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CONTEMPORARY STUDIES IN ECONOMIC AND FINANCIAL ANALYSIS VOLUME 87
DEVELOPMENTS IN LITIGATION ECONOMICS EDITED BY
PATRICK A. GAUGHAN Fairleigh-Dickinson University, USA
ROBERT J. THORNTON Lehigh University, USA
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CONTENTS LIST OF CONTRIBUTORS
vii
LITIGATION ECONOMICS Patrick A. Gaughan and Robert J. Thornton
1
THE FORENSIC ECONOMICS OF MEDICAL MONITORING DAMAGES IN THE UNITED STATES George A. Barrett and Michael L. Brookshire
9
SECURITIES FRAUD DAMAGES Bradford Cornell, John I. Hirshleifer and John N. Haut
29
RECENT DEVELOPMENTS IN THE ANALYSIS OF EMPLOYMENT PRACTICES Joan G. Haworth, Janet R. Thornton and Paul F. White
59
THE CALCULATION AND USE OF RETIREMENT AGE STATISTICS: A RECAP SINCE 1970 Tamorah Hunt, Joyce Pickersgill and Herbert Rutemiller
83
RECENT DEVELOPMENTS IN THE MEASUREMENT OF LABOR MARKET ACTIVITY Gary R. Skoog and James E. Ciecka
119
RESEARCH AND PRACTICE ISSUES IN PERSONAL INJURY AND WRONGFUL DEATH DAMAGES ANALYSIS Frank Slesnick, James Payne and Robert J. Thornton
159
v
vi
CONTENTS
ECONOMICS AND ECONOMISTS IN MERGER ANTITRUST ENFORCEMENT Lawrence J. White
205
THE ECONOMICS OF PUNITIVE DAMAGES: POST STATE FARM V. CAMPBELL Patrick A. Gaughan
217
NEW DEVELOPMENTS IN BUSINESS VALUATION Patrick L. Anderson
267
ESTIMATING ECONOMIC LOSS FOR THE MULTIPRODUCT BUSINESS Carroll Foster and Robert R. Trout
307
LIST OF CONTRIBUTORS Patrick L. Anderson
Anderson Economic Group, MI, USA
George A. Barrett
Michael L. Brookshire & Associates, WV, USA
Michael L. Brookshire
Marshall University, WV, USA
James E. Ciecka
DePaul University, IL, USA
Bradford Cornell
California Institute of Technology, CA, USA
Carroll Foster
University of California, CA, USA
Patrick A. Gaughan
Farleigh-Dickinson University, NJ, and Economatrix Research Associates, NY, USA
John N. Haut
CRA International, CA, USA
Joan G. Haworth
ERS Group, FL, USA
John I. Hirshleifer
CRA International, CA, USA
Tamorah Hunt
Formuzis, Pickersgill & Hunt, CA, USA
James Payne
Illinois State University, IL, USA
Joyce Pickersgill
Formuzis, Pickersgill & Hunt, CA, USA
Herbert Rutemiller
California State University, Fullerton, USA
Gary R. Skoog
Legal Econometrics, Inc. IL, USA and DePaul University, IL, USA
Frank Slesnick
Bellarmine University, KY, USA
Janet R. Thornton
ERS Group, FL, USA
Robert J. Thornton
Lehigh University, PA, USA vii
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LIST OF CONTRIBUTORS
Robert R. Trout
Lit.Econ LLP, CA, USA
Lawrence J. White
Stern School of Business, New York University, NY, USA
Paul F. White
ERS Group, DC, USA
LITIGATION ECONOMICS Patrick A. Gaughan and Robert J. Thornton The field of litigation economics has grown dramatically over the past quarter of a century. Sometimes referred to as forensic economics, the field consists of the application of economics and finance to litigated matters. In practicing in the field of litigation economics, economists often render opinions on the measurement of damages as well as on liability-related issues such as in employment litigation. As a reflection of the development of the field, there are now two major peer-reviewed professional journals, the Journal of Forensic Economics and the Journal of Legal Economics. These professional journals are the official research outlets of the two principal organizations of forensic economists in the US today – the National Association of Forensic Economics and the American Academy of Economic and Financial Experts. The chapters in this volume highlight recent developments in the field while pointing out the diverse ways in which economics is applied to litigated matters. In doing so, the book covers the major fields in which economics is applied in lawsuits. They include the most common form of litigation, personal injury cases, but also securities, employment, antitrust, and commercial lawsuits as well. The goal of this volume is to focus on relevant recent developments in each of these areas while also providing the reader with some background. All of the chapters have been written by economists who work extensively in the respective areas. As with most other areas of economics, the field of litigation economics continues to evolve. This is due in large part to legal decisions in the various
Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 1–7 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87001-9
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PATRICK A. GAUGHAN AND ROBERT J. THORNTON
areas. In addition, as economic research advances, new techniques and tools are applied by economists in lawsuits. The authors of the various chapters have sought to provide readers with information on both types of developments.
OVERVIEW OF VOLUME The first chapter in the volume, by George A. Barrett and Michael L. Brookshire, is entitled ‘‘The Forensic Economics of Medical Monitoring Damages in the United States.’’ It focuses on a relatively new category of compensatory damages, the measurement of the costs of monitoring the medical condition of a group of designated individuals. These individuals may have alleged that they were adversely affected by the tortuous conduct of certain defendants. Barrett and Brookshire explain the legal parameters, which govern the ways such costs may be measured. They also provide a listing of the relevant cases across different states and in federal courts. When testing the condition of a defined population, different test results can give rise to varying responses, which in turn, may warrant further testing and treatments. The authors use a decision tree approach to describe the process that experts can outline for litigants. Once the process has been defined, costs of the overall process can be estimated using statistical analysis. The next chapter in the volume, ‘‘Securities Fraud Damages,’’ is authored by Bradford Cornell, John I. Hirshleifer and John Haut (CHH). It focuses on the various methods used to measure the losses of securities holders as a result of such events as ‘‘fraud on the market.’’ The authors discuss those issues that are relevant to class action lawsuits, such as materiality, scienter, causality, and reliance. They then describe how methods such as event studies are used to measure losses of plaintiffs. When applying such techniques, experts must define the class period and the extent to which a stock price may have been inflated. Inflation is the difference between the ‘‘fraudaffected’’ stock price and the price that would have prevailed without the fraud. CHH also cite relevant case law, such as Basic v. Levinson and Green v. Occidental Petroleum. CHH then explain various trading models, such as the proportional, accelerated, and multiple trader models, used to measure the number of securities affected by the alleged fraud. In discussing the models, they provide an overview of how losses are typically measured by economic experts in securities lawsuits.
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The chapter by Joan Haworth, Janet Thornton, and Paul White (HTW) – ‘‘Recent Developments in the Analysis of Employment Practices’’ – discusses the application of economics and statistical methods to employment litigation. Economists have long been utilized as experts in lawsuits in which plaintiffs have alleged that an employer’s hiring, promotion or retention policies are biased against some group. In such cases, economists often apply statistical methods to determine whether a company has engaged in practices having an adverse effect on the group. Among such practices are reverse discrimination – programs put in place to increase diversity but which might also have adverse effects on other groups. The chapter examines both the legal environment and various corporate, government, and higher education policies aimed at bringing about greater diversity, along with the challenges that such policies create. HTW then proceed to describe the various ways that statistical analysis can be used in employment litigation. For example, an expert can use statistical methods to facilitate the class certification process. Once a class has been certified, further statistical analysis may be applied to determine whether the class has experienced disparate treatment. The authors also point out the role that the level of ‘‘statistical significance’’ plays in the conclusions that an expert reaches. They trace the positions of courts on the accepted level of significance from some of the early cases, such as the Hazelwood decision in 1977. One important distinction they note is the difference between statistical significance, which can be enhanced by an increased sample size, and ‘‘practical importance.’’ In other words, a difference may be statistically significant but may not necessarily ‘‘mean a whole lot.’’ The volume next moves on to the most common application of economics in litigated matters – personal injury litigation. Three chapters are devoted to this area. The first, by Tamorah Hunt, Joyce Pickersgill, and Herbert Rutemiller (HPR), is entitled ‘‘The Calculation and Use of Retirement Age Statistics – A Recap Since 1970.’’ This chapter discusses the evolution of worklife statistics that have been generated since 1950. HPR focus on both worklife expectancy as well as on the number of years to final separation from the labor force – a measure for which the authors are wellknown. They first describe what has become known as the ‘‘conventional model’’ and turn to a more refined technique – the increment-decrement (or Markov) method of the US Bureau of Labor Statistics. They then discuss the years-to-final-separation measure, comparing and contrasting it with the other worklife measures. Finally, they focus on how these different measures are used by economists to predict the future retirement behavior of workers in today’s labor force.
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PATRICK A. GAUGHAN AND ROBERT J. THORNTON
The chapter by Gary R. Skoog and James E. Ciecka, ‘‘Recent Developments in the Measurement of Labor Market Activity,’’ continues the worklife expectancy discussion by describing still further advances in worklife statistics. They note that prior worklife measures, such as those published by the Bureau of Labor Statistics, focused exclusively on the mean value of worklife. However, the Skoog-Ciecka statistics provide more complete descriptions of the probability distributions of the worklife measures. These enable economists to compute and utilize measures of central tendency (the mean, median, and mode) as well as measures of the dispersion and shape of the worklife distribution. In the process, Skoog and Ciecka discuss how their worklife statistics differ from years-to-final-separation statistics. This discussion is particularly useful for practitioners who use both measures. Skoog and Ciecka conclude their chapter with an explanation of the flaws in the so-called ‘‘disabled worklife tables.’’ They explain how these tables are beset with ‘‘severe methodological and data problems and a variety of biases’’ which they claim ‘‘render [them] invalid for their intended use.’’ ‘‘Research and Practice Issues in Personal Injury and Wrongful Death Damages Analysis’’ is the next chapter, written by Frank Slesnick, James Payne, and Robert Thornton. The chapter is a review, update, and critique of the major forensic economic research conducted over the past 15 years in five key subject areas involving the estimation of damages in personal injury and wrongful death (PI/WD) cases. These key subject areas are: the estimation of earning capacity, the calculation of fringe benefits, discount rate issues, the personal consumption deduction, and the use of age-earnings profiles. Most of the research summarized in the chapter has been drawn from the pages of the Journal of Forensic Economics and the Journal of Legal Economics. The authors also devote an appendix to a discussion of the Victim’s Compensation Fund. The Fund was established after the September 11, 2001, terrorist attacks and was designed to provide compensation to individuals (or their personal representatives) injured or killed in the terrorist-caused aircraft crashes on that day. Anti-trust economics is the subject of the next chapter in the volume. Authored by Lawrence White, its title is ‘‘Economics and Economists in Merger Antitrust Enforcement.’’ After two intense merger waves in the 1980s and 1990s, merger and acquisition activity in the US slowed with the onset of the 2001 recession. However, with the subsequent pickup in the economy, such activity has begun to rise again. Economists have long served as experts in hearings and lawsuits related to antitrust issues, more generally referred to as ‘‘competition policy.’’ White reviews the merger guidelines used by the Justice Department and the Federal Trade Commission. He
Litigation Economics
5
explains the main characteristics of these guidelines, such as how they define markets and how they treat such issues as entry, impact on competitors, seller concentration and efficiency considerations. He also describes how these issues have varied in importance over the passage of time. White then explains the different ways that economists are used in the antitrust aspect of mergers. They may work in-house at governmental agencies, or they may be retained by one or both of the merging parties. In discussing the various antitrust issues that may be involved in a typical merger or acquisition, he concludes with a review of the proposed merger between Staples and Office Depot. This case is an interesting one because it shows how economic analysis may initially indicate that a deal will not have an adverse impact on competition, while a more detailed analysis of the market and the transaction may well yield a very different conclusion. Patrick A. Gaughan’s chapter, ‘‘The Economics of Punitive Damages: Post State Farm v. Campbell,’’ reviews the legal standards that govern the potential application of punitive damages. He explains that the purpose of punitive damages is to facilitate punishment and deterrence. However, such damages often yield little, if any, deterrence. Furthermore, sometimes defendants have already incurred significant punishment, such as through other similar lawsuits for the same product. He also explains that punitive damages may have adverse effects on innocent parties, such as the various stakeholders that have an interest in major corporations. These stakeholders include shareholders, employees, suppliers, and communities. Usually these parties will have had nothing to do with the alleged wrong, but they may still bear the adverse effects of the punishment imposed with punitive damages. Gaughan then explains that sometimes experts put forward by plaintiffs introduce flawed reasoning for juries to rely upon when deciding the appropriateness and magnitude of punitive damages. Some of the proffered measures are net worth, which may include substantial intangible components that cannot be used to pay a punitive award. An even more inappropriate measure is market capitalization, which is not even an asset of the typical defendant corporation and which should be irrelevant to the punitive damage determination process. The overall thesis of the Gaughan chapter is that punitive damages are a blunt and imprecise tool and often totally inappropriate for many corporate defendants. Other processes may be available, such as regulatory processes, which may better achieve the desired deterrence. Patrick L. Anderson’s chapter, ‘‘New Developments in Business Valuation,’’ covers a topic which has attracted many articles and books over the past 20 years. The literature has been developed by both economists and accountants. In his chapter, Anderson summarizes this literature while
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PATRICK A. GAUGHAN AND ROBERT J. THORNTON
highlighting (in the context of a lawsuit) the main methods used to value businesses: the market, asset, and income approaches. He then proceeds to describe the drawbacks of each as they are applied to a litigation framework. For example, when using the market approach, experts may find that the data, such as sales data, may not be reported in a consistent manner across the different types of businesses being used to establish the ‘‘market.’’ Other approaches, such as the asset approach, have their own drawbacks when the market value of an asset differs significantly from its historical value. Anderson points out that the income method is the most commonly used approach. However, this method is not without its own potential drawbacks when used by a naı¨ ve ‘‘expert.’’ The method can result in flawed estimates when, for example, an expert blindly extrapolates historical growth rates without allowing for the fact that such growth rates might not be reasonable when extended far into the future. Other problems can occur when the capital asset pricing model is misused, and betas derived from one industry are applied to firms that are inappropriately included in that same industry category. He points out that the application of discounts and premiums can also be a source of problems. So too can the discounting process which is used to convert projected future income and cash flow values to presentvalue terms. After discussing the more traditional approaches, Anderson then proceeds to discuss situations in which other techniques, such as dynamic programming and real options methods, can be used to develop values of businesses. In any case, whatever methods are relied upon by an economic expert to arrive at the value of a business must be able to withstand the challenges that can arise in a Daubert hearing. Anderson closes his chapter with a discussion of some of these Daubert-related issues. The final chapter, ‘‘Estimating Economic Loss for the Multi-Product Business’’ by Robert Trout and Carroll Foster, expands upon some of the earlier work that the authors have done in the field of commercial damages. They describe various models used to measure lost profits, such as those that may occur as a result of a business interruption. They explain how basic time-series models and curve-fitting techniques can be used to project lost sales in these types of cases. They then show how these methods can be applied to cases involving small businesses that may have suffered a loss as a result of a particular event occurring at a certain time. The authors demonstrate how more advanced time series methods, such as ARIMA models, can be used to develop more accurate forecasts of lost revenues, while detailing the various steps that must be taken to develop reliable forecasts using such models.
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After their methodological discussion, Trout and Foster then proceed to discuss methods that may be used to measure the losses of a multi-product business. They show how more advanced time series methods, such as vector autoregressive techniques, can be used to estimate the losses of plaintiff companies. Although these methods have had various applications in economics, such as for macroeconomic forecasting, they have not been commonly applied to business-interruption lawsuits.
CONCLUDING COMMENTS As readers will surmise from the chapter overview, the field of litigation economics is a broad one. Even so, the topics treated by the various chapters do not depict the entire scope of the field, which continues to expand. Our purpose in this volume is to feature some of the more prominent developments. Finally, we have tried to orient the treatment of the material so it may be of benefit to a broad audience of economists as well as practitioners in other disciplines – e.g., attorneys, vocational experts, and accountants. While the various chapters in this volume all deal with technical economics topics, most of the material is presented in a manner that should be understandable to readers without graduate training in economics.
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THE FORENSIC ECONOMICS OF MEDICAL MONITORING DAMAGES IN THE UNITED STATES George A. Barrett and Michael L. Brookshire 1. INTRODUCTION The cost of medical monitoring is a relatively new category of compensatory damages in the United States. It emerged in the late 1980s, received increasing attention by the courts through the 1990s, and remains a highly controversial area of economic damages. Medical monitoring may be defined, in the litigation context, as the recovery of long-term diagnostic testing necessary to detect latent diseases that may develop as a result of tortuous exposure to toxic substances (Bower v. Westinghouse, 1999). Proponents of medical monitoring say that monitoring both saves lives and may actually lower defendant costs because wrongful deaths and serious illnesses are avoided. Critics worry that medical monitoring damages are a dangerous exception to the general rule that compensatory damages must involve a current injury or illness. They also argue that if medical monitoring damages may be awarded as a lump sum, plaintiffs need not spend their award on the prescribed protocol of medical examinations and tests. This subject has certainly been explored in the legal literature (see, for example, DiPaola & Roberts, 2000; Gonzales & Valori, 2001; Klein, 1998; Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 9–27 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87002-0
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GEORGE A. BARRETT AND MICHAEL L. BROOKSHIRE
Lee, 1994; Maskin, Cailteux, & McLaren 2000; Tanner, 1998; Whiting, 2002; Wolfe, 2000). The use of Markov analysis in costing medical screening protocols has also been discussed in the medical literature (Briggs & Sculpher, 1998). Yet, the economic and forensic economic literature is sparse on appropriate methods for developing and costing medical monitoring protocols, as outlined by the courts (Barrett & Brookshire, 2002). The overall purpose of this chapter is to describe and explain the current status of medical monitoring damages and of methods and issues related to the appropriate calculation of these damages. The chapter is organized as follows to accomplish this purpose. First, the legal parameters are described which affect the estimation of medical monitoring damages. Ten questions are developed and answered in a review of relevant cases from 19 states and the District of Columbia. Second, the appropriate method for calculating such damages is explained. Third, the decision-tree method is more fully demonstrated with reference to a sample medical monitoring protocol. Fourth, the sensitivity of cost estimates to important variables in the medical monitoring protocol is shown with reference to the sample case. Finally, further issues are described which may face the forensic economist in particular cases.
2. THE LEGAL PARAMETERS As is shown in Table 1, medical monitoring claims have thus far been litigated in the District of Columbia and 19 states. The cases cited include a few cases wherein a federal judge opined that medical monitoring claims would be allowed in the listed state. The forensic economist, of course, needs to know any of the statutory or case law parameters, which might affect the nature and calculation of medical monitoring damages. We have used both state supreme court opinions (see, especially, Bourgeois v. A. P. Green Industries, 1998 and Bower v. Westinghouse, 1999) and our own experience with these cases to develop ten parameters that may be relevant to economic damages. These ten parameters have been phrased as the following questions: Question ]1: Question ]2: Question ]3: Question ]4:
Must there be significant exposure? Must this exposure be to a proven hazardous substance? Is this exposure because of the tortuous conduct of the defendant(s)? Is a proximate result of the exposure an increased risk of contracting a serious latent disease relative to the general population?
Legal Parameters Affecting Medical Monitoring Claims in the 20 Jurisdictions, Where Such Claims Have Been Litigated.
Jurisdiction
Case Citations (Sources)
Ten Parameters From Case Law ]1
]2
]3
]4
]5
]6
]7
]8
]9
]10
Arizona
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
California
Y
Y
Y
Y
Y
S
Y
Y
Y
Y
Colorado
Y
Y
Y
Y
Y
Y
Y
S
S
N
Connecticut
Y
Y
Y
Y
Y
Y
S
S
N
S
11
Burns v. Jaquays Mining Corp., 752 P.2d 28 (Ct. App. Ariz. 1988) Potter v. Firestone Tire & Rubber Co., 863 P.2d 795(Cal. 1993) Miranda v. Shell Oil co., 15 Cal.Rptr.2d 569 (1993) Cook v. Rockwell Intern. Corp., 755 F.Supp.1468 (D. Colo. 1991), 151 F.R.D. 378 (D. Colo. 1993), 181 F.R.D. (D. Colo. 1998) Rule 23(b)(2) Doe v. City of Stamford, 699 A.2d 52 Bowerman v. United Illuminating, 1998 WL 910271 (Conn. Supper. 1998) Goodall v. United Illuminating, 1998 WL 914274 (Conn. Supp. 1998)
Economics of Medical Monitoring
Table 1.
12
Table 1. (Continued ) Jurisdiction
Case Citations (Sources)
Ten Parameters From Case Law ]2
]3
]4
]5
]6
]7
]8
]9
]10
District of Columbia
NA
NA
Y
Y
Y
S
S
S
Y
NC
Florida
Y
Y
Y
Y
Y
Y
Y
S
Y
N
Illinois
S
S
S
S
S
S
S
S
S
S
Kansas
S
S
Y
S
Y
S
S
S
Y
Y
Kentucky
Y
Y
Y
Y
Y
Y
S
Y
N
S
Friends For All children, Inc. v. Lockheed Aircraft Corp., 746 F.Supp. 816(D.C. Cir. 1984) W. R. Grace & Co. v. Galvagna, 633 A.2d 25 (D.C. 1993) Petito v. A.H. Robins Co., Inc., 750 So.2d 103 (Fla. Dist. Ct. App. 1999) Carey v. Kerr-McGee Chem., 1999 WL 966484(N.D.Ill. Sept. 30, 1999) Elliott v. Chicago Housing Authority, 2000 WL 263730 (N.D.Ill. Feb. 28, 2000 R.23(b)(2) Burton v. R.J. Reynolds Tobacco Co., 884 F.Supp. 1515 (D. Kan. 1995) Bocook v. Ashland Oil, Inc., 819 F.Supp. 530(S.D.W.Va. 1993) Wood v. Wyeth-Ayerst, No. 2000-SC-1067-DG,
GEORGE A. BARRETT AND MICHAEL L. BROOKSHIRE
]1
Y
Y
Y
Y
Y
Y
S
Y
N
S
Michigan
Y
Y
Y
Y
Y
Y
S
Y
Y
S
Minnesota
Y
Y
Y
S
S
S
S
S
N
S
Missouri
Y
NC
S
Y
Y
Y
Y
Y
N
S
New Jersey
Y
Y
Y
Y
Y
Y
S
Y
Y
Y
New York
Y
Y
Y
Y
Y
Y
Y
S
Y
N
Economics of Medical Monitoring
Louisiana
13
Ky Sup Ct (August 22, 2002) Bourgeois v. A.P. Green Ind., Inc., 716 So.2d 355 (La. 1998) superseded by statute, La.Civ.Code Ann. Art. 2315 [1999] Meyerhoff v. Turner Const. Co., 509 N.W.2d 847 (Mich. App. 1993), vacated, 575 N.W.2d 550 (Mich. 1998) Werlein v. United States, 746 F.Supp. 887 (D. Minn. 1990), vacated in part on other grounds, 793 F.Supp. 898(D. Minn. 1992) Missouri, W.D. (1994). Thomas v. FAG Bbearings Corp., Inc., 846 F.Supp. 1400,Rule 23(b)(3). Ayers v. Township of Jackson, 525 A.2d 287 (N.J. 1987) Theer v. Philip Carey Co., 628 A.2d 724 (N.J. 1993) Gibbs v. E.I. DuPont De Nemours & Co., Inc., 876 F.Supp. 475 (W.D.N.Y. 1995) Rule 23 (b)(2)
14
Table 1. (Continued ) Jurisdiction
Case Citations (Sources)
Ten Parameters From Case Law ]2
]3
]4
]5
]6
]7
]8
]9
]10
Ohio
Y
Y
Y
Y
Y
NC
NC
Y
Y
NC
Pennsylvania
Y
Y
Y
Y
Y
Y
Y
S
Y
NC
Utah
Y
Y
Y
Y
Y
Y
Y
Y
Y
NC
Vermont
S
S
S
Y
S
S
S
S
Y
S
West Virginia
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Day v. NLO, 851 F.Supp. 869 (S.D. Ohio 1994) Rule 23(b)(2) In re Teletronics Pacing Systems, 168 F.R.D. 203 (S.D. Ohio 1996) Redland Soccer Club, Inc. v. Dept. of the Army, 696 A.2d 137 (Pa. 1997) Simmons v. Pacor, Inc., 674 A.2d 232 (Pa. 1996) Merry v. Westinghouse Elec. Corp., 684 F.Supp. 847 (M.D. Pa. 1988) Hansen v. Mountain Fuel Supply Co., 858 P.2d 970(Utah 1993) Stead v. F.E. Myers Co., Div. Of McNeil Corp., 785 F.Supp. 56 (D. Vt. 1990) Bower v. Westinghouse Electric Corp., 522 S.E.2d 424 (W.Va. 1999)
GEORGE A. BARRETT AND MICHAEL L. BROOKSHIRE
]1
Economics of Medical Monitoring
Question ]5:
Question ]6: Question ]7:
Question ]8: Question ]9: Question ]10:
15
Does the increased risk make it reasonably necessary to undergo periodic medical examinations or testing different from that prescribed absent the exposure? Do monitoring procedures exist that make the early detection of a disease possible? Must monitoring damages be the ‘‘anticipated,’’ ‘‘expected,’’ or ‘‘likely’’ costs of the medical monitoring protocol? Must there be some demonstrated clinical value in the early detection and diagnosis of the disease? Do medical monitoring claims relate to those who do not (yet) have the disease(s), or symptoms? May payment for medical costs be in the form of a lump sum versus only in the form of a court-supervised fund?
These questions are answered in Table 1 for the District of Columbia and 19 states, with citations provided. The possible answers from case reviews were limited to the following: Y: N: S: NC: NA:
YES NO SILENT NOT CLEAR NOT APPLICABLE
In most cases, the answers given in this multi-jurisdiction review were obvious, especially since the relevant case language in these states was often similar. Some of the questions and answers in Table 1 do not directly relate to economic methods employed in calculating the cost of a medical monitoring protocol. They do, however, relate directly to how a class of persons might be defined, who are thereby eligible to move through the monitoring protocol. A forensic economist may or may not play a role in class definition issues. Affirmative answers to questions ]4 and ]5, taken together, strongly imply that monitoring activities must be those that are beyond what is necessary for the general population. This is clearly important as a monitoring protocol is constructed and costed because only the incremental medical or related costs would be considered. An annual physical for a person in the
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protocol might be questioned, since it is recommended that adults have an annual physical anyway. It may be different, on the other hand, if this visit to the doctor is specifically geared to the monitoring process at issue. The answer to question ]7 is directly relevant to economic calculations in a particular jurisdiction. If the answer is affirmative, it seems to follow that an appropriate economic model must embody many probabilities regarding the likely paths of persons through a protocol. Probabilities would also need to be assigned to departures from the protocol in each time period. If the answer to question ]10 was affirmative, the ]7 answer was automatically made affirmative. With a court-supervised fund, only costs actually incurred will be paid. The answer to question ]9 may be the most important of the group. If the answer is negative, then an actual present injury must exist for any person allowed into a medical monitoring protocol. It is argued that medical monitoring claims, especially in the form of class actions, are unlikely to develop when an actual injury and/or symptoms must be present. In five of the 20 jurisdictions in Table 1, an actual injury must be present, so that the issue of medical monitoring claims would only arise in the other 15 jurisdictions. Finally, the answer to question ]10 affects the importance of accurate projections and, in particular, the needed accuracy of the branching probabilities. With a court-supervised fund, payments will only be made if monitoring events actually occur; estimation errors will not result in payouts that are too large. With lump-sum payments to class members, the present value payout could be too large or too small. At the federal level, the US Supreme Court addressed medical monitoring issues in a 1997 decision (Metro-North Commuter R.R. Co. v. Buckley, 521 U.S. 424, 117 S. Ct. 2113, 1998) involving a railroad worker and asbestos exposure. The Court held that an asymptomatic railroad worker exposed to asbestos could not recover lump-sum damages in a separate cause of action under the Federal Employers’ Liability Act. A current injury was required for this type of recovery. In terms of the answer to question ]9 (above), the answer is therefore negative at the federal level. It should be noted, however, that Justice Ginsburg, dissenting in the case, pointed out that medical monitoring claims had only been ruled out for lump-sum payments, not payments made via a court-monitored program. In Table 2, relevant citations are shown for the US Supreme Court decision and for relevant decisions by US Circuit Courts of Appeal in various circuits. None of these decisions are inconsistent with the US Supreme Court requirement that an actual injury be present in federal claims for medical monitoring damages (also see Whiting, 2002).
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Economics of Medical Monitoring
Table 2. Court
Federal Case Citation
US Supreme Court 3rd Circuit Court
4th Circuit Court 5th Circuit Court
9th Circuit Court 10th Circuit Court
Federal Court Decisions on Medical Monitoring.
Metro-North Commuter Railroad v. Buckley, 521 US 424, 117 S.Ct. 2113 (1997) In re Paoli Railroad Year PCB Litigation, 916 F.2d 829 (3rd Cir. 1990) (Paoli I), 35 F.3d 717 (3rd Cir. 1994) (Paoli II), 113 F.3d 444 (3rd Cir. 1997) (Paoli III) Ball v. Joy Tech., Inc., 958 F.2d 36 (4th Cir. 1991) Hagerty v. L&L Marine Services, Inc., 788 F.2d 315 (5th Cir. 1986), modified, 797 F.2d 256 (5th Cir. 1986) Abuan v. General Elec. Co., 3 F.3d 329 (9th Cir. 1993) Building & Construction Dept.; AFL-CIO v. Rockwell Intern. Corp., 7 F.3d 1487 (10th Cir. 1993)
3. THE DECISION–TREE MODEL An experienced forensic economist approaches medical monitoring cost calculations from a background in costing medical and other components of a life care plan (see Brookshire, 1987; Slesnick, 1990). Medical doctors and, more likely, life care planners provide necessary detail on when a certain treatment or service starts and stops, its frequency, and its cost. Most treatments, medications, and services extend to life expectancy. The forensic economist then forecasts cost increases into the future, discounts future costs to a present value at trial, and ensures, for example, that only the incremental costs due to the injury or illness are being costed. A medical monitoring protocol is fundamentally different, however, from a life care plan involving a future flow of medical and related services. In a life care plan, a person moves automatically from a treatment or service item in one period to the same treatment or service item in the following period. The effects of a treatment or service event seldom matter in a cost calculation, as the forensic economist simply cumulates the present value costs over time. In a medical monitoring protocol, the results of each monitoring event must matter, so that the path of a person through a protocol will vary according to the results of the various medical tests or other events. If the results of medical monitoring events did not matter, why would the medical monitoring be done? Thus, a model to cost medical monitoring protocols
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GEORGE A. BARRETT AND MICHAEL L. BROOKSHIRE Box B Branch 1 p = .03
EXIT TO TREATMENT
Box C Branch 2 p = .20 Box A INITIAL MEDICAL TEST X $100
MEDICAL TEST Y $500
Box D Branch 3 p = .07
CEASE PARTICIPATION
Box E Branch 4 p = .70
Fig. 1.
MOVE TO A REPEAT OF TEST X IN NEXT PERIOD
Decision-Tree Schematic of a Medical Monitoring Protocol.
must involve a ‘‘branching’’ of outcomes from each monitoring event, as pictured in the simple decision-tree illustration of Fig. 1. Markov analysis has previously been used in costing medical screening programs as the medical monitoring category of compensatory damages was emerging (see Briggs & Sculpher, 1998). Markov chains involve a branching process, they are stochastic in nature, and they have often been used to model random processes, which evolve over random trials. They are useful, therefore, in modeling economic damages because both outcomes and costs can be concurrently managed in a time progression. The estimation of medical monitoring costs need not be so complex that calculations cannot be explained to triers of fact. The decision-tree model used in the decision sciences meets the requirements of scientific costing, and the reliability of conclusions largely depends upon the accuracy of probability estimates for alternative outcomes. The decision-tree model is also an expected value model. The branching process is evident in Fig. 1, which is an
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illustrative schematic of one part of a medical monitoring protocol. Such a schematic can be used to explain the costing process at trial. In Fig. 1, a person or a cohort of persons first enters Box A for an initial medical test. Suppose that a life care planner has estimated the current cost of this test in the relevant geographic area as $100. Actually, an important probability will already have been examined in determining the cohort of persons who will flow into Box A. Some eligible class members, for a variety of reasons, will never take the first test. The probability that persons in a defined class enter Box A is thus less than 100 percent and must be considered. The results of Test X will be the basis for four branches, as shown in Fig. 1. The probability estimates are controlled by opinions of medical experts, but the sum of the probabilities of all branches must be 1.0. The attachment of probabilities to branches in the protocol is a substantial task of the forensic economist while working with various medical and scientific experts. In the illustration, three percent (p ¼ 0.03) of those taking Test X will have such bad results that they will immediately move to treatment (Box B). These persons exit the monitoring protocol when treatment begins. This is one of two ‘‘leakages’’ from a protocol, which may occur in any time period. In the illustration, another 20 percent of those tested will have results from Test X which are sufficiently worrisome that more intensive monitoring is required (Box C). These persons take medical test Y, which is also more expensive at $500. (Another branching will then flow out of Box C, depending upon results from medical test Y.) Seven percent of persons will leave the protocol after Test X (Box D). This is the second of two leakages from a protocol over time; in Markov analysis, these leakages would be labeled ‘‘absorbing states.’’ Some persons cease participation because of their fear of learning about a medical problem, while others may quit because one test or a series of past tests have produced good results and they become complacent. Some persons, of course, die as a cohort of persons moves through a monitoring protocol, and US Government data on life expectancies are used to estimate this specific leakage in each time period. Finally, seventy percent of the persons in the Fig. 1 illustration have good test results and will simply move to another Test X in the next monitoring period (Box E). Obviously, the model must be applied to a specific time period, and decisions on start and stop dates also involve interactions with the medical and scientific experts. An end date of exposure must be established, so that flows of new persons into the protocol will cease. Monitoring may only begin for class members who attain a certain age. The medical monitoring protocol
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may extend for the life expectancy of those entering the protocol, or it may extend for a fixed period of years. A forensic economist, of course, must also forecast medical cost inflation into the future and discount future costs to a present value at trial.
4. SAMPLE CASE A sample case is now provided as a method of demonstrating the procedures necessary to accurately estimate the present value lump sum required to adequately fund a medical monitoring protocol. It is assumed that a class of 1,000 individuals has been certified by the court. It would be illogical to contend that all members of this certified class would even begin the medical screening procedures; therefore, a reduction might be incorporated to effectively capture the ‘‘claiming rate’’ of the eligible class members. In this sample case, it has been assumed that 15 percent, or 150, of the 1,000 members will choose not to participate in the medical monitoring protocol. Therefore only 850 persons begin the first series of medical screenings. Figure 2 illustrates the flow of persons from left to right during the first year of the monitoring protocol. This sample protocol will essentially consist of two distinct batteries of tests, which have been labeled as Tier I and Tier II tests. The difference between these two test groupings is that Tier I is intended to be an annual baseline screening, while Tier II tests will only be necessary when the results of Tier I tests suggest that further investigation is necessary to detect the latent disease in question. For purposes of simplicity and because the task of identifying the individual costs of specific medical screenings is typically beyond the expertise of economists, only the total costs for Tier I and Tier II tests are relevant to this explanation. Here, a qualified medical professional, such as a physician, and a certified life care planner have provided the current total annual costs of Tier I and Tier II tests as $925 and $398, respectively, for each member of the participating class. Although 850 class members have elected to participate in the monitoring protocol, simply adding the total annual costs for the first year of Tier I and Tier II testing together and multiplying by the total participating class size is not the proper methodology for accurately estimating the anticipated costs of monitoring these 850 individuals. Instead, it is necessary for the medical monitoring protocol to address not only the tests, which need to be administered, but also the results of these examinations as they are learned. Tier II testing is contingent upon the results learned from Tier I testing, and
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Economics of Medical Monitoring YEAR 1
YEAR 2
p=0.05
p=0.025
p=0.20
TIER II TESTS 170 PERSONS @ $398 EACH
EXIT PROTOCOL FOR TREATMENT 8.5 PERSONS
EXIT PROTOCOL DUE TO ATTRITION 4.3 PERSONS
p=0.925 TIER I TESTS 850 PERSONS @ $925 EACH
p=0.725 p=0.05
p=0.85
TIER I TEST 773.5 PERSONS @ $947.57 EACH
EXIT PROTOCOL FOR TREATMENT 42.5 PERSONS p=0.025
p=0.15 DO NOT PARTICIPATE 150 PERSONS
EXIT PROTOCOL DUE TO ATTRITION 21.3 PERSONS
Year 1 Cost of Medical Monitoring $853,910
Fig. 2.
Sample Case: Flow of Individuals through the First Year of Medical Monitoring.
not all of the 850 participating persons will receive Tier II testing, even in the first year. Given the information provided by the medical experts, the annual cost of Tier I testing is $925 dollars, with 850 members participating in Tier I testing during the first year. Therefore, the total cost of Tier I monitoring in Year 1 is $786,250 ($925 850). Additional information provided by the medical experts allows the economist to determine what happens next to this group of 850 persons. It is estimated that 2.5 percent of the initial participating class will simply elect to discontinue their participation in the protocol; these 21.3 ð850 0:025Þ individuals exit the protocol due to fear, complacency, or other reasons. Similarly, the medical experts opine that the results of Tier I testing during the first year of the protocol will likely determine that 5 percent, or 42.5 ð850 0:05Þ; of the 850 participating members will be diagnosed with an illness consistent with the toxic exposure and will therefore exit the protocol for treatment. The medical experts also explain that 20 percent of the initial participating class, or 170.0 ð850 0:20Þ individuals, will need to enter Tier II testing to receive more focused screenings. Finally,
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the protocol explains that the remaining individuals will simply continue on to the second year of medical testing. This means that the process will begin anew for these 616.3 persons, or 72.5 percent of the initial 850 class members. They will enter the Tier I testing of Year 2 directly from Tier I testing of the preceding year. Since 20 percent, or 170, of the first 850 members of the class entered Tier II testing during the first year, and the total annual cost of each Tier II test is $398, the total Tier II cost in Year 1 is $67,660. For these 170 individuals participating in Tier II tests, the medical experts have opined that 2.5 percent, or 4.3 ð170 0:025Þ persons, will decide to voluntarily withdraw from the protocol, while 5.0 percent, or 8.5 ð170 0:05Þ persons, will be diagnosed with an illness and therefore will exit the protocol for treatment. The remaining 157.3 individuals, who represent 92.5 percent of the 170 persons participating in Tier II testing in Year 1, will simply proceed to Tier I testing in Year 2. Combining the total estimated costs of Tier I and Tier II medical monitoring examinations, the cost of the first year of medical monitoring for this class is $853,910 ($786,250+$67,660). It is quite possible that the first year of a medical monitoring protocol will be unique among all other years of the protocol. Medical experts will determine the final structure of the protocol given the recommended nature and frequency of specific testing. Assume that this sample medical monitoring protocol continues for a total of 20 years, with no changes to the probabilities associated with treatment and attrition exits, Tier I entry, and Tier II entry. Establishing the proper methodology for estimating the average annual growth rate of medical costs and the average annual interest (discount) rate is beyond the scope of this chapter. For our example, the last 20 years (1983–2003) of historical data for the Total Medical Care Cost Index, interest rates on 91-day US Treasury Bills, and the Consumer Price Index are used to estimate the present value of costs for this 20-year protocol. Total Medical Care costs from 1983–2003 increased by 2.44 percentage points annually above the rate of general price inflation. The annual costs of monitoring in the sample case have therefore been increased by 2.44 percent per year to incorporate the effect of price increases. During the same time period, the average real rate of interest on US Treasury Bills with a 91-day maturity have averaged 2.23 percent. Therefore, the annual costs of monitoring in the sample case have been discounted to present value by this 2.23 percent discount rate. The present value lump sum necessary to fund this sample protocol is $8,158,268. It is obvious that the decision tree approach to medical monitoring damages differs greatly from its alternative, which is to simply quantify a
Economics of Medical Monitoring
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medical monitoring protocol based upon the traditional ‘‘life care plan’’ method. Using the ‘‘life care plan’’ method, an economist simply assumes that the number of individuals entering the class, 1,000 in our example, would participate in each test available with no regard for the outcomes of each particular examination and no reductions in the 1,000 participants over time. While the present value of the medical monitoring costs of the 20-year protocol using the decision tree approach totaled $8,158,268, the same medical monitoring protocol would be valued at $25,555,122 under a ‘‘life care plan’’ method – an estimate that would be 213 percent too high.
5. SENSITIVITY ANALYSIS The sensitivity of the $8,158,268 estimate to various changes in the protocol specification may be usefully examined. For example, assume that the protocol length is halved from 20 years to 10 years. The total present value lump sum necessary to fund the shorter program is $5,837,801. The cumulating effect of leakages for treatment and attrition is significant. Of the 850 individuals who begin the protocol, only 331 would remain after 10 years, with this number decreasing to 128 by the end of a 20-year protocol. It is also useful to study the effects of changes in variables within the medical monitoring protocol. Increases in the probabilities associated with test outcomes can have either a profound or an insignificant impact upon the estimate, depending upon which probabilities are revised. For example, a 10 percentage point addition to the probability that Tier I testing will lead to a Tier II test is found to decrease costs by $119,519 (or 1.4 percent) in the 20-year present value total of medical monitoring. When the probability of treatment exits for both Tier I and Tier II tests are increased from 5 percent each to 10 percent each, the protocol cost is reduced by $2.6 million to $5,527,180. In this sample case, a 10 percentage point increase in the need for Tier II testing would at first seem to substantially increase the total cost of the protocol as more class members are required to undergo more specific testing each year. However, despite the fact that additional individuals will receive Tier II testing, these additional participants will then face the added probability of a detection of illness. This would remove the individuals from the protocol, as would the likelihood that individuals would also voluntarily withdraw from the protocol. This combined effect offsets the increases in the cost of monitoring. It should be noted that because the total probabilities flowing from each box in the decision tree must add to 1.0, the 10 percent
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increase in Tier II testing is assumed to correspond to a 10 percent reduction in the number of persons flowing directly from Tier I testing in Year 1 to Tier I testing in Year 2. Rather than 72.5 percent following this path, only 62.5 percent would pass directly from Tier I to Tier I. On the other hand, when the probability of treatment exits are increased by 5 percent for Tier I and Tier II tests during each year of the protocol, substantial numbers of individuals are excused from the protocol each year. In fact, by the end of the 20-year protocol, a 10 percent probability of illness detection within each test group causes the final number of class members remaining to be only 32 of the 850 who began two decades earlier. As previously explained, an increase in the probability of treatment must dictate a corresponding reduction in the probabilities stemming from the same box(es). Here, the probability of persons moving from Tier I testing in Year 1 to Tier I testing in Year 2 is decreased by 5 percentage points to 0.675, and those moving from Tier II testing in Year 1 to Tier I testing in Year 2 are also decreased by 5 percentage points to 0.875. When leakage probabilities increase, the total cost of monitoring decreases substantially. An additional sensitivity analysis can be conducted by studying the effect of changing the cost of each monitoring event. In the sample case, suppose the cost of Tier I testing is doubled from $925 per person per year to $1,850. Because most individuals in the protocol will receive Tier I testing, the effect of doubling these tests is quite profound, with the total cost of monitoring increasing by more than $7 million (92 percent). Interestingly, the effect of doubling the annual cost of Tier II testing does not significantly change the estimate. Doubling the annual cost of Tier II testing from $398 to $796 only increases the total cost of the 20-year protocol by $646,425 (8 percent). Only 20 percent of participants each year are involved in Tier II testing, and leakages cumulate these numbers downward.
6. ESTIMATION AND TESTIMONY ISSUES A first estimation issue is the complexity of the branching model to be used; we have not in our experience seen benefits from use of a Markov analysis, which outweigh the added complexity compared to the use of a straightforward decision-tree model. The forensic economist will face a variety of issues in each medical monitoring case depending upon the roles, which he or she accepts. The economist obviously deals with the economic issues of medical cost inflation and discount rates. The economist may be involved early in the case as the relationships between the nature of a protocol, the class definition,
Economics of Medical Monitoring
25
and needed data are discussed. If age will be important in the monitoring protocol, this data element becomes important in data gathering. In collecting and managing data, the economist may play a large or small role. Similarly, the economist may play a more-or-less active role in facilitating the process by which medical and scientific opinions are pulled together into a coherent whole. Probabilities adding to 1.0 may be the product of several foundation experts, and leakages must be considered in the branching specifications. The economist may also be asked to estimate the costs of administering a court-supervised process and fund. The forensic economist must ensure that incremental costing is used, which also may involve interaction with the medical experts. Incremental calculations are grounded in the fifth question about legal parameters, which was discussed in a previous section. Does the increased risk make it reasonably necessary to undergo periodic medical examinations or testing different from that prescribed absent the exposure? In every surveyed jurisdiction where this legal parameter was clear (Table 1), the calculation of incremental costs is prescribed. Thus, if two physical examinations were required under the protocol, but if persons of the relevant age were advised to have only one annual examination, then only the incremental examination would be costed. The same is true for medical tests which might be specified in the monitoring protocol but which are also recommended for the general population at a specified frequency. Difficulties arise, of course, when the dividing lines between general monitoring events and events specified in a monitoring protocol are unclear. Specific monitoring protocols present specific calculation issues and challenges. For example, the first monitoring event may involve a ‘‘score’’ which is the joint outcome of several medical tests and questionnaire results involving medical histories. A different branching may emerge from a box depending upon smoking status, for example. Or the costs of a smoking cessation program may be worked into a monitoring protocol if allowed under applicable legal guideposts. Attempts have also been made to include the costs of targeted medical research in a medical monitoring protocol. The forensic economist may be asked to estimate travel costs to monitoring sites and/or lost wages. The economist may need to consider the necessary geographic area for a combination of medical facilities necessary to accommodate the new monitoring just as price discounts for ‘‘bulk’’ monitoring may also be a consideration. Possible or likely changes in medical monitoring technology may be at issue, and alternative monitoring protocols may need to be costed either for this reason or simply to show the sensitivity of costs to important assumptions.
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GEORGE A. BARRETT AND MICHAEL L. BROOKSHIRE
One testimony-related issue arises because of a difference in typical personal injury damages versus medical monitoring damages. Large dollar amounts may result in the former cases because one or a few persons have large damages. Large dollar amounts in monitoring cases might exist not because dollar damages for individuals to be monitored are large, but because there are a large number of individuals involved. In calculation examples and charts, a protocol and its costing might be shown for one person and an expected present value calculated per person. Total cost calculations for all persons might be deferred to the end of the presentation. Alternatively, all calculations and demonstrative evidence might be in terms of total cohort numbers and total dollars moving through the monitoring period. Forensic economists on the plaintiff or defense side of these cases may evaluate alternative methods of presenting this information differently, even if cost conclusions are exactly the same. Finally, the nature of testimony may be affected by whether or not the form of paying these compensatory damages is a lump-sum payment to each plaintiff, which he or she is assumed to use for the payment of monitoring costs. As is seen for column ]10 in Table 1, only four states appear to allow for lump-sum payments, but the status of lump-sum payments in most of the other States is unclear. Four states require that the form of payment be a court-supervised fund. Court-supervised funds have the disadvantage that they can be complicated and costly. On the other hand, they reduce the stress over the precision of branching probabilities assumed in the estimation model. This includes the assumed leakages of persons out of the protocol and out of its costing. To the extent that the estimate does not turn out to be perfect, the actual costs of monitoring will only be paid when monitoring events actually occur. Of course, the assumed probabilities for beginning and continuing through monitoring can also be underestimated, and provision would need to be made for upward flexibility in court-controlled funds. With lump-sum payments, the defense will surely argue that some percentage of the payments will be used for purposes other than medical monitoring. In the context of the decision-tree model, this is an issue of the quality of the leakage assumptions as a monitoring process unfolds.
7. CONCLUSION The cost of medical monitoring is a new and often controversial category of compensatory damages, which has been considered and allowed in a
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significant number of US jurisdictions. A 10-fold categorization of legal parameters from these jurisdictions provides several guideposts for calculations. A straightforward decision-tree analysis is recommended as the calculation model. In this chapter, the model has been applied to the facts of an illustrative case. The sensitivities of estimates to changes in important calculation values have been shown, and major issues of calculation and economic testimony have been described.
REFERENCES Barrett, G. A., & Brookshire, M. L. (2002). The forensic economics of medical monitoring protocols. Litigation Economics Review, 5(2), 15–26. Bourgeois v. A.P. Green Industries, Inc. (1998), 716 So.2d 355 (Supreme Court of Louisiana 1998). Bower v. Westinghouse Electric Corporation (1999), 522 S.E.2d 424 (West Virginia Supreme Court of Appeals 1999). Briggs, A., & Sculpher, M. (1998). An introduction to Markov modelling for economic evaluation. PharmacoEconomics, 13, 397–409. Brookshire, M. L. (1987). Economic damages: The handbook for plaintiff and defense attorneys (pp. 75–91). Cincinnati, OH: Anderson. DiPaola, T. A., & Roberts, G. W. (2000). Back to the future, recognition of medical monitoring claims in Florida. The Florida Bar Journal, 74(11), 28–41. Gonzales, E. A., & Valori, R. W. (2001). Medical monitoring claims are viable in Florida. The Florida Bar Journal, 75(1), 66–70. Klein, A. (1998). Rethinking medical monitoring. Brooklyn Law Review, 64(1), 1–38. Lee, J. R. (1994). Medical monitoring damages: Issues concerning the administration of medical monitoring programs. American Journal of Law & Medicine, XX(3), 251–275. Maskin, A., Cailteux, K. L., & McLaren, J. M. (2000). Medical monitoring: A viable remedy for deserving plaintiffs or tort law’s most expensive consolation prize. William Mitchell Law Review, 27(1), 521–550. Slesnick, F. (1990). Forecasting medical costs in tort cases: The role of the economist. Journal of Forensic Economics, 4(1), 83–99. Tanner, M. A. (1998). Medical monitoring trusts: A win-win situation under FELA. MetroNorth Commuter R.R. Co. v. Buckley, 117 S. Ct. 2113 (1998). Land and Water Law Review, 33(1), 399–416. Whiting, H. R. (2002). Remedy without risk: An overview of medical monitoring. Washington Legal Foundation, Contemporary Legal Notes Series, 42, 1–34. Wolfe, S. L. (2000). The recovery of medical monitoring costs: An argument for the fund mechanism in the wake of Bower v. Westinghouse. West Virginia Law Review, 103(1), 103–124.
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SECURITIES FRAUD DAMAGES Bradford Cornell, John I. Hirshleifer and John N. Haut1 Between January 2001 and January 2003, over 700 securities class action lawsuits were filed.2 With the collapse of large companies such as Enron, Adelphia, and WorldCom, these lawsuits have taken on a new importance, particularly because of issues surrounding the integrity of management and the effectiveness of outside directors and auditors. The purpose of such litigation is to obtain monetary awards for damages allegedly suffered by shareholders, who purchased shares of these companies during periods of time within which frauds were alleged to exist, but were not disclosed (‘‘class periods’’), and who either sold during the class periods or held their shares until the alleged frauds were disclosed. This chapter discusses how damages in securities class actions should be estimated and examines the various issues that should be considered when estimating such damages. A logical starting point for such a discussion is a description of the required elements of a securities class action lawsuit under Rule 10b-5 of the Securities and Exchange Act of 1934 that must be proved in order for the plaintiffs to prevail. The importance of performing an event study will also be discussed, as will issues surrounding the appropriate class period for estimating damages. Methodologies for estimating inflation per share (the difference between a stock’s price per share and its value absent the alleged fraud) will be examined, as will ‘‘bounce-back’’ provisions relating to the Private Securities Litigation Reform Act of 1995 (1995). Finally, the use of trading models to estimate aggregate damages will be explored, as will Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 29–57 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87003-2
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adjustments to the defendant company’s outstanding shares and trading volume during the class period.
1. ELEMENTS OF A CLASS ACTION LAWSUIT UNDER RULE 10B-5 OF THE SECURITIES EXCHANGE ACT OF 1934 A private right of action is not expressly mentioned in either y10(b) or Rule 10b-5 of the Securities Exchange Act of 1934, and hence such a right must be implied. To justify a reasonable cause of action, the plaintiff must prove: (1) a material omission or misstatement; (2) made by the defendant with ‘‘scienter’’ (defined later); (3) which was the actual and proximate cause of injury to the plaintiff; (4) and was relied upon by the plaintiff.3 To reach the issue of damages, defendants’ liability in terms of satisfying the above four elements must be assumed.
1.1. Materiality The Rule 10b-5 standard for materiality is found in TSC Industries v. Northway, 426 US 438 (1976), which stated that: [a]n omitted fact is material if there is a substantial likelihood that a reasonable shareholder would consider it important in deciding how to vote.y Put another way, there must be a substantial likelihood that the disclosure of the omitted fact would have been viewed by the reasonable investor as having significantly altered the total mix of information available (p. 449).
Although TSC Industries arose in a proxy solicitation context, the Supreme Court expressly adopted this standard for use in Rule 10b-5 cases.4 Thus, any omission or affirmative misstatement by the particular defendant in a Rule 10b-5 action will be material if it alters the ‘‘total mix’’ of information available to a reasonable plaintiff, i.e., a reasonable plaintiff would consider the additional information important in making a decision regarding investment in the security. A possible method of testing whether an omission (or misstatement) is material is to wait until it is discovered and then measure whether the impact of its disclosure on share prices was statistically significant (Macey et al., 1991, p. 1036, n.60). Methodologies for measuring statistical significance will be discussed later in this chapter.
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1.2. Scienter The Supreme Court established the standard for scienter in Rule 10b-5 cases in Ernst & Ernst v. Hochfelder.5 In this opinion, the Court defined ‘‘scienter’’ as ‘‘a mental state embracing intent to deceive, manipulate, or defraud,’’ and specifically avoided addressing the question of whether recklessness would suffice in a Rule 10b-5 civil liability action. However, the Court did admit that recklessness was considered intentional conduct for purposes of imposing liability in some areas of the law. Appellate courts have generally accepted the rule that such recklessness alone satisfied the requirement for scienter. This recklessness has been defined post-Hochfelder as: y a highly unreasonable omission, involving not merely simple, or even inexcusable negligence, but an extreme departure from the standards of ordinary care, and which presents a danger of misleading buyers or sellers that is either known to the defendant or is so obvious that the actor must have been aware of it.6
Recklessness of this type can be seen as approaching the bounds of intentional behavior and can be used to prove scienter when the defendant claims to lack the requisite intent.7 However, the Supreme Court has been unwilling to extend y10(b) and Rule 10b-5 of the Securities and Exchange Act of 1934 to impose liability for negligent conduct.8
1.3. Actual and Proximate Cause of Plaintiff’s Injury Under Section 28(a) of the Securities Exchange Act of 1934, a shareholder who is a class member may not recover ‘‘a total amount in excess of his actual damages on account of the act complained of.’’9 Thus, applicable law requires the application of a measure of damages, under which the plaintiff may only recover those losses actually caused by the fraudulent conduct. This measure of damages is calculated by subtracting the difference in the trading price and true value of the stock at the date of disclosure of the fraud from the difference in the purchase price and the true value of the stock at the date of purchase.10 In addition, market-wide, industry, and non-fraudulent company-specific effects on the stock price should be filtered out in order to accurately assess the effect of the alleged fraudulent conduct upon the defendant company’s stock price. For example, assume that Mr. Smith buys XYZ Oil Company stock at $50 per share. At the time of Mr. Smith’s purchase, XYZ publicly
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announces that its costs to clean up a spill off the coast of Alaska will amount to $100 million when, in fact, such costs are known by the company to amount to $2 billion. Assume that the true value of XYZ stock at the time of Mr. Smith’s purchase, in light of the $2 billion cleanup cost, is $20 per share. When the fraud is publicly disclosed, absent market or industry developments, XYZ’s stock price will drop to $20, its true value. Thus, the trading price and the true value on the disclosure date will be equal and the difference between the two will be zero.11 The difference between the purchase price per share and the stock’s true value on the purchase date will be $50 minus $20, or $30 per share. Total out-of-pocket damages in this example will thus amount to $30 per share.
1.4. Reliance In class actions, actual reliance cannot readily be proved for each individual class member. To help solve this problem, the Supreme Court adopted the ‘‘fraud on the market’’ theory in Basic v. Levinson. In Basic, the Court held that a plaintiff in a class action is entitled to a rebuttable presumption that he or she relied upon the ‘‘integrity of the market price’’ in making investment decisions where the security in question trades on an organized exchange or other efficient market.12 This presumption is rebuttable for both class and individual plaintiffs and is not available for securities trading in inefficient markets.13 An efficient market may be defined as one in which: (1) the stock price reacts quickly to new information; and (2) the reaction to such information results in an accurate pricing at that time (Langevoort, 1992; Fama, 1991; Basic, p. 246). There is a considerable body of finance literature that suggests that most stocks follow the ‘‘semi-strong’’ form of the efficient markets hypothesis (EMH) most of the time. This form of the EMH maintains that the present price of a given security reflects all publicly available information at that point in time and suggests that stock prices in an efficient market react quickly to new information (Fama, 1991).14 However, there is also evidence that, although stock prices react to new information quickly, those reactions do not necessarily result in an accurate pricing at the time (Fama, 1991, p. 1602; Langevoort, 1992, p. 856). The semi-strong form also incorporates the weak form of the hypothesis, which holds that current security prices reflect all past price information (Fama, 1991, p. 1576). There is direct evidence in contradiction of the strong form of the EMH, which maintains that current security prices reflect all available information, both public and
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private (Fama, 1991, p. 1576), as this form would indicate that insider traders are unable to earn risk-adjusted returns in excess of the market return (Fama, 1991, p. 1607). Furthermore, if the strong form were true, it would imply that there could be no fraud on the market. Under Basic’s ‘‘fraud-on-the market’’ theory, a plaintiff relies on a semistrong efficient market to accurately incorporate all publicly available information into the security price. The untrue aspect of any misstatement would not constitute public information, nor would the nature of any omission. Hence, neither would be incorporated into the market price until it was at least partially disclosed. A problem exists with the ‘‘fraud on the market’’ theory that works to the detriment of defendants and may (but probably does not) make the EMH component superfluous with respect to reliance, but not with respect to damage computation.15 This problem, as pointed out by Hiller and Ferris (1990), is that ‘‘[a] statement by the plaintiff that he relied on the integrity of the market to reflect [the security’s] true value would be very difficult, if not impossible, to disprove because of its subjectivity’’ (p. 548). In other words, all that would appear to be necessary for the fraud-on-the market theory to be applicable to a given case would be that the class of plaintiffs claim to have relied upon the integrity of the market price, regardless of whether they assert that the market is efficient. However, for the purpose of damage computation, the market’s ability to accurately price stocks relative to the stock price prior to the news item in question would have to be taken into account, because damages cannot be reasonably ascertained without some indication of the stock’s hypothetical ‘‘true value’’ on which to base hypothetical inflation. A further defense to the fraud-on-the market theory is that the market did not ‘‘react to the misrepresentation’’ or that market makers did not believe the misleading information (Macey & Miller, 1991, p. 1021). The market’s potential failure to incorporate the information can be analyzed by using an event study as described below.
2. EVENT STUDIES AS ANALYSIS TOOLS An event study is a tool for analyzing the behavior of a stock’s price and volume in reaction to news items. It is thus particularly useful for examining causation, materiality, and reliance. The purpose of an event study in a fraud-on-the-market case is to assist people, including the Court or the jury, in understanding the information that led to material movements in the
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stock price of a subject company and its industry over a period of time which includes, but does not necessarily have to be limited to, an alleged class period. While there are variants of the event study methodology commonly utilized in securities fraud cases, all event studies typically include a day-by-day listing of: (a) (b) (c) (d)
the subject company’s stock price; its daily trading volume; its daily percentage return; the daily percentage return on an index of comparable companies (or a predicted return from a regression model that may incorporate comparable companies and market proxy indices); (e) the daily percentage residual return (which is the company’s stock price return after the return on the comparable company index is netted out); (f) a statistic that measures the significance of the daily percentage residual return; (g) relevant news items on a daily basis that may have an effect upon the stock price. An event study is an invaluable tool for evaluating various questions in a securities case, such as whether the underlying news releases support a plaintiff’s contention of either causation and/or disclosure of information that reasonably can be linked to alleged frauds. It can also be useful in analyzing materiality. It is particularly useful in evaluating how a company performed in relation to comparables, determining which day’s return seems to be unusual, and whether there is news that may help to prove or disprove a plaintiff’s claims. A well-crafted event study provides enough information for each day to give the reader a solid understanding of all of the news released to the market on that day. This helps the analysts identify documents that should be studied in greater detail. As explained later, an event study can also be used to help estimate per share inflation, if such inflation is determined to exist. In a typical securities fraud case, plaintiffs assert that material misstatements or omissions are revealed to the market on discrete dates. The subject company’s stock price reactions on these dates can be analyzed using an event study. In order to evaluate the significance of the news revealed on an alleged fraud disclosure date, an analyst will study the nature of the news revealed on that date and attempt to relate the news to the stock price movement on that day. The analyst will also review the company’s stock price movement net of any movements in an index of comparable companies (or net of the predicted returns from a regression model), so that the degree
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of ‘‘unusualness’’ of the company’s price movement can be assessed. When analyzing the impact of the release of news, normally the stock price return is evaluated over the single day in which the news release occurs. The rationale for this is the numerous empirical studies that support the view that the market responds very quickly to new information.16 In some instances where news is disclosed later in a day, the period analyzed could conceivably encompass the day of disclosure plus one additional day, based on a presumption that the market had not had a chance to fully react to the news. Clearly, the next day is relevant to the analysis if the news in question was released after the market was closed. It should be noted that if material news becomes available to the market, but the stock price does not respond promptly, that constitutes market inefficiency, which undermines the presumption of reliance on the integrity of the market price.
2.1. Calculation of Daily and Residual Returns A daily stock price percentage return is calculated using the following equation: ROR ¼
Ptþ1
Pt þ Dividend Pt
where ROR is the rate of return on security, Pt the price of security at the end of trading day t, and Ptþ1 the price of security at the end of the trading day t þ 1; where t þ 1 is one day after trading day t. The residual, or company-specific, return is estimated by subtracting a market or industry-based return from the subject company’s return, for the date that is being analyzed. One approach to measuring the residual return is to use the average return on an index of comparable companies to net out the market and industry effects.17 More specifically, the residual return is given by: RES ¼ ROR
IND
where RES is the daily residual rate of return, and IND is the return used to net out market and industry effects. Because companies in the same industry should also be expected to react to general market news in a similar way, a properly identified set of comparables should give the analyst a good feel for the impact of both industryspecific and general market effects occurring on that day. Presumably, these
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effects are not related to any alleged frauds, which is why they must be netted out. For example, if it were alleged that a fraud was revealed with respect to XYZ Oil Company on June 1, 2000, causing its stock price to decline by 10%, a concomitant decline of 10% in an index of oil companies similar to XYZ Oil Company on the same day would strongly suggest that XYZ’s stock price decline was caused entirely by industry-related market forces.
2.2. Testing for Significant Daily Residual Returns A non-zero residual return for a given day means that the company’s return on that day cannot be attributed entirely to the market or industry-wide events. This does not mean, however, that there was necessarily companyspecific information released to the market. Numerous studies have shown that individual stock prices move up and down continuously for unexplainable reasons (Roll, 1988; French & Roll, 1986). Furthermore, most of the movements are so small that they cannot be distinguished from random noise. The first step, therefore, is to use a statistical test to isolate residual returns that are ‘‘significantly’’ different from zero. The standard technique for determining whether a given residual return is different from zero is to employ a z-test. This test is based upon the following equation: Z¼
Daily Residual Standard Deviation of Residual Returns
A key conceptual issue that arises when applying the z-test in the context of a securities fraud case is determining what data to use to estimate the standard deviation of residual returns. The problem is that the release of fraud-related information can affect the estimate of the standard deviation and, thereby, bias the z-test. The common solution to this problem is to use stock return data from a ‘‘clean’’ period either before the initial release or after the final disclosure of the alleged fraud-related information to estimate the standard deviation. Unfortunately, in some cases, such as those involving new issues, clean periods may be difficult to come by. The standardized z-value resulting from the above formula is compared with a standardized value in a statistical significance table for a desired level of significance. Typically, a 5% level of significance is selected. If the z-value for the residual return on a particular day is greater than the tabular z-value (or less than its negative), it means that there is less than a 5% total chance
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that the observed residual return was a result of random chance. It should be noted that the standard z-test is based on the assumption that security returns are normally distributed. According to Brown and Warner (1985), when daily data are used for individual securities, the probability distribution of security returns tends to be fat-tailed, not normal. As a result, the standard z-test is more likely to classify returns as abnormal when, in fact, they are not (pp. 9–10). A significant z-value identifies days when abnormally large residual price movements occurred, but that is only a first step. To calculate damages, that residual price movement must be related to an alleged fraud. The problem is that residual price movements may be due to the release of fraud-related information, non-fraud-related information or no information at all. The Roll (1988) and French and Roll (1986) articles cited earlier reveal that, even statistically significant residual price movements are often associated with what has been called noise trading rather than the release of information. To further complicate matters, the residual on any particular day may reflect a combination of all three factors: fraud-related information, non-fraudrelated information, and noise trading. Sorting out these interacting factors requires a detailed study of news releases associated with significant residual returns.
2.3. Analyzing News with an Event Study Event studies proceed by recording all news related to the subject company that is released on every day during the class period. Attention is focused on days for which there were statistically significant residual returns. The problem is that for a major company, say Microsoft, there are numerous stories in the press every day. Furthermore, days on which there were large stock price movements are likely to be characterized by an even greater number of releases. Unfortunately, the event study approach does not identify which, if any, of the releases was responsible for that day’s residual return. Here, judgment comes into play. Using fundamental valuation analysis in conjunction with judgment and experience, the researcher must determine how the news releases are related to the stock price movement on that day. For instance, if there are multiple news items revealed on a given day and only one of them relates to the present or future cash flow of the subject company, the import of that one item should be segregated from the others. The more qualitative the disclosure on a particular day, the greater the difficulty in segregating and estimating its effect, if any, on stock price
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behavior. In other words, news disclosures that do not discuss specific, quantifiable economic consequences are much harder to evaluate with respect to their effects on stock price. On days where analysis indicates that both fraudulent and non-fraudulent information has been revealed, and both jointly cause a material stock price movement, an added complication arises. To estimate damages, the analyst must parse the residual return into fraud-related and non-fraud-related components. One way to do this is to make use of intraday data. By examining trade by trade data, as suggested by Schwab and Kroll (1992), it is often possible to determine more accurately the impact of a specific information release on the subject company’s stock price (pp. 19–20). In addition, fundamental valuation analysis can be employed. It may be the case that one announcement has clear implications for value-relevant variables such as earnings and cash flow, while the other does not. Although these tools are helpful, it is still often the case that judgment comes into play. There are no hard and fast rules for attributing components of a residual return for a given day to specific information releases. Thus far, it has been implicitly assumed that fraud-related and nonfraud-related information can be unambiguously distinguished. Such is not always the case. As an example, consider a news item regarding an announced SEC investigation into possible fraud, without any admissions, restatements, or conclusive findings at the time of the news release. This information alerts the market that the SEC has significant concerns about a company, and the market usually reacts negatively in order to incorporate the possibility that the SEC will eventually take adverse actions against the company. Consequently, significantly negative residual returns are typically observed after such announcements have been made. At that time, however, the market has no idea what the SEC’s finding will ultimately be. While the market at that point is on notice that something could be amiss, and perhaps there could be a fraud, it does not know with certainty that a fraud will be found, nor does it know the economic magnitude of potential frauds. Thus, any stock price movement in this scenario is not a reaction to a specific fraud disclosure. Of course, it is possible that the ‘‘reserve’’ that the market impounds in the stock price to cushion against potential bad news may prove, retrospectively, to be large enough to incorporate the economic impact of actual fraud, if it is later determined to exist. In situations such as this, plaintiffs and defendants typically disagree re garding whether the stock price drop should be included in estimates of damages.
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2.4. Defining the Class Period Investors who are eligible to collect damages are those who purchased during the class period. The class period is defined by the duration of the alleged fraud. It begins when the company receives material information about the value of its stock but withholds that information from the market. It ends when the required information is released to the market. There is, of course, some ambiguity in deciding what information must be released. Clearly, a company does not have to disclose its trade secrets, such as the formula for Coca-Cola Classic. On the other hand, if a software company knows that its product is buggy and cannot be brought to market, but still claims, nonetheless, that it is ready for release, it is an obvious fraud. It should be stressed that partial disclosures will not end the class period.18 The class period ends only when the market is fully and fairly informed. For instance, in the software example above, the class period would begin when the company announced that the product was ready for shipping knowing that it was buggy. If the company subsequently announced that the product was ‘‘delayed,’’ that would be a partial disclosure. However, the class period would not end until the full extent of the bugs (including expected economic consequences) had been revealed. As discussed below, partial disclosures complicate damage analyses because they imply that the extent of mispricing, or inflation, varies during the class period.
3. MEASURING STOCK PRICE ‘‘INFLATION’’ Damages in securities class action cases are premised on the notion that frauds are associated with overvaluation. That is, during the period in which the fraud is operative, the market price of a security exceeds its true value because the market is misinformed. The difference between the market price and the true value is commonly referred to as the inflation in the share price. In his precedent-setting concurring opinion in Green v. Occidental Petroleum, Judge Sneed laid down a procedure for calculating damages based on the idea of inflation. Judge Sneed argued that an investor was damaged to the extent that the inflation at time of purchase exceeded the inflation at the time of sale, or the inflation at the date of full disclosure if the investor did not sell the stock. However, the inflation at the date of full disclosure is
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usually zero because with full information the market price and value converge by definition.19 Judge Sneed envisioned depicting inflation as the difference between two lines: the price line, which is a daily plot of the actual stock price, and the value line, which depicts the true value of the stock on a daily basis. During the class period, the price line and value line diverge because of the alleged fraud. The difference between the two lines is the inflation.20 In light of Judge Sneed’s opinion, it is clear that measuring damages in a securities case requires estimation of inflation, or equivalently the value line, on a daily basis. There are two basic approaches to measuring inflation: the comparable index method and the event method. For both approaches, there are a number of nuances that arise. Both the comparable index method and the event method start with the assumption that at the end of the class period price and value are equal. The price line can be plotted backward in time by simply downloading stock price data. The value line, however, must be constructed. The comparable index and event methods use different approaches for calculating the value line backward in time from the end of the class period to the beginning.
3.1. Comparable Index Method The comparable index method is based upon the assumption that, but for the effects of the alleged fraud, the defendant company’s stock would have behaved exactly as did the comparable index during the class period. Therefore, the value line can be constructed backward in time by substituting the return on a comparable company index for the security’s own return. Specifically, commencing with the day following the last day of the class period and working backward, the equation used to calculate the hypothetical true price for each day in the class period is given by: Prior day hypothetical pricet
1
¼
End of day pricet 1 þ Comparable Index Returnt
where t is any single day during the class period, and t 1 is the day before day t. An example of a security price line and value line for XYZ Oil Company using the comparable index method and the assumptions discussed earlier under causation is shown in Fig. 1. The greatest weakness of the comparable index method is that it effectively assumes that all differences between the price movements of the defendant company and those of the comparable index are related to fraud.
41
Securities Fraud Damages $60 XYZ Oil Co. Price Line
$50
Stock Price
$40 Full Disclosure
Inflation
$30
o
$20 True Value Line
$10 $0
1
5
Fig. 1.
9
13
17
21 25 Day
29
33
37
41
45
Inflation per Share: Comparable Index Approach.
Therefore, it includes in the damages the effects of non-fraudulent firmspecific events that affect a company’s stock price, relative to the comparable companies, over the course of a class period. For instance, if during a hypothetical class period for a lawsuit involving Apple Computer the company announced a delay in its new operating system, an event unrelated to the alleged fraud, the resulting drop in the stock price, relative to comparable computer companies, would increase the measured inflation during the class period despite the fact that it was unrelated to the fraud.
3.2. Event-Study Method The event-study method is based on the notion that the extent of inflation in a company’s stock price can be measured by the decline in the stock price that occurs when the true information is released. Consequently, the event study proceeds by examining the residual returns on the days when curative disclosures occurred and uses them to construct the value line backward in time from the date of final disclosure. More specifically, the event-study method assumes that the defendant company’s stock price would have behaved exactly as it did, except on those dates that frauds or omissions occurred and when frauds were revealed. The value line for the event method is constructed in a similar fashion to that for
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the comparable index method, except that the daily total return on the defendant company stock is used on those days where no events that are deemed to be related to the alleged fraud occur. On those days where fraud-related events are deemed to occur, a daily return on an index of comparable companies is substituted for the defendant company’s return. The equation used to compute the hypothetical true values of the security during the class period is the same as that used in the comparable index method, except that the stock’s own daily total return is used where no fraud or fraud revelation has occurred. Unlike the comparable index method, the event-study method is designed to filter out from damages company-specific stock price movements that are not related to alleged frauds. However, this requires proper interpretation of the event study. First, days on which fraud-related information was released and in which the residual return was significant must be isolated. Second, the residual return on those days must be partitioned into fraud-related and non-fraud-related components. Too often, plaintiffs simply assume that if fraud-related information was released, it accounts for the entire residual return. This assumption is over-simplified and can lead to erroneous estimates of damages. As an example, we revisit the XYZ Oil Company example used earlier in this chapter. In this example, there is only one disclosure date at the end of the class period. Recall that, at the end of the class period, XYZ disclosed that cleanup costs from an oil spill off the coast of Alaska would amount to $2 billion instead of the originally announced $100 million and that no other company-specific news was released. Upon this announcement, XYZ’s stock price declined from $50 to $20. For purposes of the value line calculation, it is assumed that on the day that XYZ disclosed that the oil spill cleanup costs would be $2 billion rather than $100 million, the OPEC cartel announced that it would reduce its price per barrel by 5% and thus a market valueweighted index of oil drilling and exploration companies declined by 5%. XYZ’s hypothetical true value line would show a decline of 5% from the previous day’s value on the last day of the class period, i.e., from $21.05 to $20. On all earlier days in XYZ’s class period prior to the disclosure date, the XYZ true value line would use XYZ’s actual returns. The event-study method is shown graphically in Fig. 2. 3.2.1. In-and-Out Traders Once the value line has been constructed, out-of-pocket damages can be estimated. For every individual trader, the damages he or she suffered equals the lesser of: (1) per share inflation at purchase minus the per share inflation at sale; or (2) the difference in the purchase price per share and the
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Securities Fraud Damages $60 XYZ Oil Co. Price Line
$50
Stock Price
$40 Full Disclosure $30
Inflation
o
$20 $10 True Value Line $0
1
5
9
13
17
21
25
29
33
37
41
45
Day
Fig. 2.
Inflation per Share: Event-Study Approach.
sale price per share times the number of shares held.21 For traders who do not sell during the class period, damages equal the per share inflation at purchase times the number of shares purchased. Traders who buy and sell during the class period are commonly called inand-out traders. The damages they suffer are more sensitive to the precise construction of the value line. For instance, if the inflation is constant until the last day of the class period, in-and-out traders suffer no damage. This leads to an important distinction between constant percentage inflation and constant dollar inflation. Another complication related to in-and-out traders is that the law, as currently interpreted, does not require traders who profited from the fraud to refund the money. It is possible, for instance, that a trader bought a stock when the inflation was $5 and sold it when the inflation was $7. Under Judge Sneed’s rule, this trader has made a $2 gain as a result of the fraud. However, that gain is not netted out when calculating aggregate damages to the class. Correct treatment of in-and-out traders is most important when a material fraud is revealed slowly over time rather than disclosed all at once at the end of the class period. In that case, the inflation will also decline slowly over time (provided that no material confounding information is also disclosed on the fraud disclosure date) and damages to in-and-out traders could well be significant.
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3.3. Constant Percentage Inflation The constant percentage inflation approach assumes that the percentage inflation remains constant as the value line is constructed backward in time. As an example, assume that GHI Company announces an accounting restatement. Upon the disclosure, the price of GHI’s stock fell from $2.00 to $1.00, a 50% decline, while the general market and GHI’s peers remained unchanged. If the constant percentage inflation method is used, inflation per share would equal 50% of GHI’s stock price throughout the class period until the alleged disclosure date. However, this means that the dollar amount of inflation changes with GHI’s stock price. As a result, at least some in-and-out traders will suffer damages. This example is shown graphically in Fig. 3. 3.3.1. Constant Dollar Inflation As its name implies, the constant dollar inflation methodology assumes that inflation related to a particular fraud is fixed at a constant dollar amount. If a single fraud occurred at the beginning of the class period, the dollar amount of inflation would be fixed over the entire class period. For instance, in the previous example of GHI Company, the inflation would be fixed at $1.00. As noted previously, this implies that there would be no in-and-out $60 $50
GHI Co. Price Line
Stock Price
$40 $30 50% Inflation $20 Full Disclosure
$10 True Value Line $0
o 1
Fig. 3.
7
13
19
25
31 Day
37
43
49
Inflation per Share: Constant Percentage Inflation Approach.
55
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damages. A graphical representation of constant dollar inflation may be found in Fig. 4. In-and-out damages may still arise under the constant dollar inflation approach if several revelations occur over the class period. When there are multiple revelations, the inflation stair steps down to zero. Investors who purchase during one stair step and sell during a later one would be damaged. When stock prices have moved sharply for reasons unrelated to the fraud, the difference between the constant percentage inflation and constant dollar inflation can be large. Reconsider, for example, the GHI Company example contained in Fig. 3 that had one corrective disclosure at the end of the class period and whose stock price dropped from $2.00 to $1.00 – a 50% decline. In this example, the company’s stock price was $50 at the beginning of the class period. According to the percentage approach, inflation would be a constant 50% of the stock price over the class period. Therefore, inflation would be estimated to be 50% of $50, or $25, at the start of the class period. This could result in huge, and inappropriate, in-and-out (and retention) damages. The constant dollar approach correctly recognizes that the in-andout damages are zero where there is only one complete disclosure of the alleged fraud. If the alleged fraud is disclosed in two or more partial disclosures, there will still be in-and-out damages under the constant dollar approach because the inflation is no longer constant during the class period. $60 $50 GHI Co. Price Line
Stock Price
$40 $1.00 Inflation
$30 $20
True Value Line Full Disclosure
$10 $0
o 1
7
13
19
25
31
37
43
49
Day
Fig. 4.
Inflation per Share: Constant Dollar Inflation Approach.
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4. INDEPENDENT ESTIMATES OF INFLATION Inflation does not have to be estimated solely by observing the behavior of the stock price on alleged disclosure dates. In many instances the value of alleged frauds can be more credibly estimated using independent valuation techniques. For instance, suppose that the alleged fraud consisted of a brokerage firm hiding $100 million in losses associated with a rogue trader. A direct estimate of the inflation associated with this fraud is $100 million divided by the number of shares outstanding. The benefit of direct valuation approaches such as this is that they are free from the random noise that makes interpretation of stock price movements so difficult. The drawback is that they are not based on market data. Plaintiffs’ damages expert witnesses in securities class actions sometimes use a constant per share value throughout the class period to measure damages. This value is usually the post-disclosure stock price and is assumed to remain constant throughout the class period. However, this methodology is severely flawed because it does not allow for fluctuations in the stock’s hypothetical true value due to market and industry considerations, firmspecific factors unrelated to the alleged fraud, and trading noise.
5. DAMAGES PROVISIONS UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF 1995 The Private Securities Litigation Reform Act (1995) contains several provisions regarding damages computation that apply to all securities class actions filed on December 22, 1995, or later.22 In an effort to limit damages to those caused by actual fraudulent inflation and not by investor overreaction to news disclosures or uncertainty, Congress enacted provisions in the 1995 Act that can potentially reduce damages to investors who purchased during the class period and held until after the full disclosure date at the end of the class period. For these investors, damages are limited to the lesser of: (1) the fraudulent inflation at purchase; (2) the difference between the purchase and sale prices of the stock; and (3) the difference between the purchase price and the mean trading price at the earlier of the date of sale or 90 calendar days after the disclosure date.23 The reasoning behind this new limitation provision is twofold: (1) investors frequently overreact to disclosures that reveal unfavorable news;24 and (2) declines in a company’s stock price may be due to reasons other than the alleged fraud.25 Moreover, the
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1995 Act limits damages during the class period to the lesser of the difference between inflation at purchase and inflation at sale, and the difference between the purchase and sale price, a departure from Judge Sneed’s original methodology.26 The 1995 Act also raises further questions about the controversial topic of using trading models to estimate aggregate damages, which will not be discussed in this chapter.
6. USE OF TRADING MODELS Both Judge Sneed’s original methodology and the revisions dictated by the 1995 Act are stated in terms of individual investors. The problem is that without proof of claim forms, data on the trading of individual investors are not available. The traditional plaintiff solution to this problem has been to use trading models based on float and volume data to estimate both the number of damaged shares bought and sold during the class period (in-andout damages) and the number of damaged shares held until the end of the class period (retention damages). Three general types of trading models of increasing sophistication have been employed in cases to date: the straight proportional trading model (PTM), the accelerated trading model (ATM), and the multiple trader model. The starting point for all of these models is data on volume. Unfortunately, aggregate volume as reported does not necessarily represent trades between final investors because of day trading and because of intermediary trades by dealers and specialists. Consequently, before a trading model can be applied, daily trading volume must be reduced to account for day trading and intermediary trading. As an example, reported volumes for a NASDAQ stock are frequently reduced by 60% – with 50% to account for trades between intermediaries, such as market makers, and an additional 10% to account for intra-day trading.27 A company’s float on a given trading day is defined as outstanding shares available for trading among members of the class. Certain reductions to total shares outstanding are made to arrive at the float. Insiders are typically defendants in securities fraud suits and therefore would not be eligible to claim damages. Consequently, their holdings and those beneficially controlled by them are not be included in the float. In addition, any shares that were purchased before the start of the class period and still held after the class period ends could not have been damaged by the alleged fraud. These shares are typically estimated by examining quarterly data and calculating the minimum institutional holdings on an institution-by-institution basis
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held from a time period before the start of the class period to the first quarterly period, after the end of the class period. Unfortunately, there are no comparable data for individual holdings, so adjustments are generally limited to institutional shares. There is some controversy regarding whether daily net increases in short interest should be added to the float, and, conversely, whether daily net decreases in short interest should be deducted. According to McCann and Hsu (1999), ‘‘Short interest increases the total number of shares that may have traded during the class period.’’28 However, Apfel, Parsons, Schwert, and Stewart (2001) assert the opposite view – that additional ‘‘shares’’ purchased from short sellers selling borrowed shares into the market are offset by the short seller’s short position, and thus the total float does not increase.29 Moreover, the issuance of such artificial ‘‘shares’’ is not controlled by the defendant company, nor does their issuance result in additional capital to the defendant company. Such ‘‘shares’’ have no voting rights with respect to Board elections and other matters dealt with at shareholder meetings. The short sale represents a pledge of collateral and cash by the short seller in exchange for borrowing a security from the brokerage house to sell in the open market. To the brokerage house, the short sale represents a loan of the security to the short seller in exchange for a liability to repay the cash collateral when the short sale is covered. This artificial share is a loan of an existing security rather than the creation of whole new security and resembles a stock appreciation right, which has been held not to be a security (p. 27). Finally, short sales and their subsequent repurchases are already included in reported daily trading volume, such that the short-selling activity is already fully taken into account with respect to trading volume that is eligible for damages. For these reasons, the float, or shares outstanding that are eligible for damages, should not be increased by the amount of net short sales.
6.1. The Proportional Trading Model (PTM) The PTM is based on the assumption that every share is as equally likely to trade as every other share. Its operation is best illustrated by an example. Suppose that company ABC has an effective float of 18 million shares. Assume, furthermore, that on Day 1 of the class period the adjusted volume for ABC is 15,000 and that on Day 2 the adjusted volume is 18,000. The PTM treats the original 15,000 shares as new purchases. The PTM assumes that on Day 2, 18,000/18 million or 0.1 percent of the float traded. Because
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all shares are assumed to be equally likely to trade, this means that 0.1 percent of 15,000 shares, or 15 shares, that were purchased on Day 1 would be sold on Day 2. These are Day 2 in-and-out traders. This algorithm is used on each day in the class period in an iterative fashion until the end of the class period is reached. The fraction of the 15,000 shares from Day 1 that remain unsold on the day after the end of the class period constitute the retention shares for that day. Unfortunately, stock trading data reveal that the PTM’s underlying assumption does not comport with reality in the vast majority of instances because shareholders have varying investment horizons. For instance, Froot, Perold, and Stein (1992) show that different types of shareholders trade with different frequencies and have varying investment holding periods. In light of such results, courts have become increasingly skeptical of the proportional trading model unless it can be buttressed by actual trading data for a subject company. For instance, the PTM was recently rejected as a result of a Daubert motion in Kaufman v. Motorola.30 In rejecting the PTM, the Kaufman court noted that the PTM has never been successfully tested against reality and, according to the court, there was no way to actually test its reliability. It further noted that the PTM has never been accepted by professional economists in a non-litigation context as an acceptable model for predicting investor behavior (pp. 3–4). Finally, the Court stated that the Motorola shareholders had an adequate remedy for any losses suffered by ‘‘having a jury determine a per share damage loss and requiring the filing of claims by each shareholder who claims that he, she or it has been damaged’’ (p. 3). In defense of the PTM, Barclay and Torchio (2001) argue that critics have not demonstrated that the PTM fails to accurately estimate aggregate damages, because studies rebutting the PTM failed to properly adjust the shares available for trading during the class period. They argue that these studies did not reflect shares that did not trade during the class period, they failed to adjust reported volume for inter-dealer trades (as described above), and they used claims data that were not an accurate reflection of the total potential claims submitted because of poor case administration.31 However, Barclay and Torchio have not affirmatively shown that the PTM accurately reflects shareholders’ trading patterns by using actual aggregate trading data from a real-world case to test the model’s basic assumptions. Further, Barclay and Torchio’s argument that looking at claims filed in a particular matter does not lead to an accurate assessment of aggregate damages begs the very question that must be answered. Namely, what are actual aggregate damages to claimants in a particular securities class action?
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As a legal matter, only those shareholders who purchased during the class period and who filed claims in a timely fashion with the claims administrator are eligible for damages. Calculating damages for shareholders who fail to file claims, as trading models do, can unfairly penalize a defendant company’s existing shareholders, who may not have purchased their shares during the class period and would not be eligible for damages. Even if unclaimed monies paid to fund a trial judgment were ultimately returned to the defendant company, shareholders could be harmed if fees paid to counsel were overestimated as a result of the size of the fund, and because the company would lose the use of those excess funds until the claims processing was completed. There is a variant of the PTM, which asserts that a share had traded during the class period is more likely to trade again during the class period than one which has not. The likelihood of this re-trading is assumed to be a multiple of the probability that a share, which had not yet traded will trade for the first time during the class period. A more comprehensive discussion of ATM may be found in the appendix.
6.2. The Multiple Trader Model The multiple trader model extends the PTM by allowing for different groups of investors with different trading characteristics. The daily trading volume and adjusted float are divided into different groups to take account of differing trading propensities and holding periods for individual shareholders within a class. As an example, the following two-trader model has been used in securities class actions:
Group 1 Group 2
Volume 80% 20%
Float 20% 80%
These two groups of traders correspond to short-term traders (Group 1), who are assumed to account for 80% of a given trading day’s volume and 20% of a given trading day’s float, and long-term investors (Group 2), who are assumed to account for the remaining 20% of a given trading day’s volume and 80% of a given trading day’s float. The straight proportional trading model in this example is divided into two separate proportional trading models. One would have daily trading volume equal to 80% of the
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adjusted daily trading volume and a daily float equal to 20% of the adjusted daily float. The other would have daily trading volume equal to 20% of the adjusted daily trading volume and daily float equal to 80% of the adjusted daily float. After the damages are computed for each group of investors, the damages for both groups are summed to arrive at the aggregate damages. The multiple trader approach can be extended to more than two classes of traders. By making different assumptions regarding trading patterns and holding periods for shareholders within each group, it might be possible to more closely approximate shareholders’ trading behavior as a whole during the class period. The problem is obtaining sufficient data to justify a set of trading assumptions for each group. Without adequate data on which to determine its parameters, a multi-trader model may not be much more accurate than the simple PTM. Because of the controversial and still unproven nature of trading models, some courts have rejected them altogether.32 The alternative approach is to construct the price line and the value and then wait for the filing of proof of claim forms to calculate damages. Given the uncertainty, future legal decisions will play a key role in the evolution of the use of trading models.
7. CONCLUSIONS Securities class actions have become increasingly prevalent in recent years with a multitude of fraud accusations being filed against companies, their management, and their auditors. A key element in these cases is arriving at an accurate estimate of damages. That estimate depends on two underlying elements: an estimate of the inflation per share on a daily basis throughout the class period and a trading model that translates per share inflation into aggregate damages. When measuring inflation per share, the starting point is generally an event study. Such a study not only illuminates how the subject company’s stock price responded to information in general during the class period, it also is critical for determining the impact of fraud-related information on stock prices. Most commonly, inflation per share is estimated by using the event study to examine how much the subject company’s stock price falls when fraud-related information is released. However, event studies are not a magic bullet because stock price reactions are usually ambiguous. Stock prices react to fraud-related information, non-fraud-related information, and sometimes no information at all. Consequently, determining the extent of inflation requires analysis beyond a standard event study. In some
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situations, intra-day data can prove helpful. It may also be possible to use fundamental valuation analysis to supplement an event study. Even with these tools, however, judgment is often required in estimating the extent of stock price inflation associated with an alleged fraud. Aggregate damages depend not only on inflation at purchase and at sale (or at the end of the class period, when it is zero) but also on how many shares were affected by the alleged fraud. The most direct way to calculate aggregate damages is to rely on proof of claim forms in which investors specify their purchases and sales. This allows precise calculation of the affected shares. In many situations, however, such as for settlement purposes, it is necessary to estimate aggregate damages before proof of claim data are available. The standard tools for this purpose are trading models based on volume and float data. Unfortunately, these models have the drawback that it is unclear how well they approximate actual trading behavior. The basic PTM was rejected by the court in Kaufman v. Motorola on the grounds that there was insufficient empirical support for the model. In response to court concerns about the PTM, a host of more sophisticated models, including multiple trader models and the ATM, have been developed. Nonetheless, it is not clear that these models are always superior to the PTM. Furthermore, they often require as input data that are not directly available. For these reasons, the use of trading models remains highly controversial. In summary, a variety of sophisticated tools have been developed for estimating damages in securities fraud cases. However, there is no turnkey method for applying these tools. The choice of tools to use and how to interpret the results depends on the specific facts of each individual case. As long as this remains true, the experience of the attorneys and the expert will continue to play an important role in the resolution of securities fraud matters.
NOTES 1. The authors of this chapter are not practicing attorneys. To the extent that they interpret legal statutes and cases in this chapter, they do so as laypersons, and their interpretations should not be construed as the rendering of legal opinions. 2. Of these cases, at least 314 dealt with allegations regarding underwriters’ practices in connection with the distribution of certain initial public offering shares. (Source: Stanford Law School Securities Class Action Clearinghouse.) 3. See Basic, Inc. v. Levinson, 485 U.S. 224 (1988). 4. Basic, 485 U.S. at 231–232. 5. Ernst & Ernst v. Hochfelder (1976). 6. Sundstrand Corporation v. Sun Chemical Corporation (1977).
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7. See Sundstrand, 553 F.2d at 1047–1048 (Defendant unsuccessfully argued lack of fraudulent intent to omit material information. Court ruled that defendant was reckless as a matter of law because the danger of misleading plaintiff by the omission was objectively obvious, even though defendant claimed he failed to appreciate the significance of the omitted information). 8. Hochfelder, 425 U.S. at 214. 9. 15 U.S.C. y 78bb(a) (Foundation Press, 1992). 10. Green v. Occidental Petroleum Corp. (1976) (Sneed, J., concurring). In most situations, the trading price is assumed to equal the hypothetical true value of the stock once the alleged fraud is fully revealed. 11. By definition, any frauds alleged to have occurred during the class period must be fully disclosed by the end of the class period. Partial disclosure of the frauds can conceivably be assumed to take place during the class period. 12. Basic, 485 U.S. at 247. 13. See Basic at 485 U.S. 248 n.27 and 249. (According to the Court of Appeals, trading of securities on an efficient market is among the elements required to be proved for the presumption to be available.) 14. As the efficient market literature has matured over 35 years, there have also been studies that raise significant questions regarding whether market price reactions absorb new information fairly, even if such information is impounded quickly. 15. See Macey and Miller (1991), at 1014, n.63. However, Easterbrook and Fischel (1985) point out that the requirement of efficiency does not mean that the market must accurately value the security, only that the market: (1) must react quickly to new information; (2) must not systematically over- or under-react to new information over time; and, (3) that the market’s assessment of a stock’s fundamental value over short time periods remain relatively stable in the absence of new information. Easterbrook and Fischel use the example of a stock’s price that always reflects 50 percent of a given firm’s true value, such that any change in the price in response to new information would give an accurate representation of the marginal value of this information, so long as the relationship remains constant. 16. Such research has generally shown that stock prices react quickly to new information, usually within one day. See, e.g., Fama (1991). 17. If daily returns are used as the event window, the difference between using industry-adjusted returns (a stock’s return minus the return on a comparable index) and a regression model that would estimate a coefficient that signifies the degree of linear relationship between the total return on a stock and the total return on the market or comparable index should be sufficiently minimal so as not to make a significant difference in the outcome. For further discussion of this topic, see Brown and Warner (1985). 18. Typically, there is controversy regarding whether disclosures are partial or complete in securities fraud-on-the-market cases. 19. This is because fraud-on-the-market cases assume that the semi-strong form of the efficient market hypothesis holds. 20. Green, 541 F.2d. at 1345. 21. This takes into account provisions of the Private Securities Litigation Reform Act (1995), which states that ‘‘the award of damages to the plaintiff shall not exceed the difference between the purchase or sale price paid or received, as appropriate, by
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the plaintiff for the subject security and the mean trading price of that security during that 90-day period beginning on the date on which the information correcting the misstatement or omission that is the basis for the action is disseminated to the market’’ 15 U.SC. 78u-4(e)(1) (CCH, 1996). If the security is sold within 90 days after the disclosure date, damages cannot exceed ‘‘the difference between the purchase or sale price paid or received, as appropriate, by the plaintiff for the subject security and the mean trading price of the security during the period beginning immediately after dissemination of information correcting the misstatement or omission and ending of the date on which the plaintiff sells or repurchases the security’’ Ibid., at 78u-4(e)(2). To apply these limitations consistently for a given class action, it seems that damages per share for shareholders who purchase and sell shares during the class period cannot exceed the difference between the purchase and sale prices. This approach has also been used by many plaintiffs’ expert damages witnesses in recent cases. 22. See 1995 Act, 51. 23. y21D(e) amending 15 U.S.C. 77a et seq. 24. The notion that investors frequently overreact to disclosures that reveal unfavorable news contradicts both the element of the efficient market hypothesis that stock prices accurately reflect all publicly available information, and the idea behind the fraud-on-the-market doctrine that investors relied upon the integrity of the market price. The reasoning behind this logical inconsistency in the law regarding damages calculation is that even though current evidence indicates that securities markets are generally efficient, pockets of inefficiency sometimes arise and may persist over relatively long time periods. Examples of this phenomenon include the market decline on October 19, 1987, and the ‘‘bubble’’ in technology stocks that began in the late 1990s and ended in the year 2000. 25. See Lev and de Villiers (1994). This article was cited in the U.S. Senate Report No. 104-98, June 19, 1995 at 406 n.58 in the 1995 Act. 26. See 1995 Act, 110. 27. Of course, the exact adjustments made may depend upon the available data in a given case. 28. See McCann and Hsu (1999, p. 3). 29. See Apfel et al. (2001, p. 11). 30. See Judge Gettleman’s order in Kaufman v. Motorola (2000). 31. See Barclay and Torchio (2001). 32. See, e.g., Judge Gettleman’s order in Kaufman v. Motorola. 33. See McCann and Hsu (1999, p. 2).
REFERENCES 15 U.S.C. y 78bb(a) (Foundation Press, 1992). Apfel, R. C., Parsons, J. C., Schwert, G. W., & Stewart, G. S. (2001). Short sales, damages, and class certification in 10b-5 actions. Working Paper No. FR 01–19. Barclay, M., & Torchio, F. C. (2001). A comparison of trading models used for calculating aggregate damages in securities litigation. Law and Contemporary Problems,(64), 105–136. Basic, Inc. v. Levinson, 485 U.S. 224 (1988).
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Brown, S. J., & Warner, J. B. (1985). Using daily stock returns: The case of event studies. Journal of Financial Economics,(14), 3–31. Easterbrook, F. H., & Fischel, D. R. (1985). Optimal damages in securities cases. University of Chicago Law Review,(52), 611–652. Ernst, Ernst v. Hochfelder, 425 U.S. 185 (1976). Fama, E. F. (1991). Efficient capital markets: II. Journal of Finance,(46), 1575–1617. French, K. R., & Roll, R. (1986). Stock return variances: The arrival of information and the reaction of traders. Journal of Financial Economics,(17), 5–26. Froot, K. A., Perold, A. F., & Stein, J. C. (1992). Shareholder trading practices and corporate investment horizons. Journal of Applied Corporate Finance,(5), 42–58. Green v. Occidental Petroleum Corp., 541 F.2d 1335, 1343 (9th Cir. 1976). Hiller, J. S., & Ferris, S. P. (1990). Use of economic analysis in fraud on the market cases. Cleveland State Law Review,(38), 535–557. Kaufman v. Motorola, No. 95 C 1069 (N.D.Ill. Sept. 19, 2000). Order of Judge Gettleman. Langevoort, D. C. (1992). Theories, assumptions, and securities regulation: Market efficiency revisited. University of Pennsylvania Law Review,(140), 851–920. Lev, B., & de Villiers, M. (1994). Stock price crashes and 10b-5 damages: A legal, economic, and policy analysis. Stanford Law Review,(47), 7–37. Macey, J. R., & Miller, G. P. (1991). The fraud-on-the-market theory revisited. Virginia Law Review,(77), 1001–1016. Macey, J. R., et al. (1991). Lessons from financial economics: Materiality, reliance and extending the reach of Basic v. Levinson. Virginia Law Review,(77), 1017–1049. McCann, C. J., & Hsu, D. (1999). Accelerated trading models used in securities class action lawsuits. Journal of Legal Economics, Winter, 1–47. Private Securities Litigation Reform Act of 1995: Law & Explanation. Commerce Clearing House, Inc., 1996. Roll, R. (1988). Presidential address: R2. Journal of Finance,(43), 541–566. Schwab, D. M., & Kroll, D. J. (1992). Damages issues in rule 10b-5 class actions that go to trial. Unpublished working paper. Sundstrand Corporation v. Sun Chemical Corporation, (1977). 553 F.2d 1033 (7 Cir.), cert. Denied 434 U.S. 875, 98 S.Ct. 225, 54 L.Ed.2d. 155.
APPENDIX. THE ACCELERATED TRADING MODEL The accelerated trading model (ATM) extends the proportional trading model by assuming that the likelihood that a share that has already traded during the class period is re-traded on a later day during the class period is a constant multiple of the probability that a share, which has not yet traded will be traded for the first time.33 Proponents of this model assert that this assumption better reflects investor behavior than the equal trading PTM. As explained by McCann and Hsu (1999), the three equations that define the ATM are given by: (1) Average turnover likelihood ¼ Total volume/Float;
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(2) Turnover likelihood of traded shares ¼ Volume of re-traded shares/ Amount of traded shares in float; and, (3) Turnover likelihood of untraded shares ¼ Volume of newly traded shares/Amount of untraded shares in float. The float can be broken down into two categories: traded shares and untraded shares. Traded shares are those that have been purchased at least once during the class period to date. The remainder of the float at any given time thus consists of shares that have not yet traded during the class period such that: Float ¼ Traded shares þ Untraded shares A stock’s daily trading volume can also be classified into two categories: re-traded shares and newly traded shares. Re-traded shares are those shares that are part of daily trading volume and that were traded out of the pool of previously Traded shares in the float. Newly traded shares are the remaining shares in the daily trading volume that were traded out of the pool of Untraded shares in the float such that: Volume ¼ Retraded shares þ Newly traded shares at any given time. The number of traded shares thus increases on a daily basis by the amount of newly traded shares in the daily trading volume, but the number of re-traded shares in the daily trading volume has no effect upon the number of traded shares in the float. One of the key assumptions of the ATM is that the ratio of the turnover likelihood of traded shares to the turnover likelihood of untraded shares remains constant over the class period. This ratio is commonly known as the turnover likelihood ratio (TLR). If the TLR is equal to 1, then the ATM should yield the same results as a PTM. However, some incarnations of the ATM are specified so that the TLR actually increases over the class period, yielding erroneous results. For instance, posited an ATM where the TLR was specified as follows: TLRKoslow ¼
VolumeRetraded =SharesTraded VolumeTotal =SharesUntraded
Koslow’s TLR is equal to the ‘‘correct’’ TLR multiplied by the ratio of total daily trading volume to newly traded shares on a given day. Although Koslow’s TLR is held constant in his ATM, the ‘‘correct’’ TLR would grow over time as the pool of traded shares grows and the number of newly traded shares in daily trading volume declines relative to total daily trading volume. Koslow’s implementation of the ATM would thus violate the premise that
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the TLR remains constant throughout the class period (pp. 22–23). Simmons and Hoyt (1993) also intended that their ATM be based on a constant turnover likelihood ratio. However, it also results in a TLR that increases over the class period. Simmons and Hoyt’s implementation is as follows: TLRSimmons and Hoyt ¼
VolumeRetraded =SharesTraded VolumeTotal =SharesFloat
The implications of these misspecifications of the ATM are that shares eligible for damages (traded shares) are limited to a fraction of the float and that the amount of re-traded volume on a given day can exceed the total volume of shares traded on that day under certain conditions (p. 26). A good stock trading model would cap traded shares at the amount of total shares available for trading over the class period and would not permit re-traded volume on a given day to exceed total volume on that day. However, even McCann and Hsu’s implementation of the ATM does not address the critical issue of whether the model accurately depicts the reality of shareholder trading patterns and holding periods with respect to a given security in a given case. They offer no tests against empirical data to validate the accuracy of the ATM in any of its forms. Thus, the accuracy of the ATM versus the PTM is uncertain at best absent testing in a given matter against actual trading records of all shareholders during a given class period.
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RECENT DEVELOPMENTS IN THE ANALYSIS OF EMPLOYMENT PRACTICES Joan G. Haworth, Janet R. Thornton and Paul F. White The passage of the Civil Rights Act of 1991 (42 U.S.C. y 1981a (2000)), which provided for compensatory damages and jury trials for plaintiffs in employment discrimination matters, modified the legal context in which expert analysis has been used in recent years. It not only affected the presentation of the analysis but has also resulted in an increase in the complexity of that analysis for litigation arising from all of the civil rights laws. In addition to the CRA, alternate means of dispute resolution (such as mediation and arbitration) have provided additional venues for the presentation of expert analysis. Consequently, economists, statisticians, and other experts who analyze employment decisions now find themselves presenting complex evidence to a much more diverse set of listeners in a modified legal context. This chapter will expand on several areas of employment analysis to discuss some of the issues that have arisen in the past few years – reverse discrimination litigation, monitoring programs, certification of a class in employment litigation, statistical aggregation issues, and wage and hour litigation.
Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 59–81 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87004-4
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1. ‘‘REVERSE’’ DISCRIMINATION LITIGATION: PARITY AND ‘‘NEED’’ The recent ‘‘reverse’’1 discrimination decisions by the Supreme Court involving the admissions decision-making policies at the University of Michigan2 illustrate the underlying need for private and public entities to justify the need to reach or maintain diversity within an organization. Clearly, the equality of the decision-making methodology and criteria used to obtain and maintain diversity was an issue, but perhaps more pressing was the question of whether such programs were necessary. The issue of parity is at the very center of these cases. If the normal admissions process would have resulted in obtaining the predicted number of minority admissions then there may no longer be a need for such programs. While the university cases have been most publicized recently, matters involving affirmative action plans and governmental programs to enhance diversity (such as minority contractor set-asides) face similar questions of parity. 1.1. University Admissions In 1977, the Supreme Court heard arguments in Bakke v. Regents of the University of California (1978). The case originated when a white male applied twice, at different times, to the medical school at the University of California at Davis. At the time, the university had two different admissions programs (the ‘‘regular’’ program and the ‘‘special admissions’’ program) and students were asked on their application for admission whether they wanted to be considered as ‘‘economically and/or educationally disadvantaged’’ applicants and members of a minority group (which consisted of African-American, Chicano, Asian, and American Indian). Both the regular program and the special admissions program included a rating score that was based upon interviews, grade point averages, and standardized test scores, among other factors. The primary difference between the two admissions programs was that the regular program summarily rejected applicants whose overall undergraduate grade point average was less than 2.5 on a scale of 4.0. Under the special admission program, candidates who were determined to be disadvantaged were not subject to the 2.5 grade point average minimum, and their rating score was not compared to those in the regular admissions program. Applying the ‘‘strict scrutiny’’ standard, the Supreme Court ruled that the University’s special admissions program violated the Equal Protection Clause of the Constitution (14th Amendment), which, as summarized by the
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National School Boards Association (2003), ‘‘requires the governmentyto treat similarly situated people in a similar manner’’ (p. 2). In its opinion, the court went further to say that the special admissions program was ‘‘not the least intrusive’’ means of achieving the compelling state goals of increasing the number of minority doctors and the number of doctors willing to treat minority patients (Bakke v. Regents, 1978, p. 279). Furthermore, since the university could not demonstrate that, absent the separate programs, Mr. Bakke would not have been admitted, the court ordered his admission into the university’s medical school. The outcome of applying the ‘‘strict scrutiny’’ requirement and the assessment as to whether or not parity was appropriately achieved is contrasted in two cases involving the University of Michigan that were addressed in 2003 by the Supreme Court, Grutter v. Bollinger (2003) and Gratz v. Bollinger (2003). In Gratz, the Court ruled that the University’s undergraduate admissions policy violates the Equal Protection Clause because it ‘‘automatically distributes 20 points, or one-fifth of the points needed to guarantee admission, to every single ‘underrepresented minority’ applicant solely because of race [and, therefore,] is not narrowly tailored to achieve the interest in educational diversity’’ (p. 270). In contrast, in the Grutter case, the University’s law school sought to enhance student diversity under the guidelines established in Bakke. The University’s law school admissions policy requires admissions officials to examine all the information in the applicant’s file, which includes the candidate’s academic achievement as well as a personal statement, letters of recommendation, an essay, etc. The admission officials must assess the candidate’s academic ability and the applicant’s ability to contribute to the educational goals of the law school. In its opinion, the court recognized this, citing the aspiration of the admissions policy to ‘‘achieve that diversity which has the potential to enrich everyone’s education and thus make a law school class stronger than the sum of its parts’’ (p. 315). Following the guidance of the Bakke case, the court ruled that racial diversity is indeed a compelling state interest and that it does not violate the Equal Protection Clause as long as the program is narrowly tailored. The National School Boards Association (2003) summarizes features that would allow a program to be considered narrowly tailored, based on guidelines provided by the court (p. 4): Other race-neutral alternatives must be considered; There must not be quotas or separate admissions programs; There can be no racial balancing;
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Race can be a ‘‘plus factor’’ but it cannot be the ‘‘defining factor’’; Non-minorities cannot be unduly burdened; and The plan must be of limited duration. Once it has reached its goals, it must be eliminated. Although University admissions may seem only tangentially related to employment litigation, in fact the basis for the decisions in these cases stems from employment law. Reverse discrimination lawsuits are often filed under the Equal Protection Clause. In Adarand Constructors, Inc. v. Pena (1995), the Supreme Court determined that if a program establishes race or gender classifications, then it will be evaluated under the ‘‘strict scrutiny’’ guidelines. The two components of the strict scrutiny guidelines are: (1) there must be a compelling state interest in the establishment and continuation of the program, and (2) the classification of employees according to race or gender is ‘‘narrowly tailored’’ enough to meet the compelling state interest without creating substantial negative consequences for those outside of the classification. These factors affect any economic or statistical analysis performed in this type of litigation. Legal challenges in ‘‘reverse’’ employment discrimination cases are generally based on the claim that an Affirmative Action Plan or a governmental program to enhance diversity in business contracting either is not related to a compelling state interest and/or it is not sufficiently ‘‘narrowly tailored’’ to prevent negative impact on employees or businesses that are not protected under the law. A number of the frequently cited reverse discrimination cases of the past few years involve universities and their admissions policies, governmental agencies and their affirmative action plans, and governmental contractors who believe they have been wrongly denied a contract in favor of a minority-owned firm. Again, the underlying question raised in these matters is whether or not there is a lack of parity and, if so, whether there was a compelling historical pattern that resulted in a lack of historical parity. Because statistical evidence is usually focused on whether or not there is a pattern and the nature of that pattern, when programs are challenged statistical evidence is often used to contrast the current pattern to the historical pattern with respect to the issue. Statistical analyses are also used to determine if parity has been reached so that there may no longer be a need to retain a particular minority or gender-focused plan. Thus, the analyses focus on whether, for example, businesses would have obtained the expected number of contracts without government intervention, students would have obtained admission to universities at the rate predicted by their interest in the school, and employees would have been selected regardless of group status (the group
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status can indicate a protected group under Title VII or an unprotected group in ‘‘reverse’’ discrimination matters) at the same rate as others. 1.2. Governmental Programs to Enhance Diversity in Business Contracting A case often cited in disputes involving minority contractor set-aside programs is the Adarand Constructors, Inc. v. Pena (1995) case mentioned above. In this case, the low bidder for a federal contract was denied a contract because preference was given to a minority-owned firm. The Supreme Court ruled that the use of a minority set-aside program for contractors prevented the plaintiff from ‘‘competing on an equal footing’’ and thus the plaintiff could claim injury (p. 211, quoting Northeastern Fla. Chapter, Associated Gen. Contractors of Am. v. Jacksonville, 1993, p. 667). It also ruled that the lower courts did not apply the strict scrutiny guidelines, and the case was remanded. However, in 1998 Congress re-enacted the Transportation Equity Act for the 21st Century (1998, Pub. L. No. 105–178 y 1101 (b), 112 stat. 107) because it found that based on statistical analysis and fact witness testimony, discrimination continued to affect the ability of minority groups to participate in transportation construction projects. Congress concluded that such programs would be an effective remedy. In 2003, the Tenth Circuit Court of Appeals reversed the District Court’s decision in Concrete Works of Colorado, Inc. v. City and County of Denver (2003) finding that a city ‘‘clearly may take measures to remedy its own discrimination or even to prevent itself from acting as a ‘passive participant in a system of racial exclusion practiced by elements of the local construction industry’’’ (Concrete Works, p. 958, quoting City of Richmond v. J. A. Croson Co., 1989, p. 492). Thus, a city ‘‘may establish its compelling interest by presenting evidence of its own direct participation in racial discrimination or its passive participation in private discrimination’’ (Concrete Works, p. 958, quoting City of Richmond, p. 492). In this matter, statistical evidence, including survey data, was used in support of the city’s position that it needed to offer a remedy to its own discrimination and its passive involvement in the discrimination of others.3 The courts expect that governmental programs that affect the ability of disadvantaged enterprises to engage in contracting will be narrowly tailored – that is, directed specifically at the industries and geographic areas in which contractors might have suffered prior disadvantages. In addition, the estimated share of business awarded to these enterprises is expected to be based on data that recognizes the firms’ capacity to perform the work, where capacity is
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measured by factors such as the age of the business and firm size. As noted in City of Richmond v. J. A. Croson Co. (1989), the purpose of the requirement for a narrowly tailored program is to ensure that ‘‘the means chosen ‘fit’ [the] compelling goal so closely that there is little or no possibility that the motive for the classification was illegitimate racial prejudice or stereotype’’ (p. 493). In this context, statistical analysis and expert testimony are expected to incorporate the narrowly tailored criteria of the courts. 1.3. Affirmative Action Plans In legal challenges to Affirmative Action Plans, the general claim made by plaintiffs is that the employer has reached the goals established in the plan and thus preferential hiring and promotion for minorities and/or females is no longer needed. In Kohlbek v. City of Omaha (2004), the plaintiffs filed reverse discrimination charges against the defendant’s practice of selecting minority firefighters out of rank order for promotions. The City of Omaha contended that it was following the rules specified in its Affirmative Action Plan, which it believed to be legally based upon the guidelines established by the Grutter case. Further, it argued that even with the selection process at issue, (a) the representation of African-Americans among entry-level firefighter hires during the same time period lagged in proportion to those who applied, and (b) the City of Omaha had failed to increase the number of African-American officers at the higher ranks within the department over the decade. In this matter, the District Court found that the processes by which the city’s Affirmative Action Plan and promotion process were constructed and implemented were indeed narrowly tailored in accordance with Grutter. When the court ruled in favor of the defendant’s summary judgment motion, it found that a historical pattern indicating a lack of parity had not been remedied by the city’s current activity and, therefore, the city had a compelling interest to remedy its past discrimination. Thus, the city’s monitoring of employment activity during the period prior to the lawsuit was used to justify its business needs and define the narrow tailoring guidelines that would form the relevant criteria for selection.
2. MONITORING EMPLOYMENT DECISION– MAKING Employers have generally not been proactive in developing and analyzing employment decision-making processes except through Affirmative Action
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Plans. Even these plans have not been generally available to managers in corporate workforces. Once an employer receives notice of forthcoming litigation, it then considers the possibility of collecting data and analyzing it for possible patterns. The only other employment analysis that is typically performed is in the Equal Employment Opportunity (EEO) office (for example, analyses required by an Affirmative Action Plan or required reports for a consent decree). This lack of analysis in a decision-making business area that could generate litigation and is fairly well regulated is surprising in a risk-managing organization. However, the fact that the analysis could be used by those suing the employer if it shows patterns that are adverse to a protected group probably reduces the willingness of most corporate counsel to encourage such analysis. A recent lawsuit that addresses a firm’s monitoring program illustrates that problem.4
2.1. Recent Legal Decisions Regarding Monitoring Despite employers’ good intentions to achieve diversity of their workforces, there will still be disagreements as to the effectiveness or the legality of such programs. For example, in Frank v. Xerox Corp. (2003), the Fifth Circuit Court of Appeals examined the plaintiffs’ claims that they were denied promotions and pay increases because they were black. The allegations arose from Xerox’s ‘‘Balanced Workforce Initiative’’ (BWF), a monitoring plan implemented by the company with the purpose of ‘‘insuring that all racial and gender groups were proportionately represented at all levels of the company’’ (p. 133). The annual targets, which were based upon local population data, showed that black employees were consistently over-represented and white employees consistently under-represented in the company’s Houston office. Subsequent company documents directed the Houston office to remedy the imbalance and set specific racial goals for each job and each grade level. Based on statistical evidence, the plaintiffs claimed that the BWF program was used to reduce the number of black employees in the Houston office. The Fifth Circuit Court ruled that regardless of whether the program directly influenced the reduction in the number of black employees, ‘‘the existence of the BWF program is sufficient to constitute direct evidence of a form or practice of discrimination’’ (p. 137). Factors that influenced the court’s decision were the fact that Xerox had explicit racial goals and that managers’ evaluations were influenced in part by how well they met their racial goals.
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Consent decrees in civil rights cases often prescribe exactly how certain employment decisions are to be made, what data will be recorded, and how the data will be analyzed. For example, in Thornton v. National Railroad Passenger Corp. (2000), the consent decree specifically required reports on promotion decisions and ordered that sufficient data be retained such that an analysis of the applicant flow data for those promotions could be conducted. Because consent decrees have specific time frames, however, employers often discontinue their reports and analysis after the consent decree term is exhausted. Given that the terms of these consent decrees are mandated by the courts, such analysis is not as likely to be the subject of additional lawsuits unless the progress mandated by the consent decree does not occur.
3. CLASS CERTIFICATION Employment monitoring, employment litigation, and Affirmative Action issues all center on the question of whether or not there is ‘‘parity’’ in the process. These cases ask whether or not decisions are neutral with respect to each employee group (e.g., male and female, minority and non-minority, older and younger). This is the center of any employment litigation allegation, regardless of whether it is a single plaintiff or class action case. However, lawsuits in which a plaintiff seeks to represent a class also focus on another issue – whether or not the plaintiff, plaintiff’s counsel, and the characteristics of the putative class meet the legal standards required of putative class actions. The increasing importance of the class certification stage of employment litigation has required more sophisticated statistical analyses at this stage in the process. This has had the secondary effect of making class certification and the merits of a case more difficult to differentiate.5 As the court recently stated in Carpenter v. Boeing Co. (2004), while the court may not decide the merits on class certification, it may ‘‘probe behind the pleadings and consider the proof necessary to establish class-wide discrimination’’ (p. 2). Once a class is certified, there is usually even more statistical analysis required because the workforce defined by the court as the ‘‘class’’ may not have been the group in the original analysis, and some of the issues initially raised by the plaintiff may not be included in the definition of the issues for which a class was certified (see Jennings v. Regents of the Univ. of Cal., 2003). In a motion for class certification, one of the underlying questions is whether or not the employment-related decisions being litigated are common
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to all areas of the proposed class. In an alleged pay disparity case, for example, the court will generally wish to know whether the pay disparity is likely to be only in the areas of the firm in which the plaintiff(s) works, only in a few of these areas, or whether the alleged pay disparities occur in all or most of the employer’s workforce. Likewise, the court may wish to know whether the alleged pay disparity is likely to occur only in certain jobs or at certain salary types or levels. In this situation, the analytical issue is the likelihood of similarity in pay practices among the different areas of the firm, jobs or salary types and levels. Whether or not there is a similar pay model in each area of the firm, or in every job, etc. is usually the issue that statisticians and economists must consider in class certification. One way to evaluate the possibility of uniform decision-making processes from organization to organization within a firm is to identify the decision maker(s) responsible for the issues in question. Typically, for class certification as well as for monitoring purposes, the analyst must determine who makes the hiring, pay, promotion, termination, and other employmentrelated decisions within a firm in order to test whether these decisions are made by one person in the firm or by hundreds, if not thousands, of decision-makers in larger firms. Even when numerous decision-makers are involved, any modeling of the decision-making processes should determine whether the employment policies are reflected in the results of the decisions. In the matter of Carpenter v. Boeing Co. (2004), the court did not certify the class, indicating that the plaintiffs’ expert failed to provide evidence of unfair treatment across the various units within the firm. The court pointed out that while the evidence revealed ‘‘pockets of disparate impact,’’ it also revealed that many class members worked in neutral or advantageous environments. As a result, the court concluded that ‘‘it would be unjust to proceed to judgment’’ with the evidence at hand (p. 7). The increased scope of statistical evidence presented at class certification as well as the accompanying increased scrutiny of expert reports have led the courts to become more involved in the specifics of statistical methods and the economic modeling of employment processes. Attorneys are much more likely to seek a motion in limine (or a ‘‘Daubert’’ motion) to exclude the expert testimony. The grounds on which such a motion would be argued are based on the criteria described in Daubert v. Merrell Dow Pharmaceuticals (1995) and Carmichael v. Kumho Tire Co. (1999). These criteria are often described as a failure to apply or use a theory or technique that is scientifically based, accepted, tested, and has a low error rate. In this context, there are many questions that may need to be addressed. These include whether or not the data on which the expert report is based
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are sufficiently accurate and complete; whether the analysis is consistent with professional standards; whether the question being addressed is relevant to the issues in the case; whether the variables included are appropriate; whether the statistical technique used is appropriate; whether the results are correctly reported; and whether the model is appropriate. For class certification, there are also questions of whether or not the decision processes analyzed are properly modeled, whether it is appropriate to combine decisions across decision-makers, and whether statistical significance alone is meaningful when examining a firm’s decisions. These questions have resulted in a closer assessment of the factors included in the economist’s and statistician’s models, the level of the analysis (by decision-maker or not), and the statistical techniques applied.
4. HOW DOES THE LEVEL OF ANALYSIS AFFECT STATISTICAL SIGNIFICANCE? Statistical significance of the difference in outcomes, the interpretive centerpiece of any statistical study, is more than a measure of mathematical certainty. It is intricately tied to the data being analyzed, the features of the modeling technique and the factors included in the model. Statistical significance in employment discrimination litigation is sensitive to the level of analysis incorporated into the model. A statistically significant difference is more likely to occur when the number of decisions included in an analysis is large because the variability in the outcomes is likely to decrease as the number of events increases. A simple way to illustrate the connection between statistical significance and level of analysis is with a coin toss experiment (Table 1). The following chart demonstrates that the smallest difference between the actual and expected number of heads that is statistically significant when you toss a coin 100 times is about 10% of the number of tosses – approximately 9.8 heads more or less than the 50 expected. If, however, you toss that coin 100,000 times, the difference that is statistically significant drops to less than 1% of the number of tosses. In other words, the minimum significant shortfall as a percent of the number of coin tosses (‘‘selections’’) decreases as the number of tosses (‘‘selections’’) increases. Because of this feature of statistical analysis, it is particularly important to prepare analyses at the appropriate level. When the analyses of hundreds of thousands of promotion, termination, and pay decisions are analyzed across all decision-makers instead of at the
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Table 1.
Number of Coin Tosses
10 50 100 500 1,000 5,000 10,000 100,000 200,000 300,000 400,000 500,000
Coin Toss Experiment.
Expected Number of Heads
Range of ‘‘Acceptable’’ Shortfall
Percent Shortfall Above Which Differences Are Statistically Significant
5 25 50 250 500 2,500 5,000 50,000 100,000 150,000 200,000 250,000
73.10 76.93 79.80 721.91 730.99 769.30 798.00 7309.90 7438.27 7536.77 7619.81 7692.96
730.99 713.86 79.80 74.38 73.10 71.39 70.98 70.31 70.22 70.18 70.15 70.14
‘‘Acceptable’’ range is based on 1.96 standard deviations.
individual decision-maker level, it may not accurately reflect the decisionmaking process at the individual decision-maker level. Such a combined analysis assumes a commonality of the decision-making process across the entire company instead of testing the question of whether or not such a commonality exists. This is particularly troublesome if great weight is given to the statistical significance of the result since the combined result is far more likely to have a statistically significant difference in employment outcomes. A proper analysis would produce statistical results that might tell us whether or not there is a uniform pattern of differences across all the decision-makers. Social scientists and statisticians have used criteria of less than 5% or less than 1% probability of occurring by chance (‘‘greater than two or three standard deviations’’) to categorize a result as ‘‘statistically significant.’’ Courts adopted this standard in voting rights cases, such as Castaneda v. Partida (1977), and have carried the standard over to equal employment issues in such cases as Hazelwood School District v. United States (1977) and International Brotherhood of Teamsters v. United States (1977). Courts have continued to rule on thresholds of statistical significance, for example, in EEOC v. Federal Reserve Bank of Richmond (1983), where the court indicated that only a difference greater than three standard deviations confirms
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an inference of adverse disparity – thus emphasizing the extent to which the appropriateness of statistical methods and modeling must be demonstrated in each and every case. Using a 5% level of significance, one would expect that 5% of the results by the decision-maker would be statistically significantly different from zero even in a random process. Thus, in a selection analysis, we would expect that the results by the decision-maker would be statistically significant 5% of the time, where 2.5% of the differences would favor the group at issue and 2.5% would be adverse to the group at issue. These characteristics permit a determination of whether the differences among the decision-makers are statistically significantly adverse with as great a frequency or greater frequency than one would predict. In Rhodes v. Cracker Barrel Old Country Store, Inc. (2003) the court found that the statistical evidence did not support a finding of commonality as there was not a consistent pattern of adverse treatment (p. 671). In this matter, the plaintiffs’ expert aggregated analyses of job level movements in more than 440 stores over nearly six years. The court criticized this approach because, given the number of selections, even a shortfall of 1 percent would be statistically significant, and because the aggregated results failed to accurately reflect the wide variation in the level of job moves (p. 661). The court, citing Abram v. United Parcel Service of America., Inc. (2001), also noted that the dangers of using aggregated data had been previously recognized: ‘‘If Microsoft-founder Bill Gates and nine monks are together in a room, it is accurate to say that on average the people in the room are extremely well-to-do, but this kind of aggregate analysis obscures the fact that 90 percent of the people in the room have taken a vow of poverty’’ (Rhodes p. 661, n. 55, quoting Abram, p. 431). In many cases, the data are sufficiently numerous that very small differences, even those of little or no practical importance, will be likely to be statistically significant. Statisticians are aware of this problem, as noted by economist and mathematician, Studenmund (1992): ‘‘The mere existence of a large t-score [number of standard deviations and, therefore, small likelihood of random occurrence] for a huge sample has no real substantive significance because if the sample size is large enough, you can reject almost any null hypothesis!’’ (p. 160). Therefore, in addition to looking at statistical significance as a criterion for assessing the results of analyses, courts also may have to determine whether or not any identified differences are sufficiently large to have practical significance as well as whether or not the analyses properly reflect the level at which the decisions were made. For example, a pay difference of one cent may be statistically significant but not practically
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significant whereas a pay difference of $5,000 that is 20% of average salary levels may be both statistically significant and practically significant. The notion of analyzing the alleged discriminatory practice by the decision-maker is not a new concept.6 However, the importance of determining the appropriate level of analysis is even greater when the issue is one of class certification. It is possible that there is no overall disparity in the employment outcomes, but that the organizations in which the named plaintiffs work or previously worked or the jobs to which the named plaintiffs aspire are adverse to their protected group. The level of analysis is also important with respect to a firm’s own monitoring of its employment decisions. An inappropriate analysis can signal to a firm that there are problems where none actually exist, or, alternatively, that there are no problems where they actually do exist. For example, firms conducting a reduction-in-force, even when they choose to monitor such decisions, may fail to omit from their analyses groups of employees that are not part of the reduction and, therefore, they may obtain an inaccurate assessment of the impact of their decisions. Clearly, therefore, it has become increasingly important to properly determine the appropriate level of analysis within a firm with respect to the protected group and the alleged discriminatory practice. The expert can often obtain that type of information from employment policies, interviews or depositions, and other correspondence.
5. IS THERE HOMOGENEITY? Experts should consider whether the results of decision-makers are so heterogeneous that they should not be aggregated. For example, the importance of job-related characteristics may not be uniform across manager, department, division, or job. To the extent that these job-related characteristics are not homogeneous, it may be useful to test whether it would be statistically correct to combine these groups without properly accounting for the differences between the groups. Recently, courts have become aware of these limitations to statistical modeling. For example, if a retail chain has several stores in which hiring decisions are made by the store manager, the hiring analysis may be prepared separately for each store. The next question is whether or not it is appropriate to aggregate the analyses of each store manager’s decisions to produce an overall result. While there may be practical reasons to aggregate the results, for example, to be responsive to an alternative analysis, statistically the
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individual store results would be aggregated only if they were found to be homogeneous. In Rhodes v. Cracker Barrel Old Country Store, Inc. (2003) the court held that for class purposes, the court should determine whether racial disparities found by plaintiffs’ experts when evaluating test failures were a common pattern across all Cracker Barrel stores or the statistically common result of aggregating the outcome across a large number of tests over a long period of time (pp. 664–65). If the latter is determined to be true, then the court will pay less attention to the aggregated disparities and more attention to the individual store results. While tests for homogeneity have been discussed in the statistical literature since 1960 (see Chow, 1960), their use in employment discrimination matters has been recent. At least two measures of homogeneity are relevant to the analysis of employment decisions, the common odds ratio and the Chow test, where the test employed depends on the type of analysis being evaluated. The appropriateness of aggregating selection analyses, such as the hiring decisions of store managers, is determined by testing the hypothesis that the odds of selection for the group at issue versus the group not at issue are equal across decision-makers. The common odds ratio test is used in this situation. With respect to a multiple factor analysis, such as a multiple regression analysis of compensation that provides the researcher the ability to control for more than one factor simultaneously, a different test is used to examine homogeneity. The appropriateness of aggregating all observations into one equation across decision-makers, such as combining all employees in the firm into one model, is decided by determining if the factors are similarly distributed across the decision-makers by the use of a Chow test. With respect to selection analyses, some firms have actual data that identifies the applicants who were interested in (‘‘posted’’ to) job openings. If all applicants are qualified, these data can be used to determine if each selection decision is neutral with respect to the group of employees or applicants at issue. It may be found that these applicants may be not equally qualified. In these situations, logistic regression analyses are developed to test whether the selection decisions are neutral with respect to the group at issue while simultaneously controlling for job-related characteristics such as the amount of experience, level of education, field of study, and other skills and training.7 Some logistic regression analyses may be the result of analyzing a sample of data rather than the entire population. As long as the estimated logistic regression incorporates the design of the sample in the estimate, a sample of appropriate size can produce reasonable results on which to base an opinion. Although logistic regression analysis was used for monitoring employment
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decisions in the late 1980s, it has not been widely used until recently. In Huguley v. General Motors Corp. (1989) the consent decree ordered the establishment of a system to monitor discretionary salary increases and promotions for five years. Included in this decree were guidelines for aggregating differences when a difference resulted in outcomes with results between 1.5 and 2.0 standard deviations in two consecutive periods. The monitoring system used a logistic regression model of promotion decisions to determine the differences between the actual and predicted promotion outcomes by race. In situations in which it is assumed that the pool of applicants for selection are equally qualified, pools analyses are often conducted that compare the composition of the selections. For example, in a promotion analysis, typically the number of actual promotions among the group at issue is compared to the number predicted by their presence in reasonably homogeneous pools. These analyses assume that all employees within the same feeder pool are equally likely to be promoted, and typically they control for the factors that are part of the promotion decision. If there are multiple feeders to a particular job each with a different likelihood of success, then an alternative pools analysis is used to construct a pool that weights the feeder jobs by the proportion of selections that came from each job. Regardless of the methodology for deriving a pools analysis, the question of whether the results of these selection pools can be aggregated is also likely to be raised. The hypothesis of homogeneity is that the ratio of the odds of selection of the group at issue to that of the group not at issue is similar across decision-makers. This research design tests the hypothesis that the differences in the odds ratio are equal to zero across selection pools.8 If the researcher fails to reject the null hypothesis, then the results from various pool-level analyses can be combined and inferences can be made from aggregated data.9 When selection pools are not homogeneous, the level of significance of the aggregated outcome is more difficult to determine. Gastwirth and Greenhouse (1987) recognized this problem when they stated that in this situation ‘‘the derivation of confidence bounds would require significant changes in theory, which we will not consider here’’ (p. 41). We do not yet have a commonly available technology for accurately determining the level of significance of a difference in aggregate, when the selection pools are not homogeneous. The issue of aggregation is primarily one of determining statistical significance of the aggregated results. However, the aggregated differences computed in calculating these results are valid even if the pools are not
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homogeneous. A review of the underlying pools or sub-aggregations (such as results by department within the overall firm) is useful when the desire is to determine where the differences are occurring. This is where practical significance becomes particularly relevant. The differences between protected and unprotected groups in the decisions made by each of the decision-makers may be within the normal range consistent with a random difference, adverse to a particular group, or may be overwhelmingly adverse and statistically significant. Alternatively, the overall difference may be only a small percentage of the selections or the differences may be isolated to a few jobs or sub-groups within an organization. We would expect that the results of the selection pools would be statistically significant 5% of the time, where 2.5% of the differences would favor the group at issue and 2.5% would be adverse to the group at issue. If one found that 50% of the selection pools were statistically significantly adverse with respect to the group at issue, then even though the statistical significance of the outcome is inappropriate because of the lack of homogeneity of the ratios of odds of selection, the overwhelming number of significant results of the pools may be of relevance to the court or to firms evaluating the decision-making process. The courts have become increasingly interested in assessing the extent to which the statistical evidence is not only carefully conducted but accurately represents the reality of the business-related processes at work within the firm in question. In Bazemore v. Friday (1986) the court ruled that the omission of variables in multiple regression analyses may render them less probative, but not necessarily unacceptable as evidence (p. 400). However, this ruling does not mandate ‘‘acceptance of regressions from which clearly major variables have been omitted – such as education and prior work experience’’ (Koger v. Reno, 1996, p. 637). In fact, as Sheehan v. Daily Racing Form, Inc. (1997) illustrates, courts routinely exclude and/or disregard statistical evidence when an expert neglects to eliminate the most common nondiscriminatory explanations for the disparity because it constitutes ‘‘a failure to exercise the degree of care that a statistician would use in his scientific work, outside the context of litigation’’ (p. 942). This theme is further supported in Munoz v. Orr (2000) where the court noted that the plaintiffs’ expert failed to ‘‘consider other variables such as education and experience as explanations for any observed discrepancy between promotion rates’’ (p. 301). The court went on to say that ‘‘failure to control for other explanatory variables makes an expert’s table ‘essentially worthless’’’ (Munoz, (p. 301), quoting Tagatz v. Marquette Univ., 1988, p. 1045). More recently in Carpenter v. Boeing Co. (2004), the court ruled that ‘‘a statistical analysis which fails to control for equally plausible non-discriminatory factors overstates the comparison
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group and, under the facts of this case, cannot raise a question of fact for trial regarding discriminatory impact’’ (p. 21). While the homogeneity tests associated with the odds of selection are relevant to such analyses, a different homogeneity test is relevant when multiple regression models (for example, compensation models) are evaluated. Recently the Chow test (an F-test) has been utilized in employment litigation to determine whether the effects of the characteristics estimated for one subset (e.g., seniority, department, or job) of the data are equal to those estimated for another subset of the data. In the case of cross-sectional data, the subsets might correspond to different organizations within a firm (see Davidson and MacKinnon, 1993, p. 375). In this context, the Chow test may be referred to as a ‘‘regime change’’ test. Specifically, the Chow test is used to determine whether characteristics included in the model have different effects on the factor of interest (such as level of compensation) in different organizations, locations, or job held. As reported by Greene (2003), it is important to determine whether the effects of the characteristics are the same across these groups because it is otherwise inappropriate to estimate a pooled model using all groups combined, without otherwise preparing a model with interactions (p. 130). If the effects of the characteristics differ by group, then the effects from the pooled model may not be a reliable estimate of a characteristic’s influence on the dependent variable for any of the groups. The effect would be understated for some organizations or jobs and overstated for others. Thus, the results of a pooled model are likely to be misleading with respect to the true effect of a characteristic like race, gender or age. If the Chow tests show that the proposed model of compensation, for example, should be analyzed separately by organization, then there are two commonly accepted options available. Either a model with interaction terms representing the analysis levels may be estimated or separate models may be estimated for each of the analysis levels that were found to be different when compared to a pooled model. If, for example, it was found that a compensation model should not be pooled across stores, then an interacted model would include variables for each store as well as the interactions for considering the differential effects of such factors as job, seniority, and education by store. Alternatively, separate equations can be estimated for each store. While intuitively it may seem easier to prepare separate equations for each store, it may not be feasible. For example, if the number of observations in most of the stores were so small as to make a regression analysis inappropriate, then the other alternative would likely be used. Alternatively, if there is a sufficient number of observations by store, then separate models can be estimated and the results compared to a normal
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distribution. Using a 5% level of significance, one would expect that 5% of the estimates by store would be statistically significantly different from zero even in a random process. Thus, in the store regression models, we would expect that the average difference in compensation between the groups at issue would be statistically significant 5% of the time, where 2.5% of the differences would favor the group at issue and 2.5% would be adverse to the group at issue. As in most cases, the issue of practical significance also applies. A further modeling consideration is the issue of combining groups of data across years with respect to multiple regression analysis. Pooling the observations across years raises serious concerns regarding the standard errors of the model because there are multiple observations for a single employee. In this case the data used in the multiple regression analysis would be unlikely to satisfy all of the fundamental assumptions that are required to be met if the results of the regression are to be unbiased and efficient. Data with both a time- and a cross-sectional component, such as these data, are often referred to as panel data. Wooldridge (2000) states, ‘‘For the econometric analysis of panel data, we cannot assume that the observations are independently distributed across time. For example, unobserved factors (such as ability) that affect someone’s wage in 1990 will also affect that person’s wage in 1991’’ (p. 409). This issue is now one that arises in certain litigation contexts.10 The practical problem with combining several years of data in only one estimated regression, for either monitoring or class certification purposes, is that it will not identify the problem year(s) unless it is modeled in such a way as to permit that result to be estimated. For example, it is possible that, overall, there is not a difference in pay with respect to the group at issue. However, if each year were to be examined separately, the results might show that differences in one year were being masked by the other years. Alternatively, a negative result from combining multiple years may be actually the effect of a very serious negative effect in one year only but not in any of the other years. Obviously, the policy responses to this kind of result are quite different from the policy responses to a statistically significant result in each year.
6. WAGE AND HOUR LITIGATION There has been a fairly substantial increase in employment cases that involve overtime payment issues, the provision of work breaks and meal periods, working without payment (‘‘off-the-clock’’), and the determination of the exempt/non-exempt status of jobs. The venue for these wage and hour cases
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varies. If brought under federal statutes, the Fair Labor Standards Act (1938, as amended, U.S.C. y 201, et seq. (2000)) will apply and results will be measured by the definitions and standards defined by this act. However, many more of the wage and hour cases are filed in state courts. Laws vary between states – both as to what can be raised as an issue and the standards to be met in each case. For example, the state of Washington has specific break and meal period requirements that are not the same as the federal laws. In that state, under Washington law, employees are allowed a 10 minutes rest break for every 4 hours worked, and there must be no more than 3 consecutive hours of work without a rest break or a meal period.11 However, these scheduled rest breaks are not required if the nature of the work allows intermittent rest breaks equal to 10 minutes during each 4 hours of work. Further, employees who work more than 5 hours are eligible for at least a 30 minutes unpaid meal period. Employees are eligible to take a meal period of up to 60 minutes after either 7 or 8 hours at the discretion of the individual store manager. These meal period eligibilities may be waived by the employee, or the employee may waive part of the meal period. The issues that usually involve economists and statisticians in these cases are unpaid time worked and exempt status. The failure to pay overtime rates for unpaid time worked is also an issue. The economic value of an individual wage and hour case is relatively small since it is rare that individuals have a very large amount of unpaid work. Of course, the unpaid work can be more substantial when it includes allegations that training was conducted during unpaid time, or collateral duties (such as caring for police dogs in canine units or cleaning uniforms) were assigned but no time was scheduled for performing those duties. However, the difference between exempt and nonexempt status can provide larger economic benefits if there is substantial overtime worked by employees given exempt status but claiming that their position should be non-exempt. In any case, most wage and hour cases that require significant expert input are brought as a ‘‘class’’ or ‘‘collective action.’’ Once again, the issue of whether the allegations are common to all the proposed class members must be addressed. A common analytical problem arises in wage and hour cases when unpaid work time is alleged because work time that is not paid is less likely to be recorded anywhere. In more recent years that problem has been resolved in fairly creative ways by various experts. For example, there may be key systems which record the date and time in which the key is used each time an employee enters the store. There may also be time records of computer use or security systems with a time stamp of entry to specific work locations or films of employees working. As the recording of employees’ activity becomes
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even more prevalent, those data will be increasingly more useful in wage and hour matters. Given the volume of data of time-keeping information that is at issue in these matters, statistical sampling is often used. If an organization has thousands of employees with daily time entry records over several years, it may not be reasonable to analyze all the data. In these situations, a sample of locations, particular months, or jobs is often used to determine the patterns that exist within the organization or to compute estimated damages. The issue that arises is whether or not the units sampled (such as the particular months) are representative of the other units that are not included in the sample.
7. SUMMARY OF ECONOMIC ANALYSIS IN EMPLOYMENT LITIGATION Economists, statisticians, and other experts who analyze employment decisions must recognize the legal context in which they work. Whether preparing the analysis for litigation or for professional review, the expert consults the professional standards and knowledge of statistics and economics as well as examples provided by case law. In recent years there have been increases in the complexity of the statistical and economic models as well as additional focus on the use of this knowledge in the courtroom. The courts have assisted analysts by defining the standards that must be met by programs that government and corporations develop to promote diversity. In the more recent cases in this area we have seen a move to use the two-pronged test of business necessity of such a program and the narrowly tailored features and requirements of the program. Therefore, the analytical issues include whether or not there are patterns of discrimination that require a governmental agency or a firm to institute a diversity program and whether the requirements of that program are narrowly tailored to the discrimination that is being remedied. Experts have approached these issues by using historical data to illustrate whether there are imbalances that provide reasons for a required program and then showing that the remedy is specific to the imbalances when found in the historical statistics. Those same criteria have been applied to monitoring programs within firms. In the class action arena, the courts have developed an interest in the standards to be applied in order to certify a class. In that regard, experts have presented analyses hat demonstrate whether the proposed class has experienced adverse disparities in pay, hiring, promotion, etc. across the entire organization or workforce. If the presentation of these analyses does
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not address the issue of common results across all the class or whether the plaintiffs’ claims are typical of the claims of the class they propose to represent, then the court may entertain arguments from other experts that the ‘‘common’’ results were merely assumed and that when separate groups are investigated there is not a common pattern or the plaintiffs’ concerns are not generally seen among the proposed class. Aggregation is central to class certification issues, and aggregation requires that the groups at issue be homogeneous in order to determine the statistical significance of the estimated differences. Thus, in recent years there has been more attention to the statistical tests for homogeneity – including the common odds ratio test and the Chow test. When the statistical or economic models are inappropriate for the issues pertinent to the case, then counsel for both sides are likely to file motions to remove the expert reports or expert testimony from the case (e.g., motions in limine and Daubert motions). The standards by which an analysis or set of analyses can be removed include relevance to the issues in the case and professional methodological techniques and assumptions. Failure to meet these standards could result in the expert report and testimony being excluded from the litigation. Finally, wage and hour cases have also begun to incorporate economic and statistical analysis. While there is great variation among the states as to the actual requirements and the standards that are applied, the economic analysis is often based on data that have been more recently collected for other purposes – such as key entry systems with time stamps in order to determine when an employee came to work and/or left work, or security systems with time stamps that film employees at work. Economic and statistical analysis of good, professional quality has assisted many courts in their deliberations and appears likely to continue to do so in the future. The challenge for experts is to produce clear and accurate analyses that assist and do not mislead the court in making its decisions.
NOTES 1. ‘‘Reverse’’ discrimination is a term that has been used to define discrimination against individuals who are not among the explicitly identified protected groups – e.g., minorities, women, and older workers. 2. Gratz v. Bollinger, 539 U.S. 244 (2003) and Grutter v. Bollinger, 539 U.S. 306 (2003). 3. Alphran (2003) provides an historical overview of the decisions involving governmental-sponsored Affirmative Action Programs. Holzer and Neumark (2000)
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also provide an overview with respect to these programs as well as university-sponsored Affirmative Action Programs. 4. See Beck v. Boeing Co., 203 F.R.D. 459, 461 (W.D. Wa. 2001). 5. See, for example, Love v. Turlington, 733 F .2d 1562 (11th Cir. 1984). 6. Haworth and Haworth (1986) addressed the problems associated with failing to properly analyze selection decisions. 7. Some of the earliest logistic regression analyses were produced in EEOC v. Sears Roebuck & Co. (1988), Csicseri v. Bowsher (1994). 8. The test for homogeneity determines whether or not the odds ratio is statistically the same across decision-makers, where the odds ratio for each decisionmaker is calculated as: Odds Ratio ¼ (# of Selections Among Group at Issue/# of Non-Selections Among Group at Issue)/(# of Selections Among Group Not at Issue/ # of Non-Selections Among Group Not at Issue). 9. Gastwirth and Greenhouse (1987) illustrate the relevance of testing homogeneity of odds ratios in employment litigation using large samples. Liang and Self (1985) provide alternative calculations for testing homogeneity when the number of observations are small. Zellen (1971) and Liu and Pierce (1993) also provide useful information regarding this subject, stating that it is a fairly standard practice to test whether the odds ratios are constant (pp. 543–556). 10. See, for example, Farrow v. Bank of America Corp. (2004). 11. Administrative Policy, State of Washington Department of Labor and Industries Employment Standards, WAC296-126–092 (1998).
REFERENCES Alphran, D. M. (2003). Proving discrimination after Croson and Adarand: If it walks like a duck. University of San Francisco Law Review, 37(4), 887–969. Chow, G. C. (1960). Tests of equality between sets of coefficients in two linear regressions. Econometrica, 28(3), 591–605. Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics. New York: Oxford University Press. Gastwirth, J. L., & Greenhouse, S. W. (1987). Estimating a common relative risk: Application in equal employment. Journal of the American Statistical Association, 82(397), 38–45. Greene, W. H. (2003). Econometric analysis (5th ed.). Upper Saddle River, NJ: Prentice Hall. Haworth, J. G., & Haworth, C. T. (1986). Employment decisions: Does your analysis of selections match the real process? Employee Relations Law Journal, 12(3), 352–369. Holzer, H., & Neumark, D. (2000). Assessing affirmative action. Journal of Economic Literature, 38(3), 483–568. Liang, K. Y., & Self, S. G. (1985). Tests for homogeneity of odds ratio when the data are sparse. Biometrika, 72(2), 353–358. Liu, Q., & Pierce, D. A. (1993). Heterogeneity in Mantel–Haenszel-type models. Biometrika, 80(3), 543–556. National School Boards Association. (2003). Grutter v. University of Michigan, Gratz v. Bollinger: Implications for K-12 diversity policies. Alexandria, VA: NSBA Federal File, Resource Document #3.
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Studenmund, A. H. (1992). Using econometrics: A practical guide (2nd ed.). New York: Harper Collins Publishers. Wooldridge, J. M. (2000). Introductory econometrics: A modern approach. Cincinnati: SouthWestern College Publishing. Zelen, M. (1971). The analysis of several 2 2 contingency tables. Biometrika, 58(1), 129–137.
Amendments, Cases and Statutes Abram v. United Parcel Serv. of Am., Inc., 200 F.R.D. 424 (E.D. Wisc. 2001). Adarand Constructors, Inc. v. Pena. 515 US 200 (1995). Bakke v. Regents of Univ. of Cal., 438 US 265 (1978). Bazemore v. Friday, 478 US 385 (1986). Beck v. Boeing Co., 203 F.R.D. 459 (W.D. Wa. 2001). Carpenter v. Boeing Co., No. 02-1019-WEB (D. Kan. Feb. 24, 2004). Carmichael v. Kumho Tire Co., 526 US 137 (1999). Castaneda v. Partida, 430 US 482 (1977). City of Richmond v. J.A. Croson Co., 488 US 469 (1989). Civil Rights Act (CRA) of 1991, 42 U.S.C. y 1981a (2000). Concrete Works of Colo. v. City & County of Denver, 321 F.3d 950 (2003). Csicseri v. Bowsher. (1994). Daubert v. Merrell Dow Pharmaceuticals, 43 F.3d 1311 (9th Cir. 1995). EEOC v. Fed. Reserve Bank of Richmond, 698 F.2d 633 (4th Cir. 1983). EEOC v. Sears Roebuck & Co. (1988). Equal Protection Clause, US Const. Amend. XIV, y1. Fair Labor Standards Act of 1938, as Amended, 29 U.S.C. 201, et seq. (2000). Farrow v. Bank of America Corp. (2004). Frank v. Xerox Corp., 347 F.3d 130 (5th Cir. 2003). Gratz v. Bollinger, 539 US 244 (2003). Grutter v. Bollinger, 539 US 306 (2003). Hazelwood School Dist. v. United States, 433 US 299 (1977). Huguley v. General Motors Corp., 128 F.R.D. 81 (E.D. Mich. 1989). Int’l Bhd. of Teamsters v. United States, 431 US 324 (1977). Jennings v. Regents of Univ. of Cal. (2003). Koger v. Reno, 98 F.3d 631 (D.C. Cir. 1996). Kohlbek v. City of Omaha, No. 8:03CV68, (D. Neb. Mar. 30, 2004). Love v. Turlington, 733 F.2d 1562. (11th Cir. 1984). Munoz v. Orr, 200 F.3d 291. (5th Cir. 2000). Northeastern Fla. Chapter of Associated Gen. Contractors of Am. v. City of Jacksonville, 508 US 656 (1993). Rhodes v. Cracker Barrel Old Country Store, 213 F.R.D. 619 (N.D. Ga. 2003). Sheehan v. Daily Racing Form, Inc., 104 F.3d 940. (7th Cir. 1997). Tagatz v. Marquette Univ., 861 F.2d 1040. (7th Cir. 1988). Thornton v. National R.R. Passenger Corp. (2000). Transportation Equity Act for the 21st Century of 1998, Pub. L. No. 105-178 y 1101(b) 112 stat. 107 (1998). Wash. Admin. Code (WAC), y 296-126-092. (1998).
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THE CALCULATION AND USE OF RETIREMENT AGE STATISTICS: A RECAP SINCE 1970 Tamorah Hunt, Joyce Pickersgill and Herbert Rutemiller 1. INTRODUCTION This chapter provides a historical overview of the data and methodologies used to measure worklife and the usefulness of such statistics for projecting future retirement behavior. Section 2 discusses the calculation of worklife expectancy (WLE), beginning with a review of the data and method of calculation using what has come to be known as the conventional model. Section 3 looks at the WLE results using the increment–decrement model and subsequent models. Sections 4 and 5 revisit the conventional model and compare the results of the conventional model to the increment-decrement model. Section 6 of the chapter discusses the data and methodologies used to calculate years to final separation (YFS), and Section 7 discusses the use of both WLE and YFS statistics in projecting future retirement behavior. Throughout the chapter, comparisons are made of the results from the various worklife calculations published since 1970. The comparisons are made by gender for all education levels combined. In order to facilitate comparison of the many studies, after the initial reference providing the author and publication data, the individual studies will be referred to by the Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 83–117 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87005-6
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year(s) of data used in the study, followed by the last initials of the author(s). The abbreviated references and their corresponding publications are outlined prior to their use for comparison purposes in the figures throughout the chapter.
2. WLE CALCULATED USING THE CONVENTIONAL MODEL 2.1. Features of the Conventional Model Prior to 1982, when the Bureau of Labor Statistics (BLS) began publishing worklife data utilizing the increment–decrement worklife model, it had periodically produced WLEs since 1950 using what has come to be called the conventional model. Under the conventional model, WLE for a general population of a given age is simply equal to the total person-years worked by that population divided by the size of the population at that age. General populations can be divided into any number of sub-categories, such as sex and level of education. To derive WLE for any group of a given age, one must calculate the total person-years worked. The conventional methodology generally derives this information from labor force participation rate (LFPR) data produced from the Current Population Survey (CPS) and published by the BLS,1 and mortality tables published by the U.S. Department of Health and Human Services. Using these two pieces of information, one can calculate the number of future person-years worked by multiplying the population at each age by the LFPR for that age, summing over all future years and dividing by the population of the initial age. The CPS is a ‘‘scientifically selected sample designed to represent the civilian noninstitutional population’’ over age 16 (see U.S. Department of Labor, 2003, p. 166). The CPS survey reflects household data collected monthly by the BLS in conjunction with the U.S. Census Bureau. Only one person in each household is interviewed by telephone and he/she answers for all the adults in the household. The monthly sample size currently includes about 60,000 occupied units eligible for interview, before reduction for the non-interview rate of about 7.5 percent. In addition, there are about 12,000 vacant or ineligible sample units. Individual households remain in the sample for 16 months and are interviewed consecutively during the first 4 months and the last 4 months. Each month, one-twelfth of the 60,000 households are added to the sample, and the rotation allows for 75 percent
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of the sample to be common from one month to the next and 50 percent to be common with the same month one year earlier.
2.2. Published WLEs Using the Conventional Method – General Population The discussion of the conventional model will focus initially on the calculation for the general population for two reasons: First, the conventional model produces WLEs for the general population, which are conceptually the same as those produced by later models employing the increment– decrement method and transition probabilities (TPs) if LFPRs are stable over the sample years used to calculate the TPs, and there is a 100 percent sample match (see Richards, 2000). Second, using the conventional model, there is no direct way of calculating WLEs separately for the active and inactive populations.2
2.2.1. WLEs Published by the BLS The last BLS publication devoted entirely to the conventional model was published in 1976 and written by Howard Fullerton and James Byrne. The 1970 worklife table produced by Fullerton and Byrne was based upon 1970 mortality tables and LFPRs from 1969 to 1971. The final BLS worklife estimates using the conventional model were prepared by Shirley Smith and published in 1982 (see U.S. Department of Labor, 1982). These results calculated using 1977 data were included in an appendix to BLS Bulletin 2135, which introduced the increment–decrement model. The 1970 WLEs reported by Fullerton and Byrne were for all men, defined as the general population, as well as for all active men. Fullerton and Byrne also reported data for the general population of women and for women by marital and parental status. The 1977 BLS data using the conventional model were reported only for the general population of men.
2.2.2. WLEs Published by Non-BLS Sources Two groups of authors have continued to publish WLEs for the general population using the conventional model. These publications include two by Hunt, Pickersgill, and Rutemiller (HPR, 1997, 2001) based on 1992/1993 and 1998/1999 data, and one published by Richards and Abele (RA, 1999) using 1990 and 1996–1998 data. Using 1992/1993 data, Hunt, Pickersgill,
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and Rutemiller (1997) published WLEs for the general population to age 70 for total men and for total women, and for the general population of men and women by education level. Hunt, Pickersgill, and Rutemiller (2001) present WLEs for the same groups by educational attainment using 1998/1999 data.3 The results of Richards and Abele (1999) using both 1990 and 1996–1998 data are presented by sex, race, and level of educational attainment.
2.2.3. Comparison of WLEs – Conventional Model – General Population Table 1 provides a list of the above-referenced WLEs that will be compared in Figs. 1 and 2. The table provides the author(s) and publication year of each study, the calendar year(s) of the data, the method used to calculate the WLE in the comparison, and the reference that will hereafter be used to facilitate comparison between the studies. The data in the above figures represent the sum of current age plus remaining WLE.4 As Fig. 1 for total males shows, the initial 1970-BLS WLEs using the conventional model were higher than the other WLEs for all ages. Although higher for all ages under 64, the 1977-BLS WLEs were closer to those using data ranging from 1990 to 1999. WLEs produced using the conventional model and data from 1990 to 1999 are quite similar, with the 1992/1993-HPR WLEs lower for most years by less than half a year, compared to the 1990-RA, 1996–1998-RA, and the 1998/1999-HPR. These results are consistent with the recent stability of retirement age for males, following a long-run decline.
Table 1.
Studies Compared in Figs. 1 and 2.
Chapter Reference
Fullerton and Byrne, BLS (1976) U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2135 Richards and Abele (1999) Hunt, Pickersgill and Rutemiller (1997) Richards and Abele (1999) Hunt, Pickersgill and Rutemiller (2001)
Labor Force Data Year(s)
Method
Condensed Reference
1970 1977
Conventional Conventional
1970-BLS 1977-BLS
1990 1992/1993
Conventional Conventional
1990-RA 1992/1993-HPR
1996–1998 1998/1999
Conventional Conventional
1996–1998-RA 1998/1999-HPR
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The Calculation and Use of Retirement Age Statistics 72.0 71.0 70.0 69.0 68.0 67.0
Current Age + WLE
66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0
18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
56.0 Age 1970-BLS
Fig. 1.
1977-BLS
1990-RA
1992/93-HPR
1996-98-RA
1998/99-HPR
Comparison of WLEs Produced Using the Conventional Model for Total Males – General Population, 1970–1998/1999.
As Fig. 2 shows, the sum of age plus WLE for the general population of total women has been increasing. This is evident when comparing the difference between the 1970-BLS WLEs (available up to age 47 only) to those based on later data, and the continued increase through the 1990s. The WLEs produced by 1990-RA and 1992/1993-HPR are almost identical. The same is true for 1996–1998-RA and 1998/1999-HPR.
TAMORAH HUNT ET AL. 71.0 70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 50.0 49.0 48.0 47.0 46.0 45.0 44.0 43.0 42.0 41.0 40.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
Current Age + WLE
88
Age 1970-BLS
Fig. 2.
1990-RA
1992/93-HPR
1996-98-RA
1998/99-HPR
Comparison of WLEs Produced Using the Conventional Model for Total Females – General Population, 1970–1998/1999.
2.3. Published WLEs using the Conventional Method – Active Population BLS WLEs using the conventional model for the active population for men and for women were produced by Fullerton and Byrne (1976) in their 1970 worklife table and by Shirley Smith for men using 1977 data. In Appendix B of BLS Bulletin 2135, Shirley Smith provides a thorough discussion of the
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problems encountered in using the conventional model to calculate WLEs for the active population. Following the technique used by Fullerton and Byrne, the BLS calculated the 1977 WLE for the active population by substituting the active population for the general population in the denominator, thus dividing the total number of future years worked by the labor force rather than by the general population. As is commonly recognized, this technique assumes that men enter and leave the labor force only once, and that women enter and leave only once in response to changes in their marital and parental status. WLEs produced by the conventional method overestimated worklife for the active population, particularly for those groups who demonstrate frequent changes in their labor force status. No comparison of the results for the active population calculated using the conventional model is included in this chapter.
3. WLE CALCULATED USING THE INCREMENT–DECREMENT MODEL 3.1. Features of the Increment–Decrement Model Beginning in 1982, the BLS published the first worklife estimates using the increment–decrement model. As with the conventional model, the increment–decrement model used to calculate WLEs must calculate the total person-years worked by the population in question. In the conventional model, this series is created by applying CPS LFPRs to the population. In the increment–decrement model this series is created by applying TPs to an initial population. The TPs measure patterns of labor force entry and exit derived from matched sample CPS data. Although both LFPRs and TPs come from the CPS, LFPRs represent a snapshot of behavior at a moment in time and TPs require matched samples, which results in loss of a substantial portion of the sample and may generate biased results. This issue will be discussed later in the chapter. In calculating TPs, the initial population can be the general, active, or inactive population. The data used to calculate TPs come from the CPS survey of households over a 16-month period. The survey questions the household on four visits to record individuals in the active and inactive state. Hence, the number of transfers per year from active to inactive and vice versa is recorded for each age and for various demographic categories, and is the basis for the four TPs, including (1) the probability of remaining
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active, p(aa); (2) the probability of going from active to inactive, p(ai); (3) the probability of remaining inactive, p(ii); and (4) the probability of going from inactive to active, p(ia). These probabilities are utilized with mortality tables to generate a stationary population showing the proportion of individuals in the active and inactive states at each exact age. The increment– decrement model uses these proportions to estimate expected worklife for the general population and for individuals currently active or currently inactive at any exact age. For those currently active at age x, the increment– decrement method sets, say, 100,000 individuals active and zero individuals inactive at exact age x, then applies the TPs to all subsequent ages to generate the number active at age x þ 1; x þ 2; etc. The expected worklife is the sum of the number of actives at age x, x þ 1; x þ 2; etc., divided by 100,000. Different studies may use different numbers of years and different smoothing techniques to calculate TPs, but all use the same general method.5 In BLS Bulletin 2135, Shirley Smith notes that in order to use TPs to create the total person-years worked for an initial group of active or inactive persons, one must make two critical assumptions. The first is relevant to the creation of WLEs for the active and inactive populations only, while the second is relevant for all groups and for both the conventional and increment–decrement methods. First it is assumed ‘‘that for any individual the probability for transition depends solely on his or her current status, sex, and exact age. It is independent of previous statuses’’ (see U.S. Department of Labor, 1982, p. 11). This is a crucial assumption, because the increment– decrement method assumes that the probability of individuals transitioning from one labor force status to another is independent of their past history. Thus, all persons currently inactive have an equally likely probability of becoming active in the next period, and all persons currently active have an equal probability of becoming inactive in the next period. It follows from this assumption that one then uses the same WLE to project future years in the labor force for an individual who is currently inactive but who has had a continuous history of labor force attachment prior to this period, as for an individual who has never been active. The increment–decrement model is called a Markov model; and to use a Markov process, current status must be ‘‘memoryless,’’ i.e., only current status determines the probability of transition. According to Shirley Smith, the second critical assumption is that ‘‘age-specific transfer rates (i.e. of entry into and withdrawal from the labor force and of death) are constant at levels observed in the reference population during the reference year’’ (see U.S. Department of Labor, 1982, p. 11). This restriction will be discussed later in the chapter.
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3.2. Published WLEs Using the Increment–Decrement Model 3.2.1. WLEs Published by the BLS From 1982 to 1986, Shirley Smith at the BLS published a number of WLE studies using the increment–decrement model (see U.S. Department of Labor, 1982, 1986). WLEs were calculated using CPS data for 1970, 1977, and 1979/1980. The WLEs were calculated for the general population of men and women and by labor force status. The later publications included a breakdown by race and education.
3.2.2. WLEs Published by Non-BLS Sources From 1995 through 2001, Ciecka, Donley, and Goldman (1995, 1997, 1999/2000, 2000, 2000/2001) published a series of WLE studies using the increment–decrement model. The 1995 paper published the WLEs for the general, active, and inactive populations for total men and total women to age 75. The results are also presented by race and education. Ciecka, Donley and Goldman reported that the TPs generated using 1992/1993 CPS data showed substantial variation from year-to-year, particularly for subsets of the total population. To reduce this variation, they used a moving average of order nine smoothing.6 They repeated this technique in later publications, including their 1997 publication using 1994/1995 CPS data for the same groups cited above and three additional articles based on 1997/1998 data (see Ciecka et al., 1999/2000, 2000, 2000/2001). In the summer of 2001, Skoog and Ciecka (2001) published two articles producing the same WLEs published by Ciecka, Donley and Goldman using 1997/1998 CPS data. They expanded their analysis to produce ‘‘probability mass functions’’ that allowed them to generate the mean, standard deviation, median, mode, skewness, and kurtosis of the ‘‘probability mass function.’’ Their assumptions are that the estimates of TPs are parameters, not estimates, that a stationary population represents cohort data exactly, and that the Markov (memoryless) conditions are valid.7 Richards and Abele (1999) produced WLEs using the increment– decrement method and CPS data from 1996 through 1998 to calculate TPs. They smoothed the TPs using 5-year running averages. Unlike the other published WLE data referenced above, Richards and Abele utilized mortality rates by age, sex, race, and for the first time educational attainment, combined with TPs for similar categories to calculate their WLEs.
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Table 2. Chapter Reference
U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2135 U.S. Department of Labor, BLS (1982)– Smith, Bulletin 2157 U.S. Department of Labor, BLS (1986) – Smith, Bulletin 2254 Ciecka, Donley, and Goldman (1995) Ciecka, Donley, and Goldman (1997) Richards and Abele (1999) Ciecka, Donley, and Goldman (1999/2000)
Studies Compared in Figs. 3 and 4. Labor Force Data Year(s)
Method
Condensed Reference
1970
Increment–Decrement
1970-BLS
1977
Increment–Decrement
1977-BLS
1979/1980
Increment–Decrement
1979/1980-BLS
1992/1993
Increment–Decrement
1992/1993-CDG
1994/1995
Increment–Decrement
1994/1995-CDG
1996–1998 1997/1998
Increment–Decrement Increment–Decrement
1996–1998-RA 1997/1998-CDG
3.2.3. Comparison of WLEs– Increment–Decrement – General Population Table 2 outlines the WLEs compared in Figs. 3 and 4, including the author(s) and publication year, the calendar year(s) of the data, the methodology used, and the condensed reference used hereafter for comparison purposes. Figure 3 compares WLEs for the general population of total males using the increment–decrement model and data from 1970 through 1998. The 1970-BLS data produced the highest WLEs, and the 1992/1993-CDG produced the lowest WLEs until converging with the other WLEs after age 60. The other WLEs from the 1977-BLS, 1979/1980-BLS, 1994/1995-CDG, 1996–1998-RA, and 1997/1998-CDG are similar to each other. Figure 4 shows that for total women, WLEs calculated using the increment–decrement model increased over time from the earliest study in 1970 to the latest in 1997/1998. Although the data converge for older women, for younger women the WLEs reflect the increasing LFPR for females since 1970.
3.2.4. Comparison of Conventional vs. Increment–Decrement – General Population The first two figures in this chapter compared WLEs calculated since 1970 for the general population using the conventional model, and the second
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The Calculation and Use of Retirement Age Statistics 72.0 71.0 70.0 69.0 68.0 67.0
Current Age + WLE
66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0
18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
55.0 Age 1970-BLS
Fig. 3.
1977-BLS
1979/80-BLS
1992/93-CDG
1994/95-CDG
1996-98-RA
1997/98-CDG
Comparison of WLEs Produced Using the Increment/Decrement Model for Total Males – General Population, 1990–1998/1999.
two figures compared WLEs calculated for the general population using the increment–decrement model. Figures 5 and 6 combine the WLEs calculated since 1990 using both models. Table 3 outlines the WLEs compared in Figs. 5 and 6, including the author(s) and publication year, the calendar year(s) of the data, the methodology used, and the condensed reference used hereafter. The condensed references begin with a ‘‘C’’ if the WLEs were calculated using the conventional model and an ‘‘ID’’ if the WLEs were calculated using the increment–decrement model.
TAMORAH HUNT ET AL. 71.0 70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 50.0 49.0 48.0 47.0 46.0 45.0 44.0 43.0 42.0 41.0 40.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
Current Age + WLE
94
Age 1970-BLS
Fig. 4.
1977-BLS
1979/80-BLS
1992/93-CDG
1994/95-CDG
1996-98-RA
1997/98-CDG
Comparison of WLEs Produced Using the Increment/Decrement Model for Total Females – General Population, 1970/1971–1997/1998.
The WLEs in Fig. 5 are for total males in the general population using 1990–1999 data. The figure reflects that the WLEs calculated using the conventional model tend to exceed those calculated using the increment–decrement model. The lowest WLEs were calculated using ID1992/1993-CDG. The highest WLEs include C1990-RA, C1996–1998RA, and C1998/1999-HPR WLEs. Excluding the ID1992/1993-CDG data, the differences between the remaining WLEs from the various studies are
The Calculation and Use of Retirement Age Statistics
95
72.0 71.0 70.0 69.0 68.0 67.0
Current Age + WLE
66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0
18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
55.0 Age C1990-RA C1996-98-RA
ID1992/93-CDG ID1996-98-RA
C1992/93-HPR ID1997/98-CDG/CS
ID1994/95-CDG C1998/99-HPR
Fig. 5. Comparison of WLEs Produced Using Conventional and Increment/ Decrement Models for Total Males – General Population, 1990–1998/1999.
approximately 1 year at earlier ages, with the differences declining to less than 1 year by age 30. Figure 6 for total women in the general population again primarily reflects increasing WLEs for women since 1990. The WLEs calculated using 1990–1994/1995 data under both the conventional and the increment–decrement models provide similar results, which are lower than those calculated
96
TAMORAH HUNT ET AL. 71.0 70.0 69.0 68.0 67.0 66.0 65.0 64.0
Current Age + WLE
63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 50.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
49.0 Age C1990-RA
ID1992/93-CDG
C1992/93-HPR
ID1994/95-CDG
C1996-98-RA
ID1996-98-RA
ID1997/98-CDG/CS
C1998/99-HPR
Fig. 6. Comparison of WLEs Produced Using Conventional and Increment/ Decrement Models for Total Females – General Population, 1990–1998/1999.
using data for later years. The WLEs calculated using 1996–1999 data under both the conventional and increment–decrement models provide higher WLEs until converging with the 1990–1994/1995 results after age 60. 3.2.5. Comparison of WLEs – Increment-Decrement – Active Population The conventional model produces WLEs for the general population. The increment–decrement model, however, produces WLEs for the general,
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Table 3. Chapter Reference
Richards and Abele (1999) Ciecka, Donley, and Goldman (1995) Hunt, Pickersgill and Rutemiller (1997) Ciecka, Donley, and Goldman (1997) Richards and Abele (1999) Richards and Abele (1999) Ciecka, Donley, and Goldman (1999/2000) Hunt, Pickersgill and Rutemiller (2001)
Table 4. Chapter Reference
U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2135 U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2157 U.S. Department of Labor, BLS (1986) – Smith, Bulletin 2254 Ciecka, Donley, and Goldman (1995) Ciecka, Donley, and Goldman (1997) Richards and Abele (1999) Ciecka, Donley, and Goldman (1999/2000)
Studies Compared in Figs. 5 and 6. Labor Force Data Year(s)
Method
Condensed Reference
1990 1992/1993
Conventional Increment–Decrement
C1990-RA ID1992/1993-CDG
1992/1993
Conventional
C1992/1993-HPR
1994/1995
Increment–Decrement
ID1994/1995-CDG
1996–1998 1996–1998 1997/1998
Conventional Increment–Decrement Increment–Decrement
C1996–1998-RA ID1996–1998-RA ID1997/1998-CDG
1998/1999
Conventional
C1998/1999-HPR
Studies Compared in Figs. 7 and 8. Labor Force Data Year(s)
Method
Condensed Reference
1970
Increment–Decrement
1970-BLS
1977
Increment–Decrement
1977-BLS
1979/1980
Increment–Decrement
1979/1980-BLS
1992/1993
Increment–Decrement
1992/1993-CDG
1994/1995
Increment–Decrement
1994/1995-CDG
1996–1998 1997/1998
Increment–Decrement Increment–Decrement
1996–1998-RA 1997/1998-CDG
active, and inactive populations. Table 4 outlines the WLEs calculated for the active population using the increment–decrement model, which are compared in Figs. 7 and 8.
98
TAMORAH HUNT ET AL. 74.0 73.0 72.0 71.0 70.0 69.0 68.0
Current Age + WLE
67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0
18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
55.0
Age 1970-BLS
Fig. 7.
1977-BLS
1979/80 BLS
1992/93-CDG
1994/95 CDG
1996-98-RA
1997/98-CDG
Comparison of WLEs Produced Using the Increment/Decrement Model for Total Males–Active Population, 1970/1971–1997/1998.
Figure 7 shows the WLEs calculated for total males for the active population using the increment–decrement model and data from 1970 to 1998. The results are quite similar to Fig. 3 for the general population, representing a decline between 1970 and 1977. Again, the lowest WLEs are generated from 1992/1993-CDG for ages under 60. The remaining WLEs are similar to each other for most years. The results in Fig. 8 are similar to those in Figs. 2, 4, and 6, reflecting the increasing LFPRs for females between 1970 and 1998.
99
73.0 72.0 71.0 70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 50.0 49.0 48.0 47.0 46.0 45.0 44.0 43.0 42.0 41.0 40.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
Current Age + WLE
The Calculation and Use of Retirement Age Statistics
Age 1970-BLS
Fig. 8.
1977-BLS
1979/80 BLS
1992/93-CDG
1994/95 CDG
1997/98-CDG
1996-98-RA
Comparison of WLEs Produced Using the Increment/Decrement Model for Total Females–Active Population, 1970/1971–1997/1998.
4. MODIFYING THE CONVENTIONAL MODEL – WLE FOR THE ACTIVE POPULATION Hunt, Pickersgill and Rutemiller (1997, 2001) modify WLEs for the general population calculated using the conventional model to account for the increased WLE for actives. As explained in Hunt et al. (1997), the increment– decrement model begins by assuming that for the initial age group, the entire
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population is active, ax ¼ l x : The conventional model utilizes the formula, ax ¼ px l x ; assuming that the active population is a certain or set proportion of the total population and is derived by multiplying the LFPR by the total population. The two expectations are quite close and are virtually identical for young ages. Initial conditions wear off quickly in Markov chains, and after about five to six transitions, ax is the same in the two models. As an estimate of WLEs for the active population, the authors set the active population equal to the total population during the first 3 years, and from year 4 on the active population is generated from the CPS participation rates. Results are presented for both sexes and by educational attainment to age 70.8
4.1. Comparison of WLE – Increment–Decrement vs. Modified Conventional for the Active Population Table 5 outlines the WLEs calculated for the active population using both the increment–decrement model and the modified conventional model Table 5. Chapter Reference
U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2135 U.S. Department of Labor, BLS (1982) – Smith, Bulletin 2157 U.S. Department of Labor, BLS (1986) – Smith, Bulletin 2254 Ciecka, Donley, and Goldman (1995) Hunt, Pickersgill and Rutemiller (1997) Ciecka, Donley, and Goldman (1997) Richards and Abele (1999) Ciecka, Donley, and Goldman (1999/2000) Hunt, Pickersgill and Rutemiller (2001)
Studies Compared in Figs. 9 and 10. Labor Force Data Year(s)
Method
Condensed Reference
1970
Increment–Decrement
ID1970-BLS
1977
Increment–Decrement
ID1977-BLS
1979/1980
Increment–Decrement
ID1979/1980-BLS
1992/1993
Increment–Decrement
ID1992/1993-CDG
1992/1993
Modified–Conventional
MC1992/1993-HPR
1994/1995
Increment–Decrement
ID1994/1995-CDG
1996–1998 1997/1998
Increment–Decrement Increment–Decrement
ID1996–1998-RA ID1997/1998-CDG
1998/1999
Modified–Conventional
MC1998/1999-HPR
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The Calculation and Use of Retirement Age Statistics
referenced above. The only difference between Figs. 9 and 10, compared to Figs. 7 and 8, is that the two WLEs calculated using the modified conventional model have been added for comparison purposes. The condensed references begin with an ‘‘MC’’ if the WLEs were calculated using the modified conventional model and an ‘‘ID’’ if the WLEs were calculated using the increment–decrement model.
74.0 73.0 72.0 71.0 70.0 69.0 68.0 Current Age + WLE
67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
55.0
Age ID1970-BLS ID1994/95-CDG
ID1977-BLS ID1996-98-RA
ID1979/80-BLS
ID1992/93-CDG
ID1997/98-CDG
MC1998/99-HPR
MC1992/93-HPR
Fig. 9. Comparison of WLEs Produced Using Increment/Decrement and Modified Conventional Models for Total Males–Active Population, 1970–1998/1999.
TAMORAH HUNT ET AL. 74.0 73.0 72.0 71.0 70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0 60.0 59.0 58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 50.0 49.0 48.0 47.0 46.0 45.0 44.0 43.0 42.0 41.0 40.0 18 .0 20 .0 22 .0 24 .0 26 .0 28 .0 30 .0 32 .0 34 .0 36 .0 38 .0 40 .0 42 .0 44 .0 46 .0 48 .0 50 .0 52 .0 54 .0 56 .0 58 .0 60 .0 62 .0 64 .0 66 .0 68 .0 70 .0
Current Age + WLE
102
Age ID1970-BLS ID1994/95 CDG
ID1977-BLS ID1996-98-RA
ID1979/80 BLS ID1997/98-CDG
ID1992/93-CDG MC1998/99-HPR
MC1992/93-HPR
Fig. 10. Comparison of WLEs Produced Using Increment/Decrement and Modified Conventional Models for Total Females – Active Population, 1970–1998/1999.
As Fig. 9 shows, if we exclude the high WLEs from ID1970-BLS and the low WLEs from ID1992/93-CDG, the WLEs produced by MC1992/1993HPR and MC1998/1999-HPR for the active population using the modified conventional model are similar to those produced by the four remaining studies using the increment–decrement method. The HPR results calculated
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103
using the modified conventional model, however, are somewhat higher for younger ages. Similar to earlier figures for females, Fig. 10 shows the increasing WLEs for total active women between 1970 and 1999. The modified conventional model of MC1992/1993-HPR and MC1998/1999-HPR produce WLEs close to those calculated using the increment–decrement model for total women in the active population for similar calendar years.
5. INCREMENT-DECREMENT VS. CONVENTIONAL MODELS 5.1. General Comparison All WLEs, whether produced using the conventional method or using the increment–decrement method, suffer a significant common problem, i.e., all of the data are cross-sectional, not longitudinal. The data are a snapshot of labor force behavior and life expectancy at a moment in time or, at most, in two or three adjacent years. Neither method follows a cohort through time. Further, to project WLEs, even if they were generated from longitudinal data, one must assume that the behavior of the population of a given age today will mirror the behavior of the population of older ages today. Thus, one is assuming that when men and women currently age 30 reach the age of 50 or 60, they will behave as 50- or 60-year olds do today. Although retirement can be involuntary, it is generally a voluntary decision and typically modeled using the theory of choice, which considers the costs and benefits of retirement. The costs and benefits of retirement are a function of the unique demographic and institutional factors facing each new generation of retirees. As mentioned earlier in this chapter, the WLEs for the general population produced by the conventional and increment–decrement methods will be identical if there is a 100 percent match for all respondents, and if the LFPRs did not change over the 1- to 2-year period used to calculate TPs from CPS data. Of course, in reality, these conditions do not hold. First, the reported non-match rate is quite high in all the studies. According to articles published by Ciecka et al. (1995, 1997, 1999/2000), the match rate ranged from 68 percent to 75 percent. Ciecka et al. (1995) cite Peracchi and Welch (1995) to support the view that TPs produced using the matched sample and discarding the unmatched portion of the sample are not biased. This implies
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that the labor force exit and entry behavior of the non-matched portion of the sample is the same as the behavior of the matched portion of the sample. Peracchi and Welch show that the characteristics of the matched and unmatched portions of the sample are similar at the time of the initial survey and conclude that, thereafter, the TPs generated from the matched sample are not biased. However, unless one tracks down the unmatched respondents, one cannot conclude that their labor force behavior remained the same as the matched respondents. The very fact that they are unmatched leads one to suspect that their labor force characteristics may have changed. Analyzing the matched and unmatched respondents over a 3-year period, 1996 through 1998, Richards (2000) shows that the TPs from active to active, and inactive to active are underestimated and those from inactive to inactive, and active to inactive are overestimated. His findings challenge the Peracchi and Welch (1995) conclusions that no systematic bias exists when the unmatched are excluded from the sample. Second, LFPRs have changed over time. The LFPR for men showed a decline for several years, has stabilized in more recent years, while the LFPR for older men has shown an increase in recent years. The LFPR for women has increased continuously, but the rate of increase in the female LFPR has slowed in more recent years. Richards (2000) examines the implications of the failure to meet the above two conditions for predicting the relative size of the WLEs produced using the increment–decrement and the conventional methods. Due to the fact that the relative sizes of the WLEs are not as predicted, Richards concludes that the increment–decrement results are biased. Increment–decrementproduced WLEs should be lower than conventional WLEs if the LFPRs of the group are falling and higher if the LFPRS are rising. For males, the increment–decrement WLEs are lower than those of the conventional model in all periods, 1970, 1977, 1979/1980, 1992/1993, and 1996–1998, but they should not have been. The reason is that male LFPRs were quite stable in 1977 and in 1996–1998, but declined over the other periods. The increment–decrement-produced WLEs for women should have been greater than those produced by the conventional model in all years, because the LFPR of women has been rising. Yet, only in 1977 and 1979/1980 do the increment–decrement WLEs exceed the conventional WLEs. In these two periods, female LFPRs were rising very rapidly. As previously discussed, a condition for using a Markov process to calculate TPs is that one’s behavior is determined only by one’s current state. Richards (2000) shows that if this is not the case, then for any age group where LFPRs at that time are greater than 50 percent, the increment–
The Calculation and Use of Retirement Age Statistics
105
decrement WLE estimates will be biased downward. Given the downward biases in the WLEs for the general population calculated using the increment–decrement method, Richards concludes that there is little or no reason to use this method if LFPRs are stable. A problem remains, however, if one wishes to calculate WLEs for the active and inactive subsets of the general population. One can use the ratio of the increment–decrement-derived WLEs of the active or inactive to the increment–decrement WLEs for the general population to adjust the WLEs for the general population, as Richards suggests. Alternatively, one can use the Hunt et al. (1997, 2001) technique described in Section 4 of this chapter to adjust the WLEs of the general population to estimate the WLEs of the active population. A new BLS working paper examines the characteristics for men not in the labor force and finds that they are not homogeneous (see Stewart, 2004). The paper concludes that ‘‘there is a small group of men that have a marginal attachment to the labor force and account for the lion’s share of the total amount of time spent not working’’ (Stewart, 2004, p. 2). Thus, when calculating the WLE for an active male or one with a long work history who has just become inactive, one is calculating the future person-years in the labor force using TPs from inactive to active that do not reflect this individual’s WLE. The results in this paper strongly suggest that there are two distinct populations, whose labor force behavior should not be intertwined. This level of heterogeneity among men not in the labor force is likely to be more pronounced for women.
6. YEARS TO FINAL SEPARATION So far in this chapter, all discussion and comparison of worklife statistics have been for WLE results. An alternative measure of worklife is years to final separation from the labor force (hereafter YFS). Recognizing that the BLS WLEs did not adequately address the concept of lost earning capacity, Nelson (1983) produced worklife estimates representing the median age at final separation from the labor force. Subtracting the individual’s current age from the median age at final separation, Nelson estimated the years the person potentially had available for work. 6.1. Published YFS Data The first YFS were median statistics published by David Nelson in the Monthly Labor Review (1983) using 1977 increment-decrement data. This
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TAMORAH HUNT ET AL.
study was followed by median YFS produced by Shirley Smith with the BLS (unpublished data) using 1979/1980 increment-decrement data and the Nelson model. In 1989, Frasca and Winger utilized 1979/1980 increment-decrement data to generate the first mean YFS. Median YFS were later updated in Hunt et al. (1997) using 1992/1993 CPS data and again in Hunt et al. (2001) using 1998/1999 CPS data. Most recently, Skoog and Ciecka (2003) have calculated both mean and median YFS using 1998/1999 data for both the active and inactive populations. In addition to calculating mean and median YFS, Skoog and Ciecka expanded their analysis to include the standard deviation, mode, skewness, and kurtosis of the YFS probability mass function.
6.2. Calculation of YFS The concept of median YFS is a simple one. The percentage of the civilian population in the labor force (the actives) gradually declines from its maximum (reached usually around age 25). While there will be some transitions from active to inactive and vice versa, these have a very small influence on the behavior of the actives, the vast majority of whom are in the labor force continuously. The gradual decline in the labor force is from mortality, disability, and retirement of the continuously active. In the Nelson paper, median YFS is defined as the number of years at which 50 percent of those in the base age group will have permanently separated from the labor force. For instance, if a sample of 10,000 males aged 50 are currently in the labor force, then the median YFS will be the years it takes for 5,000 males to remain in the labor force. Mean YFS is defined as the expected number of years before a person of a particular age will permanently leave the work force, compared to WLE, which was defined earlier in this chapter as the mean number of years that persons of a particular age will participate in the labor force over the remainder of their lives. Mean YFS always exceeds WLE, because YFS includes temporary inactive time. Similarly, median YFS exceeds median worklife. The median should be a more reliable measure of YFS than the mean for two reasons: First, the calculation of the mean requires a complete record of labor force behavior by age through the cutoff age, say 76. The estimates of TPs are least reliable for very old individuals due to small sample size and frequent non-matching during re-sampling. The median calculation requires data on labor force behavior only through the 50th percentile, which is
The Calculation and Use of Retirement Age Statistics
107
usually in the early or mid-60s. Second, medians are insensitive to consistent bias, since the median will be unaffected if the measured LFPRs are all too high or too low. For example, if LFPRs are underestimated (or overestimated) by a few percent throughout the age distribution, the mean will be correspondingly biased, but the median will be virtually unchanged. According to Frasca and Winger (1989, p. 105), the mean YFS ‘‘weights each worker’s experience by the years to final separation.’’ Using crosssectional data, Frasca and Winger calculated the mean YFS indirectly using TPs. They first calculated the probability that a currently active person would be active at age n (the age at final separation). Second, they calculated the probability that someone active at age n would become and remain inactive until death. Third, the product of these probabilities was then used to weight each possible age for final separation. Skoog and Ciecka’s (2003) mean and median YFS values are derived from their ‘‘probability mass function’’ of YFS, based on assumptions outlined by the authors.9 That is, they have listed, for each exact age x, the probability that final separation from the labor force will occur at age x, x þ 1; etc., out to age 75, beyond which we assume that individuals do not participate in the labor force. Indeed, if such a probability distribution was achievable, then all statistical parameters could be calculated, including mean, median, higher moments, quintiles, etc. According to Skoog and Ciecka, the Frasca and Winger results would be equivalent to their mean YFS ‘‘if appropriate adjustments were made for midpoint transitions’’ (see Skoog & Ciecka, 2003, p. 55).
6.3. Calculating YFS for Younger Ages A problem with the method of calculating median YFS used by Nelson, Smith, and Hunt, Pickersgill, and Rutemiller occurs when one tries to estimate median YFS for very young ages. The LFPR is low for individuals in their early 20s, because participation is delayed, primarily for additional education. Nearly all these individuals will eventually be in the labor force, and the labor force will grow. One can approximate the YFS by using the same retirement age for those below age 25 as for individuals at age 25 (or at whatever age the LFPR reaches a maximum percentage). Skoog and Ciecka avoid the problem of calculating YFS for younger ages by considering actives and inactives separately, but this produces a distortion. These authors use a memoryless Markov model, which treats all inactives as equally likely to become active. Essentially, they designate the
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TAMORAH HUNT ET AL.
large group of students in their early 20s (almost certainly to become labor force members later) as inactives, thereby increasing WLE and median YFS for all inactives and decreasing these estimates for actives at very young ages.
6.4. Comparison of YFS Table 6 outlines the above-referenced YFS10 results for the active population that will be compared in Figs. 11 and 12. The comparison will be limited to median results. One can see in Fig. 11 that the 1998/1999-SC median YFS for all males exceeds the median YFS for all males produced in the other studies by more than 2 years for most ages up to approximately age 60. At this point, the 1998/1999-SC median YFS transitions to become the lowest YFS by age 68. The 1979/1980-BLS reports the lowest median YFS for ages less than 60, lower than the 1977-BLS, 1992/1993-HPR and 1998/1999-HPR YFS results by up to 1.25 years. At age 60, the 1979/1980-BLS transitions to become the highest YFS by age 64. The 1977-BLS, 1992/1993-HPR and 1998/1999-HPR results are fairly close to one another for most years up to about age 60. Figure 12 for all females shows similar relationships, with the 1998/1999SC median YFS higher by more than one year for most ages up to age 60, after which the 1998/1999-SC transitions to become the lowest YFS by age 64. Again, the 1979/1980-BLS provides the lowest YFS for all ages up to 52, after which the 1979/80-BLS transitions to become the highest YFS by age 61 (Figs. 13 and 14). Table 6. Chapter Reference
Nelson, BLS (1983) Smith, BLS (unpublished) Frasca and Winger (1989) Hunt, Pickersgill and Rutemiller (1997) Hunt, Pickersgill and Rutemiller (2001) Skoog and Ciecka (2003)
Studies Compared in Figs. 11–14. Labor Force Data Year(s)
Mathematical Statistic
Condensed Reference
1977 1979/1980 1979/1980 1992/1993
Median Median Mean Median
1970-BLS 1979/1980-BLS 1979/1980-FW 1992/1993-HPR
1998/1999
Median
1998/1999-HPR
1998/1999
Mean, Median
1998/1999-SC
109
The Calculation and Use of Retirement Age Statistics 75.0 74.0 73.0 72.0 71.0
Current Age + YFS
70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0
.0
.0
69
.0
67
.0
65
.0
63
.0
61
.0
59
.0
57
.0
55
.0
53
.0
51
.0
49
.0
47
.0
45
.0
43
.0
41
.0
39
.0
37
.0
35
.0
33
.0
31
.0
29
27
25
.0
60.0 Age 1977-BLS
1979/80-BLS
1992/93-HPR
1998/99-HPR
1998/99-SC
Fig. 11. Comparison of Median YFS for Total Males – Active Population, 1977–1998/1999.
Considering the problems with mapping a stationary population to cohorts and the difficulties in survey-sampling methods (including nonresponse problems), median YFS estimates are surprisingly stable. The reason is simple. Retirement is largely a conscious choice, dominated by pension plans such as social security. One should therefore expect median
110
TAMORAH HUNT ET AL. 75.0 74.0 73.0 72.0 71.0
Current Age + YFS
70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0
.0
.0
69
.0
67
.0
65
.0
63
.0
61
.0
59
.0
57
.0
55
.0
53
.0
51
.0
49
.0
47
.0
45
.0
43
.0
41
.0
39
.0
37
.0
35
.0
33
.0
31
.0
29
27
25
.0
60.0 Age 1977-BLS
Fig. 12.
1979/80-BLS
1992/93-HPR
1998/99-HPR
1998/99-SC
Comparison of Median YFS for Total Females – Active Population, 1977–1998/1999.
YFS estimates to be in the early 60s (after discounting for mortality and disability). Indeed that is what a comparison of the Nelson, Smith, and Hunt, Pickersgill, and Rutemiller methods show, even though Nelson and Smith used TPs to generate LFPRs and Hunt, Pickersgill, and Rutemiller used LFPRs directly. Given identical data and a 100 percent match of the
111
The Calculation and Use of Retirement Age Statistics 76.0 75.0 74.0 73.0 72.0 71.0
Current Age + YFS
70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0
25 .0 27 .0 29 .0 31 .0 33 .0 35 .0 37 .0 39 .0 41 .0 43 .0 45 .0 47 .0 49 .0 51 .0 53 .0 55 .0 57 .0 59 .0 61 .0 63 .0 65 .0 67 .0 69 .0
60.0 Age 1979/80-FWMEAN
Fig. 13.
1979/80-BLSMED
1998/99-SCMEAN
1998/99-SCMED
Comparison of YFS Data for Total Males – Active Population, 1979/1980 and 1998/1999 (Mean and Median).
sample, the calculation of median YFS by Hunt, Pickersgill, and Rutemiller using LFPRs and YFS by Nelson and Smith using TPs should give identical estimates of YFS. Both estimates use participation rates by age, but these rates must be estimated indirectly when TPs are used. LFPRs are simpler to determine and less subject to bias than TPs due to attenuation of the resampled population.
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TAMORAH HUNT ET AL. 76.0 75.0 74.0 73.0 72.0 71.0
Current Age + YFS
70.0 69.0 68.0 67.0 66.0 65.0 64.0 63.0 62.0 61.0
25 .0 27 .0 29 .0 31 .0 33 .0 35 .0 37 .0 39 .0 41 .0 43 .0 45 .0 47 .0 49 .0 51 .0 53 .0 55 .0 57 .0 59 .0 61 .0 63 .0 65 .0 67 .0 69 .0
60.0
Age 1979/80-FWMEAN
Fig. 14.
1979/80-BLSMED
1998/99-SCMEAN
1998/99-SCMED
Comparison of YFS Data for Total Females – Active Population, 1979/1980 and 1998/1999 (Mean and Median).
7. USING WLE AND YFS TO FORECAST FUTURE EARNINGS AND EARNING CAPACITY There are many factors influencing LFPRs and the age of final separation from the labor force that produce differences among groups at a moment
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in time and changes for all groups over time. Both conventional and increment–decrement models attempt to capture differences among subsets of the total population, but neither model captures changes in labor force behavior over time. Yet, we know that behavior has changed dramatically over time and that WLEs produced in an earlier period would not have been good predictors of actual worklife as history unfolded. The YFS produced from the 1970s to date have been more stable, but they too may show significant change in the future as a result of changes in demographics and the laws and institutions affecting the marginal costs and marginal benefits of retirement. Several changes have in fact taken place recently that affect the retirement decision. The literature surveyed in the remainder of this chapter is not statistical in nature and does not examine or test hypotheses regarding the role individual factors play in the retirement decision. The surveys do not analyze which of these factors have been important, but rather attempt to simply reflect the retirement choices that have already been made. For a review of the literature on recent retirement behavior, see Gendell and Siegel (1992), Purcell (2000), Wiatrowski (2001), and EBRI (2003).
7.1. Social Security Social Security is an important factor influencing age at retirement. The introduction of the Social Security Act in 1935 and its expanded coverage, including the addition of Medicare beginning in 1965, have been important factors in reducing retirement ages. According to Purcell (2000), empirical evidence shows that more retirements have occurred at ages 62 and 65 than at any other age. The ability of those born prior to 1937 to receive reduced benefits at age 62 and full benefits at age 65, provided one was not working, created a powerful incentive to retire between those two ages. Recent changes in the Social Security Act beginning in the 1980s and the implementation of age discrimination laws have increased the benefits from later retirement. To this end, the minimum age to collect full benefits now increases gradually from age 65 for those born in 1937 to age 67 for those born in or after 1960. Furthermore, the penalty for early retirement at age 62 increases gradually from 20 percent for those born in 1937 to 30 percent for those born beginning in 1960 (see Treanor, Detlefs, & Myers, 2003). One can now work and collect benefits after full retirement age, regardless of the level of one’s employment income. This factor should work to extend the average age of retirement. The benefit payments from deferring social
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security benefits beyond full retirement age have also risen, further increasing the incentive to delay retirement (see Purcell, 2000). Due to increased U.S. life expectancies and the declining worker/retiree ratio, economists and policymakers have recognized the need to reduce the future cost of social security. This may take the form of reduced benefits, a further increase in the minimum age to collect full benefits, an increased penalty for collecting benefits before full retirement age, reduced cost of living adjustments (COLAs) upon retirement, and a delay in the eligibility age for Medicare. All of these changes would increase the incentive to delay retirement.
7.2. Private Pensions and Other Forms of Deferred Compensation The traditional private and public defined-benefit pension plan contained many features, which created incentives for early retirement. Many plans incorporated a ceiling on the maximum years of service credit used in the formula to calculate pension benefits. Full benefits were often available before age 65, with unreduced benefits available at 62 and reduced benefits at 55. Under defined benefit plans, workers are unable to collect their retirement benefits and continue working for the same employer or perhaps in the same industry, except in unusual circumstances. Defined benefit pension plans are currently being replaced by defined contribution plans, which do not penalize a worker for postponing retirement. The present value of most defined benefit plans reaches a maximum between ages 62 and 65, while the present value of defined contribution plans continues to increase for as long as one continues to work. In addition, defined contribution plans provide less certain retirement benefits than traditional retirement plans, as the recent decline in the stock market has reminded us.
7.3. Trends in Health and Health Insurance Funding Americans increasingly work in jobs that are less physically demanding, while living longer, healthier lives. Both of these factors increase the capacity to work longer, not to mention the desire for higher levels of retirement income. According to the U.S. Department of Health and Human Services (1994, 2002), the life expectancy at birth in the United States increased from 75.4 years in 1990 to 76.9 years in 2000, an average annual
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increase of 1.8 months per year. Such continued increases would add another year of life expectancy every 6.7 years. There are increasing concerns about the cost of health care during retirement, given that employers have become less likely to provide health insurance coverage for retirees. This, too, will increase the incentive to remain employed.
8. CONCLUSION A review of the methodology and the results of current models used to calculate WLE and YFS, as well as a consideration of changing incentives to work and retire, should caution the users of these studies as to the accuracy of such statistics for predicting future retirement behavior. All WLE and YFS calculations are approximations based on the behavior of the labor force during the sample period. The calculated results are based on crosssectional data, not longitudinal data, which would provide data on the labor force entries and exits of a specific worker throughout his worklife. Even with longitudinal data, given the increased life expectancy in the U.S. and the institutional changes involving social security and private pensions, current WLE and YFS are likely to underestimate the labor force attachment of workers over the next several decades. Calculations of standard deviations and other properties of WLE and YFS, even if accurate, would only apply to behavior in the base year and certainly not to people retiring many years in the future. The studies discussed in this chapter are not without value. It is important to understand such studies and the different methods used to produce worklife statistics. The calculations of WLE and YFS, however, are statistical analyses of past events. They are even approximations of historical WLE and retirement ages due to data limitations. There are issues, major and/or minor, with each study. Furthermore, by their very design, the studies are devoid of economic theory and are not designed to be predictive. They do not model labor force choices or consider the economic and institutional variables affecting the retirement decision.
NOTES 1. An exception to this is the Richards and Abele results using 1990 Census data, which will be discussed later in this chapter.
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2. The active population includes those employed or looking for work, and the inactive population includes those not employed and not looking for work. 3. HPR (2001) omitted WLEs for the total general population, but these have been calculated and used to compare HPR results to those of other authors discussed in this paper. 4. WLF does not represent continuous years of labor force participation from current age. 5. See BLS Bulletin 2135 for a description of the methodology. 6. Using a moving average smoothes out sudden bumps in transition probabilities. In this case, each year’s transition probabilities are the mean value for the most recent nine collection periods. 7. Skoog and Ciecka do not state these three major assumptions, but they are necessary to assert that a probability mass function has been obtained. 8. See Hunt et al. (1997, pp. 177–205). 9. For an explanation of their methodology, see Section 3 of Skoog and Ciecka (2003). 10. In this chapter, the comparison of YFS will be limited to ages 25 and over.
REFERENCES Ciecka, J., Donley, T., & Goldman, J. (1995). A Markov process model of worklife expectancies based on labor market activity in 1992–93. Journal of Legal Economics, 5(3), 17–41. Ciecka, J., Donley, T., & Goldman, J. (1997). A Markov process model of worklife expectancies based on labor market activity in 1994–95. Journal of Legal Economics, 7(1), 2–25. Ciecka, J., Donley, T., & Goldman, J. (19992000). A Markov process model of work-life expectancies based on labor market activity in 1997–98. Journal of Legal Economics, 9(3), 33–68. Ciecka, J., Donley, T., & Goldman, J. (2000). A Markov process model of work-life expectancies for ages 66–75 based on labor force activity in 1997–98. Journal of Legal Economics, 10(2), 27–36. Ciecka, J., Donley, T., & Goldman, J. (20002001). A Markov process model of work-life expectancies by educational attainment based on labor force activity in 1997–98. Journal of Legal Economics, 10(3), 1–22. Employee Benefit Research Institute (EBRI) (2003). The 2003 retirement confidence survey, summary of findings. Washington, DC. Frasca, R., & Winger, B. (1989). An investigation into the Nelson median and the mean age at final separation from the labor force. Journal of Forensic Economics, 2(3), 103–114. Fullerton, H. N., & Byrne, J. J. (1976). Length of working life for men and women, 1970. Monthly Labor Review, 99(2), 31–35. Gendell, M., & Siegel, J. S. (1992). Trends in retirement age by sex, 1950–2005. Monthly Labor Review. (July), 22–29. Hunt, T., Pickersgill, J., & Rutemiller, H. (1997). Median years to retirement and worklife expectancy for the civilian U.S. population. Journal of Forensic Economics, 10(2), 171–205. Hunt, T., Pickersgill, J., & Rutemiller, H. (2001). Recent trends in median years to retirement and worklife expectancy for the civilian U.S. population. Journal of Forensic Economics, 14(3), 203–228.
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Nelson, D. M. (1983). The use of worklife tables in estimates of lost earning capacity. Monthly Labor Review, 106(4), 30–31. Peracchi, F., & Welch, F. (1995). How representative are matched cross-sections? Evidence from the current population survey. Journal of Econometrics, 68, 153–179. Purcell, P. J. (2000). Older workers: Employment and retirement trends. Monthly Labor Review, 123(10), 19–30. Richards, H. (2000). Worklife expectancies: Increment–decrement less accurate than conventional. Journal of Forensic Economics, 13(3), 271–289. Richards, H., & Abele, J. (1999). Life and worklife expectancies. Tucson: Lawyers and Judges Publishing Company. Skoog, G. R., & Ciecka, J. E. (2001). A Markov (increment–decrement) model of labor force activity: New results beyond work-life expectancies. Journal of Legal Economics, 11(1), 1–22. Skoog, G. R., & Ciecka, J. E. (2001). The Markov (increment–decrement) model of labor force activity: Extended tables of central tendency, variation, and probability intervals. Journal of Legal Economics, 11(1), 23–87. Skoog, G. R., & Ciecka, J. E. (2003). Probability mass functions for years to final separation from the labor force induced by the Markov model. Journal of Forensic Economics, 16(1), 51–86. Smith, S. (unpublished) Median age of final labor force separation: 1979/80. Unpublished data. Office of Employment and Unemployment Statistics, Bureau of Labor Statistics, U.S. Department of Labor. Stewart, J. (2004). What do male nonworkers do? Working Paper Series: No. 371. Office of Employment and Unemployment Statistics, Washington, DC. Treanor, J. R., Detlefs, D. R., & Myers, R. J. (2003). 2003 social security and medicare. Kentucky: Mercer Human Resource Consulting, Inc. U.S. Department of Health and Human Services (1994). Vital statistics of the United States, 1990, life tables. Hyattsville, Maryland. U.S. Department of Health and Human Services (2002). Vital statistics of the United States, 2000, life tables. Hyattsville, Maryland. U.S. Department of Labor, Bureau of Labor Statistics (BLS) (1982). Bulletin 2135, tables of working life: The increment–decrement model. Washington, DC. (Prepared by Shirley Smith). U.S. Department of Labor, Bureau of Labor Statistics (BLS) (1982). Bulletin 2157, new worklife estimates. Washington, DC. (Prepared by Shirley Smith). U.S. Department of Labor, Bureau of Labor Statistics (BLS) (1986). Bulletin 2254, worklife estimates: Effects of race and education. Washington, DC. U.S. Department of Labor, Bureau of Labor Statistics (BLS). (2003). Employment and Earnings, 50(11), 166. Wiatrowski, W. J. (2001). Changing retirement age: Ups and downs. Monthly Labor Review, 124(4), 3–12.
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RECENT DEVELOPMENTS IN THE MEASUREMENT OF LABOR MARKET ACTIVITY Gary R. Skoog and James E. Ciecka 1. WORKLIFE EXPECTANCY AND RECENT ADVANCES BEYOND WORKLIFE EXPECTANCY 1.1. Brief History of Worklife Expectancy Tables in the United States In the most recent survey of members of the National Association of Forensic Economics (NAFE) (Brookshire, Luthy, & Slesnick, 2003), the authors write that ‘‘it is clear that issues related to worklife are at the top of the list’’ of the members’ preferences for forensic economics research. Worklifedisabled, worklife-self-employed, and worklife-general were ranked #1, #2 and #5 among 20 categories. This chapter addresses two out of these three topics. Worklife of the self-employed is not addressed, and the authors are not aware of any quantitative papers on this point. The U.S. Bureau of Labor Statistics (BLS, 1950, 1957, 1982, 1986) has calculated worklife expectancies spanning the entire twentieth century. For example, Garfinkle (1955) estimated a worklife expectancy (WLE) of 39.4
Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 119–157 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87006-8
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years for 20-year-old men (whose remaining life expectancy was only 42.2 years) for 1900; further, he predicted a WLE of 45.1 years for 20-year-old men for 2000, with a life expectancy of 53.8 years based on a Social Security Administration study. BLS Bulletin 1001 (1950) contained worklife tables for men by race and urban-rural residence for 1940 and 1947. Bulletin 1204 (1957) dealt with worklife expectancies for women by marital status for 1940 and 1950. Wolfbein (1949) published worklife estimates independently from the BLS for men for 1940, using methods similar to an earlier study that produced worklife estimates based on labor market activity for 1890–1900. Fullerton and Byrne (1976) reported worklife expectancies for men and women (by marital status and birth of the last child) using 1970 data. All of this work was based on what the BLS calls the conventional model: ‘‘Men enter and leave the labor force only once, and (that) women enter and leave only as the result of specific changes in marital and parental status’’ (BLS, Bulletin 2135, 1982). The BLS made a dramatic break from its conventional model in Bulletin 2135 when it introduced the Markov, or increment–decrement, model which viewed people as ‘‘entering and leaving the labor market repeatedly during their lifetimes, with nearly all participating for some period during their lives.’’ The BLS used the Markov model to produce worklife estimates for men and women by labor force status (i.e., initially active and inactive) and without regard to the labor market status for 1977 (Bulletin 2135) and for men and women by labor force status and with and without regard to status by education or race for 1979–1980 (Bulletin 2254, 1986). Regardless of whether the conventional model or the Markov model was used, the main objective of all the foregoing work was to produce a single number WLE, given the age, gender, and other characteristics (that varied from one study to another) such as education, marital status, and parental status. WLE is the expected value, or mean, of years of labor market activity; but until recently, no one was able to answer basic questions including: What are the values of other measures of central tendency like the median and mode? What is the shape of the distribution of years of activity (YA)? What is the probability that YA will fall within an interval of a given length, and what is the length of a YA interval given a certain probability level? In short, what is the entire probability distribution of YA? Although these questions can be successfully answered within the context of both the conventional model and the Markov model, the theoretical and empirical work we report below is based on the Markov model, which is superior to the conventional model.
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1.2. Recent Theoretical Developments in Analyzing Time in the Labor Force and Time to Final Separation from the Labor Force The Markov model employs probabilistic concepts (transition probabilities, (i.e., the probability of changing labor force status or remaining in the same status from one age to the next age) with embedded mortality probabilities) that permit one to determine various mathematical expectations. Before our recent work with the Markov model, no one had thoroughly exploited the model’s probabilistic implications. There had been no discussion of sample paths, i.e., the statistical distribution of functions of statuses several years into the future, conditional on current status. Once a model is analyzed and/or augmented so as to permit the specification of such general distribution functions, one has broken through the barrier that had restricted previous study only to expectations. Our theoretical framework permits the study of natural random variables, such as YA and years to final labor force separation (YFS), among several others. Any statistic involving these random variables, such as the mean, median, or mode, may now be studied in the population and in a sample. We may thus compare an estimator claimed to be estimating some ‘‘median’’ with proper estimators of the median, within the context of any particular model.1 We now have estimates of the entire probability distributions of YA and YFS, and we have estimated many of its parameters (and can compute any others that may be of interest). For example, we have constructed probability intervals that are consistent with the ideas of economic and statistical certainty such as ‘‘more probable than not’’ and ‘‘to within a reasonable degree of economic certainty.’’ In this section of the chapter, we summarize our recent work in analysis of YA and YFS. YA only counts time spent in the labor force, but YFS includes all time (whether in or out of the labor force) until the last exit from the labor force. We treat both YA and YFS as random variables that possess probability mass functions (pmfs). The goal is to find the pmf or statistical distribution for YA and YFS, and thereby to be able to compute for YA and YFS any characteristic of interest. (A pmf assigns a specific probability value (i.e., mass value) to every possible outcome of a random variable. For example, consider the years-of-activity random variable YA for people currently active in the labor force that takes on half-integer values of 0.5, 1.5, 2.5, yyears due to the mid-point transition assumption. The pmf gives the probability that YA ¼ 0:5 years, YA ¼ 1:5 years, YA ¼ 2:5 years, etc. Of course, the sum of these probabilities must be 1.0.) Our
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tables show three measures of central tendency (mean, median, and mode), the standard deviation as a measure of dispersion, two measures of shape (skewness (lack of symmetry) and kurtosis (thickness of the tails and height of the peak of the pmf)), and three probability intervals (the smallest interval that contains 50% of all probability mass, the inter-quartile range (the interval, which excludes 25% of the probability mass in each tail), and an interval, which excludes 10% of the probability from each of the tails of the pmf). The minimal 50% interval and the inter-quartile range may be of special interest because they capture the idea of YA and YFS being accurate to a reasonable degree of economic and statistical certainty, or what is more probably true than not true. The theoretical and empirical work we present here can be found in Skoog (2002b) and in Skoog and Ciecka (2001a, b, 2002, 2003). The defining features of the Markov model of labor market activity are that labor force transitions occur between the current state (a (for active), or i (for inactive)) and the next period’s state (a, i, or d), transition probabilities depend only on the current state, and only the death state (d) is absorbing. Transitions can occur at the beginning, end, or mid-point of a period, which is taken to be one year. A pmf is defined by a set of global conditions (which hold whether transitions occur at the beginning, end, or mid-point), boundary conditions describing the mass functions near zero additional years (which generally depend on when transitions occur), and main recursions, which define probability mass values beyond those specified in the boundary conditions. See Skoog and Ciecka (2001a) for a heuristic discussion of pmfs. Let YAx;m denote the years-of-activity random variable with pYA ðx; m; yÞ being the probability that a person who is in state m at exact age x will accumulate YAx;m ¼ y years of labor force activity in the future. Similarly, let YF Sx;m denote the years-to-final-separation random variable with pYFS ðx; m; yÞ being the probability that a person who is in state m at exact age x makes a final separation from the labor force in YF S x;m ¼ y years. The probability that a person who is in state m at age x will be in state n at age x þ 1 is denoted by m pnx where m A{a,i}, n A{a,i,d} and, a pax þ a pix þ pdx ¼ 1; i pax þ i pix þ pdx ¼ 1; where, as is customary, we assume a pdx ¼ i pdx pdx : We assume that transitions between state m at age x and state n at age x þ 1 occur at age x þ 0:5 (i.e., mid-period transitions). We define BA (beginning age) to be the earliest exact age at which labor force activity becomes possible. Define TA (truncation age) to be the youngest exact age at which everyone is dead. On the assumption that labor force activity is
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always possible if a person is alive at age BA or beyond, TA is the youngest exact age at which no labor force activity can occur. Everyone alive at age TA 1 dies at age TA 0:5; so a pdTA 1 ¼ i pdTA 1 ¼ 1 since the only transition at age TA 1 is to the death state. That is, a pax ¼ a pix ¼ i pax ¼ i i px ¼ 0 for x TA 1: The YA and YFS pmfs with mid-period transitions for initial actives and inactives are specified in the boxes below. The global conditions in the first box are identical for YA and YFS. Neither negative YA or YFS can occur, nor can YA or YFS exceed the number of years until death must occur. At the truncation age TA (taken to be age 111), it is certain that there is no activity or inactivity because everyone has died, that is, all transitions at age TA 1 are to the death state. In the first YA boundary condition, we observe that an active person at age x must accumulate some positive amount of activity because transitions occur at the mid-point of the age interval (x; x þ 1). The second YA boundary condition accounts for the probability of a person active at age x accumulating exactly one-half year of future activity by dying in mid-year or turning inactive in mid-year and staying inactive thereafter. The last boundary condition expresses the observation that there are only two ways a person inactive at age x can experience no additional YA: die or remain inactive a year and repeat the process. The remaining probability mass values for YA are defined by the main recursions. The right-hand side of the first main recursion is the sum of two terms that contribute to the probability that an active person age x will accumulate y years of activity: pðx þ 1; a; y 1Þ and pðx þ 1; i; y 0:5Þ are the probabilities of experiencing y 1 and y 0:5 active years when being active and inactive at age x þ 1; respectively. If one remains active, part of the probability of y years of activity results when the former probability, which aggregates sample paths resulting from the remaining active y 1 years from age x þ 1; is multiplied by a pax : The same treatment of the sample paths resulting from an active to inactive transition, multiplied by this probability, a pix ; completes the recursion. By multiplying pðx þ 1; a; y 1Þ by a pax ; accumulated YA change from y 1 to y; similarly, y 0:5 years increase to y years when pðx þ 1; i; y 0:5Þ is multiplied by a pix : The second main recursion works in a similar manner. Transition probabilities for people who start age x as inactive are i a px and i pix ; in order to accumulate y years of activity, these probabilities must be multiplied by probabilities pðx þ 1; a; y 0:5Þ and pðx þ 1; i; yÞ for people age x þ 1 who have already accumulated y 0:5 active years and y years, respectively since i pax produced another half year of activity but i pix adds no additional amount of active time.
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In regard to YFS, if one is active, since the next transition takes place onehalf year later, one must accumulate at least one-half of an additional year of time until the final separation. Further, if one ever transitions into the active state again, one or more full years until final separation are added, so that the function pYFS ðx; a; yÞ is non-zero only on the half integers and zero on the integers. The first boundary condition recognizes that zero probability occurs for integer values of YFS. If a person is initially inactive at age x and will never return to inactivity, either that person dies at age x þ 0:5 and so realizes y ¼ 0; or that person transitions into activity and forestalls separation by 1.5, 2.5,yyears. The domain of pYFS ðx; i; yÞ where this function is positive includes zero and the half integers, skipping 0.5; and it is zero for YFS ¼ 0:5; 1; 2; 3;y The latter statement is the second YFS boundary condition. The third boundary condition gives the probability of one-half year until final separation for an active person age x as the probability of dying before age x þ 1 (thereby being credited with a half year before final labor force separation) plus the probability of zero years to final separation at age x þ 1 weighted by the probability of a transition (between age x and x þ 1) from active to inactive status (thus accumulating a half year before final separation). In the last boundary condition, an inactive person age x can have zero years before final separation by dying before age x þ 1 or by having had zero years before separation at age x þ 1 weighted by the probability of remaining inactive (thereby accumulating no time before final separation) from age x to x þ 1: In regard to the first main YFS recursion, the right-hand side is the sum of two terms that contribute to the probability that there will be y years before an active person finally separates from the labor force: pYFS ðx þ 1; a; y 1Þ and pYFS ðx þ 1; i; y 1Þ are the probabilities of separating y 1 years after age x+1 when active and inactive at age x+1, respectively; the probability of y years before final separation (from age x) results when the former probability is multiplied by a pax and the later by a pix : The last main recursion works the same way. Since i pax and i pix are the probabilities for people who start age x as inactive, multiply i pax by pYFS ðx þ 1; a; y 1Þ and i i px by pYFS ðx þ 1; i; y 1Þ; the sum of these products is the separation probability of y years for an inactive person age x. In both of the YFS main recursions, the probability pYFS ðx þ 1; m; y 1Þ; for m A{a, i}, i m when multiplied by a pm x and px ; changes the reference age from x+1 to x and adds one year to final separation time by ‘‘pushing back’’ the age index one year.
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Global conditions for random variables RV 2 fYA; YFSg with midpoint transitions. if yo0 or y4TA pRV ðx; a; yÞ ¼ pRV ðx; i; yÞ ¼ 0 pRV ðTA; a; 0Þ ¼ pRV ðTA; i; 0Þ ¼ 1 a d px ¼ i pdx ¼ 1 for x TA 1
0:5
x
YA pmfs for YAx;m ¼ y for m A{a, i} with mid-point transitions. Boundary conditions pYA ðx; a; 0Þ ¼ 0 pYA ðx; a; 0:5Þ ¼ a pdx þ a pix pYA ðx þ 1; i; 0Þ pYA ðx; i; 0Þ ¼ i pdx þ i pix pYA ðx þ 1; i; 0Þ for x ¼ BA; . . . ; TA
1
Main recursions pYA ðx; a; yÞ ¼ a pax pYA ðx þ 1; a; y
1Þ þ a pix pYA ðx þ 1; i; y
0:5Þ;
y ¼ 1:5; 2:5; 3:5 . . . TA x 0:5 pYA ðx; i; yÞ ¼ i pax pYA ðx þ 1; a; y 0:5Þ þ i pix pYA ðx þ 1; i; yÞ; y ¼ 1; 2; 3; . . . ; TA
x
0:5 for x ¼ BA; . . . ; TA
1
YFS pmfs for YF S x;m ¼ y for m A{a, i} with mid-point transitions Boundary conditions pYFS ðx; a; yÞ ¼ 0; y ¼ 0; 1; 2; 3; . . . ; TA pYFS ðx; i; yÞ ¼ 0; y ¼ 0:5; 1; 2; 3; . . . ; TA
1 1
pYFS ðx; a; 0:5Þ ¼ a pdx þ a pix pYFS ðx þ 1; i; 0Þ pYFS ðx; i; 0Þ ¼ i pdx þ i pix pYFS ðx þ 1; i; 0Þ for x ¼ BA; . . . ; TA 1 Main recursions pYFS ðx; a; yÞ ¼ a pax pYFS ðx þ 1; a; y 1Þ þ a pix pYFS ðx þ 1; i; y 1Þ pYFS ðx; i; yÞ ¼ i pax pYFS ðx þ 1; a; y 1Þ þ i pix pYFS ðx þ 1; i; y 1Þ for x ¼ BA; . . . ; TA
1 and y ¼ 1:5; 2:5; 3:5; . . . ; TA
x
0:5
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1.3. Some Illustrative Empirical Results Flowing from Recent Theoretical Advances Tables 1–8 show YA and YFS characteristics for initially active and initially inactive men and women without regard to education (see Skoog & Ciecka (2001a, 2003) for additional tables by educational attainment for initially active and inactive statuses for men and women). Figures 1–4 illustrate the pmf for 30-year-old initially active and inactive men and women without regard to education. Although different in appearance, pmfs could be graphed for each age in Tables 1–8. The characteristics of the YA and YFS random variables depend on age. For example, the mass function for an active 20-year-old male is skewed to the left: the mean or WLE (37.28 years) is less than the median (38.29), which is less than the mode (40.50) and the skewness coefficient is 1.14 (see Table 1). The standard deviation of YA is 9.39 years, and the minimal 50% probability interval is (35.58, 44.50). WLE is closer to the left end point of this interval than the right end point because of the negative skewness. By mid-life (say age 45), the YA pmf is approximately symmetrical about the mean with skewness of 0.15; and it is approximately normal with kurtosis of 2.94. The pmf for YA is skewed to the right at later ages. At age 65, for example, the skewness coefficient is 1.02 and the mean (4.20 years) exceeds the median (2.99), which exceeds the mode (0.50). The YFS random variable possesses some similar characteristics to YA. YFS also is skewed to the left at young ages, approximately normal (as indicated by approximate zero skewness and kurtosis approximately 3.0) in mid-life, and skewed to the right at older ages. However, given the age and labor force status, YFS has a larger mean, median, mode, standard deviation, and wider probability intervals than YA. For example, the separation expectancy YFSE (34.18 years) of YFS for 30-year-old active men is 4.83 years longer than WLE (see Fig. 1 and Tables 1 and 5). The standard deviation of YFS is approximately two years bigger than the standard deviation of YA, and probability intervals are somewhat wider for YFS. Figure 2 shows the pmf for 30-year-old men who are initially inactive. The separation expectancy (34.17 years) of YFS exceeds YA’s mean by 6.63 years. Although active 30-year-old men have a WLE 1.81 years longer than their inactive counterparts, the means of YFS for active and inactive men are the same within one-tenth of a year. At older ages, the separation expectancies for actives and inactives grow apart somewhat. However, not until age 44 do the separation expectancies differ by more than one-half
127
Recent Developments in the Measurement of Labor Market Activity
Table 1.
YA Characteristics for Initially Active Men, Regardless of Education. Minimal 50% PI
Inter-Quartile PI
10–90% PI
Age
WLE Mean
Median
Mode
SD
SK
KU
Low
High
25%
75%
10%
90%
16 17 18 19 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
39.47 39.01 38.50 37.95 37.28 36.63 35.94 35.20 34.42 33.62 32.79 31.95 31.09 30.22 29.35 28.48 27.61 26.75 25.89 25.03 24.17 23.32 22.47 21.62 20.77 19.94 19.11 18.29 17.46 16.64 15.82 15.01 14.21 13.42 12.63 11.86 11.10 10.37 9.66 8.97 8.30
40.58 40.10 39.57 38.99 38.29 37.61 36.87 36.09 35.28 34.44 33.58 32.69 31.79 30.88 29.97 29.05 28.14 27.23 26.32 25.41 24.50 23.59 22.68 21.78 20.87 19.98 19.09 18.20 17.31 16.43 15.55 14.67 13.80 12.94 12.09 11.25 10.43 9.63 8.85 8.09 7.35
42.50 42.50 41.50 41.50 40.50 39.50 38.50 38.50 37.50 36.50 35.50 34.50 33.50 32.50 31.50 30.50 29.50 28.50 27.50 26.50 26.50 25.50 24.50 23.50 22.50 21.50 20.50 19.50 18.50 17.50 16.50 15.50 14.50 13.50 12.50 11.50 10.50 9.50 8.50 8.50 7.50
9.88 9.77 9.65 9.51 9.39 9.26 9.12 8.99 8.87 8.75 8.63 8.52 8.41 8.31 8.19 8.08 7.96 7.84 7.72 7.59 7.46 7.34 7.21 7.08 6.94 6.80 6.66 6.52 6.38 6.24 6.10 5.96 5.82 5.67 5.53 5.38 5.23 5.07 4.91 4.76 4.60
1.21 1.20 1.18 1.16 1.14 1.11 1.08 1.05 1.02 0.98 0.95 0.92 0.88 0.85 0.81 0.78 0.74 0.70 0.66 0.62 0.58 0.54 0.49 0.45 0.40 0.36 0.31 0.26 0.20 0.15 0.10 0.04 0.01 0.07 0.13 0.19 0.26 0.32 0.39 0.46 0.53
5.22 5.18 5.13 5.07 4.99 4.91 4.82 4.72 4.61 4.50 4.40 4.30 4.21 4.11 4.02 3.92 3.83 3.74 3.65 3.57 3.49 3.41 3.34 3.27 3.20 3.14 3.08 3.03 2.98 2.94 2.90 2.87 2.85 2.83 2.82 2.83 2.84 2.87 2.90 2.95 3.01
37.50 37.29 36.50 36.50 35.58 34.66 34.50 33.50 32.89 31.96 31.02 30.07 29.13 28.18 27.23 26.50 25.50 24.50 23.50 22.54 21.61 20.68 19.75 19.50 18.50 17.50 16.50 15.50 14.50 13.50 12.55 11.66 11.50 10.50 9.50 8.50 7.50 6.58 6.50 5.50 4.50
46.81 46.50 45.62 45.50 44.50 43.50 43.26 42.18 41.50 40.50 39.50 38.50 37.50 36.50 35.50 34.71 33.65 32.59 31.52 30.50 29.50 28.50 27.50 27.16 26.07 24.97 23.87 22.77 21.66 20.56 19.50 18.50 18.21 17.07 15.92 14.76 13.60 12.50 12.22 10.99 9.75
34.66 34.22 33.74 33.22 32.57 31.92 31.25 30.53 29.75 28.94 28.12 27.28 26.43 25.57 24.69 23.82 22.95 22.09 21.24 20.40 19.56 18.71 17.87 17.03 16.21 15.40 14.60 13.79 12.99 12.20 11.42 10.63 9.86 9.10 8.36 7.64 6.92 6.25 5.60 4.96 4.37
45.37 44.84 44.26 43.63 42.89 42.16 41.38 40.57 39.72 38.86 37.97 37.06 36.14 35.21 34.27 33.33 32.39 31.46 30.52 29.59 28.66 27.72 26.79 25.86 24.93 24.00 23.08 22.16 21.23 20.31 19.39 18.47 17.57 16.68 15.79 14.91 14.04 13.18 12.34 11.51 10.73
26.79 26.43 26.02 25.60 25.02 24.50 23.90 23.28 22.61 21.89 21.17 20.42 19.65 18.87 18.10 17.35 16.60 15.85 15.12 14.41 13.69 12.98 12.29 11.61 10.92 10.27 9.63 8.99 8.37 7.73 7.10 6.52 5.91 5.35 4.78 4.25 3.75 3.28 2.84 2.45 2.03
49.41 48.85 48.24 47.56 46.81 46.06 45.26 44.41 43.55 42.67 41.77 40.86 39.93 38.99 38.05 37.10 36.15 35.21 34.26 33.31 32.36 31.41 30.46 29.51 28.57 27.63 26.70 25.77 24.84 23.90 22.97 22.04 21.12 20.20 19.28 18.37 17.47 16.59 15.74 14.89 14.06
128
GARY R. SKOOG AND JAMES E. CIECKA
Table 1. (Continued ) Minimal 50% PI Age 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Inter-Quartile PI
10–90% PI
WLE Mean
Median
Mode
SD
SK
KU
Low
High
25%
75%
10%
90%
7.65 7.04 6.48 5.97 5.51 5.12 4.77 4.47 4.20 3.96 3.74 3.53 3.36 3.19 3.01 2.81 2.61 2.44 2.26
6.65 5.99 5.38 4.83 4.34 3.92 3.55 3.26 2.99 2.74 2.52 2.35 2.22 2.10 1.94 1.76 1.58 1.50 1.38
6.50 5.50 4.50 3.50 2.50 2.50 1.50 1.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
4.44 4.28 4.13 3.97 3.82 3.66 3.51 3.37 3.22 3.08 2.94 2.81 2.67 2.52 2.37 2.22 2.06 1.90 1.73
0.60 0.67 0.74 0.80 0.86 0.91 0.95 0.99 1.02 1.04 1.06 1.06 1.05 1.05 1.05 1.06 1.06 1.07 1.13
3.08 3.16 3.25 3.35 3.44 3.53 3.61 3.68 3.73 3.76 3.78 3.77 3.75 3.75 3.76 3.79 3.83 3.94 4.19
3.50 2.75 2.50 1.50 1.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
8.50 7.50 6.93 5.62 5.28 3.92 3.55 3.26 2.99 2.74 2.52 2.35 2.22 2.10 1.94 1.76 1.58 1.50 1.38
3.79 3.26 2.78 2.36 2.01 1.72 1.48 1.30 1.14 1.02 0.90 0.79 0.71 0.66 0.59 0.52 0.50 0.50 0.50
9.96 9.22 8.52 7.89 7.30 6.79 6.32 5.92 5.53 5.23 4.94 4.64 4.38 4.14 3.88 3.62 3.36 3.08 2.72
1.67 1.34 1.04 0.79 0.59 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
13.25 12.45 11.73 11.05 10.39 9.82 9.29 8.80 8.33 7.91 7.47 7.13 6.78 6.39 5.99 5.48 5.08 4.63 4.24
year. At age 50 the separation expectancy for actives exceeds that of inactives by 1.2 years and by 1.76 years at age 55. Figures 3 and 4 show related results for women. Active (inactive) 30-yearold women have mean YFS approximately seven (nine) years longer than for YA. As with men age of 30, there is practically no difference in the separation expectancy of YFS with respect to labor force status. By age 43, the separation expectancy of actives is 0.54 years longer than for inactive women; the difference is 2.43 years at age 55. The mean YFS gender gap between active (inactive) men and women is only 1.85 (1.87) years, but WLE differs by 4.18 (4.77) years at age 30. That is, younger men and women are more similar in regard to YFSE than WLE. This also tends to be the case for other characteristics for YFS and YA at younger ages. However, older men and women are less similar in regard to YFSE than WLE. By age 60, the YFS mean gender difference for actives (inactives) is 1.66 years (2.25 years), but it is only 0.89 years (0.98 years) for YA, respectively.
129
Recent Developments in the Measurement of Labor Market Activity
Table 2.
YA Characteristics for Initially Inactive Men, Regardless of Education. Minimal 50% PI
Age
WLE Mean
Median
Mode
SD
SK
KU
Pr(0)
Low
High
Inter-Quartile PI 25%
75%
10–90% PI 10%
90%
16
38.27
39.87
42.00
9.88
1.20
5.19
0.00
36.78
46.00
33.95
44.67
26.08
48.72
17
37.87
39.45
41.00
9.78
1.19
5.14
0.00
36.00
45.16
33.57
44.21
25.77
48.24
18
37.32
38.87
41.00
9.67
1.17
5.08
0.00
35.91
45.00
33.03
43.60
25.32
47.60
19
36.63
38.15
40.00
9.54
1.14
5.00
0.00
35.00
43.99
32.36
42.84
24.73
46.82
20
36.02
37.51
39.00
9.42
1.12
4.92
0.00
34.08
43.00
31.75
42.16
24.21
46.12
21
35.35
36.80
38.00
9.29
1.09
4.83
0.00
34.00
42.87
31.09
41.41
23.65
45.35
22
34.63
36.04
38.00
9.17
1.06
4.73
0.00
33.00
41.79
30.38
40.62
23.01
44.53
23
33.87
35.25
37.00
9.05
1.02
4.63
0.00
32.27
41.00
29.62
39.80
22.36
43.70
24
33.09
34.43
36.00
8.93
0.99
4.51
0.00
31.32
40.00
28.83
38.96
21.67
42.85
25
32.27
33.58
35.00
8.82
0.95
4.40
0.00
30.36
39.00
28.00
38.09
20.92
41.97
26
31.38
32.65
34.00
8.72
0.92
4.29
0.00
29.39
38.00
27.10
37.15
20.10
41.02
27
30.46
31.69
33.00
8.63
0.88
4.17
0.00
28.41
37.00
26.16
36.18
19.23
40.05
28
29.51
30.71
32.00
8.54
0.84
4.06
0.00
27.43
36.00
25.19
35.20
18.34
39.07
29
28.54
29.70
31.00
8.47
0.80
3.94
0.01
26.42
35.00
24.19
34.19
17.41
38.07
30
27.54
28.67
30.00
8.39
0.76
3.82
0.01
25.46
34.00
23.16
33.17
16.45
37.05
31
26.53
27.61
29.00
8.32
0.71
3.69
0.01
24.46
33.00
22.10
32.13
15.45
36.01
32
25.48
26.53
28.00
8.26
0.67
3.57
0.01
23.46
32.00
21.00
31.06
14.41
34.95
33
24.41
25.42
27.00
8.19
0.62
3.44
0.01
22.46
31.00
19.89
29.97
13.34
33.87
34
23.35
24.33
26.00
8.12
0.58
3.33
0.01
21.46
30.00
18.79
28.90
12.30
32.80
35
22.32
23.26
25.00
8.06
0.53
3.21
0.01
20.00
28.52
17.70
27.84
11.27
31.76
36
21.27
22.17
24.00
8.00
0.48
3.10
0.02
19.00
27.50
16.60
26.77
10.23
30.70
37
20.20
21.06
23.00
7.93
0.43
2.99
0.02
18.00
26.47
15.48
25.68
9.17
29.61
38
19.15
19.95
22.00
7.85
0.38
2.89
0.02
17.00
25.42
14.37
24.60
8.13
28.54
39
18.12
18.87
21.00
7.77
0.33
2.80
0.03
15.65
24.00
13.28
23.53
7.14
27.48
40
17.09
17.78
19.00
7.67
0.27
2.71
0.03
14.76
23.00
12.20
22.46
6.16
26.42
41
16.09
16.72
18.00
7.57
0.22
2.64
0.04
13.89
22.00
11.15
21.40
5.23
25.38
42
15.10
15.66
17.00
7.45
0.16
2.57
0.04
13.00
20.96
10.11
20.35
4.33
24.33
43
14.12
14.60
16.00
7.31
0.09
2.51
0.05
12.00
19.77
9.09
19.29
3.48
23.28
44
13.19
13.59
0.00
7.16
0.03
2.47
0.06
11.00
18.54
8.12
18.27
2.68
22.25
45
12.29
12.60
0.00
7.01
0.03
2.43
0.07
10.00
17.29
7.19
17.27
1.96
21.25
46
11.42
11.63
0.00
6.84
0.10
2.41
0.08
9.02
16.00
6.29
16.28
1.30
20.26
47
10.55
10.65
0.00
6.66
0.17
2.41
0.10
8.35
15.00
5.41
15.28
0.68
19.26
48
9.71
9.69
0.00
6.46
0.25
2.43
0.11
7.73
14.00
4.55
14.29
0.00
18.26
49
8.90
8.75
0.00
6.25
0.33
2.46
0.13
7.00
12.84
3.74
13.32
0.00
17.27
50
8.13
7.83
0.00
6.02
0.42
2.52
0.15
5.64
11.00
2.98
12.36
0.00
16.30
51
7.38
6.94
0.00
5.79
0.51
2.61
0.17
5.17
10.00
2.27
11.41
0.00
15.34
52
6.67
6.07
0.00
5.54
0.61
2.73
0.19
4.00
8.25
1.62
10.47
0.00
14.37
53
5.97
5.22
0.00
5.28
0.72
2.89
0.22
3.40
7.00
1.02
9.53
0.00
13.41
54
5.31
4.39
0.00
5.00
0.83
3.10
0.25
2.11
5.00
0.00
8.60
0.00
12.43
55
4.69
3.62
0.00
4.71
0.95
3.36
0.28
1.00
3.12
0.00
7.70
0.00
11.47
130
GARY R. SKOOG AND JAMES E. CIECKA
Table 2. (Continued ) Minimal 50% PI
Inter-Quartile PI
10–90% PI
WLE Mean
Median
Mode
SD
SK
KU
Pr(0)
Low
High
25%
75%
10%
90%
56
4.15
2.95
0.00
4.43
1.07
3.65
0.32
1.00
2.45
0.00
6.88
0.00
10.58
57
3.67
2.35
0.00
4.15
1.19
3.99
0.35
1.00
1.85
0.00
6.11
0.00
9.75
58
3.23
1.80
0.00
3.88
1.32
4.37
0.39
1.00
1.30
0.00
5.38
0.00
8.96
59
2.84
1.32
0.00
3.62
1.45
4.80
0.42
0.00
0.82
0.00
4.73
0.00
8.20
60
2.50
0.91
0.00
3.38
1.57
5.26
0.46
0.00
0.41
0.00
4.13
0.00
7.48
61
2.20
0.53
0.00
3.15
1.70
5.76
0.49
0.00
0.03
0.00
3.57
0.00
6.86
62
1.94
0.00
0.00
2.93
1.82
6.29
0.53
0.00
0.00
0.00
3.10
0.00
6.27
63
1.71
0.00
0.00
2.73
1.95
6.86
0.56
0.00
0.00
0.00
2.65
0.00
5.72
64
1.51
0.00
0.00
2.54
2.08
7.50
0.60
0.00
0.00
0.00
2.24
0.00
5.21
65
1.32
0.00
0.00
2.35
2.23
8.24
0.63
0.00
0.00
0.00
1.85
0.00
4.69
66
1.15
0.00
0.00
2.17
2.38
9.09
0.66
0.00
0.00
0.00
1.46
0.00
4.21
67
0.99
0.00
0.00
1.99
2.55
10.08
0.69
0.00
0.00
0.00
1.14
0.00
3.73
68
0.85
0.00
0.00
1.80
2.73
11.28
0.72
0.00
0.00
0.00
0.82
0.00
3.26
69
0.72
0.00
0.00
1.63
2.93
12.70
0.75
0.00
0.00
0.00
0.00
0.00
2.80
70
0.60
0.00
0.00
1.45
3.16
14.44
0.78
0.00
0.00
0.00
0.00
0.00
2.34
71
0.49
0.00
0.00
1.28
3.41
16.51
0.80
0.00
0.00
0.00
0.00
0.00
1.94
72
0.41
0.00
0.00
1.13
3.66
18.83
0.83
0.00
0.00
0.00
0.00
0.00
1.53
73
0.34
0.00
0.00
0.99
3.91
21.30
0.85
0.00
0.00
0.00
0.00
0.00
1.28
74
0.28
0.00
0.00
0.87
4.15
23.98
0.86
0.00
0.00
0.00
0.00
0.00
1.06
75
0.23
0.00
0.00
0.75
4.41
26.99
0.88
0.00
0.00
0.00
0.00
0.00
0.83
Age
2. CRITICISMS OF THE MARKOV MODEL 2.1. Importance of Initial Labor Force Status We have elsewhere (Skoog & Ciecka, 2004) discussed at length the comparisons of the Markov model with other models, notably the conventional model. If one does not distinguish between whether the current state is active or inactive, one is implicitly assuming that a pax and i pax are equal. It does not take elaborate statistical hypothesis testing to see that this is rejected by the data. Further, the conventional model assumes that, beyond an age of peak participation, any exit from activity is the final exit: in other words, that i pax ¼ 0 for these ages, again inconsistent with the data. Rather than rejecting such models, critics of the Markov model, including Hunt, Pickersgill, and Rutemiller (HPR), (2001) and elsewhere, and Richards (1999, 2000) appear willing to ignore the information in the current activity status and confine the domain of worklife calculation to the entire population – the mixture distribution of those inactive and those active. Their
131
Recent Developments in the Measurement of Labor Market Activity
Table 3.
YA Characteristics for Initially Active Women, Regardless of Education. Minimal 50% PI
Inter-Quartile PI
10–90% PI
Age
WLE Mean
Median
Mode
SD
SK
KU
Low
High
25%
75%
10%
90%
16 17 18 19 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
34.40 33.85 33.27 32.66 32.03 31.40 30.75 30.09 29.41 28.73 28.04 27.33 26.62 25.90 25.17 24.45 23.72 22.98 22.24 21.50 20.76 20.02 19.27 18.53 17.78 17.04 16.30 15.56 14.83 14.10 13.37 12.65 11.96 11.27 10.60 9.94 9.30 8.68 8.08 7.53 6.99
34.52 33.97 33.38 32.76 32.12 31.48 30.83 30.16 29.47 28.78 28.08 27.36 26.63 25.90 25.16 24.42 23.67 22.91 22.16 21.40 20.63 19.86 19.09 18.32 17.55 16.77 16.00 15.22 14.45 13.68 12.91 12.14 11.40 10.66 9.93 9.22 8.52 7.84 7.19 6.57 5.98
36.50 35.50 35.50 34.50 33.50 33.50 32.50 31.50 31.50 30.50 29.50 28.50 28.50 27.50 26.50 25.50 25.50 24.50 23.50 23.50 22.50 21.50 20.50 19.50 19.50 18.50 17.50 16.50 15.50 15.50 14.50 13.50 12.50 11.50 10.50 10.50 9.50 8.50 7.50 6.50 5.50
8.78 8.72 8.66 8.60 8.54 8.47 8.41 8.34 8.27 8.19 8.11 8.03 7.94 7.85 7.76 7.67 7.58 7.48 7.38 7.28 7.18 7.07 6.96 6.85 6.73 6.61 6.49 6.36 6.23 6.09 5.95 5.81 5.65 5.49 5.33 5.17 5.00 4.83 4.65 4.47 4.29
0.47 0.46 0.44 0.43 0.42 0.41 0.40 0.39 0.37 0.36 0.35 0.34 0.33 0.31 0.30 0.28 0.27 0.25 0.23 0.21 0.19 0.17 0.15 0.12 0.10 0.07 0.04 0.00 0.03 0.07 0.11 0.15 0.20 0.25 0.30 0.35 0.41 0.46 0.52 0.59 0.66
3.50 3.46 3.42 3.37 3.33 3.30 3.26 3.22 3.19 3.16 3.13 3.10 3.07 3.04 3.02 2.99 2.96 2.93 2.91 2.88 2.85 2.83 2.80 2.78 2.76 2.74 2.72 2.71 2.70 2.69 2.69 2.69 2.71 2.73 2.76 2.79 2.84 2.90 2.98 3.07 3.17
30.50 30.19 29.50 29.30 28.36 27.50 27.49 26.57 25.63 25.50 24.81 23.90 23.50 22.50 22.19 21.30 20.42 19.52 18.62 18.50 17.50 16.97 16.09 15.21 14.50 13.50 12.59 12.50 11.50 10.50 10.19 9.37 8.56 7.76 6.97 6.21 5.50 4.72 4.50 3.50 3.50
40.87 40.50 39.76 39.50 38.50 37.58 37.50 36.50 35.50 35.28 34.50 33.50 33.01 31.91 31.50 30.50 29.50 28.50 27.50 27.26 26.15 25.50 24.50 23.50 22.66 21.54 20.50 20.27 19.12 17.98 17.50 16.50 15.50 14.50 13.50 12.50 11.54 10.50 9.99 8.67 8.34
28.52 27.98 27.43 26.83 26.22 25.62 24.99 24.36 23.71 23.06 22.41 21.73 21.05 20.38 19.69 19.00 18.32 17.63 16.92 16.23 15.54 14.83 14.13 13.44 12.74 12.03 11.35 10.66 9.97 9.30 8.63 7.97 7.34 6.73 6.14 5.58 5.03 4.52 4.03 3.60 3.18
39.99 39.41 38.80 38.15 37.48 36.81 36.12 35.41 34.70 33.97 33.22 32.45 31.68 30.91 30.12 29.33 28.52 27.72 26.91 26.10 25.28 24.45 23.63 22.80 21.97 21.14 20.30 19.46 18.62 17.79 16.96 16.12 15.30 14.48 13.68 12.89 12.10 11.33 10.58 9.88 9.19
22.56 22.05 21.54 20.97 20.40 19.82 19.24 18.65 18.04 17.45 16.83 16.22 15.61 14.97 14.36 13.74 13.12 12.51 11.88 11.26 10.65 10.03 9.44 8.82 8.22 7.64 7.06 6.52 5.95 5.43 4.90 4.42 3.95 3.54 3.10 2.71 2.33 1.97 1.68 1.44 1.21
44.51 43.92 43.28 42.60 41.91 41.21 40.48 39.75 39.00 38.23 37.44 36.65 35.85 35.04 34.21 33.38 32.54 31.71 30.88 30.03 29.18 28.32 27.46 26.60 25.75 24.89 24.03 23.16 22.29 21.41 20.54 19.69 18.84 17.99 17.14 16.30 15.46 14.65 13.88 13.11 12.35
132
GARY R. SKOOG AND JAMES E. CIECKA
Table 3. (Continued ) Minimal 50% PI Age 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Inter-Quartile PI
10–90% PI
WLE Mean
Median
Mode
SD
SK
KU
Low
High
25%
75%
10%
90%
6.47 5.97 5.50 5.08 4.69 4.37 4.08 3.82 3.60 3.39 3.21 3.07 2.93 2.79 2.61 2.41 2.20 2.01 1.83
5.40 4.86 4.36 3.90 3.48 3.16 2.87 2.60 2.38 2.17 2.01 1.91 1.84 1.75 1.59 1.42 1.26 1.15 1.01
4.50 3.50 2.50 2.50 1.50 1.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
4.12 3.94 3.78 3.62 3.47 3.31 3.17 3.03 2.90 2.77 2.64 2.52 2.38 2.22 2.07 1.91 1.75 1.59 1.43
0.73 0.80 0.87 0.93 0.99 1.04 1.08 1.12 1.14 1.15 1.14 1.12 1.09 1.08 1.09 1.12 1.15 1.20 1.31
3.28 3.40 3.53 3.65 3.77 3.87 3.96 4.02 4.04 4.03 3.98 3.90 3.85 3.85 3.91 4.02 4.18 4.45 4.95
2.50 2.35 1.50 1.11 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
6.99 6.50 5.26 4.50 3.48 3.16 2.87 2.60 2.38 2.17 2.01 1.91 1.84 1.75 1.59 1.42 1.26 1.15 1.01
2.78 2.40 2.05 1.73 1.46 1.25 1.08 0.94 0.84 0.71 0.60 0.54 0.50 0.50 0.50 0.50 0.50 0.50 0.50
8.50 7.88 7.27 6.70 6.19 5.73 5.32 4.98 4.66 4.39 4.19 4.00 3.80 3.54 3.29 3.03 2.75 2.42 2.12
0.99 0.79 0.61 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
11.62 10.94 10.27 9.63 9.09 8.55 8.12 7.69 7.31 6.94 6.55 6.24 5.92 5.54 5.15 4.68 4.22 3.75 3.33
chief criticism is that the matching process ‘‘can be biased due to attenuation of the sample over the one year period’’ (HPR, 2001, p. 204). Richards (2000, p. 26) writes that in his 1996–1998 study and with his matching algorithm (about which no details are supplied) ‘‘matching resulted in lower second period labor force participation rates than occurred in the total population, transition probabilities from active to active and inactive to active were underestimated, and transition probabilities from inactive to inactive and active to inactive were overestimated.’’ (‘‘Matching’’ refers to an empirical requirement encountered when estimating transition probabilities. A specific person’s labor force status must be observed at a certain point in time and again one year later. This is not a trivial exercise because survey data are not coded to be individual specific and people simply drop out of sample over a yearly time period.) Our first observation is that, even if true, the cure – ignoring initial status – is worse than the disease. If we observe a 50–year-old male, from Table 1 the WLE is 12.63 years if active and, if inactive, 8.13 years. Whichever status is observed, the bias will be less in choosing between the relevant worklife than to announce the 85% – 15% weighted average (if the participation rate
133
Recent Developments in the Measurement of Labor Market Activity
Table 4.
YA Characteristics for Initially Inactive Women, Regardless of Education. Minimal 50% PI
Age
WLE Mean
Median
Mode
SD
SK
KU
Pr(0)
Low
High
Inter-Quartile PI 25%
75%
10–90% PI 10%
90%
16
33.21
33.83
35.00
8.79
0.46
3.49
0.00
29.66
40.00
27.82
39.30
21.86
43.86
17
32.76
33.37
35.00
8.73
0.45
3.45
0.00
29.00
39.29
27.38
38.82
21.46
43.34
18
32.22
32.83
34.00
8.68
0.44
3.41
0.00
28.75
39.00
26.86
38.26
20.95
42.76
19
31.54
32.13
33.00
8.63
0.42
3.36
0.00
27.80
38.00
26.19
37.54
20.32
42.03
20
30.79
31.38
33.00
8.57
0.41
3.31
0.00
27.00
37.15
25.47
36.77
19.62
41.23
21
30.10
30.68
32.00
8.51
0.40
3.27
0.00
26.89
37.00
24.78
36.04
18.97
40.47
22
29.36
29.93
31.00
8.46
0.38
3.23
0.00
25.95
36.00
24.06
35.27
18.28
39.69
23
28.60
29.15
30.00
8.41
0.37
3.19
0.00
25.01
35.00
23.31
34.47
17.57
38.87
24
27.81
28.35
29.00
8.35
0.36
3.15
0.00
24.01
34.00
22.54
33.65
16.82
38.03
25
26.99
27.52
29.00
8.30
0.34
3.12
0.00
23.10
33.00
21.73
32.80
16.05
37.16
26
26.14
26.66
28.00
8.24
0.33
3.08
0.00
23.00
32.85
20.89
31.92
15.26
36.26
27
25.28
25.79
27.00
8.18
0.31
3.04
0.00
22.00
31.78
20.05
31.02
14.47
35.34
28
24.43
24.92
26.00
8.12
0.29
3.00
0.00
21.00
30.70
19.22
30.12
13.67
34.42
29
23.59
24.07
25.00
8.05
0.28
2.97
0.00
20.00
29.62
18.41
29.24
12.90
33.52
30
22.77
23.22
24.00
7.98
0.26
2.93
0.01
19.46
29.00
17.61
28.37
12.15
32.63
31
21.94
22.38
23.00
7.90
0.24
2.90
0.01
18.55
28.00
16.80
27.49
11.41
31.74
32
21.11
21.53
23.00
7.82
0.22
2.86
0.01
17.65
27.00
15.99
26.60
10.65
30.83
33
20.28
20.69
22.00
7.74
0.21
2.83
0.01
16.77
26.00
15.19
25.72
9.91
29.93
34
19.50
19.89
21.00
7.66
0.19
2.80
0.01
16.00
25.11
14.44
24.89
9.21
29.06
35
18.72
19.09
20.00
7.58
0.17
2.77
0.01
15.00
24.00
13.69
24.06
8.52
28.20
36
17.94
18.29
19.00
7.50
0.15
2.73
0.01
15.00
23.89
12.92
23.22
7.80
27.34
37
17.14
17.47
18.00
7.42
0.12
2.70
0.02
14.00
22.75
12.14
22.37
7.07
26.46
38
16.31
16.61
18.00
7.34
0.09
2.66
0.02
13.00
21.60
11.32
21.48
6.30
25.55
39
15.47
15.74
17.00
7.25
0.06
2.62
0.03
12.56
21.00
10.49
20.59
5.53
24.65
40
14.63
14.88
16.00
7.17
0.03
2.58
0.03
11.75
20.00
9.64
19.70
4.74
23.75
41
13.79
14.00
15.00
7.07
0.01
2.54
0.04
10.96
19.00
8.79
18.81
3.94
22.84
42
12.94
13.10
14.00
6.98
0.05
2.50
0.05
10.00
17.81
7.91
17.90
3.14
21.93
43
12.05
12.15
0.00
6.87
0.10
2.47
0.06
9.00
16.53
6.98
16.94
2.30
20.96
44
11.14
11.16
0.00
6.74
0.17
2.44
0.08
8.00
15.19
6.02
15.95
1.48
19.97
45
10.24
10.17
0.00
6.59
0.24
2.43
0.09
7.22
14.00
5.07
14.95
0.70
18.97
46
9.37
9.19
0.00
6.42
0.31
2.45
0.11
6.68
13.00
4.14
13.96
0.00
17.98
47
8.53
8.22
0.00
6.23
0.40
2.48
0.14
6.00
11.80
3.26
12.98
0.00
17.00
48
7.71
7.24
0.00
6.02
0.49
2.55
0.17
5.00
10.19
2.40
11.98
0.00
16.00
49
6.90
6.25
0.00
5.78
0.60
2.67
0.20
4.00
8.50
1.58
10.96
0.00
14.97
50
6.13
5.29
0.00
5.51
0.71
2.83
0.23
3.00
6.73
0.84
9.93
0.00
13.94
51
5.42
4.38
0.00
5.22
0.83
3.04
0.27
1.00
3.88
0.00
8.94
0.00
12.92
52
4.79
3.56
0.00
4.93
0.96
3.30
0.30
1.00
3.06
0.00
8.01
0.00
11.95
53
4.21
2.81
0.00
4.63
1.09
3.62
0.34
1.00
2.30
0.00
7.11
0.00
11.01
54
3.68
2.11
0.00
4.33
1.22
4.01
0.38
1.00
1.61
0.00
6.25
0.00
10.08
55
3.20
1.49
0.00
4.03
1.37
4.47
0.42
0.00
0.99
0.00
5.43
0.00
9.20
56
2.77
0.95
0.00
3.73
1.52
5.01
0.46
0.00
0.44
0.00
4.67
0.00
8.33
134
GARY R. SKOOG AND JAMES E. CIECKA
Table 4. (Continued ) Minimal 50% PI
Inter-Quartile PI
10–90% PI
WLE Mean
Median
Mode
SD
SK
KU
Pr(0)
Low
High
25%
75%
10%
90%
57
2.40
0.00
0.00
3.45
1.68
5.64
0.50
0.00
0.00
0.00
3.97
0.00
7.51
58
2.06
0.00
0.00
3.18
1.84
6.36
0.54
0.00
0.00
0.00
3.31
0.00
6.77
59
1.78
0.00
0.00
2.92
2.01
7.17
0.58
0.00
0.00
0.00
2.72
0.00
6.07
60
1.52
0.00
0.00
2.68
2.19
8.10
0.62
0.00
0.00
0.00
2.19
0.00
5.38
61
1.30
0.00
0.00
2.45
2.38
9.16
0.66
0.00
0.00
0.00
1.69
0.00
4.77
62
1.11
0.00
0.00
2.24
2.57
10.31
0.69
0.00
0.00
0.00
1.26
0.00
4.20
63
0.95
0.00
0.00
2.04
2.76
11.58
0.72
0.00
0.00
0.00
0.89
0.00
3.66
64
0.81
0.00
0.00
1.86
2.97
13.01
0.75
0.00
0.00
0.00
0.50
0.00
3.18
65
0.69
0.00
0.00
1.68
3.18
14.59
0.78
0.00
0.00
0.00
0.00
0.00
2.70
66
0.59
0.00
0.00
1.53
3.39
16.25
0.80
0.00
0.00
0.00
0.00
0.00
2.30
67
0.50
0.00
0.00
1.39
3.60
18.06
0.82
0.00
0.00
0.00
0.00
0.00
1.95
68
0.43
0.00
0.00
1.25
3.84
20.20
0.84
0.00
0.00
0.00
0.00
0.00
1.56
69
0.36
0.00
0.00
1.12
4.11
22.83
0.86
0.00
0.00
0.00
0.00
0.00
1.26
70
0.30
0.00
0.00
0.99
4.42
26.16
0.88
0.00
0.00
0.00
0.00
0.00
0.96
71
0.24
0.00
0.00
0.86
4.80
30.58
0.89
0.00
0.00
0.00
0.00
0.00
0.61
72
0.19
0.00
0.00
0.74
5.23
36.23
0.91
0.00
0.00
0.00
0.00
0.00
0.00
73
0.15
0.00
0.00
0.63
5.72
43.28
0.93
0.00
0.00
0.00
0.00
0.00
0.00
74
0.11
0.00
0.00
0.53
6.29
52.39
0.94
0.00
0.00
0.00
0.00
0.00
0.00
75
0.09
0.00
0.00
0.44
6.92
63.55
0.95
0.00
0.00
0.00
0.00
0.00
0.00
Age
is 85%) for the population as a whole. It is better to have an approximate answer to the relevant question than to have a precise answer to an irrelevant question. We do not however accept the premise that significant ‘‘bias’’ in the Markov worklives has been established, and turn to that issue. 2.2. Predicting the Future First, the critics above view the exercise being undertaken differently from us. The Markov model implements the same synthetic cohort assumption employed in current or period U.S. life tables: assuming no change from the most recent data (two or one years, respectively), the question asked is ‘‘What are the long-term implications?’’ No one criticizes the National Vital Statistics System for not undertaking the project of extrapolating mortality trends throughout the remainder of the current century. In fact, such life tables are available to forensic economists from the Social Security Administration and are not used. We do not see ourselves as responsible for undertaking the much more ambitious economic and actuarial projections
135
Recent Developments in the Measurement of Labor Market Activity
Table 5.
YFS Characteristics for Initially Active Men, Regardless of Education. Minimal 50% PI Inter-Quartile PI
YFSE Age Mean Median Mode 16 17 18 19 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
47.29 46.34 45.40 44.46 43.53 42.59 41.66 40.73 39.80 38.86 37.93 36.99 36.05 35.12 34.18 33.25 32.33 31.40 30.48 29.56 28.64 27.72 26.81 25.89 24.98 24.07 23.17 22.26 21.36 20.47 19.57 18.68 17.80 16.92 16.05 15.19 14.34 13.50 12.68 11.88 11.09
48.40 47.41 46.43 45.44 44.46 43.47 42.49 41.50 40.52 39.54 38.56 37.57 36.59 35.61 34.63 33.65 32.67 31.70 30.72 29.75 28.77 27.80 26.83 25.86 24.90 23.93 22.97 22.01 21.05 20.10 19.14 18.19 17.25 16.31 15.37 14.44 13.52 12.61 11.71 10.83 9.96
47.50 46.50 45.50 44.50 43.50 42.50 41.50 40.50 39.50 38.50 37.50 36.50 35.50 34.50 33.50 32.50 31.50 30.50 29.50 28.50 27.50 26.50 25.50 24.50 23.50 22.50 21.50 20.50 19.50 18.50 17.50 16.50 15.50 14.50 13.50 12.50 11.50 10.50 9.50 8.50 7.50
SD 11.70 11.60 11.49 11.37 11.25 11.13 11.01 10.89 10.77 10.66 10.55 10.44 10.34 10.24 10.14 10.03 9.92 9.81 9.69 9.58 9.47 9.36 9.25 9.13 9.02 8.91 8.79 8.68 8.56 8.45 8.33 8.22 8.10 7.98 7.86 7.73 7.60 7.46 7.32 7.16 7.01
10–90% PI
SK
KU
Low
High
25%
75%
10%
90%
1.08 1.05 1.01 0.97 0.93 0.89 0.84 0.80 0.76 0.72 0.68 0.64 0.60 0.56 0.52 0.48 0.44 0.40 0.35 0.31 0.27 0.22 0.18 0.13 0.08 0.04 0.01 0.06 0.11 0.16 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.56 0.61 0.67 0.73
5.31 5.20 5.09 4.97 4.85 4.74 4.62 4.51 4.40 4.30 4.21 4.12 4.03 3.95 3.87 3.79 3.71 3.64 3.56 3.49 3.43 3.36 3.30 3.25 3.20 3.15 3.10 3.07 3.03 3.01 2.98 2.97 2.96 2.96 2.96 2.98 3.00 3.04 3.08 3.14 3.21
43.00 42.00 41.00 40.00 39.00 38.00 37.00 36.00 35.00 34.00 33.00 32.00 31.00 30.00 29.00 28.00 27.00 26.00 25.00 24.00 23.00 22.00 21.00 20.00 19.00 18.00 17.02 16.08 15.14 14.20 13.27 12.35 11.44 10.53 9.64 8.77 7.00 6.11 5.33 4.60 3.91
54.81 53.80 52.78 51.76 50.74 49.71 48.69 47.66 46.64 45.61 44.59 43.57 42.54 41.51 40.48 39.45 38.42 37.39 36.35 35.31 34.27 33.23 32.19 31.14 30.09 29.04 28.00 27.00 26.00 25.00 24.00 23.00 22.00 21.00 20.00 19.00 17.08 16.00 15.00 14.00 13.00
42.58 41.60 40.63 39.67 38.70 37.74 36.78 35.82 34.86 33.90 32.94 31.98 31.01 30.05 29.09 28.13 27.18 26.23 25.28 24.33 23.39 22.45 21.51 20.57 19.64 18.71 17.79 16.87 15.96 15.04 14.13 13.22 12.32 11.43 10.56 9.69 8.85 8.03 7.23 6.45 5.71
54.42 53.43 52.44 51.45 50.46 49.47 48.48 47.49 46.51 45.52 44.53 43.54 42.55 41.57 40.58 39.60 38.61 37.63 36.65 35.67 34.69 33.71 32.73 31.75 30.78 29.80 28.83 27.85 26.88 25.91 24.94 23.98 23.02 22.06 21.10 20.15 19.21 18.26 17.33 16.40 15.48
33.56 32.68 31.82 30.98 30.12 29.27 28.42 27.58 26.75 25.91 25.06 24.20 23.34 22.49 21.65 20.82 20.01 19.18 18.35 17.54 16.74 15.94 15.13 14.33 13.54 12.76 11.99 11.22 10.45 9.70 8.97 8.23 7.51 6.83 6.16 5.51 4.91 4.32 3.78 3.26 2.78
60.25 59.26 58.27 57.27 56.28 55.29 54.30 53.31 52.32 51.32 50.33 49.34 48.35 47.36 46.37 45.38 44.39 43.41 42.42 41.43 40.45 39.46 38.48 37.49 36.51 35.53 34.55 33.56 32.59 31.61 30.63 29.65 28.68 27.70 26.73 25.76 24.80 23.83 22.87 21.92 20.96
136
GARY R. SKOOG AND JAMES E. CIECKA
Table 5. (Continued ) Minimal 50% PI Inter-Quartile PI YFSE Age Mean Median Mode 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
10.33 9.59 8.88 8.22 7.60 7.04 6.52 6.05 5.61 5.22 4.85 4.52 4.22 3.94 3.67 3.40 3.13 2.90 2.66
9.12 8.30 7.53 6.80 6.13 5.54 4.99 4.54 4.11 3.76 3.47 3.20 2.99 2.82 2.62 2.41 2.22 2.11 1.94
6.50 5.50 3.50 2.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
SD
SK
KU
6.84 6.66 6.47 6.26 6.04 5.80 5.55 5.29 5.03 4.77 4.51 4.26 4.00 3.75 3.50 3.27 3.04 2.81 2.58
0.79 3.29 0.85 3.39 0.92 3.52 0.99 3.67 1.06 3.84 1.13 4.05 1.20 4.29 1.28 4.56 1.36 4.85 1.43 5.17 1.50 5.52 1.57 5.90 1.65 6.32 1.72 6.80 1.81 7.36 1.90 8.00 2.00 8.74 2.13 9.72 2.31 11.06
10–90% PI
Low
High
25%
75%
10%
90%
2.31 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
11.00 9.18 7.53 6.80 6.13 5.54 4.99 4.54 4.11 3.76 3.47 3.20 2.99 2.82 2.62 2.41 2.22 2.11 1.94
5.01 4.35 3.76 3.24 2.80 2.44 2.15 1.92 1.73 1.58 1.45 1.32 1.24 1.17 1.10 1.02 0.92 0.87 0.87
14.57 13.67 12.78 11.92 11.09 10.29 9.54 8.82 8.15 7.53 6.94 6.43 5.94 5.56 5.16 4.77 4.36 3.92 3.57
2.34 1.96 1.61 1.33 1.11 0.94 0.81 0.72 0.65 0.59 0.55 0.50 0.47 0.45 0.43 0.41 0.37 0.35 0.35
20.01 19.08 18.15 17.22 16.31 15.41 14.53 13.65 12.79 11.95 11.17 10.42 9.69 8.96 8.31 7.66 6.98 6.40 5.78
involved in projecting labor force participation and mortality. The determinants of labor force participation at and beyond middle age and retirement are the subjects of intense research interest by economists: how will baby boomers respond to policy changes in Social Security and Medicare, for example? In addition, how will those facing retirement react to the receipt of inherited wealth, their alleged ‘‘undersaving’’ for retirement, and the switch from most pension plans being defined benefits to defined contributions, and their increased longevity? If these are open questions, the projection of future political and social policy responses is even less clear. In addition to these long-run considerations, transition probabilities a few years into the future may vary with the business cycle, a topic typically and properly ignored in the long-term calculations of forensic economics. We could, of course, take our crack at projecting how all of these forces will change the evolution of transition probabilities, but our work would require users to accept our projections. For these reasons, we see no interest in looking back to the 1970s or to 1992–1993 and comparing the participations implicit in conventional or Markov models over the last 30 years or the last 5 years with what actually had happened. Those modelers performing those
137
Recent Developments in the Measurement of Labor Market Activity
Table 6.
YFS Characteristics for Initially Inactive Men, Regardless of Education. Minimal 50% PI
Age
YFSE Mean
Median
Mode
SD
16
47.28
48.40
47.50
17
46.34
47.41
46.50
18
45.40
46.43
19
44.46
20
Inter-Quartile PI
10–90% PI
SK
KU
Pr(0)
Low
High
25%
75%
10%
90%
11.72
1.09
5.37
0.00
43.00
54.70
42.58
54.42
33.56
60.25
11.62
1.06
5.25
0.00
42.00
53.69
41.60
53.43
32.68
59.26
45.50
11.51
1.02
5.14
0.00
41.00
52.67
40.63
52.44
31.82
58.27
45.44
44.50
11.39
0.98
5.03
0.00
40.00
51.65
39.67
51.45
30.98
57.27
43.52
44.46
43.50
11.27
0.94
4.91
0.00
39.00
50.62
38.70
50.46
30.12
56.28
21
42.59
43.47
42.50
11.15
0.90
4.79
0.00
38.00
49.60
37.74
49.47
29.27
55.29
22
41.66
42.49
41.50
11.03
0.86
4.68
0.00
37.00
48.58
36.78
48.48
28.42
54.30
23
40.72
41.50
40.50
10.90
0.81
4.56
0.00
36.00
47.56
35.82
47.49
27.58
53.31
24
39.79
40.52
39.50
10.79
0.77
4.45
0.00
35.00
46.53
34.86
46.51
26.74
52.32
25
38.86
39.54
38.50
10.67
0.73
4.35
0.00
34.00
45.51
33.90
45.52
25.91
51.32
26
37.92
38.56
37.50
10.57
0.69
4.26
0.00
33.00
44.48
32.94
44.53
25.06
50.33
27
36.98
37.57
36.50
10.47
0.66
4.18
0.00
32.00
43.45
31.98
43.54
24.20
49.34
28
36.04
36.59
35.50
10.37
0.62
4.11
0.00
31.00
42.41
31.01
42.55
23.34
48.35
29
35.10
35.61
34.50
10.28
0.59
4.04
0.01
30.00
41.36
30.05
41.57
22.48
47.36
30
34.17
34.63
33.50
10.19
0.56
3.97
0.01
29.00
40.31
29.09
40.58
21.64
46.37
31
33.23
33.65
32.50
10.09
0.52
3.91
0.01
28.00
39.25
28.13
39.60
20.81
45.38
32
32.29
32.67
31.50
10.00
0.49
3.86
0.01
27.00
38.19
27.18
38.61
19.98
44.39
33
31.36
31.69
30.50
9.92
0.46
3.80
0.01
26.00
37.11
26.22
37.63
19.13
43.41
34
30.42
30.72
29.50
9.84
0.43
3.75
0.01
25.00
36.03
25.27
36.65
18.28
42.42
35
29.48
29.74
28.50
9.76
0.41
3.70
0.01
24.05
35.00
24.31
35.67
17.43
41.43
36
28.53
28.77
27.50
9.70
0.38
3.66
0.02
23.14
34.00
23.36
34.69
16.57
40.45
37
27.58
27.79
26.50
9.64
0.36
3.61
0.02
22.25
33.00
22.40
33.71
15.69
39.46
38
26.63
26.82
25.50
9.60
0.34
3.56
0.02
21.37
32.00
21.45
32.73
14.80
38.48
39
25.67
25.84
24.50
9.56
0.32
3.51
0.03
20.51
31.00
20.49
31.75
13.88
37.49
40
24.70
24.87
23.50
9.52
0.30
3.45
0.03
19.66
30.00
19.52
30.77
12.94
36.51
41
23.73
23.89
22.50
9.49
0.28
3.38
0.04
18.82
29.00
18.55
29.79
11.95
35.52
42
22.76
22.92
21.50
9.47
0.26
3.30
0.04
18.00
27.99
17.58
28.82
10.90
34.54
43
21.78
21.94
0.00
9.45
0.23
3.22
0.05
17.00
26.79
16.59
27.84
9.78
33.56
44
20.79
20.97
0.00
9.43
0.20
3.13
0.06
16.00
25.58
15.60
26.86
8.56
32.58
45
19.81
19.99
0.00
9.40
0.17
3.03
0.07
15.00
24.36
14.59
25.89
7.21
31.60
46
18.82
19.00
0.00
9.38
0.13
2.94
0.08
14.00
23.11
13.56
24.91
5.55
30.62
47
17.82
18.02
0.00
9.35
0.09
2.84
0.10
13.17
22.00
12.51
23.94
3.05
29.64
48
16.83
17.03
0.00
9.31
0.04
2.74
0.11
12.48
21.00
11.42
22.97
0.00
28.67
49
15.84
16.03
0.00
9.26
0.01
2.66
0.13
12.00
20.18
10.30
21.99
0.00
27.69
50
14.85
15.04
0.00
9.20
0.07
2.58
0.15
11.00
18.81
9.13
21.02
0.00
26.72
51
13.88
14.03
0.00
9.11
0.14
2.51
0.17
10.59
18.00
7.86
20.05
0.00
25.75
52
12.91
13.01
0.00
9.02
0.21
2.46
0.19
10.00
16.95
6.42
19.09
0.00
24.78
53
11.96
11.98
0.00
8.90
0.28
2.43
0.22
9.00
15.44
4.63
18.12
0.00
23.81
54
11.03
10.93
0.00
8.76
0.37
2.43
0.25
9.00
14.85
0.00
17.15
0.00
22.84
55
10.12
9.86
0.00
8.59
0.45
2.45
0.28
8.78
14.00
0.00
16.18
0.00
21.88
56
9.26
8.77
0.00
8.39
0.55
2.50
0.32
8.47
13.00
0.00
15.22
0.00
20.91
138
GARY R. SKOOG AND JAMES E. CIECKA
Table 6. (Continued ) Minimal 50% PI
Inter-Quartile PI
10–90% PI
YFSE Mean
Median
Mode
SD
SK
KU
Pr(0)
Low
High
25%
75%
10%
90%
57
8.45
7.64
0.00
8.16
0.64
2.59
0.35
8.22
12.00
0.00
14.26
0.00
19.96
58
7.67
6.46
0.00
7.91
0.75
2.71
0.39
8.06
11.00
0.00
13.29
0.00
19.00
59
6.94
5.19
0.00
7.63
0.85
2.87
0.42
7.96
10.00
0.00
12.33
0.00
18.06
60
6.27
3.71
0.00
7.33
0.96
3.08
0.46
8.00
9.07
0.00
11.37
0.00
17.12
61
5.64
1.38
0.00
7.02
1.08
3.32
0.50
7.00
7.08
0.00
10.42
0.00
16.18
62
5.06
0.00
0.00
6.70
1.19
3.62
0.53
0.00
0.00
0.00
9.46
0.00
15.25
63
4.53
0.00
0.00
6.36
1.32
3.97
0.56
0.00
0.00
0.00
8.50
0.00
14.33
64
4.04
0.00
0.00
6.02
1.45
4.39
0.60
0.00
0.00
0.00
7.52
0.00
13.40
65
3.57
0.00
0.00
5.68
1.59
4.88
0.63
0.00
0.00
0.00
6.51
0.00
12.48
66
3.15
0.00
0.00
5.34
1.74
5.46
0.66
0.00
0.00
0.00
5.46
0.00
11.57
67
2.77
0.00
0.00
5.00
1.90
6.14
0.69
0.00
0.00
0.00
4.33
0.00
10.65
68
2.41
0.00
0.00
4.66
2.08
6.96
0.72
0.00
0.00
0.00
3.03
0.00
9.74
69
2.09
0.00
0.00
4.34
2.27
7.92
0.75
0.00
0.00
0.00
0.00
0.00
8.82
70
1.80
0.00
0.00
4.02
2.47
9.05
0.78
0.00
0.00
0.00
0.00
0.00
7.91
71
1.55
0.00
0.00
3.71
2.69
10.36
0.80
0.00
0.00
0.00
0.00
0.00
6.99
72
1.33
0.00
0.00
3.42
2.92
11.86
0.83
0.00
0.00
0.00
0.00
0.00
6.10
73
1.14
0.00
0.00
3.14
3.15
13.57
0.85
0.00
0.00
0.00
0.00
0.00
5.20
74
0.98
0.00
0.00
2.88
3.40
15.52
0.86
0.00
0.00
0.00
0.00
0.00
4.29
75
0.84
0.00
0.00
2.63
3.67
17.78
0.88
0.00
0.00
0.00
0.00
0.00
3.31
Age
benchmark calculations were simply not attempting to answer those questions at the time. 2.3. The Markov Model’s Alleged Underestimation of Participation Rates Implicit in the Model Another criticism of the Markov model is that for the population as a whole, its participation-weighted average WLE is lower than the conventional model’s WLE. Finch (1983) asserted that the Markov and the conventional models, applied to the same data, would produce the same overall WLE, and Shirley Smith (1983) agreed. This equivalence has been reasserted by the more recent critics above, but has never been proved. In fact, it is wrong, and when participation rates fall with age, we have proven a theoretical inequality, which for all males results in the conventional worklife exceeding the Markov worklife by 0.16–0.33 of a year or so. Let t PPx denote the labor force participation rate in period t for a popN m n d denote the conditional-onulation age x, and let M p p = 1 p t t x t x x survival transition probability from state M in period t to state N in period
139
Recent Developments in the Measurement of Labor Market Activity
Table 7.
YFS Characteristics for Initially Active Women, Regardless of Education. Minimal 50% PI
Inter-Quartile PI
10–90% PI
Age
YFSE Mean
Median
Mode
SD
SK
KU
Low
High
25%
75%
10%
90%
16 17 18 19 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
46.01 45.03 44.05 43.08 42.10 41.12 40.14 39.16 38.18 37.21 36.23 35.25 34.28 33.30 32.33 31.36 30.39 29.42 28.45 27.49 26.53 25.57 24.61 23.66 22.71 21.77 20.83 19.90 18.98 18.07 17.16 16.27 15.39 14.53 13.69 12.86 12.05 11.26 10.50 9.77 9.07
46.53 45.53 44.54 43.54 42.55 41.55 40.56 39.56 38.57 37.57 36.58 35.58 34.59 33.60 32.60 31.61 30.62 29.63 28.64 27.65 26.66 25.67 24.68 23.70 22.72 21.73 20.75 19.78 18.80 17.83 16.87 15.91 14.96 14.01 13.08 12.17 11.27 10.38 9.53 8.70 7.91
46.50 45.50 44.50 43.50 42.50 41.50 40.50 39.50 38.50 37.50 36.50 35.50 34.50 33.50 32.50 31.50 30.50 29.50 28.50 27.50 26.50 25.50 24.50 23.50 22.50 21.50 20.50 19.50 18.50 17.50 16.50 15.50 14.50 13.50 11.50 10.50 9.50 8.50 7.50 6.50 5.50
9.77 9.72 9.67 9.62 9.57 9.53 9.48 9.44 9.40 9.35 9.31 9.27 9.22 9.18 9.13 9.08 9.03 8.98 8.92 8.87 8.81 8.75 8.68 8.62 8.54 8.47 8.38 8.29 8.20 8.09 7.98 7.86 7.73 7.59 7.44 7.27 7.10 6.92 6.73 6.52 6.30
0.69 0.65 0.62 0.59 0.56 0.53 0.50 0.47 0.44 0.42 0.39 0.36 0.33 0.31 0.28 0.25 0.22 0.19 0.16 0.13 0.10 0.07 0.04 0.01 0.03 0.07 0.10 0.15 0.19 0.23 0.28 0.33 0.38 0.44 0.50 0.56 0.62 0.69 0.76 0.84 0.92
5.02 4.89 4.76 4.64 4.53 4.42 4.32 4.23 4.14 4.05 3.97 3.89 3.82 3.75 3.68 3.61 3.54 3.48 3.42 3.37 3.32 3.27 3.22 3.18 3.14 3.10 3.08 3.05 3.03 3.02 3.02 3.03 3.05 3.08 3.12 3.18 3.26 3.35 3.47 3.62 3.80
41.00 40.00 39.00 38.00 37.00 36.00 35.00 34.00 33.00 32.00 31.00 30.00 29.00 28.00 27.00 26.01 25.02 24.04 23.05 22.07 21.08 20.10 19.13 18.15 17.18 16.21 15.25 14.30 13.35 12.42 11.49 10.59 9.70 8.85 8.00 7.00 5.49 4.81 3.19 2.68 1.24
52.12 51.11 50.10 49.10 48.09 47.08 46.07 45.06 44.06 43.05 42.04 41.03 40.02 39.01 38.00 37.00 36.00 35.00 34.00 33.00 32.00 31.00 30.00 29.00 28.00 27.00 26.00 25.00 24.00 23.00 22.00 21.00 20.00 19.00 17.98 16.78 15.00 14.00 12.00 11.00 9.00
40.86 39.87 38.88 37.89 36.90 35.91 34.92 33.94 32.95 31.96 30.97 29.99 29.00 28.02 27.03 26.05 25.07 24.09 23.11 22.13 21.16 20.19 19.22 18.25 17.29 16.34 15.39 14.45 13.52 12.60 11.69 10.81 9.95 9.10 8.28 7.50 6.75 6.05 5.38 4.78 4.22
51.98 50.98 49.99 48.99 47.99 47.00 46.00 45.00 44.01 43.01 42.02 41.02 40.03 39.03 38.04 37.04 36.05 35.06 34.06 33.07 32.08 31.09 30.10 29.11 28.12 27.13 26.14 25.16 24.18 23.19 22.21 21.24 20.26 19.29 18.33 17.37 16.42 15.47 14.54 13.62 12.72
34.47 33.50 32.53 31.56 30.59 29.63 28.66 27.69 26.72 25.76 24.79 23.83 22.87 21.92 20.96 20.01 19.06 18.11 17.17 16.23 15.30 14.38 13.47 12.56 11.68 10.81 9.96 9.12 8.30 7.52 6.78 6.08 5.40 4.79 4.21 3.67 3.18 2.74 2.37 2.07 1.81
57.72 56.72 55.72 54.72 53.73 52.73 51.73 50.73 49.74 48.74 47.74 46.75 45.75 44.75 43.76 42.76 41.76 40.77 39.77 38.78 37.78 36.79 35.80 34.80 33.81 32.82 31.83 30.83 29.84 28.86 27.87 26.88 25.89 24.91 23.93 22.95 21.97 21.00 20.03 19.07 18.11
140
GARY R. SKOOG AND JAMES E. CIECKA
Table 7. (Continued ) Minimal 50% PI Age 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
YFSE Mean
Median
Mode
SD
SK
8.40 7.75 7.13 6.56 6.03 5.57 5.14 4.76 4.42 4.10 3.82 3.58 3.37 3.15 2.91 2.67 2.43 2.20 1.99
7.15 6.44 5.77 5.16 4.64 4.18 3.79 3.45 3.14 2.88 2.69 2.57 2.47 2.35 2.17 1.96 1.80 1.68 1.53
4.50 3.50 2.50 1.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
6.08 5.86 5.63 5.39 5.15 4.89 4.64 4.38 4.13 3.89 3.65 3.41 3.18 2.95 2.73 2.52 2.32 2.12 1.93
1.00 1.09 1.17 1.26 1.34 1.43 1.51 1.59 1.68 1.75 1.82 1.89 1.97 2.08 2.22 2.38 2.57 2.79 3.11
Inter-Quartile PI
10–90% PI
KU
Low
High
25%
75%
10%
90%
3.99 4.22 4.48 4.77 5.10 5.47 5.89 6.35 6.85 7.38 7.95 8.59 9.37 10.37 11.61 13.12 14.97 17.32 20.56
0.88 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
8.00 6.44 5.77 5.16 4.64 4.18 3.79 3.45 3.14 2.88 2.69 2.57 2.47 2.35 2.17 1.96 1.80 1.68 1.53
3.70 3.21 2.77 2.39 2.07 1.84 1.64 1.48 1.37 1.23 1.11 1.04 0.99 0.98 0.93 0.86 0.79 0.72 0.70
11.83 10.96 10.14 9.36 8.62 7.93 7.33 6.78 6.30 5.86 5.48 5.12 4.79 4.45 4.06 3.77 3.43 3.03 2.70
1.55 1.32 1.13 0.95 0.80 0.70 0.63 0.56 0.52 0.47 0.43 0.41 0.40 0.39 0.37 0.35 0.32 0.29 0.28
17.16 16.22 15.29 14.38 13.48 12.61 11.76 10.93 10.17 9.47 8.79 8.15 7.54 6.91 6.32 5.72 5.10 4.63 4.09
t þ 1; M; N 2 fA; Ig; where A denotes active and I denotes inactive. By A A I conditioning transition probabilities on survival, we have A t px þ t px ¼ 1 I I I A and t px þ t px ¼ 1: In addition, as the x-year-old population in period t ages one year, its participation rate at age x þ 1 in period t þ 1 would be given by tþ1 PPxþ1
A I A ¼A t px t PPx þ t px ð1
t PPx Þ
tþ1 PPMarkov . xþ1
(1)
If applied to the matched sample, (1) would be an identity. We expect the left- and right-hand side of (1) to be approximately equal empirically, especially absent in- or out migration or under the assumption that migrants exhibit the same labor force behavior as non-migrants, provided that the matched sample was similar to the unmatched sample. The reader may compare (1) with Finch’s (1983) Eq. (5), after adjusting for mortality. Some authors (e.g., Richards and HPR) criticize the Markov model on the grounds that estimated transition probabilities are or may be biased – the source of the bias being attributed to unmatched people being excluded from calculated transition probabilities and the assumption that the unmatched undergo significantly different transitions than the matched. This
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Recent Developments in the Measurement of Labor Market Activity
Table 8.
YFS Characteristics for Initially Inactive Women, Regardless of Education. Minimal 50% PI Inter-Quartile PI 10–90% PI
YFSE Age Mean Median Mode SD 16 17 18 19 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
46.01 45.03 44.05 43.08 42.10 41.12 40.14 39.16 38.18 37.20 36.22 35.24 34.26 33.28 32.30 31.33 30.35 29.37 28.39 27.41 26.42 25.43 24.44 23.44 22.44 21.42 20.40 19.36 18.30 17.24 16.17 15.11 14.05 12.99 11.94 10.93 9.97 9.04 8.16 7.34 6.56
46.53 45.53 44.54 43.54 42.55 41.55 40.56 39.56 38.57 37.57 36.58 35.58 34.59 33.59 32.60 31.61 30.62 29.62 28.63 27.64 26.65 25.66 24.67 23.67 22.68 21.68 20.68 19.67 18.66 17.63 16.60 15.55 14.49 13.40 12.28 11.13 9.95 8.71 7.38 5.93 4.13
46.50 45.50 44.50 43.50 42.50 41.50 40.50 39.50 38.50 37.50 36.50 35.50 34.50 33.50 32.50 31.50 30.50 29.50 28.50 27.50 26.50 25.50 24.50 23.50 22.50 21.50 20.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
9.77 9.73 9.68 9.63 9.58 9.54 9.49 9.45 9.41 9.38 9.34 9.30 9.27 9.23 9.20 9.16 9.13 9.10 9.07 9.05 9.03 9.01 9.00 9.00 9.01 9.02 9.04 9.07 9.11 9.13 9.14 9.13 9.10 9.05 8.96 8.83 8.65 8.44 8.19 7.92 7.61
SK
KU
Pr(0)
Low
High
25%
75%
10%
90%
0.69 0.66 0.63 0.60 0.57 0.54 0.51 0.48 0.46 0.44 0.41 0.39 0.37 0.35 0.33 0.31 0.30 0.28 0.26 0.25 0.23 0.22 0.21 0.20 0.18 0.17 0.15 0.13 0.11 0.07 0.03 0.03 0.10 0.17 0.26 0.35 0.46 0.57 0.68 0.81 0.93
5.06 4.93 4.80 4.68 4.57 4.47 4.38 4.29 4.21 4.14 4.07 4.01 3.95 3.90 3.84 3.79 3.74 3.70 3.65 3.60 3.55 3.50 3.45 3.40 3.33 3.26 3.18 3.08 2.97 2.86 2.74 2.64 2.55 2.48 2.44 2.43 2.47 2.55 2.67 2.85 3.08
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.05 0.06 0.08 0.09 0.11 0.14 0.17 0.20 0.23 0.27 0.30 0.34 0.38 0.42 0.46
41.00 40.00 39.00 38.00 37.00 36.00 35.00 34.00 33.00 32.02 31.04 30.06 29.08 28.11 27.14 26.17 25.21 24.26 23.31 22.37 21.44 20.53 19.64 18.77 17.93 17.00 16.00 15.59 14.91 14.00 13.00 12.18 11.71 11.00 10.96 10.00 9.40 9.00 9.00 8.00 8.00
52.08 51.07 50.07 49.06 48.05 47.04 46.03 45.01 44.00 43.00 42.00 41.00 40.00 39.00 38.00 37.00 36.00 35.00 34.00 33.00 32.00 31.00 30.00 29.00 28.00 26.89 25.68 25.00 24.00 22.71 21.29 20.00 19.00 17.69 17.00 15.32 14.00 12.81 11.96 10.03 9.00
40.86 39.87 38.88 37.89 36.90 35.91 34.92 33.94 32.95 31.96 30.97 29.99 29.00 28.02 27.03 26.05 25.06 24.08 23.09 22.11 21.13 20.14 19.15 18.15 17.15 16.13 15.10 14.04 12.94 11.79 10.58 9.29 7.86 6.16 3.80 0.00 0.00 0.00 0.00 0.00 0.00
51.98 50.98 49.99 48.99 47.99 47.00 46.00 45.00 44.01 43.01 42.02 41.02 40.03 39.03 38.04 37.04 36.05 35.05 34.06 33.07 32.08 31.08 30.09 29.10 28.11 27.11 26.12 25.13 24.13 23.13 22.13 21.13 20.12 19.11 18.09 17.07 16.04 15.01 13.97 12.93 11.87
34.47 33.50 32.53 31.56 30.59 29.62 28.66 27.69 26.72 25.76 24.79 23.83 22.87 21.91 20.95 19.99 19.03 18.07 17.11 16.14 15.17 14.18 13.18 12.15 11.08 9.95 8.71 7.31 5.58 2.94 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
57.72 56.72 55.72 54.72 53.73 52.73 51.73 50.73 49.74 48.74 47.74 46.75 45.75 44.75 43.76 42.76 41.76 40.77 39.77 38.78 37.78 36.79 35.79 34.80 33.81 32.81 31.82 30.83 29.83 28.84 27.85 26.86 25.86 24.87 23.88 22.89 21.89 20.90 19.91 18.92 17.93
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Table 8. (Continued ) Minimal 50% PI Inter-Quartile PI 10–90% PI YFSE Age Mean Median Mode SD 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
5.84 5.18 4.57 4.02 3.52 3.08 2.68 2.32 2.00 1.72 1.48 1.26 1.06 0.89 0.73 0.60 0.49 0.40 0.32
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
7.28 6.94 6.58 6.22 5.85 5.48 5.11 4.75 4.39 4.05 3.72 3.40 3.10 2.81 2.54 2.29 2.06 1.86 1.67
SK 1.07 1.21 1.36 1.52 1.68 1.85 2.04 2.23 2.45 2.68 2.93 3.22 3.56 3.94 4.39 4.90 5.45 6.06 6.70
KU
Pr(0)
Low
High
25%
75%
10%
90%
3.37 3.73 4.16 4.68 5.30 6.03 6.90 7.94 9.19 10.69 12.52 14.79 17.65 21.27 25.86 31.54 38.44 46.69 56.21
0.50 0.54 0.58 0.62 0.66 0.69 0.72 0.75 0.78 0.80 0.82 0.84 0.86 0.88 0.89 0.91 0.93 0.94 0.95
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10.80 9.72 8.61 7.47 6.27 4.99 3.49 1.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
16.94 15.95 14.96 13.97 12.98 11.99 11.00 10.00 9.00 7.99 6.96 5.90 4.78 3.53 1.90 0.00 0.00 0.00 0.00
alleged problem is thought to be so damning that critics eschew the Markov model in favor of the conventional model in spite of all of the unrealistic assumptions of that model. Finch claimed that, when Markov transition probabilities of the time were used to compute tþ1 PPMarkov ; this implied participation was too low. xþ1 He adjusted the Markov transition probabilities upward, to match the larger tþ1 PPxþ1 : His adjustments were less important than the underlying reasoning. The source of this bias is caused by the participation in the (second period) matches which, as a result of the matching process, is too low (assuming no net immigration of workers who participate more than those here in the last period) relative to the unmatched or the population as a whole. If matches give too low a value for the left-hand side in (1), then there is too little to allocate to the transitions into the active state on the right-hand side and WLE, which varies directly with these, will be biased downward. We do take the issue of potential bias seriously. First, as Peracchi and Welch (1995 p. 173) say: ‘‘We conclude that, although selecting the matched individuals does bias measures of participation, especially for men, no
143
Recent Developments in the Measurement of Labor Market Activity 0.07 YFS
YA
0.06
Probability
0.05 0.04 0.03 0.02 0.01 0 0
10
20
30
40 Years
50
60
70
80
Probability Mass Functions for Years of Activity and Years to Final Separation for Initially Active Men of Age 30.
Fig. 1.
0.07 YFS
YA
0.06
Probability
0.05 0.04 0.03 0.02 0.01 0 0
10
20
30
40
50
60
70
80
Years
Fig. 2.
Probability Mass Functions for Years of Activity and Years to Final Separation for Initially Inactive Men of Age 30.
systematic bias appears in the estimates of transitions after controlling for sex, age, and labor force status at the time of the first survey.’’ A few points should be made. We emphasize their bottom line conclusion – no bias in the transition probabilities. Finis Welch is not just any author when it comes to data issues; he has a reputation among labor economists for extremely careful treatment of data. In fact, he founded (and is currently the President of) Unicom Research in Santa Monica in 1979, a company, which ‘‘has
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GARY R. SKOOG AND JAMES E. CIECKA 0.06 YFS
YA
10
20
Probability
0.05 0.04 0.03 0.02 0.01 0 0
Fig. 3.
30
40 Years
50
60
70
80
Probability Mass Functions for Years of Activity and Years to Final Separation for Initially Active Women of Age 30.
0.06 YFS
YA
Probability
0.05 0.04 0.03 0.02 0.01 0 0
Fig. 4.
10
20
30
40 Years
50
60
70
80
Probability Mass Functions for Years of Activity and for Years to Final Separation for Initially Inactive Women of Age 30.
produced the CPS Utilities, a set of data, documentation and extraction software, since the early 1990s. The CPS Utilities provides easy access to over 40 years of data from the Current Population Survey along with comprehensive documentation and original survey questionnaires.’’ Few possess knowledge of the Current Population Survey (CPS) as thorough as Welch, who has personally discussed this issue with one of the authors. Second,
Recent Developments in the Measurement of Labor Market Activity
145
without further sampling adjustments, which may be made to eliminate the matching-participation discrepancy altogether as discussed below, the direction of the bias in the critics’ argument has now reversed itself – the matched probabilities from the Markov model were higher, a decade later. Yet the critics’ argument did not change, rather they continue to assert Markov’s underestimation. Below, we propose taking another look at the alleged bias in the estimated transition probabilities by using (1). First, we compute the left-hand side of (1). This is not done with data from only a matched sample but with the same participation rates that the BLS would have calculated from the entire CPS sample if it had calculated age-specific participation rates rather than the age-group rates it typically reports. Next, transition probabilities are calculated from a matched sample from the CPS. This, along with the previously estimated participation rates, enables us to evaluate the right-hand side of (1). Now we compare. Significant sample selection problems that lead to severely biased estimated transition probabilities would cause large discrepancies between the separately estimated left- and right-hand sides of (1). Close agreement between the estimates of the left- and right-hand sides of (1) would be further evidence of little bias. Kurt Krueger (2004) has compiled a set of transition tables for 1998– 2003, extending the work of his PhD dissertation (Krueger, 2003). His transition tables contain weighted and sample counts of the entire U.S. civilian population, its active and inactive subpopulations, and transitions (between adjacent years) from inactive to inactive, inactive to active, active to inactive, and active to active states at each exact age 16–90 from the CPS. Months in sample (MIS) 4 and 8 are used exclusively; but by using the outgoing rotation weights and adjusting the weights of the matched MIS 4,8 records, the MIS 4,8 data ‘‘forces the combined MIS4 and MIS8 sub-sample of the CPS to sum to the composite estimates of employment, unemployment and not in the labor force for each month by age, race and sex’’ (Krueger, 2003, p. 134). Krueger calculated transition tables for men and women with less than high school, high school, some college, college, and without regard to education. We utilize the Krueger data for all men and women, without regard to education, below, and thank Kurt Krueger for making his data available to us. Figure 5 shows participation rates for males for 1998–1999, which HPR cite in their most current paper on what they refer to as ‘‘median years to retirement’’ (2001) and which they indicate were produced by the BLS from CPS microdata files. The figure also shows average participation rates for 1998–1999 that we computed from Krueger’s transition tables for all males.
Participation Rate
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GARY R. SKOOG AND JAMES E. CIECKA
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Computed from Krueger Data
18
Participation Rate
Fig. 5.
22
26
30
34
38
HPR
42
46 Age
50
54
58
62
66
70
74
Male Participation Rates (1998–1999) Computed from Krueger Data and Rates Cited by HPR.
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
RHS of (1)
18
22
26
Actual LHS of (1)
30
34
38
42
46
50
54
58
62
66
70
74
Age
Fig. 6.
Actual Participation Rates for Men in 1999 and Rates Computed from (1).
To the eye, there appears to be only one series plotted in Fig. 5 because both series are practically identical. Figure 6 shows the left- and right-hand sides of (1), keeping in mind that the right-hand side of (1) depends on transition probabilities. One is struck by the close agreement of these two series. To be sure, they are not identical, but the average difference (actual tþ1 PPxþ1 less calculated value of the right-hand side of (1)) is only 0.004. Figures 7 and 8 are for all women, regardless of education. Figure 7 shows HPR participation rates that are once again practically identical to those computed from Krueger’s data. The left- and right-hand sides of (1) are displayed in Fig. 8.
147
Participation Rate
Recent Developments in the Measurement of Labor Market Activity 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 18
Fig. 7.
HPR
Computed from Krueger Data
22
26
30
34
38
42
46 Age
50
54
58
62
66
70
74
Female Participation Rates (1998–1999) Computed from Krueger Data and Rates Cited by HPR.
0.9
Participation Rate
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
RHS of (1)
Actual LHS of(1)
0 18
Fig. 8.
22
26
30
34
38
42
46 Age
50
54
58
62
66
70
74
Actual Participation Rates for Women in 1999 and Rates Computed from (1).
These curves also are in close agreement; the average difference (actual tþ1 PPxþ1 less calculated value of the right-hand side of (1)) is 0.002. Thus, the underestimation bias thought to cause bias in transition probability estimation found by Richards in earlier data and with a different algorithm, and warned against by HPR, is not present in the first years of the Krueger data, which cover the years 1998–2003.
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GARY R. SKOOG AND JAMES E. CIECKA
2.4. Participation Rates Computed by BLS and from Matched Samples Krueger’s 2003 dissertation used data from 1998 through 2002. He studied sources of potential bias in the CPS for these purposes in over 100 pages – more thoroughly than anyone else. He considered the probabilities each of the four possible one year apart matches would provide, considered rotation group, and looked at how characteristics such as employment were affected by the months in the sample at which they were observed. He noted that not only the final weights used by others, but also the BLS’s composite weights, outgoing rotation weights as well as the use of no weights, represented choices available to the researcher. He read the BLS weight construction literature and determined that he could select the MIS4 and MIS8 sample, minimize biases for matching, employ these outgoing weights, and perform a final ‘‘raking’’ of the sample to eliminate almost entirely any participation discrepancy in the matched sample. At page 145, he plotted graphs of labor force participation by age, for males and females separately. In each graph, the overall participation rate and the participation rates in the matched samples, for MIS1–4, are plotted. While the graphs are very similar, one sees that, if anything, the participation rates in the matched samples are a little higher – opposite to the Finch result but consistent with that of Peracchi-Welch. On the other hand, Krueger noted in Table 4.14 that male activity participation percentages were lower in the MIS1–4 matches than in the overall (matched and unmatched) MIS1–4 averages, which in turn differ from the MIS1–8 (official) averages when the composite weightings are used. Using his extended data set, and employing his preferred MIS4–8 matches with raked outgoing rotation weights, Krueger compared the official BLS participation rates with those from his composite weighted matches used to calculate Markov transition probabilities. Additionally, he took a weighted average of the overall participation probability weighted by the number of years in the interval, WLP, which appears at the bottom (see Table 9). The conclusion is that, with the exception of the younger ages where transitions of students are notoriously hard to track, by careful statistical techniques transition probabilities will not be affected by discrepancies in the matched participation probabilities because they are minimal and because they vanish on average. The CPS data used in our recent work come from 1997–1998, a different time period from Krueger’s. Further, we did not restrict attention to the MIS4 and MIS8 samples, so we used the ordinary rather than the rotation weights. Our matching algorithm was also slightly different. Despite these
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Recent Developments in the Measurement of Labor Market Activity
Table 9. Average of BLS Participation Rates and Participation Rates Computed from MIS4 and MIS8 Matched Sample with Composite Weights for All Males and All Females. (a) MIS4 Matched Sample (1998–2002) All Males (1998–2002)
Average of BLS Published Data
MIS4 Matched Weighted with Composite Weight
All Females (1998–2002)
Average of BLS Published Data
MIS4 Matched Weighted with Composite Weight
18–19 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–61 62–64 65–69 70–74 75 and over
63.4 81.8 92.2 93.7 93.0 92.1 90.3 86.8 77.8 66.9 47.9 29.8 17.5 7.9
63.2 81.6 92.2 93.8 93.0 92.2 90.3 86.9 77.8 67.4 47.2 29.7 17.5 7.8
18–19 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–61 62–64 65–69 70–74 75 and over
60.5 72.8 76.5 75.3 75.8 78.2 78.6 73.9 62.0 49.2 35.1 19.3 10.2 3.3
60.5 73.1 76.6 75.4 75.8 78.2 78.8 74.0 61.9 49.2 35.0 19.1 10.1 3.2
WLP
42.2
42.2
WLP
34.5
34.6
Average of BLS Published Data
MIS8 Matched Weighted with Composite Weight
59.2 72.4 75.9 75.0 75.5 78.0 78.6 74.2 62.8 50.5
57.5 70.9 76.4 75.6 76.2 78.8 79.6 75.2 63.5 51.4
(b) From MIS8 matched sample (1999–2003). All Males (1999–2003)
18–19 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–61
Average of BLS Published Data
MIS8 Matched Weighted with Composite Weight
62.2 81.4 91.8 93.6 93.0 91.9 90.0 86.6 77.7 66.9
58.7 78.2 91.6 93.9 93.6 92.8 90.9 87.3 78.5 68.0
All Females (1999–2003)
18–19 20–24 25–-29 30–34 35–39 40–44 45–49 50–54 55–59 60–61
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GARY R. SKOOG AND JAMES E. CIECKA
Table 9. (Continued ) (b) From MIS8 matched sample (1999–2003). All Males (1999–2003)
Average of BLS Published Data
MIS8 Matched Weighted with Composite Weight
All Females (1999–2003)
Average of BLS Published Data
MIS8 Matched Weighted with Composite Weight
62–64 65–69 70–74 75 and over
48.4 30.8 18.0 8.1
49.0 31.2 17.7 7.9
62–64 65–69 70–74 75 and over
36.1 20.3 10.6 3.6
36.4 20.6 10.4 3.4
WLP
42.2
42.2
WLP
34.6
34.8
Source: Tables produced by Kurt Krueger and provided to the authors by e-mail correspondence on September 29, 2004.
differences, when we ran Krueger’s data through our software, the WLEs differ only slightly. Since Krueger’s data do not possess the sources for the alleged biases, and our data operationally produce results very close to his, issues involving our data have been removed from the table, and comparisons between the Markov and conventional model may revert to the merits of these models. Our conclusion is that, while we would tolerate a small amount of bias to have a model capable of answering most of the interesting questions that could be put to it, we do not need to do so; the work of Peracchi-Welch and of Krueger do not suggest the presence of the biases warned against.
3. TABLES PURPORTEDLY MEASURING DISABLED WORKLIFE EXPECTANCY 3.1. The VEI and Disability Worklife Expectancy – Background and Methods Vocational Econometrics Inc. (VEI) and Anthony M. Gamboa, Jr., also co-owner of Vocational Economics, Inc. (VE) produce tables which claim to measure the WLEs for persons with and without disabilities. The latest version of the tables referenced in this paper were published in 2002
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(Gamboa, 2002), hereinafter ‘‘the Gamboa Tables’’ or simply the ‘‘Tables.’’ These Tables are typically used only in litigation by plaintiffs to support an opinion about the duration of the remaining length of working life of individuals who have suffered an injury. Frequently, their use is in cases where the plaintiff has returned to some work, or is capable of employment, perhaps in another line of work, which gives rise to an earnings differential. The effect of the Tables is to shorten the postinjury worklife in the new, lower paying job chosen in mitigation and to overstate the preaccident WLE. Unfortunately, severe methodological and data problems and a variety of biases render these tables invalid for their intended use. The remainder of this section highlights these data problems and biases; more details are provided in the references. The VE/VEI concept of worklife differs from all generally accepted definitions of WLE ever used by the BLS as well as from those currently used in the forensic economics literature. The BLS has itself never published ‘‘disabled worklife expectancy tables.’’ Rather, the model of worklife employed in these Tables derives from the living, participation, and employment (LPE) model, a model never used by the BLS and which, when applied to sex and education groups within the entire population, is used by only a small and shrinking minority of forensic economists – 7.6% as per the latest 2003 survey of NAFE members, down from 17.3% in 1997 (Brookshire et al., 2003). The LPE model, like the conventional model, does not consider the subject’s initial state – whether active or inactive – and we have seen that the worklives of an active and of an otherwise identical inactive individual (in the tables in Section 1) may show significant differences. Bringing unemployment into the definition of worklife creates a further departure from the BLS’s conventional model. Skoog (2002a) and Skoog & Ciecka (2004) discussed the difficulties, even assuming unbiased disability data, of analyzing disability within the currently accepted paradigm of the Markov model: one would need to validly and reliably estimate transitions into and out of a multitude of disabled states. Necessary and sufficient conditions to be able to aggregate many disability states into fewer states were derived. The vast heterogeneity of disability, in light of the aggregation conditions, renders this practically impossible for current or contemplated data sets. For readers who have not run across them, in the Tables, individuals in CPS are grouped into one of the three categories: not disabled, severely disabled, or not severely disabled, on the basis of answers to screener questions, which are designed to ascertain those individuals receiving some form of disability income. These questions therefore do not attempt to define any notion of disability (Hale, 2001) and consequently have not undergone
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validity and reliability testing (Hale, 2001 and the Census web site (see U.S. census URL in references) disclaimer). It has long been understood by properly trained statisticians working with survey data that one should not run cross tabulations and report results about characteristics of a population on the basis of such screener questions, and economists at the BLS have cautioned against doing this (Rones, 1981; Hamel, 1994). These observations alone should have been enough to deter VEI from running cross tabulations and reporting the results. When one is truly severely disabled, the inability to participate in the labor force is evident, and there is no need of tables to state the obvious. It is the classification of ‘‘non-severe disability’’ which has lead to widespread abuse, and which is therefore the focus of this section. The definition of nonseverely disabled involves answering ‘‘yes’’ to one or more of the following three questions: (a) ‘‘Do you have a health problem or disability which prevents working or which limits the kind or amount of work?’’ (b) ‘‘Have you ever retired or left a job for health reasons?’’ (c) ‘‘Do you receive Veterans’ payments for disability?’’ while answering ‘‘no’’ to four other questions determines the presence of a ‘‘severe disability’’. Probabilities of employment are then calculated. Not surprisingly, the probability of employment is lower for those self-reporting a ‘‘non-severe work disability’’ and is lower still for those self-reporting a ‘‘severe work disability.’’ The partial circularity of the very definition is apparent – people claiming to trouble working will not be observed working as much! The Tables go on to multiply the joint probability of employment and participation with survival probabilities taken from the U.S. Life Tables, sum the product over future years to age 90, and report the result as a ‘‘worklife expectancy.’’ An inspection of the questions suggests additional problems. The presence of the word ever in (b) and the presence of Veterans’ payments in (c), as well as the use of the Tables by VE’s employees and affiliates, makes being ‘‘nonseverely disabled’’ a permanent condition. This is obviously absurd – people have been known to recover from disabilities! Equally absurd, when the Tables calculate ‘‘worklife expectancy’’ for those who are not now disabled, they implicitly assume that the individual will never become disabled in the future. Evidently, the ensuing higher worklife from someone magically insured against becoming disabled in the future can logically have no role as a comparator in personal injury and wrongful death litigation. This does not stop VE employees and affiliates from using this upwardly biased worklife as a base, from which they subtract a downwardly biased disabled worklife to produce a difference which is doubly biased, overstating economic damages.
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To be useful, the characteristics embedded in a worklife table must be permanent. Thus, current tables embed sex and education. The use of proper tables, of course, may involve judgment; application of our tables to a very young person who might change his or her educational attainment would be ill advised without proper qualification. The BLS abandoned its calculation of worklife for females by marital status almost 30 years ago, undoubtedly influenced by the lack of permanence of marital status. The lack of permanence of impairments (‘‘disability’’ in the present context) is still another reason militating against the use of the Tables. A reading of the questions defining non-severe ‘‘work disability’’ also reveals their compound nature and ambiguity. Health problems are mixed with disabilities; any connection of the resulting population with those possessing similar impairments to those in the subject lawsuit would be a remarkable coincidence. Further, what does it mean to be ‘‘limited’’ – does this refer to any past job or to one’s immediate past job, or to one’s current job? It is hard to conjecture what CPS respondents believe they should be answering. Any link between leaving a previous job for health reasons and one’s ability to participate in a different present job or a contemplated future job is tenuous.
3.2. Main Econometric Criticisms of VEI Tables Another major flaw in the Tables is sample selection bias – if a sample is not random, statistical inference which does not correct the lack of randomness is flawed. Here, a subset of the underlying entire (‘‘CPS’’) sample, those who self-report one of the ‘‘non-severe disability’’ criteria, does not represent a random sample of those with any kind of impairment or condition, since by construction the sample includes those whose impairment presents a workrelated problem; systematically missing are those with the same impairment that is not work-limiting. Consequently, the measurement of the probability of a work-related outcome, specifically whether or not one is participating in the labor market and is also employed, or averages of the salaries for such individuals, will be biased. The reason is that those with a similar impairment or condition for whom there is no such ‘‘work limitation’’ will be underrepresented in this non-random sample. In less careful words, the very definition of ‘‘work disability’’ is partially statistically circular. A second econometric difficulty plagues the construction of the Tables – the failure of econometric exogeneity. Quite simply, this technical term refers to the lack of clear-cut causation from the presence of the impairment
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to the purported effect, the inability to participate in the labor market or to be employed. In addition to the desired explanation for the association of impairment and lowered employment, the presence of a feedback relation or reverse causation is also present: people may first decide that they do not wish to work, and then seek a socially acceptable and remunerative explanation in declaring themselves disabled. The typical use of these Tables is illustrated by a simple example. Suppose, that a carpenter injures his back and can no longer perform carpentry. Subsequently, he becomes a housing inspector. Now the fact that he left his carpentry job because of a back injury need not have any measurable effect on his capacity to work as an inspector, a job chosen so as to accommodate his back injury. By mixing the plaintiff into a population with many others with more serious injuries do impact the ability to participate in the labor force, however, a spurious statistical loss of a few years of ‘‘worklife expectancy’’ will be erroneously created by these Tables. Skoog and Toppino (2002) and Ciecka, Rodgers and Skoog (2002) refer to the cause of this phenomenon as heterogeneity, a third econometric problem; its presence permits the Tables to indicate specious economic loss where no loss exists. The Tables have been critically discussed in the forensic economics literature, first in the book review by Corcione (1995) and later in full-scale peer-reviewed articles (Skoog & Toppino, 1999, 2002; Ciecka & Skoog, 2001; Rodgers, 2001; Ciecka et al., 2002). In addition, they have been discussed in professional conferences and on internet listserves. There has been no serious intellectual defense of these Tables and no defense that has attracted any following of informed PhD economists. This research has shown that the Gamboa disability tables are unreliable, invalid, misleading, biased, and inappropriate.
4. CONCLUSION The Markov or increment–decrement model remains the centerpiece of WLE. Its vitality and scope have been expanded with recent theoretical developments. Also, like other good models, it has implications, extensions, and the richness to undertake questions which have only recently been asked and answered, such as the probability distributions of YA and YFS, and questions which have not heretofore been asked of it, such as the statistical distribution of time to and in retirement. We have summarized the research documenting several problems which render the VEI Tables, based on CPS data, unreliable and invalid. Severe problems, notably heterogeneity and
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lack of exogeneity, will persist even if 2000 Census data were used instead of CPS data.
NOTES 1. For example, the Hunt, Pickersgill and Rutemiller (1997, 1999, & 2001) estimator is claimed to estimate the ‘‘median’’ of the years to final separation random variable, YFS, within the Markov model, but it is an inappropriate estimator for this model since it is not statistically consistent. It is shown (Skoog & Ciecka, 2004) to be consistent instead for only the BLS’s conventional model for certain ages, and in the presence of regularity conditions not present in the Hunt, Pickersgill, and Rutemiller data.
REFERENCES Brookshire, M. L., Luthy, M. R., & Slesnick, F. (2003). Forensic economists, their methods and their estimates of forecast variables – A 2003 survey study. Litigation Economics Review, 66(2), 28–44. Bureau of Labor Statistics. (1950). Tables of working life, length of working life for men. Bulletin 1001. Washington, DC: U.S. Department of Labor. Bureau of Labor Statistics. (1957). Tables of working life for women, 1950. Bulletin 1204. Washington, DC: U.S. Department of Labor. Bureau of Labor Statistics. (1982). Tables of working life: The increment–decrement model. Bulletin 2135. Washington, DC: U.S. Department of Labor. Bureau of Labor Statistics. (1986). Worklife estimates: Effects of race and education, Bulletin 2254. Washington, DC: U.S. Department of Labor. Ciecka, J. E., Rodgers, J., & Skoog, G. R. (2002). The new Gamboa tables: A critique. Journal of Legal Economics, 12(2), 61–85. Ciecka, J. E., & Skoog, G. R. (2001). An essay on the new worklife expectancy tables and the continuum of disability. Journal of Forensic Economics, 14(2), 135–140. Corcione, F. P. (1995). The new worklife expectancy tables: Revised 1985 for persons with and without disability by gender and level of education. Journal of Forensic Economics, 8(3), 295–297. Finch, J. L. (1983). Worklife estimates should be consistent with known labor force participation. Monthly Labor Review, 106(6), 34–36. Fullerton, H. N., & Byrne, J. J. (1976). Length of working life for men and women, 1970. Special labor force report 187. Bureau of Labor Statistics. Gamboa, A. N. (2002). The new worklife expectancy tables: Revised 2002 by gender, level of educational attainment, and level of disability. Louisville, KY: Vocational Econometrics, Inc. Garfinkle, S. (1955). Changes in working life for men, 1900–2000. Monthly Labor Review, 78(3), 297–300. Hale, T. W. (2001). The lack of a disability measure in today’s current population survey. Monthly Labor Review, 124(6), 38–40.
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Hamel, H. (1994). Personal response letter to American Board of Vocational Experts Board member Lindette L. Mayer, dated 1/18/94, on US Department of Labor, Bureau of Labor Statistics letterhead. Hunt, T., Pickersgill, J., & Rutemiller, H. (1997). Median years to retirement and worklife expectancy for the civilian US population. Journal of Forensic Economics, 10(2), 171–205. Hunt, T., Pickersgill, J., & Rutemiller, H. (1999). Median years to retirement. In: H. Richards (Ed.), Life and worklife expectancies (pp. 111–121). Tucson, AZ: Lawyers and Judges Publishing Company, Inc. Hunt, T., Pickersgill, J., & Rutemiller, H. (2001). Median years to retirement and worklife expectancy for the civilian US population. Journal of Forensic Economics, 14(3), 203–227. Krueger, K.V. (2003). A first order increment–decrement estimation of remaining years of lifetime productive activity participation. Ph.D. dissertation, University of Missouri-Kansas City. Krueger, K.V. (2004). Private communication regarding transition tables. Peracchi, F., & Welch, F. (1995). How representative are cross sections? Evidence from the current population survey. Journal of Econometrics, 68(1), 153–179. Richards, H. (2000). Worklife expectancies: Increment–decrement less accurate than conventional. Journal of Forensic Economics, 13(3), 271–289. Richards, H. (1999). Life and worklife expectancies. Tucson, AZ: Lawyers and Judges Publishing Company, Inc. Rodgers, J. (2001). Exploring the possibility of worklife expectancies for specific disabilities. The Earnings Analyst, 4, 1–37. Rones, P. (1981). Can the current population survey be used to identify the disabled? Monthly Labor Review, 104(6), 37–38. Skoog, G. R. (2002a). Worklife expectancy:Aggregation theory, with special reference to disability. Seattle, WA: Western Economic Association. Skoog, G. R. (2002b). Worklife expectancy: Theoretical results. Atlanta, GA: Applied Social Science Association. Skoog, G. R., & Ciecka, J. E. (2001a). The Markov (increment–decrement) model of labor force activity: New results beyond worklife expectancies. Journal of Legal Economics, 11(1), 1–21. Skoog, G. R., & Ciecka, J. E. (2001b). The Markov (increment–decrement) model of labor force activity: Extended tables of central tendency, variation, and probability intervals. Journal of Legal Economics, 11(1), 23–87. Skoog, G. R., & Ciecka, J. E. (2002). Probability mass functions for labor market activity induced by the Markov (increment–decrement) model of labor force activity. Economics Letters, 77(3), 425–431. Skoog, G. R., & Ciecka, J. E. (2003). Probability mass functions for years to final separation from the labor force induced by the Markov model. Journal of Forensic Economics, 16(1), 49–84. Skoog, G. R., & Ciecka, J. E. (2004). Reconsidering and extending the conventional/demographic and LPE models: The LPd and LPi restricted Markov models. Journal of Forensic Economics, 17(1), 47–94. Skoog, G. R., & Toppino, D. (1999). Disability and the new worklife expectancy tables from vocational econometrics, 1998: A critical analysis. Journal of Forensic Economics, 12(3), 239–254.
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Skoog, G. R., & Toppino, D. (2002). The new worklife expectancy tables’ critique: A rejoinder. Journal of Forensic Economics, 15(1), 81–97. Smith, S. (1983). Labor force participation rates are not the relevant factors. Monthly Labor Review, 106(6), 36–38. U.S. Census Bureau’s web site data warning. http://www.census.gov/hhes/www/disable/cps/ cpstableexplanation.pdf. Wolfbein, S. L. (1949). The length of working life. Population Studies, 3(3), 286–294.
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RESEARCH AND PRACTICE ISSUES IN PERSONAL INJURY AND WRONGFUL DEATH DAMAGES ANALYSIS Frank Slesnick, James Payne and Robert J. Thornton 1. INTRODUCTION Over the past 15 years or so, a very large proportion of the forensic economics literature has been devoted to research concerning better ways of estimating damages in cases involving personal injury and wrongful death (PI/WD). This is probably not surprising since the largest fraction of consulting income for forensic economists (at least those in the National Association of Forensic Economics, NAFE) comes from such cases. In this chapter we review and critique the important forensic economics research that has been put forth over the last decade and one-half with respect to five key subject areas involving PI/WD damages calculation. These key areas are: 1. Earning capacity 2. Fringe benefits 3. Discount rate issues
Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 159–203 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87007-X
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4. Personal consumption deduction 5. Age-earnings profiles In addition, we devote an appendix to discussing the Victim’s Compensation Fund, established after the September 11, 2001, terrorist attacks and designed to provide compensation to individuals (or their personal representatives) who were injured or killed as a result of the terrorist-related aircraft crashes on that day.
2. EARNING CAPACITY The measure of economic loss as required by many courts of law is lost earning capacity rather than lost expected earnings. Thus, it is very important that the forensic economist understand what these terms mean in order to calculate economic loss according to the appropriate legal parameters. Perhaps the most succinct description of these concepts is that expected earnings equal what one expects to earn in the future while earning capacity is what the person is capable of earning. However, reasonable precision is generally easier when measuring expected earnings since earning capacity relates to the potential of an individual that may never be reached. Furthermore, estimation of the latter is subject to ‘‘moral hazard’’ problems, given that a high estimate of earning capacity can unduly inflate economic loss. Horner and Slesnick (1999) made an initial foray into this topic by developing a rough set of guidelines that would assist practicing forensic economists to distinguish between expected earnings and earning capacity. As the authors state, ‘‘We have seen that earning capacity is distinguished from actual earnings, and thus expected earnings, by the fact that some people have preference functions that differ from ‘higher wages are better.’ Therefore, their past actual earnings and expected future earnings may not equal their earning capacity’’ (p. 29). Expected earnings, then, are usually driven by a utility function that emphasizes factors other than earnings. Earning capacity, on the other hand, is usually not affected by voluntary, non-binding choices and preferences that are subject to change in the future. Horner and Slesnick also point out, however, that postulating a level of income higher than expected earnings is often viewed with skepticism by the courts. There are a number of hurdles that must be faced if the forensic economist can claim that future earning capacity is greater than expected earnings. Frequently, the supply and demand conditions of the alternative, higher-paying job that may form the basis for the earning capacity
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estimation are not adequately considered. For example, if the individual is currently a business manager but his assumed alternative job is that of a high-priced attorney, it is likely that his skills have deteriorated. Further, law firms may be wary of hiring a former attorney who quit a high-paying job in order to follow his ‘‘life’s dream.’’ Thus, the demand for the individual’s services in an alternative job may be lacking. The analysis of earning capacity can be usefully divided between a ‘‘value’’ dimension and a ‘‘quantity’’ dimension. The value dimension relates to the amount of earnings per time period and from a practical perspective concerns the type of occupation chosen. The quantity dimension refers to the amount of time worked per time period and the number of time periods over a lifetime – i.e., work life. The former would involve examination of whether the individual works overtime or perhaps in a second job. The latter explores whether the individual may work beyond normal retirement age. Ireland (1999a) examined the general issue of earning capacity, with respect to both the value and quantity dimensions. For Ireland, ‘‘Earning capacity is, by definition, a hypothetical maximum earnings stream an individual could have choseny. Presumably, the term earning capacity refers to the maximum earnings an individual could have achieved if the individual had chosen to maximize the full potential of his or her earnings’’ (p. 74). For Ireland, earning capacity greater than expected earnings is equivalent to insurance. ‘‘Further, the extra earning capacity represents an insurance value to the worker. In the event of a financial exigency, the worker could postpone retirement and use the extra capacity to generate extra earnings to help with the exigency’’ (p. 79). The intriguing notion in Ireland’s article is that individuals may develop a portfolio of skills for the purpose of diversifying their investment in human capital. If conditions change in the future, a well-diversified portfolio of skills will better serve the individual than putting all his eggs in one basket. A related idea is that alternative skills may be viewed as an option that could be exercised in the future should appropriate economic conditions arise. If an individual possesses certain skills (human capital) but is not currently using them for any of a variety of reasons, the maintenance of such skills may be useful given an uncertain future. If conditions do change in the future, the option to utilize these hitherto unused skills could then be exercised. But since such skills deteriorate over time, especially if unused, the individual will have to make specific efforts to maintain them through ongoing investment of time and money. Most of the remaining research found in the forensic economics literature concerning this topic focuses on the quantity dimension of earning capacity.
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Corcione and Thornton (1991) attempted to distinguish between voluntary and involuntary reasons for withdrawing from the labor force. Given that many of the reasons women do not participate in the labor force are of a voluntary nature, the authors calculated work life with adjustments only for those indicating they desired a job (but could not attain it) and those who have ill health or a disability. Ciecka (1994) surveyed different approaches to estimating work life. The first three that he examined related to using a fixed retirement period, median years to retirement, and mean years to retirement. The remaining ones he surveyed are based on attempts to estimate actual years in the labor force and are some variant of work-life tables or the Life-Participation-Employment (LPE) model. The article indicated that any one of the first three was probably a good choice if the focus is on earning capacity. The other models were better if expected earnings are to be calculated. However, Ciecka did not explain what is meant by the concept of earning capacity or why one of the first three models was a reasonable approximation. Krueger (1999) projected the number of healthy years remaining as a function of age. It was suggested that this estimate could be used for calculations that involve some activity over a lifetime, such as the provision of household services. However, the author indicated that years of healthy life may also be useful with reference to the number of years that a person who is already retired could work if he so desired. Thus far, forensic economists have not generally accepted the concept of healthy life, although it has intuitive appeal with reference to earning capacity. Skoog and Ciecka (2001) published a recent article that may also have application to the concept of earning capacity. The authors derive a probability mass function for estimating the probability that an individual with certain characteristics will be in the labor force for a given number of years. With such a function, it is relatively straightforward to then calculate the mean and the standard deviation of work life (as well as other statistical measures). One could then postulate that earning capacity with reference to work life is equal to, say, one standard deviation above the mean for individuals with similar characteristics. To the extent that number of years worked is greatly affected by personal choice, this number would reflect the years that could be worked should the individual so choose. A potentially valuable aspect of this approach is that the calculation is rooted in actual data. However, there is no ‘‘scientific’’ basis for the assumption that worklife capacity is necessarily equal to the average work life plus one standard deviation (or plus any other value, for that matter), and thus such a standard would likely require some kind of judicial sanction.
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It should be noted in passing that a similar approach could be used with reference to the value dimension of earning capacity as well. Given a sufficiently robust model, earnings could be estimated as a function of certain specified human capital variables. The model would then generate expected values plus some confidence range above and below the expected value given specific values of the independent variables. This range would provide ‘‘reasonable’’ upper and lower limits for estimating future income that would serve as a proxy for earning capacity. The assumption made would be that individuals in the defined upper range are likely to be income maximizers and could therefore serve as an empirical benchmark for estimating earning capacity. Two other articles have discussed earning capacity in the context of situations where expected earnings as reported in tax returns may significantly underestimate earning capacity – namely, farmers and the self-employed. Ralph Brown (1995) argues that the typical Schedule F for reporting farm income should be modified when calculating economic loss. He concludes that it is reasonable to use the opportunity cost approach, especially in estimating management services. Specifically, this might involve calculating the cost of a management fee as a percent of total receipts or more directly by estimating the value of hours required. Brown believes that this approach could also be used in other situations as well. For example, he indicated that the losses of a self-employed trucker who was injured could be evaluated by substituting the cost of a replacement trucker. Spizman and Floss (2002) pursued these ideas more fully when they examined the problems that arise with respect to the self-employed. Aside from the proper accounting of under-reported income, the self-employed (as is true with farmers) receive a great deal of utility from being their own boss. Such non-pecuniary benefits are one explanation of why the self-employed generally earn less than employees with similar backgrounds. As the authors explain, ‘‘But for the death, the decedent could have worked for someone else if he or she did not think the non-pecuniary benefits received by the household were worth the reduced income due to self-employment’’ (p. 15). Death, or permanent disability, precludes this economic option from occurring in the future. Although earning capacity seems to be the generally accepted legal criterion in many jurisdictions, it is an extraordinarily difficult concept to measure empirically. Furthermore, as suggested above, there is a moral hazard problem that pervades discussion of earning capacity since one could claim that virtually anyone has at least some small chance of earning a very large income. What Spizman and Floss emphasize is that, although moral
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hazard is a real problem, it can be avoided in the case of the self-employed since the alternative skills examined are generally in the same occupation. That seems to be the key in considering earning capacity. The alternative income is likely to be higher than expected earnings, but it must not be speculative. Using terminology from the finance literature, the value of the option of choosing the alternative income is directly related to the feasibility of acquiring it should the person choose to do so.
3. FRINGE BENEFITS Fringe benefits are an important part of estimating economic loss. Conceptually, such benefits are part of the total compensation package, and therefore the forensic economist normally must consider the value of such benefits which are funded by the employer. One important issue is what specific items are to be considered as fringe benefits. Launey (1990) focused on this issue. As he explains, it is clear that pay for time not worked, such as vacation and sick pay, normally do not count since they already show up on the W-2. In addition, accident/disability insurance premiums and unemployment insurance are normally excluded, given that the individual’s estimated loss reflects full-time earnings. Other benefits are more complicated. Some benefits, such as options, are very hard to estimate; and others, such as college tuition, may or may not be utilized. The forensic economics literature also has included a discussion of how time off should be valued. Wisniewski (1990) stated that two jobs that pay exactly the same should be valued differently if they include different amounts of time off. Most economists would concur, but would not necessarily agree on how the difference should be valued. Another problem related to measurement is whether consumption should be deducted from fringe benefits. If it should, then in a death case it is only the costs to the survivors for comparable benefits that are to be included. As pointed out by Jennings and Mercurio (1989) concerning health benefits, ‘‘Thus, recovery for medical insurance coverage paid for by the deceased’s employer would be limited to that portion of medical insurance cost paid by the employer and for the benefit of the deceased spouse and children’’ (p. 75). Frasca (1992) also examined the same issue and looked at common data sources if specific employer data were not available. At the time he examined the Employer Cost for Employee Compensation data (ECEC). The ECEC data do not cover everything, such as reimbursed business-related expenses, and tend to ignore benefits that are relatively uncommon among
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the general population but more common among higher income individuals (such as club memberships). The availability of common data sources is of ongoing interest to forensic economists since many cases relate to individuals who have little or no work history. Much debate has centered on how fringe benefits should be measured. Romans and Floss (1989) distinguished three ways of measuring fringe benefits – cost of benefit to employer, benefit to the employee, and cost of replacing the benefit. These approaches differ because of administrative costs, tax issues, and adverse selection problems. For example, employers will likely enjoy economies of scale in purchasing health insurance, so administrative costs per individual will be lower if purchased through the employer rather than individually. Furthermore, insurance purchased individually is subject to moral hazard problems where a person who needs more health care is more likely to purchase a full-coverage premium. Company plans avoid this problem since virtually all employees sign up through the company where they work. DeBrock and Linke (2002) reexamined the three basic methods of measuring fringe benefits. They stated that the employer cost method is commonly used both because it is easy to calculate and understand, and because it is supported by economic logic. But the other two approaches are also employed. For example, if the forensic economist uses the cost of purchasing a COBRA policy after an injury or termination, then he or she is utilizing the replacement cost approach. If the economist estimates the loss of retirement benefits during the period of retirement rather than the contribution of the employer during the period of work, he or she is utilizing the value-to-the-employee approach. DeBrock and Linke also indicated that the difference in the approaches was not insignificant. It is not difficult to demonstrate scenarios where the post-incident loss of social security income is very large. Because it is a government program, the link between payments into the program and benefits received is weak. After a certain number of years, there is also no link between Medicare payments and medical payments. It is common, in fact, for forensic economists to ignore the value of the 1.45% Medicare tax completely. It is clear that the different perspectives on the issue stem primarily from whether the focus is on the loss to the employee rather than to the employer or society at large. In the DeBrock and Linke article, the authors stated that FICA contributions should be valued at the cost to the employer rather than the value to the employee. They argued first that, based upon economic theory, the total cost to the employer, both wages and fringe benefits, was equal to the marginal revenue product of the employee. Furthermore, social
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security has a social dimension in terms of reducing economic insecurity for those who are older or retired. ‘‘Those forensic economists who argue against valuing employer FICA contributions at employer cost do not attach any value to the widely recognized social-good dimension of FICAtype programs’’ (p. 170). James Rodgers (2000, 2002) has written two important articles concerning retirement benefits which measure the loss from the perspective of the employee. The article in the Earnings Analyst (2000) focused on lost social security benefits while the article in the Journal of Forensic Economics (2002) examined all retirement benefits. In the 2002 article, Rodgers first discussed the different types of retirement plans, including defined contribution plans, defined benefit plans, and mixed plans. The second section developed some general concepts related to retirement plans. The first issue considered in this section was under what circumstances it is appropriate to utilize the generally accepted methodology of estimating fringe benefits as a fixed percentage of earnings. Rodgers indicated that it was appropriate when the retirement is funded by a defined contribution plan, the individual is young, or there is little known about the earnings history of the individual. Given that plans are increasingly characterized as defined contribution, such a fixed percentage rule seems more appropriate today than in the past. According to Rodgers, it is less appropriate to use a fixed percentage rule when the individual is covered by a defined benefit plan. In such a plan, there is only a loose relationship between benefits contributed by the employer and benefits received. In that case it may make more sense to use the loss to the employee standard rather than the cost to the employer standard. Rodgers also examined lost social security benefits, which is a type of defined benefit plan. The author came to much the same basic conclusions as Rosenman and Fort (1992) who described the deficiencies of the FICA tax approach eight years earlier. Lost employee benefits may be substantially above or below employer contributions depending upon the circumstances. As Rodgers stated in his year 2000 article, ‘‘The major conclusion arrived at from this analysis is that the FICA tax method provides inaccurate estimates of social security benefit loss arising from reductions in earningsy. Rather than use the FICA tax method, it would be preferable to follow one of two alternative courses of action: (a) directly compute the present value of social security benefit losses, taking account of the FICA taxes saved due to the reduction in earnings or (b) ignore social security benefits entirely’’ (p. 19). It should be noted that calculation of railroad pensions is even more complex than social security (see Ciecka & Donley, 1997).
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Ben-Zion (2001–2002) focused upon pension benefits that were defined benefit plans. Losses in these plans are unusually difficult to calculate because of the weak relationship between contributions and benefits, especially in the short run. The author raised a number of issues, but one of significant interest is that it is often important to distinguish between the annuity certain for a given life expectancy and a life annuity. If the life expectancy of a male age 40 is another 37 years, the former method would require estimating pension benefits as the discounted present value between the presumed age of retirement and age 77. In contrast, the latter method would require incorporating the probability of living each year over a maximum possible survival life (120 years). Although the total number of years alive is the same for both methodologies, the present values will usually differ. Defined benefit plans can be further complicated when the pension is indexed to inflation or when there are unusual tax consequences. Besides the article by Ben-Zion, the Journal of Legal Economics has published several articles on fringe benefits generally and pensions characterized by defined benefit plans in particular. Stoller (1992) and Allman (1993) provided an overview of pensions, focusing on issues that can easily result in large differences in estimating the value of the pension. Bowles and Lewis (1995) examined tax consequences of fringe benefits, noting that many forensic economists ignore tax consequences because they assume that taxes are not applicable. However, some benefits are taxable and many are only tax-deferred rather than tax-free. The final topic covered in this section relates to a question which is important for all estimates of economic loss. Specifically, how quickly do losses rise relative to the discount rate? Forensic economists usually focus upon the net discount rate (NDR) because it is more stable over time than the individual components. Although most forensic economic research has been directed to earnings and interest rates, the same question can be raised with regard to fringe benefits. The topic can quickly become technical, focusing upon the question whether the NDR is stable or not. Ewing, Payne, Piette, and Thompson (2002) examined the question of whether the NDR was stationary over time with regard to fringe benefits and net earnings. If a series is stationary, then it will return to its long-run value after a shock. In that case, using a long-run historical average may be a sensible methodology. If the series is non-stationary, then using the most recent observation may be more accurate for forecasting future values. The Ewing study is notable in that differences between negative and positive shocks are accounted for. Ten different sectors or classifications were
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examined for the years 1982 through 2001. The results of the unit root tests showed that the series were stationary and that the NDRs returned to their long-run averages regardless of the direction of the shock. Ewing et al., conclude that ‘‘for forensic economists, these findings suggest that the value of fringe benefits grow[s] in a fashion similar to that of earnings relative to the interest or discount rate’’ (p. 179). Despite the findings of Ewing et al., evidence exists that at least for health care insurance there is significant uncertainty concerning the future of this important benefit. Health insurance has traditionally been purchased through the employer for many well-documented reasons, although Henderson and Taylor (2002) make the case that the U.S. may be forced to move away from this solution. The authors see one possible solution encompassing defined contribution plans, which will put more of the cost-control burden on the patient and simultaneously distance the employer from health care decisions that can lead to medical malpractice suits. The proposal would include more consumer choice and would provide a range of plans from complete coverage to insurance only for catastrophic events. It should be noted that a similar movement is also occurring with regard to retirement plans. Traditional pension plans are becoming less common, while defined contribution plans that allow flexibility and control over investments are becoming more popular. Benefits represent a complex area for the forensic economist, and it is unlikely that the subject will get any simpler in the future. Benefit plans often change rapidly, and measuring the value of benefits can be difficult. This is certainly an area where more research is needed.
4. THE DISCOUNT RATE Most cases characterized by personal injury or death require forecasting losses into the future and discounting these losses back to the present at a determined discount rate(s). The discount rate chosen can have a major impact on the amount of estimated loss, especially if losses occur for many years into the future. For example, losses may extend for over 70 years if lifetime medical costs are calculated for an infant. A 1% change in the discount rate can result in a 25% change (or more) in present value. As expected, the plaintiff’s side prefers low-discount rates while the defense side prefers the opposite. It is up to the forensic economist to remain neutral in a situation where there may be subtle pressure to ‘‘shade’’ the discount rate up or down. The forensic economist must not only contend with the fact that he
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or she has been hired by one side or the other, but must also be aware that different states have different legal guidelines. The surveys of the NAFE membership by Brookshire and Slesnick (1991) have usually contained questions concerning discount rates. The survey questions discussed below have been taken from an article by Brookshire, Luthy, and Slesnick (2004), and results from the previous surveys are identified as S1 (the earliest) through S5 (the most recent). The first question listed below examines what is usually termed the ‘‘net discount rate’’ (NDR), the difference between the discount rate and the rate of increase in earnings (or some other damages amount such as compensation or medical costs). As will be seen later in this section, much of the voluminous forensic economics literature concerning this topic examines discount rates in terms of NDR. Question 1: Assume that the judge instructs that you MUST estimate a net discount rate in your forecast of economic loss for a 30-year period. The net discount rate may be based upon either nominal or real values. (Please note that for this question the net discount rate is equal to the interest rate minus the general rate of wage increase for all U.S. workers.) Complete the sentencey ‘‘I would use _______% per year as the average net discount rate over 30 future years.’’
The results of the two most recent surveys (1999 and 2003) are given below. Mean (%) Median (%)
S4 2.13 2.00
S5 1.89 2.00
In S5 the average discount rate was 1.89%, a significant increase compared to the estimates from the first three surveys, although down slightly from the previous survey (S4) which asked an identical question. The middle 50% range was 1.25–2.30%. Approximately, 11% of respondents indicated that the NDR was 0.5% or below, and 7% that the rate was 0% or below. One of the rules used by a few states is that the NDR should be zero, commonly known as the total offset rule. Clearly, such a choice is not popular among forensic economists who responded to this survey. The next question referred to the issue of portfolio maturity where future work life was 30 years. Question 2: Assume that an injured worker has 30 additional years of work-life expectancy. Regardless of your mix of government securities versus other securities that you might consider, what is the maturity of securities that you would emphasize in selecting an interest rate(s)? (Please check only one of the options below.)
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Short-term securities (maturing in less than one year). Intermediate-term securities (maturing in one to ten years). Long-term securities (maturing in more than 10 years). A ‘‘mixed’’ portfolio incorporating a variety of maturity lengths. Other (if you select this option, please explain below).
The number responding to this question in the current survey (S5) was 172. Comparison with previous surveys indicated the following:
Short-term (%) Intermediate-term (%) Long-term (%) Mixed (%) Other (%)
S1 17.8 18.9 24.4 32.2 6.7
S2 20.1 20.1 26.2 23.5 10.1
S3 20.3 22.6 24.9 27.1 5.1
S4 22.2 17.1 26.11 29.0 5.9
S5 16.3 15.1 23.3 37.2 8.1
There are two strong conclusions that can be formed based upon the above data. First, there is consistency in the percentage using the various portfolios of securities over the years of the survey. Second, there is little agreement concerning the appropriate maturity of the portfolio itself. Although short-term securities are the choice of a smaller percentage of respondents in the current survey (S5) compared to the previous survey (S4), the results are virtually the same as the very first survey (S1) conducted in 1990. The percentage of those who utilized long-term securities has been unchanged for over a decade. Although the percentage that chose a ‘‘mixed’’ portfolio seems to have increased, only future surveys can help determine whether this is a temporary or permanent change. The next survey question related to the use of Treasury Inflation-Indexed Securities. These securities guarantee certain real rates of return. Some economists estimate both the rate of increase in earnings and the interest rate in real (inflation-adjusted) terms so these rates could potentially be very useful. Question 3: Do you use Treasury Inflation Indexed Securities (TIIS) in developing an estimate of the interest rate or net discount rate? (check one)
_____ YES If you checked ‘‘Yes’’, please explain in developing an estimate of the interest rate or net discount rate.
_____ NO | | | |
If you checked ‘‘No’’, please elaborate how you use TIIS.
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The number responding to this question in the current survey (S5) was 172. Comparison with the previous survey (S4) where the identical question was asked is as follows: S4 14.12 85.88
Percentage checking ‘‘Yes’’ (%) Percentage checking ‘‘No’’ (%)
S5 20.96 79.04
There has been a small increase in the percentage of individuals who use TIIS when calculating discount rates. Whether future surveys reveal that this trend will continue is uncertain. Previous surveys have shown apparent short-term trends with regard to other related questions that did not hold up in later surveys. The final survey question examined here refers to the issue whether current or historical interest rates should be used. Question 4: When determining the interest rate for present value purposes over 30 future years, I generally usey(check one):
_____ Current interest rates. _____ Some historical average of interest rates: I use a historical period of _____years. _____ Some other method (please explain) _____ Not applicable (please explain in Comments section). The number of respondents to this question in the current survey (S5) was 170. In the current survey (S4), this question was slightly different than the comparable question in other surveys. In earlier surveys, there was a category ‘‘Other or not applicable.’’ In the current and the previous survey, this option was broken into two separate possibilities. The results were as follows (with S5 again the current survey):
Historical average (%) Current rates (%) Other (%) Not applicable (%)
S1 57.6 24.6 17.8 —
S2 48.0 34.2 17.1 —
S3 49.4 31.4 19.2 —
S4 49.7 31.6 14.6 4.1
S5 37.7 47.1 14.1 1.2
Comparing the last two surveys, the use of historical averages dropped by approximately 10 percentage points while use of current rates rose by 15
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percentage points. Again, caution should be used when interpreting the significance of these changes. The changes may be temporary (with reversion back to previous values) or perhaps signal even further changes in the future. For those who use historical rates, the average period used was 26.31 years, and the range was from 5 to 62 years. In an early discussion, Gilbert (1991b) laid out nicely the important issues when choosing the appropriate discount rate, some of which are reflected in the survey questions discussed above: (1) Should one use current or past rates? (2) What is the proper maturity of the rates? (3) Should the selection of rates be limited to government securities? (4) Is it proper to use real or nominal values? Another question that could be considered is whether discount rates should be linked to the rate of increase in earnings to calculate a NDR or should the two values be calculated independently. In most cases, the risk-free criterion as established by statute or case law requires that something similar to U.S. securities be utilized. There seems to be little controversy with this conclusion, at least with reference to personal injury and death cases. There has been some discussion that if future income is uncertain, then the appropriate discount rate should reflect this uncertainty. Alternatively, one could lower the expected future losses so these values can be viewed as what is termed a certainty equivalent. However, to the authors’ knowledge, this line of thinking has not been widely accepted. Gilbert notes, however, that what is meant by ‘‘risk free’’ is subject to interpretation. If its only meaning relates to default risk, then virtually any US government security will do. However, if one also considers other types of risk such as interest-rate risk and inflation risk, then other issues arise, such as the maturity of the assets purchased. If future loss is expressed in nominal terms, then a risk-free criterion would seem to require that the forensic economist estimate a series of zerocoupon bonds that mature in the periods indicated. If the bonds are backed by the US government, there is no risk of default. If they are zero-coupon bonds, there is no reinvestment rate risk; and as long as they are held to maturity, changes in their price are immaterial. Finally, since loss is expressed in nominal terms and not real terms, then changes in the rate of inflation need not be considered. However, losses expressed in nominal terms are not common. It can arise when there is a contractual obligation that was abrogated or a pension that specified a fixed number of dollars in the future, but the estimate of lost earnings or profits is more commonly expressed in real terms. An individual’s future earnings in nominal terms are highly unpredictable, depending
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upon future rates of inflation. When economic loss is expressed in real terms, it is appropriate to use a real rather than nominal discount rate. In terms of maturity of the purchased portfolio, if loss is expressed in nominal terms, as indicated above, it is appropriate to utilize a portfolio of zero-coupon bonds with varying maturities. But when future loss is expressed in real terms, the decision is more difficult. What is required is that the individual purchase some portfolio of assets that guarantees, to the extent possible, some real rather than nominal rate of return. Writing in 1991, Gilbert did not discuss Treasury Indexed Inflation Bonds (which were not in existence at the time) and so was only able to consider securities where returns were in nominal values. Although his opinion is far from unanimous among forensic economists, the author indicated that the portfolio should be placed in short-term government securities to minimize the risk from inflation. If an individual held long-term bonds and inflation accelerated unexpectedly, the purchasing power of the bond would fall and the subsequent rise in interest rates would lower the price of the bond. Investment in a coupon bond rather than a zero-coupon bond would provide a partial hedge against inflation since the coupon interest could be reinvested at current rates. If one accepts Gilbert’s conclusion that in most cases it is proper to use real discount rates and that the discount rate should reflect the return on short-term U.S. securities, the next question is what is the appropriate rate? No matter how one calculates real interest rates, the historical record shows that they fluctuate significantly over the business cycle even though real rates fluctuate less than nominal rates. Gilbert concluded that one should use historical rather than current rates. Given that he opted for a short-term portfolio, this conclusion is not at all surprising. What his article does not address, but what is an issue discussed extensively in later years, is what historical period is appropriate. An even more fundamental question is whether any historical information is useful in determining the proper discount rate, whether real or nominal. As mentioned previously, one can either calculate the rate of increase in earnings loss and the discount rate separately or combine them together and calculate what is again termed a NDR, which is usually defined as the difference between these two values. Ireland (1999b) examined the NDR from the perspective of the so-called total offset rule which normally assumes that the two values are equal. In this case, the NDR is zero. However, the term can also be used with reference to the relationship between interest rates and a number of other variables such as fringe benefits, after-tax earnings, and medical inflation. Ireland looked at total offset rules with
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reference to three criteria: (1) legal constraints; (2) accuracy; and (3) ease of understanding. It should be noted that, even though the total offset rule is the focus of his article, the implications are more general. If total offset is not accurate, it is important to determine what NDR should be used, given that accuracy is important. Ireland considered a number of different offset rules with regard to the three criteria stated above. In terms of legal constraints, some courts have required specific discount rates. For example, Alaska formerly required that the economist equate the rate of increase in earnings and the discount rate. This rule not only made it relatively easy to calculate economic loss, but it also meant that the jury did not have to listen to testimony, often conflicting, concerning the appropriate discount rate. There are, however, several problems with such rules. First, as Ireland pointed out, they are usually inaccurate. For example, the Pennsylvania Rule requires that interest rates equal the rate of inflation so that real rates are set equal to zero. This result is rarely valid except perhaps for short periods of time, and then only for short-term government securities. Another example relates to those states which require use of the total offset rule where the rate of increase in earnings equals the discount rate. Payne, Ewing, and Piette (2001), however, provide empirical evidence to suggest that the use of the total offset method is generally invalid. Second, such rules are not always clear cut. Forensic economists practicing in the Commonwealth of Kentucky are frequently told that they should use total offset when estimating present value based upon case law. But the appropriate cases are not clear, and they may be interpreted in a number of ways. Further uncertainty occurs because, when the rule is inaccurate, it follows that a more accurate rule will favor one side or the other. This situation leads to an ongoing battle where either the plaintiff or defense is trying to change the rule through testing its interpretation through the appeals process. To use one example, Egge (1989) examined the issue of legislated discount rates in Minnesota. The rate was not truly fixed but rather varied according to current and historical data. The purpose of the law was to ‘‘set a uniform discount rate, increase the ability to predict trial outcomes, promote settlements, ensure equal treatment under the law, obviate the need for economic testimony, and reduce transactions costs’’ (p. 7). This conflict between economic accuracy and other such goals shows up repeatedly in other articles that discuss legislatively determined discount rates. Egge also described how economists entered the fray, which was characterized by both economic discussion and agendas for certain groups such as insurance companies and trial lawyers.
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Perhaps no issue within the topic of discounting has stirred more academic interest than an examination of the stability of the NDR. In a 1991 article, Lewis (1991) concluded that the NDR was not stable and likely was no more stable than either the interest rate or wage growth separately. This implies there is no significant information that can be derived from historical data. The author also recommended that interest rates should be based on ‘‘stripped’’ or zero-coupon bond securities. These rates, along with an estimate of the increase in nominal earnings, determine the NDR. An interesting twist was added when Lewis examined the implications should the forecast of the NDR prove inaccurate. For example, if the forensic economist believes that the NDR will equal 2% but it turns out to equal 1% (perhaps because wages increase more rapidly than predicted) the plaintiff will not have sufficient money to fund future losses. Given that the court decides that the defendant should bear the risk, a contingency fund could be established that would be utilized given that insufficient money is available. This approach would require that the court remain involved in the case over time. A less intrusive alternative might be for the economist to utilize a lower NDR than expected as a type of ‘‘insurance’’ against possible adverse changes in the economy (from the plaintiff’s perspective). Since 1991 there have been numerous articles concerning both the stability as well as stationarity of the NDR and the individual components of that rate. Specifically, if the NDR is difference stationary (i.e., contains a unit root), then the forensic economist should only use the most recent information to forecast the NDR. On the other hand, if the NDR is trend stationary, then past information is valuable for forecasting the NDR. With respect to the NDR associated with earnings, the studies by Bonham and La Croix (1992), Gamber and Sorensen (1993), and Payne, Ewing, and Piette (1998) found evidence to suggest the NDR is difference stationary. However, once the presence of a structural shift in the relationship between interest rates and earnings around 1979 to 1980 was recognized, a majority of more recent studies have provided evidence to suggest the NDR is trend stationary (see Haslag, Nieswiadomy, & Slottje, 1991, 1994; Gamber & Sorensen, 1994; Pelaez, 1996; Payne, Ewing, & Piette, 1999a,b; Hays, Schreiber, Payne, Ewing, & Piette, 2000; Sen, Gelles, & Johnson, 2000). This structural shift was due to a number of reasons, including deregulation of the financial industry and a greater effort to control inflation. In the case of a structural break, the forensic economist should use the trend function in the post-break period to forecast the NDR. Moreover, if the trend term is statistically insignificant, then one could simply use the average over the post-break period. As pointed out by Johnson and Gelles (1996)
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and Horvath and Sattler (1997), forensic economists should pay particular attention to structural breaks in the use of historical data. Of course, the preceding literature is not helpful in anticipating structural breaks in the future. It should be noted that those economists who are concerned with the stability issue focus on short-term securities. In that case, the portfolio will turn over frequently, and it is necessary to make explicit forecasts of future interest rates. However, for many forensic economists, the question of whether the NDR is stable over time is largely irrelevant. They primarily rely on current interest rates and use either a fixed maturity or a ‘‘laddered’’ maturity structure to determine the relevant discount rate. For example, if the loss period extends for 20 years, an economist might utilize the return on a series of zero-coupon bonds currently available in the market to match the timing of future losses. Weckstein (2001) took this approach one step further and argued for a laddered maturity using indexed rather than nominal Treasury securities. Such securities are obviously superior in terms of purchasing power risk and have little interest-rate risk if held to maturity. Furthermore, real interest rates are generally more stable than nominal rates. Although indexed securities may face liquidity risks and problems in terms of taxes, Weckstein felt that these problems were of minor consequence. The discount rate problem is a topic that has probably been researched more than any other in the forensic economics literature, but it is one that is still unresolved. There is little agreement concerning the use of real vs. nominal rates, short-term vs. long-term (or laddered) maturities, and the value of using historical data for predicting future values. About the only item that most forensic economists agree upon is that the interest rate should reflect returns from a fairly safe investment. The reason for this agreement is that it is what most courts require. No doubt if this restriction were not imposed by the court, the level of risk would be subject to controversy as well.
5. CONSUMPTION 5.1. Background The basis of damages in wrongful death cases in the United States is the financial loss to the survivors of the deceased. In many states, this loss to survivors is described in court decisions and in statutes as being equal to the
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contributions that the decedent might reasonably have been expected to make to them. Economists typically estimate these contributions residually by calculating the earnings of the decedent and deducting from those earnings the decedent’s ‘‘personal consumption.’’ The rationale for such a deduction is straightforward. If the person had not died, he would have spent a certain amount of income exclusively on himself, and this amount would not have been available to his estate or to his surviving relatives. However, considerable differences exist with respect to the treatment of personal consumption across the various states. In a few states, Kentucky for example, no deduction for the decedent’s personal consumption is permitted. At the federal level (Federal Tort Claims Act actions and Federal Employer’s Liability Act actions) and in most states, the consumption deduction in death cases is the decedent’s likely or expected consumption expenditures. Several other states, classified as ‘‘maintenance consumption’’ or ‘‘personal maintenance’’ states, restrict the deduction. For example, Pennsylvania courts define maintenance expenses as those costs to the decedent ‘‘which would have been reasonably necessary for him to incur in order to keep himself in such a condition of health and well-being that he would maintain his earnings power.’’ Operationally, maintenance expenditures are to be calculated as ‘‘that necessary and economical sum which a decedent would be expected to spend, based upon his station in life, for food, clothing, shelter, medical attention, and some recreation’’ (McClinton v. White). In addition to Pennsylvania, several other states also view the decedent from an economic perspective as a producer of earnings for the purpose of estimating the deduction – e.g., Rhode Island, New Hampshire, and Connecticut. Not only do various statutes and court decisions treat personal consumption/maintenance differently, but there are also significant differences in the methods and data sources used by forensic economists in the calculation of the deduction, even within the same state. It is largely for this reason that in NAFE surveys forensic economists have rated personal consumption as one of the most important areas for further forensic economic research. For example, in the 1999 survey 62% of those responding to the survey selected personal consumption as an area of ‘‘high’’ or ‘‘somewhat high’’ research need, second only to the area of household services (65%) (Brookshire & Slesnick, 1999). In this section, we explain the various ways that forensic economists calculate the consumption/maintenance deduction (hereafter, simply consumption deduction) and the light that recent forensic economic research has shed upon the topic.
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5.2. Conventional Methods and Sources for Estimating Personal Consumption In their article, Thornton and Schwartz (1989) enumerated the various data sources and methods that forensic economists at the time tended to use in calculating the consumption deduction, along with the problems associated with each (see also Dulaney, 1991). Among these were: 1. The ‘‘equivalence scales’’ constructed by the U.S. Department of Labor (1968) from its Urban Family Budgets data. A major problem with these scales is that the Urban Family Budget series were discontinued in 1981 because the expenditure data on which the budgets were based were even at that time over 20 years old. An Expert Committee on Family Budget Revisions (the Watts Committee), under contract with the U.S. Department of Labor, estimated a new set of scales in a 1980 report.1 However, the committee did not fully endorse the new scales and instead recommended further research on the question (Johnson, Rogers, & Tan, 2001). 2. The personal consumption estimates formulated by Earl Cheit (1961), which show a family head’s consumption expenditures as a percentage of total family expenditures. The Cheit percentages face several difficulties, however; they are very old (Cheit’s book was published in 1961); the percentages do not vary with family income; the percentages only deal with the consumption of the family head and not of other family members; and Cheit provides very little explanation as to how the percentages were developed. Despite these shortcomings, though, Cheit’s percentages as well as the BLS equivalence scales, continue to be used by some forensic economists. The reasons for their continued use are most likely, as Roy Gilbert observed in 1991a, their simplicity as well as the paucity of superior alternatives. 3. The use of the reciprocal of family size as the fraction for estimating the percentage of family consumption that a family head consumes. Sometimes called ‘‘naı¨ ve equivalence scales,’’2 this approach also suffers from a number of difficulties. For example, family heads may have higher consumption expenditures than dependents. Also, there is no allowance made for either economies of scale or the fact that some family goods are jointly consumed (i.e., the ‘‘public good’’ nature of some family expenditures). The latter is related to the fact that many consumption items (a house or a refrigerator are good examples) are non-divisible, and the death of one family member cannot therefore be expected to reduce such expenditures proportionately.
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Over the past 15 years or so, a number of additional data sources and methods have come to be widely used by forensic economists in the calculation of consumption expenditures in wrongful death cases. Among those sources put out by the federal government, forensic economists probably make heaviest use of the U.S. Department of Labor’s Consumer Expenditure (CEX) Survey. The current CEX Survey program was begun in 1980 (although earlier surveys had been done) and has several desirable features. It is based on two independent samples of consumer units – the Diary survey and the Interview survey – both of which are representative of the U.S. population. It also contains information on consumer expenditures in a large number of detailed categories, which allows the forensic economist to select only those expenditure categories that are appropriate for calculating either consumption or maintenance expenditures. Finally, the CEX data are cross classified by income, age, consumer unit size, sex, region, and selected Metropolitan Statistical Areas (U.S. Department of Labor, 2004). While this last feature of the CEX allows forensic economists to ‘‘tailor’’ their consumption estimates, it also means that there may be some subjectivity involved in deciding which particular classification should be used. There are several potential problems with using CEX data without adjustments when calculating personal consumption in death cases, however. First, not all expenditures that the CEX survey reports deal with goods and services that are actually consumed. Rather some expenditures simply increase individual or household wealth. Also, as noted above in the shortcomings of ‘‘naı¨ ve’’ (1/n) equivalence scales, problems of non-divisibility, the ‘‘public good’’ nature of some expenditures, economies of scale, and differential consumption by children and adults also apply to the CEX data.3 Recognition of these shortcomings led Nelson and Patton (1984) to construct percentage estimates of their own for the incremental consumption of an adult in households with two or more individuals. Using CEX Survey data, Patton and Nelson (P–N) assigned each of the various detailed types of CEX expenditures4 into one of the four categories: C1: Expenditures that are either non-divisible (e.g., most housing expenditures) or that can be attributed completely to children (such as educational expenses); C2: Expenditures that tend to be equal for each family member (e.g., food at home); C3: Expenditures made only by adults (such as alcoholic beverages); and C4: Expenditures made only by adults but that differ by gender (e.g., clothing and hair care).
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Patton and Nelson then calculate the incremental consumption of an adult j (in percentage terms) in a household with two or more persons according to the following equation: ½ðC 1 0 þ C 2 =n þ C 3 =2 þ C j4 Þ=Y 100 where n is the number of family members and Y the family income. In short, the P–N estimates simply treat the various categories of CEX expenditures differently for the purpose of estimating incremental personal consumption with some expenditures included in toto, some averaged across the number of family members, and some not included at all. Nelson and Patton’s original article was published in 1984 in a Washington State bar news publication and did not immediately attract widespread attention. It was also based on CEX Survey data that at the time were nearly 12 years old. However, an updating and refinement of their original estimates based on more recent CEX data appeared in the Journal of Forensic Economics (JFE) in 1991. In their update, Patton and Nelson provided both a table of personal consumption percentages (based on various income levels, gender, and family size according to the classification equation explained above) and also regression equations for estimating consumption percentages for income levels not matching those provided in the table. Since their 1991 article, the original Patton and Nelson (1991) tables have been updated several times (with first Lierman and later Ruble added as coauthors) using more recent CEX data.5 There has been some criticism of the P–N tables, although most of it has been mild. Gilbert (1991a), for example, has suggested that the personal consumption of an individual should be computed as a percentage of total family consumption expenditures rather than as a percentage of family income as Patton and Nelson do. Boudreaux (1999) makes a similar case for using total family consumption expenditures, arguing that the numerator of the P–N percentages include consumption expenditures from all sources (not just current income) while the denominator is simply current family income. Because lower-income families on average have expenditures that exceed current income, Boudreaux argues that the P–N percentages contain an upward bias for this group. (The bias would be negative for higher-income families.) Dividing by family expenditures rather than income would remove this bias, according to Boudreaux. In his alternative tables, he finds the consumption percentages to be relatively ‘‘flat’’ with respect to income changes, unlike in the P–N tables. What is more, Boudreaux’s consumption percentages turn out to be fairly similar in magnitude to those of Cheit and to the BLS equivalency scales
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(p. 264). In a response to Boudreaux, however, Ruble, Patton, and Nelson (2001) contend that using family expenditures rather than income in the denominator of the P–N percentages is ‘‘inappropriate.’’ They argue instead that ‘‘at issue is the determination of what portion of family income would have been personally consumed by the decedent’’ (p. 175). Other modifications to the P–N methodology have been suggested by Bell and Taub (2002), who argue that consumer units of two or more persons as defined by the CEX Survey do not always signify two or more adults, a fact overlooked by P–N. Furthermore, Bell and Taub disagree on the P–N allocation of certain expenditures across family members – for example, apparel and services, entertainment, and telephone expenses. In their latest update (2000–2001) of the P–T tables, Rubin, Patton, and Nelson (2002) incorporate a number of the suggestions of Bell and Taub; however, they find that the revisions ‘‘make little difference’’ in the latest consumption percentages. In addition to the P–N approach, the forensic economics literature has seen a number of other approaches for measuring personal consumption in recent years. In a 1990 article, Harju and Adams (1990) (H–A) suggest a procedure for estimating personal consumption that is very similar to that of Patton and Nelson. They first propose dividing total family consumption expenditures into variable, fixed, and adult-only categories. They then calculate ‘‘family support percentages’’ for families of varying sizes and quintile income levels. Any given family support percentage (P) is simply the percentage of the former family expenditure level that, in the event of the loss of a family member, would allow consumption expenditures of the remaining family members to be the same as they had been (Of course, 1-P would thus represent the decedent’s personal consumption percentage). The H–A estimates, though, have received relatively little attention in the forensic economics literature, nor have they been periodically updated. Curiously, neither H–A nor P–N make reference to the other’s methods, despite their similarity and their both being published in the Journal of Forensic Economics. In a 1992 article, James Ciecka (1992) uses the concept of ‘‘service flows’’ within the family to estimate self-consumption percentages in wrongful death cases. The family service-flow notion was developed originally by Lazear and Michael (1980) and is based on the concepts of public goods, economies of scale, and the division of labor within the family. When the size and composition of a family is altered because of the death of one of its members, the ability of the family to produce the former flow of services is changed. From this it becomes possible to estimate the amount of income
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that would lead to the same per capita service flows as before and, equivalently, the self-consumption deduction. Ciecka constructs a table showing self-consumption deductions as families are reduced in size by one member. Interestingly, in comparing his self-consumption percentages with those of several other studies (e.g., Cheit, and Harju and Adams), he finds his estimates to be ‘‘quite closeyexcept when a family is reduced to only one person after a wrongful death occurs’’ (p. 113). Despite a sound theoretical base, the Ciecka/Lazear-Michael method does not seem to be widely used in wrongful death cases, most likely because of its complexity and the fact that the percentages it produces are not substantially different than those of other methods. Trout and Foster (1993) applied regression analysis to more than 5,000 individual household units from the CEX Survey in an attempt to estimate more precisely the effects of income, family size, and age on consumption. According to the authors, this approach obviates the need for ‘‘arbitrary assumptions about joint vs. individual consumption’’ ala P–N. When compared to the personal consumption percentages of other studies, though, the Trout–Foster estimates tended to be much lower, although the authors cautioned that their results could not be considered to be ‘‘definitive’’ (p. 149). The Trout–Foster estimates were criticized by William Landsea (1994), who showed that they produced some anomalies and even nonsensical results, such as absolute consumption expenditures falling when income rose (p. 211). David Jones (1996), in a later comment, argued that the savings rates implied by the Trout–Foster estimates were ‘‘four to six times the national average’’ (p. 53) and hence ‘‘not credible.’’ A variant of the Trout–Foster method has been used recently by John Scoggins (2002) with ungrouped data from the CEX Survey. Scoggins relies on the life-cycle and permanent income hypotheses in formulating his model; but since permanent income is not directly observable, he formulates an instrumental-variables model of personal consumption. The personal consumption percentages that he estimates are generally lower than those estimated in other studies such as Patton and Nelson, although not as low as those of Trout and Foster. Ajwa, Martin, and Vavoulis (AMV, 2000) have noted that most studies that estimate personal consumption have ignored household savings, which they say can be reasonably viewed as a form of delayed consumption. This is especially true for higher-income families. By ignoring savings, AMV argue that personal consumption percentages estimated in previous studies may be too low. They then estimate their own set of percentages using expenditure data from the CEX Survey and breaking the data down in a fashion much
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like that done by Patton and Nelson. Unlike Patton and Nelson, though, AMV include savings as part of consumption in two alternative ways: (1) by defining savings as gross earnings less taxes, social security, pensions, and expenditures. This may be considered as savings available for immediate consumption; and (2) by defining savings as in (1) above but not subtracting social security and pensions. This second definition views savings as available for consumption over a longer time span. AMV then present tables of consumption percentages (they also provide regression equations for estimation purposes, as do Patton and Nelson) that ‘‘fall within the range of results from comparison studies’’ (p. 9). To a great degree, personal consumption during retirement years has either been ignored or treated no differently than personal consumption during the work-life period by forensic economic research. However, Shik Young (1995) argues that household consumption decisions may change considerably during retirement. Using data from the CEX Survey, Young divides household expenditures into four categories (which he calls fixed, semi-variable, variable, and exclusive) and computes regression equations for estimating the consumption of a retired head of household on the basis of income and the presence or absence of spouse and dependents. Young’s ‘‘consumption-to-income ratios,’’ as he puts it, ‘‘may be significantly different than the one[s] used for the work period’’ (p. 79), although he provides no comparisons with percentages estimated in other studies.6 In a recent article, Roger Kaufman (2003) criticizes the usual current methods of calculating post-retirement consumption and then offers his own methodology. Kaufman argues that many forensic economists ignore postretirement consumption altogether. Others tend to follow one of the several approaches to indirectly estimate post-retirement consumption (p. 3). Ruble, Patton, and Nelson (2000), for instance, recommend assuming that retirement consumption will be exactly offset by pension and social security income (p. 307). Other forensic economists implicitly assume that a decedent’s consumption after retirement would be equal to some fraction of social security and pension benefits. For example, some exclude all future employer and employee contributions to social security and pension plans in estimating lost future earnings. Others exclude only future employer contributions. As Kaufman points out, however, there are problems with each of these approaches. Kaufman instead proposes an explicit three-step process to measure postretirement consumption. First, an estimate of total retirement income plus asset depletion is made. Kaufman indicates that this could be either individual or family, although he does not explain which method is methodologically
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preferable. Next, comes an estimate of consumption for the entire household had the tort not occurred during this time period. Third, the percentage of household consumption attributable to the deceased is made. The most difficult part of Kaufman’s estimating process relates to postretirement income. This requires a calculation of social security income, private pensions, interest and dividends, other income such as rents and royalties, the rate of depletion of non-retirement assets, and the tax rate on income. Some of these components (such as non-retirement assets) or income sources (such as rents and royalties) are especially troublesome. Fortunately, the largest components of retirement income, social security, and private retirement benefits, are relatively easy to estimate provided that the forensic economist can accurately project future wage earnings. The second step, estimating total household consumption out of total household income, is potentially another difficult task. However, Kaufman indicates that for most households, the propensity to consume out of retirement income is close to 1.0. The exception, of course, is upper-income households, which are more likely to leave bequests. He does address this difference between households and provides a separate estimate of consumption based on household income. The third step involves calculating the percentage of household consumption attributable to the deceased. Given that the denominator is consumption rather than income, the rate is somewhat higher than those found in various studies such as Ruble et al. (2000) and Bell and Taub (2002). Consumption expenditures would be calculated over a normal life expectancy. Kaufman concludes by contrasting his approach with several other standard methodologies assuming such different scenarios as single individuals, married couples, families with one spouse working or both spouses working, and different levels of earnings. Not surprisingly, the difference between the Kaufman approach and other approaches varies according to the particular scenario. Although his approach appears to be more accurate than other approaches (which were mainly rules-of-thumb), the question remains whether the additional time required for a detailed analysis of the plaintiff’s post-retirement income is warranted.
5.3. Which Methods Are ‘‘Best’’? As the above discussion has shown, forensic economists now have at their disposal a fairly large number of approaches when it comes to estimating the
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personal consumption deduction in wrongful death cases. But which methods do they tend to use most? Which methods are most defensible? Have any fallen out of favor? Although various NAFE surveys have asked forensic economists what numerical percentage consumption deduction they would use in a particular scenario, only one has contained a question about which general method or source is preferred. In their 1990 survey, Brookshire and Slesnick found that, in responding to the question ‘‘My favored data source for obtaining the consumption percentage is___,’’ over half mentioned either the Cheit study or the BLS equivalency scales. The number responding to the question, however, was small (n ¼ 68), and the NAFE survey is restricted to those who are members of NAFE. Interestingly, no other source received more than four responses (p. 127). Respondents to later surveys have sometimes volunteered comments on the particular method or source that is used. While the comments seem to be all over the board, the P–N method and the CEX Survey are most commonly mentioned. Even so, as Martin (2003) has noted, most of the research studies done on the subject have yielded consumption percentages that are ‘‘tightly clustered.’’ And in his book Determining Economic Damages, he presents averages of the results of the various studies for possible use by forensic economists (p. 5-5, Table 22C). Finally, in a recent article Thomas Depperschmidt (1997/1998) discusses some of the implicit assumptions and philosophical issues underlying the personal consumption deduction. These include its purpose or focus – is it to estimate the consumption share of a decedent’s income, or is it to estimate the change in the standard of living of those surviving the decedent? The two approaches will not necessarily yield the same results. He also discusses some problems that arise in dealing with the public good aspect of some consumption expenditures. P–N and others, as we have seen, do not count nondivisible goods (such as housing) in estimating a decedent’s consumption expenditures. But, as Depperschmidt points out, this raises the free rider issue: ‘‘Someone does have to pay for the public good for it to exist and thereby make possible others’ free riding. Should not the decedent also pay for his consuming a share of that good?’’ (pp. 6–7). He also argues that greater precision may not always result from categorizing some consumption as ‘‘individual specific’’ and some as ‘‘joint’’ in the P–N tradition. Questions such as ‘‘How much did the decedent drive the car?’’ and ‘‘If alcohol is not consumed by children, are breakfast sugar puffs not consumed by adults?’’ point to the impossibility of precisely determining consumption (p. 15). In light of these and other difficulties, Depperschmidt
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remains unconvinced ‘‘that the uncluttered 1/n approach to personal consumption is either unworkable or wrong’’ (p. 17), even though it has been labeled by some as ‘‘naı¨ ve.’’
6. AGE-EARNINGS PROFILES A common task of the forensic economist is to project lost earnings in the formulation of economic damages. The age-earnings profile recognizes the fact that earnings tend to vary with age and is commonly used in cases where the individual has little or no prior earnings history. The P-60 series published by the Department of Commerce provides the latest data on ageearnings profiles, usually reported in 10-year brackets. In addition to general wage increases, age-earnings adjustments are made to account for individual productivity growth factors related to age – for example, promotions, job advancements, and on-the-job training. In light of these factors, the typical age-earnings profile tends to display an inverted U-shape: earnings of younger individuals rise as human capital is acquired, with a leveling off of earnings for individuals in the middle stages of their work life, followed by a decline in earnings for workers nearing retirement. While there is a general consensus that earnings vary with age, there are a number of issues related to the use of age-earnings profiles as discussed by Gohmann, McCrickard, and Slesnick (1998). First, given the cross-sectional, point-in-time nature of reported age-earnings profiles, there is no assurance that the age-earnings profile for the specific demographic cohort will be a valid representation of the individual’s true age-earnings profile over time. Second, the cross-sectional nature of the data also means that the comparison involves individuals in different cohorts at different ages. In other words, it is unlikely that a 25-year-old male today will in 20 years have the same labor market experience and wages as a 45-year-old male today. Third, the different age cohorts can vary in size due to demographic shifts over time. Thus, the size of the age cohorts will influence the relative wages among age cohorts. Moreover, the returns to human capital, hence relative wages, may very well change as technology and the industrial structure of the economy changes. Finally, do age-earnings profiles change significantly over time? Indeed, if the age-earnings profiles are relatively stable over time, then the use of the cross-sectional data for projecting earnings losses into the future may be valid; however, if the age-earnings profiles change significantly over time, then the forensic economist needs to recognize these systematic changes.
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We begin this section by reviewing the major forensic economics literature that addresses the various issues related to age-earnings profiles. Applying standard human capital theory, Lane and Glennon (1985) argued that the use of one earnings growth rate for an age cohort will provide misleading results in the determination of economic damages if the influences of educational level, race, sex, and occupation of an individual are not incorporated into the analysis. Using cross-sectional 1980 census data, they estimated an earnings equation which includes human capital variables (such as experience and education) as well as labor supply controls (such as the number of children, marital status, and age). They also captured the effect of discrimination by race, sex, and age with dummy variables. Census regional dummy variables were used to capture differences in regional preferences and living costs. Likewise, dummy variables were used to measure differences between rural vs. urban and central city vs. suburban labor markets, along with the occupational and industrial composition. Lane and Glennon also argued that the use of cross-sectional data eliminates both inflationary bias in the data as well as the influence of business cycle fluctuations; however, they recognize the fact that the results will still not be as precise as in a longitudinal study. Given their earnings equation, the estimated age-earnings profiles of specific individuals identified by their characteristics can be generated by allowing age to vary. Bryan and Linke (1988) questioned the results of Lane and Glennon since their predicted growth rate of earnings for a college graduate was identical to that of a high school graduate, a result contrary to human capital theory, which would suggest that more education should lead to higher earnings. Lane and Glennon (1988) replied to the issue raised by Bryan and Linke of different earnings growth rates for individuals with different educational levels with the inclusion of an interaction term for age and education. Furthermore, Gohmann (1992) addressed three other problems with the Lane and Glennon study: large declines in the growth rates for older workers partially due to the inclusion of partial retirees with older full-time workers, the absence of higher order education and tenure variables, and the absence of age-interaction variables. Using the Retirement History Survey for the years 1969–1975, Gohmann estimates an earnings equation which includes the interactions of all variables with age along with the use of only full-time workers where a smaller decline in the growth rates of older workers is observed. Abraham (1988a, b) argued that in the calculation of economic damages, the growth in earnings is sometimes double counted when using the ageearnings profiles. His reasoning is that adding earnings growth obtained
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across age brackets to some measure of productivity growth leads to such double counting. In response to Abraham’s claim, Saurman (1988), Ciecka (1988), and Jones (1988) essentially argued that using age-earnings growth rates and the growth in general productivity over time in the same calculation is not double counting productivity changes. Saurman (1988) elaborated by stating that the preferred method is to follow a given cohort through time which would provide a more representative picture of earnings growth over time, than a comparison of different cohorts at a specific point in time. Extending the discussion on the shortcomings using age-earnings profiles at a specific point to measure earnings growth over time, Lewis (1989) argued there is no theoretical justification for using cross-sectional ageearnings profiles for projecting earnings of an individual into the future. By incorporating all factors that affect wage growth (overall labor productivity, inflation, and age-earnings factors), Lewis develops a time series profile of a specific cohort using earnings data for the years 1949, 1959, 1969, and 1979 compiled by sex and 10-year age categories. For instance, the 25–34 year-old male cohort in 1949 was the 35–44 year-old cohort in 1959, etc. In response to Lewis’s study, de Seve (1991) provided an additional rationale for the decline in earnings for older workers observed in age-earnings profiles. Specifically, de Seve suggests that ‘‘cross-sectional samples of earnings for older workers inherently increase the weighting of lower paid workers in the mix as a function of age. Because higher paid workers tend to retire earlier than their lower paid counterparts, average-earnings are pulled down with increasing weight past age 55. Thus, a cross-section may be an accurate representation of employed workers by age, while not being a good proxy for a longitudinal age-earnings profile’’ (de Seve, 1991, p. 68). De Seve (1991) continues by stating: y [T]he cross-section can be an accurate representation of earnings by age for those working and still not be an accurate age-earnings profile. An ideal profile will express age-related earnings, ceteris paribus. That means that other factors, including life expectancy, labor participation, employment probabilities and hours worked, must be constant throughout the lifetime earnings cycle covered by the profile. If they vary, the use of such a profile will double count LPE factors used elsewhere in the projection of earnings as well as impose other biases (p. 69).
Brookshire and Mathis (1993) improved the accuracy of the age-earnings profile for a given year by examining individual data rather than grouped data. Specifically, whereas previous analyses relied upon data grouped by age, sex, and race or age, sex, and education, Brookshire and Mathis used individual data on age, sex, race, and education for five-year intervals.
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Gilbert (1994) also used individual data from the 1990 census to provide more accurate estimates of age-earnings profiles for a given year. Using census data along with data from the Panel Study of Income Dynamics (PSID), Rodgers, Brookshire, and Thornton (RBT, 1996) re-emphasize the issues surrounding the use of cross-sectional age-earnings profiles to project future earnings. According to RBT, the construction of the earnings path of an individual given a certain education level depends on three effects. Period effects consist of the effects of inflation and the general productivity growth rate for the economy which impact earnings over time. The age effect represents the impact that an individual’s age and experience has on the growth of earnings. The cohort effect reflects the birth category into which an individual is born. For instance, individuals born into the baby boomer cohort, a relatively large cohort, will experience lower earnings relative to individuals in other cohorts. RBT stress that cross-sectional age-earnings profiles should not be interpreted as a ‘‘path’’ which the earnings of individuals can be expected to follow over time. They also point out that it is difficult to discern between the age and cohort effects in the formulation of future earnings. For instance, for a given age-earnings profile, the change in earnings between adjacent age categories may not reflect the effect of age alone, but also a cohort effect based on the relative number of workers in the adjacent age brackets. Moreover, the decline in earnings of older workers observed in age-earnings profiles can be attributed to differential earnings growth rates across age categories, the retirement of higher earning workers, and perhaps a reduction in the number of hours worked. Comparing age-earnings profiles from the cross-sectional census data with longitudinal PSID data, RBT find that young high school and college graduates experience more rapid earnings growth than older cohorts. This finding is consistent with the usual interpretation of the more rapid rise in earnings for younger workers in cross-sectional earnings profiles as an age/experience effect. Also, cohort data support the conclusion that nominal earnings of males do not decline with age until around age 60. It is obvious from the literature reviewed that the cross-sectional nature of age-earnings profiles for different demographic cohorts at a point in time means that such profiles may not be representative of the true earnings paths of an individual or group of individuals over time. Furthermore, age-earnings profiles themselves may change over time. Gohmann et al. (1998) use data from the 1980 and 1990 Public Use Micro Data File 1% sample from the Census of the Population to examine whether the age-earnings profiles for white men and women have changed over time. Specifically, the changes in age-earnings profiles differ by educational level. Individuals with lower
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levels of education experienced declining age-earnings profiles over time. As a result, the use of cross-sectional age-earnings profiles from one year will tend to overestimate lost future earnings. In conclusion, RBT (1996) provide several suggestions for future research on age-earnings profiles (p. 208): 1. Forecasts that splice together cohort data to include enough years to make up an entire working life. 2. Comparative analysis of educational attainment levels between those of high school graduates and bachelor degree holders. 3. Analysis of hours-worked data in the PSID for developing estimates of lifetime hours worked. These data could be compared with the projected lifetime hours worked for such approaches as the LPE or work-life expectancy tables. 4. Determination of sampling errors and confidence intervals in regards to the PSID as well as a comparison between the PSID and census data. 5. The addressing of possible selection bias issues with respect to PSID and census data. Gohmann et al. (1998) also offer some additional recommendations for further research on age-earning’s profiles (p. 187): 1. Use of cross-sectional and time-series data such as the National Longitudinal Survey of Youth (NLSY) to construct more accurate estimates of the earnings paths that individuals follow over time. 2. Comparison of the results from the NLSY with P-60 data series to determine the bias in cross-sectional data relative to the time-series data.
7. CONCLUSION In this chapter, we have reviewed recent forensic economic research in several of the most critical areas involving the proper calculation of damages in wrongful death and personal injury cases. As readers will have noticed, a good number of the research studies discussed have been drawn from the pages of the Journal of Forensic Economics, the official organ of the NAFE, and the Journal of Legal Economics, published by the American Academy of Economic and Financial Experts. Prior to the creation of these two bodies in the late 1980s, there existed few outlets for forensic economic research. Consequently, what some have referred to as the ‘‘first generation’’ of forensic economists were pretty much on their own when it came to utilizing
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or developing appropriate methodology and data sources (Thornton & Ward, 1999, p. 110). Today, with these and several other established journals dealing with forensic economics issues and practice, a considerable knowledge base has been established, as this chapter has attempted to show.
NOTES 1. See Harold Watts (1980), ‘‘Special panel suggests changes in BLS family budget program,’’ Monthly Labor Review, Vol. 103, No. 12, March 1980, pp. 3–10. 2. Edward Lazear and Robert Michael, ‘‘Family size and the distribution of real per capita income,’’ American Economic Review, March 1980, Vol. 70, pp. 91–107. Also, in referring to this method Cris Lewis (1992) states that ‘‘the ultimate in naı¨ vete would simply assign an offset factor of 1=n to a member of an n-person family unit.’’ C. Lewis, ‘‘The rationale and quantitative evidence for the personal consumption offset in wrongful death actions,’’ Journal of Legal Economics, July 1992, p. 4. 3. There is also the problem that consumption expenditures of low-income families exceed actual income by a substantial amount, as Gilbert (1991, p. 177) points out. 4. Patton and Nelson excluded all expenditures on taxes, pensions, and social security. 5. See Walter Lierman, Robert Patton, and David Nelson (1998), ‘‘Patton–Nelson personal consumption tables updated,’’ Journal of Forensic Economics, Winter 1998, Vol. 11, No.1, pp. 3–7. Michael Ruble, Robert Patton, and David Nelson (2002), ‘‘Patton–Nelson personal consumption tables 1997–1998 update,’’ Journal of Forensic Economics, Fall 2000, Vol. 13, No.3, pp. 303–307. Michael Ruble, Robert Patton, and David Nelson, ‘‘Patton–Nelson personal consumption tables 2000–2001,’’ Journal of Forensic Economics, Fall 2002, Vol. 15, No. 3, pp. 295–301. 6. One question that emerges in the context of retirement is whether the forensic economist should deduct consumption from fringe benefits as well as from income. To use a simple example, suppose that before his death John Smith earned $50,000 per year and that he contributed $5,000 out of this towards his retirement, as did his employer. If one assumes for simplification that consumption in retirement years is basically the same as during working years (which, of course, is probably not true), then John’s consumption would be calculated as some percentage of his entire $50,000 income plus some percentage of the $5,000 contribution by the employer. Thus, if the forensic economist counts the value of retirement benefits at the time they are being contributed, the usual case, then he should deduct consumption from the employer contributions. As an alternative, the economist could count the contributions when they would have been received, which is probably the more accurate (but arduous) approach. Whether consumption should be deducted from other employer-provided fringe benefits is a more difficult question. They should probably not be deducted from health care benefits. If anything, the cost of health insurance for the surviving family will likely be even greater than the cost before even though the family is now smaller.
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There also arises the question of whether consumption should be deducted from the value of household services. For example, if Mrs. Smith did 10 hours of cooking per week for the four-person family, the total cooking time required for the remaining three members may only be eight hours. Two hours of cooking were, in effect, selfconsumption. Moreover, Mrs. Smith may have previously spent 15 hours a week cleaning and now needs to only clean 5 hours a week because her former husband was a ‘‘slob’’ (We can’t think of a milder way to put it.) The ‘‘slob effect’’ means that after the deceased is gone the survivors are faced with fewer hours of housework, not more.
ACKNOWLEDGMENT The authors would like to thank Frank Tinari for his helpful comments on the Victim’s Compensation Fund appendix.
REFERENCES Abraham, F. J. (1988a). Pitfalls to using the real rates or age-earnings profile models in calculating economic loss. Journal of Forensic Economics, 1(2), 77–81. Abraham, F. J. (1988b). Pitfalls to using the real rates or age-earnings profile models in calculating economic loss: A reply. Journal of Forensic Economics, 2(1), 149–151. Ajwa, M., Martin, G., & Vavoulis, T. (2000). Estimating personal consumption with and without savings in wrongful death cases. Journal of Forensic Economics, 1(13), 1–10 (AMV). Allman, P. (1993). Four economic issues in pension valuations. Journal of Legal Economics, 3(2), 61–68. Bell, E., & Taub, A. (2002). Adult consumption ratios: An alternative approach. Journal of Forensic Economics, 15(1), 1–18. Ben-Zion, B. (2001–2002). The valuation of the loss of future pension income. Journal of Legal Economics, 11(3), 1–24. Bonham, C., & La Croix, S. (1992). Forecasting earnings growth and discount rates: New evidence from time series analysis. Journal of Forensic Economics, 5(3), 221–231. Boudreaux, K. (1999). Patton–Nelson personal consumption revisited: Is income important? Journal of Forensic Economics, 12(3), 255–265. Bowles, T., & Lewis, W. C. (1995). Estimating lost retirement benefits: Tax considerations. Journal of Legal Economics, 5(3), 59–68. Brookshire, M., Luthy, M., & Slesnick, F. (2004). Forensic economists, their methods and estimates of forecast variables: A 2003 survey study. Litigation Economics Review, 6(2), 28–44. Brookshire, M., & Slesnick, F. (1991). A 1990 survey study of forensic economists. Journal of Forensic Economics, 4(2), 125–149. Brookshire, M., & Slesnick, F. (1999). A 1999 survey study of forensic economists – their methods and their estimates of forecast variables. Litigation Economics Digest, 4(2), 65–96.
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Brookshire, M. L., & Mathis, G. L. (1993). The calculation and application of age-earnings adjustments. Journal of Legal Economics, 3(3), 23–42. Brown, R. (1995). Loss of earning capacity in the case of a farmer. Litigation Economics Digest, 1(1), 1–11. Bryan, W. R., & Linke, C. M. (1988). The estimation of the age/earnings profiles in wrongful death and injury cases: Comment. Journal of Risk and Insurance, 55, 168–173. Cheit, E. (1961). Injury and recovery in the course of employment. New York: Wiley. Ciecka, J. (1988). Real rates and age-earnings models: Comment. Journal of Forensic Economics, 2(1), 145–146. Ciecka, J. (1992). Self-consumption allowances, family size and family structure. Journal of Forensic Economics, 5(2), 105–114. Ciecka, J. (1994). A survey of the structure and duration of time periods for lost earnings calculations. Journal of Legal Economics, 4(2), 39–50. Ciecka, J., & Donley, T. (1997). The calculation of lost pension benefits for railroad workers. Litigation Economics Digest, 2, 136–150. Ciecka, J., Donley, T., & Goldman, J. (2000–2001). A Markov process model of work-life expectancies by educational attainment based on labor force activity in 1997–1998. Journal of Legal Economics, 10(3), 1–21. Corcione, F., & Thornton, R. (1991). Female work experience: Voluntary versus involuntary labor force activity. Journal of Forensic Economics, 4(2), 163–174. DeBrock, L., & Linke, C. (2002). Valuing employer FICA contributions in an analysis of diminished earnings capacity. Journal of Forensic Economics, 15(2), 165–172. Depperschmidt, T. (19971998). A law and economics perspective on the personal consumption deduction in wrongful death litigation. Journal of Legal Economics, 7(3), 1–22. de Seve, C. W. (1991). Relationship between age, earnings, and the net discount rate revisited. Journal of Forensic Economics, 5(1), 67–70. Dulaney, R. (1991). Estimating decedents’ consumption expenditures in wrongful death actions: Some refinements. Journal of Legal Economics, 1(2), 94–98. Egge, K. (1989). Legislatively imposed net discount rates: Minnesota’s tort reform. Journal of Forensic Economics, 2(3), 7–14. Ewing, B., Payne, J., Piette, M., & Thompson, M. (2002). Unit roots and asymmetric adjustment: Implications for valuing fringe benefits. Journal of Forensic Economics, 15(2), 173–179. Frasca, R. (1992). The inclusion of fringe benefits in estimates of earning loss: A comparative analysis. Journal of Forensic Economics, 5(2), 127–136. Gamber, E., & Sorensen, R. (1993). On the testing for the stability of the net discount rate. Journal of Forensic Economics, 7(1), 69–79. Gamber, E., & Sorensen, R. (1994). Are net discount rates stationary? The implications for present value calculations: Comment. Journal of Risk and Insurance, 61(3), 503–512. Gilbert, R. (1991a). Estimating personal consumption of a deceased family member. Journal of Forensic Economics, 2(4), 175–185. Gilbert, R. (1991b). Forensic discount rates. Journal of Legal Economics, 1(3), 40–51. Gilbert, R. F. (1994). Estimates of earnings growth rates based on earnings profiles. Journal of Legal Economics, 4(2), 1–19. Gohmann, S. F. (1992). Age-earnings profile estimates for older persons in wrongful death and injury cases. Journal of Risk and Insurance, 59(1), 124–135.
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Gohmann, S. F., McCrickard, M. J., & Slesnick, F. (1998). Age-earnings profiles estimates: Do they change over time? Journal of Forensic Economics, 11(3), 173–188. Harju, M., & Adams, C. (1990). Estimating personal expenditure deductions in multi-income families in cases of wrongful death. Journal of Forensic Economics, 4(1), 65–81. Haslag, J., Nieswiadomy, M., & Slottje, D. J. (1991). Are net discount rates stationary? The implications for present value calculations. Journal of Risk and Insurance, 58(3), 505–512. Haslag, J., Nieswiadomy, M., & Slottje, D. J. (1994). Are net discount rates stationary? Some further evidence. Journal of Risk and Insurance, 61(3), 513–518. Hays, P., Schreiber, M., Payne, J., Ewing, B., & Piette, M. (2000). Are net discount ratios stationary? Evidence of mean reversion and persistence. Journal of Risk and Insurance, 67(3), 439–450. Henderson, J., & Taylor, B. (2002). Employer-sponsored health insurance: Past, present and future. Journal of Forensic Economics, 15(2), 181–194. Horner, S., & Slesnick, F. (1999). The valuation of earning capacity: Definition, measurement and evidence. Journal of Forensic Economics, 12(1), 13–32. Horvath, P., & Sattler, E. (1997). Calculating net discount rates – It’s time to recognize structural changes: A comment and extension. Journal of Forensic Economics, 10(3), 327–332. Ireland, T. (1999a). ‘Lost earning capacity’ vs. ‘expected lost earnings’ in wrongful death analysis. The Earnings Analyst, 2, 73–86. Ireland, T. (1999b). Total offsets in forensic economics: Legal requirements, data comparisons, and jury comprehension. Journal of Legal Economics, 9(2), 9–23. Jennings, W., & Mercurio, P. (1989). Risk-adjusted employer-paid benefits in wrongful death cases. Journal of Forensic Economics, 3(1), 75–76. Johnson, D., Rogers, J., & Tan, L. (2001). A century of family budgets in the United States. Monthly Labor Review, 124(5), 34. Johnson, W., & Gelles, G. (1996). Calculating net discount rates: It’s time to recognize structural changes. Journal of Forensic Economics, 9(2), 119–129. Jones, D. (1996). A reality check on decedent’s consumption: A comment. Journal of Forensic Economics, 9(1), 51–53. Jones, L. D. (1988). Pitfalls to using the real rates or age earnings profile models in calculating economic loss: A comment. Journal of Forensic Economics, 2(1), 147–148. Kaufman, R. (2003). Conceptual and empirical issues in calculating post-retirement consumption. Journal of Forensic Economics, 16(2), 1–21. Krueger, K. (1999). Health life expectancy. Litigation Economic Digest, 4(1), 1–13. Landsea, W. (1994). The questionable reasonableness of Trout and Foster’s method of estimating a decedent’s consumption in wrongful death cases: A comment. Journal of Forensic Economics, 7(2), 211–212. Lane, J., & Glennon, D. (1985). The estimation of age/earnings profiles in wrongful death and injury cases. Journal of Risk and Insurance, 52(4), 686–695. Lane, J., & Glennon, D. (1988). The estimation of the age/earnings profiles in wrongful death and injury cases: Author’s reply. Journal of Risk and Insurance, 55, 174–179. Launey, G. (1990). On valuing lost fringe benefits in death cases. Journal of Forensic Economics, 3(2), 85–86. Lazear, E., & Michael, R. (1980). Family size and the distribution of real per capita income. American Economic Review, 70, 91–107.
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Lewis, C. (1991). On the relative stability and predictability of the interest rate and earnings growth rate. Journal of Forensic Economics, 5(1), 9–25. Lewis, C. (1992). The rationale and quantitative evidence for the personal consumption offset in wrongful death actions. Journal of Legal Economics, 2(2), 1–17. Lewis, W. C. (1989). On the relationship between age, earnings, and the net discount rate. Journal of Forensic Economics, 2(3), 69–77. Lierman, W., Patton, R., & Nelson, D. (1998). Patton–Nelson personal consumption tables updated. Journal of Forensic Economics, 11(1), 3–7. Martin, G. (2003). Determining Economic Damages. Costa Mesa, CA: James Publishing. Nelson, D., & Patton, R. (1984). Estimating personal consumption in wrongful death and survival actions. Washington State Bar News, 43–51. Patton, R., & Nelson, D. (1991). Estimating personal consumption in wrongful death cases. Journal of Forensic Economics, 4(2), 233–240. Payne, J., Ewing, B., & Piette, M. (1998). Stationarity of the net discount rate: Additional evidence. Litigation Economics Digest, 3(1), 27–32. Payne, J., Ewing, B., & Piette, M. (1999a). An inquiry into the time series properties of net discount rates. Journal of Forensic Economics, 12(3), 215–223. Payne, J., Ewing, B., & Piette, M. (1999b). Mean reversion in net discount rates. Journal of Legal Economics, 9(1), 69–80. Payne, J., Ewing, B., & Piette, M. (2001). Total offset method: Is it appropriate? Evidence from ECI data. Journal of Legal Economics, 11(2), 1–17. Pelaez, R. (1996). Mean reversion in the net discount rate: Evidence from the manufacturing sector. Journal of Legal Economics, 6(2), 20–39. Rodgers, J. (2000). Estimating the loss of social security benefits. The Earnings Analyst, 3, 1–27. Rodgers, J. (2002). Valuing losses of pension benefits. Journal of Forensic Economics, 15(2), 205–231. Rodgers, J. D., Brookshire, M. L., & Thornton, R. J., (RBT) (1996). Forecasting earnings using age-earnings profiles and longitudinal data. Journal of Forensic Economics, 9(2), 169–210. Romans, J. T., & Floss, F. (1989). Three concepts of the value of fringe benefits. Journal of Forensic Economics, 3(1), 69–73. Rosenman, R., & Fort, R. (1992). The correct value of social security contributions in personal injury and wrongful death settlements. Journal of Forensic Economics, 5(2), 149–158. Ruble, M., Patton, R., & Nelson, D. (2000). Patton–Nelson personal consumption tables 1997–1998 update. Journal of Forensic Economics, 13(3), 303–307. Ruble, M., Patton, R., & Nelson, D. (2001). It’s all about income! A response to ‘Patton and Nelson personal consumption revisited: Is income important?’. Journal of Forensic Economics, 14(2), 175–176. Ruble, M., Patton, R., & Nelson, D. (2002). Patton–Nelson personal consumption tables 2000–2001. Journal of Forensic Economics, 15(3), 295–301. Saurman, D. S. (1988). Pitfalls to using the real rates or age earnings profile models in calculating economic loss: A comment. Journal of Forensic Economics, 2(1), 128–143. Scoggins, J. (2002). Estimating personal consumption: An instrumental variables model. Journal of Forensic Economics, 14(3), 229–242. Sen, A., Gelles, G., & Johnson, W. (2000). A further examination regarding the stability of the net discount rate. Journal of Forensic Economics, 13(1), 23–28.
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Skoog, G., & Ciecka, J. (2001). A Markov (increment–decrement) model of labor force activity: Extended tables of central tendency, variation, and probability intervals. Journal of Legal Economics, 11(1), 23–87. Spizman, L., & Floss, F. (2002). Loss of self-employed earning capacity. Journal of Legal Economics, 12(1), 7–21. Stoller, M. (1992). Estimating the present value of pensions: Why different estimators get varying results. Journal of Legal Economics, 2(3), 49–61. Thornton, R., & Schwartz, E. (1989). The uneasy case for the personal maintenance deduction. Journal of Forensic Economics, 1(1), 10–18. Thornton, R., & Ward, J. (1999). The economist in tort litigation. Journal of Economic Perspectives, 19(2), 101–112. Trout, R., & Foster, C. (1993). Estimating a decedent’s consumption in wrongful death cases. Journal of Forensic Economics, 6(2), 135–150. U.S. Department of Labor, Bureau of Labor Statistics, (USDOL). (1968). Revised equivalence scales for estimating equivalent incomes or budget cost by family type. Bulletin 1570–2. Washington, DC: USGPO. U.S. Department of Labor, Bureau of Labor Statistics (USDOL). (2004). Consumer expenditures in 2002. Report 974. Watts, H. (1980). Special panel suggests changes in BLS family budget program. Monthly Labor Review, 103(12), 3–10. Weckstein, R. (2001). Real discounting and inflation in indexed treasury securities. Journal of Forensic Economics, 14(3), 261–270. Wisniewski, S. (1990). Vacation benefits and lost earning capacity. Journal of Forensic Economics, 3(2), 91–93. Young, S. (1995). Personal consumption during retirement in wrongful death analysis. Journal of Legal Economics, 5(3), 69–80.
APPENDIX: VICTIM’S COMPENSATION FUND On March 8, 2002, the final ruling was made concerning how the Victim’s Compensation Fund (VCF) would be distributed. The complete text can be found at http://www.usdoj.gov/victimcompensation/finalrule.pdf. It is 56 pages long, but is worth reading. The purpose of this appendix is to summarize it, with a view toward comparing the ruling with standard forensic practice. To the best of the authors’ knowledge, there have been no journal articles discussing this document, although there has been a significant amount of informal discussion. Further, many forensic economists have been hired by attorneys to evaluate economic loss in cases arising from the September 11 disaster. The Fund was established by a law signed by the President shortly after the September 11 terrorist attacks and ‘‘authorizes compensation to any individual (or the personal representative of a deceased individual) who was physically injured or killed as a result of the terrorist-related aircraft crashes
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on that day’’ (p. 1). The final rule was a product of numerous discussions on the part of the Department of Justice with victims, their families, and various experts. The Special Master, Kenneth Feinberg, stated that the Fund is a unique situation and ‘‘provides an alternative to the significant risk, expense, and delay inherent in civil litigation by offering victims and their families an opportunity to receive swift, inexpensive, and predictable resolution of claims’’ (p. 2). Feinberg also pointed out that many of the unpopular rulings, such as those related to collateral source, were mandated by Congress and beyond his control. It was clear that speed was important, and there was a tradeoff in terms of accuracy in estimating the loss for each victim. Such goals often do conflict. The alternative for the victims was protracted lawsuits that may not have come to trial for years and whose outcomes were highly uncertain. Many claimed it was important that the victims know precisely how much the Fund would provide ahead of time so they could make a choice whether to accept the money or seek an alternative. Others, however, argued just the opposite since each situation was somewhat unique, and hence a final judgment could not be made until a hearing for the victim was held. The final ruling on page 8 involved a compromise. The Act requires that no binding award be granted prior to a hearing. However, to allow applicants to make intelligent decisions concerning what course to follow, they would be provided a rough estimate of the possible range of awards based upon tables of presumed awards. Feinberg emphasized that there was no cap on the awards and that an individual could request that a recommended award be adjusted due to special circumstances. As discussed above, the awards were for those injured in the September 11 events. It included individuals who were physically injured. Thus, a person who lost his job due to the September 11 events would receive no compensation. Because awards were related to physical injuries, they were tax-free. If one filed for compensation, the person waived any right to file a civil action. Both eligibility and amount of the award was to be determined by the Special Master, and claims had to be filed before December 21, 2003. There was an interesting public discussion of the initial rules. One of the debates concerned whether there should be a fund in the first place. There have, after all, been other national disasters. Some cynically commented that the Fund was largely a bailout for the airline industry. Others went in the opposite direction and criticized the limitations imposed on suing various parties if payment from the Fund was accepted. The Act itself gave very broad discretion to the Special Master in determining the awards. Congress
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provided no guidelines, nor was there any appeal possible. To provide some guidance for victims in terms of whether they should proceed with claiming money from the Fund, a set of guidelines was set up by the Special Master. The ruling also talked about the purpose of the awards. If the purpose of the awards was to mirror the amount given in past airline litigation, then the amounts proposed were clearly too little – especially for higher-income victims. On the other hand, if the purpose of the awards was to provide immediate and basic relief to families, one could argue that there should be little or no disparity between awards based upon income. Part of the controversy was centered on these conflicting goals. Overlaying the argument was the necessity of coming up with a set of rules that were fair, yet that did not get bogged down in the kind of detail common to most civil trials. Some modifications in the rules were made to comply with the goal of greater fairness for certain groups, but there was no attempt to mirror results found in past civil trials. The final ruling did allow awards to be based upon income. The question was which income should be examined? When a forensic economist projects income into the future, the historical time period examined is always controversial. Which time period is indicative of the future? What if the person would likely have received a big promotion in the future so that no historical time period would be relevant? In a civil trial, these complications are generally sorted out; but when fine tuning is not possible, a rule had to be established which would clearly be ‘‘unfair’’ in many situations. There was also a controversial rule that awards cannot be based on incomes higher than the 98th percentile of US income earners. As expected, some thought this was unfair to low-income families. Others thought this was unfair to the individuals who were in the top 2%. Some economists noted that a simple adjustment could have been made by using the income distribution of New York city rather than the entire country. It should be noted that there is no cap to an award. An individual could claim special circumstances if he thought an award too low. However, the Special Master’s ruling was final. The report also listed criticisms leveled at the initial ruling. In most death cases, consumption of the deceased is deducted from economic loss because it is the loss to the survivors that is important. However, there is considerable controversy concerning how much a person consumes out of family income, and that controversy came up in these discussions. Another issue was that, for young individuals just starting out in their careers, historical earnings are not indicative of future earnings. Thus, using a specific time period to forecast future earnings is unfair to young, well-educated persons. Others claimed that survivors of victims may, in fact, remarry and begin
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working. In that case, awards need not be as generous as originally calculated. Page 22 began a discussion of the specific changes made in calculating awards. What is of interest to forensic economists is that this final ruling cited specific data sources and specific economic assumptions relied upon. It will be interesting to see whether courts look to these sources as more ‘‘authoritative’’ than other sources. As an example, estimates of work life were taken from one particular publication (Ciecka, Donley, & Goldman, 2000–2001). It is a good source, but certainly not the only source. As another example, the estimate of future inflation was 2% and that of real wage growth 1%. At least for the time being, will these be the accepted values? Of further interest was that life-cycle wage increases were based upon data for males for all claimants. Will the decision to use data for males in all situations become the accepted norm? As a final example, the relevant discount rate reflected current yields. Many forensic economists use an average over a historical time period, such as the last 20 years. Will use of current interest rates become the accepted standard? There was also an extensive discussion of non-economic damages such as pain and suffering, loss of enjoyment of life, and mental anguish. Because such losses are so difficult to calculate, there were ‘‘presumed’’ non-economic loss awards proposed. From a statistics perspective, the presumed awards are like testing a null hypothesis. A claimant who thinks the presumed award is unfair will have to show that there is sufficient evidence to contradict that null hypothesis. But as noted earlier, the original amount proposed was raised in the final ruling. The final ruling spent a great deal of time discussing the collateral source issue. Collateral sources of income can normally be excluded as offsets to any estimated award. The list of items considered as collateral sources specifically excluded life insurance and death benefits. The argument concerning life insurance is instructive. First, Congress mandated this requirement so the Special Master had little discretion. More importantly, the argument relates to a much larger issue – namely, what is the purpose of an award? An award in a civil court has two primary purposes. First, it is designed to compensate a victim for economic loss caused by the harm done. To this extent, it may make sense to say that life insurance proceeds should count against any court award. Otherwise, the plaintiff could get compensated twice. However, an award also has the purpose of setting up proper incentives for future tortfeasors (those who could bring harm to others). If the tortfeasor does not have to pay a victim any money because the victim had the foresight to have life insurance, that sends the wrong signal. That is why
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in civil trials life insurance is normally not considered. What is being discussed here is that the primary purpose of the Fund was the first purpose, that of compensation. To that extent, it may be proper to consider sources such as life insurance. After all, the purpose of the Fund is to make sure the victims and their families can adequately take care of themselves – not to promote a set of proper economic incentives governing future behavior. It is evident in reading through this document that collateral source issues were a major point of controversy. The Special Master did have the discretion to change some of these rules. As suggested earlier, victims could meet with special consultants to approximately determine the impact of collateral source. The Ruling also discussed the question of eligibility at length. Eligibility was limited to those who suffered physical harm. One interesting wrinkle concerned who was entitled to act as a personal representative in a death case. For example, do domestic partners include surviving partners of gays and lesbians? For legal reasons, the final rule relied on state law for determination of the personal representative. The distribution of awards was to be a lump sum rather than payments over time. This is the same method as used in civil courts and therefore requires discounting future losses back to the present. There was discussion of providing means so that victims could avoid spending such awards too quickly, such as through annuities and special financial planning devices. It may be useful to provide some brief comments about the section titled ‘‘Explanation of Computing Presumed Economic Loss.’’ It is 14 pages long and established in more detail the terms of calculating the presumed awards. 1. As suggested earlier, income was established by looking at recent tax returns. These tax returns also provided evidence of the individual’s aftertax earnings. Note that in many state courts it is pre-tax earnings that serve as the basis for calculating economic loss. 2. Fringe benefits were based upon actual data of the victim; but if such data were not available then a standard calculation was made. 3. Increases in income over time were a function of three factors – inflation (estimated at 2%), real general wage growth (estimated at 1%), and individual productivity factors such as advancements and promotions. The third factor for all victims was taken from data provided by the government estimates of age-earnings factors of males. The 1% real wage growth corresponded to the figure used by the Social Security Administration (SSA), but the 2% inflation figure was below what the SSA has forecast. A table was provided which showed the estimated increases
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5.
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7.
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combining all three factors by age bracket. Of significant importance was that the data were not broken down by level of education. There were also deductions for self-consumption in death cases using data from Consumer Expenditure Survey, 1999. Consumption varied as to the size of the household and level of income. Since household size can vary over time for such reasons as children leaving to work or attend college, the calculations took these changes in family size into account. The discount (interest) rate was based upon mid-to long-term U.S. Treasury securities adjusted for income taxes. An average tax rate of 18.44% was used, which included federal, state, and local taxes. The after-tax discount rate was applied to after-tax earnings to determine present value. However, it is not clear why a specific tax rate to estimate the after-tax discount rate was used. Since the calculation procedure required that the Special Master estimate the tax rate of each applicant, it would have been straightforward to use an individualized tax rate to determine the after-tax discount rate as well. For example, if John Smith has an individual tax rate of 20% and the pre-tax discount rate is 5.1%, the after-tax discount rate would be 5.1(1-0.2) ¼ 4.08%. One source of controversy among forensic economists is the so-called NDR. This is the difference between the interest (or discount) rate and the rate of wage increase. Focusing on before-tax values, one can discern the presumed NDR used by the Special Master. If one looks at Table 5, the pre-tax interest rate for those under 55 ranges from 4.8 to 5.1%. The rate of wage increase is 3%, which is the sum of the expected rate of inflation (2%) and real wage growth (1%). Thus, the NDR is approximately 2% (5.1 or 4.8% minus 3%). The description went out of its way to show that the assumptions were generally ‘‘liberal’’ in that they tend to make awards higher. Some forensic economists also attempt to use liberal or conservative assumptions, depending upon which side they are on. An outsider would think that the economist might use liberal assumptions if hired on the plaintiff side and conservative assumptions if on the defense side. More frequently, however, the opposite is true. The plaintiff’s economist will often go out of his or her way to adopt conservative assumptions. Such a strategy is designed to show the jury that he is not just a ‘‘hired gun’’ and is trying to be more than fair in terms of calculating loss. A defense economist may adopt a similar strategy by using liberal assumptions. However, most experienced forensic economists believe the best strategy is to use the same set of assumptions in all cases. The philosophy is that even though one side or
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the other hires the economist, the first duty is to provide fair and accurate estimates for the trier of fact, the jury. 8. The last several pages give the present value of economic loss as a function of (a) age, (b) marital status, (c) income, and (d) number of dependents. The figures are prior to deduction of any collateral income sources. It does provide a very rough idea of what an award will be before any adjustments. Examination of the table indicates that the larger the family, the larger the present value of economic loss. The reason is that a larger family implies less consumption is deducted with reference to the deceased. 9. Perhaps the most surprising part of the method of analysis is that there is no compensation for lost household services. This is a standard calculation in civil litigation and often can be of significant value. As a very rough estimate, suppose a woman dies who is 30 years old and has two children. Studies indicate that such an individual provides around 25 hours of household services per week, given that she is working. On a 50-week basis, that is 1,250 hours/year. A conservative estimate of the value of such services would be $8 per hour, which results in an annual value of $10,000. Over a 40-year period (services are provided beyond retirement), that adds up to $400,000. However, as noted previously, the Special Master was given the flexibility to adjust figures from the prescribed formulas for estimating loss. In the case of lost household services, this was commonly done – especially when young husbands who had died left a wife and several children. In their 2004 survey of members of the NAFE, Brookshire, Luthy, and Slesnick (2004) asked questions concerning whether respondents had been involved in cases related to the World Trade Center attack. The question posed and accompanying commentary is given below. Since September 11 (the date of the attacks on the World Trade Center Towers), have you taken any cases stemming from the attack involving forensic economics yon a pro bono basis for consulting? yat a discounted rate from what you normally charge for consulting? yat your normal rate for services?
The question asked the respondent to indicate ‘‘Yes’’ or ‘‘No’’ to each option. It is difficult to evaluate because the number who answered was not the same for each option – specifically, the respective numbers are 167, 157, and 152. Further, it is certainly possible for an individual to answer ‘‘Yes’’ to more than one option if he was hired in more than one case related to the
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World Trade Towers. The results were as follows:
yon a pro bono basis for consulting? (%) yat a discounted rate? (%) yat your normal rate for services? (%)
Yes 15.56 8.91 5.26
No 84.44 91.09 94.74
Of those who did consulting for this type of case, the majority did not charge. The total percentage who did any type of consulting cannot be determined by adding up the percentages indicating ‘‘Yes’’ since, as suggested above, some individuals could respond ‘‘Yes’’ to more than one question. Of all 172 individuals who responded to any part of the question, 133 indicated ‘‘No’’ to all three parts. This implies that 22.67% worked on cases related to the attack on the World Trade Center Towers. To summarize, the VCF has attempted to walk a tightrope between standardizing the awards process and providing ‘‘fair’’ estimates to each individual victim. Only time will tell if it has been successful.
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ECONOMICS AND ECONOMISTS IN MERGER ANTITRUST ENFORCEMENT Lawrence J. White 1. INTRODUCTION Economics and economists today play an active role in merger antitrust enforcement in the United States. Both of the federal antitrust agencies – the Antitrust Division of the US Department of Justice (DOJ) and the Federal Trade Commission (FTC) – that are responsible for merger enforcement have sizable staffs of trained economists who routinely become involved in merger analysis, merger litigation, and the development of merger enforcement policy. Private parties also now routinely hire expert economists for assistance in analysis and litigation in instances where the merging parties anticipate a challenge by the enforcement agencies. This chapter will briefly describe this role. Because the DOJ-FTC Merger Guidelines are so important in structuring the analysis of mergers, Section 2 will summarize the logic and structure of the Guidelines. Section 3 will then describe the specific roles that economists play. Section 4 will use the Staples1 case as an example of the productive use of economic analysis in merger enforcement. Section 5 will provide a brief conclusion.
Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 205–216 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87008-1
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2. THE MERGER GUIDELINES Since 1982, the DOJ-FTC Merger Guidelines have provided the dominant paradigm for the analysis of mergers in an antitrust enforcement context.2 Economists were important in the development of these Guidelines and their revisions.3 The logic of the Guidelines is that the US antitrust laws4 are intended to prevent the creation or enhancement of significant market power by means of a merger.5 To this end, the Guidelines’ analysis can be classified into six categories: (1) market delineation;6 (2) theories of competitive harm; (3) seller concentration levels (and changes in the levels) that would cause heightened enforcement concern; (4) the role of entry; (5) other market conditions that could alleviate or heighten enforcement concern; and (6) efficiency considerations as a potential offset. We will address each in turn.
2.1. Market Delineation Since the major public policy concern is that a merger will create or enhance the exercise of market power, market delineation is an essential part of the analysis. The essence of the Guidelines’ market delineation paradigm is that a relevant market is one in which market power could potentially be exercised or enhanced; and then the remainder of the Guidelines’ analysis tries to determine whether the specific merger that is being considered is likely to change market conditions sufficiently so as to create or enhance that market power. More formally, the Guidelines define a relevant market as a product (or group of products) that is sold by a group of sellers who, if they acted in concert (as a ‘‘hypothetical monopolist’’), could bring about ‘‘a small but significant and nontransitory increase in price’’ (SSNIP).7 These principles apply to the delineation of geographic markets as well as product markets.8 The SSNIP test identifies sellers who could potentially exercise market power; it also includes groups of customers in instances where they could be the targets of sustained price discrimination.
2.2. Theories of Competitive Harm The Guidelines embody two theories of competitive harm that could arise as a consequence of a merger. First, there is the ‘‘traditional’’ theory of oligopolistic coordinated interaction.9 The foundation for this view is the
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‘‘structure–behavior–performance’’ paradigm: Sellers in more concentrated markets (i.e., those with comparatively few sellers), and where entry is difficult, etc., are more likely to succeed in maintaining prices at higher levels than are sellers in less concentrated markets. This approach dominated merger enforcement thinking in the 1980s and has received a revival of interest in the early twenty-first century.10 The second approach, which received substantial attention during the 1990s, focuses on the ‘‘unilateral effects’’ that might arise from a merger of two firms that sell differentiated product substitutes and for which a substantial number of customers have the two merging firms as their first and second choices.11 This second approach rests on two crucial concepts: first, product differentiation in some markets is an important empirical phenomenon; and second, in the context of differentiation, there may be a significant number of buyers whose preferences for the two merging firms’ products are strong. If this is the case, then the merged firm could find it worthwhile to raise prices (as compared to pre-merger levels) generally or even just raise prices to the buyers with the strong preferences (if price discrimination toward them were feasible).12
2.3. Seller Concentration The traditional oligopolistic coordinated interaction approach has, at its center, a focus on seller concentration. The Guidelines embody this approach, using the Herfindahl–Hirschman Index (HHI) as its tool for measuring seller concentration. The HHI is calculated by summing the squares of the market shares of each seller in the relevant market; i.e., HHI ¼ Ss2i ; where si is the market share of the ith seller in the market. In the antitrustrelated discussions and calculations, the market shares are expressed as percentages (rather than as decimals), so that the possible values for the HHI range from close to 0 (for an atomistic industry with a large number of tiny sellers) to 10,000 (for a monopoly, the market share of which is 100%, so that HHI ¼ 1002 ¼ 10; 000). As a further illustration, a two-firm duopoly, where the two firms had market shares of 70% and 30%, respectively, would have an HHI of 5800 (since 702 þ 302 ¼ 5800). The Guidelines provide a specific set of post-merger HHI levels (and changes in the HHI caused by the merger) that would trigger enforcement attention. The Guidelines describe a market with an HHI above 1800 as ‘‘highly concentrated,’’ a market with an HHI in the range of 1000–1800 as ‘‘moderately concentrated,’’ and a market with an HHI below
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1000 as ‘‘unconcentrated.’’ A merger in a market that has a post-merger HHI level that is below 1000 is unlikely to be challenged. A merger in a market that has a post-merger HHI that is above 1800 and for which the merger itself has caused an increase in the HHI of 100 or more,13 is presumed to be anticompetitive, although other market conditions (discussed below) can offset this presumption; if the post-merger HHI is above 1800 and the merger causes an increase in the HHI that is between 50 and 100, the merger warrants heightened scrutiny. Finally, a merger in a market that has a post-merger HHI that is between 1000 and 1800 and for which the merger itself caused an increase in the HHI of 100 or more will receive an intermediate level of scrutiny.14 Despite these specific demarcation points in the Guidelines, however, actual enforcement practice has informally used higher HHI levels as the triggers of concern.15 Rarely have mergers with post-merger market HHIs of below 2000 been challenged, and mergers in markets with substantially higher post-merger HHIs have also escaped challenge. In essence, the merging parties in such instances have been able to convince the enforcement agencies that the other characteristics of the market and/or the merger make the post-merger exercise of market power unlikely. The Guidelines also specify a post-merger market share of 35% for the merged firm (and indications of strong customer preferences for the two firms’ products) to deal with concerns about unilateral effects.
2.4. Entry The Guidelines recognize that the conditions of entry can influence the likelihood of the post-merger exercise of market power. The Guidelines specify that, for entry to obviate such concerns, it must be ‘‘timely, likely, and sufficient in magnitude, character, and scope.’’ Timeliness requires entry to occur within two years. The criterion of likelihood is satisfied if the entrant would be profitable in the post-entry market. Sufficiency in magnitude, character, and scope requires that the entrant be capable of restoring the degree of competitiveness that is lost as a result of the merger – that is, the entrant should be as capable and vigorous an entity as the firm that is eliminated by the merger. The Guidelines acknowledge that high levels of ‘‘sunk costs’’ can be a significant barrier to entry. Sunk costs are the acquisition costs of tangible and intangible assets that are ‘‘uniquely incurred to serve the relevantymarket’’ and that cannot be completely recouped by redeploying
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them elsewhere. Examples include specialized production equipment, marketing costs, training costs, research and development expenditures, advertising, etc. The Guidelines specifically ask whether, despite the presence of sunk costs, sufficient entry would be likely to occur within two years in response to a merger-induced price increase. Firms that could enter the market easily (i.e., without expenditure of significant sunk costs) within one year are considered to be in the market and are included in the market delineation procedure described above.
2.5. Other Market Conditions Other market characteristics can influence the likelihood that a group of firms could coordinate their behavior sufficiently so as to maintain a heightened level of prices.16 The Guidelines focus especially on: the level of price transparency in the market (since greater transparency may make easier the ‘‘policing’’ of any understanding among sellers); typical pricing or marketing practices (which may make the enforcement of any understanding among sellers easier or more difficult); the level of concentration on the buyers’ side of the market (since the presence of a few large and knowledgeable buyers is more likely to induce price cutting among sellers and thereby undermine any understanding); the degree of complexity in the quality and service dimensions of the product or products at issue (since greater complexity is likely to interfere with the policing of an understanding among sellers); and the antitrust history of the sellers in the market (which may indicate something about the proclivities of the sellers to reach an understanding).
2.6. Efficiencies Among the most difficult issues for merger analysis is how to assess the forecasted efficiencies that accompany virtually every merger that is analyzed by the enforcement agencies. The dilemma, of course, is that efficiencies are easy for merger applicants to promise, but the actual post-merger achievement of those efficiencies may be difficult. Further, even if they can be achieved, the cost savings may accrue largely or wholly to the owners of the merged entity, while the customers pay the higher prices that arise because of the creation or enhancement of market power. In essence, even if
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the social benefit–cost calculation that is implied by any offset test is positive, that calculation nevertheless involves one group in society gaining the benefits while another group experiences the costs. The Guidelines try to strike a compromise among these dilemmas, stating that the agencies ‘‘will not challenge a merger if cognizable [i.e., merger-specific and verifiable] efficiencies are of a character and a magnitude such that the merger is not likely to be anti-competitive in any market.’’ A recent proposed merger in which the issue of forecasted efficiencies figured heavily was the proposed ‘‘baby food’’ merger of 2000, in which Heinz proposed to purchase Beech-Nut.17 The baby food market is highly concentrated. The leading firm, Gerber, had a 65% market share (as of 2000), Heinz had 17%, and Beech-Nut had 15%. The merging parties argued that their two brands were substantially different – Beech-Nut was perceived by baby-food buyers as a ‘‘premium’’ brand, while Heinz was perceived as a ‘‘discount’’ or ‘‘value’’ brand. Further, most grocers stocked only two brands, Gerber and one of the other two, so that Heinz and BeechNut really did not compete with each other. Most important, the parties argued that the specific efficiency gains that were uniquely available through this merger would allow the merged entity to compete more vigorously against Gerber. The FTC, in deciding to challenge the merger, argued that the two companies did indeed compete with each other – at the wholesale level, in competing for the grocers’ decisions as to which firm was going to be the second brand on the shelf – and that the post-merger entity would be likely to compete less vigorously against Gerber. Further, the agency argued that the claimed efficiencies could be achieved individually and did not require the merger. When the FTC’s challenge was initially considered by a federal district court, the FTC lost.18 But, on appeal, the FTC’s challenge was upheld, and the proposed merger was abandoned.19
2.7. A Summing Up The Merger Guidelines represent a coherent approach to merger enforcement that has at its root a concern about the post-merger creation or enhancement of market power. The Guidelines have a strong flavor of economic analysis. This is no accident. Economists were involved in their drafting at their inception and have continued to be involved in their revisions and implementation.
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3. THE ROLE OF ECONOMISTS As the previous section indicated, economists have been actively involved in the formulation, revision, and implementation of the Merger Guidelines. It is the implementation to which we now turn. As was discussed in the Introduction, both federal enforcement agencies have sizable staffs of trained Ph.D. economists. These economists are involved, alongside the agencies’ lawyers, in the mundane day-to-day screening of the thousands of transactions that annually pass through the agencies. Their economics training is brought to bear in helping to identify circumstances where the creation or enhancement of market power might be possible and then helping determine whether the specific proposed merger could pose market power problems. They help to gather and analyze the available data, often using sophisticated econometric techniques.20 If an agency decides to challenge a merger and must prepare a formal court case, economists are involved in litigation support and may sometimes appear as expert witnesses. The merging parties are also likely to employ economists to gather and analyze data, especially when agency challenges are anticipated. The economists often accompany the merging companies’ senior managements (and their lawyers) to the meetings with agency officials that may precede any agency decision. If a trial is anticipated, the economists will similarly become involved in litigation support and/or appear as expert witnesses. Indeed, a small ‘‘industry’’ of economics consulting firms that specialize in antitrust has arisen over the past three decades, with almost all of them having sizable offices (if not their headquarters) in Washington, DC. They offer their consultancy services to the enforcement agencies (to supplement the agencies’ staffs) as well as to potential and actual defendants. We now turn to a brief discussion of the use of economics in an important merger enforcement case, FTC v. Staples, 970 F. Supp. 1066 (1997).21
4. THE STAPLES CASE In September 1996, Staples Inc. announced its intention to acquire Office Depot, Inc.22 The two companies operated the first and second largest chains of ‘‘office super stores’’ (OSSs) in the US. The OSS concept had been pioneered by Staples in 1986; Office Depot was a quick follower. The OSS concept involved large-volume retail outlets for office supplies and other business-related items. The prices at OSSs were often substantially below the
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prices for the same items that were being sold in local stationery stores and other retail outlets. At first glance, the merger of the two OSS chains appeared to pose no antitrust problem. After all, the two chains together accounted for less than 10% of the total US retail sales of office supplies. However, the initial staff investigation at the FTC showed a consistent result for simple price comparisons of like items sold at OSSs across different metropolitan areas. Where only a single OSS chain was present in a metropolitan area, the OSS’s prices for these items tended to be the highest; where two OSS chains were present in a metropolitan area, the prices tended to be lower; where three chains23 were present, the prices were the lowest.24 These preliminary results were then subjected to more sophisticated econometric testing (which involved the inclusion of additional information about the metropolitan areas that were being compared, including cost data, income levels, the presence of other major retailers, such as Wal-Mart, etc.). The FTC staff concluded from these more sophisticated analyses that the basic results continued to hold.25 These price data carried two strong antitrust implications: first, OSS sales of office supplies in metropolitan areas constituted relevant antitrust markets for the purposes of merger analysis, since higher prices could be charged (and were being charged) when fewer OSS sellers were present. In these OSS metropolitan markets, the HHIs were already quite high, and the merger promised to raise them substantially. Second, the price data could be used to predict directly what would happen after the merger in the various metropolitan area markets (a) where only Staples and Office Depot were present (so that the merger would reduce the number of OSS chains from two to one) and (b) where Staples, Office Depot, and OfficeMax were all present (so that the merger reduced the number of OSSs from three to two). This evidence on past price differentials across markets was supported by company documents that indicated that Staples and Office Depot focused primarily on the other firm and on Office Max, and mostly not on other retailers, in their consideration of pricing, marketing, and expansion plans. The FTC staff also developed evidence that indicated that entry into OSSs was not easy and that the claimed efficiencies from the merger were not credible. Consequently, the FTC in April 1997 decided to challenge the merger. As a technical legal matter, this decision meant that the FTC would seek a preliminary injunction (PI) to stop the merger. The merging parties contested the FTC’s decision, which technically meant that they would challenge the FTC’s request for a PI. However, the practice for the past two decades has been that the legal clash over the
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request for the PI becomes an accelerated ‘‘mini-trial’’ on the merits of the antitrust challenge to the merger itself. Indeed, this is what occurred. The trial took place in May 1997 and lasted for seven days. The economic evidence discussed above concerning the relevant markets, the likely price effects, and the likely efficiencies were presented by both sides: in filed documents and in court testimony. Economists testified for both sides. In June 1997, Federal District Court Judge Thomas F. Hogan ruled in favor of the FTC and granted the PI. The defendants chose not to appeal (or to engage in the lengthy administrative proceeding on the merits of the merger within the FTC), and the merger was abandoned.
5. CONCLUSION Economics and economists are clearly an important part of merger antitrust enforcement in the US, and this role is likely to be sustained. Further, as telecommunications and transportation technologies improve and costs decrease, commerce in many fields is likely to become more global, and mergers are likely to involve wider markets and wider jurisdictions. The market delineation paradigm described above can encompass wider markets. Whether and how wider jurisdictions will encompass economics and economists remains to be seen. This author’s informal impression, however, is that the basic logic of the DOJ-FTC Merger Guidelines is being embraced by jurisdictions outside the US, such as the EU, Canada, and Australia. Even within a common paradigm, different parties, with different perspectives, may reach different conclusions and make different decisions.26 Nevertheless, the spread of the paradigm itself does provide an international ‘‘market test’’ of its value and of the value of economics in providing a highly useful framework for illuminating the important issues in the antitrust analysis of mergers.
NOTES 1. FTC v. Staples, 970 F. Supp. 1066 (1997). 2. The 1982 Guidelines superseded an earlier set that had been promulgated in 1968. Since 1982 the Guidelines have been revised in 1984, 1992, and 1997, but the essential structure that was established in 1982 has been retained. For further discussion, see, e.g., White (1987) and Kwoka and White (2004). The current version of the Guidelines can be found at http://www.usdoj.gov/atr/public/guidelines/ horiz_book/hmg1.html. 3. See, for example, White (2000).
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4. For the purposes of merger enforcement, this is primarily the Clayton Act. 5. Although the policy concerns about market power are usually expressed in terms of the ‘‘monopoly’’ power exercised by sellers, they apply equally to the ‘‘monopsony’’ power that could be exercised by buyers, and the analysis described below can be modified appropriately to apply to concerns about monopsony power. 6. This is frequently described as ‘‘market definition.’’ 7. A 5% increase that can be sustained for a year is the SSNIP value that the enforcement agencies typically use. As Werden (2002) has pointed out, the first use of the ‘‘hypothetical monopolist’’ paradigm was apparently by Adelman (1959). 8. The essential determining factor is demand substitutability: How readily can buyers switch (in response to a price increase) to other sellers (who are not included in the provisional delineation of a relevant market) of other goods and/or who are located in other geographic areas. In principle, a relevant geographic market could be as small as a neighborhood or as large as the entire global economy. Supply substitutability enters primarily through the consideration of entry conditions. 9. See, for example, Stigler (1964). 10. See, for example, Kolasky (2002), Sibley and Heyer (2003) and Coleman, Meyer, and Scheffman (2003). 11. See, for example, Ordover and Willig (1993). 12. A simplified discussion of this possibility can be found in Kwoka and White (2004). 13. A quick method for determining the change in the HHI that is due to the merger of two sellers is to multiply the pre-merger market shares of the two firms and then double that multiplication result; e.g., if a 20% share firm merged with a 10% share firm, the change in the HHI would be 400, since ð20 10Þ 2 ¼ 400: The mathematical basis for this method can be seen by noting that the merger of a firm with market share si with a second firm that has a market share of sj creates a merged firm with a market share of sij ¼ si þ sj : In calculating the post-merger HHI, the merged firm’s squared market share will be s2ij ¼ ðsi þ sj Þ2 ¼ ðs2i þ s2j þ 2si sj Þ: Thus the calculated difference between the pre-merger HHI and the post-merger HHI that is due to merger is the 2sisj term. 14. There are two ways of translating the HHI threshold points into more familiar terms. First, an HHI of 1000 would be yielded by a market with 10 equal-size sellers (each having a market share of 10%), while an HHI of 1,800 would be yielded by a market with between five and six equal-size sellers. Second (since most markets do not have equal-size sellers), the two nominal decision points translate empirically (based on simple correlations) to four-firm concentration ratios of approximately 50% and 70%, respectively (Kwoka, 1985). 15. See, for example, Leddy (1986) and Kolasky (2002). 16. See Stigler (1964). 17. For a more complete discussion, see Baker (2004). 18. See FTC v. H.J. Heinz Co., 116 F.Supp. 2d 190 (2000). 19. See FTC v. H.J. Heinz Co., 246 F.3d 708 (2001). 20. As is discussed in Section 4, they may be able to use historical price data to infer directly the delineation of markets. Or they may use the price data to develop estimates of elasticities of demand, which are then used to infer the dimensions of markets (e.g., by employing the elasticities to infer a ‘‘critical cost ratio’’ and then
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comparing that critical cost ratio to the historical cost data). Where the theory of competitive harm involves unilateral effects, the demand elasticities become the basis for simulations of the post-merger pricing behavior of the merged firm. See, for example, Werden and Froeb (1994) and Werden (1998). 21. Other examples of discussions (written by economists) of the use of economics and economists in merger cases can be found in Kwoka and White (2004) and in earlier editions of that volume, Slottje (1999, 2002), Katz (2002), Scheffman and Coleman (2002), Sibley and Heyer (2003, 2004), Coleman et al. (2003), and Froeb, Hosken, and Pappalardo (2004). 22. More detailed discussions of this case can be found in Baker (1999), White (2002), and Dalkir and Warren-Boulton (2004). 23. OfficeMax, Inc., was the third major operator of OSSs. 24. For further details, see Dalkir and Warren-Boulton (2004). 25. The merging parties came to a different conclusion, based on their econometric analyses of the same data. For a discussion of these results and the dispute concerning them, see Baker (1999) and Dalkir and Warren-Boulton (2004). 26. Such was the case, for example, with respect to the U.S. and EU perspectives on the GE-Honeywell merger. See, for example, Nalebuff (2004).
ACKNOWLEDGEMENTS The author was the Director of the Economic Policy Office (‘‘Chief Economist’’) of the Antitrust Division of the U.S. Department of Justice, 1982–1983. An earlier version of this paper was presented at the Seminar on Global Enforcement of the Antitrust Laws and Business Response Tokyo, Japan December 15, 2003. Thanks are due to Patrick Gaughan and Robert Thornton for valuable comments on an earlier draft.
REFERENCES Adelman, M. A. (1959). Economic aspects of the Bethlehem opinion. Virginia Law Review, 45, 684–696. Baker, J. B. (1999). Econometric analysis in FTC v. Staples. Journal of Public Policy & Marketing, 18, 11–21. Baker, J. B. (2004). Efficiencies and high concentration: Heinz proposes to acquire Beech-Nut. In: J. E. Kwoka, Jr., & L. J. White (Eds), The antitrust revolution: Economics, competition, and policy (4th ed., pp. 150–169). New York: Oxford University Press. Coleman, M. T., Meyer, D. W., & Scheffman, D. T. (2003). Empirical analyses of potential competitive effects of a horizontal merger: The FTC’s cruise ships merger investigation. Review of Industrial Organization, 23, 95–119. Dalkir, S., & Warren-Boulton, F. R. (2004). Prices, market definition, and the effects of merger: Staples-Office Depot (1997). In: J. E. Kwoka Jr. & L. J. White (Eds), The antitrust
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revolution: Economics, competition, and policy, (4th ed.) (pp. 52–72). New York: Oxford University Press. Froeb, L., Hosken, D., & Pappalardo, J. (2004). Economics research at the FTC: Information, retrospectives, and retailing. Review of Industrial Organization, 25, 353–374. Katz, M. L. (2002). Recent antitrust enforcement actions by the U.S. Department of Justice: A selective survey of economic issues. Review of Industrial Organization, 21, 373–397. Kolasky, W. J. (2002). Coordinated effects in merger review: From dead Frenchmen to beautiful minds and mavericks. Address before the ABA Section of Antitrust Law, April 24, 2002; available at http://www.usdoj.gov/atr/public/speeches/11050.htm. Kwoka, J. E. (1985). The Herfindahl index in theory and practice. Antitrust Bulletin, 30, 915–947. Kwoka, J. E., Jr., & White, L. J. (Eds) (2004). The antitrust revolution: Economics, competition, and policy, (4th ed.). New York: Oxford University Press. Leddy, M. (1986). Recent merger cases reflect revolution in antitrust policy. Legal Times, November 3, p. 2. Nalebuff, B. (2004). Bundling: GE-Honeywell (2001). In: J. E. Kwoka Jr. & L. J. White (Eds), The antitrust revolution: Economics, competition, and policy, (4th ed.) (pp. 388–412). New York: Oxford University Press. Ordover, J., & Willig, R. (1993). Economics and the 1992 Merger Guidelines: A brief survey. Review of Industrial Organization, 8, 139–150. Scheffman, D. T., & Coleman, M. T. (2002). Current economic issues at the FTC. Review of Industrial Organization, 21, 357–371. Sibley, D. S., & Heyer, K. (2003). Selected economic analysis at the antitrust division: The year in review. Review of Industrial Organization, 23, 95–119. Sibley, D. S., & Heyer, K. (2004). The year in review: Economics at the antitrust division 2003–2004. Review of Industrial Organization, 25, 375–394. Slottje, D. J. (Ed.) (1999). The role of the academic economist in litigation support. Amsterdam: North-Holland. Slottje, D. J. (Ed.) (2002). Measuring market power. Amsterdam: North-Holland. Stigler, G. J. (1964). A theory of oligopoly. Journal of Political Economy, 72, 55–69. Werden, G. J. (1998). Demand elasticities in antitrust analysis. Antitrust Law Journal, 66, 363–414. Werden, G. J. (2002). The 1982 Merger Guidelines and the ascent of the hypothetical monopolist paradigm. Paper presented at the U.S. DOJ conference: The 20th anniversary of the 1982 Merger Guidelines: The contribution of the Merger Guidelines to the evolution of Antitrust Doctrine (June 10, 2002); available at: http://www.usdoj.gov/atr/hmerger/ 11256.htm#N 5. Werden, G. J., & Froeb, L. (1994). The effects of mergers in differentiated products industries: Logit demand and merger policy. Journal of Law, Economics, and Organization, 10, 407–426. White, L. J. (1987). Antitrust and merger policy: A review and critique. Journal of Economic Perspectives, 1, 13–22. White, L. J. (2000). Present at the beginning of a new era for antitrust: Reflections on 1982–1983. Review of Industrial Organization, 16, 131–149. White, L. J. (2002). Staples-Office Depot and UP-SP: An antitrust tale of two proposed mergers. In: D. J. Slottje (Ed.), Measuring market power (pp. 153–174). Amsterdam: North-Holland.
THE ECONOMICS OF PUNITIVE DAMAGES: POST STATE FARM V. CAMPBELL Patrick A. Gaughan 1. INTRODUCTION Punitive damages is a controversial topic in the legal profession and in the field of economics. This chapter explores the economics of punitive damages as they relates to corporate defendants. The economic difference between large corporations and other potential defendants, such as individuals or smaller closely held companies, causes the effects of a punitive award to be different. In some circumstances, these differences raise significant questions as to the appropriateness of punitive damages when imposed on large corporations.
2. RECENT DECISIONS ON PUNITIVE DAMAGES BY THE U.S. SUPREME COURT Punitive damages have been with us for many years. Their roots can be traced back to English common law and beyond that (Owen, 1976). Some have even seen early versions of punitive damages in the Code of Hammurabi, the Bible, and the laws of the Hittites (Klugheit, 2002; Gotanda, 2004). Others can trace Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 217–266 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87009-3
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their roots to as far as the days of the Romans (Geraci, 2004). Punitive damages are a penalty that is applied in addition to compensatory damages in situations where a defendant’s conduct is determined to be reprehensible (Second Restatement of Torts, 1979). Punitive damages have twin goals: punishment and deterrence. The U.S. Supreme Court has been clear that these are the goals of punitive damages. For example, in Pacific Mutual Life Insurance Co. v. Haslip (1991), it was stated that ‘‘punitive damages are imposed for purposes of retribution and deterrence.’’ In later decisions, the Court has consistently reaffirmed these purposes. For example, in Cooper Industries, Inc. v. Leatherman Tools Group, Inc. (2001) the Court stated: ‘‘Punitive damages may properly be imposed to further a State’s legitimate interests in punishing unlawful conduct and deterring its repetition.’’ The Supreme Court has been concerned for some time about the fairness of punitive damages. In Browning-Ferris Industries of Vermont v. Kelco Disposal, Inc. (1989), it had registered its potential willingness to consider due process limitations of punitive damages in cases where they may violate the due process clause of the Fourteenth Amendment. In fact, this due process clause of the Fourteenth Amendment seems to have become somewhat of a norm by which the excessiveness of punitive awards is tested (Hines, 2004). In TXO Prod. Corp. v. Alliance Resources (1993), the Court seemed to move in the opposite direction and muddied the waters by upholding a punitive damages award of $10 million with a compensatory damages amount of $19,000. In this case, punitive damages were 526 times compensatory damages. At that time, some had concluded that arguing that the use of such high ratios of punitive to compensatory damages is a violation of due process was a dead issue (Stuart, 1994). This interpretation was clearly wrong. In fact, even in TXO, the court still recognized due process limitations on punitive damages. Nonetheless, it clouded the issue of the magnitude of the punitive/compensatory multiplier owing to the fact that in that case the Court also considered potential, not just actual, compensatory damages. Thus, the TXO decision was not an endorsement by the Supreme Court of such a high multiplier, as it considered a denominator that was potentially significantly higher. It has been pointed out how the plurality opinion in TXO also introduced other potential problems in suggesting that evidence of a defendant’s wealth and out-of-state conduct could justify a given punitive award (Franze & Scheuerman, 2004). It would not be until the State Farm v. Campbell decision that the Court would clarify this issue. Just one year after TXO, the Supreme Court, in Honda Motor Corp. v. Oberg (1994), refocused on the dangers of a violation of due process rights
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which could result in an unlawful taking of private property. Two years later in BMW of North America v. Gore (1996), the U.S. Supreme Court found that an award of $145 million in punitive damages and $1 million in compensatory damages, a punitive/compensatory multiple of over 100 times, violated the due process clause of the Fourteenth Amendment of the U.S. Constitution. In reaching its decision, the Gore court set forth three factors or guideposts which courts should consider when reaching a decision on punitive damages: 1. the degree of reprehensibility of the defendant’s conduct, 2. the disparity between the actual and potential harm, and 3. the disparity between a jury’s award of punitive damages and civil penalties imposed in other cases. In Copper Industries, Inc. v. Leatherman Tool Group, Inc. (2001) the Supreme Court stated that the due process clause prohibited the imposition of ‘‘grossly excessive or arbitrary punishments’’. In this decision the Court stated that a trial court’s application of the Gore guideposts was subject to de novo review. The Court stated that such a review would help ‘‘stabilize the law.’’ In April 7, 2003, the Court more explicitly addressed the punitive multiplier as well as other factors which may be taken into account when determining a punitive damages award. In State Farm Mutual Automobile Insurance Co. v. Campbell, et al. (2003), the Court applied the Gore factors to a Utah case involving an insured’s claims against their automobile insurance company. In going through the factors, the Court clarified how they apply to different lawsuits. The Campbell court was reluctant to set forth a specific multiplier, but it did state that ‘‘few awards exceeding a single digit ratio between punitive and compensatory damages will satisfy due process.’’ Indeed, the Court, in citing Haslip, did say that ‘‘an award of more than four times the amount of compensatory damages might be close to the line of constitutional propriety.’’ The Court found this ratio to be ‘‘instructive.’’ This decision was also noteworthy in that it was only the second time that the Supreme Court reduced a punitive damages award that was handed down by a jury. Even though BMW of North America v. Gore seemed to lend some stability to the process of arriving at and evaluating punitive awards, various state courts seem to have awarded punitive damages without bound or a reasonable basis. In Engle v. R.J. Reynolds Tobacco Co. (2000), a class action suit alleging smoking-related injuries in the State of Florida, a jury in 2002 awarded an unprecedented $144.8 billion. The fact that this award far exceeds the defendant’s ability to pay seemed to be lost in
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the verdict determination process. What was even more troubling was the specious analytical grounds upon which the verdict was based. The decision was later reversed by Florida’s Third District Court of Appeal and the class was decertified. In an individual tobacco lawsuit in 2002, Bullock v. Philip Morris, a California jury awarded $28 billion in punitive damages. Such mega-punitive awards are not just restricted to the tobacco industry. For example, a $5 billion award occurred in the Exxon Valdez case. And in 1999 a Los Angeles county jury awarded $4.8 billion in punitive damages against General Motors in a suit brought by six burn victims who rode in a Chevrolet Malibu that was rear-ended and caught fire. In a more recent decision, an Alabama court in November 2003 awarded the plaintiffs $63.6 million in compensatory damages while awarding $11.8 billion in punitive damages in a natural gas royalty dispute where Exxon/Mobil Corp. was the defendant. These cases are mentioned because they show that punitive damages remains a thorny and not fully understood problem for courts, particularly in the field of mass torts (Barr, 2001). Moreover, when the Campbell case was returned to the Utah Supreme Court, that court concluded that since the U.S. Supreme Court had sent the case back to review the damages, it could exercise its discretion within the Campbell limits. It thereby arrived at a punitive multiple of nine when it returned a punitive damages amount of $9 million. The Utah Supreme Court stayed within the Supreme Court’s single digit limit but chose to go beyond the Haslip range of up to four which the U.S. Supreme Court found to be instructive. Some have theorized that part of the purpose of the Court’s decision in BMW of North America v. Gore was to send a message to lower courts to ‘‘tighteny[their] grip on punitive awards’’. If this is the case then it is clear that many state courts have yet to hear the message (McKee, 1996). While Campbell has added greater clarity on the issue of how courts should interpret Gore, lower courts seem not to be applying the Campbell reasoning consistently (Sud, 2005). Even various federal courts have shown that they are unconstrained by the single-digit-multiple limits. For example, the Seventh Circuit, in Mathias v. Accor Economy Lodging, Inc. (2003), concluded that a punitive multiple of 37 was not excessive. In that decision, Judge Posner described circumstances where a ‘‘wealth calibrated’’ award may be appropriate. These would be where the conduct was particularly reprehensible and the compensable damages were relatively small. In another recent decision, Williams v. Kaufman County (2003), the Fifth Circuit upheld a 150:1 ratio in a civil rights action (actual damages were only $100). These courts, however, were dealing with cases where the behavior was reprehensible while the actual damages that could be awarded plaintiffs were small.
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The courts were concerned that defendants could escape justice when plaintiffs may not be able to finance litigation which would provide such little gain. Since the above cited cases deal with situations where actual damages are small, it seems that cases where actual damages are potentially more significant may still be limited to the single digit Campbell ratios. However, such ratios can still be troublesome for many defendants.
3. FREQUENCY OF PUNITIVE DAMAGES Punitive damages tend to be awarded relatively infrequently. The majority of cases do not go to trial; and of those that do go as far as a verdict, only a small percentage award punitive damages. Landes and Posner (1986) found that only 2% of product liability cases result in punitive damages. Another study showed an even smaller frequency. In looking at certain localities, a Rand study found punitive damages occurred in only 1/10 of 1% of such cases in Cook County, Illinois, and even less frequently in San Francisco (Peterson et al., 1987). Rustad’s (1992) research uncovered only 344 cases with punitive damages in a quarter century. Other studies showed a somewhat higher incidence of punitive damages. For example, the American Bar Foundation study found punitive damages in 4.9% of all verdicts in their research sample (Daniels & Martin, 1990). A study conducted by the Justice Department found a somewhat higher rate – 6% (DeFrances et al., 1995). However, as we will discuss later, punitive damages may play a major role in settlements, and settlements are much more common than trials (Polinsky, 1997).
4. PREDICTABILITY OF PUNITIVE DAMAGE AWARDS Not only is the frequency of punitive damages a controversial issue, but also the predictability of such damages has drawn much debate. The concern is that if punitive damages vary in an unpredictable manner, then defendants might be denied the right to due process. Eisenberg, Goerdt, Ostrom, Rottam, & Wells (1997) attempted to assess the predictability of punitive damages by examining the relationship between compensatory and punitive damages with data on such damages from Cook County, Illinois, and California over a 25-year period. They purported to find that there was a strong correlation between compensatory and punitive damages when they were
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expressed in logarithms, and concluded that punitive damages are as predictable as compensatory damages. Others, such as Mitchell Polinsky, contend that they have misinterpreted their results. He shows that their results are actually consistent with a world in which punitive damages are ‘‘significant, unpredictable and irrational’’ (Polinsky, 1997). Moreover, he has explained that punitive awards – even if they are generally insignificant in trial cases – may have had a significant effect on settlement amounts. Since settlements are more common, their outcomes are of greater relevance than those cases that make it to trial. In a later study, the Eisenberg group purported to have found a comparable relationship between compensatory and punitive damages, with the value of the compensatory award being the best predictor of that amount (Eisenberg, LaFountain, Ostram, & Rottam, 2002). However, the same criticisms of Polinsky still apply to this study. One of the thorny issues with punitive damages in the United States is that a high percentage of the larger punitive awards come from jury trials as opposed to judges. The Eisenberg, LaFountain, Ostram and Rottam claimed that punitive damages were not affected by whether the trial was before a judge or jury. However, Hersch and Viscuisi have pointed out that this work is beset with certain statistical flaws, such as the presence of multicollinearity, which biased the results (Hersch & Viscusi, 2004). In a review of punitive awards of at least $100 million over the period January 1985 through June 2003, Hirsch and Viscusi found that juries made 95% of these mega-punitive awards. Their findings are consistent with what we notice in other legal systems, such as Canada, where damages are set by judges not juries. In Canada, punitive damages are relatively rare.
5. THE SHADOW EFFECT OF PUNITIVE DAMAGES Some of the aforementioned research on the frequency of punitive damages could lead one to incorrectly conclude that punitive damages are so infrequently awarded that they need not be a major source of concern. As we have already noted, this research fails to consider that the threat of punitive damages permeates the negotiations of many lawsuits and may appear not only in verdicts but also in settlements. Defendants, concerned about the potential for high punitive damages, may agree to a settlement that implicitly incorporates their probability-adjusted estimate of their punitive damages exposure. This is what is known as the shadow effect of punitive damages. Given that it is not explicitly designated in settlements, the shadow effect is difficult to quantify. However, Thomas Koenig’s (1998) study using
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insurance adjustor data was able to measure the component of total settlements that they allocated to punitive damages (Koenig, 1998). He found that 11% of the total settlement amounts were attributed to punitive damages. At first, an 11% value may seem relatively small; but when this percentage is considered in light of the frequency of punitive damages, it becomes more and more significant.
6. TAXES, INSURANCE AND THE INCIDENCE OF PUNITIVE DAMAGES In settlement agreements, both parties, but especially the plaintiff, have an incentive to not identify settlement amounts as punitive damages. Under Section 104 of the Internal Revenue Code, settlement amounts designated as compensatory damages are not subject to federal taxation. When federal tax laws were amended by the Omnibus Budget Reconciliation Act of 1989, this law specifically excluded punitive damages (Dodge, 1992). If a settlement amount is stated as punitive damages, the net after-tax benefits to the plaintiff will be lower. Often the defendant is indifferent as to whether settlement amounts are designated punitive or compensatory damages. However, some courts have been reluctant to enforce insurance agreements for punitive damages. In other cases, a defendant may not be covered under insurance for punitive damages. If this is the case, then the defendant may also want settlement amounts designated as compensatory rather than punitive damages (Priest, 1989). The economics of punitive damages dictates that designating parts of settlements as punitive damages reduces the plaintiff’s benefit and sometimes may also raise the defendant’s costs. We know that punitive damages are embodied within settlement amounts, but we do not expect to find specific components designated as such. It is ironic that plaintiffs in mass tort suits sometimes argue that punitive damages are justified because the defendant, who may have paid millions if not billions in prior settlement amounts, had yet to pay punitive damages. In reality such defendants may have paid very substantial sums for what they considered punitive exposure.
7. PURPOSES OF PUNITIVE DAMAGES It is well established that the dual purposes of punitive damages are punishment and deterrence (Second Restatement of Torts, 1979). In its recent
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decisions relating to punitive damages, Cooper Industries v. Leatherman and State Farm Mutual v. Campbell, the U.S. Supreme Court has reaffirmed this. Punitive damages are ‘‘not compensation for injury. Instead, they are private fines levied by civil juries to punish reprehensible conduct and to deter its future occurrence’’ (Gertz v. Robert Welch, Inc., 1974). They are awarded for acts that are so extreme that the trier of the facts seeks additional penalties beyond compensatory damages. Deterrence can be broken down into two types: specific and general deterrence (Ellis, 1982). Specific deterrence focuses on a particular defendant whereas general deterrence considers parties other than the defendant. Of the two goals of punitive damages, some contend that deterrence is the more important one (Owen, 1994). As with many other economic measures, there is an optimal amount of deterrence. Over-deterrence or under-deterrence is suboptimal. When too many resources are devoted to achieving deterrence, we have over-deterrence. On the other hand, when too few resources are allocated to deterrence, the result is under-deterrence. The economically efficient outcome or optimal outcome is in the area between under- and over-deterrence. While this issue is quite relevant to the determination of punitive damages, it has been discussed elsewhere in the literature and is not the focus of this paper (Polinsky & Shavell, 1998).
8. CORPORATE GOVERNANCE AND THE CHALLENGE OF CORPORATE PUNISHMENT Punishing a corporation is a very different exercise than punishing an individual. When a judge or jury decides that an individual defendant needs to be punished, one has greater assurance that the specific individual defendant will bear the punishment. With corporate defendants, it may be more likely that parties other than the wrongdoers may bear the effects of the punishment (Coffee, 1981). This is due to the nature of corporate organizations. Shareholders are the owners of corporations. They elect directors who, in turn, select managers who run the company on a day-to-day basis. However, a broader group of individuals have a ‘‘stake’’ in corporations (Shleifer & Vishny, 1997). That is, corporations are groupings of various stakeholders working towards some common economic activity. Freeman (1984) has defined stakeholders to be ‘‘any group or individual who can affect or is affected by the achievement of the organization’s objectives.’’ However, management theorists have differed on just how broad or narrow to define
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stakeholders (Mitchell, Agle, & Wood, 1997). Such stakeholders may or may not have an equity interest in the corporation. Groups who do not have an equity interest in the company include employees, management, suppliers, communities, recipients of tax receipts and possibly others depending on the circumstances.
8.1. Corporate Punishment and Spillover Effects Punishment imposed upon a corporation may end up being borne by parties other than the wrongdoers. This may be a by-product of the legal doctrine of vicarious liability where an employer may be held liable for actions of its employees. Another name for this is the respondent superior rule. The appropriateness of the application of this legal principle to punitive damages has long been a subject of debate (Morris, 1931). Economists, however, refer to such effects that result from the application of this rule as spillover effects. The term spillover effects is well known in microeconomics – especially in the field of public finance. Yet another name for such effects is externalities. One definition of an externality or spillover effect is ‘‘a cost or benefit resulting from some activity or transaction that is imposed or bestowed on parties outside the activity or transaction. Sometimes the terms spillovers or neighborhood effects are substituted for the term externalities’’ (Case & Fair, 2002). Punitive damages are a very blunt tool for a judge or jury to use to try to punish wrongdoers. Owing to its lack of precision, and sometimes lack of timeliness, it may be more likely that innocent parties will bear the adverse effects of such an imprecise instrument while the guilty individuals may have ‘‘long departed the scene.’’ In cases where the trial takes place many years after the alleged wrongful acts, the likelihood of being able to isolate wrongdoers may be pretty low. Good examples of this are tobacco and asbestos litigation. In such cases, it may be more likely that equity and nonequity stakeholders may bear the effects of the punishment.
8.2. Punishment and Equity Stakeholders Stock is the first security to be issued when a corporation is formed and the last to be retired. As owners of the company, equity holders hope to gain from corporate profitability. Such gains may come from dividends and/or
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capital gains. Plaintiffs often argue that since shareholders gain from the corporation’s business activities, they should also bear the effects of punitive damages. Unfortunately, such simplistic reasoning is beset with flaws. The first flaw is a function of the nature of stock ownership of large corporations. In closely held companies there may be little difference between shareholders and the firm’s management and decision-makers. Such firms may be managed more like sole proprietorships which are seeking the limited liability protection of the corporate business form. With small, closely held companies there may be some assurance that corporate penalties will in some way be borne by the parties who made the decisions that led to the wrongful acts and who may have also profited from them. This situation may also be somewhat true for smaller publicly held companies where share ownership is concentrated in the hands of few shareholders who may also take an active role managing the company. The situation changes significantly as one’s focus moves to larger publicly held corporations. Here the separation of ownership and control becomes a more important issue. Shareholders in large publicly held companies tend to have little, if any, control of the company. The larger the number of shares outstanding and the more widely distributed the equity base is, the less likely that any particular shareholder has significant control over the actions of the corporation. 8.3. Separation of Ownership and Control While shareholders are the ‘‘owners’’ of the company, they are not owners in the sense that a closely held company may have owners. For shareholders in large market capitalization companies, the shareholders have an investment in the company but are not active in its management. This separation of ownership and control has been a topic that has been discussed in corporate finance for many years (see Berle & Means, 2003). Part of this debate has centered on the agency problem where shareholders select agents to maximize the value of their investments (Jensen, 1986). This can be a problem because these agents have their own agenda and may not take all of the actions that are needed for the betterment of shareholders. The agency problem underscores the limitations that shareholders face in the corporate governance arena. 8.4. Stock Ownership of U.S. Corporations Share ownership of U.S. corporations has become increasingly concentrated in the hands of institutions as opposed to individuals (Brancato & Gaughan,
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Table 1.
Institutional Holdings for Dow Jones Industrial Averages.
Company
Ticker
Institutional Holdings (%)
Number of Institutions
ALCOA INC AMER INTL GROUP BOEING CO CITIGROUP CATERPILLAR INC DU PONT CO WALT DISNEY CO GENERAL ELEC CO GENERAL MOTORS HOME DEPOT INC HONEYWELL INTL HEWLETT-PACKARD INTL BUS MACHINE INTEL CORP JOHNSON & JOHNSON JP MORGAN CHASE COCA COLA CO MCDONALDS CORP 3 M COMPANY ALTRIA GROUP MERCK & CO MICROSOFT CP PFIZER INC PROCTER & GAMBLE SBC COMMS UNITED TECH CP VERIZON COMMS WAL-MART STORES EXXON MOBIL
AA AIG BA C CAT DD DIS GE GM HD HON HPQ IBM INTC JNJ JPM KO MCD MMM MO MRK MSFT PFE PG SBC UTX VZ WMT XOM
76.45 60.64 61.78 65.14 73.15 57.94 62.46 51.84 75.25 60.62 74.20 63.42 54.85 55.57 60.91 66.76 57.72 71.08 70.29 67.62 57.19 52.60 63.11 56.65 51.95 77.43 53.82 35.97 50.47
1,749 2,931 1,317 3,398 1,333 1,694 2,061 3,080 1,189 2,407 1,520 2,307 2,703 3,141 2,869 2,339 2,049 1,770 1,986 2,174 2,576 3,442 3,592 2,554 2,112 1,955 2,299 2,418 2,775
Average 61.62
Average 2,335.86
Source: Vickers Database, July 1, 2004.
1988). For example, Table 1 shows that the institutional holdings percentage of the Dow Jones Industrial Average companies was 61% as of July 2004. The largest groups of institutions are mutual funds, pension funds and insurance companies. Each holds shares as investments for those for whom they have a fiduciary responsibility. The individuals for whom the shares are held by such intermediaries typically have little control or even contact with the corporations. The institutions themselves have become somewhat more
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active over the past decade; but due to the fact that their portfolios tend to be diversified and that each company represents only a fraction of the total equity it manages, they cannot devote significant resources to the micromanagement of the companies in their portfolios (Ross, Westerfield, & Jordan, 2004). In addition, as Table 2 shows, the largest shareholders of major companies typically hold fewer than 10% of the total shares outstanding.
Table 2.
Largest Shareholders of DJIA Companies.
Company
Ticker
ALCOA INC AMER INTL GROUP BOEING CO CITIGROUP CATERPILLAR INC DU PONT CO WALT DISNEY CO GENERAL ELEC CO GENERAL MOTORS HOME DEPOT INC HONEYWELL INTL HEWLETT-PACKARD INTL BUS MACHINE INTEL CORP JOHNSON & JOHNSON JP MORGAN CHASE COCA COLA CO MCDONALDS CORP 3 M COMPANY ALTRIA GROUP MERCK & CO MICROSOFT CP PFIZER INC PROCTER & GAMBLE SBC COMMS UNITED TECH CP VERIZON COMMS WAL-MART STORES EXXON MOBIL
AA AIG BA C CAT DD DIS GE GM HD HON HPQ IBM INTC JNJ JPM KO MCD MMM MO MRK MSFT PFE PG SBC UTX VZ WMT XOM
Holder Barclays Bank Plc Star International Company, Inc. Davis Selected Advisers, LP Capital Research and Management State Street Corporation Capital Research and Management State Street Corporation Barclays Bank Plc Barclays Bank Plc State Street Corporation FMR Corporation State Street Corporation Axa State Street Corporation Barclays Bank Plc Barclays Bank Plc Berkshire Hathaway FMR Corporation State Street Corporation Capital Research and Management Barclays Bank Plc William H. Gates III Barclays Bank Plc Barclays Bank Plc Capital Research and Management State Street Corporation FMR Corporation Barclays Bank Plc Barclays Bank Plc
% Out
Company Company
Company
Company
5.43 11.93 5.23 5.59 4.88 5.4 4.27 3.76 3.65 17.64 5.44 11.84 4.87 7.38 4.52 4.62 8.21 5.42 7.73 7.35 4.56 10.36 4.35 3.51 5.7 11.74 4.74 3.16 4.17 Average 6.46
Source: Yahoo Finance. http://finance.yahoo.com, as of June 29, 2004.
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While institutions as a group may hold a large percentage of the total shares outstanding, even majority percentages, it is unusual for any one institution to hold a controlling position in a given corporation. This is due to the fact that institutions often limit their holdings and may also face other restrictions designed to prevent any one company from becoming too large a percentage of a company’s investments (Roe, 1996). There are exceptions and cases where certain shareholders may hold at least 51 percent of shares, but that is not the norm (Holderness & Sheehan, 1988). This is one distinction between corporate share ownership in the US compared to that in other parts of the world. In Europe, for example, such high controlling share positions are more common (Franks & Mayer, 1990).
8.5. Non-Equity Stakeholders Non-equity stakeholders can be categorized into two groups: internal and external. Internal stakeholders are employees, who can be managerial and non-managerial employees. Each has a vested interest in the success and growth of the company. Decisions are made at all levels of employment with broader policies usually being established at higher levels of management and more narrowly defined decisions being made at lower levels of authority. For larger companies with many layers of management, the various layers become increasingly removed from each other. The more numerous the layers of management, the greater the probability that upper management may not even be aware of certain decisions made by middle or lower level managers. Such decisions could be ones which are the subject of the litigation. In addition to management, other stakeholders include non-management employees. At most corporations, the ranks of the non-management employees are larger than those of management. In addition to employees, still other stakeholders include suppliers, who may depend on a defendant’s corporation for an important component of its business. Suppliers benefit directly when corporations increase purchases and are hurt when such sources of business decline. Corporations that incur increased costs, such as litigation-related costs, may be forced to curtail the scope of their operations. If this is the case, such actions may have an adverse effect on the utilization of inputs in their production process and the non-equity stakeholders who are providers of these inputs: employees and suppliers. Another group of non-equity stakeholders who have an interest in the operations of a corporate defendant are creditors. They may have made
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large investments in a given company through their provision of debt capital. Increases in costs through litigation payments such as punitive damages could have an adverse effect on their investments and their own stakeholders. Debt financing providers may have bargained with the debtor defendant to gain certain controls to protect their investment; but controls over potential actions, such as those which might give rise to the lawsuit, are unlikely to be parts of such agreements (Smith & Warner, 1979).
8.6. Effects on Equityholders Litigation costs will lower corporate profitability and reduce the pool of monies available for dividends and, thereby, impede capital gains. This is true for any cost, and litigated-related costs are no different. For this reason, the exposure to potentially large and unpredictable litigation payments can have an adverse effect on stock prices. Research studies have confirmed the impact that litigation can have on stock prices (Bizjak & Coles, 1995). This impact can be very significant. A good example of this was the 42% decline in the stock price of the Halliburton Company in response to a $30 million verdict in December 2001 in favor of five plaintiffs (Banerjee, 2001). This was one of many asbestos cases that were brought against the company.1 Over the prior quarter century, the company had settled almost 200,000 asbestos claims although many of them were settled for relatively modest amounts. The market reacted to the large verdict and what it implied about the potential litigation exposure that would occur if the other cases had a similar result. Another was the declines of Bayer AG’s stock price in response to the first Baycol trials beginning in Texas in 2001 (see Fig. 1). The company’s stock price fell from $43.36 at the end of January 2001 to $20.02 by September 10, 2001, and declined even further to $17.96 by the end of October of that year. Later in 2003, when Bayer AG received a favorable verdict, the stock rebounded. Towards the end of 2004, Pfizer’s market capitalization lost approximately $30 billion over a couple of trading days as a result of concerns that were being expressed about a possible relationship between heart problems and some of its anti-inflammatory drugs. The market fell even though no firm relationship between ailments and those drugs was known at that time and not a single lawsuit had been filed. For companies with large litigation exposure, such as tobacco and asbestos defendants, the adverse shareholder wealth effects can be quite significant. Securities analysts have attempted to measure the magnitude of the large tobacco liabilities of Philip Morris Companies, Inc., which is now
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Baycol is introduced in the U.S.
Baycol is recalled First trial begins in Texas
Price ($)
45
30
Bayer's Baycol receives FDA approval 15
Jury verdict
Fig. 1.
7/21/2003
1/21/2003
7/21/2002
1/21/2002
7/21/2001
1/21/2001
7/21/2000
1/21/2000
7/21/1999
1/21/1999
7/21/1998
1/21/1998
7/21/1997
1/21/1997
0
Bayer AG’s Stock Price Reacting to Events Surrounding. Source: Yahoo Finance. http://finance.yahoo.com. June 1, 2003.
called Altria. Table 3 shows that over the past three years, Philip Morris USA, the tobacco subsidiary of Altria, as well as other divisions of the food/ tobacco company, were the object of many lawsuits, including class actions and multiple plaintiff cases (Altria Annual Report, 2003). In February 2001, Goldman Sachs issued a report that featured a ‘‘sum of the parts’’ analysis which computed total enterprise value and the value of each of the company’s corporate divisions that composed the total enterprise value. The various parts or business segments were valued using comparable multiples that were relevant to the four industry segments that made up the parent firm – Philip Morris Companies, Inc.2 This comparable multiples analysis is an accepted method of valuing businesses (Gaughan, 2004). The Goldman Sachs analysis measured what has been termed the ‘‘litigation overhang’’ and found it to be equal to $91.5 billion (Goldman Sachs Analyst Report, 2001)! Without the litigation exposure, their analysis showed that the value of the equity of Philip Morris Companies, Inc. would have equaled approximately $200 billion, compared to the market value of the equity as of that time which was $108.7 billion. Goldman Sachs attributed this large difference to the market’s allowance for the uncertain tobacco liabilities.
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Table 3.
Tobacco Lawsuits against Altria: 2001–2003.
Type of Case
Individual smoking and health cases Smoking and health class actions and aggregated claims litigation Health care cost recovery actions Lights/ultra lights class actions Tobacco price cases Cigarette contraband cases Asbestos contribution cases
No. Cases Pending as of 12/31/2003
No. Cases Pending as of 12/31/2002
No. Cases Pending as of 12/31/2001
423
250
250
12
41
37
13 21 28 5 7
41 11 39 5 8
45 10 36 5 13
Litigation-related liabilities are but one form of relevant information that markets consider when determining equity values. Increases in such liabilities due to punitive damages may cause stock prices to decline, adversely affecting shareholders. Markets tend to be somewhat efficient (with exceptions) in processing relevant information.3 Some might argue that the company should reduce dividend payments to shareholders and allocate those monies to litigation payments, thereby making shareholders pay punitive and other damages in this manner. Unfortunately, this method also has farreaching spillover effects that will hurt shareholders in other ways. Announcements of dividend reductions and/or elimination usually cause the announcing company’s stock price to fall. For example, Cigna announced in February 2004 that it was undergoing a major restructuring and would cut its dividend from $.33 per share to $.025. As can be seen from Fig. 2, the market reacted in the expected manner with a sharp falloff in the stock price and market capitalization. Such dividend-cut-related stock collapses can have even more far-reaching effects, as a company can then become a target for a takeover, which, if completed, effectively ends the existence of the company in its prior form. These are spillover effects that need to be considered when contemplating actions that affect dividends and share values. While shareholders may lose some or all of the value of their investment, they are generally not involved in the decision making process that may have led to the award. Some may assert that shareholders can use the corporate election process to try to bring about changes in management’s behavior. However, this is a very expensive and difficult process that is usually unsuccessful – even for shareholders holding sizeable stock positions (see
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Price ($)
60
55
Fig. 2.
3/ 8/ 20 04
3/ 1/ 20 04
4 2/ 23 /2 00
4 2/ 16 /2 00
2/ 9/ 20 04
2/ 2/ 20 04
50
Cigna’s Stock Price Reacting to Announcement of Major Restructuring. Source: Yahoo Finance. http://finance.yahoo.com. June 1, 2003.
Pound, 1989). Given the expected shareholder wealth effects, it may be useful for juries to be made aware of these effects which have an impact on shareholders regardless of whether the shares are owned directly or indirectly through institutions. Another factor that should be considered when contemplating imposing a punitive award that will have various adverse effects on shareholders is the average holding period for stocks. There have been many reports on how the average holding period for stocks has declined over time as investors have become more short-term oriented. The holding period for many stocks is shorter than the time between when wrongful acts may be committed by employees of a corporation and the date of trial. Atkins and Dyl found that the median holding period for NASDAQ stocks was 3.38 years, while for New York Stock Exchange stocks it was an even shorter 2.43 years (Atkins & Dyl, 1997). Data on the time period between the filing of a personal injury suit and a trial date show that the mean value is 615 days (Cornell University Data Base, 1998). This time is in addition to the lag between the alleged act and the filing of a complaint. The importance of these research
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findings is that by imposing a penalty that shareholders will bear, we force shareholders as of the date of trial to pay for the alleged wrongdoing of employees in corporations with which they may not have had any connection at the time of the alleged wrongdoing. Such an outcome hardly seems fair. Defendants may be able to demonstrate this through an analysis of the shareholdings at different relevant points in time.
8.7. Potential Impact on Regional Economies Other corporate stakeholders may include communities where the defendant corporations do substantial business. These communities may be recipients of tax receipts and charitable contributions. For smaller communities with a less diversified economic or industrial base, changes in the level of these expenditures can have a significant impact on regional economies. In such communities plant closures can have dramatic adverse effects that might be reflected in rising unemployment and declining regional output. Increases in costs caused by large litigation liabilities may cause companies to shrink the size of their work force. Displaced workers may be forced to try to replace higher paid manufacturing jobs with lower paying ones (Patch, 1995). These effects may be more pronounced during weak economic times when there are fewer opportunities for workers to mitigate their damages due to a soft employment market. If unionized manufacturing jobs are lost, they may be replaced by lower paying service positions (Ehrenberg & Smith, 2000). One well-known example of such concentrated regional economic effects occurred in communities such as Allentown and Bethlehem, Pennsylvania, when the steel industry contracted in the 1980s and companies were forced to lay off workers and close plants (Strohmeyer, 1994). If the costs of litigation cause a defendant corporation to downsize or limit expenditures that it would have devoted to other stakeholders, such as communities (an example would be corporate charitable contributions), we may incur still other litigation-related spillover effects. We know from macroeconomic theory that such cutbacks in expenditures will have total adverse effects that are a multiple of the original reduction. These effects are well known and are explained in major principles of economic textbooks in the context of Keynesian expenditure multipliers (see Samuelson & Nordhaus, 1998). Insofar as the affected corporations may have a concentrated presence within a given region, these adverse effects may be even more pronounced. Regional expenditure multipliers that attempt to measure the aggregate impact of expenditures may be used to quantitatively measure the
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total adverse impact that a cutback in corporate expenditures might have. These multipliers measure how many dollars of expenditures are ultimately generated when a given dollar is spent. Economic models exist, which attempt to measure the magnitude of such multipliers (Rickman & Schwer, 1995). Such multipliers may be one tool that can be employed when trying to measure the adverse impact of a reduction in expenditures caused by punitive awards or other litigation-related costs.
8.8. Consumers Still another group affected by spillover effects may be consumers of the defendant’s products. Litigation-related costs, like any other increase in costs, may put upward pressure on prices. Two prime examples are the tobacco and pharmaceutical industries. Cigarette prices increased in response to the ‘‘Master Settlement Agreement Between the States and the U.S. Tobacco Producers’’ (1998) and its billion dollar payments (Capehart, 2001). Research has showed that drug prices are higher in a more active litigation environment, such as the United States, compared to Canada where punitive damages are relatively rare (Manning, 1997). Litigationrelated price increases are like per-unit or excise taxes which microeconomic theory has shown to be a form of regressive taxation. As Stiglitz (1997) states, ‘‘Taxes on tobacco and alcohol are examples of regressive taxes, since poor individuals spend a larger fraction of their income on these goods.’’ Punitive or other litigation-related expenses can cause corporations to respond by increasing prices, and this will have an adverse effect on consumers – especially poorer consumers who may bear a disproportionate burden relative to their income levels. How much prices may increase when a producer’s costs rise will be a function of the product’s price elasticity of demand as well as other factors. If a product’s demand is price inelastic, price changes will have a lesser effect on quantity demanded than in the case of a more elastic demand. Economists have long established that various factors determine a product’s price elasticity, including availability of substitutes, tastes and preferences, and the percentage of an individual’s total budget that the product constitutes (Taylor, 2004). In the case of cigarettes, various estimates of elasticities exist. One such estimate is that the short-run price elasticity of demand is 0.4 and the long run is 0.7, both of which are in the inelastic range (Grossman, 2001). However, these estimates were drawn from a different world in which prices were lower and quantity demanded was less price elastic than it now appears to be.
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Microeconomic theory tells us that in the long run demand curves tend to be more elastic than in the short run. (Perloff, 1999) This is due to a possible greater availability of substitutes in the long run. The time dimension of the price elasticity of cigarette demand is quite apparent when considering the responsiveness of quantity demanded to price changes caused by the Master Settlement Agreement (MSA) and tax increases. The initial responsive of the market was somewhat sluggish; but soon consumers began to adjust, and the major cigarette manufacturers began to feel the effects of the consumer adjustment process. In the initial period after the price increases, presumably due to the inelastic nature of the demand for the product, manufacturers were able to maintain profitability even though unit sales declined. Consumers then began to pursue lower cost cigarettes manufactured by smaller manufacturers (Fairclough, 2002). When the MSA was first signed, the major cigarette manufacturers had a combined market share in the high 1990s. By 2002, the lesser known manufacturers accounted for 10% of the total U.S. cigarette market (Federal Trade Commission, 2004). It is ironic that tobacco regulation today focuses mainly on the major manufacturers while the more rapidly growing segment of this industry ‘‘moves below the radar’’ of regulators. However, the Federal Trade Commission recognized the growing competition from the small discount cigarette manufacturers when it approved the 2004 $2.6 billion merger between RJ Reynolds and Brown and Williamson. Sometimes it is difficult to know in advance the precise price effects and resulting impact on consumers. Often data on historical elasticities are limited, and in any case knowledge of such elasticities may not be that helpful if prices change significantly and we move into a new, more responsive or elastic part of the demand curve (assuming the curve does not shift due to other factors). However, juries need to understand that when a company’s costs change, it may have to adjust its prices and possibly its level of business activity. Punitive damages are a cost, and corporations respond to changing costs. These price effects may bring about a change in quantity demanded, the magnitude of which will depend on the relevant price elasticity of demand. This may be an area in which an economic expert may provide insight to a jury.
9. CORPORATE PUNISHMENT AND ISOLATING THE WRONGDOERS The fact that punitive damages may spill over to various corporate stakeholders is not new and has been explained in law journals for decades
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(Coffee, 1980). The actions that gave rise to the lawsuit could be the product of middle level managers. These employees may even have long left the employ of the corporation prior to a trial. Given the many layers of management in large Fortune 100 companies, it may be the case that upper management of the company was not aware of the actions of these employees. Those acts, however, may give rise to lawsuits in later years even though, again, upper management may be unaware of them at the time they occurred. Employee turnover, including turnover at the highest ranks of corporations, makes the problem of isolating the wrongdoers even more difficult. One study has showed that the average tenure of a chief executive is eight years (Brickley, 1999). A later survey by Booz Allen Hamilton (2003) indicates that the rate of CEO turnover may be increasing. Still another study showed that the average tenure of corporate directors is nine years (Hameralin & Weisbach, 1988). Given the time gap between an alleged wrongful act and a trial date, it may be the case that many, if not all, of the alleged wrongdoers are no longer in the employ of the defendant as of the trial. Particularly in cases where the alleged wrongdoers are no longer with the company, the effects of punitive damages imposed on the corporation will necessarily be borne by those others. While a punitive award may not have any impact on alleged wrongdoers, it may cause various stakeholders to pay a financial penalty for actions in which they had no part. This is even more likely to be the case when there is a long lag between when the alleged wrongdoing and the trial date. This is an issue of which the jury should be made aware so that they can make decisions based upon a more complete information set.
10. DETERRENCE THEORY AND THE CURRENT LITIGATION ENVIRONMENT The theoretical relationship between the probability of detection and deterrence has been analyzed in detail by Polinsky and Shavell (1998). Their analysis, however, is not totally novel as these ideas were originally introduced in the late 1800s by Jeremy Bentham and the Utilitarians. Polinsky and Shavell put forward a theoretical framework for how the probability of detection could be incorporated into the process of determining a punitive award. Given the desire to avoid both under-and over-deterrence, they reasoned that total damages should equal the harm caused. In cases where the
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probability of being found liable is less than one, punitive damages could be used to bring about the equality between the probability-adjusted harm (p)H and total damages where p stands for the probability of being found liable. A damages and punitive multiplier can be arrived at as follows: Damages Multiplier ¼ 1=p ; (1) where H is the harm caused, p is the probability of being found liable, and D is the total damages D ¼ H=p ¼ H 1=p ; (2) while the Punitive Damages Multiplier ¼ [(1 p)/p] When trying to apply this reasoning, we have to consider the potential differences between the probability of detection as of the time the alleged wrongful act was committed and the trial date. If a jury were to try to apply this probability analysis, it should differentiate between ex ante and ex post probabilities. The probability of being found liable as of the time the act is committed is the ex ante probability. The ex post probability is the one that prevails as of the trial date. From a deterrence perspective, the ex post probability is the more relevant one. This is the case because deterrence is forward looking while punishment is backward looking (Ellis, 1982). For industries that are the target of very aggressive plaintiff attorneys and/or are the object of careful regulatory scrutiny, the ex post probability may be quite high. The development of the plaintiff’s bar, such as evidenced in the new round of asbestos litigation or the numerous high profile pharmaceutical and tobacco lawsuits, gives weight to such a conclusion. A very aggressive, organized and well-financed plaintiff’s bar stands ready to attack potentially liable deep-pocketed defendants (France, 2001). Corporate defendants may have enjoyed financial advantages over plaintiff attorneys in the past, but this has become less likely to be so in recent years. The gains of the plaintiff’s bar are underscored in the following excerpts from an article about the increasing volume of lawsuits against pharmaceutical companies: These days the battle between the drug companies is no longer one between corporate goliaths and individual advocates on a shoestring budget. ‘‘We’ve got plenty of a war chest,’’ said J. Michael Papantonio, a lawyer in Pensacola, Fla., who is a leader in drug litigation. ‘‘It’s a different day out there. It’s not like they’re going to look across the table from us and say, ‘We’re going to dry you up.’ ’’
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Plaintiffs’ lawyers can now finance enormously complicated suits that require years of pre-trial work and substantial scientific expertise, in the hope of a multi-billion-dollar payoff. Scores of firms collaborate on a case, with some responsible for finding claimants, others for managing the millions of documents that companies turn over, others for the written legal arguments, and still others for presenting the case to a jury. Some 60 firms have banded together, for example, in the Baycol litigation (Berenson, 2003, p. 29).
While the Polinsky and Shavel probability analysis is an interesting academic discussion, recent research shows that it may not be capable of being applied to actual trials. Professor Kip Viscusi sought to have a sample of 500 jury-eligible individuals apply probability-based negligence rules (Viscusi, 2001). He found that they were unable to properly apply the probabilities to arrive at multipliers. This is a reasonable result as many people do not have a background in probability theory.
11. CORPORATE GAINS AND LOSSES AND DETERRENCE In cases where a company has been the target of mass tort lawsuits, it may have made very substantial litigation payments prior to a given trial. Sometimes these payments may rise to the level of billions of dollars. For example, as of the end of 2004 the pharmaceutical corporation Wyeth had paid in excess of $14 billion in diet drug litigation (Wyeth, 2004). Prior payments, particularly when they are large sums, are a factor that a jury may want to consider when evaluating whether further payments will accomplish any more deterrence. A comparison between the payments made, including settlements as well as litigation expenses, and the profits derived from the product may be useful. This comparison should include all litigation-related costs, including adverse publicity that the company may have incurred as a result of the lawsuits. (Karpoff & Lott, 1999). The impact of adverse publicity will be further discussed later in this chapter. When making this type of comparison, it may be the case that the costs far outweighed the gains. In general, corporations try to pursue projects which will pay a rate of return that is in excess of a particular threshold, such as the cost of capital (Keown, Martin, Petty, & Scott, 2002). Companies do not want to pursue projects where cash outflows greatly exceed inflows. In some cases this difference may be dramatic. This may be relevant for both specific and general deterrence as other companies, seeing the plight of a defendant who has made very significant payments while
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receiving comparatively small financial gains, would not want to put themselves in a similar situation.
12. REGULATION AND DETERRENCE Punitive damages are naturally a very imprecise tool to use to try to achieve deterrence. Other means, such as regulatory processes, may be much better ways of accomplishing deterrence. These processes may be both internal and external. Internal processes refer to the measures a defendant may take to ensure that the actions that brought about the lawsuit will not take place in the future. This may be an issue on which corporate witnesses may provide testimony. External regulation may come from governmental or industry groups that may oversee the industry. An example drawn from the tobacco industry is the regulatory strictures and oversight provided under the MSA. The agreement and the various limitations, such as marketing and advertising restrictions, imposed on the major tobacco companies are overseen by the National Association of Attorneys Generals (NAAG). NAAG has a specific tobacco committee which monitors the industry and is empowered to take aggressive legal actions if it determines that the companies have violated the MSA. (While NAAG closely monitors the marketing activities of the major tobacco companies, it appears that some of the smaller manufacturers have at times ‘‘fallen through the cracks.’’) If, for example, a jury wanted to deter one of the major tobacco companies from engaging in improper marketing activities in the future, it should be made aware that NAAG would be better able to prevent such actions than a jury. The jury would have to evaluate whether an additional punitive penalty for an act that may have occurred many years before, in addition to the billions of dollars in payments that this industry has and will have made through the MSA, would add to the deterrence already in place. In addition, the jury would have to consider the other organizations, such as health-related and anti-smoking organizations, that monitor the industry and determine if a punitive award would add deterrence that internal controls, NAAG, and these various groups do not already provide. Regulation varies by industry, with some industries being regulated closely while others are not. One industry that is closely regulated is the U.S. insurance industry. As a result of the McCarran-Ferguson Act of 1945, insurance regulation occurs primarily at the state level. All states have a separate insurance department, which regulates companies that offer insurance in a given state (Rejda, 2003). Insurance companies must be authorized
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to do business in each state where they market insurance. State insurance regulators are empowered to restrict the ability of an insurance company to do business if it fails to adhere to that state’s insurance requirements (Black & Skipper, 2000). Regulators focus on a variety of activities of insurers, including their sales practices as well as their financial stability and ability to make required payments to their policy holders. This process, while imperfect, works better than the court system at achieving deterrence. Examples of this are the many vanishing premium lawsuits that have been brought against life insurance companies. These suits allege that life insurance companies did not properly inform purchasers of insurance that premiums for certain types of insurance policies could possibly not vanish if investment gains in the value of the policy were not sufficient. By the time many of these lawsuits worked their way to the trial stage, the problem (to the extent that it ever did exist – an issue disputed by defendants) was already dealt with by the regulators of the industry. The National Association of Insurance Commissioners puts forward model regulations that tend to be subsequently adopted by the various state insurance regulators. With respect to vanishing premium suits, a specific model regulation was put forward to regulate the representations that insurance company sales people could make. This underscores how regulators can identify problems relatively quickly and then implement a solution. Jurors should be made aware of the regulatory structures that may already be in place at the time of the trial so they can determine if a punitive award will add to the deterrence that may already exist. In cases where there is a long time lag between the alleged wrongful acts and the trial, a jury may be able to look back and see that deterrence has already been achieved.
13. DETERRENCE, PUNISHMENT, AND MERGERS AND ACQUISITIONS Over the past quarter century we have had an unprecedented number of mergers and acquisitions (Gaughan, 2002). In acquisitions an acquirer typically adds the assets while assuming the liabilities of the target corporation. Unfortunately, some of these liabilities, such as off balance sheet liabilities involving litigation obligations, are difficult to predict and even foresee. Such contingent liabilities can be so difficult to assess that they may not be carried on the balance sheet as a known liability. It can possibly take many years before an acquirer is able to know the extent of the liabilities that it
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may have incurred as a result of an acquisition. The potential of looming off balance sheet liabilities was discovered in the 1990s when various acquirers became a target of a whole new wave of asbestos lawsuits. Some of them were forced into bankruptcy as a result of these acquired liabilities. One example is Halliburton Corporation, which filed for Chapter 11 bankruptcy protection due to asbestos liabilities it assumed when it acquired Dresser Industries in 1998 for $7.7 billion. The byproduct of this acquisition was 200,000 asbestos claims (Clark & Woellert, 2002). Another example of huge acquired asbestos liabilities is McDermott International, Inc., which incurred them through its acquisition of Babcok & Wilcox. Still another example of a company which inherited large litigation-related liabilities is ABB, the Zurich-based international conglomerate. It inherited these asbestos liabilities as a result of its $1.6 billion acquisition of Combustion Engineering in 1989 (ABB Completes Acquisition, 1989). Ironically, ABB sold Combustion’s operations in 2000, but was forced to still bear the claims that Combustion Engineering was responsible for causing asbestos exposure involving insulation in boilers. We will discuss the impact of the mounting asbestos claims on the viability of various U.S. corporations towards the end of this chapter. While punitive damages may often be inappropriate for companies not involved in acquisitions, it may be even more difficult to justify in the case of acquired entities. The management of the acquiring entity may have no knowledge of the actions that may result in these lawsuits in the future. In addition, it may never have engaged in the alleged acts and thus may not need to be deterred. However, if punitive damages are imposed, the acquirer’s stakeholders may be punished while the acquirer may have no responsibility for the wrongful acts. Critics may assert that the acquisition process could be used to avoid punishment to wrongdoing. This is not a valid criticism, however, as the jury would be asked to determine if this was the purpose of the deal based upon what they may be presented on this issue. When a lawsuit is pursued against an acquirer that has merged the target into its operations, the plaintiff may seek to substitute the financial resources of the acquirer for the target and to use the acquirer’s assets as some type of gauge for the magnitude of punitive damages. If this is allowed, the magnitude of punitive damages could be far greater if a target is acquired by a large ‘‘deep-pocketed’’ corporation.4 How can it be reasonable to have one level of punitive damages if the company remains independent and another far greater level of punitive damages if this corporation is acquired? Clearly, the acts of the wrongdoers are the same; and the magnitude of the harm, for which compensatory damages has presumably fully compensated the
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plaintiffs, is invariant. The only factor that differs is the resources of the two corporations. Such an outcome makes little sense.
14. TYPICAL FINANCIAL MEASURES INTRODUCED IN COURT FOR THE DETERMINATION OF PUNITIVE DAMAGES The wealth of the defendant is often allowed to be introduced as a factor for the jury’s consideration when determining the magnitude of a punitive award (Frank, Kelkar, & Sulkowski, 2001). While many punitive damages statutes discuss net worth, the simplistic application of net worth can often be of little value to a jury and at times can actually be very misleading. The U.S. Supreme Court addressed the use of net worth in its 2003 decision in State Farm Mutual Automobile Insurance Co. v. Campbell et al. The Court had already expressed reservations about this issue in BMW v. Gore when it stated that the wealth of the defendant ‘‘provides an open-ended basis for inflating awards when the defendant is wealthy (Justice Breyer concurring).’’ In Campbell the Court expressed reservations about the use of evidence concerning a defendant’s wealth when it stated that ‘‘reference to its assets (which of course are what other insured parties in Utah and other states must rely upon for payment of claims) had little to do with the actual harm sustained by the Campbells. The wealth of the defendant cannot justify an otherwise unconstitutional punitive damages award.’’ In addressing the plaintiff’s attempts to introduce the wealth of the defendant, the Supreme Court expressed concern that the wealth of a large corporate defendant could bias the jury and possibly result in an award that bore little relationship to the actual harm caused. If the wealth of a defendant is allowed to be a factor for the jury’s consideration, then higher net worth defendants could face higher punitive/compensatory multiples for the same acts. Such a result could compound the problem that the Supreme Court in Campbell was concerned about – multiples greater than single digits. Also, such a result raises concerns about fairness and equal treatment under the law.
14.1. Net Worth Net worth is defined as the difference between the value of a company’s assets and liabilities on its balance sheet (Moyer, McGuigan, & Kretlow,
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2006). Balance sheets are not prepared for the purpose of serving as a guide for juries to assess punitive damages. They show the assets of a company and the claims on those assets in the form of both debt and equity claims. The assets include both tangible and intangible assets. Intangible assets are assets that do not possess physical substance (Weygandt, Keiso, & Kimmel, 2003). Within the intangible category are assets such as goodwill. Goodwill is created in acquisitions and is an accountant’s way of dealing with the difference in the value of a previously acquired company’s assets and the total purchase price of the company (Pratt, 2003). Clearly, it is very difficult for a defendant to use goodwill or other possibly intangible assets to pay a punitive penalty. Yet, since various courts allow net worth to be considered, these assets are part of what courts have said juries can look to when determining the magnitude of a punitive award. If we are determined to use net worth, a partial remedy to its drawbacks would be to substitute tangible net worth. Here we only consider tangible assets and leave out intangible assets prior to deducting total liabilities. This is not a complete solution as higher tangible net worth defendants may still face higher awards. For many companies the difference between total and tangible worth can be significant. For example, Table 4 shows that in 2001 the net worth of AOL Time Warner equaled $152 billion (Annual Report of AOL Time Warner, 2002). Of this total, $127.4 billion was goodwill. By 2002 shareholder equity had fallen by approximately $100 billion. Most of this decline was a decrease in goodwill, which had fallen to $37 billion from $127.4 billion! Accounting principles and policies required that companies regularly revisit goodwill to determine if an impairment exists (FAS 142). If such an impairment exists, such as when the carrying value of the goodwill is greater than its fair market value, then the company is required to take an impairment loss. AOL Time Warner responded to the adoption of this accounting rule change enacted in January 1, 2002. As part of that evaluation, AOL Time Warner took a charge of $54.199 billion when the rule was first enacted and then another charge at the end of that year equal to $45.538 billion. Table 5 shows that intangibles constitute approximately 40% of the total net worth of the 30 companies included in the Dow Jones 30 Industrial Average.
14.2. Net Worth and the Capitalization of Corporations When punitive damages are made partially a function of shareholder equity, companies exposed to the risk of such damages may have an incentive to
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Table 4.
AOL Time Warner Inc. Consolidated Balance Sheet.
Dollars in Millions ASSETS Current Assets: Cash and cash equivalents Receivables, less allowances of $2.379 and $1.889 billion Inventories Prepaid expenses and other current assets Total current assets Noncurrent inventories and film costs Investments, including available-for-sale securities Property, plant and equipment, net Intangible assets subject to amortization Intangible assets not subject to amortization Goodwill Other Assets Total Assets LIABILITIES AND SHAREHOLDERS’ EQUITY Current Liabilities: Accounts payable Participations payable Royalties and programming costs payable Deferred revenue Debt due within one year Other current liabilities Total current liabilities Long-term debt Deferred income taxes Deferred revenue Other liabilities Minorities interests SHAREHOLDERS’ EQUITY Series LMCN-V common stock, $0.01 par value, 171.2 million shares outstanding in each period AOL Time Warner common stock, $0.01 par value, 4.305 and 4.258 Billion shares outstanding Paid in capital Accumulated other comprehensive income (loss), net Retained earnings (loss) Total shareholders’ equity Total Liabilities and Stockholders’ Equity Source: Annual Report of AOL Time Warner (2003).
2002
2001
$1,730 5,667 1,896 1,862 11,155 3,351 5,138 12,150 7,061 37,145 36,986 2,464 $115,450
$719 6,054 1,791 1,687 10,251 3,490 6,886 12,669 7,289 37,708 127,420 2,791 $208,504
$2,459 1,689 1,495 1,209 155 6,388 13,395 27,357 10,823 990 5,023 5,048
$2,266 1,253 1,515 1,451 48 6,443 12,976 22,792 11,231 1,048 4,839 3,591
2
2
43
42
155,134 (428) (101,934) 52,817 $115,450
155,172 49 (3,238) 152,027 $208,508
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Table 5.
Net Worth and Intangibles for Dow Jones Industrial Average Companies: 2003. Goodwill
Intangibles
Total Intangibles
Total Assets
Net Worth
Total Intangibles as % of Net Worth
ALCOA AMER EXPRESS CO BOEING CO CITIGROUP CATERPILLAR INC DU PONT CO WALT DISNEY CO EASTMAN KODAK GENERAL ELEC CO GENERAL MOTORS HOME DEPOT INC HONEYWELL INTL HEWLETT-PACKARD INTL BUS MACHINE INTEL CORP INTL PAPER CO JOHNSON & JOHNSON
6,549.0 0.0 1,913.0 27,581.0 1,398.0 1,939.0 16,966.0 1,348.0 0.0 0.0 0.0 5,789.0 14,894.0 6,921.0 3,705.0 5,341.0 5,390.0
0.0 0.0 1,035.0 13,881.0 239.0 3,278.0 8,991.0 0.0 55,025.0 1,479.0 0.0 1,098.0 4,356.0 574.0 0.0 0.0 6,149.0
6,549.0 0.0 2,948.0 41,462.0 1,637.0 5,217.0 25,957.0 1,348.0 55,025.0 1,479.0 0.0 6,887.0 19,250.0 7,495.0 3,705.0 5,341.0 11,539.0
31,711.0 175,001.0 53,035.0 1,264,032.0 36,465.0 37,039.0 49,988.0 14,818.0 647,483.0 448,507.0 34,437.0 29,344.0 74,708.0 104,457.0 47,143.0 35,525.0 48,263.0
12,075.0 15,323.0 8,139.0 98,014.0 6,078.0 9,781.0 23,791.0 3,264.0 79,180.0 25,268.0 22,407.0 10,729.0 37,746.0 27,864.0 37,846.0 8,237.0 26,869.0
54.24 0.00 36.22 42.30 26.93 53.34 109.10 41.30 69.49 5.85 0.00 64.19 51.00 26.90 9.79 64.84 42.95
PATRICK A. GAUGHAN
Companies
8,511.0 1,029.0 1,665.1 2,419.0 27,742.0 1,085.4 3,128.0 11,132.0 1,611.0 4,801.0 9,329.0 9,882.0 0.0 6,069.0
6,480.0 2,960.0 0.0 274.0 11,803.0 864.0 384.0 2,375.0 0.0 499.0 0.0 0.0 0.0 4,058.1
14,991.0 3,989.0 1,665.1 2,693.0 39,545.0 1,949.4 3,512.0 13,507.0 1,611.0 5,300.0 9,329.0 9,882.0 0.0 10,127.1
770,912.0 27,342.0 25,525.1 17,600.0 96,175.0 40,587.5 79,571.0 43,706.0 100,166.0 47,988.0 34,648.0 104,912.0 174,278.0 156,512.2
46,154.0 14,090.0 11,981.9 7,885.0 25,077.0 15,576.4 61,020.0 16,186.0 38,248.0 13,956.0 11,707.0 43,623.0 89,915.0 28,267.7
32.48 28.31 13.90 34.15 157.69 12.52 5.76 83.45 4.21 37.98 79.69 22.65 0.00 40.37
The Economics of Punitive Damages
JP MORGAN CHASE COCA COLA CO MCDONALDS CORP 3 M COMPANY ALTRIA GROUP MERCK & CO MICROSOFT CP PROCTER & GAMBLE SBC COMMS AT & T CORP UNITED TECH CP WAL-MART STORES EXXON MOBIL Averages
Source: Balance Sheets 2003, www.marketguide.com.
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adjust their capital structure and utilize more debt and less equity (Boyd & Ingberman, 1999). If we assume that the company already had what it believed to be an optimal capital structure, one that would provide it with its lowest cost of capital, then such an adjustment would move the company to a less optimal capital structure and increase its cost of capital. The increased use of financial leverage would raise the risk profile of the company. In addition, if deterrence were a truly a function of the amount of net worth that would be at risk, then adjustments in corporate capital structures which reduce shareholder equity could fail to promote deterrence. However, while there is a theoretical rationale for implying that punitive damages may have adverse effects on the capitalization of corporations, this has not yet been convincingly demonstrated empirically.
14.3. Court-Recognized Flaws Inherent in Net Worth One of the first drawbacks associated with the presentation of evidence on the defendant’s net worth is that it introduces a potential bias against deeppocketed defendants. While this was noted in Campbell, it was not the first time that the U.S. Supreme Court expressed this concern. In 1994 the Court noted that net worth presentations can be biased against defendants, especially those which may lack a significant local presence (Honda Motor Co. v. Oberg., 1994). However, bias-related problems are not the only source of judicial concerns about the use of net worth. Courts have recorded their reservations about whether net worth is even a good measure of the defendant’s financial resources. In Mathias et al. v. Accor Economy Lodging, Inc. et al. (2003), the Seventh Circuit noted the following: As a detail (the parties having made nothing of the point), we note that ‘‘net [*678] worth’’ is not the correct measure of a corporation’s resources. It is an accounting artifact that reflects the allocation of ownership between equity and debt claimants. A firm financed largely by equity investors has a large ‘‘net worth’’ ( ¼ the value of the equity claims), while the identical firm financed largely by debt may have only a small net worth because accountants treat debt as a liability. (Mathias v. Accor Economy Lodging, 2003)
Judge Easterbook discussed the deficiencies of net worth as a guide for punitive damages as follows: Courts take account of a defendant’s wealth when ‘‘an amount sufficient to punish or to deter one individual may be trivial to another.’’ Black v. Iovino, 219 III. App. 3rd 378, 394, 580 N.E.2d 139, 150, 162 III. Dec. 513 (1st Dist. 1991). See also Douglass v. Hustler
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Magazine, Inc., 769F.2d 1128, 1145 (7th Cir.1985). For natural persons the marginal utility of money decreases as wealth increases, so that higher fines may be needed to deter those possessing great wealth (‘‘May be’’ is an important qualifier; the entire penalty includes extra-judicial consequences, such as loss of business and other future income, that is likely to greater for wealthier defendants.) Corporations, however, are not wealthy in the sense that persons are. Corporations are abstractions; investors own the net worth of the business. These investors pay any punitive awards (the value of their shares of decreases), and they may [**28] be of average wealth. Pension trusts mutual funds, aggregating the investments of millions of average persons, own the bulk of many large corporations. Seeing the corporation as wealthy is an illusion, which like other mirages frequently leads people astray. (Zazu Designs v. L’Oreal S.A., 1992)
14.4. Punitive Damages and the Future Viability of the Defendant Punitive damages are designed to punish and promote deterrence, not to destroy the defendant. The future viability of the defendant is important – particularly if the corporate defendant provides societal economic benefits such as being a source of employment for its workers. The Fifth Circuit in Jackson v. Johns Manville Corp (1984) expressed concerns that punitive damages could result in the destruction of the corporate defendant. This concern was also expressed by other courts (Arab Termite & Pest Control of Florida, Inc. v. Jenkins (1982) and Vasbinder v. Scott, 976 F.2d 118 (2d Cir. 1992)). Some courts have attempted to deal with this problem by limiting the amount of any punitive award to some ceiling level of net worth. When evaluating total or tangible net worth, juries need to also understand the uses and roles of the various corporate assets that go into the different net worth measures. Assets can be categorized into two broad groups: liquid or current assets and non-current assets (Brigham, 2004). Current assets include liquid assets such as cash, marketable securities, inventories, and accounts receivable, while non-current assets include longer term assets such as plant and equipment (Weston, 1992). A certain level of liquid assets is necessary to maintain a firm’s solvency. Firms manage the level of their current assets as they tend to pay a lower return than other less liquid assets (Gallagher, 2003). Other assets, such as illiquid equipment and real estate, may be required to maintain the operations and continuity of the business. For example, for AOL Time Warner, property, plant and equipment equal approximately $12.15 billion – almost a quarter of unadjusted total shareholder equity. Net worth is not designed for being a gauge by which a jury can determine punitive damages. However, in spite of its obvious flaws, other measures, such as market capitalization, are even worse.
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14.5. Market Capitalization Market capitalization is defined as the product of a company’s number of outstanding shares and its stock price. Plaintiffs may try to introduce this value as an alternative to net worth as it is usually a higher number than the net worth one would derive from a company’s balance sheet. As an example, Table 6 shows the value of the net worth of the companies that are included in the Dow Jones Industrial Average. At the time the data were assembled for Table 6, market capitalization was several times higher than net worth as of April 2004. Part of the reason for this difference is that assets are not recorded on a company’s balance sheet at market values. However, another reason is that market capitalization reflects the market’s evaluation of the company’s ability to generate earnings and cash flow in the future. It is heavily influenced by the state of the market, which, in turn, can vary considerably. The most basic flaw of market capitalization as a gauge for a jury to consider in determining punitive damages is that it is not an asset of the defendant corporation. It represents the value of the collective equity assets of all shareholders. It is not something that the defendant owns. Instead, it is a claim that equity holders have against the future gains of the company. Earlier in this chapter we have already explained the fact that shareholders may not have any responsibility, or possibly not even any knowledge, of the acts that are the subject of the litigation. Using market capitalization as part of the punitive damages decision-making process raises serious questions of fairness. Since the company is not in a position to use these assets to pay a punitive award, the usefulness of market capitalization becomes totally inappropriate. Market capitalization is not a stable measure, and its value varies with the vagaries of the market. The variability of share prices has been well established (Barsky & DeLong, 1990). This is relevant to punitive damages as awards are based upon an unstable measure and will vary, sometimes significantly, depending on the state of the market at the time of trial even though the conduct would have been unchanged over that period. High awards may occur in up markets while lower awards may occur if the market happens to be down. This variability of an award may have nothing to do with the behavior of the defendant. As an example, lets us say that the Schering-Plough Corporation has been found liable for punitive damages and that the jury chose to base the amount of the award on the market capitalization of the company as of April, 2003. The amount of the award would be very different from the value that prevailed for the prior year. This
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is shown in Fig. 3, which reveals that stock price of Schering had fallen from $32.81 on March 1, 2002, to $17.53 just a year later – a decline of almost 50%.5 Some of this decline can be attributed to a decline in the market and the drug sector in particular while another part is attributable to companyspecific factors. This decline in the value of the stock implies that if the trial were held in the first quarter of 2002, the jury would be using a substantially higher gauge to determine punitive damages than what would prevail if the trial were delayed a year. The example of AOL Time Warner is even more extreme: here the company’s stock price fell from $51.25 in January 2001 to $10.85 by April 2003. As if the aforementioned flaws were not enough, market capitalization also tends to be quite sensitive to the anticipatory nature of the market’s internalization of new information. If a significant award is made, the market will react to the news of the verdict, perhaps even in advance of the actual event, and the stock price may decline as a function of the magnitude of the verdict. One example was the recent decline in the price of Altria’s stock in response to the aforementioned Miles verdict (Susan Miles et al. v. Philip Morris Companies, Inc., 2003). The decline in the Altria stock price around that announcement date is shown in Fig. 4. Once the news of an adverse punitive verdict reaches the market, the declining stock price causes the company’s market capitalization to be significantly lower after the announcement. This means that on the date that the company would have to make the payment, market capitalization would be lower than the value that the jury might have used to reach the verdict. For corporate subsidiaries, market capitalization poses even further problems. A parent company may ‘‘hold’’ several corporate subsidiaries. The parent company’s stock represents equity claims to the earnings and cash flows of its various subsidiaries. A subsidiary of a public company may not have a separate stock price. In some instances, the company may have issued a tracking stock, which is stock that tracks the performance of a specific subsidiary that remains a part of the parent company. For example, AT&T issued the largest stock offering in U.S. history when it sold $10.6 billion in AT&T Wireless tracking stock in April, 2000 (Smart, Megginson, & Gitman, 2004). However, most companies do not have tracking stocks. In fact, the popularity of tracking stocks has greatly diminished and companies are not issuing them as often. Nonetheless, it is the norm that a subsidiary does not have a separate stock and thus does not have its own market capitalization. Citing the market capitalization of the parent company may be irrelevant. Cases such as this show that market capitalization is not a viable measure to consider.
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Table 6.
Current Components for Dow Jones Industrial Averages. Ticker
Share Price as of 04/04
Traded Volume
Mkt Cap as of 04/04 ($Bn)
Net Worth as of 04/04 ($Bn)
Difference (%)
ALCOA INC AMERICAN EXPRESS CO BOEING CO CITIGROUP CATERPILLAR INC DU PONT CO WALT DISNEY CO EASTMAN KODAK CO GENERAL ELEC CO GENERAL MOTORS HOME DEPOT INC HONEYWELL INTL HEWLETT-PACKARD INTL BUS MACHINE INTEL CORP INTERNATIONAL PAPER CO JOHNSON & JOHNSON JP MORGAN CHASE
AA AXP BA C CAT DD DIS EK GE GM HD HON HPQ IBM INTC IP JNJ JPM
32.490 50.360 42.510 49.180 82.260 44.540 24.670 26.560 30.690 49.190 36.580 34.700 21.750 91.380 27.490 43.120 53.739 38.340
2,942,100 3,243,200 1,308,700 8,228,300 3,013,000 3,114,800 6,580,200 2,553,600 15,821,500 3,556,400 3,516,900 1,692,000 10,294,900 4,177,800 57,702,392 2,861,200 5,196,600 6,338,500
28.25 64.97 34.06 253.62 28.28 44.44 50.51 7.61 309.31 27.64 82.01 29.80 66.37 155.29 178.25 20.94 159.49 78.91
11.12 15.32 8.14 98.01 6.08 9.78 24.03 2.92 79.18 25.27 22.26 10.73 37.75 27.86 37.85 8.24 26.87 46.15
154 324 318 159 365 354 110 160 291 9 268 178 76 457 371 154 494 71
PATRICK A. GAUGHAN
Company
KO MCD MMM MO MRK MSFT PG SBC T UTX WMT XOM
50.980 27.410 88.190 55.770 46.710 27.500 104.990 25.420 18.340 88.560 59.070 43.000
6,017,000 3,901,900 4,738,500 3,623,900 3,417,500 245,175,168 1,776,400 8,750,600 10,374,100 1,961,600 6,013,400 7,293,700
124.05 34.58 69.11 114.14 103.90 296.85 135.69 84.10 14.55 45.64 253.81 281.97 105.94
14.09 11.98 7.89 22.83 15.58 69.34 18.57 38.25 13.54 11.71 42.17 74.60 27.94
780 189 776 400 567 328 631 120 7 290 502 278 279
Note: Difference (%) shows how much higher the market cap is over net worth (equal to Stockholders’ Equity), which is taken from the company’s balance sheet (4th Quarter). Source: Yahoo Finance. http://finance.yahoo.com. June 1, 2003.
The Economics of Punitive Damages
COCA COLA CO MCDONALDS CORP 3 M COMPANY PHILIP MORRIS MERCK & CO MICROSOFT CORP PROCTER & GAMBLE SBC COMMS AT & T CORP UNITED TECH CP WAL-MART STORES EXXON MOBIL Average
253
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PATRICK A. GAUGHAN 40
Price ($)
30
20
10
Fig. 3.
6/ 6/ 20 03
3/ 6/ 20 03
/2 00 2 12 /6
9/ 6/ 20 02
6/ 6/ 20 02
3/ 6/ 20 02
0
Stock Prices of Schering-Plough: 2002–2003. Source: Yahoo Finance. http:// finance.yahoo.com. June 1, 2003.
15. SIMPLISTIC COMPARISONS TO THE FINANCES OF INDIVIDUALS Sometimes damage experts retained by plaintiffs put forward simplistic comparisons of possible punitive penalties to the impact of a fixed fine on an average household (Dillman, 1993). Sometimes they try to measure median household income and wealth from surveys that are conducted by governmental entities such as the Federal Reserve Bank’s Survey of Consumer Finances (2001). They may put forward comparisons of the impact of a specific monetary penalty, such as $100 or $1,000, on a household’s wealth. The percentage of household wealth that these amounts constitute is then applied by some plaintiff witnesses to the net worth of the defendant corporation. Some assert that it is analogous to ‘‘common size statement’’ analysis that is done in corporate finance (Dillman, 1993). This may be appealing to plaintiff’s attorneys suing large corporate defendants, as the amounts of money that a typical juror would consider large appear relatively small when compared to a defendant’s net worth or annual income. Plaintiff’s attorneys may then encourage a jury to set a punitive award that
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The Economics of Punitive Damages 36 3-21-03 Miles verdict against Altria. 35
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Altria’s Stock Performance before and after Miles’ Verdict. Source: Yahoo Finance. http://finance.yahoo.com. June 1, 2003.
would have a similar effect on the corporation as a given fine would on a household. While this exercise is computationally easy, the comparison of the finances of a corporation to that of a household is irrelevant and misleading. Corporations are far more complex organizational entities than families. As we have already discussed, major corporations involve the complex interactions of various different stakeholders, many of whom are far removed from the decision making process. Corporations operate in a competitive world where they compete with other companies for market share and maintain resources so as to retain and enhance their competitive position. The fact that they engage in many other unrelated activities, such as acquiring other corporations, highlights the stark differences between corporate structures and families. Still another problem with the simplistic comparison of corporate financial measures to net worth data for family finances has to do with the quality of the sources of the data for each. Data on the worth of households derived
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from the Survey of Consumer Finances are not as reliable as data from corporate financial statements developed through an audit process. Federal Reserve researchers have long been aware of the concerns about the reliability of their household net worth data which are derived from voluntary surveys with respondents who are sometimes asked to provide instant recall to complex questions about their finances. Such questions include ones about the value of closely held businesses they may own (Kennickell, 2002). Some respondents may simply not know the answers to the questions, and others may not want to respond accurately. Obviously, data gathered through an accountant’s auditing process are of very different quality. The comparison of the two inherently different data sets makes for a very misleading result. The researchers at the Federal Reserve designed the Survey of Consumer Finances for research purposes, such as telling the central bank about trends in banking and savings behavior of households. While the researchers may find the measure they derived useful for their research purposes, it should not be applied to a purpose for which it was never intended.
16. REPUTATIONAL COSTS Corporations usually work to develop a positive image in the marketplace. Towards that end they may devote significant expenditures in public relations. This is based upon the belief that having a good image in the market and being considered a ‘‘good citizen’’ is good business. Conversely, having a negative image creates a more difficult sales environment. Being the target of punitive damages claims, whether legitimate or not, carries with it costs beyond the direct monetary penalties the defendant faces. These costs have been documented in various research studies, and Karpoff and Lott (1999) have shown that such costs can be substantial. They measured these costs by examining the stock market declines around the announcements of suits involving punitive claims. They found that the market declined by more than what could be explained by compensatory and punitive damages awarded. They also had conducted earlier studies showing how reputational penalties are reflected in stock market declines (Karpoff & Lott, 1993). Other economists have found that media coverage of punitive verdicts was skewed. Steven Garber (1998) found that coverage of punitive verdicts was higher the greater the size of the award while defense verdicts garnered virtually no newspaper coverage. The same was true when large awards were reduced – the reductions received minimal coverage. Given the orientation
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of the media in its treatment of punitive damages, companies have great incentives to try to avoid being the target of such suits.
17. THE UNCERTAINTY OF THE LITIGATION PROCESS Companies, and the market in general, are often not good at predicting what the volume and outcome of future lawsuits will be. Defendants who are targets of multiple lawsuits or serial tort suits may take charges and acknowledge liabilities based upon their best estimates of the magnitude of the litigation-related exposure. As discussed earlier, such liabilities are referred to as contingent liabilities, and accounting rules require that they be accrued when they are highly probable and estimable (Pratt, 2003). Specifically the Financial Accounting Standards Board (FASB) states that the following factors should be considered whether an accrual or disclosure of a litigation liability is necessary: 1. The period in which the underlying cause (i.e., the cause of action) of the pending or threatened litigation or of the actual or possible claim or assessment occurred. 2. The degree of probability of an unfavorable outcome. 3. The ability to make a reasonable estimate of the amount of loss. (FASB No. 5) Some firms have attempted to apply sophisticated statistical analysis to calculate litigation reserves (Allen & Savage, 2003). One assumes that a public company’s financial statements represent its best estimates; however, the number and outcome of current and future cases are often quite uncertain. This was particularly true in the 1990s and early 2000s when the volume of certain types of cases grew dramatically. A notable example is the asbestos lawsuits (Olson, 2003). A settlement was entered into on January 15, 1993, that was supposed to include all future claims against the entity founded by the asbestos defendants – the Center for Claims Resolution (Georgine v. Amchem, 1993). In 1997, however, the U.S. Supreme Court decided that the settlement did not meet the requirements for class certification under the Federal Rule of Civil Procedure 23. Following this decision and the onslaught of asbestos suits, many previously healthy companies were forced to file for Chapter 11 bankruptcy. Table 7 shows that the list of companies filing for Chapter 11 due to asbestos liabilities includes some who are leading names in American industry.
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Table 7. Companies Filing for Bankruptcy due to Asbestos Litigation. Year
1976 1982
1983 1984 1985 1986
1987
1988
1989
1990 1991 1992 1993 1995 1996 1998
1999
Company
North American Asbestos Corporation UNR Industries Johns-Manville Amatex Corporation Waterman Steamship Corp. H & A Construction Wallace & Gale Forty-Eight Insulations United States Lines
Year
2000
2001
Standard Insulations Inc. Prudential Lines Pacor Todd Shipyards Nicolet Gatke Corp. Chemetron Brunswick Fabrications Asbestec Raytech Corporation Lone Star Steel Hillsborough Holdings Delaware Insulations Celotex National Gypsum Eagle Picher Industries H.K. Porter Co. Cassiar Mines Kentile Floors American Shipbuilding Keene Corporation Lykes Brothers Steamship Rock Wool Manufacturing Atlas Corporation Fuller-Austin Insulation M.H. Detrick Harnischfeger Industries Rutland Fire & Clay
Source: www.asbestos solution.org.
2002
2003
2004
Company
Stone and Webster Pittsburgh Corning Owens Corning Fiberglass E.J. Bartells Burns & Roe Enterprises Babcock & Wilcox Armstrong World Industries W.R. Grace Washington Group International U.S. Mineral U.S. Gypsum Swan Transportation Skinner Engine Company G-I Holdings Federal Mogul Eastco Industrial Safety Corporation Bethlehem Steel Western MacArthur Shook & Fletcher Porter Hayden Plibrico North American Refractories (NARCO/RHI) Kaiser Aluminum and Chemical JT Thorpe Harbison Walker ARTRA (Synkoloid) A.P. Green AC & S A-Best CE Thurston Combustion Engineering Congoleum Kellogg Brown & Root/DII Muralo Flintkote Pfizer/Quigley Utex Industries
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Many of the asbestos defendants believed that the litigation was contained by means of the Georgine settlement. However, the uncertainty is underscored by the dramatic reversals that this litigation took. Defendants who are the target of mass tort lawsuits need to have the outstanding volume of litigation and its potential impact on the company’s viability considered in the punitive damages determination process. One example of the difficulties involved in predicting the impact of potential litigation exposure on the financial well being of a corporation can be found in Owens Corning Fiberglass Corporation v. Roy Malone et al. (1998). In this case the Supreme Court of Texas agreed with the trial court and the court of appeals in concluding that a punitive award would not have an adverse effect of the financial health of Owens Corning. The court stated: The trial court considered OCF’s ‘‘enough is enough’’ evidence from the post-trial hearing and determined that OCF’s financial position is not so precarious that further punitive damages awards against it should be disallowed. We agree. The evidence is that OCF is a solvent, healthy company. In 1993, shortly before this case was tried, OCF reported to its shareholders that ‘‘at the end of 1991, our company was valued by the market at $932 million; 12 months later, the market value of the company was in excess of $1.5 billion, an increase of 60%!’’ Moreover, in March 1993 OCF reported to the SEC that ‘‘the additional uninsured and unreserved costs which may arise out of pending personal injury and property damages asbestos claims and additional similar claims filed in the future will not have a materially adverse effect on the Company’s financial position.’’ We cannot say that the prior paid punitive damage awards against OCF, combined with the punitive damage awards here, have exceeded the goals of punishment and deterrence (Owens Corning Fiberglass Corporation v. Roy Malone et al.).
During the trial the court evaluated what the defendant indicated about its viability in light of the volume of lawsuits it faced and concluded that the company had to be in a better position than the court in assessing the impact on the company. If the defendant represents that it is viable and is not in danger of failure, how is the court able to conclude otherwise? In retrospect, however, both the defendant and the court were wrong. Armed with the hindsight that the company and the Texas Appeals Court did not have at the time, we now know that such reasoning did not prove to be correct. The lesson we can take from this is that, in spite of the optimistic statements a company may make in its filings and submissions to shareholders, the company may not be able to accurately assess the potential exposure from future lawsuits, particularly when there are many of them outstanding. The world of litigation has become so difficult to predict that it is very hard to forecast just what the future litigation volume will be. At a minimum, we can conclude that the jury should at least be able to consider the volume of other
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cases. It is one of many pieces of information that a jury can take into account when trying to come to a fully informed decision.
18. PUNITIVE DAMAGES AND APPORTIONMENT In addition to considering the outstanding volume of cases, it may be misleading to present to a jury in a particular venue the total value of whatever financial measures are to be presented. Defendants who are targets of mass tort lawsuits may incur a level of punishment well in excess of what any jury would intend if the full value of the various financial measures, such as total corporate net worth, are introduced in each and every action. The combined value of the punishment could end up being well in excess of the company’s total financial resources. One possible solution to this problem would be to apportion the aggregate financial values that are presented at trial to be consistent with the volume of the defendant’s business in the products and/ or services that are at issue in the locality where the trial is taking place. As an example, defendants in a state-wide class action might present a percentage of the total measures, let us say net worth (assuming for the purposes of this example that unadjusted net worth were an appropriate measure), that reflects the share of the defendant’s total national business in the relevant products or services that the state comprises. The U.S. Court of Appeals for the Ninth Circuit indicated that apportionment was appropriate in White v. Ford Motor Company (2002) where the court concluded that the jury should consider only the business in the State of Nevada, as opposed to the national sales of the product in question. Experts must be aware that this percentage may vary over time. Therefore, they may have to evaluate more than one year of data when putting forward a percentage. It is also important to note that disaggregating sales to specific states may not always be relevant. For example, it may be more relevant to narrow down the area of division even more precisely when considering a single case being tried in a given county.
19. CONCLUSION Punitive damages continue to be hotly debated in both the law and economics fields. This is true even though they are awarded in only a small percentage of all trials. It should not be construed that this relative infrequency implies that punitive damages are not an important issue, however.
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Many have held that punitive damages vary in an unpredictable manner. Also, just looking at trial verdicts disguises the pervasiveness of punitive damages, which are often explicitly incorporated into settlement values. This phenomenon is referred to as the ‘‘shadow effect’’ of punitive damages. The dual purposes of punitive damages are punishment and deterrence. However, punishment and deterrence of corporations are a very different exercise than that which would apply to individual defendants. Corporations represent a grouping of various stakeholders who may be affected very differently by a punitive verdict. These stakeholders include shareholders, management and non-management employees, consumers, suppliers, and communities. When a company incurs a punitive damage award, in effect it incurs a cost which it reacts to like any other cost. These costs can have various effects on the different stakeholders. The potential spillover effects of a punitive award is a factor that a jury should be made aware of prior to its rendering a verdict. In addition to the spillover effects of a punitive damage award, a jury needs to determine what deterrence effect, if any, punitive damages will have. In order to do this the jury needs to know what deterrence is already in place. Such deterrence could include the internal deterrence that has occurred. This may come in the form of various actions the defendant may have taken to prevent such an occurrence in the future. In addition to the defendant’s own internal deterrence, regulatory processes may impose their own deterrence upon the defendant. Punishment is backward looking, although its effects are forward looking. Deterrence, on the other hand, is forward looking. Plaintiffs often try to introduce various financial measures of a company’s wealth at trial. Often, however, using such simplistic measures can be quite misleading for the jury. It is here that the defendant needs to offset biased and overly simplistic presentations with a more balanced presentation that includes important information that may not have been presented to the jury. This may include adjustments to a total net worth measure so as not to include intangible assets. It may also include a more complete description of the use of various assets by the defendant. Furthermore, it may include a more complete explanation of market capitalization and why it is not an asset of the company, along with further details on why it may be a very inappropriate measure for presentation at trial. Litigation can be unpredictable. Defendants in mass torts need to be aware of this and must be able to present such issues to a jury. Litigation liabilities have forced many major corporations that are otherwise viable to file for bankruptcy. Juries should be made aware of the volume of
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outstanding litigation a company may face so as to make sure that a total level of punishment is not imposed that, when considered in the aggregate, is in excess of what should occur.
NOTES 1. It should be noted that Halliburton’s stock price had been declining since May 2001, when the stock price was as high as $49.25, owing to not only asbestos liabilities but also to a general market decline as well as fallout from the Enron debacle. However, the sharp decline on December 7, 2001, can be more directly attributed to the recent asbestos verdict. 2. Since the issuance of that report, Philip Morris Companies, now Altria, has merged its Miller Brewing subsidiary into the South African Brewing Company to form SABMiller plc. 3. There is abundant literature on corporate finance on market efficiency, which refers to the speed with which markets process and respond to relevant information. There is still a wide debate in finance as to just how efficient markets are and to what extent there exist market anomalies or exceptions to market efficiency. 4. The acquirer may be insulated from such exposure through its corporation structure, depending on how the deal was structured. This is often a topic of debate in the litigation. 5. The stock price trends of Schering-Plough are used as an example to show the variation in a company’s equity values. No separate investigation has been done on the source of this equity variation.
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FURTHER READING AOL Time Warner Annual Report. (2003). Bentham, J. (1881). Theory of legislation. Brigham, E. F., & Houston, J. F. (2004). Fundamentals of Financial Management (10th ed., pp. 78–79) New York: South-Western. Bullock v. Philip Morris Inc. Superior Court of California. (2002). Klughiet, M. (2002). Where the rubber meets the road: Theoretical justifications versus practical outcomes in punitive damages litigation. Syracuse Law Review, 52, 803–846. Morris, C. (1989). Punitive damages in tort cases. Harvard Law Review, 44(8), 1173–1209. Parkin, M. (2005). Economics (7th ed.). New York: Addison Wesley. Weston, J. F., & Copeland, T. E. (1992). Managerial finance (9th ed.). Fort Worth, Texas: Dryden. White v. Ford Motor Company et al. (2002). U.S. App. Lexis 24364. Wyeth Annual Report. (2003). Yahoo Finance. http://finance.yahoo.com. June 1, 2003.
NEW DEVELOPMENTS IN BUSINESS VALUATION Patrick L. Anderson 1. INTRODUCTION The purpose of this chapter is to outline new methodological developments in business valuation, with particular attention to how those developments are being used in litigation involving lost profits and the value of operating businesses. In addition to methodological developments, the chapter also includes a discussion of recent legal developments, particularly selected cases that affect the use and standards for business valuation techniques within litigation settings. Finally, the chapter includes a mathematical appendix. The chapter is broken down as follows: 1. Introduction. 2. Review of standard approaches and sources for those approaches, including newer treatises on methods in business evaluation. 3. Weaknesses in the standard approach, including: critiques of the use of ‘‘historical cost’’; recognition of the failure of the net-present-value rule; problems with common use of capitalized income, Capital Asset Pricing Model (CAPM) models, and typical rules of thumb; and the support or lack of support for earnings estimates used in practice. 4. Methodological developments in valuation technique, including: ‘‘real option’’ methods; recognition of the option to wait; conditions when the net present value rule is wrong; quantitative methods used in standard Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 267–306 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87010-X
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approaches, such as iterative methods for estimating the cost of capital; and the new dynamic programming valuation method. 5. Legal developments, including developments in allowable methods; the abandonment of the ‘‘excess earnings’’ method; and new case law. As this chapter is designed to capture new developments, it will invariably suffer from two limitations: First, new developments are, by definition, not those that have stood the test of time. Thus, some of the items discussed will be of passing interest, while others will assume increasing importance in the years to come. Second, new methods will not have standard nomenclature, nor will they be well documented when compared with their antecedents. Furthermore, any selection of important ‘‘new’’ ideas relies heavily on the subjective opinions of the reviewer. I have endeavored to capture new techniques and developments with an eye toward identifying the most important and potentially broadly applicable. Invariably, some have been missed, and others will seem much more important to one observer than another.
2. STANDARD APPROACHES 2.1. Generally Accepted Three Approaches As this chapter is written, one can still say there are ‘‘three generally accepted approaches to valuing a business.’’ These approaches are typically defined as: 1. the market approach, based on the market value of similar firms; 2. the asset approach, based on the value of the various assets that make up a company; and 3. the income approach in which an estimated value is calculated by discounting expected future returns. This is sometimes loosely called the ‘‘discounted cash flow’’ (DCF) approach. While these are still the ‘‘generally accepted’’ approaches, cracks are starting to develop in this easy categorization. In particular, commonly used methods in both the asset approach and the income approach are vulnerable to serious, fundamental criticisms. We will deal with these weaknesses in the section entitled ‘‘Weaknesses in the Standard Approaches.’’ In addition, we discuss newer methodologies – some of which call into question the categorization above – in the ‘‘Methodological Developments’’ section.
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2.2. References for Standard Approaches Practitioners in business valuation and litigation economics typically refer to one of a handful of references. To summarize the basic methods, I would characterize these references as largely falling into two styles: 1. those based fundamentally on accounting methods, adapted to valuation; and 2. those based fundamentally on economics methods, adapted to valuation. We describe the differences in perspective that appear in these references and cite the important texts for each style below. 2.2.1. Accounting-Based References The most popular texts in the field of business valuation have, in the past, been written by accountants. These references tend to start with accounting as a basis for business valuation, and then move toward valuing the firm by incorporating techniques from the disciplines of economics or its subdiscipline, finance.1 Among these are the following: 1. Shannon Pratt, Reilly, and Schwiess, Valuing a Business (1996, 2000). Probably the most widely used reference, this comprehensive guide is very heavy on the basic analysis of income statements, cash-flow statements, and other basics of the accounting profession. It contains extensive source notes and excellent practice guides. 2. Aswath Damodaran, Investment Valuation (1996, 2002). The Damodaran text takes a different tack from that of Pratt et al., by focusing more on finance than on accounting. In particular, his text analyzes capitalization rates extensively and systematically dissects the cost of capital for a firm. The finance approach is based on the venerable CAPM model, which will be discussed later in the ‘‘Weaknesses in the Standard Approaches’’ section. Damodaran’s text is supplemented by an extensive website, which contains much useful information on publicly traded firms and historic data on large publicly traded firms. 3. James Hitchner, editor, Valuation (2003). This very large book contains much secondary material that has been reprinted and collected in one volume. It is light on the derivation of formulas and frequently provides topical ‘‘tips’’ that would be useful for a new practitioner (and good advice for a veteran). However, the different chapters vary significantly in rigor and occasionally duplicate each other.
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The extensive reprinted material from other sources, particularly from IRS documents, is quite useful. 4. Jay Abrams, Quantitative Business Valuation (2001). Abrams ratchets up the mathematical rigor in his text, which derives discount formulas that are often summarized in other texts. In addition, he suggests two innovations that we will discuss further: a log-size model for estimating equity cost of capital, and a method for iteratively calculating the cost of capital for an entire firm. This book does not attempt to comprehensively present valuation techniques, but it is important for its innovation and rigorous treatment of formulas that are often used carelessly. There are, of course, other texts that are used in this field and which largely follow the perspective taken by these authors.2 2.2.2. Economics-Based References There have been fewer business valuation texts starting from the basis of economics.3 However, the relative dearth of sources from the economics perspective has been filled by at least two texts that have been recently published. These are: 1. Patrick Gaughan, Measuring Business Interruption Losses (2003). Gaughan’s book begins with an extensive discussion of the source of earnings for companies and describes how those earnings can be estimated. It also describes various legal underpinnings for determining lost profits and explains important concepts in litigation economics that are relevant for any practitioner in the field. The Gaughan text does explain the ‘‘generally accepted’’ three approaches, although it does so in less detail than the accounting-based texts. Instead, he spends more time connecting the concepts used in the valuation calculations with those developed in an economic and industrial analysis. Reflecting the economics perspective shared by books of this style, the analysis of the economy and industry that underlie the forecasted future earnings are prominently and extensively discussed. In addition, Gaughan specifically describes the analysis of lost profits for businesses, which is not described at any length in the accountingbased references cited above. 2. Patrick Anderson, Business Economics and Finance (2004b). This text matches the economics perspective taken by Gaughan. It begins its discussion of business valuation with an entire chapter devoted to modeling the economics of a firm. Anderson notes there are two main
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factors that must be determined to value a firm using the capitalized income approach: forecasted future earnings, and a discount rate for those earnings. Anderson argues that properly forecasting earnings is often given short shrift in the valuation literature, and that such omissions lead to systematic errors in valuation. The Anderson text is also unique in that it describes two topics that are generally missing from other references: the role of uncertainty in forecasted cash flows, and the dynamic programming valuation method. These are both described later in this chapter under ‘‘Methodological Developments.’’ 2.3. Reconciling the Styles It is worth noting the differences in perspective among the authors noted above. However, one should not overstate them. In particular, we note that all the ‘‘economics’’ texts rely on accounting concepts for their analysis of businesses. Furthermore, the ‘‘accounting’’ texts recognize the need to adjust accounting records toward economic income. For example, Pratt et al., (1996, p. 151) states: It may be worthwhile to define the term economic income, as we will use it in this discussion of the income approach to valuation. As the term implies, we define income according to the economists’ definition and not the accountant’s definition.
All the texts listed above assume that a spreadsheet software program is used in the analysis. Most texts, particularly the accounting-based ones, almost exclusively describe techniques done in a spreadsheet.4 This is consistent with the author’s informal survey of software use among forensic economists.5 However, there are a handful of books that extend mathematically beyond what is commonly done in spreadsheets. In particular, the Abrams text describes the use of Visual Basic routines within spreadsheets; the Gaughan text describes certain statistical measures of markets; and the Anderson text describes the use of a mathematical programming environment to create simulation and iterative models.
3. WEAKNESSES IN THE STANDARD APPROACHES In this section we describe weaknesses that have been identified in the three ‘‘generally accepted’’ standard approaches. The reader will note that these ‘‘weaknesses’’ run the gamut from expected limitations that do not undermine
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the fundamental strength of the approach, to severe weaknesses that in many cases mean that the approach is unsuitable. We take these in order. 3.1. The Market Approach The market approach should be the strongest approach for the valuation of a firm, because it closely matches the definition of ‘‘market value’’: the price agreed to by a willing buyer and a willing seller, neither under any compulsion, and both having adequate information.6 If there is market evidence available, there is no reason why it should not be given the strongest weight. However, we then come to grips with a fundamental problem: there is not market evidence available for most closely-held companies. This problem is compounded by the fact that most companies are closely-held companies. Indeed, despite the voluminous examinations of publicly-held companies and the enormous amount of data on market values for equities in those firms, most companies are not publicly traded, and therefore cannot be easily valued using stock-market data. 3.2. Critique: Inconsistent Reporting of Business Sales In an attempt to fill this gap, there are a small number of data sources that have been built up from reported sales of closely held companies. These databases provide some indication of how market values have been actually determined for closely held firms. However, a recent analysis by Wolpin (2003) provided ample evidence that these databases should be used with caution. The author identified significant weaknesses in these databases, related to the following: 1. lack of consistency in reporting, with users reporting sales on multiple different bases; 2. nonrandom reporting, which severely limits the usefulness of the data for inferring information about the general population of companies; and 3. selection bias, which the author felt occurred for both the submitters of data and those that record it. Wolpin performed a series of statistical tests that support his contentions that the commonly used business data should be used with caution. In particular, he argues that the collectors of data have a vested interest in their
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use and have exaggerated their reliability. He argues that the data should only be considered reliable when they reflect an active market with sufficient observations. Wolpin does not argue that these databases are useless. Indeed, such an argument would overstretch his findings, which indicate that the data cannot be used to reliably infer information (such as the mean) about the population as a whole. His critique is a useful warning against naively using these databases as if they were a random sample of actual business sales.
3.3. The Asset Approach The asset approach includes valuation methods that begin with cost information for specific assets within a firm. By the accounting identity, the assets of a firm must equal the sum of liabilities and equity. However, this identity becomes less useful when we speak not of the accounting balance sheet, but of the value of the firm in the market. We discuss below the critiques of the asset approach when applied to an operating business.7
3.4. Critique: Historical Costs Do Not Predict Market Value There is no principle that so neatly summarizes the epistemological difference between accountants and economists than reliance on ‘‘historical cost’’ accounting records in business valuation. This ambivalence in the business valuation community is reflected in the differences in perspective taken by authors of valuation references. But the question is not merely one of perspective or style; many business valuations begin with an examination of accounting records based on the historical cost principle. Furthermore, some valuation techniques classified as part of the ‘‘asset approach’’ are based on the validity of those records as indicators of market value. Others, at least in practice, rely almost entirely on these records as predictors of the future. The classic accounting method is built around the principle of historical cost, and indeed could not exist without it. A brief history of accounting reveals how important its development has been for commerce and for the growth of the world economy since the Renaissance.8 Given that the market value of a firm will fluctuate while its accounts must have some stability, the historical cost principle seems to be the strongest foundation for
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reporting the assets, liabilities, and income of a firm. From an accounting perspective, the use of historical costs is a vital principle, which ensures an objective measurement of an actual transaction and is the basis for accounting statements.9 On the other hand, economists from Adam Smith onward have debated whether historical costs have any meaning at all.10 Economists have typically focused on the labor inputs, the scarcity, or ‘‘supply and demand’’ to derive value. Advances in finance over the past several decades have resulted in an extensive theory of the market value of financial assets, based on the avoidance of arbitrage and the use of replicating portfolios.11 In these settings, historical cost is the basis for an accounting record, not an indicator of value. However weak the theoretical basis for their use in estimating future market value, the historical cost principle is a powerful and beneficial one when viewing the current financial status of a firm. Indeed, even economicsbased valuation texts suggest starting a valuation exercise with an examination of the fundamental accounting records, all of which are based on historical costs. Still, while historical cost accounting records are essential to understanding a business, they are not indicators of market value.
3.5. Critique: The Failure of the ‘‘Excess Earnings’’ Method Problems arise when historical cost records are used to predict the market value of an operating firm. In general, the ‘‘asset’’ approach of valuation is founded on the notion that historical costs predict, in some sense, the market value of an asset. One business valuation method is firmly based on this notion. Known as the ‘‘excess earnings’’ or ‘‘formula’’ method, it arose from a 1920 U.S. Treasury method of valuing the lost earnings from breweries shut down by Prohibition.12 The IRS restated it in a 1968 Revenue Ruling, with very specific warnings and restrictions on its use.13 The excess earnings method is based on the premise that income above a certain return on tangible assets constitutes ‘‘excess’’ earnings, and therefore is the basis (assuming continuation of those earnings) for the market value of intangible assets. This premise, given the hindsight of over 80 years, should be recognized for its prescience about future developments in portfolio theory and valuation techniques.14 However, as a valuation technique today, it is deeply flawed.15 Indeed, the IRS guidance on this from 1968 starts with the admonition that the formula approach should ‘‘only be used when there is no better basis available for making the determination.’’
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Neither the flawed assumptions of this method nor its disrepute has stopped its use, however. Valuation estimates using this method continue to be produced. Furthermore, the method is still described – although with significant caveats – in references such as Pratt et al., (1996) and Hitchner (2003).16 This should change. Recently, the ‘‘excess earnings’’ method has been explicitly and roundly denounced by Anderson (2004b). Gaughan (2003) and Damodaran (1996) do not mention it as a method. The better texts that include it repeat the admonition of the IRS against its use and recount one or more ways it can produce erroneous results. Even if one simply adopts the IRS guidance from 1968 (to use the method only when there is ‘‘no better basis available’’), it is difficult to conceive of a business that could not be valued with another method. At this point, no practitioner should use an ‘‘excess earnings’’ method, nor should it be presented as a practical method to predict the market value of a firm.
3.6. The Income Approach The income approach (sometimes loosely called ‘‘discounted cash flow’’)17 is the workhorse method for many valuations of closely held firms. Without market prices on similar firms, and with assets recorded at historical cost having only a tangential relationship with the firm’s value, the capitalized income approach is often the most reliable. The specific methods used within this approach are well described in many texts.18 The fundamental tasks under the income approach are forecasting business income (often measured by cash returns to shareholders or to the business enterprise as a whole19) and capitalizing it by using a discount rate appropriate for time and risk. Often, the resulting estimate is further adjusted by certain discounts or premia. We highlight critiques below that reveal newer developments in this field.
3.7. Critique: Inadequate Analysis of Forecasted Income The first critique has been made forcefully by Anderson (2004b), who notes that many valuation references give short shrift to the essential task of forecasting income. Indeed, it is still common to see valuation estimates that are based on the naive, and almost always incorrect, assumption that the last period’s reported earnings will grow at a constant rate forever.20 Even if the growth rate seems ‘‘reasonable,’’ no buyer will invest money based on an
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unsupported assumption of perpetual growth. The lack of strong foundation for an earnings forecast is often the weakest point of a valuation estimate done under the income approach.21 Forecasting earnings requires an analysis of the industry, the economy as a whole, and the company. The economic reasoning required for this is apparently not well taught to many practitioners. There is strong theoretical and empirical evidence to reject the naive ‘‘continued growth forever’’ assumption. Earnings in any one period depend heavily on business conditions in that period, including business conditions determined by unpredictable events, fluctuations in the economy as a whole, changes in the industry, and unexpected actions by humans within the organization itself. Thus, there is no theoretical reason to expect currentperiod earnings to grow at a constant rate. The empirical evidence is almost as conclusive. In a little-noticed analysis published over 40 years ago, Little (1962) found that strong earnings growth in one period was not positively correlated with strong earnings growth in the next. Damodaran (1996, Chapter 7) updated the analysis using data from the 1980s. Again, he found that the correlation coefficient for earnings growth over two periods was not significantly different from zero. The implication for those forecasting earnings is clear: there is neither theoretical nor empirical justification for assuming that past earnings growth rates will simply continue onward indefinitely. A deeper analysis, involving the industry, economy, and company, must support the forecast. On this point, the IRS guidance is quite clear. Since Ruling Revenue 59-60, issued in 1960, the IRS has explicitly required an examination of the underlying industry, competitive position of the firm, and future earning power of the firm in a valuation analysis.22 Regardless of the specific method used under the capitalized income approach, the forecasted income must be based on an analysis of the industry and the firm’s position in it. Valuations that ignore this step (and simply assuming the trend growth rate will continue is ignoring this step) are quite vulnerable to challenge. The importance of this point may seem obvious, but it has been neglected in practice and not emphasized enough in many reference texts.23 Recent texts by Gaughan (2004) and Anderson (2004b) place more emphasis on this task and suggest how it should be done.24 Practitioners today must – if they wish to properly complete a capitalized income valuation estimate – base their earnings estimate on an analysis of the economy and industry. For practitioners with only an accounting background, it may require the participation of an economist on the valuation team.
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3.8. Critique: Naive Use of CAPM Model The CAPM model, even with its many critics, has been the most powerful organizing paradigm in finance for about 40 years. The CAPM model was based on the mean–variance framework for evaluating large portfolios within the universe of equity investments. This approach was pioneered by Harry Markowitz and extended by William Sharpe in the 1950s and 1960s.25 The CAPM model describes how, under certain quite limiting circumstances, the equity discount rate for a firm can be determined from a linear combination of a small group of factors: the risk-free rate, the ‘‘equity premium’’ for equities as a whole, and the ‘‘beta’’ factor that relates the earnings volatility of firms in one industry with those of the market as a whole.26 Together with the leverage of the firm (the share of its market value that is supported by equity), this model seems to provide a straightforward manner of estimating the cost of capital for most firms. There are compelling critiques of the CAPM model, many of which focus on the benefits of adding additional factors to the model to better predict the discount rate.27 However, the general principle–that much of the risk and return characteristics in portfolios containing equities of large, publicly traded firms can be captured within the mean–variance framework–continues to be solid. The discussion above was careful to place the CAPM model within the mean–variance framework, which operates under significant limiting assumptions. Among these assumptions is the availability to the investor of a wide variety of equities, including those that ‘‘span’’ the risk characteristics of the subject firm; good information on these equities; publicly trading in these equities; and minimal transaction costs. Consider now the use of this framework for privately-held firms. Investors generally cannot purchase shares in such firms. The key data used to analyze publicly-traded firms – earnings, expenses, capital expenditures, etc., – are also generally not available. The shares in the firms are typically not traded very often. There is no traded asset that matches the underlying risks in the firm. Finally, transaction costs are quite high, especially if the due diligence costs are included. In sum, every one of the listed assumptions used to derive the CAPM model is violated in most small business valuations. This should cause concern about using the straightforward CAPM model for small firms. The following example illustrates the problems. There are many sources for ‘‘beta’’ parameters for publicly-traded companies in large industrial segments. While we might question how accurate these are, for this discussion we
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assume that they are quite accurate. What does this tell us about a small firm in the same industry? It may tell us very little. For example, there are major alcoholic beverage brewers that are publicly traded and whose business is brewing beer. There are many distributors that take these products and distribute them to retailers. Are these companies in the same ‘‘beer’’ business, and, if so, is a beta calculated for a national brewer indicative of the risks faced by a local distributor? The answer to the first question is mixed, as the distributor also relies on the general market for beer in general and certain brands, in particular. However, the distributor is primarily in a distribution business, not a beer business. It may also have other lines (wine, soft drinks, other brands of beer) and can prosper based on good local service even when its brands are not growing. The answer to the second question is then clear: the brewery’s risk is quite different from that of the distributor.28 Indeed, it may be that the most comparable publicly traded businesses are in the distribution business, or the retail business, or are similarly dependent on a local area’s economy. Therefore, the beta for a big brewer cannot be used to calculate the cost of capital of a local distributor. The generalization of this example is simple: the ‘‘beta’’ parameters calculated for large firms are often unreliable estimators of the risk in a small firm, even if that firm is in the same broad industry. Without a reliable beta estimate, the CAPM technique of estimating discount rates falls apart. This does not mean that the capitalized income approach does not work, but it does mean that a CAPM-based technique for estimating the discount rate does not work. This critique also applies to ‘‘build-up’’ discount rate estimates that are based on CAPM model.
3.9. Critique: Excessive Use of Discounts and Premia A significant literature has arisen describing various discounts and premia that should be used when adjusting a capitalized income estimate of the value of a firm. In many cases, these discounts or premia provide a useful and necessary adjustment for factors that are outside the standard discount rate analysis. The workhorse capitalized income approach typically produces a preliminary value estimate that should be further refined through the use of discounts and premia. These adjustments should reflect the particular characteristics of the company or the type of equity investment allowed in the company.
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However, a review of the use of the adjustments would observe the breadth, severity, and ubiquity of such factors. This observation motivates the following critique of the excessive and improper use. First, consider the range of discounts and premia: 1. One well-developed concept is the discount for marketability on stock or other equity that is burdened by resale restrictions. Basic economics would indicate that the ownership of an asset implies the right to sell it; restricting that right should reduce the asset’s value. A series of empirical analyses have demonstrated convincingly that restrictions on resale cause securities to be priced less than identical securities without the restrictions. Thus, both theory and practice coincide on this concept. 2. Other discounts and premia have been proposed and used for contingent liabilities, minority interests, ‘‘blockage,’’ control, size, nonhomogeneous assets, and other factors.29 Indeed, there is now at least one book devoted entirely to discussing discounts and premia.30 3. Some discount factors are applied to the firm as a whole; some to particular interests in the firm; and some to the cost of capital for the firm. With this range in mind, we now critique the excessive use of discounts and premia in three categories, and then conclude with two warnings for practitioners. Some of the ‘‘discounts’’ in the second category above appear to extend beyond an adjustment to a well-established value, and are instead a ratio of that value to that of a fundamentally different entity. In particular: A company with significant contingent liabilities or assets is not the same as a company without them. A ‘‘discount’’ or ‘‘premium’’ should be an adjustment to the value of the particular entity, not the difference between the value of one company and another. An analogy will illustrate this: the cost of a Chevrolet sedan will typically be smaller than that of a Cadillac sedan. The difference in price is not a ‘‘discount’’ off the price of the Cadillac – it is a lower price for a less valuable vehicle. A contingent liability should be valued separately and recognized as such. Calling the reduction in value due to contingent liabilities a ‘‘discount’’ is at least mislabeling; it may be a gross error. A significant contingent asset – say a patent or license – is not cause for a premium over the discounted cash flow value–implied value. It is an additional source of future cash flow and should be valued separately. Nonhomogeneous assets may need to be valued separately, and considered as separate entities.31 This is particularly the case if the entity as a
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whole is going to be sold. A simple ‘‘nonhomogeneous’’ discount will probably not capture the costs, or benefits, of this step. A small-sized company is often a qualitatively different entity than a large-sized entity. This difference can arise from access to capital, dominance of one or more key persons, the form of organization, and the ability to offer publicly traded securities.32 These differences imply changes in other aspects of the valuation analysis rather than a simple ‘‘size discount.’’ Furthermore, some of the discounts are based on similar factors. The use of two discount factors – both related to the same underlying factor – is double counting, or ‘‘double discounting.’’33 For example: A historical analysis underlying a size premium or discount may capture factors such as discounts for marketability. Studies of discounts for marketability probably include companies with controlling interests and other factors. Thus, one cannot apply two or more discount factors that account for the same underlying risk. Many common methods of estimating the cost of capital rely on discounts and premia. Practitioners using these approaches should consider the following: Historical cost-of-capital data are usually derived from large, publiclytraded firms. Cost-of-capital estimates for firms that match the characteristics of these data should be subjected to minimal adjustments; firms that do not should be adjusted once for each characteristic that differs. In particular, CAPM models that use ‘‘beta’’ factors to estimate the cost of capital of specific firms already have adjustments for the typical firms in the sample for these industries.
3.10. Warnings for Practitioners Practitioners should keep in mind the following cautions when applying discounts or premia to the discount rate or the underlying cash flows: 1. The indiscriminate use of premia and discounts should be recognized, discouraged, and criticized. The use of ‘‘double discounts’’ or simple application of ‘‘average’’ discounts should be classified as an error and avoided. This critique has recently been made by other authors.34
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2. The use of discounts and premia when estimating the cost of capital should be done with caution when a subsequent discount is used on the overall valuation estimate. In many such cases, only one discount factor should be employed. 3. When the entity being valued has fundamentally different characteristics – such as contingent liabilities or assets, nonhomogeneous assets, or an unusual capital structure – than a standard model incorporates, the practitioner should use a different model. A discount or premium applied to an estimate produced by a standard model will generally be incorrect.
3.11. Implication: Weakness in the Capitalized Income Method There is a more fundamental implication of this critique. Even in cases where discounts are properly applied, it appears that they can easily range upward of 50% of the amount of a straightforward capitalized income value estimate. This could mean two things: adjustments are big in this world, or the fundamental method is broken. The lack of good data on actual market transactions both creates the need for methods like capitalized income and limits the ability to test it. However, if we assume that the limited data available imply that discounts or premia routinely exceed 25% of the estimate derived using a standard method, we should ask ourselves the following question: Is the standard estimation method sound? At this point, the evidence from good valuation practice indicates that the standard method, well applied, is sound. However, we should expect that the next decade will result in the question being posed more forcefully.
4. METHODOLOGICAL DEVELOPMENTS 4.1. Log-Size Discount Model Jay Abrams has proposed a simple and robust model for estimating discount rates for firms that fit into the small- and medium-sized categories. This ‘‘log-size’’ model uses a simple logarithm of the size of the assets of the firm to arrive at a discount rate. The model is described well in Abrams (2001). Abrams provides empirical evidence to support the method. Aside from Abrams’ data on the log-size model, there is ample evidence of a ‘‘size
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effect’’ on the returns of private firms. This shows up in tests of the CAPM model, and in straightforward analyses of the cost of capital.35 There is no rigorous theoretical construct from which the log-size model can be derived. Therefore, if the assumptions underlying a CAPM or other model are fulfilled in a certain case, it should be preferred over another approach lacking theoretical support. However, the critiques of the CAPM are serious, especially for small firms and those firms not represented in the universe of publicly traded companies. Therefore, practitioners should consider whether a simpler, more robust model deserves precedence in such cases.
4.2. Iterative Cost-of-Capital Model A common error in valuations under the capitalized income approach stems from a misuse of the historical cost–balance sheet when weighting the debt and equity parts of the capital structure. When calculating a weighted average cost of capital (WACC), many practitioners commonly use as weights the book value of debt and equity. The actual weights should be the market value of debt and equity. For most operating firms, the market value of equity will typically be a much higher share of the total capitalization than the book value. Reading a balance sheet for a firm, based on historical cost accounting, and using those figures to weight the cost of capital will often result in a substantial overestimate of the market value of a firm.36 While one source of this error is simple ignorance, the other is unfamiliarity with iterative methods to solve the mathematical problem of estimating one variable (value) when an input to that calculation (cost of capital) depends partially on the variable one is trying to estimate. Three recent texts (noted below) describe a practical iterative method to solve the mathematical problem: 1. First, use the book value to prepare a first guess of market value and use these weights to prepare a first guess of WACC; 2. Use this initial WACC estimate to, in turn, prepare a second guess of market value; 3. Use the second guess of market value to prepare the second guess of WACC; and 4. Continue until the results are close enough to warrant no further iterations.
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These iterations are not difficult to perform manually on a standard spreadsheet, and Abrams (2001, Chapter 6) describes such a method. The entire process can be programmed into a more sophisticated mathematical model, which is described by Anderson (2004b, Chapter 11). Pratt (2002, Chapter 7) also describes the iterative method and highlights how failure to properly weight the capital structure can produce serious errors in value estimates. A related application is presented in Anderson (2004b, Chapter 10), in which an iterative method is used to properly estimate the value of income-producing real estate.
4.3. Investment Under Uncertainty One of the most powerful critiques in recent decades, and one that is only now surfacing in the standard texts,37 is a direct attack on one of the most hallowed rules of finance: the net present value rule of investment. The net present value rule can be stated as follows: if the expected net present value of the cash flows from an investment exceed the amount required to make the investment today, one should make the investment. There is no trick in this statement; the investor (or manager of a company) should, according to the rule, estimate the future returns, taking into account the relative probability of future events, and discount them. The resulting expected NPV should be compared with the amount of the investment. If the expected NPV is greater, the investor should go ahead with the transaction. This rule will, if funds are sufficient to outlast random fluctuations, make one rich in a casino.38 In the business world, following the NPV rule has long been taught as the foundation for managers attempting to maximize shareholder value.39 Consider the standard NPV rule used in most investment texts, such as the following: Theory of Valuation ythe value of an asset is the present value of the expected returns.40
This is echoed in corporate finance texts: Value today always equals future cash flow discounted at the opportunity cost of capital.41
The essence of the attack on this rule is that it ignores a powerful source of value: the option to wait. Indeed, the option to wait and make the investment
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later is an essential part of actual markets. Ignoring a consideration used by most investors is theoretically unsound. In other words, the standard NPV investment rule is wrong. This critique was well developed in the seminal book by Dixit and Pindyck (1994), Investment Under Uncertainty. They summarize previous research conclusively showing that the option value in many investment management decisions was significant enough to cause decisions made with the straightforward NPV rule to lose money by comparison. Such examples have also been used in a handful of other economics and finance books.42 However, as cited above, the NPV investment rule is still enshrined in many investment and valuation texts. Most human analysts understand the natural human tendency to wait until the time is ripe to make the deal. As will be discussed in the following sections, there are now a number of analytical tools that can be used to make such judgments explicit.
4.4. The ‘‘Real Options’’ Method The explosive growth of the market for derivative securities has pushed – and been pushed in return – by the development of analytical tools to estimate the value of financial options. Since the publication of the seminal paper identifying the Black–Scholes option valuation formula in the 1970s, a number of innovative financial option models have been developed.43 These include various binomial tree models, Monte Carlo methods, and variations on the classic Black–Scholes model.44 4.4.1. Valuing the Equity as an Option One of the most intriguing insights emerging from the original Black and Scholes article was the observation that the equity in a corporation could be viewed as a call option on the value of the firm, with the strike price being the value of the debt. They noted that equity holders have the residual claim on the firm’s assets. If the firm is liquidated, the proceeds will first pay off all bondholders, and anything left will go to the equity holders. For going concern firms, stocks are equivalent to ‘‘in the money’’ call options on the value of the firm. These securities can be sold and re-sold indefinitely, as long as the market perceives the firm’s value as higher than its debt.
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4.4.2. The ‘‘Real’’ Option In the past decade, a number of authors have developed a ‘‘contingent claim’’ approach to valuing firms, based on this insight.45 Because equity in a firm can be viewed as a call option on ‘‘real’’ assets (the firm being an actual, rather than a financial, asset), this approach is sometimes called ‘‘real options.’’ Real option methods are particularly suited in the following situations: 1. When valuing firms with significant contingent assets or liabilities. In such cases, contingent claims approaches are obviously better suited to the underlying asset or liability. 2. When firms are in financial distress, or the ‘‘going concern’’ assumption is not warranted or is questionable. 3. When firms have particularly promising technologies or intellectual property such as patents or licenses, which could result in significant cash flows in the future. Real option methods are not as well developed as most other valuation techniques. Furthermore, they often rely on standard approaches (such as capitalized income) to value the expected earnings of operating entities. Option methods are then used to value contingent claims. Note that the key ‘‘risk’’ involved in option methods is not the same as ‘‘equity risk,’’ or even equity risk adjusted for the ‘‘beta’’ of a particular industry.46 The key measure of risk in standard option valuation formulas is the volatility of the underlying asset, on which a contingent claim exists. The more volatile such an asset, the more likely it will end up ‘‘in the money’’ even if it is currently ‘‘out of the money.’’47 Note that the traditional implication of volatility in returns is a higher rate of return, meaning a lower present value. In the standard analysis of an out-of-the-money call option, more volatility implies higher value. This difference in the effect of volatility on market value is not, when properly considered, a complete contradiction.48 We do not describe real option methods here. Damodaran (1996, 2002) provides the most extensive treatment among the standard references. Hitchner (2003) contains a very brief summary. Anderson (2004b) describes the approach as part of an overall presentation on risk and the options available to managers and shareholders, and also introduces the related Dynamic Programming method.49 Like all other valid methods, a properly completed option-method valuation, given good information, will provide a similar estimate of fair market value. However, at this point the real options approach has not been widely used in practice and would benefit from more development.
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4.5. Modeling Risk: Uncertainty in Future Earnings Forecasting earnings is the primary task in a capitalized income approach. Typically, such earnings are forecasted based on past performance. The critique above describes weaknesses in this practice, due to inadequate (or nonexistent) review of the underlying economic and industrial conditions.50 We consider below methodological innovations in the treatment of risk in earnings, assuming that the underlying economic and industrial analysis has been properly completed.
4.6. Complex Uncertainty in Future Earnings Most valuation texts discuss uncertainty primarily with respect to the cost of capital. More volatile earnings in the past are associated with higher expected returns, and therefore a higher discount rate on future earnings. However, the uncertainty in other business variables should be considered as even more important. In particular, the uncertainty in expected future revenue and earnings is more important to most business valuation exercises than the analysis of past earnings rates. Anderson (2004b) describes techniques for modeling different types of uncertainty in cash flows, including: 1. Simple deviation around a trend. This appears to be the most common modeling of uncertainty in valuation exercises; most examples presented in the standard texts show forecasted earnings following a very strong trend, often with no deviation around it.51 2. Complex uncertainty, involving both a drift and a random variation around the drift. The well-known ‘‘random walk’’ motion is an example of a process with such uncertainty. A more developed model is known as ‘‘geometric Brownian motion,’’ and appears to well represent stock prices. 3. Complex uncertainty involving ‘‘jump’’ processes, which we discuss in the next section. Dealing with uncertainty is a fundamental concern in financial economics. Mathematical techniques such as stochastic calculus are now commonly employed to model asset prices in the academic literature.52 While some of these techniques are more esoteric than needed for applied work, there is an unsettling gulf between the treatment of uncertainty in most valuation texts and its treatment in both the academic literature and in the financial markets.53
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Anderson (2004b) presents a set of tools to model these kinds of uncertain cash flows. We discuss one such innovation with broad application in business valuation below.
4.7. ‘‘Jump’’ Processes and Risks of Termination Most treatments of risk in earnings are based on the assumption that periodic returns are distributed normally (or at least symmetrically) around a mean return. The distribution of returns can then be largely described by two ‘‘moments’’ of the distribution: the mean, and the variance.54 This is the basis of the ‘‘mean–variance’’ framework for analyzing investment portfolios, on which the familiar CAPM model and its many variants are based. Using this assumption, revenue, earnings, and other important business variables are often modeled as a trend line subject to symmetric, normally distributed random disturbances.55 However, there are a certain class of variables subject to risks that are not well modeled by random deviation around a trend random walks, or even by geometric Brownian motion. In particular, some variables are subject to sudden, unexpected changes that may dramatically alter the prospects of a business. This type of behavior is often considered a ‘‘jump process,’’ because when graphed the line appears to ‘‘jump’’ at one point. The risks borne by insurance companies are an obvious example of such risks. The chance that any one building will burn down is small, but the number of buildings they insure is large. Nonfinancial companies also bear such risks. For example, companies that manufacture or distribute products under a franchise agreement, or sell predominantly ‘‘brand name’’ products, bear the risk that the brand itself will decay, the products will no longer be produced, or that they will lose franchise rights. Investors bear a default risk that may be small, but is not negligible, for many classes of bonds. Almost all parties to contracts bear a risk of nonperformance by other parties. Businesses with operations in foreign countries bear risk of war, closure of borders, or confiscation.56 Some important business variables change infrequently, but when changed cause either catastrophic losses or large gains. These cannot be assumed to behave like one of many, individually small, random occurrences that are adequately modeled in a mean–variance framework. Anderson (2004a) derives a formula incorporating risks modeled by a ‘‘jump’’ process into a discounted present-value calculation. The formula is based on the Poisson distribution, which is described in the ‘‘Mathematical Appendix’’ of this chapter. This formula can be used as a basis for
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estimating the value of business income that could be terminated at some point in the future, due to an unexpected event that has a low chance of occurring. The expected net present value of a stream of income p, with profit in year one p1, discount rate r, and the periodic growth rate g, for the time periods t ¼ 1; . . . ; 1; where the income stream is subject to termination risk governed by a Poisson process, is:57 p1 , (1) E ðNPVÞ ¼ r gþl where l ¼ mean arrival rate of a Poisson process, or the chance that the event will occur in any one period.58 This formula is deceptively simple; the familiar ‘‘Gordon Growth Model’’ equation (for perpetual, constantly growing cash flows without uncertainty) is: p1 NPV ¼ . (2) r g Thus, the effect of an event that would end the stream of income, and has a 2% chance of occurring in any one year, is similar to increasing the discount rate on the stream of income by 2%.59
4.8. Uses for Jump Processes: Franchised Firms Many valuation tasks involved franchised firms, including both the manufacturers (typically the ‘‘franchisor’’) and the retailers or distributors (typically the ‘‘franchisee’’). Even for well-developed franchises there is a nonnegligible risk that the franchise will fail, meaning that the products and services sold under the brand will no longer be produced or sold. In such cases, some franchised firms would suffer catastrophic losses and may cease doing business. Anderson (2004a) suggests an ‘‘Oldsmobile rule’’ for estimating the specific brand risk for franchised firms. He notes that even the most firmly established brands eventually go out of business, and cites the Oldsmobile brand as establishing the upper limit of the likely tenure for most brands. Oldsmobile automobiles were continuously produced for 100 years before the brand was terminated by General Motors. Anderson states that franchised firms bear a brand risk that can be modeled as a Poisson distribution. He then characterizes the brand risk in
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many franchised firms as a Poisson process with a mean arrival rate equal to 1/100 or higher.60 A mean arrival rate of 1/100 means that one expects the termination of the brand to occur about once every century. Firms with weaker brands – and most franchises will be weaker than Oldsmobile – should be modeled with a higher mean arrival rate. One implication of this research is that firms with significant, specific income termination risks are improperly modeled with a standard CAPMbased discount rate. For example, consider a ‘‘beta’’ derived from a study of large publicly traded firms in a certain industry, none of which are dependent on a single patent, franchise, supplier, customer, or market. Now consider a firm in the same industry that has earnings subject to termination risk, albeit a small risk in any one year. Many practitioners would simply use the beta for the industry, perhaps modify it for the size of the firm, and estimate a discount rate using a CAPM-derived formula. Such an approach would probably result in an overestimate of the market value of the firm, stemming from ignoring the risk of termination of income. Indeed, Monte Carlo testing of the formula shown in the first equation, using a very low mean arrival rate, confirms that it properly estimates the lower net present values that will be generated by cash flows that are subject to small risks of termination in any one year.61
4.9. Dynamic Programming Valuation Method A method of solving complicated, multi-stage optimization problems called dynamic programming was originated by American mathematician Richard Bellman in 1957.62 Like most brilliant insights, the method promised a radical simplification of some intransigent problem. However, the method was usually difficult, or even impossible, to implement in practice until quite recently. Developments in both analytical and computational methods now make it possible to use this method in business valuation. The use of dynamic programming for business valuation was introduced by Anderson (2004b). We very briefly summarize it here as a method that, while novel in practice, has great potential to improve valuation in the future. The essence of this approach is Bellman’s insight that an optimization problem can be segmented into two parts: the current benefit (the return on an investment in the current period) and the change in the value at the end of this period (the change in the discounted future benefits). This is,
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for business valuation, analogous to estimating the value of a firm that originates from two parts: 1. The income expected in the current period; and 2. The value of the firm at the beginning of the next period, taking into account the prospects for future earnings at that point. Note that many discounted cash flow schedules represent data in a similar way: the first columns show income during the next few periods, during which the income can be explicitly forecasted, and then the last column shows a ‘‘terminal value’’ which is the expected value at that time. However, there is a key difference between the approaches: the dynamic programming approach requires the management to optimize the sum of the value arising from current-period income and future-period expected earnings. Thus, in contrast to the income statements common to valuation projections,63 the dynamic programming method assumes that managers will change expenditures when revenues change. Furthermore, it does not implicitly assume that the growth rate for revenue, or ratio of expenses to revenue (even for ‘‘variable’’ expenses) will remain the same.
4.10. Advantages of the Dynamic Programming Approach One key advantage of this method is its proper assertion of the primary importance of management policy. Traditional valuation methods often assume a very passive role for managers.64 In contrast, dynamic programming puts management policy front-and-center. It is the manager who is assumed to optimize the sum of current earnings and discounted future value. Owners of a firm, of course, have the same such incentives. The mathematics of solving dynamic programming models, while arcane and difficult, at least have the cardinal virtue of mimicking the actual incentives of business owners. This is not true in typical discounted cash flow models; management is often assumed away, becoming almost unimportant. On the other hand, dynamic programming assumes that the manager (or owner) optimizes the sum of current earnings and future discounted earnings, matching the mathematical techniques to the actual motivation of owners. Thus, dynamic programming methods should, ceteris paribus, lead to better valuation estimates, as they explicitly consider policy actions that are largely ignored in traditional cash-flow models. Underlying this assertion of management importance is a superior treatment of uncertainty. The dynamic programming method incorporates the notion of the management of
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a firm changing its policies as business conditions change. By contrast, most discounted cash flow schedules described in the texts cited as references assume passive management and stable business conditions. We briefly describe the technique in the Mathematical Appendix. A recent description of potential practical uses in Anderson (2005).
4.11. Disadvantages of the Dynamic Programming Method While this method has important theoretical advantages, it suffers at this time from significant practical disadvantages. In particular, it has just been introduced, there are yet no practical software tools, and there are few texts on its use in this field. We expect this to change, however, and suggest that practitioners interested in cutting-edge techniques anticipate much development in this technique.
5. LEGAL DEVELOPMENTS Since the seminal decisions in Daubert and Kumho Tire, courts have been systematically restricting the use of expert testimony through the application of what are commonly called ‘‘Daubert standards.’’65 These standards, given the relative newness of the seminal decisions, are more like an evolving consensus than a clear universal standard. Given the vital importance of this issue, we describe below the most important developments for litigation economics covering business valuation in the evolving Daubert standards. For a broader summary, see Gaughan (2003).
5.1. Daubert Standards Apply in Business Valuation One of the most important decisions in this area was Ullman-Briggs, Inc. v. Salton/Maxim Housewares, Inc., 1996 WL 535083, (N.D. Ill. 1996). In this case, the court applied the Daubert standards to business valuation, stating: While business valuation may not be one of the ‘‘traditional sciences,’’ it is nevertheless a subject area that employs specific methodologies and publishes peer-reviewed journals.
The court rejected the request of the plaintiff in this case to offer as ‘‘expert’’ testimony in business valuation a person who was a business broker and
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who provided an estimate of the value of firm based largely on his experience in selling businesses. The court concluded that ‘‘an expert that supplies nothing but a bottom line supplies nothing to the judicial process.’’66 The Ullman-Briggs decision is already influencing other courts, as will be seen in the discussion below. 5.2. Economics Experts Must Show Methodology and Data Recent court cases have affirmed the common-sense rule that the expert’s report could only be given credence if it included both the methodology used to arrive at the decision and the information on which the decision is based. Rules 26 and 702 of the Federal Rules of Civil Procedure already require this (for federal cases), but courts are beginning to enforce it with some vigor in cases involving business economics. Indeed, a recent brief by the U.S. Department of Justice in United States v. First Data Corporation provides a rendition of the many possible legal attacks against a report given by a person of some business expertise, but whose conclusion was produced without adequate discussion of methodology and data. This anti-trust case turns to some degree on the question of whether two different payments methods are competing products. A business executive with no economics training produced an opinion on this question, which the Department of Justice moved to exclude with a withering series of arguments: It is well established that an expert witness must have a grounding in the methods and procedures of a particular field, and that expertise must be applied in a way that enables the witness to draw conclusions about the particular issues in the case. See Daubert, 509 U.S. at 590-91. These requirements are not abandoned when a witness attempts to rely solely or primarily on experience as a basis for non-scientific opinions. Under those circumstances, ‘‘[t]he trial court’s gatekeeping function requires more than simply ‘taking the expert’s word for it.’ ’’ Fed. R. Evid. 702 2000 Advisory Committee Notes. Instead, the court must require the witness to explain ‘‘how that experience leads to the conclusion reached, why that experience is a sufficient basis for the opinion, and how that experience is reliably applied to the facts.’’ Id. See, e.g., United States v. Jones, 107 F.3d 1147 (6th Cir. 1997) (Handwriting examiner, who had years of practical experience and extensive training, explained his methodology in detail.) Indeed, the advisory committee notes to Rule 702 quote with approval the Fifth Circuit’s admonition that ‘‘[i]t seems exactly backwards that experts who purport to rely on general engineering principles and practical experience might escape screening by the district court simply by stating that their conclusions were not reached by any particular method or technique.’’ Watkins v. Telsmith, Inc., 121 F.3d 984, 991 (5th Cir. 1997). ‘‘[N]othing in either Daubert or the Federal Rules of Evidence requires a district court to admit opinion evidence that is connected to existing data only by the ipse dixit of the
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expert. A court may conclude that there is simply too great an analytical gap between the data and the opinion proffered.’’ General Elec. Co. v. Joiner, 522 U.S. 136, 146 (1997). Because there is no methodological link between [the proposed expert’s] industry experience and his opinions, his testimony fails to meet the standards of Rule 702.67 yIt is elementary that an expert cannot simply point to his resume and then engage in unfettered speculation. Similarly, a witness with industry experience cannot just offer a ‘‘hunch’’ based on his business sense. Ullman-Briggs, Inc. v. Salton/ Maxim Housewares, Inc., 1996 WL 535083 (N.D. Ill. 1996). As noted above, ‘‘[t]he trial court’s gatekeeping function requires more than simply ‘taking the expert’s word for it.’ ’’
The brief in this case is important for several reasons: first, it summarizes (from the perspective of the party attempting to restrict an expert’s report) the recent relevant cases and federal rules governing this issue within the field of business economics. Second, the plaintiffs in the case include not only the U.S. Department of Justice, but also the attorneys general of six states and the corporation counsel of the District of Columbia. It therefore also represents a repository of legal arguments that will be widely shared. However, readers should note that it is a brief, not a decision. There have been other cases that support this trend toward increasing scrutiny of experts. The California Appeals Court affirmed the exclusion of one expert’s testimony after the expert failed to provide meaningful responses to valuation methodology questions in deposition.68 The Arkansas Court of Appeals affirmed the exclusion of another expert’s testimony, who had the credentials of a ‘‘certified financial analyst’’ but had no experience in business valuation.69 The court, instead accepted the testimony of a courtappointed business appraiser using two different methods.70 5.3. General Business Experience Does Not Qualify as Economic Expertise The same Department of Justice motion cited above contains a valuable summary of the arguments that can be made to exclude the testimony of a person whose expertise comes largely from general business experience in the industry, but who has no specific economics training. A court should ‘‘exclude proffered expert testimony if the subject of the testimony lies outside the witness’s area of expertise.’’ 4 Weinstein’s Fed. Evid. y 702.06[1], at 702–52 (2000). Although [proposed expert] has experience in the ‘‘payments industry’’y , he lacks any education or training in economics or industrial organization. [He] thus does not have the requisite training or experience to determine whether PIN debit and signature debit are in the same product market. General industry experience does not qualify a witness to conduct the analysis required to define a product market for purposes of an antitrust case, and [the proposed expert] is
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no more qualified to testify about relevant markets than other non-economist witnesses who have been precluded from offering such testimony in similar circumstances. In Berlyn v. Gazette Newspapers, 214 F. Supp. 2d 530, 536 (D. Md. 2002), for example, the plaintiffs’ proposed expert witness had considerable experience in publishing, having held several prominent positions with newspapers throughout his career. Id. at 533. Nonetheless, the court determined that the witness was not qualified to opine that the relevant product market was community newspapers and some editions of metropolitan newspapers because the witness’s background was ‘‘completely devoid of specific education, training or experience in economics or antitrust analysis.’’ Id.; see also id. at 536 (‘‘[G]eneral business experience unrelated to antitrust economics does not render a witness qualified to offer an opinion on complicated antitrust issues such as defining relevant markets’’). Similarly, in Virginia Vermiculite, Ltd. v. W.R. Grace & Co., 98 F. Supp.2d 729 (W.D. Va. 2000), the court prevented a geological engineer with some background in economics and substantial mineral industry experience (including experience performing market analyses for clients) from testifying as an expert about the geographic market for vermiculite. Id. at 732–734. The court noted that ‘‘there are differences between an analysis for business investment and an analysis for antitrust purposes,’’ that ‘‘market analyses for antitrust markets generally require some expertise in the field of industrial organization,’’ and that individuals with experience in analyzing the mineral market but not in antitrust ‘‘would not possess the skill and training of a professional economist necessary to define a relevant market for antitrust purposes.’’71
As stated above, an economic analysis of the industry, rather than just accounting records, must be used to estimate future earnings. In certain areas of law, specific economic analyses are required. However, such economic analyses need not be performed by an economist. A Federal Court of Appeals decision in the Ericsson v. Harris patent infringement case highlights this allowance. The Court’s review of the law was that to support a finding of lost profits, the relevant markets must be analyzed and a causal link found between the infringement and the lost sales. The Court then stated: Such market reconstruction must be supported by ‘‘sound economic proof of the nature of the market and likely outcomes with infringement factored out of the economic picture.’’72
Despite this straightforward requirement for economic analysis, the plaintiff’s expert on damages was an accountant. The expert presented detailed market analyses, which included a segmentation of the relevant markets, consideration of barriers to entry, and actual sales records. The opposing counsel attacked the analysis as lacking a specific economic test for crosselasticity of demand between two products.
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However, the court accepted the argument that the analysis was developed ‘‘using an approved methodology’’ and was ‘‘supported by testimonial and documentary evidence.’’73 Therefore, the Court affirmed that ‘‘substantial evidence supports the jury’s damages award for lost profits due to lost sales.’’74
5.4. Lost Profits in Franchised Businesses A growing number of businesses operate under franchise agreements, which allocate to the franchisor (usually the manufacturer) the right to establish a distinctive brand and set forth advertising, quality, and other standards, while the franchisee actually sells or distributes the products. The question of damages arises naturally in cases involving a claim of improper termination of the franchise, and a small body of case law has developed in this area. Important cases in this area were summarized in Fitzgerald and Anderson (2004). A terminated franchisee’s remedy for improper termination is generally money damages, not the continued use of the franchisor’s brand.75 The franchisee must present sufficient evidence of the damages; and if lost profits are claimed, they must be proved with reasonable, though not exact, certainty.76 When there is a sufficient history of sales, a ‘‘before and after’’ comparison can be used to establish damages.77 State courts have consistently found that improperly terminated franchisees are eligible for damages for lost future profits.78 In addition, a number of state and federal laws provide specific protections to franchisees.79
5.5. Conclusion: Case Law on Valuation and Damages From this survey we can observe a handful of themes in recent case law. These include: Continued development of the ‘‘Daubert’’ standards for expert testimony. Requirement for actual economic knowledge of markets or business valuation methodology, rather than simple credentials or ‘‘business experience’’. Awareness of the nature of franchises. Requirements for data and methodology to support a valuation or damages estimate.
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NOTES 1. Complete citations of these and other sources are given in the reference list at the end of this chapter. Where more than one edition of a text is in common use, we have noted both in this section. 2. These include Reilly and Schwiess (1999); Copeland, Koller, and Murrin (2000), and others. 3. This contrasts strongly with the literature on financial assets viewed as part of an investor’s portfolio, which is almost entirely based on economics, finance, and mathematics. See, e.g., Cochrane (2001); Duffie (2001); Markowitz (1991), or LeRoy (1991). 4. Of course, they typically summarize financial market research, such as CAPM models, that were parameterized by linear regression or other statistical techniques. However, such analysis is typically assumed to have been done by others. 5. A survey question posed by the author on the bulletin board of the National Association of Forensic Economics in July 2004 elicited about 20 responses, almost all of which indicated heavy use of spreadsheet software for business valuation or lost earnings for individuals analysis. Only a fraction (on the order of magnitude of 10%) indicated regular use of statistical, mathematical, or simulation software. 6. Many of the references listed below provide background for the definition; see, in particular, Hitchner (2003) and Anderson (2004b). 7. We do not discuss here the use of this approach when determining the salvage value of hard assets, such as in a liquidation or bankruptcy case. 8. The first statement of accounting is generally credited to Luca Pacioli (1447–1517), a Franciscan monk and mathematician in what is now Italy. He published Summa de Arithmetica, Geometrica, Proportioni et Proportionalite in 1494, summarizing mathematical knowledge of the time. See Anderson (2004b), Chapter 11. 9. See, e.g., Larson and Miller (1993, Chapter 1), stating the ‘‘cost principle’’ in the 13th edition of their accounting text. This is consistent with their definition of accounting: ‘‘the function of accounting is to provide useful information to people who make rational investment, credit, and similar decisions,’’ quoting the Financial Accounting Standards Board, ‘‘Statement of Financial Accounting Concepts Number 1,’’ (1978) paragraph 34. 10. See Adam Smith, Wealth of Nations (1776), Book I, Chapter 6. A review here must also note the contributions of David Ricardo (on the labor theory of value) and Alfred Marshall (on the introduction of the ubiquitous supply demand curves to determine price). Karl Marx and his followers have developed a literature devoted to the study of the differences between value and price, almost all of which is without practical use in this field. 11. See, e.g., Duffie (2001) for a mathematically rigorous reference of asset valuation in complete markets, based on the avoidance of arbitrage. Many other mathematical economics references, such as Ljungvist and Sargent (2004), contain summaries of this approach. 12. Treasury Department Appeals and Review Memorandum 34 (‘‘ARM 34’’), 1920. See Hitchner (2003, Chapter 4). 13. IRS Revenue Ruling 68–609.
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14. In particular, the 1920 observation about the sources of equity returns predates the development of modern portfolio theory by approximately 40 years. Considering that most analyses of historical returns start with data from after 1920, one can gain an appreciation of how ahead of its time it was. 15. Among other problems, it is intended only to value intangible assets, but is often misused to value entire businesses; proper use requires the use of market value estimates of tangible assets, but the book values are often used; it is unclear how the intangible value of a firm’s assets can be estimated using the known market value of its tangible assets, given that the two are probably intertwined; and the tricky use of different capitalization rates is bound to produce frequent errors. 16. Indeed, Pratt (2002, Chapter 17) indicates that the method is usually described in a full chapter of valuation references, citing both the third edition of his widely used text and the fourth edition (Pratt et al., 1996, 2000), as well as Fishman, Pratt, Griffith, and Wells (2001). He then proceeds to detail a ‘‘sanity check’’ for the calculation and offers a number of comments on the ‘‘vagaries’’ of its use. 17. There is some ambiguity and confusion about the nomenclature here; some authors use ‘‘capitalized income’’ to refer to a family of models that discount (capitalize) future earnings; others use ‘‘capitalized income’’ to only refer to a subset of the income approach in which a constant stream or earnings are discounted by a constant discount rate. There is even confusion in the literature on whether ‘‘discounted cash flow’’ is, in any sense, equivalent to ‘‘capitalized income.’’ Part of this stems from the accounting convention that defines ‘‘cash flow’’ differently than ‘‘earnings.’’ However, from the point of view of the investor (not the CFO of the company itself) distributed cash to shareholders is the return on the ownership interest, and would commonly be considered ‘‘income.’’ Indeed, the ‘‘capitalized income’’ that arises from dividends on a stock is theoretically its market value. (This arises from an absence of arbitrage, as well as the time value of money.) The derivation of the present value formula for a perpetual constant series of cash flows (pv ¼ cf =r) typically arises from an assumption of a constant flow of future dividends. See, e.g., LeRoy (1991); Anderson (2004b). Note that the dividend-paying firm’s accounting cash flow, like other accounting concepts, never enters into the formula. In this sense, ‘‘discounted cash flow’’ is only equivalent to market value when, again under certain conditions, it is equivalent to capitalized income. 18. All the references in the ‘‘Standard Approaches’’ section describe these methods. The discussion there highlights the different emphases placed by different authors on certain aspects of the methods. 19. Although the nomenclature varies, these methods are often called ‘‘free cash flow to equity’’ and ‘‘free cash flow to the firm.’’ Here ‘‘free cash flow’’ (or ‘‘net cash flow’’) is the distributable cash to investors or to the firm as a whole. 20. This assumption is often incorrect on both grounds: last period’s earnings will usually not closely predict the earnings under new management or ownership, and the growth rate of a firm never stays constant. This latter assumption is later treated more closely in the sections titled ‘‘Methodological Developments’’ as well as in ‘‘Evidence: Past Earnings Not Sufficient Predictor.’’ 21. The author has seen this error carried to its logical extreme. In one valuation estimate he reviewed, a distribution firm whose franchise had been terminated for
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cause was projected to have earnings blithely continue for years at a constant growth rate. The counter analysis was fairly simple: forecasted earnings of zero continuing perpetually. 22. Hitchner (2003) contains the most extensive discussion of RR 59–60. He counts eight categories in RR 59–60, namely: (a) nature and history of business, (b) economic outlook for industry, (c) book value of the stock, (d) earning capacity, (e) dividend capacity, (f) whether the firm has goodwill or intangible value, (g) sales of stock, and (h) market price of stock in similar business (‘‘Selected Revenue Rulings,’’ reprinting RR 59–60, Section 4.01 (a)–(h)). See also Gaughan (2004) for a corroborating opinion and Anderson (2004b) for a new synthesis of the factors required by the IRS. 23. Damodaran (1996, Chapter 7) is a good example. The importance of properly forecasting income using the industrial and economic fundamentals is made quite clear to a thorough reader, who would also discover empirical evidence confirming the failure of naive constant growth estimates. However, the methods described (time-series models, and averages of historical rates) are largely based on extrapolating past growth. Thus, for many readers, extrapolating past growth seems to be the easiest path. 24. Two of the recent accounting-perspective references also have an increased emphasis on proper forecasting of income. Abrams (2001, Chapter 2) places the forecasting of revenues and expenses at the beginning of his treatise and describes the use of regression analysis using independent variables (such as GDP) to help identify the relationship between the firm’s earnings and the economy as a whole. Hitchner (2003, Chapter 2) explicitly instructs analysts to obtain ‘‘external information’’ regarding the future earnings of the firm. 25. The classic references include Markowitz (1952), Markowitz (1970), and Sharpe (1964). An excellent summary is also contained in Markowitz (1991). 26. This derivation is described most extensively in Damodaran (1996), although all the references in the ‘‘Standard Approaches’’ section contain discussions. 27. Among these are the Fama-French 3-factor model and the Arbitrage Pricing Theory. In the ‘‘Methodological Developments’’ section, we will discuss a simple logsize model and other discount rate innovations. 28. We describe below one specific risk faced by franchised businesses: termination of franchise rights. See ‘‘Modeling Income Subject to Termination Risk’’ in the appendix. 29. Among the general valuation references, Pratt et al., (1996) and Hitchner (2003) have the most comprehensive discussions. 30. Business Valuation Discount and Premiums, Pratt (2001). 31. By ‘‘nonhomogeneous’’ we mean assets of a different type that cannot be easily combined in an enterprise. 32. The cost-of-capital factors here may be appropriate to recognize as a discount or premium in the cost of (equity) capital. The cost of debt should already be adjusted to the firm’s specific characteristics. 33. In practice, it may be closer to one-and-a-half-times discounting, which is bad enough. 34. Pratt (2001, Chapter 20) lists the ‘‘indiscriminate use of average discounts or premiums’’ as a common error. Hitchner (2003, Chapter 8) states that ‘‘the blind
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application of discounts, without a thorough understanding of the subject company as compared to the data underlying the discounts, can lead to misleading valuation results.’’ He further warns against ‘‘double discounts’’ caused by applying two discount factors arising from the same characteristic. 35. For a summary of the standard analyses of the size effect – which are sometimes interpreted as evidence that the CAPM model is flawed – see Damodaran (1996). Pratt (2001, Chapter 11) devotes an entire chapter to the size effect. 36. In the (normal) case where the cost of debt is lower than the cost of equity, understating the equity portion will result in an artificially low WACC estimate, resulting in an artificially high valuation estimate. 37. Among the valuation texts cited above, Anderson (2004b) and Damodaran (2002) explicitly cover it. Other texts often describe option valuation as an offshoot of the Black-Scholes model for valuing certain financial options, but ignore the much more common option to wait to purchase most investments. 38. Of course, the expected net present value of a dollar bet in a casino is less than a dollar. Therefore, it is the casino owners that routinely follow the rule! 39. See, e.g., Brealey and Meyers (1981), which was the first edition of the longrunning corporate finance book. See also the additional citation from the fourth edition of this line of textbooks, below. The text was released in a seventh edition in 2003. 40. Reilly (1994), quoted in Pratt et al., (1996). 41. Brealey and Myers (1992), quoted in Pratt et al., (1996, Chapter 9). 42. See, in particular, Anderson (2004b), which models different types of uncertainty and directly incorporates managerial options in the discussion of valuation; and Schwartz and Trigeorgis (2001), whose compilation of important articles on this subject provide ample theoretical foundation for the insights on the value of managerial flexibility. Among the standard valuation texts, Damodaran (1996) has extensive discussions of ‘‘contingent claims’’ analysis which rely on this insight. See the section on ‘‘The Real Option’’ in the next section. Damodaran (2002) covers the option to wait explicitly. 43. The original article was Black and Scholes (1973). 44. There are many references to financial options and methods to value them; most valuation references instead include a basic summary of call and put options for use in discussing contingent claims. Those interested in financial options should consult one of the texts devoted exclusively to this topic. 45. Damodaran (1996) goes as far as calling the ‘‘contingent claim’’ approach one of the three main approaches; he combines the market and asset methods into a ‘‘relative value’’ approach and retains the capitalized income approach. 46. In particular, the standard ‘‘beta’’ is a measure of the covariance of the returns from firms in one industry with that of the market as a whole. The equity premium is an average of the excess returns for equities above risk-free securities. Neither of these are the same as the contingent claim risk on one firm. 47. An ‘‘in the money’’ option is one that has an intrinsic value at the current time, such as a call option on a stock that is trading above the strike price. An option on a stock that is quite volatile, even if the current price is below the strike price, will tend to be valued more highly than one that is expected, quite steadily, to remain ‘‘out of the money.’’
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48. Most importantly, a discounted cash flow analysis of a profitable operating business would be the analogy of a financial call option that was deeply ‘‘in the money.’’ 49. See the section on ‘‘Dynamic Programming Valuation Method’’ and the references there, particularly Dixit and Pindyck (1994). 50. See the earlier section on ‘‘Critique: Inadequate Analysis of Forecasted Income.’’ 51. Indeed, it is common to see forecasted earnings (or revenue) grow at a constant rate with no deviation. Some texts describe two-stage or three-stage forecasts, in which growth rates remain smooth but decline after an initial set of high-growth periods. In both these cases, there is little or no incorporation of uncertainty in the forecasted revenue. 52. See, e.g., Duffie (2001), one of the standard graduate texts in finance. 53. For a broad survey of advanced methods, which includes management firms as well as equity research and trading firms, see Facardi and Jonas (1997). This survey shows the intellectual ferment in areas that appear to be disconnected from the standard discounted cash flow methods in the (professional) valuation literature. 54. The ‘‘method of moments’’ is a very old method in statistics. The mean is the first moment of the distribution about zero, and the variance is the second moment about the mean. 55. An appeal to the Central Limit Theorem of Statistics is often made to justify an assumption of normally distributed disturbances. This may be justified if there are a very large number of small risk factors that are uncorrelated. Such an assumption is close to correct when dealing with a large, publicly traded firms. See Anderson (2004b, Chapter 10) for a discussion of various types of uncertainty in revenues, starting with variation around a trend and continuing through its processes and geometric Brownian motion. 56. These risks in the United States are normally considered negligible. However, especially in the areas of litigation risk and environmental liability, they are often not negligible even in the U.S. 57. This discussion is based on Anderson (2004a). See also Anderson (2004b, Chapter 10). The basic derivation of the NPV formula for a constant series governed by Poisson risk is in Dixit and Pindyck (1994). A more rigorous mathematical discussion is in Duffie (2001). 58. More precisely, the ‘‘mean arrival rate’’ is the average number of events that occur each period over a large number of periods. The Greek letter lambda is often used to indicate this parameter. 59. We say ‘‘the effectyis similar’’ because the formula can be simplified into a form similar to the Gordon Growth model equation. The underlying cash flows are not at all similar, and one calculates an expectation while the other calculates a certainty. See the discussion below. 60. See Anderson (2004a). 61. Anderson (2004a) used a mean arrival rate of 1/100, periods of 100 years, a discount rate of 8%, and a growth rate of 4%. Over 100 trials, the formula and the average of the randomly-generated trials were fairly close, while ignoring the termination risk produced a significant overestimate of the net present value.
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62. Bellman (1957). Bellman’s introduction to his slim book of nearly 50 years ago is still useful reading. 63. The common presentation of discounted cash flow schedules is a projection of income growing at a constant rate, along with variable and fixed expenses growing also at constant rates, with no deviation around the trend. See, e.g., most of the discounted cash flow examples in the accounting-based literature listed in the ‘‘Standard Approaches’’ section. 64. Indeed, our critique of insufficient analysis of earnings forecasts above indicates that some valuation estimates literally assume no role for management; they simply extrapolate future earnings from current earnings, as if they would magically appear no matter who minds the store. 65. Daubert v. Merrell Dow 509 U.S. S. Ct. 579 (1993); Kumho Tire v. Carmichael, No. 97-1709, 526 U.S. 137, 119 S. Ct. 1167 (1999). 66. See the discussion of this case in Gaughan (2003, Introduction). 67. Memorandum of law in support of motion to exclude witness, United States v. First Data Corporation and Concord EFS Inc., U.S. District Court for the District of Columbia, 2003. Because this is a memorandum, not a decision; because the reply brief was not available; and because the purpose for quoting the memorandum extensively was to include a number of potential legal challenges to expert witnesses in general; I have excluded the name of the witness. It is provided for reasons noted in the text, and not as the final decision in this case, or as a balanced summary of all cases discussing this issue. 68. Phase 2 Developers Corp v. Citicorp Real Estate, no. B160111, Cal. App. 2d Dist, (2004), unpublished. Summarized in Stockdale (2004). 69. Thomas Sanders v. Heidi Sanders, no. 03-738, Ark. App. (2004), unpublished. Summarized in Stockdale (2004). 70. The summary, cited in the note above, indicates that the appraiser used both the excess earnings and discretionary cash-flow method to determine that there was no ‘‘salable goodwill’’ in the business. As noted above, the excess earnings method is of doubtful credibility, but at least was intended to value intangible property. If backed up by a sound discounted cash flow analysis, a finding of no goodwill value in a business would probably be sound. 71. Memorandum of law in support of motion to exclude witness, United States v. First Data Corporation and Concord EFS Inc., U.S. District Court for the District of Columbia, 2003. See cautionary note above and in the text. 72. Ericsson et. al. v. Harris Corporation et. al., U.S. Court of Appeals for the Federal Circuit, no. 02-1571, -1603 (2003); Section B.2. The quoted section of the excerpt is from Grain Processing Corp. v. Am. Maize-Prods. Co., 185 F.3d 1341, 1350 (Fed. Cir. 1999). 73. The methodology was asserted to be set forth in Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (6th Cir. 1978), 74. Ericsson, cited above, B.2. 75. Burger King v. Jajeed, 805 F. Supp. 994, 6 FLW Fed D 481 (SD Fl, 1992). 76. See Blair (1988); Atlantic Sports Boat Sales v. Cigarette Racing Team, 695 F. Supp. 58 (Mass, 1988); Lindevig v. Dairy Equipment Co. 150 Wis 2d 731, 442 NW2d 504 (1989). 77. C.A. May Marine Supply Co. v. Brunswick Corp., 64g F.2d 104g (5th circuit, 1981).
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78. Fitzgerald and Anderson (2004) list cases from California, Florida, Illinois, Indiana, Iowa, Minnesota, Missouri, Montana, Nebraska, New Jersey, Pennsylvania, Puerto Rico, South Carolina, and South Dakota, as well as federal court decisions. 79. Automobile dealers and beer and wine wholesalers are often covered by specific state statutes; there are also federal statutes for service station operators and auto dealers. 80. This has implications in many fields, including finance. In particular, if there are not a wide variety of securities that create a risk-reward frontier or that could, under additional assumptions, be expected to have normally distributed returns or risk characteristics, many of the nice, standard conclusions of modern portfolio theory are undermined. 81. The probability density function shows that the third equation can produce non-integer numbers, but these are probabilities of certain integer values, not the values themselves. Random Poisson numbers always produce integers. For example, a Monte Carlo run of random Poisson numbers with l ¼ 0:25 produced 100 numbers: mostly zeroes, some ones, and one two. The sum of all 100 numbers was 21; 21/ 100 is close to the mean arrival rate of l ¼ 0:25: 82. More complete explanations of the dynamic programming method for optimization problems in economics and other fields are Miranda and Fackler (2002); Chiang (1999); Rustagi (1994), and Ljungqvist and Sargent (2004). 83. The ‘‘state’’ vector captures information about the state of the world at any one point. State variables can include those summarizing the business, the industry, or the economy as a whole. 84. This is best described in Rustagi (1994) and Chiang (1999). Chiang notes that this is not a mapping from real numbers to real numbers, which would be a function. Instead, it is a mapping from paths to real numbers, the real numbers being the quantities being optimized. 85. For the mathematical proofs that solutions are possible and unique, see Stokey and Lucas (1989).
ACKNOWLEDGMENTS I also wish to acknowledge the suggestions offered on earlier manuscripts by Patrick Fitzgerald, Patrick Gaughan, David Goldenberg, Mike Hanrahan, Bill King, and Loren Williams as well as the respondents to the survey question posted on the National Association of Forensic Economics mail server.
REFERENCES Abrams, J. B. (2001). Quantitative business valuation. New York: McGraw-Hill. Anderson, P. L. (2004a). Valuation and damages for franchised businesses. Paper presented at ASSA Conference, San Diego, California (January 2004). Available as AEG Working Paper no. 2003-12 at: http://www.andersoneconomicgroup.com.
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Anderson, P. L. (2004b). Business economics and finance: Using Matlab, simulation models, and GIS. New York: CRC Press. Anderson, P. L. (2005). Practical dynamic programming for business and forensic economics. Paper presented at the National Association of Forensic Economics international conference, Dublin, Ireland (May 2005). Available as AEG Working Paper no. 2005-5 at: http://www.andersoneconomicgroup.com. Bellman, R. (1957). Dynamic programming. Princeton University Press; reissued at Mineola, New York by Dover Press, 2003. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political economy, 81, 637–654. Blair, R. D. (1988). Measuring damages for lost profits in franchise termination cases. Franchise Law Journal, 8, 3. Brealey, R., & Myers, S. (2003 [1991] [1981]). Principles of corporate finance. New York: McGraw-Hill. Chiang, A. C. (1999). Elements of dynamic optimization. Longrove, IL: Waveland Press. Cochrane, J. H. (2001). Asset pricing. Princeton. NY: Princeton University Press. Copeland, T., Koller, T., & Murrin, J. (2000). Valuation: Measuring and managing the value of companies (3rd ed.). New York: Wiley. Damodaran, A. (2002 [1996]). Investment valuation. New York: Wiley (References in the text of this article are to the first edition). Dixit, A., & Pindyck, R. (1994). Investment under uncertainty. New York: Princeton University Press. Duffie, D. (2001). Dynamic asset pricing theory (3rd ed.). New York: Princeton University Press. Facardi, S., & Jonas, C. (1997). Modeling the market: New theories and techniques. New Hope, PA: Frank J. Fabozzi Associates. Fishman, J., Pratt, S., Griffith, J. C., & Wells, M. (2001). Guide to business valuations (12th ed.). Fort Worth, TX: Practitioners Publishing Company. Fitzgerald, P. W., & Anderson, P. L. (2004). Valuation and damages for franchised businesses: Overview of important case law and a proposed new methodology for estimating damages. Paper presented at the international meeting of the National Association of Forensic Economics, Edinburgh, Scotland (May 2004). Gaughan, P. A. (2003). Measuring business interruption losses and other commercial damages. New York: Wiley. Hitchner, J. R. (Ed.) (2003). Financial valuation: Applications and models. New York: Wiley. Larson, K., & Miller, P. (1993). Fundamental accounting principles (13th ed.). California: Irwin. LeRoy, S. F. (1991). Present value. In: J. Eaton, M. Milgate & P. Newman (Eds), The new Palgrave: A dictionary of economics. New York: Stockton. Also in the slimmer volume The new Palgrave: Finance. New York: Stockton. Little, I. M. D. (1962). Higgledy piggledy growth. Oxford Institute of Economic & Statistics, 24(4), 387–412. Cited in Damodaran (1996, Chapter 7). Ljungqvist, L., & Sargent, T. J. (2004 [2000]). Recursive macroeconomic theory (2nd ed.), Massachusetts: MIT Press. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91. Markowitz, H. M. (1970). Portfolio selection: Efficient diversification of investments. New Haven: Yale University Press (Reprinted New York: Wiley). Markowitz, H. (1991). Mean variance analysis. In: The new Palgrave: A dictionary of Economics. New York and London: Stockton and MacMillan.
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Miranda, M. J., & Fackler, P. L. (2002). Applied computational economics and finance. Massachusetts: MIT Press. Pratt, S. (2001). Business valuation discount and premiums. New York: Wiley. Pratt, S., Reilly, R., & Schwiess, R. (1996). Valuing abusiness (3rd ed.). New York: McGrawHill. A fourth edition was released in 2000. References in the text of this article are to the 3rd edition). Pratt, S. P. (2002). Cost of capital (2nd ed.). New York: Wiley. Reilly, F. K. (1994). Investment analysis and portfolio management. Hinsdale, IL: Dryden Press. Reilly, R. F., & Schwiess, R. (1999). Handbook of advanced business valuation. New York: McGraw-Hill. Rustagi, J. S. (1994). Optimization techniques in statistics. New York: Academic Press. Schwartz, E., & Trigeorgis, L. (Eds) (2001). Real options and investment under uncertainty: Classical readings and recent contributions. Massachusetts: MIT Press. Smith, A. (1776). Wealth of Nations, originally published 1776; Cannan’s edition published (1907). Reissue Chicago: University of Chicago Press (1976). Stockdale, J. J. (2004). Business valuation cases in brief. Business Valuation Review, 47(1). Stokey, N., & Lucas, R. E., Jr. (1989). Recursive methods in economic dynamics (with Prescott, E. C.). Harvard, MA: Harvard University Press. Wolpin, J. B. (2003). Examining the reliability of small business transaction databases. Valuation Strategies, 8(Nov–Dec), 24.
MATHEMATICAL APPENDIX Modeling Income Subject to Termination Risk We consider in this section random events that have a small probability of occurring in any one year. The normal distribution, or at least a nice symmetrical distribution of events, typically cannot be used to describe the risk of such events.80 Instead, we suggest the Poisson distribution as an appropriate model for such risks. This statistical distribution is close to that of a binomial distribution in which the number of trials is very high and the probability of success in each trial is low. The binomial is often used to model events that have close to a 50% chance of occurring, such as a coin flip. The Poisson is typically used in studies of errors, breakdowns, queuing behavior, and other phenomena where the chance of any one subject facing a specific event is small, but where the number of subjects is large. A Poisson process is governed by the following probability density function: PðxÞ ¼
e l x l ; x!
x ¼ 0; 1; 2; . . . .
(3)
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note that the Poisson is a discrete probability distribution; it provides positive probabilities only for integers x ¼ 0; 1; 2; . . . :81
The Dynamic Programming Method We present below a simplified description of the method of dynamic programming, originally developed by Bellman (1957) and recently applied to business valuation by Anderson (2004b).82 In this derivation, we model the management of a business as a multi-period optimization problem. 1. A business is an organization which will live through multiple periods and for which a mixture of both reasonably predictable, and unknowable, events will occur. These events will present the management of the company with information, which can be summarized as data in a state vector.83 At each time period, holding the information available, the management takes certain actions, such as hiring, firing, purchasing, pricing, advertising, and selling. 2. The challenge (the ‘‘optimization problem’’) presented to the managers of the company is to take actions in a manner that maximizes the value of the firm. If we take the value of the firm to be the expected future profits, discounted for time and risk, we can express this optimization problem in the following functional equation: (4) V ðs; tÞ ¼ max f ðs; xÞ þ bE ½V ðstþ1 ; xtþ1 Þ . x
Here, V(s,t) is the value of the firm given the state s at the time period t. This value consists of two parts: the current profit of the firm f(s, x) and the expected value of the firm in the next period, after discounting by the factor b. The discount factor is equivalent to (1=1 þ r), where r is the discount rate on the capital employed and is often considered to be around 15% in applied work. The maximization problem involves the control variables or actions x, so the maximization operator references this variable or vector of variables. Because both the current profit and the future profits of the firm depend on the actions of the firm’s management, the action variable is an argument to the profit and value functions. The fourth equation is known as a functional equation because the expression V(s,t) is not, strictly speaking, a function of just the variables s and t, but instead the maximization of a family of functions.84 We will refer to it as the Bellman equation for this optimization problem.
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Actually solving the problem we have now stated has been the greatest difficulty in using this technique.85 Among the problems are the ‘‘curse of dimensionality,’’ because the size of the problem is magnified exponentially by the number of variables; properly specifying the state variable; properly specifying the objective function; and the computational techniques. There are a number of methods for solving dynamic programming problems, including: a. Recursively solving the problem, backward, from a known terminal value; this is known as ‘‘backward recursion.’’ b. Iterating on the values created at each step with variations in the policy created by the application of the control variables; this is known as ‘‘policy iteration.’’ c. Specifying an initial set of values for all variables, calculating the value function at these points, and then iteratively searching for higher values until such searches yield no further improvement. This is known as ‘‘function iteration.’’ The mathematics underlying this approach, including a rigorous derivation of the conditions under which the technique can be expected to produce a unique solution, is outlined in Stokey and Lucas (1989). Ljungqvist and Sargent (2004) provide a set of applications to academic problems and notes on its applications to macroeconomics. A computational approach, along with a series of examples from the academic literature, was developed by Miranda and Fackler (2002). They also provide computer code that can be used with the vector-processing mathematical software environment Matlab. The application to business valuation and damages was developed by Anderson (2004b), with practical applications for both business valuation and lost wages presented in Anderson (2005).
ESTIMATING ECONOMIC LOSS FOR THE MULTI-PRODUCT BUSINESS Carroll Foster and Robert R. Trout 1. INTRODUCTION The basic model for estimating economic losses to a company that has some type of business interruption is well-documented in the forensic economics literature. A summary of much of this literature is contained in Gaughan (2000). The general method used to measure damages is essentially the same regardless of whether the loss occurs because of some type of natural disaster (as in insurance claims resulting from flood, fire, or hurricane) or whether it is caused by the actions of another party (as with potential tort claims). The interruption prevents the firm from selling units of product, which would otherwise have been supplied to the market. Economic damage is the loss of revenues less the incremental production costs of the units not sold, plus or minus some adjustment factors described in Gaughan (2000, 2004), and elsewhere. Damage analysis usually begins with the estimation of lost sales (units or dollars of revenue) over some past, current, and/or future time period. Business interruptions can be categorized as follows:1 Closed loss period – the interruption has ended, and production and sales have returned to normal, as of the time of the analysis. Developments in Litigation Economics Contemporary Studies in Economic and Financial Analysis, Volume 87, 307–325 Copyright r 2005 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 1569-3759/doi:10.1016/S1569-3759(05)87011-1
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Open loss period – the interruption of normal operations is still continuing as of the time of the analysis, but an end of the loss period is foreseeable and can be estimated. Permanent loss – due to the interruption, the firm has to (or will soon) go out of business. Typically, forensic economists use some type of time-series or econometric model to estimate lost revenues. The model is used to forecast what revenues would have been, absent the interruption. Forecasted revenue minus actual revenue determines the total revenue loss. The economist then subtracts the attendant incremental costs and makes other adjustments (taking into account ‘‘extraordinary’’ expenditures incurred to minimize or recover from the effects of the interruption) to arrive at what is generally termed the ‘‘lost profits.’’ It is often the case that the estimation/forecasting of revenue losses over time can be accomplished by employing relatively simple single-equation forecasting models: 1. Deterministic time series models, 2. Single-equation econometric models. The main thrust of this chapter will be to show that in some instances, such as with a firm that has suffered losses in two or more product lines or where a regression model error term exhibits a complex dynamic structure, a set of more elaborate forecasting techniques may be required: 3. Statistical Autoregressive Integrated Moving Average (ARIMA) methods for time-series analysis of residuals (TSAR), 4. Multiple-equation econometric models. Despite the differences in terminology, all of the above models are estimated with time-series data in the applications discussed in this paper. They require, at a minimum, quantitative data on the past history of the variable to be forecasted (sales revenues or units). In the case of econometric models, data on other relevant ‘‘causal’’ or ‘‘explanatory’’ variables must also be acquired.2 The first two classes of forecasting models are described and illustrated in Part 2. ARIMA models and TSAR are introduced in Part 3. Multipleequation econometric modeling will be presented in Part 4, in the context of a specific recent business interruption case.
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2. SIMPLE SINGLE-EQUATION MODELS In the discussion to follow, S represents sales (measured in units or value) and is the variable to be forecasted. Observations St are available for t ¼ 1; :::; n; where t is an index of time. Forecasting model parameters are denoted by Greek letters (a, b, g), and the estimates of those parameter values by the corresponding English letters (a, b, c).
2.1. ‘‘Deterministic’’ Time-Series Models In deterministic models, S is presumed to follow an exact function of time, y(t), called the ‘‘deterministic trend component.’’ Actual data observations on S will also include unobservable random errors.3 For the additive error term ut we would write: S t ¼ yðtÞ þ ut ;
t ¼ 1; :::; n
The linear trend is probably the simplest deterministic model formulation: S t ¼ a þ bt þ ut Here, y(t) ¼ a+bt. Ordinary least squares (OLS) is commonly used to estimate intercept and slope parameters a and b. For any time period t, the forecasted sales level is denoted as follows (where a and b are the OLS estimates of a and b): S^ t ¼ a þ bt If one believes that sales grow (or decay) at a constant proportional rate, a deterministic exponential growth model might be appropriate: St ¼ aebt eu In this model, y(t) ¼ aebt, where b is the constant growth or decay rate. It is unlikely that this model would accurately project sales over a lengthy future forecast horizon, as the implied exponential trend goes to 0 (if bo0), or N (if b40). There exist a host of other non-linear deterministic (‘‘curve fitting’’) models that are often useful in describing historic patterns in sales. A few are
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shown below: Modified exponential : S t ¼ a þ begt þ ut Gompertz curve : St ¼ aeb expðgtÞ Yield curve : St ¼ a þ ðb þ gtÞedt For the modified exponential curve, if go0, sales will asymptotically approach a40 from above or below. The Gompertz curve will fit the ‘‘S-shape’’ pattern common with sales of newly introduced products, approaching upper asymptote a40. The third model above, used to estimate bond yield curves, is applicable to a very general set of patterns in time-series data. With any of these model specifications, the effect of some nonquantitative event on the sales of a business is usually captured by including a binary (dummy) variable in the equation. The dummy variable Dt equals 1 during periods affected by the event, and equals 0 otherwise. If the dummy represents the period of interruption, then the linear trend model would appear as follows: S t ¼ a þ bt þ gDt þ ut Dt ¼ 1 during the interruption period, and g measures the average difference between normal and interrupted sales levels during the interruption, providing a direct estimate of average sales loss per period. Another common use of dummy variables is to account for seasonal patterns in the data. If there are M seasons per year (e.g., M ¼ 12 for monthly data), then one can introduce dummy variables DðjÞt ; j ¼ 2:::M; into the model. For linear trend and additive seasonality: S t ¼ a þ bt þ g2 Dð2Þt þ þ gM DðMÞt þ ut In season 1, the average level of sales is a+bt. The gj coefficients measure the difference between season 1 and season j sales levels. It is often the case that only one- or two-months’ sales are significantly different from the norm, thereby requiring only one or two monthly seasonal dummies in the model. The deterministic models discussed thus far require only data on the single variable S. The parameters of the linear trend model are easily estimated by OLS, and some of the others can be transformed to make them amenable to OLS estimation. The more complicated curves require nonlinear estimation routings based on Maximum Likelihood (MLE) or Nonlinear Least Squares (NLS) algorithms.4 Deterministic trend and curve-fitting models are easy to estimate and utilize, and they are applicable to both closed and open interruptions. In the
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case of a closed interruption, a curve which closely fits the data pattern before and after the loss period should provide a good educated guess as to what the values of the dependent variable would likely have been during the period if there had been no interruption to normal business operations.5 Trend line or curve-fitting models can also be extended into the future, as would be required with an open interruption; but forecast accuracy usually leaves much to be desired over long forecast horizons.
2.2. Deterministic Model Example – A Small Commercial Business A business was affected by a flood, which swept through the town and caused the business to be closed for most of a three-month time period. The full effect of the flood lasted several months after the business had reopened, and the neighborhood had been cleaned up. The sales data for the full time period from January 1990 through May 1996 are shown in Figure 1, titled ‘‘Copy Shop Sales.’’ The solid line depicts the actual monthly sales while the dashed line depicts a curve fitted by the following estimated model: S t ¼ 6170 þ 42:13t þ 2400LnðtÞ þ 5102DðMarchÞt DðMarchÞ ¼ 1 in the month of March, which has abnormally large sales, and 0 otherwise. Note the large decline in January 1993, when the flood hit. Sales during the next two months were also seriously affected. 35000
Copy Shop Sales Sales = f(time, log time, March)
Monthly Sales $
30000
Flood Period >--
25000 20000 15000 10000
Sales
Sales Forecast
5000 1990
1991
Fig 1.
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Copy Shop Sales.
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35000
Copy Shop Sales Including the Effect of the Flood Sales = f(time, ln time, ST flood, LT flood & March)
Monthly Sales $
30000 25000
Flood Period >--
20000 15000 10000 Sales
Sales Forecast
5000 1990
Fig. 2.
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Copy Shop Sales Including the Effect of the Flood.
Figure 2 models sales but takes the flood into account by adding two indicator (dummy) variables: DðshortÞ ¼ 1 in January, February, and March, 1993; DðlongÞ ¼ 1 in all months after March 1993. The dashed line shows the fitted values of this expanded model. Figure 3 adds a projection of uninterrupted sales to the previous figure. The vertical distance between the two dashed lines measures lost sales for all months after January 1993 by comparing the forecasted sales without the flood with the projected sales including the effect of the flood.
2.3. Single-Equation Econometric Models By ‘‘econometric model’’ we mean a forecasting model, which uses independent or explanatory variables, other than a time index and binary event dummies, to explain and predict a variable of interest. Consider the following example for illustration. A maker of a product used in curing concrete suffered an interruption to sales for several months. A plot of quantities shipped (Q) revealed neither a recognizable pattern nor a visibly obvious change during the loss period. It turned out that the variation in shipments during the out-of-interruption period was well explained by a product category price index (P), monthly housing starts (H), an index of street and highway construction (S), and an overall index of public and private construction spending (C). A linear
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35000
Copy Shop Sales Comparison of Projected Sales With No Flood v. Forecast Sales = f(Time, Ln Time, March, ST Flood & LTFlood)
Monthly Sales $
30000 Flood Period >-25000 20000 15000 Sales Sales Forecast Sales - Proj. No Flood
10000 5000 1990
Fig. 3.
1991
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1995
Copy Shop Sales Comparison of Projected Sales with No Flood v. Forecast.
regression specification was used. Qt ¼ b1 þ b2 Pt þ b3 H t þ b4 St þ b5 C t þ ut ; t ¼ 1 42; 71 89 After estimating the coefficients b1 ... b5, the ‘‘but for’’ values of shipments during the loss period were easily calculated. The final computations showed that the company had lost nearly $175,000 of sales revenue. The case above was a ‘‘closed’’ interruption. Econometric models are particularly useful in such an application because values of the explanatory or right-hand-side (RHS) variables will be available during the loss period. A weakness of these models when applied to open interruptions is that assumed or separately computed ex ante values of the RHS variables will be necessary. An example of this type of problem, and approaches to its solution, will be discussed in Part 4. As any student of econometrics knows, the linear regression specification used can be subjected to innumerable modifications and tests. In particular, the nature of the error term ut is crucial. If the errors can legitimately be assumed to possess zero mean, constant variance, and no internal dynamic pattern (such as serial correlation), then OLS will usually be an appropriate technique for estimating regression parameters and producing forecasts.6 When there is a dynamic structure to the error term, additional steps to model that structure produce better coefficient estimates and more accurate forecasts. This issue is treated next.
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3. ARIMA METHODS USED FOR TIME-SERIES ANALYSIS OF RESIDUALS 3.1. Single-Equation ARIMA Models Most economic time-series display a dynamic pattern, where the value of a variable at time t depends on its previous values and on random errors, which may themselves affect the variable in a cumulative and dynamic fashion. For example, a relatively simple model of a time series might look as follows: xt ¼ f1 xt
1
þ f2 xt
2
þ ut ; where ut ¼ t þ y1 t
1
Here, xt is determined by its two previous values, and is subject to a random input ut which is itself an accumulation of two consecutive random influences (or ‘‘innovations’’) et and et 1. The economist who needs to forecast X over an interruption period will estimate the parameters ji and yj, then compute forecasts x~ tþs : Most applicable computer programs estimate these parameters using non-linear least-squares and MLE hill-climbing algorithms. There are a number of things to be noted about these dynamic time-series models. First, they are referred to in the literature as ‘‘Box–Jenkins’’ or ‘‘Autoregressive Integrated Moving Average’’ (ARIMA) models. The number of lags of the variable determines the order (p) of the autoregressive component, while the number of lagged innovations in the random term determines the order (q) of the moving average component. The Box– Jenkins approach to forecasting can only be applied to a time series which is ‘‘stationary,’’ which implies, among other things, that the ‘‘statistical process’’ which generates the series has a constant and finite mean and variance. Many economic time series display a non-constant mean in the form of a trend. In order to remove such trends from a series, one can take first or second consecutive differences. The number of consecutive differences needed to achieve a stationary series determines the order (d) of integration in the full ARIMA (p,d,q) model. If one begins with raw series yt and successfully removes a trend with a first consecutive difference, then the series which is subject to ARIMA modeling will be xt ¼ Dyt ¼ yt 2yt 1 : The model illustrated above is denoted by xt ARMAð2; 1Þ; which implies that yt ARIMAð2; 1; 1Þ:7 Second, it is to be noted that Box-Jenkins modeling does not incorporate economic theory and requires no data on other ‘‘explanatory’’ variables.
Estimating Economic Loss for the Multi-Product Business
315
The series is taken as given, and the problem is to find a dynamic pattern in the series which can be utilized to project the series forward in time. The technique can be useful for open interruptions if information on related explanatory variables is not available, but one needs at least 50–75 observations from the period before the onset of the interruption to estimate parameters with any accuracy. ARIMA models should not be attempted with closed interruptions because the patterns cannot easily be estimated over periods with gaps in the data series. ARIMA forecasting proceeds in stages: Stationarity – a non-stationary series yt must first be transformed into a stationary series xt. Consecutive differencing and logarithmic transformations are commonly employed here. Identification – one must determine the AR and MA order of the generating process. Autocorrelations rs ¼ corr (xt, xt s), s ¼ 1; 2; :::; are estimated and graphed as an autocorrelation function (ACF). A similar set of ‘‘partial autocorrelations’’ is graphed as the PACF. From patterns in the ACF and PACF (see below), the forecaster makes an educated guess as to what ARMA (p,q) process might have produced the series xt. Estimation – parameters of the ARMA model are estimated and fitted values x~ t computed. Diagnostic checking – goodness-of-fit of the estimated model is evaluated by various means. Ljung-Box Q-statistics may be used on model residuals for w2 tests of the null hypothesis that the first s autocorrelations r1 ¼ r2 ¼ y rs ¼ 0. If the null cannot be rejected, the residuals may well be zero-mean white noise (ZMWN), indicating a good model. It is commonplace to go through several tentative models before finding one that is satisfactory, and to end up with more than one tenable model specification at the end of this process. Ex ante forecasting – each satisfactory model may be used to produce separate forecasts, and one may combine forecasts into one joint forecast if desired. Some ACF/PACF patterns associated with typical non-seasonal ARMA (p,q) process are described briefly and illustrated in Figure 4.
AR (p) – ACF dies out, PACF spikes at lags s ¼ 1; 2; . . . p: MA (q) – ACF spikes at lags s ¼ 1; 2; . . . q; PACF dies out. ARMA (p,q) – ACF and PACF die out after lag s4max {p, q}. ZMWN – no significant spikes in both the ACF and PACF.
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ACF
PACF
s
s
Typical AR (3) Model
Typical MA (1) Model
s
ACF
Fig. 4.
s
PACF
ACF/PACF Patterns with ARMA Models.
3.2. Time-Series Analysis of Residuals Only rarely will a forensic economist directly apply Box-Jenkins methods to forecast sales or other variables in business loss cases. But ARIMA modeling can be helpful even if only simple curve-fitting or single-equation econometric models are employed. The estimation of such models by OLS is correct only if the error terms have no dynamic structure. An OLS residual series has zero mean and will, in all likelihood, be stationary and therefore suitable for ARIMA modeling. Box-Jenkins methods are then applied to determine the dynamic structure of u˜t. If there is no structure, the residuals are ZMWN, and the equations estimated by OLS can be used for forecasting without further ado. More often, u˜ does possess a structure. In the case
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Estimating Economic Loss for the Multi-Product Business
of first-order serial correlation, u¯ ARMA ð1; 0Þ: u¯ t ¼ f¯ut 1 þ t : More complicated structures are frequently evident. But once the analyst has identified a particular structure u~ ARMA ðp; qÞ; the equation can be reestimated with the error term modeled appropriately. Modern statistical programs like EViews permit, in one pass, the efficient estimation of both regression parameters bi and error process parameters fi and yj. The end result is better fit and more accurate forecasts. A specific case will facilitate the discussion. A club with a growing membership list was forced to relocate. This event was alleged to have curbed the club’s rate of increase in membership. The analysis began with the following hybrid trend/econometric model: N t ¼ b1 þ b2 Dt þ b3 NIndext þ b4 LnðtÞ þ ut N ¼ club membership, explanatory variable NIndex ¼ membership at similar nearby institutions, and Ln(t) is a logarithmic trend term. Dt ¼ 1 for all periods after the forced relocation. The model was first estimated by OLS. Figure 5, called Club OLS Model, shows the residuals and the fitted values of N. The tracking pattern of the residuals in the bottom part of the chart is associated with serial-correlation of the error term. The ACF and PACF of the OLS residuals suggested an AR (1) or AR (2) process. Trial-and-error modeling led to a choice of u~ ARMA ð1; 1Þ: Incorporating this structure and re-estimation resulted in a much-improved fit
Residual
Actual
16000 15500
Fitted
15000 400
14500
200
14000
0 -200 Event -->
-400 1999
2000
Fig. 5.
2001
Club OLS Model.
2002
Membership
16500 Club OLS Model Actual and Fitted Values and Residuals
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CARROLL FOSTER AND ROBERT R. TROUT
Residual
Actual
16000 15500
Fitted
15000
300 200
14500
100
14000
Membership
16500 Club ARMA(1,1)Model Actual and Fitted Values and Residuals
0 -100 -200
Event -->
-300 1999
2000
Fig. 6.
2001
2002
Club ARMA (1,1) Model.
and a final residual series which more closely resembled ZMWN, as can be seen by comparing Figures 5 and 6 (Club OLS and Club ARMA).8
4. MODELING LOSSES FOR A MULTI-PRODUCT BUSINESS 4.1. The Business Interruption A regional industrial company had its business interrupted by an explosion and fire which disrupted output. Production was completely halted for several weeks and partially interrupted for about 8 months. The business produced a variety of finished products that were categorized in three generic product groups related to their method of production. We refer to them herein as Products A, B and C.9 All of the product lines required the same basic raw material inputs; but each had its own set of buyers for finished products, and each had competition from imports and, for some of the lines, from domestic producers as well. The monthly quantities of sales, prior to the fire, for each of the three product lines are shown in Fig. 7, called Industrial Company Sales. It is clear that unit sales had begun declining for several months prior to the fire. This was due to lack of regional demand for its products as well as significant competition from foreign companies.
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Estimating Economic Loss for the Multi-Product Business
Industrial Company Sales by Product Line
50000
Monthly Sales Units
40000 30000 20000 Fire --> 10000 0 1996
1997 Product A
Fig. 7.
1998
1999 Product B
2000
2001 Product C
Industrial Company Sales by Product Line.
This business interruption was an ‘‘open’’ interruption. The analytical task was to forecast quantities and prices of all three product lines forward from the time of the fire to the present (ex post) and then out to a future period specified by the insurance carrier (ex ante). The simultaneous forecasting of six variables (three product quantities and their corresponding prices) necessitated use of simultaneous equations modeling.
4.2. Simultaneous Equation Econometric Models Macroeconomists know well the cliche´ that ‘‘everything depends on everything else.’’ Personal consumption spending depends on disposable income, which in turn depends on GDP and taxes; but taxes depend on GDP, and GDP depends on consumption and investment. Investment depends on GDP and interest rates, but the latter are determined by money supply and money demand, which of course depends upon GDP, etc. Economists have learned through experience that a useful way to sort out complicated interrelations among variables is to model components of a system mathematically with simultaneous equations. The simplest textbook illustration starts with the market for a single product and models the supply function and demand function, and then imposes a market equilibrium condition. Suppose that quantity supplied (Qs) is a function of price (P) and
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production cost (C), while quantity demanded (Qd) depends on price and consumer income (Y). Such a system could be represented as follows: Qd Qd
¼ ¼
a1 P þ a2 C b1 P þ b2 Y
Qs
¼
Qd
The equation system above is known as the model’s ‘‘structural form.’’ Variables Qs, Qd, and P are ‘‘endogenous’’ variables, in that their values are determined by the economic forces represented within the model. Other variables, which influence but are not influenced by the system, are called ‘‘exogenous’’ (variables C and Y in the model above). If the objective is to estimate the structural form parameters ai and bj, then relatively sophisticated means, such as Two-Stage Least Squares (2SLS), must be employed to overcome problems associated with ‘‘simultaneous equations bias.’’10 If, however, the objective is merely to forecast the endogenous variables, then a simple expedient is to recast the model in its ‘‘reduced form.’’ For the supply/demand model above, one can obtain by algebraic substitution: Q ¼
p11 C þ p12 Y þ u
P
p21 C þ p22 Y þ v
¼
Q ¼ Qs ¼ Qd in equilibrium, and P is the equilibrium market price; u and v are regression error terms. The equations of the reduced form are not subject to simultaneous equations bias. There is one reduced form equation for each endogenous variable; only exogenous variables appear on the RHS of these equations; and, in general, every exogenous variable in the structural form system appears on the RHS of each reduced form equation. If the error terms are well-behaved ZMWN, the pij parameters of each equation can be estimated separately by OLS, and forecasts produced the same way as described earlier in Part 2. Of course, things are seldom that simple. It is typical for the structural form to include lagged values of endogenous variables, (Qt 1 or Pt 1, Pt 2, for example). The lagged variables are treated as exogenous (or ‘‘predetermined’’), but they may well be correlated with the error terms. If, in addition, the error terms are serially correlated, then estimation techniques other than OLS are required to obtain efficient and unbiased estimates of the pij.
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Estimating Economic Loss for the Multi-Product Business
4.3. The Industrial Case Reduced Form Equations One would naturally hypothesize that the output prices and quantities for the three product lines were generated in the context of some structural form equation system. The precise nature of this system is neither simple to deduce nor necessary for forecasting. Among the relevant exogenous variables in the structural form, certainly input costs would affect production/supply. User-demand would depend on conditions in the users’ product markets and on the extent to which they substituted imported product in place of purchases from the domestic firm. An initial specification of the 6-equation reduced form system modeled the endogenous variables QðjÞt and PðjÞt; j ¼ 1 . . . 3; as linear functions of input cost variables {C}, regional and macroeconomic market indexes {M}, current and lagged values of import prices, and quantities of each of the three product types {S}. Separate estimates of these equations quickly revealed that lagged values of the endogenous variables should also be included, as predetermined variables, on the RHS of the equations. It would make sense to do so, given cost-saving production-smoothing considerations and the fact that the firm was meeting the requirements of customer contracts of uneven duration. A new large contract to be met in 3 month’s time might raise output levels for 3 consecutive months, establishing a strong correlation between Qt and Qt 1, for example. The introduction of predetermined variables greatly increased the complexity of the estimation problem. For illustration, assume two product lines, where only output quantities Q(1) and Q(2) are to be forecasted, and one exogenous (cost, market, or import) variable X. If only lagged values of the endogenous variable are introduced in that variable’s equation, the model looks like this: Qð1Þt
¼
p11 þ p12 X t þ p13 Qð1Þt
1
þ ut
Qð2Þt
¼
p21 þ p22 X t þ p23 Qð2Þt
1
þ vt
Each of these equations can be estimated separately and TSAR used to model residuals. Forecasting ex ante is relatively simple, as each new forecast value becomes the lagged value for the next forecast iteration. But the model ignores possible cross effects. A random change to ut affecting Q(1) at time t may well cause a shifting of resources or production plans which affect Q(2) at time t+1 or later. This cross effect would be felt in the Q(2) error term vt: corr(vt, ut 1) 6¼ 0. This, of course, is a type of structure in the error terms; and as with TSAR, if this structure can be exploited, goodness
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of fit and forecast accuracy will be enhanced. In this example, Q(2) is affected, after a lag, by perturbations in Q(1), and the model would be amended as follows: Qð1Þt Qð2Þt
¼ ¼
p11 þ p12 X t þ p13 Qð1Þt p21 þ p22 X t þ p23 Qð2Þt
þ ut 1 þ p24 Qð1Þt
1
1
þ vt
Each of these equations could still be estimated separately, but forecasts of both Q(1) and Q(2) from one time period are needed to generate forecasts of Q(2) for the next period. Fortunately, this inconvenience is easily overcome by use of vector autoregression.
4.4. Vector Autoregression The vector autoregression (VAR) is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the system of variablesy . [It] sidesteps the need for structural modeling by modeling every endogenous variable in the system as [a] function of the lagged values of all the endogenous variables in the system. [Eviews 3, (1997), p. 493]
A VAR estimates and forecasts a vector of endogenous variables. The equations form a type of reduced form system, called a ‘‘VAR in standard form,’’ in which each endogenous variable is a linear function of the same set of exogenous variables and of one or more lagged values of every endogenous variable. For our example of two quantity variables Q(1) and Q(2), with one endogenous lag, the VAR is written as follows: Qð1Þt Qð2Þt
¼ ¼
p11 þ p12 X t þ p13 Qð1Þt p21 þ p22 X t þ p23 Qð2Þt
þ p24 Qð2Þt 1 þ p24 Qð1Þt 1
þ ut 1 þ vt 1
All pair-wise lagged cross effects are allowed for. The system is not simultaneous in that contemporaneous values Q(1)t and Q(2)t do not appear on the RHS of any of the equations. A VAR program conveniently estimates the pij parameters and produces joint forecasts of the endogenous variables.11 Analysis of residuals from the estimated equation can be used to determine the desired number of lags of endogenous variables. If u˜t and/or v˜t in the sample VAR above appeared to be serially correlated AR(1), Q(1)t 2 and Q(2)t 2 would both be added to the RHS of both equations. VAR was used in preparing the final set of forecasts for the industrial company interruption case. We estimated the future quantities and prices
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Estimating Economic Loss for the Multi-Product Business
50000
VAR Model Forecasted Sales by Product Line
Monthly Sales Units
40000
30000
20000 Fire --> 10000
0 1998
1999
Product A
Fig. 8.
2000 Product B
2001 Product C
VAR Model Forecasted Sales by Product Line.
for each of the three product lines using the VAR model. For the quantities, we first introduced the historic quantities for each of the three product lines in the VAR model as the endogenous variables. We used a two-period lag model based on an examination of the coefficients of the second period lagged coefficients and on the various lag order selection criteria provided within the EViews program itself. The program includes six different criteria for selecting an appropriate lag period; and, of course, the different criteria seldom agree on the specific number of lags to use, so judgment is required. Serial correlation for the model was tested by using the EViews residual serial correlation LM test which is part of the VAR output. This test indicated that there was no serious serial correlation in the residuals of the two-lag specification. VAR quantity forecasts for the three products are graphed in Fig. 8. Prices are not shown herein.
5. CONCLUSIONS This chapter presents several economic and econometric models that an economist can apply to data in business interruption or business loss cases.
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The objective of the models is to use past sales data and the inclusion of exogenous events as well as exogenous industry variables to accurately estimate the sales that would have been made some ‘‘event’’ not to occur. We have presented models to use for simple single product or single service firms, which can be applied to open or closed business interruption cases. We have also presented models to use for more complex multi-product or multi-service firms that experience some business interruption. In this context, we are convinced that the EViews program is an excellent example of econometric software permitting correct analysis of models used to estimate business losses.
NOTES 1. See Foster and Trout (1989, 1993). 2. Where possible, data pertaining to relatively short time intervals (weekly or monthly) are preferred, so as to model short-term cyclical or seasonal influences. Obviously, information on costs and profit margins are ultimately necessary for completion of the loss analysis. 3. The error contains all influences on S which are not specifically modeled in the forecasting equation, including the effects of omitted variables, data recording errors, and ‘‘purely random’’ shocks. 4. Fortunately, non-linear estimation modules are part of most modern statistical packages. The authors have found the EViews program to be particularly flexible and useful in business interruption applications. The forecasts presented in this paper were all produced using the EViews program. 5. There are other types of deterministic forecast models based upon classical decomposition and smoothing techniques, but these, along with the ARIMA models in Part 3, are very cumbersome when there are gaps in a data series, as is the case with closed interruptions. 6. Such an error term is known as zero-mean white noise (ZMWN). 7. Box-Jenkins models can be extended to time series displaying seasonal patterns by including seasonal differences and seasonal lags along with consecutive differences and lags. Alternatively, one can begin ARIMA modeling with a seasonally adjusted time series. Classical Decomposition and the Holt-Winters smoothing models are among the ways of computing seasonally adjusted time series. For the basics of ARIMA theory, see Enders (1995, Chapter 2). 8. The estimated ARMA process was unstable, perhaps due to non-stationary residuals resulting from misspecification of the trend term. The improved fit of this model was what mattered in this instance, but ex ante forecasts would have been questionable. Unstable AR processes drive the variable to 7N , possibly with explosive oscillation. 9. The actual identity of the firm and its specific products are withheld for obvious reasons.
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10. There is also a so-called ‘‘identification problem.’’ Roughly speaking, there must be exogenous variables in the system, which are excluded from each equation, and in sufficient numbers. If identification conditions are not met, parameters cannot be estimated. See Ramanathan (2002, Chapter 13) on simultaneous equations models in general. 11. VAR is an analytical as well as a forecasting tool. ‘‘Impulse response functions’’ measure lagged impacts of changes in one endogenous variable on subsequent values of the others. This feature was not utilized in the industrial company case. A good discussion of VAR theory and application can be found in Enders (1995, Chapter 5).
REFERENCES Eviews 3 User’s Guide. (1997). Quantitative micro software. Irvine, CA. Enders, W. (1995). Applied econometric time series. New York, NY: Wiley. Foster, C., & Trout, R. R. (1989). Computing losses in business interruption cases. Journal of Forensic Economics, 3(1), 9–22. Foster, C., & Trout, R. R. (1993). Economic analysis of business interruption losses. In: P. Gaughan. & R. Thornton (Eds), Methods and issues in litigation economics. New York: JAI Press. Gaughan, P. (2000). Measuring commercial damages. New York: Wiley. Gaughan, P. (2004). Measuring business interruption losses and other commercial damages. New York: Wiley. Ramanathan, R. (2002). Introductory economics with applications (5th ed.). New York: Harcourt.
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