Research in Labor Economics, Volume 28

RESEARCH IN LABOR ECONOMICS Series Editor: Solomon W. Polachek IZA Co-Editor: Konstantinos Tatsiramos Volume 23: Accoun...

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RESEARCH IN LABOR ECONOMICS Series Editor: Solomon W. Polachek IZA Co-Editor: Konstantinos Tatsiramos Volume 23:

Accounting for Worker Well-Being Edited by Solomon W. Polachek

Volume 24:

The Economics of Immigration and Social Diversity Edited by Solomon W. Polachek, Carmel Chiswick and Hillel Rapoport

Volume 25:

Micro-Simulation in Action Edited by Olivier Bargain

Volume 26:

Aspects of Worker Well-Being Edited by Solomon W. Polachek and Olivier Bargain

Volume 27:

Immigration: Trends, Consequences and Prospects for the United States Edited by Barry R. Chiswick

RESEARCH IN LABOR ECONOMICS

VOLUME 28

WORK, EARNINGS AND OTHER ASPECTS OF THE EMPLOYMENT RELATION EDITED BY

SOLOMON W. POLACHEK Department of Economics, State University of New York at Binghamton and IZA

KONSTANTINOS TATSIRAMOS IZA

United Kingdom – North America – Japan India – Malaysia – China

JAI Press is an imprint of Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2008 Copyright r 2008 Emerald Group Publishing Limited Reprints and permission service Contact: [email protected] No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center. No responsibility is accepted for the accuracy of information contained in the text, illustrations or advertisements. The opinions expressed in these chapters are not necessarily those of the Editor or the publisher. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-7623-1397-6 ISSN: 0147-9121 (Series)

Awarded in recognition of Emerald’s production department’s adherence to quality systems and processes when preparing scholarly journals for print

LIST OF CONTRIBUTORS Catalina AmuedoDorantes

Public Policy Institute of California (PPIC), San Diego State University, San Diego, CA, USA

Michael Bognanno

Department of Economics, Temple University, Philadelphia, PA, USA; IZA, Bonn, Germany

Hielke Buddelmeyer

Melbourne Institute of Applied Economic and Social Research, Melbourne, Australia

Lorenzo Cappellari

Universita` Cattolica, Milano, Italy

Anabela Carneiro

Faculdade de Economia (Faculty of Economics), Universidade do Porto, Porto, Portugal

Lisa Delgado

Department of Economics, Temple University, Philadelphia, PA, USA

Joseph Deutsch

Department of Economics, Bar-Ilan University, Ramat-Gan, Israel

Gil S. Epstein

Department of Economics, Bar-Ilan University, Ramat-Gan, Israel; CReAM, London; IZA, Bonn, Germany

Anders Frederiksen

Hoover Institution, Stanford University, Stanford, CA, USA; Aarhus School of Business, Aarhus University, Aarhus, Denmark; IZA, Bonn, Germany

Ebbe Krogh Graversen

The Danish Centre for Studies in Research and Research Policy, Aarhus University, Aarhus, Denmark vii

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LIST OF CONTRIBUTORS

Andrew Grodner

Department of Economics, East Carolina University, Greenville, NC, USA

Alan L. Gustman

Department of Economics, Dartmouth College, Hanover, NH, and NBER, USA

Jorgen Hansen

Department of Economics, Concordia University, Montreal, Quebec, Canada

Odelia Heizler (Cohen)

Department of Agricultural Economics and Management, Hebrew University, Jerusalem, Israel

Stephen P. Jenkins

Institute for Social and Economic Research (ISER), University of Essex, Colchester, UK

Thomas J. Kniesner

Center for Policy Research and Department of Economics, Syracuse University, Syracuse, NY, USA

Magnus Lofstrom

Public Policy Institute of California, San Francisco, CA, USA; IZA, Bonn, Germany

Miguel A´. Malo

Department of Economics, Universidad de Salamanca, Salamanca, Spain

Gilles Mourre

European Commission, DG Economic and Financial Affairs, and Free University of Brussels (ULB), Brussels, Belgium

Paul Oyer

Graduate School of Business, Stanford University, Stanford, CA, USA; NBER, Cambridge, MA, USA

Pedro Portugal

Faculdade de Economia (Faculty of Economics), Universidade Nova de Lisboa, Lisboa, Portugal; Banco de Portugal (Central Bank of Portugal), Lisboa, Portugal

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List of Contributors

Jacques Silber

Department of Economics, Bar-Ilan University, Ramat-Gan, Israel

Nina Smith

Department of Economics, University of Aarhus, Aarhus, Denmark; IZA, Bonn, Germany

Thomas L. Steinmeier

Department of Economics, Texas Tech University, Lubbock, TX, USA

John Tyler

Education Department, Brown University, RI, USA; NBER, Cambridge, MA, USA

Roger Wahlberg

Department of Economics, Go¨teborg University, Go¨teborg, Sweden

Melanie Ward

European Central Bank, Frankfurt, Germany; IZA, Bonn, Germany

PREFACE Who works, how much one works, and what one earns are the cornerstones of labor economics. However, determining the answers to these questions can be tricky because many factors are involved in estimating labor supply, explaining the implications of labor demand, and determining the resulting earnings. This volume contains 13 chapters on these components of the labor market. Five deal directly with labor supply; four deal with labor demand, most notably the effect of cyclical demand ﬂuctuations; and the remaining four deal with compensation, particularly wages, wage distributions, and fringe beneﬁts. The usual labor supply function examines work behavior from the perspective of individual characteristics, that is how one’s wage, gender, marital and child status affect employment hours. One often ignored factor is the inﬂuence of the behavior of other individuals in one’s own social group. However, frequently individuals do not act alone, but instead in concert with others, patterning their behavior on the conduct of neighbors. In the ﬁrst chapter, Andrew Grodner and Thomas Kniesner model the inﬂuence of neighborhood externalities on individual labor supply decisions. They deﬁne neighborhood in two ways: ﬁrst based on demography, and second based on geography. Their resulting econometric model then allows the data to reveal reference groups that are multidimensional in demographic and geographic closeness with the weights given as estimated regression parameters. They ﬁnd that regression models that ignore spillovers in labor supply underestimate labor supply wage elasticity measures by about 40%, and that regression models that ignore endogenous social interactions underestimate the wage elasticity by over 60%. Similarly usual labor supply functions rarely include sufﬁcient information on overtime and hours in secondary jobs. Yet omitting these can lead to biased labor supply elasticity estimates because such methods miscalculate wages for marginal hours of work. As a consequence they fail to account for nonlinearities in the wage constraint governing time allocation. To combat these difﬁculties, Anders Frederiksen, Ebbe Krogh Graversen, and Nina Smith utilize data collected by Statistics Denmark in 1996 containing detailed information on wages and overtime hours worked in primary and xi

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PREFACE

secondary jobs. They ﬁnd labor supply elasticities to be highly sensitive to speciﬁcation. Utilizing information on overtime and moonlighting wages increases numerical elasticity values compared to standard models, while allowing for more ﬂexible treatment of wage constraint non-convexities decreases elasticity values. Another aspect of labor supply is how an individual’s type of work changes from one time period to another. Put simply, can individuals easily transition from unemployment to a high-paying job, or are most of the unemployed relegated to a viscous ‘‘low-pay no-pay’’ cycle? Lorenzo Cappellari and Stephen Jenkins answer this question with the British Household Panel Survey by utilizing a general ﬁrst-order Markov model. They ﬁnd substantial persistence in being unemployed and in low-paid employment. Low-paid men had about twice the chance of unemployment as high-paid men, and similarly unemployed men had a substantially higher chance of being low-paid rather than high-paid upon ﬁnding a new job. Their results also indicate greater turnover in low-paid jobs than in highpaid jobs, and the magnitudes are stronger than in studies not accounting for endogeneity, selection, and sample attrition. Whereas state dependence affects labor market outcomes, so do the business cycle as well as structural and institutional factors. Hielke Buddelmeyer, Gilles Mourre, and Melanie Ward use a cross-country panel analysis to parcel out time-invariant structural and time-varying cyclical phenomena to get at why part-time employment rose so substantially over the 1983–1993 period in the 15 European Union countries. They ﬁnd that increased female labor force participation is one of the main structural variables to explain the rise in part-time work. Similarly, the relaxation of legislation on part-time work particularly in Belgium, Spain, Portugal, and the Netherlands is a factor, as well. On the other hand, these increases in part-time work are mitigated by decreases in fertility. Although part-time work diminishes as the economy strengthens, indicating a counter-cyclical business cycle effect, the overall business cycle effects turn out to be negligible compared to structural effects. Another aspect of labor supply is retirement, the time when one leaves the labor market permanently. At least in the United States, policies prior to 1980 encouraged retirement by age 65, or earlier. However, as a result of population aging, namely the decline in the working age population needed to support the retired, the 1983 Social Security reforms as well as other legislation ensued to encourage work beyond age 65. By and large these policies include eliminating mandatory retirement, requiring that pension beneﬁts give credit for work after normal retirement age, as well as a

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movement to deﬁned contribution retirement plans. Other plans under consideration included the elimination of the Social Security earnings test, an increase in the age of beneﬁt entitlements, and relaxing prohibitions from receiving at least partial pension beneﬁts while still at work. Alan Gustman and Thomas Steiner study the effects of these changes in pension law. They ﬁnd that despite most of these proposals being actuarially fair, ‘‘contrary to predictions from a simple retirement equations, these policies will nevertheless affect retirement, primarily as a result of a mismatch between certain persons’ rates of time preference and the discount rate implicit in the design of the pension.’’ Using a model that allows one to separate the decision to claim beneﬁts and the decision to retire, they estimate the extent to which individuals fully or partially retire and the extent to which individuals claim beneﬁts. Among their results, they ﬁnd that the share of married men claiming Social Security beneﬁts would increase 10% if the earnings test were abolished between early and full retirement ages. Abolishing the requirement that individuals need work full-time or not at all would lead to a 10–15% decline in fully retired individuals 62–69 years old. Higher average portfolio returns coming about from voluntary personal accounts would lead to a decline in full-time employment in the fraction of 62 year olds. Employment depends not just on supply, but also on demand. Cognizant of this, Gil Epstein and Odelia Heizler (Cohen) investigate employers’ demand, concentrating on the demand for legal versus illegal immigrants. They show that demand is a function of the effective minimum wage, the pay gap between legal and illegal workers, as well as the penalty for employing illegal workers. In particular, increasing the minimum wage has an ambiguous effect on the number of employed local workers but raises the stock of illegal immigrants working in the host country. Based on their conclusion, they consider various migration policies. Overall, the effect of changes in the minimum wage on the optimal enforcement budget depends on the political strength of the groups. If the workers’ union is strong, then increasing the minimum wage increases the optimal enforcement, and vice versa if the capital owners are the strong group. Cyclical changes in demand can lead to worker job displacement. Job displacement and its effects on worker wages are well studied using United States data. Indeed, in the US, failing ﬁrms account for roughly 25% of the total job destruction. However, studying job displacement in Japan might be particularly interesting because the Japanese economy tanked between 1990 and 2003, witnessing a rise in unemployment from 2.1 to 5.3%, while at the same time having a reputation of lifetime employment. Yet there are very few empirical studies of job displacement in Japan. Using more detailed data

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than previously studied, Michael Bognanno and Lisa Delgado analyze the effects of Japanese job displacement. They ﬁnd that displacement costs to employees increase with their age. For each year older a worker is, displacement costs increase by the equivalent of over $1,000. Clearly, these wage penalties arise when workers change ﬁrms, but are even greater when workers change industries, consistent with speciﬁc training models. Anabela Carneiro and Pedro Portugal also examine worker displacement arising from demand shocks that raise the risk of plant closings. They employ a longitudinally matched worker-ﬁrm data set for Portugal, a country where plant formation and plant failure account for almost a half the total gross employment ﬂows. By utilizing a simultaneous equations model to account for the endogeneity of wages and plant closure, they ﬁnd that an increase in a ﬁrm’s failure rate affects wage changes adversely because workers seek to avoid the risk of displacement. This is an interesting and novel result. First, it explains an empirical result counter to the predictions of a number of compensating wage differential studies which argue that risky jobs should command higher wages. Second, it shows that low-wage ﬁrms employing high proportions of minimum wage earners fail more often than other ﬁrms because minimum wage restrictions preclude the possibility of wage concessions. Generally the less rigid the degree of labor market regulation, especially with respect to work dismissal, the greater the employer ﬂexibility and the higher the probability of worker displacement. During the decade 1984–1994 employment regulation in Spain changed to permit permanent workers to be hired on short-term ﬁxed-duration contracts. As a result, from the early 1980s to the late 1980s temporary employment there grew from less than 10% of wage and salary workers to over 30%. In the next chapter, Catalina Ameudo-Dorantes and Miguel Malo utilize establishment employment practices by type of work contract from the 1993–2002 Spanish Encuesta de Coyuntura Laboral establishment data containing detailed quarterly information on employment stocks and ﬂows. Based on these, they examine how ﬁrms respond to changing expectations via creating new ﬁxed-term hires compared to conversions from ﬁxed to permanent contracts. They ﬁnd evidence that establishments use ﬁxed-term contracts both as a buffer to cushion themselves from short-run demand ﬂuctuations and as a screening device before employing workers permanently. Once in the labor market, education is not the only signal of a worker’s potential earnings. Of late, at least in the US, there has been a growing literature on the beneﬁcial value of the Generalized Education Development (GED) certiﬁcate, a credential awarded to roughly a quarter of the half-million

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xv

high school dropouts who pass a test administered by the American Council on Education (ACE). At issue is how GED recipients compare to high school dropouts non-credentialed by the GED. In the next chapter, Magnus Lofstrom and John Tyler seek to answer this question by utilizing data from a natural experiment taking place in Texas after the ACE arbitrarily increased the minimum passing score. Essentially, by comparing labor market performance of those with a high enough score to have passed the exam before the change to those with the same score but who now did not pass, they are able to identify the signaling value of the GED. They ﬁnd no evidence that the GED credential is positively related to higher earnings. However, they ﬁnd some evidence that this result might have arisen because Texas’s particularly low passing threshold remained in place for an extended period. Another signal of earnings differentials is occupation. If occupation is exogenous to one’s human capital and other characteristics, then one can achieve a lower wage if assigned to a low-paying occupation. As is well known, men and women have different occupational distributions, and some believe this occupational segregation is responsible for the gender wage gap. Much evidence for the US indicates that occupational segregation is not an important factor. However, Sweden is a country characterized by pro-family government policies promoting women’s abilities to simultaneously raise a family and work. As a consequence, the gender wage gap is small by international standards, but occupational segregation appears to be relatively high. Consistent with the human capital model, Jorgen Hansen and Roger Wahlberg ﬁnd that women choose occupations in which the penalty for work interruptions is low, but because of greater withinoccupation wage equalization in Sweden as much as 30% of the overall gender wage gap might be ascribable to occupational segregation. The decomposition technique is one approach often used to disentangle the factors related to gender (and race) wage differences. However, not only do males and females differ in wage level, but their entire wage distributions differ, as well. Further, typical decomposition techniques concentrate on analyzing wage differences only between two demographic groups at a point in time. In the next chapter, Joseph Deutsch and Jacques Silber generalize the Blinder-Oaxaca decomposition technique in three ways. First, they extend the approach to account for any number of groups. Second, they extend the approach to allow one to analyze changes in wage gaps over time. Finally, and more importantly, they extend the approach to analyze the determinants of the overall wage distribution differences. They illustrate their innovations by examining wage differences between 1982 and 1998 for new Israeli immigrants, Israeli natives, and older Israeli immigrants.

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Not all pay is in the form of salary. Often both employers and employees ﬁnd advantages to provide and receive in-kind fringe beneﬁts. Paul Oyer builds and tests a model showing how employee beneﬁts are correlated with ﬁrm and worker attributes based on a theoretical model in which ﬁrms choose their beneﬁts packages to maximize proﬁts. The model takes account ﬁrst of ﬁrms’ economies of scale in providing certain beneﬁts, second of differences in the way employees evaluate beneﬁts based on their characteristics, and third of labor-saving efﬁciencies certain beneﬁts have. The model introduces two considerations not currently in the literature, namely that ﬁrms provide beneﬁts to increase worker effort, and that ﬁrms provide certain beneﬁts to decrease the costs of ﬁnding available workers. From the model Oyer derives a number of theorems that he tests using the NLS-Y data. As with past volumes, we aimed to focus on important issues and maintain the highest levels of scholarship. We encourage readers who have prepared manuscripts that meet these stringent standards to submit them to Research in Labor Economics (RLE) via the IZA website (http:// www.iza.org/rle) for possible inclusion in future volumes. For insightful editorial advice in preparing this volume, we thank Paul Althous, Ann Bartel, Andrea Beller, David Blau, Nancy Chau, Karen Smith Conway, Ludo Cuyvers, Andy Dickerson, Debra Dwyer, John Sutherland Earle, Rob Euwals, Gary Fields, Carlo Fiorio, Belton Fleisher, Anders Frederiksen, Eric French, Stefano Gagliarducci, Bernhard Ganglmair, Christopher Hanes, Steinar Holden, Todd Idsen, Ben Kriechel, Anil Kumar, Mark Lino, Lance Lochner, David MacPherson, David Marsden, Alfonso Miranda, Lena Nekby, Luca Nunziata, Andreas Pape, Trond Petersen, Melinda Pitts, Barbara Rossi, Christy Spivey, Arne Uhlendorff, Jose Vareja˜o, Bruce Weinberg, Phani Wunnava, and Ken Yamada. Solomon W. Polachek Konstantinos Tatsiramos Editors

LABOR SUPPLY WITH SOCIAL INTERACTIONS: ECONOMETRIC ESTIMATES AND THEIR TAX POLICY IMPLICATIONS Andrew Grodner and Thomas J. Kniesner ABSTRACT Our econometric research allows for a possible response of a person’s hours worked to hours typically worked by members of a multidimensional labor market reference group that considers demographics and geographic location. Instrumental variables estimates of the canonical labor supply model expanded to permit social interactions pass a battery of speciﬁcation checks and indicate positive and economically important spillovers for adult men. Ignoring or incorrectly considering social interactions in male labor supply can misestimate the response to tax reform by as much as 60%.

1. INTRODUCTION Social interactions, the situation where individuals respond to the actions of people with whom they interact, may have a biological basis or stem from

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 1–23 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28001-5

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ANDREW GRODNER AND THOMAS J. KNIESNER

information gathering. Social interactions are a potentially important aspect of economic behavior because interdependencies can affect how people react to the expected and unexpected changes in their environment, including ones caused by public policy. We investigate the econometric nuances and empirical importance of social interactions in labor supply with taxes where the interdependence is a response of the individual to the hours worked by the members of a reference group. We ﬁnd evidence of a positive spillover effect in hours worked and demonstrate their quantitative importance for tax policy. The presence of social interactions in labor supply means that individuals respond to others’ hours worked by a non-negligible amount. When there is a social interaction, effect is important because the policy affecting the wages or another independent variable of a subgroup will not only affect the individual but also others in the individual’s reference group. We therefore focus on the consequences of interdependence for the estimated effect of wages on labor supply, which economists use widely in examining tax reform proposals. Our research contribution is to implement a tractable labor supply model with spillover effects and then demonstrate the value of econometric estimates of the importance of social interactions in labor supply for tax policy. Theoretical solutions to optimal static or dynamic taxation in the presence of social interactions externalities use the parameters of the utility and attendant consumption and labor supply functions (Kooreman & Schoonbeek, 2004; Abel, 2005). To ﬂesh out brieﬂy the enriched policy implications of a labor supply model with social interactions, consider a basic proportional tax reduction applied to married men in a case with potential social interactions effects. Suppose the proportional tax rate change applied only to families with disabled children. The subpopulation affected would be relatively small and scattered geographically; reference group effects could be ignored safely. Alternatively, suppose we were examining the effect of a proportional state income tax change on the highest earners in a state such as California, where many would live in the same area or interact regularly in professional settings. Now feedback effects would be present. The labor supply elasticity to consider would then include non-negligible social interactions effects. Put simply, the beneﬁts of empirical social interactions research are that, after identifying any interdependencies, the economist can perform a more complete welfare analysis. Identiﬁcation of social interactions is econometrically complex (Soetevent, 2006; Lee, 2007a, 2007b). The primary challenge a researcher must confront

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3

is what is the correct reference group (Durlauf, 2004). There is a wideranging belief that people in close proximity can have a signiﬁcant effect on the individual’s labor supply decisions (Weinberg, Reagan, & Yankow, 2004). Similarly, there is labor supply research where reference points come from others who are demographically similar but need not live near each other (Woittiez & Kapteyn, 1998). Here we synthesize the two possibilities. We explore an econometric model that allows the data to reveal reference groups that are multidimensional in demographic and geographic closeness with the weights left as free parameters to be estimated. In summary, we address many of the practical issues related to identifying the effect of endogenous social interactions on an individual’s actions. We create a ﬂexible measure of the economic distance, approximating the level at which individuals interact among one another. We deﬁne the economic distance between individuals as a combination of personal characteristics and physical distance. Our measure reﬂects the varying costs of interaction as higher economic distance implies higher cost of interaction, which implies a lower level of interaction. We then deﬁne the reference groups, each of which consists of persons who are in a close economic proximity, and compute hours worked for each person in the reference group (endogenous social interactions). We create and verify the econometric validity of using the mean of hours worked for persons in the adjacent reference group for the purpose of instrumenting endogenous social interactions. The speciﬁcation lets us examine the core issue of whether the hours supplied by persons in close economic proximity are related. To frame the importance of social interactions, we purposely use crosssectional data from 1976 so as to anchor our research to the seminal and oft cited cross-sectional studies of male labor supply by Hausman (1981) and MaCurdy, Green, and Paarsch (1990). Our econometric results suggest positive and non-negligible social interactions in hours worked. Focal results are that US male labor supply data (1) reject a model ignoring social interactions against one with spillovers and (2) reject a model with spillovers treated as exogenous against one with spillovers treated as endogenous. A regression model that ignores spillovers in labor supply underestimates the wage elasticity of labor supply by about 40%; if one uses a social interactions model but ignores endogenous interactions, s/he underestimates the wage elasticity by over 60%. We conclude with a demonstration of how improperly accounting for social interactions can lead to substantial under- or overestimation of the labor supply effects of tax reform.

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2. CONCEPTUAL FRAMEWORK AND ECONOMETRIC MODEL Theories of social interactions have a fairly long history in the economic literature. Becker (1974) ﬂeshes out the consequences when utility of the individual is somehow affected by either utility or choices made by members of a reference group, who are people with whom the individual interacts. More recent theoretical research delves into the details of how information and species survival considerations may be the source of equilibrium social interactions in utility (Samuelson, 2004; Rayo & Becker, 2007a, 2007b) and what differentiates situations where individuals emulate versus deviate from peer behavior (Clark & Oswald, 1998; Grodner & Kniesner, 2006). The utility function that leads to our labor supply-estimating equation is the utility function derived by Hausman (1980, 1981), amended to include social interactions, which yields a linear labor supply function that is linear in the means of the reference group behavior. This anchors our results to Hausman’s and MaCurdy’s inﬂuential research, which facilitates judging the economic importance of adding social interactions to labor supply. In the empirical work to follow, we regress individuals’ hours worked on average hours worked in their reference groups, ceteris paribus. A positive coefﬁcient on labor supplied by the reference group indicates the presence of a positive spillover effect in hours worked (Woittiez & Kapteyn, 1998; Aronsson, Blomquist, & Sackle´n, 1999). When econometrically implementing the spillover model of individual labor supply, we estimate the familiar linear in means model, that is, the canonical linear labor supply model with social interactions added (Brock & Durlauf, 2001, 2002; Grodner & Kniesner, 2006). Speciﬁcally, for an individual i in a reference group g, hi ¼ y þ aoi þ bui þ gxi þ d1 hðiÞg þ d2 x ðiÞg þ i

(1)

where o is the after-tax real wage, u the after-tax virtual income, x a vector of individual control covariates, hðiÞg the reference group g’s average labor supplied excluding the ith worker, x ðiÞg the vector of control covariate averages for the reference group excluding the ith worker, e the error term, and y, a, b, g, r, d1, and d2 parameters to estimate. From Eq. (1), an increase in average hours worked in the reference group spills over so that the individual also increases hours worked. We now ﬂesh out the econometric details involved with examining possible exogenous and endogenous social interactions in individual labor

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supply and suggest an approach that synthesizes two avenues in the current literature. 2.1. Labor Supply Variables The net wage rate (o) uses a marginal tax rate t provided by the Panel Study of Income Dynamics (PSID) and is o ¼ ð1 tÞw. Virtual income (u) also uses the marginal tax rate from the PSID.1 To control for possible endogeneity when estimating (3), we instrument both the after-tax wage and virtual income using last year’s gross wage and nonlabor income (Ziliak & Kniesner, 1999). The control covariates in labor supply include a number of children less than six years old, family size, an indicator if the person is more than 45 years old, the equity that the family has in their house, and an indicator of a physical or nervous condition that limits the amount of work, which are standard exogenous explanatory variables in labor supply studies. Finally, in some speciﬁcations, x includes hours worked in the previous year (h1) to allow for the possibility noted by Rayo and Becker (2007a, 2007b) that the reference point in utility may depend not only on reference group outcomes but also on the individual’s habits. 2.2. Social Interactions Variables The mean labor supplied by the reference group is the sample average of hours worked for other people who are close in the economic distance to the worker. In computing the average, we exclude the individual for whom we are computing a reference group mean outcome. The estimated value of the parameter d1 represents the effect of endogenous social interactions in hours worked. Next, we create a proxy variable summarizing the information in the exogenous covariates. Speciﬁcally, we use factor analysis and take the ﬁrst factor as a proxy variable for exogenous information. The new variable is standardized to have zero mean and unit variance and is highly correlated here with all the exogenous variables as well as the individual’s hours worked. The mean in the reference group for the created (factor analytic) proxy variable uses the same range of the economic distance variables as we use for computing mean hours worked, again excluding the person for whom we are computing the reference group mean. The proxy variable controls the common characteristics of the reference group, and the estimated coefﬁcient d2 will indicate any presence of exogenous social interactions.

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2.3. Identifying Social Interactions The labor supply equation, Eq. (1), can identify the presence of both endogenous (in the dependent variable) and exogenous (in the independent variables) social interactions. If the reference groups are completely separable, then a randomly distributed shock that affects hours worked for some individuals but not others can help identify endogenous social interactions (Manski, 1993; Mofﬁtt, 2001). When reference groups overlap, there are a variety of empirical approaches, including repeated samples (Aronsson et al., 1999), structural models (Brock & Durlauf, 2002; Kapteyn, van de Geer, van de Stadt, & Wansbeek, 1997; Krauth, 2006), aggregated data (Glaeser, Laibson, & Sacerdote, 2002), within versus between variation (Graham & Hahn, 2005), or spatial econometric techniques (Kelejian & Prucha, 1998; Lee, 2007a, 2007b). Alternatively, suppose there are workers who belong to more than one reference group, and we use them to compute the (endogenous) mean for reference group hours worked. Hours worked by people in the adjacent reference group can now be an instrument; this is similar to using past values of the dependent variable in a dynamic panel data model (Arellano & Bond, 1991). Here we use, as an instrument, the mean for workers in the adjacent reference groups, which are deﬁned by a social grid with two social coordinates from factor analysis. The instrument is correlated with mean hours worked in the individual’s reference group (endogenous social interactions) because people in the speciﬁc and adjacent reference groups belong to the same economic neighborhood. The instrument should also be uncorrelated with unobservables affecting individual labor supply because the particular individual does not belong to the adjacent reference group.2 In any event, the instrumental variable (IV) approach that we use will be checked in the usual ways for weak instruments and that the overidentifying restrictions are satisﬁed, and if the checks are passed, then we are no less comfortable with our approach than with any other IV application. Fig. 1 illustrates our particular identiﬁcation strategy. We present the hypothetical two-dimensional social coordinate space with two reference groups: g1 and g2. Suppose that individual h0g1 belongs to the reference group g1 and responds to the outcomes of the members of the reference group, represented by the observations labeled as h1g1 and h2g1 g2 (empty and grayﬁlled circles). If we use the mean of all h1g1 and h2g1 g2 observations (referred ð0Þ further as h g1 ) as an independent variable in the regression (1) to try to identify endogenous social interaction in h0g1 , the coefﬁcient will be biased.

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Social Coordinate 2

Labor Supply with Social Interactions

Boundary for reference group g2

Boundary for reference group g1 0

h g1

1

h g1 h3g2

2

h g1g2 Inner Boundary for instrument group Outer boundary for instrument group

Social Coordinate 1

Fig. 1.

Demonstration of the Identiﬁcation Strategy for the Endogenous Social Interactions.

Observations h1g1 and h2g1 g2 are also affected by the outcome h0g1 , which causes endogeneity in h ð0Þ g1 . However, if there are observations in the reference group g1 that also belong to the neighboring reference group g2, then part of h ð0Þ attributed to the outcomes h2g1 g2 can be instrumented by the outcomes g1 of the members of the reference group g2, denoted by h3g2 . If the usual diagnostic checks are passed plus an additional one developed in Lee (2007b) that the reference group size varies, then we can reasonably use IV estimation. The h3g2 are valid instruments because they are correlated with all h2g1 g2 observations since they belong to the same reference group, and h3g2 are not correlated with the error terms associated with either h0g1 or h1g1 observations since they do not belong to the same reference group.3

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In practice, if we instrument observations h2g1 g2 with outcomes h3g2 , there may still be observations h1g1 that are not instrumented and thus will make a part of the h ð0Þ endogenous, which is the case presented in Fig. 1. Instead g1 of using just one reference group, we can imagine using a full set of observations in the adjacent reference groups that form the ring around the particular reference group (represented by the dotted circle).

3. DATA We use data from the University of Michigan’s PSID collected in 1975 and 1976 (PSID Wave IX). One reason for using the PSID is that it is the most frequently used data to study US labor supply (Blundell & MaCurdy, 1999; Ziliak & Kniesner, 1999). We purposely chose the 1976 cross section of the PSID data because we seek to understand the possible importance of social interactions in labor supply by anchoring our estimates to the inﬂuential research of Hausman (1980, 1981) and MaCurdy et al. (1990), who use the same data to examine how taxes affect labor supply without modeling social interactions.

3.1. Sample We follow the sample selection process described in Eklo¨f and Sackle´n (2000), who compare the studies by Hausman (1981) and MaCurdy et al. (1990) to which we anchor our research. Both studies estimate an almost identical linear labor supply model with income taxation. We select observations according to the following criteria: married males 26–55 years old with positive hours worked in 1974 and 1975 (but no higher than 5,096 annual hours), who are heads of households in the crosssectional random subsample; there were no changes in the family composition of the head or wife (others can change) in 1974–1975; the head is not retired or permanently disabled, or a housewife, student, or other; the household resides in the United States; and the head is not self-employed or a farmer. Using our exclusion criteria for the 1976 PSID, we obtain 1,077 observations, which are close to the Hausman sample of 1,084 and the MaCurdy sample of 1,018 as reported by Eklo¨f and Sackle´n (2000).4

Labor Supply with Social Interactions

9

3.2. Individual Regression Variables The wage rate comes from a direct question in the PSID, including an imputed value for workers who are not paid by the hour. We also estimate a wage equation to impute hourly wages for observations with unobserved or truncated wages. In particular, we use observations that have positive and not top-coded wage rates (839 observations) to estimate a Tobit regression that uses, as the dependent variable, observed (un)truncated wages on a constant term, age, age squared, years of schooling, years of schooling squared, college degree, and family size. We then use the estimated wage equation to produce a ﬁtted value for all wages. The procedure is similar to that in Hausman (1981), so our mean hourly wage is $6.17, which is nearly identical to the $6.18 reported by Hausman. Hours worked, the dependent variable, also comes from a directly asked question in the PSID. Nonlabor income is a constructed variable that is the difference between the total 1975 taxable income of the husband and the wife and the total 1975 labor earnings of the husband. The hours worked and the nonlabor income measures we use are also those of MaCurdy et al. (1990). Other independent variables include the number of children less than six years old (KIDSU6), family size (FAMSIZ), an indicator variable for individuals more than 45 years old (AGE45), the amount of equity the family had in its house (HOUSEQ), and an indicator of a physical or nervous condition that limited the amount of work the respondent could do (BHLTH). Appendix presents descriptive statistics for all regression variables.

3.3. Reference Group and Economic Distance Specifying the composition of the individual’s reference group is the researcher’s central decision in any study of interdependence (Manski, 1993, 2000). Implementing the reference group concept means acknowledging that people who are in relative economic proximity to each other may interact with one another because the cost of interactions is low. We use the concept of economic distance among individuals as an indicator of the potential signiﬁcance and magnitude of workers’ interdependencies (Conley, 1999). We take people who are in close economic distance as belonging to the same reference group. Economic distance is a combination of whether the workers are similar demographically and live in close physical proximity. We use a combination

10

ANDREW GRODNER AND THOMAS J. KNIESNER

of personal and family characteristics to deﬁne demographically similar persons and use the distance between centers of countries in which people reside for their relative geographic locations. There are multiple difﬁculties involved with selecting from a large variety of characteristics to measure economic distance. Acknowledging that each characteristic measure has a different scale and determining the relative importance of each input variable on economic distance, we use a statistical model of factor analysis (Woittiez & Kapteyn, 1998). The factor analytic model naturally deals with characteristics having different measurement scales; the procedure standardizes individual variables and then ﬁts a linear model to ﬁnd common latent variables called factors (Bai & Ng, 2002; Bai, 2003). The intuition is that there are unobservable variables (factors) that are orthogonal to one another and strongly correlated with observed variables. We use the factors as social coordinates to establish reference groups. Because the typical variables explaining labor supply can affect whether workers interact with each other by being related to economic distance, our factor analysis inputs all independent variables from the econometric labor supply model (3). We also use physical coordinates indicating the location by the center of the country where the person resides. We use two factors to summarize demographic and physical coordinates because there is usually a much better ﬁt with multiple factors than with only one factor, but using too many factors tends to be uninformative.5 By using two factors, we have the convenient feature that the computed latent variables serve as two social coordinates (SocCoord1, SocCoord2) for where individuals are located on a social interactions grid with economic distance measured by the Euclidean distance between two points.

4. ECONOMETRIC RESULTS: LABOR SUPPLY WITH SOCIAL INTERACTIONS Because there is no clearly deﬁned reference group in our study, we ﬁrst select persons likely to have interdependent labor supplies by using the two social coordinates to deﬁne overlapping neighborhoods. As the reference group is now deﬁned, we then estimate the labor supply model in (1) using instrumental variables for identiﬁcation. If the appropriate econometric speciﬁcation checks are satisﬁed, we then interpret the social interactions effects in terms of endogenous versus exogenous wage effects.

Labor Supply with Social Interactions

11

4.1. Selecting the Reference Group Because we do not have direct information on who belongs to the reference group for a particular person, we use a statistical procedure to infer it from the location and characteristics of the group’s members. We believe that our observations are representative of working married men in terms of their individual characteristics and spatial distribution. We can think of the reference group as a ring of certain radius centered around the individual in two-dimensional social coordinate space (Fig. 1). The problem is then to select the radius best representing the borders of the reference group. The border selection problem is important because we use sample observations to compute the characteristics of close-by individuals. Each observation establishes possible multiple reference groups so that careful selection of borders is critical here for identiﬁcation. To ﬁnd borders for the membership groups, we use a result from spatial econometrics that, as the reference group size expands, the coefﬁcient on endogenous social interactions tends to minus inﬁnity (Kelejian & Prucha, 2002).6 In our application, endogenous social interactions are represented by the mean of hours worked by others in the worker’s reference group, AnnHSRG_0_R, where R indicates the radius dimension of the reference group’s circle. If social interactions are present at a certain size of the reference group, then the upward bias because of reference group labor supply endogeneity will overcome the statistical tendency for d^ 1 in (3) to become negative as the neighborhood size increases (Anselin, 2001). The reference group with the most positive d^ 1 in exploratory estimates of (3) then reveals the size of the worker’s reference group. Table 1 presents results from baseline labor supply regressions with a social interactions variable AnnHSRG_0_R. Estimation starts with the radius indicator R=1, which means that the average of hours worked uses nearby workers in the social space within the distance of 0.1 or less. When the indicator R ¼ 1, the reference group has around 13 workers. As the size of the reference group increases in the social space (the radius indicator R increases), the number of persons who are considered to be economically close to a worker increases from 44 to about 271 in Table 1. As expected a priori, the coefﬁcient on average hours worked by neighboring persons is increasingly negative across the columns of Table 1, going from about 0.2 to 1.5 as the reference group size increases. Such a tendency will be observed for any estimator, including the IV regressions of Table 1 (Kelejian & Prucha, 2002). Critical to our research is that the

910 44.53 WageRate75, NLIncome75

879 13.33

WageRate75, NLIncome75

0.0626 (0.1432)

WageRate75, NLIncome75

918 89.19

0.2042 (0.2411)

(35.4610) 0.0040 (0.0058)

(35.9633) 0.0031 (0.0058)

52.5361 (36.3663) 0.0034 (0.0059) 0.1978 (0.0867)

71.6107

68.4734

WageRate75, NLIncome75

922 142.56

0.4982 (0.3231)

(35.8352) 0.0047 (0.0057)

71.8010

Annual Hours

(4)

WageRate75, NLIncome75

922 204.13

0.9685 (0.3566)

(35.6676) 0.0051 (0.0057)

68.8683

Annual Hours

(5)

WageRate75, NLIncome75

1.5021 (0.4709) 922 271.21

68.9533 (35.4563) 0.0055 (0.0057)

Annual Hours

(6)

Notes: Standard errors in parentheses. Endogenous variables’ coefﬁcients in bold. Weak instrument check statistics appear in Table 2. Additional control variables: KIDSU6, FAMSIZ, AGE45, HOUSEQ, BHLTH, constant. Signiﬁcant at 10%. Signiﬁcant at 5%. Signiﬁcant at 1%.

Observations Average observations in reference group Identifying instruments

AnnHSRG_0_6

AnnHSRG_0_5

AnnHSRG_0_4

AnnHSRG_0_3

AnnHSRG_0_2

AnnHSRG_0_1

VirtualInc

AfterTaxWage

Annual Hours

Annual Hours

Annual Hours

(3)

(2)

Selection of the Reference Group Using IV Regression.

(1)

Table 1.

12 ANDREW GRODNER AND THOMAS J. KNIESNER

Labor Supply with Social Interactions

13

reference group labor supply coefﬁcient is most signiﬁcantly positive at the size of the reference group, where radius indicator R ¼ 2. The importance of Table 1 is that the pattern of regressions reveals the group size with the largest upward bias due to endogeneity of the AnnHSRG variable. The endogeneity caused by labor supply interdependencies is most positive for the range (0,0.2), so we pick 0.2 as the radius most closely capturing the true size of the reference group. Results from a Moran I test (Anselin, 2001, p. 323) support the presence of social interactions in hours worked; the radius we adopt to deﬁne the reference group based on the preliminary regression in Table 1 also maximizes the Moran I statistic measure of association. The practical consequence of our speciﬁcation search is that the average reference group contains about 44 persons, which indicates that the groups are small enough to guarantee sufﬁcient outcome variation across groups but large enough that the computed average hours worked are meaningful and have relatively small error due to aggregation. Our results also satisfy the identiﬁcation condition for general spatial econometric models established in Lee (2007b) that groups vary in size (standard deviation is 38 and maximum size is 139).7

4.2. Social Interactions Effects The focus of our research is on examining interdependence in hours worked, using the canonical model of labor supply applied to cross-sectional data. This anchors our results for purposes of interpretation to the inﬂuential labor supply research by Hausman (1980, 1981) and MaCurdy et al. (1990). We ﬁrst conﬁrm that our estimates for the uncompensated wage and income elasticities are similar to the results of Hausman and MaCurdy et al. The ﬁrst column of Table 2 presents IV regression wage and income coefﬁcients for their canonical models of labor supply. The uncompensated wage elasticity at the means is 0.14, and the income elasticity at the means is 0.008; both values are typical estimates in the standard econometric labor supply literature that serves as our starting point for judging the importance of social interactions. Our focal regression results are presented in the second column of Table 2, where we include both habits and social interactions. We also use as a regressor, the average of the proxy variable for the exogenous variables constructed via factor analysis (IndVORG_2_6). The estimated social interactions effect is that a 10 h increase in the reference group labor supplied would increase an individual’s hours worked by about 6 h.

14

ANDREW GRODNER AND THOMAS J. KNIESNER Table 2.

Dependent Variable Annual hours worked AfterTaxWage VirtualInc IndVRG_0_2

IV Regressions with Social Interactions.

(1)

(2)

Baseline

Social interactions and habits

Only habits Only social interactions

66.6982 (35.5604) 0.0031 (0.0058) 318.8201 (381.9788)

38.5373 (28.6798) 0.0000 (0.0047) 317.4740 (307.9343) 0.6379 (0.2689) 910 0.212 0.645 WageRate75 NLIncome75 AnnHSORG_2_6 IndVORG_2_6

30.5734 (28.1246) 0.0011 (0.0045) 284.0008 (302.0874)

AnnHSRG_0_2 Observations 910 Sargan test P-value Identifying WageRate75 instruments NLIncome75

(3)

910

WageRate75 NLIncome75

(4)

81.6429 (37.3766) 0.0055 (0.0061) 385.0609 (401.1535) 1.3128 (0.3532) 910 0.081 0.776 WageRate75 NLIncome75 AnnHSORG_2_6 IndVORG_2_6

Notes: Standard errors in parentheses. Endogenous variables’ coefﬁcients in bold. F(Shea partial R2) ¼ 53.0(0.189), 368.1(0.621), 51.9(0.188). Additional control variables in all equations: KIDSU6, FAMSIZ, AGE45, HOUSEQ, BHLTH, constant. Additional control variable in (2) and (3): AnnualHours75. Signiﬁcant at 10%. Signiﬁcant at 5%. Signiﬁcant at 1%.

Comparing columns 2 and 3 of Table 2 yields the important result that the estimated social interactions effect is signiﬁcant statistically and economically reasonable in magnitude only when habits in labor supply are part of the speciﬁcation.8 It is important to reemphasize that the estimated endogenous social interactions effect, d^ 1 , which is the impact of average hours worked by persons in the worker’s reference group (AnnHSRG_0_2), has the expected sign and economically reasonable magnitude only after we instrument for interdependence, which we do in Table 2. Because they suggest the presence of endogenous social interactions, the estimates in Table 1 are statistically inconsistent (Durbin–Wu–Hausman test rejects exogeneity at the 5% level). The difference between the results in Tables 1 and 2 emphasizes that we must be clear about the method we use to construct the instrument for social interactions in labor supply. As noted, there are no obvious variables to provide exogenous variation with which to instrument reference group work effort, so we use the

Labor Supply with Social Interactions

15

structure of the data to construct an instrument for the reference group’s labor supplied. Taking reference groups as overlapping with boundaries as ﬁxed, average hours worked by persons in the adjacent reference groups can be instruments. The outer boundary of the persons for the instrument group will be exactly twice the size of the radius for each neighborhood because there may be workers who are located exactly on the boundary for both the reference group of interest and the adjacent reference group.9 We construct hours worked by individuals in the outside ring in Fig. 1 (0.2, 0.6), which has an average of 226 observations for each instrument group. First-stage goodness of ﬁt and Sargan test results for the regressions in Table 2 conﬁrm that our instruments (for all three right-hand-side endogenous regressors: after-tax wage, virtual income, and reference group average labor supplied) are valid in terms of passing the standard checks for weak instruments and that the overidentifying restrictions are satisﬁed. Equivalently, the strength of our identifying instruments, here, means that the potential bias of the IV estimator of the endogenous social interactions effect in Table 2 is small: less than 4% of the potential bias of OLS (Hahn & Hausman, 2003; Stock & Yogo, 2005).

4.3. Additional Econometric Validity Checks of the Reference Group It is instructive to examine how our results may or may not be robust to the sizes of the reference group or adjacent groups comprising the instrument set. How might our results change by (1) shrinking the outer circle boundary in Fig. 1, which leaves the reference group size the same but decreases the number of observations viewed as nearest neighbors for the reference group, or (2) shrinking the inner reference group circle boundary in Fig. 1, which makes the reference group smaller? In the ﬁrst sensitivity experiment, as the instrument group shrinks, the IVestimated social interactions effect is similar while becoming statistically less precisely estimated. Our interpretation is that the instrument loses power as the size of the instrument set shrinks. In the second sensitivity experiment, we ﬁnd that when the reference group size shrinks, the estimated social interactions effect is also unchanged, although the statistical efﬁciency of the estimate again decreases. We interpret the result of the second sensitivity experiment as indicating that the range for the reference group is well chosen because, within the group, there should be a similar level of interactions, and we are just choosing progressively smaller and small subgroups that still interact.

16

ANDREW GRODNER AND THOMAS J. KNIESNER

Having discussed the sensitivity results of our instrument construction, we now turn our attention to the economic interpretation and policy implications of our estimated social interactions effects in male labor supply.

4.4. Interpreting the Importance of the Estimated Social Interactions Effect Social interactions in labor supply mean that individuals respond to others’ hours worked by an economically signiﬁcant amount. A social interactions effect is important because a policy affecting the wages or another independent variable of a subgroup will affect not only the individual but also others in the reference group. We therefore focus on the direct versus the indirect effect of interdependence. In particular, we consider the consequences of interdependence for the estimated effect of wages on labor supply, which economists use widely in welfare effect simulations of tax reform proposals (Kniesner & Ziliak, 2008). Taking the mean values in Eq. (1) and focusing on hours worked and wages, þ d1 h ) h ¼ a h ¼ ao

1 o 1 d1

(2)

where 1=ð1 d1 Þ is known as the global social multiplier because it represents the effect of social interactions at the highest level of aggregation (Glaeser, Sacerdote, & Scheinkman, 2003). The total uncompensated effect of a wage change in the static linear model can be decomposed into @h a ad1 ¼ ¼aþ @o 1 d1 1 d1

(3)

where a is the exogenous effect and ðad1 Þ=ð1 d1 Þ the endogenous effect. Notice that the endogenous effect depends on both the magnitude of the initial exogenous change and the social multiplier. the uncompensated elasticity is h, Multiplying Eq. (3) by o= Zhw; total ¼ Zhw; exogenous þ Zhw; endogenous

(4)

For d1 o0:5, h and Zhw; endogenous ¼ ad1 o=ð1 where Zhw; exogenous ¼ ao= d1 Þ h. the exogenous effect is larger than the endogenous effect, but for d1 40:5, the endogenous effect is larger. As we will later emphasize, the decomposition in Eq. (4) underscores how ignoring labor supply interdependencies may have serious consequences for the elasticity estimates of interest.

Labor Supply with Social Interactions

17

Using the values from the second column of Table 2, the total uncompensated wage elasticity of labor supply at the means is 0.22, with an exogenous part of 0.08 and an endogenous part of 0.14. In comparison, the baseline model results from column 1 of Table 2 are an uncompensated net wage elasticity of 0.13. If we purposely ignore social interactions, the estimated exogenous wage effect is about 60% too high; the positive bias in the canonical model happens because the single (wage) coefﬁcient estimate also imbeds the effect of labor supply interdependencies. The twin ﬁndings that (1) the wage elasticity has two unequal and sizeable parts in the social interactions model and (2) the wage coefﬁcient of the traditional model has sizeable omitted variable bias have important consequences for evaluating tax policy. 4.5. Implications for Tax Policy Calculations We have noted that numerical solutions to optimal income taxation need appropriate econometric estimates. Further, our core results are that, for US male labor supply, a regression model that ignores spillovers in labor supply underestimates the wage elasticity of labor supply by about 40%; if one uses a social interactions model but ignores the endogenous interactions component, s/he underestimates the wage elasticity by over 60%. It is less obvious how we should apply estimates where the policy-maker considers wage elasticity segments with and without social interactions. Some back-of-the-envelope calculations for the proportional tax rate case are instructive. The preferred model in Table 2, column 2, implies that a 10% comprehensive tax rate cut would raise male labor supply by as much as 2.2% when social interactions are considered; ignoring social interactions would lead to about a 60% underestimate of the labor supply effect of the tax cut (0.8%). How can one use our decomposition of the total wage elasticity into its exogenous component (þ0.08) and its endogenous social interactions component (þ0.14) in policy calculations? Suppose there is a proportional tax rate change applied only to families with disabled children. The subpopulation affected would be relatively small and scattered geographically; the reference group effects could be ignored safely, and the appropriate elasticity to use would be closer to 0.08 than 0.22. Alternatively, suppose we were discussing the effect of a proportional state income tax change on the highest earners in a state, such as California, where many would live in the same area or interact regularly in business. Now feedback effects would be present. The elasticity to use would then include nonnegligible social interactions effects and probably be closer to 0.22 than 0.08.

18

ANDREW GRODNER AND THOMAS J. KNIESNER

The importance of gauging what is the correct elasticity in terms of the exogenous and endogenous parts is useful only if we can deﬁne whether a particular group will be affected by interactions. If the persons who are affected do not belong to the same reference group, then most likely we would observe only the exogenous effect, and the elasticity would be overestimated if we used an elasticity that contained both exogenous and endogenous components, which was the ﬁrst example in the previous paragraph. If the tax reform applied to members of a reference group, though, then there would be a full-blown feedback effect, and the elasticity that used only an exogenous component would underestimate the total labor supply effect, which was the second example in the previous paragraph.

5. CONCLUSION Our research uses the canonical (linear-in-means) model of labor supply that adds possible social interactions in hours worked. We ﬂesh out the econometric nuances of testing whether an increase in hours worked by the members of the reference group increases hours worked for the individual (endogenous social effect). The reference group here contains persons in close economic distance to each other. Our measure of economic distance uses factor analysis, which allows mapping multiple economic neighborhood variables into a two-dimensional social space. Our identiﬁcation strategy builds on the likelihood that some persons belong to more than one reference group, so that their hours worked may be used to instrument for endogenous labor supply of individuals in the worker’s reference group. As in any other IV exercise, we apply checks of instrument strength and that the overidentifying restrictions are satisﬁed. In our regression model of married men’s labor supply, if social interactions are treated as exogenous, there is no estimated effect of the reference group behavior on the individual worker’s behavior. When we instrument mean hours worked of the reference group and include individual habits in labor supplied, we ﬁnd a social interactions effect that is reasonable both statistically and economically. The estimated total wage elasticity of labor is 0.22, where about one-third is due to the exogenous wage change and two-thirds are due to social interactions effects. The policy implications are that if one is to fully understand the labor supply and welfare effects of income taxes, which may be conditioned on demographic and location information, a model including social interactions is best. Equally important is a proper interpretation of the social

Labor Supply with Social Interactions

19

interactions model results. We demonstrate how a mis-speciﬁed model or a properly speciﬁed model that is misapplied can easily lead to misestimates of the labor supply effects of tax reform by as much as 60%.

NOTES 1. u ¼ [NLIþ(t(TT/(TINLI)) (TINLI))], where NLI is nonlabor income, TT are total taxes, and TI is taxable income (Ziliak & Kniesner, 1999). For a survey of income tax effects on labor supply, including over the life cycle, see Kniesner and Ziliak (2008). 2. Similarly, Case and Katz (1991) instrument for the endogenous effect using the average levels of adjacent neighbors’ characteristics that are supposedly exogenous, and Evans, Oates, & Schwab (1992) instrument school composition with citywide variables for the unemployment rate. 3. In practice, if we instrument observations h2g1 g2 with outcomes h3g2 , there may still be observations h1g1 that are not instrumented and thus will make a part of the ð0Þ hg1 endogenous, which is the case presented in Fig. 1. Instead of using just one reference group, we can imagine using a full set of observations in the adjacent reference groups that form the ring around the particular reference group (represented by the dotted circle). 4. The difference between the number of observations used by MaCurdy et al. (1990) and our study comes from the fact that we dropped two observations because the head’s age was missing and that we did not exclude persons who were selfemployed and farmers in 1975 but not in 1976 (changed employment status). Due to restricting the sample to individuals who also reported hours worked for 1974, we have a ﬁnal sample of 910 men. 5. The ﬁrst factor loads primarily on demographics and explains about 75 percent of the total variation in the variables. The second (rotated) factor loads primarily on location and then explains about 15 percent of the information. 6. The intuition behind the result is that as the size of the group used to produce the average grows, it approaches a similar value for everyone and becomes increasingly collinear with the regression constant term. 7. As yet another check on the reasonableness of how our econometric model reveals groups, we examined the intragroup correlation of the members’ characteristics variables and the correlation of the same variables in an identicalsized group selected randomly. In all cases, the model’s groupings had much higher intragroup correlations (typically greater than þ0.90) versus among the members of randomized groups of similar size (typically less than þ0.02). 8. The coefﬁcient on the hours worked for the reference group needs to be less than 1.0; otherwise, a 1 h increase in the mean hours worked for the reference group would induce a worker to increase his labor supply by more than one hour, which would cause a domino effect where, in the limit, all workers choose the maximum feasible hours. The coefﬁcient of the lagged dependent variable in both columns (2) and (3) is 0.59 with a standard error of 0.03. In a cross-sectional regression, it will

20

ANDREW GRODNER AND THOMAS J. KNIESNER

reﬂect both habits and additional worker-speciﬁc heterogeneity. One needs panel data to separate the two effects. 9. The result stems from symmetric boundaries around each member. We thank Dan Black for that observation.

ACKNOWLEDGMENTS We are grateful for ﬁnancial support from the MacArthur Research Network on Social Interactions and Economic Inequality and thank Gerald Auten, Badi Baltagi, Dan Black, Gary Engelhardt, Bo Honore, Bill Horrace, Will Kniesner, Jeff Kubik, Anil Kumar, Lung-fei Lee, Joseph Marschand, Christian Meghea, Andrew Oswald, Jan Ondrich, and two anonymous referees for their helpful comments.

REFERENCES Abel, A. B. (2005). Optimal taxation when consumers have endogenous benchmark levels of consumption. Review of Economic Studies, 72(1), 21–42. Anselin, L. (2001). Spatial econometrics. In: B. H. Baltagi (Ed.), A companion to theoretical econometrics (pp. 310–330). Malden, MA: Blackwell Publishers, Inc. Arellano, M., & Bond, S. (1991). Some tests of speciﬁcation for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies, 58(2), 277–297. Aronsson, T., Blomquist, S., & Sackle´n, H. (1999). Identifying interdependent behaviour in an empirical model of labour supply. Journal of Applied Econometrics, 14(6), 607–626. Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135–171. Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221. Becker, G. S. (1974). A theory of social interactions. Journal of Political Economy, 82(6), 1063–1093. Blundell, R., & MaCurdy, T. (1999). Labor supply: A review of alternative approaches. In: O. Ashenfelter & D. Card (Eds), Handbook of labor economics (Vol. 3A, pp. 1559–1695). Amsterdam: Elsevier Science, North-Holland. Brock, W. A., & Durlauf, S. N. (2001). Interactions-based models, (SSRI). In: J. J. Heckman & E. Leamer (Eds), Handbook of econometrics (Vol. 5, pp. 3297–3380). Amsterdam: Elsevier Science, North-Holland. Brock, W. A., & Durlauf, S. N. (2002). A multinomial-choice model of neighborhood effects. American Economic Review, 92(2), 298–303. Case, A.C., & Katz, L.F. (1991, May). The company you keep: The effects of family and neighborhood on disadvantaged youths. Working Paper No. 3705. National Bureau of Economic Research (NBER).

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Clark, A. E., & Oswald, A. J. (1998). Comparison-concave utility and following behaviour in social and economic settings. Journal of Public Economics, 70(1), 133–155. Conley, T. G. (1999). GMM estimation with cross sectional dependence. Journal of Econometrics, 92(1), 1–45. Durlauf, S. N. (2004). Neighborhood effects. In: J. V. Henderson & J.-F. Thisse (Eds), Handbook of urban economics (Vol. 4, pp. 2173–2242). North-Holland: Elsevier Science. Eklo¨f, M., & Sackle´n, H. (2000). The Hausman-MaCurdy controversy: Why do the results differ across studies? Journal of Human Resources, 35(1), 204–220. Evans, W. N., Oates, W. E., & Schwab, R. M. (1992). Measuring peer group effects: A study of teenage behavior. Journal of Political Economy, 100(5), 966–991. Glaeser, E. L., Sacerdote, B., & Scheinkman, J. A. (2003). The social multiplier. Journal of the European Economic Association, 1(2–3), 345–353. Glaeser, E. L., Laibson, D., & Sacerdote, B. (2002). An economic approach to social capital. Economic Journal, 112(483), F437–F458. Graham, B. S., & Hahn, J. (2005). Identiﬁcation and estimation of the linear-in-means model of social interactions. Economics Letters, 88(1), 1–6. Grodner, A., & Kniesner, T. J. (2006). Social interactions in labor supply. Journal of the European Economic Association, 4(6), 1226–1248. Hahn, J., & Hausman, J. (2003). Instrumental variable estimation with valid and invalid instruments. Unpublished paper, Department of Economics, MIT, Cambridge, MA. Hausman, J. A. (1980). The effect of wages, taxes, and ﬁxed costs on women’s labor force participation. Journal of Public Economics, 14(2), 161–194. Hausman, J. A. (1981). Labor supply. In: H. J. Aaron & J. A. Pechman (Eds), How taxes affect economic behavior (pp. 27–83). Washington, DC: The Brookings Institution. Kapteyn, A., van de Geer, S., van de Stadt, H., & Wansbeek, T. (1997). Interdependent preferences: An econometric analysis. Journal of Applied Econometrics, 12(6), 665–686. Kelejian, H. H., & Prucha, I. R. (1998). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics, 17(1), 99–121. Kelejian, H. H., & Prucha, I. R. (2002). 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Regional Science and Urban Economics, 32(6), 691–707. Kniesner, T. J., & Ziliak, J. P. (2008). Evidence on tax-induced individual behavioral responses. In: J. W. Diamond & G. R. Zodrow (Eds), Fundamental tax reform: Issues, choices, and implications. Cambridge, MA: MIT Press. Kooreman, P., & Schoonbeek, L. (2004). Characterizing pareto improvements in an interdependent demand system. Journal of Public Economic Theory, 6(3), 427–443. Krauth, B. (2006). Simulation-based estimation of peer effects. Journal of Econometrics, 133(1), 243–271. Lee, L.-F. (2007a). GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics, 137(2), 489–512. Lee, L.-F. (2007b). Identiﬁcation and estimation of econometric models with group interactions, contextual factors and ﬁxed effects. Journal of Econometrics, 140(2), 333–374. MaCurdy, T., Green, D., & Paarsch, H. J. (1990). Assessing empirical approaches for analyzing taxes and labor supply. Journal of Human Resources, 25(3), 415–490. Manski, C. F. (1993). Identiﬁcation of endogenous social effects. Review of Economic Studies, 60(204), 531–542.

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Manski, C. F. (2000). Economic analysis of social interactions. Journal of Economic Perspectives, 14(3), 115–136. Mofﬁtt, R. A. (2001). Policy interventions, low-level equilibria and social interactions. In: S. Durlauf & H. P. Young (Eds), Social dynamics (pp. 45–82). Washington, DC: MIT and Brookings Institution Press. Rayo, L., & Becker, G. S. (2007a). Evolutionary efﬁciency and happiness. Journal of Political Economy, 115(2), 302–337. Rayo, L., & Becker, G. S. (2007b). Habits, peers, and happiness: An evolutionary perspective. American Economic Review, 97(2), 487–491. Samuelson, L. (2004). Information-based relative consumption effects. Econometrica, 72(1), 93–118. Soetevent, A. R. (2006). Empirics of the identiﬁcation of social interactions: An evaluation of the approaches and their results. Journal of Economic Surveys, 20(2), 193–228. Stock, J. H., & Yogo, M. (2005). Testing for weak instruments in linear IV regression. In: D. W. K. Andrews & J. H. Stock (Eds), Identiﬁcation and inference for econometric models: Essays in honor of Thomas Rothenberg (pp. 80–108). New York: Cambridge University Press. Weinberg, B. A., Reagan, P. B., & Yankow, J. J. (2004). Do neighborhoods affect hours worked? Evidence from longitudinal data. Journal of Labor Economics, 22(4), 891–924. Woittiez, I., & Kapteyn, A. (1998). Social interactions and habit formation in a model of female labour supply. Journal of Public Economics, 70(2), 185–205. Ziliak, J. P., & Kniesner, T. J. (1999). Estimating life cycle labor supply tax effects. Journal of Political Economy, 107(2), 326–359.

AnnualHours AnnualHour75 AfterTaxWage WageRate WageRate75 VirtualInc NLIncome NLIncome75 AnnHSRG_0_2 AnnHSORG_2_6 IndVORG_2_6 IndVRG_0_2 KIDSU6 FAMSIZ AGE45 HOUSEQ BHLTH

Variable

910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910 910

Observations 2236.864000 2247.385000 4.692693 6.272303 5.479915 5138.557000 3710.268000 3298.155000 2210.108000 2214.600000 301892.000000 352303.000000 0.445055 3.873626 1.748352 18511.900000 0.051648

Mean 536.701100 540.086500 1.198573 1.794132 0.636453 4364.210000 4700.172000 3984.506000 134.322300 53.725650 5444115.000000 0.035230 0.696331 3.873626 3.108485 16930.990000 0.221438

Standard Deviation 288.000000 320.000000 0.542700 0.670000 3.655642 965.000000 7900.000000 10000.000000 1180.000000 2009.458000 1.534880 1.760330 0.000000 2.000000 0.000000 5000.000000 0.000000

Minimum

APPENDIX. DESCRIPTIVE STATISTICS

4917.000000 4500.000000 7.488000 9.900000 6.837162 45593.000000 57640.000000 26000.000000 2950.667000 2477.579000 1.369547 1.598270 3.000000 9.000000 11.000000 120000.000000 1.000000

Maximum

Labor Supply with Social Interactions 23

OVERTIME WORK, DUAL JOB HOLDING, AND TAXATION Anders Frederiksen, Ebbe Krogh Graversen and Nina Smith ABSTRACT Labor supply data seldom include detailed information on hours and wages in secondary job or overtime work. Based on survey information on hours and wages in overtime work and second job which is merged to administrative register information on income taxes and deductions we estimate a ‘‘Hausman labor supply model,’’ which allows for a detailed treatment of nonconvexities. Including explicit information on overtime pay and second job wages increase the estimated elasticities compared to a standard labor supply model without this information. However, allowing a more ﬂexible treatment of nonconvexities the estimated elasticities are reduced; even below the estimates of the baseline results. In simulations we show that these ﬁndings have signiﬁcant consequences when evaluating the degree of self-ﬁnancing of various tax reforms.

1. INTRODUCTION A major criticism of many labor supply models is that hours cannot be varied freely within jobs and that the decision to work overtime or to enter a Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 25–55 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28002-7

25

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ANDERS FREDERIKSEN ET AL.

second job is different from the work hours decision in the main occupation.1 In general, overtime wages exceed the wages in main occupation and second jobs typically imply additional ﬁxed costs of work. The purpose of this paper is to examine the role overtime work and duel job holding plays for the labor supply decision of men and women. The use of additional information on overtime and second job gives a more ﬂexible and realistic modeling of the actual labor supply. The explicit modeling of ﬁxed costs of work, overtime payments, and wages in second jobs is expected to be very important when analyzing potential tax reforms. The main reason is that tax reforms that changes the marginal income tax rates potentially changes the budget segment where the individual’s optimal labor supply is positioned. In particular, a tax reform with tax cuts increases the individual’s incentives to work overtime or take a second job. Thus, it is important that the estimated model takes the nonlinearities of the budget constraint related to this decision into account. Despite the vast literature on labor supply models, there are relatively few studies focusing on the implications of overtime work and dual job holding (cf. Hart, 2004). One of the ﬁrst studies, which explicitly model these aspects of the supply decision, is Ashworth and Ulph (1981). They ﬁnd numerically larger elasticities when overtime and second job wages are explicitly modeled compared to a model where the budget constraint is linearized around the point of observation. In this paper, we apply a piecewise linear approach, for simplicity denoted a ‘‘Hausman approach,’’ which allows for an explicit treatment of the nonlinearities imposed by the tax system. This approach is known to be sensitive to the speciﬁcation of functional forms and measurement errors in the hours and wage variables. In addition, the Hausman model is very demanding with respect to the information required to construct the budget constraint (see, for instance, Blundell & MaCurdy, 1999). Introducing information on overtime work and dual job holding requires two extensions of the traditional Hausman approach. First, the number of budget segments is increased to capture variation in wages between main job, overtime work, and second job. Second, we anticipate that some workers will have additional costs associated with working in a second job. The extensions are found to be empirically relevant for both men and women. The estimated model is a generalization of a Tobit model that accounts for the joint participation and hours decision which is especially important when we look at female labor supply where a signiﬁcant part of the women are nonparticipants.2 In addition, we take measurement errors in the labor supply as well as unobserved heterogeneity in preferences into account.

Overtime Work, Dual Job Holding, and Taxation

27

The model is estimated on a survey collected by Statistics Denmark in 1996. The survey information is merged with very detailed information from administrative registers on incomes and taxes. The main feature of the data which is explored extensively in this paper is the detailed information on individual labor supply and wages in a person’s main job, overtime work, and second job. Our results show that the labor supply elasticities are highly sensitive to the inclusion of the information on overtime work and secondary job and to the handling of ﬁxed costs of work. The additional information increases the estimated elasticities as in Ashworth and Ulph (1981). However, the subsequent introduction of ﬂexibility reduces the estimated elasticities considerably compared to traditional labor supply models without explicit information on overtime pay and second job wages. Hence, our new results show that omitting crucial information related to work hours exceeding the hours in the main job may lead to signiﬁcant overestimates of the labor supply effects and the degree of self-ﬁnancing of tax reforms. The economic consequences of this shortcoming may be large. The theoretical framework is discussed in the next section. In Section 3 we present the data and show descriptive statistics. The choice of empirical model is motivated in Section 4. We give a detailed discussion of the models assumptions and propose various empirical model speciﬁcations in Section 5. The results from the estimations are presented in Section 6. These results are used for simulation of four hypothetical tax reforms in Section 7. Finally, Section 8 concludes the paper.

2. THE THEORETICAL MODEL We model the individual labor supply decision using a piecewise linear approach which is known as the Hausman model.3 The individuals choose bunches of consumption and hours of work, (C,h), which maximizes their utility function U(C,h), given the piecewise linear budget constraint. The constrained utility maximization implies a labor supply function, which depends on the after-tax wage rate and after-tax income. The traditional Hausman model relies on the assumption that workers face one exogenously given wage rate which is independent of the number of hours supplied. Embedded in this approach is that the individual can vary the number of hours freely at a given wage rate ignoring all institutional settings in the market such as labor laws requiring overtime compensation and limits to the number of hours an individual can supply in a given job. Since these restrictions are important in labor markets, we extend the

28

ANDERS FREDERIKSEN ET AL.

conventional model and explicitly integrate information on overtime and second job into the individual-speciﬁc budget constraint. This means that instead of one wage, individuals are now facing three exogenous wage rates in the market; i.e., a wage in the main job, an overtime wage, and a second job wage.4 This results in the following budget constraint: C ¼ ðwm hm FCm Þ þ wo ho þ ws hs þ Y þ V tðIÞ

(1)

where C is annual consumption, wm, wo, and ws are the hourly wage rates in main occupation, overtime work, and second job, respectively, hm, ho, and hs, annual labor supply in main occupation, overtime work, and second job. Y is annual taxable nonlabor income, V, annual nontaxable nonlabor income, including spouse’s after-tax income if married or cohabiting. t(I) is the tax function, where I is annual assessed income, I=SwhþYD, and D is annual deduction. FCm are the ﬁxed money costs of work, e.g., costs of transport and childcare, associated with the job. We consider two speciﬁcations for hours.5 First, we apply the ‘‘hours constraints’’ speciﬁcation outlined in Shisko and Rostker (1976) who assume that hours supplied to different types of jobs have similar disutility, i.e., h ¼ hmþhoþhs. Further, hours constraints and institutional factors in the main occupation is the primary motivation for multiple job holding. Second, we use the ‘‘heterogeneous-job’’ speciﬁcation discussed in Conway and Kimmel (1998) and Heineck and Schwarze (2004) and explore how variation in the nonpecuniary beneﬁts or unobservable costs associated with different jobs can account for the observed variation in hours. This is implemented by allowing the disutility of work between the main employer (main hours and overtime hours) and work in a second job to differ in the econometric speciﬁcation. Because these costs are nonmonetary, they do not show up in Eq. (1). The nonlinear budget constraint is characterized by its kinks, the after-tax wage rates and virtual incomes on the linear segments. These can be obtained using a simple iterative procedure as long as nonlabor income, gross wage rates, labor supply, and the tax system are known. Fig. 1 exempliﬁes a budget constraint for a person who has both overtime work and a second job in addition to the main occupation. The person was subject to the Danish tax system in 1996 which had four tax segments and three kink points. The marginal tax rates on the four segments were 7%, 47.2%, 51.8%, and 65.8% and the distribution of individuals in the sample is shown in Table 1 for men and women, separately. In general, the marginal tax rates in Denmark are high compared to most other OECD countries

29

Overtime Work, Dual Job Holding, and Taxation C

Ws(1-t 4) y6 y4 y3 y2 y0

.

y1 O y5

Wo(1-t 4)

Wm(1-t 4)

Wm(1-t 3) Wm(1-t 2) Wm(1-t 1)

H H0 H1

H2

H3

H4

H5

H6

Fig. 1. The Piecewise Linear Budget Constraint with Fixed Costs of Work and Six Linear Segments due to Nonlinear Income Taxes and Different Wages in Main Occupation, Overtime Work, and Second Job. Note: The difference between y1 and y0 in Fig. 1 is the sum of ﬁxed costs of work and reductions in unemployment or social welfare beneﬁt. It is assumed that the unemployment and social welfare beneﬁt disappears when the ﬁrst hours is worked in accordance with the rules in Denmark in 1996.

Table 1.

Men Women All

Distribution of Men and Women by Marginal Tax Rates.

Marginal Tax Rate r7%

Marginal Tax Rate 47.2%

Marginal Tax Rate 51.8%

Marginal Tax Rate 65.8%

All (%)

1% 3% 2%

10% 34% 23%

58% 54% 56%

31% 9% 19%

100 100 100

(see, for instance, OECD, 1996) and the actual marginal tax rates are considerably higher for men than for women. This reﬂects the higher level of earnings and nonwage income of men, but it also reﬂects the Danish tax system which is dominated by a separate taxation of spouses (see Smith, Dex, Vlasblom, & Callan, 2003). Labor supply up to H4 in Fig. 1 represents work in main occupation, excluding overtime work, with an hourly gross wage rate, wm. The person is assumed to have an income in main occupation, excluding overtime work, which passes the three thresholds or kinks of the progressive income tax

30

ANDERS FREDERIKSEN ET AL.

scheme. If the person works more than standard hours, he is assumed to get an overtime compensation, which exceeds the standard wage in the main occupation. This is represented by the hours range from H4 to H5. Further, the person may have a second job. In Fig. 1, it is assumed that the net wage in second job equals the hourly main job wages. A different budget constraint arises if the person has a relatively low hourly wage rate in main occupation – or a very large tax deduction – which implies that kink points from the tax schedule may lie in the hour ranges for overtime work or second job. There are of course a number of possible combinations of hypothetical budget constraints, depending on the size of Y, V, D, the wage rates and the job opportunities faced by the individual. The after-tax wage rate on segment j is given as wij ¼ wi ð1 tj Þ where tj is the marginal tax rate on segment j, and wi is the hourly wage rate in either main occupation, overtime work, or second job (i ¼ m, s, o). To simplify notation, we drop the subscript i in the following. The virtual income on the ﬁrst budget segment is given as y1 ¼ VþYt(YD)FCm. The virtual income corresponding to segment j can be found iteratively as yj ¼ yj1 þ ðwj1 wj ÞH j1 ; 8j 2. Given the deﬁnition of yj, wj, and Hj above, the individual’s optimization problem becomes the following, where k is the maximum number of segments (k ¼ 6 in Fig. 1). 8 Max UðC; hÞ > > s:t: > > < y1 if h ¼ H 0 (2) C¼ > wj h þ yj if H j1 ohoH j j ¼ 1; . . . ; k > > > : wk H k þ yk if h ¼ H k Hk corresponds to the total time allocation. The solution to the maximization problem is obtained from an algorithm that compares all local optima for the complete budget constraint and returns the global optimum, which is the maximum of all local optimal utilities. The ﬁrst step of the algorithm is to identify the locally optimal choice of labor supply from the desired hours function, f(wj, yj), for each linear segment of the budget constraint. If the locally optimal solution is calculated to be within the range of hours over which the linear segment is deﬁned, it is said to be ‘‘feasible.’’ If we have a ‘‘convex’’ kink and the locally optimal solution on a segment lies above the feasible range and if the locally optimal solution on the following segment lies below the feasible range, we have a kink between two segments as a feasible solution. An interior ‘‘nonconvex’’ kink can never

Overtime Work, Dual Job Holding, and Taxation

31

be a feasible solution (while the corner solution at h ¼ 0 may be both optimal and feasible). Hence, this ﬁrst step yields a vector of information about the segments and kinks where an element takes the value one if the segment is feasible and zero otherwise. Second, after all feasible local optima have been identiﬁed, the algorithm ﬁnds the global optimum by calculating which is the feasible local optima that generates the maximum utility. When the direct utility function is only implicitly available, the maximum must be calculated using the indirect utility function. It is easily done for all the feasible segments, but no deﬁnitive wage rate exists at the kink points. However, we can evaluate the inverse demand function, w ¼ w(h, y), at the hours corresponding to the kink point and ﬁnd a ‘‘support’’ wage rate and virtual income. By duality, the substitution of the ‘‘support’’ wage rate and income into the indirect utility function at the kink point hours is sufﬁcient to evaluate the level of direct utility at the kink point (cf. Duncan, 1993).

3. DATA The data used in this study are based on a survey of 4,000 Danes collected by Statistics Denmark in 1996. The initial sample covers the age range of 16–74 years. In the present study we restricted the sample to individuals aged 18–59 years to limit the inﬂuenced of human capital accumulation and retirement (early retirement schemes are available from age 60). We include married, cohabiting, as well as single individuals in the sample, but exclude individuals with long-term illness, students, self-employed persons, and their spouses. The exclusion of the two latter groups is made because we are unable to calculate their income taxes and hence to construct their budget constraints because the Danish tax rules for self-employed families requires more information than is available in the database. The exclusions result in a sample of 2,441 individuals. The labor supply of unemployed individuals is determined by questions on their search behavior. Unemployed individuals who are on unemployment insurance beneﬁts or social welfare are asked the conventional questions from labor force surveys on search behavior. Based on the answers to these questions, we divide the unemployed into two groups, those who satisfy the ILO conditions of being unemployed (involuntarily unemployed) and those who do not (voluntarily unemployed). The ILO criteria for being categorized as (involuntarily) unemployed are that the person has been seeking for a job actively within the latest month and that

32

ANDERS FREDERIKSEN ET AL.

he or she is able and willing to start in a new job within the next two weeks. If the person satisﬁes these conditions, he or she is assumed to have a desired labor supply of 37 h weekly if full-time insured against unemployment and 20 h weekly if part-time insured against unemployment.6 If the person does not satisfy the ILO criteria, he is categorized as voluntarily unemployed with a desired labor supply of 0 h. Euwals and van Soest (1999) and Bingley and Walker (2001) have applied a similar identiﬁcation procedure using data for the Netherlands and the UK, respectively. The sample includes survey information on weekly normal hours in main occupation, normal working hours in second job, if the person holds a second job, and number of hours in overtime work in the week prior to the survey week.7 Tables 2 and 3 show the distribution on employment states and average weekly hours in main job, overtime work, and second job for the 1,150 men and 1,291 women included in the empirical sample. The majority of the sample has only a main job. More men than women tend to work overtime or have a second job, and a higher proportion of women are nonparticipants. Twelve percent of the individuals in the sample are either unemployed or observed as nonparticipants, 64% have only one job and no overtime hours, and 24% have a second job or work overtime beside their main occupation. Out of these 24%, 18% – points only work overtime, 5% – points only have a second job, while a little more than 1% – point is observed to have overtime hours as well as a second job.8 The weekly number of working hours is relatively low in Denmark compared to other European countries. On average, an employed man works more than an employed woman in all three job types: main job, overtime, or second job (cf. Table 3). Table 2. Distribution of Men and Women in Nonparticipation, Unemployment, and Employment in Main, Overtime, and Second Job Occupation. Nonparticipants Unemployed

Men Women All

0.03 (36) 0.08 (101) 0.06 (137)

0.06 (72) 0.07 (86) 0.06 (158)

Main Main and Occupation Overtimea Only Occupation

0.60 (694) 0.67 (864) 0.64 (1,558)

0.22 (254) 0.14 (187) 0.18 (441)

Main and Main, Second Job Overtimea and Occupation Second Job Occupation 0.06 (72) 0.03 (45) 0.05 (117)

0.02 (22) 0.01 (8) 0.01 (30)

Total

0.99 (1,150) 1.00 (1,291) 1.00 (2,441)

Note: Number of observations in parentheses. a 130 men and 81 women with observed overtime (main hours exceeding 37 per week) did not get any compensation for their overtime work. These observations are included in Column 3 (Main Occupation Only).

33

Overtime Work, Dual Job Holding, and Taxation Average Weekly Hours in Main Occupation, Overtime, and Second Job, Conditional on Participation.

Table 3.

Main Occupation (h)

Overtime Work (h)

Second Job (h)

Total (h)

37.9 34.5 36.1

2.1 1.0 1.5

1.0 0.4 0.7

41.0 35.9 38.3

Men Women All

Table 4.

Observed Average Hourly Wages in Main Occupation, Overtime Work, and Second Job. Main Occupation

Men Women

Overtime Work

Second Job

N

Wage, DKK

N

Wage, DKK

N

Wage, DKK

1,042 1,104

133.7 107.0

276 195

170.1 148.6

94 53

140.5 135.9

In the survey we have detailed information on individual wages in each of the three job types: main job, overtime, and second job. Hence, we know for instance if a person working overtime is compensated beyond his main job wage. The compensation or extra payment for overtime work is determined by union-speciﬁc collective agreements with Danish employers. Standard working hours is 37 h per week and additional work taking place at the main employer is considered overtime work. Hourly or weekly paid manual workers typically get overtime payments or they are allowed to take time off later on. Monthly paid nonmanual workers seldom get overtime pay. In some cases, they may have the right to take time off later on (see Smith, 1998). The sample values of average observed wage rates (conditional on participation) in main occupation, overtime work, and second job are shown in Table 4. Overtime payments exceed the payments for standard hours in main occupation and second job with a considerable amount, while second job wages on average are higher than main job wages but lower than hourly overtime payments. More detailed cross tabulations show that individuals with low hours in main occupation tend to have relatively low hourly wages in second job, while individuals with a full-time job have higher wages in a second job (see Frederiksen, Graversen, & Smith, 2001). This may reﬂect that individuals with few hours in main occupation have to supplement their income with a second job in order to

34

ANDERS FREDERIKSEN ET AL.

work the preferred hours, i.e., they are restricted from having a full-time job in their main occupation (see Trejo, 1993). At the other extreme, for individuals who hold both a full-time and a second job, the jobs often seem to be complements, i.e., professors with complementary consultancy jobs (see Paxson & Sicherman, 1996). In these cases the second job may improve the career opportunities hence they are not accepted only to increase current wage income. This is a point which is discussed further in Section 5. The construction of individual budget constraints requires a speciﬁcation of income both when the individuals are working and not working. The required information is obtained from different administrative registers (tax, income, social welfare and other income transfers, and UI-beneﬁt registers), which have been merged to the survey information. Thus, we have information on total annual earnings, capital income and income from other sources, tax deductions, UI beneﬁts, social welfare payments, child and housing subsidies. The income when not working (y0) is calculated as follows: For individuals insured against unemployment (about 80% of the employees), we include potential unemployment beneﬁts in the budget constraint. Unemployed individuals who are insured in an UI fund receive an hourly compensation of 90% of prior hourly wages up to a ﬂat rate. The UI compensation in Denmark is independent of other sources of income and independent of the income of a spouse. In contrast to working individuals, we have no information on hourly wage rates for nonworking individuals. Hence, we use the predicted wage rate based on selectivity-corrected wage regressions to construct the budget constraint.9 About 5% of the individuals are observed as involuntarily unemployed, i.e., they are not working but have a desired positive labor supply according to the ILO criteria (cf. Table 2). Another group of the same size does not have a positive labor supply according to the ILO criteria. Both groups do not have an observed wage rate and for these individuals we use predicted hourly wage rates based on estimations of selectivity-corrected wage functions. Similar wage regressions are estimated for the missing wage rates on overtime and second jobs. The sample includes married as well as single individuals. In the estimations, we model the individual labor supply decision, i.e., not a household decision. For married or cohabiting individuals we treat the spouse’s net income after taxes and means-tested income transfers as exogenous nonlabor income. Thus, we only allow for an income effect between spouses’ labor supply behavior and not a cross-substitution effect.

35

Overtime Work, Dual Job Holding, and Taxation

Other Danish empirical studies ﬁnd quite low cross substitution and family income effects between spouses (see Smith, 1995, among others).10 An overview of a number of demographic and regional variables used in the estimations is given together with sample means and deviations in Table A1 in the appendix.

4. THE EMPIRICAL MODEL SPECIFICATION In order to specify the empirical model, we have to select a functional form of the labor supply function and a stochastic structure. In this study, we select a ﬂexible nonlinear speciﬁcation, which allows for backward bending labor supply as in Duncan (1993). The speciﬁcation is nonlinear in the wage rates but linear in the nonlabor income. However, the direct utility function does not exist in a closed form, so instead we use the indirect utility function in the algorithm described above to ﬁnd the desired labor supply.11 Consider the following empirical speciﬁcation, which is linear in all the parameters to be estimated, y. h ¼ f ðwj ; yj Þ ¼ xj y þ n h^j þ n;

j ¼ 1; . . . ; k

(3)

xj is a vector of explanatory variables. The error component, n, represents heterogeneity in preferences with n Nðmn ; s2n Þ and it is assumed to be uncorrelated with observable variables in xj. The after-tax wage rate and virtual income enter the labor supply function by the nonlinear term bln(wj)þg(yj/wj). This speciﬁcation allows for a backward bending supply curve for some or all individuals if bo0 and go0. The model is well speciﬁed in a utility-maximizing sense as long as the Slutsky condition holds, i.e., (bg(yj/wj))/hg W0 (cf. MaCurdy, Green, & Paarsch, 1990). Heterogeneity of preferences, represented by n, tends to generate clusters of observations around the convex kink points and to disperse observations away from nonconvex kink points (see Mofﬁtt, 1986). The empirical data normally show no bunching or dispersion of individuals at or around the kink points, but usually there is a large concentration of observations at h ¼ 0 and at the standard number of hours in a full-time job (37 h weekly in Denmark in 1996) which may reﬂect different constraints on labor supply or ﬁxed costs of work in second job, as discussed in Section 2. In order to capture optimization errors or measurement errors, we add an additive random error term to the model. Let the observed labor supply, h, be a function of desired hours, h, and an error component, e, so h ¼ hþe, where

36

ANDERS FREDERIKSEN ET AL.

e Nð0; s2e Þ and Eðn; Þ ¼ 0. Now the problem is that the observed h is neither sufﬁcient to allocate individuals to their correct budget segment nor sufﬁcient to identify their marginal tax rate. Only the information on h reveals this. Since the individuals’ desired segment choice is not directly observable, one has a discrete-data version of an errors-in-variables problem, and the resulting stochastic model speciﬁcation becomes the following: 8 H0 þ if h^1 þ n H 0 Lower limit > > > > < h^j þ n þ if H j1 oh^j þ n H j Segment j; j ¼ 1; . . . ; k (4) hn ¼ > Hj þ if h^jþ1 þ noH j oh^j þ n Kink j; j ¼ 1; . . . ; k 1 > > > : Hk þ if h^k þ n H k Upper limit This combines the discrete and continuous parts of the choice in an estimable econometric model. The likelihood function becomes Y Y Y L¼ Gðhni ¼ 0Þ gðhni Þ Gðhni ¼ H k Þ (5) i¼I

i¼J

i¼K

where G( ) is the cumulative density function, and g( ), the derivative of G( ) w.r.t. x, dG( )/dx I, the index set for the nonparticipants (h ¼ 0), J, the index set for the individuals with a positive labor supply less than Hk (0ohoHk), and K measures the individuals who work Hk hours or more (hZHk). The exact expression of the density gðhni Þ and the probability Gðhni ¼ 0Þ is given in the appendix. Maximization of the likelihood, L, provides point estimates of the parameters in the labor supply function.12

5. BUDGET CONSTRAINTS AND MODEL SPECIFICATIONS In order to estimate the Hausman model, a complete speciﬁcation of the budget constraint is required. For this reason, we will discuss the underlying assumptions which are necessary to construct the empirical budget constraints. The traditional Hausman model relies on the assumption that workers face one exogenously given wage, which is independent of the number of hours supplied. However, the empirical evidence presented in Tables 3 and 4 contradicts this assumption since a substantial part of the individuals are observed to work more than standard hours at overtime or

Overtime Work, Dual Job Holding, and Taxation

37

second job wages, which often are different from the wage in the main occupation. First, we propose models which follow the ‘‘hours constraints’’ speciﬁcation (see models I–III below). These models assume (as discussed in Section 2) that labor supply at the main employer may be constrained and that institutional settings will distinguish hours supplied to the main job from overtime hours. Thus, underemployment in the main occupation and institutions may lead to overtime work and dual job holding. Further, these speciﬁcations assume that the disutility of work is similar across job types. These assumptions can be applied directly to the Danish case since collective agreements set standard hours to 37 per week and work beyond that at the main employer is considered overtime. Second, in model IV, we explore the ‘‘heterogeneous-job’’ speciﬁcation by allowing the disutility of work to vary across jobs. In model I, we estimate a ‘‘standard’’ Hausman model where the labor supply equals the sum of hours in main and second job plus overtime hours, but we ignore information on overtime payments and second job wage rates. This ‘‘baseline model’’ corresponds to the deﬁnitions of wage rates and working hours in Blomquist (1983) and Graversen (1998) and resembles many labor supply models estimated which have not explicitly focused on overtime work and second job information. In model II, we add information on wages in second job and overtime payments. Thus, we improve the Hausman approach by allowing for a more realistic modeling of the labor supply decision. This will increase the marginal wage rates for most individuals working overtime and for some individuals in second job. Hence, other things being equal, the wage coefﬁcient will increase together with the corresponding wage elasticity. When including information of second job and overtime work, we have to impose a number of assumptions concerning behavior and outside restrictions in order to construct the budget constraint. First, we introduce the assumptions of ‘‘hours constraints’’: individuals supply overtime and second job hours because they are underemployed in main occupation and because institutions require main job hours to be distinguished from overtime hours. The disutility of work is assumed to be similar across jobs. The budget constraint is easy to construct for employees working overtime but not in a second job. The reason is that collective agreements state that all work beyond 37 h per week at the main employer is overtime. Hence, when an employee works more than 37 h and receives an overtime premium, there will be a nonconvex kink at this point. When there is no overtime premium, the last main job segment is extended linearly as in the traditional Hausman model.

38

ANDERS FREDERIKSEN ET AL.

Individuals working multiple jobs allocate most of their time (typically 37 h or more) to one of the jobs and only a few hours to the other (see Table 3). We use this observation to deﬁne an employee’s main occupation as the job with most hours. Of course this assumption may be challenged by the few cases where the wage in the second job exceeds the main job wage but often these lucrative second jobs are only available to the individual conditional on holding the main job, i.e., professors working as consultants. Thus, this ordering of jobs seems natural. Most employees who work more than standard hours have either a second job or they work overtime. However, a small group of individuals (about 1% according to Table 2) work both overtime and have a second job. In order to construct the budget constrains for these individuals we need to specify an ordering between these two types of jobs. We assume that overtime hours are preferred to a second job. There are at least two economic arguments supporting this assumption. First, on average overtime wages are empirically much higher than wages in a second job (see Table 4). Second, working in a second job is very likely to have additional ﬁxed costs, i.e., transportation etc. which does not apply to overtime hours because these hours are an extension to the workday at the current employer. Thus, when an individual is observed to work in a second job, it is assumed that the overtime option has been exhausted. Finally, we assume that individuals who are observed to work only in their main job can vary their labor supply as in the traditional Hausman model. If the individual is observed to have only a main job, there are in principle three alternative interpretations: (i) the individual may not have the option to work overtime or cannot ﬁnd a second job; or (ii) he may have had, but not used, the option to become compensated for overtime work or the option of a second job where the wage exceeds the compensation in the main job; or (iii) he had the option of overtime work or second job, but at a salary which is too low. In case of (i), there may be institutional regulations preventing him from varying hours freely. In our model, this is captured by the error term e. If (ii) applies, the budget constraint will have a nonconvex kink at observed hours. As a nonconvex kink cannot be an optimal allocation for the individual, it must be the case that the option of a higher compensation for overtime work or in a second job does not exist. Finally, in case (iii) the option of overtime payment at a lower wage level than in the main job can be ruled out because of institutional settings, while we cannot rule out the possibility of a convex kink because of the option of a second job with a lower net wage than in the main job.

Overtime Work, Dual Job Holding, and Taxation

39

In model III, we introduce a more ﬂexible speciﬁcation related to the nonconvexity at H0 due to the inclusion of UI beneﬁts and social welfare. The nonconvexity forces the indifference curve to become very ﬂat for individuals who are observed to work for instance in a fulltime job, in spite of the fact that their economic gain is quite low compared to being unemployed and receiving UI beneﬁts, i.e., point [H0,y0] in Fig. 1. This reﬂects that the economic disincentive problems are quite large in Denmark, see Pedersen and Smith (2002) who show that about 10% of all employees have a lower disposable income when working full time compared to being on UI beneﬁts. In addition, the state as nonparticipant/voluntarily unemployed may imply a stigmatization effect for individuals who are unemployed and receive social welfare or UI beneﬁts. The stigmatization may reﬂect that there is a negative effect on individual utility from being on public income support because of lower ‘‘reputation among neighbors’’ etc. Or, it may reﬂect that the individual is aware that being on public income support is a negative signal for a potential future employer. The stigmatization effect may also capture effects from administrative rules concerning availability for the labor market etc. In order to take these potential effects into account, we propose a more ﬂexible speciﬁcation where an indicator variable is added to the right-hand side of Eq. (3) for individuals who are observed working.13 Finally, in model IV we extend the model by including a ‘‘heterogeneousjob’’ effect. The disutility of work at the main employer may be different from the disutility of work in a second job. We implement this by adding a second indicator on the right-hand side of Eq. (3) for individuals who are observed to work in a second job. The second job dummy is intended to capture the discontinuity effects due to missing information on ﬁxed costs (time and money costs of transportation and equipment) in second job as well as nonpecuniary beneﬁts. We expect that adding this ﬂexibility into the model may decrease the wage elasticity when the nonpecuniary beneﬁts dominate since the number of hours and income in the second job in this case is less important and more likely a participation decision, i.e., a career or income improving action. In sum, four versions of the labor supply model are estimated in order to evaluate how sensitive the estimation results are with respect to additional information on overtime payments and second job wage rates and the assumptions concerning the budget constraint. The strategy is successively to add more survey information and allow the model to be increasingly ﬂexible.

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ANDERS FREDERIKSEN ET AL.

6. EMPIRICAL RESULTS 6.1. The Hausman Model The empirical results are presented separately for men and women in Tables 5a and 5b. The key ﬁnding is that the detailed information on overtime payments and second job wages and the added ﬂexibility of the Hausman model speciﬁcation are important. First, the estimated wage and income coefﬁcients are affected signiﬁcantly. Second, the associated elasticities are Table 5a.

Estimation of Labor Supply Functions (Men 1996). I Baseline

0.736 (0.143) ln(wnet)/10 (y/wnet)/100 0.079 (0.029) Controls for Yes demographic variables Stigma effect – Second job dummy – se (measurement, 0.090 (0.002) optimization) su (heterogeneity) 0.055 (0.003) log(L) 904 Number of observations 1,150 Elasticitiesa eucw_net ecw_net ey

0.277 (0.009) 0.358 (0.010) 0.078 (0.002)

II Information on Overtime and Second Job 1.281 (0.142) 0.097 (0.015) Yes

III IIþStigma Effect

IV IIIþSecond Job Dummy

0.333 (0.080) 0.169 (0.039) 0.016 (0.003) 0.001 (0.001) Yes Yes

– – 0.097 (0.001)

0.329 (0.009) – 0.046 (0.002)

0.341 (0.008) 0.071 (0.011) 0.024 (0.001)

0.059 (0.003) 877 1,150

0.079 (0.003) 1,034 1,150

0.083 (0.002 1,195 1,150

0.413 (0.022) 0.496 (0.022) 0.143 (0.021)

0.103 (0.065) 0.052 (0.034) 0.119 (0.063) 0.053 (0.034) 0.018 (0.060) 0.006 (0.023)

Note: The elasticities are calculated from the following expressions and evaluated at average sample values:

eucw

a

! xy y 1 ; ey ¼ F pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ b g w h s22 þ s2n ! xy y wh ; and ecw ¼ eucw ey : ¼ F pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ g 2 2 wh y s2 þ sn

Dependent variable is weekly hours. Standard deviations in parentheses.

41

Overtime Work, Dual Job Holding, and Taxation Table 5b.

ln(wnet)/10 (y/wnet)/100 Controls for demographic variables Stigma effect Second job dummy se (measurement, optimization) su (heterogeneity) log(L) Number of observations Elasticitiesa eucw_net ecw_net ey

Estimation of Labor Supply Functions (Women 1996). I Baseline

II Information on Overtime and Second Job

III IIþStigma Effect

IV IIIþSecond Job Dummy

1.111 (0.245) 0.022 (0.014) Yes

3.326 (0.175) 0.220 (0.041) Yes

0.363 (0.130) 0.032 (0.022) Yes

0.488 (0.093) 0.004 (0.002) Yes

– – 0.115 (0.002)

– – 0.065 (0.001)

0.071 (0.006) – 0.032 (0.022)

0.074 (0.002) 0.003 (0.025) 0.030 (0.001)

0.059 (0.005) 569 1,291

0.209 (0.007) 445 1,291

0.115 (0.003) 1,247 1,291

0.117 (0.003) 1,247 1,291

0.360 (0.005) 0.381 (0.005) 0.040 (0.001)

0.760 (0.019) 0.907 (0.022) 0.137 (0.005)

0.137 (0.034) 0.169 (0.034) 0.030 (0.025)

0.148 (0.038) 0.152 (0.038) 0.007 (0.053)

Note: See Note in Table 5a. a Dependent variable is weekly hours. Standard deviations in parentheses.

altered substantially. The estimated wage effect is signiﬁcantly positive in all models while the income effect is negative, but often insigniﬁcant. In the baseline model, model I, the estimated average wage elasticity (uncompensated elasticity of substitution) is 0.277 for men and 0.360 for women, while the average income elasticity is estimated to be 0.078 for men and 0.040 for women.14 This is in accordance with earlier Danish studies using the Hausman approach (see, for instance, Graversen, 1998). As expected from the literature, adding information on overtime and second job (model II) implies that the estimated wage elasticities increase considerably. The average uncompensated wage elasticity increases to 0.413 for men and 0.760 for women and the numerical size of the income effect also rises. However, the numerically larger elasticities are reduced when we extend the traditional Hausman approach and allow for a more ﬂexible treatment of nonconvexities in the budget constraint. In model III, we add the stigma effect which is intended to capture negative stigma or signaling effects from receiving public income transfers instead of income from work. This reduces the numerical size of the estimated coefﬁcients and elasticities considerably.

42

ANDERS FREDERIKSEN ET AL.

Adding the second job dummy (model IV) which controls for nonconvexities due to unobserved ﬁxed costs or nonpecuniary beneﬁts of second job reduces the size of the estimated coefﬁcients for men even further. The estimated stigma effect in model III is high and it is quite stable when adding the second job dummy in model IV. Thus, the introduction of the ﬂexibility terms into a traditional Hausman model seems to have large effects on the estimated coefﬁcients and elasticities. For women, nonconvexity due to stigma effects etc. are important, while nonconvexities due to second job only play a minor role. Both the stigma and the estimated second job effects are signiﬁcant for men. This clearly indicates a career effect among men, but the effect seems to be absent among women. The more ﬂexible speciﬁcation used here compared to the traditional Hausman approach drives the estimated average wage elasticity for men from 0.41 to 0.10 (model III) and 0. 05 (model IV), while for women the average wage elasticity drops from 0.76 to 0.14 (model III) and 0.15 (model IV). The average estimated income elasticities also reduce to an average close to 0. The size of the average elasticities found in the ﬁnal model IV is lower than the results found in previous Danish studies using a Hausman approach (see Graversen, 1998). In a recent study using a nonparametric Hausman approach, Blomquist, Eklo¨f, and Newey (2001) have found wage elasticities for Swedish men of about 0.08 which is lower than earlier Swedish studies based on parametric Hausman models (see Blomquist & Hansson-Brusewitz, 1990). In general, the elasticities estimated from model IV are positioned at the lower end of the scale compared to estimates from other studies using the Hausman method (see Blundell & MaCurdy, 1999, for a survey). The variance of both the measurement error and the heterogeneity error is signiﬁcant in all speciﬁcations for both men and women except model III for women. Hence, the inclusion of the two error terms seems to be of importance. The size of the variance of the measurement and optimization error is approximately the double of the heterogeneity error variance in the baseline model I but it decreases the more information on overtime work and second job that is included in the models II, III, and IV, i.e., the more ﬂexible the estimated model becomes.

6.2. Alternative Model Speciﬁcations One question of particular interest is if the substantial variation in the parameters due to the inclusion of information on overtime and second job

Overtime Work, Dual Job Holding, and Taxation

43

is unique to the Hausman model or if it can be observed in other model speciﬁcations as well. We explore this by estimating a set of linear regressions. In the ﬁrst two models we only use wage information from the main job. Thus, we regress weekly hours on income and the wage in the main occupation (the marginal main job wage) ignoring overtime pay and second job wages. In the ﬁrst model we use the gross wage, and in the second model the net wage. In the third model we include information on overtime and second job, which implies that the marginal net wage may include an overtime premium or be the net wage in a second job. There are other ways to use the additional information and the example provided here is only intended to illustrate the point that the estimated labor supply effects in a linear model are altered signiﬁcantly when information on wages in overtime and second job is included. We present the results from the linear regressions in Table 6. In the ﬁrst model we ﬁnd that the coefﬁcient on the gross main job wage is positive and signiﬁcant and the coefﬁcient on income is negative for both men and women. Using the net wage instead changes the sign on the wage and reduces the coefﬁcient on income to zero. Including information on overtime and second job alters the coefﬁcient on the net wage signiﬁcantly but recovers the negative signiﬁcant sign on income. This implies that both the uncompensated wage elasticity of hours of work and the income effect are negative which resembles the early literature on labor supply reviewed by Pencavel (1986). Important in this context is that the presumption that the point estimates in the linear model are signiﬁcantly altered when introducing information on overtime and second jobs is supported by the data. Hence, the result found in the Hausman model also applies to the linear framework. Another important question is if the large variation in parameters is driven by the nonconvexities following the introduction of information on overtime and second job. One way to address this issue is to follow the work by MaCurdy et al. (1990) and ‘‘convexify’’ the budget set. Our model IV shows only minor deviations from the original results when the budget constraint is convexiﬁed as can be seen when the last two columns of Table 6 are compared with the results of Table 5. This suggests that it is not the treatment of the nonconvexity, i.e., how the applied algorithm allocates individuals to the optimal segment, but instead the introduction of additional information which is driving the results presented in this paper. In the next section we analyze the effect of potential tax reforms using the results obtained from model speciﬁcation IV since this model represents the most ﬂexible speciﬁcation and the highest likelihood value is obtained in this model.

Yes

Men

Women

Net wage when information on overtime and second job is included

Yes

Yes

0.000 (0.000) Yes

Yes

Yes

0.000 (0.000) 0.002 (0.000) 0.003 (0.000)

1.710 (0.303) 0.049 (0.002) 0.062 (0.002) 0.020 (0.001) 0.044 (0.002)

0.115 (0.043) 0.194 (0.032)

1.194 (0.243)

Note: Dependent variable is weekly hours. Standard deviations in parentheses.

w/10 ln(wnet)/10 y/100 (y/wnet)/100 Controls for demographic variables Stigma effect Second job dummy se (measurement, optimization) su (heterogeneity)

Women

Men

Men

Women

Net main job wage

Linear Regression Models

Alternative Model Speciﬁcations.

Gross main job wage

Table 6.

0.372 (0.131)

Women

0.071 (0.006) 0.001 (0.026) 0.032 (0.001) 0.115 (0.003)

0.137 (0.006) 0.066 (0.015) 0.033 (0.003) 0.088 (0.003)

0.001 (0.001) 0.032 (0.022) Yes Yes

0.190 (0.047)

Men

‘‘Convexiﬁed’’

Hausman Models Using Speciﬁcation IV

44 ANDERS FREDERIKSEN ET AL.

Overtime Work, Dual Job Holding, and Taxation

45

7. LABOR SUPPLY RESPONSES TO TAX REFORMS In an analysis of the potential labor supply responses to a tax reform it is important to know the distribution of the substitution and income elasticities because it is the distributions and not the average elasticities which determine the degree of self-ﬁnancing of a given tax reform. For this reason the sample distributions of the substitution and income elasticities for the preferred model (model IV) are shown in Fig. 2. The distributions of the uncompensated substitution elasticities are unimodal and fairly symmetric around the mean for both men and women, but with long tails and a higher mean for women. The distributions of income elasticities are slightly bimodal and more compressed for men than women (note that the scales on the axes are different for the distributions of income and substitution effects). Four potential tax reforms are simulated. Reform A, B, and C (described below) each have an initial effect on public revenue corresponding to 1% of GDP, whereas reform D only affects initial revenue by 0.5%. The reforms are chosen such that they will target different income brackets. The micro simulations are partial in the sense that they do not include general equilibrium effects and thus, the results from these simulations should be interpreted with care. Further, they are not modeled as budget-neutral reforms.15 In reform A, the upper income tax bracket (the ‘‘top tax’’) is removed (see Fig. 3). For the year 1996, this meant that the highest marginal tax rates were reduced from 65.8% to 51.8% for those with the highest incomes, about 20% of the sample according to Table 1. In reform B, the marginal tax rates in segments three and four are reduced by about 4.5 percentage points (this corresponds to a removal of the so-called medium tax which is relevant for about 75% of the sample, according to Table 1). Reform C reduces the marginal tax rates for tax payers by 1.8 percentage points in segments 2–4, which are relevant for more than 98% of the sample, according to Table 1. Compared to reform A, reform B and especially reform C imply much more moderate reductions of the highest tax rates, but for a much larger proportion of the population. In reform D, the kink point between the third and fourth tax segment is moved upwards, i.e., fewer tax payers face the highest marginal tax rate of 65.8%. The coefﬁcients from the ﬁnal model IV in Tables 5a and 5b are used in the prediction of labor supply responses.16 The revenue effects of the four tax reforms are described by the rate of self-ﬁnancing, i.e., the tax revenue from increased labor supply as a percentage of the initial revenue loss due to the reform (see Table 7). These revenues differ substantially across the four reforms due to the large

46

ANDERS FREDERIKSEN ET AL. Men

Women

60

40

20

0 -.05

-.1

0

.05

E_y Men

Women

30

20

10

0 0

.1

.2

.3

E_ucw

Fig. 2.

Kernels for the Simulated Income and Substitution Elasticities.

47

Overtime Work, Dual Job Holding, and Taxation t%

65.8 51.8 47.2

7.0 income Baseline system Reform A

Reform D

Reform B Reform C

Fig. 3. The Danish Income Tax System in 1996 (‘‘Baseline’’ System and Alternative Tax Reforms). Note: It is assumed that the person lives in a municipality with ‘‘average’’ tax rates, and that he does not have any positive or negative capital income or other income and no allowances beside the zero-rated allowance for local and state taxes.

Table 7.

Public-Sector Revenue Effects Based on Alternative Hypothetical Tax Reformsa. Public-Sector Revenue, Rate of Self-Financing

Reform A: Remove fourth segment (highest marginal tax rates reduced from 65.8% to 51.8%) Reform B: Remove third tax segment and lower marginal tax rates in highest tax segment (reduction of highest marginal tax rates by about 4.5% points in third and fourth tax segments) Reform C: Reduce marginal tax rate in all tax segments by 1.8% Reform D: Shift third tax kink upwards (fewer pay the highest marginal tax rates) a

0.21 0.39

0.12 0.58

Reforms A, B, and C have almost the same initial revenue effect (excl. labor supply effects) on public budgets, while the initial revenue effect of reform D is only about half of this effect. Simulations are based on the results from model IV.

48

ANDERS FREDERIKSEN ET AL.

Table 8. Predicted Labor Supply and Public-Sector Revenue Effects Based on Alternative Model Speciﬁcations: Tax Reform A: Highest Marginal Tax Rates Reduced to 51.8% on Average.

Public-sector revenue, rate of self-ﬁnancing

I Baseline

II Information on Overtime and Second Job

III IIþStigma Effect

IV IIIþSecond Job Dummy

0.65

1.90

0.46

0.21

2.2 0.9

0.7 0.7

Labor supply effects (relative change of weekly hours) (%) Men 2.2 7.0 Women 3.6 6.3

variation in the labor supply responses. The proposed reforms have a rate of self-ﬁnancing ranging from 12% for reform C to 58% for reform D. A reduction of the marginal tax rates for virtually all tax payers (reform C) will be fairly expensive for the public ﬁnances, while the dynamic effects from a moderate reform (D) which reduces the number of tax payers in the highest tax bracket will be relatively large and make this type of reform closer to being self-ﬁnancing. The predicted effects of the proposed tax reforms are known to be sensitive to the underlying econometric speciﬁcation (see, for instance, Blundell & MaCurdy, 1999). In order to analyze more closely the consequences for the results presented above, we have calculated the predicted labor supply responses and the rate of self-ﬁnancing for reform A based on the four econometric speciﬁcations presented in Tables 5a and 5b (see Table 8).17 The results show that the rates of self-ﬁnancing are highly sensitive to the speciﬁcation of the model. In general, the inclusion of detailed information on hours and wages in overtime work and second job and the added ﬂexibility to the model reduce the labor supply effects of the tax reform compared to the results from a traditional labor supply ‘‘Hausman model.’’

8. CONCLUSION In this paper, we have estimated labor supply functions for men and women in Denmark using a piecewise linear Hausman model to account for nonlinear taxes. We compare the estimated labor supply responses based on budget constraints reﬂecting detailed information on overtime work and second job with the traditional approach where information on overtime and second job

Overtime Work, Dual Job Holding, and Taxation

49

wages is not taken into account. Our proposed extensions of the Hausman model give a more ﬂexible and realistic modeling of the actual labor supply decision. A natural further extension would be to allow for joint household or family decisions which are not modeled explicitly in the present study. Our main ﬁndings are that the results are highly sensitive to the speciﬁcation and the ﬂexibility of the labor supply model. The estimated average wage elasticities for men vary from 0.41 to 0.05 depending on speciﬁcation and for women from 0.76 to 0.14. The variation in estimated income elasticities is also relatively large. As found in previous studies the information on overtime payment and second job wages increases the numerical values of the estimated elasticities relative to a standard model which ignores this information. However, allowing for a more ﬂexible treatment of the nonconvexities in the model speciﬁcation, the numerical values of the estimated elasticities are reduced. We analyze four hypothetical tax reforms, each targeting different income brackets. Since the estimated labor supply elasticities are fairly moderate, the tax cuts proposed are not fully self-ﬁnancing through dynamic labor supply effects. The reform, closest to self-ﬁnancing reduces the marginal tax rate for median income earners. The two reforms reducing the marginal tax rates for high-income earners or reducing the marginal tax rates for low-income earners (and hence for high-income earners too) are relatively expensive. One of the main lessons from this study is that when analyzing the effects of tax reforms based on a Hausman-model approach, it is important to allow for sufﬁcient ﬂexibility at the nonconvex part of the budget constraints and to have as much information on the budget constraints as possible, i.e., information on overtime and second job wages. For the Danish tax system analyzed in this paper, the results indicate that strictly using a traditional Hausman approach may result in much too large estimates of the labor supply effects and hence incorrect predictions of the degrees of self-ﬁnancing of tax reforms.

NOTES 1. See, for example, Aaberge, Colombino, and Strom (1999), van Soest (1995), and Hart (2004) for a discussion of the free choice of work hours or rather work packages, and Paxson and Sicherman (1996) and Frederiksen, Graversen, and Smith (2005) for a discussion of the dual job holder characteristics. 2. Contrary to papers like Blomquist (1983) and Flood and MaCurdy (1992), our male sample is not restricted to workers with positive hours, but we allow the small group of nonworking men to inﬂuence the results.

50

ANDERS FREDERIKSEN ET AL.

3. The ambition in this study is to analyze the sensitivity of the Hausman approach to more ﬂexible speciﬁcations and additional information on overtime and second job. An alternative approach to the Hausman model is a choice-based model such as the random utility model (see for instance Aaberge, Colombino, & Strom, 2004). Choice-based models may provide complementary information on how variation in relative wages across different types of jobs affects the composition of labor supply. 4. See Averett and Hotchkiss (1997) for a discussion of the exogeneity of the budget constraint in the context of the part-time/full-time labor supply decision. 5. A third approach is to see dual job holding as an insurance against unemployment. There are two reasons why we ignore this hypothesis. First, the existing empirical evidence based on a study of the British Household Panel provides only weak evidence for the hypothesis (see Bell, Hart, & Wright, 1997). Second, the high unemployment beneﬁts level in Denmark suggests that the insurance argument is unlikely to be the main motivation for dual job holding in the present study. 6. The Danish UI-beneﬁt rules allow a person to insure either as a part-time worker or as a full-time worker. If insured as a part-time worker, the insurance premium and the UI beneﬁts in case of unemployment are lower than if full-time insured. 7. It may be criticized that the time dimension is not the same for overtime work, second job, and work in main occupation. We prefer to use ‘‘the normal work hours’’ as a measure of the labor supply since it gives a smoothed measure of the desired labor supply. Unfortunately, this information for overtime hours is not available in our data set. Instead, we use the ‘‘best’’ approximation available. 8. The incidence of overtime in Denmark seems to be considerably lower than in the UK where overtime incidence (for males) is found to be about 40% (see Kalwij & Gregory, 2005). For the US, Trejo (1993) ﬁnds that the dual-job-holding rate is about 6% for both men and women in the 1991 CPS sample which is based on observations in a given survey week. When using annual data, the dual-job-holding rate is considerably higher, 21% for men and 12% for women. Similarly, Paxson and Sicherman (1996) ﬁnd rates on 20% and 12% based on US PSID data for 1976–1989 for men and women separately. Since our data are based on a question on ‘‘normal weekly hours in second job,’’ the larger ﬁgures are probably the relevant ﬁgures to compare. 9. Three selectivity-corrected wage regressions are used in this study: main occupation, overtime work, and second job. Similar to Blomquist and HanssonBrusewitz (1990), we estimate a wage rate function on the subgroup with observable wage rates, taking account of sample selection bias by a Heckman procedure. Identiﬁcation is secured by including additional survey and register information on demographic variables etc. (child variables, information on marriage or cohabitation, and ownership of house) in the participation relation, and information on tenure, occupational level, and regional variables in the wage function. Subsequently, the regression results are used to predict wages. All wage functions are available from the authors upon request. 10. Aaberge et al. (1999, 2004) also ﬁnd low cross-substitution effects among middle class and especially among rich households. Similarly, van Soest (1995) ﬁnds low cross-substitution effects and low family income effects on Dutch data. Thus, we do not expect that this shortcoming of our approach will seriously bias the results.

Overtime Work, Dual Job Holding, and Taxation

51

11. As an alternative, we have used the linear labor supply speciﬁcation, which was also used in Blomquist (1983) and Flood and MaCurdy (1992). It is linear in both wage rates and nonlabor income, and the direct utility function has an explicit closed form. Contrary to the results found in other studies, we do not ﬁnd, that the results (measured by average elasticities for different demographic groups) are very sensitive to choice of speciﬁcation (see Sackle´n, 1996). Since the nonlinear speciﬁcation is the more ﬂexible and since it performs statistically slightly better, we present the results from the nonlinear speciﬁcation. 12. The sample used is a nonrepresentative sample where unemployed persons are over-sampled. Therefore, the likelihood function in Eq. (5) is weighted by the appropriate weights. 13. Another way to obtain something similar would be to exclude the nonworking individuals. 14. The elasticities are calculated for each individual in the sample according to Note below Table 5a. The average of theses elasticities are presented in the text and tables. 15. It should be mentioned that the analysis is also partial in the sense that we do not include dynamic effects, i.e., potential effects on consumption and indirect tax revenues. If these effects are included, the rate of self-ﬁnancing of the tax reforms analyzed above will increase, since disposal income will increase for all income groups. The potential effects of taxation on the wage formation process are not included either (see for instance Bingley & Lanot, 2002). 16. The labor supply response to a given tax reform is determined as the difference in predicted pre- and postreform labor supply. 17. We only present the results from reform A since it is exactly the same pattern of variation which appears for all the reforms analyzed in Table 7.

ACKNOWLEDGMENT The data set used in this study was created and ﬁnanced by the Rockwool Research Foundation which has also partly ﬁnanced the research project. The presented analysis is solely the authors’ responsibility.

REFERENCES Aaberge, R., Colombino, U., & Strom, S. (1999). Labour supply in Italy: An empirical analysis of joint household decisions, with taxes and quantity constraints. Journal of Applied Econometrics, 14, 403–422. Aaberge, R., Colombino, U., & Strom, S. (2004). Do more equal slices shrink the cake? An empirical investigation of tax-transfer reform proposals in Italy. Journal of Population Economics, 17(4), 767–785. Arrufat, J., & Zabalza, A. (1986). Female labor supply with taxation, random preferences, and optimization errors. Econometrica, 54(1), 47–63.

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Ashworth, J., & Ulph, D. (1981). Endogeneity I, estimating labor supply with piecewise linear budget constraints. In: C. V. Brown (Ed.), Taxation and labor supply. London, UK: Allen & Unwin Chap 6. Averett, S. L., & Hotchkiss, J. L. (1997). Female labour supply with a discontinuous, nonconvex budget constraint: incorporation of a part-time/full-time wage differential. Review of Economics and Statistics, 79, 461–470. Bell, D., Hart, R. A., & Wright, R. E. (1997). Multiple job holding as a ‘hedge’ against unemployment. CEPR Discussion Paper No. 1626. Bingley, P., & Lanot, G. (2002). The incidence of income tax on wages and labour supply. Journal of Public Economics, 83(2), 173–194. Bingley, P., & Walker, I. (2001). Household unemployment and the labour supply of married women. Economica, 68(270), 157–185. Blomquist, S. (1983). The effect of income taxation on the labor supply of married men in Sweden. Journal of Public Economics, 22, 169–197. Blomquist, S., Eklo¨f, M., & Newey, W. (2001). Tax reform evaluation using non-parametric methods: Sweden 1980–1991. Journal of Public Economics, 79, 543–568. Blomquist, S., & Hansson-Brusewitz, U. (1990). The effect of taxes on male and female labour supply in Sweden. Journal of Human Resources, 25, 317–357. Blundell, R., & MaCurdy, T. (1999). Labor supply: A review of alternative approaches (Chap. 27). In: O. Ashenfelter & D. Card (Eds), Handbook of labor economics. Amsterdam: Elsevier. Conway, K. S., & Kimmel, J. (1998). Male labor supply estimates and the decision to moonlight. Labour Economics, 5, 135–166. Duncan, A. (1993). Labour supply decisions and non-convex budget sets: The case of National Insurance Contribution in the UK. In: A. Heimler & D. Meulders (Eds), Empirical approaches to ﬁscal policy. London: Chapman and Hall. Euwals, R., & van Soest, A. (1999). Desired and actual labour supply of unmarried men and women in the Netherlands. Labour Economics, 6(1), 95–118. Flood, L., & MaCurdy, T. (1992). Work disincentive effects of taxes: An empirical analysis of Swedish men. Carnegie-Rochester Conference Series on Public Policy, 37, 239–278. Frederiksen, A., Graversen, E., & Smith, N. (2001). Overtime work, dual job holding and taxation. IZA Discussion Paper No. 323, Forschungsinstitut zur Zukunft der Arbeit, Bonn. Frederiksen, A., Graversen, E., & Smith, N. (2005). Tax evasion and work in the underground sector. Labour Economics, 12(5), 613–628. Graversen, E. (1998). Labour supply and work incentives. PhD thesis 1998–2002, University of Aarhus, Aarhus. Hart, R. A. (2004). The economics of overtime working. Cambridge, UK: Cambridge University Press. Heineck, G. & Schwarze, J. (2004). Fly me to the moon: The determinants of secondary jobholding in Germany and the UK. IZA Discussion Paper. No 1358. Kalwij, A. S., & Gregory, M. (2005). Overtime hours in Great Britain over the period 1975–1999: A panel data analysis. Journal of the Royal Statistical Society, Series A, 168(1), 207–231. MaCurdy, T., Green, D., & Paarsch, H. (1990). Assessing empirical approaches for analyzing taxes and labor supply. The Journal of Human Resources, XXV(3), 415–490. Mofﬁtt, R. (1986). The econometrics of piecewise-linear budget constraints. A survey and exposition of the maximum likelihood method. Journal of Business and Economic Statistics, 4(2), 317–328.

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OECD. (1996). Employment outlook, Paris Paxson, C. H., & Sicherman, N. (1996). The dynamics of dual job holding and job mobility. Journal of Labor Economics, 14(3), 357–393. Pedersen, P., & Smith, N. (2002). Unemployment traps and ﬁnancial disincentives to work. European Sociological Review, 18(3), 271–288. Pencavel, J. (1986). Labor supply of men: A survey (Chap. 1). In: O. Ashenfelter & R. Layard (Eds), Handbook of labor economics. Amsterdam: Elsevier. Sackle´n, H. (1996). Essays on Empirical Models of Labor Supply: Economic Studies (Vol. 27). Uppsala: Department of Economics, Uppsala University. Shisko, R., & Rostker, B. (1976). The economics of multiple job holding. American Economic Review, 66(3), 298–308. Smith, N. (1995). A panel study of labour supply and taxes in Denmark. Applied Economics, 27, 419–429. Smith, N. (1998). Arbejde, incitamenter og ledighed (In Danish). Aarhus: The Rockwool Foundation Research Unit and Aarhus Universitetsforlag. Smith, N., Dex, S., Vlasblom, J. D., & Callan, T. (2003). The effects of taxation on married women’s labour supply across four countries. Oxford Economic Papers, 55(3), 417–439. Trejo, S. J. (1993). Overtime pay, overtime hours, and labor unions. Journal of Labor Economics, 11(2), 253–278. van Soest, A. (1995). Structural models of family labor supply: A discrete choice approach. The Journal of Human Resources, 30(1), 63–88.

APPENDIX The Likelihood Function The probability Gðhni ¼ 0Þ can be written as Gðhni ¼ 0Þ Z H 0i Z ¼

H 0i h^li

j1 ½hni H 0 ; vi dvi di

1 1 k Z h^ji X

Z

H ji h^ji

þ

j¼1

þ

1

k1 Z X j¼1

Z

H ðj1Þi h^ji

H ji

Z

H ki

Z

Segment j; j ¼ 1; . . . ; k

j1 ½hni H ji ; vi dvi di

Kink j; j ¼ 1; . . . ; k 1

1

þ 1

j2 ½hni h^ji ; vi dvi di

H ji h^ðjþ1Þi

H ji h^ji

1

Lower limit

H ki h^ki

j1 ½hni H k ; vi dvi di

Upper limit

54

ANDERS FREDERIKSEN ET AL.

and the density gðhni Þ can be written as Z

n

gðhi Þ ¼ þ

H 0i h^0i

j¼1

þ

n

j1 ½hi 1 k Z H ji h^ji X H ðj1Þi h^ji

k1 Z X j¼1 Z 1

H 0 ; vi dvi

Lower limit

j2 ½hni h^ji ; vi dvi

Segment j; j ¼ 1; . . . ; k

H ji h^ðjþ1Þi

H ji h^ji

þ H ki h^ki

j1 ½hni H ji ; vi dvi

j1 ½hni H k ; vi dvi

Kink j; j ¼ 1; . . . ; k 1

Upper limit

There are no individuals with hni ¼ H k . Hence, Gðhni ¼ H k Þ is not in the likelihood we maximize. Arrufat and Zabalza (1986) give expressions for both G( ) and g( ). F1( , ) and F2( , ) are bivariate normal density functions of (e,v) and (eþv,v) with means, variances, and covariance (0; 0; s2e ; s2v ; 0) and (0; 0; s2e þ s2v ; s2v ; s2v ), respectively. There is no a priori reason to expect the heterogeneity and measurement errors to be correlated. Hence, we assume no correlation as almost all other studies in the area (cf. Mofﬁtt, 1986).

Table A1. Descriptive Statistics. Variable

Men Mean

Weekly labor supply, given participation Main occupation 37.9 Overtime work 2.1 Second job 1.0 Hourly gross wage rate, DKK Main occupation 133.7 Overtime work 170.1 Second job 140.5 Weekly nonlabor income, 2,725.4 DKK Marginal tax rate (%) 54.7 Age 39.1 Owner of house (0/1) 0.64

Women

Standard deviation

Mean Standard deviation

5.0 5.1 4.3

34.5 1.0 0.4

6.5 2.8 2.2

53.8 53.3 110.6 1,401.3

107.0 148.6 135.9 3,170.3

26.9 66.1 126.9 1,439.9

13.1 11.1 0.49

48.0 39.1 0.69

15.2 10.4 0.46

55

Overtime Work, Dual Job Holding, and Taxation Table A1. (Continued ) Variable

Men Mean

Region Copenhagen Major cities Country Children 0–2 years (0/1) Children 3–6 years (0/1) Number of children Civil state Single Married Cohabiting Number of observations

Women

Standard deviation

Mean Standard deviation

0.30 0.34 0.36 0.13 0.11 0.75

0.46 0.48 0.49 0.34 0.33 0.96

0.32 0.32 0.36 0.15 0.11 0.85

0.46 0.46 0.47 0.35 0.32 0.95

0.24 0.58 0.18

0.42 0.50 0.39 1,150

0.22 0.62 0.16

0.41 0.48 0.37 1,291

TRANSITIONS BETWEEN UNEMPLOYMENT AND LOW PAY Lorenzo Cappellari and Stephen P. Jenkins ABSTRACT We model transitions between unemployment, low-paid and high-paid employment by British men using a ﬁrst order Markov model with endogenous switching that also takes into account the endogeneity of initial conditions, selection into employment, and sample attrition. Our estimates indicate that all three selectivity issues are non-ignorable. We demonstrate several interrelationships between the dynamics of (un)employment and low-paid work between one year and the next, represented by forms of (cross-)state dependence. Controlling for heterogeneity, the probability of a man having a low-paid job in one year depends not only whether he had a job a year before but also whether that job was low paid. The probability of his being employed at all depends on whether he had a job the previous year.

1. INTRODUCTION There is a great interest in Britain in the extent to which individuals who are employed in a low-paid job are more likely to become unemployed than high-paid individuals are, and the extent to which those who are currently unemployed are more likely to become low-paid employees rather than

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 57–79 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28003-9

57

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LORENZO CAPPELLARI AND STEPHEN P. JENKINS

high-paid ones when they get a job. In this paper, we provide new evidence about these transitions using a ﬁrst order Markov model for multi-state labour market dynamics. The emphasis of recent British labour market policy has been on getting unemployed people into a job. These jobs have often been low-paid ones (albeit supplemented with in-work beneﬁts such as the Working Families Tax Credit). If there is a strong ‘low pay no pay cycle’, then most of these jobs do not last very long, and there is churning between the ranks of the unemployed and the low paid. Put another way, there is a form of labour market segmentation, with a division between a primary sector (high-paid jobs) and a secondary sector comprising the individuals churning between unemployment and low-paid employment with little chance of climbing up the pay ladder. We shed light on these issues by modelling the annual rates of transition between being high-paid, low-paid, or being unemployed. A more speciﬁc question addressed is whether the individuals who remain in the secondary sector do so because they have poor educational qualiﬁcations and other disadvantageous characteristics, or because of the experience of unemployment or of low-paid employment itself. With regard to the latter (state dependence), we are also concerned to explore cross-state effects; whether for example, the chances of unemployment depend not only on past unemployment but also experience of low-paid employment (often work of generally poor ‘quality’). Although there has been much recent research for Britain about earnings mobility on the one hand, and unemployment dynamics on the other hand – see for example Stewart and Swafﬁeld (1999) about the former, and Arulampalam, Booth, and Taylor (2000) about the latter – the interrelationships between the dynamics of low-paid employment and unemployment have received less attention. Stewart (2007) modelled the probabilities of unemployment and low pay, using dynamic random effects probit regressions for each process controlling for endogenous initial conditions. Using pooled transition data from the British Household Panel Survey (BHPS) waves 1–6, he found that the chances of becoming low paid were signiﬁcantly more likely for unemployed individuals than for high-paid employees and, among employed individuals, the chances of entering unemployment were larger for individuals who had low-paid rather than high-paid jobs. There was also evidence that low pay acted as a conduit to repeat unemployment: unemployed people who found a low-paid job were more likely to fall back into unemployment than those who had found a high-paid job. In this paper we provide new evidence about labour market transitions for British men. Using BHPS data, we model annual transitions between unemployment and low- and high-paid employment using a ﬁrst order

Transitions between Unemployment and Low Pay

59

Markov model that allows for interrelationships between the dynamics of low pay and unemployment in a novel manner. In addition, we take account of three potentially endogenous selection processes: initial conditions in lowpaid employment, selection into employment, and panel attrition. Low-pay dynamics have also been modelled using random effects dynamic panel models (cf. Stewart, 2007). In these models, estimation is based on a wave-by-wave sequence of observations starting at the ﬁrst panel wave, with each followed until panel drop-out, so that individuals joining the panel subsequently are not included, and nor are individuals who return to the panel after one or more non-response waves – this excludes a relatively large number of cases. By contrast, our approach includes panel joiners and those with incomplete panel participation patterns. Panel attrition is typically not modelled in applications of the random effects dynamic panel model (Arulampalam et al., 2000; Stewart, 2007), whereas we model it explicitly. Our approach also differs by allowing regressors to have different impacts on the outcome variable depending upon outcomes in the previous period (endogenous switching). Our results suggest that all three potential sources of endogeneity (initial conditions, selection, attrition) are non-ignorable when estimating rates of transition between unemployment and low- and high-paid jobs. Put another way, estimates of transition probabilities based on models that do not account for these phenomena yield biased estimates. Controlling for observed and unobserved individual heterogeneity, we ﬁnd some evidence of labour market ‘scarring’ effects, but they operate across labour market states as well as within them. For example, the probability of a man having a low-paid job in one year depends not only whether he had a job a year before but also whether that job was low paid. The probability of his being employed at all depends on whether he had a job the previous year.

2. DATA AND OVERALL PATTERNS OF TRANSITIONS BETWEEN LABOUR MARKET STATES Transition rates between labour market states were studied using data from waves 1 to 10 (survey years 1991–2000) of the BHPS.1 We consider transitions between states measured at consecutive annual interviews, call these year t and t1, using a sample that pools transitions (as did Stewart & Swafﬁeld, 1999). The focus is on men in order to avoid addressing issues of endogenous female labour supply. We analyse the experience of men who were aged 16–64 years in year t1 who were either unemployed or employees, and not full-time students. Following Arulampalam et al. (2000)

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LORENZO CAPPELLARI AND STEPHEN P. JENKINS

and Stewart (2007), we do not model the endogeneity of being economically active or of self-employment. We also exclude from the estimation sample, the 4.7% of cases that were characterised as employees but who did not report valid earnings. A man was deﬁned to be unemployed if he was not working and had been looking for a job during the four weeks prior to the interview. The low pay threshold was deﬁned as 60% of median hourly earnings, in August 2000 prices. Table 1 reports the raw transition rates for our sample.2 The table shows, for example, that the chances of being low paid in one year were four times greater for those who were unemployed rather than high-paid the previous year. On the other hand, the probability of being unemployed in one year was three times more likely among those who were low-paid rather than high-paid in the previous year. Of those who left unemployment, 37% ( ¼ 17.8/(17.8þ29.35)) got a low paid job, which is almost three times the cross-sectional low pay probability (13% in our sample). Overall, the evidence suggests that there is substantial churning between unemployment and low-paid employment. There also appears to be persistence in the experience of low paid work and unemployment. Among those unemployed in year t1, the probability of unemployment in year t was 53%, compared to 6.5% of those who were low-paid and less than 2% for those high-paid. Similarly, the probability of having a low paid job in year t was 52% for those who were low-paid at year t1, but 18% for those who were unemployed, and only 4% for those who were high-paid. Together the evidence of churning and of persistence indicates a strong association between a man’s labour market state this year

Table 1.

Transition Rates between Labour Market States for British Men.

Year t–1 State

Unemployed Low-paid employment High-paid employment

Year t State Unemployed (%)

Low-paid employment (%)

High-paid employment (%)

Dropped out of sample (%)

52.85 (31.91) 6.51 (5.11) 1.95 (1.69)

17.80 (10.74) 51.87 (40.67) 4.14 (3.60)

29.35 (17.72) 41.61 (32.62) 93.91 (81.53)

(39.63) (21.60) (13.18)

Notes: Adult men aged 16–64 years, excluding full-time students and those who were selfemployed. Transitions pooled from British Household Panel Survey, waves 1–10. Numbers in parentheses are transition rates for the case in which sample dropout in included as a fourth destination state. Sample size ¼ 18,372 (22,081). The low-pay threshold is 60% of median contemporary hourly earnings.

Transitions between Unemployment and Low Pay

61

and his state in the previous year. The extent to which such ‘aggregate state dependence’ is due to (observed or unobserved) heterogeneity or to ‘genuine state dependence’ (labour market scarring) is an issue that we address below. Table 1 also shows the transition rates obtained when attrition from the sample was included as a fourth destination state at year t: these are the estimates shown in parentheses. Sample dropout rates were highest among those who were unemployed at year t1 (40%), smaller for those were lowpaid (22%), and lower still among those who were high-paid (13%). This pattern suggests that attrition probabilities depend on labour market state, and hence econometric analysis of transitions between states needs to take account of potential correlations between the unobserved factors affecting attrition and transition probabilities (i.e. endogenous attrition). We do this.

3. A MODEL OF TRANSITIONS BETWEEN LABOUR MARKET STATES In order to estimate an econometric model of transitions between unemployment, low-paid and high-paid employment, several issues need to be addressed. First, the dynamic nature of the model means that unobserved factors affecting transitions between states may be correlated with those determining the origin state – the ‘initial conditions problem’ (Heckman, 1981a). Second, earnings are observed only for individuals who have a job, and it is well known from the labour economics literature that parameter estimates of earnings equations for the population as a whole derived from a sample restricted to workers may be subject to ‘selection biases’ (Heckman, 1974; Keane, Mofﬁtt, & Runkle, 1988). This endogenous selection issue is also relevant to our application: employed men may have propensities for low-paid employment that are systematically higher than the propensities for unemployed men. Third, as Table 1 suggested, sample attrition might not be random. Finally, in order to distinguish between heterogeneity and state dependence as explanations for the persistence in labour market states that is observed, one needs to allow for correlations between the unobserved factors in the relevant processes (Heckman, 1981b). We address all four issues by developing a multivariate probit model with endogenous selection and endogenous switching. We specify a model for labour market transitions between two consecutive years, t1 and t, t ¼ 2, y, T. Consider a man, indexed by i ¼ 1, y, N, observed in either unemployment, low-paid employment, or higher-paid employment in year t1, the base year of a given transition. Transitions between the three states for individual i can be observed only if

62

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

he is also observed in year t. Let the unobserved sample retention propensity between the two waves, rnit , be a linear function of observable attributes at t1, plus a composite error term ait distributed as standard normal: rnit ¼ c0 xit1 þ ait ;

ait Nð0; 1Þ

ait ¼ ai þ xit

(1) (2)

Whenever rnit is greater than some threshold that can be set to zero without loss of generality, individual i is observed at successive waves t1 and t. Let Rit ¼ Iðrnit 40Þ be a dichotomous indicator for that event, where the indicator function I( ) equals one if its argument holds, and zero otherwise. The composite error term is the sum of two orthogonal components: an individual speciﬁc effect ai representing time-invariant unobserved heterogeneity, and a purely idiosyncratic effect xit, each of which is assumed to be independent of xit1. Since rnit is unobserved, the variance of the composite error term is normalised to one. (This is a random effects panel model, except that we do not specify the variances of ai or xit, since, given our pseudo-likelihood estimation approach, discussed below, they are not an argument of the sample likelihood function. See below and also Cappellari & Jenkins, 2004). Assume that employment chances in year t1 can be written in terms of an unobserved latent employment propensity, enit1 , a linear function of observable characteristics plus a composite error term bit1 distributed as standard normal and independent of observable characteristics. We write this as the sum of two orthogonal components, one summarising timeinvariant unobserved heterogeneity (ki) and the other an idiosyncratic effect (eit1): enit1 ¼ b0 zit1 þ bit1 ;

bit1 ; Nð0; 1Þ

bit1 ¼ ki þ it1

(3) (4)

Let E it1 ¼ Iðenit1 40Þ be a variable indicating whether i is employed in year t1 rather than unemployed. If individual i is employed at t1, earnings can be observed, and assume that they can be speciﬁed as: f ðwit1 Þ ¼ g0 mit1 þ cit1 ;

cit1 Nð0; 1Þ

cit1 ¼ ui þ uit1

(5) (6)

Transitions between Unemployment and Low Pay

63

where f( ) is a suitable monotonic transformation of earnings such that the composite error term cit1 has a standard normal distribution and is independent of regressors, mit1. (This speciﬁcation follows that used by Stewart & Swafﬁeld, 1999). Let tt1 be the low pay threshold for year t1. An individual is low-paid whenever wit1ott1 or, equivalently when f(wit1)of(tt1). By subtracting both sides of Eq. (3) from f(tt1), this expression may be rewritten as: l nit1 ¼ d0 mit1 þ d it1

d it1 Nð0; 1Þ

d it1 ¼ vi þ vit1

(50 ) (60 )

where l nit1 f ðtt1 Þ f ðwit1 Þ. The intercept term in parameter vector d is the difference between f(tt1) and the intercept term in vector g. The other parameters in d are the same as the corresponding ones in g, but have the opposite sign: niui and vit1uit1. If the latent variable l nit1 is positive, individual i is low paid. Let the low pay binary indicator Lit1 ¼ Iðl nit1 40Þ characterise that event.3 If individuals do not drop out of the sample, their status in year t can be observed in addition to their status at t1. In order to characterise probabilities of transition between unemployment and low pay and to allow for interrelationships between processes, we condition both year t states on t1 states. Clearly, one cannot do this by including Eit1 and Lit1 among the regressors of the year t equations, since low pay status at t1 is observed only for men who were employed at t1. Because of this, we allow there to be two different speciﬁcations for the year t equations depending on the value of Eit1 (i.e. there is endogenous switching), and we include Lit1 among the explanatory variables for the case when Eit1 ¼ 1. For example, we specify year t employment propensities as: enit ¼ E it1 ðl01 h1it1 þ ye Lit1 Þ þ ð1 E it1 Þl02 h2it1 þ git git ¼ mi þ oit

git Nð0; 1Þ (7) (8)

As with the previous equations, the composite error term is assumed to be the sum of two orthogonal components, one representing time-invariant unobserved heterogeneity and the other an idiosyncratic error, which are normally distributed and independent of the regressors. Observe that lagged low pay status, Lit1, is included among the regressors for men who were employed in t1. Moreover, the set of explanatory variables, and the effects of any particular variable, are allowed to differ depending on past

64

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

employment. In particular, the vector of observables h1it1 will contain all the variables present in h2it1 plus some job and ﬁrm characteristics. A variable like age, included in both h2it1 and h2it1, may have different effects on employment at t depending on employment status at t1. We measure regressors at date t1 in order to avoid simultaneity between changes in employment propensities and changes in regressors. We characterise year t employment status by means of a binary indicator variable, E it ¼ Iðenit 40Þ. Note that Eq. (9) is conditional on Eqs. (1), (3) and (7). The ﬁnal processes to be speciﬁed are those characterising low pay at date t, which are observed only if Rit ¼ 1 and Eit ¼ 1. Moreover, the equations need to be conditioned on the state at t1, whether employed, high- or lowpaid. Arguments similar to the ones we made about the speciﬁcation of the latent employment propensity enit point to the need to allow for endogenous switching in this case as well. We specify the process determining low pay at t directly in terms of a low pay propensity, l nit , which can be derived from a equation for earnings at t in a fashion similar to the one used to relate l nit1 to earnings at t1: l nit ¼ E it1 ðj01 k1it1 þ y1 Lit1 Þ þ ð1 E it1 Þj02 k2it1 þ nit nit ¼ pi þ Zit

nit Nð0; 1Þ (9) (10)

Our earlier remarks about the impact of regressors differing according to lagged employment status, and about the nature of the error components comprising the composite error, also apply here, suitably modiﬁed. The set of regressors k1it1 and k2it1 may differ according to t1 employment status, and a variable that is common to each vector may have a different impact on the outcome. Note too the potential dependence of current low pay status on lagged low pay status for those employed at t1. Let Lit ¼ Iðl nit 40Þ be the binary indicator summarising observed low pay status at t. We assume that the composite errors in the ﬁve equations are jointly distributed as ﬁve-variate normal with zero means, unit variances, and unrestricted correlations: ðait ; bit1 ; d it1 ; git ; nit Þ N 5 ð0; SÞ

(11)

Because each composite error is the sum of a time-invariant individual component and an idiosyncratic white noise component, the correlation coefﬁcients in S are identically equal to the cross-equation covariances of

Transitions between Unemployment and Low Pay

65

the time-invariant individual components. The distribution of timeinvariant unobserved heterogeneity is therefore parameterised by the correlation coefﬁcients forming the off-diagonal elements of S. Estimation of the cross-equation correlations allows for the endogeneity of panel attrition, of lagged states and selection into employment, and tests of the null hypothesis of exogeneity of the various processes can be performed by testing the statistical signiﬁcance of the elements of S (see below). In sum, our econometric model is a ﬁve-variate probit regression model with an endogenous dummy variable (lagged low pay), endogenous switching (in year t equations), and endogenous selection (of year t equations with respect to attrition, and of pay equations with respect to employment). The likelihood function involves normal integrals of various dimensions, the largest being ﬁve. The integrals are evaluated by simulation, employing the GHK simulator. The model is estimated pooling annual transitions from BHPS interview waves 1–10, with t ¼ 1992, y, 2000. There are repeated observations on the same individual for each man who was a respondent at least two interviews. These repeated observations mean that the i.i.d. assumption is violated, since each time-invariant individual-speciﬁc effect is correlated with itself over transitions, and we do not model such correlation. To address this issue, we used a pseudo maximum simulated likelihood (PMSL) estimator, as follows. The survey statistics literature has developed methods for adjusting the estimates of the parameter covariance matrix to account for sample clustering, using formulae that allow for arbitrary correlations between observations within the same sample cluster, an individual in our case. See inter alia Huber (1967) and Binder (1983) and, for an independent derivation in the econometrics literature, White (1982). The sample loglikelihood is a ‘pseudo-likelihood’ in this case (Gourieroux & Monfort, 1996), from which can be derived a ‘robust’ variance estimator of the parameter estimates using Taylor-series linearisation. Our estimator is a PMSL estimator because the pseudo-likelihood was evaluated using the GHK simulator. An alternative approach, in principle, would be to model the individual effects and to integrate them out. We eschewed this approach because of the substantial computational complexities implied by it, over and above those implied by addressing the various endogenous selections. Our approach is computationally tractable, at the cost of being unable to identify the variances of the multivariate distribution of time-invariant individual unobserved heterogeneity. However, this is not a problem (in the current context), because we do not use these variances. We are able to identify the

66

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

parameters of interest in the distribution of unobserved heterogeneity, namely the covariances: it is these that characterize and induce endogenous selectivity. Exclusion restrictions are required if the model is to be identiﬁed by other than its non-linear functional form. Our instrument for attrition is a binary variable summarising whether the year t1 interview was assessed as being problematic by the interviewer on matters such as eyesight, hearing, reading, English, language and interpretation. Our identiﬁcation strategy assumes that, conditional on educational attainment and health status (indicators used as explanatory variables in every model equation), the occurrence of problems during the year t1 interview shifts the likelihood of sample retention but does not have an independent effect on labour market transitions.4 Stewart (2007) suggested instrumenting employment equations using variables summarising the characteristics of an individual’s ﬁrst-ever employment spell. In addition, recent papers have reported that wages are less sensitive to unemployment in the United Kingdom than they are elsewhere (see Barth, Bratsberg, Naylor, & Raaum, 2002; Montuenga, Garcy´a, & Fernandez, 2003). This suggests that measures of labour market tightness as the unemployment vacancy ratio in the relevant travel-to-work area could also be used as instruments in employment equations. We found that, whereas these variables worked well as instruments for identifying employment at t1, measures of the characteristics of the ﬁrst employment spell performed better in equations for employment at t. (The measures were binary indicators of whether the ﬁrst spell was in full-time work, and whether the information was missing). Finally, as instruments for initial conditions, we used a series of binary indicators summarising parental socio-economic status measured when the respondents were aged 14 (primarily occupation variables, plus variables to indicate no parent or missing information), as a way of proxying factors pre-dating labour market entry that affect the initial conditions but not the transitions (Heckman, 1981a). Because our model controls for observed and unobserved heterogeneity, it allows assessment of the extent to which the observed persistence in labour market states is due to the experience of adverse states per se, and whether there are cross-state effects. As a benchmark for assessing ‘genuine state dependence’, parameter estimates can be used to compute the equivalent of the raw overall differences in transition rates shown in Table 1. In particular, we generate predicted transition rates for each sample member and then take their averages over the relevant subsamples.

Transitions between Unemployment and Low Pay

67

The absence of genuine state dependence can be investigated by testing whether there is a difference in the parameters associated with the different states at t1, i.e. whether the past has any inﬂuence on the probabilities of current states after controlling for observed and unobserved heterogeneity. To investigate the effects of lagged low pay, this amounts to testing whether ye and yl are statistically different from zero (see Eqs. (4) and (5)). For lagged employment, according to which the whole set of coefﬁcients (not only the intercept term) switches, we test the equality of the coefﬁcients estimates for the two employment states at t1, i.e. H01: l 1 ¼ l2 and H02: j ¼ j , where a ‘’ denotes vectors deprived of coefﬁcients that have no 1 2 counterparts in the equations for the unemployed of t1. Measures of the degree of genuine state dependence need to quantify the shift in the probabilities of year t states corresponding to changes in year t1 states while abstracting from heterogeneity. To assess the impact of lagged low pay versus lagged higher pay, one can compute the ‘marginal effects (MEs)’ associated with the coefﬁcient on Lit1 in the equations for year t outcomes. This is what is usually done in dynamic random effects models in which state dependence is characterised in terms of the coefﬁcient on a lagged binary dependent variable (see e.g. Arulampalam et al., 2000). In our model, this strategy is infeasible for measures of dependence involving lagged employment since conditioning upon lagged employment is achieved via endogenous switching rather than by inclusion of a lagged employment dummy. An alternative measure of genuine state dependence for such cases was proposed by Cappellari and Jenkins (2004). Consider, for example, state dependence in (current) unemployment due to a change of lagged states from, say, low pay to unemployment. Such a probability shift can be computed at the individual level, using the parameter estimates, as Pr(Eit ¼ 0|Eit1 ¼ 0; l2)Pr(Eit ¼ 0|Lit1 ¼ 1; l1 ye), where it is made explicit that these individual probability shifts are a function of model coefﬁcients (i.e. analogously to the ME on lagged low pay, which is a function of the coefﬁcient on the lagged dependent dummy). This difference in probabilities measures state dependence at the individual level and therefore abstracts from heterogeneity. The sample mean of each of these differences over the relevant cases (i.e. non-attrited observations that were either unemployed or low paid in t1) provides a measure of the degree of genuine state dependence. Similarly, measures can be also computed for the other probability shifts of interest, namely: Pr(Eit ¼ 0|Eit1 ¼ 0; l2)Pr(Eit ¼ 0|Lit1 ¼ 0; l1); Pr(Lit ¼ 1|Lit1 ¼ 1; j1, yl)Pr(Lit ¼ 1|Eit1 ¼ 0; j2); Pr(Lit ¼ 1|Eit1 ¼ 0; j2)Pr(Lit ¼ 1|Lit1 ¼ 0; j1).

68

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

4. RESULTS 4.1. Correlations between Unobserved Individual Components, and Tests for Endogenous Selection The estimated correlation structure of the unobserved individual components is shown in Table 2, together with test statistics for the ignorability of the retention, initial conditions and employment processes. Unobserved factors in the retention equation were positively associated with those in the lagged employment equation and negatively associated with the ones in the current low pay equation. This echoes the pattern in Table 1 noted earlier, i.e. that men dropping out of the sample were concentrated among the unemployed and the low paid. The correlation between unobserved factors affecting initial employment and conditional current employment was negative and statistically signiﬁcant. Given the endogenous switching structure adopted, this parameter measures the correlation between unobserved heterogeneity in Table 2.

Correlation Structure of Unobservables, and Tests of the Ignorability of Endogenous Selection Processes.

Correlations in Unobservables Retention and employment at t1 (r1) Retention and employment at t (r2) Retention and low-paid employment at t1 (r3) Retention and low-paid employment at t (r4) Employment at t–1 and employment at t (r5) Employment at t–1 and low-paid employment at t1 (r6) Employment at t–1 and low-paid employment at t (r7) Employment at t and low-paid employment at t1 (r8) Employment t and low-paid employment at t (r9) Low-paid employment at t–1 and at t (r10) Test Ignorability of retention H0: r1 ¼ r2 ¼ r3 ¼ r4 ¼ 0 Ignorability of lagged employment H0: r1 ¼ r5 ¼ r6 ¼ r7 ¼ 0 Ignorability of lagged low-paid employment H0: r3 ¼ r6 ¼ r8 ¼ r10 ¼ 0 Ignorability of unobserved heterogeneity in employment/ low-paid employment H0: r6 ¼ r7 ¼ r8 ¼ r9 ¼ 0

Estimate

|t|

0.349 0.086 0.003 0.314 0.270 0.372 0.363 0.090 –0.269 0.163

(19.70) (0.23) (0.10) (1.86) (2.24) (2.99) (2.58) (1.25) (1.07) (1.57)

w2

p-Value

391.06

0.0000

447.09

0.0000

14.05

0.0071

9.98

0.0408

Transitions between Unemployment and Low Pay

69

initial employment and in current employment conditional on past employment status. The parameter’s negative sign can be interpreted as an example of Galtonian regression towards the mean in employment propensities. (See Stewart & Swafﬁeld, 1999; Cappellari, 2002 for analogous ﬁndings in the context of other models of labour market transitions). The correlation between unobserved factors in the lagged employment and lagged low pay equations was positive and precisely estimated, indicating that earnings potential was higher for men who were not employed compared to men who were, other things being equal. This fact might reﬂect higher reservation wages for unemployed men compared to employed men, or higher hiring probabilities in low-wage industries or workplaces compared to high-wage ones. Alternatively, it might reﬂect a higher chance of losing jobs during recessions among high-wage workers than among low-wage ones, as Keane et al. (1988) found for the United States. A similar interpretation can be given to the positive correlation estimated between unobserved factors determining lagged employment and current low pay. On the other hand, the correlations between unobserved factors in the current employment and low pay equations were not precisely estimated. Finally, the correlation between unobserved factors in the two low pay equations was positive, although statistically signiﬁcant only at the 20% level. (Taken at face value, it appears that, after controlling for differences in observed characteristics and in lagged low pay states, there remains some unobserved heterogeneity in low pay). Overall, the data support the proposed estimation strategy. According to the tests reported at the bottom of the table, none of the three endogenous selection processes considered should be ignored in the estimation of low pay/unemployment transitions: the null hypothesis that all the correlation coefﬁcients that ‘load’ a given selection process into the model are jointly equal to zero is rejected at conventional conﬁdence levels.

4.2. Employment Transition Probabilities In Table 3 we provide estimates of the coefﬁcients in the equations for the probability of employment. In the ‘full model’, probabilities differ depending on employment status (and low pay) at t1; hence the two columns of estimates. The table also reports the MEs associated with each variable, evaluated at the sample means of explanatory variables. For comparative purposes, the table also includes the estimates from ‘univariate’ models. These result from the estimation of the employment probability

(1.10) (0.74) (2.14) (0.64) (1.00)

(3.68) (2.49) (2.68)

Number of reported health problems 1 0.003 0.056 2 0.003 0.058 3 0.017 0.262 4þ 0.009 0.151 Lived in South East 0.003 0.054

0.238 0.057 0.001

|t|

(0.86) (1.06) (0.93) (1.79) (2.47)

0.004 0.004 0.004 0.007 0.010

0.013 0.005

Coeff.

0.085 0.087 0.078 0.149 0.240

Education Other qualiﬁcation O-level A-level Other higher degree First degree or higher

Married Age Age squared

ME

Pr(Et ¼ 1|Et–1 ¼ 1) Coeff.

|t|

0.220 0.402 0.666 0.517 0.654

0.011 0.032 0.072 0.229 0.065 0.209 0.161 0.439 0.012 0.035

0.076 0.141 0.245 0.187 0.242 (0.39) (1.67) (0.92) (1.19) (0.35)

(1.67) (3.03) (4.53) (3.78) (3.77)

0.063 0.193 (1.68) 0.069 0.012 (0.38) 0.00005 (0.12)

ME

Pr(Et ¼ 1|Et–1 ¼ 0)

0.003 0.004 0.017 0.009 0.002

0.004 0.005 0.004 0.007 0.010

0.013 0.006

ME

0.058 0.072 0.260 0.150 0.051

0.083 0.098 0.092 0.158 0.237

0.245 0.048 0.001

Coeff.

(1.15) (0.96) (2.18) (0.67) (0.91)

(0.89) (1.24) (1.11) (2.03) (2.47)

(4.52) (3.53) (3.92)

|t|

Pr(Et ¼ 1|Et–1 ¼ 1)

0.021 0.104 0.105 0.152 0.020

0.110 0.209 0.312 0.259 0.308

0.058 0.024

ME

|t|

0.054 0.267 0.268 0.386 0.050

0.276 0.533 0.825 0.671 0.822

(0.64) (1.88) (1.16) (1.04) (0.46)

(2.01) (4.04) (5.74) (5.00) (4.65)

0.146 (1.32) 0.003 (0.13) 0.00003 (0.09)

Coeff.

Pr(Et ¼ 1|Et–1 ¼ 0)

(2) Univariate Models

Estimates of Employment Transition Probabilities.

(1) Full-Joint Model

Table 3.

70 LORENZO CAPPELLARI AND STEPHEN P. JENKINS

21,935

28,035

0.042 0.125

[192]

0.760

0.126 0.365

0.031 0.097

0.000 0.002 0.005

0.0000

(1.18) 0.008 (3.06) 0.003 0.020 (1.16)

(0.71)

17,074

1,873

0.152 0.054 0.316 0.539

0.000 0.044 0.119

[27]

(2.35) (0.72) (5.04) (2.10)

(0.00) (0.39) (0.95)

0.0000

0.074 0.155

0.043

1,298

824

0.544

0.185 0.391

0.108

[24]

(1.32)

(1.62) (3.07)

(0.72)

Notes: ME: marginal effect. The GHK simulator for the full-joint model (1) used 150 random draws. MEs were computed at the means of explanatory variables over the relevant subsamples. For example, in the Pr(Et ¼ 1|Et1 ¼ 1) column, means were computed over non-attrited cases in employment at t1. For dummy variables, MEs show the change in the relevant probability when the variable changes from 0 to 1. For age, the ME is the change in probability when age changes from 26 to 45 (the sample 25th and 75th percentiles). |t|: robust asymptotic t-ratio for estimated coefﬁcient. The reference man was not married, had no educational qualiﬁcations, did not report any health problems, lived outside the South East or London areas, and worked in a small ﬁrm in an unskilled occupation. His ﬁrst labour market spell was not fulltime employment, and he was high-paid at t1. All regressions include controls for survey year.

0.0000

(2.23) (0.72) (1.45) (0.62)

First labour market spell Full-time employment 0.007 0.140 Missing information 0.003 0.054 Low paid at t1 0.011 0.194 Constant 0.371

Log likelihood Model p-value [df] Number of observations

(0.08) (0.51) (0.95)

0.0003 0.003 0.005

0.006 0.057 0.118

Lived in London Firm size W 100 Skilled occupation

Transitions between Unemployment and Low Pay 71

72

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

equations without controlling for endogenous attrition, selection into employment, or initial conditions.5 Looking ﬁrst at the full model estimates, we ﬁnd that the probability of unemployment is about one percentage point higher for a man who was low-paid in t1 rather than high-paid, other things being equal. As this ME is calculated holding observed and unobserved personal attributes ﬁxed, it is an indication of the extent of genuine state dependence in employment with respect to low-paid work. Taking the probability of unemployment for men who were high-paid at t1 as a benchmark (1.95%, see Table 1), our estimates imply that, by itself, having a low-paid job raises unemployment probabilities by about a half. The corresponding ME in the univariate model is twice the size of that in the full model (2%), suggesting that not accounting for unobserved heterogeneity, in this case, would lead to an overstatement of the impact of lagged low pay on the probability of employment by nearly 100%. Also the relevant coefﬁcient in the univariate model is precisely estimated (with a p-value less than 0.05, compared to the one in the full model, for which the p-value is 0.147). Being married was associated with higher employment probabilities if one was already employed, and with a lower probability for the previously – unemployed. In the ﬁrst case the effect may reﬂect the presence of family responsibilities that favour employment stability; in the second case, it might reﬂect the presence of the partner’s incomes that lengthen job search duration, other things being equal. Employment probabilities had an inverse-U relationship with age, but life-cycle variation was limited: the probability was 0.5% higher for a man aged 45 rather 26 years (these are the third and ﬁrst quartiles of the sample age distribution). Having better educational qualiﬁcations had a positive impact on employment probabilities, especially for those who were previously unemployed. For example, the probability of getting a job was about 25% higher for an unemployed man with a university degree compared to an unemployed man with no educational qualiﬁcations. It is noteworthy that these effects would have been estimated to be even larger – by approximately 5% – if (wrongly) endogeneity issues had been ignored. (See the univariate model estimates). The presence of health problems, on the other hand, seems to be associated with higher probabilities of becoming unemployed. 4.3. The Probabilities of Low-Paid Employment Estimates of the models of the probabilities of low-paid employment are reported in Table 4. The ﬁrst two columns of numbers show the full model,

(2.88) (4.12) (5.97) (7.19) (8.09) (2.12) (2.47) (4.41) (2.69) (3.18) (3.68)

Number of reported health problems 1 0.010 0.080 2 0.021 0.149 3 0.063 0.384 4þ 0.079 0.454 Lived in South East 0.017 0.142 Lived in London 0.028 0.262

0.023 0.028 0.041 0.052 0.061

Education Other qualiﬁcation O-level A-level Other higher degree First degree or higher

(3.50) (9.81) (9.62)

|t|

0.203 0.251 0.406 0.482 0.692

0.024 0.182 0.007 0.142 0.002

Coeff.

Married Age Age squared

ME

0.088 0.097 0.042 0.073 0.087 0.063

0.105 0.062 0.120 0.073 0.253

0.058 0.203

ME

0.284 0.334 0.125 0.245 0.257 0.186

0.304 0.188 0.349 0.218 0.695

0.184 0.168 0.002

Coeff.

ME

0.018 0.025 0.036 0.043 0.051

(2.52) 0.009 (1.58) 0.018 (0.27) 0.052 (0.53) 0.062 (1.84) 0.015 (1.11) 0.024

(1.42) (0.98) (1.60) (1.06) (2.68)

0.079 0.154 0.368 0.418 0.143 0.260

0.191 0.260 0.420 0.477 0.699

0.162 0.123 0.001

Coeff.

(2.06) (2.56) (4.20) (2.53) (3.26) (3.87)

(2.80) (4.49) (6.59) (7.62) (8.75)

(3.39) (12.15) (11.24)

|t|

0.132 0.168 0.061 0.130 0.117 0.084

0.125 0.098 0.163 0.124 0.271

0.059 0.020

ME

0.349 0.432 0.169 0.336 0.328 0.234

0.361 0.270 0.476 0.351 0.895

0.156 0.200 0.002

Coeff.

(2.84) (1.86) (0.33) (0.66) (2.06) (1.27)

(1.54) (1.40) (2.26) (1.74) (3.35)

(0.87) (6.56) (5.58)

|t|

Pr(Lt ¼ 1|Et1 ¼ 0)

(2) Univariate Models Pr(Lt ¼ 1|Et1 ¼ 1)

(1.14) 0.018 (4.84) 0.008 (4.57)

|t|

Pr(Lt ¼ 1|Et1 ¼ 0)

(1) Full-Joint Model

Estimates of Probabilities of Low-Paid Employment.

Pr(Lt ¼ 1|Et1 ¼ 1)

Table 4.

Transitions between Unemployment and Low Pay 73

0.0000 21,935

0.042 0.436 0.037 0.362 0.254 1.139 2.124

Coeff.

28,035

(4.14) (3.26) (6.21) (6.17)

|t|

ME

[192]

3.406

Coeff.

(6.50)

|t|

Pr(Lt ¼ 1|Et1 ¼ 0)

0.0000

0.034 0.031 0.327

ME

16,644

3,591

0.426 0.370 1.443 1.599

Coeff.

[25]

(4.07) (3.24) (28.31) (7.57)

|t|

Pr(Lt ¼ 1|Et1 ¼ 1)

0.0000

ME

612

338

3.004

Coeff.

[22]

(5.74)

|t|

Pr(Lt ¼ 1|Et1 ¼ 0)

(2) Univariate Models

Notes: ME: marginal effect. The GHK simulator for the full-joint model (1) used 150 random draws. MEs were computed at the means of explanatory variables over the relevant subsamples. For example, in the Pr(Et ¼ 1|Et1 ¼ 1) column, means were computed over non-attrited cases in employment at t1. For dummy variables, MEs show the change in the relevant probability when the variable changes from 0 to 1. For age, the ME is the change in probability when age changes from 26 to 45 (the sample 25th and 75th percentiles). |t|: robust asymptotic t-ratio for estimated coefﬁcient. The reference man was not married, had no educational qualiﬁcations, did not report any health problems, lived outside the South East or London areas, and worked in a small ﬁrm in an unskilled occupation. His ﬁrst labour market spell was not fulltime employment, and he was high-paid at t1. All regressions include controls for survey year.

Log likelihood Model p-value [df] Number of observations

Firm size W 100 Skilled occupation Low paid at t1 Constant

ME

Pr(Lt ¼ 1|Et1 ¼ 1)

(1) Full-Joint Model

Table 4. (Continued )

74 LORENZO CAPPELLARI AND STEPHEN P. JENKINS

Transitions between Unemployment and Low Pay

75

with coefﬁcients varying with lagged employment status and, for those previously employed, whether the job was low-paid or not. The ‘univariate model’ estimates are those derived from models that did not control for any endogenous selections. The ME associated with having been low-paid at t1 indicates that the probability of low-paid employment would be about 25 percentage points higher for a man who was low-paid at year t1 rather than high-paid. Given that the average low-pay probability in year t among men who were highpaid at t1 is 4%, the large ME indicates that the chances of being low-paid are closely associated with the experience of low pay in the past. This association can be interpreted as causal in the sense that both observed and unobserved heterogeneity have been taken into account. Had unobserved heterogeneity been overlooked (univariate models), the resulting ME would have been 33% (and the associated t-ratio would have changed from 6.2 to 28.3). These results suggest that probability of being low-paid is inﬂuenced by sizeable genuine state dependence effects. Being married was associated with lower low pay probabilities for formerly employed men, whereas among formerly unemployed men, the effect was positive but imprecisely estimated. Low pay probabilities had a U-shaped relationship with age. A man aged 45 rather than 26 had a slightly lower probability of low pay if they were employed at t1, but the effect was much larger (20%) if they were unemployed at t1. The corresponding ME in the model that did not control for endogenous selection was only 2%. Since coefﬁcients associated with age are rather stable across columns, part of the change must be attributable to changes in the other coefﬁcients, which enter the computation of the baseline probabilities. Having better educational qualiﬁcations was associated with lower chances of being in low-paid employment, and the two points already made about employment probabilities also apply in this case. First, the MEs associated with having educational qualiﬁcations are larger for men who were unemployed rather than employed at t1. Second, for the previously unemployed, controlling for the endogenous selections reduces the estimated impact of having educational qualiﬁcations. There were also statistically signiﬁcant associations between low pay probabilities and region, ﬁrm size, and occupation. Probabilities were lower for men living in London and the South East, for men who worked in large ﬁrms, and for those who worked in a skilled occupation. Variations in the parameter estimates associated with the two alternative states at t1 are consistent with existence of genuine state dependence effects. The hypothesis of an absence of a genuine state dependence effect

76

LORENZO CAPPELLARI AND STEPHEN P. JENKINS

from having low-paid employment at the previous interview is overwhelmingly rejected in the equation for low-paid employment in year t, whereas rejection is more marginal in the equation for year t employment ( p ¼ 0.15): see the estimates associated with lagged low pay dummies in Tables 3 and 4. Tests of equality of coefﬁcients across the two employment states at t1 (see Section 3) overwhelmingly reject the null hypothesis of no differences (results, not reported, are available upon request).

4.4. Predicted Transition Rates and State Dependence Table 5, rows 1–6, reports transition rates computed from the model estimates, and the predicted rates correspond well with the raw transition rates reported in Table 1.6 Measures of aggregate state dependence were calculated as differences in transition rates for men with different initial labour market states (as explained earlier): see rows 7–12. The estimates of genuine state dependence are the MEs associated with lagged low pay indicators or the alternative measure presented in Section 3. The estimates indicate that genuine state dependence is a non-trivial share of aggregate state dependence. In particular, when looking at unemployment probabilities (rows 10–12), genuine state dependence accounts for almost all of the Table 5.

Predicted Transition Rates and State-Dependence Effects. Predicted Transition Rates

1. 2. 3. 4. 5. 6.

Pr(Lt ¼ 1|Lt1 ¼ 1) Pr(Lt ¼ 1|Lt1 ¼ 0) Pr(Lt ¼ 1|Et1 ¼ 0) Pr(Et ¼ 0|Lt1 ¼ 1) Pr(Et ¼ 0|Lt1 ¼ 0) Pr(Et ¼ 0|Et1 ¼ 0)

51.19 4.82 16.12 3.71 1.79 57.72

State Dependence

7. 8. 9. 10. 11. 12.

Pr(Lt ¼ 1|Lt1 ¼ 1)Pr(Lt ¼ 1|Lt1 ¼ 0) Pr(Lt ¼ 1|Lt1 ¼ 1)Pr(Lt ¼ 1|Et1 ¼ 0) Pr(Lt ¼ 1|Et1 ¼ 0)Pr(Lt ¼ 1|Lt1 ¼ 0) Pr(Et ¼ 0|Et1 ¼ 0)Pr(Et ¼ 0|Lt1 ¼ 1) Pr(Et ¼ 0|Et1 ¼ 0)Pr(Et ¼ 0|Lt1 ¼ 0) Pr(Et ¼ 0|Lt1 ¼ 1)Pr(Et ¼ 0|Lt1 ¼ 0)

Aggregate

Genuine

46.36 35.07 11.29 54.01 55.93 1.91

25.40 29.09 3.76 48.86 52.92 1.11

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observed state dependence, indicating that human capital depreciation or negative signalling may be important in those cases. The effects computed conditional on what the labour market state was at t1 are informative about interrelationships between transitions. For example, the estimates indicate that differences in the probability of lowpaid employment at year t between men who were low-paid at t1 rather than unemployed at t1 were largely due to state dependence, whereas heterogeneity drives the differential in the low-paid employment probability between men who were unemployed rather than in a higher-paid job. (The fraction of state dependence that is genuine in line 8 is larger than the corresponding fraction in line 9). This ﬁnding is consistent with the arguments in the Section 1 about the labour market having a primary and a secondary sector (unemployment or low-paid work), as there appear to be few heterogeneity effects differentiating the chances of those who were unemployed rather than low paid. This suggests a common set of policies for this relatively homogenous group.

5. CONCLUDING REMARKS There is substantial persistence in the chances of being unemployed and being in low-paid employment. More than one half of the men who were in either of these two states were in the same states a year earlier. Unemployment and low-paid employment are also labour market states that are closely linked. Becoming unemployed in one year was more likely for men with a low-paid job in the previous year and, among unemployed men who got a job, the chances of that job being a low-paid one were about three times the unconditional low pay probability. To gain greater understanding of these patterns, this paper has modelled transitions between unemployment and low pay versus high pay using data for men from the BHPS, with particular attention given to controlling for the endogeneity of associated processes, in initial conditions, selection into employment, and in attrition from the panel. None of the three processes was found to be exogenous in the estimation of the transitions of principal interest. The interrelationship between the chances of being unemployed and the chances of being low paid remained strong, even after controlling for the three endogenous selections and for observed characteristics. Men who had been in low-paid employment had higher probabilities of unemployment than high-paid men, and men who had been unemployed had higher chances

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of being low-paid rather than high-paid were they to get a job. The ﬁrst ﬁnding suggests that low-paid jobs are characterised by greater turnover than high-paid jobs. The second ﬁnding suggests that the experience of unemployment leads to lower quality jobs. This would be consistent with the idea that an individual’s human capital depreciates the longer he is unemployed or, alternatively, employers use unemployment duration as a signal of poor quality workers. In general, there appear to be genuine state dependence effects helping to determine men’s chances of being low-paid or unemployed. Hence policies targeted on unemployed men may reduce the chances of being low-paid once they get a job, and measures designed to raise the earnings potential of the low-paid may also reduce their chances of becoming unemployed in future.

NOTES 1. The BHPS is documented at http://www.iser.essex.ac.uk/ulsc/bhps/ 2. Stewart (2007) pooled data for men and women, and reported higher low pay transition rates and lower unemployment transition rates than those show in Table 1 below. When we pooled data for men and women, we found transition rates to be close to the rates reported by Stewart. 3. One advantage of working with the dichotomous low pay indicator rather than with a continuous earnings variable in the multivariate normal context of this paper is that we avoid having to assume that earnings or log-earnings are normally distributed. Instead, normality is assumed only up to an arbitrary monotonic transformation of earnings (Stewart & Swafﬁeld, 1999). 4. In addition to health and education, another variable that may be related with interview problems, particularly language problems, is ethnicity. We experimented with speciﬁcations that included indicators of ethnic group membership and found their effects on labour market transitions to be very imprecisely estimated. We therefore decided not to report the estimates for these models. 5. We also estimated the model excluding the sample retention process only. The estimates (available from the authors) were similar to the ones presented here, with some exceptions. First, some of the cross-process correlation coefﬁcients – namely, the ones that were statistically signiﬁcant at conventional levels of conﬁdence in Table 2 – were estimated to be larger in absolute value, possibly a consequence of using information over a smaller parameter space. Second, the restricted model tended to underestimate transitions into unemployment from low pay, which suggests that attrited cases include low-paid workers who would have had a large propensity to become unemployed had they remained in the sample. 6. Predictions were derived for each man, and then averaged over the relevant subsamples. For example, predicted low pay persistence is the predicted probability of low pay at t conditional on low pay at t–1 and retention, averaged over those who were low paid at t–1 and did not drop out of the sample during the transition.

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ACKNOWLEDGEMENTS Research supported by a Nufﬁeld Foundation New Career Development Fellowship and by ISER’s core funding from the University of Essex and the UK Economic and Social Research Council for the Research Centre on Micro-Social Change and the United Kingdom Longitudinal Studies Centre. We are grateful for the comments of two anonymous referees.

REFERENCES Arulampalam, W., Booth, A. L., & Taylor, M. P. (2000). Unemployment persistence. Oxford Economic Papers, 52, 24–50. Barth, E., Bratsberg, B., Naylor, R. A., & Raaum, O. (2002). How wage curves differ: Theory and evidence for the US, UK and Norway. Unpublished manuscript, University of Oslo, February. Binder, D. A. (1983). On the variances of aymptotically normal estimators from complex surveys. International Statistical Review, 51, 279–292. Cappellari, L. (2002). Do the ‘working poor’ stay poor? An analysis of low pay transitions in Italy. Oxford Bulletin of Economics and Statistics, 64, 87–110. Cappellari, L., & Jenkins, S. P. (2004). Modelling low income transitions. Journal of Applied Econometrics, 19, 593–610. Gourieroux, C., & Monfort, A. (1996). Simulation based econometric methods. Oxford: Oxford University Press. Heckman, J. J. (1974). Shadow prices, market wages, and labor supply. Econometrica, 42, 679–694. Heckman, J. J. (1981a). The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process. In: C. F. Manski & D. McFadden (Eds), Structural analysis of discrete data with econometric applications. Cambridge, MA: MIT Press. Heckman, J. J. (1981b). Statistical models for discrete panel data. In: C. F. Manski & D. McFadden (Eds), Structural analysis of discrete data with econometric applications. Cambridge, MA: MIT Press. Huber, P.J. (1967). The behaviour of maximum likelihood estimators under non-standard conditions. In: Proceedings of the Fifth Berkeley Symposium in Mathematical Statistics and Probability, University of California Press, Berkeley, CA. Keane, M., Mofﬁtt, R., & Runkle, D. (1988). Real wages over the business cycle: Estimating the impact of heterogeneity with micro-data. The Journal of Political Economy, 96, 1232–1266. Montuenga, V., Garcy´a, I., & Fernandez, M. (2003). Wage ﬂexibility: Evidence from ﬁve EU countries based on the wage curve. Economics Letters, 78, 169–174. Stewart, M. B. (2007). The inter-related dynamics of unemployment and low-wage employment. Journal of Applied Econometrics, 22, 511–531. Stewart, M. B., & Swafﬁeld, J. K. (1999). Low pay dynamics and transition probabilities. Economica, 66, 23–42. White, H. (1982). Maximum likelihood estimation of misspeciﬁed models. Econometrica, 50, 1–25.

WHY EUROPEANS WORK PART-TIME? A CROSS-COUNTRY PANEL ANALYSIS Hielke Buddelmeyer, Gilles Mourre and Melanie Ward ABSTRACT This paper aims to identify the relative contribution of the business cycle and structural factors to the development of part-time employment in the 15 Member States of the European Union before the 2004 enlargement (EU-15) over the 1980s and 1990s. To do so, it exploits both crosssectional and time series variations in available data over the past two decades. Key results include the business cycle that is found to exert a short-term negative effect on part-time employment developments, although this effect fades away over the two-decade period considered. This ﬁnding is consistent with ﬁrms utilising part-time employment as a means of adjusting their labour force to economic conditions. Correspondingly, involuntary part-time employment is found to be counter-cyclical, being higher in troughs of economic activity. Splitting our sample reveals a very signiﬁcant effect of the business cycle on the rate of part-time work for young and male prime-age workers. Conversely, the effect is very weak for women and insigniﬁcant for older workers. Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 81–139 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28004-0

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Institutions and other structural factors are also found to be signiﬁcant, longer run determinants of the rate of part-time employment. Changes in legislation affecting part-time employment are found to have a strong and positive impact on part-time employment developments. Moreover, employment protection legislation is positively correlated with the parttime employment rate (PTR), which is consistent with the use of parttime work as a tool for enhancing ﬂexibility in the presence of rigid labour markets. Less robust evidence suggests the presence of unemployment traps for some potential part-time workers. Cross-country evidence also indicates that the lower labour costs borne by ﬁrms when employing part-time workers have a large and positive inﬂuence on the PTR. Overall, a contribution analysis shows that the main structural and institutional variables generally explain the development in the part-time rate in the EU countries fairly well, while this is obviously not the case in the United States.

1. INTRODUCTION A growing part-time employment share has been a main feature of a number of industrialised countries over the past two decades. While the United States experienced a slight fall in the share of part-time employment in total employment during the late 1980s and 1990s, the latter increased strongly in the 15 Member States of the European Union before the 2004 enlargement (EU-15),1 Japan and Canada in the same period (see Annex A for the trends in part-time employment). From a macroeconomic standpoint, the increase in the share of part-time work may have a dampening effect on aggregate wage growth,2 and some recent papers have shown that the total employment growth (in terms of persons employed) in the 1990s beneﬁted from the development of part-time employment in the European countries (Garibaldi & Mauro, 2002; Mourre, 2006). Furthermore, from an economic policy perspective, the promotion of part-time work may be an important measure through which the ﬂexibility of labour markets can be increased. On the labour demand side, it may allow employers to adjust hours worked to cyclical conditions more easily, facilitating adjustment of production and labour costs. On the labour supply side, part-time work may increase the labour market choices open to individuals and may draw people who were previously unwilling or unable to work into the labour market. Part-time employment may therefore increase potential output in the EU (see the economic strategy

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and the targets for the EU employment rates set by the European Councils held in Lisbon in 2000 and Stockholm in 2001). At the same time, part-time work may have its drawbacks. Part-time workers may be subject to lower wages, be less likely to receive fringe beneﬁts and face reduced chances for promotion (for a discussion, see OECD, 1999). For employers, part-time work may be connected with higher ﬁxed costs, such as recruitment and training costs. Furthermore, part-time jobs may crowd out full-time positions. Broadly speaking, the literature on part-time job developments to date can be divided into two main vintages. A ﬁrst branch relies on microeconometric analysis based on ﬁrm surveys. The purpose of this work is to identify the microeconomic and individual determinants of part-time work (Haskel, Kersley, & Martin, 1997; Houseman, 2001), to illustrate the role of part-time work as a ﬂexible work arrangement (Haskel et al., 1997; Farber, 1999; Barrett & Doiron, 2001) or to explain the transition between part-time jobs and other labour market states (Blank, 1994; O’Reilly & Bothfeld, 2002; Buddelmeyer, Mourre, & Ward, 2005a). The second vintage deals with the comprehensive description of part-time employment developments based on macro-data and includes sociological and institutional qualitative evidence (Smith, Fagan, & Rubery, 1998; Delsen, 1998; OECD, 1999; Walwei, 1998). In this vein, some papers focus on international comparison (Lemaıˆ tre, Marianna, & Van Bastelaer, 1997) and attempt to understand the reason why part-time work is so low in some countries such as Spain and Portugal (Ruivo, Gonzalez, & Varejao, 1998) or so different across countries (Pfau-Efﬁnger, 1998). This paper belongs to the second vintage of the literature, while extending it through the use of a country panel of time-varying institutions and structural variables covering most EU-15 Member States. This latter methodological approach can be associated with another branch of the labour market literature (initiated by Scarpetta, 1996 and extended by Belot & van Ours, 2000; Blanchard & Wolfers, 2000; Nickell, Nunziata, & Ochel, 2002) that uses cross-sectional or pooled-time-series data on indicators of labour market performance and labour market institutions to account for unemployment differentials across countries. This paper therefore ﬁlls a gap in the literature by analysing the cause of part-time job developments systematically in a Europe-wide perspective, including the ex post impact of changes in legislation regarding part-time employment.3 This paper also considers the effect of the business cycle on part-time employment. Although the counter-cyclicality of the relative growth of part-time employment compared to full-time employment has often been mentioned

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in the literature (Delsen, 1998; Lester, 1999) and tackled indirectly through the cyclicality of hours worked (Millard, Scott, & Sensier, 1999), no systematic econometric investigation has been carried out using macroeconomic data. Thus the purpose of this paper is threefold. First, it reviews the determinants of part-time employment as identiﬁed by the economic literature. Second, it aims to identify the role of the business cycle and structural factors in the development of part-time employment in the EU-15 countries by exploiting both cross-sectional and time series variations. This may enable us to comment on whether part-time jobs have been used as a ﬂexible work arrangement by ﬁrms in the EU-15, as has been shown for some speciﬁc countries and sectors within the micro-econometric literature. Third, the main payoff of this paper is to measure the relative weight of each determinant of part-time employment over time. This justiﬁes the macroperspective of this paper and its comprehensive approach (encompassing a large set of determinants) since the relative contribution of the relevant macroeconomic, policy and institutional factors could not have been obtained with a micro-analysis or study focusing on a speciﬁc factor of parttime employment. This paper is organised as follows: Section 2 surveys the determinants of part-time work offered by theory. Section 3 introduces the simple econometric setting to be utilised in the remainder of this paper and describes our data sources. Section 4 analyses the impact of the business cycle on part-time employment developments and involuntary part-time work. Section 5 considers the role of part-time legislation, labour market institutions and other structural features (of demographic, sociological or economic nature) on the rate of part-time work within EU-15 countries. Section 6 concludes.

2. SOME THEORY: THE FACTORS INFLUENCING PART-TIME EMPLOYMENT This subsection reviews the various determinants of part-time work offered by a theory that will be consequently important for our econometric analysis in the following sections. The determinants can be grouped under sections (i) Business Cycles, (ii) Labour Market Institutions and (iii) Other Structural Factors. While the economic literature generally suggests that the business cycle plays some role in the short-to-medium run, it also stresses the

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importance of various institutions and policies as well as other structural factors of sociological, demographic or economic nature in the longer run.

2.1. Business Cycles Business cycles affect movements in the part-time employment rate (PTR)4 in the short-to-medium term. This implies that the rate of part-time work may respond differently to business cycle effects relative to full-time employment. The literature has identiﬁed a number of ways in which the business cycle affects the share of part-time employment (OECD, 1995; Delsen, 1998). On the demand side, two effects may be at play. First, there is a compositional effect. As noted by Lester (1999), shifts between sectors arise because sectors with a higher share of full-time employees, such as manufacturing and construction, are generally affected earlier and more strongly by the cycle than other sectors. Therefore, part-time employment may be less responsive to business cycle effects than total employment and may show a counter-cyclical pattern. Second, shifts within sectors may boost part-time employment during downturns as employers offer part-time employment as a way to adjust hours worked over the cycle, while continuing to hoard labour (Delsen, 1998). This enables employees in place to avoid dismissal and job seekers to avoid long-term unemployment. Thus, during a downturn, employers may reduce the number of hours worked by their current workforce or hire new workers in part-time jobs. However, as suggested by Lester (1999) for Australia, and Farber (1999) for the United States, it seems that a nonnegligible proportion of full-timers moving to part-time work does not stay in their current ﬁrm, going through a period of unemployment.5 Moreover, as some employers use part-time jobs to screen workers for full-time positions (Houseman, 2001) and ﬁrms may be more demanding and more risk averse before hiring new staff in bad times, they may prefer to systematically recruit part-timers rather than full-timers in periods of economic slowdown. In an upswing, employers may offer full-time contracts to their part-time workers (so called ‘‘tap effects’’) in order to increase their total stock of labour resources, as this was the case in Sweden in the 1980s (Sundstro¨m, 1991). We will label the use of part-time work by employers as a means to regulate the size of their workforce in response to the economic cycle as the ‘‘ﬂexibility effect’’. We would therefore expect the ﬂexibility

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effect to exert a counter-cyclical impact on the rate of part-time employment.6 On the supply side, in an environment of falling economic activity and/or rising unemployment, workers may be more willing to consider part-time work as an alternative to their preferred labour supply choice of full-time employment. This third effect can also be viewed as a consequence of the ‘‘ﬂexibility effect’’, as it also reﬂects the mismatch between job seekers, preferably looking for a full-time job, and ﬁrms mainly offering a part-time job. Conversely, in a period of expanding output and/or falling unemployment, workers with a preference for full-time work may be less willing to work part-time. This ‘‘involuntary part-time work effect’’ is expected to be negatively related to the part-time rate. An additional labour supply effect is the ‘‘added worker effect’’. Here, the unemployment of a household member leads to an increase in the labour supply of other household members (Mincer, 1962; Layard, Barton, & Zabalza, 1980; Maloney, 1991). Typically, a recession causes job losses in single-breadwinner household, urging the other partner (often female) to work part-time so as to limit the income loss. The empirical evidence to date, however, suggests that this effect is small. A ﬁfth effect, also of labour supply, is known as the ‘‘discouraged worker effect’’ (Long, 1953). A lasting period of unemployment reduces the probability of ﬁnding a job and may induce groups of disadvantaged groups not to enter in the labour market, awaiting better opportunities, given that searching for a job is a costly activity. A large set of empirical studies reports evidence supporting the discouraged worker hypothesis (Clark & Summers, 1982; Blundell, Ham, & Meghir, 1998; Darby, Hart, & Vecchi, 2001). During a period of economic contraction or slowdown, labour supply from low-skilled or initially inactive females, who are more likely to look for parttime jobs, may be reduced, given the lesser prospect of ﬁnding a job. Thus, the discouraged worker effect is likely to be negatively related to the parttime rate. Thus, the effect of the cycle on the rate of part-time work will be positive or negative depending on the relative importance of these ﬁve effects (Table 1). The ﬁnding of a signiﬁcant counter-cyclical effect could suggest that (i) labour demand is one of the main driving forces behind developments in part-time employment and (ii) employers use these types of jobs to adjust to the general economic situation. Indeed, the labour supply effects going in the same direction are supposed to be weak (‘‘added worker effect’’) or the mirror of cyclical labour demand conditions (‘‘involuntary part-time effect’’). In contrast, the ﬁnding of no or weak cyclical patterns of part-time

Why Europeans Work Part-Time? A Cross-Country Panel Analysis Table 1.

87

Five Effects of Business Cycle on Part-Time Employment Rate.

Labour demand () Compositional effect (concentration in less cyclical sectors) () Flexibility effect (adjustment of hours worked along the cycle) Labour supply () Involuntary part-time effect (enhanced willingness to work part-time to avoid unemployment) () Added worker effect (unemployment of a household member causing an increase in labour supply of another household member) (þ) Discouraged worker effect (withdrawal from the labour market of part-time job seekers) - Overall effect uncertain, but likely negative correlation between output gap and part-time increase Notes: Reading: () means countercyclical effects; (þ) means procyclical effects.

work relative to total employment may indicate that developments in part-time jobs rather reﬂect structural factors, such as the design of labour market institutions. 2.2. Labour Market Institutions While the business cycle affects the short-to-medium term, developments in part-time employment, institutional and sociological factors are likely to inﬂuence the longer-term level of the part-time rate. Smith et al. (1998) survey the factors affecting the growth of part-time work in Europe. Some of these factors are not mutually exclusive and might reinforce each other. Speciﬁc regulations on part-time work (statutory or collectively bargained) can affect part-time employment developments through three mechanisms, as described by Smith et al. (1998). First, some regulations directly affect the working-time system by restricting the use of part-time work. Second, some regulations indirectly inﬂuence part-time employment through wage regulation, the social protection system or the tax and beneﬁt systems. For example, in some countries (e.g. Portugal), hourly wages for part-time and full-time work are restricted by law to be equal (pro rata clause). Such legislation may change the structure of non-wage costs for employers, such as hours or earnings thresholds for social insurance contributions or special subsidies or tax rebates for ﬁrms hiring part-time staff.7 Lower pension entitlements can also restrict the labour supply of part-time jobs (Ginn & Arber, 1998). A third type of regulation facilitates the conversion of full-time jobs into voluntary part-time employment in

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order to reconcile personal and professional lives (Genre, Gomez-Salvador, Leiner-Killinger, & Mourre, 2003). Employment protection legislation (EPL) has become a more and more important reason for hiring part-time employees. In the late 1990s, in a context of increasing competition and uncertainty, ﬁrms realised the advantages of ‘‘atypical jobs’’, which were considered to be more ﬂexible and less expensive. Part-time employment was quickly acknowledged as offering such a job type, together with temporary jobs, help agency employment, shift work, on-call jobs and atypical working hours (nights and weekends). Bentolila and Dolado (1994) call this new search for ﬂexible stafﬁng arrangements the ‘‘new reasons’’ for hiring part-time workers. The stringency of job protection legislation may have two conﬂicting effects. First, it can encourage the use of part-time work so as to circumvent highly rigid employment legislation affecting full-time jobs. Second, EPL in some countries can directly and adversely affect part-time employment by strictly limiting its use. In any case, as part-time employment in the EU-15 mostly corresponds to permanent contracts (above 80% in the late 1990s), EPL for regular contracts seems more relevant for understanding the level of parttime work over time and across countries. However, the small proportion of ﬁxed-term part-time employment can be affected by EPL for temporary contracts.8 The effect of child beneﬁts on part-time work is ambiguous. In general, the provision of child beneﬁts can create an ‘‘unemployment trap’’, if beneﬁts are only granted below a certain level of income.9 Moreover, some child beneﬁts grant additional income to parents who renounce to work in order to take care of their young children. These can have a strong adverse effect on female participation (Laroque & Salanie´, 2003). On the other hand, the lack of childcare beneﬁts or a subsidised childcare system is a major disincentive to taking up employment. Therefore, the overall effect may depend on the shape and the composition of child beneﬁt systems. Unemployment beneﬁt systems (together with other beneﬁts) may create an ‘‘unemployment trap’’ through high net replacement rates and long beneﬁt durations. As stated by Doudeijns (1998), this ﬁnancial disincentive to take up a job has a signiﬁcant impact on the decision to work part-time since part-time jobs are not likely to yield high earnings. Conversely, ‘‘in-work beneﬁts’’, the tightening of eligibility criteria and enhanced controls of their implementation may help alleviate such a disincentive. The tax system and, in particular, high income tax rates may deter parttime work. Where the income tax is computed on the basis of a couple’s earnings rather than on an individual basis, the second earner in the couple

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may be taxed at a relatively high marginal rate, creating an ‘‘unemployment trap’’. Moreover, the existence of a dependent partner’s allowance may create disincentives for the second earner to take up a job, especially lowpaid part-time jobs (Jaumotte, 2003). Trade unions have generally fought against part-time work – seen as a threat to full-time standards. Houseman (2001) found some econometric evidence of a negative relationship between trade union density and parttime employment for the United States, although reverse causation cannot be ruled out.10 This can also explain the low part-time rate in highly unionised sectors such as manufacturing, while the services sector, which is less unionised, is more part-time intensive. However, high unemployment has started to change trade unions’ attitude. In this context, a high level of co-ordination between unions may facilitate the conclusion of tripartite agreements, involving the government, that aim at reducing unemployment via some ‘‘work sharing’’ or improving working conditions by encouraging voluntary part-time employment (Genre et al., 2003). The share of temporary jobs (short-term contracts help agency employment) could exert a crowding-out effect on part-time employment. In Portugal and Spain (until 1994), the favourable legislation on ﬁxed-term contracts and the sharp development in this type of job have led to a weak development in part-time employment. Nonetheless, in many cases, the development in part-time jobs goes hand in hand with that of ﬁxed-term contracts as complementary ﬂexible stafﬁng arrangements.11

2.3. Other Structural Variables The rise in female participation has occurred hand in hand with an increase in the part-time rate in many countries. Part-time employment has been the main way of integrating women in the labour market in countries where the participation rate was low in the 1960s and 1970s. Sociological and cultural reasons, such as the separation of tasks within the household and the family model, combined with institutional reasons (e.g. the lack of childcare facilities), explain in part why women are more inclined to work part-time than men. For instance, a ‘‘male breadwinner’’ model of family encourages women to work part-time rather than full-time (Fagan & O’Reilly, 1998). Likewise, an increase in the fertility rate and the number of children per family may increase the need for working part-time instead of working fulltime so as to reconcile professional and family life, especially when the childcare system is insufﬁcient. However, in some countries, such as

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Finland, the male breadwinner model was never dominant, and the rise in female participation was mainly due to the increase in full-time employment (Pfau-Efﬁnger, 1998). However, these variables may suffer from endogeneity problems. The share of employment in services is also an important determinant of part-time work in the literature to date. Traditionally, employers hire parttime workers in order to deal with regular and predictable peaks of demand (‘‘rush hours’’) or to extend opening hours on evenings or weekends, beyond what the hours worked by a full-timer in a single shift would allow.12 This situation particularly concerns some service sectors, where part-time work is concentrated (retail trade, hotels and restaurant, personal services). Conversely, mass-production and capital-intensive industries rely far more on full-time workers. Part-time work may also be used to substitute for absent employees (on maternity or sick leave) or to meet unexpected orders. Part-time staff therefore acts as a backup for full-time employees (Delsen, 1995). In addition, as mentioned by Delsen (1998), the issue of ‘‘gender ﬂexibility’’ plays a role. Many services rely predominantly on female employees, who are more prone to accept working part-time, while maledominated sectors (industry, construction) have been more reluctant. The schooling rate of the population aged 15–24 is likely to positively inﬂuence the PTR, as the latter is currently highest for those aged 15–24 within the EU. From the labour demand side, students offer relatively cheap and ﬂexible labour.13 From the labour supply side, students are mainly looking for part-time jobs to ﬁnance their studies. Moreover, some newly graduated students may be ready to accept working part-time in bad times in order to build up professional experience and avoid unemployment spells, which might be stigmatising. The differential in wages and non-wage costs between part-time and fulltime employment may make part-time work advantageous to ﬁrms. OECD (1999) showed that both the hourly wage rate and the beneﬁts received by part-time workers were lower than that of full-time workers in most OECD countries.14 This remains true even after controlling occupational characteristics of part- and full-time jobs. The gap between part-time and fulltime earnings is 10% on average. One reason for this may be that part-time workers tend to receive less job-related training than full-timers. As suggested by Houseman (2001), a second reason might be that part-timers belong to a ‘‘secondary’’ labour market and might not have as strong a bargaining position as full-time workers. Likewise, part-timers are less likely to beneﬁt from an ‘‘efﬁcient wage’’ policy, given their lower contribution in terms of the number of hours to the ﬁrm.15

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3. THE FRAMEWORK OF THE EMPIRICAL ANALYSIS This section explains the estimation strategy and the data used to show empirically how important the factors mentioned in the previous section are in the determination of the rate of part-time work in EU-15 countries.

3.1. Estimation Strategy The part-time employment rate follows a clear positive trend over time in Europe, and the presence of a unit root is conﬁrmed in most countries by running the augmented Dickey–Fuller test and Phillips–Perron test. We ﬁrst use the annual change in the PTR (DPT) as the dependent variable in order to address the issue of non-stationarity. As this variable offers a limited time series dimension by country (i.e. 18-time observations at most), we pool annual data across EU-15 countries. Therefore, for our analysis of the effect of the business cycle on the PTR, we ﬁrst use the following simple ﬁxedeffect speciﬁcation (1), where OG denotes a measure of the cyclical position of the economy and ai are i country dummies:16 DPT it ¼ ai þ bOGit þ it

(1)

Under this model (1), the business cycle OG is proxied by (i) estimates of the output gap and (ii) real GDP growth. The former is preferred since it offers a better measure of the cyclical ﬂuctuation of economic activity, while real GDP growth also encases variation in potential output growth across countries. The output gap is deﬁned as the difference between actual GDP and potential GDP as a percentage of potential GDP. The latter, also called potential output and calculated using the production function method, corresponds to the productive capacity of the economy, that is, the level of sustainable output, compatible with a stable inﬂation rate. However, since output gaps are derived from model-based estimates of potential output and are consequently ‘‘non-observable’’ variables, real GDP growth is used to check the robustness of the results. In this model, we also include lagged independent variables. According to a Wald test, two period lags are found to be sufﬁcient for our model, as the removal of further lags (three and four) does not affect the results signiﬁcantly. Since the effect of the business cycle on the part-time rate may be asymmetric, we also regress the output gap (with lags) interacted with a

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dummy variable, which indicates whether the output gap is positive or negative. Finally, one may conjecture that the ‘‘ﬂexibility effect’’ mentioned earlier would be more acute for countries experiencing strong structural rigidities. In these countries, which are likely characterised by a high unemployment rate, ﬁrms would use part-time work as a means of circumventing structural rigidities and adapting resources according to ﬂuctuations in economic activity. Moreover, in the case of very high unemployment, workers may be more willing to accept a part-time job, enhancing the involuntary part-time work effect. Therefore, we also use the output gap interacted with a dummy reﬂecting a high unemployment country to investigate whether the countries hit by high unemployment witness a more pronounced cyclical pattern. Model (1) is straightforward, breaking down the PTR into a cyclical component and a linear country-speciﬁc trend.17 It easily resolves the problems arising from the use of non-stationary variables. However, the results are constrained by the absence of quarterly data for part-time employment, which would have been more suitable to investigate its cyclical behaviour. Annual data are by deﬁnition less frequent; tend to smooth out quarterly pattern and lose information about the start of upturns and downturns. For sake of robustness, we also complement this model in ﬁrst differences with a more comprehensive model in levels. The structural changes brought out by reforms in the regulatory or legal framework of part-time employment may cause acceleration in part-time developments, which is not captured by the linear trend of model (1). This may disturb, somewhat, the empirical estimation of the cyclical component of part-time employment. Thus, our model (1) considers the level of the PTR across countries and over time as well as the impact of structural factors and institutions. It also allows us to check the robustness of the cyclical effect and the control for possible omitted variable bias by taking into account additional explanatory variables. It is expressed as follows: PT it ¼ ai þ at þ bOGit þ

K X k¼1

ak X k it þ

J X

bj X j it þ it

(2)

j¼1

where ai are i country dummies and at t time dummies. Xk are k variables representing institutions and Xj j variables capturing structural factors (of societal, demographic or economic nature). This speciﬁcation is close to that used by Nickell, Nunziata, Ochel, and Quintini (2001) to explain OECD unemployment, but the variables for

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short-term macroeconomic shocks (labour demand shock, real import price shock, real interest rate, etc.) are replaced by the output gap. Moreover, the lagged dependent variable is dropped as its presence introduces correlation between the errors and the regressors, which can bias the GLS estimate of parameters.18 As most variables are not stationary, it is crucial to check that they are linked together in the long run through a cointegrating relationship and thus that the residuals of the equation are stationary. In order to test for unit roots in the residuals, we use the Fisher–Maddala–Wu test, which was suggested by Maddala and Wu (1999) on the basis of previous work by Fisher (1932). This non-parametric test is used here since it does not require a balanced panel. It is also easy to run as it combines the observed signiﬁcance levels of any type of unit-root test performed individually on N countries. If Pi denotes P the p-value from the unit test on the ith country time series, then 2 ln Pi follows a w2 distribution with 2N degrees of freedom. However, this test assumes the absence of cross-sectional correlation, that is, the observations are generated independently across countries. When this assumption is violated, which is often the case in practice, the standard test may suffer from a large size distortion, as evidenced by Maddala and Wu (1999), who have computed the exact distribution of the test and corrected the critical value by bootstrapping. Here, following Nunziata (2005), we control cross-country correlation using time dummies (which capture cross-sectional dependency caused by common time-speciﬁc components), and then we utilise the standard distribution of the test. Under the Fisher–Maddala–Wu test and using Phillips–Perron tests for individual countries, the null of no cointegration (non-stationarity of the residual) is strongly rejected for all equations in Table C1.19 For instance, using equation 1 of Table C1, the test statistics is w2(40) ¼ 79.2, with a p-value of 0.02%. The test clearly rejects the hypothesis of the residuals having a unit root and points to the existence of a cointegrating relationship between the regressors.20 As some heteroskedasticity and ﬁrst-order autocorrelation are detected in both models (1) and (2), all equations are estimated by feasible generalised least squares (Nickell et al., 2001; Nunziata, 2001).21 To tackle possible endogeneity problems, we also use an instrumental variable method, namely, the two-stage feasible generalised least squares. Although the causality may mainly run from GDP/output gaps to part-time employment, the growth rate of ﬁxed capital investments (along with its lagged values) and the growth rate of trade and services exports are used as instruments in speciﬁcation (1). Indeed, whereas employment developments

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directly inﬂuence output growth through household disposable income and consumption, trade and services exports and ﬁxed capital investments are not driven by national employment, at least in the short run. Instead, they are strongly correlated with the output, and Table C3 shows that the two variables are important explanatory factors of the output gap.22 This suggests that the two-stage least squares estimate should not suffer from the weak-instrument problem. In order to further gauge the robustness of the results to the possible endogeneity of regressors, we also run Granger-causality type of equations (1u), where the business cycle variable is lagged by one year. The estimate (1u) conﬁrms the signiﬁcance and the sign of the output gap coefﬁcient, although its magnitude is lower than in estimates (1) (Table C4). DPT it ¼ ai þ bOGi t1 þ it

(10 )

In speciﬁcation (2), the issue of endogeneity is very likely to particularly affect the relationship between the PTR and participation. Moreover, a growing share of part-time jobs might make policy makers more responsive to part-time worker preferences. In this respect, the EU directive on parttime work could be seen as an EU-wide response to the growing importance of part-time workings.23 Therefore, we instrument the structural and institutional variables by their values lagged by two years. One-year lag does not sufﬁce because of the presence of ﬁrst-order autocorrelation in the residuals.

3.2. Data The data used in this paper are presented more in detail in Annex B. The PTR is deﬁned as the percentage of workers working part-time relative to total employment. The PTR, as well as the share of involuntary part-time employment, is derived for each country from the European Community Labour Force Survey, which has been conducted every year in the spring since 1983 and compiled by Eurostat. The deﬁnition of ‘‘part-time’’ is based on individuals’ declarations of working status (part-timer versus full-timer), rather than on a precise measure of hours worked. Data on business cycle (output gap, GDP growth) come from OECD Economic Outlook. The output gap is measured as the percentage difference between actual GDP in constant prices and potential GDP estimated by the OECD.24

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Data on labour market institutions and structural variables are taken from various sources, in particular the recent macroeconomic literature on labour markets. Most of these data on national labour market institutions were available only until 1997–1998 when the study was carried out. It should be noted that the empirical models are estimated with annual data, which may underestimate the full effect of the business cycle by not taking into account intra-annual cyclical variations. Indeed, the annual indicator of output tends to smooth out the real cyclical ﬂuctuations. The choice of annual data relates to statistical limitations. While cyclical indicators can be available on a quarterly basis, part-time employment series are available only on an annual basis and as data on labour market institutions and structural variables. The use of panel data approach, however, increases the number of observations and circumvents this lack of time length.25 The series capturing the effect of part-time regulation on the part-time rate deserve particular attention. This is a vector of country-speciﬁc trends that start from the year in which regulations of part-time employment were relaxed in each country.26 The motivation for the creation of this variable is that we wish to capture the additional annual increase in the PTR that follows the change in part-time regulation.27 The latter is identiﬁed using information provided by EIRO and OECD (1999). The starting date of each trend therefore varies by country. For the countries where part-time regulation has not changed (Ireland, Portugal, Sweden and the United Kingdom), the value of the variable is set at zero for the complete period 1983–2001. To avoid an ‘‘outlier’’ bias, we have also constructed the ‘‘policy’’ variable excluding the trend for the Netherlands, which experienced a much sharper increase in part-time employment than other EU countries did (Euwals & Hogerbrugge, 2004).28

4. THE EFFECT OF THE BUSINESS CYCLE ON PART-TIME EMPLOYMENT IN THE SHORT-TO-MEDIUM RUN Results derived from model (1) are presented in Table C2. Noteworthy results include, ﬁrst, that the output gap is found to signiﬁcantly and negatively affect the increase in the PTR – see column 1. When the economy operates above its potential, the PTR tends to decline, or in other words, part-time employment grows to a lesser extent than full-time employment. Conversely, the PTR tends to increase when the economy operates below its potential.29

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The negative effect of the economic cycle on the PTR is also shown when running country-by-country OLS equations, as seen in Table C5. The coefﬁcient of the output gap (either contemporaneous or one year lagged) is negative for all countries except for Denmark, although of different magnitude across countries. Given the very small size of the sample for each country, the statistical inference is problematic and the value of the t-test might not be reliable. Therefore, we formally test the poolability of the country results. A standard Chow test does not reject the hypothesis of common-output-gap coefﬁcient across countries. Panel data analysis, also called pooled-time-series estimation, increases the number of observations and degrees of freedom, allowing for better inference and providing more efﬁcient estimators. The negative effect of the economic cycle on the PTR is consistent with the ﬂexibility effect outlined in Section 2.1. The counter-cyclical pattern of the PTR is less marked in periods of strong economic activity than in periods of weak activity, as shown by column 7. Indeed, this would indicate that part-time employment enables employers to react ﬂexibly in the presence of increasing economic uncertainty, for example, in the event of recession or the very start of economic recovery. Moreover, as most parttime jobs are created in the services sector, it is not surprising that the counter-cyclical relationship is highly signiﬁcant when the cycle is measured by the value-added growth in the services sector (column 6). This result is fully consistent with the aforementioned compositional effect. Table C6 (ﬁrst row) shows a highly signiﬁcant and negative impact of the business cycle on the share of involuntary part-time employment. This would conﬁrm the existence of a ﬂexibility effect and involuntary part-time effect. The bulk of the effect of the cycle on the involuntary PTR seems to occur within the same year. This contemporaneous effect of the business cycle holds for both the total and involuntary share of part-time work. Therefore, the expansion of economic activity recorded in the late 1990s likely reduced involuntary part-time employment, which continuously declined from 21.8% of total part-time employment in 1997 to 16.4% in 2001, as displayed by Annex A. Our results generally indicate that, although strongly signiﬁcant, the effect of the economic cycle on the part-time share appears limited in magnitude. The use of an annual model, for statistical reasons, may slightly underestimate the impact of the business cycle, as the intra-annual cyclical variations are not taken into account, although this measurement effect should not be overstated, given that the output gap is smoothed out over a relatively short period of four quarters. A negative output gap of 1% is

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associated with an increase in the total PTR of around 0.06 percentage points at most. Regarding the period 1992–1999, which was characterised by continuously negative output gaps, the cycle explained less than one-ﬁfth (17%) of the total increase in the PTR recorded in the EU as a whole.30 This result is likely to be related to the fact that involuntary part-time work represented less than 20% of total part-time jobs in the EU in the 1990s. This also gives some support to the idea that other factors of structural nature, which are considered in Section 5, have been far more important in the explanation for the upward trend in part-time employment developments. The remainder of this section separately considers the importance of the business cycle on the development of part-time work for four different groups of workers: young workers, prime-age males, prime-age females and older workers. As displayed in Table C4, the ﬁndings for each group are broadly conﬁrmed by the Granger-causality approach, which is used to check the robustness of the estimates to possible endogeneity issues. Table C7 presents results for model (1) for the PTR of young workers. The effect of the economic cycle, captured either by the output gap or real GDP movements, is found to be highly signiﬁcant. The coefﬁcient of the output gap lies between 0.15 and 0.21 across regressions. Taking a median elasticity of 0.18, the cycle would have accounted for around 25% of the total increase in the youth PTR recorded in the EU in the period 1992–1999, which is clearly stronger than the impact of the cycle on the total PTR. The more acute cyclical pattern in countries displaying high unemployment might suggest that the need for higher ﬂexibility for youth is larger in the presence of strong structural rigidities. Moreover, the effect of the cycle on the share of involuntary youth part-time employment is statistically signiﬁcant, but smaller compared to other groups. This would suggest that ﬁrms’ labour demand generally matches the desire of young people who are mainly looking for part-time jobs to ﬁnance their studies. The second group we consider is prime-age males. Table C8 suggests that the effect of the economic cycle on the PTR for this group is again highly signiﬁcant, with an elasticity of around 0.26 on the output gap (column 3). Thus the cycle would have explained around 20% of the total increase in the PTR recorded in the EU in the period 1992–1999, which is slightly stronger than the impact of the cycle on the total PTR.31 This is consistent with the fact that the share of prime-age male involuntary part-timers appears highly cyclical with a negative output gap of 1% increasing the proportion of involuntary part-timers by 0.34 percentage points (Table C6). For prime-age females, the effect of the cycle on the PTR is unclear and in any case very weak, as seen in Table C9. Although the effect of the

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contemporaneous output gap appears highly signiﬁcant and relatively high in magnitude (columns 1 and 3), it does not turn out to be signiﬁcant anymore once instrumented by ﬁxed capital investment and total exports (column 4). When regressing the female PTR on the output gap lagged by one year so as to examine the Granger causality, the coefﬁcient is signiﬁcant only at 10% and its magnitude almost halved (Table C4). Moreover, an alternative indicator of the business cycle, such as real GDP growth, is not signiﬁcant (column 2). The cycle could only explain between 8% and 15% of the total increase in the female PTR recorded in the EU in the period 1992–1999. This impact is very small and lower than the impact of the cycle on the total PTR.32 Thus, the upward trend in the female PTR in the 1990s, as seen in Annex A, is likely to have mainly been the result of structural factors considered in the next section. An alternative explanation could be related to the fact that most female part-timers are working in the services sector, which is much less cyclical than industry. However, when considering speciﬁcally an indicator of cyclicality in the services sector (value-added growth), the effect on female part-time work remains insigniﬁcant. Finally, we consider workers aged 50 and over. Table C10 reveals no clear effect of the cycle on the PTR for this group; neither real GDP growth nor the output gap is signiﬁcant.33 This result suggests that either part-time work is particularly unattractive for this group or employers do not typically use older workers in their attempts to increase the ﬂexibility of their workforce through part-time work.

5. THE INFLUENCE OF INSTITUTIONS AND OTHER STRUCTURAL VARIABLES ON THE PART-TIME EMPLOYMENT RATE IN THE LONGER RUN In addition to the impact of the business cycle, macro-panel data analysis (model 2) allows us to shed some light on the effect of the institutional and structural factors described in Sections 2.2 and 2.3 on part-time employment.

5.1. Using a Panel of OECD Countries with General Labour Market Institutions Covering the main OECD countries, Table C1 shows the impact of general labour market institutions on the rate of part-time employment. As most of institutional data are available only until 1998 and display low time series

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variations, we ﬁrst include non-EU OECD countries into the sample in order to better exploit the cross-sectional dimension of institutions.34 The ﬁndings in columns 1–3 do not include instrumental variables. Correcting for possible reverse-causality issues (columns 4–6), the instrumental variable technique (two-stage GLS) broadly conﬁrms the signiﬁcance of labour market institutions in inﬂuencing the PTR.35 The output gap is found to be negatively correlated with the PTR and appears highly signiﬁcant in all equations, conﬁrming the results displayed in Section 4. The labour market participation rate is found to be positively related to the PTR in equations 1, 2, 3 and 6, in line with the predictions in Section 2.36 While the measure of EPL for temporary contracts is not found to be statistically signiﬁcant in the explanation for the PTR, EPL for regular jobs is found to be signiﬁcantly and positively related to the PTR (columns 2, 3, 5 and 6). This is consistent with very stringent EPL for regular jobs, making it necessary for ﬁrms to develop ﬂexible stafﬁng arrangements. This is also in line with the fact that most part-time jobs are permanent. Unionisation is found to be negatively related to the PTR, possibly reﬂecting the reluctance of some trade unions towards the introduction of ﬂexible work arrangements. Likewise, the unemployment beneﬁt replacement ratio is negatively linked to the PTR, signalling the possible existence of ‘‘unemployment traps’’, which may particularly affect part-timers, given their relatively low level of earnings compared to full-timers. The labour tax rate is also negatively and highly signiﬁcantly correlated with the PTR. A plausible interpretation of this ﬁnding could refer to the high marginal rate of taxation borne by the second earner of a couple.

5.2. Employing a Panel of EU Countries with Additional Institutional and Structural Variables The recent literature on the effect of labour market institutions on unemployment has argued that the institutions in Europe may be different from those in other OECD countries and signiﬁcantly more rigid and affect labour market output variables, such as unemployment, in signiﬁcantly different ways than in the United States (see Nickell et al., 2001 for the impact on overall employment and unemployment). This ﬁnal subsection therefore restricts our analysis to a consideration of European countries. Furthermore, we deepen our analysis of the determinants of part-time work through the collection of other structural and institutional variables,

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which are expected to speciﬁcally inﬂuence part-time employment. Indeed, a further critique of the analysis in the previous speciﬁcation could be, for example, that the general labour market institutions affect the labour market as a whole rather than the market for part-time work. Table C11 shows the results for this focus on EU-15 countries. Some ﬁndings emerge from equations 1 to 9, which are broadly conﬁrmed when using instrumental variable techniques (column 10).37 First, the negative inﬂuence of output gap is conﬁrmed. Its signiﬁcance is very strong in equations 1 and 9, where there are no time dummies. Indeed, time dummies, used in other equations, tend to capture the common component of the output gap across the EU-15, which is fairly important, given the degree of synchronisation of European business cycles. Thus, the output gap coefﬁcient in equations with time dummies mostly points to the country-speciﬁc component of the business cycle. As regards the magnitude of the business cycle inﬂuence, the output gap coefﬁcient ranges from 0.07 to 0.11, which is in line with the results of Section 4, albeit slightly higher. Second, some institutions and policies appear to have a clear inﬂuence on the PTR as expected by the economic theory. The change in part-time regulation turns out to have a very signiﬁcant impact on the part-time employment developments (column 4). This still holds true when excluding the Netherlands (columns 1, 2, 3, 5, 8 and 9), although the magnitude of the effect decreases somewhat. Another noteworthy result is the strong, negative and highly signiﬁcant effect of child beneﬁts on the PTR, which acts as a disincentive to working part-time and makes it less attractive for individuals to (re-)enter the labour market. The reasoning behind this phenomenon may be that the beneﬁt alters the trade-off between work and leisure towards a more family-oriented life. Broadly conﬁrming the results of Section 5.1, EPL on regular jobs is found to be highly signiﬁcant, while overall EPL is signiﬁcant only at a 10% level. The temporary employment rate is found to be positively correlated with the PTR (columns 7, 8 and 10), which suggests that the absence of substitution between part-time employment and temporary employment and these two ﬂexibility schemes are complementary in circumventing the rigidity of European labour markets. Lastly, as in Section 5.1, unemployment beneﬁt replacement ratios are found to be negatively correlated with the PTR, but the statistical signiﬁcance of this variable and the magnitude of its effect are not robust across equations. Third, some institutions do not seem to drive the PTR. The unemployment beneﬁt duration is not signiﬁcant. Reﬂecting the theoretical uncertainty concerning its overall impact (e.g. income versus substitution effects), total labour taxes do not seem to be signiﬁcant. The total labour tax rate probably

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remains too aggregated to identify the relative tax burden borne by part-timers compared to full-timers. In particular, it does not take into account the difference between the tax rate borne by the second earner in a household and that undergone by a single-wage-earner household. Likewise, union density is not found to be signiﬁcant (see column 6), which may mirror the changing attitude of trade unions toward part-time work in the EU countries in the 1990s. Fourth, some structural factors of sociological, demographic or economic nature are also found to be an important determinant of the PTR. The lagged female-participation rate is positively related to the PTR. This is fully consistent with the fact that, since the 1970s, part-time employment has been allowing numerous cohorts of women willing to work to access the labour market massively in many countries where female participation was initially low. Part-time jobs can indeed be seen as a way for women to reconcile family and professional lives, especially after their childbirth. Likewise, an alternative regression using the female share of employment instead of female participation also shows a clear positive relationship with the PTR. The fertility rate is found to be strongly and positively correlated with the PTR, which suggests that part-time work creates an opportunity for women to combine taking care of their children with market work. Similarly, the schooling rate of the population aged 15–25 and the share of employment in the services sector are also found to positively affect the PTR. The relative hourly wage of part-time workers vis-a`-vis full-time workers exerts a strong and highly signiﬁcant effect on the PTR; therefore, the use of part-time work may be partly accounted for a reduction of hourly labour costs borne by ﬁrms (equation 11). Looking further, the cross-sectional relationship between the PTR and the relative wage seems to be stronger for men than women (Figs. C1–C3). Lastly, the two types of models reviewed in Sections 5.1 and 5.2 seem to well explain part-time developments over time and across countries. The ﬁtted value for OECD countries is broadly close to the actual series, with the exception of Denmark and the United States (Fig. C4). The ﬁtted value for European countries derived from Table C11 yields even better results, as shown by Fig. C5.38 5.3. The Relative Importance of the Business Cycle and Institutional and Structural Variables: A Contribution Analysis The contribution analysis is one important value added to this paper, as it measures the relative weight of each relevant factor over time. This justiﬁes the macroeconomic perspective and the comprehensive approach of this

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paper (encompassing a large set of determinants) since the contribution of relevant factors could not have been obtained with a micro-analysis or study focusing on one speciﬁc factor of part-time employment. The contribution analysis is carried out using the baseline version of the model (model 1 in Table C11). As the model is static, the contribution of each variable to the development in the PTR is the product of the regression coefﬁcient and the change in the variable at stake over the period considered. In Fig. C6, the contribution of the main structural and institutional variables generally explains the development in the part-time rate in the EU countries rather well over the full period 1983–1998. This is especially true for Belgium, Germany, Spain, France and Italy, while other (unobserved) factors have also contributed to increasing the PTR in the United Kingdom, Ireland, the Netherlands and Portugal. By contrast, the main structural and institutional factors do not explain the decline in the US PTR.39 As we might expect, female participation appears to be the main driving force behind the development in part-time employment. The countries experiencing the strongest increase in their PTR were those recording a surging female-participation rate. However, part-time job dynamism was slightly dragged down by declining fertility, especially in Ireland and Spain and to a lower extent in Italy. On the institutional side, the relaxation of the legislation on part-time jobs in Belgium, Spain and France played a major role in the rising rate of part-time work, explaining some 2 percentage points of the rise. Other institutions played a more marginal role, except in Spain and Portugal, where the reduction in EPL stringency signiﬁcantly weighed upon part-time job developments, and the Netherlands, where the cut in child beneﬁts further boosted part-time employment. It should be noted that the (negative) effect of the business cycle was quite negligible over the full period 1983–1998, not even reaching half a percentage point, which stresses the principally structural nature of the upward trend in part-time employment. Indeed, cyclical movements in different directions offset each other over the full period, as EU economies experienced broadly similar positions in the business cycle at the start and the end of the time sample. In order to better identify the cyclical factors, we split the period into two sub-periods – 1983–1990 (Fig. C7) and 1990–1998 (Fig. C8). While the contribution of output gap was negative (between half and one percentage points) in most countries in the 1980s, it was slightly positive (of around onefourth percentage point) in the 1990s, when EU economies were running slightly below their potential. Therefore, the business cycle has contributed to explaining the generally stronger developments in part-time employment in the 1990s compared with the 1980s, albeit to a modest extent.

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As regards structural and institutional indicators, their individual roles in the 1980s and 1990s differ across countries. However, some general features emerge. The (either positive or negative) effect of the fertility rate was stronger in the 1980s. Child beneﬁts had an unambiguously positive contribution in 1980s, while their impact was weaker or negative in the 1990s. Conversely, the change in part-time employment laws and in EPL for regular contracts only played a real role in the 1990s.

6. CONCLUSION The analysis of pooled data for EU-15 countries has considered to what extent the business cycle and structural variables have inﬂuenced the rate of part-time work in the EU over the past two decades. Indirectly, it allows us to see the extent to which part-time work may offer a means of increasing the ﬂexibility of labour markets. The business cycle, as measured by both the output gap and the real GDP growth, is found to exert a negative effect on part-time employment developments, when using panel data techniques. This counter-cyclical effect is consistent with ﬁrms utilising part-time employment as a way to adjust their labour force (in terms of hours worked) to economic conditions. We hypothesise that, during economic downturns, employers reduce the number of hours worked by current staff and/or hire new workers in parttime jobs. In an upswing, net employment creation consists mostly full-time jobs in order to meet the increased demand for labour resources by ﬁrms. We ﬁnd that, consistent with this hypothesis, involuntary part-time employment is cyclical, being higher in troughs of economic activity. Splitting our sample by age and gender groups reveals a very signiﬁcant effect of the cycle on young and male prime-age workers. Conversely, the effect is unclear for women and clearly insigniﬁcant for older workers. This paper also considers the role of structural factors and institutions in explaining the rate of part-time employment. Looking at institutions, changes in legislation favourable to part-time employment are found to be effective, having a strong impact on actual part-time employment developments. Moreover, while overall EPL has no clear-cut effect, EPL for permanent contracts is found to be positively related to the PTR, which is consistent with the use of part-time work as a tool for enhancing ﬂexibility in the case of rigid labour markets. Given the negative impact of child beneﬁts and, to a much lesser extent, unemployment beneﬁts, the econometric results support an ‘‘unemployment trap’’ story affecting part-time employment.

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Turning to other structural variables, societal and demographic, the fertility rate is found to be strongly and positively correlated with the PTR. This result suggests that part-time work creates an opportunity for women to combine taking care of their children with market work. In line with conventional stylised facts, the share of the services sector in the economy and the proportion of youth in tertiary education are also signiﬁcant predictors of the part-time employment rate. Besides, a cross-sectional analysis underscores the positive impact of the differential in hourly wages between part-timers and full-timers on the PTR. This suggests that relative hiring in part-time employment compared to fulltime employment seems to be fairly sensitive to relative wages. This also reﬂects that part-time work is often used as a ‘‘precarious’’ form of employment, in line with the ‘‘insider/outsider’’ theory. Finally, a contribution analysis shows that the main structural and institutional variables generally explain the development in the part-time rate in the EU countries fairly well over the full period 1983–1998, while this is obviously not the case in the United States. Moreover, in some EU countries, such as the United Kingdom, Ireland, the Netherlands and Portugal, other factors not captured by the analysis have also contributed to increasing the PTR. While female participation, not surprisingly, appears to be the main driver of the development in part-time employment, declining fertility rates exert a dampening effect in some countries. Looking at labour market institutions, the relaxation of the legislation on part-time jobs in Belgium, Spain and France played a major role. Other institutions also played some part in Spain and Portugal (easing of EPL for permanent jobs) and in the Netherlands (the cut in child beneﬁts). Lastly, while the effect of the business cycle was quite negligible over the full period, it has contributed, albeit to a limited extent, to explaining the generally stronger developments in part-time employment seen in the 1990s compared with the 1980s.

NOTES 1. That is, the European Union, before its enlargement in May 2004, comprising 15 member states. 2. This is because, ﬁrst, the increase in the part-time employment rate mechanically decreases the average hours worked per individual, reducing total average compensation per employee, ceteris paribus. This is a pure measurement effect. Second, some studies have shown that the hourly wage rate received by parttime workers is lower than that of full-time workers (OECD, 1999). Both of these two dampening effects on aggregate wage growth may increase with a rise in parttime employment.

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3. It should be noted that the vast economic literature on European employment laws tends to focus primarily on the distinction between permanent versus short-time contracts, rather than full-time and part-time contracts. 4. The percentage of those working part-time relative to total employment. 5. Farber (1999) for the United States found that job losers are signiﬁcantly more likely than non-losers to get an involuntary part-time job, which may suggest that workers, formally in full-time jobs, go through an (short) unemployment spell before occupying a part-time job. 6. In other words, the ﬂexibility effect reduces the negative cyclical responsiveness of the number of those working part-time compared to those working full-time, thereby causing a counter-cyclical effect on the share of part-time employment in total employment. 7. For instance, in 1993–2000, a speciﬁc social security contribution rebate was granted to ﬁrms in France for recruitment in part-time work, in addition to some additional social security contribution cut for the recruitment of low-paid parttimers. This coincided with a boom in part-time employment over the same period. As reported by Ruivo et al. (1998), the legislation on part-time work underwent important changes in Spain in 1994 (relaxation of the maximum daily and weekly working hours, reduction in social security contribution). This resulted in a strong increase in the part-time employment rate between 1994 and 1995. 8. A low level of EPL for temporary contracts may also make the use of part-time contracts less necessary as temporary employment can meet the need for more ﬂexible stafﬁng arrangements. 9. If child beneﬁts are means tested, this increases the marginal rate of taxation around the income threshold above which the incumbents are not eligible to these beneﬁts. This might deter one member of the couple to take up a job because this may mean the loss of child beneﬁts. However, if the eligibility threshold is high, this could encourage taking a part-time job rather than a full-time job. 10. Firms or sectors with a high proportion of part-timers are generally considered to be harder to unionise. 11. In France, part-time jobs increased strongly in the services sector in the 1980s and 1990s, while temporary jobs and particularly agency employment ﬂourished in manufacturing. 12. Therefore, employers avoid underemployment of staff in off-peak times and overtime payment in busy periods. 13. Young workers may be considered as ‘‘outsiders’’, allowing ﬁrms to make them bear a higher proportion of adjustment costs in terms of wages and working conditions. Youth labour may often consider their part-time job as temporary, limiting the risk to the ﬁrm of recruiting an inefﬁcient worker. 14. See OECD Employment Outlook, June 1999. 15. More tentatively, another reason for an increase in part-time employment might be the demographic ageing, as the elderly may need more care, often provided by part-timers, and young generations may ﬁnd part-time jobs more appealing. However, given the slow nature of demographic changes, these effects, playing in different directions, are likely to be of second order. Likewise, the substantial immigration observed in some EU countries might inﬂuence part-time employment, although the theoretical bond is unclear. 16. In speciﬁcation (1), we do not use time dummies because they would bias the estimation of the effect of the economic cycle. Indeed, they would capture the

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component of the business cycles that is common across countries, and the coefﬁcient of the output gap would only take into account the country-speciﬁc component instead of the full cyclical effect. 17. The linear country-speciﬁc trends correspond to country-ﬁxed effects (i.e. country-speciﬁc intercept), as model (1) is written in ﬁrst differences. 18. Given the fairly short time series dimension of the data, this bias may not be negligible. 19. The results are conﬁrmed when using Dickey–Fuller test as country-bycountry unit-root test. 20. Under the Fisher–Maddala–Wu test and using Phillips–Perron tests for individual countries, the null of no cointegration (non-stationarity of the residual) is strongly rejected for all equations in Table C1. For instance, using equation 1 of Table C1, the test statistics is w2(40) ¼ 79.2, with a p-value of 0.02%. This test relies on no cross-country correlation. The introduction of time dummies in speciﬁcation (2) is likely to capture much of the cross-correlation in the data. 21. For instance, on the basis of regression 1 in Table C2, the hypothesis of homoskedastic residuals is strongly rejected by an LR test (w2(13) ¼ 72.8), while the hypothesis of non-serially correlated residuals is clearly rejected by an LM test (w2(1) ¼ 94.2). 22. The instruments are selected from equation 1, which contains the largest number of highly signiﬁcant variables. 23. Possible endogeneity with other policy variables is less obvious. Indeed, it is reasonable to assume that the developments in labour market institutions and policies in EU countries have been inﬂuenced by the general situation of the labour market in each country (as reﬂected by the unemployment rate), and the causation from part-time employment rate to institutions seems to be fairly unlikely. Moreover, as pointed out by Nunziata (2001), the reasons behind institutional and policy changes are far from evident. The pattern of political decision making in each country would tend to indicate that other important factors such as the timing of election, the policy makers’ agenda and the average voters’ preference may have played a crucial role in shaping the institutional and policy changes. 24. For further details, see Giorno, Richardson, Roseveare, and van den Noord (1995). 25. A panel data analysis appears adequate. A cross section study only exploiting the time average of each variable would face the problem of the relatively limited cross-sectional dimension (21 OECD countries and 14 EU countries) and will lose some time series information. Table B1 shows that the time variation (‘‘within’’) is relatively important for some structural variables (female participation, fertility rate, schooling rate) and not negligible for some labour market institutions such as total tax rate, EPL and bargaining co-ordination. The section on contribution analysis (Section 5.3) will more intuitively conﬁrm that the importance of institutions in each country varies between the 1980s (Fig. C7) and the 1990s (Fig. C8). 26. Technically, this vector corresponds to ‘‘pooled after-reform country trends’’. We have stacked the observations country by country to compose the vector. Within each block, we have a trend that is 0 before any policy change and 1 after the ﬁrst year, following the easing of part-time regulations, 2 the second year, n the nth year,

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etc. In principle, we could have separately estimated each country block. However, given the relatively limited time series dimension, we stacked them and restricted the coefﬁcients to be the same across countries in order to increase the efﬁciency of the estimate and capture the overall effect of reforms. 27. The rise in PTR induced by the regulatory change is likely to disappear in the long run, as it corresponds to the dynamics towards the new steady state implied by the reform of part-time regulation. 28. More technically, as the change in the regulatory framework for part-time jobs in the Netherlands occurred before the start of the sample (i.e. 1982), the ‘‘policy’’ variable for the Netherlands cannot really measure the effect of the change in regulation. It would instead simply capture the trend of increase in PTR. 29. Other ancillary results suggest the robustness of the ﬁndings mentioned above (Table C2). The counter-cyclical pattern still holds when taking real GDP growth as our measure of the cycle in column 2. The cyclicality appears even stronger when using instrumental variables for the output gap to treat possible problems of endogeneity between the output gap and the PTR (column 5). Column 8 suggests that the cyclical effect on part-time work is not very different between countries with high unemployment and other countries. 30. In this period, the cycle explained 0.09 p.p. only out of the 0.51 p.p. increase in PTR recorded on average each year in the EU-15 as a whole. In the period 1992–1997, the cyclical effect reached its maximum, that is, 23% of the total increase in PTR. 31. The effect of negative output gaps on the PTR of prime-age males is found to be stronger when lagged by one year, while that of positive output gaps is strongest when contemporaneous. The negative output gap effect outweighs the positive output gap effect. One interpretation of these results again follows our ﬂexibility effect argument: Firms prefer to hire staff on ﬂexible contracts when the economic outlook is uncertain (recession or very start of economic recovery). When the economy recovers, ﬁrms’ need for part-time contracts decreases, as the uncertainty concerning future economic activity fades away gradually. 32. The relatively small impact of the output gap on involuntary female part-time work, compared to prime-age men (Table C6), further illustrates the unclear effect of the business cycle on prime-age female part-time employment. 33. The only exception to this result is for relatively high unemployment countries (Spain, France, Italy and Finland), where the cycle is found to have a modest negative impact on changes in PTR. 34. Australia, Canada, Japan, New Zealand, Norway, Switzerland and the United States. 35. The effect of EPL for regular work on the rate of part-time work is clearly positive and signiﬁcant, while the coefﬁcient for EPL on temporary jobs displays a smaller magnitude. The negative effect of unionisation and the labour tax rate are also conﬁrmed. However, the total participation rate changes sign, and the coefﬁcient of unionisation, beneﬁt replacement ratio, unemployment beneﬁt duration and labour tax rate appear extremely strong compared to the results shown in columns 2 and 3, likely reﬂecting statistical artefacts. The latter results are not intuitive and should be interpreted with caution, as the instruments used (lagged exogenous variables) are imperfect, albeit widespread in the literature.

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36. The surprising results found in equations 4 and 5 could be explained by the high degree of colinearity between the participation rate and some institutional variables in the context of instrumental variable estimations. This can be seen through the very high value of some coefﬁcients. 37. Results for EU-15 displayed in Table C11 show that the impact of the output gap is negative, supporting our previous ﬁndings. It is clearly signiﬁcant when the equation is estimated without time dummies (columns 1 and 9). Indeed, these dummies take out the component of the cycle common across countries. 38. Equation 2 in Table C1 and equation 2 in Table C11 have been chosen to make simulations because they are comparable to each other and use EPL indicators broken down by types of contracts (regular and temporary) that provide better results than using simply the overall EPL indicator. 39. This is possibly due to the ﬂexibility of permanent contracts in the United States, which makes the use of part-time jobs less necessary for ﬁrms. Even more importantly, the already high rate of female participation and the culture of much longer working hours compared with Europe could explain the stalling part-time employment rate in the United States. 40. The concept stricto sensus refers to employment, that is, the number of jobs rather than the number of people employed. As a result, two part-time jobs held by the same individual are not counted as a full-time job but as two different jobs. Moreover, full-time and part-time employment can either correspond to selfemployment or wage-earning jobs and, alternately, to ﬁxed-term contracts or permanent positions. 41. A detailed description of the sampling methods and adjustment procedures used to compile these data can be found in the latest Labour Force Survey – Methods and deﬁnitions, 1998. Part-time employment series are available only on an annual basis. Some quarterly series of part-time employment rate exist for some countries but remain rather short and display a very strong seasonal pattern, which is risky to correct, given the poor time series dimension of the data. 42. Data have been made available for 2002. The estimations in this chapter used data until 2001. 43. This split corresponds to the main age categories presented by Eurostat for the LFS. 44. The correlation coefﬁcient between the two measures of output gap is 0.96. 45. Also called union density. This is the percentage of reported union members between wage and salaried employees. 46. For the most recent observations, see also Nickell, S., Nunziata, L., & Ochel, W. (2002, May). Unemployment in the OECD since the 1960s. What do we know? Bank of England. 47. The wage differential for the United States used in Section 6 comes from OECD (1999).

ACKNOWLEDGEMENTS We would like to thank particularly two anonymous referees, Willi Semmler, Rob Euwals, Salvador Barrios, Giuseppe Carone, Ve´ronique

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Genre, J.J. Dolado, J. van Ours and G. Laroque and other participants of the 4th ECB/CEPR Labour Market Workshop and the 2005 ASSA annual conference in Philadelphia for their helpful comments or suggestions on a preliminary version of this paper.

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Nicoletti, G., Scarpetta, S., & Boylaud, O. (2000). Summary indicators of product market regulation with an extension to employment protection legislation. OCDE Working Paper no. 266. Nunziata, L. (2001, December). Institutions and wage determination: A multi-country approach. Nufﬁeld College Working Papers in Economics (2001-W29). Nunziata, L. (2005). Institutions and wage determination: A multi-country approach. Oxford Bulletin of Economics and Statistics, 67(4), 435–466. OECD. (1995, July). Employment outlook. Paris: OECD. OECD. (1999, June). Focus on part-time work. Employment Outlook. O’Reilly, J., & Bothfeld, S. (2002). What happens after working part-time? Integration, maintenance or exclusionary transitions in Britain and western Germany. Cambridge Journal of Economics, 26, 409–439. Pfau-Efﬁnger, B. (1998). Culture or structure as explanations for differences in part-time work in Germany, Finland and the Netherlands. In: J. O’Reilly & C. Fagan (Eds), Part-time prospects: An international comparison of part-time work in Europe, North America and the Paciﬁc Rim. London: Routledge. Ruivo, M., Gonzalez, M. P., & Varejao, J. M. (1998). Why is part-time work so low in Portugal and Spain? In: J. O’Reilly & C. Fagan (Eds), Part-time prospects: An international comparison of part-time work in Europe, North America and the Paciﬁc Rim. London: Routledge. Scarpetta, S. (1996). Assessing the role of labour market policies and institutional settings on unemployment: A cross-country study. OECD Economic Studies no. 26, pp. 43–82. Smith, L., Fagan, C., & Rubery, J. (1998). Where and why is part-time work growing in Europe? In: J. O’Reilly & C. Fagan (Eds), Part-time prospects: An international comparison of part-time work in Europe, North America and the Paciﬁc Rim. London: Routledge. Sundstro¨m, M. (1991). Part-time work in Sweden: Trends and equity effects. Journal of Economic Issues, 25(1), 167–178. Turner, D., Richardson, P., & Rauffet, S. (1996). Modelling the supply side of the seven major OECD economies. OECD Economics Department Working Paper no.167. Walwei, U. (1998). Part-time work: A threat to labour standards? In: J. O’Reilly & C. Fagan (Eds), Part-time prospects: An international comparison of part-time work in Europe, North America and the Paciﬁc Rim. London: Routledge.

ANNEX A. TRENDS IN PART-TIME WORK IN EU-15 COUNTRIES A thorough description of the trends in part-time work in EU-15 countries can be found in Buddelmeyer, Mourre, and Ward (2005b). A growing part-time employment share has been a main feature of a number of industrialised countries over the past two decades. Fig. A1 shows a signiﬁcant increase in the share of part-time employment in total employment in the EU-15, Japan and Canada during the late 1980s and 1990s, while the United States experienced a slight fall in the part-time employment

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share. Fig. A2 plots the proportion of part-time work across EU-15 countries in 2001, which varies considerably by country, ranging from 4.5% to 42%, with the EU-15 average at 18%. As shown by Fig. A3, the Netherlands exhibits the highest rate of part-time work, with 42% of its workers working part-time. Relatively low rates of part-time work are found in Finland, Luxembourg and Portugal (at around 11%), in Italy and Spain (at 8%) and in particular in Greece (at 4.5%). The broad stylised facts for part-time employment in the EU-15 countries in 2001 by age group and gender can be summarised as follows: EU

Euro area

USA

Japan

Canada

25

20

15

10

19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01

5

Fig. A1.

Part-Time Employment Rate (%). Source: OECD, Eurostat (Labour Force 7Surveys).

Fig. A2.

L N

JP N AU S

E H

U K

N ZL

C

L

SE

E D

IS

R

D K

BE

O N

un io n C AN

IE

FR

AT

Eu ro pe an

FI U Eu SA ro ar ea

LU

IT

PT

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R TU R

KO

G R

45 40 35 30 25 20 15 10 5 0

Part-Time Employment Rate in 2001 (%). Source: OECD, Eurostat (Labour Force Surveys).

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45 40 35 30 25

Medium Belgium France Sweden

Ireland Denmark United Kingdom

Austria Germany

30 25 20 15 10

85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02

84

19

19

19

83

5

Low Finland Italy

15

Luxembourg Greece

Spain Portugal

10

5

02

20

01

00

Part-Time Employment Rate (%).

20

99

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19

98

19

97

19

96

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95

19

94

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93

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91

19

90

89

Fig. A3.

19

88

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19

87

86

19

85

19

19

84

19

19

83

0

2002

2001

2000

1999

1998

1997

1996

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1983

20

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20 15 10

0

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

5

Fig. A4.

Part time employment

The part-time employment share is currently highest for 15- to 24-yearolds, at nearly 23% on average within the EU-15, and lowest for prime-age workers (i.e. those aged 25–49), at just over 16%. Older workers have a parttime employment share of 21%. Young workers experienced the fastest rate of growth in part-time work during the 1990s in the EU-15 as a whole, although the growth rate has ﬂattened out more recently. Part-time workers are much more likely to be women, with the female PTR standing at 34% and the male rate at 6.2% in 2001 in the EU-15. This pattern of a signiﬁcantly higher rate of female part-time employment holds across time and for all EU-15 countries. Since the early 1990s, growth in part-time work has also generally been strongest among female workers. The majority of part-time work is voluntary. Nonetheless, 14.2% of parttime workers were involuntarily working part-time in the EU-15 in 1992, with this rate rising to 19.1% in 1997, before falling back to 14.4% in 2001 (Figs. A4 and A5). The rate of involuntary part-time work within the EU-15 stood at 20% for men in 2001 but at a signiﬁcantly lower 13% for women. Rates of involuntary part-time employment tend to be lower among young and older age groups.

45 40 35 30 25 20 15 10 5 0

y = -0.53x + 27.008 R 2 = 0.4631

0

5

10

15

20

25

30

35

40

45

50

Share of involuntary part time in 2001

Share of Involuntary Part-Time – EU 12 and Relation with Part-Time Employment Rate.

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

Fig. A5.

115

Share of Involuntary Part-Time as Percent of the Total Part-Time Employment (%).

ANNEX B. DATA Part-Time Employment The PTR is deﬁned as the percentage of part-time employment relative to total employment.40 The annual PTR, as well as the share of involuntary

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part-time employment, is derived for each country from the annual European Community Labour Force Survey, which has been conducted every year in the spring since 1983 and compiled by Eurostat.41 Although data on part-time employment are generally available from 1983, no information is available for countries before they joined the EU (i.e. for Spain and Portugal, prior to 1986; for Austria, Sweden and Finland, prior to 1995).42 Thus, for some countries, such as Finland and Sweden, data have been back cast using OECD Annual Labour Force Statistics, when available. These data are considered the most harmonised existing data source on part-time work. Moreover, data are available by age groups and gender. For this study, four age/gender categories have been considered: those aged 15–24, men aged 25–49, women aged 25–49 and those aged 50 and over.43

Business Cycle Indicators We mainly focus on annual output gaps stemming from the OECD Economic Outlook database. The use of the output gaps computed by the European Commission (DG-ECFIN-AMECO database) leads to very similar results.44 The output gap is measured as the percentage difference between the actual GDP in constant prices and the estimated potential GDP. Its construction is precisely documented in Giorno et al. (1995) and Turner, Richardson, and Rauffet (1996). The estimated potential GDP is estimated by the OECD using a production function approach for all countries but Portugal. This approach takes into account the capital stock, total factor productivity, changes in labour supply and the nonaccelerating wage rate of unemployment (NAWRU) for each OECD country. By contrast, potential output for Portugal is calculated using a Hodrick–Prescott ﬁlter of actual output. It should be stressed that the estimated levels of potential output are subject to signiﬁcant margins of error. Unemployment data were also obtained from this database. Matching the frequency of part-time employment data, the business cycle is measured using annual data to match the long time series of the PTR. Although the annual frequency does not allow for a precise measurement of the dynamic adjustment to the cycle, the number of available observations appears satisfactory by pooling annual time series.

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

117

General Labour Market Institutions Data are taken from the recent macroeconomic literature on labour markets. Data on EPL, in particular for regular contracts and temporary contracts, are the OECD summary series (Nicoletti, Scarpetta, & Boylaud, 2000). Data on total taxes on labour, unionisation45 and wage-bargaining co-ordination, beneﬁt replacement rates and beneﬁt duration are those collected by Nickell and Nunziata (2001), with an update provided by Nickell et al. (2002).46 Most of these data on national labour market institutions are available only until 1997–1998. An indicator for the provision of child beneﬁts (drawn from Eurostat) is also used.

Other Structural Variables In addition to labour market institutions, we collected various structural data that, on the basis of Section 3, were likely to inﬂuence part-time employment developments. Most of these data are available for the EU countries and relatively harmonised across countries. Demographic variables, including fertility rates and the schooling rates of 15- to 24-year-olds, are provided by the World Bank’s World Development Indicators database. Series for total and female-participation rates come from the OECD Annual Labour Force Survey database. Data on structural aspects of national labour markets include social protection data for European countries (such as child/family beneﬁts) drawn from Eurostat European Social Statistics, Expenditure and receipts dataset for 1980–1999, which gather levels of beneﬁts in ECU/Euros for all European countries. These variables are expressed as a percentage of GDP. Data on temporary employment as well as the share of employment in the services sector stem from Community Labour Force Surveys (Eurostat). The Wage Differential between Part-Time and Full-Time Employment The wage differential (i.e. the ratio of the median hourly wage excluding overtime of part-time workers to that of full-time employees) is computed from the Eurostat Survey of the Structure of Earnings, implemented in 1995. This variable is time invariant.47

Share of involuntary PT prime-age men (%)

Share of involuntary PT 15–24 (%)

Share of involuntary PT (%)

Part-time employment rates prime-age 50–64 (%)

Part-time employment rates prime-age women (%)

Part-time employment rates prime-age men (%)

Part-time employment rates 15–24 (%)

16.51

5.37

21.38

15.55

26.49

2.88

16.87

13.86

Part-time variables Total part-time employment rates (%) Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within

Mean

Variables

8.31 8.15 2.19 13.77 14.10 5.48 2.04 1.87 0.78 16.14 15.77 2.83 9.27 8.69 3.27 11.53 11.56 3.91 3.21 2.81 1.51 9.99 9.38 3.23

Std. Dev.

3.8 5.0 3.4 3.6 5.6 7.7 0.7 1.6 0.2 5.6 7.7 19.9 1.4 6.5 10.8 2.3 6.5 13.1 0.2 0.7 0.4 2.9 5.2 4.7

Min.

Table B1. Summary Statistics on the Variables of Interest 1983–1998.

38.8 31.6 21.3 61.6 41.0 37.4 9.9 8.4 5.0 68.2 64.0 37.8 39.6 33.0 25.4 44.8 38.9 33.4 12.6 9.6 10.0 35.8 31.1 24.0

Max.

N n T N n T N n T N n T N N T N n T N n T N n T

216 15 14.4 191 15 12.7 181 14 12.9 197 15 13.1 196 15 13.1 184 15 12.3 169 14 12.1 164 14 11.7

Observations

118 HIELKE BUDDELMEYER ET AL.

EPL for regular jobs

EPL

Children beneﬁts (%)

Change in part-time regulation (more favourable) excluding the Netherlands

Institutions Change in part-time regulation (more favourable)

GDP growth (%)

Economic activity Output gap (%)

Share of involuntary PT prime-age 50–64 (%)

Share of involuntary PT prime-age women (%)

Between Within Overall Between Within Overall Between Within Overall Between

Overall Between Within Overall

Overall Between Within Overall Between Within

Overall Between Within Overall Between Within

2.60

2.71

2.18

0.31

0.94

2.60

1.12

3.51

12.67

0.55 0.95 0.96 0.98 0.30 1.03 1.02 0.29 0.94 0.96

2.80 2.43 1.52 1.09

2.62 0.82 2.50 2.25 0.85 2.09

7.03 7.32 3.04 1.91 1.88 0.84

0.0 1.4 0.3 0.4 1.3 0.5 0.5 2.0 0.7 0.7

0.0 0.0 6.6 0.0

10.5 2.4 9.1 6.3 1.6 6.1

1.4 4.2 4.7 0.2 1.3 1.5

1.8 5.6 4.6 4.0 3.3 4.2 4.0 3.2 5.0 4.7

17.0 9.5 8.4 7.0

5.5 0.2 6.4 13.2 5.1 12.9

29.9 27.2 23.4 8.1 6.4 6.0

n T N n T N n T N n

N n T N

N n T N n T

N n T N n T

15 16 223 15 14.9 224 14 16 224 14

240 15 16 240

224 14 16 224 14 16

173 15 11.5 167 14 11.9

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 119

Unionisation

Total labour tax rate

Share of temporary jobs

Unemployment beneﬁt duration

Unemployment beneﬁt replacement ratios

EPL for temporary jobs

Variables

Table B1.

Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within 0.45

0.38

0.10

0.50

0.32

2.82

Mean

(Continued ).

0.17 1.44 1.38 0.55 0.14 0.13 0.05 0.26 0.27 0.08 0.07 0.06 0.02 0.08 0.07 0.02 0.22 0.23 0.05

Std. Dev.

2.0 0.3 0.3 1.4 0.00 0.08 0.08 0.00 0.05 0.23 0.02 0.03 0.04 0.23 0.25 0.31 0.10 0.12 0.36

Min.

3.0 5.3 5.0 3.7 0.71 0.59 0.44 1.02 0.80 0.71 0.35 0.30 0.17 0.53 0.46 0.47 0.91 0.85 0.66

Max.

T N n T N n T N n T N n T N n T N n T

16 224 14 16 224 14 16 210 14 15 195 15 13 218 14 15.6 206 13 15.8

Observations

120 HIELKE BUDDELMEYER ET AL.

Between Within

Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall Between Within Overall

Overall Between Within

Note: Unless indicated, the variables are not expressed as percentages.

Ratio of part-time hourly wage/full-time hourly wage (time invariant)

Share of employment in services

Schooling rate of the population aged 15–25 (%)

Fertility rate

Total participation rate (%)

Other structural variables Female-participation rate (%)

Bargaining co-ordination

0.77

0.64

55.87

1.61

68.19

62.18

2.14

0.14 0.00

13.70 13.90 5.69 7.80 7.89 1.56 0.25 0.21 0.14 8.45 8.03 5.01 0.08 0.07 0.03 0.14

0.50 0.46 0.23

0.54 0.77

33.0 46.5 47.7 55.1 57.7 63.8 1.15 1.31 1.29 34.3 43.5 42.8 0.44 0.51 0.56 0.54

1.0 1.0 1.5

1.06 0.77

87.7 86.1 76.2 82.9 80.6 73.5 2.74 2.14 2.21 72.0 71.1 67.1 0.77 0.73 0.71 1.06

3.0 2.9 2.8

n T

N n T N n T N n T N n T N n T N

N n T

15 16

201 15 13.4 240 15 16 240 15 16 191 15 12.7 192 13 14.8 240

208 13 16

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 121

268 20 No

8.952 (2.66) 11.638 (2.12)

268 20 No

9.211 (2.75) 9.905 (1.78)

0.946 (0.73)

296 20 No

12.247 (3.23)

0.154 (0.96) 0.824 (2.05)

0.439 (8.51) 0.113 (3.91)

(3)

295 20 Yes

295 20 Yes

92.142 (4.89) 94.336 (4.42)

36.259 (2.87) 77.921 (4.61) 89.041 (4.38)

38.211 (3.02)

9.836 (2.08) 2.677 (3.38) 58.491 (3.16)

(1.88) (4.08) (2.23) (3.75) (3.48)

0.487 (2.75) 1.291 (4.31)

(5)

0.823 4.961 10.289 3.026 67.703

0.398 (2.44) 1.018 (3.84) 2.076 (2.32)

(4)

303 20 Yes

6.815 (0.97)

1.273 (2.48) 3.873 (3.40)

0.173 (1.81) 1.578 (3.29)

(6)

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrstorder serial correlation. Each equation contains country dummies to account for cross-country heterogeneity as well as a speciﬁc dummy taking into account the German reuniﬁcation. When indicated, the two-stage least squares within estimator (ﬁxed-effect regression estimator with instrumental variables) have also been used as an alternative method to correct possible endogeneity. The instruments used are the variables lagged by two years. The panel is unbalanced, as part-time employment series are starting later for some countries (Austria, Finland, Norway, Sweden and Switzerland). Sources: OECD; Nickell et al. (2002); Nickell and Nunziata database (2001). Signiﬁcant at 10% (value of t-statistics in parentheses) Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a OECD countries included Australia, Austria, Belgium, Canada, Denmark, Germany, Finland, France, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom and the United States.

Observations Number of countries Instrumented

0.810 (0.63)

4.764 (2.11) 0.135 (0.36) 4.970 (1.92)

(0.33) (1.84) (2.02) (0.63) (2.00)

0.260 (4.30) 0.124 (3.83)

0.248 (4.09) 0.122 (3.74) 0.227 (0.71) 0.053 0.731 4.486 0.235 5.136

(2)

(1)

Effects of Institutions on Part-Time Employment Rates. Dependent Variable: The Part-Time Employment Rate (%) (OECD Panela 1983–1998).

Total participation rate Output gap EPL EPL for temporary jobs EPL for regular jobs Unionisation Bargaining co-ordination Unemployment beneﬁt replacement ratios Unemployment beneﬁt duration Labour tax rate Constant

Table C1.

ANNEX C. ECONOMETRIC RESULTS 122 HIELKE BUDDELMEYER ET AL.

No 228

0.059 (2.10) 0.022 (0.54) 0.04 (1.66)

No 228

0.033 (1.62) 0.045 (1.90) 0.012 (0.57)

(2)

No 228

0.060 (4.51)

(3)

No 228

0.032 (2.31)

(4)

Yes 223

0.121 (3.81)

(5)

No 228

0.052 (2.95)

(6)

No 228

0.064 (3.12) 0.055 (1.63)

(7)

0.053 (3.22) 0.077 (3.27) No 228

(8)

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrst-order serial correlation. Each equation contains country dummies to account for cross-country heterogeneity as well as a speciﬁc dummy taking into account the German reuniﬁcation. When indicated, the two-stage generalised least squares (ﬁxed-effect regression estimator with instrumental variables) have also been used to tackle possible problems of endogeneity. The instruments are the growth rate of ﬁxed capital investments (and its value lagged by one and two years) and the growth rate of trade and services exports. The ﬁrst-stage equation of the instrumental variable estimation is displayed in Table C3 (equation 1). Sources: Eurostat Labour Force Surveys; OECD Annual Labour Force Statistics and Economic Outlook (2001). Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden and the United Kingdom. b OECD. c Spain, France, Italy and Finland.

Instrumented variables Number of observations

Output gap in low and medium unemployment countries

Output gap in high unemployment countriesc

Positive output gap

Negative output gap

Value-added growth in services sector

GDP growth (2)

GDP growth (1)

GDP growth

Output gap (2)

Output gap (1) (GAP-1)

Output gapb (GAP)

(1)

Table C2. Cyclical Pattern of Total Part-Time Employment Rates. Dependent Variable: Annual Change in the Part-Time Employment Rate (p.p.) (EU-15 Countries Except Luxembourga 1984–2001).

257 14

0.071 (3.88)

0.081 (4.63) 0.063 (3.32)

(3)

(4)

(6.53) 0.083 (7.44) (7.65) 0.082 (7.68) (7.19) 0.071 (7.03) (1.98) 2.407 (4.13) 1.369 1.47 257 266 257 14 14 14

(3.53)

(2)

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrstorder serial correlation. Each equation contains country dummies. Sources: Eurostat Labour Force Surveys; OECD Annual Labour Force Statistics and Economic Outlook (2001). Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses).

Observations Number of countries

Growth rate of ﬁxed capital investments 0.078 Growth rate of ﬁxed capital investments lagged by one year 0.087 Growth rate of ﬁxed capital investments lagged by two years 0.071 Constant 1.648

Growth rate of trade and services exports lagged by two years

0.055 0.016 0.93 0.018 1.09 (6.96) 0.075 (8.23) 0.084 (7.19) 0.071 (1.80) 1.835

0.048 (3.34)

(1)

First-Stage Equation of the Instrumental Variable Estimation (EU-15 Countries Except Luxembourg 1984–2001).

Dependent variable: Output gap (%) Growth rate of trade and services exports Growth rate of trade and services exports lagged by one year

Instruments

Table C3.

124 HIELKE BUDDELMEYER ET AL.

0.380 0.103 0.316 0.154 0.048

Dependent variable: Share of involuntary part-time employment Overall 0.252 (3.98) Youth 0.050 (2.85) Men aged 25–49 0.268 (4.69) Women aged 25–49 0.090 (2.43) Older workers 0.022 (1.60)

(6.58) (6.50) (5.21) (4.33) (3.56)

(4.51) (4.76) (4.42) (3.12) (1.87)

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrstorder serial correlation. While some heteroskedasticity has been detected, there is no evidence of serial correlation. Sources: Eurostat Labour Force Surveys; OECD Annual Labour Force Statistics and Economic Outlook (2001). Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses).

0.060 0.168 0.037 0.099 0.043

0.032 0.078 0.028 0.058 0.002

Output gap

(2.32) (2.21) (3.28) (1.95) (0.08)

Dependent variable: Part-time employment rate Overall Youth Men aged 25–49 Women aged 25–49 Older workers

Output gap lagged by one year

Explanatory Variable

Table C4. Granger Causality from the Output Gap to Part-Time Employment Rates (EU-15 Countries Except Luxembourg 1984–2001).

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 125

w2(13) ¼ 17.7

0.062 0.008 0.002 0.103 0.084 0.027 0.170 0.124 0.084 0.041 0.075 0.169 0.022 0.096 (0.169)

(0.29) (0.22) (0.02) (0.67) (3.02) (1.28) (3.96) (3.02) (0.80) (0.94) (0.79) (0.86) (0.40) (1.77) w2(13) ¼ 11.47

0.156 0.041 0.038 0.160 0.012 0.008 0.101 0.100 0.050 0.014 0.103 0.034 0.011 0.056 (0.572)

(1.17) (0.56) (0.35) (1.16) (0.24) (0.41) (1.53) (2.43) (0.53) (0.20) (1.13) (0.34) (0.29) (1.02)

(2) Output Gap Lagged by One Year

6 18 18 18 14 18 18 18 18 18 18 18 15 13

Number of Observations

Notes: The equations are estimated by OLS with Newey–West standard errors allowing for heteroskedastic errors and serial correlation. For Chow’s poolability test, the p-value is shown in parentheses. Sources: Eurostat Labour Force Surveys; OECD Annual Labour Force Statistics and Economic Outlook (2001).

Chow’s poolability test

Austria Belgium Germany Denmark Spain Finland France United kingdom Greece Ireland Italy Netherlands Portugal Sweden

(1) Output Gap

Cyclical Pattern of Total Part-Time Employment Rates by Country. Dependent Variable: Annual Change in the Part-Time Employment Rate (p.p.) (OLS Country-by-Country Equation 1984–2001).

Explanatory Variable

Table C5.

126 HIELKE BUDDELMEYER ET AL.

(2) Output gap (1) 0.265 (4.15) 0.0542 (2.99) 0.275 (4.77) 0.097 (2.58) 0.025 (1.82)

(1) Output gap 0.415 (7.10) 0.1172 (7.19) 0.337 (5.43) 0.171 (4.70) 0.0575 (4.12)

Explanatory Variables

Notes: The equations are estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrst-order serial correlation. Each equation contains country dummies to account for cross-country heterogeneity as well as a speciﬁc dummy taking into account the German reuniﬁcation. Sources: Eurostat Labour Force Surveys. Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, the Netherlands, Portugal and Spain, Sweden and the United Kingdom.

Total part-timers Youth Men aged 25–49 Women aged 25–49 Older workers

Groups Involved

Table C6. Cyclical Pattern of Involuntary Part-Time Employment. Dependent Variable: Annual Change in the Share of Involuntary Part-Time Employment in Total Employment (p.p.) (EU-15 Countries Except Luxembourga 1984–2001).

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 127

(2)

(3)

(4)

(5)

(6)

No 209

No 209

No 209

Yes 204

No 209

No 209

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrstorder serial correlation. Each equation contains country dummies to account for cross-country heterogeneity as well as a speciﬁc dummy taking into account the German reuniﬁcation. When indicated, the two-stage least squares within estimator (ﬁxed-effect regression estimator with instrumental variables) have also been used to tackle possible problem of endogeneity. The panel is unbalanced as part-time employment series start later for some countries (Austria, Finland and Sweden). Sources: Eurostat Labour Force Surveys; OECD Economic Outlook (2001). Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden and the United Kingdom. b The high unemployment countries are Spain, France, Italy and Finland.

Instrumented variables Number of observations

0.177 (4.92) 0.251 (3.58) Output gap (GAP) 0.206 (3.09) Output gap (1) (GAP-1) 0.003 (0.03) Output gap (2) 0.075 (1.22) GDP growth 0.104 (2.14) GDP growth (1) 0.057 (1.19) GDP growth (2) 0.047 (1.09) Negative output gap 0.227 (3.45) Positive output gap 0.114 (1.53) 0.255 (3.57) Output gap in high unemployment countriesb Output gap in low and medium 0.144 (3.48) unemployment countries

(1)

Table C7. Cyclical Pattern of Part-Time Employment Rates for Youth. Dependent Variable: Annual Change in the Part-Time Employment Rate for Those Aged 15–24 (p.p.) (EU-15 Countries Except Luxembourga 1984–2001).

128 HIELKE BUDDELMEYER ET AL.

129

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

Table C8. Cyclical Pattern of Part-Time Employment Rates for Prime-Age Males. Dependent Variable: Annual Change in the Part-Time Employment Rate for Those Aged 25–49 (p.p.) (EU-15 Countries Except Luxembourga 1984–2001). (1)

(2)

(3)

(4)

(5)

(6)

(7)

Output gap (GAP) 0.005 (0.31) Output gap (1) (GAP-1)

Output gap (2)

0.066 (2.97)

0.026 0.072 (3.05) (4.92)

0.054 (3.67)

GDP growth 0.094 (0.79) GDP growth (1)

0.029 (2.64)

GDP growth (2) 0.016 (1.62) Negative output gap

0.038 (2.68)

Negative output gap (1) 0.020 (1.37) Positive output gap (1)

0.039 0.033 (1.88) (1.75)

Output gap in high unemployment countries (1) Output gap in low and medium unemployment countries (1) Instrumented variables Number of observations

0.023 (1.64) 0.029 (2.60) No 209

No 209

No 209

Yes 204

No 209

No 209

No 209

Note: For further details, see Table C7. Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, The Netherlands, Portugal, Spain, Sweden and the United Kingdom.

(2)

(3)

(4)

(5)

(6)

(7)

No 209

No 209

No 209

Yes 204

No 209

No 209

No 209

Note: For further details, see Table C7. Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden and the United Kingdom. b Spain, France, Italy and Finland.

Instrumented variables Number of observations

0.094 (2.96) 0.056 (0.86) Output gap (GAP) 0.127 (2.04) Output gap (1) (GAP-1) 0.047 (0.52) Output gap (2) 0.0162 (0.28) GDP growth 0.049 (1.02) GDP growth (1) 0.0199 (0.37) GDP growth (2) 0.047 (0.97) Value-added growth in 0.0473 (1.19) services sector Negative output gap 0.049 (0.88) Positive output gap 0.156 (2.25) 0.132 (2.72) Output gap in high unemployment countriesb Output gap in low and 0.068 (1.64) medium unemployment countries

(1)

Table C9. Cyclical Pattern of Part-Time Employment Rates for Prime-Age Females. Dependent Variable: Annual Change in the Part-Time Employment Rate for Women Aged 25–49 (p.p.) (EU-15 Countries Except Luxembourga 1984–2001).

130 HIELKE BUDDELMEYER ET AL.

No 209

Instrumented variables Number of observations

No 209

0.055 (1.52) 0.059 (1.56) 0.024 (0.73)

(2)

No 209

0.042 (1.76)

(3)

No 209

0.0009 (0.04)

(4)

Yes 204

0.073 (1.54)

(5)

No 209

0.001 (0.02) 0.118 (1.59)

(6)

No 209

0.008 (0.15)

0.053 (2.02)

(7)

Note: For further details, see Table C7. Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). a Austria, Belgium, Denmark, Germany, Greece, Finland, France, Ireland, Italy, the Netherlands, Portugal and Spain, Sweden and the United Kingdom.

0.078 (1.58) 0.008 (0.11) 0.06 (1.26)

Output gap (GAP) Output gap (1) (GAP-1) Output gap (2) GDP growth GDP growth (1) GDP growth (2) Negative output gap Positive output gap Output gap in high unemployment countries Output gap in low and medium unemployment countries

(1)

Table C10. Cyclical Pattern of Part-Time Employment Rates for Older Workers. Dependent Variable: Annual Change in the Part-Time Employment Rate for Those Aged 50–64 (p.p.) (EU-15 Countries Except Luxembourga 1984–2001).

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 131

Unionisation

Total labour tax rate

Unemployment beneﬁt replacement ratios Unemployment beneﬁt duration Share of temporary jobs

EPL for temporary jobs

EPL EPL for regular jobs

(5.44) 0.072 (0.42) 1.877 (2.09) 0.790 (0.80)

2.512

1.448 (1.39) 1.090 (0.99)

0.622 (1.73)

1.437 (3.49)

1.679 (4.53)

1.383 (3.56)

1.938 (3.50) 0.059 (0.35) 0.789 (0.37) 0.253 (023)

0.165 (2.10)

0.071 (1.53)

(3)

0.165 (2.32)

0.075 (1.73)

(2)

0.334 (5.68)

0.116 (3.47)

(1)

2.207 (4.65) 0.126 (0.93) 1.029 (1.25) 0.099 (0.12)

1.045 (3.10)

0.349 (6.26)

0.075 (1.93)

(4)

0.430 (1.05) 0.390 (1.81) 15.17 (3.29) 1.736 (1.18)

1.324 (2.49)

0.384 (5.24)

0.075 (1.46)

(5)

8.224 (1.61) 1.728 (0.56)

2.38 (5.66) 0.0306 (1.73) 3.77 (2.89) 1.61 (1.53)

2.146 (5.14)

0.0506 (0.51)

0.0628 (1.50)

(6)

0.115

2.276 (4.74) 0.050 (0.30) 2.058 (2.36) 0.853 (0.89) 6.514 (1.99)

1.478 (4.09)

(1.57)

0.061 (1.44)

(7)

2.004 (5.02) 0.171 (1.12) 1.636 (2.13) 1.431 (1.69) 7.285 (2.52)

1.551 (4.52)

0.125 (1.94)

0.025 (0.65)

(8)

1.961 (3.51) 0.337 (2.25) 2.622 (2.62) 0.087 (0.09) 4.168 (1.19)

0.881 (2.42)

0.375 (6.74)

0.090 (2.74)

(9)

(11)

4.600 (3.65) 0.684 (1.51) 3.631 (1.63) 5.340 (1.67) 15.593 (2.17)

2.999 (3.88)

0.029 (0.25)

0.350 0.055 (2.52) (0.88)

(10)

Determinants of Part-Time Employment Rates. Dependent Variable: The Part-Time Employment Rate (%) (European Countriesa 1983–1998).

Institutions Change in part-time regulation (more favourable) Change in part-time regulation (more favourable) excluding the Netherlands Child beneﬁts

Output gap

Table C11.

132 HIELKE BUDDELMEYER ET AL.

172 14 Yes No No

14.382 (3.24)

9.77 (3.31)

172 14 No No No

0.401 (12.14) 4.424 (5.48) 0.079 (3.41)

0.374 (16.5) 3.425 (4.05) 0.029 (2.63)

172 14 Yes No No

13.637 (2.45)

0.381 (10.30) 4.886 (5.35) 0.033 (1.34)

172 14 Yes No No

11.933 (2.75)

0.354 (12.25) 2.313 (3.29) 0.082 (3.79)

18.16 (2.79) 154 14 Yes No No

17.557 (2.48)

4.296 (3.88) 0.028 (1.04)

172 14 No Yes No

0.3497 (10.22) 4.704 (5.39) 0.0568 (2.19)

170 14 yes no no

15.275 (4.08)

0.397 (12.40) 4.885 (6.05) 0.072 (3.22)

154 14 yes no no

42.834 (7.31)

0.317 (9.43) 8.230 (6.96) 0.051 (2.32) 22.875 (2.85)

154 14 no no no

2.079 (0.78)

0.010 (0.45) 7.767 (1.18)

0.271 (7.84)

154 14 yes no yes

231 15b Yes No no

43.724 4.409 (4.04) (1.43)

0.327 0.325 (5.18) (12.06) 6.489 (2.86) 0.169 0.076 (3.11) (2.27) 30.200 (1.67) 11.850 (4.94)

Notes: The equations are generally estimated by generalised least squares allowing for heteroskedastic errors and common-across-group ﬁrstorder serial correlation. Each equation contains country dummies, intercepts and a speciﬁc dummy taking into account the German reuniﬁcation. When indicated, the two-stage least squares within estimator (ﬁxed-effect regression estimator with instrumental variables) have also been used as an alternative method to correct possible endogeneity. The instruments used are the variables lagged by two years. The panel is unbalanced as data are starting later for some countries (Austria, Finland, Norway and Sweden). Sources: Eurostat Labour force surveys; Eurostat European Social Statistics; OECD Economic Outlook (2001); OECD labour market database; World Bank’s World Development Indicators database; Nickell et al. (2002); Nickell and Nunziata database (2001). Signiﬁcant at 10% (value of t-statistics in parentheses). Signiﬁcant at 5% (value of t-statistics in parentheses). Signiﬁcant at 1% (value of t-statistics in parentheses). a Countries included all the European Union member states except Luxembourg (Belgium, Denmark, Germany, Greece, Spain, France, Ireland, Italy, the Netherlands, Austria, Portugal, Finland, Sweden and the United Kingdom). b The United States is also included to increase the cross-sectional dimension, as the ratio of part-time hourly wage to full-time hourly wage is time invariant, corresponding to its 1995 value (Eurostat Survey of Structure of Earnings). For the same reason, equation 9 was estimated without country dummies (GLS with time dummies).

Observations Number of countries Time dummies Country trends Instrumented variables

Schooling rate of the population aged 15–25 Share of employment in services Ratio of part-time hourly wage/full-time hourly wage (time invariant) Constant

Fertility rate

Other structural variables Female-participation rate

Why Europeans Work Part-Time? A Cross-Country Panel Analysis 133

HIELKE BUDDELMEYER ET AL. Median wage of part-timers compared to fulltimers (%)

134 110 100 90 80 70 60

y = -1.0659x + 90.268

50

R 2 = 0.1626

40 0

5

10

15

20

25

30

35

Part-time employment rate (%)

Median wage of male part-timers compared to male full-timers (%)

Fig. C1.

Part-Time Employment Rate and Relative Wages of Part-Time Workers (%) – Both Genders.

140 130 120 110 100 90 80

y = -3.9836x + 95.031 R 2 = 0.2415

70 60 50 40 0

Fig. C2.

2

6 4 8 10 Male part-time employment rate (%)

12

14

Part-Time Employment Rate and Relative Wages of Part-Time Workers (%) – Males.

135

Median wage of female part-timers compared to female full-timers (%)

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

120 110 100 y = -0.4344x + 97.737 R 2 = 0.0922

90 80 70 60 50 40 0

10

20

30

40

50

60

Female part-time employment rate (%)

Fig. C3.

Part-Time Employment Rate and Relative Wages of Part-Time Workers (%) – Females.

1985 1990 1995 2000 2005 time

esp

1985 1990 1995 2000 2005 time

10

20

0

1985

1985

1990 1995 2000 time

fin

1990 1995 2000 time

aut

2005

2005

10

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0

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1985 1990 1995 2000 time

fra

1985 1990 1995 2000 time

che

2005

2005

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2005

0

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0

10

20

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10

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1985

1985

1990 1995 2000 time

swe

1990 1995 2000 time

jpn

2005

2005

Actual part-time employment rate Fitted value

1985 1990 1995 2000 2005 time

prt

1985 1990 1995 2000 2005 time

ita

0

0

10

20

0

10

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0

1985 1990 1995 2000 time

usa

1985 1990 1995 2000 time

nld

2005

2005

0

10

20

1985 1990 1995 2000 2005 time

nor

1985 1990 1995 2000 2005 time

gbr

1985 1990 1995 2000 2005 time

deu

Fig. C4. The Fitted Value of Part-Time Employment Rate for OECD Countries (Model 2 of Table C1) (%).

0

10

20

0

0

2005

10

10

1985 1990 1995 2000 time

20

ire

20

0

0

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136 HIELKE BUDDELMEYER ET AL.

137

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

deu

dnk

esp 20

20 20 10

10

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0

0 1985 1990 1995 2000 2005 time

0 1985 1990 1995 2000 2005 time

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1985 1990 1995 2000 2005 time

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ire 20

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0 1985 1990 1995 2000 2005 time

0 1985 1990 1995 2000 2005 time

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1985 1990 1995 2000 2005 time

nld

20

prt 20

10

10

20 10 0

0 1985 1990 1995 2000 2005 time

0 1985 1990 1995 2000 2005 time

1985 1990 1995 2000 2005 time

Actual part-time employment rate Fitted value

Fig. C5.

The Fitted Value of Part-Time Employment Rate for EU Countries (Model 2 of Table C11) (%).

14

14

12

12

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

BE

DEU

ESP

FRA

UK

IRE

ITA

NLD

PT

USA

Schooling rate

EPL for regular contracts

Output gap

Fertility rate

Child benefits

Part-time rate

Female participation

New PT law

Fig. C6.

Change in Part-Time Employment Rate (in Black) and Contribution of Each Determinant over the Full Period (1983–1998) (Model 1 of Table C11) (Percentage Points).

10

10 8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4 BE

DEU

ESP

FRA

UK

IRE

ITA

Schooling rate

EPL for regular contracts

Fertility rate

Child benefits

Female participation

New PT law

NLD

PT

USA

Output gap Part-time rate

Fig. C7. Change in Part-Time Employment Rate and Contribution of Each Determinant in the 1980s (1983–1990) (Model 1 of Table C11) (Percentage Points).

139

Why Europeans Work Part-Time? A Cross-Country Panel Analysis

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

BE

DEU

ESP

FRA

UK

IRE

ITA

NLD

PT

USA

Schooling rate

EPL for regular contracts

Output gap

Fertility rate

Child benefits

Part-time rate

Female participation

New PT law

Fig. C8. Change in Part-Time Employment Rate and Contribution of Each Determinant in the 1990s (1990–1998) (Model 1 of Table C11) (Percentage Points).

PROJECTING BEHAVIORAL RESPONSES TO THE NEXT GENERATION OF RETIREMENT POLICIES Alan L. Gustman and Thomas L. Steinmeier ABSTRACT Using data from the Health and Retirement Study, we examine behavioral responses to a new generation of retirement policies that on average are actuarially neutral. Although many conventional models predict that actuarially neutral policies will not affect retirement behavior, our model allows those with high-time preference rates to ﬁnd that the promise of an actuarially fair increase in future rewards does not balance the loss from foregone current beneﬁts. Thus together with liquidity constraints facing those with high-time preference, we ﬁnd that actuarially neutral policies do affect retirement behavior. One such policy follows on the elimination of the Social Security earnings test for those over normal retirement age, and would eliminate the earnings test between early and normal retirement age. Another of these policies would increase the ages of beneﬁt entitlement. Still another such policy emerges from a central focus of the past few years on the adoption of personal accounts. Although Social Security beneﬁts are currently paid in the form of an annuity, beneﬁts from either deﬁned beneﬁt plans or from personal Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 141–195 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28005-2

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accounts may be made available as an annuity or as a lump sum of equivalent actuarial value. A related policy choice between actuarially equivalent beneﬁts emerges on the pension side. There has been discussion of relaxing the current IRS prohibition against paying a pension beneﬁt when a person remains at work, instead allowing partial pension beneﬁts to be paid to those who partially retire on a job.

Until the 1980s, both the federal government and employer policies encouraged workers to retire by age 65. Employers were free to mandate retirement by age 65, and many did. In addition, the dominant type of pension plan, the deﬁned beneﬁt plan, often stopped crediting work at age 65. When a person worked an additional year, one year’s pension was lost, but future pension payments were not increased to compensate. Similarly with Social Security, when a person worked after age 65 and lost beneﬁts to the retirement test, future Social Security beneﬁts were not increased by an amount that would compensate for the lost beneﬁts. Other features of pensions, including availability of early beneﬁts, and supplements to pensions taken at early ages, encouraged even earlier retirement. However, with the baby boomers approaching retirement age, in the past few decades both the government and employers have done an about face. They not only eliminated policies that encouraged retirement by age 65 or earlier, but also adopted policies to encourage older persons to delay their retirements. Some of these policies, such as the 1983 Social Security reforms, increase adjustments in future beneﬁts to compensate for beneﬁt payments lost to the earnings test, or to otherwise compensate when beneﬁt claiming is delayed. Other public policies encourage later retirement by outlawing age discrimination, mandatory retirement, and by requiring that pension beneﬁts give credit for work after normal retirement age, or that they are otherwise adjusted on an actuarially fair basis.1 The trend from deﬁned beneﬁt to deﬁned contribution plans and the adoption of hybrid plans also encourage delayed retirement.2 Today, beneﬁt structures in pensions and Social Security are now roughly actuarially fair, in that disincentives from inadequate beneﬁt accrual rates for those who postpone retirement have been eliminated. Now a new generation of retirement policies is under consideration. Although actuarially neutral, these policies are likely to affect retirement outcomes. One such policy follows on the elimination of the Social Security earnings test for those over normal retirement age, and would eliminate the

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143

earnings test between early and normal retirement age. Another of these policies would increase the ages of beneﬁt entitlement. Still another such policy emerges from a central focus of the past few years on the adoption of personal accounts. Although Social Security beneﬁts are currently paid in the form of an annuity, beneﬁts from either deﬁned beneﬁt plans or from personal accounts may be made available as an annuity or as a lump sum of equivalent actuarial value. A related policy choice between actuarially equivalent beneﬁts emerges on the pension side. There has been discussion of relaxing the current IRS prohibition against paying a pension beneﬁt when a person remains at work, instead allowing partial pension beneﬁts to be paid to those who partially retire on a job. Unfortunately, when it comes to distinguishing between these and other policies offering choices between actuarially equivalent outcomes, many of the tools that have been used to analyze the effects of retirement policies on retirement behavior either fall silent, or suggest counter to their likely effects that these policies will have no impact on retirements. In particular, a central feature of many retirement equations is the pension or Social Security delta, the change in present value of beneﬁts with continued work. In the case of actuarially fair policies, these deltas are zero, so the prediction is that the policies will have no effect on retirement. This paper examines the effects on retirement of certain proposals that are part of the new generation of actuarially neutral policies. As we show, contrary to predictions from simple retirement equations, these policies will nevertheless affect retirement, primarily as a result of a mismatch between certain persons’ rates of time preference and the discount rate implicit in the design of the pension or Social Security. Consider some of the policies noted above. Although the earnings test taxes away beneﬁts from earnings above the disregard amount, subsequent yearly beneﬁts are increased to compensate for beneﬁts lost. Compensation carries an implicit interest rate speciﬁed in the law. However, among those with high time preference rates, that interest rate is not adequate. Those with high time preference rates will not consider beneﬁt adjustments under current law adequate to compensate them for postponing retirement or beneﬁt claiming. Once the earnings test is abolished, in this case between the early and normal retirement age, they are no longer subject to inadequate compensation for postponing retirement, and therefore they may delay their retirement. Similarly, allowing beneﬁts from pensions or Social Security to be paid as a lump sum encourages those with high time preference rates to accelerate their retirement. Those with high time preference rates and consequently little saving will prefer a lump sum settlement, even though the annuities are actuarially equivalent in

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value. Increasing the age of eligibility for beneﬁts will reduce retirements as those with high time preference rates who retire to avoid waiting for beneﬁts under the current system will instead ﬁnd postponing retirement no longer reduces their Social Security beneﬁts while still at work (Gustman & Steinmeier, 2005a). Of course, these substitution effects will not always dominate. If there are wealth effects, or assets become available at particular ages to a person who is liquidity constrained, these effects must also be considered. Once again, most retirement equations will fall silent, especially about any liquidity effects. A key to analyzing this next generation of policy initiatives is to incorporate differences in time preference rates into the underlying behavioral model of retirement. To do that, one must relax the assumption of perfectly operating capital markets and consider the joint determination of retirement and saving. As long as one cannot borrow extensively on the basis of future pension and Social Security payments, those with different time preference rates may have different valuations for beneﬁts received at different times, even if the beneﬁts are actuarially equivalent, e.g., for lump sum versus an annuity or other deferred payouts. This type of distinction is not included in the ﬁrst generation of retirement models. We will estimate and apply an extended version of a model developed in Gustman and Steinmeier (2005a, 2005b) to analyze the retirement implications of these newer policies. A major extension of the model is that the present version incorporates the decision to claim beneﬁts as separate and distinct from the decision to retire. Thus the decisions analyzed in the model we estimate include whether to fully or partially retire, to claim beneﬁts, to participate in voluntary personal accounts, to take beneﬁts as an annuity or lump sum, and how much to save. These decisions determine the course of beneﬁt and tax payouts. Another extension more systematically extends the role of minimum hours constraints in shaping retirement. Section 1 discusses our retirement model and its estimation. Section 2 analyzes the likely effects of abolishing the retirement earnings test between early and normal retirement age, and compares the effect of abolishing the earnings test with the policy of raising the Social Security early entitlement age. We then turn to Section 3 for an analysis of the differential effects on retirement of eliminating institutional barriers, having ﬁrms and the IRS adopt policies that would permit ﬂexible retirement on most jobs where minimum hours constraints and pension rules now prohibit them. Section 4 analyzes how voluntary personal accounts would affect retirement,

Projecting Behavioral Responses to the Next Generation of Retirement Policies

145

including the effects of adopting actuarially equivalent lump sum or annuity payouts to systems of voluntary personal accounts, as well as the effects of adopting various structural components of personal account schemes. Section 5 concludes.

1. THE RETIREMENT MODEL AND ITS ESTIMATION This section presents a structural model of retirement and saving. It then discusses the approach to estimation of the model, the data used in the estimation, and the results of the estimation.

1.1. The Retirement Model The model estimated here jointly explains retirement and saving, and allows for heterogeneity in both time preference and in tastes for leisure. In the basic model, the individual is assumed to maximize a utility function of consumption and leisure over time. The constraints include an asset accumulation equation and an uncertain lifetime.3 In this model, there are two labor market paths to retirement, full-time work to full-retirement, and full-time work to partial retirement to full retirement. Because retirement is not modeled stochastically, there are no reversals from states of lesser to states of greater work.4 1.1.1. Utility In the model, the individual is assumed to maximize a utility function of consumption and leisure over time: ( ) T 3 X X 1 a rt X t bþ 1 g U¼ L e sm;t C m;t þ e a; go1 a g m;t t¼0 m¼1 In this equation, T is the maximum lifespan and m refers to the family structure at time t (both spouses alive, only the husband alive, or only the wife alive). sm,t is the probability of family structure m at time t, C consumption, and L the leisure, which takes on a value of 0 for full-time work, 1 for full retirement, and 1/2 for partial retirement, assuming that partial retirement involves half-time work.5 X includes a constant, age, health status, and vintage. The age variable in X causes leisure to become

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gradually more attractive as the individual ages. X does not contain any binary age variables or splines in age that might encourage retirement at a particular age.

1.1.2. Heterogeneous Elements of Utility These preferences allow for three types of heterogeneity. The time preference term r is a ﬁxed effect, and the leisure preference term e is a random effect drawn from a normal distribution. The parameter g, which governs how desirable partial retirement is relative to full-retirement or full-time work, is also a random effect. It is taken so that the term (1/2)g g comes from the exponential distribution f ½ð1=2Þg ¼ kedð1=2Þ deﬁned over g (1/2) A[1/2, 1], which is the theoretically acceptable range of (1/2)g for gA[0, 1]. k is the constant necessary for the density function to integrate to unity, as it must. If g is close to unity, then full-time leisure has about half the value of half-time leisure, and the individual regards the utility of an hour of leisure (and the disutility of an hour of work) as about the same regardless of whether the work is full-time or part-time. If g is close to zero, then part-time leisure is almost as valuable as full-time leisure. In this case, the individual does not mind part-time work too much but really dislikes having to work full-time. Since partial retirement seems to become relatively more attractive as the individuals age, we specify d to be increasing in age: d=doþda Age. There is a literature (e.g., see McGarry, 2004; Bound et al., 2006) that is rightly concerned with the potential correlation of reported health with unobserved heterogeneity, and thus directly or indirectly with the measures of time preference and preference for full-retirement and part-time leisure speciﬁed in the model. Although this literature clearly shows that self-reports of health status do contain considerable information, there is always the possibility that correlation between reported health and unobservables will bias the coefﬁcients on the health measure. Since the effect of health on retirement is not a central concern of this paper, we consider this to be second order concern in this context. That is, to the extent that self-reported health is picking up the effects of unmeasured preferences, it is unlikely that any remaining correlation will bias our estimates of the effects of policy changes on retirement. A related issue concerns the relation of g to health. Experimentation indicates that when a health problem causes an individual to retire, it usually causes complete retirement rather than partial retirement. Accordingly, when the individual reports a health problem, g is set equal to one.

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1.1.3. The Budget Constraint The asset accumulation over time is given by Am;t ¼ ð1 þ rÞAk;t1 þ W m;t ð1 Lm;t Þ þ E m;t þ Bm;t C m;t ;

with

Am;t 0

where Am,t is the level of real assets at time t in survival state m, r the real interest rate, Wm,t the real wage rate, Em,t the earnings of the spouse, and Bm,t the level of Social Security and/or pension beneﬁts at time t. The equation must hold for any legitimate transition between survival state k at time t1 and survival state m at time t. If the individual is working, the wage rate may depend on whether the work is full- or part-time. Workers are allowed to partially retire, usually in different jobs from those held in prime working age. Work when partially retired on a new job reduces ﬁrm-speciﬁc human capital to zero, and may involve relaxation of other job requirements. As a result, partial retirement on a job not held during prime working years typically pays a lower wage rate (Gustman & Steinmeier, 1983, 1985). Social Security enters as income in the asset accumulation equation in the years that beneﬁts are received. The earnings and pension beneﬁts of the spouse are treated as exogenous in this paper. The model does not account for health insurance, but it does a good job of accounting for other facts. We leave health insurance for future research.6 The level of beneﬁts Bm,t at time t depends on the previous decisions of the individual as to when to leave full-time employment and when to retire fully, as well as the current survival state.7 Note that this model does not calculate the value of accruals to Social Security and pensions directly, but the value of the accruals is implicit in the model because work during one period will affect the value of Social Security and pension beneﬁts in later periods. The implicit value of these accruals, of course, depends strongly on the time preference rate. It also depends on the decision of the individual as to when to apply for Social Security beneﬁts; obviously, no beneﬁts can be paid until the individual has applied for them. This means that a delay in the application will result in increased beneﬁts later.

1.2. Estimation Estimation is based on the general method of simulated moments.8 The calculation of the simulated moments follows from the following

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decomposition of the utility function: " # "X # T X 3 T X 3 X 1 1 g U¼ ert sm;t C am;t ert sm;t eX t b Lm;t e þ a g t¼0 m¼1 t¼0 m¼1 A crucial observation is that the ﬁrst part of the utility function does not depend on the random effects e and g, and the second part does not depend on consumption or the budget set. For all possible combinations of partialand full-retirement ages, and for all possible ages for initial Social Security claims, the budget set is calculated. Given the budget set, and given values of a and r, optimal consumption is calculated by solving the dynamic programming model. The associated utility of the optimal consumption stream is UC(r1, r2, a; a, r), where r1 is the age of partial retirement, r2 the age of full retirement, and a the claiming age. If there is no partial retirement, r1=r2. The optimal claiming behavior for particular values of r1 and r2 is just the value of a which maximizes U C : U C ðr1 ; r2 ; a; rÞ ¼ max U C ðr1 ; r2 ; a; a; rÞ. a

Next, 10,000 random values of e and g are chosen per individual, and for each set the value of the second part of the utility function is evaluated for each combination of r1 and r2. This utility depends on the retirement dates and the value of b: UL(r1, r2; e, g, b, r). Note that the calculation of UL does not require the solution of a dynamic programming model and hence can be done quickly. For each set of e and g, the total utility is evaluated for each set of retirement dates r1 and r2, and the retirement dates are the ones, which maximize the total utility: U(e, g, r; a, b)=max [UC(r1, r2; a, r)þUL(r1, r2; e, r1 ;r2

g, b, r)]. Thus, given r and values for the parameters a and b, the distribution of retirement ages is built up from the 10,000 values of e and g. The next issue is: where do we get the value for the ﬁxed effect r? To resolve this, we use the actual retirement dates (if retirement occurs within the sample) or the individual’s reported expected retirement dates (if it does not). Given a value of a, we then pick a value of r and solve the consumption problem described above. Using the optimal consumption values and the asset accumulation equation, we can solve for assets at the beginning of the sample period, which is 1992 for the HRS. If these assets are larger than the assets actually observed, we adjust r upward; otherwise we adjust r downward. The ﬁxed effect is the value of r for which the calculated accumulation just matches the actual assets.9 Note that this ﬁxed value depends on the value of a and so must be recalculated each time the estimation procedure considers a new value of a.10

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For a given set of parameters, these simulations give simulated sample moments. In the generalized method of simulated moments, these simulated sample moments are compared to the actual sample moments, and the procedure adjusts the parameters to minimize the differences between the simulated moments and the actual moments. In the minimization, the moments are weighted so as to provide the most precise estimates possible with the data. The estimation is based on 46 moments. Thirteen of the moments are the percentages working full-time at each age between 54 and 66. The remaining moments are calculated at ages 55, 58, 60, 62, and 65 and include ﬁve moments for the percentage fully retired at the indicated ages, the percent of those with a health problem who are working full-time, the percent of those with a health problem who are fully retired, the percent of those born before 1934 who are working fulltime, the percent of those born after 1938 who are working full-time, the percent of those with lifetime incomes below $1,250,000 who are working full-time, and the percent of those with lifetime incomes above $1,900,000 who are working full-time. The income ﬁgures and vintages are chosen to divide the sample roughly into thirds. Two moments are lost because those born before 1934 could not have been 55 in the survey time frame, and those born after 1938 could not have reached 65 within this time frame. The model has eight parameters to be estimated. These include the consumption parameter a; four elements of b including the constant and coefﬁcients for age, poor health, and birth year; two elements of d including a constant and a coefﬁcient of age; and the standard deviation of retirement preferences given by se. In calculating test statistics, each individual is a single observation. There are 46 possible moments for each individual, and they are arranged in the 46 element vector mi, where i refer to the individual. The moments may refer to different ages; thus one moment may be for retirement at age 55 and another may be for retirement at age 62. Let mij be the jth moment for the ith individual. Then mij is the difference between the jth retirement outcome for the ith individual and the corresponding probability of the outcome from the model. Since many of the moments refer to years in which the individual was not interviewed, not all of the moments are observed for each individual. The unobserved moments in mi are assigned a value of zero, as in Hayashi, Altonji, and Kotlikoff (1996). The retirement outcomes are binary variables for a particular individual. Let m=S mi and mj be the jth element of m. Thus, if there are nj individuals for whom the jth moment is observed, then (1/nj) mj is simply the difference between the observed fraction of the

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sample in the retirement state and the fraction that would be predicted from the model. Under the null hypothesis that the model is correct, all moments have an expected value of zero, i.e., E(m)=0. The matrix mi mui is a 46 46 matrix of the squares and cross products for the moment vector of individual i. The sum of these matrices W=S mi mui is thus an estimate of the variances and covariances of the vector m=S mi. The diagonal elements of W are estimates of the variances of the moments, and the off-diagonal elements of W are estimates of the covariances between two different moments. Note that since various elements of mi refer to different years for the same individual, the off-diagonal elements of W account for any correlations for the same individual over time on account of the unobserved differences in r, e, and g. m is a function of the outcomes and the parameters and hence can be written as m(y, h). Because E(m)=0 under the null hypothesis that the model is correct, we may write m(y, h)=e, where E(e)=0 and W is approximately equal to the variance–covariance matrix of e. Linearizing m(y, h) around the true value of h, which can be denoted as ho, we have m(y, ho)þG(hho)=e, where the matrix G is the partial derivatives of the elements of m with respect to the elements of h. This may be rewritten as m(y, ho)Gho=Ghþe. In this format, the GMM of h can be viewed as the GLS estimator of –G on [m(y, ho)Gho], since it minimizes e W1e=m(y, h) W1 m(y, h). The variance of the GLS estimator is given by [Gu W1 G]1. Some additional corrections would normally be required since we use simulated moments rather than calculated moments, but because we use 10,000 simulations per observation to obtain the simulated moments, the differences between the simulated and calculated moments should be small enough that the additional corrections can probably be ignored. The simulations proceed in almost exactly the same manner as the estimates, except that only the estimated values of the parameters need be considered. Tallies can be made for almost any aspect of the model, including the percentages fully retired and partially retired at different ages, the percentage claiming Social Security beneﬁts, the distribution of time preference rates, and the amount of Social Security taxes and beneﬁts by age. Simulations are accomplished by simply making the appropriate changes in the budget sets and simulating the results. Simulations include married men only. The simulations use a real interest rate of 4.31% per year as the assumed return on investments in personal accounts. This is the average compounded rate from 1926 to 2002 of an asset basket of 50% large

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151

cap stocks, 5% long-term bonds (treasury bonds), and 45% treasury notes, as measured by Ibbotson Associates (2002).

1.3. Data Used in the Model Estimation The model is estimated for married men who are career workers from the original cohorts of the Health and Retirement Study, using observations from the ﬁrst six waves of the survey, every other year from 1992 through 2002, including restricted Social Security and pension data collected in the initial year of the survey. The selection of the sample, and reasons for deleting observations, are reported in appendix Table A1. The deﬁnition of retirement in this study is a hybrid one relying both on objective and subjective measures. Individuals working at least 30 h per week and 1,560 h per year are counted as full-time. Individuals working at least 100 h per year but no more than 25 h per week or 1,250 h per year are counted as part-time, and individuals not doing any work at all are counted as fully retired. Individuals who fall between full-time and part-time or between part-time and retired are classiﬁed on the basis of self-reports. Earnings proﬁles are taken from Social Security records or, if these are not available, from the retrospective information in the respondent surveys. Future potential earnings are projected on the basis of tenure and experience coefﬁcients of earnings regressions. Pension beneﬁts, conditional on tenure in the job providing the pension, are based on information in the summary pension descriptions, provided by the employers. Social Security beneﬁts are based on the earnings histories and ﬁgured according to the Social Security rules.

1.4. Parameter Estimates Table 1 reports parameter estimates. There are 46 moments in the estimation, leaving 38 degrees of freedom. The cutoff points of the w2 distribution are 53.15 for 5%, so the model is not rejected at the 5% signiﬁcance level. The coefﬁcients are of similar magnitudes to those in our earlier estimates. Everything except the vintage coefﬁcient is signiﬁcant. A key to understanding these results is in the time preference rates. These rates are heterogeneous, with 45% of the population exhibiting time

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER Table 1.

Symbol

Estimated Results.

Description

a Parameters in b b0 ba bh bc

Consumption parameter Constant Coefﬁcient of agea Coefﬁcient of healthd Coefﬁcient of cohortb,d (year of birth)

Parameters in d d0 da se q value Number of observations

Constant Coefﬁcient of agec Standard deviation of ed 52.11 2,231

Coefﬁcient Value t-Statistic 0.16 10.01 0.084 4.71 0.03 3.75 0.56 5.11

2.60 246.52 4.78 4.54 0.28 5.93 2.66 6.06

Notes: Several variables are differenced from their approximate means in the sample in order to facilitate estimation. a The actual variable is age – 62. b The actual variable is cohort – 1,936. c The actual variable is age – 65. d These coefﬁcients are all relative to the age coefﬁcient, again to facilitate estimation.

preference rates above 5%, and one third exhibiting time preference rates of 20% or greater.11 These rates are consistent with Samwick (1998).

1.5. Comparison of Observed and Predicted Outcomes As is well known, in recent years, the most prominent spike in retirement occurs around the age of early entitlement to Social Security beneﬁts, age 62. Roughly 15% of the relevant sample of males retires at age 62, about 9% more than those retiring in surrounding years. About 9% of the population retires from full-time work at age 65, about 3.5% more than those retiring in neighboring years. Note that these percentages are percentages of the population retiring at different ages, not the hazard rates for retirement at particular ages. Table 2 reports observed retirement outcomes, and simulated retirement outcomes under the current program, with each included individual having the work history actually experienced, and reﬂected in own Social Security earnings record and reported job history. An indication of the ability of the

4.1 0.9 2.7 2.0 2.1 3.1 1.9 4.0 3.0 3.6 6.0 6.3 15.1 5.6 6.7 9.1 4.5 2.8 3.1 1.7

From FT work

3.3 0.0 2.2 1.1 1.3 2.7 2.1 3.2 2.1 2.1 6.4 5.5 12.5 3.4 6.7 6.7 3.9 2.9 3.3 4.6

Fully

Percentage retiring

4.1 5.0 7.6 9.7 11.8 14.9 16.8 20.8 23.8 27.4 33.4 39.7 54.8 60.4 67.1 76.2 80.7 83.5 86.7 88.4

From FT work 3.3 3.3 5.5 6.6 7.9 10.6 12.7 15.9 18.0 20.1 26.4 31.9 44.4 47.9 54.6 61.3 65.2 68.1 71.4 76.0

Fully

Cumulative percentage retired

Observed Retirement Percentages

243 361 510 621 712 801 907 990 1,064 1,132 1,121 1,043 986 909 843 744 658 565 472 379

Observations

4.5 1.4 1.7 1.5 1.9 3.2 3.2 3.5 4.2 4.5 6.5 5.4 14.8 6.2 5.9 6.0 4.5 4.2 3.7 3.0

From FT work 3.1 0.9 1.2 1.1 1.4 2.4 2.4 2.8 3.4 3.6 5.3 4.3 10.3 4.9 4.9 5.3 4.1 4.0 3.3 2.6

Fully

Percentage retiring

4.5 5.9 7.6 9.1 11.0 14.2 17.4 20.9 25.1 29.6 36.1 41.4 56.2 62.4 68.2 74.2 78.7 82.9 86.6 89.7

From FT work

3.1 4.1 5.3 6.4 7.8 10.2 12.6 15.4 18.8 22.4 27.6 32.0 42.2 47.1 52.0 57.3 61.3 65.3 68.6 71.3

Fully

Cumulative percentage retired

Projected Retirement Percentages

Observed and Projected Retirement Percentages.

Note: Total number of observed respondents=2,231.

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Age

Table 2.

Projecting Behavioral Responses to the Next Generation of Retirement Policies 153

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

model to ﬁt the data can be seen by comparing the baseline simulations of the retirement outcomes at different ages. The spike in retirements from full-time work at age 62 and 65 are approximately the right height. Comparing the ﬂow into full retirement, the spikes at both 62 and 65 are a couple of points too low. More speciﬁcally, comparing the retirement rates from full-time in the baseline simulation results, with the observed retirement rates, the simulations catch the spike in retirements at age 62, where 14.8% of the population is simulated to retire from full-time work, where 15.1% actually retire at age 62. At 65 the actual spike in retirements from full-time work is 9.1%, while the simulations generate a peak of 6%. The underestimate of the spike in retirement at age 65 is probably due to the fact that we have not included employer health insurance. With regard to the numbers fully retiring from the labor force, the simulations catch 10.3% out of the 12.5% found to retire in the raw data at age 62, and 5.3% out of 6.7% at age 65. Table 3 presents descriptive statistics on beneﬁt claiming by age and Table 4 presents the simulated values obtained from the model. The model tracks the fraction of the population claiming Social Security beneﬁts between ages 62 and 65 fairly well, understating claiming behavior on average by a modest amount, and missing the mark most severely at age 63. According to the last column of Table 3, 47.5% of all married men claim their beneﬁts at age 62. The last column of Table 4 simulates a claiming rate of 41.3% at age 62. While the claiming rate at age 62 is affected by the fact that it is a transition year (Olson, 1999), the projected claiming rate for the

Table 3. Age

62 63 64 65 66 67 68 69

Social Security Beneﬁt Receipt by Age and Retirement Status, 1994–2002.

Retirees from Full-Time Work

Fully Retired

Partially Retired

Full-Time Working

All

72.0 83.7 86.1 92.2 92.9 95.4 92.7 94.4

75.1 86.5 87.3 91.9 93.0 94.7 93.6 95.2

60.8 73.1 80.9 93.5 92.6 98.1 89.1 90.8

9.8 17.3 24.6 59.9 74.8 76.6 79.1 81.7

47.5 61.7 68.4 84.6 89.4 92.0 91.1 93.1

Notes: Observations for 1992 were excluded because unlike the questions in later years, the 1992 question on Social Security beneﬁt receipt referred to receipt in the previous year.

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Projecting Behavioral Responses to the Next Generation of Retirement Policies Table 4. Baseline Projections of the Percentage of Married Men Collecting Social Security Beneﬁts (Assuming the Earnings Test is in Place and People Optimally Apply for Beneﬁts). Age

62 63 64 65 66 67 68 69

Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

59.9 65.1 77.1 92.3 94.8 97.2 98.5 99.2

53.5 60.0 74.8 92.0 94.4 97.1 98.4 99.1

76.4 79.0 84.0 93.3 96.1 97.7 98.7 99.2

19.4 22.7 27.8 65.8 79.2 87.0 92.3 94.7

41.3 48.1 60.1 84.7 91.0 95.2 97.4 98.5

full sample at age 63 is 48.1%, compared to an actual claiming rate of 61.7%. For ages 64 and 65, the claiming rates are 68.4 and 84.6%, while the projected claiming rates are 60.1% at age 64, and 84.7% at age 65. Again it is at age 63 that the projected claiming behavior falls furthest below the mark. Tables 3 and 4 also report actual and projected claiming rates conditional on retirement status. For example, from Table 3, ﬁrst column, the actual claiming rates for those who have left full-time work are 72.0, 83.7, and 86.1% for those 62, 63, and 64, respectively, while from the ﬁrst column in Table 4, the projections are 59.9, 65.1, and 77.1%, respectively. Table 5 strengthens our ﬁndings by demonstrating that although our model underestimates take-up rates, by allowing for heterogeneity in time preference rates it does a much better job than estimates with homogeneous time preference. While Table 5 does not involve any new estimation, the simulations set the time preference rates for all the respondents to 4%. It can be seen that at a standard time preference rate, the take-up rate on Social Security is very small. Using a constant time preference rate of 4% yields take-up rates of 7.5, 12.0, and 33.6% at ages 62, 63, and 64 compared to the observed percentages of 47.5, 61.7, and 68.4. Allowing for heterogeneous time preferences yields take-up rates of 41.3, 48.1, and 60.1. Thus heterogeneous time preference takes us most of the way to the observed values, despite the fact that the take-up rate is not used in the GMM procedure as one of the moments in the estimation. That is, without any input on observed take-up rates used in the estimation, the model still

156

ALAN L. GUSTMAN AND THOMAS L. STEINMEIER Table 5. Projections of the Percentage of Married Men Collecting Social Security Beneﬁts with Constant Time Preference Rate of 4% (Assuming the Earnings Test is in Place and People Optimally Apply for Beneﬁts).

Age

62 63 64 65 66 67 68 69

Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

7.8 12.2 43.2 85.0 89.8 94.7 97.4 98.7

7.6 11.6 43.2 85.3 89.9 94.7 97.4 98.7

8.8 15.9 43.4 83.1 88.4 94.5 97.1 98.5

7.3 11.8 21.3 62.1 74.4 83.7 90.7 94.1

7.5 12.0 33.6 76.9 85.2 92.0 96.1 98.0

Table 6. Projections of the Percentage of Married Men Collecting Social Security Beneﬁts Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62 (Assuming the Earnings Test is in Place and People Optimally Apply for Beneﬁts). Age

62 63 64 65 66 67 68 69

Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

69.6 83.5 91.9 96.7 97.7 98.5 99.0 99.4

64.7 82.0 92.3 97.1 97.7 98.5 99.0 99.4

82.0 87.3 90.4 95.7 97.7 98.5 99.0 99.3

22.5 26.7 31.6 69.8 84.8 89.8 93.4 95.1

47.6 60.1 70.4 88.6 94.3 96.5 98.0 98.7

produces take-up rates that are much closer to the observed values than would be true using standard time preference rates. Benitez-Silva, Dwyer, Heiland, and Sanderson (2007) have argued that the high take-up rate upon eligibility for Social Security beneﬁts may reﬂect a lack of conﬁdence in the Social Security system. In this spirit, the simulations in Table 6 assume that individuals expect their beneﬁts to be reduced by 1.7% per year after age 62.12 The resulting take-up percentages

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157

at ages 62–64 are within a couple of percentage points of the observed values. The 1.7% reduction rate seems to be the rate (to the nearest 0.1%), which makes the simulated percentage accepting beneﬁts in the 62–65 year range as close as possible to the reported actual percentages.

2. ABOLISHING THE RETIREMENT EARNINGS TEST BETWEEN EARLY AND NORMAL RETIREMENT AGE The Senior Citizens Freedom to Work Act of 2000 (PL 106–182) abolished the Social Security earnings test for those between the full-retirement age and 70 years of age.13 It is expected that abolishing the earnings test for those between the early and full-retirement age would further encourage later retirement.14 This is despite the fact that postponing beneﬁts results in increases in future beneﬁts that are, for many individuals, better than actuarially fair.15 2.1. Overview of the Earnings Test Issue To understand the effects of abolishing the earnings test for those between 62 and the normal retirement age, one must understand not only how retirement responds to the immediate reward for work against the beneﬁt payments that would be received should the person retire, but how different people in the population value the increased beneﬁt payments in future years that are paid when one postpones retirement. The valuation of the tradeoff between current and future beneﬁt payments may not be determined by the market interest rate alone. As we have seen in the discussion of the retirement model above, a person with a high rate of time preference and no ability to borrow at the lower rate said to obtain in the market will discount future beneﬁt adjustments more heavily than the market rate suggests.16 Heterogeneity in time preference rates may help to explain the prevalence of beneﬁt claiming at the early entitlement age, a phenomenon that researchers have had difﬁculty explaining (Coile, Diamond, Gruber, & Jousten, 2002).17 Although policy analysts are well aware of the relation of the earnings test to the timing of beneﬁt claiming (Gruber & Orszag, 1999), empirical studies of the role of the earnings test have not focused on its implications for the timing of beneﬁt claiming. Rather, much of the discussion of the earnings test has focused on the labor market behavior of those who are collecting beneﬁts. In particular, it has long been recognized

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that many people who are collecting Social Security beneﬁts, but who work part-time, stop working when their earnings just reach the annual exempt amount (Gordon & Blinder, 1980; Burtless & Mofﬁtt, 1984). Abolishing the earnings test is simulated by allowing immediate beneﬁt claiming between the early and full-retirement age without reducing beneﬁts in accordance with a person’s earnings. For those who have a high discount rate, there will be an interaction between the earnings test, beneﬁt claiming and retirement. Because beneﬁts can be claimed immediately, the opportunity cost of continued work is reduced. Before the abolition of the earnings test, the current beneﬁt is lost, and the increase in future beneﬁts is inadequate to compensate, so the individual with a high discount rate may choose to retire. After the earnings test is abolished, the same individual will be able to continue at work without having to forego the beneﬁt payment, and so may choose to stay at work. The resulting changes in full-time and part-time work among other things depend on the distributions of time and leisure preference, as well as the opportunity set, all of which are estimated by the model.

2.2. Simulations of the Effects of Abolishing the Retirement Earnings Test between 62 and Full-Retirement Age In this section we use the model, including the modiﬁcation in which people are free to choose when to claim their beneﬁts, to simulate the effects of abolishing the earnings test. This affects all respondents before age 65 and, for a substantial fraction of the sample, respondents who had already reached age 65 before the year 2000. Outcomes simulated include the effects of the earnings test on full and partial retirement and beneﬁt claiming. To brieﬂy summarize our overall ﬁndings, from age 62 through the fullretirement age, the remaining earnings test reduces the share of married men who work full-time by about four percentage points, which entails a reduction of about 10% in the number of married men of that age at fulltime work. In terms of the cash ﬂow of the system, abolishing the earnings test would have an adverse effect, at least initially. If the earnings test were abolished between the early and full-retirement ages, the share of married men claiming Social Security beneﬁts would increase by about 10 percentage points, and the average beneﬁt payments would increase by about $1,800 per recipient. The initial increase in beneﬁt payments would eventually be reversed, over a time span of decades, because the annual beneﬁt amounts

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would eventually be reduced by more than an actuarially fair amount due to the earlier collection of beneﬁts. Our model also allows us to compare the effects of abolishing the earnings test with a policy that has a more favorable effect on the cash ﬂow of the system. Instead of increasing the employment of older persons by abolishing the earnings test, their employment can be increased (by an even greater amount) by raising the early entitlement age under Social Security. A major difference on the funding side is that abolishing the earning test results in an earlier ﬂow of beneﬁt payments from Social Security, worsening the cashﬂow problems of the system, while increasing the early entitlement age delays the ﬂow of beneﬁt payments from the system, improving its liquidity. 2.2.1. Implications for Retirement Outcomes Table 7 reports the differences in retirement outcomes between a simulation in which the earnings test is eliminated and the baseline results. There are two notable effects on retirement from abolishing the earnings test. As seen in the next to last column, from ages 62 to 65, the percentage retired from full-time work is reduced by about four percentage points per year. With less than half the labor force still at full-time work, this entails an increase of about 10% in full-time work by that population. Some of those who remain at full-time work come from the ranks of the partially retired. As a result, there is a much smaller effect on the fraction of Table 7. Differences in Retirement Outcomes between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Testa. Age

60 61 62 63 64 65 66 67 68 69 a

Percentage Retiring

Cumulative Percentage Retired

From full-time work

Fully

From full-time work

Fully

0.0 0.0 3.8 0.3 0.1 0.1 0.8 0.5 0.5 0.4

0.0 0.0 1.3 0 0.2 0.1 0.3 0.0 0.1 0.1

0.0 0.1 3.9 4.2 4.3 4.2 3.5 2.9 2.5 2.2

0.1 0.1 1.3 1.3 1.6 1.7 1.4 1.3 1.2 1.1

Figures in the table are calculated as the retirement outcome predicted without an earnings test in place minus the retirement outcome predicted with an earnings test in place.

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the labor force that is fully retired, ranging between a 1 and 2 percentage point decrease. Notice the effect on the retirement spike at age 62 from abolishing the earnings test. The earnings test creates a link between the reward to work from continuing at full-time employment and the desire to claim Social Security beneﬁts at age 62 for those with a high discount rate or low actuarial reward to postponed beneﬁt receipt. This link encourages 3.8% of the population to retire at age 62 who would not otherwise retire if that link were not there. Therefore abolishing the earnings test would reduce the spike in retirements at age 62 by about 3.8 percentage points. One other ﬁnding should be noted. In these simulations, abolishing the earnings test between early and full-retirement age increases by 2–3 percentage points the fraction at full-time work throughout the age range from 66 to 69. There are two reasons for this ﬁnding. First, a number of those in the sample were born too soon to beneﬁt from the abolition of the earnings test for those over the age of 65 in 2000. Second, others in the sample who were born in later years are facing an age 66 of entitlement for full beneﬁts. 2.2.2. Implications for the Percent Collecting Social Security Beneﬁts by Age and the Flow of Social Security Beneﬁts and Taxes Table 8 projects the likely effect of abolishing the retirement earnings test on beneﬁt claiming. The increase in claiming by the population ages 62–64, seen in the last column of Table 8, is 10–13% of the sample. By far the bulk of the increase in beneﬁt payments are projected to come from the ranks of those Table 8. Differences in Percent Collecting Social Security Beneﬁts between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Test. Age

62 63 64 65 66 67 68 69

Differences in Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

2.1 1.6 0.5 0.3 0.0 0.2 0.1 0.0

1.5 1.0 0.8 0.1 0.1 0.0 0.1 0.1

1.3 0.8 1.6 1.9 0.9 0.8 0.6 0.3

26.2 30.8 40.2 22.4 12.9 9.1 6.4 4.8

10.5 11.0 13.2 6.4 3.1 1.9 1.2 0.8

Projecting Behavioral Responses to the Next Generation of Retirement Policies

161

Table 9. Differences in Social Security Taxes and Beneﬁts between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Test. Age 50 55 60 61 62 63 64 65 66 67 68 69 70 75 80 85 90 95

Taxes

Beneﬁts

0 3 2 3 84 90 101 111 90 79 67 57

4 34 98 161 1,487 1,813 2,322 1,722 1,020 674 310 80 503 809 750 574 380 210

holding full-time jobs, with 20–40% of persons remaining at full-time work claiming beneﬁts at each year of age between 62 and 64 should the earnings test be abolished, with claiming increased through the age of 69. Table 9 details the changes in Social Security taxes paid and beneﬁts received between simulations with and without the earnings test. Both taxes and beneﬁts are weighted by the probability the individual survives to pay or collect them. The changes in Social Security taxes paid and beneﬁts received are dependent both on changes in claiming behavior and on changes in employment induced by the removal of the earnings test. For those between the ages of 62 and 66, beneﬁts are increased substantially after the abolition of the earnings test, ranging from $1,000 to $2,300 in additional beneﬁts at each year of age. To attain actuarial balance, from age 70 onward, beneﬁts are substantially reduced. Thus the abolition of the earnings test accelerates beneﬁt payments by the Social Security Administration forward, and although reclaimed from a generation within the span of its lifetime, these payments are not reclaimed for the system for many years. That is, because the system is actuarially fair or more than actuarially fair, there is no loss to the system in present value terms from abolishing the earnings test, and perhaps even a small gain over the individual’s lifetime. However, by the

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time the accelerated payments made to the ﬁrst generation are recaptured, younger cohorts will be enjoying accelerated payments. Thus the system will take a hit to its liquidity on a one-time basis that in a simple steady state would perhaps never be offset.

2.3. Abolish the Retirement Earnings Test between Early and Normal Ages or Raise the Early Entitlement Age to 64? In an earlier paper, we examined the effects of increasing the early entitlement age for Social Security beneﬁts from 62 to 64 (Gustman & Steinmeier, 2005a). This is a policy that we expect to have similar effects on retirement as eliminating the earnings test between early and full-retirement age. But we also expect raising the early entitlement age to have a more favorable effect on the liquidity of Social Security ﬁnances.18 2.3.1. Implications for Retirement Outcomes Column 3 of Table 10 indicates that increasing the early entitlement age to 64, leaving the earning test in place, would reduce the ranks of those retired from full-time work by over 7 percentage points at ages 62 and 63. In contrast, Table 7 suggested that eliminating the earnings test would Table 10. Age

58 59 60 61 62 63 64 65 66 67 68 69 a

Effect on Retirement of Increasing the Early Entitlement Age to 64a. Percentage Retiring

Cumulative Percentage Retired

From full-time work

Fully

From full-time work

Fully

0.1 0.1 0.2 0.4 6.5 0.5 7.3 0.2 0.2 0.2 0.2 0.1

0.1 0.1 0.2 0.4 4.1 0.4 5.1 0.1 0.2 0.2 0.2 0.2

0.2 0.3 0.4 0.8 7.3 7.8 0.6 0.4 0.3 0.0 0.1 0.2

0.3 0.3 0.5 0.8 4.8 5.2 0.2 0.1 0.1 0.3 0.5 0.7

Figures in the table are calculated as the retirement outcome predicted an age 64 early entitlement age minus the retirement outcome predicted with an age 62 early entitlement age.

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Projecting Behavioral Responses to the Next Generation of Retirement Policies

reduce the ranks of the retired by about 4 percentage points at each year of age from 62 to 66, and by a smaller amount at older ages. Counting the labor market effects after age 66, eliminating the earnings test appears to have a more powerful effect on the percentage at full-time work, primarily due to the fact that the earnings test still affected many in the HRS sample who turned 65 before the year 2000. On the other hand, raising the early entitlement age appears to have a larger effect on the rolls of those who are fully retired. Overall, the percent retired from full-time work will be higher with an age 64 early entitlement age than under a regime where the earnings test is abolished. Compared to a regime with no earnings test, a regime with age 64 early entitlement would have 3.4 and 3.6 percentage points fewer people retired at ages 62 and 63, an additional 3.7 and 3.8 percentage points retired at 64 and 65, and would exhibit a 2.4–3.2 percentage point increase in the percentage retired from full-time work at each year of age from 66 to 69.

2.3.2. Implications for Beneﬁt Claiming Table 11 shows the strong and obvious effect on beneﬁt claiming of raising the early entitlement age to 64. From the last column in Table 11, we see that raising the early entitlement age to 64 would reduce the overall claiming by more than 40 percentage points at ages 62 and 63, and by more than 50 percentage points as compared to a scenario where the earnings test is eliminated. The comparison continues to be negative after age 64, largely

Table 11.

Effect on Beneﬁt Claiming of Increasing the Early Entitlement Age to 64.

Age

62 63 64 65 66 67 68 69

Differences in Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

59.9 65.1 0.6 0.2 0.1 0.1 0.0 0.0

53.5 60.0 0.6 0.2 0.1 0.1 0.0 0.0

76.4 79.0 0.6 0.3 0.3 0.1 0.0 0.0

19.4 22.7 0.7 0.5 0.1 0.0 0.2 0.2

All 41.3 48.1 0.5 0.1 0.1 0.1 0.0 0.0

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

because the elimination of the earnings test increases beneﬁt claiming by those who remain at full-time work.

2.3.3. Implications for the Flow of Taxes and Beneﬁts In Table 12, we see the effect of increasing the age of early entitlement on the ﬂow of taxes and beneﬁts. The impact on the ﬂow of taxes is relatively minor. However, postponing the early entitlement age to 64 would result in a reduction in beneﬁt payouts. It would take 15 or 20 years before the missed beneﬁts are compensated for by higher subsequent beneﬁt payments, thus working in the direction of reducing, at least for a time, the cash-ﬂow problems of the system. In sum, the earnings test and increased early entitlement age have similar effects on retirement and taxes, while the effects of raising the early entitlement age is beneﬁcial from the perspective of the liquidity problems of Social Security, with more favorable take-up rates and reductions in receipt of beneﬁts at younger ages.

Table 12. Age 50 55 60 61 62 63 64 65 66 67 68 69 70 75 80 85 90 95

Effect on Social Security Taxes and Beneﬁts Claiming of Increasing the Early Entitlement Age to 64. Taxes

Beneﬁts

0 1 13 23 166 176 10 6 2 3 8 10

5 42 175 313 2,738 3,532 529 502 436 82 249 433 545 825 774 609 420 239

Projecting Behavioral Responses to the Next Generation of Retirement Policies

165

2.4. How are Policy Estimates Affected if Respondents Expect Future Reductions in Social Security Beneﬁts? One might argue that the underestimation of the take-up rates by our model will affect the estimates of the policy simulations, particularly the simulation of abolishing the earnings test. In this next exercise, we compare the effects of the earnings test using a model, which better reproduces the actual takeup rates with the effects of the earnings test in the base model. Speciﬁcally, we compare two simulations where the beneﬁts are expected to be reduced by 1.7% per year from promised levels. One simulation uses the actual earnings test and the other eliminates it. The baseline simulation where Social Security was expected to introduce a beneﬁt reduction of 1.7% was presented in Table 6. When the earnings test is eliminated, the effects of the earnings test on retirement are little changed. Maintaining the 1.7% reduction in beneﬁts throughout, the effects of abolishing the earnings test on retirement can be seen in appendix Table A2, which is comparable to Table 7 where beneﬁts are not expected to decline. The effects on take-up are somewhat greater in appendix Table A3 than in Table 8 at ages 65 and earlier. The effects on taxes (appendix Table A4 vs. Table 9) are minimal (which we would expect if retirement is not much changed), and the effects on beneﬁts are 20–30% greater. Comparable ﬁndings simulating the effects of raising the early entitlement age are found in appendix Tables A5–A7.

3. EFFECTS OF CHANGING MINIMUM HOURS CONSTRAINTS A minimum hours constraint is a limitation imposed by the ﬁrm requiring a minimum number of hours of work for a speciﬁed job. It has been known for some time that most jobs do not permit a person to retire gradually by reducing hours of work.19 The choice facing most workers on their longterm jobs is to work full-time or not at all. Theory tells us that in the absence of any constraints (minimum hours constraints or a ﬁxed cost of work), most people would prefer to reduce their time at work gradually as they age. Moreover, given the higher wage paid on jobs held for a long time, they would prefer to partially retire on their long-term jobs. As a result of the minimum hours constraints imposed by their employers, however, they are not free to do so.20 Consequently, the predominant retirement path is from

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

full-time work to complete retirement, with a signiﬁcant fraction, but still a minority, passing through partial retirement (Gustman & Steinmeier, 1984b, 2000).21 Should tighter labor markets encourage ﬁrms to relax their minimum hours constraints, the frequency of partial retirement will increase, while both full-retirement and full-time work will become less common. To simulate the effects of removing minimum hours constraints, all individuals are assumed to be able to switch to partial retirement in their full-time job with no change in wage rate, so they are paid half the earnings for half the work. This affects all respondents except those in full-time jobs which began prior to age 50 and which would allow half-time work in those jobs. Implicitly, this assumes that respondents could collect their full pensions at the age they change from full-time work to part-time work. Thus the simulation assumes the policy change deals with two of the major issues limiting part-time work; hour’s constraints are relaxed and in addition, the current law prohibiting paying a pension to a person who continues to work for the ﬁrm is eliminated.22 A comparison of panel 2 with panel 1 of Table 13 clearly indicates that if demand side changes persuaded ﬁrms to allow partial retirement at the same hourly wage as earned on the long-term job, this would generate a major change in retirement outcomes. The percent of the labor force that passed through partial retirement would increase from about three tenths to about two thirds. To make the differences easier to follow, the ﬁrst panel of Table 14 reports the difference in retirement outcomes between a simulation

Table 13.

Results of Retirement Simulations from Relaxing the Indicated Factor (Numbers Reported are in Percentages).

Age

55

58

60

62

65

67

69

Percent into Partial Retirement

Full sample baseline Percent fully retired Percent partially retired Percent not retired

8.8 4.1 87.1

17.5 6.4 76.1

26.5 8.7 64.8

40.2 13.5 46.3

56.5 15.7 27.8

66.1 15.5 18.4

76.7 13.0 10.3

29.9

No hours limits Percent fully retired Percent partially retired Percent not retired

6.4 11.9 81.7

12.8 18.6 68.6

19.6 24.8 55.6

29.7 33.5 36.8

42.4 37.8 19.8

50.8 36.7 12.5

62.9 29.9 7.2

66.9

Notes: Sample size=2,231. Based on model with parameter estimates as shown in Table 3.

Projecting Behavioral Responses to the Next Generation of Retirement Policies Table 14. Age

167

Retirement Outcomes: No Constraints on Partial Retirement Versus Current Restrictions (Numbers Reported are in Percentages). 55

58

60

62

65

67

69

Percent fully retired 2.4 4.7 6.9 10.5 14.1 15.3 13.8 Percent partially retired 7.8 12.2 16.1 20.0 22.1 21.2 16.9 Percent not retired 5.4 7.5 9.2 9.5 8.0 5.9 3.1

Percent into Partial Retirement 37.0

where there are no constraints on partial retirement and a simulation with the current restrictions on partial retirement. From the ﬁrst row, when partial retirement is unconstrained, the fraction fully retired declines by 4.7 to 14.1 percentage points at each year of age between 58 and 65. For ages 67 and 69, the number who are fully retired falls by 15.3 and 13.8 percentage points, respectively. From row three, the percent who are not retired at all also declines. The percentage not retired falls at each age, from a reduction of 7.5 percentage points at age 58 to a reduction of 8 percentage points at age 65. The reductions in full-time work and in complete retirement ﬂow into the ranks of the partially retired. Comparing the change in the percent fully retired from full-time work with the change in the percent partially retired, the effect on total earnings is roughly a wash, or perhaps suggests a slight decline. The increase in partial retirement is roughly twice the reduction in full-time work. Since the simulation suggests twice as many hours worked in a full-time job as when partially retired, this change suggests that work lost through acceleration of retiring from full-time work is roughly balanced by the fact that twice as many people now work part-time. On balance, roughly half the increase in partial retirement comes from full-time work, and half comes from full retirement, but the amount coming from full retirement increases with age, while the amount coming from the ranks of the not retired is greatest in the age range from 58 to 65. For those 65–69, the opportunity to work part-time increases the number partially retired by about 20 percentage points. It reduces the number working full-time by 8, 5.9, and 3.1 percentage points at ages 65, 67, and 69, respectively. Consequently, for those 65 and above, the increase in part-time workers is much greater than twice the decline in full-time workers, suggesting a 3–5 percentage point increase in full-time work equivalents from ages 65 to 69. In this age range, partial retirement becomes three or four times more common than full-time work, as compared to being roughly equally common in the current environment.

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4. HOW DO PROVISIONS OF VOLUNTARY PERSONAL ACCOUNTS AFFECT RETIREMENT? To simulate behavioral responses to voluntary personal accounts, we use current law projections, meaning that the population is assumed to have been covered over their full lifetimes by the ﬁnal set of Social Security rules now on the books. These rules include a normal retirement age of 67, a delayed retirement credit of 8%, and a payroll tax contribution of 10.6% of wages. The policies are simulated by altering the budget constraint described above to build a baseline partial, voluntary personal account system, and then to simulate the effects of changing various features of the system. The incentives created by each alternative proposal generate behavioral responses. Given the resulting earnings histories and the choice to participate in a voluntary personal account, there is a string of tax contributions to the conventional system and to the personal accounts. The course of the conventional beneﬁts depends both on the offset rule adopted for reducing conventional beneﬁts when a person chooses to participate in a voluntary personal account, and on claiming behavior. Alternative policies will create different substitution and wealth effects. Under the current system, beneﬁt recomputation means that a person who has been working 35 years enjoys a gain in beneﬁts from another year of work that depends on the relation of earnings in the marginal year to the lowest indexed earnings used in computing Average Indexed Monthly Earnings (AIME) among all previous years of work. After discounting, the marginal value of any additional future beneﬁts less the value of foregone beneﬁts will be added to the wage to determine the value of total compensation from continued work. If there are partial voluntary personal accounts, and if the interest rate earned on assets in the personal account is high enough, the substitution effect from a personal account may encourage a further delay in retirement. As long as beneﬁts are higher with the personal account than without it, there also will be a wealth effect; but that will encourage earlier retirement. A major caveat pertains to the absence of adjustments for risk. The additional beneﬁts resulting from the higher return on personal accounts are not risk adjusted. We use a long run historical return for a mixed stock and bond portfolio that is meant to be reasonably conservative. Thus we assume that 45% of the portfolio is invested in treasury notes. However, we do not assume here that participants treat the equity premium, any additional returns to stocks over bonds, as due solely to risk. As a ﬁrst approach to

Projecting Behavioral Responses to the Next Generation of Retirement Policies

169

dealing with risk, we vary the discount rate. In particular, we use a lower interest rate than 4.31% real. Thus one way to interpret these results is as a sensitivity analysis to risk adjustment of the returns to the portfolio. Another is as a sensitivity analysis to the assumed level of returns in the absence of risk adjustment. It is important to note that because we ignore the risk of further declines in Social Security beneﬁts, there is some balance in our assumptions. That is, although there is no risk adjustment in the returns to the personal accounts, there also is no risk adjustment to Social Security beneﬁts under to reﬂect perceived political risk. Only one type of risk is explicitly taken into account. Respondents do value the insurance provided by the annuity.

4.1. Structure of Baseline Voluntary Personal Accounts We begin by specifying a baseline voluntary personal account, and then explore the effects of changing some of its key characteristics. The baseline voluntary personal accounts are presumed to work the following way. At the time the individual registers for beneﬁts, the Primary Insurance Amount (PIA) is reduced to take into account the contributions to the personal accounts.23 The resulting amount is the modiﬁed PIA. The voluntary personal account is divided into two parts. One part is required to be annuitized into a real annuity at the real interest rate and brings the total of the PIA plus the required annuity up to a minimal level. The other part is allowed either to be taken as a lump sum or annuitized, as the individual prefers. Further details of the process are contained in the following paragraphs. The baseline accounts are ﬁnanced with a 4 percentage point payroll tax rate taken from current payroll taxes. It is assumed that the accounts are voluntary. Accordingly, total utility is calculated both with and without the personal accounts, and the individual is presumed to choose whichever yields the most utility. This is an either/or decision; either the individual eschews voluntary personal accounts completely or invests in them to the permissible amount. We do not examine the case where the contribution decisions can differ year to year. Nor do we examine cases where the wife’s participation decision is different from the husband; if the husband chooses personal accounts, the wife does as well. In the baseline package, there is a minimum required annuity. The sum of the traditional beneﬁt (PIA) plus required annuities from the personal accounts for the two spouses must reach the family poverty level. After that the beneﬁciary is free to take the payment as a lump sum, beginning at age

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

62.24 At the time of the individual’s application, the sum of the individual’s PIA plus the spouse’s then current PIA is subtracted from the family poverty level. The difference is what the two required annuities must cover. The required annuity for the individual is the total required annuity times the ratio of the individual’s PIA to the sum of the two PIA’s. There are other assumptions underlying the speciﬁcation of the basic package of voluntary personal accounts. The earnings test is assumed to apply proportionately to the two beneﬁts. That is, the test is applied to the sum of the traditional beneﬁts plus the required annuities to calculate the percent of beneﬁts that are lost.25 Any sum accumulated in the personal accounts above the required level of annuitization is presumed to be available as a lump sum payment at age 62.26

4.2. Participation in Voluntary Personal Accounts Each simulation is done twice, one in which personal accounts are available and one in which they are not. The one with the highest lifetime total utility is presumed to be chosen. Since there is no uncertainty regarding the returns, almost all of the middle- and high-income households choose personal accounts, and most of the low-income households do as well, especially those who retire at younger ages. Participation in these voluntary personal accounts is very high. This is not a behavioral outcome, but is the result of construction of the model. We have assumed away uncertainty in the returns to the account. When we tabulate the proportion choosing personal accounts, since there is no stock market investment risk in this model, most people choose to participate. Only about 2% of all husbands from two-earner households choose not to participate, and among the bottom third of earners, 5% choose not to participate. When the individual is allowed to fully withdraw beneﬁts in the form of a lump sum, participation in personal accounts rises to above 99%, with 98% of the low earners choosing to participate.

4.3. Voluntary Personal Accounts and Retirement Outcomes Table 15 presents retirement outcomes at age 62 under alternative speciﬁcations of systems of personal accounts. The ﬁrst three columns report the cumulative levels of the fractions of married men who are not

Projecting Behavioral Responses to the Next Generation of Retirement Policies Table 15.

171

Retirement Outcomes under Alternative Systems of Voluntary Personal Accounts. Retirement Status at Age 62 Retirement Rate Not Partially Fully from FT retired retired retired Work

Program features (variation from base package) 1. Current law projections of traditional Social Security

41.9

14.3

43.8

15.6

Revised systems with voluntary personal accounts 2. Base package of personal accounts 3. Total conversion to personal accounts 4. Full annuitization required 5. Annuitization optional, full lump sum withdrawal permitted

32.8 27.9 36.7 31.2

9.6 8.9 15.0 8.5

57.6 63.2 48.3 60.3

21.6 23.3 18.9 23.0

retired, partially retired, and fully retired. The last column reports the percent retiring from full-time work at age 62. For purposes of comparison, line 1 of Table 15, and subsequent tables, report retirement outcomes assuming provisions of current law were fully implemented for the entire work lives of the sample of married HRS respondents. By age 62, almost 44% of the population of married men is projected to be fully retired, with almost 42% reporting themselves as not retired. At age 62, column 4 indicates that 15.6% of married men are retiring from full-time work. Line 2 indicates retirement under the baseline reform package of personal accounts. As seen by comparing lines 1 and 2 of Table 15, the base package of voluntary personal accounts substantially increases retirements by age 62, raising the percent fully retired from 43.8% to 57.6%, while reducing the fraction not retired by 9.1 percentage points, and reducing the fraction partially retired by 4.7 percentage points.27 There are a number of major forces operating to inﬂuence retirement under the baseline system of voluntary personal accounts. First, there are the conventional substitution and income effects. Given the higher return to investment, the system of voluntary personal accounts raises total beneﬁts in retirement, creating an income effect encouraging earlier retirement. On the other hand, under a system of personal accounts, there is a greater reward to continued work for higher income people who otherwise would be in the 15% PIA bracket.

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

Row 3 of Table 15 reports retirement outcomes under a system where the conventional Social Security payroll tax may be entirely converted to a voluntary personal account. Comparing lines 2 and 3 thus allows comparison of a system with partial conversion to personal accounts, i.e., a system based on 4 percentage points of a payroll tax, with a system where the full 10.6% payroll tax may be converted to a voluntary personal account. While the fraction fully retired at age 62 is 57.6% under a system where the account may include up to 4 percentage points of the payroll tax, it is 63.2% where the full payroll tax may be included in the account. The fraction not retired would decline from 32.8% under a partial system of personal accounts, to 27.9% if the full payroll tax could be included in the personal account, and there would be a 0.7% difference in the fraction partially retired. To clarify the reasons for differences in retirements between the current system and a system of voluntary personal accounts where lump sum beneﬁts are not permitted, it is useful to compare retirement outcomes between rows 1 and 4 of Table 15. Row 1 represents the current law projections, while row 4 represents a system of partial personal accounts where full annuitization is required, so that the option to take lump sum beneﬁts does not cause those with high time preference to choose the personal accounts. We see that labor force participation is about 5 percentage points higher at age 62 under the current system than under a system of partial personal accounts that require full annuitization. The main reason is the wealth effect resulting because the level of beneﬁts is higher for most of the population under the partial personal accounts, noting that we reduce assumed returns in light of risk, and the caveats about implicit risk attached to Social Security versus the failure to discount the equity premium in the mixed portfolio we have chosen. Complicating any comparison, the effects are not evenly distributed throughout the population. For one thing, the differences in beneﬁt levels depend on the level of earnings, and in particular on where the individual’s earnings fall relative to the bend points in the PIA formula. Second, for similar reasons, there are different marginal returns to continued work under the two systems. For some lower earners with intermittent job histories, they may be higher under the current system. Not only is a low earner subject to a much higher replacement rate under the AIME formula, but also under beneﬁt recomputation, if the individual did not work for 35 years, any earnings are replacing a zero in the AIME formula. Under voluntary personal accounts, marginal returns to continued work are likely to be higher for those with higher earnings than they are under the current formula. The marginal increase in beneﬁts under the

Projecting Behavioral Responses to the Next Generation of Retirement Policies

173

current PIA formula will be 32%, or for many higher earners, 15%. High earners who have worked for 35 years will ﬁnd that their AIME increase from another year of work is smaller as current earnings replace the lowest earnings year in their work history, rather than a year with zero earnings for a very low earner. Thus the differences in the marginal reward to continued work after age 62 depend not only on the level of earnings, but also on the length of work life and the slope of the earnings proﬁle over the life cycle (ﬂat or steep). The differences in marginal rewards to continued work under the two systems will also depend on the spouse’s AIME from own earnings.

4.4. The Choice between Lump Sum Payments and Annuitized Beneﬁts Deﬁned contribution pension plans often offer the option of a lump sum. Indeed, DC plans rarely offer the option of annuitizing beneﬁts. In the case of personal accounts, the presumption is that even though the system is switching from a deﬁned beneﬁt to a deﬁned contribution approach, the deﬁned contribution plan will come with an annuity. Retirement may be affected by whether beneﬁts are offered only as an annuity as under the conventional Social Security program, or whether beneﬁts may be taken as a lump sum. Those with high time preference rates, especially those in the population with a time preference rate well above the interest rate, who are more likely to accrue little saving, are more likely to value a lump sum beneﬁt over an annuity that is of equal present value. For these people, allowing lump sum payouts may create a stronger incentive to retire early. When a lump sum is claimed by those with little other saving, it is likely to be consumed over the next few years, driving down the marginal utility of income from work. As a result, many of those with a high rate of time preference will leave work at age 62. Lines 4 and 5 of Table 15 clarify the effects on retirement of allowing lump sum beneﬁts. The simulation in line 4 pertains to a system requiring that all beneﬁts from personal accounts be fully annuitized. The higher return to personal accounts creates a wealth effect that exceeds the substitution effect, and thus encourages earlier retirement. The underlying interest rate is well below the time preference rates estimated above for an important fraction of the population, so these individuals will retire early just as they did when facing the conventional beneﬁt structure. However, they do not receive a lump sum beneﬁt, and thus place a higher value on work around age 62 than they would if a lump sum beneﬁt were available.

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

Requiring complete annuitization of beneﬁts from the personal account would reduce the fraction fully retired at age 62 down to 48.3%. Remember that the availability of lump sum beneﬁts at age 62 is not conditioned on whether a person is working. The earnings test applies only to beneﬁts from the conventional system plus beneﬁts from the annuities paid out of the personal account. The present simulations do not provide a mechanism for clawing back any lump sum payments at age 62 should the individual continue working in a job offering long-term employment. Comparing rows 1, 2, and 4 helps us to decompose the decrease in retirement when transitioning from the current system to the baseline system of partial voluntary personal accounts. This comparison suggests that 9.3 percentage points of the increase in the fraction fully retired (column 3, row 2 minus row 4) results from the depressing effect of the lump sum payment at age 62 on the marginal utility of work, and 4.5 percentage points of the increase in retirements (row 4 minus row 1) is due to the income effect from receiving higher retirement beneﬁts, net of substitution effect resulting from a higher reward to work at later ages. Analogously, the fraction retiring at age 62 is 18.9% when full annuitization is required, up from 15.6% under the current system, but would rise to 21.6% under the basic, voluntary partial personal account plan. There is a further effect from introducing personal accounts. Speciﬁcally, a 4.7 percentage point reduction in the fraction partially retired appears to be almost entirely due to the effects of making lump sum payments available at age 62, with their depressing effects on the marginal utility of consumption for those with high discount rates, rather than to the wealth effect of the higher returns to personal accounts. When the package of voluntary personal accounts is introduced, partial retirement falls from 14.3% to 9.6%. Accordingly, introducing personal accounts reduces work effort by reducing both full-time work and partial retirement.28 However, 15% of the population chooses partial retirement when voluntary personal accounts are introduced, but lump sum beneﬁts are not available, so the income effect from personal accounts explains almost none of the decline in partial retirement. Column 4 of Table 15 shows that the fraction leaving full-time work increases from 15.6% under the current system to 21.6% under the basic voluntary system. Alternatively, as seen in Row 5 of Table 15, if complete lump sum withdrawals were permitted, i.e., even those with below poverty incomes were not forced to annuitize a minimum beneﬁt, full retirement would rise to 60.3%, with only 31.2% not retired at age 62. We also conducted a number of other simulations. One result is that the choice of offset method used to reduce traditional beneﬁts has little effect on

Projecting Behavioral Responses to the Next Generation of Retirement Policies Table 16.

175

Wealth by Age Conditional on Both Spouses Living (in 1992 Dollars, Unadjusted for Mortality). 61

62

70

Program features (variation from base package) 1. Current law Social 140,028 148,305 155,113 Security 2. Base package of 111,601 138,839 123,891 personal accounts 3. Total conversion to 83,907 132,864 115,582 personal accounts 4. Full annuitization 113,228 120,313 111,607 required 5. Annuitization 111,600 140,271 124,077 optional, full lump sum permitted

75

80

85

90

122,812

88,634

56,404

29,148

95,909

67,239

41,430

20,545

88,687

61,425

37,339

18,108

87,957

62,797

39,205

19,528

96,008

67,277

41,448

20,551

Notes: Base package=current law traditional beneﬁts, voluntary, partial (4% of contribution) accounts, prorated traditional beneﬁts, annuitize to family poverty level, joint and 2/3 annuity, required personal accounts subject to earnings test.

retirement outcomes.29 Further simulations show the larger the required annuitization, and thus the smaller the lump sum beneﬁts that can be claimed, the lower the retirement rate as a result of adopting personal accounts. To provide symmetric results for saving behavior, Table 16 shows the total value of non-pension, non-Social Security wealth that is accumulated under alternative plans. Components of wealth measured by the HRS include retirement assets such as IRAs, real estate, business and ﬁnancial assets, and other forms of wealth (see Gustman & Steinmeier, 1999 for a detailed analysis). Comparing rows 1 to 3 at various ages, total non-pension, non-Social Security wealth is lower where voluntary personal accounts are more valuable, suggesting there is some substitution between personal accounts and these other forms of wealth. As seen in Table 17, simulations for the basic package of personal accounts suggests that 46.2% will choose a lump sum payment, 48.5% will choose a voluntary annuity, and 5.4% will not have sufﬁcient annuitized beneﬁts to allow them to take a lump sum. That is, they will not have an annuity equal to the family poverty level. The earlier one retires the greater the proportion choosing to accept a lump sum payment from their personal accounts rather than annuitizing funds available for a voluntary annuity. For example, as seen in Table 17, for the base package of personal accounts, almost two thirds of those retiring in their early ﬁfties choose to take a lump

176

ALAN L. GUSTMAN AND THOMAS L. STEINMEIER Table 17.

Percent Choosing Voluntary Annuities under Base Package of Voluntary Personal Accounts.

Age Retired from FT Work 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 All

No Funds Available

Lump Sum

Voluntary Annuity

9.0 3.9 3.9 1.1 1.5 1.6 3.0 1.6 2.7 3.0 3.2 3.8 7.2 8.3 8.9 6.5 5.5 3.0 4.6 6.2 8.8 5.4

60.9 64.9 64.2 63.3 57.3 56.5 49.5 50.4 45.5 46.7 40.1 46.4 69.7 20.5 18.8 20.6 19.9 20.6 22.0 22.7 37.0 46.2

30.1 31.2 31.9 35.6 41.2 41.8 47.5 48.1 51.8 50.2 56.7 49.8 23.1 71.1 72.3 72.8 74.6 76.4 73.4 71.1 54.2 48.5

sum settlement when they reach age 62, while 40–47% of those retiring between 58 and 62 choose a lump sum settlement. Seventy percent of those retiring at exactly 62 choose a lump sum settlement. Among those retiring from age 63 on, only about a ﬁfth will choose a lump sum settlement over annuitized beneﬁts. Table A8 in the appendix shows how the proportion choosing lump sum versus voluntary annuities out of the discretionary funds in the voluntary personal accounts varies among the different plans. Discretionary funds are those in excess of any annuity that is required to ensure that retirement income meets the minimum level speciﬁed in the plan. For most variations of the personal account plans, about half of participants choose to take their beneﬁts from the personal account as a lump sum. We will see below that the decision to accept a lump sum beneﬁt will affect the distribution of retirement income at different ages.

177

Projecting Behavioral Responses to the Next Generation of Retirement Policies

4.5. Beneﬁts by Age Despite having only modest effects on retirement, the features of these alternative systems have major effects on retirement incomes of the covered populations. Where annuitization is not mandatory, as noted in Table 17, many will choose to take lump sum payments at age 62. Thus we see in Table 18A in those programs where lump sum payments are permitted, i.e., in rows 2, 3, and 5, the average beneﬁt taken at age 62 (in 1992 dollars) is equal in dollar amount to two to four times the average yearly annuitized beneﬁt paid at age 70. In contrast, as seen in row 4 of Table 18A, in plans for voluntary personal accounts where full annuitization is required, the average beneﬁt taken at age 62 is much lower than the average beneﬁt at age 70, as many put off beneﬁt claiming until a later age. Moreover, within those plans allowing a lump sum payment, the lower the required annuity, and the higher the permitted lump sum, the smaller the yearly beneﬁt at older ages compared to the beneﬁt at age 62. One issue is how widows will fare if lump sum beneﬁts are claimed at age 62, either by the family when both spouses are alive, or by the widow. Table 18B shows that spouses on average will be just as well off under the

Table 18A. Traditional Social Security Beneﬁts Plus Beneﬁt from Voluntary Personal Accounts by Age of Receipt, Assuming Husband and Wife are Alive (Unadjusted for Mortality, in 1992 Dollars). 62 Program features (variation from base package) 1. Current law projections of 3,679 traditional Social Security 2. Base package of personal 48,147 accounts 3. Total conversion to personal 92,830 accounts 4. Full annuitization required 7,044 5. Annuitization optional, full lump 52,012 sum withdrawal permitted

70

75

80

85

16,139

16,906

17,059

17,059

18,665

17,444

17,347

17,407

21,791

21,432

21,113

21,192

20,978 18,386

21,898 17,110

22,078 16,999

22,128 17,061

Notes: Base package=current law traditional beneﬁts, voluntary, partial (4% of contribution) accounts, prorated traditional beneﬁts, annuitize to family poverty level, joint and 2/3 annuity, required personal accounts subject to earnings test.

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

Table 18B. Traditional Social Security Beneﬁts Plus Beneﬁt from Voluntary Personal Accounts by Age of Receipt, Assuming Only Wife is Alive (Unadjusted for Mortality, in 1992 Dollars). 62 Program features (variation from base package) 1. Current law projections of 1,061 traditional Social Security 2. Base package of personal 45,127 accounts 3. Total conversion to personal 89,992 accounts 4. Full annuitization required 3,861 5. Annuitization optional, full lump 49,001 sum withdrawal permitted

70

75

80

85

9,546

10,780

10,999

11,061

12,400

11,364

11,296

11,367

15,091

14,469

14,098

14,166

13,304 12,237

14,244 11,149

14,413 11,067

14,461 11,140

Notes: Base package=current law traditional beneﬁts, voluntary, partial (4% of contribution) accounts, prorated traditional beneﬁts, annuitize to family poverty level, joint and 2/3 annuity, required personal accounts subject to earnings test.

baseline system of partial privatization as under the current program, assuming the 4.31% real return to the personal account portfolio. Scanning down the beneﬁts by program for 85 year olds, widow’s beneﬁts will be higher than under the current program only if there is complete conversion of the current system to personal accounts, or if under a plan with partial personal accounts, annuitization is mandatory. The average beneﬁts by program and by age do not tell the full story. There will be a distribution of beneﬁts at each age that depends on the distribution of choices made as to whether to participate in the personal account (most will), and as to whether to take a lump sum beneﬁt, or to fully annuitize the assets in the personal account. 4.6. Taxes and Beneﬁts under Personal Accounts Total taxes and beneﬁts over the lifetime are shown in Table 19, where taxes and beneﬁts are shown in 1992 dollars, adjusted for mortality, but not discounted. Total taxes paid decline by 1.2% under the baseline voluntary personal account program, compared to the current law projections for traditional Social Security beneﬁts. In addition to the decline in total taxes paid, there is a much larger decline in taxes paid into the trust fund as taxes are diverted to personal accounts. For the baseline personal account program,

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Table 19. Taxes and Expected Family Beneﬁts from Social Security and Voluntary Personal Accounts (in 1992 Dollars, Adjusted for Mortality, but not Discounted). Sum Over Lifetime Sum Social Security Personal account Total taxes beneﬁts beneﬁts beneﬁts Program features (variation from base package) 1. Current law projections of traditional 171,428 Social Security 2. Base package of personal accounts 169,304 3. Total conversion to personal accounts 167,331 4. Full annuitization required 169,886 5. Annuitization optional, full lump sum 169,151 withdrawal permitted

328,955

0

328,955

199,878 0 199,540 199,330

210,556 574,346 251,026 207,820

410,434 577,009 450,566 407,150

Notes: Base package=current law traditional beneﬁts, voluntary, partial (4% of contribution) accounts, prorated traditional beneﬁts, annuitize to family poverty level, joint and 2/3 annuity, required personal accounts subject to earnings test.

the maximum decline in taxes paid into the trust fund due to diversion of taxes from conventional beneﬁts to personal accounts is 37.7% (4/10.6).30 Table 19 also shows the decline in lifetime beneﬁts from $328,955 to $199,878, or almost 40%. Thus the decline in beneﬁts and taxes from adoption of voluntary personal accounts are roughly of the same proportion. However, because taxes are reduced years before beneﬁts are reduced, the movement to personal accounts does present a solvency problem. Given the assumption of a real return to the personal account portfolio of 4.31% per year, and the heavy pattern of participation in these accounts, the increase in total beneﬁts, i.e., the sum of beneﬁts from the traditional system and from personal accounts, is substantial, rising from $328,955 to $410,434.31

5. CONCLUSIONS This paper has examined retirement and related responses to a number of policies. We call these the next generation of policies because the changes they introduce are, on average, roughly actuarially neutral. They are in contrast to decades of policy changes that removed disincentives to continued work from unfair actuarial adjustments. Nevertheless, retirement

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is affected by these actuarially neutral policies as those with high time preference rates do not ﬁnd the promise of additional future rewards to balance the loss in current beneﬁts. We can summarize our ﬁndings with regard to four different types of policy initiatives, none of which involves a primary manipulation of the actuarial reward to deferred beneﬁt receipt.

5.1. Abolishing the Retirement Earnings Test versus Increasing the Early Entitlement Age For persons between the early entitlement and full-retirement age, the earnings test is actuarially fair, or better than fair. Future beneﬁts are increased so that at the interest rate used in the calculation, they at least compensate for any beneﬁt reductions from the earnings test for earnings that exceed the annual exempt amount. Consequently, a prediction of life cycle models with perfectly operating capital markets is that the earnings test should not affect retirement behavior. Nevertheless, we have found that a number of people have high rates of time preference, and they do not consider the restoration of beneﬁts on an actuarially fair basis, using the government’s interest rate, to be an attractive tradeoff. From age 62 through the full-retirement age, the earnings test reduces the share of married men who work full-time by about four percentage points, which entails a reduction of about 10% in the number of married men of that age at full-time work. In terms of the cash ﬂow of the system, abolishing the earnings test would have an adverse effect, at least initially. If the earnings test were abolished between the early and full-retirement ages, the share of married men claiming Social Security beneﬁts would increase by about 10 percentage points, and the average beneﬁt payments would increase by about $1,800 per recipient. The initial increase in beneﬁt payments would eventually be reversed, over a time span of decades, because the annual beneﬁt amounts would eventually be reduced by more than an actuarially fair amount due to the earlier collection of beneﬁts. As an alternative to increasing work effort by abolishing the earnings test, one can increase the employment of older persons by increasing the early entitlement age under Social Security. A major difference on the funding side is that abolishing the earning test results in an earlier ﬂow of beneﬁt payments from Social Security, worsening the cash-ﬂow problems of the system, while increasing the early entitlement age delays the ﬂow of beneﬁt payments from the system, improving its cash ﬂow.

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5.2. Policies to Relax Minimum Hours Constraints Minimum hours constraints, that is the requirements on many jobs that an individual work full-time or not at all, are a major ﬁrm-side factor affecting the course of retirements. Should minimum hours constraints be abolished, among the population ages 62–69 that has a long-term commitment to the labor market, the percentage fully retired will decline by 10–15 percentage points, depending on age. The fraction in this age group working in partial retirement jobs will increase by roughly 20 percentage points. Were minimum hours constraints abolished, more than twice as many people would enter partial retirement as would leave full-time work, so that total full-time equivalent (FTE) employment would increase. But the change in FTE employment is much smaller than the increase in partial retirement employment. When ﬁrms decide whether to relax minimum hours constraints, they will consider not just the very modest effect on FTE employment from relaxing these constraints. They will also consider how minimum hours constraints contribute to productivity and reduce costs. Fixed costs of employment to the ﬁrm, the role of interdependence in production and many other factors have encouraged ﬁrms to adopt minimum hours constraints in the ﬁrst place. Moreover, although our simulations have assumed that constraints on partial retirement from current pension rules are eliminated, health insurance and other beneﬁts made available on a per employee, rather than per hour basis, increase costs when ﬁrms provide a partial retirement option. Our ﬁndings also suggest that if ﬁrms relaxed minimum hours constraints, this would have conﬂicting effects on the ﬂow of funds from Social Security. Relaxing minimum hours constraints would encourage individuals to leave full-time work at younger ages to enter partial retirement. As a result, they would begin to draw down their beneﬁts at an earlier age, increasing the ﬂow of funds out of Social Security. However, they would remain in partial retirement jobs past the point where they currently retire, and during this period they would draw fewer beneﬁts. The proportion of earnings subject to the earnings test will also be subject to conﬂicting forces. The fraction of earnings exempt from the earnings test will increase, but the fraction of earnings beyond the reaches of the earnings test will decline. Lastly, behavior would change under proposed reforms that would include voluntary personal accounts as part of Social Security. Should ﬁrms relax minimum hours constraints to encourage more partial retirement by older individuals, demand for early withdrawals from personal accounts would increase. This would increase the importance of terms and conditions regulating the timing of withdrawals from personal accounts.

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5.3. Introducing Voluntary Partial Personal Accounts with Lump Sum or Annuity Payouts Particular features of voluntary personal accounts will affect retirement behavior, saving, and participation in personal accounts. These choices in turn will affect the ﬂow of beneﬁts and taxes, and ultimately the adequacy of beneﬁts. Among our ﬁndings, under a system of partial voluntary personal accounts, with higher average returns on portfolios than under the current formula (unadjusted for risk), total retirement beneﬁts would increase by about a quarter, while the fraction of 62 year olds at full-time work would decline by about 22% compared to the current system. If the current system were replaced fully by personal accounts, total retirement beneﬁts would increase by about 75% and the fraction at full-time work would decline by about a third. Retirement responses are relatively modest, but the predicted increase in retirements from adopting partial voluntary personal accounts should nevertheless be of concern to policy makers. Increased retirements will further reduce the labor supply of older workers beyond the decline caused by the retirement of the baby boom. If all beneﬁts from voluntary personal accounts could be taken as a lump sum, the fraction not retired at age 62 would fall by about 5 percentage points compared to a system where there is mandatory annuitization of beneﬁts. When annuitization is voluntary, there will be substantial diversion of beneﬁts to age 62. When annuitization is mandatory, beneﬁts received in one’s 70s and 80s may be increased by 20% or more. These ﬁndings suggest that the ongoing transition from annuitized beneﬁts to systems with increased availability of lump sum payouts will encourage increased retirement. This side effect of transitions to plans offering lump sum payouts will act to undermine the thrust of the ﬁrst generation of policies designed to encourage later retirements.

5.4. In Summary As we have emphasized throughout this paper, a key to understanding the effects on retirement of this next generation of policies is to understand saving and the role of heterogeneity in time preference. A signiﬁcant fraction of people in the labor market has a high time preference rate. These people will not ﬁnd tradeoffs between foregone present beneﬁts and increased

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future beneﬁts at actuarially fair rates to be an attractive bargain. Some policies that are expected to have a large effect on retirements by introducing actuarially fair beneﬁt adjustments will have smaller effects than expected. Other policies that are expected to have no effect on retirement because they involve transitioning from one actuarially fair beneﬁt structure to another, such as abolishing the retirement earnings test between early and full-retirement ages, nevertheless will affect retirements. In the case of abolishing the retirement earnings test, that policy will increase labor force activity and accordingly will encourage postponed retirements. On the other hand, some policy changes, which again appear to be actuarially neutral, such as the trend to paying out retirement plan beneﬁts as a lump sum instead of an actuarially equivalent annuity, will have the effect of encouraging earlier rather than later retirements. Models that jointly explain retirement and saving, and allow for heterogeneity of time preference rates, are required to understand the direction and size of the effects of these and related policies on retirement.

NOTES 1. The 1983 Social Security reforms signiﬁcantly increased the incentive to postpone retirement after age 65. Among other things, the delayed retirement credit was gradually increased from 3% to 8%, and the normal retirement age was raised. Subsequently, the earnings test was abolished for those over the normal retirement age. Age discrimination rules abolished mandatory retirement at age 65 for most jobs, and eliminated certain (but not all) actuarial penalties found in deﬁned beneﬁt pensions that effectively reduced the reward to work after age 65. 2. Anderson, Gustman, and Steinmeier (1999) quantify the effects on retirement of changes in Social Security rules, abolition of mandatory retirement, changes in deﬁned beneﬁt structures and substitution of DC for DB plans. See also Friedberg and Webb (2003). 3. Structural models in the spirit of the present model, where capital markets are not operating perfectly, have been estimated by Rust and Phalen (1997), French (2005), van der Klaauw and Wolpin (2006), and Bound, Stinebrickner, and Waidmann (2006). These models have different purposes than the one we estimate here, and develop those aspects of the model that are aimed at their speciﬁc focus in greater detail than we do. However, given their different emphases, each assumes away one or another feature that is central to the present analysis, simplifying the representation of incentives from deﬁned beneﬁt pensions, ability to borrow, joint determination of saving and retirement, or inclusion of partial retirement, among others. None of these models fully analyzes joint decision making within the household. Our model takes the labor market decision of the spouse as exogenous. For models of joint decision making by couples, which simplify other dimensions of

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retirement and retirement decision making in comparison to the present model, see Gustman and Steinmeier (2004) and Blau and Gilleskie (2006). 4. For a similar model that includes reversals from full-retirement to full-time work, but does not allow partial retirement, see Gustman and Steinmeier (2002). 5. In recognition that consumption is more valuable while both spouses are alive, the consumption function is adjusted so that the marginal utility for a surviving spouse is approximately equal to that for a couple consuming 40% more. 6. Our own work on the role of employer provided retiree health insurance (Gustman & Steinmeier, 1994) suggests that role is minor. This ﬁnding has been supported in the work of Blau and Gilleskie (2006) and others, but is sensitive to model speciﬁcation. 7. Estimates of rates of survival are taken from the Social Security survival tables, which are divided according to sex and birth cohort. 8. For a more detailed description, see Pakes and Pollard (1989), Dufﬁe and Singelton (1993), and Greene (2000). 9. This calculation is slightly modiﬁed in the cases of extremely high, or zero wealth. When an individual has more assets than would be calculated even at a zero time preference rate, this is taken as a signal of a low time preference rate, and a value of zero for the time preference rate is assigned. An individual who has zero assets, even allowing for a deﬁned contribution lump sum which would be available at retirement, is at a corner solution with regard to assets. Although the time preference rate for such an individual cannot be completely determined, only an individual with a very high time preference rate would have zero assets on the verge of retirement. Such an individual is assigned an arbitrarily high time preference rate, causing each period’s income to be fully consumed. 10. Samwick (1998) uses a similar approach and ﬁnds wide heterogeneity in time preference rates. 11. Distribution of Time Preference Rates: Rate 0–0.05 0.05–0.1 0.1–0.15 0.15–0.2 0.2–0.25 0.25–0.3

No. of Obs. Rate No. of Obs. Rate No. of Obs. Rate No. of Obs. 474 759 170 59 29 22

0.3–0.35 0.35–0.4 0.4–0.45 0.45–0.5 0.5–0.55 0.55–0.6

12 10 4 8 4 2

0.6–0.65 0.65–0.7 0.7–0.75 0.75–0.8 0.8–0.85 0.85–0.9

1 4 2 1 1 2

0.9–0.95 0.95–1 W1

1 2 664

12. At age 63, beneﬁts would be 98.3% of what they would otherwise be, at age 64 they would be 96.6% (98.5% times 98.3%) of what they would have been, and so on. The idea is to reﬂect the feeling that beneﬁts might be reduced because of the ﬁnancing problems. This could have been done, say, with a 20% reduction in 10 years, but it was simpler to do a percentage reduction. Note that, as long as inﬂation is more than 1.7%, beneﬁts would increase over time in nominal terms, but not by as much as inﬂation. Although this simulation assumes that recipients believe that beneﬁts will be cut, the ﬁgures in the taxes and beneﬁts section of the simulation are

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calculated as though the beneﬁts are not cut in the end. Note also that parameter values have not been reestimated for this simulation. 13. Under current Social Security law, beneﬁts are reduced for each year one claims beneﬁts before the full retirement age. This means that for every year beneﬁts are not claimed after age 62, future beneﬁts are adjusted upward. For example, a person born by January 1, 1938, who has a full retirement age of 65, would receive 80% of full beneﬁts upon retiring at age 62. Therefore, postponing beneﬁt receipt until age 63 would increase yearly beneﬁts by 8.38% (0.067/0.8) for the rest of his life. The earnings test has a similar effect. For those between ages entitling them to early and full beneﬁts, the Social Security earnings test reduces beneﬁts received by 50 cents for every dollar earned over the exempt amount ($11,520 in 2003). A person expecting a yearly Social Security pension of $10,000 at age 62 would ﬁnd the entire beneﬁt reduced to zero if earnings reached $31,520. Beneﬁts lost to the earnings test are restored in future years, again at a rate that for many is better than on an actuarially fair basis. 14. For those born in 1937 or earlier, who attained age 62 by 1999, the full retirement age is 65. The full retirement age is then increased two months per year until reaching 66 for those born in 1943, staying at 66 between 1943 and 1954, and increasing in two-month increments per year of birth between 1955 and 1960, where it reaches age 67. 15. At a 3% real interest rate, and for many taking into account the effect of postponing own beneﬁts on beneﬁts paid to their spouse, given current life tables this adjustment is better than actuarially fair (Gordon & Blinder, 1980; Feldstein & Samwick, 1992). 16. Studies of the effects of abolishing the earnings test rely either on changes in the earnings test kink point (Friedberg, 2000), or on the observed change in employment patterns between workers affected by the abolition of the earnings test and those who are not. Disney and Smith (2002) examine the effects of the abolition of the earnings test in Britain. Song (2002), Song and Manchester (2006), and Tran (2002) examine the effects of abolishing the earnings test for those over the normal retirement age in the United States. 17. Friedberg (2000) produces a reduced form analysis of the retirement earnings test. Her analysis falls silent on the question of beneﬁt acceptance and the wide distributions of time preferences that characterize the population. 18. Gruber and Orszag (1999) suggest that eliminating the earnings test will have unfavorable effects on the distribution of beneﬁts because those who claim their beneﬁts early are left with lower beneﬁts in later years, and those with lower lifetime earnings are more likely to claim their beneﬁts early. Indeed, one consideration that mitigated against eliminating the earnings test between early and full retirement age by the Clinton Administration in 2000 was the specter of poor widows whose low beneﬁts reﬂected the fact that their husband’s elected to receive beneﬁts early. Gruber and Orzag provide relevant descriptive numbers. They also note that the earnings test may favor high-income individuals if their life expectancy is longer than those who are entitled to lower beneﬁts. In the latter case, abolishing the earnings test may have a progressive impact on the distribution of beneﬁts paid over the lifetime. 19. Gustman and Steinmeier (1983, 1984a) document the existence of minimum hours constraints facing retirement age workers. Even and Macpherson (2004) use

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HRS data to discuss the relation between coverage by pension plans of different types and minimum hours constraints. 20. Gustman and Steinemeier (1983) and Hurd (1996) list a number of reasons why ﬁrms choose to adopt minimum hours constraints, including ﬁxed costs of employment, team production, and other factors. 21. Gustman and Steinmeier (1986) demonstrate the importance of including minimum hours constraints in structural retirement models. When these constraints are the reason most workers proceed directly from full-time work to complete retirement, but a model assumes workers are free to work part-time on their main job but choose not to, the resulting estimates will suggest that work and leisure are very close substitutes. Thus the model will generate corner solutions, with most individuals moving immediately from the corner with full-time work to the corner with full retirement. Once it is recognized that minimum hours constraints prohibit most older workers from phasing smoothly into retirement, preference estimates will show that in the absence of these constraints, most people would prefer to reduce their time at work smoothly as they phase into retirement, but their ﬁrms’ policies prevent them from doing so. 22. The simulations also eliminate the disincentive to partial retirement by those with DB plans who might ﬁnd their beneﬁts reduced when part-time wages earned at the end of the life cycle are counted when computing the average wage measure used in a ﬁnal average salary beneﬁt formula. When we abolish the hours constraint and let individuals draw on pensions when they partially retire, the pensions are calculated as though they quit at that point. Earnings and service during the period of partial retirement are not included in the pension calculation. For further discussions of the ERISA rule prohibiting a person from working part-time while collecting a pension beneﬁt from a long-term employer, see Fields and Hutchens (2002), Even and Macpherson (2004), and Penner, Perun, and Steuerle (2002). 23. We assume that beneﬁts in the traditional account are reduced via a pro-rata method. The pro-rata method uses two hypothetical accounts. The ﬁrst accumulates the contributions to the private accounts at the offset rate of 2.5% real, which is the interest rate speciﬁed in the President’s Commission’s model 3. The second accumulates cumulatively the contributions to the traditional system, also at 2.5% real. Beneﬁts are reduced by the percentage of the sum of the cumulative accounts that is due to the contributions to the private accounts. In the current law projection case, with partial accounts this is 4.0/10.6=37.7%, which is the amount by which traditional beneﬁts are reduced. This applies to the individual’s own beneﬁts and the spouse’s spouse and survivor beneﬁts, which are due to the individual’s earnings. 24. We also consider the effects of requiring the sum of the adjusted traditional PIA plus the required annuities to reach the single person poverty level or the sum of the adjusted traditional PIA plus the required annuities to reach the unadjusted traditional PIA level (which is the amount that would be calculated from the current formula). The larger the required annuity, the less inﬂuential lump sum beneﬁts are on retirement and retirement beneﬁts. 25. It is difﬁcult to conceive of a system that would apply the earnings test to the lump sums, since the lump sums are almost by deﬁnition amounts that are above the amounts required to achieve the desired level of annual beneﬁts. Similarly, the fate of

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any new contributions to the personal accounts depends on the status of the accounts. If the required annuities do not exhaust the accounts, then the contributions would be available, plus interest, in the next year. If, however, the accounts are insufﬁcient to bring the total annuities up to the required levels, then any new contributions would go to purchase additional annuities to narrow the shortfall. For instance, suppose that traditional beneﬁts are $8,000 and the required annuities from the personal accounts are $4,000. If the earnings test limit is $6,000 with a $1 reduction for every $2 in earnings above that amount, and if earnings are $20,000, then $7,000 [=0.5 (20,000–6,000)] in beneﬁts are lost. Two thirds of this ($4,667) are lost from the traditional beneﬁts and one third ($2,333) is lost from the required annuities from the personal accounts, since the unreduced traditional beneﬁts are two-thirds [=8,000/(8,000þ4,000)] of total unreduced beneﬁts. The lost traditional beneﬁts increase later traditional beneﬁts in the usual fashion. For the beneﬁts that are lost from the required annuity, the lost beneﬁts are invested at the real rate of return, and the following year the amount is annuitized and added to the previous required annuity. 26. We also analyzed whether the required and optional annuities purchased from the personal accounts are to be single life or joint and two-thirds annuities. The presumption is that the eventual regulations would probably require joint annuities, but this investigates whether there is any substantial change in behavior as a result. When single annuities are permitted, there is little change in retirement. But total beneﬁts are higher under single annuities. A disproportionate amount of these beneﬁts are taken at age 62, so that beneﬁts received in one’s late 70’s or 80’s are lower than in the basic package, despite the fact that total beneﬁts are higher. 27. There is a secondary spike at age 70, but that is an artifact of the simulations, which assume that all individuals retired at that age. Although the returns on personal accounts can average out over time, there is a problem when the accounts are annuitized. If the annuities are variable annuities, similar to the annuities TIAA-CREF offers, the value of the beneﬁts will ﬂuctuate year-to-year, sometimes by substantial amounts, and this runs counter to having a reliable income stream during retirement. If the annuities are ﬁxed in real terms, then it may make a great deal of difference when the annuitization takes place. An individual who annuitized in 2000, for instance, would have twice the annuity as another individual with similar lifetime earnings and contributions who annuitized in 2003. The unequal treatment of roughly equal individuals would make the differences involved in the ‘‘notch generation’’ debate small by comparison, and that debate generated a fair amount of heat. This annuitization problem may be substantial. 28. The increase in the lifetime value of personal account beneﬁts when the personal account must be fully annuitized is a reﬂection of the effect of additional work on earnings, and thus on beneﬁts. 29. Using an alternative offset method similar to that used by the President’s Commission did not have major effects on the ﬁndings. In simulations with offsets, it was assumed that the personal accounts were mandatory. With certain returns in the personal accounts that were higher than the offset interest rate, the model would show that everyone would prefer the personal accounts were they voluntary. Here

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the contributions to the personal accounts are cumulated at the offset rate of 2.5% real. The resulting amount is then discounted to the normal retirement age at 2.5% real and transformed into a single annuity at the same interest rate. This puts the offset computations on a comparable basis with the PIA, which is the traditional beneﬁt available at normal retirement. Traditional beneﬁts are then reduced by the ratio of this annuity to the PIA. The reduction applies to the individual’s own beneﬁt only, and not to any spouse or survivor beneﬁts which depend on the individual’s earnings record, since the offset account is annuitized with a single life annuity. A joint annuity would be very difﬁcult to compute, since the spouse beneﬁts depend on the relation of half of the individual’s PIA to the spouse’s PIA, and the applicable spouse’s PIA may well not have been determined at the time the individual applies for beneﬁts. For further discussion of alternative offset methods, see Gustman and Steinmeier (2005c). There we show that the offset method adopted by the President’s Commission essentially taxes away the principal created in the private account from payroll tax deposits made in the name of the covered individual. That reduces the insurance the account would otherwise provide against unforeseen changes in Social Security beneﬁts that might be adopted in the future. 30. The actual decline in taxes is slightly less than 37.7% since 5% of covered workers will choose not to accept the personal account, and these will mainly come from the ranks of low-income workers. 31. Again, this calculation does not take into account any risk premium either for stock market investment, or the political risk to current Social Security promises.

ACKNOWLEDGMENTS The research reported herein was conducted pursuant to grants UM03-03, UM04-01, and UM05-02, from the US Social Security Administration (SSA) to the Michigan Retirement Research Center (MRRC), with subcontracts to the National Bureau of Economic Research (NBER). The model was developed with support from the National Institute on Aging in a grant 1R01AG13913 to NBER. The ﬁndings and conclusions expressed are solely those of the authors and do not represent the views of SSA, any agency of the Federal Government, the MRRC, or the NBER.

REFERENCES Anderson, P. M., Gustman, A. L., & Steinmeier, T. L. (1999). Trends in male labor force participation and retirement: Some evidence on the role of pension and social security in the 1970s and 1980s. Journal of Labor Economics, 17(4, Part 1), 757–783. Benitez-Silva, H., Dwyer, D. S., Heiland, F., & Sanderson, W. C. (2007). A dynamic model of retirement and social security reform expectations: A solution to the new early retirement puzzle. Stony Brook, Working Paper.

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Blau, D. M., & Gilleskie, D. B. (2006). Health insurance and retirement of married couples. Journal of Applied Econometrics, 21(7), 935–953, available on line, November, http://www3.interscience.wiley.com/cgi-bin/fulltext/113453619/PDFSTART Bound, J., Stinebrickner, T. R., & Waidmann, T. (2006). Health, economic resources and the work decisions of older men. Paper presented at NBER Summer Institute on Aging. Burtless, G., & Mofﬁtt, R. (1984). The joint choice of retirement age and postretirement hours of work. Journal of Labor Economics, 3(2), 209–236. Coile, C., Diamond, P., Gruber, J., & Jousten, A. (2002). Delays in claiming social security beneﬁts. Journal of Public Economics, 84, 357–385. Disney, R., & Smith, S. (2002). The labor supply effects of the abolition of the earnings rule for older workers in the United States. The Economic Journal, 112, C136–C152. Dufﬁe, D., & Singleton, K. J. (1993). Simulated moments estimation of Markov models of asset prices. Econometrica, 61(4), 929–952. Even, W. E., & Macpherson, D. A. (2004, September). Do pensions impede phased retirement? Xeroxed. Discussion Paper No. 1353, Institute for the Study of Labor, Bonn, ideas.repec.org/p/iza/izadps/dp1353.html Feldstein, M., & Samwick, A. (1992). Social security rules and marginal tax rates. National Tax Journal, 45, 1–22. Fields, V., & Hutchens, R. (2002). Regulatory obstacles to phased retirement in the for-proﬁt sector. Beneﬁts Quarterly, 18(3), 35–41. French, E. (2005). The effects of health, wealth and wages on labor supply and retirement behavior. Review of Economic Studies, 72, 395–427. Friedberg, L. (2000). The labor supply effects of the social security earnings test. The Review of Economics and Statistics, 82(1), 48–63. Friedberg, L., & Webb, A. (2003). Retirement and the evolution of the pension structure. NBER Working Paper 9999. Gordon, R. H., & Blinder, A. S. (1980). Market wages, reservation wages and retirement. Journal of Public Economics, 14, 277–308. Greene, W. H. (2000). Econometric analysis. Upper Saddle River, NJ: Prentice Hall. Gruber, J., & Orszag, P. (1999, July). What to do about the social security earnings test? Issue in brief no. 1. Boston, MA: Center for Retirement Research at Boston College. Gustman, A. L., & Steinmeier, T. L. (1983). Minimum hours constraints and retirement behavior. Contemporary Policy Issues, a supplement to Economic Inquiry, No. 3 (April), 77–91. Gustman, A. L., & Steinmeier, T. L. (1984a). Partial retirement and the analysis of retirement behavior. Industrial and Labor Relations Review, 37(3), 403–415. Gustman, A. L., & Steinmeier, T. L. (1984b). Modeling the retirement process for policy evaluation and research. Monthly Labor Review, 107(7), 26–33. Gustman, A. L., & Steinmeier, T. L. (1985). The 1983 social security reforms and labor supply adjustments of older individuals in the long run. Journal of Labor Economics, 3(2), 237–253. Gustman, A. L., & Steinmeier, T. L. (1986). A structural retirement model. Econometrica, 54(3), 555–584. Gustman, A. L., & Steinmeier, T. L. (1994). Employer provided health insurance and retirement behavior. Industrial and Labor Relations Review, 48(1), 124–140. Gustman, A. L., & Steinmeier, T. L. (1999). Effects of pensions on savings: Analysis with data from the health and retirement study. Carnegie-Rochester Conference Series on Public Policy, 50, 271–324.

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Gustman, A. L., & Steinmeier, T. L. (2000). Retirement outcomes in the health and retirement study. Social Security Bulletin, Perspectives, 63(4), 3–17. Gustman, A. L., & Steinmeier, T. L. (2002, December). Retirement and the stock market bubble. NBER Working Paper 9404. Gustman, A. L., & Steinmeier, T. L. (2004). Social security, pensions and retirement behavior within the family. Journal of Applied Econometrics, 19(6), 723–738. Gustman, A. L., & Steinmeier, T. L. (2005a). The social security early retirement age in a structural model of retirement and wealth. Journal of Public Economics, 89(2–3), 441–463. Gustman, A. L., & Steinmeier, T. L. (2005b). Retirement effects of proposals by the president’s commission to strengthen social security. National Tax Journal, 58(1), 27–49. Gustman, A. L., & Steinmeier, T. L. (2005c). Offsetting the principal in the new social security accounts. Tax Notes, 107(1), 109–114. Hayashi, F., Altonji, J. G., & Kotlikoff, L. (1996). Risk-sharing between and within families. Econometrica, 64(2), 261–294. Hurd, M. D. (1996). The effect of labor market rigidities on the labor force behavior of older workers. In: D. A. Wise (Ed.), Advances in the Economics of Aging (pp. 11–58). Chicago, IL: University of Chicago Press. Ibbotson Associates. (2002). Valuation edition 2002 yearbook. Chicago, IL: Ibbotson Associates. McGarry, K. (2004). Health and retirement: Do changes in health affect retirement expectations? Journal of Human Resources, 39(4), 624–648. Olson, J. A. (1999). Who is ‘‘62 Enough’’? Identifying respondents eligible for social security early retirement beneﬁts in the health and retirement study. Social Security Bulletin, 62(3), 51–56. Pakes, A., & Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica, 57(5), 1027–1057. Penner, R. G., Perun, P., & Steuerle, C. E. (2002). Legal and institutional impediments to partial retirement and part-time work by older workers. http://www.urban.org/ url.cfm?ID=410587 President’s Commission to Strengthen Social Security. (2001). Strengthening social security and creating personal wealth for all Americans. Washington, DC. http://www.commtostrengthensocsec.gov/reports/Final_report.pdf Rust, J., & Phalen, C. (1997). How social security and medicare affect retirement. Econometrica, 65(4), 781–831. Samwick, A. (1998). Discount rate heterogeneity and social security reform. Journal of Development Economics, 57, 117–146. Song, J. G. (2002, November). Evaluating the effects of the removal of the retirement earnings test in 2000. Mimeo. Social Security Administration. Song, J. G., & Manchester, J. (2006, June). New evidence on earnings and beneﬁt claims following changes in the retirement earnings test in 2000. US Social Security Administration, Ofﬁce of Policy. ORES Working Paper no. 107. Tran, B. V. (2002, November). The effect of the repeal of the retirement earnings test on the labor supply of older worker. Xeroxed. College Park, MD: University of Maryland at College Park. van der Klaauw, W., & Wolpin, K. I. (2006). Social security and the retirement and savings behavior of low income households. Mimeo.

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APPENDIX Table A1.

Reasons for Deletions of Observations.

Total sample individuals Not male Not married Spouse not interviewed Not a career worker Ambiguity about whether jobs are covered by social security No full-time earnings amounts available No self-reported earnings and social security earnings over limit Relatively large business assets No pension provider record in last job Full-time years unavailable for spouse

Observations Dropped

Observations Left

6,785 1,578 133 497 49

12,652 5,867 4,289 4,156 3,659 3,610

36 31

3,574 3,543

291 865 156

3,252 2,387 2,231

Table A2. Differences in Retirement Outcomes between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Test Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62a. Age

60 61 62 63 64 65 66 67 68 69 a

Percentage Retiring

Percentage Retired

From full-time work

Fully

From full-time work

Fully

0.0 0.1 4.0 0.3 0.3 0.2 0.9 0.6 0.5 0.3

0.0 0.0 1.4 0.1 0.3 0.1 0.5 0.1 0.1 0.1

0.0 0.0 4.1 4.3 4.7 4.4 3.5 3.0 2.5 2.2

0.0 0.0 1.5 1.5 1.9 1.9 1.4 1.2 1.1 1.0

Figures in the table are calculated as the retirement outcome predicted without an earnings test in place minus the retirement outcome predicted with an earnings test in place.

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Table A3. Differences in Percent Collecting Social Security Beneﬁts between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Test Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62. Age

62 63 64 65 66 67 68 69

Differences in Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

1.4 0.0 0.7 0.7 0.3 0.2 0.2 0.0

1.2 0.4 0.5 0.1 0.0 0.0 0.1 0.0

0.2 2.4 5.2 3.0 1.3 0.9 0.6 0.4

34.8 46.7 54.3 25.6 12.1 8.4 6.0 4.5

15.0 18.8 19.5 8.1 3.4 2.1 1.2 0.8

Table A4. Differences in Social Security Taxes and Beneﬁts between Simulations after Eliminating the Earnings Test and Simulations with the Earnings Test Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62. Age 50 55 60 61 62 63 64 65 66 67 68 69 70 75 80 85 90 95

Taxes

Beneﬁts

0 2 1 3 90 98 115 118 92 79 67 58

4 34 98 161 2,015 2,655 3,002 1,806 899 539 165 228 679 954 859 642 413 221

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Table A5. Effect on Retirement of Increasing the Early Entitlement Age to 64 Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62a. Age

58 59 60 61 62 63 64 65 66 67 68 69

Percentage Retiring

Cumulative Percentage Retired

From full-time work

Fully

From full-time work

Fully

0.1 0.1 0.1 0.4 6.7 0.6 7.3 0.2 0.2 0.2 0.2 0.1

0.1 0.1 0.2 0.3 4.1 0.4 5.2 0.2 0.2 0.2 0.2 0.2

0.2 0.3 0.4 0.7 7.5 8.0 0.7 0.5 0.3 0.2 0.0 0.1

0.2 0.3 0.4 0.8 5.0 5.4 0.2 0.2 0.0 0.2 0.4 0.6

a

Figures in the table are calculated as the retirement outcome predicted an age 64 early entitlement age minus the retirement outcome predicted with an age 62 early entitlement age.

Table A6. Effect on Beneﬁt Claiming of Increasing the Early Entitlement Age to 64 Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62. Age

62 63 64 65 66 67 68 69

Differences in Percent Collecting Social Security Retirees from full-time work

Fully retired

Partially retired

Full-time work

All

69.6 83.5 0.4 0.1 0.1 0.1 0.0 0.0

64.7 82 0.2 0.1 0.0 0.1 0.0 0.0

82 87.3 0.6 0.1 0.1 0.1 0.0 0.0

22.5 26.7 0.2 0.5 0.1 0.0 0.1 0.1

41.3 48.1 0.5 0.1 0.1 0.1 0.0 0.0

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ALAN L. GUSTMAN AND THOMAS L. STEINMEIER

Table A7. Effect on Social Security Taxes and Beneﬁts Claiming of Increasing the Early Entitlement Age to 64 Assuming Individuals Expect Beneﬁts to be Reduced by 1.7% per Year after Age 62. Age 50 55 60 61 62 63 64 65 66 67 68 69 70 75 80 85 90 95

Taxes

Beneﬁts

0 1 12 23 173 185 13 9 4 1 5 8

5 42 175 313 3,153 4,434 421 389 338 15 343 525 633 899 828 643 437 244

Table A8. Percent Choosing Lump Sum versus Voluntary Annuities.

Program features (variation from base package) 1. Current law projections of traditional Social Security

No Funds Available

Lump Sum

Voluntary Annuity

100.0

0.0

0.0

46.2 0.0 50.1

48.5 0.0 49.3

45.9 50.9

49.2 44.1

46.5

48.7

Revised systems with voluntary personal accounts 2. Base package of personal accounts 5.4 3. Full annuitization required 100.0 4. Annuitization optional, full lump sum 0.6 withdrawal permitted 5. Total conversion to personal accounts 4.8 6. Mandatory personal accounts, using 5.0 offset accounts 7. Mandatory personal accounts 4.8

Projecting Behavioral Responses to the Next Generation of Retirement Policies Table A8.

195

(Continued). No Funds Available

8. Annuitize to single person poverty level 9. Annuitization up to currently scheduled PIA 10. Single annuities 11. Required personal accounts not subject to earnings test

Lump Sum

Voluntary Annuity

7.0 4.8

45.6 52.9

47.4 42.4

4.5 5.4

63.1 45.9

32.4 48.6

Notes: Base package=current law traditional beneﬁts, voluntary, partial (4% of contribution) accounts, prorated traditional beneﬁts, annuitize to family poverty level, joint and 2/3 annuity, required personal accounts subject to earnings test.

ILLEGAL MIGRATION, ENFORCEMENT, AND MINIMUM WAGE Gil S. Epstein and Odelia Heizler (Cohen) ABSTRACT This paper examines the connection between illegal migration, minimum wages, and enforcement policy. We ﬁrst explore the employers’ decision regarding the employment of illegal migrants in the presence of an effective minimum wage. We show that the employers’ decision depends on the wage gap between those of the legal and illegal workers and on the penalty for employing illegal workers. We consider the effects a change in the minimum wage has on the employment of illegal immigrants and local workers. We conclude by considering the optimal migration policy taking into consideration social welfare issues.

1. INTRODUCTION Illegal immigration is a very hot social and economic issue facing many technologically advanced countries. Despite efforts to limit the number of immigrants allowed into these countries, the illegal immigrant stock is rising. It is difﬁcult to accurately estimate the number of illegal immigrants.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 197–224 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28006-4

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At the beginning of 2000, some OECD countries published ofﬁcial ﬁgures of unauthorized immigrants.1 In the USA, estimates were between 4 and 7 million,2 which is about 1.5% of the population. In Greece, it was about 3% and in Italy about 0.5%. The increasing stock of illegal immigrants has turned it into a central issue in numerous elections throughout the Western Hemisphere. The effect of legal immigration on the host country’s welfare is controversial. Some studies found that the immigrants are a beneﬁt to the local population and others claimed the opposite (see, for example, Berry & Soligo, 1969; Rivera-Batiz, 1982; Borjas, 1995). However, it is widely believed that illegal immigration is detrimental to the host country. This is because the illegal immigrants impose additional costs by the essence of their illegality, in addition to the burden imposed by their illegality, i.e., the replacement of local workers. The illegal immigrants tend not to pay taxes and are often involved in clandestine activities both as felons and as victims. Furthermore, their existence serves as a signal to the natives that the government does not enforce the law or that illegality is acceptable, thus causing them to avoid paying taxes (see Epstein & Weiss, 2006). Many articles discuss the government’s efforts to control illegal immigration (for example, Ethier, 1986; Chiswick, 1988; Zimmermann, 1995; Djajic, 1999; Gaytan-Fregoso & Lahiri, 2000 and more recently Guzman, Haslag, & Orrenius, 2008). Efforts to reduce illegal immigration utilize a number of instruments. The main instrument is the allocation of resources for apprehending illegal immigrants. This is implemented via border controls which block the entry of undesirable elements as well as internal enforcement, whereby such people are apprehended and expelled from the country. Some countries also provide foreign aid to the country of origin in order to reduce income differentials and thus the incentive to immigrate. An additional way to minimize illegal immigration, which has recently become very common, is to grant amnesties to illegal immigrants who have been in the country for an extended period of time. The Immigration Reform and Control Act (IRCA) of 1986 in the USA represents an attempt to control illegal immigration by imposing ﬁnes on employers who hire unauthorized workers. Employers who knowingly hire illegal alien workers are subject to civil money penalties of $250–2,000 per worker for a ﬁrst offense and $3,000–10,000 per alien for a third offense3 (see, for example, Cobb-Clark, Shiells, & Lowell, 1995). Western European countries, such as France and Germany, also enacted employer sanctions in the mid-1970s. In France, employers are liable for penalties of up to 1,000 times minimum wage, while in Germany the maximum ﬁne is $52,600.

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In UK employer sanctions exist since 1997 and the maximum ﬁne is $8,000 per illegal worker hired (Martin & Miller, 2000). A vast literature exists on migration policy (see, for example, Benhabib, 1996; Bauer, Lofstrom, & Zimmermann, 2000), but only few articles examine the interaction between economic and political processes. Amegashie (2004) studied a model in which the number of immigrants allowed into a country is the outcome of a costly political lobbying process between a ﬁrm and a union, using the all-pay auction contest. Epstein and Nitzan (2006) have recently presented a model for the endogenous determination of quotas, viewing the quota as the outcome of a two-stage political contest between two interest groups, i.e., workers and capital owners. Garcia (2006) explained why the control of immigration may be a relevant issue in elections and demonstrated that rightist parties have an advantage of winning in countries where immigration control is a relevant issue in the election. Grether, Melo, and Muller (2001) determined the migration policy as result of the electorate’s preferences. Epstein and Hillman (2003) presented migration policy implications of the efﬁciency wage setting. Although many studies deal with the issue of illegal immigration, as mentioned above, there are almost no references to the employers’ decision regarding the number of legal and illegal workers. The majority of these studies simply assume that when the expected penalty faced by the employer increases, the number of illegal immigrants decreases (see, for example, Epstein, Hillman, & Weiss, 1999). In our study we consider the relationship between the number of illegal immigrants and the employer’s beneﬁts (wage gap between legal and illegal workers) and costs of employing them (expected penalty). There is well-established literature on the minimum wage law. For example, the pioneer study of Ashenfelter and Smith (1979) examined the incentive of proﬁt-maximizing ﬁrms to comply with the minimum wage law and the government’s strategy to enforce the law. Change and Ehrlich (1985) expanded this model by adding references to the role of the gap between the minimum wage and the free market wages, the level of elasticity of labor demand, and the effect of the sanctions on the employer’s noncompliance decision. Yaniv (2001) presented portfolio-choice approach to this employer’s decision. Sun and Tawada (2007) analyze illegal migration by assuming that the source country is a developing country in which there is a minimum wage policy. They examine how the minimum wage of the source country and enforcement by the host affects factor prices, migration, unemployment, and economic welfare. They ﬁnd that the

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enforcement effect is clear and intuitive, but the qualitative effect of the minimum wage depends on the wage elasticity of employment in the source country. Epstein and Nitzan (2007) presented a political economy approach whereby the minimum wage is determined by interaction between the politician and the interest group, the workers’ union, and the capital owners. However, the literature has not examined the effect of the minimum wage in the destination country on the employers’ decision regarding employing illegal immigrants. This paper also deals with this issue by answering the question of how a change in the minimum wage affects illegal immigrants and the local workers. Another purpose of this study is to examine the optimal migration policy. The low wage requested by foreign workers encourages capital owners to employ them. The policy maker may protect the unskilled workers by establishing a minimum wage law and allocating resources to catch the noncomplying employers (i.e., employers who employ illegal workers). In our model two interest groups are directly affected by the migration policy: the capital owners who beneﬁt from illegal immigrants and the unskilled workers who suffer from them. The public is affected indirectly by illegal immigration. The politician determines the optimal policy by taking into account all the factors: the capital owners’ and the unskilled workers’ utility, the public interest and the ﬁnancing cost. This paper is organized as follows. The following section presents the decision faced by the illegal workers and the employers. Section 3 determines the optimal enforcement budget. The last section contains a brief summary and conclusion.

2. THE EMPLOYERS’ AND THE WORKERS’ DECISIONS 2.1. The Employer’s Decision Consider a small open and competitive economy where the employers are risk neutral and may employ local unskilled workers or foreign workers in return for a wage that is lower than the equilibrium wage of a closed economy. In order to protect these workers and to prevent the decrease of wages to the level of the foreign workers’ wage, the government establishes a minimum wage, wM, (which is higher than the requested wage of foreign workers and is lower or equivalent to the equilibrium wage of a closed

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economy) for all workers. Moreover immigration law forbids employing foreign workers who lack employment authorization. The employer’s proﬁts equal: PE ¼ VFðNÞ NwM

(1)

where N is the number of unskilled workers, F(N), the production function, which satisﬁes F 0 ðNÞ40; F 00 ðNÞo0, and V, the product price. Denote the optimal number of unskilled workers by N, which satisﬁes VF 0 ðNÞ ¼ wM

(2)

We assume that the employer may employ illegal workers, I, who are perfect substitutes for the legal workers. The wage which paid for a foreign illegal worker, wI, is lower than the wage of a legal workers, wM (below we will determine the foreign illegal worker’s wage, wI). It should be emphasized that in our model the employer pays a wage which is lower than the minimum wage only for the illegal immigrants despite the fact that there are some local workers who are willing to work in return for a similar wage to that of the illegal workers (assuming that their supply increases from left to right). The reason for this assumption is that the illegal foreign workers stay in the country illegally, thus they are afraid to turn to the authorities to complain on being paid a lower wage than the minimum wage. When an illegal worker is apprehended, both the worker and the employer are affected: the illegal worker is expelled from the country, and sanctions against the employer are implemented. Moreover, the local workers are aware of their rights and paying part of them a lower wage than the minimum creates frustration which may harm the production. Therefore the ‘‘illegal workers’’ are herewith called ‘‘illegal immigrants.’’ The enforcement budget to control illegal immigration is implemented via border controls blocking entrance to undesired elements and via internal enforcement, whereby illegal immigrants are apprehended and expelled from the country and their employers are punished. Our model deals with the illegal immigrants who are currently in the country (whether by evading border controls or by entering a country legally for temporary employment and then overstaying when their visas expire (see Epstein et al., 1999), hence we deal with the internal enforcement which is directed at those illegal immigrants and their employers. It is assumed that an employer who employs illegal immigrants may be detected and punished with probability p. The policy maker can regulate, p, by an (internal) enforcement budget, E, i.e., p(E) such that p0 ðEÞ40;

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GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

p00 ðEÞo0. The penalty for employing illegal workers depends on the number of illegal immigrants, yðIÞ, such that yð0Þ ¼ 0 and y0 ðIÞ40; y00 ðIÞ40.4 Moreover, we assume that y000 ð0Þ ¼ 0. This assumption simpliﬁes our calculations. Below we show how this assumption is used and that it is not critical for our results. Lastly, it has been assumed that at the beginning of each period, the employer decides on the number of legal and illegal workers to employ. The employer’s expected proﬁt is given by EðPE Þ ¼ VFðNÞ LwM IwI pyðIÞ

(3)

N ¼LþI

(30 )

such that

The employer determines the optimal number of workers and illegal immigrants. Therefore, the ﬁrst-order conditions for interior solution of maximizing the proﬁts are5,6 @EðPE Þ ¼ VF 0 ðNÞ wM ¼ 0 @N

(4)

@EðPE Þ ¼ wM wI py0 ðIÞ ¼ 0 @I

(5)

and

We obtain that the wages will equal wM ¼ wI þ py0 ðIÞ

(6.1)

VF 0 ðNÞ ¼ wI þ py0 ðIÞ

(6.2)

and

At equilibrium, the marginal cost of employing an illegal immigrant equals the wage of a legal worker – the minimum wage, wM. The employer employs illegal immigrants as long as the cost for employing them, wI þ py0 ðIÞ, is lower or equal to the minimum wage. Afterwards, he continues to employ legal workers as long as their wage, wM, is lower or equal to the marginal value of production, VF 0 ðNÞ. This result is supported by Yaniv’s (2001) conclusions that the employer reduces employment to the point where the marginal value of the production equals the minimum wage but the total number of workers does not change as a result of violating the migration law.

Illegal Migration, Enforcement, and Minimum Wage

203

Lemma 1. A positive relationship exists between the stock of employed illegal immigrants and the level of minimum wage. Proof. Using the inverse function rule with Eq. (6.1) we obtain @I 1 1 ¼ 00 ¼ @wM dwM =dI py ðIÞ

(7)

As assumed above, y00 ðIÞ40, hence ð@I=@wM Þ40. 2.2. The Illegal Immigrants’ Decision Much has been written about the individual’s decision to immigrate; a substantial part of this literature has focused on the illegal immigrant’s decision. All the immigrants are motivated by the expected income in the destination country relative to the source country (which includes the probability of employment) and the costs of migrating abroad. Those costs include the adjustment cost that stems from living in an unfamiliar environment and moving costs (see, for example, Levine, 1999; Chiswick, 1999). However, the illegal immigrant who is subject to apprehension and deportation by the authorities takes into the consideration additional costs: the probability of being apprehended and deported as well the equilibrium wage which is included as an implicit tax which is imposed by employers who pay the illegal immigrants less than the market wage (see Todaro & Maruszko, 1987). Following Todaro and Maruszko (1987) and others it is assumed that the wage in the destination country is higher than the wage in the source country and immigrants face adjustment costs and potential costs if apprehended. The potential immigrant will therefore agree to immigrate illegally if the wage received in the destination country, wI, is higher than the wage in the source country, wH, including the penalty if he is apprehended, lp, and the adjustment cost in the host country, c. The condition for illegal immigration can be written as follows: wI wH þ c þ pl

(8)

Note that this condition is written for one period.7 The employer pays the illegal immigrants the minimal wage that they are willing to accept. Setting Eq. (8) into (5) gives pðEÞ ¼

wM wH c l þ y0 ðIÞ

(9)

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GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN) (a) N Ne = Ie

Ne = N *

Ne = Le = N *

N*

(b)

(c)

(d)

Le = 0

wM − wH − c

wM − wH − c

+ ′(N *)

+ ′(0)

p

Legend: legal workers total workers

Fig. 1. The Optimal Total Number of Workers and Illegal Workers.

Eq. (9) determines the conditions for the optimal number of illegal immigrants, Ie, that are employed for a given enforcement budget, E. Let us explain this equality by looking at Fig. 1 that represents Eq. (9): the solid line represents the number of employed workers, Ne, whereas the dashed line represents the number of legal workers (local and foreign), Le. The gap between these lines represents the number of illegal workers, Ie. At point (a) the government does not allocate resources against illegal immigration (i.e., pðEÞ ¼ 0), the employers employ only illegal immigrants and their number is higher than N, the number of workers whose marginal product value equals the minimum wage (see Eq. (2)). In area (b) the probability of being detected increases and the number of illegal immigrants decreases. However, the employer continues to employ only illegal immigrants and

Illegal Migration, Enforcement, and Minimum Wage

205

their number is higher than N. In area (c) the employer employs both legal and illegal workers such that the cost of employing illegal workers equals the cost of employing legal workers, i.e., the minimum wage. The number of all the workers equals N. In area (d) the probability of being detected is so great that the employer complies with the law and employs only legal workers. To summarize, Proposition 1. (see Fig. 1): (a) If p=0 then Ne=Ie=N and Le=0. Therefore, Ne satisﬁes VF 0 ðN e Þ ¼ wH þ c

(10)

(b) If p 2 ð0; ððwM wH cÞ=l þ y0 ðN ÞÞÞ then N e ¼ I e 4N and Le=0. Therefore, Ie satisﬁes VF 0 ðI e Þ ¼ wH þ c þ pl þ py0 ðI e Þ (c) If p 2 ððwM wH cÞ=l þ y0 ðN Þ; ðwM wH cÞ=l þ y0 ð0ÞÞ Ne=N, I e 2 ðN ; 0Þ and Le 2 ð0; N Þ. Therefore, Ie satisﬁes wM ¼ wH þ c þ pl þ py0 ðI e Þ

(11) then (12)

(d) If p4ðwM wH cÞ=l þ y0 ð0Þ then N e ¼ Le ¼ N and Ie=0. Therefore, Le satisﬁes VF 0 ðLe Þ ¼ wM

(13)

Proof. (a) From setting p=0 in Eqs. (8) and (6.1), we obtain wI ¼ wH þ c and wM 4wI (wM is constant), respectively. This means that the cost of employing an illegal immigrant is lower than in the case of p>0 and than the wage for a legal worker. The employer therefore employs only illegal workers. From Eq. (6.2) we obtain that the number of employed workers hold VF 0 ðN e Þ ¼ wH þ c ¼ wI . (b) From Eqs. (8) and (6.1) it follows that the cost of employing an illegal immigrant is higher than the cost of case (a), but is still lower than the wage for a legal worker. The employer thus continues to employ only illegal workers. From Eq. (6.2) together with (8), we obtain that the number of employed illegal workers hold VF 0 ðI e Þ ¼ wH þ c þ pl þ py0 ðI e Þ.

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(c) From Eqs. (6.1), (6.2), and (8) it follows that VF 0 ðN e Þ ¼ wM ¼ wI þ py0 ðI e Þ such that wI ¼ wH þ c þ pl. This means that the cost of employing illegal immigrants equals the wage for legal workers and equals the marginal product. (d) From Eq. (6.1) it follows that the cost of employing legal workers is higher than the wage for legal immigrants, i.e., wM owI þ py0 ðIÞ. The employer therefore employs only legal workers and their number hold VF 0 ðLe Þ ¼ wM . Area (c) which presents employing both illegal and legal workers is the common case. In this case, the total number of workers is identical to the number of workers that would be employed if only legal workers are employed (d).

3. OPTIMAL POLICY Let us ﬁrst examine how a change in the minimum wage affects the number of local workers employed. The legally employed workers consist of the legal native workers, LL, and the foreign workers, LF. We assume that the supply of the local workers increases from left to right (the supply function is for example, LL ¼ a0 þ a1 w). We assume also that each employer has an immigration quota. The employer ﬁrst employs the local workers, and if there is a surplus demand for legal workers then he may import foreign workers (it is assumed that immigration quotas have non-effective limits). The number of employed local workers is given by LL ¼ N LF I

(14)

Fig. 2 describes the effect of increasing the minimum wage to w1M 4wM on the optimal number of workers, N. From Eq. (2) and from the sign of the second derivative of F(N) (i.e., F 00 ðNÞo0), it follows that dN=dwM o0. Thus, the optimal number of workers decreases from N to N. It is also easy to see that the boundaries described above, wM wH c=l þ y0 ðN Þ and wM wH c=l þ y0 ð0Þ, move to the right to w1M wH c=l þ y0 ðN Þ and w1M wH c=l þ y0 ð0Þ, respectively. Hence, area (b) – the area of employing only illegal workers – expands and area (d) – the area of employing only legal workers – diminishes. This is supported by Lemma 1, which stated that ðdI=dwM Þ40. This means that if the government wants to prevent the rise in the stock of illegal immigrants resulting from the increase in the minimum wage, it must allocate

207

Illegal Migration, Enforcement, and Minimum Wage N

N* N**

(d)

(b) (c) Le = 0

w1M − wH − c

w1M − wH − c

+ ′(N **)

+ ′(0)

p

Legend: legal workers total workers

Fig. 2.

The Effect of Increasing the Minimum Wage.

more resources to counteract illegal immigration (moving to the right in Fig. 2). An additional effect of the rise in the minimum wage is described as follows: the supply of local workers who wish to work for the current wage increases and the number of legal foreigners decreases, i.e., ðdLF =dwM Þo0 (the illegal immigrants and the local workers replace them). A change in the minimum wage affects the number of legal workers and equals dL dN dI ¼ dwM dwM dwM

(15)

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GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

Proposition 2. a. In the case of area (c), the area of employing both legal and illegal workers, raising the minimum wage decreases the number of legal workers employed if the new minimum wage is lower than the equilibrium wage of a closed economy. The change in the number of legal workers is greater than the change in the number of all workers. b. Raising the minimum wage has an ambiguous effect on the number of local legal workers employed. Proof. a. dL=dwM ¼ ðdN=dwM Þ ðdI=dwM Þo0 the LHS, the change in the number of legal workers, equals the change in the number of all workers plus the negative term ðdI=dwM Þ. b. When the minimum wage increases, the supply of local workers increases and they replace the legal foreign workers. However, the total number of workers diminishes and the number of illegal workers rises. If the former effect is bigger than the latter, then the number of local workers increases, and vice versa if the former effect is smaller than the latter. dLL =dwM ¼ ðdN=dwM Þ ðdI=dwM Þ dLF =dwM , the two ﬁrst terms of RHS are negative and the last term is positive. Therefore, it is impossible to know the sign of dLL =dwM . It should be noted that recent studies have indeed found zero or even a positive effect of minimum wage on employment in monopsony markets (Dickens, Mechim, & Manning, 1999). However, other studies show that raising the minimum wage has a negative effect on employment (see Yaniv, 2001). Our model differs from the existing type of models in the literature. Let us present a numerical example which illustrates pﬃﬃﬃﬃ our results. Suppose that the production function is FðNÞ ¼ 2; 000 N , the penalty equals yðIÞ ¼ I 3 =6, V ¼ 1; wM ¼ 100; pﬃﬃﬃﬃ wH ¼ 40; c ¼ 10; and l ¼ 150. We may calculate that F 0 ðNÞ ¼ 1; 000= N and y0 ðIÞ ¼ I 2 =2. It is easy to see that the optimal number of workers (which satisfy VF 0 ðNÞ ¼ 100) equals 100. Now we can calculate the boundaries of employing only illegal immigrants and those employing only legal workers. The former is wM wH c 100 40 10 ¼ ﬃ 0:01 l þ y0 ðN Þ 150 þ ð1002 =2Þ

Illegal Migration, Enforcement, and Minimum Wage

209

and the latter is wM wH c 100 40 10 ¼ 0:33 ¼ l þ y0 ð0Þ 150 þ 0 This means that if the enforcement budget is so low such that the probability of being apprehended is less than 1%, then only illegal immigrants will be employed. However, if the level of enforcement is high and the probability of being apprehended is more than 33%, then the employer employs only legal workers. Suppose now that the minimum wage increases to 150. The optimal number of workers (which satisfy VF 0 ðNÞ ¼ 150) decreases to 44, less than half of the previous quantity. The new boundaries become wM wH c 150 40 10 ¼ ﬃ 0:09 l þ y0 ðN Þ 150 þ ð442 =2Þ and wM wH c 150 40 10 ¼ 0:66 ¼ l þ y0 ð0Þ 150 þ 0 We obtain that after the increase in the minimum wage the employers employ only illegal workers as long as the probability of being apprehended is less than 9% (instead of about 1% previously). The employer employs only legal workers with a very high level of enforcement which creates a probability of being apprehended equal to 66% (instead of 33% previously). If the policy maker wishes to ensure that the rate of the illegal workers is the same he/she must increase the enforcement budget dramatically.

3.1. The Optimal Enforcement Budget In our model the politician determines the optimal enforcement budget. We assume that the politician wishes to maximize social welfare, including the costs and beneﬁts of the unskilled workers, the capital owners, and the economic as well as social costs as a result of illegal immigration. It should be noted that if the politician determines the optimal minimum wage and the struggle between the unskilled workers and the capital owners is over the minimum wage rather than over the enforcement level, our main results will not change.8

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When the enforcement budget increases, the capital owners reduce the number of illegal immigrants for two reasons: (1) the probability of being detected and the expected penalty increase; (2) the wage requested by the illegal immigrants also increases (see Eq. (8)). Hence, increasing the enforcement budget causes a decrease in the capital owners’ proﬁts. The main costs of the existence of illegal immigration are displacement of the local unskilled workers and a reduction in received wages. It is thus clear that increasing the enforcement budget decreases the number of immigrants staying in the host country, the unemployment of local unskilled workers decreases and their utility increases. The secondary costs are caused by the essence of their illegality. For example, the undocumented immigrants are often involved in clandestine activities and are used as signals to the public that the government does not enforce the law. Raising the resource allocation to enforce the immigration law, i.e., the enforcement budget, reduces the social cost, but it has a price – the alternative use. This means that these resources are allocated to nonproductive activities. The unskilled workers are interested in raising the enforcement budget, while the capital owners are interested in reducing it. The government’s objective function is represented by9 G ¼ aPL þ ð1 aÞPE bCðIÞ gE

(16)

where E is the enforcement budget, a, the workers’ relative political strength ð0oao1Þ, PL , the local workers’ earning,10 PE , the proﬁts of the capital owners as given in Eq. (3), C, the social harm resulting from the existence of illegal immigrants, such that Cð0Þ ¼ 0; C 0 ðIÞ40; C 00 ðIÞo0, and b and g denote the weights of this social harm and the enforcement budget ð0ob; go1Þ, respectively. Eq. (16) can be rewritten as G ¼ aLL wM þ ð1 aÞðVFðNÞ wM ðN IÞ IwI pyðIÞÞ bCðIÞ gE (17) The optimal enforcement budget equals: dG @LL @I @I @wI @p @I 0 ¼a wM wI I yðIÞ py ðIÞ wM þ ð1 aÞ dE @E @E @E @E @E @E @I g¼0 ð18Þ bC 0 ðIÞ @E The regulator faces a given employers’ and illegal immigrants’ behavior as presented at the ﬁrst part of this paper. After setting experience with yield

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211

from the employers’ and illegal immigrants’ behavior and some mathematical work (which is presented at Appendix A.1), we can obtain that the optimal enforcement is given by11 a

@LL @I @P ¼ g þ ð1 aÞ ðIl þ yðIÞÞ wM bC 0 ðIÞ @E @E @E

(19)

The ﬁrst term of the RHS presents the increase in the local workers’ wages as a result of increasing the enforcement multiplied by their relative political strength. The second term of the RHS presents the decrease in the social harm resulting from illegal immigration multiplied by the public’s weights. The ﬁrst term of the LHS presents the cost of the enforcement budget and the last term presents the decrease in the proﬁts of the capital owners multiplied by their relative political strength. We see that the policy maker determines enforcement budget which takes into account all the different sectors and the interest groups.

3.2. Comparative Statics Suppose that an exogenous change in the minimum wage has taken place.12 Let us now examine how this change affects the optimal enforcement budget. As shown above, raising the minimum wage decreases the number of employed workers and increases the number of illegal immigrants working in the host country. We also see that the effect, of raising the minimum wage for the local workers’ employment, is not clear. The unskilled workers and the capital owners are affected by the migration policy and struggle in order to change the enforcement budget. Indeed, the capital owners suffer from the additional cost of illegal immigration and ﬁnance the enforcement. However, their direct beneﬁt from illegal immigration is higher. We can therefore say that the unskilled workers have an interest in a large enforcement budget, while the capital owners have the opposite interest. Denote the optimal enforcement budget (which satisﬁes (19)) by E. Let us now examine how an exogenous change in the minimum wage affects E. To simplify we ignore @2 C=@wM @E.13 It can be veriﬁed that @E @2 GðÞ=@E@wM ¼ 2 @wM @ GðÞ=@E 2

(20)

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GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

By the second-order condition, @2 GðÞ=@E 2 is assumed to be negative, so 2 @E @ GðÞ sign ¼ sign (21) @E@wM @wM After some mathematical work which is presented at Appendix A.2 we obtain that 2 @E @ LL @LL @I sign wM þ (22) ¼ sign a þ ð1 aÞ @E @wM @wM @E @E The ﬁrst term in RHS denotes the effect of a change in the enforcement budget on the unskilled workers’ wages, whereas the second term denotes the effect of a change in the enforcement budget on the capital owners’ proﬁts. It is obvious that there is a negative relationship between the enforcement budget and the capital owners’ proﬁts (i.e., @I=@Eo0). However, the effect of a change in the enforcement budget on the unskilled workers’ wages is ambiguous. Let us calculate the sign of @E =@wM . We ﬁrst study the case that local workers are willing to work for the minimum wage, so the employer employs local workers but does not need to employ legal foreign workers, i.e., LF=0 (see Fig. 3(1)). Where the government raises the enforcement budget, the stock of illegal immigrants decreases and the number of local workers increases, i.e., @LL =@E40; @2 LL =@wM @E40 (see Appendix B). The ﬁrst component of RHS in Eq. (22) is therefore positive and the second is negative.

wM

N LL

Fig. 3(1).

I

There Are Local Workers Willing to Work for the Minimum Wage.

Illegal Migration, Enforcement, and Minimum Wage

213

Proposition 3. The effect of changes in the minimum wage on the optimal enforcement budget depends on the political strength of the groups. If the workers’ weight, a, is higher than @LL =@E 1 o 2 2ð@LL =@EÞ þ ð@ LL =@E@wM ÞwM 2 then a positive relation exists between the optimal enforcement budget and the minimum wage. Whereas if ao

@LL =@E 2ð@LL =@EÞ þ ð@2 LL =@E@wM ÞwM

then a negative relation exists between the optimal enforcement budget and the minimum wage. Proof. See Appendix C. The intuition behind this proposition is as follows: as stated in Lemma 1, raising the minimum wage causes an increase in the illegal immigrants employed in the host country. It is also clear that as the total number of workers and the total production decreases, the expected penalty increases and the capital owners’ proﬁts decrease (see Appendix D). This is followed by an increase in the number of employed illegal immigrants, the unemployment among the local workers increases, and therefore the utility of the local workers decreases. If the workers have a high political strength relative to the capital owners’ then the policy maker raises the resource allocation against illegal migration with an increase in the minimum wage. The reason for this is that increasing the budget enforcement prevents an increase in the stock of illegal immigrants and possible harm to the local workers’ utility. However, if the capital owners have strong political strength, the policy maker reduces the enforcement budget with an increase in the minimum wage since increasing the minimum wage decreases the capital owners’ proﬁts. The politician wishes to raise, or at least maintain, the utility of the strong group, and achieves this by reducing the enforcement budget. Another case that can occur is that there are no local workers willing to work at the minimum wage (see Fig. 3(2)). In this case the demand for legal workers is higher than the local supply. Thus, the employer should employ legal foreign workers, i.e., LF 40. Raising the enforcement budget reduces the stock of illegal workers, increases the number of legal foreign workers,

214

GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

wM

N LL

Fig. 3(2).

LF

I

There Are No Local Workers Willing to Work for the Minimum Wage.

but does not affect the number of employed local workers, i.e., @LL =@E ¼ 0 and @2 LL =@wM @E ¼ 0 (in this zone, the change in the minimum wage has no affect @LL @LL =@E ¼ 0). Setting @LL =@E ¼ 0; @2 LL =@wM @E ¼ 0 into Eq. (22), gives dE @I sign o0 (23) ¼ sign ð1 aÞ @E dwM Thus, when the minimum wage increases and there are no local workers willing to work for this wage, the policy maker decreases the enforcement budget. In this case, as a result of increasing the minimum wage the utility of one group, the capital owners, decreases while the utility of the other group, the local workers, does not change (the illegal immigrants displace the legal foreign workers but not the legal local workers). The politician may increase the capital owners’ proﬁts without harming the local workers’ utility. The politician therefore reduces the enforcement budget as long as there is no harm in the local workers’ employment. After that he behaves as described in ﬁrst case. Our results depend on the relative strength of the workers and the capital owners, a and 1a, respectively. In our model we assume that those parameters are exogenous, but they can be endogenous. For example, Epstein and Nitzan (2006) presented a political framework of competition over migration quotas between two interest groups: the workers’ union and the capital owners. In the ﬁrst stage of the game, the interest groups select,

Illegal Migration, Enforcement, and Minimum Wage

215

noncooperatively, their proposed policies of migration quotas. In the second stage, they engage in a contest over the approval of the proposed policy. The politician’s determination about which policy is approved depends on two parameters: the lobbying efforts of the interest group and the weighted average of the excepted social effort. The interest groups can affect the politician’s decision by investing lobbying efforts, but it has costs. The authors showed that lobbying efforts cause the interest groups to moderate their proposed policy, but the equilibrium policy proposals do not coincide. Finally let us examine how a change in the strength of one of the parties, for example, as result of change in the lobbing effort, affects the optimal enforcement budget. In a way similar to (22) we obtain:

dE sign da

@LL @P ðIl þ yðIÞÞ 40 wM þ ¼ sign @E @E

(24)

It is clear that increasing the workers’ relative political strength raises the enforcement budget and vice versa if the capital owners’ relative political strength increases. From the above and from Proposition 3 it follows that if the minimum wage increases as a result of increasing the relative political strength of the workers, it is expected that the enforcement budget will also increase.

4. CONCLUSION We examined two policy measures designed to protect the unskilled workers and the public: preventing a decrease in wage by a minimum wage law and allocating resources to enforce the immigration law. We have focused on the employers’ behavior and on the consequent migration policy. As opposed to studies assuming a negative relationship between the enforcement budget and the stock of illegal workers, we ﬁnd the relationship between the number of employed illegal immigrants and the enforcement budget: at low budget levels employers employ only illegal workers and their number is higher than the total number of workers at higher budget levels. At high budget levels the employer complies with the immigration law and employs only legal workers. In our story we consider a small open economy. The employer may employ legal workers and either pay them minimum wage or not. However, the employer prefers to discriminate against the foreign workers by paying

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GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

them a lower wage than the local workers, because they are in the country illegally and may be afraid to complain to the authorities. Thus, foreign illegal workers are willing to work for a wage which is lower than that of the native workers’ wage and is higher than the wage they would obtain in the home country. The ﬁrst main issue discussed in the paper is the effect of increasing the minimum wage on the domestic workers and the illegal workers. The existing literature deals in detail with the subject of the effect of the minimum wage on employment (see Dickens et al., 1999; Yaniv, 2001). However, there is no reference to the effect on the various groups: illegal immigrants and local workers. Our results show that increasing the minimum wage may increase, decrease, or not change the number of employed local workers, but also raises the stock of illegal immigrants working in the host country. This result supports the established claim in the literature that a positive correlation exists between the wage in the host country and the number of immigrants (legal and illegal) (see Chiswick, 1999; Hanson & Spilimbergo, 1999). However, in our model, the rise in the stock of illegal immigrants is caused by the increased employers’ demand, while in the others the reason is hidden in the increase in the immigrants’ supply which is triggered by a wage differential. The second main issue deals with the optimal enforcement budget. The politicians determine the optimal enforcement budget taking into consideration the employers’ and the illegal immigrants’ behavior and the public interest. Following Epstein and Nitzan (2006), we assume two interest groups: native unskilled workers who are harmed by the illegal immigration and the capital owners who beneﬁt from it. Finally, we study the effect of a change in the minimum wage on the optimal enforcement budget. We show that the relationship between the optimal enforcement budget and the minimum wage depends on the groups’ relative strength. If the workers’ union is strong, then increasing the minimum wage increases the optimal enforcement, and vice versa if the capital owners are the strong group.

NOTES 1. See http://www.oecdobserver.org/news/fullstory.php/aid/190 2. See http://www.cis.org/topics/illegalimmigration.html 3. In some countries sanctions are less effective at deterring illegal entry and employment for several reasons, including among others, allocation of few resources, the spread of false documents and insufﬁcient cooperation between government agencies.

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4. Indeed, in a lot of countries, the ﬁne is constant for each employee, but when marginal production decreases then the apprehension of a worker increases the costs to the employer in a nonlinear way. In addition, the ﬁnancial cost of the ﬁne (for instance, the marginal interest) increases as the total ﬁnes increases. 5. The second-order conditions for maximum are satisﬁed. 6. If the employer employs only illegal immigrants, i.e., N=1, then the ﬁrst-order condition satisﬁes VF 0 ðNÞ ¼ VF 0 ðIÞ ¼ wI þ py0 ðIÞ. The employer employs only illegal workers as long as the cost of employing them, wI þ py0 ðIÞ, is lower than the cost of employing legal workers, i.e., wM . 7. For simplicity, we ignore the one-time moving cost. But it can be assumed that this cost is divided over all the periods. 8. Since it is known that

@E @2 GðÞ=@E@wM @wM @2 GðÞ=@wM @E ¼ ¼ 2 ; @wM @E @ GðÞ=@E 2 @2 GðÞ=@w2M the second-order conditions exist and from Young’s theorem which claimed @2 G= @E@wM ¼ @2 G=@wM @E we obtain that signf@E =@wM g ¼ signf@wM =@Eg (where G is the politician’s objective function, E, the enforcement budget, E, the optimal enforcement budget, wM, the minimum wage, and wM is the optimal minimum wage). 9. Another scenario is that the enforcement budget is ﬁnanced by the ﬁnes and taxes imposed. The public bears the tax burden paying for the enforcement (as in Guzman et al., 2008) and takes part in the struggle over illegal immigration. It is clear that the utility of the public, U public , decreases while the enforcement budget increases. Hence, the government’s objective function will be

G ¼ aPL þ bPE ð1 a bÞU public such that U public ¼ ðCðIÞ þ tðEÞÞ t ¼ E pyðIÞ

8

t0

where t is the tax which is paid by the public for the enforcement budget and it is equal to the gap between the enforcement budget and the government expenditures from penalties on employers. The other variables are similar to the paper’s body. The core of the results does not change and will be provided on request. 10. We use the workers’ wages, and not the workers’ surplus, because the declared main goal of the minimum wage is to maximize the total income transfer to minimum wage workers (Sobel, 1999). Furthermore, the labor supply curve is unknown (except for the fact that it increases) and when the workers’ total wages increase – the ‘‘workers’ surplus’’ also increases. 11. It is assumed that the sufﬁcient second-order conditions are satisﬁed. 12. The changes in the minimum wage can be caused by a change in the average wage, while the minimum wage is adjacent to it or inﬂation occurs and the minimum wage is eroded, or the government is subjected to political constraints to raise the minimum wage (see Sobel, 1999). 13. The essence of the results does not change – proof will be provided on request.

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ACKNOWLEDGMENTS We are grateful to the editors and two anonymous referees for their helpful and important comments. We thank the participants of Annual Meeting of the Israel Economic Association (2007) and the seminar participants at the Department of Agricultural Economics, the Hebrew University of Jerusalem for helpful and constructive comments. Part of the paper is based on one of the chapters from Odelia Heizler’s thesis written at Bar-Ilan University, Israel. Financial support from the Adar Foundation of the Economics Department of Bar-Ilan University is gratefully acknowledged.

REFERENCES Amegashie, J. A. (2004). A political economy model of immigration quotas. Economics of Governance, 5, 255–267. Ashenfelter, O., & Smith, R. S. (1979). Compliance with the minimum wage law. Journal of Political Economy, 87(2), 333–350. Bauer, T. K., Lofstrom, F., & Zimmermann, K. F. (2000). Immigration policy, assimilation of immigrants and natives’ sentiments towards immigrants: Evidence from 12 OECDcountries. Swedish Economic Policy Review, 7, 11–53. Benhabib, J. (1996). On the political economy of immigration. European Economic Review, 40, 1737–1743. Berry, R. A., & Soligo, R. (1969). Some welfare aspects of international migration. Journal of Political Economy, 77, 778–794. Borjas, G. J. (1995). The economic beneﬁts of immigration. Journal of Economic Perspectives, 9, 3–22. Change, Y., & Ehrlich, I. (1985). On the economics of the compliance with the minimum wage. Journal of Political Economy, 93(11), 84–92. Chiswick, B. R. (1988). Illegal immigration and immigration control. Journal of Economics Perspective, 2(3), 101–115. Chiswick, B. R. (1999). Are immigrants favorably self-selection? American Economic Review, 89(2), 181–185. Cobb-Clark, D. A., Shiells, C. R., & Lowell, B. L. (1995). Immigration reform: The effects of employer sanctions and legalization on wages. Journal of Labor Economics, 13(3), 472–498. Dickens, R., Mechim, S., & Manning, A. (1999). The effect of minimum wage on employment: Theory and evidence from Britain. Journal of Labor Economic, 17(1), 1–22. Djajic, S. (1999). Dynamics of immigration control. Journal of Population Economics, 12, 45–61. Epstein, G. S., & Hillman, A. L. (2003). Unemployed immigrants and voter sentiment in the welfare state. Journal of Public Economics, 87, 1641–1655. Epstein, G. S., Hillman, A. L., & Weiss, A. (1999). Creating illegal immigrants. Journal of Population Economics, 12(1), 3–21. Epstein, G. S., & Nitzan, S. (2006). The struggle over migration policy. Journal of Population Economics, 10(4), 703–723.

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Epstein, G. S., & Nitzan, S. (2007). Endogenous public policy and contest. Berlin: Springer. Epstein, G. S., & Weiss, A. (2006). The why, when and how of immigration amnesties. Working paper. Ethier, W. J. (1986). Illegal immigration: The host country problem. American Economic Review, 76, 56–71. Garcia, A. S. (2006). Does illegal immigration empower rightist parties? Journal of Population Economics, 19(4), 649–670. Gaytan-Fregoso, H., & Lahiri, S. (2000). Foreign aid and illegal immigration. Journal of Development Economics, 63, 515–527. Grether, J., Melo, J., & Muller, M. (2001). The political economy of international migration in a Ricardo–Viner model. CERP Discussion Paper, No. 2714. Guzman, M. G., Haslag, J. H., & Orrenius, P. M. (2008). On the determinants of optimal border enforcement. Economic Theory, 34(2), 261–296. Hanson, G. H., & Spilimbergo, A. (1999). Illegal immigration, border enforcement, and relative wages: Evidence from apprehensions at the US–Mexico border. American Economic Review, 89(5), 1337–1357. Levine, P. (1999). The welfare economics of immigration control. Journal of Population Economics, 12, 23–43. Martin, P., & Miller, M. (2000). Employer sanctions: French, German and US Experiences. International Migration Papers, Number 36. Rivera-Batiz, F. L. (1982). International migration, non-traded goods and economics welfare in the source country. Journal of Development Economics, 11, 81–90. Sobel, R. S. (1999). Theory and evidence on the political economy of the minimum wage. Journal of Political Economy, 107(4), 761–785. Sun, S., & Tawada, M. (2007). The economic effects of illegal migration under the minimum wage policy of a source country. Papers in Regional Science, 86(2), 321–331. Todaro, P. T., & Maruszko, L. (1987). Illegal migration and US immigration reform: A conceptual framework. Population and Development Review, 13(1), 101–114. Yaniv, G. (2001). Minimum wage noncompliance and the employment decision. Journal of Labor Economics, 19(3), 596–603. Zimmermann, K. F. (1995). Tackling the European migration problem. Journal of Economics Perspectives, 9, 45–62.

APPENDIX A. 1 The difference between the minimum wage and the illegal workers’ wage at equilibrium equals the expected penalty (see Eq. (6.1)): py0 ðIÞ ¼ wM wI

(A.1.1)

In addition, from Eq. (8) it follows that @wI @p ¼l @E @E

(A.1.2)

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From setting Eqs. (A.1.1) and (A.1.2) into (18), we obtain dG dE

@LL @I @I @p @I wM wI ðIl þ yðIÞÞ ðwM wI Þ wM þ ð1 aÞ @E @E @E @E @E @I g¼0 ðA:1:3Þ bC 0 ðIÞ @E

¼a

Rearranging Eq. (A.1.3) gives dG @LL @p @I ¼a ðIl þ yðIÞÞ bC 0 ðIÞ g¼0 wM ð1 aÞ dE @E @E @E Hence, the optimal enforcement is given by a

@LL @I @P ¼ g þ ð1 aÞ ðIl þ yðIÞÞ wM bC0 ðIÞ @E @E @E

(A.1.4)

(A.1.5)

APPENDIX A. 2 It is known that LL ¼ LL ðwM Þ and I ¼ IðwM Þ, hence @ðð@LL =@EÞwM Þ @LL @2 L L þ ¼ wM @wM @E @E@wM and @ðIl þ yðIÞÞ @I @I ¼l þ y0 ðIÞ @wM @wM @wM Hence, from Eq. (A.1.4) we obtain @2 GðÞ @LL @2 LL @p @I @I 0 l þ ¼a wM ð1 aÞ þ y ðIÞ @E@wM @E @wM @wM @E @E@wM (A.2.1) From Eq. (9) and the quotient rule, we obtain @p ðwM wH cÞy00 ðIÞ @I ¼ @E @E ðl þ y0 ðIÞÞ2

(A.2.2)

Illegal Migration, Enforcement, and Minimum Wage

Setting Eq. (A.2.2) into (A.2.1) gives: @2 GðÞ @LL @2 LL þ ¼a wM @E@wM @E @E@wM ðwM wH cÞy00 ðIÞ @I @I @I 0 l þ y ðIÞ þ ð1 aÞ @E @wM @wM ðl þ y0 ðIÞÞ2

221

ðA:2:3Þ

Eq. (A.2.3) can be written as @2 GðÞ @LL @2 LL ðwM wH cÞy00 ðIÞ @I @I þ ¼a wM þ ð1 aÞ @E@wM l þ y0 ðIÞ @E @wM @E @E@wM (A.2.4) Setting Eq. (9) into (A.2.4) affords @2 GðÞ @LL @2 LL @I @I þ ¼a wM þ ð1 aÞpy00 ðIÞ @E@wM @E @wM @E @E@wM After setting Eq. (7) into (A.2.5), we obtain 2 @2 GðÞ @ LL @LL @I wM þ ¼a þ ð1 aÞ @E@wM @E @wM @E @E Hence, by Eqs. (20) and (A.2.6) it follows that 2 @E @ LL @LL @I wM þ sign ¼ sign a þ ð1 aÞ @E @wM @wM @E @E

(A.2.5)

(A.2.6)

(A.2.7)

APPENDIX B Proof that when LF ¼ 0 then @2 LL =@wM @E40. The intuition is as follows: when the minimum wage rises more local workers wish to work, unemployment among the local population increases, and the effect of change in the enforcement budget on the employed local workers (i.e., @LL =@E) increases. The formal proof: If LF ¼ 0, then LL ¼ N I, hence @LL @N @I ¼ @E @E @E

(B.1)

222

GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

It is known that @N=@E ¼ 0, so from Eq. (B.1) we obtain @LL @I ¼ @E @E

(B.2)

From Eq. (B.1) it follows that @wM ¼ py00 ðIÞ @I

(B.3)

@I 1 ¼ @wM py00 ðIÞ

(B.4)

Hence,

From Eq. (B.4) it follows that @2 I ðð@P=@EÞy00 ðIÞÞ þ py000 ðIÞð@I=@EÞ ¼ @E@wM ðpy00 ðIÞÞ2

(B.5)

Under the assumptions mentioned above, the third derivative of the penalty y000 ðIÞ equals zero. This assumption simpliﬁes matters. Alternatively, it can be assumed that py000 ðIÞð@I=@EÞ is very small or equals zero. Hence, @2 I o0 @E@wM

(B.6)

From Eq. (B.2) together with (B.6), we obtain @2 L L 40 @E@wM

(B.7)

APPENDIX C Proof of Proposition 3: From setting @I=@E ¼ ð@LL =@EÞ (see Appendix B) into Eq. (A.2.6), we obtain @E @2 L L @LL sign wM þ ð2a 1Þ ¼ sign a @wM @wM @E @E

Illegal Migration, Enforcement, and Minimum Wage

223

The sign of @E =@wM is positive if and only if a4

@LL =@E 2ð@LL =@EÞ þ ð@2 LL =@E@wM ÞwM

all the components of this expression are positive, so @LL =@E 1 o 2 2ð@LL =@EÞ þ ð@ LL =@E@wM ÞwM 2 And vice versa, if ao

@LL =@E 2ð@LL =@EÞ þ ð@2 LL =@E@wM ÞwM

then the employers’ political strength, 1 a, is high and signf@E =@wM go0.

APPENDIX D The effect of raising the minimum wage on the capital owners’ proﬁts: From Eq. (3) we obtain @EðPE Þ @N @N @I 0 ¼ VF ðNÞ ðN IÞ wM dwM @W M @wM @wM @I @I wI py0 ðIÞ ðD:1Þ @wM @wM From Eqs. (6.1) and (6.2), we obtain py0 ðIÞ ¼ wM wI and VF 0 ðNÞ ¼ wM

(D.2)

Substituting (D.2) into (D.1) gives @EðPE Þ @N @N @I ¼ wM ðN IÞ wM dwM @W M @wM @wM @I @I wI ðwM wI Þ @wM @wM

ðD:3Þ

224

GIL S. EPSTEIN AND ODELIA HEIZLER (COHEN)

Eq. (D.3) can be rewritten as @EðPE Þ ¼I N dwM It is clear that N4I, hence @EðPE Þ=dwM o0.

(D.4)

EARNINGS LOSSES FOLLOWING JOB CHANGE IN JAPAN: EVIDENCE FROM A JOB PLACEMENT FIRM$ Michael Bognanno and Lisa Delgado ABSTRACT The costs of job displacement are examined on a sample of Japanese workers successfully provided job placement services from 2000 to 2003, a period of economic stagnation and structural change in Japan. We ﬁnd that displaced workers suffer a loss of approximately $1,100 for each additional year of age. Workers also incur a large penalty when they change industries after being displaced. The age–earnings loss relationship is consistent with the operation of a delayed compensation scheme in large ﬁrms.

1. INTRODUCTION Structural changes in the Japanese economy and sluggish growth in the 1990s and beyond have imposed hardships on workers with both social and economic consequences. The high cost to workers of job change was one

$

This paper was previously titled ‘‘Job Displacement Penalties in Japan’’.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 225–250 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28007-6

225

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MICHAEL BOGNANNO AND LISA DELGADO

aspect of the economic consequences. In this paper, we use a unique data set from a job placement ﬁrm to study the impact of job change on the wages of workers in large ﬁrms and to quantify the impact of age, gender, education, tenure, hierarchical level, initial ﬁrm size (employment), days of unemployment, and industry change on job displacement penalties. During the sample period from 2000 to 2003, we ﬁnd evidence of worker job displacement costs that increase strongly with age at a rate of approximately $1,100 per year. We also ﬁnd large penalties associated with industry change and the number of days spent in job search when these are treated exogenously. Between 1990 and 2003, the overall unemployment rate in Japan crept up from 2.1% to 5.3%. Despite a worsening labor market, older, full-time male workers with signiﬁcant tenure were largely shielded from unemployment in the 1990s through the buffering effect of traditional human resources practices. These practices include reducing hours and overtime pay, reducing the hiring of college graduates, and transferring workers to other ﬁrms either temporarily (shukko) or permanently (tenseki).1 While the media has deemed lifetime employment over, Kato (2001) argues against this notion.2 He documents that for workers from 30 to 44 with ﬁve or more years of ﬁrm tenure, there was only a very slight drop in 10-year retention rates between the two periods of 1977–1987 and 1987–1997. Lifetime employment, always something of a misnomer, cannot be said to have ceased for the older workers with substantial tenure. Nevertheless, concern continues to be expressed over the continued retention of the relatively privileged core workers, along with pessimism about their ability to leave the secondary labor market once unemployed.3 Though the ﬁrst concern over core worker retention rates has yet to be empirically justiﬁed, the second concern may have some validity. Our data document the high cost of job displacement for workers from large, wellknown Japanese ﬁrms and the movement to smaller ﬁrms upon reemployment. The results give some credibility to the concern expressed over the consequences facing workers that fall from large ﬁrms into the secondary labor market. The literature on job displacement is large, and the effects of job displacement on wages have been well documented in the United States.4 Earnings have been estimated to fall between 15% and 40%, and these losses increase with both ﬁrm tenure and labor market experience (Topel, 1993). Earning losses were shown by Ruhm (1991) and Jacobson, LaLonde, and Sullivan (1993) to persist four and ﬁve years after job displacement. Tenure in the initial job increases earnings in both initial and new jobs but is valued less in the new employment (Addison & Portugal, 1989; Kletzer,

Earnings Losses Following Job Change in Japan

227

1989). Farber (1993) found job displacement penalties to increase by 1% for every year of ﬁrm tenure. Poor labor market conditions and workers changing industries also increase job displacement penalties. There is little empirical research on the consequences of job displacement in Japan due in large part to the difﬁculty in obtaining data, particularly income information at the individual level. Despite Japan’s status as the world’s second largest economy, we are aware of only one published study on job displacement in Japan. Abe, Higuchi, Nakamura, Kuhn, and Sweetman (2002) review features of the Japanese and Canadian labor markets and analyze the incidence and consequences of job displacement in Japan and Canada. They ﬁnd median unemployment durations resulting from job displacement in Japan of less than two months in the mid-1990s. Further, they ﬁnd virtually no impact on mean wages from job displacement for workers under about 50 years of age in Japan. Only 8.7% of displaced Japanese men and 4.3% of Japanese women faced wage reductions greater than 30%. Large wage increases in Japan were also uncommon. Only 2% of men and 3% of women had gains over 30%. Job displacement cost increased with age in Japan. For men over 55, mean wages fell 10–15%. In contrast with Canadian workers under 55, displaced Japanese workers had shorter unemployment spells and were less likely to have large wage reductions. At the same time, because displacement costs rise more strongly with age in Japan than in Canada, more senior Japanese workers experience greater hardships from displacement than Canadian workers do. This study contributes little to what is known about the costs of job displacement in Japan, particularly for those from large ﬁrms and ﬁnding employment through job placement services. In comparison to Abe et al., our data are smaller in size, less representative of the population, and subject to various types of selection in entering the sample. Selection bias may exist because workers ﬁnding well-paid jobs without the involvement of the placement service do not appear in the data. This would serve to inﬂate the cost of job loss. On the other hand, the provision of job placement services itself is a beneﬁt that may mitigate earnings losses but is not available to all displaced workers. Unfortunately, the study does not have a control group against which to compare the earnings changes of the displaced workers. However, our data are better in important respects. All of the data available to Abe et al. are categorical. For instance, the income changes available in their data are coded into ﬁve categories according to the percentage change, such as an income loss of over 30%, between 10% and 30%, and so forth. Because they only know the category of the percentage

228

MICHAEL BOGNANNO AND LISA DELGADO

change in income, the average penalty from job change cannot be computed without error because it is not known how income changes are distributed within each income change category. Our data contain worker income in both jobs, and income changes can be computed directly. Another beneﬁt of this study is that it is more recent and covers a period of greater economic stagnation. The study by Abe et al. was conducted on job displacements that took place in 1995. GDP was growing at 2.4% in 1995, and unemployment stood at 3.2%. During our sample period from January 2000 to May 2003, GDP grew at an average annual rate of only 1.5% and unemployment averaged 4.8%. We also explore factors that inﬂuence job loss penalties that have not been studied. Additionally, though ﬁrm tenure was not available to Abe et al. and is not available in our data, we impute tenure based on a national survey of Japanese workers that provides mean tenure broken down by year, industry, gender, educational level, ﬁrm size, and ﬁve-year age categories. Hence, we can examine the role of tenure on displacement penalties. The next section discusses a theory relevant to job displacement. Section 3 describes the data. Section 4 presents the empirical results, and conclusions follow in Section 5.

2. THEORY It is tempting to think about the primary sector of the Japanese labor market in terms of Lazear’s (1979) well-known model of delayed compensation in which wages and the marginal product of workers are not equal. When the opportunity for long-term employment exists, the delayed compensation model suggests that it may be beneﬁcial to underpay workers relative to their marginal product early in their careers and overpay them later. This compensation scheme is hypothesized to have desirable consequences because workers are provided with the incentive to exert enough effort to remain in the employment of the ﬁrm throughout their careers. The Japanese labor market may be relatively well suited to operating according to a delayed compensation model for two reasons. First, the risk to the ﬁrm of workers not retiring and collecting compensation in excess of their marginal product longer than anticipated does not exist in Japan. This is because mandatory retirement is both legal and, as noted by Clark and Ogawa (1992), an important part of the employment contract.5 Second, Hashimoto and Raisian (1985) note that job attachment is greater in Japan than in the United States. Long-term employment contracts exist for many

Earnings Losses Following Job Change in Japan

229

workers in Japan, particularly at the larger ﬁrms, such as those represented in our data. Accounts in the popular press and results in the literature suggest that delayed compensation contracts do operate in Japan.6 Clark and Ogawa (1992) ﬁnd direct empirical support for the delayed compensation model. Since delaying compensation leads to more steeply sloped tenure–earnings proﬁles, the ﬁnding by Hashimoto and Raisian (1985) that the earnings growth attributable to tenure is greater in Japan than in the United States is consistent with a greater prevalence of such contracts in Japan. One implication of delayed compensation contracts is that, since young workers are underpaid relative to their market wage and old workers are overpaid, older workers with more years of ﬁrm tenure should experience larger reductions in pay due to job change. More generally, there are several theories that relate to the cost of job separation. Fallick (1996) notes four reasons to expect lower wages for displaced workers than their nondisplaced counterparts: the loss of speciﬁc human capital, a superior job match, possible union or industry wage premiums, and seniority. These factors also link the cost of job separation to job tenure. Assuming that both speciﬁc human capital and the quality of the job match increase with job tenure, job separation costs should be larger for older workers with greater tenure. If the last of Fallick’s reasons, seniority, exhibits an effect on pay independent of worker productivity, it could be considered within the delayed compensation model advanced by Lazear. Since the speciﬁc human capital, job-matching, and delayed compensation models all predict the cost of job separation to increase with tenure, it is difﬁcult to distinguish between them on this basis. We simply note that ﬁnding evidence of this relationship is consistent with the delayed compensation model and also other theories. We also expect measures of general human capital, such as years of education, to maintain their value in reemployment.

3. DATA A ﬁrm engaged in job placement services in Japan provided the data set. During the period covered, January 2000–May 2003, the ﬁrm had served over 1,000 job seekers. The data set contains information on 622 successfully placed workers initially employed in 65 generally large ﬁrms and going to 525 new, generally smaller ﬁrms.7 Workers excluded from the data set include those who fell out of contact with the placement ﬁrm, found new

230

MICHAEL BOGNANNO AND LISA DELGADO

employment on their own, began their own business, had quit looking for work, or were continuing clients still looking for work.8 The placement ﬁrm contracts only with other ﬁrms; there are no contracts with independent job seekers. The ﬁrm reports that it successfully places about 85% of its job seekers. Middle-aged workers are more likely to receive placement services, and the older a worker is, the longer is the period of search. Job seekers typically receive a job offer through the placement company after an average wait of about four months. Job seekers rarely pass up this offer, but when they do so, it is most commonly because they cannot accept the culture of the new ﬁrm. The data provided by the placement ﬁrm includes earnings before and after displacement, age, gender, years of education, college major, hierarchical position of the initial job, certiﬁcations, occupation, and characteristics of the initial ﬁrm and the new ﬁrm. The data set does not contain any direct information on job tenure with the initial ﬁrm. Because tenure is a variable of interest, we impute tenure using national Japanese statistics.9 Tables 1–4 provide descriptive statistics for the data set. Table 1 compares our data set with Japanese national averages in terms of education, earnings, and industry representation. Table 2 lists the breakdown of workers in our data set by the position in hierarchy, ﬁrm size, and industry in the initial ﬁrm and the new ﬁrm. Table 3 lists educational characteristics, unemployment duration, and wage changes by the age category of workers in our data set. Table 4 describes the characteristics of the initial and new ﬁrms of employment. Table 1 shows the differences between the sample analyzed in this paper (labeled ‘‘Displacement Data’’) and national summary statistics from a survey of educational attainment of the adult population collected by the OECD in regard to education, a survey of 33,000 establishments conducted by the Japanese Ministry of Health, Labour and Welfare in regard to earnings, and a survey of the labor force conducted by the Statistics Bureau, MPHPT (now known as MIT), in regard to industry. It is evident that our sample is more educated than the general Japanese population. The table also shows that Japanese workers of all age categories, except ages 20–24, 30–34, and 50–54, had a slight increase in their earnings from 2000 to 2002. However, our sample shows large declines in earnings after being displaced from the initial ﬁrm for all age categories, except ages 30–34. Focusing on a comparison of mean earnings in US dollars across age groups in Japan and the mean earnings for the same age groups in our data before and after displacement, we ﬁnd that most of the workers in our data made above-

28,406 36,116 44,533 51,462 54,721 56,292 57,821 53,389 37,434

28,350 36,384 44,822 52,160 55,580 57,279 58,164 54,680 39,712

28,338 36,171 44,125 51,674 55,447 57,076 57,161 54,224 38,847

2002

0.2 0.2 0.9 0.4 1.3 1.4 1.1 1.6 3.8

% Change from 2000 to 2002

64.1 0.0 1.3 19.2 9.8 4.6 1.0

32.4 1.2 7.0 11.6 7.8 26.0 14.1 49.5 0.0 434.6 39.6 20.8 468.5 0.0

20.5 0.5 6.4 22.9 3.8 26.7 19.2

20.0 0.5 6.3 23.0 3.7 27.6 18.9

19.3 0.5 6.3 22.7 3.8 28.5 18.8

5.9 1.8 1.4 0.7 1.0 6.9 2.0

Firm 1 (%) Firm 2 (%) % Change between Firms 2000 (%) 2001 (%) 2002 (%) % Change from 2000 to 2002

23.7 12.0 6.2 0.4 14.8 20.8 23.4 28.5 41.9 40.0

2001

Education data for Japan were obtained through the OECD (http://www.oecd.org/dataoecd/52/38/33669031.xls). The following statistics for Japan were used to match with our data: Jr. high school ¼ below upper secondary; Sr. high school ¼ upper secondary; Jr. college or vocational school ¼ tertiary type B institutions; university or more ¼ tertiary type A institutions. b Earnings data for Japan were obtained from the Japan Basic Survey on Wage Structure (http://www.mhlw.go.jp). c Industry data for Japan were obtained through the Statistics Bureau, MPHPT (http://www.stat.go.jp).

a

Manufacturing Electricity, gas, heat, and water supply Transport and communications Wholesale and retail trade Finance, insurance, and real estate Services Other

Industryc

50,430 26,760 33,408 42,272 53,992 54,080 56,858 53,174 43,217 56,304

66,088 30,419 35,617 42,113 63,369 68,302 74,247 74,391 74,446 93,840

Ages 20–59 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–64

% Change between Firms

2000

Firm 2

Firm 1

Earningsb

16.3 47.4 16.0 20.0

2002 (%)

2000–2002 (%)

7.2 31.4 9.0 52.5

National Averages

Displacement Data

Comparison between Displacement Data Set and National Data.

Education Jr. high school Sr. high school Jr. college or vocational school University or more

a

Table 1. Earnings Losses Following Job Change in Japan 231

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MICHAEL BOGNANNO AND LISA DELGADO

average earnings before displacement and below-average earnings after displacement. Finally, Table 1 shows that industry changes in our sample are similar to the changes taking place overall in the Japanese workforce. The movement out of the manufacturing, wholesale, and retail trade, ﬁnance, insurance, and real estate industries to the services industry that occurred nationally is also reﬂected in the industry changes occurring in our data. Not surprisingly, the industry shifts are more pronounced for the displaced workers than for all workers. Nearly two-thirds of the workers in our sample lost jobs in manufacturing, reﬂecting the 5.8% decline nationally in manufacturing’s share of total employment between 2000 and 2002. The industry to expand most strongly nationally in the wake of the economic changes taking place was the services industry. Reﬂecting this, the employment share in the services industry increased in our data from 4.6% to 26%.10 Table 2 describes workers according to their hierarchical position and ﬁrm size in both the initial ﬁrm and the new ﬁrm. Level, deﬁned by the 1–8 scale in the table, is slightly higher on average for workers after job change. However, when the sample is restricted to workers with the level reported both before and after job change, the average level falls by 0.41. It should be noted that the differences between levels are not constant in any sense, nor would a given title necessarily connote the same status across ﬁrms. We can

Table 2.

Change in Hierarchical Level and Firm Size from Job Separation. Percentage of Workers

Average level Stacho (president, 8) Bucho (department manager, 7) Kacho (section chief, 6) Kakaricho (chief clerk, 5) Jicho (vice chief, 4) Supervisory duties (3) No supervisory duties (2) Noncorporate position (1) Large ﬁrm (W10,000 employees) Medium ﬁrm (W1,000 employees, o10,000 employees) Small ﬁrm (o1,000 employees)

Before separation

N

After separation

N

3.1 0.0% 2.4% 17.0% 2.9% 23.8% 9.2% 6.3% 38.3% 35.7% 31.8%

206 0 5 35 6 49 19 13 79 198 176

3.4 0.5% 10.3% 8.8% 3.4% 21.1% 17.2% 18.6% 20.1% 0.8% 17.2%

204 1 21 18 7 43 35 38 41 2 45

32.5%

180

82.0%

214

Earnings Losses Following Job Change in Japan

233

also see that the displaced workers are being reemployed at smaller ﬁrms. Employment in ﬁrms with fewer than 1,000 employees rose from 32.5% to 82% as the result of job placement for workers in this sample. Table 3 summarizes characteristics of the displaced workers by age. Unemployment duration, which is four months on average, rises with age. The marginal effect of being an extra year older is about two additional days of unemployment. The oldest workers, those over 55, experience the largest losses in earnings from job displacement. Similarly, while the average loss in earnings across the sample is 25.7%, the earnings loss for workers over 40 is signiﬁcantly greater than for those under 40. Workers in their early 30s actually have a slight increase in income. Last, it appears in Table 3 that changing industry is positively correlated with the income loss due to job displacement. This relationship is explored in estimations in the next section. The results in Table 3 contrast with those of Abe et al. in regard to the magnitude of job displacement costs. They found that displacement had no mean impact on the wages of those under 50 and only a 10–15% reduction for those over 55. The contrast with Abe et al. suggests that the impact of job separation on wages has risen perhaps because of the slower economic growth during the sample period. The size of the displacement costs must be interpreted with caution, however, because of the special nature of the sample. There are two primary reasons for this. First, the workers were displaced from high-paying large ﬁrms. Second, the workers were of higher income in their initial ﬁrms than if they were paid according to national averages, given their industry, age, ﬁrm size, education, and gender categories. Even assuming that the results are applicable only to workers being displaced from primary sector ﬁrms, possible selection bias must be taken in account. One potential source of selection bias that would inﬂate displacement costs is workers ﬁnding well-paid jobs on their own because they will not appear in the data. There are also two potential sources of bias that might reduce the estimated displacement costs. First, the provision of job placement services was to the advantage of the workers in the sample. Second, though some workers might ﬁnd well-paid jobs on their own, others not appearing in the data are those who quit looking for work, were still looking for work, or were unable to ﬁnd jobs even with the help of placement services. This source of selection bias also exists in the national data used by Abe et al. since reemployment at a ﬁrm with at least ﬁve employees is also necessary to enter their sample. Overall, while no conclusive statement can be made about the net inﬂuence of selection bias,

621 43 40 89 91 105 156 94 3

20–68 20–29 30–34 35–39 40–44 45–49 50–54 55–59 60–68

89.9% 77.5% 80.0% 85.2% 93.3% 91.3% 94.8% 91.4% 66.7%

(551) (31) (32) (75) (84) (95) (146) (85) (2)

Male

52.5% 58.8% 62.5% 72.4% 65.0% 44.2% 49.1% 42.5% 0.0%

(117) (10) (10) (21) (13) (19) (27) (17) (0)

University Graduate

35.0% (41) 40.0% (4) 30.0%(3) 45.0% (9) 41.7% (5) 20.0% (4) 34.6% (9) 36.8% (7) 0.0% (0)

Engineering/ Math Major

54.7% 60.0% 50.0% 50.0% 41.7% 70.0% 53.8% 52.6% 0.0%

(64) (6) (5) (10) (5) (14) (14) (10) (0)

Business/ Law Major

10.3% 0.0% 20.0% 5.0% 16.7% 10.0% 11.5% 10.5% 0.0%

(12) (0) (2) (1) (2) (2) (3) (2) (0)

Other Major

120 (618) 70 (43) 97 (40) 102 (89) 117 (91) 118 (103) 139 (154) 142 (94) 159 (3)

3.1 3.4 2.1 3.6 3.7 2.4 3.6 2.7 2.5

(206) (15) (17) (25) (18) (38) (53) (37) (2)

Average Average Level Duration of Unemployment Firm 1

3.4 2.4 2.6 3.9 3.8 3.8 3.3 3.0 1.0

(204) (10) (8) (21) (24) (42) (66) (31) (1)

Average Level Firm 2

23.0% 14.0% 17.5% 16.9% 20.9% 29.5% 26.9% 23.4% 0.0%

(143) (6) (7) (15) (19) (31) (42) (22) (0)

Pct. Level Increase

66.2% 72.1% 40.0% 49.4% 78.0% 67.6% 69.2% 72.3% 100.0%

(412) (31) (16) (44) (71) (71) (108) (68) (3)

Pct. Industry Change

Worker Characteristics and Job Separation Outcomes by Age. Average Income Firm 2

67,774 (379) 50,357 (513) 34,429 (35) 32,330 (37) 42,113 (20) 42,272 (29) 63,369 (73) 53,992 (75) 80,784 (51) 53,989 (71) 74,247 (55) 56,858 (86) 74,391 (84) 53,174 (136) 74,446 (60) 43,217 (76) 93,840 (1) 46,958 (2)

Average Income Firm 1

25.7 6.1 0.4 14.8 33.2 23.4 28.5 41.9 50.0

Pct. Change in Income (%)

Notes: The number of observations is in parentheses. The duration of unemployment is measured in days. Incomes are measured in 2000 US dollars. Pct. level increase is the percent of reemployed workers who experience an increase in level based on the 1–8 scale in Table 2.

Total Number of Workers

Ages

Table 3.

Earnings Losses Following Job Change in Japan

235

the placement ﬁrm maintains that it places all but 15% of those referred to it, limiting to some extent the bias from workers ﬁnding employment on their own or not being placed at all. Table 4 summarizes ﬁrm characteristics of the initial and new ﬁrms by worker age cohort. It is evident that workers in all age categories are going to smaller ﬁrms upon reemployment, and ﬁrms displacing workers have negative proﬁts that average $60 million. This suggests that displacements were ﬁnancially motivated. However, only 39% of displaced workers came from ﬁrms with negative proﬁts. Of those workers at ﬁrms with negative proﬁts, 42% came from ﬁrms losing nearly $1 billion in the year of job displacement. These large losses caused the mean to be negative when the majority of workers came from ﬁrms that were not losing money. Younger displaced workers come disproportionately from manufacturing. In this data set, over 90% of those displaced workers under the age of 34 come from manufacturing. Due to missing data for the new ﬁrms, we have few observations for these characteristics.

4. ESTIMATION OF JOB DISPLACEMENT PENALTIES The analysis of job displacement penalties takes place in three parts. First, we graphically present the estimated age–earnings and tenure–earnings proﬁles in order to provide a sense of the large magnitude of the job separation penalties in these data. Second, separate estimates of the earnings equations for the initial ﬁrm and the new ﬁrm are presented. Third, the change in earnings between the initial ﬁrm and the new ﬁrm is analyzed. The change in earnings is also compared against the results of two previous studies, Abe et al. for Japan and Farber (1997) for the United States. 4.1. Earnings Proﬁles Fig. 1 shows the extent to which age is more highly rewarded in initial employment than in new employment in the Japanese labor market and the cost of job separation for older workers.11 In addition to providing the age– earnings proﬁles for workers in their initial job (Firm 1) and new job (Firm 2), we have included an age–earnings proﬁle that displays what workers in the sample would earn if they were paid according to national averages.12 This proﬁle is included for comparison purposes. Workers in their initial jobs in

Average proﬁts

2,749,428 (14) 16,645 (2) – (0) – (0) 60,161,819 (3) 921,997 (4) 941,908 (2) 74,860,850 (3) – (0)

63,379,682 (384) 104,491,548 (32) 130,931,892 (20) 67,464,351 (49) 3,619,945 (55) 82,375,366 (67) 81,573,538 (94) 216,222,951 (65) 261,095,782 (2)

Firm

Note: The number of observations is in parentheses.

1,604,948,247 (25) 395,429,889 (4) – (0) – (0) 518,857,226 (3) 32,340,654 (8) 33,053,880 (7) 12,165,104,180 (3) – (0)

After separation 20–68 793 (261) 20–29 4,593 (9) 30–34 711 (12) 35–39 986 (33) 40–44 794 (29) 45–49 607 (57) 50–54 541 (75) 55–59 556 (45) 60–68 – (0)

Average sales

9,334,530,082 (390) 12,033,786,661 (32) 4,733,301,005 (21) 4,684,946,430 (52) 6,662,860,017 (56) 10,425,651,218 (68) 10,087,342,843 (94) 13,418,254,672 (65) 4,953,899,318 (2)

Average number of workers

Before separation 20–68 7,766 (554) 20–29 11,419 (41) 30–34 3,567 (35) 35–39 4,948 (83) 40–44 5,254 (80) 45–49 8,017 (94) 50–54 8,653 (132) 55–59 11,382 (85) 60–68 5,011 (3)

Ages

Table 4.

1,721,021,874 650,162,305 – (0) – (0) 9,578,435,647 0 (0) 24,383,323 0 (0) – (0) (4)

(1)

(6) (1)

10,644,224,828 (331) 12,391,232,098 (32) 4,797,003,826 (20) 5,942,739,490 (40) 7,893,780,804 (44) 11,819,709,925 (55) 12,397,878,012 (77) 13,618,658,122 (61) 5,142,090,643 (2)

Average assets

(393) (42) (36) (52) (52) (53) (81) (73) (3)

32.4% (167) 26.8% (11) 75.0% (24) 31.6% (25) 17.1% (12) 37.9% (33) 29.7% (38) 29.5% (23) – (0)

64.1% 97.7% 90.0% 59.1% 57.8% 51.0% 53.6% 78.5% 100.0%

Manufacturing

Firm Characteristics by Worker Age.

(118) (0) (1) (11) (18) (31) (47) (10) (0)

11.6% (60) 2.4% (1) 0.0% (0) 10.1% (8) 18.6% (13) 18.4% (16) 14.1% (18) 5.1% (4) – (0)

19.2% 0.0% 2.5% 12.5% 20.0% 29.8% 31.1% 10.8% 0.0%

Wholesale/ trade/retail

(60) (1) (2) (24) (7) (9) (13) (4) (0)

7.8% (40) 4.9% (2) 0.0% (0) 17.7% (14) 11.4% (8) 4.6% (4) 5.5% (7) 6.4% (5) – (0)

9.8% 2.3% 5.0% 27.3% 7.8% 8.7% 8.6% 4.3% 0.0%

Bond/ ﬁnancial

Industry

(28) (0) (0) (1) (9) (9) (6) (3) (0)

26.0% (134) 34.1% (14) 12.5% (4) 21.5% (17) 25.7% (18) 17.2% (15) 30.5% (39) 34.6% (27) – (0)

4.6% 0.0% 0.0% 1.1% 10.0% 8.7% 4.0% 3.2% 0.0%

Services

(14) (0) (1) (0) (4) (2) (4) (3) (0)

22.3% (115) 31.7% (13) 12.5% (4) 19.0% (15) 27.1% (19) 21.8% (19) 20.3% (26) 24.4% (19) – (0)

2.3% 0.0% 2.5% 0.0% 4.4% 1.9% 2.6% 3.2% 0.0%

Other

237

Earnings Losses Following Job Change in Japan $85,000

$75,000

$65,000

$55,000

$45,000

$35,000 Income Firm 1

$25,000

Income Firm 2 Imputed Income

$15,000

$5,000 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 1.

Age–Earnings Proﬁles.

the sample are more highly paid and on a steeper pay proﬁle than if paid according to the national averages, given their industry, age, ﬁrm size, education, and gender. This may contribute to the large cost of job loss for these workers. Fig. 2 shows the tenure–earnings proﬁles of the workers in initial and new employment and displays the extent to which job separation costs rise with tenure.13 These ﬁgures can be interpreted in light of Lazear’s model of delayed compensation. The implications that older workers, with more years of ﬁrm tenure, should experience larger reductions in pay as a result of job separations are borne out by the ﬁgures. The ﬁgures clearly display older, more tenured workers losing more income upon job change.

4.2. Earnings Equations The ﬁrst model speciﬁcation investigated is a regression model in which income at the initial ﬁrm and in the new ﬁrm is tied to age, estimated tenure, and other individual characteristics. The estimations treat the data as two cross sections, ﬁrst considering worker income in the initial job and then in the new job. Years of education and level in the initial ﬁrm’s hierarchy cause a large number of observations to be lost, so these are not entered into all of

238

MICHAEL BOGNANNO AND LISA DELGADO

$85,000

$75,000

$65,000

$55,000

$45,000

$35,000 Income Firm 1 Income Firm 2 Imputed Income

$25,000

$15,000

$5,000 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Fig. 2.

Tenure–Earnings Proﬁles.

the regressions reported. Tenure is also not entered into all regressions because it is imputed.14 We estimate these models to determine the difference in the value placed on worker characteristics between the initial ﬁrm and the new ﬁrm. Human capital theory suggests that general training in the form of years of education should be valued in both jobs. Estimated tenure should have reduced value in subsequent employment according to the delayed compensation model and both the speciﬁc human capital and job-matching theories. The model is speciﬁed as follows: ln I ij ¼ Z i g þ ij where ln Iij is the logarithm of income of individual i at ﬁrm j measured in real $2,000 (deﬂated annually and converted at a constant exchange rate of 107.1 yens to the dollar); Zi is a vector of individual-speciﬁc attributes, including age, age2, gender, education, imputed tenure, and initial hierarchical level. Recall that tenure is imputed on the basis of the individual’s cell in the Basic Survey on Wage Structure categories that include year, industry, age category, ﬁrm size, education level, and gender. The effect of imputed tenure can be estimated because of the exclusion of industry and ﬁrm size dummy variables; eij is a random shock (iid) with a mean of zero. Two panels of regression results are presented in Table 5.15 The dependent variable in the ﬁrst panel is log income at the initial ﬁrm. The

377

0.34

370

0.34

0.1291 (2.3)

0.0012 (6.4)

0.1191 (7.6)

0.1251 (8.2)

0.0012 (6.9)

8.1725

8.0140

(2)

Note: t-statistics are in parentheses.

Total obs.

R

2

Level in Firm 1 hierarchy

Imputed tenure

Years of education

Gender (female ¼ 1)

Age

2

Independent variables Intercept Age

(1)

Table 5.

135

0.39

0.0188 (1.5)

0.0556 (0.6)

0.0011 (3.5)

0.1115 (4.4)

7.9789

(3)

370

0.36

0.0196 (2.8)

0.0918 (1.6)

0.0010 (5.0)

0.0911 (4.9)

8.6887

(4)

Log Income 1

110

0.46

0.0184 (1.1)

0.0775 (0.7)

0.0011 (3.4)

0.1164 (4.3)

8.0540

(5)

105

0.50

0.0248 (1.4)

0.0377 (3.2)

0.0051 (0.3)

0.1639 (1.5)

0.0008 (2.3)

0.0696 (2.2)

8.9737

(6)

509

0.15

0.0017 (9.1)

0.1523 (9.3)

7.5639

(1)

Dependent Variable

500

0.16

0.1725 (3.1)

0.0017 (8.6)

0.1451 (8.8)

7.7425

(2)

192

0.16

0.0366 (2.6)

0.1075 (1.1)

0.0015 (4.3)

0.1316 (4.5)

7.4167

(3)

500

0.17

0.0111 (1.6)

0.1484 (2.6)

0.0016 (7.6)

0.1292 (6.8)

8.0383

(4)

Log Income 2

Income Regressions in Initial and Subsequent Employment.

175

0.19

0.0360 (2.5)

0.0210 (0.2)

0.0016 (5.1)

0.1551 (5.3)

7.5883

(5)

160

0.23

0.0455 (2.7)

0.0214 (2.0)

0.0057 (0.4)

0.0890 (0.8)

0.0014 (4.1)

0.1173 (3.7)

7.9501

(6)

Earnings Losses Following Job Change in Japan 239

240

MICHAEL BOGNANNO AND LISA DELGADO

dependent variable in the second panel is log income at the new ﬁrm. Age is valued in both initial and subsequent employment. The negative sign on age2 gives the earnings proﬁles the familiar concave shape. Age and age2 alone explain one-third of the variation in log income at the initial ﬁrm but only half as much at the new ﬁrm. Comparing column 1 in each of the log income panels of Table 5, the marginal effect on earnings of aging one year for a 40-year-old is 2.5% in initial ﬁrms and 1.1% in new ﬁrms. This ﬁts with the ﬂatter trajectory of the age–earnings proﬁle for workers in new employment displayed in Fig. 1. Comparing column 6 in each of the panels in Table 5 and also accounting for tenure advancing as well as age, the marginal effect on earnings of aging one year for a 40-year-old is 4.4% in initial ﬁrms and 2.5% in new ﬁrms. This indicates a job loss cost that is increasing with age. The premium received by displaced workers for years of education increases in new employment and becomes statistically signiﬁcant. Column 3 in the ﬁrst two panels of Table 5 shows the premium for an additional year of education to be about 1.9% and not signiﬁcant in initial employment and 3.7% and signiﬁcant in new employment. This ﬁnding offers some support for the ﬁnding of Podgursky and Swaim (1987) that higher levels of education may reduce earnings losses. Tenure has a positive and signiﬁcant effect on income in the initial job but a smaller effect in subsequent employment. This corresponds to the ﬁnding in the literature that tenure in the initial ﬁrm falls in value in the new ﬁrm. Columns 4 and 6 in both panels of Table 5 indicate that age is more inﬂuential than tenure in determining pay. However, the coefﬁcient on tenure may be biased toward zero as this variable was imputed and is therefore measured with error.

4.3. Displacement Costs The second model speciﬁcation investigated is a regression model in which the change in income between the initial ﬁrm and the new ﬁrm is tied to age and other individual and ﬁrm characteristics. The estimations treat the data as a single cross section. The model is speciﬁed as follows: DI ij;k ¼ Z ig þ ij;k where DIij,k=IijIik is the change in the income of individual i between the initial ﬁrm j and the new ﬁrm k measured in real US dollars; Zi is a vector of individual-speciﬁc attributes (age, gender, education, tenure, total

Earnings Losses Following Job Change in Japan

241

employment in the initial ﬁrm, initial hierarchical level, days of unemployment, binary change of industry indicator, and binary occupation, certiﬁcation, and major indicators); eij,k is a random shock (iid) with a mean of zero. Table 6 examines the change in income brought about by job separation.16 In the ﬁrst column of Table 6, we see that workers lose about $1,100 for every additional year of age when involuntarily changing jobs. The marginal effect of an additional year of both age and tenure for a 40year-old in column 5 is to increase earning losses by $1,115. In this computation, the inﬂuence of age is several times greater than the inﬂuence of tenure, though both serve to inﬂate losses for older, more senior workers. To conclude that greater earnings losses for older workers result primarily from age itself and not much from the tenure lost at the initial job would be premature, however, given that the tenure variable is imputed. A gender effect appeared in the level estimates in Table 5. Females, in initial and new employment, earned less than males did when controls for education and level were omitted. However, gender has a statistically insigniﬁcant effect on the change in earnings. The size of the initial ﬁrm is also insigniﬁcant. In Table 5, education was more highly rewarded in new employment. The analysis of income change in Table 6 shows the effect of education to be positive, but the estimate is statistically insigniﬁcant. Some of the difﬁculty in achieving statistically signiﬁcant results for education on the change in income may be due to the relatively small sample size caused by missing values for education. We also saw in Table 5 that the returns to tenure were smaller in new employment. In Table 6, we see that tenure in the initial ﬁrm increases job displacement costs, but the estimate is not statistically signiﬁcant after controlling for age. It is highly signiﬁcant if age is excluded, but we cannot establish that it has an independent effect. Level in the initial ﬁrm’s hierarchy does not have signiﬁcant effect on the change in income. As with education, level in the hierarchy has many missing values and makes statistically signiﬁcant estimates difﬁcult to obtain because of the small sample size. Longer spells of unemployment appear to increase the cost of job separation by about $45 a day when the term is treated as exogenous. This is not an inconsequential amount because our average worker is in job search for about three months. Column 8 of Table 6 shows that when treating the length of the unemployment spell as endogenous and instrumenting it with the monthly unemployment rate and imputed tenure, it becomes statistically insigniﬁcant.

0.25 341

30,597 1,110 (10.7)

(1)

0.27 341

25,053 1,678 (1.9) 33 (3.1)

(2)

0.27 334

19,550 1,402 (1.5) 30 (2.7) 1,657 (0.5)

(3)

0.38 114

9,243 696 (0.5) 23 (1.3) 780 (0.2) 0.18 (1.3) 459 (0.6)

(4)

0.32 311

271 (0.6)

27,274 1,910 (1.7) 34 (2.9) 1,858 (0.6) 0.14 (1.3)

(5)

91

0.40

283 (0.3)

19,102 1,806 (1.0) 38 (1.9) 4,025 (0.6) 0.20 (1.1)

(6)

0.36 311

45 (3.8) 5,086 (2.8)

8,385 1,171 (1.4) 25 (2.5) 1,255 (0.4) 0.18 (1.9)

(7)

Dependent Variable ¼ Income Change (Income 2Income 1)

Change in Income Brought about by Job Separation.

0.30 311

29 (0.2) 10,636 (0.5)

8,250 1,156 (0.8) 28 (1.3) 1,920 (0.6) 0.15 (1.1)

(8)

0.27 341

7,466 (2.2) 11,219 (3.1) 15,868 (4.4) 23,996 (7.4) 33,629 (9.4)

2,737

(9)

Notes: t-statistics are in parentheses. Column 8 is estimated with two-stage least squares, and days of unemployment and industry change are instrumented the monthly unemployment rate and imputed tenure.

R2 Total obs.

Ages 55–59

Ages 50–54

Ages 45–49

Ages 40–44

Level in Firm 1 hierarchy Days of unemployment Change of industry Ages 35–39

Gender (female ¼ 1) Employment Firm 1 (1,000s) Years of education Imputed tenure

Age

Intercept Age

Independent Variables

Table 6. 242 MICHAEL BOGNANNO AND LISA DELGADO

Earnings Losses Following Job Change in Japan

243

Changing industries carries a high-wage penalty, and workers switching industries lose about $5,000 when industry change is treated exogenously. This suggests that the labor market values the experience workers gain in a particular industry, and the workers suffer when they cannot apply that industry training in new employment. The changing distribution of employment in Japan, away from manufacturing and into the services industry, caused workers in manufacturing to disproportionately lose more jobs and forced many of these workers to ﬁnd work in different industries. About two-thirds of the workers in our sample changed industries upon gaining new employment. Treating industry change as endogenous and instrumenting it with the monthly unemployment rate at the start of the workers’ unemployment spell and imputed tenure does not reduce its impact as in the case of the spell of unemployment, but it ceases to be statistically signiﬁcant. Table 7 also presents the change in income between the initial ﬁrm and the new ﬁrm but with a speciﬁcation that allows for a comparison between results with our job placement data, Abe et al.’s 1995 sample from the Japanese Employment Mobility Survey and Farber’s sample from the US Displaced Workers Survey for the period 1981–1995. The dependent variable is the change in log real annual income in our placement data, the percentage wage change in the Japanese Employment Mobility Survey, and the change in log real weekly earnings in the US Displaced Workers Survey. The coefﬁcients can be interpreted comparably in all columns, though columns 1, 2, and 4 are simple regression results while column 3 comes from the estimation of a censored regression model with a doubly truncated dependent variable (Abe et al., 2002, Table 3.18, col. 2A).17 The technique employed in column 3 is because the percentage wage change variable is categorical with truncation in both tails (loss over 30%, 30% to 10%, 10% to 10%, 10% to 30%, gain over 30%). The estimation reported in column 3 pertains to males who underwent involuntary job separations resulting from management convenience, contract termination, and mandatory retirement. Abe et al. do not report results for an estimation that pools males and females. Additional control variables employed but not reported in Table 7 include ﬁrm size, part-time status, industry change, industry wage premium, and year for Abe et al. and year, reason for job displacement, years since job loss, and non-white for Farber. Considering the age controls, the cost of job displacement rises strongly with age in both Japan and the United States though the differences between the three studies are marked. For workers under the age of 45, the consequences of job loss are not statistically signiﬁcant in Japan across

244 Table 7.

MICHAEL BOGNANNO AND LISA DELGADO A Comparison of Job Displacement Costs with Earlier Results for Japan and the US.

Independent Variables

Dependent Variable Change in log annual income

Intercept Ages 25–34 Ages 35–44 Ages 45–54 Ages 55–64

(1) Japan (placement data)

(2) Japan (placement data)

0.126 0.07 (0.142) 0.067 (0.137) 0.295 (0.137) 0.557 (0.142)

0.315 0.328 (0.224) 0.026 (0.214) 0.213 (0.208) 0.400 (0.215) 0.208 (0.142)

Educationo12 Education ¼ 12 Education 13–15

0.072 (0.060)

0.035 (0.110) 0.058 (0.074) 0.092 (0.106)

0.267 335

0.347 119

EducationZ16 Gender (female ¼ 1) R2 Total obs.

Percentage wage change

Change in log weekly earnings

(3) Japan (Abe et al.)

(4) US (Farber)

0.008 (0.007) 0.039 (0.008) 0.113 (0.007)

0.070 (0.014) 0.156 (0.015) 0.19 (0.017) 0.338 (0.022) 0.043 (0.014)

0.020 (0.006) 0.053 (0.014) 0.013 (0.008)

4,603

0.012 (0.011) 0.079 (0.013) 0.004 (0.009) 0.024 18,595

Notes: Standard errors are in parentheses. Those over 64 are deleted from the sample in estimating columns 1 and 2. Column 3 comes from the estimation of a censored regression model with a doubly truncated dependent variable using the 1995 Japanese Employment Mobility Survey (Abe et al., 2002, Table 3.18, col. 2A). They employ this technique because their percentage wage change variable is categorical with truncation in both tails (loss over 30%, 30% to 10%, 10% to 10%, 10% to 30%, gain over 30%). The estimation reported pertains to males who underwent involuntary job separations resulting from management convenience, contract termination, and mandatory retirement. Additional control variables employed but not reported here include ﬁrm size, part-time status, industry change, industry wage premium, and year. Column 4 comes from Farber’s (1997, Table 10, column 1) use of the Displaced Workers Survey for the period 1981–1995. Not reported here are Farber’s coefﬁcients on dummy variables for year, reason for job displacement, years since job loss, and nonwhite.

Earnings Losses Following Job Change in Japan

245

columns. Young US workers 25–34 and 35–44 suffer wage changes of 7% and 16%. For older workers, for workers 45–54 and 55–64, our data show income changes of 30% and 56% without educational controls and 21% and 40% with educational controls. These changes were estimated to be only 4% and 11% in 1995 by Abe et al. and 19% and 34% in the United States in the 1980s and the early 1990s. While age relatedness is apparent in all three data sources, our data show the highest degree of age relatedness and one that is closer to the United States than to the earlier Japanese data. The suggestion that the age relatedness of job loss penalties has increased so markedly should be viewed with caution, given the nature of our Japanese sample. Japan and the United States share an educational system in which secondary education is completed in 12 years, and an undergraduate university degree takes an additional four years. The education dummy variables in Table 7 are coded similarly across the estimations, but the omitted categories are high-school graduates in columns 2 and 4 and those not completing high school, in column 3. In the placement data, parameter estimates with such a small sample size are not signiﬁcant but appear to suggest that education buffers workers to a small extent from the income losses due to job change. This is true for the United States, where college graduates fare 8% better than high-school graduates and non-high-school graduates fare 4% worse. Abe et al.’s estimates indicate that those with higher education levels suffer larger declines in income. High-school graduates and junior college graduates (included here in the education 13–15 row) have income changes of 2% and 5% relative to non-high-school graduates. Fig. 3 depicts the total loss in earnings suffered by displaced workers, assuming their anticipated retirement age is 60. For this calculation, we would like to take the present value of the difference between the worker’s wage proﬁles to retirement with and without job separation. Since we do not observe these proﬁles, we assume that the difference between them remains constant in real terms and is equal on an annual basis to the change in earnings observed between initial and new employment. The total cumulative loss in earnings for each age category is generated by summing the immediate loss for each age cohort from the median age of the cohort to age 60. The immediate earnings loss from job separation for each ﬁve-year age cohort is presented in column 9 of Table 6. Though the immediate loss in earnings is greatest for older workers, if projected out in the simple way we have, workers in their 40s suffer the largest aggregate losses until retirement. The calculation of these penalties is simplistic and may overstate the overall ﬁnancial impact of job displacement for a couple of reasons. First, some

246

MICHAEL BOGNANNO AND LISA DELGADO

300,000 250,000 200,000 150,000 100,000 50,000 20-34

35-39

40-44

45-49

50-54

55-59

Fig. 3. Total Loss in Earnings with Retirement at Age 60.

researchers suggest that earnings increase in new employment in Japan at a greater rate than in continued employment. Second, displaced workers are almost always provided a severance payment or additional retirement allowance for leaving before the mandatory age of retirement. These payments are typically tied to the worker’s monthly salary, years of service, and reason for leaving and would reduce the ﬁnancial impact of job displacement, especially on those older workers with more ﬁrm tenure. To get some idea of the size of these payments, public sector workers receive at least one month of pay for each year of service for leaving due to illness or injury.

5. CONCLUSION This study estimated the penalties associated with job change at a time when Japan was undergoing a transition to a less-manufacturing-based economy and suffering from economic stagnation. Our primary ﬁnding is that the income premium for each year of age, while positive in post-displacement employment, is about $1,100 less than the income premium received in initial employment. Therefore, we ﬁnd that the older the worker, the greater the loss in annual income due to job loss. The ﬁndings regarding the job loss penalty are consistent with models of delayed compensation, job matching, and speciﬁc human capital.

Earnings Losses Following Job Change in Japan

247

It should be noted that the large job displacement costs found in this study came from a sample that was employed initially at large ﬁrms and paid slightly higher than the national averages for their industry, age, ﬁrm size, education, and gender. Additionally, selection bias might have inﬂuenced the estimated job displacement costs to some extent. The decline of the manufacturing sector in Japan caused many workers to ﬁnd employment in other industries. Changing industry markedly increased job displacement penalties, and we speculated that this was due to the loss of industry-speciﬁc capital. Additionally, we have found that years of education continue to be highly valued throughout a worker’s career and may have a larger effect on subsequent earnings. Thus, general training might help to mitigate the losses caused by job displacement. In comparison to the results of Abe et al. using nationally representative data from 1995, our results using 2000–2003 data show markedly larger job displacement costs that are more strongly correlated with age and no evidence of education increasing displacement costs. The question is whether these differences are due to the nature of our sample or the changes that took place in the Japanese labor market. Further research is necessary to conﬁrm the suggestion of an increasing trend in job displacement penalties and the extent to which they are age related.

NOTES 1. See Kato (2001) for applications of these practices in ﬁrm case studies. 2. Genda and Rebick (2000) also argue that job protection strengthened in the past decade in Japan and that institutional practices changed slowly relative to the pace of change in the labor market. 3. Fujiki, Nakada, and Tachibanaki (2001) state: From the viewpoint of the core Japanese workers, typically full-time male workers who have accumulated ﬁrm-speciﬁc skills through on-the-job training, their relatively favorable employment opportunities may not be sustained during the current recession, and once they lose their position they must stay in the secondary labor market forever. 4. For surveys of this literature, see Farber (1997), Fallick (1996), and Hamermesh (1989). 5. Since 1998, the earliest age at which mandatory retirement may be imposed is 60 (Abe et al., 2002). 6. Nakagawa, Nishizaki, and Kamiya (2002) write in the popular press: ‘‘Under this system [the lifetime employment system], workers are normally underpaid and overworked in their early years and only reap the rewards when their salaries surge in their mid-40s.’’ 7. The average employment level in the 65 initial ﬁrms was over 3,500. Since larger ﬁrms displaced more workers, the average worker originated in a ﬁrm of over 7,500.

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Though some of the new ﬁrms were large, the average worker was employed in a new ﬁrm with fewer than 1,000 employees. 8. The tables and regressions also exclude one individual with a drop in earnings of $650,000. The regressions also exclude workers over 59 and potentially subject to mandatory retirement. 9. To impute tenure, we ﬁrst categorized workers in our data by the categories used in the ‘‘Basic Survey on Wage Structure’’ collected by the Japanese Ministry of Health, Labour and Welfare. The Basic Survey categories included year (2000, 2001, and 2002), industry (all, manufacturing, communication, and transport, wholesale and retail trade, ﬁnancial and insurance, and service), age (all, 17 and under, 18–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65 and above), ﬁrm size (all, 10–99 employees, 100–999 employees, 1,000þ employees), education level (all, junior high-school graduate, senior high-school graduate, junior college/ vocational school graduate, university graduates), and gender (all, male, female). The mapping from the placement data to the categories in the Basic Survey was straightforward, but a few things should be noted. In cases where a missing value in the placement data prevented the assignment to a category, we used the data listed under ‘‘all’’ in the Basic Survey. The placement data runs through 2003 while the Basic Survey extends only to 2002. We applied the 2002 Basic Survey data to our placement data for both 2002 and 2003. We categorized the ﬁrms in the placement data listed as ‘‘systems/software,’’ ‘‘professional,’’ and ‘‘security’’ in the ‘‘services’’ industry in the Basic Survey. Firms listed as ‘‘stock’’ were assigned to the ‘‘ﬁnancial and insurance’’ industry in the Basic Survey. We then applied the ratio of mean tenure to mean age that existed in each year, industry, age category, ﬁrm size, education level, and gender cell in the Basic Survey to the age of the individual in the placement data to impute the estimated tenure. 10. Among workers in initial employment, both the transport and communications industry and ‘‘other’’ categories (electronics, communications, and information technology industries) are underrepresented in comparison to the national employment shares in these industries. Upon reemployment, the employment shares in our data rise much closer to the national employment shares. This growth in employment shares likely stems from the underrepresentation of these industries initially and not from shifting employment shares at the national level. 11. The age–earnings proﬁles depicted are generated from the following regression estimates: Income Firm 1 ¼ 82,682þ5986.91 Age – 56.79 Age2 with t-statistics 5.7 and 4.6 for Age and Age2, N ¼ 377 and R2 ¼ 0.24; Income Firm 2 ¼ 90,587þ6690.11 Age – 75.95 Age2 with t-statistics 8.3 and 8.1 for Age and Age2, N ¼ 509 and R2 ¼ 0.13; Imputed Income ¼ 49,318þ4064.47 Age – 38.94 Age2 with t-statistics 11.5 and 9.5 for Age and Age2, N ¼ 609 and R2 ¼ 0.41. 12. In the same way we imputed tenure, we impute income at national averages. Workers in our data are grouped by the categories used in the ‘‘Basic Survey on Wage Structure’’ collected by the Japanese Ministry of Health, Labour and Welfare. The Basic Survey categories included year, industry, age, ﬁrm size, education level, and gender. After mapping from the placement data to the categories in the Basic Survey, we applied the ratio of mean contractual cash earnings to mean age that existed in each year, industry, age, ﬁrm size, education, and gender cell in the Basic Survey to the age of the individual in the placement data to arrive at imputed income.

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13. The tenure–earnings proﬁles depicted are generated from the following regression estimates: Income Firm 1 ¼ 20,301þ4381.48 Tenure 82.21 Tenure2 with t-statistics 5.4 and 3.0 for Tenure and Tenure2, N ¼ 377 and R2 ¼ 0.25; Income Firm 2 ¼ 25,163þ3069.67 Tenure 82.48 Tenure2 with t-statistics 4.9 and 4.0 for Tenure and Tenure2, N ¼ 509 and R2 ¼ 0.07; Imputed Income ¼ 26,598þ1,576 Tenure – 2.30 Tenure2 with t-statistics 6.5 and 0.29 for Tenure and Tenure2, N ¼ 609 and R2 ¼ 0.57. 14. The coefﬁcient on tenure may be biased toward zero due to measurement error and the standard errors invalid. 15. Excluding from the sample those over age 55, under the presumption that they are simply being retired, resulted in minimal changes to signs or signiﬁcance of the estimated parameters. The monthly unemployment rate was never statistically signiﬁcant, and speciﬁcations including it are not presented. A model that controls unobserved heterogeneity between initial ﬁrms with the same variable speciﬁcations as in Table 5 was also estimated. The same basic results were found. Firm effects could be controlled because the average initial ﬁrm is displacing about 10 employees. These results are available from the authors upon request. 16. A parallel model that also controls unobserved heterogeneity between initial ﬁrms was estimated with similar results except that the sign on gender changes, though remaining statistically insigniﬁcant. These results are available upon request. 17. Since Abe et al.’s estimates were in percentage changes, with 20% entered as 20 rather than 0.2, the decimals in Abe et al.’s coefﬁcients have been shifted two places to the left for comparability between the columns.

ACKNOWLEDGMENTS We thank Charles Swanson, Tsuyoshi Tsuru, and two referees for their comments. All errors are our own. The support of a Marie Curie Fellowship for the Transfer of Knowledge is gratefully acknowledged by Bognanno.

REFERENCES Abe, M., Higuchi, Y., Nakamura, M., Kuhn, P., & Sweetman, A. (2002). Worker displacement in Japan and Canada. In: P. J. Kuhn (Ed.), Losing work, moving on: International perspectives on worker displacement (Chapter 3). Kalamazoo, MI: W.E. Upjohn Institute for Employment Research. Addison, J. T., & Portugal, P. (1989). On the costs of worker displacement: The case of dissipated ﬁrm-speciﬁc training investments. Southern Economic Journal, 56(1), 166–182. Clark, R. L., & Ogawa, N. (1992). The effect of mandatory retirement on earnings proﬁles in Japan. Industrial and Labor Relations Review, 45(2), 258–266.

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Fallick, B. C. (1996). A review of the recent empirical literature on displaced workers. Industrial and Labor Relations Review, 50(1), 5–16. Farber, H. S. (1997). The changing face of job loss in the United States, 1981–1995. In: Brookings papers on economic activity: Microeconomics (pp. 55–142). Washington, DC: Brookings Institution Press. Farber, H. S. (1993). The incidence and costs of job loss: 1982–91. In: Brookings papers on economic activity: Microeconomics (pp. 73–132). Washington, DC: Brookings Institution Press. Fujiki, H., Nakada, S. K., & Tachibanaki, T. (2001). Structural issues in the Japanese labor market: An era of variety, equity, and efﬁciency or an era of bipolarization? Monetary and Economic Studies, 19(February, special edition), 177–211. Genda, G., & Rebick, M. (2000). Japanese labour in the 1990s: Stability and stagnation. Oxford Review of Economic Policy, 16(2), 85–102. Hamermesh, D. S. (1989). What do we know about worker displacement in the U.S.? Industrial Relations, 28(1), 51–59. Hashimoto, M., & Raisian, J. (1985). Employment tenure and earnings proﬁles in Japan and the United States. The American Economic Review, 75(4), 721–735. Jacobson, L., LaLonde, R., & Sullivan, D. (1993). Earnings losses of displaced workers. The American Economic Review, 83(4), 685–709. Kato, T. (2001). The end of lifetime employment in Japan?: Evidence from national surveys and ﬁeld research. Journal of the Japanese and International Economies, 15(4), 489–514. Kletzer, L. G. (1989). Returns to seniority after permanent job loss. American Economic Review, 79(3), 536–543. Lazear, E. (1979). Why is there mandatory retirement? The Journal of Political Economy, 6, 1261–1284. Nakagawa, T., Nishizaki, K., & Kamiya, T. (2002, July 30). Workers face the need to swallow their market prices. The Asahi Shimbun (IHT/Asahi). Podgursky, M., & Swaim, P. (1987). Job displacement and earnings loss: Evidence from the displaced worker survey. Industrial & Labor Relations Review, 41(1), 17–29. Ruhm, C. J. (1991). Are workers permanently scarred by job displacements? American Economic Review, 81(1), 319–324. Topel, R. (1993). What have we learned from empirical studies of unemployment and turnover? American Economic Review, 83(2), 110–115. Papers and Proceedings of the Hundred and Fifth Annual Meeting of the American Economic Association.

WAGES AND THE RISK OF DISPLACEMENT Anabela Carneiro and Pedro Portugal ABSTRACT In this paper a simultaneous-equations model of ﬁrm closing and wage determination is speciﬁed in order to analyse how wages adjust to unfavorable product demand shocks that raise the risk of displacement through ﬁrm closing, and to what extent an exogenous wage change affects the exit likelihood. Using a longitudinal matched worker-ﬁrm data set from Portugal, the estimation results suggest that, under the existence of noncompetitive rents, the fear of job loss leads workers to accept wage concessions, even though a compensating differential for the ex ante risk of displacement might exist. A novel result that emerges from this study is that ﬁrms with a higher incidence of minimum wage earners are more vulnerable to adverse shocks due to their inability to adjust wages downward. Indeed, minimum wage restrictions were seen to increase the failure rates.

1. INTRODUCTION The extent of job destruction and, in particular, ﬁrm closing and job loss due to sector reallocation, has been a matter of great concern in recent years,

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 251–276 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28008-8

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with empirical research on gross job and worker ﬂows experiencing a tremendous growth over the past two decades. The studies on the decomposition of net employment ﬂows emphasize the importance of job creation and job destruction through the entry and exit of ﬁrms. According to Davis, Haltiwanger, and Schuh (1996), about one-fourth of annual job destruction in the United States takes places at plants that shut down, while startups account for one-sixth of annual job creation. In Portugal, annual job ﬂows produced by both plant births and plant deaths account for almost half of total gross employment ﬂows (Blanchard & Portugal, 2001). The literature on ﬂows of jobs is, however, mostly employment accounting, without any direct information about the magnitude of the wage or output elasticities of employment changes through the births and deaths of establishments (or growth or contraction in existing establishments). Recently, a considerable number of studies examined how the wages of displaced workers evolve (over a long-term period) in comparison with the wages of workers who were not displaced (see, among others, Jacobson, LaLonde, & Sullivan, 1993; Stevens, 1997; Margolis, 1999). Nonetheless, few studies have yet analyzed how exogenous wage changes affect the probability of displacement. In fact, the theoretical and empirical research on the role of wages on plant closings is remarkably sparse. Most of the empirical literature on plant closings has concentrated on the effect of unions in the probability that a ﬁrm (plant) shuts down.1 Hamermesh (1988) was the ﬁrst to address this issue explicitly, offering a model in which workers and ﬁrms contract over wages and employment probabilities.2 Based on the theoretical framework of Hamermesh’s model (1988, 1991, 1993), this study will examine how wages adjust to a negative demand shock that raises the risk of displacement through ﬁrm closing and to what extent wages affect the exit likelihood. The role of a mandatory minimum wage on the ﬁrm’s exit decision will also be analyzed. This work attempts to contribute to the empirical literature on wages and the risk of displacement on three distinct grounds. The ﬁrst is related to the use of a simultaneous-equations approach in order to account for the possible endogeneity of wages and the probability of displacement. As it seems clear that an increase in the ﬁrm’s failure rate may affect wage changes because it raises the risk of displacement, it also seems clear that a wage change may affect the exit likelihood because it reduces, all else being equal, the ﬁrm’s proﬁtability.

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Second, this study makes a signiﬁcant contribution by examining the effect of a mandatory minimum wage on the failure rate. Despite the great effort dedicated to research on the effect of minimum wages on unemployment, namely, youth unemployment, we are not aware of any study that explicitly looks at the relationship between minimum wages and ﬁrms’ exits. Are ﬁrms with a higher proportion of minimum wage earners more vulnerable to product shocks due to their inability to adjust wages downward? Finally, the third is related to the use of an appropriate and representative data set to analyze the relationship between wages and the risk of displacement. In fact, the Portuguese data from Quadros de Pessoal (QP) can be described as a longitudinally matched worker-ﬁrm sample with a rich set of information on workers’ characteristics, their wages, and their work environment. This will enable us to address a number of questions that cannot be adequately answered in the absence of ﬁrm or worker data. The plan of the paper is as follows. Section 2 presents the theoretical framework. Section 3 describes the empirical counterpart of the simultaneous-equations model of ﬁrm closing and wages. In Section 4 the data set is described and the basic hypothesis regarding which factors should matter for exit and the wage determinants are also discussed. Section 5 reports the empirical results and some tantalizing robustness checks. Section 6 concludes.

2. THEORETICAL FRAMEWORK Hamermesh’s theoretical model (1988, 1991, 1993) constitutes the basis of our own approach. Hamermesh modeled the relationship between wage changes and the probability of job displacement due to plant closing, in order to determine the necessary wage concessions to keep plants from closing.3 The model is set within a contract theory framework in which workers contract with their employers for a package that includes a probability that the job will exist and a wage premium above the entry-level wage (reservation wage). In fact, when workers sort themselves among ﬁrms, one of the risks they consider is that exogenous product-market shocks may cause the ﬁrm to close down. The idea underlying the model is that since an internal labor market may operate with employers and employees sharing the rents originated by ﬁrmspeciﬁc human capital, the adjustment to negative shocks may be partially absorbed through wage concessions.

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Thus, in a given period t, the level of wages includes two components and can be deﬁned as: W t ¼ W Rt þ ðW t W Rt Þ The ﬁrst component corresponds to the reservation wage, WRt, the market-wage rate that makes the worker indifferent between that ﬁrm and at least another one. The reservation wage includes a compensating differential for the ex ante expected probability of closing. The second component, WtWRt, corresponds to the deviation of wages over the reservation wage and should reﬂect the returns to ﬁrm-speciﬁc human capital investments. Two main predictions emerge from Hamermesh’s model. The ﬁrst, points to a negative relationship between the excess of wages over the reservation wage and the probability of closing, suggesting that shocks that increase the probability of displacement reduce the magnitude of the wage increase. The second, points to the existence of a positive relationship between the reservation wage and the probability of closure due to the existence of compensating differentials for the ex ante risk of displacement. In order to disentangle between these two effects, i.e., to analyze how wages adjust to unfavorable shocks that raise the risk of displacement through ﬁrm closing, and to what extent an exogenous wage change affects the exit likelihood, a simultaneous-equations model of ﬁrm closing and wage determination is adopted in this study. In this framework wages are determined through negotiation between the ﬁrm and its workers. It is also assumed that the existence of product/labor market power generates rents that can be shared by employees in the form of higher wages. From the perspective of the contractual relationship between employers and employees, the existence of noncompetitive rents may be viewed as a buffer that can cushion against negative shocks and, thus, partially insulate the ﬁrm from unfavorable market conditions. The possibility of wage concessions is, of course, precluded if workers are paid legal minimum wages. The basic model consists of two equations. In essence, the ﬁrst deﬁnes the probabilistic event of a displacement due to plant closure. This equation is a discrete labor demand function that describes the impact of wages on the probability of displacement through ﬁrm closing and, thus, on employment. The effect of wage levels on the probability of ﬁrm closing may be ambiguous. One would expect that, all else being equal, ﬁrms with lower wages would have higher expected proﬁts, and thus be more likely to

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survive. But, in the absence of proper productivity measures, high wages may simply be viewed as mirroring high productivity and, thus, there might be no correlation. The second equation of the model is a wage bargaining function. The market-wage equation allows us to examine whether, under imperfect competition in the labor market, the risk of being ﬁred due to ﬁrm closing leads workers to accept wage moderation in order to avoid the ﬁrm’s shutdown. This hypothesis is consistent with the idea that pay is ﬁxed in a bilateral bargain where the fear of unemployment acts to weaken workers’ bargaining position (Blanchﬂower, 1991).

3. THE EMPIRICAL MODEL OF FIRM CLOSING AND WAGES 3.1. Purpose The empirical model of ﬁrm closing and wages presented in this section attempts to grasp three important elasticities. The ﬁrst will give a measure of how wages adjust to a negative demand shock that raises the probability of displacement through ﬁrm closing – elasticity of wages with respect to the probability of ﬁrm closure. The second will determine how wages themselves affect the exit likelihood – quasi-elasticity of ﬁrm closure with respect to wages. The third, measures the effect of a mandatory minimum wage on the failure rate – quasi-elasticity of ﬁrm closure with respect to minimum wage incidence. At this point the reasons that led to choosing a model of ﬁrm closing and not plant closing should be mentioned. The option to use information at the ﬁrm level instead of at the plant level is justiﬁed by two main reasons. First, the important management bargaining decisions in a multiplant ﬁrm are made at the corporate level, not at the plant, and reﬂect the priorities of the ﬁrm as a whole. In particular, wage policies are mainly relevant at the ﬁrm level. Second, it seems that when it is the ﬁrm that is at risk of closing, the unemployment threat is stronger than when it is an establishment of a multiplant ﬁrm. In large multiplant ﬁrms, plant shutdowns may be used in addition to layoffs as a means of reducing capacity in face of unfavorable shocks in the product demand. A plant shutdown may even occur with no layoffs, as workers from closing plants are reemployed in other plants of the same ﬁrm. Indeed, in some situations the shutdown of a plant may be a less

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costly bargaining strategy and, thus, would be preferable to a wage concession strategy. The empirical evidence for Portugal suggests that due to higher adjustment costs (mainly the costs of ﬁring workers) and in the face of unforeseen temporary shocks, it is preferable for employers, under certain circumstances, to close down instead of adjusting their level of employment by laying off workers (Blanchard & Portugal, 2001).

3.2. The Empirical Model The failure equation is speciﬁed as: pnijt ¼ a1 X jt1 þ a2 W nRijt1 þ a3 FðW Mit1 Þ þ u1ijt

(1)

where Y ijt ¼ 1 if pnijt o0 and Y ijt ¼ 0 if pnijt 0. pnijt is a latent variable reﬂecting the future proﬁtability of ﬁrm j. In the data it is not possible to observe pnijt . All we can say is whether pnijt is or is not below a given threshold (the minimum level of proﬁts that guarantees the ﬁrm’s continued existence). In the latter case, the ﬁrm will continue its operations, otherwise it will close down. Thus, the dummy variable Yijt equals one if worker i was displaced in year t due to ﬁrm closure, zero otherwise. The probability of displacement through ﬁrm closing is deﬁned as Pijt Prðpnijt o0Þ. Xjt1 is a vector of ﬁrm and local labor market characteristics and W nRijt1 the natural logarithm of the entry-level wage (reservation wage) paid to worker i by ﬁrm j. We decided to include the level of reservation wages instead of the level of wages per se in the failure equation in order to make comparisons across ﬁrms less ambiguous. Adjusting the level of wages by subtracting the impact of tenure circumvents the possibility that wages may be merely reﬂecting the impact of ﬁrmspeciﬁc human capital investments on the failure rate.4 FðW Mit1 Þ denotes the probability of a given worker receiving the minimum wage.5 a’s are the parameters to be estimated and u1ijt is a normally distributed random variable with zero mean and unit variance. This speciﬁcation is fundamentally different from Hamermesh’s own empirical failure equation. In fact, since a control for ﬁrm-speciﬁc demand shocks is added to the failure equation deﬁned in (1), the probit equation merely captures the effect of the level of wages on the probability of closing. The failure equation gives, for each wage rate, the probability that the ﬁrm will close, holding product demand shocks constant. In this sense, it can be viewed as a discrete version of a labor demand equation. The effect of the

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probability of closing on wages is estimated in the market-wage equation, which can be interpreted as a discrete version of a labor supply equation. Generically, the market-wage equation is deﬁned as: W nijt1 ¼ b1 Z ijt1 þ b2 U jt1 þ b3 pnijt þ u2ijt1

(2)

where W ijt1 ¼ MaxðW Mit1 ; W nijt1 Þ and W Mit1 is the mandatory minimum wage in period t1. The wage paid to worker i in ﬁrm j is a function of a set of workers’ characteristics included in vector Zij, local labor market characteristics deﬁned in vector Uj and pnij .6 b’s are the unknown parameters to be estimated and u2ijt1 is a normally distributed random variable (zero mean and constant variance).

4. THE DATA 4.1. Sample Description The data set used in this study was obtained from QP and includes all workers that lost their jobs in 1994, 1995, or 1996 due to ﬁrm closure and were present in the QP registers in the year that preceded the displacement. A control group made up of a random sample of workers who were employed in the year prior to the displacement in ﬁrms that did not close in the following year is also included. QP is an annual mandatory employment survey collected by the Portuguese Ministry of Employment, which covers virtually all ﬁrms employing paid labor in Portugal.7 Each year, every establishment with wage earners in the private sector is legally obliged to ﬁle a standardized questionnaire. Reported data cover the establishment itself (location, economic activity, and employment), the ﬁrm (location, economic activity, employment, sales and legal framework), and each of its workers (gender, age, education, skill, occupation, tenure, earnings, and duration of work). Each ﬁrm entering the database is assigned a different identiﬁcation number and the Ministry implements several checks to ensure that a ﬁrm that has already reported to the database is not assigned a different identiﬁcation number. In particular, an exit from the database should signal a ﬁrm that has ceased its activity. This criteria, however, is not entirely accurate, due to the fact that some of the ﬁrms temporarily exit the database. A temporary exit may occur for a number of reasons other than

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cessation of activity, a very likely reason being that the survey form was not received in the Ministry of Employment before the date when the recording operations were closed. Almost all of these temporary exits last less than two years, but can still cause an identiﬁcation problem if they occur in the terminal years. In order to account for this problem, the information on the last two years after displacement was used solely to control for temporary exits in the intermediate years.8 To ensure that we are in the presence of ﬁrms’ true closures and not mergers or acquisitions, we also excluded from the sample those workers that appeared in the database in the period after displacement with a year of admission in the new job less than the year of displacement minus one.9 The survey has three characteristics that make it particularly suitable for the analysis of the relationship between wages and the risk of ﬁrm closing. The ﬁrst is its coverage. By law, the questionnaire is made available to every worker in a public space of the establishment. This requirement facilitates the work of the services of the Ministry of Employment that monitor compliance of ﬁrms with the law (e.g., illegal work). The administrative nature of the data and its public availability implies a high degree of coverage and reliability. Second, this survey is conducted on a yearly basis and since unique identiﬁers are available for both ﬁrms and workers, ﬁrms and individuals can be tracked over the years. Third, it contains a rich set of information on both ﬁrms and its workers, which will enable us to address a number of questions that cannot be adequately answered in the absence of ﬁrm or worker data. In order to be allowed to construct the variables that account for ﬁrm’s recent evolution, we impose that workers be present in the QP registers in each of the three years that preceded the ﬁrm shutdown and employed with the same employer over those years.10 This requirement means that an individual must have at least two years of tenure in the year prior to displacement. This selection rule, although primarily dictated by data availability considerations, results in an overrepresentation of employed individuals with a stable contractual relationship.11 Nevertheless, this restriction should not be of greater concern since the possibility of wage concessions is particularly relevant for workers with a higher employment attachment. On average, the sampled individuals have 26 years of labor force experience and over 11 years of employer tenure. We also limited the sample to full-time workers aged between 18 and 64 in the year prior to displacement. Since the minimum wage is deﬁned as a monthly wage, the full-time job requirement allows us to identify minimum wage earners more accurately.12 In this context, wages are measured as monthly wages.

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We have also excluded those individuals for whom information was incomplete for the year before displacement (or for the three years before displacement in the case of the variable sales), namely those with no reported wage. Finally, and in order to minimize the effects of the presence of outliers, we drop the 0.1% top and the 0.1% bottom observations for the wage and sales variables. After these exclusions we obtained a sample of 35,922 full-time workers that were displaced between 1994 and 1996 due to ﬁrm closing, aged between 18 and 64 and with at least two years of tenure in the year prior to displacement. The control group includes three subsamples and was constructed in the following way. For each year prior to the displacement year we obtained a random sample of around 300,000 workers that were employed in ﬁrms that did not close.13 For each of these three groups we excluded those individuals that were not present in the QP ﬁles in each of the three years before displacement and those who were not employed in the same ﬁrm over those years. The sample was also limited to full-time workers aged between 18 and 64 in the year prior to displacement. After excluding those observations with missing values on the explanatory variables and the extreme observations (outliers) for wages and sales, we obtained a control group of 230,102 nondisplaced workers. Table 1 presents the descriptive statistics of the sample for the two groups of workers: displaced and non-displaced. As shown in Table 1, on average, displaced workers are slightly younger, less qualiﬁed, and with fewer years of tenure and education. They also earn, on average, less than non-displaced workers. The subsample of displaced workers includes more females and minimum wage earners. According to ﬁrms’ characteristics, the proportion of displaced workers that comes from small, young, and single-plant ﬁrms is higher when compared to the sample of non-displaced workers. For the former the real average growth rate of ﬁrms’ sales in the last three years is negative (7.6%), while for the latter that same rate is positive (1.4%). Displaced workers are also employed in ﬁrms with a reduced market power (as measured by market share).

4.2. Variables Deﬁnition 4.2.1. Failure Equation The dependent variable in the failure equation is a binary variable that takes the value of one if the worker was displaced in year t due to ﬁrm closure,

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ANABELA CARNEIRO AND PEDRO PORTUGAL Table 1.

Sample Characteristics (Means and Standard Deviations).

Characteristics

Workers’ characteristics Age (in years) Tenure (in years) Education (in years) Proportion of female Proportion of minimum wage earners Qualiﬁcation levels (proportion of workers) Top executives Intermediary executives Supervisors Highly skilled and skilled professionals Semiskilled and unskilled professionals Apprentices Non-deﬁned

Displaced

Non-Displaced

Mean

St. dev.

Mean

St. dev.

37.3 9.8 5.8 0.442 0.143

0.113 0.082 2.830

38.5 11.9 6.4 0.368 0.056

0.107 0.085 3.231

0.018 0.017 0.051 0.527 0.279 0.057 0.051

0.029 0.031 0.057 0.543 0.262 0.034 0.044

Firms’ characteristics Size (total employment) Past sales growth Market share Proportion of foreign capital Proportion of multiplant ﬁrms

108.4 0.076 0.013 0.031 0.165

Firm age (proportion of workers) 2–5 years 6–10 years W10 years Real sales per worker (in logs) Real monthly wage (in logs) Number of observations

0.134 0.181 0.685 8.419 1.111 10.973 0.432 35,922

426.2 0.391 0.060 0.161

1135.1 0.014 0.118 0.094 0.413

2701.2 0.354 0.250 0.269

0.046 0.086 0.869 8.825 1.172 11.175 0.490 230,102

Notes: (a) all variables, except past sales growth, are measured in the year prior to displacement; (b) sales per worker and the monthly wage are in 1991 PTE (escudo); 1 EUROR200.482 PTE.

zero otherwise. A set of ﬁrm variables that may affect the ﬁrm’s decision to close are identiﬁed below. In order to control the exogenous demand shocks that may affect the probability of ﬁrm closing, the average growth rate of real sales in the last three years is used as a proxy for ﬁrm-speciﬁc shocks.14 Controlling for ﬁrmspeciﬁc (idiosyncratic) shocks enables one to examine whether, in the face of

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an identical exogenous shock, and all else being equal, ﬁrms with lower wages are less likely to close down or not. Even though ﬁrm demand shifts certainly affect the rate of ﬁrm closing, other forces are also at work. Jovanovic (1982) showed that patterns of employer growth and ﬁrm (plant) failure are consistent with a process of within-industry selection in which inefﬁcient producers decline and fail. This selection process leads to substantial variation in the probability of exit across ﬁrms (plants) within an industry. In fact, while plant deaths are part of the normal process of the entry and exit of ﬁrms, the post-entry patterns of growth and failure vary considerably with employers’ observed characteristics (Dunne, Roberts, & Samuelson, 1989). This reasoning suggests that the risk of displacement due to ﬁrm closing varies not only with the demand for the ﬁrm’s output but also with employer’s efﬁciency relative to competing ﬁrms in the same industry. In this sense, a set of ﬁrm characteristics that are related to its performance in the output market may affect the ﬁrm’s own probability of survival. The factors to be included in the empirical model as exit determinants will now be identiﬁed. With the exception of past sales growth, all variables are measured in the year that precedes the potential exit event (period t1). It has been largely shown in the empirical literature on ﬁrm survival that ﬁrm size and ﬁrm age are negatively associated with failure rates (see, e.g., Kumar, 1985; Evans, 1987; Hall, 1987; Dunne et al., 1989; Audretsch & Mahmood, 1994; Mata & Portugal, 1994; Mata, Portugal, & Guimara˜es, 1995). These results are consistent with Jovanovic’s (1982) model of industry evolution, according to which ﬁrms start with no knowledge about their efﬁciency. As time goes by and ﬁrms observe their performance in the product market, they gradually learn about their efﬁciency. This information is then incorporated into their current size. Efﬁcient ﬁrms grow and survive, while inefﬁcient ones contract and fail. Thus, large and old ﬁrms are successful ﬁrms, and, for this reason, they should have higher survival probabilities. Measures of the size and age of the ﬁrm are, thus, included in the failure equation. The size of the ﬁrm is deﬁned as the natural logarithm of its total employment. Since the information about the date of a ﬁrm’s creation is only available after 1993, and in order to use the same criteria to measure age in the 1993–1995 period, we used as a proxy for ﬁrm age the tenure (in years) of the worker with the longest tenure within the ﬁrm.15 A linear spline function is used to deﬁne the effect of the age of the ﬁrm. The ﬁrm’s market share is used as a measure of product market competition. Monopoly power generates monopoly rents and consequently higher proﬁts. If employers are able to appropriate part of these rents, it

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should be expected that ﬁrms with increased market share are less likely to fail. The market share is obtained by the ratio between a ﬁrm’s sales and total (ﬁve-digit) industry sales. Firm ownership characteristics may affect the exit likelihood. Two indicators of ownership type will be used, namely the number of establishments with which each ﬁrm operates and the proportion of foreign capital. For the former a dummy variable that takes the value one if the ﬁrm is a multiplant ﬁrm (0 otherwise) will be included in the model. Even though the empirical evidence suggests that multiplant ﬁrms use the shutdown margin more often than their single-plant counterparts, it seems reasonable to admit that exit of a multiplant ﬁrm is less likely since it implies the simultaneous failure of all its plants (see Mata & Portugal, 1994; Machin, 1995; and the recent studies of Addison et al., 2004; Bernard & Jensen, 2002). The proportion of foreign capital may itself be an indicator of the ﬁrm’s unobserved managerial ability and may affect the probability of closure. Doms and Jensen (1998) found that multinational plants have superior observable characteristics. But, it is also well known that multinationals have a higher propensity to relocate production within ﬁrms, which may lead to an increased probability of closure (see, e.g., Harris & Hassaszadeh, 2002). To analyze the effects of individual wage levels on the probability of ﬁrm closing, it is necessary to use a measure of revenue per employee in order to be able to compare ﬁrms. Firms that have higher variable costs, holding revenue ﬁxed, are less likely to cover their ﬁxed costs in the long run and thus more likely to close down. Real sales per worker (in logs) is used as a measure of ﬁrm’s revenue per employee. Finally, and in order to control for local labor market conditions, a set of industry (one-digit) and regional dummies (Nuts II), as well as the regional unemployment rate, are included in the failure equation.16,17 Since the data include ﬁrm closures that occurred in 1994, 1995, and 1996, two time dummies were also added to the model in order to control for aggregate economic conditions. 4.2.2. Wage Equation The dependent variable in the wage equation is deﬁned as the natural logarithm of the real monthly base wage paid to an individual worker in the year that precedes the displacement. The monthly base wage was deﬂated by the Consumer Price Index (CPI; base ¼ 1991). The reservation wage is measured as the monthly base wage minus an adjustment equal to the effect of tenure (and its square) on wages.

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The wage equation includes a set of controls for personal characteristics such as: gender (female ¼ 1), education (in years), age and its square (in years), tenure and its square (in years), and qualiﬁcation level. A set of dummies are used for the levels of qualiﬁcation. Seven categories are considered: top executives, intermediary executives, supervisors, highly skilled and skilled professionals, semiskilled and unskilled professionals, non-deﬁned (a residual category), and apprentices (the reference category). In order to assure that the effect of a higher risk of unemployment on wages is due to ﬁrm shutdown and not due to differences in the risk of layoff in the local labor markets, the local unemployment rate is used to control for those differences. The local unemployment rate is deﬁned at the disaggregated level of Nuts III.18 A set of industry (one-digit), regional (Nuts II), and time dummies are also added to the wage equation.

5. ESTIMATION AND EMPIRICAL RESULTS 5.1. Estimation Procedure In order to estimate the simultaneous-equations model of ﬁrm closing and wages presented in Section 3, it will be necessary to choose an adequate method of estimation. It is well known that the ordinary least squares (OLS) estimator is, in general, inconsistent when applied to a structural equation in a simultaneous-equations system. Beyond this difﬁculty, our empirical model of ﬁrm closing and wages is nonstandard, since one of the endogenous variables is a binary variable while the other is a censored variable. In fact, while the failure equation is speciﬁed as a probit model, the wage equation is a tobit model with lower censoring at the minimum wage. Thus, we are in the presence of a simultaneous-equations model with mixed dichotomous and censored variables. The conventional method for estimating simultaneous-equations models is the method of instrumental variables. As suggested by Maddala (1983), a two-stage procedure will allow us to estimate a two-equation model in which one of the variables is censored while the other is only observed as a dichotomous variable. The two-stage estimation method involves the following steps. The ﬁrst step is to write the reduced-forms equations for the endogenous variables. Next, estimate the reduced-forms equations and keep the predicted values. Finally, estimate the structural equations

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replacing the endogenous variables by the predicted values obtained from the reduced-forms regressions. The empirical model deﬁned by Eqs. (1) and (2) speciﬁes both the probability of closure and wages as endogenous. Hence, the reduced form of the equation system in the latent variables is: pnijt ¼ P1 K ijt1 þ 1ijt ; W nijt1 ¼ P2 K ijt1 þ 2ijt1 ;

Y ijt ¼ 1ðpnijt o0Þ

W ijt1 ¼ MaxðW Mit1 ; W nijt1 Þ

(3) (4)

where K includes all the exogenous variables in X, Z, and U. The reduced-form parameters can be estimated by maximum likelihood methods applied to the probit and tobit models in Eqs. (3) and (4), respectively. Estimating the reduced-form for pnijt by the probit method will allow us to ^ obtain the predicted probability of displacement through ﬁrm closing, P. n Estimating the reduced-form for W ijt1 by the tobit method will enable us to dn ) and the estimated obtain the predicted value of the monthly wage (W d probability that a given observation is a limit observation, FðW M Þ. In other d words, FðW M Þ measures the estimated probability of a given worker receiving the minimum wage. This procedure is unconventional, but provides a simple and elegant solution to the speciﬁcation of the two sources of endogeneity from wages to failure rates. On the one hand, the impact of the level of wages on the chances of ﬁrm closure, and, on the other, the inﬂuence of minimum wage restrictions on the ability to accommodate negative shocks. The structural wage equation is estimated in the second-stage tobit after replacing the probability of displacement through ﬁrm closing (P) by its ^ The structural failure equation is estimated in the predicted value ðPÞ. second-stage probit after replacing the monthly reservation wage ðW nR Þ by dn ðp^ Tenure p^ Tenure2 Þ and after includdn ¼ W its predicted value W R

21

22

19 d ing the estimated probability of being a minimum wage earner, FðW M Þ. This last procedure will enable us to examine the effect of a mandatory minimum wage on the failure rate.

5.2. Identiﬁability Issues The speciﬁcation of our simultaneous-equations model is based, as usual, on a delicate compromise between parsimony, on the one hand, and the

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informational limitations of the data, on the other. It has to be admitted from the outset that the identiﬁcation obtained from the nonlinearities of the model, while helpful, is not fully convincing. Apart from this source of identiﬁcation, we rely on the information of the ﬁrm’s past sales growth as an indication of exogenous demand shocks, which arguably affect the closure decision but not the wage equation. What is assumed is that past sales growth solely impact on wages through the increase of the probability of ﬁrm closure (raising the ‘‘fear of unemployment’’ and weakening workers’ bargaining power). In short, we are using past sales growth as a valid instrument for the probability of closure and we are conﬁdent that the unemployment threat can be legitimately captured in the probability of closure. By the same token, we included the worker qualiﬁcation levels, which are used to deﬁne the base wages determined by collective bargaining, in the wage equation but not in the failure equation. We are fairly conﬁdent that this classiﬁcation is orthogonal to the exit decision by the ﬁrm, being, in our interpretation, a proxy for bargained wages. We also made, with some trepidation, additional exclusion restrictions: in essence, we excluded from the wage equation variables characterizing the ﬁrm and we excluded worker variables from the failure equation. These restrictions are admittedly ad-hoc but do not play any decisive role in the estimation results as we shall see.

5.3. Empirical Results 5.3.1. Main Results The parameter estimates of the simultaneous-equations model of ﬁrm closing and wages are presented in Table 2 (structural failure equation) and Table 3 (structural wage equation).20 The estimation strategy consists of having, as far as possible, a complete set of controls to examine whether a robust association between wages and the probability of ﬁrm closing (and vice-versa) can be identiﬁed. Columns 1 and 2 of Table 2 report results (coefﬁcients estimates and marginal effects, respectively) for a speciﬁcation in which the probability of ﬁrm closing depends on an extensive set of ﬁrm characteristics, the regional unemployment rate, monthly reservation wage (predicted), and the estimated probability of being a minimum wage earner. A set of dummy variables for industries, regions, and years are also included. High-wage paying ﬁrms face higher hazard rates than low-paying ﬁrms, ceteris paribus. After controlling for an extensive set of employers’

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ANABELA CARNEIRO AND PEDRO PORTUGAL Table 2.

Failure Equation – Two-Step Probit Results, Full-Time Workers (N ¼ 266,024), Dependent Variable: Displaced ¼ 1.

Variables Past sales growth Firm size Firm age Age Age S5 Age S10 Market share Multiplant ﬁrm Proportion of foreign capital Sales per worker Regional unemployment rate Monthly reservation wage (predicted) FðW M Þ (predicted) Constant Log-likelihood Chi-squared

Coefﬁcient

Marginal Effect

0.327 (31.1) 0.242 (77.2)

0.049 0.037

0.059 (5.3) 0.007 (0.6) 0.073 (24.6) 1.436 (29.0) 0.066 (6.9) 0.206 (11.4) 0.055 (13.8) 0.055 (7.3) 0.063 (3.2) 0.192 (5.9) 0.741 (3.4) 88628.6 33350.4

0.009 0.001 0.011 0.217 0.010 0.031 0.008 0.008 0.010 0.029 0.112

Notes: (a) a set of industry, regional and time dummies are included in the speciﬁcation; (b) age S5 ¼ (age-5) if ageW5, 0 otherwise; age S10 ¼ (age-10) if ageW10, 0 otherwise; (c) asymptotic t-statistics are in parentheses. Statistically signiﬁcant at 1%.

characteristics and for local labor market conditions, the results reveal that ﬁrms that pay higher entry-level wages, holding revenue per employee ﬁxed, are less likely to survive. In fact, the marginal effect of a 10% increase on the monthly reservation wage in the probability of displacement is 0.1 percentage points (see column 2 of Table 2). Since the average job displacement rate through ﬁrm closing in the population is around 6.3%, a 10% wage increase is associated with a 1.6% increase in the probability of job displacement through ﬁrm closing. The evidence of a positive relationship between reservation wages and failure rates is consistent with the idea of higher entry-level wages due to the existence of compensating differentials for the ex ante risk of displacement, which may accelerate the closure process in the short-run. Alternatively, it may merely reﬂect the scarcity of labor. Finally, the two-step probit results report a positive and signiﬁcant effect of the probability of receiving the minimum wage on the failure rate, suggesting that ﬁrms with a higher incidence of minimum wage workers face

267

Wages and the Risk of Displacement Table 3. Wage Equation – Two-Step Tobit Results, Full-Time Workers (N ¼ 266,024), Dependent Variable: Log of Real Monthly Wage. Variables Female Education Age/100 Age/100 squared Tenure/100 Tenure/100 squared Qualiﬁcation levels Top executives Intermediary executives Supervisors Highly skilled and skilled professionals Semiskilled and unskilled professionals Non-deﬁned Regional unemployment rate Probability of displacement (predicted) Constant Log-likelihood s^

Coefﬁcient

Marginal Effect

0.170 0.054 2.873 2.712 0.331

(86.5) (118.4) (44.0) (33.8) (7.9) 0.093 (0.8)

0.162 0.051 2.745 2.592 0.317 0.088

0.762 (62.4) 0.575 (61.2) 0.445 (58.5) 0.214 (33.7) 0.089 (13.8) 0.377 (43.9) 0.058 (25.1) 0.933 (75.7) 10.064 (703.7) 82468.0 0.32

0.728 0.549 0.425 0.204 0.086 0.361 0.056 0.892 9.616

Notes: (a) a set of industry, regional and time dummies are included in the speciﬁcation; (b) asymptotic t-statistics are in parentheses. Statistically signiﬁcant at 1%.

higher exit rates than those with a smaller incidence. A one percentage point increase in the proportion of minimum wage earners increases the probability of displacement by 0.029 percentage points. Since, on average, the proportion of minimum wage earners in the population is around 13% and the average job displacement rate is 6.3%, a 10% increase in the proportion of minimum wage earners increases the probability of displacement through ﬁrm closing by 0.60%. In fact, the possibility of wage concessions is precluded if workers are paid legal minimum wages. Thus, ﬁrms with a higher proportion of minimum wage earners may have lower chances of survival due to their inability to adjust wages downward in the face of a negative demand shock. Past sales growth, ﬁrm size, age, market share, multiplant ﬁrm, proportion of foreign capital, and sales per worker are signiﬁcantly correlated with the probability of ﬁrm closing. In particular, the results reveal that ﬁrms experiencing a decline in sales growth are clearly more

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likely to close. This seems to imply that sales contraction can be used as a strong predictor of ﬁrm failure. Indeed, the fact that a ﬁrm has grown in the past signals that it has been performing well. Moreover, the estimates reported in Table 2 show that small ﬁrms are clearly more likely to close than large ﬁrms. This result is conventional enough and, in particular, is in line with the one obtained for Portugal in the study of Mata et al. (1995) using a sample of newly born manufacturing plants. The estimates of the coefﬁcients on the ﬁrm’s age using splines indicate a negative and signiﬁcant effect of age on the probability of displacement. However, after a decade, the negative effect of age starts to vanish, becoming slightly positive for very old ﬁrms (more than 54 years). The variable market share has a strong negative effect on the probability of closing, suggesting that monopoly power generates rents that may function as a buffer that cushions against negative shocks. As expected, workers that are part of a multiplant ﬁrm are less likely to be displaced due to ﬁrm closing than workers that are part of a single-plant ﬁrm. The same is true for workers that are part of ﬁrms with a large proportion of foreign-owned capital. Sales per worker, a proxy for productivity, have a negative impact on the probability of ﬁrm closing. Thus, low productivity ﬁrms, all else being equal, are more likely to close down. The coefﬁcient estimate of the regional unemployment rate is positive and statistically signiﬁcant, suggesting that local economic conditions may affect the viability of some types of ﬁrms. Table 3 reports the two-step tobit results of the wage equation. The basic speciﬁcation includes a set of controls for workers’ characteristics, the regional unemployment rate, and the (instrumented) probability of displacement due to ﬁrm closing. A set of industry, regional and time dummies are also included in the speciﬁcation. All the exogenous variables (excluding tenure squared) are statistically signiﬁcant at the 1% level of signiﬁcance and have the expected signs. The effect of the probability of closing on monthly wages is negative and also statistically signiﬁcant. Converting the coefﬁcient of 0.892 to an elasticity results in a value of 0.056 evaluated at the mean failure rate in the sample (i.e., 6.3%). This implies that if the probability of displacement doubles, say from 6.3% to 12.6%, wages decrease by 5.6%, all else being equal.21 This empirical result indicates that average wages grow less rapidly in plants that will soon close, suggesting that ﬁrms’ adjustment to negative shocks are partially absorbed into wages.22

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5.3.2. Robustness Checks: Alternative Speciﬁcations At this point it should be noted that our main results remain valid regardless of changes in the model speciﬁcation. In fact, to further evaluate the robustness of our results, namely their sensitivity to changes in speciﬁcation, our model was reestimated including a detailed set of workers’ characteristics in the failure equation following previous studies such as Cooper, Gimeno-Gascon, and Woo (1994) and Mata and Portugal (2002), who found human capital to be a good predictor of survival. The results reported in column 1 of Table 4 show that including a set of controls for workers’ characteristics (such as gender, age, education, and tenure) in the failure equation does not affect our previous results. Indeed, this change increases the positive impact of wages on the probability of closing, suggesting that wages may be correlated with workers’ characteristics across ﬁrms. Moreover, and even though the impact of the proportion of minimum wage earners in the ﬁrm is reduced, it remains positive and statistically signiﬁcant at the conventional levels.23 Some other alternative speciﬁcations were tested, namely with the introduction, in the wage equation, of ﬁrms’ characteristics that might constitute an important determinant of wages, such as size and sales per worker. Again, these changes did not alter our main qualitative results (see column 2 of Table 4).24 Table 4.

Robustness Checks – Two-Step Results (Coefﬁcient Estimates), Full-Time Workers (N ¼ 266,024). Failure Equation (1)

(2)

Wage Equation (3)

(1)

(2)

(3)

0.933 (75.7) 0.479 (37.0) 0.933 (75.7)

Probability of displacement (predicted) 0.251 (8.3) 0.063 (3.2) Monthly reservation wage (predicted) FðW M Þ (predicted) 0.080 (2.2) 0.192 (5.9) Monthly wage (predicted)

0.181 (5.4) 0.052 (2.6)

Notes: (i) speciﬁcation (1) includes a set of human capital variables (gender, education, tenure and its square, age dummies) in the failure equation; speciﬁcation (2) includes ﬁrm size and sales per worker in the wage equation; speciﬁcation (3) uses the monthly wage instead of the monthly reservation wage in the failure equation; (ii) asymptotic t-statistics are in parentheses; (iii) all coefﬁcients are signiﬁcant at the 1% or 5% level.

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Finally, it should be pointed out that the effect of wages and the proportion of minimum wage earners in the failure equation remains virtually unchanged if the level of wages is measured as the monthly base wage with no correction for tenure effects (see column 3 of Table 4). In sum, these robustness checks reveal that the relationships between wages (including minimum wages) and the risk of displacement are robust to the inclusion of workers’ and ﬁrms’ characteristics in the failure and wage equation, respectively, i.e., our main conclusions stand regardless to changes in the model speciﬁcation.

6. CONCLUSIONS In this paper we have investigated how wages adjust to unfavorable shocks that raise the risk of displacement through ﬁrm closing, and to what extent a wage change affects the exit likelihood. For this purpose, a simultaneousequations model was speciﬁed and tested using a large longitudinally linked employer–employee data set of workers displaced due to ﬁrm closing. Three main conclusions emerge from this exercise. First, after controlling for employers’ heterogeneity and local labor market conditions, the results indicated that, although modest, wages have a positive impact on the failure rate. High-wage paying ﬁrms face higher exit rates than low-paying ﬁrms, ceteris paribus. Indeed, a 10% increase in monthly reservation wages raises the probability of displacement through ﬁrm closing by 1.6%. Second, a negative and strong effect of the probability of closing on wages was found, favoring the hypothesis that the risk of unemployment depresses wages. Doubling the average risk of displacement depresses wages by around 6%. This robust empirical evidence reinforces the hypothesis that under a bargaining approach workers in ﬁrms at risk are able to agree upon wage concessions/moderation in order to avoid the ﬁrm’s shutdown. Third, minimum wage restrictions were seen to increase the failure rates. A high proportion of minimum wage earners in a ﬁrm may preclude the possibility of wage concessions in response to unfavorable shocks, and thus accelerate the exit decision. In other words, ﬁrms with a higher incidence of minimum wage earners are more vulnerable to adverse demand shocks due to their inability to adjust wages downward. In fact, beyond the direct effect of wages on the failure rate, a 10% increase in the incidence of minimum wage earners (just around 1.3 percentage points) raises the probability of displacement by 0.6%.

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NOTES 1. See Addison, Bellmann, and Ko¨ling (2004) for a summary of the international evidence of union effects on plant closings for Britain and the United States. Their own study is about the effects of worker representation on plant closings in Germany. 2. Two other notable exceptions are the studies of Dunne and Roberts (1990) and Blanchﬂower (1991). 3. For a more detailed approach see Hamermesh (1988, 1991, 1993). 4. To better understand the relationship between ﬁrm-speciﬁc human capital and plant closing see Hamermesh (1988). 5. Even though minimum wage earners can be identiﬁed directly, the estimated probability of a given worker receiving the minimum wage will be included in the probit equation in order to account for the endogeneity of wages, including minimum wages. 6. Notice that since a control for tenure in the job will be included in the wage equation it is indifferent, from a theoretical point of view, whether the dependent variable is deﬁned as the level of wages (W) or the excess of wages over the reservation wage (WWR). 7. Thus, this source does not cover operated family businesses without wageearning employees and self-employment. Public administration is also excluded. 8. Since we have information over the 1991–1998 period, a ﬁrm is classiﬁed as an exiting ﬁrm in 1996 if it is present in the QP ﬁles in 1995, but absent in 1996, 1997, and 1998. The same reasoning applies for exits in 1994 and 1995. 9. If, for example, a worker’s displacement year is 1994 and he (she) appears in the database in the post-displacement period with a year of admission in the new job of 1992 or less, he (she) is excluded from the sample. 10. Hence, for workers displaced in 1994 the data should be available for the 1991–1993 period, for workers displaced in 1995 for the period of 1992–1994, and for workers displaced in 1996 for the 1993–1995 period. 11. We also believe that this restriction minimizes a potential selectivity problem generated by the (possibly nonrandom) departure of workers before closure. 12. See Appendix A for a more detailed description of the minimum wage legislation in Portugal. 13. The sample was drawn using a random number generator. 14. Sales in year t correspond to annual sales of the previous year. Sales were deﬂated using the CPI (base ¼ 1991). 15. This solution has been largely adopted and validated by other studies that use the QP data set. 16. At one-digit level there are nine sectors according to the Portuguese Classiﬁcation of Economic Activities (CAE). 17. At Nuts II mainland Portugal is split into ﬁve geographical areas. 18. It should be noted that for the period of analysis of this study (1993–1995), unemployment rates are only deﬁned at the regional level at Nuts II. In order to have a proxy for unemployment at a more disaggregated level of Nuts III (28 geographical areas for mainland), the ratio between annual job applications registered in each employment center and total employment (deﬁned at Nuts III using data from QP) will be used. The information on job applications registered in each employment

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center was obtained from Monthly Statistics – Institute for Employment and Vocational Training (IEFP). 19. The estimates of the tenure coefﬁcients (p^ 21 and p^ 22 ) were obtained with the estimation of the reduced form for W. 20. In both equations the asymptotic t-ratios correspond to the corrected covariance matrix for the two-step estimator using the methodology developed by Murphy and Topel (1985). d0 is the predicted wage in a ﬁrm with an average failure probability of 21. If W d1 is the predicted wage in a ﬁrm with a double probability of failure, 0.063 and W b 1 =W d0 Þ ¼ ½ð0:892Þ then the relative wage differential is calculated as ln ðW ð0:063Þ ¼ 0:056. 22. It should be noted that in Portugal nominal wage reductions are forbidden. Periods of high inﬂation favor, of course, larger downward real wage adjustments. In the period under analysis, inﬂation rates reached 8.1% in 1993, 6.1% in 1994, and 4.6% in 1995. 23. See Table B1 of Appendix B for the full results of the failure equation. 24. See Table B2 of Appendix B for the full results of the wage equation. 25. The only exceptions are 1982, when it was not updated, and 1989, when it was updated twice. 26. Source: Earnings Survey – Statistics Department of the Ministry of Employment.

ACKNOWLEDGEMENTS We are grateful to Daniel S. Hamermesh and John T. Addison for helpful comments and suggestions. The usual disclaimer applies. We thank Lucena Vieira for excellent computational assistance. We also thank CETE and Fundac- a˜o para a Cieˆncia e Tecnologia for ﬁnancial support (research grant POCTI/ECO/35147/99). CETE is a Research Centre supported by Fundac- a˜o para a Cieˆncia e a Tecnologia, Programa de Financiamento Plurianual through the Programa Operacional Cieˆncia, Tecnologia e Inovac- a˜o (POCTI)/Programa Operacional Cieˆncia e Inovac- a˜o 2010 (POCI) of the III Quadro Comunita´rio de Apoio, which is ﬁnanced by FEDER and Portuguese funds.

REFERENCES Addison, J., Bellmann, L., & Ko¨ling, A. (2004). Unions, works councils and plant closings in Germany. British Journal of Industrial Relations, 42(1), 125–148. Audretsch, D., & Mahmood, T. (1994). The rate of hazard confronting new ﬁrms and plants in US manufacturing. Review of Industrial Organization, 9, 41–56. Banco de Portugal. (1999). Annual Report 1998. Lisboa: Banco de Portugal.

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Bernard, A. B., & Jensen, J. B. (2002). The Death of Manufacturing Plants. NBER Working Paper no. 9026. Blanchard, O., & Portugal, P. (2001). What hides behind an unemployment rate: Comparing Portuguese and US labor markets. American Economic Review, 91, 187–207. Blanchﬂower, D. (1991). Fear, unemployment and pay ﬂexibility. Economic Journal, 101, 483–496. Cooper, A., Gimeno-Gascon, F., & Woo, C. (1994). Initial human and ﬁnancial capital as predictors of new venture performance. Journal of Business Venturing, 9, 371–395. Davis, S. J., Haltiwanger, J. C., & Schuh, S. (1996). Job creation and destruction. Cambridge: MIT Press. Doms, M. E., & Jensen, J. B. (1998). Comparing wages, skills, and productivity between domestically and foreign-owned manufacturing establishments in the United States. In: R. Baldwin, et al. (Eds), Geography and ownership as bases for economic accounting, NBER studies in income and wealth (Vol. 59, pp. 235–255). Chicago: University of Chicago Press. Dunne, T., & Roberts, M. J. (1990). Wages and the Risk of Plant Closings. CES Working Paper no. 90-6. Dunne, T., Roberts, M. J., & Samuelson, L. (1989). The growth and failure of US manufacturing plants. Quarterly Journal of Economics, 104, 671–698. Evans, D. (1987). The relationship between ﬁrm growth, size, and age. Journal of Industrial Economics, 35, 567–581. Hall, B. H. (1987). The relationship between ﬁrm size and ﬁrm growth in the United States manufacturing sector. Journal of Industrial Economics, 35, 583–606. Hamermesh, D. S. (1988). Plant closings and the value of the ﬁrm. Review of Economics and Statistics, 70, 580–586. Hamermesh, D. S. (1991). Wage concessions, plant shutdowns, and the demand for labor. In: J. Addison (Ed.), Job displacement: Consequences and implications for policy (pp. 83–106). Detroit: Wayne State University Press. Hamermesh, D. S. (1993). Labor demand. Princeton: Princeton University Press. Harris, R. I., & Hassaszadeh, P. (2002). The impact of ownership changes and age effects on plant exits in UK manufacturing, 1974–1995. Economics Letters, 75, 309–317. Jacobson, L. S., LaLonde, R. J., & Sullivan, D. G. (1993). Earnings losses of displaced workers. American Economic Review, 83, 685–709. Jovanovic, B. (1982). Selection and the evolution of industry. Econometrica, 50, 649–670. Kumar, M. (1985). Growth, acquisition activity and ﬁrm Size: Evidence from the United Kingdom. Journal of Industrial Economics, 33, 327–338. Machin, S. (1995). Plant closures and unionization in British establishments. British Journal of Industrial Relations, 33, 55–68. Maddala, G. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press. Margolis, D. (1999). Part-year employment, slow reemployment, and earnings losses: The case of worker displacement in France. In: J. Haltiwanger, et al. (Eds), The creation and analysis of employer–employee matched data: Contributions to economic analysis (pp. 375–416). North-Holland: Elsevier Science B.V. Mata, J., & Portugal, P. (1994). Life duration of new ﬁrms. Journal of Industrial Economics, 42, 227–245. Mata, J., & Portugal, P. (2002). The survival of new domestic and foreign owned ﬁrms. Strategic Management Journal, 23, 323–343.

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Mata, J., Portugal, P., & Guimara˜es, P. (1995). The survival of new plants: Start-up conditions and post-entry evolution. International Journal of Industrial Organization, 13, 459–481. Murphy, K. M., & Topel, R. H. (1985). Estimation and inference in two-step econometric models. Journal of Business and Economic Statistics, 3, 370–379. Stevens, A. H. (1997). Persistent effects of job displacement: The importance of multiple job losses. Journal of Labor Economics, 15, 165–188.

APPENDIX A. MINIMUM WAGE LEGISLATION A mandatory minimum monthly wage was set for the ﬁrst time in Portugal in 1974, covering workers aged 20 or older and excluding agriculture and domestic servants. Currently, there is a unique legal minimum that applies to all workers. Workers formally classiﬁed as apprentices receive just 80% of the full rate. The minimum pay cannot be reduced by means of collective agreements or individual contracts. The minimum wage is deﬁned as the base monthly wage and is updated annually by the parliament, under government proposal.25 Decisions on the level of the minimum wage are taken on a discretionary basis, usually taking into account past and predicted inﬂation and after consulting the social partners. According to the 1998 annual report of the Banco de Portugal (1999), in 1995, the minimum monthly wage represents around 43% of the average monthly base wage in the private sector. Data for 1995 also indicate that the proportion of workers that received the minimum legal wage or a subminimum was about 13%, although this percentage has steadily declined since 1985. The coverage of the legal minimum wage is maximum in the furniture industries and in the sector of restaurants and hotels (coverage higher than 20% in 1995). Coverage is also larger in ﬁrms employing fewer than 10 employees.26

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APPENDIX B Table B1.

Failure Equation – Two-Step Probit Results, Full-Time Workers (N ¼ 266,024), Dependent Variable: Displaced ¼ 1.

Variables Past sales growth Firm size Firm age Age Age S5 Age S10 Market share Multiplant ﬁrm Proportion of foreign capital Sales per worker Regional unemployment rate Female Education Worker age 18–24 25–34 35–54 Tenure/100 Tenure/100 squared Monthly reservation wage (predicted) FðW M Þ (predicted) Constant Log-likelihood Chi-squared

Coefﬁcient

Marginal Effect

0.322 (30.7) 0.253 (75.8)

0.048 0.038

0.056 (5.0) 0.007 (0.5) 0.069 (23.1) 1.386 (28.4) 0.066 (6.9) 0.248 (13.4) 0.070 (15.8) 0.072 (9.5) 0.151 (15.5) 0.016 (7.2)

0.009 0.001 0.010 0.208 0.010 0.037 0.010 0.011 0.023 0.002

0.058 (3.1) 0.050 (3.4) 0.041 (3.2) 1.759 (11.3) 4.442 (10.0) 0.251 (8.3)

0.008 0.007 0.006 0.264 0.668 0.038

0.080 (2.2) 0.974 (3.1) 88432.4 33742.8

0.012 0.146

Notes: (a) a set of industry, regional and time dummies are included in the speciﬁcation; (b) age S5=(age-5) if ageW5, 0 otherwise; age S10=(age-10) if ageW10, 0 otherwise; (c) asymptotic t-statistics are in parentheses. Statistically signiﬁcant at 1%. Statistically signiﬁcant at 5%.

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Table B2. Wage Equation – Two-Step Tobit Results, Full-Time Workers (N ¼ 266,024), Dependent Variable: Log of Real Monthly Wage.

Variables Female Education Age/100 Age/100 squared Tenure/100 Tenure/100 squared Qualiﬁcation levels Top executives Intermediary executives Supervisors Highly skilled and skilled professionals Semiskilled and unskilled professionals Non-deﬁned Regional unemployment rate Sales per worker Firm size Probability of displacement (predicted) Constant Log-likelihood s^

Coefﬁcient 0.158 0.050 2.643 2.499 0.479 0.492 0.742 0.542 0.421 0.198

(100.8) (160.6) (52.6) (40.7) (15.0) (5.3) (101.5) (84.6) (77.0) (43.5)

0.075 (16.2) 0.349 0.060 0.070 0.016 0.479

Marginal Effect 0.152 0.048 2.536 2.397 0.460 0.472 0.712 0.520 0.404 0.190 0.072

(58.4) (35.9) (90.2) (23.8) (37.0)

0.335 0.058 0.067 0.016 0.459

9.356 (678.1) 76453.8 0.31

8.976

Notes: (a) a set of industry, regional and time dummies are included in the speciﬁcation; (b) asymptotic t-statistics are in parentheses. Statistically signiﬁcant at 1%.

HOW ARE FIXED-TERM CONTRACTS USED BY FIRMS? AN ANALYSIS USING GROSS JOB AND WORKER FLOWS Catalina Amuedo-Dorantes and Miguel A´. Malo ABSTRACT Using Spanish establishment-level data on temporary and permanent job and worker ﬂows, we examine ﬁrms’ relative usage of ﬁxed-term contracts in response to changes in their prior net employment expectations for the short-run and the long-run – viewed as proxies of how a wide variety of future shocks are ultimately perceived by establishments. The employment response of establishments to changing net employment expectations for the short-run is, primarily, suggestive of their reliance on ﬁxed-term contracts as a buffer to cushion short-run changes in demand as well as to shield permanent workers from downward workforce adjustments. In contrast, their response to changes in net employment expectations for the long-run mostly hints on the use of ﬁxedterm contracts as a screening device. Therefore, policies providing ﬁnancial incentives to convert ﬁxed-term into permanent contracts – thus targeting ﬁrms’ using ﬁxed-term contracts as a screening device, are likely to only have limited effectiveness.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 277–304 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28009-X

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1. INTRODUCTION During the 1980s, several countries implemented labor market reforms with the intent of lowering unemployment levels by deregulating employment and promoting the use of ﬁxed-term contracts.1 As opposed to open-ended or permanent work contracts, ﬁxed-term or temporary work contracts provided employers with substantially lower dismissal costs.2 These reduced discharge costs consisted of limited severance payments and nonexistent judicial procedures available to workers wanting to sue employers for unfair dismissals. From a legal point of view, ﬁxed-term contracts were conceived to be used as a buffer or cushion to address temporary changes in employment needs due to changes in product demand characteristic of seasonal industries, such as tourism or construction, or to ﬁll vacancies on a temporary basis. However, in part fueled by the cost advantages described above, ﬁxed-term contracts became widely used by ﬁrms for other purposes, for example, as a buffer for workers with open-ended contracts during economic downturns or to screen workers for permanent positions at a relatively low cost. In some instances, as was the case with Spain from 1984 to 1994, the employment regulation was changed to allow for the use of ﬁxed-term contracts to hire workers fulﬁlling permanent jobs. Owing to the characteristics of the data we work with, we focus on two of the most discussed usages of ﬁxed-term contracts in the labor literature, that is, on their use as a buffer and on their use as a screening device. Spain is the most prominent case of an extensive use of ﬁxed-term contracts and constitutes an unparallel example given its unprecedented growth in temporary employment, which grew from less than 10% of the wage and salary workforce in the early 1980s to approximately 30% by the second half of the 1980s (Dolado, Garcı´ a-Serrano, & Jimeno, 2002). In fact, the proportion of temporary workers has barely changed since then despite the legalization of temporary help agencies and the passage of various labor market reforms aimed at reducing establishments’ reliance on temporary contracts (Toharia & Malo, 2000). Hence, there is growing interest in gaining a better understanding of establishments’ employment practices by type of work contract. We use Spanish data from the Encuesta de Coyuntura Laboral (ECL) to examine establishments’ employment practices by type of work contract. The ECL is a quarterly longitudinal survey that contains detailed information on stocks and gross ﬂows of workers at the establishment level. In addition, it provides information on establishments’ net employment expectations for the next quarter and year. These expectations furnish

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detailed plant-level information on how establishments perceive that a wide variety of short- and long-run shocks may be affecting their future employment needs. For the purpose of this study, we use data on establishments having 500 or more workers during the period 1/1993–1/ 20023 to ﬁrst examine the extent to which establishments accurately forecast their short- and long-run employment needs by comparing their expected net employment changes for any given quarter to their realized gross job and worker ﬂows. Subsequently, we examine the dynamics of gross job and worker ﬂows by type of work contract and contract conversion ﬂows from ﬁxed-term to permanent at the establishment level in response to changes in net employment expectations for the short- and the long-run. We ﬁnd that establishments’ response to changing net employment expectations for the short-run are, primarily, suggestive of their reliance on ﬁxed-term contracts as a buffer to cushion short-run changes in demand as well as to shield permanent workers from downward workforce adjustments, whereas their response to changes in net employment expectations for the long-run mostly hint on the use of ﬁxed-term contracts as a screening device.

2. LITERATURE REVIEW AND HYPOTHESES TO BE TESTED An extensive literature has examined the dynamics of labor demand in terms of the employment and worker-hours response to changes in adjustment costs.4 However, despite the theoretical evidence on higher dismissal costs reducing total job reallocation and worker turnover rates (e.g., Blanchard & Portugal, 2001), the literature does not provide a clear prediction of the dynamics of gross job and worker ﬂows by type of work contract (Bentolila & Saint-Paul, 1992). Some researchers have addressed this gap with an analysis of the impact that the availability of ﬁxed-term contracts may have on the dynamics of gross job and worker ﬂows. The studies, nonetheless, differ in their geographic focus as well as in their reliance on employee versus ﬁrm-level data. For instance, Goux, Maurin, and Pauchet (2001) discuss how the availability of ﬁxed-term contracts affects average (temporary and permanent) employment levels in France from a theoretical perspective. They argue that ﬁxed-term contracts provide the ﬁrm with greater stafﬁng ﬂexibility. According to the authors, low dismissal costs associated to ﬁxed-term contracts allow ﬁrms to respond to short-term increases in demand through the hiring of temporary workers despite prospects of a future economic downturn.

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Yet, Goux et al. (2001) do not empirically test this hypothesis regarding the use of temporary workers as a buffer. Other studies have done that for other countries. Most of the literature has relied on employee level data, for example Houseman and Abraham (1993) and Booth, Francesconi, and Frank (2002). Both studies use individual level or employee level data to examine, in the ﬁrst case, whether Japanese women are used as a buffer and, in the second case, whether women and ethnic minorities are used as a buffer in the United Kingdom. Making use of ﬁrm-level data and focusing on Spain, Garcı´ a-Serrano (1998) provides some descriptive evidence on worker turnover and job reallocation being higher for ﬁxed-term contracts, which account for the majority of job creation, job destruction, and for the difference between worker turnover rates and job reallocation rates (also called ‘‘churning’’). However, Garcı´ a-Serrano’s analysis displays a descriptive nature and is based on just two years of data (i.e., 1993 and 1994). More importantly, this study does not examine establishments’ temporary and permanent job and worker ﬂows’ dynamics in response to their changing employment expectations for the short- and long-run. Yet, the link between establishments’ prior net employment expectations and their job and worker ﬂows by type of contract reveals important information on how a variety of economic and noneconomic shocks are perceived to affect employment at the plant level and, in turn, on how these expectations impact their temporary and permanent employment practices. Another study using ﬁrmlevel data is that by Houseman, Kalleberg, and Erickek (2001), who examine whether temporary workers are used as a buffer by US hospitals and ﬁrms in the auto supply industries. Lastly, Varejao, and Portugal (2003) provide yet another example of a study relying on ﬁrm-level data to analyze how ﬁrms use ﬁxed-term contracts. They conclude that screening workers for permanent positions is by far the most important reason behind Portuguese ﬁrms’ usage of ﬁxed-term contracts. Despite the similarity in some of their objectives, their study differs from ours in various aspects. First, they focus on Portugal, while our focus is on Spain. Second, their dataset lacks information on our variable of interest, that is, ﬁrms’ employment expectations, as well as on total gross ﬂows by contract type. Therefore, they are unable to analyze the role played by the ﬁrm’s employment expectations on total gross ﬂows by contract type and on their temp-toperm conversion rate – as it is the purpose of the present study. In addition to the descriptive analysis by Garcı´ a-Serrano (1998), other studies with a Spanish focus examining ﬁrms’ temporary employment practices include the analyses by Jimeno and Toharia (1993a) and Bentolila

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and Dolado (1994), who examine the hypothesis of temporary workers being used as a buffer, although from a collective bargaining point of view. In their models, wage gaps between permanent workers – also called ‘‘insiders’’ – and temporary workers – or ‘‘outsiders’’ – are accentuated via collective bargaining. In particular, the authors argue that permanent workers feel protected (with a very limited exposure to unemployment) in their higher salary requests by the existence of temporary workers who can be easily dismissed in the event of any labor adjustment needs. As a result, according to these authors, salaries become relatively independent of the unemployment rate dynamics. Hernanz (2003) has questioned the aforementioned models on the basis that they are only valid when workers with temporary and permanent workers are considered substitutes. In contrast, if temporary workers and their counterparts with open-ended contracts are considered complements, both will be hired simultaneously, although in different proportions given the lower cost associated to ﬁxed-term contracts. Yet, a valid test of whether temporary and permanent workers are complements or substitutes requires information on the ﬁrm’s production function. Finally, in a recent study, Polavieja (2006) argues that ﬁxed-term contracts are mainly used as a screening device by Spanish ﬁrms. However, he recognizes that the use of ﬁxed-term contracts as a screening device does not rule out ﬁrms’ reliance on ﬁxed-term contracts as a buffer or cushion to address short-term increases in demand or downward labor adjustments owing to ﬁxed-term contracts’ lower dismissal costs. Therefore, in light of the aforementioned explanations regarding the usage of temporary work contracts by ﬁrms, we hypothesize that: (a) If temporary contracts are used as a screening device, temporary hires and job creation should increase (diminish) in establishments adjusting to growing (declining) employment expectations for the long-run. Additionally, any contract conversion ﬂows would signal the use of ﬁxed-term contracts as a screening device. Nonetheless, given the permanent nature of the new contract, changes in net employment expectations for the longrun should induce greater contract conversions than temporary changes in net employment expectations for the short-run. (b) When temporary job and worker ﬂows are used as a buffer, any labor adjustments to address diminishing employment expectations are primarily carried out via changes in temporary job and worker ﬂows. Speciﬁcally, as formulated by Goux et al. (2001), only if temporary employment is used as a buffer for permanent employment will we observe that establishments foreseeing a decline in net employment in

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the long-run opt to increase their temporary job or worker ﬂows to accommodate their current demands while still keeping future dismissal costs low. Additionally, establishments’ greater reliance on ﬁxed-term contract to address growing net employment expectations for the shortrun also reﬂects their usage of temporary employment as a cushion or buffer against such changes. A priori, we do not subscribe to one particular use of temporary job and worker ﬂows by ﬁrms. After all, in large establishments, it is reasonable to expect temporary and permanent workers to take on a variety of responsibilities and tasks. Furthermore, as noted by Polavieja (2006), the use of ﬁxed-term contracts as a screening device by the establishment is not disputed with the use of temporary employment in some instances as a buffer or cushion to address changes in employment needs. Since establishments’ net employment expectations can be considered proxies of how a wide variety of future shocks are ultimately perceived by establishments, we use changes in establishments’ net employment expectations for the short- and long-run to gauge the extent to which establishments use ﬁxed-term contracts to meet their changing employment needs, drawing conclusions on establishments’ use of ﬁxed-term contracts as a screening device and/or as a buffer.

3. INSTITUTIONAL BACKGROUND Before proceeding any further, it is important to brieﬂy review some of the institutional aspects of the Spanish labor market most relevant to our analysis. Before the passage of the Workers’ Statute in 1980, ﬁxed-term or temporary contracts were only allowed in sectors characterized by their seasonal employment needs under the so-called ‘‘causality principle.’’5 In addition, interim contracts of a temporary nature were permitted in exceptional occasions. The 1984 reform of the Workers’ Statute liberalized ﬁxed-term employment introducing a new contract (the so-called ﬁxed-term contract for employment promotion) that did not require the ‘‘causality principle.’’ As such, ﬁrms could use ﬁxed-term contracts to hire workers for all types of positions – temporary as well as permanent.6 The intent was that the introduction of this new contractual ﬁgure would help lower the very high unemployment rate characterizing that time period. This reform increased employment ﬂexibility at the margin by exclusively altering the dismissal costs of temporary contracts, while leaving the regulation of indeﬁnite-term or permanent work contracts unchanged. In part fuelled by the cost advantages

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of ﬁxed-term contracts, temporary employment expanded very rapidly. On the demand side, ﬁrms used ﬁxed-term contracts as a means to cut down employment costs. On the supply side, youngsters relied on these contractual arrangements as a means to enter the labor market. As reference of the fast growth of temporary employment, it is worth noting that, before the 1984 reform, approximately 10% of wage and salary workers held temporary work contracts (Fina, Meixide, & Toharia, 1989). By 1992, this proportion had grown to account for 33% of wage and salary workers according to data from the Spanish labor force survey or Encuesta de Poblacio´n Activa (Toharia & Malo, 2000; Dolado et al., 2002). The extended use of ﬁxed-term contracts was only weakly linked to industry changes and became a common feature of all Spanish industries (Toharia, 2005). Furthermore, temporary employment rates remained stable since the early 1990s despite the legalization of temporary work agencies in 1994, the passage of two labor reforms in 1994 and 1997 intended to reduce temporary employment rates, or the business cycle. With regards to business cycles, Fig. 1 depicts the evolution of temporary employment and GDP growth rates. Temporary employment increased between 1988 and 1992 at a time when GDP growth rates were slowing down. This relationship switched sign between 1993 and 1995 and, from 1996 onwards, temporary employment rates have remained fairly stable regardless of ﬂuctuations in the growth rate of GDP. Therefore, temporary employment rates seem to exhibit limited sensitivity to the business cycle. What about the potential impact of the two labor reforms of 1994 and 1997? The 1994 reform introduced two types of changes. First, it legalized temporary work agencies – whose intermediation was only restricted in sectors with high injury rates, in Health Services and in the Public Administration.7 Second, the 1994 legal reform tried to limit the use of ﬁxed-term contracts through the restoration of the causality principle for temporary employment and the elimination of the ﬁxed-term contract for employment promotion introduced in 1984. However, as Toharia and Malo (2000) show, the proportion of temporary contracts remained fairly unchanged following the reform, even if the composition of temporary employment by type of contract differed. In particular, the ﬁxed-term contracts for employment promotion were replaced by the so-called per-task contracts. Additionally, the new legislation allowed for ‘‘small’’ collective dismissals8 to be treated as individual workers’ dismissals as long as they were based on economic grounds9 to reduce ﬁrms’ dismissal costs.10 As the rate of temporary employment remained fairly high after the passage of the 1994 reform, a new legal reform was implemented in 1997. This

Fig. 1.

5.0

4.0

3.0

2.0

1.0

0.0

-1.0

-2.0

35

30

25

20

15

10

5

0

GDP Growth Rate (right)

Temporary Employment and GDP Growth Rates. Source: Labor Force Survey and National Accounts.

Temp. Rate (left)

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

6.0

40

284 CATALINA AMUEDO-DORANTES AND MIGUEL A´. MALO

An Analysis Using Gross Job and Worker Flows

285

new reform also targeted ﬁrms’ prominent reliance on ﬁxed-term contracts with two new measures: (1) a new open-ended contract characterized by lower dismissal costs and (2) the promotion of temp-to-perm contract conversions through monetary incentives from the Public Administration.11 Yet, despite all these institutional labor market changes, temporary employment has remained at about one third of the wage and salary workforce up to the present decade.12 Since other ﬂexible work contracts (e.g., part-time contracts) have been scarcely used in Spain, ﬁxed-term contracts constitute the predominant work arrangement used by Spanish employers in order to increase their employment ﬂexibility (Toharia, 2005).

4. DATA AND DESCRIPTIVE ANALYSIS 4.1. Data The data for this research come from the ECL. The ECL is a longitudinal survey carried out on a quarterly basis since the second quarter of 1990 by the Spanish Ministry of Labor and Social Affairs. It surveys establishments with more than ﬁve workers in nonagriculture industries, with the exception of Public Administration, Defense and Social Security, diplomatic delegations, and international and religious organizations in the service sector. In 1997, the ECL underwent important methodological changes involving the inclusion of establishments with less than ﬁve workers in the survey sample along with a new sample stratiﬁcation methodology. We use data on establishments having more than 500 employees during the period 1/1993–1/2002. This is the only stratum of micro data and the only time period for which detailed information on establishment level gross employment ﬂows (employment stock at the moment and at the end of the previous quarter, as well as the number of arrivals and separations by type of work contract during the quarter) has been made publicly available. Furthermore, this is the only stratum of establishments unaffected by the 1997 changes to the survey methodology. Finally, this stratum of establishments with 500 employees constitutes the Spanish universe of large ﬁrms and, therefore, observations do not need to be weighted. The number of such large establishments is around 1,000 in a given quarter.13 In particular, due to new establishment creation, we work with an unbalanced panel consisting of 1,811 establishments and 27,381 observations during the 1/1993–1/2002 period. On average, this stratum represents approximately 15% of nonagriculture employment. About 20% of their workforce holds ﬁxed-term contracts

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depending on the time period under examination (Garcı´ a-Serrano, 1998). Since approximately 30% of wage and salary workers hold temporary work contracts in Spain, our gross and net temporary ﬂows may, in any event, be considered underestimates of the gross and net temporary ﬂows in the entire universe of Spanish establishments. There are a couple of reasons as for why this is the case. First, our sample consists of large establishments for which the percentage of workers with ﬁxed-term contracts is smaller than for small- and medium-size establishments not included in the sample. Second, for any given worker, the ECL does not record hires and separations taking place within the same establishment during the same month. For instance, if a worker is hired in the ﬁrst month of the quarter, separated in the second month, and re-hired in the third month during any given quarter, the ECL records two hires and one separation within that establishment during that quarter. However, if a worker is hired, separated, and re-hired during the same month, the ECL only records one hiring. Hence, the ECL provides underestimates of gross and net temporary ﬂows of short duration. Despite these shortcomings, the high frequency and longitudinal information on establishment level gross employment ﬂows (by type of work contract) and the information on the establishments’ net employment expectations for the short-run and for the long-run make the ECL a unique and well-suited survey for the analysis proposed in this study.

4.2. Gross Job and Worker Flows by Contract Type Our methodology follows the empirical approach outlined in Davis and Haltiwanger (1990, 1992) to construct job and worker ﬂows. Worker turnover (or worker reallocation) can be divided into two components: worker mobility due to gross job reallocation (i.e., job creation and job destruction processes) and worker mobility in excess of job reallocation (i.e., worker rotation or worker shufﬂing). Because our dataset contains information on hires and separations at the establishment level, it is possible for us to construct measures of worker reallocation and distinguish among its components. First of all, let us consider total gross worker turnover. Given the size of establishment i at times t (Ei,t) and t1 (Ei,t1), the average size of establishment i between t1 and t is deﬁned as follows: Ni,t=(Ei,tþEi,t1)/2. By aggregating, it is possible to obtain the size of the whole economy: Nt=Si Ni,t. The hiring (separation) rate is deﬁned as the proportion of the number of workers arriving in (leaving) establishments between t1 and t

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with respect to the employment stock: H i;t S i;t hi;t ¼ si;t ¼ N i;t N i;t Then, by aggregating, we may calculate the aggregate hiring rate: X N i;t WPOS t ¼ hi;t Nt i and the aggregate separation rate: WNEGt ¼

X N i;t i

Nt

si;t

The sum of both rates is the worker turnover or worker reallocation rate (WRt): WRt ¼ WPOS t þ WNEGt Now let us consider job reallocation. The employment growth rate in each establishment is deﬁned as follows: gi,t=(Ei,tEi,t1)/Ni,t=(Hi,tSi,t)/Ni,t. In other words, the employment growth rate can be calculated as the difference between current and past employment stocks, or as the difference between hires and separations in the corresponding period of time.14 Then, for the whole economy, we can deﬁne the job creation rate as: X N i;t JPOS t ¼ g ; for gi;t 40 N t i;t i and the job destruction rate as: X N i;t g ; JNEGt ¼ N t i;t i

for gi;t o0

The job reallocation rate (JRt) is the sum of both rates. It provides us with an estimate of worker mobility due to job creation and job destruction: JRt ¼ JPOSt þ JNEGt Worker turnover (RRt) can then be deﬁned as the extent of worker reallocation taking place in excess of job ﬂows: RRt ¼ WRt JRt ¼ 2 min ðH t ; S t Þ Finally, aggregate net employment growth rates are given by the difference between both job creation and job destruction rates. They may also be

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computed as the difference between total hires and total separations. Hence: NET t ¼ JPOS t JNEGt ¼ WPOS t WNEGt Using data on the employment stock by contract type, we compute the indicators of job creation and job destruction for temporary, permanent, and total plant-level employment. Similarly, we exploit the information on hires and separations by contract type at the establishment level to construct indicators of gross worker ﬂows, gross temporary worker ﬂows, and gross permanent worker ﬂows. Finally, we derive net ﬂows for temporary, permanent, and total employment. All indicators are computed in thousands. Additionally, we compute the average employment stock between t and tþ1 to then gauge the fraction of the adjustment made through changes in temporary versus permanent employment. We thus have measures of all gross temporary and permanent employment ﬂows, with total gross ﬂows being the sum of both. The database also includes information on the number of new permanent contracts signed with workers previously hired by the establishment on a ﬁxed-term basis each quarter. Therefore, we are also able to compute conversion rates. Such a rate is deﬁned as WPOS t , with the only difference that hit now refers to these new permanent contracts instead of all new permanent contracts. Finally, it is worth noting that new permanent contracts resulting from contract conversions are included in the calculation of permanent hires in the same way that the ﬁxed-term contracts converted to a permanent basis are considered temporary employment separations. Otherwise, these permanent and temporary worker ﬂows would be miscalculated. 4.3. Net Employment Expectations and Gross Job and Worker Flows by Contract Type The main purpose of this study is to learn about how establishments adjust their temporary and permanent job and worker ﬂows to ﬂuctuations in their future employment needs as captured by changes in their prior net employment expectations. Therefore, we create two sets of dichotomous variables to capture establishments’ net employment expectations for the following quarter and for the following year. These dummies are created using the responses of establishments’ human resource and personnel departments when asked whether they expect their employment stock to increase, remain unchanged, or decrease in the short-run (next quarter) and

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in the long-run (next year). In particular, establishments’ human resource and personnel departments are asked to ‘‘Indicate the foreseen employment changes for the following two time periods: (a) for the upcoming trimester, that is, between the ﬁrst and last days of the upcoming trimester, and (b) for the upcoming year, that is, between the ﬁrst and last days of the upcoming twelve months.’’ Survey respondents then choose among three options regarding their expected future net employment: increasing (se aumentara´), unchanged (permanecera´ estable), and diminishing (disminuira´). Because the survey universe consists of large establishments with 500 plus workers, human resource and personnel departments are typically well informed and, in any case, assisted by the statistical survey team in interpreting and answering the questions posed by the professional interviewers. Furthermore, to the extent that the information on establishments’ net employment expectations is used on a quarterly basis by the Ministry of Labor to publicize industries’ employment outlooks, establishments’ responses to this question are carefully checked across quarters to ensure data reliability. Past research has used industry or regional information regarding changes in sales, shipments, output prices, or other observable shocks to gauge changes in labor demand (e.g., Hamermesh, 1993). In this study, we make use of information on establishments’ net employment expectations for the upcoming quarter and year. As the term indicates, these expectations do not exclusively reﬂect a frictionless target but, rather, expected changes in the employment needs of the establishment given its adjustment costs and overall human resource strategy. Because of the lack of information on establishments’ adjustment costs or human resource strategies, most studies using measures of observable shocks run into an omitted variable problem that biases their estimate of the establishment’s reaction to the shock. In this regard, the usage of individualized information on establishments’ net employment expectations for the upcoming quarter and year constitutes an ideal measure to address a related, yet slightly different, question we pose ourselves in this study. The latter refers to establishments’ employment practices vary by type of work contract and, in particular: to which extent do establishments use temporary employment as a screening device and/or as a buffer when adjusting to their changing net employment expectations? Additionally, the usage of establishments’ net employment expectations for the upcoming quarter and year provides some advantages over more conventional measures of observable shocks. First, instead of proxying for changes in labor demand via changes in sales, shipments, or output prices, establishments’ net employment expectations directly capture how a variety of shocks are ultimately perceived by plants as reﬂected by their expectations regarding future employment needs. Second,

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survey data provide us with information regarding changes in establishments’ net employment expectations for the short-run and the long-run. In this manner, we are able to distinguish how establishments rely on speciﬁc contract types depending on the temporal proximity of the expected change in their employment needs. Third, establishments’ net employment expectations are measured at the establishment level instead of at the industry or regional level. As such, they constitute a more valuable measure considering that establishments may respond differently to future shocks depending on the accuracy of their information and their economic standing. Table 1 displays average gross job and worker ﬂows according to the sign of establishments’ net employment expectations for the next quarter and year.15 For the most part, employment expectations are met with temporary and permanent employment adjustments of the same sign. This is particularly true in the short-run. For instance, establishments seem to respond to increasing net employment expectations from a previous quarter by expanding their temporary and permanent workforces by 37 and 8 workers per 1,000, respectively. Likewise, diminishing net employment expectations from a previous quarter are met with reductions in both temporary and permanent employment of 6 and 11 workers per 1,000, correspondingly. As such, ﬁxed-term contracts seem to be used as a shock absorber or buffer in the short-run, particularly to respond to growing net employment expectations. Additional evidence of the usage of temporary employment as a buffer is provided by the fact that net temporary employment is positive for establishments with unchanged or with diminishing net employment expectations for the long-run. This statistic supports the predictions from the dynamic labor demand model presented by Goux et al. (2001), who argue that establishments will continue to hire temporary workers in the presence of a long-run economic downturn in order to satisfy current demand as they will be able to use them as a buffer for permanent employees at a future date. Is there any evidence of the usage of temporary employment as a screening device? Yes. The simultaneous use of ﬁxed-term and permanent contracts to address both growing as well as diminishing net employment expectations for the short-run is suggestive of the usage of ﬁxed-term contracts as a screening device. Additional evidence regarding the use of ﬁxed-term contracts to screen workers is provided by establishments’ conversion ﬂows. The ratio of permanent hires to conversions remains at about 2.5 regardless of the change in net employment expectations. The sole exception occurs when establishments adjust to diminishing employment expectations for the next year, in which case this rate rises to approximately 3.6 as fewer temp-to-perm contract conversions take place. The relatively

32.86 18.35 8.27

Permanent Job Creation

90.83 52.11 24.29

Temporary Job Creation

12.81 6.06 6.23

Permanent Job Creation

50.41 22.30 13.64

14.03 20.69 49.87

Permanent Job Destruction

18.07 20.37 12.64

Temporary Job Destruction

4.80 6.88 16.88

Permanent Job Destruction

12.96 15.33 19.78

Temporary Job Destruction

84.62 56.81 31.68

Permanent Hires

932.13 551.48 184.06

Temporary Hires

23.36 14.16 11.89

Permanent Hires

247.93 139.54 65.03

Temporary Hires

65.79 59.15 73.28

Permanent Separations

859.37 519.75 172.41

Temporary Separations

15.35 14.98 22.55

Permanent Separations

210.48 132.56 71.17

Temporary Separations

18.84 2.34 41.60

Net Permanent Employment

72.76 31.73 11.65

Net Temporary Employment

8.01 0.82 10.66

Net Permanent Employment

37.45 6.98 6.14

Net Temporary Employment

37.16 21.97 8.68

Conversions

– – –

–

9.04 5.36 4.24

Conversions

– – –

–

Note: Gross ﬂows are measured following Davis–Haltiwanger methodology as explained in the main text. Source: Authors’ tabulations using the ECL. ‘‘Conversions’’ refers to permanent hires proceeding from immediately previous temporary contracts with the same workers. By deﬁnition, the amount of conversions is as much as permanent hires.

Increasing Unchanged Diminishing

Expectations for Next Year (Perms)

Increasing Unchanged Diminishing

Expectations for Next Year (Temps)

Increasing Unchanged Diminishing

Expectations for Next Quarter (Perms)

Increasing Unchanged Diminishing

Temporary Job Creation

Gross Flows by Contract Type and by Establishments’ Net Employment Expectations (All Figures in per Thousands).

Expectations for Next Quarter (Temps)

Table 1.

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stable proportionality between permanent hires and conversion ﬂows is suggestive of the usage of ﬁxed-term contracts as a screening device, possibly as part of the establishments’ long-run employment strategies. In sum, establishments seem to primarily rely on temporary employment ﬂows to meet increases in their net employment expectations as would be expected if ﬁrms use ﬁxed-term contracts as a shock absorber or buffer. Likewise, establishments increase their temporary employment when they are either uncertain or expect a decline in their future net employment – both signs of establishments’ possible reliance on temporary employment as a buffer for permanent employment. However, establishments also raise their net permanent employment to meet growing net employment expectations, suggesting that ﬁxed-term and open-ended contracts are used in a complementary manner by some ﬁrms as would be the case when ﬁxedterm contracts are used as a screening device.

5. EMPIRICAL METHODOLOGY Our main purpose is to learn about establishments’ employment practices by type of work contract and, speciﬁcally, assess the extent to which establishments use temporary employment as a screening device and/or as a buffer when adjusting to their changing net employment expectations. In modeling establishments’ temporary and permanent net employment, gross job and worker ﬂows, and temp-to-perm contract conversions, we account for a variety of variables possibly inﬂuencing establishments’ employment practices ranging from general establishment characteristics to institutional and macroeconomic controls. In the ﬁrst category of general establishment descriptors, we include information regarding the establishment size, industry and sector. Smaller establishments may be more likely to rely on temporary workers as a means to respond to changes in their product demand or ﬁnancial constraints.16 Likewise, establishments in certain industries, such as services, and sectors, as is the case with the private sector, experience a higher volume of job and worker rotation. In addition to the aforementioned establishment level characteristics, we account for various institutional aspects, such as the presence and scope of a collective bargaining agreement due to its potential impact on the establishment’s employment practices.17 Finally, we incorporate regional dichotomous variables as well as quarterly and yearly dummies. The regional dummies allow us to take into account changes in the economic and institutional environment in which establishments operate, as in the case of regional economic booms/

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crises or variations in payroll taxes/subsidies. Additionally, we incorporate year and quarter dummies to purge our estimated coefﬁcients from the impact of nationwide labor market reforms and seasonal ﬂuctuations in establishments’ job and worker ﬂows, respectively. A description of the variables used in our regression analysis, along with their means and standard deviations, is provided in Table A1 in the appendix. Given the longitudinal nature of our dataset, the aforementioned discussion suggests the following panel data model: yit ¼ X it b þ Z i d þ mi þ it

(1)

where yit represents the ratio of temporary to permanent gross job and worker ﬂows being examined; Xit a vector of time-varying characteristics – including the establishment’s net employment change expectations, lagged size, internal collective bargaining, industry, and other establishments’ size and workforce composition – and sets of dummies for each quarter in our sample; Zi a vector including information on time-invariant characteristics of the establishments in our sample, such as their location and whether they belong to the public sector; mi the unobserved establishment speciﬁc and time-invariant effect, assumed to have zero mean, ﬁnite variance s2u , and to be identically distributed (i.i.d.) over the panel; and eit the idiosyncratic error, also assumed to have zero mean, ﬁnite variance s2e , and to be i.i.d. over all the observations in our panel. To determine whether unobserved plant level ﬁxed characteristics should be modeled as ﬁxed- or random-effects, we examine whether mi is uncorrelated with other explanatory variables in our model. If the unobserved establishmentspeciﬁc effect is potentially correlated with some explanatory variables, the ﬁxed-effects method is needed since the use of random-effects would yield inconsistent estimates. Both the Breusch and Pagan Lagrangian multiplier and the Hausman speciﬁcation tests suggest the speciﬁcation of the individual effects to be ﬁxed.18 Hence, we estimate Eq. (1) via OLS as a ﬁxed-effect model and, in this manner, we obtain consistent and efﬁcient estimates of b and d.

6. RESULTS 6.1. Net Employment Expectations and Temporary to Permanent Job and Worker Flows Table 2 displays the estimates from the ﬁxed-effects regression analysis of the ratios of temporary to permanent gross job and worker ﬂows. In particular, columns 1 and 2 present the estimates for the ratios of

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temporary to permanent job creation and job destruction rates, columns 3 and 4 show the estimates for the ratios of temporary to permanent hires and separation rates, and the last column (column 5) presents the estimates corresponding to the ratio of temporary to permanent net employment change at the establishment level. The results displayed in Table 2 are supportive of the hypothesis that establishments use ﬁxed-term contracts with screening purposes as well as a buffer. Speciﬁcally, the positive sign on establishments’ prior employment growth expectations for the long-run when examining ratios of temporary to permanent job creation ﬂows signals that establishments create nearly 37% more temporary than permanent positions when envisioning a long-run growth period. This behavior is suggestive of establishments using temporary work contracts as a screening device to meet long-run employment needs. However, the ﬁgures in Table 2 also provide some evidence of the usage of temporary work contracts as a shock absorber or buffer to meet other changes in establishments’ employment expectations. For instance, the positive signs on establishments’ prior employment growth expectations for the short-run when examining the ratios of temporary to permanent job creation ﬂows are indicative of their greater reliance on temporary employment to meet short-run changes in their product demand and other immediate employment needs. Similarly, the fact that establishments respond to diminishing employment expectations for the long-run by creating temporary positions at more than twice the rate of permanent positions suggests, once more, their partial usage of temporary contracts as a buffer that allows them to avoid the future costly dismissal of permanent employees, according to Goux et al.’s (2001) prediction. Also signaling the usage of temporary contracts as a shock absorber or buffer is the change in the ratio of temporary to permanent job destruction among establishments facing employment growth and employment decline expectations in the short-run. Establishments are signiﬁcantly less likely to destroy temporary (relative to permanent) positions when faced with employment growth expectations for the short-run. However, establishments destroy temporary positions at two and a half the rate that they destroy permanent positions when addressing diminishing employment expectations for the short-run. Yet another sign of the usage of ﬁxed-term contracts as a shock absorber or buffer is the fact that establishments are six times more likely (and four times less likely) to hire workers on a temporary (as compared to a permanent) basis when faced with employment growth (decline) expectations, which hints that temporary hiring is primarily used by ﬁrms to meet short-run increases in demand.

1.372 (0.798) 2.304 (1.270)

Expectations for next year Increasing Diminishing

8,466 1,509 4.67 0.0000

16,212 1,664 13.09 0.0000

0.402 (0.035) 1.072 (0.459) 1.531 (1.271) 1.597 (1.444) 2.029 (1.253) 1.123 (1.034) 2.161 (1.708) 1.334 (0.974) 0.597 (0.704) 0.304 (0.661)

0.664 (0.409) 0.663 (0.497)

2.451 (0.393) 2.651 (0.367)

Job Destruction

21,414 1,744 5.16 0.0012

0.213 (0.170) 4.443 (2.293) 16.072 (7.789) 14.511 (9.134) 10.108 (7.647) 9.869 (6.373) 4.559 (10.030) 4.230 (5.644) 3.222 (4.410) 3.531 (3.653)

2.810 (1.968) 0.199 (2.386)

6.157 (1.870) 3.713 (2.191)

Hires

24,759 1,772 2.08 0.0000

0.628 (0.270) 5.715 (3.555) 2.527 (11.231) 1.037 (12.783) 1.055 (10.847) 0.353 (9.139) 2.512 (14.999) 4.199 (8.275) 2.521 (6.241) 0.837 (5.570)

1.690 (3.058) 0.526 (3.494)

4.620 (2.896) 1.883 (3.198)

Separations

24,678 1,781 4.14 0.0000

0.123 (0.050) 1.136 (0.664) 1.588 (2.112) 0.052 (2.429) 1.632 (2.035) 0.672 (1.727) 5.218 (2.776) 0.614 (1.540) 1.566 (1.156) 0.982 (1.034)

0.421 (0.567) 0.335 (0.646)

2.680 (0.537) 3.279 (0.595)

Net Employment

Notes: The regressions include a constant term as well as dummies for each quarter in our sample. Unchanged employment expectations and ‘‘other services’’ are used as reference categories. Gross ﬂows used to construct the ratios are measured following Davis–Haltiwanger methodology as explained in the main text. Indicates signiﬁcance at the 10% level. Indicates signiﬁcance at the 5% level. Indicates statistical signiﬁcance at the 1% level.

Regression ﬁt statistics No. of observations Number of groups F statistic ProbabilityWF

0.175 (0.072) 2.313 (1.013) 5.743 (4.743) 0.596 (5.632) 4.025 (4.187) 0.214 (3.908) 4.231 (5.349) 0.998 (2.891) 0.979 (2.423) 0.001 (1.856)

1.951 (0.756) 0.500 (1.180)

Expectations for next quarter Increasing Diminishing

Establishment characteristics Establishment size at (t1) Collective bargaining at ﬁrm level Energy Chemicals, rubber, plastics Machinery Other manufacturing Construction Trade Transportation & communications Finance & insurance

Job Creation

Fixed Effects Estimates of Ratios of Quarterly Temporary to Permanent Gross Job and Worker Flows (S.E. in Parentheses).

Independent Variables

Table 2.

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Finally, the last column of Table 2 displays the response of the ratio of temporary to permanent net employment ﬂows to prior changes in net employment expectations for the short-run. Because net employment ﬂows are the sum of all job/worker ﬂows – whether positive or negative – this ratio signals establishments’ relative adjustments in temporary (as compared to permanent) employment when faced with changing net employment expectations. In this regard, it is interesting to note that adjustments in temporary employment are about three times greater than adjustments in permanent employment when establishments address diminishing employment expectations. This behavior is suggestive of the use of ﬁxed-term contracts as a buffer for workers with permanent contracts. However, temporary employment adjustments are about three times smaller than adjustments in permanent employment when establishments face employment growth expectations. If temporary contracts were being used as a buffer, we would expect the opposite that is, greater temporary employment adjustments when establishments respond to short-run growing employment expectations (perhaps resulting from the hiring of new temporary workers to address the short-run increases in demand). Instead, it seems as if establishments use their temporary work contracts with screening purposes and do not bother to make substantial changes to their temporary workforce in the face of what they envision as only short-run changes in their employment expectations. Consequently, the response of temporary to permanent net employment ﬂows provides mixed evidence of the potential uses of ﬁxed-term contracts by establishments. In sum, establishments do not seem to use ﬁxed-term contracts with just one purpose. Instead, the response of establishments to changing net employment expectations for the short-run is mainly suggestive of their reliance on ﬁxed-term contracts as a shock absorber or buffer, whereas their response to changes in net employment expectations for the long-run mostly alludes to their usage of ﬁxed-term contracts as a screening device. Finally, it is also worth noticing that, the ratio of temporary to permanent job creation is smaller among larger sized establishments suggesting that the creation of temporary employment is relatively more frequent among smaller sized establishments. However, the ratios of temporary to permanent job destruction, job separations and, as such, the sum of temporary to permanent ﬂows, are all greater among larger establishments. It is also interesting to note that the presence of collective bargaining at the ﬁrm level signiﬁcantly raises the ratio of temporary to permanent job creation, job destruction, hires, and, overall, net employment ﬂows. This effect conﬁrms the reduced ﬂuctuations in permanent employment often observed in the presence of unions and employment protection measures.

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Finally, establishments’ ratios of temporary to permanent job and worker ﬂows do not seem to vary much by industry. The only exceptions are the relatively smaller ratios of temporary to permanent net employment ﬂows in the construction industry compared to more seasonal industries in the tourism and alike services.

6.2. Net Employment Expectations and Temporary to Permanent Contract Conversions Another means to gain a better understanding of how establishments make use of temporary work contracts is to examine their temporary to permanent contract conversions. This analysis not only informs on the usage of ﬁxed-term contracts as a screening device but, also, on how tempto-perm contract conversions are affected by changes in establishments’ net employment expectations for the upcoming quarter and year. According to the ﬁgures in Table 3, establishments decrease (increase) their temporary to permanent contract conversions when faced with growing (diminishing) employment expectations for the short-run. Why? The reason may be that ﬁrms attempt to keep a temporary workforce to deal with the (expected) future increase in demand. Nonetheless, it should be noted that the decrease in temporary to permanent contract conversions when faced with growing employment expectations for the short-run is only statistically signiﬁcant at the 10% level. Alternatively, if establishments do not use ﬁxed-term contracts as a shock absorber or buffer, they may not increase their temporary job creation and hires to address employment growth expectations that they envision as temporary. That is, establishments may view ﬁxed-term contracts as a screening device. Therefore, any temp-to-perm contract conversions constitute employment practices with long-term effects. Under such scenario, establishments may not alter their contract conversions in the face of what are viewed as short-run or temporary diminishing employment expectations. Additional evidence of the use of ﬁxed-term contracts as a screening device stems from the fact that establishments increase (decrease) their temporary to permanent contract conversions by approximately one contract per quarter to adjust to employment growth (decline) expectations for the long-run. Finally, it is worth discussing the lower temporary to permanent contract conversion rates among establishments with collective bargaining at the ﬁrm level. Permanent workers, also called the ‘‘insiders’’ in the collective bargaining literature (e.g., Jimeno & Toharia, 1993a; Bentolila & Dolado,

298 Table 3.

CATALINA AMUEDO-DORANTES AND MIGUEL A´. MALO Fixed Effects Estimates of Quarterly Gross ‘‘Temp-to-Perm’’ Contract Conversion Flows (S.E. in Parentheses).

Independent Variables

Temp-to-Perm Conversions

Expectations for next quarter Increasing Diminishing

0.564 (0.336) 1.634 (0.382)

Expectations for next year Increasing Diminishing

0.879 (0.352) 0.951 (0.419)

Establishment characteristics Establishment size at (t1) Collective bargaining at ﬁrm level Energy Chemicals, rubber, plastics Machinery Other manufacturing Construction Trade Transportation & communications Finance & insurance

0.023 (0.032) 0.840 (0.421) 0.923 (1.389) 0.406 (1.554) 0.069 (1.283) 0.347 (1.125) 0.954 (1.813) 0.075 (0.991) 0.002 (0.751) 1.496 (0.675)

Regression ﬁt statistics No. of observations Number of groups F statistic ProbabilityWF

29,345 1,858 6.24 0.0000

Notes: The regressions include a constant term as well as dummies for each quarter in our sample. Unchanged employment expectations and ‘‘other services’’ are used as reference categories. Gross ﬂows are measured following Davis–Haltiwanger methodology as explained in the main text. Indicates signiﬁcance at the 10% level. Indicates signiﬁcance at the 5% level. Indicates statistical signiﬁcance at the 1% level.

1994), typically have more clout in any agreements reached at the ﬁrm level than temporary workers. Therefore, any collective bargaining agreement at the ﬁrm level is more likely to ensure, ﬁrst, better working conditions for permanent workers. The latter may, in some instances, come at the cost of allowing for the use of temporary work contracts as a shock absorber or buffer (resulting in fewer contract conversions) to cut labor costs when faced with a downturn (as, e.g., Bentolila & Dolado, 1994, alleged in their theoretical model). Finally, industry-wise, the results indicate that

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establishments in the ﬁnance and insurance industries are less likely to use temporary work contracts as a screening device than other establishments in the service industry.

7. CONCLUSIONS Previous theoretical (Goux et al., 2001) as well as empirical work (Garcı´ aSerrano, 1998) has stressed the importance of distinguishing between ﬁxedterm and open-ended work contracts when examining ﬁrms’ employment practices. The literature also recognizes a variety of ways in which ﬁrms use temporary employment. In this paper, we focus on two of the most salient and discussed uses in the literature on ﬁxed-term employment: (a) the use of ﬁxed-term contracts as a buffer to cushion short-run changes in demand as well as to shield permanent workers from downward workforce adjustments, and (b) the usage of ﬁxed-term contracts as a screening device. Using gross job and worker ﬂows data on Spanish establishments, we examine establishments’ employment practices by type of work contract and discuss the extent to which establishments use temporary employment as a screening device or as a buffer when adjusting to changes in prior employment expectations. Establishments’ prior employment expectations provide us with detailed plant-level information on how a wide variety of short- and long-run shocks are ultimately perceived by establishments as reﬂected by changes in their expectations regarding future employment needs. Using data from Spain, the country with the highest rate of temporary employment in the European Union, we ﬁnd that establishments appear to use ﬁxed-term contracts for a variety of purposes. On one hand, establishments seem to rely on ﬁxed-term contracts as a buffer to meet expected shortrun changes in employment needs. Some examples of this behavior are establishments’ greater temporary to permanent job creation and hiring ratios when responding to employment growth expectations for the short-run; yet, the also greater rate at which they destroy temporary positions when faced with diminishing employment expectations for the short-run. On the other hand, establishments also appear to create temporary jobs at a higher rate than permanent jobs to address long-run employment growth expectations, which hints on the usage of ﬁxed-term contracts as a screening device to satisfy long-term employment needs. We also look closely at establishments’ temporary to permanent contract conversions to better understand their determinants. We ﬁnd that, not surprisingly, conversions are more (less) likely to occur following

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employment growth (decline) expectations for the long-run, whereas the opposite occurs in the presence of changes in establishments’ prior employment expectations for the short-run. That is, establishments continue to convert ﬁxed-term contracts to permanent when adjusting to diminishing employment expectations for the short-run – perhaps owing to their temporary nature – and they are not likely to go forward with temporary to permanent contract conversions when facing employment growth expectations for just the short-run. In sum, establishments appear to use ﬁxed-term contracts both as a screening device and as a buffer. However, the use of ﬁxed-term contracts as a buffer seems to be the most prominent when responding to changing net employment expectations for the short-run. In contrast, the response of establishments to changes in net employment expectations for the long-run is mainly suggestive of their usage of ﬁxed-term contracts as a screening device. What policy implications stem from these ﬁndings? Most notably, policies consisting of ﬁnancial incentives to convert ﬁxed-term into permanent contracts are likely to have a limited effectiveness when ﬁrms also use ﬁxed-term contracts as a buffer. At any rate, the possibility still exists that establishments’ response to changing employment expectations in small- and medium-size establishments not included in our sample differs from that observed in large establishments. While the literature (e.g., Davis et al., 1996, Chapter 4) has shown that gross ﬂows are mainly driven by the behavior of large ﬁrms, the availability of detailed employment stock and ﬂow data for small- and medium-size establishments should prove useful in furthering our understanding of establishments’ employment practices by type of work contract.

NOTES 1. See Bertola and Ichino (1995) for a comparative analysis of legal reforms in Europe in the last two decades. 2. Throughout the paper, we will use the terms ﬁxed-term and temporary, as well as the terms open-ended and permanent, interchangeably. 3. This is the only stratum of establishments for which detailed longitudinal information on gross ﬂows is made available. 4. See, for example, Hamermesh (1993) for a synthesis of this theoretical and empirical literature. 5. This legal principle stated that ﬁxed-term contracts should be exclusively used for temporary needs of the ﬁrm and open-ended contracts for permanent needs. 6. These ﬁxed-term contracts could not last less than 6 months or more than 3 years with the same worker. However, ﬁrms were able to hire new employees using the same type of ﬁxed-term contract to continue to cover the permanent position.

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301

7. The most extended evaluation of the impact of the temporary work agencies on the high use of temporary contracts in Spain concludes that, while they are not responsible for the high rate of temporary employment in Spain, they have shortened the duration of ﬁxed-term contracts (Toharia, 2005). 8. Dismissals should not involve more than 10% of the workforce. 9. Economic grounds refer to relevant technological changes in the ﬁrm and, in general, to economic downturns. 10. However, the Tribunals’ interpretation of economic grounds for individual dismissals was controversial because of the lack of an objective deﬁnition of what constitutes an economic reason for dismissal. 11. See Toharia and Malo (2000) for further details on these reforms. 12. Some authors, as Dolado et al. (2002), document a smooth decline in the private sector after 1997. In 2006, new political measures have been implemented following the 1997 labor market reform to curb down the high rate of temporary employment. 13. When a ﬁrm is occasionally below the threshold of 500 employees, it is maintained in our stratum and it is only eliminated when the ﬁrm does not recover the level of 500 employees during two additional quarters. 14. In both instances, this growth rate provides us with insights on the establishment’s net job creation or destruction rate. See, for example, Davis, Haltiwanger, and Schuh (1996) , chapter 2. 15. Gross job and worker ﬂows indicators are computed at the establishment level. 16. Establishments’ size is lagged one period in order to guarantee its predetermined character. 17. Due to the institutional framework of Spanish collective bargaining, collective agreements extend to any establishment of the sector. Therefore, the relevant distinction is not whether or not there is a collective agreement applicable to the establishment’s employees but, rather, the scope of the collective agreement in place. See, for example, Jimeno and Toharia (1993b) or Garcı´ a-Serrano and Malo (2002) for greater details on collective bargaining in Spain. 18. Results are available from the authors upon request.

ACKNOWLEDGMENTS The data used in this study were provided by the Social and Labour Statistics Ofﬁce from the Spanish Ministry of Employment and Social Affairs. We are indebted to Carmen Salido for her assistance with our requests. We are also grateful to Ce´sar Alonso, Cynthia Bansak, Susan Houseman, and to participants at the conference on Microeconomic Analyses of Labour Reallocation sponsored by IZA, the W.E. Upjohn Institute for Employment Research, and the William Davidson Institute for their helpful suggestions. This study also beneﬁted from comments received at the Fifth Spanish Labour Economics Meetings and at the Ramo´n Areces Foundation.

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REFERENCES Bentolila, S., & Dolado, J. J. (1994). Labour ﬂexibility and wages: Lessons from Spain. Economic Policy: A European Forum, 9(18), 53–99. Bentolila, S., & Saint-Paul, G. (1992). The macroeconomic impact of ﬂexible labor contracts, with an application to Spain. European Economic Review, 36(5), 1013–1047. Bertola, G., & Ichino, A. (1995). Crossing the river: A comparative perspective on Italian employment dynamics. Economic Policy, 21, 359–415. Blanchard, O., & Portugal, P. (2001). What hides behind an unemployment rate: Comparing Portuguese and US labor markets. American Economic Review, 91(1), 187–207. Booth, A., Francesconi, M., & Frank, R. (2002). Labour as a buffer: Do temporary workers suffer? IZA Working Paper no. 673. Davis, S. J., & Haltiwanger, J. C. (1990). Gross job creation and destruction: Microeconomic evidence and macroeconomic implications. In: S. Fischer & O. Blanchard (Eds), NBER Macroeconomics Annual 1990. Cambridge, MA: MIT Press. Davis, S. J., & Haltiwanger, J. C. (1992). Gross job creation, gross job destruction and employment reallocation. Quarterly Journal of Economics, 107(3), 819–863. Davis, S. J., Haltiwanger, J. C., & Schuh, S. (1996). Job creation and job destruction. Cambridge, MA: MIT Press. Dolado, J. J., Garcı´ a-Serrano, C., & Jimeno, J. F. (2002). Drawing lessons from the boom of temporary jobs in Spain. Economic Journal, 112(480), F270–F295. Fina, Ll., Meixide, A., & Toharia, L. (1989). Reregulating the labor market amid an economic and political crisis: 1975–1986. In: S. Rosenberg (Ed.), The state and the labor market. New York: Plenum Press. Garcı´ a-Serrano, C. (1998). Worker turnover and job reallocation: The role of temporary contracts. Oxford Economic Papers, 50, 709–725. Garcı´ a-Serrano, C., & Malo, M. A. (2002). Worker turnover, job turnover and collective bargaining in Spain. British Journal of Industrial Relations, 40(1), 69–85. Goux, D., Maurin, E., & Pauchet, M. (2001). Fixed-term contracts and the dynamics of labour demand. European Economic Review, 45, 533–552. Hamermesh, D. S. (1993). Labor demand. Princeton, NJ: Princeton University Press. Hernanz, V. (2003). El Trabajo Temporal y la Segmentacio´n: Un Estudio de las Transiciones Laborales. Madrid: Economic and Social Council (Consejo Econo´mico y Social). Houseman, S., & Abraham, K. (1993). Female workers as a buffer in the Japanese economy. American Economic Review, 83(2), 45–51. Houseman, S., Kalleberg, A. L., & Erickek, G. A. (2001). The role of temporary help employment in tight labor markets. Upjohn Employment Institute, Working Paper no. 01-73. Jimeno, J. F., & Toharia, L. (1993a). The effects of temporary employment on wages: Theory and evidence from Spain. Investigaciones Econo´micas, 17(3), 475–494. Jimeno, J. F., & Toharia, L. (1993b). Spanish labour markets: Institutions and outcomes. In: J. Hartog & J. Theeuwes (Eds), Labour market contracts and institutions (pp. 299–322). Amsterdam: Elsevier Science. Polavieja, J. (2006). Temporary contracts and labour market segmentation in Spain: An employment-rent approach. European Sociological Review, 19, 501–517. Toharia, L. (dir.) (2005). El problema de la temporalidad en Espan˜a: Un diagno´stico. Madrid: Publications Service of the Spanish Ministry of Employment.

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Toharia, L., & Malo, M. A. (2000). The Spanish experiment: Pros and cons of the ﬂexibility at the margin. In: G. Esping-Andersen & M. Regini (Eds), Why deregulate labour markets (pp. 307–335). Oxford: Oxford University Press. Varejao, J., & Portugal, P. (2003). Why do ﬁrms use ﬁxed-term contracts (DP 2003-10). Portugal: Faculdade de Economia, Universidade do Porto.

APPENDIX Table A1. Description, Means, and Standard Deviations. Variables

Description

Ratios of quarterly ﬂows by contract type JPOSRATIO Establishment’s ratio of quarterly temp to perm creation ﬂows JNEGRATIO Establishment’s ratio of quarterly temp to perm destruction ﬂows WPOSRATIO Establishment’s ratio of quarterly temp to perm WNEGRATIO Establishment’s ratio of quarterly temp to perm separations WNETRATIO Establishment’s ratio of quarterly temp to perm employment ﬂows

Mean

S.D.

5.9067

23.6145

2.5828

13.4375

24.0556

112.7021

17.7020

150.2000

0.3078

26.3056

1.4889

9.4991

0.1497

0.3568

0.6983

0.4590

0.1489

0.3560

job

job

hires

net

Establishment’s quarterly temp to perm contract conversion ﬂows Expectations for next quarter Increasing Dummy variable indicative of increasing net employment expectations for the next quarter Unchanged Dummy variable indicative of unchanged net employment expectations for the next quarter Diminishing Dummy variable indicative of diminishing net employment expectations for the next quarter

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CATALINA AMUEDO-DORANTES AND MIGUEL A´. MALO Table A1.

Variables

(Continued ).

Description

Expectations for next year Increasing Dummy variable indicative of increasing net employment expectations for the next year Unchanged Dummy variable indicative of unchanged net employment expectations for the next year Diminishing Dummy variable indicative of diminishing net employment expectations for the next year Other establishment characteristics Establishment size Establishment’s size last quarter at (t1) in hundreds of workers Collective Establishment-level collective bargaining bargaining dummy Energy Industry dummy Chemicals, rubber, Industry dummy plastics Machinery Industry dummy Other Industry dummy manufacturing Construction Industry dummy Trade Industry dummy Transportation & Industry dummy communications Finance & Industry dummy insurance Other services Industry dummy Source: Authors’ tabulations using the ECL.

Mean

S.D.

0.1461

0.3532

0.7179

0.4500

0.1360

0.3428

12.5883

15.0206

0.3882

0.4874

0.0342 0.0412

0.1818 0.1988

0.1170 0.0494

0.3214 0.2166

0.0162 0.0909 0.0833

0.1262 0.2874 0.2764

0.0749

0.2632

0.4640

0.4987

MODELING THE SIGNALING VALUE OF THE GED WITH AN APPLICATION TO AN EXOGENOUS PASSING STANDARD INCREASE IN TEXAS Magnus Lofstrom and John Tyler ABSTRACT In this paper, we develop a simple model of the signaling value of the General Educational Development certiﬁcate (GED) credential. The model illustrates necessary assumptions for a difference-in-differences estimator that uses a change in the GED passing standard to yield unbiased estimates of the signaling value of the GED for marginal passers. We apply the model to the national 1997 passing standard increase, which affected GED test takers in Texas. We utilize unique data from the Texas Schools Micro Data Panel (TSMP) that contain demographic and GED test score information from the Texas Education Agency linked to pre- and post-test-taking Unemployment Insurance quarterly wage records from the Texas Workforce Commission. Comparing Texas dropouts who acquired a GED before the passing standard was raised in 1997 to dropouts with the same test scores who failed the GED exams after the passing standard hike, we ﬁnd no Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 305–352 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28010-6

305

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evidence of a positive GED signaling effect on earnings. However, we ﬁnd some evidence suggesting that our ﬁnding may be due to the low GED passing threshold that existed in Texas for an extended period.

1. INTRODUCTION The General Educational Development certiﬁcate (GED) is an exam-based credential awarded to about 500,000 high school dropouts in the United States each year, representing almost 15% of all high school diplomas, or credentials, issued. For high school dropouts lacking a high school diploma to certify successful completion of their secondary schooling experience, the GED is the ﬁrst, and often only, credential. One reason many dropouts seek a GED is a belief that it will lead to greater labor market success. Several studies over the last decade have attempted to determine whether this is indeed the case, with the research questions breaking along two lines: How do GED holders compare to regular high school graduates? And, how do GED holders compare to other uncredentialed high school dropouts? Most observers agree that the ﬁrst question has been answered rather convincingly by Cameron and Heckman (1993). They ﬁnd that GED holders fare consistently worse than regular high school graduates on any number of labor market outcomes. These results were notable but hardly surprising, given the differences in human capital opportunities between students who drop out and pursue a GED and students who stay in school until graduation. The most recent data on GED preparation time indicates that the median study time was only about 30 h (Baldwin, 1990), substantially less than the 410 h spent on a high school’s core curriculum in a typical school year and probably insufﬁcient time for meaningful human capital accumulation. An answer to the second question – how do GED holders fare relative to uncredentialed dropouts – is somewhat more contentious. Again, the relatively low levels of time spent preparing for the GED suggest to many that pursuit of the GED credential could hardly have a substantial human capital component. This, of course, leaves open to question the potential of the GED as a labor market signal, a proposition studied by Tyler, Murnane, and Willett (2000). Using interstate variation in the standard required to pass the GED exams and acquire the credential, they ﬁnd GED ‘‘signaling effects’’ of between 10% and 19% on annual earnings.

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307

Similar to Tyler, Murnane, and Willett, the research strategy in this paper also utilizes different passing standards faced by different groups of dropouts. We use a 1997 change in Texas in the GED passing standards to identify the signaling value of the GED on the labor market outcomes of dropouts in that state. We argue that the changes in Texas give rise to a natural experiment that can be exploited to identify the labor market signaling effects of the GED on earnings, reducing the endogeneity due to correlation between the outcome of passing/not passing and unobserved individual heterogeneity that may bias Ordinary Least Squares (OLS) estimates. The American Council on Education (ACE) administers the nation’s GED testing program and sets the minimum requirements for obtaining the credential. States can set, and regularly have, state level passing standards above the ACE-mandated minimum. Prior to 1997, Texas was one of the few states whose passing standard was at the ACE minimum level. As a result, Texas had one of the country’s least stringent GED passing standards. In 1997, the ACE mandated a nationwide increase in the minimum passing standard, a change that was arguably exogenous to Texas. Given these changes and data on individuals containing GED test scores, we can identify an ‘‘affected score group’’ of GED candidates whose eventual GED status is ‘‘affected’’ by the change in the passing standard. Members of the ‘‘affected score group’’ who took the GED exams before 1997 had high enough scores to be awarded a GED, while dropouts in this group with the exact same scores but who attempted the GED exams after the passing standard hike in January 1, 1997, would have scores below the passing threshold and hence not be awarded the credential. Since only the passing threshold but not the GED exams themselves changed in January 1997, and the raising of the threshold was by the ACE in Washington, D.C., rather than Texas policy makers, this occurrence provides us with a clearly deﬁned natural experiment that can be exploited to estimate the impact of the GED on labor market outcomes. Because we are comparing individuals who have the same test scores but differ in GED status according to the year in which they attempted the exams, a strict interpretation of our results is that they estimate the labor market signaling value of the GED.

2. THE GED AND THE EARNINGS OF DROPOUTS The GED is an exam-based credential that is awarded based on the scores on ﬁve different exams: math, science, social studies, reading, and writing.

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All of the test items in the GED exam battery are of multiple-choice type, except for a section in the writing exam that requires GED candidates to write an essay.1 The total exam battery takes about 7½ h, and GED examinees who fail to score sufﬁciently high to ‘‘pass’’ may, under certain circumstances, retake any or all of the exams in the battery. The growth in this education credential has coincided with substantial research efforts over the last decade. Cameron and Heckman (1993) ﬁrst drew attention to the GED credential and the fact that male GED holders are not the labor market equivalents of regular high school graduates. Studies that followed their research focused on the question of how GED holders compare to dropouts in the labor market who lack the credential. That is, once the dropout decision has been made, does the GED buy you anything in the labor market? While the answer has been somewhat mixed, two recent studies – each of which uses a different data set and a different empirical strategy – offer evidence that lower-skilled GED holders have higher earnings than comparably low-skilled dropouts who lack a GED (Murnane, Willett, & Tyler, 2000; Tyler et al., 2000). In addition, Murnane et al. (2000) offer a discussion of how these more recent results can be reconciled with the earlier Cameron and Heckman ﬁndings. Later work by Heckman, Hsse, and Rubinstein (2000) ﬁnds that failing to control time-invariant heterogeneity between low-skilled credentialed and uncredentialed dropouts may lend an upward bias to estimates of a GED treatment effect. However, estimates from both individual ﬁxed-effects models and a regression discontinuity design (Tyler, 2004) provide additional evidence that acquisition of a GED can improve the earnings of dropouts. To summarize recent research, it is fair to say that while there is still some ambiguity about the causal effect of the GED on labor market outcomes, the recent research tends to support a view that the credential has beneﬁcial effects for the least skilled dropouts. The data in this paper contain information on the quarterly earnings of dropouts who attempt to acquire a GED credential. For those dropouts who pass the GED exams, there are several mechanisms through which acquisition of a GED could impact the quarterly earnings of dropouts. First, employers may use the GED as a signal of productive attributes in a pool of dropouts, choosing to hire GED holders over uncredentialed dropouts (Spence, 1973). If this were the case, then we would expect to see higher employment rates among the GED holders. Also, conditional on being employed, employers may use the GED as a positive signal of productivity and hence offering and assigning higher wages and/or more

Modeling the Signaling Value of the GED

309

hours of work. In all cases, we would expect the earnings of GED holders to be higher than the earnings of uncredentialed dropouts. Second, there could be a human capital impact on the wages. Dropouts obtain a GED by gaining a passing score on a ﬁve-test examination battery that takes about 7½ h to complete. To the extent that school dropouts have to work and prepare to increase their cognitive skills in order to achieve a passing score on the GED exams, then the opportunity to be awarded the credential could lead to human capital gains. As mentioned earlier, the only available data on time spent studying for the GED indicates a median study time of about 30 h, too little for human capital accumulation. However, the Baldwin (1990) study generating those estimates did not distinguish between successful and unsuccessful GED candidates, nor did it include the time that dropouts might have spent in Adult Basic Education, English as a Second Language, or pre-GED classes in the estimate. As a result, the time spent by successful candidates could be longer than the study estimate. It may also be the case that today’s dropouts, especially foreign-schooled immigrants, may spend more time in GED preparation than the survey respondents in the 1990 study. Thus, the extent to which the GED program fosters human capital accumulation is still arguably an empirical question. Third, GED holders can use the credential to gain access to, and funding for, postsecondary education. Most degree-granting postsecondary education programs require applicants to possess a high school diploma or a GED. Also, Pell grants and guaranteed federal student loans for postsecondary education require applicants to demonstrate an ‘‘ability to beneﬁt’’ from the funding. Dropout applicants for these federal monies can satisfy this requirement if they possess a GED. It should be pointed out that previous research indicates that relatively few GED holders obtain substantial amounts of postsecondary education. Murnane, Willett, and Boudett (1997) report that only 12% receive at least one year of college schooling and 3% obtained an associate degree. As with any program evaluation in which the selection process cannot be adequately modeled, we are concerned about the role of individual unobserved heterogeneity. We address this problem by exploiting the natural experiment that resulted when the passing standard required to obtain a GED in Texas was raised for everyone who took the GED exams on or after January 1, 1997. In simplest terms, we will compare the labor market outcomes of GED candidates who have the same GED test scores but vary in GED status depending on whether they tested in the years before the hike in the passing standard or after the hike. We will also account for changes in overall labor market conditions for low-skilled workers by

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subtracting out changes in earnings experienced by GED test takers whose scores were not affected by the passing standard change. Although the GED credential may have a human capital effect on earnings, our approach assesses the signaling value of the GED. Hence, we will present a simple signaling model that illustrates the necessary assumptions for our approach to be valid. To implement the above strategy, we deﬁne three score groups: a group whose scores were too low to pass under either passing standard (All Fail), a group whose scores were sufﬁciently high that they would pass under either passing standard (All Pass), and a group whose scores were in the range such that the outcome was affected by the passing standard (Affected Score Group). Speciﬁcally, a GED candidate is deﬁned to be in the affected score group if the person’s scores are such that either the minimum score on the ﬁve GED exams is at least 40 or the average of the ﬁve scores is at least 45, while simultaneously the candidate does not have a minimum score of 40 and an average of at least 45. We identify individuals in the three score groups both before and after the passing standard hike, yielding six distinct groups. The deﬁned groups are: 1. The group of individuals who tested under the old passing standard and whose scores were too low to pass under either standard. This group attempted the GED in 1995 (All Fail–Pre). 2. The group of individuals who tested under the new passing standard but whose scores were too low to pass under either standard, including the old standard. This group attempted the GED in 1997 (All Fail–Post). 3. The treatment group of individuals who barely passed the GED exams before the change in the passing standard. This group attempted the GED in 1995 (ASG–Pre). 4. The comparison, or control, group of individuals with the same GED test scores as the treatment group but who lack a GED because they tested under the new, higher standard. This group attempted the GED in 1997 (ASG–Post). 5. The group of individuals who tested under the old regime but whose scores were high enough so that they would have passed under the new standard. This group attempted the GED in 1995 (All Pass–Pre). 6. The group of individuals who tested under the new regime and whose scores would have been passing under either passing standard. This group attempted the GED in 1997 (All Pass–Post). Next, we develop a simple signaling model using the above outcome groups to assess the signaling value of the GED.

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311

3. A SIMPLE SIGNALING MODEL We utilize the well-known signaling model based on the work by Spence (1973) and Stiglitz (1975). In this model, workers choose education not to increase their productivity, as in the human capital model, but to signal to employers their productivity. The general model assumes k kinds of workers with unobserved ability yj, j ¼ 1,2,yk and k1 educational levels, ED. Let y1Wy2Wy3WyWyk, i.e., y1 is more ‘‘able,’’ or productive, than y2. Firms are assumed to be risk neutral and are operating in competitive markets. The single ability characteristic, y, is known to the worker, possibly imperfectly, but not known to the ﬁrm. The population proportion of ability worker j with education level ED is h(yj, ED). Furthermore, it is prohibitively costly for ﬁrms to determine y, the worker’s true productivity. However, a worker can signal to an employer his ability by investing in education as a signal. Let cost, c(y, ED), of obtaining the signal be negatively correlated with productivity and positively with education level. The earnings by workers, yED, depend on the signal obtained by them. Workers are assumed to solve: Max yED cðy; EDÞ ED

(1)

The relevant group to study the impact of the GED credential on earnings is high school dropouts. Among this group, we assume that there are three types of workers, i.e., k ¼ 3, and two levels of educational attainment outcomes among high school dropouts: obtaining the General Educational Development credential (G) and no GED (NG). We further assume that y’s map into GED score groups in such a way that both high- and low-ability workers’, y1 and y3, test-taking outcomes will not be affected by the 1997 passing standard hike while the medium-ability workers’, y2, test-taking outcomes will be affected. That is, y1 represents the All Pass group, y2 the Affected Score Group, and y3 the All Fail group. The earnings received for signaling education levels ED are deﬁned as ( yNG ifED ¼ No GED (2) yED ¼ yG ifED ¼ GED To this point, a person’s earnings, or wage, are determined by the beliefs of employers of the meaning of the signal, i.e., the GED credential, and not directly by the ability of the worker. We enrich the model by allowing for wages to be also affected by a vector X of characteristics that are observable

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to both the employer and the econometrician (e.g., race/ethnicity) and by a characteristic u that is observable to employers but not to the econometrician. English language ability is an example of such earnings characteristic u, which is particularly relevant to Texas with its large immigrant population. We assume that y and u are correlated. The wage then is determined by the composition of ability workers in the education group, by X, and by u. As stated above, ﬁrms do not observe y and are consequently going to pay yED based on the average marginal revenue product, MRP, of workers of educational attainment level ED, with a given set of other productivity-related characteristics, X and u: X yED ¼ hðyj ; EDÞMRPðyj jX; uj Þ (3) j

The cost for a worker to obtain the GED credential as a signal includes both the opportunity cost and the ‘‘psychic cost’’ of studying and preparing for the exams and then taking the ﬁve-test battery of exams. The total cost is a function of ability and also depends on the passing standard. In the prepassing-standard-increase (Pre-PS) period, the cost of obtaining a GED is deﬁned as cG ðy3 jPre-PSÞ4cG ðy2 jPre-PSÞ4cG ðy1 jPre-PSÞ

(4)

This inequality illustrates that it is more expensive for low-ability workers to obtain a GED signal than for high-ability workers. The higher cost of obtaining the GED credential for relatively low ability workers is due to the greater time and mental effort necessary for these individuals to pass the exam compared to relatively high ability individuals.2 Furthermore, we assume that in the Pre-PS period, obtaining the signal is too costly for some individuals but affordable for some in the following way: -PS yPre-PS 4c ðy jPre-PSÞ4c ðy jPre-PSÞ cG ðy3 jPre-PSÞ4yPre G 2 G 1 G NG

(5)

According to inequality (5), in equilibrium, the cost to individuals of ability y1 and y2 of obtaining a GED is less than the return on that investment and so we see them with a GED. The y3 individuals, on the other hand, are willing to invest in the GED, but given their ability, they do not invest sufﬁciently to obtain the credential. The fact that we see them investing at all and showing up to take the exams can be explained by the fact that they may know their true productivity only imperfectly or by an assumption on their part that the GED exams measure true productivity

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with some error giving them a nonzero probability of obtaining a GED by chance. The model and assumptions described above lead to a separating equilibrium. Note that there exist multiple equilibria in the model. If employers sufﬁciently change their beliefs about what the signal means, a new equilibrium will be reached. However, employers are likely to change their beliefs only if the observed average marginal revenue product changes. Furthermore, it is theoretically possible that the cost of obtaining the signal is either too low or too high so that all individuals, or no individual, would invest in the signal, i.e., a non-separating equilibrium. Given that we observe some dropouts actually receiving the GED credential, while others do not, suggest that neither of these are relevant practical equilibria. Lastly, in the conclusions, we discuss the possibility that non-pecuniary factors may be involved in the decision to acquire the GED credential.

3.1. The Signaling Value of the GED – Before and after the Passing Standard Increase An increase in the passing standard, such as the one that took place in 1997, can be viewed as an increase in the cost of obtaining the GED credential (i.e., increased preparation time and mental effort necessary to pass the battery of tests). Of course, if some individuals now fail to invest sufﬁciently to obtain the signal under a higher passing standard, the wage received in equilibrium will change since the composition of the GED group will change. For example, if the cost changes, so that the cost and signaling value of investing in the signal are now cG ðy3 jPost-PSÞ4cG Post ðy2 jPost-PSÞ4yPost G yNG 4cG ðy1 jPost-PSÞ, y2 ability individuals will no longer obtain the GED due to the greater effort now necessary to pass the battery of exams.3 We assume that this is the case and there exists a group of ‘‘marginal’’ GED candidates who would obtain a GED in the pre-period but do not obtain the credential in the post-period, i.e., y2 ability workers. The composition of GED holders will differ in the pre- and post-passingstandard-hike periods. In the period before the hike, GED holders consisted both y1 and y2 ability workers, i.e., GPre(y1, y2), while in the post-period, only the highest ability dropouts hold the GED credential, GPost(y1). As employers learn about the compositional changes, the earnings of GED holders will increase since all GED holders now are of the highest ability, y1, and hence the average marginal revenue product increases. With the addition of relatively higher ability workers, y2, wages of non-GED holders

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will also increase since this group’s average marginal revenue product also rises. One important group is, however, negatively affected by the passingstandard-hike, y2 ability, individuals. In our analysis, this group will constitute the ‘‘marginal’’ group, which is affected by the passing standard hike with respect to the GED outcome. The new educational attainment equilibrium can be deﬁned as cG ðy3 jPost-PSÞ4cG ðy2 jPost-PSÞ 4yPost G Post Pre Post Pre yPost 4 c ðy jPost-PSÞ. Note that since both y 4y and y 4y G 1 NG G G NG NG , it is unclear whether the GED earnings premium will increase, yPost yPost G NG 4 Pre Pre Post Post Pre Pre Post yG yNG , stay the same, yG yNG ¼ yG yNG , or decrease, yG yPost NG Pre oyPre G yNG . In the above signaling model, the signaling value of the GED is given by PS yPS G yNG , where PS represents whatever passing standard is in effect at the time. However, as discussed above, the ability composition of workers, with and without the GED, will change with a passing standard hike. Our empirical approach outlined below will speciﬁcally focus on the signaling value of the GED credential for the ‘‘marginal’’ group. That is, the group whose GED status is most directly affected by the change in the passing standard. Based on the assumption of three ability types and two educational outcomes, we deﬁne the following individual conditional earnings:4 Pre yPre ðy1 ; y2 Þ; X; u1 Þ G;1 ¼ EðyjG Pre ðy1 ; y2 Þ; X; u2 Þ yPre G;2 ¼ EðyjG Pre ðy3 Þ; X; u3 Þ yPre NG;3 ¼ EðyjNG Post ðy1 Þ; X; u1 Þ yPost G;1 ¼ EðyjG Post ðy2 ; y3 Þ; X; u2 Þ yPost NG;2 ¼ EðyjNG Post ðy2 ; y3 Þ; X; u3 Þ yPost NG;3 ¼ EðyjNG

Note that the conditional earnings are identical for individuals with a given u and a speciﬁc GED outcome, holding X constant. For example, in the pre-period, employers cannot distinguish between y1 and y2 workers of a given level of u. That is, using our example of English ability, all individuals with the GED and who are ﬂuent in English, holding X constant, will receive the same wage. However, employers can distinguish between individuals with different levels of u, say u1 and u2, with the same GED outcome. We assume that u and y are correlated, plausibly positively, meaning that in our example, higher ability workers are also more likely to be proﬁcient in English than lower ability workers.5 The difference in the conditional

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earnings between workers with a given GED outcome is then due to differences in both y and u. Pre- and post-passing-standard-hike difference estimators of the total value of the GED may be deﬁned as Pre Pre ðy1 ; y2 Þ; X; uÞ EðyjNGPre ðy3 Þ; X; uÞ yPre G yNG ¼ EðyjG Post Post ðy1 Þ; X; uÞ EðyjNGPost ðy2 ; y3 Þ; X; uÞ yPost G yNG ¼ EðyjG

However, neither of these estimators represents the ‘‘true’’ signaling value of the GED for the marginal, y2, group since neither represents the relevant counterfactual for y2 individuals. The arguably relevant situation is one in which y2 workers are observed both with and without the GED in separate labor market regimes, with the subsequent compositional changes in the groups with (G) and without (NG) the GED. The problem with the above differences is that the former estimator utilizes a group of non-GED holders that does not include y2 individuals while the later uses a group of GED holders that does not include y2 workers. Instead, for a given passing standard, the ‘‘true’’ GED premium for the marginal-ability group can be deﬁned as PS PS PS yPS G yNG ¼ EðyjG ðy1 ; y2 Þ; X; uÞ EðyjNG ðy2 ; y3 Þ; X; uÞ

Given the above signaling framework, at a given point in time, we do not observe y2 workers with and without the GED, and hence this cannot be directly estimated. However, given the change in the passing standard, we observe y2 individuals with the GED credential in the pre-passing hike period and without the signal in the post-period. A possible estimator of the GED signaling value is then Pre Post yPre ðy1 ; y2 Þ; X; u2 Þ EðyjNGPost ðy2 ; y3 Þ; X; u2 Þ G;2 yNG;2 ¼ EðyjG

The difference estimator yields unbiased estimates of the signaling value of the GED credential, for y2 individuals, under the assumptions that u’s impact on earnings remains constant between the pre- and post-periods (u2 will simply be subtracted out in the difference), or that u2 is uncorrelated with the GED outcome. Unbiased estimates using the difference estimator above also require the assumption that there is no pre–post change in the labor market conditions and environment. However, the labor market conditions may indeed be different across periods. This can be alleviated by subtracting out changes in earnings for the groups who were not affected by the passing standard hike, i.e., y1 and y3 ability workers, giving us the

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following difference-in-differences estimators. Post Pre Post ½yPre G;2 yNG;2 ½yNG;3 yNG;3

¼ ½EðyjGPre ðy1 ; y2 Þ; X; u2 Þ EðyjNGPost ðy2 ; y3 Þ; X; u2 Þ ½EðyjNGPre ðy3 Þ; X; u3 Þ EðyjNGPost ðy2 ; y3 Þ; X; u3 Þ Post Pre Post ½yPre G;2 yNG;2 ½yG;1 yG;1

¼ ½EðyjGPre ðy1 ; y2 Þ; X; u2 Þ EðyjNGPost ðy2 ; y3 Þ; X; u2 Þ ½EðyjGPre ðy1 ; y2 Þ; X; u1 Þ EðyjGPost ðy1 Þ; X; u1 Þ Each of these estimators subtracts out the pre–post change in the earnings among non-GED and GED holders, respectively, and will differ depending on how earnings have changed over time. The ﬁrst difference-in-differences estimator is the preferred one if the general earnings trend of y2 individuals are more similar to y3 workers, and the latter one is more appropriate if y1 workers represent the more suitable comparison group. Importantly, if u, which is an unobserved characteristic to the econometrician but observable to the employer, is not correlated with the GED outcome, the difference-indifferences estimators reduce to estimators of the differences in earnings between GED and non-GED holders in the pre- and post-period, respectively. Post Pre Post Pre Pre Pre Pre ½ yPre G;2 yNG;2 ½ yNG;3 yNG;3 ¼ ½ yG;2 yNG;3 ¼ ½ yG yNG

Post Pre Post Post Post Post Post ½ yPre G;2 yNG;2 ½ yG;1 yG;1 ¼ ½ yG;1 yNG;2 ¼ ½ yG yNG

However, if u is correlated with the GED outcome, the difference-indifferences estimators do not collapse to the difference estimators. The difference-in-differences estimators will yield unbiased estimates if the change in the passing standard does not change the within-group, yj, relationship between yj and u and u’s impact on earnings remain the same in the pre- and post-period or if it changes equally for the relevant yj’s (i.e., y3 and y2 or y1 and y2). Using the example of a characteristic that may be observable to the employer but not to the econometrician, English ability, we need to assume that English ability is a relevant earnings characteristic, that it is correlated with the deﬁned score groups, and that the English earnings premium remains constant in the pre- and post-period, or if it changes, that it changes equally for the relevant score groups.

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3.2. Changes in the Labor Market Environment – Earnings Regime The above framework assumes that pre-passing-standard-hike individuals work in a labor market environment where both y1 and y2 individuals obtain the GED credential. However, the earnings regime will change in the postperiod, and y2 individuals will no longer obtain the signal. In other words, in the (at least immediate) post-period, GED holders still consist both y1 and y2 workers.6 Over time, the proportion of pre-passing-standard-hike GED holders will decrease, suggesting that, all else constant, earnings among both non-GED (y3) and GED holders (y1) will gradually increase while the earnings of the marginal group (y2) will gradually decrease. These changes will stop when the compositions are the ones given above (i.e., all nonGEDs are y2, and y3 and only y1 hold the GED credential). We detail our data, research design, and empirical models in the next sections.

4. DATA This paper brings new and unique data to bear on the GED question, in an attempt to better estimate the counterfactual and provide answers to questions about the economic impact of the GED, particularly regarding the labor market signaling value of this credential. We employ a specially constructed panel data set that contains GED test scores, basic demographic variables, and administrative earnings records in both the pre- and postpassing-standard-hike periods for a sample of male dropouts who all last attempted the GED exams in Texas either in 1995 or 1997. The key feature of these data is that we have data on GED test takers in Texas before and after January 1, 1997, the date on which the passing threshold for the GED exams in Texas (and several other states) was raised. The data utilized in this paper are from the Texas Schools Microdata Panel (TSMP). Data from two sources, the Texas Education Agency (TEA) and the Texas Workforce Commission (TWC), were linked to the TSMP data. The TEA data contain information on GED test date, GED test scores, age at test attempt, highest grade attained prior to dropping out of school, gender, ethnicity, GED test language, and GED test center. The TWC data contain information on employer-reported Unemployment Insurance (UI) quarterly earnings. In these data, we have quarterly earnings records from the ﬁrst quarter of 1989 through the last quarter of 2002. When there is no wage record in a quarter, we impute a value of zero.

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Although our analysis is of the ﬁrst 20 quarters following the test-taking date, we also generate pre-test-taking work experience and earnings for the six years prior to attempting the GED. The sample utilized in this paper is restricted to males who last attempted the GED in either 1995 or 1997, were between the ages of 16 and 40 at the time of the test, and did not attempt the GED while incarcerated. We choose 1995 as the period to examine before the passing standard hike because there is some evidence of a change in testing behavior in 1996 in anticipation of the 1997 increase in the scores required to pass the GED exams. Simply put, there appears to be less of a rush in 1995 to test before the passing standard changed than is the case in 1996. The sample restrictions we impose yield a sample of 52,251 dropouts who last attempted the GED exams in either 1995 or 1997.7

5. DESCRIPTIVE STATISTICS Sample descriptive statistics and graphs are presented in Tables 1 and 2, and Figs. 1 and 2. Fig. 1 plots the quarterly earnings by quarters from the time individuals attempted the GED, both before and after, by GED status. The raw quarterly earnings of eventual GED holders and GED candidates who will, eventually, fail the exams appear similar in the quarters prior to attempting the GED, with some relatively weak indication of slightly higher earnings in the quarters immediately before taking the GED among eventual passers. About a year after the GED attempt, the unadjusted earnings of those who passed the exams, and hence were awarded the credential, begin to diverge from the uncredentialed GED candidates. The patterns in the Texas data are similar to what has been observed in other UI quarterly earnings data on GED candidates. In particular, they are very close to what Tyler (2004) found using data from Florida. Two differences are the ﬂattening of the earnings proﬁle of both groups just prior to attempting the GED and the increase in mean quarterly earnings for both groups immediately after the GED attempt. One possible reason for the pretest ﬂattening of the proﬁle is test preparation in which individuals spend less time working in the quarter before, and of taking, the GED test. This is consistent with the observed proportion of individuals with positive earnings, i.e., roughly employment rates, which we discuss next. Fig. 2 shows the percentage in each group, successful and unsuccessful GED candidates, who have positive earnings in each quarter around the GED attempt. Unlike the raw mean earnings proﬁles of Fig. 1, the proﬁles

319

Modeling the Signaling Value of the GED Table 1.

Summary Statistics by Year of Attempting the GED. Year Attempted the GED

Difference

1995

1997

(1997–1995)

Highest grade attained Age when took GED Non-hispanic white Hispanic African American Asian All other GED in Spanish

9.82 21.41 42.0% 39.1% 14.1% 1.2% 3.7% 3.9%

9.75 21.31 42.6% 38.9% 13.0% 1.3% 4.3% 5.0%

0.06a 0.10a 0.5% 0.1% 1.1%a 0.1% 0.6%a 1.1%a

Test scores Writing skills Social studies Science Interpreting lit. & the arts Mathematics Average score Min. score Passed the GED

45.45 48.60 49.47 47.69 47.38 47.72 42.98 78.7%

45.70 49.77 49.94 48.61 48.42 48.49 43.66 68.7%

0.25a 1.17a 0.47a 0.92a 1.04a 0.77a 0.68a 10.0%a

7.56

7.59

0.03

Average quarterly earnings Six years prior to attempting the GED Five years prior to attempting the GED Four years prior to attempting the GED Three years prior to attempting the GED Two years prior to attempting the GED One year prior to attempting the GED

$528 $623 $697 $824 $1,025 $1,214

$490 $568 $681 $852 $1,050 $1,241

$39a $55a $16 $28 $25 $27

Number of individuals

28,449

24,734

Pre-test-taking employment and earnings experience (quarters)

a

Indicates difference is statistically signiﬁcantly different from zero at a 5% signiﬁcance level or less.

in Fig. 2 indicate that eventual GED holders were more likely to be employed in the quarters before the GED attempt than candidates who would eventually fail the GED exams. Also, the employment advantage does not appear to widen after the successful candidates were awarded their GED. The higher pre-test-taking employment rates among eventual GED passers suggest that this group has accumulated greater work experience prior to taking the GED. This may partially explain their relatively greater

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MAGNUS LOFSTROM AND JOHN TYLER Table 2.

Summary Statistics by GED Outcome Group. GED Outcome Group All fail

1995

Affected score group

1997

comparison

Passed 1995

Failed 1997

1995

Highest grade attained Age when took GED Non-hispanic white Hispanic African American Asian All other Took the GED in Spanish

9.62 22.57a 27.1% 46.4% 20.5% 1.3% 4.7% 2.5%

9.52 22.16a 27.6% 45.3% 20.5% 1.6% 5.1% 2.2%

9.67 21.22a 31.9% 44.7% 18.5% 1.3% 3.9% 1.8%a

9.59 21.53a 30.7% 42.7% 20.4% 1.4% 4.8% 2.7%a

9.94 21.03 51.1%a 34.4%a 10.2% 1.2% 3.2%a 5.1%a

9.85a 20.97 49.3%a 36.2%a 9.6% 1.2% 4.0%a 6.2%a

Test scores Writing skills Social studies Science Interpreting lit. & the arts Mathematics Average score Min. score

39.35 40.95a 41.83 40.38a 40.20 40.54a 36.86a

39.48 41.42a 41.85 41.03a 40.40 40.84a 37.16a

42.69a 44.59 45.42 44.02 43.87 44.12 39.88

42.23a 44.63 45.25 44.05 44.11 44.06 40.13

48.72a 52.88a 53.75a 51.73 51.30a 51.67 46.36

48.33a 53.35a 53.39a 51.86 51.80a 51.75 46.41

7.82

7.60

7.19a

7.85a

7.59

7.56

$656a

$549a

$451

$464

$506a

$470a

$763a

$609a

$528

$564

$602a

$553a

$815a

$709a

$601

$692

$684

$670

$918

$859

$727a

$866a

$820

$848

$1,104a

$1,004a

$914a

$1,072a

$1,032

$1,065

$1,229a

$1,152a

$1,089a

$1,247a

$1,251

$1,274

6,311

6,303

5,590

1,532

16,548

16,899

Average quarterly earnings Six years prior to attempting the GED Five years prior to attempting the GED Four years prior to attempting the GED Three years prior to attempting the GED Two years prior to attempting the GED One year prior to attempting the GED Number of individuals a

a

1997

a

Pre-test-taking experience (quarters)

a

Treatment

All pass

Indicates whether 1997–1995 within GED outcome group difference is statistically signiﬁcantly different from zero at a 5% signiﬁcance level or less.

321

Modeling the Signaling Value of the GED 3,500

Quarterly Earnings ($)

3,000 2,500 2,000 1,500 1,000 500 -

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

18

20

Quarters From Time Attempted GED Passed GED

Fig. 1.

Failed - GED

Quarterly Earnings by Quarter from Time Attempted the GED – Men, Ages 16–40. 70%

Percent with Reported Earnings

60% 50% 40% 30% 20% 10% 0% -8

-6

-4

-2

0

2

4

6

8

10

12

14

16

18

20

Quarters From Time Attempted GED Passed GED

Fig. 2.

Failed - GED

Percent with Reported Earnings by Quarter from Time Attempted the GED – Men, Ages 16–40.

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earnings growth, and levels, in the period after having received a GED credential. Table 1 provides information on GED candidates in Texas in the two testing years, 1995 and 1997. The central message of the table is that the two cohorts of candidates appear quite similar on the observable individual characteristics. There are, however, some small but statistically signiﬁcant differences. GED test takers in the 1997 sample completed slightly less schooling, are somewhat younger, and consist fewer African Americans and more Spanish test takers. The table shows that test scores are signiﬁcantly higher among 1997 test takers relative to 1995 test takers. Given our discussion above on a simple signaling model, it is not surprising that the test scores are higher since the implicit cost has increased with the higher passing standard and is likely to deter, in particular, some medium-ability individuals from attempting the GED. Also, as might be expected, the percentage of candidates who passed the exams declined – 10% fewer candidates passed in 1997, after the passing standard was raised, than in 1995. One factor that should not go unnoticed is that the number of dropouts who attempted the GED exams in 1997 was substantially lower than in 1995. This observation has potential implications for our identiﬁcation strategy, a point we address in a later section. Table 2 displays information on the six distinct groups created by the passing standard change. The groups of particular importance, given our empirical strategy, are the treatment and comparison groups, i.e., those in the ‘‘affected score group.’’ To validate our identiﬁcation strategy, the assignment into these groups needs to be random, or more speciﬁcally, in the models deﬁned below, assignment into the groups controlling for observables – including differences across the other pre- and post-passingstandard-change groups – must be uncorrelated with the disturbance term. According to Table 2, the treatment and comparison groups appear quite similar across the dimensions on which we have data.8 There are, however, some differences. For example, the percentage of African Americans is slightly larger in the comparison group. The comparison group also has slightly greater pre-test-taking work experience, about two-thirds of a quarter, and higher pre-test-taking quarterly earnings. A difference between the 1997 and 1995 group pre-test-taking earnings also exists for the failing groups, i.e., groups 1 and 2, in the two years prior to attempting the GED, although it is smaller. The test score statistics in Table 2 suggests that the score distribution within the affected score group did not change

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323

appreciably. There appears, however, to be a slight within-group shift to the right in the score distribution among the All Fail group. It should also be pointed out that the sample size of the treatment and comparison groups are quite different, with the latter being smaller. There are at least two explanations for this 1995-to-1997 drop in the sample size of the affected score group. The ﬁrst explanation lies in the necessary deﬁnition and restriction of test takers. We have restricted our sample to individuals who last attempted the GED in either 1995 or 1997. A test taker in this score group who took the exam in 1995 has no incentive to come back and test again since that person has already received high enough scores to obtain the credential. However, a 1997 test taker in this score group is quite close to passing but did not receive the credential. Some individuals with scores in this range are likely to return later to try again. If these individuals returned for another attempt in 1998 or later, they would be excluded from our sample. To address this potential complication, we will perform robustness tests, including a restriction of our sample only to individuals who attempted the GED in either 1995 or 1997. A second explanation is that some individuals who would be potential affected-score-group members in 1997 are deterred by the higher passing standard and never attempt the GED. To the extent that these potential ‘‘no-shows’’ are not a random subsample from the affected score group, their absence from the estimation could bias our results. A third and related explanation is that individuals who attempted fewer than all ﬁve exams in 1997 were placed in the ‘‘all-failer’’ group in our analysis. To the extent that some of these individuals would have been in the affected score group, had they completed all of the exams, they are essentially ‘‘mis-assigned’’ by us. Again, to the extent that these individuals are a nonrandom subsample of the affected score group, their potential ‘‘mis-assignment’’ could bias our estimates. We return to these two related, potential sources of bias later in this paper.

6. EMPIRICAL SPECIFICATIONS 6.1. Natural Experiment Lacking a true experiment that would generate exogenous variation in GED status, we exploit the 1997 change in GED passing standards in Texas as a

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natural experiment that simulates random assignment of the credential. We will utilize the six groups deﬁned above. There are two key assumptions in our identifying strategy. The ﬁrst is that any difference in outcomes between the individuals in the treatment and comparison groups are solely the result of differences in GED status and in the years in which they tested and, hence, entered the labor market. The second key assumption is that the individuals in group 1 relative to group 2 and those in group 5 relative to group 6 differ only in the years in which they attempted the GED exams, and as a result, these individuals can be used to purge the treatment group versus comparison group contrast of any differences related to whether they attempted the GED before or after the change in the passing standard. These assumptions, or restrictions, can be relaxed somewhat and still yield unbiased estimates of the signaling value of the GED. As long as the assignment into the deﬁned score groups is uncorrelated with the disturbance term, the estimates of the GED effect are unbiased. The difference-in-differences estimator that captures this idea is given by the following speciﬁcation: yit ¼ a0 þ YrsPostit a þ b0 Beforei þ YrsPostit Beforei b þ d0 ASGi þ YrsPostit ASGi d þ g0 ASGi Beforei þ YrsPostit ASGi Beforei c þ Z0 AllPassi þ YrsPostit AllPassi g þ l0 AllPassi Beforei þ YrsPostit AllPassi Beforei k þ Xit p þ Timet s þ uit where yit ¼ quarterly earnings for individual i at time t; AllPassi ¼ dummy variable indicator for those whose score would place them above the passing threshold either before or after the change in the passing standard; ASGi ¼ dummy variable indicator for those whose scores place them in the affected score group; Beforei ¼ dummy variable indicator for having taken the GED exams before the passing standard was raised, i.e., 1995 test takers; ASGi Beforei ¼ identiﬁes individuals in the treatment group – individuals in the affected score group who have a GED; YrsPostit ¼ a vector of dummy variables indicating whether earnings were measured in the second, third, fourth, or ﬁfth years after the GED attempt; Xit ¼ matrix containing

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325

a set of individual control variables including age, highest grade completed, race/ethnicity, and pre-test-taking earnings and experience;9 Timet ¼ vector capturing time ﬁxed effect. It is straightforward to show that, given this speciﬁcation, the parameters yielding the GED signaling value estimator, utilizing the group of failers as the comparison group, are g0 and g0þgt, the ﬁrst of which is the difference in mean outcomes between the treatment and comparison individuals in the ﬁrst year after the GED attempt, after the 1995-to-1997 change for the failers have been differenced out. In other words, this is the difference-in-differences estimator for the ﬁrst post-attempt year’s earnings, under the assumption that low-ability workers’ pre–post changes in earnings most closely resemble the overall changes in the labor market earnings of the medium, or marginal, ability group. The parameter g0þgt is the difference-in-differences estimator for the tth year’s earnings. Similarly, the parameters of interest using the all-passer group to purge time effects are g0l0, for the ﬁrst year after taking the GED exam, and (g0þgt)(l0þlt) represents the estimator for the tth year since taking the GED. OLS estimates of the parameters from this speciﬁcation will be unbiased if, controlling for relevant changes in the labor market environment, the comparison groups accurately estimate the counterfactual of what would have happened to the treatment group had they not been awarded a GED. It is worth reemphasizing here that, by construction, the members of the treatment and comparison groups have the same GED test scores. Thus, to the extent that GED test scores capture dropouts’ levels of human capital, g0 and g0þgt [alternatively, g0l0 and (g0þgt)(l0þlt)] estimate the signaling value of the GED. Speciﬁcally, and importantly, our estimates represent the signaling value of the GED for ‘‘marginal’’ GED holders, i.e., y2 workers, or differently put individuals who barely passed the GED exam. This is similar to the estimation strategy used by Tyler et al. (2000), who utilize state variation in passing standards. To the extent that there is a human capital component to the GED credential, the difference-in-differences estimator will underestimate the total impact of the GED on earnings. Similarly, if employers are able to infer productivity of individuals with the GED credential based on observable characteristics, i.e., the GED outcome, and X are correlated, our estimators will represent the average GED signaling value across X for ‘‘marginal’’ passers. Similar arguments can also be made for the Tyler et al.’s (2000) research approach.

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6.2. OLS Speciﬁcation As a ﬁrst step in the empirical work, we ﬁt simple OLS models to establish that the Texas data do not generate unique patterns relative to earlier work. Our OLS speciﬁcation is yit ¼ b0 þ b1 GEDi þ b2 Beforei þ YrsPostit g þ YrsPostit GEDi tt þ Xit n þ Timet a þ it where y is the quarterly earnings for individual i in year-quarter; t the quarter after the GED attempt in which earnings are measured and tA(1,2,y,20); GED an indicator variable for possessing a GED; Before an indicator variable for attempting the GED in 1995; YrsPost a vector of dummy variables indicating whether earnings were measured in the second, third, fourth, or ﬁfth years after the GED attempt. The interaction between GED and YrsPost allows earnings to grow differently for GED and non-GED holders. The matrix X contains the set of individual control variables deﬁned above as well as GED scores. Time is a vector of year-quarter dummy variables, i.e., time ﬁxed effects that control macroeconomic conditions. There are two interpretations that can be given to estimates based on the OLS speciﬁcation. First, to the extent that the X matrix, including GED test scores, captures an individual’s stock of human capital, b1 is an estimate of the signaling value of a GED on the ﬁrst year’s earnings and b1þtt an estimate of the signaling value of the GED on earnings in the tth year. If one thinks that the matrix X and GED test scores capture only some portion of an individual’s level of human capital, then b1 is an estimate of some combination of the signaling value plus the return to the unexplained (by X and GED test scores) portion of human capital of a GED on the ﬁrst year’s earnings, and b1þtt are estimates of the same for the tth year. The important point here is that under either interpretation, b1 and b1þtt are unbiased estimates of the causal impact of the GED only if the variable GED is uncorrelated with e. The latter is, however, against our simple signaling model in which earnings is also a function of the unobserved heterogeneity, i.e., u. The assumption that COV(G, u)W0 would lead to an upward bias of the OLS estimator of the GED signaling value. 6.3. Fixed-Effects Speciﬁcation The next two speciﬁcations are comparable to those used in earlier research, speciﬁcally Tyler (2004). These speciﬁcations attempt to address potential

Modeling the Signaling Value of the GED

327

unobserved heterogeneity of dropouts who do and do not obtain a GED, and we include them here to establish that the Texas data yield similar results to those of Tyler (2004). The ﬁrst of these speciﬁcations is a ﬁxedeffects model that controls time-invariant individual unobserved heterogeneity. The speciﬁcation is yit ¼ bi þ b1 GEDit þ YrsPostit g þ YrsPostit GEDi tt þ Ageit l0 þ Age2it l1 þ Timet a þ it Note that in this speciﬁcation, to be able to identify the GED effect, we include observations prior to the GED attempt. As opposed to all other models estimated, where t ¼ 1,2,y,20, we now add in the observation for the six quarters before the person took the GED, i.e., t ¼ 6,5,y,20. This implies that the variable GED is set to zero in all quarters before the GED attempt for all individuals and one in the quarters after the GED attempt for those who receive passing scores. In this speciﬁcation, bi is the individual ﬁxed effect. The vector YrsPost is deﬁned as in the above simple OLS speciﬁcation. The model also includes time ﬁxed effects and controls for age, which is the only time-varying individual variable in our data. If unobserved individual heterogeneity is time invariant, as is assumed in our simple signaling model, the estimates of b1 and b1þtt will be unbiased. However, if unobserved heterogeneity is time varying, possibly reﬂecting a positive change in motivation, which coincides with the decision to take the GED, the ﬁxed-effects speciﬁcation will also yield a biased estimate of the causal impact of the credential.

6.4. Regression Discontinuity Speciﬁcation Tyler (2004) also takes advantage of the fact that there is a cutoff, or discontinuity, in the average score, holding minimum score at 40 on each of the ﬁve components, in order to obtain the GED credential. In our Texas data, this strategy can most clearly be applied to the individuals who took the GED in 1997 since there does not exist an equally well-deﬁned discontinuity prior to the passing standard hike.10 Hence, in this speciﬁcation, we limit our sample to individuals who attempted the GED in 1997. yit ¼ b0 þ b1 GEDi þ b2 MeanScorei þ YrsPostit g þ YrsPostit GEDi tt þ Xit n þ Timet a þ it

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MAGNUS LOFSTROM AND JOHN TYLER

The model to be estimated, given our third speciﬁcation, is similar to the OLS speciﬁcation except that we include mean GED score, as opposed to all individual scores. Furthermore, the model is ﬁtted using test takers who scored a minimum of 40 and whose mean score was between 40 and 50. The latter restriction is imposed since the relationship between earnings and average scores may not be linear over the full range of mean scores. Unbiased estimates of b1 and b1þtt in this model rest on the assumptions that, in a narrow range around the passing cutoff, the conditional earningsmean score relationship is linear and captures the relevant unobserved heterogeneity, and that any vertical shift in the regression line at the cutoff is due solely to acquisition of the credential. We note that while the ﬁxed-effects speciﬁcation of Eq. (2) estimates the total impact of the GED, regression discontinuity estimates based on Eq. (2) capture the signaling value of the credential.

7. EMPIRICAL RESULTS We begin the empirical investigation by ﬁtting models based on variations of the simple OLS speciﬁcation. Coefﬁcient estimates and test statistics are displayed in Table 3. The estimated GED effects in Table 3 are summarized in Table 4 across the years, including standard errors and tests of the null hypothesis of no GED effect. Results from Model 1 in column 1 are from a simple model that includes time ﬁxed effects, to control differences in macroeconomic conditions, and controls for highest grade attained, age, and race/ethnicity, whether the Spanish language version of the GED was taken and whether the test was taken in 1995 or 1997. These baseline results indicate that in the ﬁrst year following the GED attempt, the mean quarterly earnings of GED holders are somewhat higher than those of dropouts who attempted, but failed, the exams. However, by the ﬁfth year following the GED attempt, the mean quarterly earnings of GED holders are about $423 ($60þ$363) higher than those of the individuals who failed the GED. A rather substantial change in the estimates appears in Model 2 when controls for pre-test-taking work experience and earnings are included. The estimates now indicate signiﬁcantly lower earnings for GED holders in the ﬁrst year after taking the GED, by $76. This is reversed in the preceding years and in the ﬁfth year following the GED attempt, and the quarterly earnings advantage is about $288. This suggests that almost one-third of the estimated GED earnings

124.67 213.10 296.66 363.00 38.52 74.83 89.66 142.88 49.53

139.92 303.49 348.15 167.27 314.07 29.96 1273.55 324.31 399.84 380.71

Other control variables Highest grade attained Age Age2/100 Age when took GED Age when took GED2/100 Hispanic African American Asian Other ethnicity Took GED in Spanish (17.73) (16.46) (9.96) (6.48) (6.05) (1.23) (43.83) (3.12) (7.25) (5.89)

(8.25) (10.38) (12.25) (13.20) (2.09) (2.44) (2.07) (2.57) (2.27) 72.83 218.43 344.34 328.74 524.70 90.83 506.25 151.14 74.79 64.38

126.26 214.72 298.39 364.28 119.79 233.73 324.53 457.26 15.67 (11.84) (12.47) (10.51) (14.57) (11.81) (4.65) (21.35) (1.68) (1.65) (1.27)

(8.36) (10.46) (12.33) (13.27) (7.13) (8.69) (8.77) (9.77) (0.89)

1178.41 (6.04) 76.12 (4.72)

Simple OLS

Simple OLS

6441.09 (27.85) 60.26 (2.74)

Model 2

Model 1

69.96 219.15 345.55 324.08 517.57 97.78 473.20 82.74 64.62 54.86

126.28 214.67 298.28 364.44 120.44 234.86 326.20 458.27 26.03 (11.30) (12.51) (10.55) (14.39) (11.67) (4.91) (19.45) (0.92) (1.43) (1.04)

(8.36) (10.46) (12.32) (13.27) (7.17) (8.74) (8.82) (9.80) (1.45)

60.35 (0.18) 129.93 (5.53)

Simple OLS

Model 3

Speciﬁcation

(1.51) (4.87) (11.27) (16.30) (12.84) (10.03) (7.23) (7.47)

373.75 (71.88) 536.78 (71.62)

18.99 60.94 141.31 204.37 157.74 147.59 131.68 159.24

3857.60 (41.21) 222.04 (26.08)

Fixed effect

Model 4

Estimated Quarterly Earnings Based on Speciﬁcations (1), (2), and (3).

Years since took the GED Second year GED holder Third year GED holder Fourth year GED holder Fifth year GED holder Second year Third year Fourth year Fifth year Attempted GED in 1995

Intercept GED holder

Variable

Table 3.

61.85 174.27 274.93 259.85 404.31 141.82 472.56 266.55 13.69

168.10 218.02 250.49 289.47 58.88 11.26 79.00 186.42

(4.82) (3.88) (3.47) (4.90) (4.02) (3.22) (9.20) (1.30) (0.13)

(4.67) (4.54) (4.43) (4.56) (1.36) (0.15) (0.74) (1.31)

2526.22 (3.69) 100.16 (1.50)

Discontinuity

Model 5

Modeling the Signaling Value of the GED 329

1,044,604 52,251 0.277

(0.01) (0.68) (1.55) (1.73) (4.09) (3.72) (1.77) (0.82) (2.97) (1.69)

0.278

Yes Yes Yes All tests

0.18 0.10 15.85 0.18 50.14 0.45 17.65 0.08 31.67 0.19

Simple OLS

Model 3

Speciﬁcation

1,414,535 52,251 0.100

Yes No No No

Fixed effect

Model 4

200,583 10,033 0.287

Yes Yes Yes Average

22.88 (2.06)

Discontinuity

Model 5

Notes: t-values based on robust standard errors are shown in parentheses. Furthermore, the standard errors are obtained assuming disturbances are independent across individuals but allows for dependence for individuals’ repeated observations over time, i.e., within-group/ individual correlation of disturbance term.

0.080

Number of observations Number of individuals R2

Yes Yes Yes No

Simple OLS

Simple OLS

Yes No No No

Model 2

Model 1

Time ﬁxed effect included Pre-test-taking experience Pre-test-taking earnings GED test scores

GED scores Writing skills Writing skills2 Social studies Social studies2 Science Science2 Interpreting lit. & the arts Interpreting lit. & the arts2 Mathematics Mathematics2 Average

Variable

Table 3. (Continued )

330 MAGNUS LOFSTROM AND JOHN TYLER

(21.96) (24.68) (27.66) (30.27) (32.76)

0.080

Number of observations Number of individuals R2

Note: Standard errors are shown in parentheses.

Yes Yes No No No

0.006 o0.001 o0.001 o0.001 o0.001

60.26 184.92 273.35 356.91 423.26

(16.14) (19.87) (23.33) (26.19) (28.97)

1,044,604 52,251 0.277

Yes Yes Yes Yes No

o0.001 0.012 o0.001 o0.001 o0.001

76.12 50.15 138.60 222.27 288.16

Simple OLS

Simple OLS

Included controls Time ﬁxed effect Age, schooling, ethnicity Pre-test-taking experience Pre-test-taking earnings GED test scores

Test H0:GED effect ¼ 0 (P-values) First year (t-test) Second year (F-test) Third year (F-test) Fourth year (F-test) Fifth year (F-test)

First year Second year Third year Fourth year Fifth year

Model 2

Model 1

(23.49) (26.44) (29.21) (31.53) (33.89)

0.278

Yes Yes Yes Yes All tests

o0.001 0.890 0.004 o0.001 o0.001

129.93 3.65 84.74 168.36 234.51

Simple OLS

Model 3

(8.51) (11.76) (11.81) (11.81) (11.84)

1,414,535 52,251 0.100

Yes Age No No No

o0.001 o0.001 o0.001 o0.001 o0.001

222.04 203.05 282.98 363.35 426.41

Fixed effect

Model 4

200,583 10,033 0.287

Yes Yes Yes Yes Average

0.133 0.348 0.133 0.072 0.033

(66.73) (72.41) (78.43) (83.66) (88.82)

Discontinuity

Model 5

100.16 67.94 117.86 150.32 189.30

Estimated Earnings Difference ¼ GED Holders Non-GED Holders

Estimated Quarterly Earnings Differences, GED Holders and Non-GED Holders, Based on Results in Table 3.

Year since Attempted the GED

Table 4.

Modeling the Signaling Value of the GED 331

332

MAGNUS LOFSTROM AND JOHN TYLER

premium is due to differences in pre-test-taking labor market outcomes between men who pass and fail the test. Model 3 in Table 3 adds controls for GED test scores. When GED test scores are added, the estimated GED effect falls by approximately 20%. Nonetheless, Model 3 estimates still indicate that by the ﬁfth year after the test attempt, GED holders earn about $234 more per quarter than do observationally similar dropouts lacking the credential. To the extent that GED test scores capture the human capital of GED examinees, these results can be interpreted as the signaling value of the GED. Under this interpretation, roughly 80% of the ﬁfth year’s GED advantage estimated using Model 2 is due to the signaling component of the GED. Of course, since we have no information on pre-GED test scores, we do not know how much, if any, of the remaining 20% is the result of human capital related to GED preparation versus human capital that GED examinees already possessed before they decided to attempt to acquire the credential. The ﬁxed-effects model speciﬁcation is presented as Model 4 in Tables 3 and 4. The results indicate a strong GED effect on earnings. In fact, the estimates suggest a statistically signiﬁcant immediate earnings advantage in the ﬁrst year since taking the GED of about $220. By the ﬁfth year, the GED premium has grown to roughly $426. The last model, Model 5 in Tables 3 and 4, utilizes the regression discontinuity strategy and the 1997 sample. The estimated impact of the GED on earnings is substantially smaller than in the ﬁxed-effects model and somewhat less than the simple OLS estimates indicate. There appears to be no effect in the ﬁrst year after taking the GED but, by the ﬁfth year, GED holders earn a statistically signiﬁcant $190 more per quarter than do dropouts who did not obtain the credential. We next turn to a comparison of the results in Tables 3 and 4 to previous ﬁndings of the impact of the GED on earnings, primarily to determine if the Texas data can generate similar results to earlier studies. In particular, we want to see if our results are close to those in Tyler (2004) that are based on GED examinees in Florida. Like our Texas data, the Florida data used in Tyler (2004) also contain demographic information, GED test scores, and UI quarterly earnings. Two comparisons are important. First, across all of the speciﬁcations represented in Tables 3 and 4, except for the regression discontinuity speciﬁcations, our estimates in Texas are quite similar to those found by Tyler. The OLS and ﬁxed-effects estimates indicate that four to ﬁve years after taking the GED, individuals who passed the exam display higher quarterly earnings by about 10–17%. Data used in the Tyler paper had a slight advantage of an additional four quarters of post-GED attempt

Modeling the Signaling Value of the GED

333

UI wage information, and the estimated differences were $266 and $310 in the ﬁfth and sixth years following the GED attempt, respectively. Regarding the regression discontinuity results, the $190, GED earnings advantage we ﬁnd after ﬁve years represents about an 8% increase over the $2,500 mean quarterly earnings that unsuccessful GED examinees exhibit ﬁve years after the attempt (Fig. 2). This is about half of the roughly 20% effect Tyler ﬁnds in Florida based on the same regression discontinuity design. We return to a discussion of these regression discontinuity estimates at the end of this paper. The second general comparison between our results and the earlier Tyler work worth noting is that similar to Tyler (2004) and others (Tyler et al., 2000), we ﬁnd that examining the ﬁrst years after the GED attempt will typically fail to reveal any substantive GED earnings advantage; it typically takes at least three years for substantively large and statistically signiﬁcant results to appear.11 These results indicate that estimates based on the Texas data quite closely replicate results using similar data from Florida. Of course, regardless of the data source, estimates based on any of our speciﬁcations are only as good as the assumptions upon which they rest. The simple OLS estimates may be biased if the GED score variables do not adequately capture productivity-related unobserved heterogeneity, including ability and motivation. Estimates based on the ﬁxed-effects speciﬁcation will be biased if there are time-varying, unobserved differences between GED candidates who do and do not obtain the credential. The validity of the regression discontinuity approach hinges on whether the earnings–mean score relationship is linear in the vicinity of the passing score cutoff and whether any unobservables related to earnings are smooth around the vicinity of the passing score cutoff. In short, identiﬁcation in all of these approaches rests on untestable assumptions. Identiﬁcation using the natural experiment in Texas also rests on untestable assumptions, namely, there are no differences in who decides to attempt the GED in the pre- and post-passing-standard-change regimes and in test preparation across these regimes. On the other hand, an advantage of the natural experiment is that there is a clear and arguably exogenous source of policy variation that is related to who does and does not receive a GED in Texas.

7.1. Natural Experiment Results Given that there are two possible comparison groups to our ‘‘marginal’’ group, individuals whose scores were not sufﬁciently high to pass under

334

MAGNUS LOFSTROM AND JOHN TYLER

either passing standard (All Fail) and individuals whose scores were sufﬁciently high to pass under either passing standard (All Pass), our speciﬁcation yields two, potentially, different estimators of the GED signaling value. As Tables 5 and 6 reveal, there are relatively small differences in the point estimates between these two estimators. Our discussion below will refer to the point estimates utilizing the All Pass comparison group. Model 1 in Table 5 presents estimates from the ‘‘pure’’ natural experiment. Based on Model 1, GED holders in the treatment group earn approximately $264 less in the ﬁrst post-attempt year than do members of the comparison group who have the same GED test scores, a result that is statistically signiﬁcant. This may be because newly minted GED holders are engaged in more post-attempt postsecondary education, training, or job search than are comparison group members lacking a GED.12 As the companion results in the ﬁrst column of Table 6 show, this negative effect becomes small enough in subsequent years so that it is not statistically signiﬁcant. The overarching message of column 1 is, however, that estimates of the impact of the GED on earnings from the natural experiment fail to ﬁnd any positive effect. If the natural experiment is doing a good job at pseudo-randomization, estimates should change little when observable control variables are added. The evidence on this in Table 5 is somewhat mixed. Estimates from Model 1 change little when time ﬁxed effects are added in Model 2 or when age, schooling, and ethnicity are added in Model 3.13 The largest changes in the estimates occur when pre-test-taking work experience and earnings are added in Models 4, 5, and 6, and all of the change associated with adding these controls accrues to the ﬁrst year GED effect. From Model 3 to Model 6, the ﬁrst year negative GED ‘‘effect’’ decreases by slightly less than 30%. Even with this less negative ﬁrst year effect, however, inferences about the impact of the GED remain unchanged from Model 3 to Model 6. In fact, the conclusion one would draw from the estimates in Model 1 that GED holders display lower earnings in the ﬁrst year after attempting the GED and earn no premium from the credential in subsequent years holds across all models. As discussed above, the lower earnings in the ﬁrst year may be due to a composition effect where relatively more productive GED holders enroll in some schooling in the ﬁrst year after receiving the GED diploma. It is also possible that, upon successfully obtaining the GED credential, an individual’s reservation wage may increase. As a result, the job search process is likely to take longer as the person is now requiring a higher wage to accept a job offer. Nonetheless, the results strongly indicate that there is

Model 1

972.48 114.37 232.83 279.85 316.44 477.39 93.94 254.81 223.58 178.85 209.84 68.82 10.29 109.42 114.92 330.43 168.58 153.05 101.04 153.95 112.26 150.64 271.54 386.00 429.58 66.71 45.14

Model 3

(14.94) 6839.01 (28.69) (4.14) 62.11 (2.40) (4.77) 132.31 (2.96) (4.01) 133.78 (2.11) (3.36) 127.86 (1.50) (8.29) 244.90 (4.02) (3.17) 83.77 (2.85) (6.13) 235.16 (5.71) (4.28) 193.64 (3.75) (2.69) 137.70 (2.11) (3.25) 271.02 (4.49) (1.51) 73.19 (1.60) (0.18) 1.24 (0.02) (1.62) 96.27 (1.42) (1.56) 97.56 (1.32) (4.35) 259.08 (3.65) (3.17) 163.49 (3.08) (2.22) 143.14 (2.07) (1.25) 85.81 (1.06) (1.72) 133.35 (1.49) (3.36) 106.30 (3.31) (6.58) 142.02 (6.20) (8.59) 254.34 (8.04) (10.70) 360.17 (9.97) (10.59) 395.21 (9.73) (1.40) 17.86 (0.40) (1.42) 47.50 (1.49)

Model 2

2022.34 99.12 205.94 237.45 257.27 368.13 75.84 224.44 177.34 111.84 188.17 72.63 2.54 97.34 99.01 182.20 163.78 143.08 86.95 134.84 5.56 142.74 255.75 362.03 397.90 0.61 47.29

(8.79) (4.01) (4.90) (4.04) (3.26) (6.95) (2.62) (5.52) (3.51) (1.77) (3.62) (1.59) (0.04) (1.44) (1.34) (2.98) (3.08) (2.07) (1.08) (1.51) (0.20) (6.23) (8.09) (10.02) (9.79) (0.02) (1.49)

Model 4

378.25 103.06 214.21 250.63 276.03 311.09 75.40 223.33 175.60 109.75 144.75 72.95 1.87 96.28 97.48 149.65 163.13 142.00 85.22 132.81 66.48 141.93 254.13 359.69 394.69 35.62 47.50

(1.84) (4.31) (5.34) (4.49) (3.69) (6.77) (2.65) (5.56) (3.53) (1.78) (3.12) (1.60) (0.03) (1.42) (1.32) (2.81) (3.07) (2.06) (1.05) (1.48) (2.80) (6.20) (8.04) (9.96) (9.72) (1.11) (1.49)

Model 5

Estimated Quarterly Earnings Based on Speciﬁcation (4) – Natural Experiment.

GED outcome and years since took the GED Constant 1756.45 (62.40) Second year 289.86 (15.41) Third year 508.75 (19.80) Fourth year 613.98 (21.18) Fifth year 589.43 (18.02) Before 39.40 (0.97) Second year before 70.36 (2.67) Third year before 23.54 (0.67) Fourth year before 133.43 (3.22) Fifth year before 337.67 (7.20) Affected Score Group (ASG) 216.98 (3.36) Second year ASG 75.11 (1.64) Third year ASG 5.53 (0.09) Fourth year ASG 102.56 (1.51) Fifth year ASG 105.87 (1.43) Before ASG 334.41 (4.40) Second year before ASG 174.05 (3.27) Third year before ASG 159.92 (2.31) Fourth year before ASG 105.38 (1.30) Fifth year before ASG 161.61 (1.80) All-passing group 116.39 (3.49) Second year all passing 147.01 (6.41) Third year all passing 268.79 (8.50) Fourth year all passing 382.04 (10.58) Fifth year all passing 424.36 (10.45) Before all-passing group 70.54 (1.48) Before second year all passing 41.59 (1.31)

Variable

Table 5.

690.53 107.97 223.94 262.66 288.84 338.65 72.35 219.21 169.28 99.81 131.08 72.86 2.07 96.52 97.81 152.16 163.28 142.22 85.66 133.37 78.90 142.14 254.56 360.28 395.48 20.03 47.44

(3.48) (4.53) (5.60) (4.72) (3.88) (7.38) (2.54) (5.45) (3.40) (1.62) (2.85) (1.60) (0.04) (1.43) (1.33) (2.87) (3.07) (2.06) (1.06) (1.49) (3.33) (6.21) (8.05) (9.98) (9.74) (0.62) (1.49)

Model 6

Modeling the Signaling Value of the GED 335

Yes No No

0.019

0.018

65.99 (1.52) 77.71 (1.52) 22.16 (0.38)

Model 2

No No No

63.05 (1.45) 73.98 (1.45) 27.25 (0.47)

Model 1

0.080

Model 4

(13.15) (8.57) (9.39) (16.10) (16.24) (0.91) (28.34) (2.57) (3.05) (1.50)

0.192

Yes Yes No

92.53 172.31 316.74 418.63 791.43 20.12 735.67 249.57 153.53 86.45

70.43 (1.62) 83.94 (1.65) 13.50 (0.23)

1,044,604 52,251

(17.52) (13.68) (9.85) (6.72) (6.11) (0.79) (43.06) (3.05) (7.12) (6.14)

Yes No No

138.25 286.31 344.47 184.40 317.65 19.48 1260.74 316.55 393.16 397.40

70.71 (1.63) 84.71 (1.66) 12.70 (0.22)

Model 3 70.73 (1.63) 84.46 (1.66) 12.87 (0.22)

Model 6

0.273

0.277

Yes Yes Yes

(14.04) 72.61 (11.79) (10.42) 184.51 (9.53) (10.63) 340.71 (10.39) (9.10) 296.67 (12.50) (8.15) 524.23 (11.78) (3.46) 92.80 (4.73) (23.41) 505.09 (21.19) (0.46) 152.99 (1.70) (2.56) 73.32 (1.62) (1.00) 61.66 (1.21) Yes No Yes

87.36 202.75 349.16 215.14 357.31 68.29 572.18 41.02 116.37 50.60

70.83 (1.63) 84.67 (1.66) 12.59 (0.22)

Model 5

Notes: t-values based on robust standard errors are shown in parentheses. Furthermore, the standard errors are obtained assuming disturbances are independent across individuals but allows for dependence for individuals’ repeated observations over time, i.e., within-group/ individual correlation of disturbance term.

Time ﬁxed effect included Pre-test-taking experience Pre-test-taking earnings Number of observations Number of individuals R2

Other control variables Highest grade attained Age Age2/100 Age when took the GED Age when took the GED2/100 Hispanic African American Asian Other ethnicity Took GED in Spanish

Before third year all passing Before fourth year all passing Before ﬁfth year all passing

Variable

Table 5. (Continued )

336 MAGNUS LOFSTROM AND JOHN TYLER

334.41 160.36 174.48 229.03 172.79

(75.99) (84.54) (95.03) (104.41) (110.80)

263.87 48.24 40.90 84.51 129.51

(76.02) (84.55) (95.04) (104.42) (110.77)

o0.001 0.056 0.062 0.028 0.111

330.43 161.85 177.39 229.39 176.48

Model 2

Model 4

Model 5

Model 6

o0.001 0.231 0.202 0.085 0.241 0.003 0.796 0.634 0.301 0.635

0.005 0.838 0.922 0.466 0.861

0.004 0.865 0.897 0.448 0.844

Comparison Group: All Fail 259.08 (71.06) 182.20 (61.07) 149.65 (53.32) 152.16 (52.95) 95.58 (79.84) 18.42 (71.28) 13.48 (65.75) 11.12 (65.30) 115.93 (90.92) 39.12 (82.17) 7.65 (77.70) 9.95 (77.12) 173.27 (100.47) 95.25 (92.17) 64.43 (88.31) 66.50 (87.72) 125.72 (107.16) 47.36 (99.64) 16.84 (96.06) 18.79 (95.48)

Model 3

o0.001 0.517 0.609 0.379 0.198

o0.001 0.678 0.743 0.447 0.225

0.001 0.667 0.687 0.890 0.509

o0.001 0.678 0.703 0.852 0.469

o0.001 0.524 0.569 0.980 0.563

Comparison Group: All Pass (68.88) 263.73 (68.93) 241.22 (64.46) 182.81 (56.00) 185.28 (49.30) 172.19 (48.92) (77.17) 50.01 (77.18) 30.22 (72.81) 28.26 (65.68) 25.35 (60.96) 38.53 (60.51) (87.33) 44.69 (87.36) 27.37 (83.58) 30.70 (76.09) 27.55 (72.19) 40.76 (71.64) (96.66) 84.97 (96.67) 70.70 (93.06) 11.92 (86.01) 15.38 (82.69) 2.07 (82.13) (102.57) 131.93 (102.54) 120.57 (99.31) 61.46 (93.04) 65.05 (89.86) 51.68 (89.32)

Test H0:GED effect ¼ 0 (P-values) First year o0.001 Second year 0.532 Third year 0.640 Fourth year 0.382 Fifth year 0.207

First year Second year Third year Fourth year Fifth year

Test H0:GED effect ¼ 0 (P-values) First year o0.001 Second year 0.058 Third year 0.066 Fourth year 0.028 Fifth year 0.119

First year Second year Third year Fourth year Fifth year

Model 1

Estimated Quarterly Earnings Differences, GED Holders and Non-GED Holders, Based on Results in Table 5.

Years Since Attempted GED

Table 6.

Modeling the Signaling Value of the GED 337

Note: Standard errors are shown in parentheses.

0.018

No No No No

Included controls Time ﬁxed effect Age, schooling, ethnicity Pre-test-taking experience Pre-test-taking earnings

Number of observations Number of individuals R2

Model 1

Years Since Attempted GED

0.019

Yes No No No

Model 2

0.080

Yes Yes No No 1,044,604 52,251

Model 3

Table 6. (Continued )

0.192

Yes Yes Yes No

Model 4

0.273

Yes Yes No Yes

Model 5

0.277

Yes Yes Yes Yes

Model 6

338 MAGNUS LOFSTROM AND JOHN TYLER

Modeling the Signaling Value of the GED

339

no evidence of a positive impact of the GED on the earnings of male dropouts when the effect is identiﬁed through the natural experiment of the passing standard change.

7.2. Robustness Checks Clearly, the above-presented results warrant thorough robustness checks. We do this by ﬁrst examining the validity of the natural experiment. Next, we see if the results can be generalized or appear to be speciﬁc to some groups in our sample population. An important advantage with our data is that we can investigate the validity of the experiment by analyzing pre-intervention differences between treatment and comparison groups. While Table 2 indicates that there are statistically signiﬁcant pre-intervention earnings differences between the 1995 and 1997 affected score groups ($1,089 versus $1,247), these differences could be the result of differing labor markets between 1994 and 1996 and/or differences in observable characteristics between the 1995 and 1997 affectedscore-group members. To account for these potential differences, we estimate a difference-in-differences model similar to Model 3 in Table 5 using observations only from the four quarters prior to the GED attempt, i.e., the year before the GED attempt. The estimated earnings difference the year before taking the GED between the treatment and comparison groups indicates that the treatment group earned roughly $75 more than the comparison group. However, the standard error is quite large, $48, suggesting no pre-intervention difference between the two groups.14 The results are virtually unchanged if we extend the pre-test-taking period to the immediate two years before the test was taken. These results suggest that the treatment and comparison groups were similar in the pretreatment years, a ﬁrst test for the validity of any experiment or natural experiment. As stated earlier, the difference in the sample size between the treatment and comparison group suggests that there may be some nonrandom assignment into these groups. There are three potential and non-mutually exclusive explanations for the relatively smaller size of the comparison group, and we examine the potential impact of each in turn. First, the 1995 test takers in the affected score group had no incentive to take the GED in later years since their score qualiﬁes them for the credential. However, 1997 test takers whose scores would place them in the affected score group failed to obtain a credential and thus had an incentive to retake the GED exams. Any of these potential comparison group members who chose to retest in

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1998 or later would not be included in our sample. Thus, the 1997 affectedscore-group members may be a selective group of individuals since they did not return to try to obtain the credential again. To address this concern, we reestimated the models shown in Table 5 and 6 using a restricted sample, including only individuals who attempted the GED once, either in 1995 or in 1997.15 The results for Model 6 speciﬁcation are presented in the ﬁrst column of Table 7. The results are quite similar to the ones shown in Table 6. For example, the estimated ﬁrst year difference between the treatment and comparison groups for Model 6 speciﬁcation, using the All Pass group as the comparison group, is $197 for the subsample of test takers who attempted the GED only once, compared to $172 in the ‘‘full’’ sample. The estimated GED effects in subsequent years become positive but are statistically insigniﬁcant. A second reason for the smaller comparison group has to do with potential behavioral changes associated with the change in passing standard. While the imposition of the passing standard hike in Texas was surely exogenous to the state, the behavior of GED preparation providers, GED examinees, and potential GED examinees may have been inﬂuenced by the passing standard change in ways that inﬂuence our results. Fig. 3 plots trends over time in the number of GED examinees in Texas and Florida. Florida, of course, is a state that did not face a passing standard hike in 1997 as did Texas, though the standard was raised slightly in Florida in June 1998, again in July 1999, and again in July 2000.16 The trend line in Texas indicates that there was a substantial increase in the number of GED examinees in Texas in 1996, the year prior to the passing standard hike, followed by a substantial falloff in the number of GED examinees in 1997. The 1996 increase in test takers is consistent with the anecdotal evidence that GED preparation providers were encouraging GED candidates to attempt to acquire the credential before the higher standards went into effect. This is the primary reason that we choose to use 1995 as a ‘‘before’’ period in our difference-in-differences estimates; we were concerned that the pool of GED examinees in Texas was different in unobservable ways in 1996, as the run-up to the January 1, 1997, deadline loomed. On the other hand, we are not able to account for the potentially different pool of GED examinees from which we draw our comparison group – those who chose to attempt the GED exams after the passing standard hike was in place in 1997. The sharp drop in the number of test takers in Texas that occurred between 1994–1996 and 1997 suggests that those who decided to attempt to obtain a GED in 1997 may be different than GED examinees of

1998 takers

White

0.005 0.781 0.974 0.504 0.676

o0.0001 0.075 0.802 0.545 0.290 0.823 0.719 0.973 0.803

Age 16–21

0.019 0.486 0.846 0.931 0.327

(61.78) 129.06 (54.95) (75.42) 49.71 (71.37) (88.03) 16.80 (86.41) (100.86) 8.74 (100.94) (109.96) 108.69 (110.81)

0.014 0.722 0.858 0.442 0.794

151.11 26.86 15.81 77.47 28.69

Nonwhite

0.024 0.230 0.374 0.475 0.715

o0.0001 0.134 0.790 0.519

0.035 0.683 0.989 0.848 0.680

0.073 0.061 0.141 0.560 0.729

0.001 0.341 0.255 0.397 0.704

Comparison Group: All Pass (77.84) 118.81 (52.48) 161.76 (45.02) 188.28 (89.08) 105.22 (58.68) 169.91 (49.88) (93.81) 78.25 (65.16) 86.57 (57.76) 46.56 (113.83) 134.92 (72.00) 61.57 (64.64) (117.13) 68.57 (77.17) 17.54 (65.98) 1.89 (138.00) 123.75 (84.14) 90.36 (79.35) (134.38) 63.17 (88.49) 47.08 (73.08) 29.75 (155.03) 56.66 (97.29) 78.80 (92.98) (143.86) 35.22 (96.53) 69.56 (168.67) 36.76 (105.97) 38.64 (101.82)

0.011 0.809 0.661 0.821 0.818

196.74 22.72 51.39 30.46 33.17

Test H0:GED effect ¼ 0 (P-values) First year Second year Third year Fourth year Fifth year

First year Second year Third year Fourth year Fifth year

Low pass/high fail

Comparison Group: All Fail (82.15) 154.87 (55.20) 176.70 (49.49) 107.38 (101.58) (98.84) 18.96 (68.04) 112.47 (63.07) 28.88 (129.23) (122.56) 2.61 (80.37) 17.93 (71.67) 56.03 (155.76) (140.30) 60.86 (91.15) 48.39 (79.85) 6.01 (174.91) (150.53) 41.57 (99.41) 47.53 (190.82)

0.036 0.845 0.611 0.916 0.619

172.68 19.29 62.33 14.74 74.83

Test H0:GED effect ¼ 0 (P-values) First year Second year Third year Fourth year Fifth year

First year Second year Third year Fourth year Fifth year

Test once

Sample

Robustness of Estimated Quarterly Earnings Differences, GED Holders and Non-GED Holders.

Years since Attempted the GED

Table 7.

Modeling the Signaling Value of the GED 341

706,638 35,332 0.277

Yes Yes Yes Yes

Test once

603,016 30,161 0.297

Yes Yes Yes Yes

Low pass/high fail

883,507 55,244 0.308

Yes Yes Yes Yes

1998 takers

Sample

448,500 22,430 0.250

Yes Yes Yes Yes

White

599,305 29,982 0.295

Yes Yes Yes Yes

Nonwhite

727,978 36,404 0.174

Yes Yes Yes Yes

Age 16–21

Notes: Standard errors are shown in parentheses. Estimated earnings difference ¼ GED holders non-GED holders. Alternative subsamples, based on Model 6 speciﬁcation, Table 5.

Number of observations Number of individuals R2

Included controls Time ﬁxed effect Age, schooling, ethnicity Pre-test-taking experience Pre-test-taking earnings

Years since Attempted the GED

Table 7. (Continued )

342 MAGNUS LOFSTROM AND JOHN TYLER

343

Modeling the Signaling Value of the GED 100000 90000

Texas Florida

80000

Number of testers

70000 60000 50000 40000 30000 20000 10000 0 1988

1990

1992

1994

1996 Year

Fig. 3.

1998

Change Change in TX in FL

2000

2002

Change Change in FL in FL

Age 16–39 GED Testing Volumes in Texas and Florida for 1989–2001.

the near-prior years. Of primary concern for us is whether those who tested and failed in 1997, our comparison group, are different in unobservable ways from those who tested and passed with the same scores in 1995, our treatment group. In particular, if the reduced pool of dropouts who decided to attempt a GED in 1997, in spite of the higher standard, has on average more productive unobservable traits than the pool of 1995 examinees, then our natural experiment estimates would be downwardly biased. Thus, if individuals in the 1997 comparison group have more motivation and determination, but are less deterred, etc., then we would expect our results to be downwardly biased. It is important to note that if these types of unobservable differences exist for everyone in the 1995 and 1997 groups, then there is no problem, as the difference-in-differences estimator will account for them. What is a problem, however, is if the individuals who are nearest the passing cutoff tend to have more unobservable productivity in 1997 than do those who are farther from the cutoff in 1995. For example, if it is the case that most of the reduction in testing numbers that occurred in Texas between 1995 and 1997 because of the decision not to test by those who would tend to

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score close to the passing standard, while there were few changes at the upper and lower ends of the skill distribution in the propensity to test, then our results could be biased. The observation, from Table 2, that there are substantial changes in the sample size of the affected score group between 1995 and 1997, while there are essentially no changes in the 1995–1997 sample sizes of the all-failer and all-passer groups, is consistent with a scenario whereby most behavioral changes were occurring around the passing score cutoff. Examining the extent to which the 1997 affected score group is systematically different from the 1995 affected score group is not something that we can do directly. One approach we could take would be to restrict the other groups, all failers and all passers, to those who were closer to the affected score group in terms of their GED test scores. That is, use only ‘‘high failers’’ and ‘‘low passers’’ in the second difference of the differencein-differences estimator. Our conﬁdence in this robustness check is contingent upon how well these high-failer and low-passer subsamples mirror any changes in the affected-score-group sample between 1995 and 1997. Unfortunately, the large drop in the 1995–1997 affected-score-group sample size is not mirrored in either the high-failer or low-passer subsamples; these more narrowly deﬁned subgroups have about the same number of test takers in 1997 as in 1995. As a result, it is not clear that either of these groups could control unobservable changes in the affected score group between 1995 and 1997 that might result from behavioral changes in who attempts the tests. Nonetheless, under the ‘‘Low pass/High fail’’ column of Table 7, we present estimates using these more narrowly deﬁned all-passer and all-failer groups that are similar to our full sample estimates. A third explanation for the drop in the affected-score-group sample size between 1995 and 1997 is that ‘‘potential’’ 1997 affected-score-group members get ‘‘mis-assigned’’ by us in the construction of the different groups. In particular, anyone who did not take all ﬁve of the GED exams as of 1997 was assigned to the ‘‘all-failer’’ group. There are potentially individuals thus assigned who, if they were to attempt all ﬁve tests, would have scores that would place them in the 1997 affected score group. If these ‘‘mis-assigned’’ individuals are, on average, less productive than the observed 1997 affected score group, our difference-in-differences estimates are downwardly biased. Unfortunately, we have no good way of directly examining this potential source of bias. However, the natural experiment results using a restricted sample of individuals who took all ﬁve exams reveal no appreciable differences in the results compared to the ones presented in Tables 5 and 6.

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Thus, sample selection between 1995 and 1997 into who does or does not decide to attempt the GED exams, given the passing standard, is a worrisome source of bias for our natural experiment estimates. One ﬁnal method for examining this issue is to reﬁt Model 6, replacing the 1997 test takers with 1998 test takers. Given that our data include earnings information up until the fourth quarter in 2002, we can only track 1998 test takers’ post-test-taking earnings for four years. As is shown, in column 3 in Table 7, the results using 1998 test takers are quite similar to the ones we obtained using 1997 test takers. However, given that Fig. 3 indicates only a slight rebound in the number of GED examinees between 1997 and 1998, it is not clear that these estimates are purged of any bias that might be associated with the 1997-based estimates. We next turn to an investigation of whether the ﬁnding of no positive GED effect may be speciﬁc to certain groups in our sample. Previous research by Tyler et al. (2000) ﬁnds no evidence that nonwhite dropouts who obtain the GED credential earn more than statistically similar nonwhites who failed to receive passing scores. To address whether our results are driven by the relatively large proportion of nonwhite minorities in our sample, close to 60%, we estimated Model 6 separately for whites and nonwhites. The results are presented in the fourth and ﬁfth result columns in Table 7. The results for the two groups are sufﬁciently similar that one would draw the same conclusions regarding the impact of the GED on earnings for both groups, lower earnings in the ﬁrst year and no effect in the subsequent years. Since the sample used in Tyler et al. (2000) consisted young dropouts, between the ages of 16 and 21, a positive GED effect may be speciﬁc to this age group. To test whether our data, and approach, may mask these effects since we include males between the ages of 16 and 40, we ﬁtted Model 6 for a sample of 16- to 21-year-old males. The results are shown in column 6, Table 7. The estimates do not suggest that there are any differences between the relatively younger dropouts and their older counterparts since the results are very similar to the ones for the 16–40 age group.17 The above sensitivity analyses, while not perfect, are all supportive of our main results, suggesting that the strategy using the natural experiment to identify the signaling value of the GED credential is reasonably robust. Furthermore, the ﬁnding of no statistical difference in pre-test-taking earnings between the treatment and comparison groups is consistent with an assumption that the 1997 affected score group serves as a good comparison group for the 1995 affected score group.

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8. SUMMARY AND CONCLUSIONS 8.1. Reconciling Differences The natural experiment estimates in this paper differ from recent results in the literature that indicate a positive impact of the GED on the earnings of low-skilled dropouts. In particular, Tyler et al. (2000) used national data and a natural experiment similar to that used in this paper to estimate the impact of the GED on annual earnings from the federal Social Security earnings ﬁle. Exploiting interstate variation in GED passing standards that existed across states in 1990 as an identiﬁcation strategy, their difference-indifferences estimates place the impact of the GED on annual earnings at around 15%. What are the potential explanations that could reconcile these different results? A ﬁrst explanation for the different ﬁndings is that the natural experiment-based estimates in this paper are biased downward. As discussed earlier, while the passing standard change is surely exogenous to Texas, under certain conditions discussed above, selection into the comparison group may not be. If so, the difference-indifference approach may yield an incorrect estimate of the causal impact of the GED on earnings. We conducted an exhaustive set of sensitivity analyses to examine this issue, and none were supportive of a scenario whereby the 1997 affected score was systematically different from the 1995 affected score group. Nonetheless, the differing sample sizes between these two groups evidenced in Table 2 is less than comforting, especially since the other groups exhibit sample size stability over this period. Given that the comparability of the treatment and comparison groups is ultimately an untestable question, we now turn to a reconciliation of results under an assumption that our natural experiment results in this paper are correct. First, it could be the case that the research design employed by Tyler et al. (2000) failed to adequately control endogenous GED passing standard policies across states in a way that leads to an upward bias in their estimates. This potential criticism is tempered by the exhaustive set of sensitivity analyses conducted in that paper. Similar to the sensitivity analyses conducted in this current paper (including an examination of pretreatment earnings between the treatment and comparison groups), Tyler et al. found consistent support for the validity of their natural experiment. Nonetheless, the mechanism behind the passing standard change that occurred in Texas is more transparent than the historical passing standard differences across states used by Tyler et al. (2000), given that some might be more inclined to

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347

believe that the earlier estimates are biased upward and the natural experiment estimates in this paper are relatively unbiased. A second explanation has to do with the different samples used in Tyler et al. (2000) and in this paper. Estimates in Tyler et al. (2000) are based on a pooled sample of males and females, and their estimated GED effect is a weighted average of the effect for males and the effect for females. Meanwhile, our estimates are based on a sample containing only males. A scenario where there are heterogeneous signaling effects of the GED by gender, with positive effects for females and small or no effects for males, would explain the differences between our results and those of Tyler et al. (2000). Support for this possibility is found in Texas data similar to that used in this paper. Preliminary work we have done with samples of females from the Texas Schools Micro Data Panel indicate positive and statistically signiﬁcant GED effects based on natural experimental speciﬁcations similar to those used for males in this paper. Exploring the extent to which heterogeneous returns by gender can reconcile the different results across papers is an important area for future research. A third explanation concerns the signaling interpretation of the natural experiment estimates. As stated earlier, since the treatment and comparison groups are balanced on both the motivation to attempt the GED exams and the GED test scores, what is being estimated is not the total impact of the GED but rather the signaling value of this education credential. Prior to 1997, Texas, along with only three other states, had for many years the lowest passing standard allowable in the GED program.18 It could be that, with such a low passing standard, the GED is a relatively useless signal of productivity to Texas employers. Evidence that supports this interpretation comes from regression discontinuity estimates of the impact of the GED using data from Florida (Tyler, 2004). In the Florida study, examinees whose GED test scores placed them just a few points on either side of the passing standard were compared. Because they were so close in score, it is reasonable to interpret the results primarily as estimates of the signaling value of the GED in Florida. The estimated impact of the GED from this regression discontinuity design was about a 20% increase in earnings, very similar to the Tyler et al. (2000) results using national data. At the time of this study, Florida had the highest GED passing standard in the nation, except for Wisconsin and New Jersey. Thus, a possible inference is that having a high GED passing standard, as in Florida, results in a separating equilibrium that provides a meaningful signal to employers about the productivity of those possessing the signal. Meanwhile, if the passing standard is too low,

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such as might have been the case in Texas prior to 1997, the mean productivity of GED holders will not be sufﬁciently different from that of uncredentialed dropouts, resulting in a credential that conveys no useful information to employers. The regression discontinuity estimates in this paper lend some support to this interpretation of how results across the studies can be reconciled. As discussed earlier, our regression discontinuity results based on the 1997 sample show a statistically signiﬁcant ﬁfth year signaling effect of about an 8% increase in quarterly earnings. This compares to the 20% effect that Tyler (2004) measured in Florida over roughly the same period, using the same regression discontinuity design. Furthermore, our regression discontinuity results using the sample of 1995 test takers fail to ﬁnd evidence of a positive pre-passing-standard-hike GED signaling effect. However, these results should be used with caution since the necessary sample restriction used to identify a discontinuity yields a small, possibly nonrepresentative, subsample of test takers. These three sets of estimates, in combination with our natural experiment estimates, are consistent with a situation where: 1. the GED is a relatively strong signal of productivity in Florida because, for many years, this state had one of the highest GED passing standards, 2. the GED in Texas was for many years a very weak signal of productivity because of the low passing standard, and 3. while still not as valuable as in Florida, the GED signal in Texas in 2001 (the year in which ﬁfth year earnings for 1997 test takers were measured) was growing in reliability, and hence value, as the GED pool became increasingly populated with individuals who had passed under the higher standard and as employers adjusted to this fact. To the extent that this explanation is correct for our results, they suggest that policy makers should think carefully about the role that passing cutoffs on high-stake tests play in determining the composition of the differing pools of ‘‘passers’’ and ‘‘failers,’’ and how the composition of these pools affects the distribution of earnings. This is a lesson that others, including Betts and Costrell (2001), have effectively illustrated. If one goal of the GED program is to allow more motivated and skilled dropouts to distinguish themselves to employers, then the hike in passing standards mandated in 1997 may well have been one of the most important decisions the American Council on Education has made in recent years.

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8.2. Why Obtain a GED if no Effect on Earnings? If the estimates in this paper represent the causal impact of the GED on earnings, the question raised is: why would dropouts continue to acquire this credential if there is no economic beneﬁt? There are several potential and non-mutually exclusive answers to this question. We ﬁrst note that, to the extent that we are estimating only the signaling value of the credential, we may be underestimating the total potential impact on earnings, composed of the returns to the signaling value and to human capital component of the credential. Putting that caveat aside, however, one explanation is that there are noneconomic beneﬁts that dropouts derive from acquiring a GED. Anecdotally, GED preparation providers report that many of the ‘‘graduates’’ of their programs report that studying for and acquiring a GED is the ﬁrst thing that they have accomplished on their own, and they proudly bring family to GED graduation ceremonies. Thus, feelings of pride and accomplishment could bring dropouts to the GED program even if there were no economic payoffs to the credential. A second explanation for why we might see dropouts pursuing the credential is that, at least in terms of direct costs, it is a relatively cheap credential. Direct costs for taking the GED exams can be as low as $35 and even free in some cases. Also, GED preparation classes are often subsidized by the government and therefore of very low cost to participants. Furthermore, if the dropout attempting to obtain a GED is unemployed or out of the labor force, then there are no opportunity costs from lost employment to participate in GED preparation classes. Less clear are the psychic costs dropouts with a history of poor academic performance incur as they sit in GED preparation classes and subsequently take examinations that take up to 734 h. Nonetheless, government subsidization of GED preparation courses appears to make for very low direct costs associated with this credential.

8.3. Conclusions Each year, some three-quarters of 1 million individuals in this nation take the GED exams in the hope of passing and acquiring their GED certiﬁcate. Our results suggest that the signaling returns to this credential for male dropouts in Texas are substantially less than what has been found in other settings since we ﬁnd essentially no returns to the GED signal in Texas. One reason for this may be that the low GED passing threshold that existed in Texas for so long resulted in a credential that conveyed little information to

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employers. This explanation is supported by regression discontinuity results in this paper in comparison with results based on a similar regression discontinuity design using data from Florida, a state with a historically high GED passing standard. This paper has attempted to use a natural experiment in Texas to provide unbiased estimates of the return to the GED credential. The nature of the experiment provides us with estimates of the signaling value of the credential, net of any human capital effects that studying for the GED might generate. While it is important and valuable to understand the causal effects of programs such as the GED, some perspective is in order here. To provide this perspective, we ask the following question: what if the ‘‘total’’ GED effect (human capital plus signaling) was reasonably well estimated by the raw differences between GED examinees who passed the exams and GED examinees who failed? Based on Fig. 2, this difference in Texas (which is similar to what one would see in Florida from Tyler’s earlier work) is about a 25% return. By any measure, this is a large economic ‘‘return.’’ Even so, in our Texas data, this translates into annual earnings of only about $12,000, instead of $10,000, ﬁve years after the GED attempt. Thus, our examination of the GED credential in Texas mirrors other research on this credential in yet another important way. Namely, even if one thought that the total return to a GED was on the order of 25%, obtaining the GED as a ‘‘terminal’’ education credential is no route out of poverty. This suggests that the direction of further GED research should be in the areas of (1) how effective is this credential as an alternative route to postsecondary education and (2) does the very presence of the GED program provide some inducement to leave school for students who are on the margin of dropping out?

NOTES 1. GED candidates are not required to take all of the ﬁve exams in one sitting. 2. The direct cost associated with obtaining the GED, the GED test fee, varies by testing center but is quite low. The direct cost of taking the GED exam in Texas can be as low as $35 and may even be free in some cases. 3. Here, we assume that medium-ability individuals still attempt the GED even after the passing standard increase. As with the y3 workers in both the pre- and post1997 period, this requires the assumption that either the GED outcome is uncertain and/or ability is imperfectly known. Furthermore, we assume that the effort and study time does not change for a given ability or score group when there is a passing standard change.

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4. For notational simplicity, we ignore the individual subscript i in the presentation of the conditional earnings. 5. Of course, u could be negatively correlated with y and hence with GED acquisition. This ﬁts with the ﬁndings of Heckman and Rubinstein (2001), who ﬁnd that GED holders have lower noncognitive skills than do uncredentialed dropouts. 6. Firms are unable to determine whether GED holders who obtained the credential in the pre-period would also pass in the post-period. Furthermore, we assume employers do not know whether the person attempted the GED in the pre- or post-period. 7. We say ‘‘last attempted,’’ because upon failing the GED exams, a dropout can, with certain minimal restrictions, retake the GED battery. We classify individuals into last-attempt years based on GED data as of December 31, 2000. 8. Of course, these two groups have similar test scores by construction. 9. Pretest experience is measured as the number of quarters in the six years prior to testing in which nonzero earnings are recorded. Pretest earnings is a vector of six variables representing the annual earnings (sum of the year’s four quarters of earnings) in each of the six years prior to testing. 10. A 1995 cutoff can be constructed using individuals who have at least one exam score below 40. Using just these individuals, a regression discontinuity would be examined around a mean score of 45. The problem with using this 1995 passing standard to examine a potential regression discontinuity is that there are relatively few individuals who have at least one score below 40 and yet have a mean score of at least 45. Nonetheless, we discuss results from this regression discontinuity design later. 11. Tyler et al.(2000) also ﬁnd that GED effects grow over time and are often negligible in the ﬁrst years after the attempt. 12. We note that, while previous work suggests that GED holders only accumulate 0.4 mean total years of postsecondary education (Murnane et al., 2000), this same work shows that up to 30% of the GED holders in the data earned at least one college credit. 13. Note that the estimates using the All Fail group appear more sensitive to adding controls for age, schooling and ethnicity than the estimates utilizing the All Pass group as the comparison group. This is not very surprising, given that we also observed somewhat greater within-group pre–post changes for the All Fail group relative to the All Pass group. 14. These estimates use the all-passer group for the second difference. Estimates using the all-failer group for the second difference are similar. 15. Speciﬁcally, the restrictions that the test taker only attempted the GED once, in 1995 or 1997, covers the period from January 1, 1990, the earliest year our data on GED test takers cover, to December 31, 2000, the latest date our GED test score data span. 16. In June 1998, Florida GED candidates had to score a minimum of 42 and a mean of 45 to be awarded a GED. In July 1999, the minimum allowable score was raised to 44, and in July 2000, the minimum allowable score was 45, giving Florida the highest GED passing standards in the nation. 17. In analysis not shown here, we examined results for white, 16- to 21-year-olds, the exact group used in Tyler et al. (2000). Estimates based on this more reﬁned sample also show no evidence of a GED effect on earnings.

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18. The other states that had a similarly low passing standard pre-1997 were Louisiana, Mississippi, and Nebraska.

ACKNOWLEDGMENTS We would like to thank Jean Kimmel, Jeffrey Kling, and Richard Murnane, and seminar participants at Concordia University, Federal Reserve Bank of St. Louis, University of Texas at Arlington, UT Dallas, 2004 SOLE annual meeting in San Antonio, and 2004 WEA annual meeting in Vancouver, Canada, for their helpful comments.

REFERENCES Baldwin, J. (1990). GED candidates: A decade of change (1). Washington, D.C.: GED Testing Service of the American Council on Education. Betts, J. R., & Costrell, R. M. (2001). Incentives and equity under standards-based reform. In: D. Ravitch (Ed.), Brookings papers on educational policy 2001 (pp. 9–74). Washington, D.C.: The Brookings Institution. Cameron, S. V., & Heckman, J. J. (1993). The nonequivalence of high school equivalents. Journal of Labor Economics, 11(1), 1–47. Heckman, J. J., Hsse, J., & Rubinstein, Y. (2000). The GED is a ‘‘Mixed Signal’’: The effect of cognitive and non-cognitive skills on human capital and labor market outcomes. Unpublished University of Chicago manuscript. Heckman, J. J., & Rubinstein, Y. (2001). The importance of noncognitive skills: Lessons from the GED testing program. The American Economic Review, 91(2), 145–149. Murnane, R. J., Willett, J. B., & Boudett, K. P. (1997). Does acquisition of a GED lead to more training, post-secondary education, and military service for school dropouts? Industrial & Labor Relations Review, 51(1), 100–116. Murnane, R. J., Willett, J. B., & Tyler, J. H. (2000). Who beneﬁts from a GED? Evidence from high school and beyond. The Review of Economics and Statistics, 82(1), 23–37. Spence, M. (1973). Job market signaling. The Quarterly Journal of Economics, 87(3), 355–374. Stiglitz, J. E. (1975). The theory of ‘screening,’ education, and the distribution of income. American Economic Review, 65(3), 283–300. Tyler, J. H. (2004). What is the value of the GED to dropouts who pursue the credential? Industrial & Labor Relations Review, 57(4), 587–598. Tyler, J. H., Murnane, R. J., & Willett, J. B. (2000). Estimating the labor market signaling value of the GED. The Quarterly Journal of Economics, 115(2), 431–468.

OCCUPATIONAL GENDER COMPOSITION AND THE GENDER WAGE GAP IN SWEDEN Jorgen Hansen and Roger Wahlberg ABSTRACT This paper examines the relationship between the gender wage gap and occupational gender segregation in Sweden. The results show that the gender wage gap varies substantially across occupations. It is small in male-dominated occupations and relatively large in female-dominated occupations. Further, as much as 30% of the overall gender wage gap in Sweden can be attributed to occupational segregation by gender. Finally, the return to work experience for women is substantially higher in maledominated occupations than in female-dominated occupations, suggesting that the cost for work interruptions are lower in female-dominated occupations than in male-dominated occupations. This ﬁnding is consistent with the hypothesis that women choose occupations in which the penalty for work interruptions is low. Thus, occupational segregation may arise because of gender differences in preferences for occupational characteristics and not necessarily because of discriminatory practices by employers.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 353–369 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28011-8

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1. INTRODUCTION In the labor economics literature there exists a general understanding that occupational segregation is present and that women are gathered disproportionally in occupations with lower earnings. Consequently, occupational segregation by gender is one of the reasons for the observed gender wage gap. However, there is no agreement on why occupational segregation by gender arises. One possibility is that women are gathered disproportionally in occupations with low earnings because they are prevented by employers from working in high-wage occupations. Alternatively, segregation by gender may be an outcome of a self-sorting mechanism. For example, if low-wage occupations have more nonwage beneﬁts than high-wage occupations and if women have a higher valuation of such beneﬁts than men, we would expect to ﬁnd more women than men in low-wage occupations. Another possibility for a higher concentration of women in low-wage occupations is that the cost of work interruptions may be lower in such occupations and women may anticipate more intermittent labor force participation over the life cycle than men. Although it is difﬁcult to empirically determine why occupational gender segregation exists, it is still important to assess the impact of this labor market phenomenon on wages and wage differences between men and women. Recently, a number of studies devoted to estimating the impact of the density of females (FEM) in certain occupations on individual wages have appeared, see for instance Bayard, Hellerstein, Neumark, and Troske (2003), Macpherson and Hirsch (1995), Sorensen (1990, 1989), England, Farkas, Kilbourne, and Dou (1988), and Johnson and Solon (1986) for applications on U.S. data, Baker and Fortin (2001) using Canadian data, Miller (1987) using data from the U.K., and le Grand (1991) using Swedish data. While the results from these studies vary, most suggest a negative relationship between the proportion of females in a given occupation and wages in that occupation.1 The role of occupational sex segregation for the gender wage gap has also been examined by Meyersson Milgrom, Petersen, and Snartland (2001) who report that it explains most of the observed gender wage gap in Sweden and also that it explains more of the gender wage gap in Sweden than in the United States. As noted by Blau and Kahn (1996), although the gender wage gap in Sweden is small by international standards, gender occupational inequality appears to be relatively high. Thus, occupational gender segregation may explain more of the gender wage gap in Sweden than elsewhere. A possible reason for higher occupational (and industrial)

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segregation in Sweden compared to other countries is the relatively high incidence of part-time work among women in Sweden (Blau & Kahn, 1996).2 A potential problem with many of the previous studies is the assumption that occupational attainment is exogenous.3 As argued by Macpherson and Hirsch (1995), there exist at least two reasons for why the exogeneity assumption may be false. First, if men and women with higher unmeasured skills (captured by the error term in the wage equation) are more likely to be sorted into male jobs and those with lower skills into female jobs, then the exogeneity assumption will obviously be violated.4 Second, the error term may also capture unobserved taste differences among workers. For instance, some female workers may expect future work interruptions due to childbearing and will therefore prefer part-time jobs or jobs where the wage ‘‘penalty’’ for work interruptions is low. In this case, the assumption of no correlation between the density of females in an occupation and the error term may also be violated. To address the endogeneity of occupational choice, Macpherson and Hirsch (1995) use longitudinal data and apply a ﬁxed-effects estimator.5 While this approach differences out any time-invariant unobserved characteristics, such as skills and preferences, it achieves identiﬁcation of the effect of occupational segregation on wages from workers that change their occupational status over time. However, few workers change their occupational status over time meaning that only a small sample of occupational movers identiﬁes the effect. Moreover, those who change their occupational status over time may also comprise a nonrepresentative portion of the sample (e.g., they may be younger and clustered in low-skill jobs). Instead of using a ﬁxed-effects estimator to address the possible endogeneity problem with occupational segregation, we use a generalized version of the standard Heckman selection model. We consider three occupational categories, male-dominated occupations (occupations with less than 33% women), intermediate occupations (occupations where the proportion of women varies between 33% and 66%) and female-dominated occupations (occupations with more than 66% females), and use an ordered probit model in the ﬁrst stage to estimate the probability of choosing a certain occupation. In the second stage, we include selection correction terms, obtained using estimates from the ﬁrst stage, along with observable characteristics in conditional wage equations. To achieve identiﬁcation, we need at least one observable characteristic that determines occupational choices but not wages. In this paper, we use age as such as a characteristic.6 The paper is organized as follows. The following section describes the data and sample used in this paper. The empirical speciﬁcation is presented in Section 3 while the results are presented in Section 4. A decomposition of

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the gender wage gap is presented in Section 5. The subsequent section discusses wage differences between public and private sector workers. A ﬁnal section contains a summary of the paper.

2. DATA The data is drawn from the 1997 Swedish Household Income Survey (HINK), matched with information on occupational segregation from the 1996 Labor Force Survey. Both of these data sources are administered by Statistics Sweden. HINK provides information on labor market activities and incomes for a random sample of Swedish households, and approximately 7,000 households are interviewed each year. We limit the analysis to individuals aged 18–65 and exclude self-employed workers. After these selections we are left with 3,995 females and 3,625 males. An interesting, and relatively unique, feature with this data set is the possibility of matching individual records with wage information provided by employers. The hourly wage rate corresponds to a worker’s contracted wage and does not suffer from the usual measurement error that is common in self-reported wages. The wage information is available for all workers in the public sector as well as for a majority of workers in the private sector.7 To construct the FEM-variable, which measures the proportion of workers who are women in a given occupation, we used information from the 1996 Labor Force Survey. The data provides information on individuals’ occupation at a two-digit level, and we were able to distinguish between 38 different occupations in the data.8 We split occupations into three groups. Occupations with less than 33% women are deﬁned as maledominated occupations while occupations with less than 33% men are deﬁned as female-dominated occupations. The remaining occupations form the integrated occupations category. In Table 1 we present descriptive statistics for females and males by occupational category. For women, the average wage is higher in maledominated occupations than in female-dominated occupations, despite the fact that women in the latter group have, on average, acquired more education. We also observe a signiﬁcant difference in the proportion of women working full-time across occupations. Among females in maledominated occupations, 77% work full-time (more than 1,500 h per year). In female-dominated occupations, this ﬁgure is only 48%. This pattern cannot be observed for male workers, conﬁrming the traditional view that male labor supply is less ﬂexible than female labor supply. Table 1 also shows that

357

Occupational Gender Composition and the Gender Wage Gap in Sweden Table 1. Characteristics

Descriptive Statistics by Occupational Type. Male-Dominated Occupation Mean

Std. dev

Wage/hour (1997 SEK) High school College/University Work experience Living in urban areas Living in medium-sized cities Single Working full-time Public sector No. of children Age No. of observations

107.7 0.53 0.13 18.9 0.31 0.37 0.18 0.77 0.16 0.8 40.3

28.4 – – 10.1 – – – – – 1.0 10.7

Wage/hour (1997 SEK) High school College/University Work experience Living in urban areas Living in medium-sized cities Single Working full-time Public sector No. of children Age No. of observations

111.0 0.65 0.08 23.2 0.27 0.41 0.14 0.76 0.16 0.8 41.8

332 32.2 – – 12.2 – – – – – 1.1 11.0 2,073

Intermediate Occupation Mean

Std. dev

Female-Dominated Occupation Mean

Std. dev

Women 106.1 31.6 0.60 – 0.16 – 21.3 10.6 0.39 – 0.37 – 0.15 – 0.67 – 0.45 – 0.7 1.0 43.1 10.8 1,650

99.3 0.67 0.20 20.4 0.29 0.39 0.15 0.48 0.89 0.9 42.5

22.2 – – 10.1 – – – – – 1.1 10.8

Men 124.8 49.2 0.58 – 0.24 – 22.5 11.9 0.43 – 0.37 – 0.13 – 0.82 – 0.23 – 0.8 1.0 42.8 10.8 1,155

121.5 0.42 0.50 21.1 0.34 0.40 0.19 0.78 0.83 0.8 43.1

2,013 46.9 – – 11.3 – – – – – 1.0 11.1 397

males in female-dominated occupations are highly educated as 50% has a college or a university degree, compared to only 8% in male-dominated occupations. Finally, public sector employment appears to be strongly correlated with the concentration of women in a given occupation. For instance, 89% of women in female-dominated occupations work in the public sector while this ﬁgure is only 16% in male-dominated occupations.

3. ECONOMETRIC SPECIFICATION As argued in the introduction, it is reasonable to assume that FEM (the proportion of women in a given occupation) is endogenously determined.

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The approach that we adopt in this paper, which attempts to control for this misspeciﬁcation, is to estimate a version of Heckman’s two-step estimator. In the ﬁrst stage, we estimate an ordered probit model that determines the probability of choosing a speciﬁc type of occupation (that is, maledominated, female-dominated, or an intermediate occupation). The parameters from the ordered probit are then used to form selection correction terms (similar to Heckman’s lambdas) that are added to the log-wage regression equation in the second stage. Formally, the model can be speciﬁed as follows: FEM nij ¼ gj Z ij þ Zij FEM ij ¼ k if

mk1 oFEM nij mk

where k ¼ 0, 1, 2, and mk1 omk and where fðm^ k1 g^ j Z ij Þ fðm^ k g^ j Z ij Þ l^ ijk ¼ Fðm^ k g^ j Z ij Þ Fðm^ k1 g^ j Z ij Þ and ln wijk ¼ yjk þ bjk X ijk þ djk l^ ijk þ ijk with ijk i:i:d:Nð0; s2 Þ Zij i:i:d:Nð0; 1Þ where index i denotes individuals, index k denotes occupation, and index j denotes gender ( j=w or m). Further, f and F are the standard normal probability density and distribution functions, respectively. The m’s are unknown parameters to be estimated jointly with the g’s. It is further assumed that ijk and Zij are correlated with correlation coefﬁcient rkj . As is the case in a standard Heckman model, the standard errors of the estimates in the log-wage regressions need to be adjusted.

4. EMPIRICAL RESULTS Table 2 shows results from the ordered probit speciﬁcation. The entries in the ﬁrst two columns present the results for males, while the last two columns show the results for females. The estimated coefﬁcients indicate that

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Occupational Gender Composition and the Gender Wage Gap in Sweden Table 2.

Ordered Probit Estimates.

Variables

High school College/University Experience Experience2/100 Living in urban areas Living in medium-sized cities Single Working full-time Public sector No. of children Age m1 m2 N Log-likelihood

Males

Females

Estimate

Std. error

Estimate

Std. error

0.182 0.669 0.039 0.004 0.276 0.100 0.006 0.149 0.878 0.044 0.042 1.482 2.755

0.054 0.075 0.009 0.015 0.054 0.052 0.063 0.052 0.048 0.023 0.006 0.161 0.165

0.320 0.258 0.012 0.031 0.038 0.036 0.092 0.361 1.380 0.022 0.006 1.152 0.624

0.050 0.067 0.009 0.018 0.051 0.049 0.055 0.042 0.045 0.022 0.004 0.129 0.129

3,625 2,942

3,995 2,989

Notes: The dependent variable takes on three values: 0 for male-dominated occupations, 1 for intermediate occupations, and 2 for female-dominated occupations.

education and occupational choices are strongly correlated and that the probability of working in a female-dominated occupation is higher for those with higher education. This result holds for both males and females. Men living in urban areas have a higher probability of working in femaledominated occupations than other men. For women, region of residence is not signiﬁcantly related to occupational choice. Further, marital status does not have a signiﬁcant impact on occupational choice among men but married women are more likely work in female-dominated occupations. The entries in Table 2 also suggest that full-time work is more common in male-dominated occupations than in female-dominated occupations. Moreover, occupations with high proportions of women are mainly found in the public sector. The estimates associated with the public sector indicator suggest a strong positive correlation between public sector jobs and female-dominated occupations, both for men and women. Finally, the number of preschool-aged children in the household does not have a signiﬁcant effect on occupational choice. The estimates associated with age, the identifying variable, on occupational choice suggest that older men are more likely to work in femaledominated occupations than younger men and that the opposite holds for women. The associated standard errors indicate that age has a signiﬁcant

360

JORGEN HANSEN AND ROGER WAHLBERG Table 3.

Variables

Wage Equation Estimates for Women, by Occupation. Male-Dominated Occupation

Intermediate Occupation

Female-Dominated Occupation

Estimate Std. error Estimate Std. error Estimate Std. error Constant 4.178 High school 0.017 College/University 0.245 Experience 0.017 Experience2/100 0.030 Living in urban areas 0.114 Living in medium-sized cities 0.038 Single 0.082 Working full-time 0.082 Public sector 0.303 No. of children 0.010 Lambda 0.156 Adj. R2 s^ p-value for agea

0.670 0.111 0.090 0.008 0.016 0.032 0.030 0.041 0.126 0.506 0.016 0.432

0.251 0.195 0.251

4.344 0.079 0.312 0.010 0.016 0.081 0.002 0.037 0.094 0.003 0.026 0.107

0.033 0.055 0.044 0.004 0.008 0.015 0.015 0.021 0.060 0.226 0.008 0.212

0.325 0.199 0.175

3.306 0.225 0.397 0.003 0.003 0.032 0.019 0.056 0.134 0.622 0.022 0.781

1.133 0.033 0.026 0.003 0.005 0.006 0.005 0.003 0.033 0.100 0.003 0.101

0.305 0.157 0.788

Note: The dependent variable equals the logarithm of hourly wage rates. a p-value when age was included in the wage equations.

effect on occupational choice for men ( p-value less than 0.0001) and that it is borderline signiﬁcant for women ( p-value equals 0.13). Table 3 contains the wage estimates for females. The results in the ﬁrst two columns refer to male-dominated occupations, while columns three and four show the results for integrated occupations and the last two columns show estimates for females working in female-dominated occupations. For all occupational categories, the estimates indicate a signiﬁcant wage premium for having a college/university degree. Completion of high school is associated with higher wages in female-dominated occupations but not in other occupations. It is reasonable to assume that workers who expect intermittent labor force participation will choose occupations where the wage penalty associated with being out of the labor force is lowest (see for instance Polachek, 1981, 1985, 2004). Such occupations will have relatively high initial wages and little wage growth. If women anticipate that they will be more absent from the labor market than men, they may therefore choose occupations with ﬂatter experience-earnings proﬁles. As a consequence, we would observe occupational segregation in the labor market. Whether

361

Occupational Gender Composition and the Gender Wage Gap in Sweden Table 4. Variables

Wage Equation Estimates for Men, by Occupation. Male-Dominated Occupation

Intermediate Occupation

Female-Dominated Occupation

Estimate Std. error Estimate Std. error Estimate Std. error Constant 4.183 High school 0.042 College/University 0.196 Experience 0.010 Experience2/100 0.014 Living in urban areas 0.015 Living in medium-sized cities 0.009 Single 0.011 Working full-time 0.163 Public sector 0.217 No. of children 0.010 Lambda 0.350 Adj. R2 s^ p-value for agea

0.044 0.015 0.050 0.002 0.004 0.019 0.014 0.018 0.015 0.048 0.007 0.081

0.266 0.206 0.176

4.678 0.001 0.032 0.015 0.021 0.020 0.025 0.052 0.294 0.446 0.019 0.398

0.111 0.033 0.077 0.004 0.008 0.038 0.030 0.034 0.031 0.076 0.013 0.091

0.308 0.271 0.579

5.115 0.020 0.090 0.014 0.015 0.035 0.035 0.038 0.130 0.297 0.020 0.349

0.284 0.058 0.099 0.004 0.010 0.043 0.034 0.037 0.035 0.093 0.015 0.121

0.374 0.246 0.102

Note: The dependent variable equals the logarithm of hourly wage rates. a p-value when age was included in the wage equations.

the experience-earnings proﬁles are indeed ﬂatter in female-dominated occupations is an empirical matter. The results in Table 3 lends some support for this hypothesis since the coefﬁcient for work experience is positive and signiﬁcant in male-dominated occupations while it is small and not statistically signiﬁcant in female-dominated occupations. Table 4 contains the wage estimates for males. The results regarding the effects of human capital imply a positive and signiﬁcant wage effect of a college/university degree in male-dominated occupations but not in other occupations. Further, the return to work experience is higher in female-dominated and intermediate occupations than in male-dominated occupations. To test if our choice of age as an instrument is valid, we report the p-value associated with the age variable when it was included in the wage equation. For women, the p-values range from 0.175 in intermediate occupations to 0.788 in female-dominated occupations. For men, the p-values range from 0.102 in female-dominated occupations to 0.579 in intermediate occupations. The relatively low p-value for men in female-dominated occupations may raise some concern about the validity of using age as an instrument in

362

JORGEN HANSEN AND ROGER WAHLBERG Table 5.

Occupation

Observed, Explained, and Unexplained Gender Wage Gaps. Observed Gap

Explained Gap

Male dominated Intermediate Female dominated

0.026 0.136 0.167

OLS 0.002 0.087 0.119

Male dominated Intermediate Female dominated

0.026 0.136 0.167

Selection corrected 0.009 0.145 0.086

Unexplained Gap

0.024 0.049 0.048 0.016 0.008 0.081

Notes: The explained wage gap is calculated as: b bmk ðX mk X wk Þ where X mk is a vector b is a vector of containing average values of observable characteristics in occupation k, and b mk estimated coefﬁcients for males in occupation k.

this context. Since the results from selection model depend on the exclusion restriction for identiﬁcation, we will complement the selection model results on the gender wage gap with results from OLS regressions. In Table 5, we present observed, explained, and unexplained gender wage differentials in the three occupational groups. The top panel shows results using OLS while the lower panel shows results using the selection model. The observed gender wage gap is smallest (2.6%) in male-dominated occupations and largest in female-dominated occupations (16.7%). As is shown in the last column, much of the observed wage difference in maledominated occupations can be attributed to differences in unobserved factors (92% using OLS and 61% using the selection model). For femaledominated occupations, more of the gender wage difference can be attributed to differences in observable characteristics, such as accumulated human capital and full-time work (29% using OLS and 49% using the selection model). Although there are differences between the results from OLS and the selection model, both methods indicate substantial heterogeneity in the gender wage differentials across occupational groups. This is an observation that, surprisingly, has received little attention in the literature. Further, regardless of estimation method, the unexplained portion of the gender wage gap is largest in male-dominated occupations. Given the strong correlation between female-dominated occupations and public sector, this result suggests that wage differences that cannot be justiﬁed based on differences in human capital and other observable characteristics are more common in the private sector than in the public sector.

Occupational Gender Composition and the Gender Wage Gap in Sweden

363

5. DECOMPOSING THE GENDER WAGE GAP Using our approach to estimate the gender wage gap enables us to decompose this gap into three mutually exclusive parts: differences in endowments, differences in occupational structure, and differences in rewards to endowments. Formally, this can be written as: X w b b b ^ ln wm ln ww ¼ ðpm k pk Þfywk þ bwk X wk þ dwk lwk g k2K

þ

X

b pm k bmk ðX mk X wk Þ

k2K

þ

X

b b ^ b b ^ pm k fðymk þ dmk lmk Þ ðywk þ dwk lwk Þg

k2K

þ

X

b b pm k X wk ðbmk bwk Þ

k2K

where the ﬁrst term on the right hand side represents the part of the average w wage gap that is due to differences in occupational structure (pm k pk ). The second term shows the part of the gap that is due to differences in observed endowments (X mk X wk ). Finally, the last two components correspond to the portion of the gap that is due to unexplained factors (such as differences in unobserved endowments and differences in rewards to endowments). The p’s measure the proportion of workers (men or women) in each occupation k, and there is a total of K occupations. The results of this decomposition are reported in Table 6 for three different speciﬁcations. In the ﬁrst column, we show the results from a model (estimated by OLS), which does not allow occupational structure to affect wages. In this case, 60% of the observed (log) wage gap between men and women can be attributed to differences in endowments (primarily education, experience, full-time work, and public sector) and 40% of the gap is left unexplained. The entries in the second column are obtained by estimating separate wage regressions for the three occupational groups. When controlling for occupational segregation, the unexplained wage gap drops to 32%. Further, 29% of the observed wage difference is due to occupational segregation. Finally, the entries in column three show results obtained using the selection model. While the proportion of the wage gap due to occupational segregation is unchanged, the unexplained wage gap drops to 14%. To summarize, we ﬁnd that approximately a third of the gender wage difference can be attributed to occupational differences and once we control for such differences, the unexplained portion of the gender wage gap drops.

364

JORGEN HANSEN AND ROGER WAHLBERG Table 6.

Decomposing the Gender Wage Gap. Model Speciﬁcation

Observed log wage gap Gap due to differences in observed endowments Gap due to occupational segregation Gap due to unobserved factors

(1)

(2)

(3)

0.107 0.064 (60%) – 0.043 (40%)

0.107 0.042 (39%) 0.031 (29%) 0.034 (32%)

0.107 0.061 (57%) 0.031 (29%) 0.015 (14%)

Notes: The different speciﬁcations are as follow: (1) OLS without controls for occupational segregation; (2) OLS with controls for occupational segregation; and (3) selection corrected speciﬁcation using age as an instrument.

However, this does not mean that the extent of labor market discrimination against women is estimated to be lower in a speciﬁcation that controls for occupational segregation since such segregation may itself be an outcome of discriminatory behavior. A second result suggests that wage growth is substantially larger in male-dominated occupations than in female-dominated occupations, where the return to work experience is small and not signiﬁcantly different from zero. While wage growth is smaller in femaledominated occupations, so is the cost of being absent from the labor market. Thus, this ﬁnding is consistent with the hypothesis that women anticipate intermittent labor force participation to a greater extent than men, and therefore choose occupations where the cost of work interruptions is low. As mentioned above, it is possible that our ﬁnding of differences in wage growth across occupations is sensitive toward identiﬁcation problems in the selection model. To explore this issue, we present estimates on the return to work experience using OLS, in addition to those obtained using the selection model, in Table 7. The OLS estimates suggest that the effect of work experience on wages for women is indeed higher in male-dominated occupations than in female-dominated occupations, although the difference is smaller than the one obtained using the selection model.

6. PUBLIC VERSUS PRIVATE SECTOR Since the data indicate that female-dominated occupations are more common in the public sector than in the private sector, and since public sector workers are overrepresented in our sample, it may be informative to consider gender wage differences across sectors instead of across different occupations. We consider results from OLS and from a selection model that

365

Occupational Gender Composition and the Gender Wage Gap in Sweden Table 7.

Returns to Work Experience for Women in Different Occupations. Model Speciﬁcation (1)

(2)

Male-dominated occupations Experience Experience2/100

0.014 (0.004) 0.026 (0.010)

0.017 (0.008) 0.030 (0.016)

Female-dominated occupations Experience Experience2/100

0.012 (0.001) 0.019 (0.003)

0.003 (0.003) 0.003 (0.005)

Notes: The different speciﬁcations are as follow: (1) OLS and (2) selection corrected speciﬁcation using age as an instrument.

Table 8.

Decomposing the Gender Wage Gap in Public and Private Sectors.

Observed log wage gap Gap due to differences in observed endowments Gap due to occupational segregation Gap due to unobserved factors

Public Sector

Private Sector

0.160 0.086 (54%) 0.010 (6%) 0.063 (40%)

0.044 0.012 (27%) 0.002 (5%) 0.030 (68%)

Note: The entries are obtained using a selection corrected speciﬁcation with age as an instrument.

attempts to control for nonrandom selection into public and private sectors using a methodology similar to that presented above. For the gender wage gap, Table 8 shows the decomposition of the gender wage gap in the public and private sector, respectively. The observed gender wage gap is much larger in public sector jobs (difference in log wages is 0.160) than in private sector jobs (difference in log wages is 0.044). This is consistent with the ﬁnding above that the observed wage gap is larger in female-dominated occupations (difference in log wages is 0.167) than in male-dominated occupations (difference in log wages is 0.026). Once we condition on sector, occupational segregation explains little of the gender wage difference. Given the correlation between sector and occupational gender segregation, this is not surprising. Finally, a larger fraction of the wage difference can be attributed to differences in unobserved factors in private sector jobs (68%) than in public sector jobs (40%). In Table 9, we present the estimated returns to work experience for women in the public and private sector, respectively. We present estimates

366 Table 9.

JORGEN HANSEN AND ROGER WAHLBERG Returns to Work Experience for Women in Public and Private Sectors. Model Speciﬁcation (1)

(2)

Public sector Experience Experience2/100

0.009 (0.001) 0.011 (0.003)

0.007 (0.012) 0.008 (0.017)

Private sector Experience Experience2/100

0.017 (0.002) 0.033 (0.005)

0.016 (0.004) 0.030 (0.010)

Notes: The different speciﬁcations are as follow: (1) OLS and (2) selection corrected speciﬁcation using age as an instrument.

using OLS and the selection corrected speciﬁcation. For the public sector, the effect of work experience is small and not signiﬁcantly different from zero. This is true regardless of estimation method. However, in the private sector, work experience signiﬁcantly increase wages, and the magnitude is similar to that found for male-dominated occupations above. Again, both OLS and the selection model yield similar estimates. Although the results on differences in wage growth across occupations above were not conclusive, these results support the ﬁnding of large differences in experience-earnings proﬁles for women across occupations.

7. CONCLUSIONS This paper studies the effects of occupational segregation on wages and on the gender wage gap in Sweden. Speciﬁcally, we studied how the gender wage gap varies across different occupations. The data showed that the gap is smallest in male-dominated occupations and largest in female-dominated occupations. Based on estimated wage equations, we decomposed the observed wage gap into explained (by differences in endowments) and unexplained parts. The results suggested that the unexplained gap is largest in male-dominated occupations. Since male-dominated occupations are generally found in the private sector, this suggests that wage differences that cannot be justiﬁed based on differences in human capital and other observable characteristics are more common in the private sector than in the public sector. Our results also showed that the experience-earnings proﬁle for women in male-dominated occupations is steeper than the proﬁle in female-dominated

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occupations. This difference in wage growth suggests that a work interruption is more costly in male-dominated occupations than in femaledominated occupations. Thus, occupational gender segregation may arise because of gender differences in anticipated work interruptions over the life cycle, as well as in gender differences in preferences for other occupational characteristics, and not because of discriminatory practices by employers. This result is similar to the main ﬁndings in Macpherson and Hirsch (1995) who argue that occupational segregation by gender exists because men and women have different valuations of certain occupational characteristics. Finally, we used our model to investigate the fraction of the observed wage gap that can be attributed to occupational segregation. The results indicated that around 30% of the gap can be attributed to segregation in the labor market. This ﬁgure is lower than that reported by Meyersson Milgrom et al. (2001) for Sweden and higher than that reported by Macpherson and Hirsch (1995) for the U.S. Ignoring occupational segregation produces signiﬁcantly higher estimates of the unexplained gender wage gap. Hence, it is important to include information on the occupational structure of the labor market when estimating the size of the unexplained wage gap. However, the importance of occupational gender segregation for the gender wage gap is directly related to the extent of such occupational segregation. Since the Swedish labor market appears to be more segregated than labor markets in other countries (see e.g., Blau & Kahn, 1996), the role of occupational gender segregation in explaining the gender wage gap may be greater in Sweden than elsewhere.

NOTES 1. A problem which is neglected in many of these studies (i.e., in Bayard et al., 2003; Sorensen, 1990; le Grand, 1991; Miller, 1987; Johnson & Solon, 1986) is the fact that the standard errors from OLS are biased since the error term is correlated across workers within occupations, see Moulton (1990). It is therefore difﬁcult to assess the signiﬁcance of the results in these studies. 2. A number of policies, such as separate taxation of spouses, generous maternity/ parental leave policies, subsidized public day care and extended employment security, may explain why part-time employment rates among women are higher in Sweden than elsewhere. Differences in preferences for work between women in Sweden and women in other countries may also explain why part-time employment is relatively common in Sweden. 3. Exceptions include Macpherson and Hirsch (1995), Sorensen (1989), and England et al. (1988). 4. Note that this kind of sorting may result from employer discrimination. 5. England et al. (1988) apply a similar strategy on a sample taken from the National Longitudinal Survey.

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6. Using age as an instrument may be valid since there is nothing in human capital theory that predicts age to be a determinant of wages, once controls for actual work experience are included in the wage equation. It should also be noted that, because of functional form assumptions, the parameters of the system of equations are identiﬁed even without any exclusion restrictions. 7. Since wages are not available for all private sector workers, our sample contains a higher proportion of public sector workers than what is observed in the population. To test if our results were sensitive toward this, we estimated models with and without sample weights. The use of sample weights had very little impact on our results. 8. Details about types of occupations and the proportion of women in each occupation are provided in Table A1 in appendix.

REFERENCES Baker, M., & Fortin, N. M. (2001). Occupational gender composition and wages in Canada: 1987–1988. Canadian Journal of Economics, 34(2), 345–376. Bayard, L., Hellerstein, J., Neumark, D., & Troske, K. (2003). New evidence on sex segregation and sex differences in wages from matched employee-employer data. Journal of Labor Economics, 21(4), 887–922. Blau, F. D., & Kahn, L. (1996). Wage structure and gender earnings differentials: An international comparison. Economica, 63(Suppl.), S29–S62. England, P., Farkas, G., Kilbourne, B. S., & Dou, T. (1988). Explaining occupational sex segregation and wages: Findings from a model with ﬁxed effects. American Sociological Review, 53, 544–558. Johnson, G., & Solon, G. (1986). Estimates of the direct effects of comparable worth policy. American Economic Review, 76(5), 1117–1125. le Grand, C. (1991). Explaining the male-female wage gap: Job segregation and solidarity wage bargaining in Sweden. Acta Sociologica, 34, 261–278. Macpherson, D. A., & Hirsch, B. T. (1995). Wages and gender composition: Why do women’s jobs pay less? Journal of Labor Economics, 13, 426–471. Meyersson Milgrom, E. M., Petersen, T., & Snartland, V. (2001). Equal pay for equal work? Evidence from Sweden and a comparison with Norway and the U.S. Scandinavian Journal of Economics, 103, 559–583. Miller, P. W. (1987). The wage effect of the occupational segregation of women in Britain. Economic Journal, 97, 885–896. Moulton, B. R. (1990). An illustration of a pitfall in estimating the effects of aggregate variables on micro units. Review of Economics and Statistics, 72, 334–338. Polachek, S. W. (1981). Occupational self-selection: A human capital approach to sex differences in the occupational structure. Review of Economics and Statistics, 63(1), 60–69. Polachek, S. W. (1985). Occupational segregation: A defense of human capital predictions. Journal of Human Resources, 20(3), 437–440. Polachek, S. W. (2004). How the human capital model explains why the gender gap narrow. IZA Discussion Paper, no. 1102, Institute for Study of Labor, Bonn. Sorensen, E. (1989). Measuring the pay disparity between typically female occupations and other jobs: A bivariate selectivity approach. Industrial and Labor Relations Review, 42(4), 624–639. Sorensen, E. (1990). The crowding hypothesis and comparable worth issue: A survey and new results. Journal of Human Resources, 25, 55–89.

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APPENDIX Table A1.

Occupational Speciﬁcation and Proportion of Women in Each Occupation.

Occupation

Proportion of Women

Science: Technical Science: Chemical and Biological Medicine, Health and Nursing Education Law Religion, Journalist, Artist Administration: Government and Business Administration: Accounting, Clerical Administration: Other Sales: Business Services, Purchase, Goods Sales: Other Agriculture, Horticulture, Forestry: Management Agriculture, Horticulture, Forestry: Workers Wildlife Protection, Hunting and Fishing Mining Transport and Communication: Air, Sea, Other Transport and Communication: Drivers, Delivery Transport and Communication: Postal Service, Telecommunication Manufacturing: Textile Manufacturing: Iron and Metal Manufacturing: Precision-Tool Manufacturing: Workshop and Construction Manufacturing: Electrical Manufacturing: Wood Manufacturing: Painting and Varnishing Manufacturing: Other Construction and Building Manufacturing: Graphics Manufacturing: Glass, Pottery, Tile Manufacturing: Dairy Manufacturing: Chemical Processing Manufacturing: Material Handling Manufacturing: Packing and Storage Manufacturing: Other Services: Civilian Protection Services: Lodging and Catering Services: Caretaking and Cleaning Services: Military Services: Other

0.111 0.612 0.880 0.703 0.299 0.581 0.465 0.906 0.448 0.385 0.542 0.117 0.295 0.038 0.027 0.189 0.077 0.579 0.658 0.071 0.400 0.104 0.147 0.146 0.027 0.003 0.262 0.292 0.286 0.256 0.049 0.296 0.317 0.182 0.767 0.603 0.037 0.677

EARNINGS FUNCTIONS AND THE MEASUREMENT OF THE DETERMINANTS OF WAGE DISPERSION: EXTENDING THE BLINDER–OAXACA APPROACH$ Joseph Deutsch and Jacques Silber ABSTRACT This paper is an extension of Blinder’s (1973) and Oaxaca’s (1973) famous decomposition. While they looked at the determinants of the wage gap between two groups, this paper not only considers any number of groups but it also proposes a decomposition technique that permits to analyze the determinants of the overall wage dispersion. The approach presented combines two techniques. The ﬁrst one, popular in the ﬁeld of income inequality measurement, concerns the breakdown of inequality by population subgroups. The second one, very common in the labor economics $

This is quite an extended version of a paper that had been presented at several seminars and conferences. The authors are grateful to an anonymous referee and to Sol Polachek for their very useful comments and suggestions. This paper was revised when Jacques Silber visited Fundacio´n de Estudios de Economı´ a Aplicada (FEDEA), Madrid, Spain, and he is very thankful to FEDEA for its warm hospitality.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 371–427 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28012-X

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literature, uses Mincerian earnings functions to derive a decomposition of wage differences between two groups into components measuring, respectively, group differences in the average values of the explanatory variables, in the coefﬁcients of these variables in the earnings functions and in the unobservable characteristics. This methodological novelty allows one to determine the exact impact of each of these three elements on the overall wage dispersion, on the dispersion within and between groups, and on the degree of overlap between the wage distributions of the various groups. This paper goes, however, beyond a static analysis in so far as it succeeds in breaking down the change over time in the overall wage dispersion and its components (between- and within-groups dispersion and group overlapping) into elements related to changes in the value of the explanatory variables and the coefﬁcients of these variables in the earnings functions, in the unobservable characteristics and in the relative size of the various groups. The empirical illustration of this paper looks at data obtained from income surveys conducted in Israel in 1982, 1990, and 1998, special emphasis being put on the comparison between the earnings of new immigrants and those of natives or older immigrants.

1. INTRODUCTION In two path-breaking papers Blinder (1973) and Oaxaca (1973) independently proposed a technique that allowed to decompose the relative wage gap between two population subgroups into two components, a ﬁrst one measuring differences between the groups in human capital characteristics, a second one, labeled ‘‘discrimination,’’ taking into account the impact of differences between the groups in the rates of return on these human capital characteristics. Such a distinction is, however, not correct (see, for example, Polachek, 1975; Borjas, 2005) because the explained portion can come about because of discrimination while the unexplained portion need not be discrimination.1 The main goal of the present study is to extend Blinder’s (1973) and Oaxaca’s (1973) approach. While they looked at the determinants of the wage gap between two groups, this paper not only extends the analysis to any number of groups but also proposes a decomposition technique that permits to analyze the determinants of the overall wage dispersion. The approach presented here combines two techniques. The ﬁrst one is popular in the ﬁeld of income inequality measurement and concerns the breakdown of inequality by population subgroups. The second one, very common in the labor economics literature, uses Mincerian earnings functions to derive a decomposition of

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wage differences between two groups into components measuring, respectively, group differences in the average values of the explanatory variables, in the coefﬁcients of these variables in the earnings functions and in the unobservable characteristics. This methodological novelty allows one to determine the exact impact of each of these three elements on the overall wage dispersion, on the dispersion within and between groups, and on the degree of overlap between the wage distributions of the various groups.2 This paper goes, however, beyond a static analysis in so far as it succeeds in breaking down the change over time in the overall wage dispersion and its components (between- and within-groups dispersion and group overlapping) into elements related to changes in the value of the explanatory variables and the coefﬁcients of these variables in the earnings functions, in the unobservable characteristics and in the relative size of the various groups. The empirical illustration of this paper looks at data obtained from income surveys conducted in Israel in 1982, 1990, and 1998, special emphasis being put on the comparison between the earnings of new immigrants and those of natives or older immigrants. The paper is organized as follows. Section 2 reviews very brieﬂy the literature on the determinants of wage inequality, the causes of the wage gap between natives and immigrants, and the speciﬁcity of the immigration to Israel. Section 3 deﬁnes the mean difference of the logarithms of wages, indicates how it may be decomposed into between- and within-groups inequality and an overlapping component. It then explains how these decomposition techniques may be applied to Mincerian earnings functions to determine the respective contributions of the explanatory variables, their coefﬁcients in the earnings functions, and unobservable characteristics to the overall wage dispersion. This decomposition technique is then applied to data from the 1982, 1990, and 1998 income surveys. Section 4 extends this breakdown to an analysis of the determinants of the change over time in the overall wage dispersion and an empirical illustration of this additional decomposition, based on the same three income surveys, is then presented. Concluding comments are ﬁnally given in Section 5.

2. ON WAGE INEQUALITY AND IMMIGRATION 2.1. The Determinants of Wage Inequality A vast literature has appeared in recent years dealing with the determinants of the increasing wage dispersion that has been observed in several

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Western countries during the past 20 years. Among the causes of this increasing inequality a distinction has usually been made between factors that affect the demand for labor, those that have an impact on the supply side, and institutional changes that are likely to have also played a role. There is a general agreement among economists that during the last quarter of the twentieth century there has been an important (positive) shift in the demand for high-skilled labor. The literature has offered two main explanations for this rise in the relative demand for skilled labor. The ﬁrst argument stresses the role of increased trade openness that has been observed throughout the world during the 1980s and 1990s. This trend toward ‘‘globalization’’ that is usually explained by a decrease in transportation and communication costs and technology transfers implies that goods may be imported at a lower price. Since many of these goods are produced by lowskilled labor, the increased degree of trade openness will, in developed countries, lead to a weaker demand for unskilled labor and hence a rise in the relative demand for skilled workers (see, for example, Freeman, 1995; Wood, 1995). Another type of explanation has emphasized the role of skill-biased technological change, a distinction being sometimes made between intensive and extensive skilled-biased technological change (see, Johnson, 1997; Krueger, 1993). One may also think of several factors that may affect the inequality of earnings via the supply side. The immigration of low-skilled immigrants that has been observed in many Western countries is a ﬁrst element to be taken into account. In most countries, however, the ﬂow of immigrants does not represent an important addition to aggregate labor supply but the effect on local labor markets may still be important if immigrants tend to stay in speciﬁc areas (see, Topel, 1997, for some illustrations). As a whole, however, the net effect of immigration seems to be small, an additional reason being that the geographic mobility of natives tends to offset the impact of immigration on local labor markets. Variations in the size of cohorts are another type of change that may have an effect on the supply side. A baby boom may thus lead, a generation later, to an important increase in the share of young cohorts in the labor force and since younger workers have lower wages than experienced workers, this may lead to an increase in overall inequality (see, for example, Welch, 1979; Berger, 1985). Changes in the female labor force participation rates may also play an important role since younger female cohorts have low experience. They may, however, have a higher level of education. Another modiﬁcation on the supply side that should indeed be mentioned is the continuous upgrading of the educational composition of the labor force in the Western

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world, a factor which leads to a decrease in the relative wage of educated workers and hence probably to a decrease in wage inequality. Although a demand and supply framework can explain the rise in educational wage differentials by assuming that the rise in the relative demand for educated workers was stronger than that of their supply, some other factors of a more institutional nature should be taken into account. There may be laws that determine the minimum wage or overtime premia and thus affect wage inequality (see, Fortin & Lemieux, 1997). The extent of collective bargaining or the relative size of the public sector are other institutional elements which may play a role. The study of Goldin and Margo (1992) has indeed clearly shown the impact of institutional change on wage inequality in the United States between 1935 and 1945. This short survey of the arguments put forth to explain the increase in wage dispersion observed in several Western countries during the past decades indicates that immigration could theoretically be an important factor, acting through the supply side but that the empirical evidence of a signiﬁcant impact is not too abundant. 2.2. The Analysis of Wage Differences between Natives and Immigrants Following Chiswick’s (1978) pioneering work, many studies tried to analyze how immigrants’ skills adapted to the host country’s labor market. For a long time, the consensus was that at the time of their arrival immigrants earn less than natives because they lack the speciﬁc skills rewarded in the host country’s labor market. However, as these skills are acquired, the human capital stock of immigrants grows relative to that of natives and immigrants experience faster wage growth (see, Borjas, 1994). There may even be a stage where immigrants have accumulated more human capital than natives, the argument being that there is a self selection process in so far as immigrants are ‘‘more able and more highly motivated’’ than natives (Chiswick, 1978). One has, however, to take into account the impact of changes in the wage structure since the latter is not likely to have similar effects on natives and immigrants. Thus, in periods where rates of return to skills increase, the relative wage of immigrants may fall even if their skills remain constant (see, Levy & Murnane, 1992). Most of the studies looking at the earnings of immigrants refer, however, to countries where the annual ﬂow of immigrants represents a small addition to the existing labor force. The case of Israel is different because at least twice during the past 50 years there have been periods of massive immigration, ﬁrst during the late 1940s, then during the early 1990s.

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2.3. On Immigration in Israel In her comprehensive survey of the research conducted on immigration in Israel, Neuman (1999) indicates that between May 1948 and August 1951 the monthly number of immigrants was 15,000–20,000 so that in about 3 years the Jewish population which included 649,500 individuals when the State of Israel was created, doubled. Forty years later, there was a massive inﬂux of immigrants from the former Soviet Union. Thus, in 1990 there were 199,500 immigrants and in 1991, 176,000. Between the beginning of 1990 and the end of 1998, 879,500 immigrants were added to the Israeli population of 4.56 million, which corresponds to a growth rate of 19.3%. It should be stressed that these immigrants, most of them from the former Soviet Union, had an exceptionally high level of education. More than half of them had academic and managerial positions before immigration. The degree and speed of assimilation in the Israeli labor market of previous immigration waves has been analyzed in several studies (see, for example, Ofer, Vinokur, & BarChaim, 1980; Amir, 1993; Beenstock, 1993; Friedberg, 1995; Chiswick, 1997), while Eckstein and Weiss (1997) analyzed the occupational convergence and wage growth of the recent large wave of immigrants from the former Soviet Union. Using panel data they found that upon arrival immigrants receive no signiﬁcant return on imported human capital but with more time spent in Israel these returns increase, a gap remaining however between the returns received by immigrants and natives. Ultimately immigrants receive the same returns on experience but convergence is slow as is occupational convergence. There have also been in the 1970s and 1980s studies looking at the wage differentials between immigrants from various countries, a distinction being usually made between Westerners (immigrants from Europe, America, or Australia) and Easterners (immigrants from North Africa or the Near East). While Weiss, Fishelson, and Mark (1978) attributed the decrease in the wage gap between Westerners and Easterners, that was observed in the early 1970s, to a decrease in human capital differences, Amir (1980) argued that the decrease in ‘‘discrimination’’ played a larger role.

2.4. Implications for the Analysis of the Link between Immigration and Wage Dispersion in Israel The quick survey of the literature that has just been conducted should lead us to the following predictions, assuming individuals are

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grouped by country or continent of origin. First, given the size of the immigration waves during the past 30 years, we may expect the kind of supply side effects mentioned earlier to be important. Second these immigrants came mainly from the former Soviet Union and they had a relatively high level of education. It is nevertheless likely that the skills of these immigrants, who came from a country with a centralized economy, did not ﬁt very well the requirements of the Israeli labor market. This should imply that, if human capital (education or experience) is measured only in years,3 the rate of return on this capital should be lower for the new immigrants. For all these reasons (high level of human capital among immigrants, but low rate of return on it), one may expect between groups gaps in wages to be more related to differences in rates of return than in human capital. These gaps are also likely to have grown over time as the share of new immigrants in the Israeli labor force became more important.4 It should be remembered, however, that the Israeli economy is a developed economy so that the demand side effects mentioned earlier and affecting most Western countries must have played also a role in Israel, this being particularly true for skilled-biased technological change. Moreover, it is well known that the Israeli economy was much more open to international trade in the 1980s and 1990s than in earlier periods. Both factors lead us to predict that wage dispersion as a whole must have increased in Israel between the early 1980s and the late 1990s. This trend is also likely to have taken place within population subgroups, if the latter are deﬁned, for example, on the basis of the country or continent of origin, and not as a function of human capital characteristics. Finally, given that we expect that both the between- and the withingroups dispersion increased over time, we cannot predict a priori what will happen to the degree of overlap between the wage distributions of the various population subgroups. Despite the relatively important number of studies dealing with the impact of immigration on the Israeli labor market, less emphasis has been given to the effect of immigration on income inequality in general, wage dispersion in particular. The next sections will provide ﬁrst a methodological framework allowing to better estimate the impact of immigration on wage dispersion, second an empirical illustration based on income surveys that have been conducted in 1982, 1990, and 1998.

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3. THE STATIC ANALYSIS OF THE DETERMINANTS OF THE DISPERSION OF WAGES 3.1. The Decomposition of the Mean Difference of the Logarithms of Incomes by Population Subgroups Although the standard deviation is the most popular measure of the dispersion of a distribution, there exists another index of dispersion, called the mean difference, MD, that is related to Gini’s famous concentration coefﬁcient (see, Gini, 1912) and is deﬁned (see, Kendall & Stuart, 1996) as X X 1 MD ¼ jy yj j (1) n2 i¼1 to n j¼1 to n i where yi and yj are the incomes of individuals i and j, and n, the number of individuals in the population. Such an index may also be used when the observations are the logarithms of incomes rather than the incomes themselves, in which case the mean difference, that will be denoted here as D, will be deﬁned as X X 1 D¼ j ln yi ln yj j (2) n2 i¼1 to n j¼1 to n Expression (2) indicates in fact that D measures the expected income gap, in percentage terms, between two individuals drawn (with repetition) from the sample of individuals on whom information on their income was collected. Let now m represent the number of population subgroups. Expression (2) may then be decomposed into the sum of two terms, DA and DW where DA refers to what may be called the ‘‘across-groups inequality’’ (see, Dagum, 1960, 1997), while DW measures the ‘‘within-groups inequality,’’ with X XXX 1 DW ¼ j ln yih ln yjk j (3) n2 h¼1 to m i2h k¼h j2k and X XXX 1 DA ¼ j ln yih ln yjk j n2 h¼1 to m i2h kah j2k

(4)

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the second sub-index (h or k) in (3) and (4) referring to the group to which the individual belongs. Let us now assume that the groups are ranked by decreasing values of the average of the logarithms of income in each group so that ln ygh, the mean logarithm of incomes5 in group h, is higher than ln yg,hþ1, the mean logarithm of incomes in group (hþ1). Expression (4) may then be written as DA ¼ Dd þ Dp

(5)

X XXX 1 Dd ¼ ðln yih ln yjk Þ with ln yih yjk n2 h¼1 to m i2h kah j2k

(6)

X XXX 1 ðln yjk ln yih Þ with ln yih oyjk n2 h¼1 to m i2h kah j2k

(7)

with

and Dp ¼

Combining (6) and (7) we derive that X XXX 1 ðln yih ln yjk Þ Dd Dp ¼ n2 h¼1 to m i2h kah j2k # X X"X X 1 2Dd Dp ¼ ðnk ðln yih ÞÞ ðnh ðln yjk ÞÞ n2 h¼1 to m kah i2h j2k

2Dd Dp ¼

X X 1 ½nk nh ðln ygh ln ygk Þ n2 h¼1 to m kah

(8)

(9)

(10)

where nh and nk represent, respectively, the number of individuals in groups h and k. Since the between-groups mean difference DB is obtained by giving each individual the average value of the logarithms of the incomes of the group to which he belongs, we may, using (2), deﬁne an index DB as X X 1 DB ¼ nh nk j ln ygh ln ygk j (11) n2 h¼1 to m kah to m

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and it may be observed, when comparing (10) and (11), that DB ¼ ðDd Dp Þ

(12)

Since expression (5) indicates that DA ¼ ðDd Dp Þ þ ð2Dp Þ

(13)

we conclude, using (1)–(5), (12), and (13), that D ¼ DW þ DB þ ð2Dp Þ

(14)

One should note that expression (7) indicates that (2Dp), the residual which is obtained in the traditional decomposition of the mean difference by population subgroups, is expressed as a simple function of the ‘‘transvariations’’6 which exist between all pairs of population subgroups. In the next section it will be shown that it is also possible to compute the contribution of each population subgroup to the value of the three components of the overall wage dispersion that have just been derived.

3.2. Computing the Contribution of Each Population Group to the Various Components of the Breakdown The results that have been derived in Eqs. (3)–(14) may be used to determine the contribution of each population group to the three components of the breakdown that have been deﬁned. The contribution Cwh of group h to the within-groups inequality DW may thus be expressed, using (3), as XX 1 j ln yih ln yjk j (15) C wh ¼ n2 i2h j2h Similarly, using (6), (7), and (12), the contribution Cbh of group h to the between inequality DB may be written as C bh

XXX 1 ¼ ðln yih ln yjk Þ with ln yih ln yjk n2 kah i2h j2k XXX 1 2 ðln yjk ln yih Þ with ln yih o ln yjk n kah i2h j2k

ð16Þ

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Finally the contribution Cph of group h to the overlapping term (2Dp) may be written, using (7) and (14) as XXX 1 ðln yjk ln yih Þ with ln yih o ln yjk (17) C ph ¼ n2 kah i2h j2k Naturally, the contribution Ch of group h to the overall inequality term D in (14) will be expressed as C h ¼ C wh þ Cbh þ C ph and it can be easily proven that D¼

X

Ch

(18)

(19)

h¼1 to m

In the next section, the various decompositions that have been previously deﬁned will be combined with Blinder’s (1973) and Oaxaca’s (1973) traditional breakdown of income differences into a ‘‘variable’’ and a ‘‘coefﬁcient’’ component7. This will allow us to analyze the impact of these two elements (the values of the variables and that of the regression coefﬁcients) not only on the difference between the average logarithms of incomes in two population subgroups, but also on the dispersion of these (logarithms of) incomes in each group and on the degree of overlapping between two distributions of (the logarithms of) incomes. We will see that in some of these decompositions there will be another component that will represent the impact of unobservable characteristics.

3.3. Estimating the Contributions of the Variables, Their Coefﬁcients in the Regressions, and the Unobservable Characteristics to the Overall Wage Dispersion The human capital model relates the earnings of an individual to the amount of his investment in human capital and, using the framework of analysis originally put forth by Mincer (1974), we may write that X ln yih ¼ blh xlih þ uih (20) l¼1 to L

where the subscripts i, h, and l refer, respectively, to the individual (i), the group to which he belongs (h), and the explanatory variable (l).

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The coefﬁcient blh is the regression coefﬁcient corresponding to the explanatory variable xlih which refers to the characteristic l of individual i who belongs to group h. Finally uih, which is the residual of the regression, refers evidently to factors that have not been taken into account. Combining now expressions (3) and (20) we derive ﬁrst the within-groups inequality ! ! X X X X X X 1 DW ¼ b x þ u b x þ u lih ih ljk jk lh lk n2 h¼1 to m i2h k¼h j2k l¼1 to L l¼1 to L ! X X X X 1 ¼ ðb x b x Þ þ ðu u Þ lih ih jh lh ljh n2 h¼1 to m i2h j2h l¼1 to L lh !# X XX " X 1 ¼ 2 ðblh xlih blh xljh Þ þ ðuih ujh Þ n2 h¼1 to m i2h j2h l¼1 to L with ln yihWln yjh so that ﬁnally (21)

DW ¼ A þ B where X XX " 1 A¼ 2 n2 h¼1 to m i2h j2h

X

!# blh ðxlih xljh Þ

with ln yih 4 ln yjh

l¼1 to L

(22) and X XX 1 B¼ 2ðuih ujh Þ; with ln yih 4 ln yjh n2 h¼1 to m i2h j2h

(23)

Expressions (21)–(23) indicate clearly that the within-groups inequality of (the logarithms of) incomes is the sum of two elements: a ﬁrst one (A) that is the consequence of differences between individuals belonging to the same group in values taken by their measured characteristics and a second one (B) that derives from differences between individuals belonging to the same group in unmeasured characteristics.

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Extending the Blinder–Oaxaca Approach

We may in a similar way derive an expression for the between-groups inequality DB since by combining (11) and (20) we may write that X X X X 1 n n b x b x DB ¼ h k l¼1 to L lh lgh l¼1 to L lk lgk n2 h¼1 to m k¼1 to m X X X 1 ¼ n n ðb x b x Þ h k lgh lgk lh lk l¼1 to L n2 h¼1 to m k¼1 to m " " ## X X X 1 ¼ nh nk ðblh xlgh blk xlgk Þ 2 n2 l¼1 to L h¼1 to m k¼1 to m with ln ygh 4 ln ygk

ð24Þ

where xlgh and xlgk are the arithmetic means of characteristic l in groups h and k, respectively. Remembering then that (abcd)=((aþc)/2)(bd )þ((bþd )/2)(ac), we ﬁnally derive (25)

DB ¼ C þ D where " X 1 C¼ n2 h¼1 to m with ln yghWln ygk and X 1 D¼ n2 h¼1 to m

X

" nh nk

k¼1 to m

## ðblh þ blk Þðxlgh xlgk Þ

(26)

l¼1 to L

k¼1 to m

X

X

" nh nk

X

# ðxlgh þ xlgk Þðblh blk Þ

(27)

l¼1 to L

with ln yghWln ygk Expressions (25)–(27) indicate that the between-groups inequality of (the logarithms of) incomes is the sum of two elements: a ﬁrst one (C) that is the consequence of differences between the groups in the average levels of the explanatory variables and a second one (D) that is explained by differences between the groups in the coefﬁcients of these variables in the regressions.8 Note that in (26) and (27) no reference is made to unmeasured characteristics since in measuring the between-groups inequality we assume that each individual in a group receives the average (logarithm of the) income of the group and that, by the deﬁnition of a regression, this average does not include a residual.

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JOSEPH DEUTSCH AND JACQUES SILBER

The third element of the decomposition of inequality of (the logarithms of) incomes measures the degree of overlap between the distributions of the various groups and, combining (7) and (20), Dp may be expressed as ! !# X X X X" X X 1 Dp ¼ blk xljk þ ujk blh xlih þ uih n2 h¼1 to m i2h kah j2k l¼1 to L l¼1 to L (28)

with ln yiholn yjk Using similar decomposition rules as before, we derive that Dp ¼ E þ F þ G

(29)

where # X X X X" X 1 blk þ blh Þ ðxljk xlih Þ E¼ n2 h¼1 to m i2h kah j2k l¼1 to L 2 with ln yiholn yjk # X X X X" X 1 xljk þ xlih F¼ ðblk blh Þ n2 h¼1 to m i2h kah j2k l¼1 to L 2

(30)

(31)

with ln yiholn yjk and G¼

X XXX 1 ½ðujk uih Þ n2 h¼1 to m i2h kah j2k

(32)

with ln yiholn yjk Expressions (29)–(32) indicate that the degree of overlapping between the distributions corresponding to the various groups is a function of three elements: a ﬁrst component (E) that reﬂects differences in the values taken by the explanatory variables among the individuals affected by the overlapping, a second element (F) that is explained by differences between the groups in the regression coefﬁcients corresponding to these variables, and a third expression (G) that is due to unmeasured characteristics among the individuals affected by the overlapping. Combining expressions (21), (25), and (29) we conclude that (AþCþE), (DþF), and (BþG) represent, respectively, the contributions of differences in the values of the explanatory variables, in the regression coefﬁcients

385

Extending the Blinder–Oaxaca Approach

corresponding to these variables, and in unobservable characteristics to the overall wage dispersion. Such a decomposition may be given a graphical interpretation that extends the usual Blinder–Oaxaca diagram. To simplify, we limit the analysis to two population subgroups and one explanatory variable, say, education. In Fig. 1 the straight lines MA and NB refer, respectively to the earnings functions (regression lines) of the two groups A and B. Let xmean,A and xmean,B correspond to the mean values (mean educational level and logarithm of earnings) of groups A and B. In reality, there is, however, a dispersion of educational levels (on the horizontal axis) in each group (between xB,min and xB,max for group B and between xA,min and xA,max for group A). There is also, at the various educational levels and for each group, a dispersion of unobservable characteristics (e.g., innate ability) on the vertical axis. Assume, for simplicity, that all the observations for group B are located in the area B1B2B3B4 and for group A in the area A1A2A3A4. We have assumed that these two areas overlap (area B1HA3K). The between-groups dispersion is (for example) decomposed into the two elements CD and DB as in the traditional Blinder–Oaxaca diagram and this dispersion depends clearly only on the regression coefﬁcients and on the average value of the educational levels of the two groups. The within-groups

B3

logarithm of incomes

group B B2 B

B4 H N

A2 A

B1

A3 D A4

M A1 A Xmin

Fig. 1.

group A

K

C A Xmean

A B Xmin X max

B X mean

B X max

education

Graphical Representation Extending the Usual Blinder–Oaxaca Diagram.

386

JOSEPH DEUTSCH AND JACQUES SILBER

dispersion corresponds to the two areas B1B2B3B4 and A1A2A3A4 and, as can be seen in the graph, this dispersion is due to within-groups differences in educational levels and in the unobservable characteristics. Finally the overlapping component, represented by the area B1HA3K depends clearly on differences in the slopes of the lines MA and NB (differences in regression coefﬁcients), in the educational levels and in the value of the unobservable characteristics. We now turn to the results of the empirical investigation.

3.4. Male Earnings Functions in Israel in 1982, 1990, and 1998 The empirical illustration that is presented in this section is based on the income surveys that are conducted each year in Israel. We have chosen to limit our analysis to three surveys: those of the years 1982, 1990, and 1998. Since one of the aims of this research is to look at the impact on earnings of the country of origin and of the period of immigration of the immigrants, we have limited our analysis to the Jewish male population and divided it in four groups: those born in Israel (group I), those born in Asia or Africa (group AA), and those born in Europe or America. However, in order to take into account what happened to the most recent immigrants we have divided the last group into two subgroups: those who immigrated to Israel before 1972 (group EA) and those who immigrated after 1971 (group NIM). It is clear that, especially for the last two surveys analyzed (1990 and 1998), most of the members of the last subgroup came from the former Soviet Union so that we will be able to focus on the earnings of this important population of immigrants. Let us ﬁrst take a look at the general characteristics of the population analyzed. The two ﬁrst columns of Table 1 give for each year the means and standard deviations of the various variables that have been introduced in the regressions. The results are given each time for the whole sample.9 It appears that the proportion of married individuals declined over the years from 87% in 1982 to 75% in 1998. The proportion of singles on the contrary increased during the same period from 10.7% to 20.9%. The other categories of marital status (divorced, widows, or separated) increased slightly from 2.3% in 1982 to 4.1% in 1998. The average number of years of schooling increased from 10.7 in 1982 to 12.6 in 1998, while the average number of years of experience correspondingly decreased from 26.2 years in 1982 to 21.7 in 1998. The proportion of the males having attended a Talmudic school

387

Extending the Blinder–Oaxaca Approach Table 1. Variable

Descriptive Statistics and Regression Results. Mean

1982 income survey (whole population) Logarithm of wage per hour 4.0184 Married 0.8672 Single 0.1068 Years of schooling 10.6754 Years of experience 26.2035 Square of years of experience 904.2872 Attended Talmudic school 0.0257 Intercept R2 0.2564 Number of observations 2,725 1990 income survey (whole population) Logarithm of wage per hour 2.5072 Married 0.8140 Single 0.1523 Years of schooling 11.6693 Years of experience 23.3972 Square of years of experience 739.5288 Attended Talmudic school 0.0202 Intercept R2 0.2810 Number of observations 3,113 1998 income survey (whole population) Logarithm of wage per hour 3.4487 Married 0.7460 Single 0.2109 Years of schooling 12.6383 Years of experience 21.6922 Square of years of experience 641.7122 Attended Talmudic school 0.0153 Intercept R2 0.2360 Number of observations 6,197

Standard Deviation

0.5723 0.3394 0.3088 3.7835 14.7535 880.5513 0.1582

0.5742 0.3891 0.3593 3.2367 13.8600 787.2934 0.1408

0.6553 0.4353 0.4080 2.8172 13.0829 679.5137 0.1229

Regression Coefﬁcients

t-Values

0.2077 0.1079 0.0681 0.0274 0.0004 0.3546 2.7680

3.46 1.55 24.03 9.66 8.57 5.85 33.76

0.1070 0.1009 0.0749 0.0385 0.0005 0.2695 1.0609

2.20 1.78 24.83 14.52 12.07 4.30 14.71

0.1554 0.0415 0.0886 0.0289 0.0004 0.1567 1.8412

4.29 0.97 32.23 12.59 9.33 2.63 31.01

(Yeshiva), a factor likely to have a downward effect on earnings, decreased from 2.6% in 1982 to 1.5% in 1998. It is difﬁcult to compare the means obtained for the various population subgroups since the younger people are more likely to be individuals born in Israel so that one would expect to observe, for these men born in Israel, a smaller proportion of married individuals and less years of schooling or experience. This is actually the case for each year. Such differences do not

388

JOSEPH DEUTSCH AND JACQUES SILBER

prevent us, however, from comparing regression results because then the age is kept constant, since we have deﬁned experience in the traditional way, that is as age minus six minus the number of years of schooling.10 The last two columns of Table 1 give, for the whole sample, the results of the Mincerian earnings functions that have been estimated for each of the three periods analyzed. It appears, for example, that the coefﬁcient of schooling increased throughout the period, being equal to 6.8% in 1982, 7.5% in 1990, and 8.9% in 1998. The coefﬁcient of the experience variable11 at the beginning of the career showed a different pattern since it rose form 2.7% to 3.9% between 1982 and 1990 but was equal to 2.9% in 1998. Individuals who were married earned on average 20.8% more than those who were divorced, separated, or widows in 1982, 10.7% more in 1990, and 15.5% more in 1998. Single individuals on the contrary earned 10.7% in 1982, 10.1% in 1990, and 4.1% less than those who were neither married nor singles. These data indicate therefore that the gap between married and single men decreased signiﬁcantly between 1982 and 1998. Similar regressions have been estimated for each of the four population subgroups that have been distinguished and are presented in Appendix A. It appears, for example, that in 1982 the coefﬁcient of schooling was much higher for those born in Israel (8.8%) than for those born in Asia or Africa (4.9%) or Europe or America (6.0% for those who came before 1972 and 5.0% for those who came after 1971). Similarly in 1998 the coefﬁcient of schooling was 12.5% for those born in Israel, 7.3% for those born in Asia or Africa, 11.0% for those born in Europe who immigrated before 1972, and 6.5% for those born in Europe who arrived in Israel after 1971.

3.5. The Components of the Overall Wage Dispersion Table 2 gives for each of the 3 years 1982, 1990, and 1998 the decomposition of the overall wage dispersion into the three components mentioned in Section 3: the between- and within-groups dispersions and the overlapping term. The number that appears in the line labeled ‘‘Total’’ gives for each year the overall mean difference of the logarithms of income, that is the expected income difference in percentage terms between two individuals chosen (with repetition) in the sample. Whereas this mean difference only slightly increased between 1982 and 1990 (from 63.6% to 64.4%), the change was very important between 1990 and 1998 since the mean difference reached the value of 73.0% in 1998. What are the reasons for such an important increase in the overall dispersion observed during 1990–1998? This is a period where

389

Extending the Blinder–Oaxaca Approach Table 2. Decomposition of the Wage Dispersion into a Between-Groups Dispersion, a Within-Groups Dispersion, and an Overlapping Component. 1982

1990

1998

Actual results Component Between groups Within groups Overlap Total

11.5 17.89 34.19 63.58

6.46 21.74 36.2 64.4

14.65 26.48 31.85 72.98

In percentage terms Component Between groups Within groups Overlap Total

18.08 28.14 53.78 100.00

10.02 33.76 56.21 100.00

20.07 36.29 43.64 100.00

in several Western countries wage dispersion increased for reasons related to technological change, increasing openness to trade and institutional change such as the weakening of the trade unions (see the short survey of the literature in Section 2). It should, however, be remembered that during the 1990–1998 period 880,000 individuals immigrated to Israel, mostly from the former Soviet Union. Since one of the population subgroups includes only those who migrated from Europe or America after 1971, the analysis presented in this section enables one to determine the impact of this immigration on the overall wage dispersion. However, the decomposition techniques presented previously give also the speciﬁc impact on the overall dispersion of incomes, and on its three components, of the between- and within-groups dispersion and the overlapping element, of the explanatory variables, their coefﬁcients, and of the unobserved characteristics. All these results will now be presented and analyzed. 3.5.1. The Relative Importance of the Between- and Within-Groups Dispersion and the Contribution of the Overlapping Component Table 2 indicates that in absolute terms the contribution of the betweengroups dispersion to the overall dispersion decreased from 11.5% to 6.4% between 1982 and 1990 but increased between 1990 and 1998 to reach 14.7% in 1998. In percentage terms, the picture is similar since the contribution of the between-groups dispersion decreased from 18.1% to 10.0% between 1982 and 1990 but was equal to 20.1% in 1998.

390

JOSEPH DEUTSCH AND JACQUES SILBER

The within-groups dispersion increased in absolute terms during both subperiods. It was equal, in absolute terms, to 17.9% in 1982, 21.7% in 1990, and 26.5% in 1998. The picture is quite similar if one looks at the relative contribution of the within groups to the overall wage dispersion since this contribution rose from 28.1% in 1982 to 33.8% in 1990 and 36.3% in 1998. For the overlapping term the pattern is as follows: in absolute terms it increased from 34.2% in 1982 to 36.2% in 1990 but fell down to a level of 31.8% in 1998. In relative terms the contribution of the overlapping term rose form 53.8% in 1982 to 56.2% in 1990 to go back to 43.6% in 1998. The picture during the 1982–1990 period is hence very different form the one observed during the years 1990–1998. During the ﬁrst period the between-groups dispersion decreased, while the within-groups dispersion rose, the overlapping term increasing only slightly. These conclusions are true in absolute and relative terms. During the second subperiod, on the contrary the between- as well as the within-groups dispersion rose, while the amount of overlapping decreased, this being again true in absolute and relative terms. Two factors at least may explain these patterns. First, there was at that time an increase in wage dispersion in several Western countries and this is probably also true for the within-groups dispersion. At the same time there is a speciﬁc Israeli story: the massive immigration of Jews from the former Soviet Union has increased, at least in a ﬁrst stage, the degree of stratiﬁcation in the Israeli society, leading thus to an increase in the between-groups dispersion. This latter effect was more important than the increase in the within-groups dispersion, that was just mentioned, since the degree of overlapping decreased during this period. To better understand these changes we now take a look at the respective role played by the explanatory variables and their coefﬁcients and by the unobserved characteristics. 03.5.2. The Contribution of the Explanatory Variables and Their Coefﬁcients and of the Unobserved Characteristics to the Wage Dispersion Table 3 indicates that in 1982, out of a total wage dispersion of 63.6%, the explanatory variables contributed in absolute terms 16.8%, their coefﬁcients 2.7%, and the unobserved characteristics 44.1%. The corresponding ﬁgures for 1990 when the overall dispersion was 64.4%, were 19.9%, 0.3%, and 44.2%. In 1998 the mean difference of the logarithms of wages was equal to 73.0%, while the three contributions previously mentioned were, respectively, equal to 21.4%, 4.8%, and 46.7%. It appears therefore that over time the contribution of the explanatory variables increased in absolute value. The contribution of unobserved characteristics on the contrary did not vary

391

Extending the Blinder–Oaxaca Approach Table 3. Decomposition of the Wage Dispersion into Components Corresponding to the Explanatory Variables, Their Coefﬁcients, and to the Unobservable Characteristics. 1982

1990

1998

Actual results Component Explanatory variables Regression coefﬁcients Unobservable characteristics Total

16.80 2.69 44.10 63.58

19.87 0.33 44.20 64.40

21.44 4.83 46.72 72.98

In percentage terms Component Explanatory variables Regression coefﬁcients Unobservable characteristics Total

26.42 4.23 69.36 100.00

30.85 0.52 68.63 100.00

29.37 6.62 64.01 100.00

very much over time, while that of the regression coefﬁcients was low and unstable. The ﬁgures are somehow different in percentage terms (see again Table 3). It appears that over time there was also an increase in percentage terms in the contribution of the explanatory variables, at least between 1982 where it was equal to 26.4% and 1990 when it reached 30.9%. There was no important change during the 1990–1998 period. The relative contribution of unobserved characteristics decreased over time, mainly during the second subperiod (from 69.4% in 1982 to 68.6% in 1990 and 64.0% in 1998). Finally the relative contribution of subgroup differences in the regression coefﬁcients varied over time since it was equal to 4.2% in 1982, 0.5% in 1990, and 6.6% in 1998. A similar analysis may be conducted at the level of each of the three components of the overall wage dispersion: the between- and within-groups dispersion and the overlapping term. The results are presented in Table 4. For the between-groups dispersion, as was mentioned previously, only the explanatory variables and their coefﬁcients play a role. It appears that the relative role of the explanatory variables varied strongly over time: it was equal to 35.4% in 1982, 57.0% in 1990, but only 11.8% in 1998. The picture is evidently the opposite for the relative contribution of the regression coefﬁcients. The very important role of the latter in 1998 indicates, for example, that, ceteris paribus, the coefﬁcient of the schooling variable is much lower among new immigrants.12

392

JOSEPH DEUTSCH AND JACQUES SILBER

Table 4. Decomposition for Each Year of the Between-Groups, Within-Groups, and Overlapping Components into Elements Corresponding to the Explanatory Variables, the Regression Coefﬁcients, and the Unobservable Characteristics Elements. Elements of the Decomposition

1982

1990

1998

Between-groups dispersion Differences in the value of the explanatory variables Differences in the regression coefﬁcients Total

35.41 64.59 100.00

56.98 43.02 100.00

11.82 88.18 100.00

Within-groups dispersion Differences in the value of the explanatory variables Differences in unobservable characteristics Total

27.61 72.39 100.000

32.35 67.65 100.000

36.00 64.00 100.000

Overlap Differences in the value of the explanatory variables Differences in the regression coefﬁcients Differences in unobservable characteristics Total

22.77 13.86 91.09 100.00

25.29 6.75 81.46 100.00

31.93 25.39 93.45 100.00

For the within-groups dispersion only two factors (see supra) play a role: the explanatory variables and the unobserved characteristics. Table 4 indicates that, in relative terms, the contribution of the explanatory variables steadily rose over time, from 27.6% in 1982, to 32.3% in 1990 and 36.0% in 1998. The trend, in relative terms, is evidently opposite for unobservable characteristics. For the overlapping component, as was mentioned previously, each of the three factors (the explanatory variables, the unobserved characteristics, and the regression coefﬁcients) plays a role. It is ﬁrst interesting to note that the data indicate that the component measuring the impact of the regression coefﬁcients had, each year, a negative contribution to the degree of overlap. This implies that if there had been no differences between the individuals involved in the overlap in the value of the explanatory variables (so that the sum of all the binary comparisons of measured characteristics, as it is given in (30), would have been assumed to be nil) or in their unobservable characteristics (so that the sum of all the binary comparisons of unobserved characteristics, as it is given in (32) would also have been nil), the betweengroups differences in the regression coefﬁcients would have led to a smaller amount of overlap. As far as the two other components are concerned, it appears that the relative importance of the explanatory variables increased over time (from

Extending the Blinder–Oaxaca Approach

393

22.8% in 1982 to 25.3% in 1990 and 31.9% in 1998). The relative contribution of unobservable characteristics on the contrary was rather unstable (91.1% in 1982, 81.5% in 1990, and 93.4% in 1998). 3.5.3. Summarizing the Empirical Results The various observations that have just been made could be summarized as follows. First during the two subperiods that have been analyzed, the between-groups dispersion ﬁrst decreased, then increased; since the same pattern has been observed, in percentage terms, for the component reﬂecting the regression coefﬁcients and given that this component contributes most to this dispersion, we may fairly assume that the regression coefﬁcients played a central role here. Second, the within-groups dispersion increased in both periods, a pattern that is observed also, in percentage terms, for the component corresponding to the explanatory variables. Although this component never represents more than a third of the within-groups dispersion, it is likely that its variation over time explains the increasing importance of the within-groups dispersion. Third, the overlapping component ﬁrst increased then decreased. This is also the pattern observed for the regression coefﬁcients, although their contribution remains negative throughout the period. We may therefore conjecture that the story of the overlap is mainly that of the regression coefﬁcients and if the share of the overlap in the overall dispersion decreased drastically between 1990 and 1998, it seems to be a consequence of the fact that the sharp decrease in the regression coefﬁcients observed among new immigrants led to a reduction in the amount of overlap between the income distributions of the four population subgroups. In the next section we extend the analysis and show how it is also possible to decompose changes over time in the dispersion of wages and in its components.

4. THE DECOMPOSITION OF THE CHANGE OVER TIME IN THE WAGE DISPERSION: METHODOLOGY AND EMPIRICAL ILLUSTRATION The breakdown of the change over time in the degree of income dispersion is quite complex and its details are given in Appendix B. It may be summarized by looking at the impact of various factors on changes in the three

394

JOSEPH DEUTSCH AND JACQUES SILBER

components of the overall dispersion, the between-groups dispersion, the within-groups dispersion, and the overlapping component. Concerning the changes in the within-groups dispersion it is shown in Appendix B that three elements play a role: the changes that take place over time within the various groups in the dispersion of the explanatory variables; the modiﬁcation that take place over time in the different groups in the regression coefﬁcients; the variations over time within the various groups in the dispersion of the unobserved characteristics. Concerning the changes in the between-groups dispersion the following elements are distinguished (see Appendix B): the changes over time in the relative size of the different groups; the variations over time in the between-groups dispersion of the explanatory variables; the modiﬁcations taking place over time in the average values of these variables; the variations over time in the between-groups dispersion of the regression coefﬁcients; the modiﬁcations that take place over time in the average values of these regression coefﬁcients. Finally concerning the overlapping component the following factors are listed in Appendix B: the changes in the dispersion of the values of the explanatory variables for those individuals involved in the overlapping at each period; the variations over time in the average values of the explanatory variables among those same individuals; the changes over time in some weighted dispersion of the regression coefﬁcients, these weights depending only on those individuals involved in the overlapping at each period; the variation over time in some weighted average of these regression coefﬁcients, here again the weights depending only on those individuals who are part of the overlapping at each period; the change over time in the dispersion of the unobserved characteristics among those individuals involved in the overlapping in each period. The results of this complex breakdown13 are given in Tables 5–7. Table 5 gives the respective impacts of changes in the between- and within-groups

395

Extending the Blinder–Oaxaca Approach Table 5. Decomposition of the Overall Change between 1982 and 1998 in the Mean Difference of the Logarithms of Wages: The Role of Changes in the Between- and Within-Groups Mean Difference and of that in the Overlapping Component. Components of the Decomposition

Change in between-groups mean difference Change in within-groups mean difference Change in overlapping component Total change in mean difference

Period 1982– 1990

Period 1990– 1998 8.19

5.04 3.85 2.01 0.8142

Period 1982– 1998 3.15

4.74 4.35 8,587

8.59 2.34 9.401

Table 6. Decomposition of the Overall Change between 1982 and 1998 in the Mean Difference of the Logarithms of Wages: The Role of Changes in the Relative Size of the Population Subgroups, in the Value of the Explanatory Variables, in the Regression Coefﬁcients, and in the Unobserved Variables. Components of the Decomposition

Impact of change in the relative size of the population subgroups Impact of changes in the value of the explanatory variables Impact of changes in the regression coefﬁcients Impact of changes in unobservables Total change in mean difference

Period 1982– Period 1990– Period 1982– 1990 1998 1998 2.91

0.28

3.94

4.98

1.70

7.71

1.35 0.10 0.8142

4.64 2.52 8.587

3.02 2.62 9.401

mean difference of the logarithms of wages as well as of variations in the overlapping component. It ﬁrst appears that in both periods (1982–1990 and 1990–1998) there was an increase in the mean difference of the logarithms of wages, this increase being much stronger during the period 1990–1998. It can in fact be observed that the variations in the overall mean difference of the logarithms of wages given in Table 5 correspond to the results given in Table 2. Given that the change in this mean difference was quite small during the period 1982–1990 we will concentrate our attention to what is observed during the period 1990–1998. As indicated in Table 2, the mean difference of the logarithms of wages increased from 64.4% to 72.98% between 1990 and 1998. In other words, the expected percentage gap in wages between two individuals drawn (with repetition) from the sample

396

JOSEPH DEUTSCH AND JACQUES SILBER Table 7.

Decomposition by Subcomponents of the Change in the Mean Difference of the Logarithms of Wages.

Subcomponents

Period 1982– 1990

Period 1990– 1998

Period 1982– 1998

0.28 3.11 0.25 0.90 4.71 8.19

3.94 1.77 0.71 3.83 0.78 3.15

1.34 1.16 2.24 4.74

3.82 0.77 4.00 8.59

1.49 1.15 0.12 1.15 1.66 2.01

0.32 2.82 0.69 2.82 0.28 4.35

3.07 1.67 0.69 1.67 1.38 2.34

0.81

8.59

9.40

(1) Changes in the between-groups wage dispersion GþJ 2.91 H 0.07 K 0.07 I 1.52 L 3.79 Total change in between-groups 5.04 dispersion (2) Changes in the within-groups wage dispersion C 2.20 D 0.11 B 1.76 Total change in within-groups dispersion 3.85 (3) Changes in the overlapping component S U T V Y Total change in overlapping component (4) Total change in wage dispersion

Note: (GþJ), effect of changes over time in the relative size of the different groups; (HþK), the impact of variations over time in the value of the explanatory variables in the various groups with; H, impact of variations over time in the dispersion of these variables; K, role of modiﬁcations taking place over time in the average value of these variables; (IþL), role played by modiﬁcations over time in the regression coefﬁcients in the different groups with; L, impact of variations over time in the dispersion over the different groups of these regression coefﬁcients; I, the role played by the modiﬁcations that take place over time in the average value of these regression coefﬁcients; C, impact of changes over time in the various groups in the dispersion of the explanatory variables; D, effect of the modiﬁcation that took place over time in the different groups in the regression coefﬁcients; B, role played by variations over time in the various groups in the dispersion of the unobserved components; S ¼ (S1þS2þS3), the effect of changes in the dispersion of the value of the explanatory variables among those involved in the overlapping at both periods; U ¼ (U1þU2þU3), impact of variations over time in the average values of the explanatory variables among those same individuals; V=(V1þV2þV3), effect of changes over time in some weighted dispersion of the regression coefﬁcients, these weights depending only on those individuals involved in the overlapping; T ¼ (T1þT2þT3), impact of the variation over time in some weighted average of these regression coefﬁcients, here again the weights depending only on those individuals who are part of the overlapping; Y, role of change over time in the dispersion of the unobserved components.

Extending the Blinder–Oaxaca Approach

397

increased in absolute terms by 8.6% (72.98–64.4), which is exactly the result which appears in Tables 5 and 6. Note that during the period 1982–1990 the increase in the between-groups dispersion would per se have led to a decrease in the amount of overlap but since at the same time the within-groups dispersion increased we also end up with an increase in the amount of overlap between the wage distributions of the four groups distinguished. Between 1990 and 1998, on the contrary, there was an increase in both the between- and the within-groups dispersion and the net result is a decrease in the amount of overlap. Table 6 analyzes this increase in wage dispersion from another angle. There we try to identify whether the increase in wage dispersion was a consequence of changes in the value of the explanatory variables, of variations in the regression coefﬁcients, of changes in the unobserved variables, or even of a modiﬁcation in the relative size of the population subgroups. Table 6 shows thus that between 1990 and 1998 more than half of the increase in the overall wage dispersion was the consequence of an increase in the contribution of the regression coefﬁcients. Table 7 combines the results of Tables 5 and 6. In addition, it makes a distinction between the contribution of changes in the average value and in the dispersion of the explanatory variables as well as in the average value and in the dispersion of the coefﬁcients of these variables in the earnings functions. In what follows we will try to give an intuitive interpretation to these various effects and then present and analyze the results of our empirical investigation.

4.1. The Determinants of the Change over Time in the Between-Groups Dispersion Let us start with the impact of the change over time in the between-groups dispersion. As proven in Appendix B, three factors may play a role here: the explanatory variables, the regression coefﬁcients, and the relative size of the population subgroups. In addition, it should be stressed that the explanatory variables have an impact on the variation over time in the wage dispersion either because their average value changes or because their dispersion varies. The intuition of this distinction is as follows. Assume ﬁrst that the average value (average computed for groups h and k together) of a given explanatory variable l increases between times 0 and 1. Then for a given gap between the coefﬁcients blh and blk of this variable l in the earnings functions of groups h and k, the between-groups h and k wage

398

JOSEPH DEUTSCH AND JACQUES SILBER

dispersion should increase, ceteris paribus. Assume now that what increased is the gap between groups h and k in the average value of a given explanatory variable l. Then for given coefﬁcients blh and blk of the variable l in groups h and k, the between-groups wage dispersion between groups h and k should increase, ceteris paribus. Assume now that the average value over groups h and k of the coefﬁcients blh and blk of variable l in the earnings function of groups h and k increased. Then for a given gap between groups h and k in the value of the explanatory variable l, the wage dispersion should increase, ceteris paribus. But if one assumes that what increased is the gap (blh–blk) between groups h and k in the value of the coefﬁcient of variable l in the earnings functions of groups h and k, then, for a given average value (over groups h and k) of variable l, the wage dispersion should increase, ceteris paribus. Finally as far as the impact of a change in relative size of the population subgroups is concerned, the idea is, without entering into the technicalities of Appendix B, that changes in the relative sizes of the groups should also affect the between-groups wage dispersion.

4.2. The Determinants of the Change over Time in the Within-Groups Dispersion The intuition for the results derived in Appendix B is here simpler. Given that when we analyze the within-groups dispersion we assume from the onset that the regression coefﬁcients in the earnings functions are the same for all the individuals belonging to a given population subgroup, a change over time in these coefﬁcients will have an impact on the withingroups wage dispersion. Similarly, assuming no change over time in these coefﬁcients, a change in the within-groups dispersion of the explanatory variables will lead to a change in the overall within-groups dispersion. Clearly a change in the dispersion of the unobservables will also have an effect on the within-groups dispersion.

4.3. The Determinants of the Change over Time in the Value of the Overlapping Component The intuitive interpretation of the various elements of the change in this overlapping component is similar to that given previously to the components

Extending the Blinder–Oaxaca Approach

399

of the change in the between- and within-groups dispersion. We will therefore not examine each component of this change but just take an example. Assume a change occurred, among those involved in the overlapping, in the dispersion of the explanatory variables. Then clearly, assuming no change in the regression coefﬁcients, there will be a modiﬁcation of the overlapping component. Similarly, assume there was no change, among those involved in the overlapping, in the dispersion of the explanatory variables, but only in the value of the regression coefﬁcients. Then, evidently, there will be a change in the value of the overlapping component. Similar interpretations may be given to the other components of the change in the overlapping component. Let us now take a look at the results presented in Table 7 and concentrate on the changes that occurred in the overall wage dispersion between 1990 and 1998. It appears that the change (8.19%) in the between-groups dispersion was almost equal to that in the overall dispersion (8.59%) because the changes in the within-groups dispersion and in the amount of overlap neutralized each other. More than half this contribution of changes in the between-groups dispersion was a consequence of variations in the dispersion of the regression coefﬁcients (L). Another important factor was the change in the dispersion of the variables themselves (H). Table 7 indicates also that, as far as changes in the within-groups dispersion are concerned, the most important contribution to this change is related to variations over time in the various groups in the dispersion of the unobserved components. Finally the most important contributions to changes in the overlapping component refer either to changes over time in the dispersion of the regression coefﬁcients or to a variation in the average value of the explanatory variables among those individuals affected by the overlapping.

4.4. The Contribution of Different Population Subgroups to the Various Components of the Change in the Overall Wage Dispersion In Section 3.2 we explained how to compute the contribution of the different population subgroups to the three components of the overall wage dispersion (the between- and within-groups wage dispersion and the overlapping component). A similar exercise may be implemented to compute the contribution of the various population subgroups to the

0.58 1.24 0.79 4.36 5.40 0.22 0.58 0.81 0.26 0.07 0.32

0.21

2.19

1.89

3.08

7.37

2.85

0.21 1.22 0.26 0.48 1.19

Change in relative size of population Change in value of explanatory variables Change in regression coefﬁcients Change in unobserved variables Total change in wage dispersion Change in betweengroups dispersion GþJ H K I L

Contribution of those Born in Asia or Africa

Contribution of those Born in Israel

1.41 0.81 0.01 0.57 0.10

0.08

4.01

3.08

0.63

0.14

1.41

Contribution of those Born in Europe or America Who Immigrated before 1972

1.50 0.28 0.25 0.08 3.10

5.05

10.62

6.88

1.34

0.90

1.50

Contribution of those Born in Europe or America Who Immigrated after 1972

0.28 3.11 0.25 0.90 4.71

8.19

8.59

2.52

4.64

1.70

0.28

All Groups Together

Contributions of the Different Population Subgroups to the Various Components of the Changes in Wage Dispersion during the Period 1990–1998.

Component of Change

Table 8.

400 JOSEPH DEUTSCH AND JACQUES SILBER

Change in within-groups dispersion C D B Change in overlap S U T V Y Total change in wage dispersion 2.42 0.58 0.09 1.93 3.19 1.18 0.03 0.48 0.03 2.43 5.40

5.30

1.81 1.05 2.44 0.78 0.48 1.06 0.22 1.06 0.64 7.37 0.38 0.03 0.78 2.96 0.68 0.10 0.17 0.10 2.31 4.01

1.12 0.49 0.02 2.51 2.58 1.70 1.83 0.16 1.83 4.37 10.62

2.99 1.34 1.16 2.24 4.35 0.32 2.82 0.69 2.82 0.28 8.59

4.74

Extending the Blinder–Oaxaca Approach 401

402

JOSEPH DEUTSCH AND JACQUES SILBER

change over time in the three components. It is even possible to combine such a breakdown by population subgroups with the decomposition in subcomponents (impact of explanatory variables, of regression coefﬁcients and of unobservable characteristics) that was given in Table 7. This complex breakdown will not be detailed14 but an illustration of its application to the period 1990–1998 is given in Table 8. Table 8 indicates thus clearly the important role played by the group of those who immigrated from Europe or America after 1972. As far as the change in the between-groups dispersion is concerned we see, as expected, the important contribution of this group to the changes in the dispersion of the regression coefﬁcients (component L) and in the relative size of the various groups (components G and J). We also can observe the important role this group of immigrants plays in affecting the change in the overlapping component via, for example, the change over time in the dispersion of the unobservables (Y) among those individuals involved in the overlap.

5. CONCLUDING COMMENTS This paper extends the original approach of Blinder (1973) and Oaxaca (1973) by proposing a methodology for analyzing the respective impact of explanatory variables, the coefﬁcients of these variables in the earnings functions, and unobservable characteristics on the overall wage dispersion and its components (between- and within-groups dispersion as well as the degree of overlap between the groups’ wage distribution, when the individuals are also characterized by the groups to which they belong). An illustration based on income surveys conducted in Israel in 1982, 1990, and 1998 and making a distinction between four population subgroups, one of them including immigrants from Europe or America who came after 1971, indicated that the approach proposed here sheds some interesting light on the evolution over time of the wage dispersion in Israel. The paper also proposed a methodology allowing to decompose changes over time in the amount of wage dispersion. When applied to the same Israeli data this approach allowed us to show, for example, that the increase in the overall wage dispersion between 1990 and 1998 was strongly connected to the increase in the between-groups dispersion which was itself related to an increase during this period in the dispersion of the regression coefﬁcients which followed the massive immigration that took place in the early 1990s in Israel.

403

Extending the Blinder–Oaxaca Approach

NOTES 1. Further, it is not true that the coefﬁcients of the ‘‘Mincerian’’ earnings function reﬂect ‘‘differences in rates of return on human capital.’’ Whereas the schooling coefﬁcient can be interpreted as the average rate of return on human capital, the experience/tenure coefﬁcient indicates both returns and amounts of investment, the constant reﬂects innate earnings power where there is no investment, and coefﬁcients of demographic variables depict differences in earnings potential, assuming similar human capital investment trajectories for each demographic group. We are thankful to an anonymous referee for stressing these points. 2. In a recent paper Fields (2003) devised also a new method that can determine how much of the income inequality in an income-generating function is accounted for by each explanatory factor. This is what Fields (2003) called the levels decomposition. His paper suggested also a way to decompose the difference in inequality between two groups into speciﬁc contributions of the various explanatory factors that were themselves broken down into a coefﬁcient, a correlation, and a standard deviation effect. Fields (2003) called this procedure the change decomposition. The technique developed in the present study goes therefore, in a way, beyond Fields’ (2003) approach, ﬁrst because it is not limited to an analysis of the between-groups inequality, second because it succeeds at the end in determining the respective contributions of coefﬁcients, explanatory variables as well as residuals to the overall inequality of the dependent variable. It should be stressed however that because the analysis includes somehow interaction effects (the overlapping component) no attempt is made to look at the speciﬁc contribution of the different explanatory variables to the overall dispersion of the dependent variable. 3. Unfortunately the information available in the income surveys that were analyzed does not give the exact year of immigration so that it was not possible in the empirical analysis to make a difference between the impacts of the human capital accumulated abroad and in Israel. 4. On the other hand, over time immigrants accumulate more human capital and this should lower the wage gap. 5. ygh is evidently the geometric mean of the incomes in group h. 6. Following Gini (1959) we may say that there exists a ‘‘Transvariation’’ between two distributions {xi} and {yj} with respect to their (arithmetic, geometric,y) means mx and my when among the nxny possible differences (xi–yj), the sign of at least one of them is different from that of the expression (mx–my), nx and ny being the number of observations in these two distributions. The importance of such a ‘‘Transvariation’’ may be measured in several ways (see, Deutsch and Silber, 1998). The reference here is to the moment m1 of order 1 which is deﬁned as

Z

Z

þ1

m1 ¼

y

gðyÞdy 1

ðy xÞf ðxÞdx 1

where g(y) and f(x) are the densities of the variables.

404

JOSEPH DEUTSCH AND JACQUES SILBER

7. It may be observed that the Blinder (1973) and Oaxaca (1973) decomposition corresponds to what was deﬁned earlier as the between-groups mean difference DB as it is deﬁned in (11), for the speciﬁc case where there are only two groups k and h, assuming their size nh and nk are equal. (Their decomposition is in fact then equal to half the mean difference DB.) 8. The decomposition given in expressions (25)–(27) corresponds to that proposed by Reimers (1983). 9. The corresponding statistics for each of the four subgroups that have been distinguished (I, AA, EA, and NIM) and for each of the years 1982, 1990, and 1998 are given in Appendix A. 10. This implies that the years spent in the army are considered as part of the working experience. 11. Since this study is based on cross sections, it is in fact impossible to make a distinction between the impact of experience and that of the business cycle, and one has to be careful in interpreting some of the changes observed, for example, between 1982 and 1990. 12. This is conﬁrmed by the results of the regressions run separately for each of the four population subgroups and which are given in Appendix A. 13. It should be observed that the breakdown proposed here goes beyond the one suggested by Blau and Kahn (1996, 1997, 2000), ﬁrst because we are able to deal with more than two groups, second because we do not limit ourselves to changes in the between-groups dispersion, third because we stress the impact of more than four determinants. The four determinants they identify are changes in the average value of productive characteristics (explanatory variables), in the prices of these productive characteristics (in the regression coefﬁcients), in the dispersion of unmeasured characteristics, and ﬁnally in the relative position of the residuals of one group in the distribution of those of the other (an effect that is somehow one of the elements determining what we called change in the overlap). 14. It may be obtained, upon request, from the authors. 15. Thus, in expression (B.19), for example, the difference (xlgh,1–xlgk,1) could be negative despite the fact that the difference (ln ygh,1–ln ygk,1) is by assumption positive. Similarly in expression (B.23) the difference (blh,0–blk,0) may be negative although, by assumption, the gap (ln ygh,0–ln ygk,0) is positive.

REFERENCES Amir, S. (1980). The wage function of Jewish males in Israel, between the years 1968/69 and 1975/76. Bank of Israel Review (52), 3–14(in Hebrew). Amir, S. (1993). The absorption process of academic immigrants from the USSR in Israel: 1978–1984. Report of the Israeli International Institute for Applied Economic Policy Review (in Hebrew). Beenstock, M. (1993). Learning Hebrew and ﬁnding a job: Econometric analysis of immigration absorption in Israel. Discussion Paper No. 93.05, The Maurice Falk Institute for Economic Research in Israel, Jerusalem. Berger, M. (1985). The effect of cohort size on earnings growth: A reexamination of the evidence. Journal of Political Economy (93), 561–573.

Extending the Blinder–Oaxaca Approach

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Blau, F. D., & Kahn, L. M. (1996). Wage structure and gender earnings differentials: An international comparison. Economica, 63(Suppl), S29–S62. Blau, F. D., & Kahn, L. M. (1997). Swimming upstream: Trends in the gender wage differential in the 1980s. Journal of Labor Economics, 15(1, part 1), 1–42. Blau, F. D., & Kahn, L. M. (2000). Gender differences in pay. Journal of Economic Perspectives, 14(4), 75–99. Blinder, A. S. (1973). Wage discrimination: Reduced form and structural estimates. Journal of Human Resources (8), 436–455. Borjas, G. J. (1994). The economics of immigration. Journal of Economic Literature, XXXII, 1667–1717. Borjas, G. J. (2005). Labor economics (3rd ed.). Columbus, OH: McGraw-Hill. Chiswick, B. R. (1978). The effect of Americanization on the earnings of foreign-born men. Journal of Political Economy, 86, 897–921. Chiswick, B. R. (1997). Hebrew Language usage: Determinants and effects on earnings among immigrants in Israel. Discussion paper No. 97.09, The Maurice Falk Institute for Economic Research in Israel, Jerusalem. Dagum, C. (1960). Teoria de la transvariacion – Sus aplicaciones a la economia. Metron, XX, 1–208. Dagum, C. (1997). A new approach to the decomposition of the Gini income inequality ratio. Empirical Economics, 22(4), 515–531. Deutsch, J., & Silber, J. (1998). The overlapping of distributions: Alternative measures and their application to the analysis of consumption patterns. In: S. R. Chakravarty, D. Coondoo & R. Mukherjee (Eds), Quantitative economics: Theory and practice (pp. 229–246). New Delhi: Allied Publishers. Eckstein, Z., & Weiss, Y. (1997). The absorption of highly skilled immigrants: Israel: 1991–1995. Paper presented at the CEPR conference ‘‘European Migration: What Do We Know,’’ Munich, November 1997. Fields, G. S. (2003). Accounting for income inequality and its change: A new method, with application to the distribution of earnings in the United States. Research in Labor Economics, 22, 1–38. Fortin, N. M., & Lemieux, T. (1997). Institutional change and rising wage inequality: Is there a linkage? Journal of Economic Perspectives, 11(2), 75–96. Freeman, R. (1995). Are your wages set in Beijing. Journal of Economic Perspectives, 9(Summer), 15–32. Friedberg, R. M. (1995). You can’t take it with you? Immigration assimilation and the portability of human capital: Evidence from Israel. Discussion paper No. 95.02, The Maurice Falk Institute for Economic Research in Israel, Jerusalem. Gini, C. (1912). Variabilita e mutabilita: Contributo allo studio delle distribuzioni e relazioni statistiche. Studi Economico-Giuridici dell’Universita di Cagliari, 3, 1–158. Gini, C. (1959). Memorie de metodologia statistica: Volume secondo – Transvariazione, Roma: Libreria Goliardica. Goldin, C., & Margo, R. (1992). The great compression: The wage structure in the United States at mid-century. Quarterly Journal of Economics, 107, 1–34. Johnson, G. E. (1997). Changes in earnings inequality: The role of demand shifts. Journal of Economic Perspectives, 11(2), 41–54. Kendall, M. G., & Stuart, A. (1996). The advanced theory of statistics. London: Charles Grifﬁn and Company Limited. Krueger, A. B. (1993). How computers have changed the wage structure: Evidence from microdata, 1984–1989. Quarterly Journal of Economics, 108, 33–60.

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Levy, F., & Murnane, R. J. (1992). US earnings levels and earnings inequality: A review of recent trends and proposed explanations. Journal of Economic Literature, 30, 1333–1381. Mincer, J. (1974). Schooling, Experience and Earnings, 1974, N.B.E.R. Neuman, S. (1999). Alyah to Israel: Immigration under conditions of adversity. IZA Discussion Paper No. 89, Bonn, December 1999. Oaxaca, R. (1973). Male-female wage differentials in urban labor markets. International Economic Review, 9, 693–709. Ofer, G., Vinokur, A., & Bar-Chaim, Y. (1980). Absorption in Israel and economic contribution of immigrants from the Soviet Union. The Maurice Falk Institute of Economic Research (in Hebrew), Jerusalem. Polachek, S. W. (1975). Differences in expected post-school investment as a determinant of market wage differentials. International Economic Review, 16, 451–470. Reimers, C. (1983). Labor market discrimination against Hispanic and black men. Review of Economics and Statistics, 65, 570–579. Topel, R. H. (1997). Factor proportions and relative wages: The supply-side determinants of wage inequality. Journal of Economic Perspectives, 11(2), 55–74. Weiss, Y., Fishelson, G., & Mark, N. (1978). Income gaps between men by continent of origin: Israel, 1969–76. The Foerder Economic Research Institute, Tel-Aviv University, June 1978. Welch, F. (1979). The effects of cohort size on earnings: The baby boom babies’ ﬁnancial bust. Journal of Political Economy, 87, S65–S97. Wood, A. (1995). How trade hurt unskilled workers. Journal of Economic Perspectives, 9(Summer), 57–80.

APPENDIX A Table A1.

Descriptive Statistics and Regression Results for the 1982 Income Survey for Each of the Four Subpopulations.

Summary Statistics for the Variables and Regression Results Variable Individuals born in Israel (I)a Logarithm of wage per hour Intercept Married Single Years of schooling Years of experience

Mean

Standard deviation

3.9943

0.6113

0.7465 0.2385 11.5657 15.7247

0.4350 0.4262 3.0633 10.4861

Coefﬁcients

2.1859 0.4441 0.1503 0.0882 0.0364

tvalues

12.70 3.17 1.03 14.73 6.23

407

Extending the Blinder–Oaxaca Approach Table A1.

(Continued ).

Summary Statistics for the Variables and Regression Results Variable

Mean

Standard deviation

Square of years of 357.2224 experience Attended Talmudic school 0.0184

Coefﬁcients

tvalues

501.4416

0.0004 3.38

0.1345

0.6728 5.36

b

Individuals born in Asia or Africa (AA) Logarithm of wage per 3.9148 hour Intercept Married 0.9226 Single 0.0566 Years of schooling 8.9885 Years of experience 29.0381 Square of years of 1,001.4319 experience Attended Talmudic school 0.0173

0.5041

0.2672 0.2310 3.8689 12.5786 787.3419

3.2380 20.73 0.0327 0.29 –0.1657 1.24 0.0491 9.99 0.0184 3.15 0.0003 3.46

0.1305

0.1877 1.55

Individuals born in Europe or America who immigrated before 1972 Logarithm of wage per 4.1880 0.5716 hour Intercept 3.2318 Married 0.9263 0.2613 0.2038 Single 0.0329 0.1784 0.1363 Years of schooling 11.3132 3.7253 0.0595 Years of experience 35.0921 14.1397 0.0131 Square of years of 1,431.3862 971.1232 0.0002 experience Attended Talmudic school 0.0474 0.2124 0.3545

(EA)c

20.41 2.17 0.97 10.13 2.29 2.88 4.04

Individuals born in Europe or America who immigrated after 1971 (NIM)d Logarithm of wage per 3.9398 0.5371 hour Intercept 2.6320 11.14 Married 0.9177 0.2747 0.2433 1.53 Single 0.0433 0.2035 0.0186 0.08 Years of schooling 11.5563 4.0091 0.0499 5.85

408

JOSEPH DEUTSCH AND JACQUES SILBER Table A1.

(Continued ).

Summary Statistics for the Variables and Regression Results Variable

Mean

Standard deviation

Years of experience 25.7078 Square of years of 861.5595 experience Attended Talmudic school 0.0130

Coefﬁcients

tvalues

14.1658 836.2168

0.0480 4.94 0.0008 5.24

0.1132

0.1072 0.39

a

Summary statistics for the regression: R2 ¼ 0.3601, SE ¼ 0.48927, F ¼ 82.32, N ¼ 868. Summary statistics for the regression: R2 ¼ 0.1700, SE ¼ 0.45953, F ¼ 30.53, N ¼ 866. c Summary statistics for the regression: R2 ¼ 0.2152, SE ¼ 0.50667, F ¼ 35.69, N ¼ 760. d Summary statistics for the regression: R2 ¼ 0.2607, SE ¼ 0.46280, F ¼ 14.52, N ¼ 231. b

Table A2.

Descriptive Statistics and Regression Results for the 1990 Income Survey for Each of the Four Subpopulations.

Summary Statistics for the Variables and Regression Results Variable

Mean

Standard deviation

Individuals born in Israel (I)a Logarithm of wage per 2.4700 hour Intercept Married 0.7289 Single 0.2460 Years of schooling 12.1911 Years of experience 16.3499 Square of years of 373.8360 experience Attended Talmudic school 0.0232

Coefﬁcients

tvalues

0.5624

0.4445 0.4307 2.6088 10.3207 472.8218

0.8836 8.26 0.0592 0.79 0.1149 1.41 0.0891 18.98 0.0435 10.61 0.0006 7.10

0.1507

0.3045 3.87

b

Individuals born in Asia or Africa (AA) Logarithm of wage per 2.4929 hour Intercept Married 0.9178

0.5411

0.2746

1.3383 0.0487

8.75 0.53

409

Extending the Blinder–Oaxaca Approach Table A2.

(Continued ).

Summary Statistics for the Variables and Regression Results Variable

Mean

Single 0.0455 Years of schooling 10.1043 Years of experience 30.3951 Square of years of 1,070.2892 experience Attended Talmudic school 0.0126

Standard deviation

Coefﬁcients

tvalues

0.2084 3.6764 12.1008 802.5076

0.1684 1.33 0.0594 10.77 0.0353 5.66 0.0005 5.56

0.1117

0.4711 3.04

Individuals born in Europe or America who immigrated before 1972 Logarithm of wage per 2.6875 0.6163 hour Intercept 1.0617 Married 0.9137 0.2808 0.1419 Single 0.0400 0.1960 0.2130 Years of schooling 11.8347 3.4586 0.0773 Years of experience 34.9189 13.1700 0.0402 Square of years of 1392.7826 936.3921 0.0006 experience Attended Talmudic school 0.0274 0.1632 0.1852

(EA)c

4.87 1.21 1.25 9.26 4.64 4.70 1.23

Individuals born in Europe or America who immigrated after 1971 (NIM)d Logarithm of wage per 2.4516 0.5949 hour Intercept 1.0504 4.42 Married 0.8221 0.3824 0.2392 1.68 Single 0.1275 0.3336 0.0334 0.18 Years of schooling 12.8473 3.1253 0.0733 6.84 Years of experience 23.0889 13.7142 0.0187 1.80 Square of years of 721.1770 734.6558 0.0002 1.24 experience Attended Talmudic school 0.0134 0.1151 0.1618 0.60 a

Summary statistics for the regression: R2 ¼ 0.3373, SE ¼ 0.45880, F ¼ 132.33, N ¼ 1,549. Summary statistics for the regression: R2 ¼ 0.2653, SE ¼ 0.52880, F ¼ 29.53, N ¼ 475. c Summary statistics for the regression: R2 ¼ 0.2653, SE ¼ 0.52880, F ¼ 29.53, N ¼ 475. d Summary statistics for the regression: R2 ¼ 0.2027, SE ¼ 0.53214, F ¼ 13.58, N ¼ 298. b

410

JOSEPH DEUTSCH AND JACQUES SILBER

Table A3.

Descriptive Statistics and Regression Results for the 1998 Income Survey for Each of the Four Subpopulations.

Summary Statistics for the Variables and Regression Results Variable

Mean

Individuals born in Israel (I)a Logarithm of wage per 3.4884 hour Intercept Married 0.6593 Single 0.3074 Years of schooling 12.7199 Years of experience 16.8355 Square of years of 399.8894 experience Attended Talmudic school 0.0186 Individuals born in Asia or Africa (AA)b Logarithm of wage per 3.4912 hour Intercept Married 0.8928 Single 0.0547 Years of schooling 11.0717 Years of experience 32.0957 Square of years of 1,162.0249 experience Attended Talmudic school 0.0098

Standard deviation

Coefﬁcients

tvalues

0.6472

0.4740 0.4614 2.4466 10.7915 469.3617

1.3567 16.96 0.1301 2.61 0.338 0.61 0.1249 33.33 0.0378 11.76 0.0004 6.12

0.1352

0.2884 4.38

0.6371

0.3094 0.2274 3.5468 11.4843 742.8596

1.9982 12.06 0.0397 0.47 0.1357 1.07 0.0727 11.95 0.0467 6.11 0.0007 5.72

0.0987

0.0205 0.11

Individuals born in Europe or America who immigrated before 1972 Logarithm of wage per 3.8053 0.6824 hour Intercept 1.4726 Married 0.9206 0.2704 0.1637 Single 0.0265 0.1605 0.1148 Years of schooling 13.0356 3.0756 0.1098 Years of experience 34.9868 11.5728 0.0380 Square of years of 1,358.0025 879.0703 0.0004 experience Attended Talmudic school 0.0224 0.1480 0.2439

(EA)c

5.36 1.36 0.56 10.88 3.40 2.83 1.34

411

Extending the Blinder–Oaxaca Approach Table A3.

(Continued ).

Summary Statistics for the Variables and Regression Results Variable

Mean

Standard deviation

Coefﬁcients

tvalues

Individuals born in Europe or America who immigrated after 1971 (NIM)d Logarithm of wage per 3.2118 0.5935 hour Intercept 2.1244 19.02 Married 0.7933 0.4049 0.2093 3.35 Single 0.1506 0.3576 0.0976 1.24 Years of schooling 13.2988 2.6319 0.0651 11.77 Years of experience 21.7888 12.3316 0.0127 2.66 Square of years of 626.8232 613.1620 0.0003 3.61 experience Attended Talmudic school 0.0089 0.0939 0.3121 2.04 a

Summary statistics for the regression: R2 ¼ 0.3819, SE ¼ 0.50891, F ¼ 343.88, N ¼ 3,331. Summary statistics for the regression: R2 ¼ 0.2119, SE ¼ 0.56595, F ¼ 41.90, N ¼ 914. c Summary statistics for the regression: R2 ¼ 0.2508, SE ¼ 0.59123, F ¼ 28.34, N ¼ 491. d Summary statistics for the regression: R2 ¼ 0.1568, SE ¼ 0.54518, F ¼ 46.25, N ¼ 1,461. b

APPENDIX B. DECOMPOSING THE CHANGE OVER TIME IN THE WAGE DISPERSION We will successively derive a breakdown of the three components of expression (14) as they have been given in expressions (21)–(23), (25)–(27), and (29)–(32).

Decomposing the Change over Time in the Within-Groups Dispersion Let the subscripts 0 and 1 refer, respectively, to time 0 and 1. Assume n0 and n1 refer, respectively, to the size of the population at times 0 and 1. Using (21) we can now express the change over time in the within-groups

412

JOSEPH DEUTSCH AND JACQUES SILBER

dispersion as DW;1 DW;0 ¼ A þ B

(B.1)

A ¼ A1 A0

(B.2)

where

with # X XX " X 1 A1 ¼ 2 b ðxlih;1 xljh;1 Þ n21 h¼1 to m i2h j2h l¼1 to L lh;1 " # X X XX 1 2A1 ¼ b ðxlih;1 xljh;1 Þ 2 n21 h¼1 to m l¼1 to L i2h j2h lh;1

ðB:3Þ

with ln yih;1 4 ln yjh;1 and # X XX " X 1 2 b ðxlih;0 xljh;0 Þ A0 ¼ n20 h¼1 to m i2h j2h l¼1 to L lh;0 " # X X XX 1 2A0 ¼ b ðxlih;0 xljh;0 Þ 2 n20 h¼1 to m l¼1 to L i2h j2h lh;0

ðB:4Þ

with ln yih;0 4 ln yjh;0 , while B ¼ B1 B0

(B.5)

B1 ¼

X XX 1 2ðuih;1 ujh;1 Þ; with ln yih;1 4 ln yjh;1 n21 h¼1 to m i2h j2h

(B.6)

B0 ¼

X XX 1 2ðuih;0 ujh;0 Þ; with ln yih;0 4 ln yjh;0 n20 h¼1 to m i2h j2h

(B.7)

with

and

413

Extending the Blinder–Oaxaca Approach

Combining (B.3) and (B.4), we derive that X X XX 1 ½b ðxlih;1 xljh;1 Þ A1 A0 ¼ 2 n21 h¼1 to m l¼1 to L i2h j2h lh;1 X X XX 1 2 2 ½b ðxlih;0 xljh;0 Þ n0 h¼1 to m l¼1 to L i2h j2h lh;0

(B.8)

where for each period 0 and 1, in each group and for each explanatory variable, the individuals are ranked by decreasing value of their income (i.e., of the logarithm of their income). Expression (B.8) may then be written as A1 A0 ¼ CC þ DD

(B.9)

where "

"

X X 1 CC ¼ ðblh;1 þ blh;0 Þ ðxlih;1 xljh;1 Þ n21 h¼1 to m l¼1 to L i2h j2h 1 2 ðxlih;0 xljh;0 Þ n0 X

X

(B.10)

and "

" X X 1 DD ¼ ðblh;1 blh;0 Þ ðxlih;1 xljh;1 Þ n21 h¼1 to m l¼1 to L i2h j2h 1 þ 2 ðxlih;0 xljh;0 Þ n0 X

X

(B.11)

Similarly, combining (B.5)–(B.7), we may express B as B ¼ BB ¼ 2

X h¼1 to m

"

X X 1 1 u Þ ðu ðuih;0 ujh;0 Þ ih;1 jh;1 2 n1 n20 i2h j2h

# (B.12)

where the unobserved elements uih are, in each period, ranked by decreasing values of the individual incomes (i.e., of the logarithms of the individual incomes).

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JOSEPH DEUTSCH AND JACQUES SILBER

Combining ﬁnally expressions (B.1), (B.2), (B.9)–(B.12), we conclude that DW;1 DW;0 ¼ CC þ DD þ BB

(B.13)

where CC measures the impact of changes over time in the various groups in the dispersion of the explanatory variables, DD the effect of the modiﬁcation that took place over time in the different groups in the regression coefﬁcients, BB corresponds to the role played by variations over time in the various groups in the dispersion of the unobserved components, and AA measures the impact of the change over time in the relative size of the population subgroups. Decomposing the Change over Time in the Between-Groups Dispersion On the basis of (25) and using again the subscripts 1 and 0 to denote the periods 1 and 0, we may express the change over time in the between-groups dispersion as DB;1 DB;0 ¼ E þ F

(B.14)

E ¼ ðE1 E0Þ

(B.15)

where

with E1 ¼

(

" #) X nh;1 nk;1 X ðblh;1 þ blk;1 Þðxlgh;1 xlgk;1 Þ n21 l¼1 to L h¼1 to m k¼1 to m X

(B.16) for ln ygh1 4 ln ygk1 , with ( " #) X nh;0 nk;0 X X E0 ¼ ðblh;0 þ blk;0 Þðxlgh;0 xlgk;0 Þ n20 l¼1 to L h¼1 to m k¼1 to m (B.17) for ln ygh0 4 ln ygk0 , while F ¼ ðF1 F0Þ

(B.18)

415

Extending the Blinder–Oaxaca Approach

with ( F1 ¼

" #) X nh;1 nk;1 X ðxlgh;1 þ xlgk;1 Þðblh;1 blk;1 Þ n21 l¼1 to L h¼1 to m k¼1 to m X

(B.19) for ln ygh1 4 ln ygk1 ( " #) X nh;0 nk;0 X X F0 ¼ ðxlgh;0 þ xlgk;0 Þðblh;0 blk;0 Þ n20 l¼1 to L h¼1 to m k¼1 to m (B.20) for ln ygh0 4 ln ygk0 . Note that in expressions (B.16)–(B.20) the groups are classiﬁed by decreasing values of the means of the logarithms of the incomes during the relevant year, that is, by decreasing values of the geometric means of the incomes in the different groups.15 Combining (B.16) and (B.17), we now derive that the difference E1E0 may be expressed as ðE1 E0Þ ¼ G þ H þ I

(B.21)

G ¼ BG1 þ BG2 þ BG3

(B.22)

H ¼ BH1 þ BH2 þ BH3

(B.23)

I ¼ BI1 þ BI2 þ BI3

(B.24)

with

where ( BG1 ¼

1XXX ððblh;1 þ blk;1 Þðxlgh;1 xlgk;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblh;0 þ blk;0 Þðxlgh;0 xlgk;0 ÞÞ n21 n20

(B.25)

416

JOSEPH DEUTSCH AND JACQUES SILBER

for the cases where ln ygh1 4 ln ygk1 and ln ygh0 4 ln ygk0 ( 1XXX BG2 ¼ ððblh;1 þ blk;1 Þðxlgh;1 xlgk;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblh;0 þ blk;0 Þðxlgk;0 xlgh;0 ÞÞ n21 n20 for the cases where ln ygh1 4 ln ygk1 and ln ygh0 o ln ygk0 ( 1XXX BG3 ¼ ððblh;1 þ blk;1 Þðxlgk;1 xlgh;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblh;0 þ blk;0 Þðxlgh;0 xlgk;0 ÞÞ n21 n20 for the cases where ln ygh1oln ygk1 and ln ygh0Wln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BH1 ¼ þ ððblh;1 þ blk;1 Þ 4 l h k n21 n20 )

(B.26)

(B.27)

(B.28)

þ ðblh;0 þ blk;0 ÞÞ½ðxlgh;1 xlgk;1 Þ ðxlgh;0 xlgk;0 Þ for the cases where ln ygh1Wln ygk1 and ln ygh0Wln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BH2 ¼ þ ððblh;1 þ blk;1 Þ 4 l h k n21 n20 )

(B.29)

þ ðblh;0 þ blk;0 ÞÞ½ðxlgh;1 xlgk;1 Þ ðxlgk;0 xlgh;0 Þ for the cases where ln ygh1W ln ygk1 and ln ygh0oln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BH3 ¼ þ ððblh;1 þ blk;1 Þ 4 l h k n21 n20 ) þ ðblh;0 þ blk;0 ÞÞ½ðxlgk;1 xlgh;1 Þ ðxlgh;0 xlgk;0 Þ

(B.30)

Extending the Blinder–Oaxaca Approach

for the cases where ln ygh1oln ygk1 and ln ygh0Wln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BI1 ¼ þ ððxlgh;1 xlgk;1 Þ 4 l h k n21 n20 )

417

(B.31)

þ ðxlgh;0 xlgk;0 ÞÞ½ðblh;1 þ blk;1 Þ ðblh;0 þ blk;0 Þ for the cases where ln ygh1Wln ygk1 and ln ygh0Wln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BI2 ¼ þ ððxlgh;1 xlgk;1 Þ 4 l h k n21 n20 )

(B.32)

þ ðxlgk;0 xlgh;0 ÞÞ½ðblh;1 þ blk;1 Þ ðblh;0 þ blk;0 Þ for the cases where ln ygh1W ln ygk1 and ln ygh0oln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BI3 ¼ þ ððxlgk;1 xlgh;1 Þ 4 l h k n21 n20 )

(B.33)

þ ðxlgh;0 xlgk;0 ÞÞ½ðblh;1 þ blk;1 Þ ðblh;0 þ blk;0 Þ for the cases where ln ygh1oln ygk1 and ln ygh0Wln ygk0. Similarly, combining (B.22) and (B.23), we derive that the difference (F1–F 0) in (B.18) may be expressed as ( ( X X X nh;1 nk;1 ðF1 F0Þ ¼ ðblh;1 blk;1 Þðxlgh;1 þ xlgk;1 Þ n21 l¼1 to L h¼1 to m k¼1 to m )) nh;0 nk;0 ðblh;0 blk;0 Þðxlgh;0 þ xlgk;0 Þ n20 (B.34) or, after some algebraic manipulations, as ðF1 F0Þ ¼ J þ K þ L

(B.35)

418

JOSEPH DEUTSCH AND JACQUES SILBER

where J ¼ BJ1 þ BJ2 þ BJ3

(B.36)

K ¼ BK1 þ BK2 þ BK3 L ¼ BL1 þ BL2 þ BL3

(B.37)

1XXX ððblh;1 blk;1 Þðxlgh;1 þ xlgk;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblh;0 blk;0 Þðxlgh;0 þ xlgk;0 ÞÞ n21 n20

(B.38)

with ( BJ1 ¼

for the cases where ln ygh1Wln ygk1 and ln ygh0Wln ygk0 (

1XXX ððblh;1 blk;1 Þðxlgh;1 þ xlgk;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblk;0 blh;0 Þðxlgh;0 þ xlgk;0 ÞÞ n21 n20 for the cases where ln ygh1Wln ygk1 and ln ygh0oln ygk0 ( 1XXX BJ3 ¼ ððblk;1 blh;1 Þðxlgh;1 þ xlgk;1 Þ 2 l h k ) nh;1 nk;1 nh;0 nk;0 þ ðblh;0 blk;0 Þðxlgh;0 þ xlgk;0 ÞÞ n21 n20 BJ2 ¼

for the cases where ln ygh1oln ygk1 and ln ygh0Wln ygk0 ( 1 X X X nh;1 nk;1 nh;0 nk;0 BK1 ¼ þ ½ðblh;1 blk;1 Þ 4 l h k n21 n20 ) þ ðblh;0 blk;0 Þ½ðxlgh;1 þ xlgk;1 Þ ðxlgh;0 þ xlgk;0 Þ

(B.39)

(B.40)

(B.41)

Extending the Blinder–Oaxaca Approach

419

for the cases where ln ygh1Wln ygk1 and ln ygh0Wln ygk0 ( BK2 ¼

1 X X X nh;1 nk;1 nh;0 nk;0 þ ½ðblh;1 blk;1 Þ 4 l h k n21 n20 )

(B.42)

þ ðblk;0 blh;0 Þ½ðxlgh;1 þ xlgk;1 Þ ðxlgh;0 þ xlgk;0 Þ

for the cases where ln ygh1Wln ygk1 and ln ygh0oln ygk0 (

1 X X X nh;1 nk;1 nh;0 nk;0 BK3 ¼ þ ½ðblk;1 blh;1 Þ 4 l h k n21 n20 )

(B.43)

þ ðblh;0 blk;0 Þ½ðxlgh;1 þ xlgk;1 Þ ðxlgh;0 þ xlgk;0 Þ

for the cases where ln ygh1oln ygk1 and ln ygh0Wln ygk0 ( BL1 ¼

1 X X X nh;1 nk;1 nh;0 nk;0 þ ½ðxlgh;1 þ xlgk;1 Þ 4 l h k n21 n20 )

(B.44)

þ ðxlgh;0 þ xlgk;0 Þ½ðblh;1 blk;1 Þ ðblh;0 blk;0 Þ

for the cases where ln ygh1Wln ygk1 and ln ygh0Wln ygk0

( BL2 ¼

1 X X X nh;1 nk;1 nh;0 nk;0 þ ½ðxlgh;1 þ xlgk;1 Þ 4 l h k n21 n20 )

þ ðxlgh;0 þ xlgk;0 Þ½ðblh;1 blk;1 Þ ðblk;0 blh;0 Þ

(B.45)

420

JOSEPH DEUTSCH AND JACQUES SILBER

for the cases where ln ygh1Wln ygk1 and ln ygh0 o ln ygk0 ( BL3 ¼

1 X X X nh;1 nk;1 nh;0 nk;0 þ ½ðxlgh;1 þ xlgk;1 Þ 4 l h k n21 n20 )

(B.46)

þ ðxlgh;0 þ xlgk;0 Þ½ðblk;1 blh;1 Þ ðblh;0 blk;0 Þ for the cases where ln ygh1oln ygk1 and ln ygh0W ln ygk0. Combining ﬁnally expressions (B.15)–(B.46), we derive that the variation (DB,1DB,0) that occurs over time in the between-groups dispersion may be written as DB;1 DB;0 ¼ ðG þ JÞ þ ðH þ KÞ þ ðI þ LÞ

(B.47)

where (GþJ), (HþK), (IþL) measure, respectively, the effect of changes over time in the relative size of the different groups, the impact of variations over time in the average value of the different explanatory variables in the various groups and the role played by modiﬁcations over time in the regression coefﬁcients in the different groups. Note that the effect (HþK) of changes in the value of the explanatory variables may be decomposed into two parts and interpreted as follows: the impact (H) of variations over time in the dispersion of these explanatory variables and the role (K) of modiﬁcations taking place over time in the average values of these variables. Similarly the effect (IþL) of changes in the regression coefﬁcients may be decomposed into two parts and interpreted as follows: the impact (L) of variations over time in the dispersion over the different groups of these regression coefﬁcients and the role (I) played by the modiﬁcations that take place over time in the average values of these coefﬁcients.

Decomposing the Change over Time in the Overlapping Component It is important, at this stage, to remember what this component refers to. Let us assume that the mean ln ygh of the logarithms of the incomes in group h is higher than the corresponding mean ln ygk in group k. Despite the fact that on average the incomes in group h are higher than those in group k,

Extending the Blinder–Oaxaca Approach

421

one cannot exclude the possibility that some individuals belonging to group k have a higher income that some other individuals who are members of group h. This is the essence of the concept of overlapping between two income distributions. In giving the correct expression for the change in the degree of overlapping we will try to determine the role played by changes in the value of the explanatory variables, in the regression coefﬁcients and in the unobserved components. Using expressions (28)–(33) the change M in the degree of overlapping may be expressed as M ¼ Dp;1 Dp;0 ¼ P þ Q þ R

(B.48)

P ¼ P1 þ P2 þ P3

(B.49)

Q ¼ Q1 þ Q2 þ Q3

(B.50)

R ¼ R1 þ R2 þ R3

(B.51)

where

and X X XXX 1 1 ½ðb þ blh;1 Þðxljk;1 xlih;1 Þ P1 ¼ 2 n21 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb þ blh;0 Þðxljk;0 xlih;0 Þ 2 n20 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.52) for ln ygh0W ln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1;

P2 ¼

X X XXX 1 1 ½ðb þ blh;1 Þðxljk;1 xlih;1 Þ 2 2 n1 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb þ blh;0 Þðxljk;0 xlih;0 Þ 2 2 n0 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.53)

422

JOSEPH DEUTSCH AND JACQUES SILBER

for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; P3 ¼

X X XXX 1 1 ½ðb þ blh;1 Þðxljk;1 xlih;1 Þ 2 2 n1 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb þ blh;0 Þðxljk;0 xlih;0 Þ 2 2 n0 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.54)

for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1; and X X XXX 1 1 Q1 ¼ ½ðb blh;1 Þðxljk;1 þ xlih;1 Þ 2 n21 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb blh;0 Þðxljk;0 þ xlih;0 Þ 2 n20 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.55) for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; X X XXX 1 1 Q2 ¼ ½ðb blh;1 Þðxljk;1 þ xlih;1 Þ 2 n21 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb blh;0 Þðxljk;0 þ xlih;0 Þ 2 n20 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.56) for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; X X XXX 1 1 Q3 ¼ ½ðb blh;1 Þðxljk;1 þ xlih;1 Þ 2 n21 l¼1 to L h¼1 to m i2h kah j2k lk;1 X X XXX 1 1 ½ðb blh;0 Þðxljk;0 þ xlih;0 Þ 2 n20 l¼1 to L h¼1 to m i2h kah j2k lk;0 (B.57) for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1;

Extending the Blinder–Oaxaca Approach

423

and R1 ¼

X XXX 1 ½ðujk;1 uih;1 Þ n21 h¼1 to m i2h kah j2k X XXX 1 ½ðujk;0 uih;0 Þ 2 n0 h¼1 to m i2h kah j2k

(B.58)

for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; X XXX 1 R2 ¼ ½ðujk;1 uih;1 Þ n21 h¼1 to m i2h kah j2k X XXX (B.59) 1 2 ½ðujk;0 uih;0 Þ n0 h¼1 to m i2h kah j2k for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; X XXX 1 R3 ¼ 2 ½ðujk;1 uih;1 Þ n1 h¼1 to m i2h kah j2k X XXX (B.60) 1 þ 2 ½ðujk;0 uih;0 Þ n0 h¼1 to m i2h kah j2k for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1. Here again expressions (B.52)–(B.60) may be further decomposed by writing that P1 ¼ S1 þ T 1

(B.61)

P2 ¼ S2 þ T 2

(B.62)

P3 ¼ S3 þ T 3

(B.63)

Q1 ¼ U 1 þ V 1

(B.64)

Q2 ¼ U 2 þ V 2

(B.65)

Q3 ¼ U 3 þ V 3

(B.66)

and

424

JOSEPH DEUTSCH AND JACQUES SILBER

where (

X X XX 1 X ½ðb þ blh;1 Þ 4 l¼1 to L h¼1 to m i¼2h kah j2k lk;1 1 1 þðblk;0 þ blh;0 Þ ðxljk;1 xlih;1 Þ 2 ðxljk;0 xlih;0 Þ n21 n0

S1 ¼

(B.67)

for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; (

X XXX 1 X ½ðb þ blh;1 Þ 4 l¼1 to L h¼1 to m i2h kah j2k lk;1 1 1 þðblk;0 þ blh;0 Þ ðxlih;1 xljk;1 Þ 2 ðxljk;0 xlih;0 Þ n21 n0

S2 ¼

(B.68)

for ln ygh0 W ln ygk0, ln ygh1 o ln ygk1, ln yjk0 W ln yih0, ln yih1 W ln yjk1; (

X XXX 1 X ½ðb þ blh;1 Þ 4 l¼1 to L h¼1 to m i2h kah j2k lk;1 1 1 þðblk;0 þ blh;0 Þ x Þ x Þ ðx ðx ljk;1 lih;1 lih;0 ljk;0 n21 n20

S3 ¼

(B.69)

for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1; and ( 1X X XXX 1 T1 ¼ ðxljk;1 xlih;1 Þ 4 l h¼1 to m i2h kah j2k n21 (B.70) 1 þ 2 ðxljk;0 xlih;0 Þ ½ðblk;1 þ blh;1 Þ ðblk;0 þ blh;0 Þ n0 for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; ( 1X X XXX 1 T2 ¼ ðxlih;1 xljk;1 Þ 4 l h¼1 to m i2h kah j2k n21 (B.71) 1 þ 2 ðxljk;0 xlih;0 Þ ½ðblk;1 þ blh;1 Þ ðblk;0 þ blh;0 Þ n0

Extending the Blinder–Oaxaca Approach

425

for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; (

1X X XXX 1 ðxlih;1 xljk;1 Þ 4 l h¼1 to m i2h kah j2k n21 1 þ 2 ðxlih;0 xljk;0 Þ ½ðblk;1 þ blh;1 Þ ðblk;0 þ blh;0 Þ n0

T3 ¼

(B.72)

for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1. Similarly we have ( 1X X XXX ½ðb blh;1 Þ U1 ¼ 4 l h¼1 to m i2h kah j2k lk;1 (B.73) 1 1 þðblk;0 blh;0 Þ ðxljk;1 þ xlih;1 Þ 2 ðxljk;0 þ xlih;0 Þ n21 n0 for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; ( 1X X XXX ½ðb blh;1 Þ U2 ¼ 4 l h¼1 to m i2h kah j2k lk;1 (B.74) 1 1 þðblk;0 blh;0 Þ ðxljk;1 þ xlih;1 Þ 2 ðxljk;0 þ xlih;0 Þ n21 n0 for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; ( 1X X XXX ½ðb blh;1 Þ U3 ¼ 4 l h¼1 to m i2h kah j2k lk;1 (B.75) 1 1 þðblk;0 blh;0 Þ ðxljk;1 þ xlih;1 Þ 2 ðxljk;0 þ xlih;0 Þ n21 n0 for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1; and ( 1X X XXX 1 V1 ¼ ðxljk;1 þ xlih;1 Þ 4 l h¼1 to m i2h kah j2k n21 (B.76) 1 þ 2 ðxljk;0 þ xlih;0 Þ½ðblk;1 blh;1 Þ ðblk;0 blh;0 Þ n0

426

JOSEPH DEUTSCH AND JACQUES SILBER

for ln ygh0Wln ygk0, ln ygh1Wln ygk1, ln yjk0Wln yih0, ln yjk1Wln yih1; ( V2 ¼

1X X XXX 1 ðxljk;1 þ xlih;1 Þ 4 l h¼1 to m i2h kah j2k n21 1 þ 2 ðxljk;0 þ xlih;0 Þ½ðblk;1 blh;1 Þ ðblk;0 blh;0 Þ n0

(B.77)

for ln ygh0Wln ygk0, ln ygh1oln ygk1, ln yjk0Wln yih0, ln yih1Wln yjk1; ( V3 ¼

1X X XXX 1 ðxljk;1 þ xlih;1 Þ 4 l h¼1 to m i2h kah j2k n21 1 þ 2 ðxljk;0 þ xlih;0 Þ½ðblk;1 blh;1 Þ ðblk;0 blh;0 Þ n0

(B.78)

for ln ygh0oln ygk0, ln ygh1Wln ygk1, ln yih0Wln yjk0, ln yjk1Wln yih1. Combining expressions (B.48)–(B.78) we ﬁnally derive that M ¼W þX þR

(B.79)

W ¼ ðS1 þ S 2 þ S 3 Þ þ ðU 1 þ U 2 þ U 3 Þ

(B.80)

X ¼ ðT 1 þ T 2 þ T 3 Þ þ ðV 1 þ V 2 þ V 3 Þ

(B.81)

R ¼ ðR1 þ R2 þ R3 Þ

(B.82)

where

where W, X, and R measure, respectively, the effect of changes in the value of the explanatory variables, in the regression coefﬁcients and in the unobserved components. Additional distinctions may be made by noting that (S1þS2þS3) measures the effect of changes in the dispersion of the values of the explanatory variables among those involved in the overlapping in each periods, while (U1þU2þU3) corresponds somehow to the impact of variations over time in the average values of these explanatory variables among those same individuals.

Extending the Blinder–Oaxaca Approach

427

Similarly (V1þV2þV3) measures the effect of changes over time in some weighted dispersion of the regression coefﬁcients, these weights depending only on those individuals involved in the overlapping, while (T1þT2þT3) corresponds to the impact of the variation over time in some weighted average of these regression coefﬁcients, here again the weights depending only on those individuals who are part of the overlapping. Finally R measures the change over time in the dispersion of the unobserved components among those individuals involved in the overlapping in both periods.

SALARY OR BENEFITS? Paul Oyer ABSTRACT Employer-provided beneﬁts are a large and growing share of compensation costs. In this paper, I consider three factors that can affect the value created by employer-sponsored beneﬁts. First, ﬁrms have a comparative advantage (e.g., due to scale economies or tax treatment) in purchasing relative to employees. This advantage can vary across ﬁrms based on size and other differences in cost structure. Second, employees differ in their valuations of beneﬁts and it is costly for workers to match with ﬁrms that offer the beneﬁts they value. Finally, some beneﬁts can reduce the marginal cost to an employee of extra working time. I develop a simple model that integrates these factors. I then generate empirical implications of the model and use data from the National Longitudinal Survey of Youth to test these implications. I examine access to employer-provided meals, child care, dental insurance, and health insurance. I also study how beneﬁts are grouped together and differences between beneﬁts packages at for-proﬁt, not-for-proﬁt, and government employers. The empirical analysis provides evidence consistent with all three factors in the model contributing to ﬁrms’ decisions about which beneﬁts to offer.

‘‘Concierge services, petsitting, nap rooms and the option to telecommute are really just sneaky new ways to get already overworked employees to toil even harder, says Jill Andresky Fraser, author of White-Collar Sweatshop. ‘These perks are often illusory.

Work, Earnings and other Aspects of the Employment Relation Research in Labor Economics, Volume 28, 429–467 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0147-9121/doi:10.1016/S0147-9121(08)28013-1

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They exist just for their publicity value,’ she says. ‘In reality, staff face resentment if they try to work from home or take family days. And free food, nap rooms and home computers just keep people tied to their work.’’’–Economist (2001)

1. INTRODUCTION Signiﬁcant effort has gone into the economic analysis of ﬁrms’ choices about what to make and what to buy. Economists have also often considered when parties to a transaction exchange goods and services rather than one side simply purchasing from the other with currency. The provision of employee beneﬁts, which are a large and growing portion of employment costs, is driven by both the make or buy decision and nonmonetary barter. The most widely discussed employer-sponsored beneﬁt is health insurance, but some employers also provide dental care, subsidized or free beverages and meals, subsidized or free child care, discounts on the ﬁrms’ products, and even inofﬁce massages.1 Given the wide use of noncash compensation, it must be the case that these workplace beneﬁts create economic beneﬁts that cannot be captured if employees make all their own consumption choices.2 In this paper, I model potential sources of this value and explore these sources empirically. As modeled by Rosen (1974) and others, beneﬁts can create value in the employment relationship when ﬁrms can purchase goods and services more cost-effectively than employees. That is, the ﬁrm acts as a buyers’ club for its employees with much of the potential cost advantage of this arrangement driven by tax treatment of beneﬁts. I develop a model that adds two elements to this ‘‘tax/buyers’ club’’ explanation of employee beneﬁts. First, I consider the potential costs of matching employees who value certain beneﬁts with ﬁrms that can procure them efﬁciently. I add an element of search costs to a model where employees have heterogeneous tastes and the ﬁrm cannot price discriminate (in the sense of tying compensation to beneﬁts consumption). In this case, hiring workers at random would reduce or eliminate the value created by employer-provided beneﬁts, so the ﬁrm trades off the cost of ﬁnding employees that value the beneﬁts it can provide efﬁciently against its procurement cost advantage. As long as employee preferences are reasonably ﬁxed, the ‘‘tax/buyers’ club’’ model, with or without search costs, suggests that beneﬁts packages will be stable over time. The second innovation in the model, on the other hand, helps explain the fact that many beneﬁts are sensitive to the business cycle.3 I consider the possibility that certain beneﬁts are provided as a means

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431

of reducing employees’ cost of effort. When the marginal product of labor is high, the employer may want to encourage the worker to extend his work week. Assuming the employee’s cost of effort is convex in hours worked, the employer is trying to buy additional hours that are very costly to the employee. By offering beneﬁts such as meals, entertainment options at the workplace, and errand services, employers lower the employee’s cost of effort. That is, by helping the employee subcontract some of his personal duties to a party that can execute these duties at lower cost, the employer can free more time for the employee to engage in high-value tasks. I derive a simple model that integrates these various factors that may lead ﬁrms to offer beneﬁts. The model generates several testable implications, which I explore using data from the National Longitudinal Survey of Youth (NLSY). In 1979, the NLSY interviewed 12,686 people born between 1957 and 1964. When possible, these same individuals were interviewed annually through 1994 and bi-annually through 2000. From 1985 to 2000, the NLSY included questions about fringe beneﬁts at the person’s main job. I use these data to perform empirical analysis in three stages. First, I examine factors associated with ﬁrms’ providing individual beneﬁts, including employerprovided or employer-subsidized meals, child care, dental insurance, and health insurance. Second, I look at how these beneﬁts are combined with other offerings to form beneﬁts ‘‘packages’’ that are likely to either attract certain types of workers or help lower the cost of employee effort. Finally, I compare the beneﬁts policies of employers in the for-proﬁt, not-for-proﬁt, and government sectors to see if the variation is consistent with expected differences in attributes of employers and workers in these sectors. I ﬁnd results that are consistent with the implications of the model. I show that employer-sponsored beneﬁts are associated with factors that proxy for employers’ costs and employees’ tastes. For example, larger ﬁrms’ which can gain greater scale economies in beneﬁts purchasing are more likely to provide all beneﬁts. Firms are more likely to provide beneﬁts related to their industry, suggesting they provide beneﬁts when they can create them at low cost. It appears people sort to ﬁrms based on their demand for beneﬁts. For example, similar to prior work, I show that people with families are signiﬁcantly more likely to hold jobs with employer-provided health insurance. I also show that sorting extends to other beneﬁts such as child care and on-the-job meals. The correlation between hours of work and some beneﬁts is highly supportive of these beneﬁts lowering the cost of effort. All beneﬁts are more likely for full-time workers than for part-time workers. However, employees who work particularly long hours are signiﬁcantly more likely to have

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employer-provided meals than other full-time workers. This relationship between long hours and beneﬁts does not hold for beneﬁts that would seem less naturally complementary to effort such as dental care and health care. Also, it seems likely that employer-provided child care can help lower the costs of switching from part-time to full-time but that people who work very long hours prefer not to keep their children at the workplace. The evidence is consistent with this notion, as employer-provided child care is signiﬁcantly more likely for full-time workers than part-time workers. However, employees who work particularly long hours are less likely to have employer-provided child care than those who work standard full-time hours. The model’s implications are also consistent with the empirical analysis of beneﬁts ‘‘packages.’’ I show that people who work long hours are relatively likely to receive a package of beneﬁts that lower the cost of effort, including meals, parking, and ﬂexible time. I also show that workers who are likely to be seeking stable employment relationships are more likely to get a package of beneﬁts that the ﬁrm can purchase efﬁciently but that do not affect the cost of effort. The ﬁnal set of empirical results shows interesting patterns in beneﬁts packages across different types of employment classes. I show that government employers are much less likely than for-proﬁt companies to provide beneﬁts that lower the cost of effort. Government and not-for-proﬁt employers are much more likely to provide a package of beneﬁts that might be valued by employees interested in long-term employment relationships. Self-employed workers show the exact opposite pattern, however. This is consistent with government and nonproﬁt employees being risk averse and seeking stable employment without long hours, while self-employed workers try to lower the burden of working hard. The theory and the empirical evidence lead to the conclusion that the optimal compensation package can be affected by numerous factors. As a result, ﬁrms get involved in the procurement of various products and services that are only related to their business because of employee preferences. Due to variations in labor market conditions, income tax structure, and purchasing economies, it is often efﬁcient for ﬁrms to expand their scope into creating employment packages rather than simply engaging in cash-only transactions with workers. This paper builds on a large existing theoretical and empirical literature on employer-provided beneﬁts. Rosen (1986) surveys the theoretical and empirical work on compensating differentials in the labor market. He outlines a model where employees sort efﬁciently and costlessly to the

Salary or Beneﬁts?

433

employer that offers the beneﬁts they value most. As he and Brown (1980) discuss, it is very difﬁcult to measure the ‘‘price’’ of employee beneﬁts in terms of lowering wages.4 To avoid this issue, I primarily analyze the existence of beneﬁts rather than the exact salary trade-off. For a more recent survey, focusing on employer-sponsored health insurance, see Gruber (2000). The paper makes several novel contributions to this literature. First, by adding search costs to prior models of workplace beneﬁts, I derive a relationship between beneﬁts and job tenure. Second, to my knowledge, the only other work on the relationship between beneﬁts and effort are papers by Rajan and Wulf (2006) and Marino and Zabojnik (2008b). The focus of Rajan and Wulf (2006) is quite different, however, as they analyze senior executives, large ﬁrms, and ‘‘perks’’ such as company jets, chauffer service, and country club membership. Marino and Zabojnik (2008b) design a model where ﬁrms use beneﬁts in addition to ﬁnancial incentives in order to lower risk costs. Their model further develops the idea of a complementarity between effort and beneﬁts that I study here. The empirical support for that general idea in this paper can be interpreted as consistent with their model, as well. Third, while the bulk of prior work studies health insurance (probably because it is such a large cost), I focus on a broader set of beneﬁts that can provide more insight into a greater variety of motivations for employers to sponsor workplace beneﬁts. Though not as large as healthrelated beneﬁts, some of these beneﬁts, such as workplace meals and child care, are growing in prevalence and have become large markets. Finally, my ﬁndings on differences in beneﬁts policies between for-proﬁt companies and other types of employers are novel and may inform understanding of differences among employer classes. The rest of this paper proceeds as follows. In the next section, I develop a model of employer-provided beneﬁts that incorporates several factors that can affect the optimal salary–beneﬁt mix and derive testable empirical implications of the model. Section 3 tests the model’s implications using selfreported data on individuals’ work-related beneﬁts. I conclude and discuss the implications of the analysis for ﬁrms and policy makers in Section 4.

2. A MODEL OF EMPLOYER-PROVIDED BENEFITS In this section, I develop a simple model of a ﬁrm’s optimal mix of compensation between salary and employer-sponsored beneﬁts. I focus on four factors that may affect the salary–beneﬁts trade-off: heterogeneity

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PAUL OYER

across ﬁrms in the cost of providing beneﬁts, heterogeneity across employees in their relative preferences for money and beneﬁts, costs to ﬁrms of ﬁnding workers that will accept the compensation packages they offer, and the possibility that some beneﬁts may lower the cost of work-related effort. I brieﬂy motivate consideration of each of these four factors. Then I develop the formal model that integrates these effects and discuss the model’s empirical implications. Employers can be efﬁcient providers of goods and services for their employees for several reasons.5 First, people interact regularly at work, so the marginal costs of organizing group buying is lowered there. Also, ﬁrms may attract people with similar tastes, enabling larger purchases. Perhaps most importantly, there can be substantial tax advantages to some beneﬁts being provided by ﬁrms relative to paying employees more money and letting them purchase goods with after-tax income. The efﬁciency of beneﬁts is also affected by differences across individuals in their taste for beneﬁts. For example, those workers who do not drink coffee will not accept a wage discount in exchange for employer-provided coffee. But, if ﬁrms can ﬁnd employees who value the beneﬁts they offer, then they can lower their total compensation expenses. Given the heterogeneity of ﬁrms and employees, random assignment of employees to ﬁrms would not allow ﬁrms to maximize the efﬁciency of beneﬁts. That is, in the absence of being able to price discriminate by lowering individuals’ salaries according to their taste for beneﬁts, ﬁrms and workers have to expend resources searching for appropriate matches. While the discussion to this point has focused on the trade-off between salary and beneﬁts, there is also a relationship between some beneﬁts and leisure. Consider a simple example. Some ﬁrms provide ‘‘concierge services’’ to their employees.6 These services help employees to subcontract out some of the necessities of their personal lives so that they can engage in higher value activities at work. That is, by taking care of details in people’s personal lives such as laundry, shopping, and even planning children’s birthday parties, concierge services lower employees’ cost of effort. To see how these issues relate to one another in a more formal context, consider a labor market where ﬁrms contract with workers who provide a set of tasks (or level of effort) e. Firms capture revenue of ye per period of an employment relationship. There is no hidden action problem, so ﬁrms offer a package of wages, beneﬁts, and effort, (w, b, e), to potential employees. b is the dollars per employee that the ﬁrm spends on beneﬁts. Firms vary in how efﬁciently they can spend their beneﬁts dollars. Let N be a parameter that captures ﬁrm heterogeneity in the cost of providing a beneﬁt. N is increasing

Salary or Beneﬁts?

435

in the amount of beneﬁts a given ﬁrm can purchase with each dollar it expends. It is convenient to think of N as the number of employees at the ﬁrm (where N is exogenously determined).7 N can also be such factors as how closely a beneﬁt is related to products the ﬁrm is already producing. For example, a ski resort can presumably provide lift tickets at relatively low cost to its employees (assuming there is at least some idle capacity on the mountain), so ski resorts would have relatively high N if the relevant beneﬁt is lift tickets. At the time of hiring, each employee is expected to work for T periods. T is driven by such factors as the nature of the work, the value of ﬁrm-speciﬁc human capital, and the stability of employee preferences.8 Employees vary in how much utility they derive from beneﬁts. In particular, person i derives diV(b, N) from the ﬁrm’s expenditure (b) on employee beneﬁts. Let di be drawn from a distribution with density f(d) and cumulative density F(d). The function V incorporates representative preferences, individual heterogeneity in preferences (through d), and the relative efﬁciency of purchasing on the part of the ﬁrm. That is, it is convenient analytically to capture the heterogeneity of both workers and ﬁrms through the representation of the individual’s utility function. This also allows the value of diV(b, N) to be interpreted as a match-speciﬁc valuation of beneﬁts. But it is important to bear in mind that b is the amount the ﬁrm spends on beneﬁts, while diV(b, N) is the amount the employee values those expenditures. I make the following assumptions about the beneﬁts valuation function. People prefer more beneﬁts to less, but the marginal value of additional beneﬁts is decreasing (i.e., VbZ0 and Vbbr0). The purchasing advantages of employers (scale economies) are concave (i.e., VNZ0 and VNNr0). Also, the marginal value to the employee of a dollar spent on beneﬁts is greater at larger ﬁrms (i.e., VbNZ0). Fig. 1 graphs V as a function of b at two different levels of N, under these assumptions. In this example, if di ¼ 1, then any level of b such that V(b, N) is below the 45-degree line is inefﬁcient because the ﬁrm is spending more on beneﬁts than it can ‘‘charge’’ the employee through a wage discount. The cost of effort completes the employee’s utility function. An employee bears personal cost of doing his job of c(e, b). Assume the standard convex cost of effort (ce(e, b)W0 and cee(e, b)W0). Now assume that beneﬁts lower the employees’ cost of effort (cb(e, b)o0). Most importantly, I assume ceb(e, b)o0. That is, the marginal cost of an extra unit of effort is decreasing in beneﬁts. This captures the notion that working late is less costly if dinner is provided, that working hard all week is less costly when a concierge is provided, or even that working is less unpleasant when attractive art is posted in the ﬁrm’s corridors.9

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High N (large) firm

V(b,N)

Low N (small) firm

45-degree line; “unprofitable” to be at any point below this line

b

Fig. 1.

Employee Valuation of Beneﬁts.

The employee has an alternative job that pays w0 in cash with e ¼ 0, so he accepts any (w, b, e) combination such that wþdiV(b, N)c(e, b)Zw0. All potential employees accept an offer of (w, b, e)=(w0, 0, 0). Ideally, the model would solve for w0 endogenously. That is, market wages would be a function of ﬁrms’ beneﬁts cost structure and employee preferences for beneﬁts. Adding this to the model would add a great deal of complication and require assumptions about the workers’ information when engaging in search. However, I believe the basic results and intuition would be unchanged. One way to avoid concern over the exogenous market wage is to interpret the current model as being about choices the employer makes regarding beneﬁts that other employers cannot provide.10 All else equal, the ﬁrm wants to lower costs of employment, which it can do by ﬁnding potential employees with the highest values of di. However, it is costly to search for such workers. To capture this in the model, I assume that it costs m to offer a job to an employee and that, at the time the job is offered, the ﬁrm does not know the employee’s preferences. As a result, the expected costs of hiring a new worker are (m/pr(accepts)), or m 1 Fððw0 w þ cðe; bÞÞ=ðVðb; NÞÞÞ

437

Salary or Beneﬁts?

The ﬁrm sets the wage such that w ¼ w0 dVðb; NÞ þ cðe; bÞ

(1)

for some critical d.11 The ﬁrm maximizes proﬁts over T periods, including both the costs of hiring and the annual cost of compensation. Substituting for w using (1), this problem can be written max y e b w0 þ dVðb; NÞ cðe; bÞ d;b;e

m Tð1 FðdÞÞ

(2)

The proﬁt function is quasisupermodular in ðd; b; eÞ and, given the assumptions of the model, satisﬁes the single crossing property in ðd; b; e; T; N; mÞ. Therefore, Theorem 4 of Milgrom and Shannon (1994) applies to the ﬁrm’s problem and I can state the following results. I do not provide formal proofs, as they are derived from various simple cross-partial derivative calculations. Implication 1. b and d are increasing in N. In words, a comparative advantage in purchasing a beneﬁt has two effects on a ﬁrm – it leads the ﬁrm to provide more of that beneﬁt and it leads the ﬁrm to invest in ﬁnding employees who value that beneﬁt relatively highly. In the model, there is efﬁcient sorting between ﬁrms that can cost-effectively supply a beneﬁt and employees that value the beneﬁt highly. Implication 2. b and d are positively correlated. In the model, beneﬁts and strong tastes for beneﬁts are complements. That is, if a ﬁrm wants to select people that have relatively high valuations for a certain beneﬁt, they will provide more of that beneﬁt. This suggests that workers with a taste for a beneﬁt will sort to ﬁrms that provide that beneﬁt. Implication 3. b and d are increasing in T. When ﬁrm–worker matches last longer, then any value that can be created by the use of beneﬁts becomes larger relative to the costs of matching ﬁrms to workers. As a result, in longer employment relationships, ﬁrms will want to offer more beneﬁts and attempt to screen more carefully for workers who will take large wage discounts for those beneﬁts.

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Implication 4. e and b are positively correlated if cebo0. Firms will provide more of the types of beneﬁts that lower the cost of effort when they ask for higher levels of effort. Empirical tests of this implication require some judgment, as not all beneﬁts are likely to lower the cost of effort. For example, while concierge services may make it easier for employees to stay at the ofﬁce, it seems unlikely that an employer can lower the cost of employee effort by providing dental insurance. Implications 1, 2, 3, and 4 are the key testable empirical hypotheses that I will analyze in the empirical section below. The model does make additional predictions, though the NLSY data that I use will not allow me to test these directly. I now brieﬂy state and discuss these implications. Implication 5. b and e are increasing in y if cebo0. When the marginal return to effort is high, ﬁrms will ﬁnd it efﬁcient to provide more of the beneﬁts that make it easier for the employee to exert effort. The use of concierge services during the boom of the late 1990s, followed by a drop in the use of such services after the boom, is consistent with this idea. During the good times, ﬁrms attempted to make high-value employees’ personal lives easier so they could stay late. But when long work weeks were no longer valuable, ﬁrms let employees take care of their personal chores. This implication could, in principle, be tested crosssectionally because I would expect higher wage employees (where wage proxies for marginal product) to receive more beneﬁts than lower-level employees. However, while this interpretation will clearly be shown to be consistent with the data in the next section, it cannot be separated from the idea that employees who value beneﬁts more (due to higher tax rates and due to lower marginal utility for cash) are more likely to receive beneﬁts. That is, this implication cannot be separated from Implication 2. Implication 6. b and d are decreasing in m. Increased search costs have the opposite effect of increasing expected length of the employment relationship in that they make the costs of ﬁnding a person who values beneﬁts higher relative to the value created by beneﬁts once the match is made. This suggests that lowering the costs to ﬁrms of ﬁnding and screening workers would lead them to make beneﬁts a larger part of compensation. Note that there is ample evidence regarding some of these implications in prior empirical studies of employer-sponsored health insurance. Implication 2, which suggests that employees will sort to ﬁrms based on beneﬁts, has been

Salary or Beneﬁts?

439

analyzed in the context of health insurance by Scott, Berger, and Black (1989), Dranove, Spier, and Baker (2000), and Levy (1998). Scott et al. (1989) study the effect of Internal Revenue Service rules that require beneﬁts to be offered on a nondiscriminatory basis in order to qualify for tax exemption. They show that this has enhanced sorting of workers into occupations that match their preferences (using income as a proxy). Dranove et al. (2000) develop a model where employers offer health insurance due to cost and tax advantages, but, in order to discourage over-consumption of this beneﬁt, require employees to make a contribution to insurance premiums. This saves the ﬁrm some expense, at the cost of some efﬁciency in the total costs to the ﬁrm and the workers, by encouraging some employees to utilize health insurance offered by their spouse’s employer. Levy (1998) draws similar conclusions by studying the relationship between employee contributions and average age of a ﬁrm’s employees. I will perform similar analyses of sorting in the health insurance context. However, I will also analyze the role of sorting workers through other beneﬁts that have not received as much attention in prior studies.12 As mentioned above, Implication 2 can be interpreted as suggesting a connection between beneﬁts and taxes. This implication has also received support from prior studies of health insurance. See, for example, Royalty (2000) and Gruber and Lettau (2004), who show that health insurance provision is highly sensitive to tax rates. The results in Gruber and Lettau (2004) are also consistent with economies of scale and, more speciﬁcally, with the assumption that VNW0 because insurance beneﬁts are, on average, signiﬁcantly higher at larger ﬁrms. I have emphasized the ﬁrm’s purchasing efﬁciency and matching of employees with ﬁrms strictly based on employee tastes. However, a ﬁrm could also use beneﬁts if employee tastes for a certain beneﬁt are correlated with productivity at the ﬁrm. Consider, for example, a ﬁrm that felt the most productive workers were those who were intellectually curious and valued education. In the context of the model, this would imply a positive correlation between y and d. The ﬁrm might offer a tuition reimbursement beneﬁt, even in the absence of any tax or purchasing advantage, as a means of inducing the most productive potential employees to signal their tastes (and, therefore, their productivity). While this suggests a somewhat different model from the one I have outlined (and one that is closely related to Salop & Salop, 1976), both emphasize the ﬁrm using beneﬁts to sort on a certain type of worker. As a result, the empirical implications (at least those that are testable) are quite similar. Therefore, at this point, I make no attempt to distinguish between sorting strictly on preferences and using beneﬁts to sort on productivity.

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3. EMPIRICAL ANALYSIS 3.1. Data I use data from the NLSY. The NLSY started with a sample of 12,686 Americans who were between the ages of 14 and 21 in 1979. Every year from 1979 to 1994, and then in the years 1996, 1998, and 2000, those members of the original sample who could be found and interviewed were asked many questions about employment and other issues.13 I use the 1985–2000 interviews because most respondents had become permanently attached to the labor force by then and these are the years with the most questions related to employee beneﬁts. The total NLSY sample size in these years varies from 10,894 to 8,033. However, because I only look at employed respondents, the usable sample size is somewhat smaller. In each year, I use responses relating to the job that the NLSY determined to be the respondent’s ‘‘main job.’’ This is the job at which he worked the most hours at the time of the interview or, if the person is not working at the time of the interview, it is the last job he held (as long as he worked there after the previous interview). Table 1 provides summary statistics of key demographic and employment variables in the NLSY sample. I use a total of 82,555 observations from 10,658 workers, with any given worker providing up to 13 observations. The summary statistics do not apply to each of the individual analyses that follow, because some of the relevant questions were not asked each year. Just under half the observations are women and just over half are married. About 60% of the observations are people with children, with the average respondent having 1.2 children at the time of an interview.14 Naturally, given that the sample ages over time, this average (as well as the marriage rate) varies across years in the sample. Fewer than 40% of 1985 respondents had children, while almost 80% of those interviewed in 2000 had at least one child. This aging and changing demographics could complicate the empirical analysis in that controls for year could also control for aging of the sample. I attempt to minimize this effect throughout the following analysis by always controlling for a full set of age indicator variables so that the year effects should pick up, for example, differences between 30-year-old workers in 1989 and 1990. The NLYS includes a measure of the unemployment rate in the local labor market for each person in the sample. The measure is crude, however, revealing only whether the unemployment rate is 0–3%, 3–6%, 6–9%, etc. Most of the variation in this variable is explained by person ﬁxed effects and

441

Salary or Beneﬁts? Table 1.

Female Married Spouse works Children indicator Number of children Local unemployment Employees Part-time More than full-time Tenure (weeks) Hourly wage ($1,990) Age Food industry Child-related industry Dental industry Health-related industry Meals provided Child care provided Dental insurance Medical insurance

NLSY Summary Statistics.

Mean

Median

Standard Deviation

Sample Size

47.0% 52.2% 74.1% 61.2% 1.225 6–9% 1,981 6.2% 27.3% 201.1 $16.26 31.26 8.1% 4.6% 0.5% 8.4% 15.1% 7.2% 56.2% 75.8%

Na Na Na Na 1 3–6% 50 Na Na 123 $8.60 31 Na Na Na Na Na Na Na Na

Na Na Na Na 1.259 Na 12,195 Na Na 211.7 $397 4.67 Na Na Na Na Na Na Na Na

82,555 82,555 43,058 82,555 82,555 81,051 79,832 82,529 82,529 81,499 82,555 82,555 23,703 69,868 82,261 82,555 23,703 69,868 82,261 82,555

Notes: Sample includes 82,255 person/year observations (from a total of 10,658 people) who hold a job and provided a positive wage. Years are 1986–1994, 1996, 1998, and 2000. Samples size varies (here and in the following tables) because respondent did not answer or the question was not asked each year. ‘‘Spouse works’’ indicates that the respondent’s spouse worked at least 1,000 hours in the calendar year preceding the interview. ‘‘Local unemployment’’ is provided in 3% bands (i.e., either 0–3%, 3–6%, etc.). ‘‘Employees’’ is the number of employees at the establishment where the respondent works. ‘‘Part-time’’ indicates people who usually work fewer than 30 h per week at their main job. ‘‘More than full-time’’ includes people who usually work more than 40 h per week at that job. ‘‘Food industry’’ includes stores that sell food and restaurants, ‘‘child-related industry’’ includes elementary and secondary schools, day care services, residential care facilities, and social services, ‘‘dental industry’’ includes dentist ofﬁces, and ‘‘health-related industry’’ includes doctors’ ofﬁces, hospitals, nursing homes, and health services.

year effects. That is, the unemployment rate does not change much in local markets during the sample, except as it moves up and down with national trends. Therefore, after controlling for year, this variable is largely a crude region indicator variable. The ‘‘employees’’ row shows the number of employees at the site where the respondent works. The NLSY has other measures of ﬁrm size, such as whether the employer has multiple locations and the total number of

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PAUL OYER

workers at all the employer’s locations. I use employees at the worker’s site for most of the analysis. The results are not sensitive to using alternative proxies for ﬁrm size. Section 3.7 discusses this and alternative interpretations to the ﬁrm size results. Over 90% of the sample regularly works 30 h/week or more, with 67% reporting working 30–40 h/week (full-time) and 27% working more than 40 h/week (more than full-time). The median wage is about $9/h (real $1,990) and the average is considerably higher. Table 1 displays the fraction working in industries related to the employee beneﬁts I analyze because these industries can presumably provide these beneﬁts at low cost. The last four rows of the sample show the fraction of employees who reported that their employer offered various beneﬁts. In 1988, 1989, and 1990, the NLSY asked respondents if their employer made ‘‘company paid or subsidized meals’’ available to them. Approximately 15% of respondents said their employer offered them this beneﬁt. From 1988 to 2000, the NLSY asked if respondents’ ﬁrms offered them ‘‘company provided or subsidized child care.’’ Only 7% said their ﬁrm provided this beneﬁt.15 Not surprisingly, healthcare-related beneﬁts were more common. Over half of the NLSY sample reported that their employer offered dental beneﬁts and about three quarters said yes when asked ‘‘Does your employer make available to you medical, surgical, or hospital insurance that covers injuries or major illnesses off the job?’’

3.2. Employer-Provided Meals Meals that employees receive at the workplace present an opportunity to investigate all four of the testable implications of the model. Implication 1 of the model says that ﬁrms with a cost advantage in providing a beneﬁt (either due to scale economies, tax savings, or simply saving individual effort of food preparation) will provide that beneﬁt. This suggests employees are more likely to receive meals from their employer when the ﬁrm is in the food business (that is, surely it is efﬁcient for restaurants to provide meals to employees) and when the ﬁrm is relatively large, allowing it to take advantage of scale economies in purchasing (especially in the case of on-site subsidized cafeterias). Implication 2 predicts that workers will sort to ﬁrms that provide beneﬁts that they value relatively highly. To proxy for value to the employee, I include children and marital status. I would expect people with families to have a higher opportunity cost of dining at the workplace and, therefore,

Salary or Beneﬁts?

443

expect these proxies to be negatively related to on-the-job meals. I also expect higher-paid workers to be more likely to receive meals at the workplace, as the tax advantages are greater for these workers. Implication 3 implies that meals will be more common with longer employment spells. The hours of work variables are potentially informative about Implication 4 of the model, which predicts that beneﬁts will be related to employee effort. As the model suggested, beneﬁts that lower the cost of effort are more valuable when greater effort is required. Therefore, Implication 4 predicts that employer-provided meals will be increasing in hours worked. Table 2 presents the results of logit regressions that test these hypotheses. The dependent variable is the indicator for whether the person receives employer-provided or employer-subsidized meals in a given year. The coefﬁcients displayed in the ﬁrst four columns are the marginal effect on the probability of receiving this beneﬁt if the explanatory variable increases by one. The ﬁfth column shows the coefﬁcients from a ﬁxed-effects (conditional) logit, using the methodology in Chamberlain (1980). Identiﬁcation in this case comes from changes in beneﬁts and changes in the explanatory variables. As a result, the sample size is smaller because anyone for whom the dependent variable is constant throughout the sample is dropped. There is no coefﬁcient for gender because it is constant for each person. The regressions provide support for the relationship between employerprovided meals and ﬁrm cost of providing beneﬁts (Implication 1). First note that a doubling of the number of employees at the work site increases the likelihood of the ﬁrm providing meals by approximately 1 percentage point. Given a base probability of 15% of receiving meals, this is a large effect. See Section 3.7 for a more detailed discussion of possible interpretations of the ﬁrm size–beneﬁts relationship. Firms that are in food-related businesses, such as bakeries and restaurants, are much more likely to provide meals. As expected, these relationships do not vary by gender and they are still strong (though the coefﬁcients are not comparable) in column 5 when controlling for person ﬁxed effects. The data are also consistent with employees who value meals more sorting to ﬁrms that provide them (Implication 2), as both marriage and children are negatively related to workplace meals. Married workers with nonworking spouses are about 20% less likely (3 percentage points on a base of 15%) to receive meals at work than single workers. Married workers with working spouses are also less likely than single workers to be offered meals at work, though less likely than married workers whose spouses do not work. This is consistent with couples where both people are busy ﬁnding it less personally costly to be at work. Both the married and working spouse effects are

(0.0063) (0.0037) (0.0065) (0.0101)

0.0188 (0.0095) 0.0086 (0.0012) 0.0330 (0.0121) 0.0390 (0.0060) 0.0052 (0.0019) 0.0197 (0.0046) 0.1989 (0.0082) 0.058 21,852

0.0019 0.0003 0.0219 0.0307

0.0019 (0.0063) 0.0004 (0.0037) 0.0216 (0.0106) 0.0290 (0.0118) 0.0021 (0.0136) 0.0184 (0.0095) 0.0086 (0.0012) 0.0328 (0.0120) 0.0389 (0.0060) 0.0052 (0.0019) 0.0197 (0.0046) 0.1986 (0.0082) 0.059 21,852

Interactions

Females

0.0094 (0.0168) 0.0102 (0.0018) 0.0234 (0.0137) 0.0312 (0.0100) 0.0061 (0.0029) 0.0084 (0.0072) 0.1897 (0.0114) 0.058 10,184

0.0015 (0.0053) 0.0217 (0.0095) 0.0110 (0.0180)

Meals.

0.0300 (0.0116) 0.0071 (0.0017) 0.0653 (0.0264) 0.0426 (0.0075) 0.0047 (0.0025) 0.0295 (0.0061) 0.2077 (0.0120) 0.062 11,668

0.0008 (0.0052) 0.0240 (0.0090) 0.0343 (0.0124)

Males

0.3582 (0.1583) 0.0585 (0.0213) 0.3973 (0.1880) 0.2731 (0.0986) 0.0393 (0.0509) 0.1037 (0.0792) 0.9916 (0.1519) 0.041 4,236

0.0580 (0.0772) 0.3324 (0.2080) 0.1507 (0.2424)

Fixed Effects

Notes: Data are from NLSY. Each column reports the results of a logit, except column 5 which is a ﬁxed-effects conditional logit. The dependent variable is an indicator that equals 1 if the respondent indicates his/her main employer provides paid or subsidized meals. Sample includes all employed people who report their wage and answer the relevant beneﬁts question. The sample is smaller in column 5 because any person for whom the dependent variable is always 1 or always 0 is dropped from the sample. Explanatory variables are described in Table 1. Each regression also includes year and age indicators. Sample years are 1988–1990. Standard errors, adjusted for correlation among multiple responses by the same person, are in parentheses. Coefﬁcients are marginal effects on the probability that the respondent’s ﬁrm provides the beneﬁt, except in column 5 where they are coefﬁicients from the conditional logit.

Female Local unemployment Children indicator Married Married children Spouse works Log employees Part-time Wfull-time Tenure ( 100) Log wage Food industry Pseudo-R2 Sample size

Base Case

Table 2.

444 PAUL OYER

Salary or Beneﬁts?

445

stronger for men than for women. Women whose spouses do not work are relatively rare, however, so it is difﬁcult to interpret this relationship. People (of either gender) with children are much less likely to be in jobs where they are offered meals. Also, higher wages are associated with workplace meals, consistent with the tax effects.16 These relationships generally hold up when using ﬁxed effects. However, probably due to lack of within-person variation in marital status and children, the marriage and children coefﬁcients are not signiﬁcant. The fact that people with longer tenure are less likely to receive meals contradicts Implication 3 of the model. This could be due to the fact that employee preferences for work-related meals are likely to change as their family status changes. The logit results on hours worked are consistent with a relationship between beneﬁts and effort costs (Implication 4). Full-time workers (the excluded category in the logit) are somewhat more likely to receive meals at work than part-time workers. However, the important effect of hours is for those who work more than full time. Employees who work more than 40 h per week have about a 7% higher likelihood of receiving meals at work than part-time workers and about a 4% higher likelihood than those who work full time. The coefﬁcients on part-time and more than full-time are both statistically different from zero at better than the 1% level. These relationships hold for both genders and when controlling for person ﬁxed effects. They are economically meaningful given an overall employerprovided meal probability of 15%. These results appear even more striking when compared to later regressions, which will show that employees who work more than full time are no more likely than full-time workers to receive beneﬁts that do not complement long hours of work. Given that work-related meals are a key example of how the beneﬁts– effort relationship can affect ﬁrms’ purchases, it is worth considering the size of these effects in the overall economy. Sodexho USA and Aramark are both large providers of meals to US businesses. Aramark, for example, states in their 2003 10-K statement: ‘‘We satisfy the business dining needs of several million people annually.’’ Both companies generate several billion dollars of revenue annually in this segment of the market, with double-digit annual growth. In addition, many work-related meals are provided by small caterers and restaurants. The estimates in Table 2 suggest that working more than full-time increases employer-sponsored meal probability by about one quarter. It therefore seems likely that a nontrivial portion of this multi-billion dollar business is related to the complementarity between meals and effort.

446

PAUL OYER

3.3. Child Care I now consider employer-provided child care. Implication 4, regarding the complementarity between effort and beneﬁts, operates quite differently in the child care context than for meals. Employees who are primarily responsible for their children seem unlikely to be swayed to work very long hours as a result of employer-provided child care. However, it is plausible that employer-provided child care can help some employees increase their working hours, if not to extreme levels. The effort complementarity idea may apply to child care on the part-time versus full-time margin rather than in leading people to work more than full-time. Table 3 shows the results of logits where the dependent variable is 1 if the NLSY respondent reports that his employer provides or subsidizes child care. The explanatory variables are the same as in Table 2, except that the child indicator now is determined by whether the respondent lives in a household with a child under the age of seven. The results support the connection between beneﬁts and ﬁrm cost structures (Implication 1). People who work in industries that are related to child services are much more likely to get child care through their employers and larger employers are far more likely to provide child care. Child-care beneﬁts are also associated with some factors that suggest employers search for those who value this beneﬁt and these employees sort to employers that provide it (Implication 2).17 For example, women and employees with higher paying jobs (and, presumably, higher tax rates) are signiﬁcantly more likely to get child-care beneﬁts. However, child-care beneﬁts are not signiﬁcantly related to marital status, working status of spouse, or even whether the employee has children.18 The interaction between being married and having children is also not signiﬁcantly related to child-care beneﬁts, so there is no evidence that single parents are particularly likely to sort to jobs with child care. The surprising lack of a connection between family characteristics and child-care beneﬁts largely holds for both genders and when controlling for person ﬁxed effects. It may be the case that people who plan to have children match to ﬁrms that provide child care, but do not need this beneﬁt during much of their relatively long tenure on the job. In any case, the overall evidence regarding child-care beneﬁts and worker sorting is, at best, mixed. The results support Implication 3 more strongly. Employer-provided child care is more common at longer tenure jobs (indicating high ‘‘T’’ in the buyers’ club model).

(0.0032) (0.0015) (0.0027) (0.0047)

0.0046 (0.0039) 0.0124 (0.0005) 0.0132 (0.0050) 0.0051 (0.0030) 0.0016 (0.0006) 0.0164 (0.0020) 0.0444 (0.0055) 0.066 64,021

0.0183 0.0095 0.0004 0.0059

0.0188 (0.0032) 0.0095 (0.0015) 0.0094 (0.0070) 0.0094 (0.0050) 0.0138 (0.0077) 0.0049 (0.0039) 0.0124 (0.0005) 0.0135 (0.0050) 0.0052 (0.0030) 0.0016 (0.0006) 0.0161 (0.0020) 0.0441 (0.0055) 0.067 64,021

Interactions

0.0000 (0.0076) 0.0145 (0.0009) 0.0114 (0.0067) 0.0067 (0.0057) 0.0022 (0.0011) 0.0151 (0.0035) 0.0576 (0.0075) 0.058 30,194

0.0095 (0.0025) 0.0011 (0.0043) 0.0031 (0.0088)

Females

Child Care.

0.0040 (0.0041) 0.0107 (0.0006) 0.0343 (0.0106) 0.0038 (0.0032) 0.0012 (0.0007) 0.0174 (0.0023) 0.0234 (0.0101) 0.071 33,827

0.0097 (0.0018) 0.0003 (0.0034) 0.0105 (0.0052)

Males

0.1141 (0.0840) 0.1726 (0.0119) 0.2548 (0.1103) 0.1067 (0.0617) 0.0646 (0.0161) 0.0713 (0.0490) 0.7314 (0.1172) 0.042 15,607

0.0476 (0.0362) 0.0054 (0.0570) 0.1196 (0.1259)

Fixed Effects

Notes: Dependent variable is an indicator that equals 1 if the respondent indicates his/her main employer provides paid or subsidized child care. Sample years are 1988–1994, 1996, 1998, and 2000. For further information, see notes to Table 2.

Female Local unemployment Children indicator Married Married children Spouse works Log employees Part-time Wfull-time Tenure( 100) Log wage Related industry Pseudo-R2 Sample size

Base Case

Table 3.

Salary or Beneﬁts? 447

448

PAUL OYER

The results are consistent with beneﬁts being used to lower employees’ effort costs (Implication 4). Full-time workers are signiﬁcantly more likely to get child care at work than part-time workers. The 1.3 percentage point decrease in child care probability for part-time workers suggests these employees are about 20% less likely to get work-related child care than fulltime workers. However, those who work more than full time are less likely to get work-related child care than those who work full time. This difference is statistically signiﬁcant at the 10% level and the point estimate indicates a large difference based on full-time versus more-than-full-time status.19 The point estimates are similar, though less signiﬁcant, for each gender. Column 5 shows that the relationship between long hours and less child care comes from cross-sectional differences. Controlling for ﬁxed effects, it appears that when people change from full-time to more than full-time jobs, they do not value employer-sponsored child care. Combined with the results on hours worked and employer-provided meals, the importance of using beneﬁts to affect effort costs is well supported by the data. The results are consistent with the idea that employers provide child care to ease the transition from part-time to full-time work and they provide meals to make it easier for employees to work long hours. Finally, employer-provided child care is more common in more competitive labor markets. An increase of 3% in the local unemployment rate is associated with a 1 percentage point reduction in child care probability (or about a one-seventh reduction). This provides some suggestive evidence that is consistent with Implication 3 in that it could indicate that, when labor markets are tight, ﬁrms use child care to increase labor supply by helping to ease the transition from part-time to full-time work.20 In unreported regressions, I found further suggestive support for this hypothesis by interacting the unemployment variable with the hours variables. The hours effects are signiﬁcantly larger when unemployment is low – that is, an unemployment/part-time interaction variable is positive, an unemployment/more-than-full-time interaction is negative, and both are at least marginally signiﬁcant.

3.4. Dental and Health Insurance The largest beneﬁt given to US employees, in terms of likelihood of receiving it and cost to ﬁrms is health insurance.21 This is as much by historical accident and due to institutional factors as it is a reﬂection of any sort of optimal allocation of resources. Nevertheless, given the tax incentives

Salary or Beneﬁts?

449

and opportunities to use such a high-cost beneﬁt to affect the employment relationship, it is well worth studying determinants of health insurance provision.22 Health insurance, as well as dental insurance, can help shed light on the relationship between beneﬁts and effort because they are different in important ways from employer-provided meals and child care. It seems unlikely that either of these beneﬁts is complementary to employee effort or hours of work (i.e., I would expect ceb ¼ 0). It does not seem likely that the value of this beneﬁt should be related to an employee’s marginal product. Therefore, if insurance also shows different prevalence for full-time workers and more-than-full-time workers, I would suspect that the results with regard to work hours for child care and meals are not driven by forces captured in the model. As Tables 4 and 5 show, however, there is no meaningful difference in insurance likelihood between full-time and morethan-full-time employees.23 This suggests that the provision of insurance is not driven by an attempt to affect effort. As might be expected, the results are highly consistent with the relationship between beneﬁts and employer costs (Implication 1). Working in a related industry (low cost of providing beneﬁt) or for a large ﬁrm (which helps amortize the ﬁxed cost of establishing a program and creates greater economies of scale) are strongly positively related to health and dental beneﬁts in all speciﬁcations. A 10% increase in ﬁrm size increases dental probability by 0.86 percentage points (which is a 1.5% increase on the unconditional 56% probability of having dental insurance). The predicted relationship between beneﬁts and employee sorting (Implication 2) also ﬁnds some support in the data, though some of the results are ambiguous in this regard. Higher pay (which proxies for tax rate) is associated with both beneﬁts. Married workers, who may want to get beneﬁts for the rest of their family, are far more likely to be offered health insurance. This relationship is limited to those with working spouses in the case of dental insurance, which could indicate these couples have relatively good jobs. Married workers may also have higher likelihood of being offered insurance because their employment relationships are more stable. People with children are less likely to receive these beneﬁts than those with no children. This could be because some children are covered by spouses’ insurance. In fact, when not controlling for marriage (in an unreported logit), children are associated with much higher rates of health insurance coverage. Column 2 of both tables shows that the negative child effect is much lower for married people, indicating that single parents are the least likely group to have health or dental insurance. This could be

(0.0081) (0.0038) (0.0081) (0.0111)

0.0339 (0.0095) 0.0856 (0.0019) 0.3130 (0.0129) 0.0067 (0.0071) 0.0210 (0.0022) 0.2464 (0.0084) 0.4225 (0.0684) 0.186 77,082

0.0705 0.0166 0.0324 0.0004

0.0708 (0.0081) 0.0168 (0.0038) 0.0608 (0.0127) 0.0214 (0.0138) 0.0436 (0.0159) 0.0357 (0.0096) 0.0856 (0.0019) 0.3144 (0.0129) 0.0064 (0.0071) 0.0208 (0.0022) 0.2457 (0.0084) 0.4237 (0.0683) 0.186 77,082

Interactions

0.0350 (0.0166) 0.0769 (0.0026) 0.2944 (0.0148) 0.0070 (0.0115) 0.0314 (0.0033) 0.2560 (0.0128) 0.4223 (0.0697) 0.196 35,968

0.0176 (0.0054) 0.0379 (0.0120) 0.0345 (0.0191)

Females

Dental Care.

0.0446 (0.0117) 0.0924 (0.0028) 0.3559 (0.0262) 0.0053 (0.0090) 0.0125 (0.0029) 0.2351 (0.0116) 0.3218 (0.2096) 0.180 41,114

0.0158 (0.0053) 0.0265 (0.0112) 0.0233 (0.0139)

Males

0.0234 (0.0454) 0.3282 (0.0072) 1.3919 (0.0577) 0.0834 (0.0313) 0.1404 (0.0098) 0.6399 (0.0317) 1.8417 (0.2870) 0.158 52,417

0.1135 (0.0192) 0.1135 (0.0192) 0.0013 (0.0626)

Fixed Effects

Notes: Dependent variable is an indicator that equals 1 if the respondent indicates his/her main employer provides paid or subsidized dental beneﬁts. Sample years are 1986–1994, 1996, 1998, and 2000. For further information, see notes to Table 2.

Female Local unemployment Children indicator Married Married children Spouse works Log employees Part-time Wfull-time Tenure ( 100) Log wage Related industry Pseudo-R2 Sample size

Base Case

Table 4.

450 PAUL OYER

(0.0046) (0.0021) (0.0048) (0.0067)

0.0158 (0.0059) 0.0558 (0.0013) 0.2424 (0.0078) 0.0330 (0.0042) 0.0364 (0.0015) 0.1471 (0.0053) 0.0259 (0.0077) 0.252 77,345

0.0286 0.0058 0.0371 0.0425

0.0287 (0.0046) 0.0059 (0.0021) 0.0476 (0.0071) 0.0323 (0.0085) 0.0186 (0.0093) 0.0166 (0.0059) 0.0558 (0.0013) 0.2430 (0.0078) 0.0329 (0.0042) 0.0364 (0.0015) 0.1469 (0.0053) 0.0261 (0.0077) 0.252 77,345

Interactions

0.0256 (0.0101) 0.0516 (0.0019) 0.2416 (0.0098) 0.0149 (0.0071) 0.0407 (0.0024) 0.1668 (0.0086) 0.0188 (0.0087) 0.275 36,072

0.0066 (0.0032) 0.0496 (0.0074) 0.0077 (0.0116)

Females

Health Insurance.

0.0272 (0.0073) 0.0585 (0.0018) 0.2451 (0.0140) 0.0390 (0.0051) 0.0323 (0.0020) 0.1266 (0.0065) 0.0560 (0.0173) 0.237 41,273

0.0048 (0.0027) 0.0263 (0.0063) 0.0546 (0.0081)

Males

0.0421 (0.0534) 0.3589 (0.0084) 1.7092 (0.0554) 0.2073 (0.0355) 0.2820 (0.0127) 0.7280 (0.0346) 0.4133 (0.0697) 0.179 43,217

0.0313 (0.0214) 0.1619 (0.0604) 0.0985 (0.0715)

Fixed Effects

Notes: Dependent variable is an indicator that equals 1 if the respondent indicates his/her main employer provides paid or subsidized ‘‘medical, surgical, or hospital insurance that covers injuries or major illnesses off the job.’’ Sample years are 1986–1994, 1996, 1998, and 2000. For further information, see notes to Table 2.

Female Local unemployment Children indicator Married Married children Spouse works Log employees Part-time Wfull-time Tenure ( 100) Log wage Related industry Pseudo-R2 Sample size

Base Case

Table 5.

Salary or Beneﬁts? 451

452

PAUL OYER

because they are insured through government programs, because they have a higher marginal utility for cash relative to insurance, or that unobserved skill/job quality is correlated with being a single parent. Implication 3 receives strong support from the logit results, as tenure is related to notably higher rates of insurance. An extra year of tenure raises the probability of dental and health beneﬁts by about 1–2 percentage points each.

3.5. Beneﬁts Packages The model and discussion to this point suggest two broad classes of justiﬁcations for ﬁrms’ choices about which beneﬁts to offer – some ﬁrms compile beneﬁts to encourage long hours (Implication 4 of the model) and some compile beneﬁts to encourage costs savings and long employment relationships (Implications 1, 2, and 3). As the model suggests, these justiﬁcations can reinforce one another. However, if ﬁrms where effort and beneﬁts complement one another are not those with comparative advantage in purchasing, these two justiﬁcations can be quite distinct. To more directly assess this distinction, I now look at groups of beneﬁts offered by individual employers. The NLSY asks for details on several other beneﬁts that can be used to deﬁne beneﬁts packages. I start by forming an ‘‘effort package’’ that consists of beneﬁts that are good candidates to help lower the cost of effort. That is, in the terminology of the model, I expect these beneﬁts to have cebo0. Unfortunately, the NLSY does not ask about many of the beneﬁts (such as concierge service, game rooms in the ofﬁce, etc. – see the quote at the beginning of the paper) that are most likely to complement effort and keep people at the workplace. I therefore deﬁne an indicator variable ‘‘effort package’’ that takes the value 1 if the employee has access to employerprovided meals, employer-provided parking, and ﬂexibility in choosing work hours. The NLSY asks about a variety of more traditional beneﬁts that can help attract employees for a long relationship. I deﬁne a ‘‘tenure package’’ indicator that equals 1 if the employee’s ﬁrm provides health insurance, dental insurance, maternity leave, on-the-job training, life insurance, and a retirement plan.24 Panel A of Table 6 provides descriptive statistics for each package, as well as each beneﬁt within the package. One thing that is immediately clear from the table is that there is signiﬁcant correlation across these beneﬁts for a

453

Salary or Beneﬁts? Table 6.

Packages of Beneﬁts.

Panel A: Summary Statistics

‘‘Effort’’ package Meals Parking Flex time ‘‘Tenure’’ package Medical insurance Dental insurance Maternity leave On-the-job training Life insurance Retirement plan

Mean

Sample size

8.3% 15.1% 58.5% 48.4% 30.7% 75.8% 56.2% 62.5% 48.6% 65.1% 59.8%

15,914 23,703 15,959 15,948 69,377 82,555 82,261 66,518 70,213 70,423 70,077

Panel B: Relationship between Packages (1989 and 1990 Only)

No ‘‘Effort’’ package ‘‘Effort’’ package Total

No ‘‘Tenure’’ package

‘‘Tenure’’ package

Total

68.7% 5.3% 73.9%

23.0% 3.1% 26.1%

91.7% 8.3% 100%

Notes: See Table 1 for sample details. Years included are 1986–1994, 1996, 1998, and 2000. Samples are smaller for some variables because respondent did not answer question or the question was not asked each year. ‘‘Effort’’ beneﬁts and ‘‘Tenure’’ beneﬁts are indicator variables that equal 1 for respondents who report having every one of the beneﬁts in the relevant category. If respondent reports not knowing if he/she receives a beneﬁt, then that beneﬁt is not included when determining if the person receives the relevant ‘‘package.’’ As a result, package sample size can be bigger than individual beneﬁt sample.

given person. That is, the 8.3% (30.7%) of people who have each element of the effort (tenure) package is almost double (six times) the fraction that would have all these beneﬁts if they were provided completely independently of each other.25 However, as Panel B shows, the correlation between the effort and tenure packages is not particularly noteworthy. While 8.3% of people have the effort package, 11.9% of those who get the tenure package also get the effort package. Similarly, while 26.1% of the relevant sample gets the tenure package, 37.3% of those who get the effort package also get the tenure package. While these numbers suggest these two groups of packages are related, the correlation is far from overwhelming. This provides some initial evidence that these types of beneﬁts ﬁt at different types of ﬁrms.

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Table 7 shows the results of logits similar to those in Tables 2–5, but with the two packages as dependent variables. Columns 1 and 2 present the logit and ﬁxed-effects logit results for the effort package. Not surprisingly, the results are similar to the meals logit, given meals are a third of the package. The ﬁxed-effects results are of little use because, given there are only 2 years in the panel, there is insufﬁcient within-person variation of the key variables to identify signiﬁcant relationships. Two results in column 1 are worth highlighting. First, the greater-than-full-time indicator is again large (and statistically signiﬁcant). The part-time indicator is not distinguishable from the less-than-full-time group, though this could be due to the small sample of less-than-full-time workers. These results mean that Implication 4 is consistent with the relationship between hours worked and availability of the effort package. Second, there is no relationship between effort-related beneﬁts and tenure. These beneﬁts do not seem to be about attracting people who place a high value on a particular beneﬁt and, therefore, stay with the ﬁrm. Rather, they appear to help induce high effort during the employee’s stay at the ﬁrm, however long that may be. Columns 3 and 4 of Table 7 show that these two results reverse when looking at the tenure package. That is, for these beneﬁts where I would not expect beneﬁts to lower the cost of effort (and, therefore, would not expect Implication 4 to hold) there is no difference between the likelihood of getting this group of beneﬁts for those working full-time and those working very long hours. Implications 1, 2, and 3 are consistent with the results for the tenure package, however. These beneﬁts are strongly associated with relatively long-term jobs. This suggests that these beneﬁts are packaged together to take advantage of ﬁrm buying power and to attract people who place a relatively high value on the beneﬁts. These conclusions are similar whether looking at the standard logit analysis (column 3) or the ﬁxed-effects logit (column 4).

3.6. Beneﬁts at Government and Nonproﬁt Organizations Conventional wisdom suggests that people work for government and nonproﬁt organizations because these employers tend to offer generous beneﬁts. A commonly heard justiﬁcation for taking jobs outside the private sector is, ‘‘The pay stinks, but the beneﬁts are good.’’ In this section, I extend the prior analysis to consider the type of ﬁrm. I show that nonproﬁt and government employers are, in fact, much more likely to provide certain

0.0123 (0.0054) 0.0030 (0.0036) 0.0071 (0.0058) 0.0280 (0.0093) 0.0145 (0.0087) 0.0024 (0.0010) 0.0118 (0.0113) 0.0177 (0.0054) 0.0018 (0.0016) 0.0006 (0.0042) 1989–1990 0.007 14,698

Logit

‘‘Effort’’ package

0.2687 (0.1745) 0.2463 (0.3656) 0.1546 (0.4895) 0.0294 (0.2955) 0.0042 (0.0351) 0.3140 (0.3116) 0.0058 (0.1752) 0.0681 (0.0853) 0.0072 (0.1093) 1989–1990 0.013 1,292

Fixed-effect logit

‘‘Effort’’ package

(2)

0.1144 (0.0069) 0.0214 (0.0035) 0.0272 (0.0071) 0.0194 (0.0103) 0.0573 (0.0085) 0.0573 (0.0013) 0.2435 (0.0140) 0.0003 (0.0060) 0.0145 (0.0015) 0.1935 (0.0068) 1988–2000 0.167 65,318

Logit

‘‘Tenure’’ package

(3)

Factors Associated with Beneﬁts Packages.

0.0783 (0.0223) 0.1249 (0.0600) 0.1777 (0.0753) 0.0998 (0.0505) 0.2537 (0.0080) 1.1719 (0.0790) 0.0238 (0.0368) 0.0449 (0.0099) 0.5317 (0.0377) 1988–2000 0.091 38,072

Fixed-effect logit

‘‘Tenure’’ package

(4)

Notes: Data are from the NLSY. Each column reports the results of a logit. Dependent variables are deﬁned in Table 6 and in the text. See Table 2 for sample and speciﬁcation details. Standard errors, adjusted for correlation among multiple responses by the same person, are in parentheses. Coefﬁcients are marginal effects on the probability that the respondent’s ﬁrm provides the beneﬁt in columns 1 and 3 and ﬁxed-effect conditional logit coefﬁcients in columns 2 and 4.

Female Local unemployment Children indicator Married Spouse works Log employees Part-time Wfull-time Tenure ( 100) Log wage Sample years Pseudo-R2 Sample size

Speciﬁcation

Dependent variable

(1)

Table 7.

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types of beneﬁts than private ﬁrms and I consider how this ﬁts with the theoretical analysis above. At least based on a stereotypical view that government work is stable and that government jobs are not high stress, government organizations should be relatively unlikely to use beneﬁts to lower effort costs. In addition, there may be political constraints that restrict government organizations from providing perquisites such as meals. Therefore, I expect meals, child care, and the effort package to be less prevalent at government employers. Because of their size and potential power in procurement, government employers are likely to be able to take advantage of scale economies in purchasing insurance. Also, people who choose the stability of government jobs are likely to be risk averse and, therefore, to value insurance. That is, Implications 1, 2, and 3 should apply at government organizations, suggesting dental and health insurance, as well as the tenure package as a whole, will be relatively common for government workers. Self-employed workers may have just the opposite proﬁle – they are likely to be relatively risk tolerant and they cannot take advantage of scale economies in purchasing insurance.26 In addition, self-employed workers may have less tax incentive to purchase health insurance, as they may be able to shield their income from taxes in other ways. Therefore, I would expect self-employed workers to be less likely to receive employment-related insurance. Self-employed workers have more to gain than other workers by providing meals at work. This is one way to shield income from taxes, for example. Also, a self-employed person need not worry as much about the variety of food preferences of a large group when purchasing meals. Table 8 displays the results of logits similar to those in Tables 2–5 and 7, except I include indicator variables for working for the government, for being self-employed, and for working for a nonproﬁt organization. The excluded category in all regressions is private company, so the coefﬁcients show the difference in probability between each type of employer and a private company. Note that I limit the analysis, when possible, to 1994 and later. From the start of the survey until 1993, the NLSY asked respondents if they worked for a private company, worked for the government, or were self-employed. Starting in 1994, the option of nonproﬁt organization was added. Before 1994, nonproﬁt employees were classiﬁed as working at private companies. The meal logit in column 1 conﬁrms that government workers are signiﬁcantly less likely to receive meals at work than people who work for companies, while self-employed workers are much more likely to get meals at work. Column 2 shows that government workers are somewhat less likely

1988–1990 0.059 21,850

0.0090 (0.0065) 0.0007 (0.0126) 0.0450 (0.0066) 1994–2000 0.071 21,263

Child care

Meals

0.0200 (0.0100) 0.0943 (0.0278)

(2)

(1)

0.1916 (0.0162) 0.3084 (0.0291) 0.1166 (0.0192) 1994–2000 0.243 21,537

Dental

(3)

0.1116 (0.0102) 0.1193 (0.0133) 0.0571 (0.0122) 1994–2000 0.299 21,595

Health

(4)

1989–1990 0.013 14,696

0.0530 (0.0091) 0.0335 (0.0252)

‘‘Effort’’

(5)

Beneﬁts and Employment-Sector Individual Data – NLSY.

0.1244 (0.0127) 0.4466 (0.0474) 0.1440 (0.0161) 1994–2000 0.198 21,595

‘‘Tenure’’

(6)

Notes: Each column reports the results of a logit. Dependent variables in columns 1–4 are the same as those used in Tables 2–5. Dependent variables in columns 5 and 6 are the same as those in Table 7. Control variables include all those used in Tables 2–5 and 7. In columns 1 and 5, nonproﬁt organizations are combined with for-proﬁt entities (which is the excluded variable). Standard errors, adjusted for correlation among multiple responses by the same person, are in parentheses. Coefﬁcients are marginal effects on the probability that the respondent’s ﬁrm provides the beneﬁt.

Government Self-employed Nonproﬁt Sample years Pseudo-R2 Sample size

Dependent Variable

Table 8.

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to get child care at work, though the effect is not signiﬁcant. Employees of nonproﬁt organizations, on the other hand, are much more likely to have employer-provided child care. This is not simply due to the fact that child care and child service providers are often nonproﬁt agencies, because the regressions control for child-oriented businesses. Perhaps this connection between nonproﬁts and child care reﬂects that some new parents who want to continue working move to the nonproﬁt sector because they ﬁnd the ‘‘work-life balance’’ better (which is a way to interpret this result as consistent with Implication 2). Nonproﬁt employers would then ﬁnd it efﬁcient to set up a child-care center given this common preference. However, there is not enough detail in the data to investigate this conjecture fully. Columns 3, 4, and 6 conﬁrm that the beneﬁts at government and nonproﬁt jobs are generous. Employees in both these sectors are much more likely to get insurance at work, as well as to have the entire tenure package. The results are statistically signiﬁcant at any reasonable level and economically large. For example, while 56% of the sample as a whole receives dental insurance, this probability is increased by 19 (12) percentage points for government (nonproﬁt) workers. Also, self-employed workers are dramatically less likely to grant themselves these beneﬁts.27 The results are consistent with Implication 2 of the model. That is, if employees with strong preferences for insurance (those who are relatively risk averse) are also those who like the stability of government and nonproﬁt jobs, then these organizations may be able to cost-effectively employ these workers. Column 5, on the other hand, shows that government workers are far less likely than corporate employees to be provided with beneﬁts that are conducive to increased effort.

3.7. Alternative Hypotheses and Historical Trends I have argued that the empirical patterns in the NLSY are driven by factors modeled in Section 2, including that workers sort to ﬁrms that costeffectively provide beneﬁts they value and that some beneﬁts lower the cost of employee effort. In this section, I brieﬂy consider a few alternative explanations and I use an alternative dataset to look at historical changes in beneﬁts (and to probe for potential weaknesses in the NLSY). The results regarding ﬁrm size are, as I have argued above, consistent with the importance of economies of scale in purchasing (and, therefore, Implication 1 of the model). However, as a large literature shows (see Oi

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459

& Idson, 1999), ﬁrm size is correlated with wages even when including extensive control variables. Therefore, there could be some omitted factor that causes large ﬁrms to have both high wages and generous beneﬁts. In fact, given the positive ﬁrm size–wage relationship, I would expect a positive ﬁrm size–beneﬁts relationship simply because employees at larger ﬁrms would consume some of the extra compensation in wages and some in beneﬁts. I therefore think of the results that relate ﬁrm size to beneﬁts as a necessary, but not sufﬁcient, condition for the economies of scale relationship suggested by Implication 1 of the model. I also found that, when combining various measures of ﬁrm size (speciﬁcally, employees at the respondent’s site, whether the ﬁrm has other locations, and whether the ﬁrm has 1,000 or more employees at other locations), each of these measures is almost always positively and signiﬁcantly related to the provision of any beneﬁt. So I cannot speciﬁcally isolate whether it is economies of scale at the ﬁrm or establishment that lead ﬁrms to provide beneﬁts. One other potential worry with the ﬁrm size variable is that the functional form assumption (log of employees at the worker’s location) is inappropriate and, therefore, it does not fully control for ﬁrm size. This could lead to inappropriate conclusions about other variables that are related to ﬁrm size. However, while I cannot fully rule that possibility out, it is reassuring that none of the other conclusions are sensitive to any alternative controls for ﬁrm size. Speciﬁcally, I reran all the analysis with no controls for ﬁrm size and then controlling for various alternative functions of ﬁrm size. This never affected any conclusions. In addition, I ran an alternative speciﬁcation that provides support for the economies of scale interpretation of ﬁrm size. If economies of scale are an important part of the ﬁrm size–beneﬁts relationship, I would expect this relationship to be weaker at ﬁrms that already have a cost advantage because of their industry. For example, while any ﬁrm that is larger might have an advantage in providing meals, the marginal effect of being large is likely to be greater at a law ﬁrm than at a restaurant. I therefore also reran all the analysis with the control for ﬁrm size interacted with the variable for being in a related industry (restaurants and food stores in Table 2, child-care centers in Table 3, etc.). In the case of all four beneﬁts in Tables 2–5, the data are consistent with the economies of scale interpretation. The coefﬁcient on ﬁrm size is always positive, as is the coefﬁcient on working in a related industry. But the coefﬁcient on the interaction between size and related industry is negative and signiﬁcant in each case.28

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An alternative explanation for ﬁrms offering some beneﬁts is agency problems. Lavish corporate beneﬁts, or perquisites, are often cited as a classic example of agency problems for executives (see Yermack, 2006). Perhaps some employees in the NLSY are also in a position to capture rents and this is easiest to do by getting the ﬁrm to add perks. Agency seems like an unlikely explanation for the components of the ‘‘tenure package’’ because nondiscrimination laws require that most of these beneﬁts be provided to all employees if they are available at all. Similarly, it is hard to imagine this explains the patterns in child-care provision because employees trying to balance work and family concerns are unlikely to be well positioned to extract rents from the ﬁrm. However, this could explain the results regarding meals if employees who work long hours are relatively powerful. If this were the case, one might imagine that this agency issue would be a bigger problem at large ﬁrms with higher monitoring costs. In an unreported regression, I reran the analysis in Table 2 and found that an interaction of greater than full time and ﬁrm size has a marginally signiﬁcant negative relationship to meals. Another alternative explanation is that ﬁrms add and remove beneﬁts to adjust to the economic climate because it is easier to adjust beneﬁts than to change wages (see Oyer, 2005). This is consistent with some of the results in Tables 2–5, as the negative coefﬁcients on local unemployment suggest that beneﬁts are higher when labor markets are tighter. This could be a contributing factor. However, low adjustment costs of beneﬁts alone cannot explain the other factors that affect beneﬁts, such as hours worked, wages, and tenure. To see how beneﬁts have changed over time and to insure there are not serious weaknesses in the NLSY, I gathered data from three surveys of workers from the 1970s. The 1970 Survey of Working Conditions and the 1973 and 1977 Quality of Employment Survey each asked approximately 1,500 workers many detailed questions about their primary job. The three surveys asked similar questions and I refer to the three surveys together as the QES. When asking about beneﬁts, the QES speciﬁcally asked if the employer makes the beneﬁt available to the respondent. As with the NLSY, there is no requirement that the person take advantage of the beneﬁt. To maximize comparability with the NLSY, I drop QES respondents that are over 45. Like the NLSY, the QES asked about free or discounted meals and health insurance for medical issues not related to work. I use the same components to form the ‘‘tenure package’’ as I used in the NLSY except maternity leave. The QES only asked women this question. The proportion of workers

Salary or Beneﬁts?

461

reporting employer-provided meals and health insurance, as well as those reporting the ‘‘tenure package’’ closely match those in the NLSY. The QES asked if the ﬁrm provided a day-care center, which is a little more speciﬁc than the NLSY question of whether the ﬁrm provides or pays for day care. Probably because of this difference in the question and because there are fewer women in the QES (24%), the day-care rate is much lower (2.2%) than in the NLSY. The QES did not ask about dental beneﬁts. Also, it did not ask about parking, ﬂex time, or other beneﬁts that could help form an ‘‘effort package.’’ I was able to construct most of the same explanatory variables that I used in the NLSY logits. The industry classiﬁcations are somewhat different in the 1970 sample, so the controls for related industry are measured with more error in that year. The QES does not include a measure of local labor market conditions. Analyses similar to those in Tables 2–7, but using the QES data, are displayed in appendix Table A1. I do not discuss them in detail, but simply highlight a few conclusions relative to the NLSY results. The connection between hours worked and meals is the most interesting result in the QES meals analysis. Conﬁrming one of the main ﬁndings of the NLSY analysis, employees who work more than full time are more than 4% more likely to receive meals than those that work full time. This suggests that effort complementarity is important in the provision of meals. However, in the QES, employees who work part time are signiﬁcantly more likely to be offered meals at work than those who work full time. While this effect is substantial and signiﬁcant, note that under 9% of the sample worked part time. The positive effect of part time is the result of 10 people in the 1970 and 1973 surveys who worked part-time in general merchandise stores or as domestic help. So, though part time workers may have been more likely to have work-related meals in the early 1970s, this affected a small portion of the workforce and was no longer true as the nature of retail stores and domestic help changed over time. If I applied a broader deﬁnition to ‘‘food-related’’ industries, the results in the QES would mimic those in the NLSY. As it is, the 1977 results do mimic the NLSY while the earlier results conﬁrm the effect of working long hours but change the result for part-time employees. The child-care results are not very enlightening, possibly because of how few women there are in the sample and/or because this beneﬁt was much less common at the time of the QES. The health care and tenure package logit results are very similar for the QES and the NLSY except that women were no more likely to get these beneﬁts in the QES. This increase in female beneﬁts by the time of the NLSY could be due to women’s

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increased attachment to the labor force and their ability to obtain higher quality jobs. In general, the conclusions from the NLSY data are robust to using data from the QES as an alternative. The changes are what might be expected, given the increase in women’s labor force participation during the 1970s and 1980s.

4. CONCLUSIONS AND FURTHER RESEARCH One of the ‘‘make or buy’’ decisions nearly every ﬁrm faces is how much to simply ‘‘buy’’ labor input with salary and how much to ‘‘make’’ employee beneﬁts that it can barter for labor services. In this paper, I analyzed several factors that go into this choice about ﬁrms’ boundaries. I developed a model where ﬁrms do some of their employees’ purchasing for them when the ﬁrm can more efﬁciently procure some items and where employee valuations of beneﬁts vary with work-related effort. Using the NLSY, I showed empirical evidence that is consistent with these theoretical considerations playing a role in ﬁrms’ decisions about which beneﬁts to provide. For some key beneﬁts that make up the bulk of beneﬁts expenditures (especially health insurance), the efﬁcient purchasing model appears to be particularly important. The relationship between beneﬁts and employee effort is strongest for company-provided meals and child care. These are both large and growing portions of the economy, which suggests that ‘‘effort complementarity’’ of beneﬁts will become more important in the overall economy in coming years. Given the reduced-form nature of the analysis and the lack of an experiment that can help evaluate policy, the results in this paper do not have direct public policy implications. However, given that beneﬁts continue to be a growing portion of employment costs and that sectors such as workrelated catering are a growing share of the economy, the paper does suggest that policy makers should consider how ﬁrms’ choice of beneﬁts will respond to any change in tax policy, overtime rules, or other policies that affect the structure of employment costs. For managers, the paper highlights the potential value that can be created in the employment relationship by crafting beneﬁts packages that combine a ﬁrm’s cost structure with employees who value certain beneﬁts. The comparative statics derived in this paper and the empirical relationships provide some evidence to suggest factors that affect ﬁrms’ decisions on provision of beneﬁts. One limitation of the analysis is that I have relied on

463

Salary or Beneﬁts?

individuals’ self-reported beneﬁts’ eligibility. To more closely tie beneﬁts to ﬁrm characteristics and to minimize measurement error, it would be informative to use a survey of ﬁrms and their beneﬁts practices. Finally, in this paper I did not address one important issue in employee beneﬁts – over-consumption. That is, one of the costs of ﬁrms’ providing beneﬁts to employees is that, if employees pay no marginal cost to receive a beneﬁt, they will consume to the point where the marginal value of their beneﬁts consumption is zero. Given that the social optimum would be for employees to consume until marginal value equals marginal cost (to the ﬁrm), there will be a deadweight loss from over-consumption. Future research could gather detailed beneﬁts usage data from individual ﬁrms to study how ﬁrms manage the trade-off between the value created by beneﬁts and the cost of over-consumption.

NOTES 1. In this paper, I only consider nonmonetary beneﬁts. I do not analyze why and how ﬁrms choose among forms of ﬁnancial compensation (i.e., cash, stock, or proﬁt sharing), nor do I look at the timing of pay (such as retirement beneﬁts). 2. This sentence suggests the potential confusion when looking at an economic model of employee beneﬁts given the natural tendency to discuss marginal costs versus marginal beneﬁts. Hereafter, I use the term beneﬁts solely to refer to noncash employee compensation and use other terms when referring to economic beneﬁts more generally. 3. For anecdotal discussions of discontinuation of beneﬁts when economic conditions weaken, see Economist (2001) and Raghavan (2003). 4. See Olson (2002) and Thaler and Rosen (1975) for evidence that workers pay for health insurance and job safety, respectively, through lower wages. 5. See Rice (1966) and Woodbury (1983) for early discussions of the potential efﬁciency of employer-sponsored beneﬁts. Theoretical foundations can be found in Rosen (1974). 6. Several companies, including Circles, VIPdesk.com, and Virtual Concierge, contract with employers to provide these services to workers. 7. Making N exogenous is obviously a somewhat strong assumption. For this and other reasons, the empirical results regarding ﬁrm size need to be interpreted cautiously as I discuss in Section 3.7. 8. One dimension on which people vary is how long they are likely to stay on the job. Beneﬁts would then have the additional value of separating quitters from stayers, as in Salop and Salop (1976). 9. Note that I assume that the complementarity between e and b is independent of the individual’s taste for beneﬁts or the ﬁrm’s purchasing power. In reality, the complementarity would likely be increasing in di and N. Allowing for this would add complexity without affecting the conclusions.

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10. See Marino and Zabojnik (2008a) for a model where employees’ reservations wages and tastes for beneﬁts are correlated, so ﬁrms use beneﬁts to extract information and lower compensation costs. 11. Given the static nature of the model, the ﬁrm picks its beneﬁts and then workers. In reality, as ﬁrm strategies and cost structures evolve, ﬁrms change their beneﬁts plans to meet the tastes of the employees they already have. While this might make the search aspects of the model a bit less important, it should not change the basic relationships or implications. 12. As Rosen (1986) discusses, workers can also be expected to sort based on the risks associated with jobs. See DeLeire and Levy (2004) for empirical evidence of such sorting. 13. The original NLSY oversampled disadvantaged youth and members of the military. These samples were reduced over the years, so attrition from these groups is higher. 14. In the analysis that follows, I use the children indicator rather than the number of children. The results are not sensitive to this choice. 15. See McIntyre (2000) for further details on the growth and prevalence of on-site day care. 16. In unreported regressions, I controlled for weekly, rather than hourly, wages. This had essentially no effect on the conclusions. 17. A similar alternative interpretation is that ﬁrms begin to offer child-care assistance when they ﬁnd that they have employees who would value this beneﬁt. 18. For the child care analysis, I set the child indicator equal to one if there is a person under the age of seven residing in the respondent’s household. Results are similar when the child indicator is one if the respondent has any children. 19. In an unreported speciﬁcation controlling for weekly (rather than hourly) wages, the negative relationship between long hours and child care is stronger and statistically signiﬁcant at the 1% level. 20. As noted above, the unemployment variable is very crude and does not vary much independently of the national economy. It does, however, indicate which labor markets are generally competitive. If child care were added and dropped regularly by ﬁrms and if this labor market measure were more accurate, the negative coefﬁcient could imply ﬁrms cut this beneﬁt when wages are rigid (as suggested by Oyer, 2005). However, the conditional logit regressions provide limited support for this conjecture. 21. This statement is somewhat dependent on the deﬁnition of employee beneﬁts. Employer-provided health insurance is about as common in the NLSY as paid vacation. However, I am thinking of paid vacation as affecting the timing, rather than the form, of compensation. 22. There is a large literature on health insurance and its effects on the U.S. labor market. Many of these issues are beyond the scope of this analysis. For further institutional detail on the U.S. employer-provided health insurance and its effects on the labor market, see Gruber (2000). 23. More-than-full-time employees are more likely to be offered health insurance than full-time employees. However, the difference is quite small economically. 24. On-the-job training and retirement plans do not necessarily meet the basic criterion I stated earlier that a beneﬁt would be something the person got from the

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ﬁrm that it could also buy externally. However, both these beneﬁts could meet that deﬁnition and, given the correlation in beneﬁts within ﬁrms, are probably more likely to meet it when provided as part of a large package of beneﬁts. 25. That is, if the components of the effort package were provided independently, roughly 4.3% (15.1 58.5 48.4%) of respondents would have the full package. 26. The NLSY sample of self-employed workers only includes those whose business is incorporated. 27. As discussed by Gruber and Poterba (1994), before the Tax Reform Act of 1986, the tax advantages of employment-based health insurance were lower for selfemployed workers than others. However, because the results in columns 3, 4, and 6 are for 1994 and later, they should be free of effects of tax differences between selfemployed workers and others. 28. The interaction coefﬁcient is marginally signiﬁcant in the case of health care, but signiﬁcant at better than the 1% level for the other three beneﬁts.

ACKNOWLEDGMENTS I thank George Baker, Victor Fuchs, Daniel Hamermesh, Ed Lazear, Scott Schaefer, Kathryn Shaw, Eric Van den Steen, Jan Zabojnik, and seminar participants at University of Southern California; National Bureau of Economic Research; the Max Planck Institute, University of Texas; Stockholm School of Economics; Massachusetts Institute of Technology; University of California, Los Angeles; New York University; Michigan State University; University of Michigan; University of California, Santa Cruz; University of British Columbia; and the 2004 European Summer Days for comments and suggestions.

REFERENCES Brown, C. (1980). Equalizing differences in the labor market. Quarterly Journal of Economics, 95, 113–134. Chamberlain, G. (1980). Analysis of covariance with qualitative data. Review of Economic Studies, 47, 225–238. DeLeire, T., & Levy, H. (2004). Working sorting and the risk of death on the job. Journal of Labor Economics, 22, 925–954. Dranove, D., Spier, K. E., & Baker, L. (2000). ‘Competition’ among employers offering health insurance. Journal of Health Economics, 19, 121–140. Economist (2001). ‘‘The unkindest cuts of all,’’ p. 64, April 5. Gruber, J. (2000). Health insurance and the labor market. In: A. J. Culyer & J. P. Newhouse (Eds), Handbook of health economics (Vol. 1a). New York: North Holland.

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Salary or Beneﬁts?

APPENDIX Table A1.

Factors Associated with Beneﬁts Individual Data – SWC and QES.

Dependent Variable

Female Children indicator Married Spouse works Log employees Part-time Wfull-time Tenure (100) Log wage Related industry Pseudo-R2 Sample size

(1)

(2)

(3)

(4)

Meals

Child care

Health

Tenure package

0.0255 (0.0190) 0.0007 (0.0160) 0.0024 (0.0214) 0.0127 (0.0185) 0.0128 (0.0034) 0.0914 (0.0256) 0.0442 (0.0148) 0.0026 (0.0027) 0.0100 (0.0072) 0.2471 (0.0234) 0.060 2,787

0.0046 (0.0060) 0.0022 (0.0051) 0.0025 (0.0064) 0.0083 (0.0059) 0.0059 (0.0011) 0.0037 (0.0098) 0.0048 (0.0048) 0.0007 (0.0008) 0.0043 (0.0018) 0.0142 (0.0067) 0.073 2,729

0.0194 (0.0185) 0.0171 (0.0156) 0.0307 (0.0201) 0.0203 (0.0185) 0.0587 (0.0036) 0.1961 (0.0273) 0.0248 (0.0145) 0.0161 (0.0033) 0.0581 (0.0094) 0.0447 (0.0268) 0.230 2,758

0.0054 (0.0235) 0.0194 (0.0182) 0.0147 (0.0235) 0.0039 (0.0203) 0.0536 (0.0042) 0.1836 (0.0528) 0.0022 (0.0165) 0.0108 (0.0029) 0.1191 (0.0279) Na 0.152 2,787

Data are from the 1970 Survey of Working Conditions and the 1973 and 1977 Quality of Employment Surveys. Each column reports the results of a logit. Dependent variables are indicators that equal 1 if the respondent indicates his/her main employer provides paid or subsidized meals (column 1), child care (column 2), or ‘‘medical, surgical, or hospital insurance that covers any illness or injury that might occur to you while off the job’’ (column 3). The dependent variable in column 4 is similar to the ‘‘tenure package’’ in Table 3 except it does not include maternity leave. Sample includes all working people age 45 or under who report a wage at their main job. Explanatory variables are similar to those in Table 1. Each regression also includes year and 5-year age indicators. Coefﬁcients are marginal effects on the probability that the respondent’s ﬁrm provides the beneﬁt.