Housing Markets in Europe: A Macroeconomic Perspective

Housing Markets in Europe

Olivier de Bandt • Thomas Knetsch • Juan Peñalosa Francesco Zollino Editors

Housing Markets in Europe A Macroeconomic Perspective

Editors Olivier de Bandt Banque de France 46-1405 DCPM rue Croix des Petits Champs 39 75049 Paris France [email protected]

Juan Peñalosa Banco de España Servicio de Estudios Alcala 48 28014 Madrid Spain [email protected]

Thomas Knetsch Deutsche Bundesbank Economics Department Wilhelm-Epstein-Straße 14 60431 Frankfurt am Main Germany [email protected]

Francesco Zollino Banca d’Italia Servizio Studi di Congiuntura e Politica Monetaria Via Nazionale 91 00184 Rome Italy [email protected]

ISBN 978-3-642-15339-6 e-ISBN 978-3-642-15340-2 DOI 10.1007/978-3-642-15340-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010936193 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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Acknowledgements

The articles published in this book were discussed by academics and economists from central banks or international organisations during the conference held in Paris on 3 and 4 December 2009 on ”The macroeconomics of housing markets”. The authors wish to express their sincere appreciation to them. This includes, in alphabetical order: C. Andr´e (OECD), J. Ayuso (Banco de Espa˜na), D. Beau (Banque de France), A. Benito (Bank of England), R. Br¨uggemann (University of Konstanz), A. Diaz (University Carlos III), S. Dubecq (Banque de France), G. Dufr´enot (University AixMarseille and Banque de France), S. Frappa (Banque de France), G. Ferri (University of Bari), I. Ghattassi (Banque de France), S. Gr´egoir (Edhec Business School), P. Jaillet (Banque de France), J.S. M´esonnier (Banque de France), P. Moutot (European Central Bank), J. Muellbauer (Oxford University), F. Panetta (Banca d’Italia), G. P´erez-Quir´os (Banco de Espa˜na), A.F Pozzolo (University of Campobasso), J.P. Redouin (Banque de France), T. Wollmersh¨auser (Ifo Institute), G. Ziebarth (Deutsche Bundesbank). In addition, they warmly thank L. Ferrara (Banque de France), B. Rouvreau (Banque de France) and F. Robert (Banque de France) who expertly assembled the different articles in LATEX.

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Preface

During the recession in years 2008-2009, the most severe for mature economies in the post-war period, housing markets have often been mentioned as having a special responsibility. During this period, housing was associated either with disruptions in the financial sector - which were triggered by crisis of the US subprime mortgage market -, or sharp shifts in the demand previously addressed to the construction sector, with effects on overall activity, or downward corrections in house prices, negatively affecting households’ wealth. From the European point of view, a central issue is to investigate whether these dynamics are country-specific or share common patterns across countries. For the conduct of the single monetary policy it is important to assess to what extent housing markets in the euro area have become more homogeneous. Another policy relevant question is to assess whether shocks in the housing sector may jeopardise financial stability. The objective of this book is to shed light on the cyclical behaviour of the housing markets, its fundamental determinants in terms of supply and demand characteristics, and its relationship with the overall business cycle. The comovements of house prices across countries are also considered, as well as the channel of transmission of house price changes to the rest of the economy. Particular attention is paid to the effects on private consumption, through possible wealth effects. The contributions focus on developments in the four largest countries in the euro area on the basis of a collection of research papers written by economists from Deutsche Bundesbank, Banque de France, Banca d’Italia and Banco de Espa˜na. It also includes an introductory lecture by Matteo Iacoviello (Federal Reserve Board and Boston College, United States), who discussed the analytical merits and challenges of incorporating a housing sector in macroeconometric models, especially Dynamic Stochastic General Equilibrium models. The conclusion of the book is that housing market cycles are still relatively heterogeneous across euro area countries, even though there is some evidence pointing towards convergence since the creation of the Economic and Monetary Union. On the other hand, housing markets may give rise to significant macroeconomic shocks, as the current crisis has shown, therefore calling for a regular monitoring of housing developments. vii

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After reviewing the main reasons why the macroeconomics of housing markets represents a relevant research area, the papers collected in this volume will be briefly summarised. It should be noted that all the articles in the book express the opinions of the authors and do not necessarily reflect the positions of Deutsche Bundesbank, Banque de France, Banca d’Italia or Banco de Espa˜na.

1 Housing markets in Europe as a relevant topic of economic research The developments in housing markets influence business cycles, play a key role in the transmission of monetary impulses to the real economy and, under unfavourable circumstances, may even affect the stability of the financial system. This is due to a variety of reasons. First, housing takes a relatively significant share in economic activity and, thus, shocks that originate in the housing sector can have a marked effect on the other macroeconomic variables. Residential investment and consumption of housing services (mostly effective and imputed rents) account for a share between 13 and 19 per cent of GDP in the four largest countries of the euro area, whereas real property assets represent more than 50 per cent of households’ total gross wealth in these economies (see table 1). This is comparable to the figures found for the United States regarding the share of housing in households’ total wealth (see Iacoviello, 2010, this volume). Table 1 Size of housing markets Housing consumption and investment as a share of GDP (in%) Housing wealth (including land) as a share of total household’s gross wealth (in % of GDP) Credit to households for housing / GDP (in%) (households’ debt/GDPin%)

Germany France Italy Spain 19 15 13 16 52 (198) 42 (61)

63 51 89 (337) (298) (557) 37 21 60 (51) (40) (84)

Source: National accounts for 2008, Monetary statistics from National Central banks

Second, purchasing a housing unit is the main motivation for entering into a debt contract by households and, accordingly, housing wealth backs a large share of banking loans. Credit for housing represents 21 percent of GDP in Italy and 60 percent in Spain, while France and Germany are in intermediate positions. To some extent, these differences reflect cross-country divergences in the share of owneroccupied housing, more developed in Spain and Italy than Germany and France. Third, given the length of the housing construction process, mismatches between

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supply and demand can be protracted, initiating swings in house prices which may feed on themselves and delay a change of direction. Thus, the housing market is prone to episodes of overvaluation which may have significant effects across the economy since it may transmit to the construction sector - as they affect firms’ expected profitability - as well as to other industries, via changes in the ability to access credit markets, and to households, leading to wealth effects on consumption. One should therefore acknowledge, following Leamer (2007), that the macroeconomic contribution of residential construction to the business cycle may go beyond its long term share in GDP, since shocks affecting housing markets may be of large amplitude at particular points in time.1 Leamer (2007) indeed shows that all recessions in the United States apart from the one in 2003 were preceded by a crisis in the residential construction market. These features may explain why housing developments also have significant macrofinancial implications. Indeed historical experience shows that many financial crises in the past originated or were exacerbated by housing-related factors. In particular, in the last decade housing markets seem to have played a substantive role in building up global macroeconomic imbalances, the US subprime crisis being the most outstanding example. Focusing on developments in the euro area, residential investment and house prices moved differently in the member states during the crisis. The degree of integration, although partly increasing since the start of Economic and Monetary Union in 1999, is still relatively modest among housing markets. This evidence, which is also one of the main conclusions drawn from the bulk of investigations collected in this volume, gives rise to a number of questions, which are both analytically challenging and relevant from a policy perspective. Among these questions are the following ones. Is the present diversity in national housing markets related to differences in institutional settings, the habits of consumers and investors and other characteristics? Which are the built-in forces of a monetary union which could balance out differences in housing markets and how can these be strengthened? How can the setting and conduct of economic policies as well as financial market regulation and supervision be designed to avoid, or at least counteract, the emergence of boom and bust cycles in real estate sectors? How can monitoring of housing market developments be improved? What lessons can be drawn from the recent crisis? These few and rather selective issues alone constitute a very ambitious research agenda. Although only tentative conclusions can be drawn from the broad spectrum of results presented in the book, one conclusion is that the convergence of residential markets within the euro area has been hampered by a mixture of factors. First, national idiosyncrasies are still of prevalent importance in housing markets, given the relevance of factors such as taxation, social housing, legislation or land restrictions. Second, the fundamentals of housing demand - for example, demographics have evolved quite distinctly across countries. Third, real interest rate differentials, while declining somewhat, were still characterised by a high degree of persistence, 1 Leamer, E. E. (2007), Housing, housing finance, and monetary policy, Federal Reserve Bank of Kansas City, Presentation to Symposium organized in Jackson Hole, August 30 - September 1, 2007.

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lengthening the asymmetric impact of real financing costs on housing demand and residential investment. The experience of the previous cycle illustrates that the regular and close monitoring of housing market trends is essential for economic policy. This requires data of high quality and cross-country comparability. The statistical measurement of housing market activity is comprehensive given that national accounts provide harmonised quarterly data on residential investment and a number of monthly indicators (e.g. building permits) are available as supplementary information, although some pieces of information, such as the stock of unsold houses, is currently lacking. The financial side of residential activity is also well documented; for instance, in the harmonised MFI statistics of lending rates and loans as well as in financial accounts. However, the statistical basis is weaker regarding the measurement of housing wealth (including the land underlying dwellings). Despite some improvements, the monitoring of house price developments in the euro area still suffers from marked information gaps, in the residential and, even more so, commercial sector. Further progress might be envisaged in terms of representativeness, consistency and timeliness of indicators. In the euro area, the mandate of monetary policy is to maintain price stability in a broad sense, suggesting that house price developments are addressed only insofar as they imply a risk to overall inflation or inflation expectations. Fiscal policy, however, might be more effective in counteracting unsustainable trends in national housing markets because a number of instruments are at the disposal of national or even regional authorities, such as real estate taxation, stamp duties or tax allowances for homebuyers. Other economic policy areas are also fundamental, such as the legislation concerning renting. The conduct of banking and financial market supervision might also be used to avoid excessive risk-taking by financial intermediaries, or even households, as the recent crisis in the subprime mortgage market has shown. We now survey in detail the main findings of the various parts of the book: • • • •

the measurement of housing cycles; the determinants of housing cycles; the impact of wealth effects; the conclusions for economic policy and financial stability.

2 Is housing a leading indicator of the business cycle? In his introductory lecture, Matteo Iacoviello (Federal Reserve Board and Boston College) stresses the extent to which housing has often been underestimated in economic research, while, in the United States for example, it accounts for half of the total capital stock, outstanding housing debt is comparable to that of public debt and house price volatility is at least twice as high as that of inflation. According to Iacoviello, on the basis of evidence from Dynamic Stochastic General Equilibrium models (DSGE), the rise in house prices, due above all to weak technological

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progress in construction, contributed significantly in the United States to private consumption growth in the first half of te years 2000s. It is therefore important to better analyse the formation of house prices, whose fluctuations show a relatively higher degree of inertia than on financial markets, by more efficiently incorporating expectations, the confidence of market participants and other financial factors (wealth effects, credit standards and banks’ credit supply capacity). The papers presented in Part II of the book then examine the links between housing cycles and general economic activity in certain countries. In line with US evi´ dence, Laurent Ferrara and Olivier Vigna (Banque de France) and Luis J. Alvarez and Alberto Cabrero (Banco de Espa˜na) find that housing market cycles in France and Spain tend to be a leading indicator of the business cycle, in contrast with the evidence by Guido Bulligan (Banca d’Italia) for Italy. Furthermore, in France, there tends to be downward price rigidity, which explains why house prices fell less sharply than in other countries and, in Spain, there are interesting asymmetries in cyclical fluctuations: contractions in GDP and housing tend to be briefer than expansions. However, it is essential to analyse housing market developments at the international level. In the four major euro area countries, GDP cycles show a high degree of comovement, most likely due to trade linkages. In contrast, housing market cycles - in which country-specific or local variables, such as land availability or regulation play a major role - show substantially weaker comovements across coun´ tries, according to a study conducted jointly by Luis J. Alvarez (Banco de Espa˜na), Guido Bulligan (Banca d’Italia), Alberto Cabrero (Banco de Espa˜na), Laurent Ferrara (Banque de France) and Harald Stahl (Deutsche Bundesbank).

Q/Q-4 in % 40

10 FR (l) IT (l)

30

DE (r) US (l)

ES (l)

8

20

6

10

4

0

2

-10

0

-20

-2

-30

82

84

86

88

90

92

94

96

98

00

02

04

06

08

-4

Fig. 1 Nominal house prices in the four largest euro area countries and United States

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These findings have been corroborated by Laurent Ferrara (Banque de France) and Siem Jan Koopman (VU University Amsterdam), who show that, for Spain, the dependence between the housing market and economic activity is stronger than elsewhere. Housing cycles appear to be correlated in France and Spain, while the German market exhibit a different cycle. Extending the analysis to OECD countries, Olivier de Bandt (Banque de France), Karim Barhoumi (Banque de France) and Catherine Bruneau (University of Paris-Ouest and Banque de France) highlight the existence of various channels of transmission of house price shocks, either direct (between housing markets, with a particular role for those originating in the United States), or indirect via other macroeconomic variables (see Fig. 1).

3 What drives housing cycles? Part III focuses more closely on the structural determinants of the housing market and their impact on the economy. R´emy Lecat and Pamfili Antipa (Banque de France) present a model showing that, in both France and Spain, residential property prices in 2007 were clearly above the level explained by their fundamentals (households’ disposable income, housing stock, interest rates, etc.). Nevertheless, this overvaluation is greatly reduced when taking into account other indicators measuring changes in financial and demographic factors. The paper by Thomas Knetsch (Deutsche Bundesbank) shows that housing market developments in Germany have been influenced by the economic consequences of German reunification for the last two decades. For a number of reasons, this event seems to have triggered a pronounced cycle in dwellings construction, exceeding previous fluctuations in duration and magnitude. In addition, there is evidence that, on the German housing market, the forces to equilibrium correction have been weakened since 1991, as the speed of adjustment in housing supply via residential investment slowed down significantly and house prices became virtually irresponsive. In a complementary study, Tobias Duemmler and Stephan Kienle (Deutsche Bundesbank) focus on the financial conditions for residential investment. Their paper shows that, in Germany, the demand for housing is significantly affected by the real user cost. Moreover, net financial wealth seems to have an impact, too, stressing the role of collaterals for bank lending in the context of imperfect information. For Italy, Filippo Scoccianti (Banca d’Italia) investigates the joint effects of low real interest rates and the reduction in downpayment requirements: his research concludes that the easing of financing conditions is beneficial to households managing to access home-ownership in that it enables them to absorb the negative impact, for their property affordability, of the rise in house prices. In contrast, middle-aged home owners, who also hold financial assets, gain on their financial wealth but lose from lower interest rates paid on their financial savings.

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4 Wealth effects from housing In order to assess the links between housing, access to credit and household consumption, and the evidence gathered in the book on possible ”wealth effects” on consumption (i. e. to what extent consumption responds to variations in households’ wealth), it is useful to refer to the work of John Muellbauer (2009). In his view, house price increases trigger a decrease in the demand for housing, because past price rises end up pricing out an increasing number of first-time potential buyers, and constrained spending on current dwellings (rental or ownership) is higher than before. This drives down private consumption and ultimately aggregate growth.2 However, for a given country, the final impact of an increase in house prices depends, on the one hand, on the owner-tenant ratio and, on the other hand, on the structure of the financial system, in particular the supply of credit. In a country with a strong rate of growth of bank credit, whose amount depends on the value of property financed or mortgaged as collateral, an increase in house prices may increase the present value of collateral, hence partially counteracting, and even sometimes reverting, the initial negative effect on consumption.

41.7

Italy

Source: National accounts

59.9 52.8

France

76.0 62.0

Euro area

91.4

63.2

Germany

89.0 66.1

Japan

99.5 86.0

Spain

124.8 100.0

United Kingdom

145.9 120.7

United States 40

50

60

70

80

% of gdp

90

100

110

120

130

155.0 140

150

160

% of gross disposible income

Fig. 2 Households’ debt ratios, fourth quarter of 2009

In the book, the measurement of wealth effects was more particularly investigated for three countries: in France (Val´erie Chauvin and Olivier Damette, Banque de France), in Italy (Antonio Bassanetti and Francesco Zollino, Banca d’Italia) and in 2

Muellbauer, J. (2009), Housing, Credit and Consumer Spending, Presentation to the Conference organized in Paris on “The Macroeconomics of Housing Markets”, Dec. 3-4 2009.

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Spain (Teresa Sastre and Jos´e Luis Fern´andez, Banco de Espa˜na). Levels of household debt vary considerably across countries (see Fig. 2). These three studies reach a number of common conclusions based on an equilibrium relationship which appears to exist at the macroeconomic level between housing wealth, financial wealth, the purchasing power of income and private consumption. According to these estimates (see Table 2), a one euro increase in financial wealth implies an increase in consumption around 4.5 cts in France and Italy, and 9.7 cts in Spain. The equivalent figures for an increase in housing wealth is less than 2 cts in Italy and Spain and in the range of 2.7-4.3 cts in France. Comparative evidence for Germany for total wealth, as found in Hamburg (2008), indicates that the impact seems to be slightly higher than in France and Italy. 3 Apart from these differences, the estimates of wealth effects available for the major continental European countries share the feature that, in general, they are below the estimates usually found in the United States and the United Kingdom,4 although one should acknowledge the existence of measurement issues, as stressed in the economic literature. It remains that wealth effects, in particular from real property, are small but non negligible in the euro area . A certain number of caveats should, however, be kept in mind. First, wealth effects only materialise as soon as households perceive the rise in housing wealth to be permanent. Second, one needs to identify the source of shocks : over the last few years, consumption behaviour has mainly reflected expectations of financial asset prices, for the United States, and income expectations, in the cases of France, Italy and Spain.

Table 2 Increase in Total Consumption (cents), after a one euro increase in households’ wealth Total wealth Financial wealth Housing wealth

Germany 4-5 -

France 0.4-1.7 4.4-4.5 2.7-4.3

Italy Spain 2.6 4-6 9.7 1.5-2 1.1

Sources: Basanetti and Zollino (2010, this volume) for Italy; Damette and Chauvin (2010, this volume) for France (non durable consumption); Sastre and Fernandez (2010, this volume) for Spain; Hamburg et al. (2008) for Germany

Supplementing this macroeconomic analysis with a microeconomic study, Luc Arrondel and Fr´ed´erique Savignac (Banque de France) analyse households’ tradeoff between housing wealth and financial wealth. Indeed, households not wishing to take excessive risk favour at times housing assets and at times equities. Preferences may vary across countries. In particular, the fact that the share of financial assets in 3 Hambourg, B. , M. Hofmann, M. and J. Keller (2008), Consumption, Wealth and Business Cycles, Empirical Economics , 34,3, 451-476. 4 For the USA, see the paper by S. Dubecq and I. Ghattassi (2009), Banque de France, Working Paper, No. 264.

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French households’ aggregate assets is lower than in other countries, is explained by the greater preference of French households for housing assets.

5 Implications for economic policy and financial stability Given that the interrelations between general economic activity, household consumption and changes in housing or financial wealth vary across countries, there is a debate among policymakers about the most suitable economic policy to be implemented in the presence of housing cycles. We distinguish here between fiscal policy and the monitoring of financial stability. There is a host of evidence that the housing cycle may be affected by fiscal policy. The existence of such a link between government housing subsidies and housing market dynamics is borne out for France by Pamfili Antipa and Christophe Schalck (Banque de France): according to this research, residential investment and the housing cycle in France appear to be sensitive to tax allowances (including tax deductibility). As regards the risks that housing markets pose for financial stability, Vladimir Borgy, Laurent Clerc and Jean-Paul Renne (Banque de France) put forward a method to identify asset-price or house price bubbles ex ante, by isolating in particular the episodes where the bursting of a bubble leads to a marked slowdown in activity. They conclude that this type of situation is found more frequently in cases where bubbles develop in housing markets than in stock markets. Moreover, it is important to analyse the level of real interest rates, credit and investment growth when house price bubbles start to form. Another indicator used to assess risks to the sustainability of house price developments is the affordability index. Affordability measures the maximum size of housing unit a household can acquire, depending on house prices, but also financial conditions (interest rates and average maturity of loans, which is affected by financial innovation), as well as households’ disposable income. In France, Italy and Spain, after a decrease in affordability until 2007 due to the steady growth of house prices, the index has been improving. In Germany, however, the affordability constraint turns out to have become looser in the last two decades owing to comparatively stable house prices, increasing disposable income and declining interest rates (see Fig. 3).

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160

Italy

Spain

Germany

France

140 120 100 80 60 40 1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

Source : Authors’s own computations. Fig. 3 Affordability index (average 1991-2009 = 100)

To conclude, the book sheds some light on the various determinants of house prices and the contribution of residential construction to macroeconomic developments. After the run-up in the early part of the years 2000s, house prices in France, Italy and Spain are now slowly converging to a more sustainable path, while the situation in Germany has been characterized by stable prices after the upswing associated with reunification. The key role that the housing sector has played recently, and which has been deeply explored in the book, invites to pay more attention in the future to its performance and to make further progress on different research areas related to that sector.

Olivier de Bandt (Banque de France), Thomas Knetsch (Deutsche Bundesbank), Juan Pe˜nalosa (Banco de Espa˜na), Francesco Zollino (Banca d’Italia)

Contents

Part I Introductory Lecture Housing in DSGE Models: Findings and New Directions . . . . . . . . . . . . . . . Matteo Iacoviello

3

Part II Housing and the Business Cycles Country Analysis Housing and the Macroeconomy: The Italian Case . . . . . . . . . . . . . . . . . . . 19 Guido Bulligan Cyclical Relationships Between GDP and Housing Market in France: Facts and Factors at Play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Laurent Ferrara and Olivier Vigna Does Housing Really Lead the Business Cycle in Spain? . . . . . . . . . . . . . . . 61 ´ Luis J. Alvarez and Alberto Cabrero Cross-Country Analysis Housing Cycles in the Major Euro Area Countries . . . . . . . . . . . . . . . . . . . . 85 ´ Luis. J. Alvarez, Guido Bulligan, Alberto Cabrero, Laurent Ferrara and Harald Stahl Common Business and Housing Market Cyles in the Euro Area from a Multivariate Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Laurent Ferrara and Siem Jan Koopman The International Transmission of House Price Shocks . . . . . . . . . . . . . . . . 129 Olivier de Bandt, Karim Barhoumi and Catherine Bruneau

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Part III Macroeconomic Models of Housing The ’Housing Bubble’ and Financial Factors: Insights from a Structural Model of the French and Spanish Residential Markets . . . . . . . . . . . . . . . . 161 Pamfili Antipa and R´emy Lecat Trend and Cycle Features in German Residential Investment Before and After Reunification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Thomas A. Knetsch User Costs of Housing when Households Face a Credit Constraint: Evidence for Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Tobias Duemmler and Stephan Kienle Causes and Welfare Consequences of Real Estate Price Appreciation . . . . 241 Filippo Scoccianti Part IV Wealth Effects Wealth Effects on Private Consumption: the French Case . . . . . . . . . . . . . . 263 Valerie Chauvin and Olivier Damette An Assessment of Housing and Financial Wealth Effects in Spain: Aggregate Evidence on Durable and Non-durable Consumption . . . . . . . . 283 Teresa Sastre and Jos´e Luis Fern´andez The Effects of Housing and Financial Wealth on Personal Consumption: Aggregate Evidence for Italian Households . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Antonio Bassanetti and Francesco Zollino Housing and Portfolio Choices in France . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Luc Arrondel and Fr´ed´erique Savignac Part V Housing, Economic Policy and Financial Stability House price Boom/Bust Cycles: Identification Issues and Macroprudential Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 Vladimir Borgy, Laurent Clerc and Jean-Paul Renne Impact of Fiscal Policy on Residential Investment in France . . . . . . . . . . . . 385 Pamfili Antipa and Christophe Schalck

List of Contributors

Academics: Luc Arrondel (CNRS - Paris Jourdan Sciences Economiques and Banque de France), Catherine Bruneau (University of Paris Ouest - Nanterre La D´efense and Banque de France), Olivier Damette (University of Paris XII - Val de Marne), Matteo Iacoviello (Federal Reserve Board, Division of International Finance), Siem Jan Koopman (VU University Amsterdam). Deutsche Bundesbank: Tobias Duemmler, Stephan Kienle, Thomas Knetsch, Harald Stahl. Contact : Deutsche Bundesbank, Economics Department, Wilhelm - Epstein - Strasse 14, 60431 Frankfurt am Main, Germany. Banque de France: Pamfili Antipa, Olivier de Bandt, Karim Barhoumi, Vladimir Borgy, Val´erie Chauvin, Laurent Clerc, Laurent Ferrara, R´emy Lecat, Jean-Paul Renne, Fr´ed´erique Savignac, Christophe Schalck, Olivier Vigna. Contact : Banque de France, Direction G´en´erale des Etudes et des Relations Internationales, 39 rue Croix des Petits Champs, 75049 Paris Cedex 01, France. Banca d’Italia: Antonio Bassanetti, Guido Bulligan, Filippo Scoccianti, Francesco Zollino. Contact : Banca d’Italia, Servizio Studi di Congiuntura e Politica Monetaria, Via Nazionale 91, 00184 Rome, Italy. ´ ˜ Luis J. Alvarez, Banco de Espana: Alberto Cabrero, Jos´e Luis Fern´andez, Juan Pe˜nalosa, Teresa Sastre. Contact : Banco de Espa˜na, Servicio de Estudios, Alcal´a, 48, 28014 Madrid, Espa˜na.

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Part I

Introductory Lecture

Housing in DSGE Models: Findings and New Directions

Housing in DSGE Models: Findings and New Directions Matteo Iacoviello

Abstract The goal of this chapter is to make the case that it is time for macroeconomists to restore the imbalance between the practical and empirical relevance of housing for macroeconomics on the one hand, and the treatment that macroeconomic models devote to housing on the other. After discussing a few stylized facts regarding the macroeconomic importance of housing markets, the chapter presents key results from the Iacoviello and Neri’s (2010) DSGE model with housing, a model that is increasingly used in quantitative monetary policy analysis. Directions for further research are then suggested, focusing on the role of financial intermediation, the determinants of house prices and their persistence, the role of economic policy to stabilize house prices and the link between housing and labour markets.

JEL codes : E32, E44, E47, E58, R21, R31 Keywords : Housing markets, housing prices, Bayesian estimation, DSGE models

1 Introduction To understand the renewed interest of academics and policy makers in the housing market, I will start with a quote that summarizes how little interest there was in the topic only nine years ago: This paper focuses on a small niche – the housing market – with limited evidence that this market has the significance that is implied for real economic activity. (July 17, 2001) M. Iacoviello Federal Reserve Board - Division of International Finance, e-mail: [email protected] The material in this chapter is based on the keynote speech delivered at the International Research Conference on ”The Macroeconomics of Housing markets” hosted by the Banque de France in Paris, 3-4 December 2009

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_1, © Springer-Verlag Berlin Heidelberg 2010

3

4

Matteo Iacoviello

This quote is from a well-known economist who has, since then, written papers on the housing market himself, probably in light of the fact that the housing market is not such a niche anymore. This quote was the justification that the economist, as editor-in-charge at a macro field journal, gave to reject a paper written by the author of this chapter. In sum, the paper was okay, but the topic – housing and the credit channel of monetary policy – was boring. Nine years later, the research on the housing market and the macroeconomy has finally become mainstream. One of the keys to this shift of ideas has been the observation that movements in housing markets are not just the consequence of wider macroeconomic developments, but also can be important impulses to business fluctuations. For instance, in his introductory remarks at a conference on Housing and Mortgage Markets, Federal Reserve Chairman Ben Bernanke (2008) noted: Housing and housing finance played a central role in precipitating the current crisis.

To summarize, while only ten years ago “housing” was not part of mainstream economic research, and was confined to a subfield of economics named “real estate economics ” , it is fair to say that, today, things have changed. Yet even now many popular undergraduate and graduate macroeconomic textbooks devote little space to housing. For instance, the word “housing” only appears once in Carl Walsh’s latest edition of the book “Monetary Theory and Policy” (in the context of a discussion of tax deductibility of nominal mortgage payments). It never appears in the Ljungqvist and Sargent or in Woodford’s books. The goal of this chapter is to make the case that it is time for macroeconomists to restore the imbalance between the practical and empirical relevance of housing for macroeconomics on the one hand, and the treatment that macroeconomic models devote to housing on the other. My comments will mostly touch upon the role of housing within the class of macroeconomic models that have become known as dynamic, stochastic, general equilibrium (DSGE) models (see Woodford, 2009, and Fern´andez-Villaverde, 2009, for recent surveys). The cost of confining my attention to DSGE models is that the chapter will not cover the growing literature that links housing with search models, with models of urban economics, or with asset pricing models, unless this research has used elements of DSGE models. The benefit is that a large portion of modern macro research – especially in central banks and international financial institutions – uses DSGE models for forecasting and for policy advice, as an alternative or as a complement to large scale non-structural macroeconomic models. My hope is that users of DSGE models who are not familiar with housing research will find this review useful.

2 Seven facts about housing and the macroeconomy There are several interesting dimensions that matter as far as housing prices, housing investment and housing wealth are concerned. To illustrate their importance, I will

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focus on seven interesting facts about housing. These facts are not new, and have been noted by other authors – including myself – before. I just want to put them together in order to organize my discussion. 1. Housing wealth (the market value of all residential capital stock, whether rented or owned) is an important component of national wealth. In fact, it accounts for almost half of household wealth in most developed economies. Figure 1 illustrates this case for the United States, using data (in billions of 2005$) from 1952 to 2008.1

2005 billions of $

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Fig. 1 Housing Wealth and Non-Housing Wealth in the United States - Both variables have been deflated with the deflator for Personal Consumption Expenditures

2. Housing wealth is larger than GDP, and fluctuates considerably over time. Figure 2 plots the ratio of nominal housing wealth to nominal GDP for the United States.2 The ratio of housing wealth to GDP has averaged around 1.5 between 1952 and 2008. However, it has moved dramatically throughout this period: it was equal to 1.27 at the beginning of the sample period; it was as low as 1.20 in 1962; and reached a value of 2.26 at the end of the 2005, at the peak of the recent housing boom.

1

The data source for housing wealth are the Flow of Funds Accounts of the United States. The details of data construction can be found in Iacoviello (forthcoming). 2 Most of the fluctuations in nominal housing wealth reflect movements in the price of housing, rather than movements in the stock.

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2.50 Housing Wealth over GDP 2.00

1.50

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Fig. 2 Ratio of Housing Wealth to GDP - Both numerator and denominator are expressed in dollar terms

3. Housing wealth and aggregate consumption expenditures tend to move together in post-World War II U.S. history. Over the 1952–2008 period, their contemporaneous correlation is 0.47 (using year-on-year real growth rates). Figure 3 illustrates the joint comovement between the two variables. This correlation is larger than the correlation between consumption and the residual components of household wealth: for instance, the contemporaneous correlation between changes in inflation-adjusted financial wealth and changes in consumption equals 0.38.3 4. Movements in housing wealth are typically accompanied by large movements in housing investment in the same direction.4 These movements in housing investment, in turn, substantially affect aggregate GDP and employment, even if the share of housing investment in GDP is relatively small.5 For instance, since its 2005 peak, the share of housing investment in GDP fell in half, from about 6 percent to 3 percent in about three years (see Figure 4): simple back-of-the-envelope economics suggests that this reduction has subtracted several percentage points from GDP growth throughout the same period. 3

It is this observation that had led many, in my view, to study the so-called housing wealth effect: see Iacoviello and Neri (2010) and Iacoviello (forthcoming) for further discussion of this topic and for additional references. 4 Part of this comovement reflect the simple fact that, by adding to the stock, an increase in housing investment will necessarily lead to an increase in housing wealth, holding prices constant. However, a larger fraction of this comovement might reflect the endogenous response of housing investment to exogenous changes in housing demand that jointly affect both the price and the quantity of housing: Iacoviello and Neri (2010) present a DSGE model that captures this mechanism. 5 The share of housing investment in GDP has been constant around 5 percent throughout the 1952-2008 period. The constant of this share reflects two offsetting forces: while real residential investment has not rises as fast as GDP over time, the price of residential investment has risen relative to the GDP deflator. See Iacoviello and Neri (2010) and Fisher (2007) for further discussion.

Housing in DSGE Models: Findings and New Directions

% 15

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Consumption, annual % change Housing Wealth, annual % change

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Fig. 3 Changes in Housing Wealth and Changes in Consumption Expenditures - Both variables are expressed in year-on-year growth rates and have been deflated with the deflator for Personal Consumption Expenditures

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Housing Investment to GDP (R) Housing Wealth, annual % change (L)

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Fig. 4 Changes in Housing Wealth and Ratio of Housing Investment to GDP - Housing Wealth has been deflated with the deflator for Personal Consumption Expenditures and is expressed in year-on-year growth rate. The Housing Investment to GDP ratio is the ratio of the two variables, both expressed in dollar terms

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5. Movements in the price of housing are only loosely connected to movements in other prices.6 Figure 5 plots consumer price inflation alongside two measures of house price inflation, the Census Price Index of new homes sold and the Freddie Mac Conventional Mortgage House Price Index.7 The contemporaneous correlation between quarter-on-quarter changes in consumer prices and house prices is in the 0.3–0.4 range, depending on the time period and the house price measure used. If anything, housing price inflation leads consumer price inflation by approximately two to three quarters, and this tendency is more pronounced in the last decades. In addition, house price inflation is more volatile than consumer price inflation: for instance, the standard deviation of quarter-on-quarter house price inflation (using the Freddie Mac Conventional Mortgage House Price index) from 1970 to 2008 is 1.19 percentage points. The corresponding number for consumer price inflation is 0.67 percentage points. This result also holds if one uses less noisy measures (such as year-on-year growth rates) of inflation.

% 20

Consumer Price (PCE) Inflation House Price Inflation (Census)

House Price Inflation (CMHPI)

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Fig. 5 House Price Inflation and Consumer Price Inflation - All variables are expressed in yearon-year growth rates

6. Housing (Residential Fixed) investment leads nonhousing (Nonresidential Fixed) investment, and is more volatile. This pattern can be seen in Figure 6.8 Peaks and troughs in housing investment generally precede peaks and troughs in business investment. This observation has led to the now-famous quote by Ed Leamer that “housing is the business cycle”.

6

My emphasis here is on unconditional correlations. It is possible that, once some other variables or exogenous shocks are factored in, conditional correlations might be larger. 7 The Census series starts in 1963. The Freddie Mac series starts in 1970. For this reason, I restrict my attention to observations from 1970 onwards only. See Rappaport (2007) for a survey of the differences between different house price measures for the U.S. 8 Fisher (2007) documents this result in detail and offers a DSGE model of housing that can explain this result. See also Davis and Heathcote (2005) for a related model.

Housing in DSGE Models: Findings and New Directions

% 60

Housing Investment Growth

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Fig. 6 Housing Investment and Nonhousing Investment - Both variables are chain-weighted and expressed in year-on-year growth rates

7. In U.S. data over the last 45 years, inflation-adjusted house prices display an upward trend, even after controlling for the boom and bust in prices of the last decade. Figure 7 illustrates this pattern. See Davis and Heathcote (2005) and Iacoviello and Neri (2010) for additional discussion on these issues.

220 200

Real House Prices, Census Real House Prices, Freddie Mac/OFHEO

180 160 140 120 100 80 1960

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Fig. 7 Real House Price Indices - Both Indices have been normalized to 100 in 1970Q1. Both series have been deflated with the deflator for Personal Consumption Expenditures

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These facts should be considered as an important yardstick to measure the success of macroeconomic models of housing. My experience with referees, discussants and colleagues tells me that, depending on tastes (as well as intellectual capital spent on each particular question), everyone has his own ranking of these facts. I do not want to take a stance here, and might have omitted other interesting facts about housing that some economist might regard as equally important.9

3 A DSGE model of housing Iacoviello and Neri (2010) add a rich housing sector to a framework that is increasingly used in quantitative monetary policy analysis. Their paper develops and estimates a DSGE model of the housing market that captures two important features of housing: on the supply side, sectoral heterogeneity allows capturing the different trend and cyclical properties of housing prices and housing investment relative to other prices and to other forms of demand; on the demand side, collateral effects of housing prices on borrowing allow for spillovers from the housing market to consumer spending. Versions of this model have been used at Riksbank (Sellin and Walentin, 2010), Norges Bank (Brubak, Elekdag and Maih, 2007), ECB (Lombardo and McAdam, 2008), European Commission (Roeger and in ’t Veld, 2009), Bank of Canada (Christensen, Corrigan, Mendicino and Nishiyama, 2009), Central Bank of Colombia (L´opez Enciso and Salamanca Lugo, 2009), IMF (Kannan, Rabanal and Scott, 2009), and elsewhere. In this section, I will briefly review the main elements of the Iacoviello and Neri model. Let me start with the production side of the economy. Iacoviello and Neri assume that the economy is best approximated by multiple sectors with different rates of technological progress. The non-housing sector produces consumption, business investment, intermediate goods (using capital and labor). The housing sector produces new homes, which add to the existing stock, using capital, labor, land, and intermediate goods. Following the lead of most of the DSGE literature, Iacoviello and Neri allow for nominal wage rigidity in both the non-housing and housing sector and allow for price rigidity in the non-housing sector. The multi-sector structure is meant to capture two important observations about the housing market: first, there is a long-run upward trend in the relative price of housing in post-world-war-II U.S. data, which is – at least in part – due to heterogeneous trend technological progress between housing and other sectors of the economy. Second, the production of hous9

I will mention here some additional facts that did not make the cut in the list above: (a) The production of housing services can be thought of as the combination of housing structures and land (Davis and Heathcote, 2005). (b) The purchase of a house is typically financed with a downpayment, with a mortgage making up for the difference between the purchase price and the downpayment. (c) Housing services can be either purchased or rented, depending on preferences, life-cycle motives, and institutional arrangements. (d) Finally, contrary to what many seem to believe, the ratio of consumption expenditures to housing expenditures tends to fall over the life cycle: in other words, old people consume relatively more housing than young people (see Yang, 2009).

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ing is land intensive: hence, the assumption that the same production mix is used to produce houses and other goods is too restrictive. On the demand side, Iacoviello and Neri split households into two types: patient (lenders) and impatient (borrowers). Patient households work, consume and accumulate housing: they own the productive capital of the economy, and supply funds to firms on the one hand, and to impatient households on the other. Impatient households work, consume and accumulate housing: because of their high impatience, they accumulate only the required net worth to finance the down payment on their home and are up against their housing collateral constraint in equilibrium. Along the equilibrium path, in turn, fluctuations in housing values affect borrowing and spending capacity of constrained households. Iacoviello and Neri use U.S. time series to estimate the model structural parameters and to ask a series of questions concerning the macroeconomic importance of housing market spillovers. Their main findings are: • The slow rate of technological progress in housing construction explains the upward trend in real housing prices of the last decades. Part of the trend growth reflects supply constraints from land, but their contribution is small (10% of the total trend increase in house prices). The remainder reflects different rates of technological progress. • The wage share of credit constrained households is estimated at around 20 percent. The credit constrained households are those who suffer (benefit) the most from drops (increases) in housing values. At the aggregate level, this fraction is large enough to amplify effects on consumption from fluctuations in housing values (especially for high values of the loan-to-value ratio). The presence of credit constrained households also reinforces the correlation between movements in consumption and movements in housing wealth.10 • Wage rigidity in the housing sector is crucial to explain important features of the data, in particular the large sensitivity of residential investment to changes in short-term interest rates: with flexible house prices, wage rigidity is important in making housing investment very sensitive to monetary shocks, something that is apparent in the data. The Iacoviello and Neri model can be used to assess sources of fluctuations in housing prices and quantities, can be used to quantify macroeconomic consequences of housing market shocks, and can be used to think about optimal responses to asset prices. In what follows, however, I will mainly indicate some directions in which I think and hope this setup can be extended to address topical questions in macroeconomics.

10

This effect occurs over and above the comovement coming from common shocks moving the two variables in the same direction.

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4 New directions 4.1 The role of financial intermediation The Iacoviello and Neri model is silent about the role of financial intermediation. In the model, financial intermediation occurs without frictions, since patient households can costlessly transform savings into loans using a constant returns to scale technology. This assumption, which is implicit in the neoclassical growth model, is equivalent to treating the financial sector as a veil. When thinking about the 2008 financial crisis, however, it is hard not to notice that one important effect of fluctuations in housing prices is linked to the potential effect of house prices movements on the balance sheet of financial intermediaries. In the Iacoviello and Neri model, it is only the borrowers who are hurt from declines in housing values: the model’s implicit assumption, in fact, is that borrowers will always honor their debts. As a consequence, lenders are virtually insulated from movements in housing wealth. Consider, instead, a financial crisis episode: reductions in house prices may lead to smaller repayments on part of the borrowers (some borrowers walk away from their obligations when the collateral is worth less than the face value of debt). The smaller repayments, in turn, may lead to reductions in the net worth of financial intermediaries. If financial intermediaries are able to absorb these losses raising capital elsewhere, the lack of repayment should be equivalent to a redistributive shock that should not generate large aggregate effects. Suppose, instead, that financial intermediaries themselves face credit constraints. In other words, assume that patient households lend resources to bankers, and that bankers lend resources to impatient households. If bankers face credit constraints (for instance, they need to satisfy some minimum capital requirement), a negative repayment shock can cause a loss for the lenders which, in turn, may cause an aggregate credit crunch. In ongoing work (Iacoviello, 2010), I develop a model along the lines developed above in order to study the role of bank in the transmission of financial shocks. This work complements the excellent work of many others who have developed models of banking and credit frictions in a general equilibrium context. A non-exhaustive list includes Gertler and Karadi (2009), Gerali, Neri, Sessa and Signoretti (2009), Angeloni and Faia (2009), Gertler and Kiyotaki (2009), Meh and Moran (2004), and Dib (2009).

4.2 The determinants of housing prices One important finding of the Iacoviello and Neri model is that a good part of the cyclical fluctuations in housing prices are viewed by the model as the outcome of “exogenous” preference shifts towards housing (the trend in house prices in U.S. data, as explained above, can be captured by heterogeneous rates of technological progress, namely slow technological progress in the housing sector relative to the

Housing in DSGE Models: Findings and New Directions

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consumption and business fixed investment sectors). This result holds even after regressing the estimated innovations to housing preferences against a large set of potential explanatory variables for housing demand that we do not explicitly incorporate in the model (such as population or mortgage origination fees or share of subprime mortgages in total mortgages). As with every shock, the issue of whether preference shocks are spontaneous, primitive and interpretable remains an open one: in the paper, we report the results of a search of newspapers’ articles for the period 1965-2006 trying to relate, from an informal standpoint, our estimated “preference” shocks to stories about the national housing market. Articles in the press often explain movements in the housing market with changes in housing demand that they could not immediately attribute to changes in fundamentals such as inflation, incomes and interest rates. To give a few examples, they refer to shifts in the housing market as coming from the “increased needs for privacy”, to “changes in tastes”, to the “desire to buy more housing than necessary”, to “faith in real estate as an investment”. Obviously, these explanations are only meant to be suggestive. It goes without saying that digging more in detail into the structural determinants of these shocks is an important topic for future research.

4.3 The time-series properties of housing price inflation Most microfounded DSGE models that incorporate asset prices (including house prices) generate – as an optimality condition of the model – an asset price equation which is purely forward looking in nature. This is true even for consumer price inflation: the baseline new-Keynesian model, for instance, predicts that inflation is a weighted average of current and future expected real marginal costs. As a byproduct of this result, house and consumer price inflation share one common – and somewhat undesirable – property: they are too forward looking relative to the data. In the data, there is a high degree of serial correlation in consumer price inflation (see for instance the survey paper by Fuhrer in the forthcoming Handbook of Monetary Economics). There are not many studies (that I know of) that have looked at the persistence properties of house price inflation, but, as Figure 5 shows, there is evidence of serial correlation in house price inflation. House price inflation persistence is slightly smaller than consumer price inflation persistence, but is present both in the Freddie Mac and in the Census measures of house prices. The Freddie Mac measure has a serial autocorrelation of 0.5. The Census measure is not serially correlated with its first lag, but has a positive correlation (around 0.25) with lags greater than the first. Why is house price inflation persistent, at least for some measures? As anybody who has bought or sold a house knows, there exist a variety of institutional features and social norms in the housing market that, at least in part, can explain sluggishness in house prices. To give some examples, one yardstick that sellers and their agent use when they first put homes on the market are “comparables”: the first listing price of a property is often based on the price of similar nearby properties sold up

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to 6 months before. Likewise, lenders will often commit to a mortgage that does not exceed the minimum between contract price and appraised price: to the extent that appraisers base their estimates on previous sales, lending criteria and ability to offer will depend on the past. In other words, there seems to be in the real estate practice lots of backward looking behavior: moreover, the potential for backward looking behavior is even larger in periods when the housing market is slow, since the decline in the number of transactions that is typical of housing slowdowns forces appraisers and real estate agents to go back further in time in an attempt to find the “right” price for a property. I am sure we would learn a lot if some of these insights could be incorporated in future DSGE models with housing.

4.4 How to stabilize house prices In earlier work (Iacoviello, 2005), I have found that monetary policy shocks affect house prices more than consumer prices: this result would suggest that, at least in principle, monetary authorities have the tools to mitigate fluctuations in housing prices. However, given the large fluctuations in house prices that are observed in the data, it is not clear whether interest rate policies only can successfully stabilize house prices, or, provided that they can do so, that they can stabilize house prices without causing excessive volatility in other macroeconomic variables. The above observation leads to a number of obvious questions: are there policy instruments that can be quantitatively successful in stabilizing house prices? Can tax credits (such as, for instance, the Worker, Homeownership, and Business Assistance Act of 2009) significantly affect housing demand and prices? Do “macroprudential” supervisory tools – such as those used by the Hong Kong Monetary Authority imposing caps on maximum loan-to-value ratios – work? Digging more into these issues – using DSGE models – seems to me a sensible way to address these questions.

4.5 Housing and the labor market The efficient functioning of an economy requires that factors of production are allocated where their marginal product is highest. This observation is especially true for the labor market in the United States, which, by most measures, features one of most dynamic labor markets in the world. However, it is possible that, when house prices fall, people are less willing to capitalize a loss on the property they own even if a better job opportunity arises elsewhere. If this argument holds, declines in house prices should impede labor mobility, and less labor mobility could have an impact on productivity. These arguments are fascinating, and one would like to see DSGE models that tackle this intuition more formally (see Head and Lloyd-Ellis, 2008, for a stylized model of housing and labor market search, and Sterk, 2010).

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5 Conclusions As the recent housing turmoil has shown, a better understanding of the workings of the housing market holds the key to a better understanding of macroeconomic fluctuations in general. My hope is that the next generation of DSGE models will devote increasing attention to modeling the housing market. Housing, for better or worse, is no small niche anymore.

References Angeloni, Ignazio, and Ester Faia (2009), A Tale of Two Policies: Prudential Regulation and Monetary Policy with Fragile Banks, Kiel Institute for the World Economy, Working Papers, No. 1569. Bernanke, Ben S (2008), Housing, Mortgage Markets, and Foreclosures, remarks at The Federal Reserve System Conference on Housing and Mortgage Markets, Washington, D.C. Brubakk, Leif, Selim Elekdag, and Junior Maih (2007), The Interactions Between Financial Frictions and Monetary Policy for Small Open Economies, IMF and Norges Bank, Working paper. Christensen, Ian, Paul Corrigan, Caterina Mendicino and Shin-Ichi Nishiyama (2009), Consumption, Housing Collateral, and the Canadian Business Cycle, Bank of Canada, Working Papers, 09-26. Davis, Morris A., and Jonathan Heathcote (2005), Housing and the Business Cycle, International Economic Review, 46, 3, 751-784. Dib, Ali (2009), Banks, Credit Markets Frictions, and Business Cycles, Bank of Canada, Working paper. Fern´andez-Villaverde, Jesus (2009), The econometrics of DSGE Models, SERIEs, 1. Fisher, Jonas D. M. (2007), Why Does Household Investment Lead Business Investment over the Business Cycle?, Journal of Political Economy, 115, 1, 141-168. Fuhrer, Jeff (2009), Inflation Persistence, in preparation for the Handbook of Monetary Economics. Gerali, Andrea, Stefano Neri, Luca Sessa, and Federico M. Signoretti (2009), Credit and Banking in a DSGE Model, Banca d’Italia, Working paper. Gertler, Mark, and Peter Karadi (2009), A Model of Unconventional Monetary Policy, NYU, Working paper. Gertler, Mark, and Nobuhiro Kiyotaki (2009), Financial Intermediation and Credit Policy in Business Cycle Analysis, NYU and Princeton, Working paper. Head, Allen, and Huw Lloyd-Ellis (2008), Housing Liquidity, Mobility, and the Labour Market, Queen’s University, Working paper. Iacoviello Matteo (2005), House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle, American Economic Review, 95, 739-764 Iacoviello, Matteo, and Stefano Neri (2010), Housing Market Spillovers: Evidence from an Estimated DSGE Model, American Economic Association, American Economic Journal: Macroeconomics, 2,2,125-64. Iacoviello, Matteo (2010),Financial Business Cycles, Federal Reserve Board, Working paper. Iacoviello, Matteo (forthcoming), Housing Wealth and Consumption, International Encyclopedia of Housing and Home, Elsevier. Kannan, Prakash, Pau Rabanal, and Alasdair Scott (2009), Monetary and Macroprudential Policy Rules in a Model with House Price Booms, IMF, Working paper. Leamer, Edward E. (2007), Housing is the business cycle, Federal Reserve Bank of Kansas City, Proceedings, 149-233.

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Lombardo, Giovanni and Peter McAdam (2008), Adding Financial Market Frictions to the NAWM, European Central Bank, Working paper. L´opez Enciso, Enrique, and Andr´es Salamanca Lugo (2009), El efecto riqueza de la vivienda en Colombia, Banco de la Rep´ublica, Colombia, Borradores de econom´ıa. Meh, Cesaire. and Kevin Moran (2004), Bank Capital, Agency Costs, and Monetary Policy, Bank of Canada, Working Paper No. 2004-6. Rappaport, Jordan (2007), A Guide to Aggregate House Price Measures, Federal Reserve Bank of Kansas City, Economic Review, issue Second Quarter: 41-71. Roeger, Werner, and Jan in ’t Veld (2009), Fiscal Policy with Credit Constrained Households, European Commission, DG ECFIN, Working paper. Sellin, Peter, and Karl Walentin (2010), Housing collateral and the monetary transmission mechanism, Riskbank, Working paper. Sterk, Vincent (2010), Home Equity, Mobility, and Macroeconomic Fluctuations, De Nederlandsche Bank and University of Amsterdam, Working paper. Woodford, Michael (2009), Convergence in Macroeconomics: Elements of the New Synthesis, American Economic Journal: Macroeconomics, 1, 1, 267-279. Yang, Fang (2009), Consumption Over the Life Cycle: How Different is Housing?, Review of Economic Dynamics, 12, 3, 423-443.

Part II

Housing and the Business Cycles

Country Analysis Housing and the Macroeconomy: The Italian Case Cyclical Relationships Between GDP and Housing Market in France: Facts and Factors at Play Does Housing Really Lead the Business Cycle in Spain?

Cross-Country Analysis Housing Cycles in the Major Euro Area Countries Common Business and Housing Market Cyles in the Euro Area from a Multivariate Decomposition The International Transmission of House Price Shocks

Housing and the Macroeconomy: The Italian Case Guido Bulligan

Abstract We present an empirical analysis of the role of the housing market and the macroeconomy in Italy. We analyze the cyclical properties of house prices and quantities and compare them with the aggregate economic cycle. We study the effects of monetary policy shocks on the housing market in a Structural VAR model with Italian data for 1990-2008. We find evidence that monetary policy strongly affects the behavior of real house prices and investment. Furthermore their response is significantly more sluggish than that of economic activity, suggesting that the housing market might contribute to the persistent propagation of the shocks hitting the economic system. Despite their influence on housing variables, monetary policy shocks are not the predominant cause of the volatility of residential investment and house prices.

JEL codes : E52, C32 Keywords : monetary policy, house price, business cycle, sign restrictions

1 Introduction In the last decade house prices in Italy have increased by almost 40 percent in real terms. The phenomenon is not specific to the Italian economy, as several industrialized countries have experienced similar and even stronger rises. It is neither new as already in the past house prices have recorded similar strong upward movements, followed by long lasting phases of stagnation or decline. However the recent financial crisis has renewed concerns that the expected downward correction associated with the end of the latest housing market expansion might occur disorderly Guido Bulligan Banca d’Italia, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_2, © Springer-Verlag Berlin Heidelberg 2010

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and hamper the already bleak economic outlook for much longer and more severely than anticipated. The debate at the academic and the policy level has highlighted the role played by several factors in the run-up of house prices, among which monetary policy has attracted particular interest. The long period of historically low nominal interest rates is often cited as one of the major causes of the increase in house prices and the associated rise in residential investment. However, other factors have also been under the spotlight. Among these the effect of innovation in the lending standards of financial institutions; on this aspect, despite a generalized convergence of credit markets spurred by greater competition and financial integration, conditions in European national markets remain substantially different. For instance, according to a survey (Mercer Oliver Wyman, 2003) on European mortgage markets the degree of market completeness varies greatly. The Italian housing finance market is ranked among the least complete: for instance, the average loan-to-value ratio, one of the variables included in the completeness index, is significantly lower than the European average; the typical mortgage duration is short, usually coinciding with the borrowers’ remaining working life; furthermore home equity withdrawal products are not available. Such institutional and economic arrangements coupled with cultural preferences for low indebtedness point to a rather limited role for financial acceleration effects and housing wealth effects on consumption.1 However, considering that the majority of outstanding and new mortgages is at variable rate, monetary policy and financial shocks might affect households’ consumption trough unexpected increases in the share of mortgage repayments over disposable income. Against this background our study explores the behavior of the Italian housing market over the business cycle with particular attention to the effect of monetary policy conditions. We exploit a house price index recently compiled at the Bank of Italy (Zollino et al., 2008) to describe the comovements of house price and residential investment with a set of macroeconomic variables over the last 40 years. Furthermore, we investigate the interplay between the housing market and monetary policy by resorting to a structural VAR (SVAR) analysis. The paper is organized as follows: section 2 has a pure statistical flavor and describes the relationship between the housing market and the macroeconomy over 40 years and sets the stage for the subsequent structural analysis. It follows both the “business-cycle” approach and the “growth-cycle” approach in describing a set of comovements and stylized facts. Section 3 expands the set of stylized facts by conditioning them on observing a restrictive monetary policy shock and assess the role of the latter in explaining the observed variability of housing prices and quantities. Section 4 concludes.

1

See Calza, Monacelli, Stracca (2007) for an analysis of the role of institutional factors on the housing channel of the transmission mechanism of shocks.

Housing and the Macroeconomy: The Italian Case

21

2 Cyclical analysis of the Italian housing market In order to investigate the relationship between the housing market and the macroeconomy we articulate the analysis in two parts. In the first one, we follow the classical “business cycle” definition of the cycle as recurrent and persistent fluctuations in the level of a time series and describe its main features in terms of duration, intensity, leading-lagging behavior at turning points, and synchronization with a set of important macroeconomic time series. The second approach followed here (“growth cycle” approach) focuses instead on deviations of a series from its long term component. Although in this case the results closely depend on a artificial and ultimately subjective decomposition of a time series into trend, cycle and short term noise, they shed light on aspects of economic fluctuations that would be otherwise left unexplained, such as periods of acceleration and deceleration, which cannot be classified as expansions and recessions in a “business cycle” sense. Furthermore by identifying a larger number of shorter cycles, the growth cycle approach allows a more robust analysis of leading/lagging relationships.

2.1 The “business cycle” approach The starting point of the classical analysis is the determination of a sequence of turning points on the level of the variables (TP, peaks and troughs), which allows to decompose a time series into a sequence of recessions and expansions. In a first stage, following a standard practice, detection of turning points is performed with the algorithm suggested by Bry and Boschan (1971). In a second stage, the sequence of selected TP is inspected in order to eliminate cyclical episodes either too shortlived or too mild to represents the medium term fluctuations that are the focus of this study. The dynamics of the real house price index suggests the following business cycle dating for the housing market: 1973Q3-1980Q1; 1980Q2-1987Q3; 1987Q41999Q1 (see figure 1 - where shaded areas signal periods of recessions in terms of house prices - and Appendix A for data description). The latest cycle started its expansionary phase in 1999 and seems to have reached a peak in 2007Q4.2 Based on this dating and excluding the ongoing cycle, expansionary phases last on average around 4 years (see Table 1), during which the average cumulated real price increase is around 40 percent. Recessions tend to last longer (on average 6 years), but the cumulated real decline in prices is significantly 2 At the time of writing the house price series was available untill the last quarter of 2008. Graphical inspection suggests that in 2008 real house prices had stabilized but not decreased yet. On the contrary, residential investment and employment in the construction sector had clearly peaked in the second half of 2007. At the end of 2009 the series of real house price has been revised and the cyclical peak estimated at the end of 2007 confirmed. Indeed, the new series shows a cyclical peak in 2008 during which the annual increase was -0.7%. In 2009 the series has further declined by 1.3 percent.

22

Guido Bulligan REAL HOUSE PRICE INDEX*

NOMINAL HOUSE PRICE INDEX

1.0

4

9.65

0.8

3

9.60

0.6

9.55

2 0.4

9.50 1

9.45

0.2

9.40

0

0.0

9.35

-0.2 1970

1975

1980

1985

1990

1995

2000

2005

-1 1970

EMPLOYMENT IN CONSTRUCTION 7.65

1975

1980

1985

1990

1995

2000

2005

85

90

95

00

05

0 1970

6.0 5.6

1980

1985

1990

1995

2000

2005

11.8

70

75

80

85

90

95

REAL OUTSTANDING MORTGAGE DEBT** 7.6 7.2

5.2

16

05

11.9 1975

EQUITY INDEX*

20

00

12.0

POLICY RATE 24

2005

12.1

4

80

2000

12.2

7.35

75

1995

12.3

8

70

1990

REAL GDP

12.4

12

7.30

1985

12.5

16

7.40

1980

12.6

7.55

7.45

1975

12.7

20

7.50

9.30 1970

INFLATION RATE (year on year) 24

7.60

7.25

REAL HOUSING INVESTMENT 9.70

6.8

4.8

12

6.4 4.4

8

0

6.0

4.0

4

5.6

3.6

70

75

80

85

90

95

00

05

3.2 1970

1975

1980

1985

1990

1995

2000

2005

5.2 1970

1975

1980

1985

1990

1995

2000

2005

Shaded areas represent housing market recessions * Deflated with CPI index ** Deflated with house price index

Fig. 1 Housing market variables and housing market recessions

smaller (23 percent) and is mainly accounted for by CPI inflation while nominal house prices stagnate. It is interesting to note how the duration of expansions has increased progressively since the 1970’s (from 1 year in the late 1970’s and early 1980’s to around 8 years in the latest upswing), while that of recessions is fairly constant. The cyclical behavior of residential investment mirrors closely that of real house prices. The series has experienced three complete cycles (from trough to trough). Qualitatively, the comparison of the turning points of the series of real prices and investment suggests a high degree of synchronization (troughs in investment leads those in prices on average by 2 quarters while peaks in the two series have on average occurred at the same time). Quantitatively, residential investment shows milder fluctuations than real prices: during expansions (recessions) cumulated increases (declines) in residential investment are around 12 percent from the previous trough (peak) level, to be compared to 40% for real prices. The close relationship between price and quantity in the housing market is also confirmed visually by the cyclical behavior of employment in the construction sector. Starting from the trough of 1979Q2, the series has experienced two complete cycles, whose turning

Housing and the Macroeconomy: The Italian Case

23

points show short leads and lags with respect to the peaks in residential activity and real house prices. Table 1 Descriptive statistics of housing market cycle House Price Sample 1970-2008 N. cycles (trough to trough) Expansions: average duration (quarters) Recessions: average duration (quarters) Expansions: average cumulated change (% points) Recessions: average cumulated change (% points) Average lead at peak (quarters)1 [min;max] Average lead at trough(quarters)1 [min;max]

Res. Inv.

Empl. Constr.

3 (4 ongoing) 3 (4 ongoing) 2 (3 ongoing) 9.3 24.7 42.3 -23.4 -

8.5 22 14.1 -11.3 0.0 [0;0] -2 [1;7]

15.8 25 9.7 -12.6 -1 [-4;1] 0.6 [-3;7]

Note to Table. House price: Real house price (deflated with CPI index). Res. Inv: Residential investment. Empl. constr: Employment in construction.; 1: + (-) corresponds to lead (lag) with respect to house price turning points.

Further support for a close relationship between price and quantity in the housing market is obtained by calculating their degree of synchronization. In table 2 we have calculated the cross-concordance index between the respective reference cycles (see Harding and Pagan, 2002). The index measures the relative amount of time two series spend in the same cyclical phase, after controlling for any lead/lag relationship, taking value of 1 at lead/lag zero for perfect positive synchronization (when the two series’ turning points exactly coincide) and a value of 0 at lead/lag zero for perfect negative synchronization (when two series’ turning point are always in opposition). According to this measure, real house prices are indeed strongly synchronized with residential activity, both measured as investment in residential construction as well as employment in the sector. In order to put such figures in the general economic context, the same analysis is repeated for GDP, inflation, a monetary policy interest rate, the real stock of mortgage debt and the real stock price index. These series have been found to be among the most important drivers of house price dynamics in several studies, reflecting the interaction between income, the opportunity cost of housing investments, credit availability and the role of housing as hedge against inflation (see for instance Sutton, 2002, Borio and McGuire, 2004, Tsatsaronis and Zhu, 2004). Significant values of synchronization are found only for the short term interest rate and inflation while in the case of GDP, the real equity price index and real stock of mortgage debt the coefficient is not significantly different from zero. The inflation cycle appears to be slightly ahead of the house price cycle.

24

Guido Bulligan

Table 2 Synchronization of cycles: cross-concordance index Real House Price with: Sample 1970-2008 Res. Inv.

Empl. Constr. GDP Inflation1 Policy rate Equity price index2 Stock of mortgage debt3

0.9∗∗∗ (0) 0.8∗∗∗ (0) 0.5 (-3) 0.6∗∗ (-1) 0.75∗∗∗ (0) 0.5 (0) 0.5 (0)

Note to Table. The table reports the maximum value of the concordance index between real house price and the variable in rows along with the quarterly lead(-)/lag(+) of the corresponding series with respect to real house prices. Res. Inv: Residential investment. Empl. constr: Employment in construction.; 1: year on year change of CPI index. 2: Deflated with CPI index. 3: Deflated with nominal house price index.** and *** significant at 5% and 1%.

2.2 The “growth cycle” approach The business cycle approach to comovements analysis is affected by the diverse frequency at which turning points occur in different series. Indeed, housing market variables show only few peaks and troughs when compared to macro variables. For instance, duration of house price cycles (from trough to trough) has varied between a minimum of 26 quarters and a maximum of 46 quarters compared to a minimum of 9 quarters and a maximum of 46 for GDP. In this section, to take into consideration such differences and to increase the robustness of synchronization measures, we focus on the cyclical comovements.3 The analysis is carried out by considering those fluctuations which are responsible for the behavior of a series at a specific cyclical horizon. In order to strike a balance between the observed durations of housing market cycles and of fluctuations in economic activity, inflation and interest rate, we focus on that component associated with fluctuations lasting between 3 and 10 years.4 Table 3 reports the maximal correlation coefficient (and the lead/lag at which it occurs) between the cyclical components of real house prices and of the other 3

The resulting (filtered) series are characterized by more cycles and therefore more turning points. The empirical literature has focused on cycles whose duration varies between 1.5 and 8 years. These values have been proposed for the US economy by Baxter and King (1999) who indirectly refer to the empirical work by Burns and Mitchell (1946). The application of these values to other economies and different time periods is therefore questionable (see Everts, 2006 and Agresti and Mojon, 2001). However results obtained with the standard parameters are similar and available from the author upon request.

4

Housing and the Macroeconomy: The Italian Case

25

variables over the period 1970-2008.5 The evidence indicates that house prices and residential investment are strongly positively correlated, with the latter leading the former by around one year.6 Further support for a leading role of quantity with respect to prices is found by looking at employment in the construction sector. The correlation between house price and GDP is not significant at lag 0, but increases at longer lags suggesting that cyclical fluctuations in real house prices follow the economic cycle with a two year delay. Further evidence is found by looking at GDP components, with households’ consumption (of durable as well as non durable) and non residential investment strongly leading house price by 1.5-2 years. Table 3 Synchronization of cycles: correlation between cyclical components Real House Price Residential investment Sample 1970-2008 Real house price

Res. Inv. Empl. Constr. GDP Inflation1 Policy rate Equity price index2 Stock of mortgage debt3

-

0.6

0.6 (-3) 0.7 (-2) 0.8 (-7) 0.8 (-3) 0.5 (-2) -0.4 (-8) -0.6 (0)

(3) 0.5 (3) 0.4 (-2) 0.6 (-1) 0.45 (4) -0.4 (-3) -0.6 (6)

Note to Table. The table reports the maximum value of the correlation coefficient between variable in column and variables in rows along with the quarterly lead(-)/lag(+) at which it occurs. Res. Inv: Residential investment. Empl. constr: Employment in construction.; 1: year on year change of CPI index. 2: Deflated with CPI index. 3: Deflated with nominal house price index.

This result is at odds with the evidence available for the Euro area (Musso et al., 2008), France, Spain and Germany, where house prices are found to be coincident or slightly leading with respect to economic activity.7 Residential investment are pro-cyclical and slightly lagging GDP, consumption and non residential investment (by 2 quarters). The result stands out when compared to the available international evidence for the Euro area (Musso et al., 2008) and US evidence (Leamer, 2007) and 5

The cyclical component is extracted with the filter proposed by Baxter and King (1999). A standard explanation for such temporal ordering is that weakness in demand affects transaction volumes and housing construction activity first, as sellers might prefer to wait before accepting to reduce their reserve price (Leamer, 2007) 7 See contributions in this volume. 6

26

Guido Bulligan

might partly be due the distorting effect of several fiscal incentives implemented in the last decade. Real house prices and to a lesser degree residential investment are positively correlated also with inflation and the policy interest rate. The lead-lag structure suggests that interest rates lag residential investment but lead house prices by few quarters. Real house prices are mildly negatively correlated with the real stock price index one year later. Finally, the cyclical component of real house prices is negatively correlated with that of the real stock of mortgage debt, suggesting that in absence of home equity withdrawal products, rising house prices have a standard negative effect on demand and therefore on mortgage applications. To add robustness to our results in Table 3 we have also computed the crosscorrelation with respect to the cyclical components of real house prices. The results bring further evidence to the lead/lag relationship uncovered so far: real house price tend to lag housing volume measures (residential investment and employment in construction) as well as aggregate economic activity. The relation with the policy rate and inflation is somewhat less strong but again there is evidence of house price lagging these variables. To summarize, the statistical evidence indicates that cycles in the housing market tend to last longer than the cycles observed in economic activity and other macroeconomic variables. Prices and quantities moves in synchronization, although prices are significantly more volatile. Expansions are usually shorter (although since the 1970’s, their duration has progressively increased) but more intense than recessions and the cumulated increases in real prices observed during the expansionary phases are only partially reabsorbed during the following recessions. Housing prices and quantities are strongly procyclical and lag economic activity by around one year. They are also positively correlated with inflation and the monetary policy interest rate. On the contrary, they are strongly negatively correlated with real mortgage debt.

3 A SVAR analysis of monetary policy and the housing market Having documented a set of stylized facts about the interaction between housing and macro variables, in this section we investigate the role of monetary policy (more specifically of its unpredictable component)in shaping the unconditional moments of the housing variables. We focus specifically on monetary policy shocks for two reasons. Firstly, the theoretical literature has studied extensively the conditions under which such shocks can be correctly identified and abundant empirical evidence is available as benchmark. Secondly, the recent debate has focused on the role that an over-expansionary monetary stance might have played in fuelling housing prices. We present two sets of results. A first set is derived from a recursive identification scheme, where the ordering of the variables critically reflects the identifying

Housing and the Macroeconomy: The Italian Case

27

assumptions. A second set of results is proposed where a structural non-recursive interpretation is given by imposing sign restrictions on the response of (some) variables to a monetary policy shock. While recursive VARs have been extensively used to make structural inference (see Christiano et al., 1999), they implicitly make strong assumptions on the temporal relationships among structural shocks. Identification of monetary policy shocks trough sign restrictions follows from acknowledging that a widespread agreement seems to have been reached among economists on the effects of monetary policy on several macroeconomic aggregates. According to Christiano et al. (1999) “The nature of this agreement is as follows: after a contractionary monetary policy shock, short term interest rates rise, aggregate output, employment, profits and various monetary aggregates fall, the aggregate price level responds very slowly [. . . ]”. Compared to a recursive scheme, a sign restriction approach seems to us more flexible as it can accommodate several models and different assumptions regarding the temporal relationships among variables. in both cases the analysis focus on the more homogeneous sample period 1990-2008. Monetary policy in Italy since the 1990’s can be well approximated by the stance of the short term interest rate, furthermore the structural relationships might have evolved from the high inflation and high volatility environment that characterized the 1970’s and the early 1980’s to the low inflation environment experienced afterward.

3.1 Housing in a monetary VAR: the recursive approach We start with a baseline model that includes a minimal set of variables necessary to analyze the interaction of monetary policy and the housing sector. In the baseline specification these variables are ordered as follows: the consumer price index (CPI), GDP, the nominal house price index (HP), residential investment (RI), and the short term interest rate (P.RATE). All variables enter in log-levels (except the policy rate; figure 1). We adopt a recursive approach to identify the structural shocks, so that the ordering of variables reflects our assumption on monetary policy and its transmission mechanism to the economy. Specifically, the non-policy block is ordered first, reflecting the view that the monetary authority sets the interest rate knowing the contemporaneous values of the price level, output, the house price level and of housing investment. It is further assumed that these variables react to interest rate changes only with a lag. Several studies adopt this ordering, claiming that output and prices are sluggish and react to policy decisions only with lags. The choice of the variables follows previous VAR studies of the interaction between monetary policy and the housing market (see for instance Giuliodori, 2004 and Vargas-Silva, 2008). The only difference consists in the fact that we use nominal house prices (HP) instead of real house prices (RHP), which however are recovered by construction from the behavior of nominal house price (HP) and that of the price level (CPI). The departure is dictated by our interest about the sign of the responses of both house prices and the general price level. Among exogenous variables, the baseline

28

Guido Bulligan

specification includes a world commodity price index, and four dummy variables.8 The first variable accounts for external price pressures, while the dummy variables mainly account for the interest rate turmoil in 1992 and 1995 and abnormal observations in the residential investment series associated with government legislative interventions; furthermore we include four lags in our VAR models in line with most quarterly VARs in the empirical literature.9 The effects of monetary policy shocks on the macroeconomy and the housing market can be analyzed through impulse-response functions and the forecast error decomposition. From the former, a one standard deviation restrictive monetary policy shock (corresponding to a 50 basis point increase in the policy rate; see figure 2) significantly affects GDP: output starts to contract significantly after three quarters and continues to decline up to six quarters after the shock, when its deviation from the baseline reaches almost 0.2 percentage points (pp).10

.0004

.0010

.002

.0005

.0000

.000

.0000 -.0004

-.002

-.0005

-.0008

-.004

-.0010 -.006

-.0015

-.0012

-.008

-.0020 -.0016 -.0020

2

4

6

8

10

CPI_L

12 CPI

14

16

18

20

-.0030

2

4

CPI_U

6

8

10

GDP_L

.002

.6

.001

.5

.000

.4

-.001

.3

-.002

.2

-.003

.1

-.004

.0

-.005

-.1

-.006 -.007

-.010

-.0025 12 GDP

14

16

18

20

4

6

8 RI_L

10

12 RI

14 RI_U

16

18

20

-.3

2

4

6

8

10

HP_L

12 HP

14

16

18

20

18

20

HP_U

.002 .000 -.002 -.004 -.006 -.008

-.2 2

-.012

GDP_U

2

4

6

8

P.RATE_L

10

12

P.RATE

14

16

18

P.RATE_U

20

-.010

2

4

6

8 RHP_L

10

12 RHP

14

16

RHP_U

continous line: median dotted lines: 16th (L) and 84th (U) percentiles

Fig. 2 Impulse-response functions: recursive approach

8

Dummy variables have been used for the following quarters:1992Q3, 1995Q2, 1995Q4, 1997Q4 and 1998Q1. 9 Lag-length criteria give discordant results so that the choice strikes a balance between non autocorrelated and normally distributed residuals and the precision of the estimated coefficients. Results not reported but available from the author. 10 The magnitude of the response is in line with results by Giuliodori (2004), Bonci and Columba (2006) and De Aracangelis and Di Giorgio (1998), after adjusting for the different size of the shocks.

Housing and the Macroeconomy: The Italian Case

29

Afterwards it slowly returns to its pre-shock level (twelve quarters after the shock the gap is no longer significant). The price level starts to decline only after two quarters, although it significantly deviates from its pre-shock level only after 6 quarters and, in line with previous studies for Italy (see Gaiotti, 1999), its response is less intense and more spread-out than output.11 Quantity and prices in the housing market react with different timing. Housing investment leads house prices by several quarters. The former start to significantly decline after 4 quarters, and the contraction is strong during the first 1.5-2 years, reaching a maximal deviation of 0.5 pp, after which it very gradually recovers. The reaction of nominal house prices is not significant during the first 8 quarters. The bulk of the effect shows up only in the third and fourth year after the shock, with a maximal deviation of 0.7 pp after 16 quarters. Overall, both quantity and prices in the housing market react more strongly to monetary policy than economic activity (at its trough the decline in investment is twice as big as that in GDP) and their return to pre-shock levels is significantly slower (it takes around 5 years for their response to be no longer significant, compared to 3 years for GDP). Given the limited reaction of the CPI index, the real house price mimics quite closely the behavior of nominal prices, declining consistently only after two years and deviating by 0.5 pp at their trough. Table 4 reports the share of the variance of each endogenous variable explained by monetary policy shocks at various horizons. They account for around 20 percent of output volatility at the 3 year horizon, while their contribution to price volatility is non-negligible only at longer horizons. With respect to price and quantities in the housing market, the analysis indicates that in the short run monetary policy shocks play a small role. Their contribution tends to increase at longer horizons (around 10 percent at the 5-year horizon).

3.2 Housing in a monetary VAR: a sign restriction approach The recursive VAR analysis suggests that monetary policy shocks have significant effects on the housing market in the medium term (3 to 4 years). However, their short run effects are not precisely estimated. Furthermore the reaction of the CPI index during the first three quarters, although insignificant, is wrong-signed. In order to check the robustness of previous results, we decided therefore to change identification strategy and to exploit theory-consistent information on the effects of monetary policy shocks.12 This approach, pioneered by Faust (1998), Canova and De Nicol’ (2002) and Uhlig (2005), consists of imposing sign restrictions on the impulse re11 In the first two quarters after the shock, the CPI index slightly increases, however the (16-84 percent) standard error bands show that the so called ”price-puzzle” is not significant. 12 Within the recursive approach the results obtained are robust to changes in the order of the variables in the VAR, to the use of different measures of interest rate (3months money market rate) and of the price level (GDP deflator) and to the inclusion of the bilateral exchange rate Lira/Deutsche Mark and of a real monetary aggregate (the real stock of M2).

30

Guido Bulligan

Table 4 Recursive VAR: forecast error variance decomposition CPI GDP HP RI P.RATE RHP Period 1 0.0 0.0 0.0 0.0 90.4 0.0 2

0.2 0.2 0.0 0.0

67.0

0.0

3

0.2 0.5 0.0 0.2

60.1

0.0

4

0.4 2.4 0.4 0.7

50.9

0.3

8

2.3 16.6 0.8 8.6

40.0

0.4

12

7.8 20.0 4.3 9.8

37.9

2.4

16

13.7 19.8 9.2 9.5

33.2

5.9

20

18.1 19.2 11.7 10.2

30.8

7.7

Note to Table. The table reports for each variable in column the share of its forecast error variance accounted for by monetary policy shocks, at several forecast horizons. CPI: Consumer Price index. GDP: Output. HP: House price index. RI: Residential investment. P.RATE: Policy rate. RHP: Real house price index.

sponse functions of some variables with respect to a set of structural shocks. By restricting the dynamic behavior of only a subset of variables, such identification scheme allows the researcher to take an “agnostic” approach on the response of the remaining variables. Furthermore, as several structural decompositions (“models”) are compatible with a given set of restrictions, it allows to quantify the uncertainty about possible outcomes, following a monetary policy shock. In other words, unlike the recursive scheme, confidence bands around the estimated impulse responses reflects the uncertainty about the true underlying model.13 We assume that after a monetary restriction, the response of the policy rate is non-negative, while that of real GDP, nominal house price and the consumer price index is non-positive. All restrictions are in place for two quarters. No restriction is placed on the response of housing investment. Such scheme leaves unrestricted the two variables of interest in the housing market: housing investment and real house prices. Indeed, recent theoretical work does not univocally pin down the effect of a monetary policy shock on the relative prices of durable goods (like housing). Following a restrictive monetary policy shock, the policy rate increases above the “optimal” level for three quarters before moving into expansionary territory for the next six quarters (see Figure 3).

13

The analysis does not take into consideration prameter uncertainty around OLS point estimates. Taking the latter into consideration would lead to wider confidence bands than those reported here (see figure 5 in appendix B).

Housing and the Macroeconomy: The Italian Case .0000

31

.0005

-.0002

.001 .000

.0000

-.0004

-.001 -.0005

-.0006 -.0008

-.002

-.0010

-.0010

-.003 -.004

-.0015

-.0012

-.005 -.0020

-.0014 -.0016

2

4

6

8

10

CPI_L

12 CPI

14

16

18

20

-.0025

-.006 2

4

6

CPI_U

8

10

GDP_L

.002

12 GDP

14

16

18

20

-.007

2

4

6

GDP_U

8

10

HP_L

.3

12 HP

14

16

18

20

18

20

HP_U

.002 .001

.000

.2

.000

-.002

-.001

.1

-.004

-.002 -.006

.0

-.003

-.008 -.010 -.012

-.004

-.1

-.005 2

4

6

8 RI_L

10

12 RI

14 RI_U

16

18

20

-.2

2

4

6

8

P.RATE_L

10

12

P.RATE

14

16

18

20

P.RATE_U

-.006

2

4

6

8 RHP_L

10

12 RHP

14

16

RHP_U

continous line: median dotted lines: 16th (L) and 84th (U) percentile

Fig. 3 Impulse-response functions: sign restriction approach

Nominal house prices decrease on impact by 0.2 pp and continue to fall up to 3 years after the initial shock, so confirming the highly inertial response obtained under the recursive scheme. Quantitatively the maximum deviation is 0.4 pp compared to 0.7 pp under the recursive scheme. Significantly different is the response of residential investment in the two identification methods considered here - namely recursive or with sign restrictions - (see Figure 4, which compares the IRFs displayed in Figures 2 and 3). Now the bulk of the response shows up on impact when investment declines by 0.6 pp (under the recursive scheme, a similar drop occurs only six quarters after the shock and coincides with the through, see figure 4).14 Afterwards, an almost steady return to equilibrium takes place. Interestingly, the response of real house prices does not change as dramatically. Real house prices fall on impact by 0.2 pp, the decline intensifying in the following 3 years, deviating by 0.3 pp at the trough (compared to a decline of 0.5 pp obtained under the recursive scheme) and then return towards their pre-shock level. Table 5 reports the percentage of model-responses compatible with a decline in residential investment and real house prices over several horizons: 80 percent of the models signal a reduction of residential investment one quarter after the policy shock. At the 4 and 8 quarter horizons, such percentage increases (to 90 percent), confirming the recursive VAR indication about the delayed reaction in the housing market. The probability of a negative response then declines to 70 percent at the 5 year horizon. Nearly all models 14 The response of residential investment is more similar to that obtained under the recursive scheme, if we impose the sign restrictions to hold for 4 quarters (results available upon request from the author).

32

Guido Bulligan

.0004

.0005

.001 .000

.0000

.0000

-.001 -.0005

-.002

-.0004 -.0010

-.003

-.0008

-.004

-.0015

-.005

-.0012

-.0016

-.0020

2

4

6

8

10

12

CPI_recursive

14

16

18

20

-.0025

-.006 2

4

6

CPI_sign

8

10

12

GDP_recursive

.000

.6

-.001

.5

14

16

18

20

4

6

8

10

12

14

16

18

20

16

18

20

HP_sign

.001 .000 -.001

.3

-.003

2

HP_recursive

.4

-.002

-.007

GDP_sign

-.002

.2 -.004 -.005

-.004

.0

-.006 -.007

-.003

.1

-.005

-.1 2

4

6

8

10

RI_recursive

12

14 RI_sign

16

18

20

-.2

2

4

6

8

10

P.RATE_recursive

12

14

16

18

20

-.006

P.RATE_sign

2

4

6

8

10

RHP_recursive

12

14

RHP_sign

continous line: recursive approach dotted Line: sign restriction approach

Fig. 4 Comparison of impulse-response functions between recursive and sign restriction approaches

are compatible with a reduction in the relative price of houses between 1 and 12 quarters after the shock. After 5 years still 60 percent of models are compatible with real house price below the pre-shock level. Overall, model uncertainty is very limited both at short and medium horizons and suggests that residential investment and relative house prices significantly react to unexpected changes in the monetary policy stance for several years after the initial shock. Table 5 Sign restricted VAR: model uncertainty Period after shock 1 4 6 8 12 20 RI 0.8 0.9 0.9 0.9 0.8 0.7 RHP 1 0.9 0.9 0.9 0.9 0.6 Note to Table. The table reports the share of admissable models that are compatible with a reduction in residential investment and in real house prices at several horizons. RI: Residential investment. RHP: Real house price index.

The analysis of the forecast error variance decomposition (see table 6) indicates that monetary shocks account for around 20 percent of residential investment volatility at the 3-year-horizon and slightly less at longer horizons. They play a smaller role in the variance of the nominal house price index (between 7 and 14 percent) and a negligible role in explaining the volatility of real house prices (between 4 and 6 percent). While the sign restriction approach leads to a slightly bigger role of monetary policy shocks in explaining housing market variability, the results are broadly in

Housing and the Macroeconomy: The Italian Case

33

line with those obtained under a recursive scheme in suggesting a marginal role for monetary policy innovations, especially with respect to real house prices. Table 6 Sign restricted VAR: forecast error variance decomposition CPI GDP HP RI P.RATE RHP Period 1 38.6 17.6 7.1 6.7 9.6 4.8 2

23.6 18.8 8.0 6.9

7.6

5.3

3

19.4 20.1 8.4 9.7

7.1

5.4

4

15.4 22.4 9.2 13.9

9.2

5.7

8

17.8 24.7 10.5 19.4

21.3

5.3

12

17.0 18.9 13.6 17.2

32.3

6.9

16

14.9 15.4 14.0 16.5

39.6

7.3

20

13.8 13.9 12.7 15.9

42.3

6.6

Note to Table. The table reports for each variable in column the share of its forecast error variance accounted for by monetary policy shocks, at several forecast horizons. CPI: Consumer Price index. GDP: Output. HP: House price index. RI: Residential investment. P.RATE: Policy rate. RHP: Real house price index.

To summarize, the VAR analysis supports the view that monetary policy shocks have significant and long-lasting effects on housing variables. Despite a greater degree of uncertainty on the quantitative size of the latter in the short term, we have found robust evidence that over the medium term horizon (3-5 years), housing investment and prices react strongly to changes in financing conditions. Furthermore the analysis also suggests that house prices react faster and more strongly than the general price level and that the return to equilibrium in the housing market is significantly slower than in the rest of the economy. Finally, variance decomposition indicates monetary policy shocks play a minor role in the observed variability of real house prices. This result does not imply that the historically low interest rates observed in Italy in the last decade have not contributed to the long expansionary phase in house prices. It points to the role of the systematic component of monetary policy (i.e. the estimated feedback rule) rather than to the deviations from it.

4 Conclusions The study extends the recent empirical literature on the role of housing markets in macroeconomic fluctuations, by providing new evidence on the Italian experience. Our results suggest that the housing market is characterized by long cycles whose

34

Guido Bulligan

duration is significantly longer than that observed for economic activity, interest rates and inflation. However, focusing on medium term fluctuations significant comovements emerge, which indicate that the housing market lags the economic cycle. The VAR-based evidence indicates that monetary policy strongly affects the behavior of real house prices and investment, furthermore their response is significantly more sluggish than that of GDP and its components, suggesting that the housing market as a whole might contribute to the persistent propagation of the shocks hitting the economic system. Despite its influence on housing variables, monetary policy shocks are not the predominant cause of the volatility of residential investment and house prices.

Acknowledgements I would like to thank Andrea Nobili, Francesco Columba, Riccardo Bonci and seminar participants at Banca d’Italia and at Banque de France. The opinions expressed are those of the author and do not involve the responsibility of Banca d’Italia. Any remaining errors are my own.

References Agresti, A. and Mojon, B. (2001) Some stylesed facts on the Euro-area business cycle, European Central Bank, Working Paper, No. 95. Altissimo F., Marchetti, D. J. and Oneto G. P. (2000) The Italian Business Cycle: Coincident and Leading Indicators and Some Stylized Facts, Banca d’Italia, Temi di Discussione, No. 377. Barsky, R, House C. and Miles K. (2007) Sticky Price Models and Durable Goods, American Economic Review, 97, 984-998. Bernanke, B. and Gertler M. (2005) Inside the Black Box: The Credit Channel of Monetary Policy Transmission, Journal of Economic Perspectives, 9, 27-48. Bonci, R. and Columba, F. (2008) Monetary Policy Effects: New Evidence from the Italian Flowof-Funds, Applied Economics, 40, 2803-2818. Borio, C. and McGuire P. (2004) Twin Peaks in Equity and Housing Prices, BIS Quarterly Review, March. Bry, G. and Boschan, C. (1971) Cyclical Analysis of Times Series: Selected Procedures and Computer Programs, NBER, Technical Paper, No. 20. Burns, A.F. and Mitchell, W.C. (1946) Measuring Business Cycles, in: NBER (eds.), Studies in Business Cycle, New York, Columbia University Press. Calza, A., Monacelli T. and Stracca, L. (2007) Mortgage Markets, Collateral Constraints, and Monetary Policy: Do Institutional Factors Matter?, CFS, Working Paper, No. 10. Canova, F. and De Nicol´o, G. D. (2002) Monetary Disturbances matter for Business Fluctuations in the G-7, Journal of Monetary Economics, 49, 1131-1159. Catte, P., Girouard N., Price R. and Andre, C. (2004) Housing Markets, Wealth and the Business Cycle, OECD, Economics department Working Paper, No. 394. Chiades P. and Gambacorta, L. (2004) The Bernanke and Blinder Model in an Open Economy: the Italian Case, German Economic Review, 5, 1-34. Christiano, L., Eichembaum, M. and Evans, C. (1999), Monetary Policy Shocks: What Have We Learned and To What End?, in: Taylor J. and M. Woodford (eds.), Handbook of Macroeconomics. Davis, M. A. and Heathcote, J. (2005) Housing and the Business Cycle, International Economic Review, 46, 751-784.

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De Arcangelis G. and Di Giorgio, G. (1998) In Search of a Monetary Policy Measure: the Case of Italy in the ’90s, Giornale degli Economisti ed Annali di Economia, 57, 297-324. De Arcangelis G. and Di Giorgio, G. (2001) Measuring Monetary Policy Shocks in a Small Open Economy, Economic Notes, 30, 81-107. Everts, M. (2006) Duration of Business Cycles, MPRA, Working Paper, No. 1219. Faust, J. (1998) The robustness of identified VAR conclusions about money, Carnegie-Rochester Conference Series in Public Policy, 49, 207-244. Fry, R. and Pagan, A. (2007) Some Issues in Using Sign Restrictions for Identifying Structural VARs, NCER, Working Paper, N. 14. Gaiotti E. (1999) The Transmission of Monetary Policy Shocks in Italy, 1967-1997, Banca d’Italia, Temi di Discussione, N. 363. Giuliodori, M. (2004) Monetary Policy Shocks and the Role of House Prices across European Countries, DNB, Working Paper, N. 15. Harding, D. and Pagan, A. (2002) Dissecting the cycle: a methodological investigation, Journal of Monetary Economics, 49, 365-381. Harding, D. and Pagan, A. (2006) Synchronization of Cycles, Journal of Econometrics, 132, 59-79. Jarocinski M. and Smets, F. (2008) House Prices and the Stance of Monetary Policy, Federal Reserve Bank of St. Louis Review, 90, 339-65. Kim S. (1999) Do Monetary Policy Shocks matter in the G-7 Countries? Using Common Identifying Assumptions About Monetary Policy Across Countries, Journal of International Economics, 48, 387-412. Kim S. and Roubini, N. (2000) Exchange Rate Anomalies in the Industrial Countries: a Solution with a Structural VAR Approach, Journal of Monetary Economics, 45, 561-586. King, R. and Baxter, M. (1999) Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series, Review of Economics and Statistics, 81, 575-593. Iacoviello, M. (2005) House Prices, Borrowing Constraints and Monetary Policy in the Business Cycle, American Economic Review, 95, 739-764. Iacoviello, M. (2000) House Prices and the Macroeconomy in Europe: Results from a Structural VAR Analysis, ECB, Working Paper, No. 18. Iacoviello, M. and Neri, S. (2007) The Role of Housing Collateral in an Estimated Two-Sector Model of the U.S. Economy, Boston College, Working Papers in Economics, No.659. Leamer, E. (2007) Housing is the Business Cycle, NBER, Working Paper, No. 13428. Lippi F. and Nobili, A. (2008) Oil and the Macroeconomy: a Structural VAR Analysis with Sign Restrictions, CEPR, Discussion Paper, No. 6830. McCarthy, J. and Peach, R. (2002) Monetary Policy Transmission to Residential Investment, Federal Reserve Bank New York Policy Review. Mercer Oliver Wyman (2003) Study on the Integration of European Mortgage Markets, European Mortgage Federation. Mishkin, F. (2007) Housing and the Monetary Transmission Mechanism, Federal Reserve Board, Finance, FEDS Working Paper, No. 40. Musso A., Neri, S. and Stracca, L. (2008) Housing Markets and the Business Cycles: What differences between the Euro Area and the US?, paper presented at the Deutsche Bundesbank and ZEW Manheim Conference on “What drive Asset and Housing Markets?”, October 20-21, 2008. Neri S. (2004) Monetary Policy and Stock Prices: Theory and Evidence, Banca d’Italia, Temi di Discussione, No. 513. Rubio-Ram´ırez, J. F., Waggoner, D. and Zha, T. (2005) Markov Switching Structural Vector Autoregressions: Theory and Application, Federal Reserve Bank of Atlanta Working Paper, No. 27. Sims, C.A. and Zha, T. (1999) Error Bands for Impulse Responses, Econometrica, 67, 1113-1156. Sutton G. (2002) Explaining Changes in House Prices, BIS Quarterly Review. Tsatsaronis, K. and Zhu, H. (2004) What drives Housing Price Dynamics: Cross-Country Evidence, BIS Quarterly Review. Uhlig, H. (2005) What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure, Journal of Monetary Economics, 52, 381-419.

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Vargas-Silva, C. (2008) Monetary Policy and the US Housing market: a VAR Analysis Imposing Sign Restriction, Journal of Macroeconomics, 30, 977-990. Zollino, F., Sabbatini, R. and Muzzicato, S. (2008) Price of Residential Property in Italy: Constructing a New Indicator, Banca d’Italia, Quaderni di Economia e Finanza, No. 17.

Appendix A - Data description House price index: Aggregate index for Italy based on Zollino et al. (2008). Source: Il Consulente Immobiliare survey. The survey is conducted every six months and reports the average price of sales made in a set of cities that currently includes all the provincial capitals and approximately 1400 other municipalities. Prices refer to three type of dwellings, according to their location (centre; semi-centre; outskirt). Prices are further divided in relation to the property’s state of repair (new houses; recently built houses). Aggregation to a national price index is obtained on the basis of the distribution of the population and of the housing stocks. Homogeneity in the time series is obtained by imputing missing observations and correcting anomalous ones at the micro-level (see Zollino et al. 2008 for further information). The quarterly series is obtained by interpolating semi-annual data on the basis of the deflator for residential investment. Residential investments: Quarterly National Accounts chain index value of investments in residential construction. Source: ISTAT. Employment in construction sector: Number of employed people. Source: ISTAT. GDP: QNA chain index value of gross domestic product. Source: ISTAT. CPI: consumer price index. Source: ISTAT. Policy rate: short-term interest rate. From 1980 to 1981: average interest rate on fixed term advances. From 1982 to 1998: auction rate on repurchase agreements between the Bank of Italy and credit institutions. From 1999: interest rate on main refinancing operations of the ECB. Source: Bank of Italy. Equity share price index: MIBTEL index (Quarterly average). Source: Datastream. Stock of mortgage debt: outstanding stock of mortgage debt. Source: Bank of Italy. Exchange rate: Lira/Deutsche mark. Source: Datastream. Commodity Price Index: commodity price index. Source: IMF.

Housing and the Macroeconomy: The Italian Case

37

Appendix B - VAR identification We assume that the model can be estimated through a VAR in reduced form: yt = B(L)yt−1 + εt

(1)

where B(L) is a lag polynomial of order p and y is a n x 1 vector of endogenous variables and ε the vector of reduced form residuals with variance-covariance matrix Σ . The corresponding structural VAR is A0 yt = A(L)yt−1 + ut

(2)

where A(L) = A0 B(L) is a lag polynomial of order p and the matrix, A0 is the matrix that describes the contemporaneous relationship among the endogenous variables and ut = A0 εt is the vector of structural shocks. Identification amounts to impose a set of restrictions to the matrix A0 that uniquely solves - up to orthonormal transformation- the following system of equations: A0 A′0 = Σ

(3)

Under a recursive scheme, the identification amounts to assume that the matrix A0 is lower triangular. This corresponds to imposing n x (n-1)/2 restrictions on the contemporaneous relationships among structural disturbances that allow to exactly identify the model. Each (n x 1) column vector a j of the matrix A0 contains the impact effects of the j-th structural shock on the n endogenous variables. By multiplying the vector a j by the lag polynomial B(L) it is possible to recover the vector of effects of responses to the j-th structural shock at any horizon k after the shock. Under a sign restriction approach a set of restrictions is imposed on the effect of the j-th structural shock on a subset of endogenous variables for K periods. For a given set of restrictions there exist a set of (n x n) matrices S0 which satisfy them. Given a matrix S0,i belonging to S, any other identification matrix can be obtained as the product of S0,i by an orthonormal matrix H. In other words, the sign restriction approach does not identify one single model but a set of admissible “models”. As a consequence, for a given set of restrictions, a set of admissible impulse response functions is identified whose distribution reflects the range of compatible “models”. When, as in the main text, the estimated coefficients of the B(L) polynomial are kept fixed, such conditional distribution can be probabilistically interpreted as “model”-uncertainty. To take into account uncertainty around OLS estimates (“sample” uncertainty), it is assumed that the posterior density for the reduced form VAR under sign restrictions is proportional to a Normal-Wishart. In figure A1 we report the median and the 16th and 84th percentile of the distribution of the impulse response functions under sample and model uncertainty.

38

Guido Bulligan .002

.004

.001

.000

.000 -.004 -.001 -.008 -.002 -.012

-.003 -.004

2

4

6

8

10

GDP_L GDP_L

12

14

GDP GDP

16

18

20

-.016

4

6

8

10

RI_L RI_L

.004

.006

.002

.004

.000

.002

-.002

.000

-.004

-.002

-.006

-.004

-.008

-.006

-.010 -.012

2

GDP_U GDP_U

12 RI RI

14

16

18

20

18

20

RI_U RI_U

-.008

2

4

6

8 HP_L HP_L

10

12 HP HP

14

16 HP_U HP_U

18

20

-.010

2

4

6

8 RHP_L RHP_L

10

12 RHP RHP

continous lines: only model uncertainty (16th 50th and 84th percentiles) circled lines: sample and model uncertainty (16th 50th and 84th percentiles)

Fig. 5 Impulse-response functions: sample and model uncertainty

14

16 RHP_U RHP_U

Cyclical Relationships Between GDP and Housing Market in France: Facts and Factors at Play Laurent Ferrara and Olivier Vigna

Abstract In this paper we focus on cycles and trends of some macroeconomic and housing market variables representative of the French economy. In a first part, we empirically show that cycles in the housing sector, measured by housing prices, housing starts, building permits, sales or residential investment, are strongly correlated to GDP cycles with a lead lying between of one and four quarters, suggesting thus that a monitoring of housing fluctuations could bring useful information for macroeconomic forecasting. Interestingly, this result is robust to the various considered approaches. Moreover, it seems that the housing sector long-term trend possesses its own dynamics, quite different from the aggregate French economic activity. Thus, in a second part, we review various structural factors that could drive housing market developments in France in the future.

JEL codes : E20, E32, R21 Keywords : Economic cycles, Housing market, France

1 Introduction Strong empirical evidence of relationships between macroeconomics and the housing sector have been recently underlined in many research papers. For example, Mullbauer and Murphy (2008) have surveyed the multiple interactions between housing markets and the macroeconomy, with applications to US and UK data, and Goodhart and Hofmann (2008) have shown evidence of a multidirectional link beL. Ferrara Banque de France, e-mail: [email protected] O. Vigna Banque de France, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_3, © Springer-Verlag Berlin Heidelberg 2010

39

40

Laurent Ferrara and Olivier Vigna

tween house prices, monetary variables and the macroeconomy, based on data for 17 industrialized countries. Among these papers, several authors have also focused on dependence among macroeconomic and housing market in term of cycles. In this respect, cyclical analyses often involve the concept of business cycle, see for example Leamer (2007) or Vargas-Silva (2007) for applications on US data. The business cycle refers to the level of the activity and delimitates periods of expansions (basically positive growth rate) from periods of recessions (negative growth rate). When dealing with European industrialized countries, especially France, recessions are a little less frequent and less intense since the end of World War II in comparison with US recessions. This stylized fact leads us to focus on the concept of deviation cycle (or growth cycle) resulting from the decompostion of variables between a long-term trend and a medium-term cycle. Recently, in France, both macroeconomic activity and housing markets have been strongly affected by the consequences of the US sub-prime crisis, as in many other ´ countries (see for example Andr´e, 2009, Alvarez et al., 2010, or Ferrara and Koopman, 2010, for recent international comparisons). For example, according to the first release of Quarterly National Accounts (QNAs) for the second quarter of 2009,1 GDP growth rate in France was negative from the second quarter of 2008 to the first quarter of 2009, that is four consecutive quarters of negative growth. At the same time, from August 2008 to July 2009, 420 764 building permits have been delivered, that is a drop of 18.7% by comparison with the same period one year before. Regarding house prices, the latest available figures at that period revealed that the quarterly hedonic index for existing dwellings estimated by notaries and Insee had experienced four consecutive falls since the third quarter of 20082. Our aim is to know whether this synchronised evolution between macroeconomics and housing markets is a stylized fact and has been already observed in the past or it is only short-lived event that will not impact on long-term fluctuations of both sectors. In this paper we focus on deviation cycles and trends of some macroeconomic and housing market variables representative of the French economy. In a first part, we empirically show that deviation cycles in the housing sector are strongly correlated with macroeconomic cycles with a significant lead, suggesting thus that a monitoring of housing fluctuations could bring useful information for macroeconomic forecasting. In a second part, it seems that long-term trend of the housing sector activity possesses its own dynamics, quite different from the aggregate economic activity in France. We review various assumptions on structural variables suggesting that the downturn in the French housing sector in 2008-09 might be temporary.

1 2

Released on August 15, 2009, by Insee, the French Statistical Institute Information Rapide released by Insee on September 10, 2009

Cyclical relationships in France

41

2 Comparison of cycles In this section, our aim is to compare macroeconomic growth cycles3 based on French GDP with some housing market variables. Regarding variables related to the housing sector, we first consider real house prices deflated with the HICP 4 . We use the index for existing dwellings as released by Insee and French notaries (see Gouri´eroux and Laferr`ere, 2009, for details), which has been internally backcalculated until 1980 Q1. Then we also consider various variables such as sales of new dwellings, household investment, employment in construction, permits, housing starts and IPI in construction. We also integrate into the analysis a survey by housing industrials carried out by the European Commission, especially the Confidence indicator in the construction sector. National account data are chain-linked and computed by Insee. In order to have a common sample size, data are analysed from 1980 Q1 to 2009 Q2.5 Note that housing starts and industrial production index (IPI) only starts respectively in 1986 and 1990 and the EC survey starts in 1985. Last, we also consider in the analysis long and short interest rates (10-years government bonds and 3-months Euribor6, respectively). From a methodological point of view, when dealing with growth cycles, the question that arises is how to extract them from macroeconomic variables, knowing that diverse methods can lead to various estimated cycles (Canova, 1998). Several statistical approaches have been put forward in the literature to decompose a macroeconomic time series between trend and cycle. In this paper, we use the 2-step version of the Hodrick-Precott (HP) filter that considers that the HP filter can be designed as a low-pass filter with a cut-off frequency ω0 and therefore enables to apply a bandpass filter by difference of two low-pass filters. This approach is described in details in the paper of Artis, Marcellino and Proietti (2004). This version of the filter avoids a too noisy growth cycle, but there is still the issue of the choice of the parameter λ in the filter. According to Artis, Marcellino and Proietti (2004), the relationship between the cut-off frequency ω0 of the HP low-pass filter and the parameter λ is given by :  −1 λ = 4(1 − cos(ω0 ))2 . For example, when dealing with quarterly data, λ = 1600 corresponds to a 10-year cycle, λ = 677 corresponds to a 8-year cycle, λ = 215 corresponds to a 6-year cycle and λ = 1 corresponds to a 1.5-year cycle. Thus a band-pass filter with a bandwidth 1.5-8 years is specified as the difference of two HP filters estimated with λ = 677 and λ = 1.

3 4 5 6

In this paper, the terms ’growth cycles’ and ’deviation cycles’ will be used interchangeably. The HICP is seasonally adjusted and back-calculated by the ECB. At the time the paper was written, only 2009 Q1 was available for prices and housing starts Data are stemming from OECD

42

Laurent Ferrara and Olivier Vigna

Preliminary results on French data have shown that non-parametric filters, such as those put forward by Hodrick and Prescott (1997), Baxter and King (1999) or Christiano and Fitzgerald (2003), provide basically the same set of turning points. ´ We refer also to the paper of Alvarez and Cabrero (2010, this volume) for a comparison of filtering methods on this kind of data. Thus, we focus only on the 2-step version of the HP filter with a window between 1.5 and 8 years. From a practical perspective, all series are taken in logs before filtering and are expressed in percentage (see Figures 7, 8 and 9, in Appendix). Estimations are carried out using the RATS sofware. We carry out the analysis until 2009 Q2, knowing that the last estimated points are subject to revision because of end-point effects inherent to filtering techniques. In this empirical analysis, we are looking for relationships between economic cycles and housing market cycles. In this respect, we provide two types of analysis, first in terms of correlation coefficients, second in terms of cyclical turning points based on concordance indexes.

2.1 Correlation analysis In this part, we aim at pointing out possible correlation between economic and housing cycles. First, we focus on contemporaneous correlation coefficients between the various variables, presented in the upper diagonal of Table 1. In the first row of Table 1, we note that GDP is highly correlated with household investment (0.80) what is an expected result insofar as it is a component of GDP, but also with employment in construction (0.72). IPI in construction and short-term interest rates present also a significant correlation with GDP. A more detailed analysis of this contemporaneaous positive correlation between GDP and short-term interest rates

Table 1 Contemporaneous correlation (upper diagonal) from 1980 Q1 to 2009 Q2. GDP H. Prices Sales Invest. Employ. Survey Short Long Permits Starts IPI

GDP Prices Sales 1 0.44 0.01 1 0.20 1

Invest. Employ. Survey Short Long Permits Starts IPI 0.80 0.72 0.57 0.68 0.53 0.32 0.45 0.60 0.60 0.54 0.48 0.18 0.19 0.61 0.62 0.26 0.23 0.21 0.10 -0.37 -0.42 0.38 0.40 -0.40 1 0.65 0.53 0.46 0.39 0.40 0.57 0.39 1 0.46 0.56 0.64 0.17 0.22 0.57 1 0.28 0.21 0.39 0.40 0.31 1 0.57 0.10 0.09 0.60 1 -0.13 0.05 0.54 1 0.67 0.13 1 0.31 1

Note: ’Short’ and ’Long’ refer to short term (3 months) and long term (10 years) interest rates, respectively.

Cyclical relationships in France

43

cycles is given below. Rather high correlation coefficients can also been observed between prices and household investment (0.60), housing starts (0.62) and permits (0.61), suggesting that housing activity in volume and house prices share common medium-term fluctuations. We also note negative correlation between housing sales and interest rates cycles (short and long interest rates cycles are mutually positively correlated), which is in line with the economic theory. Overall, those contemporaneous correlation measures appear quite small in comparison to what could be expected. In this respect, we focus now on cross-correlation coefficients. In order to take leads and lags into account, we compute cross-correlations among all the deviation cycles. The various cross-correlations with GDP are presented in Figure 10 (in Appendix). High correlation coefficients for negative values on the x axis indicate that the series is leading the business cycle, and conversely positive values imply a lagging behaviour of the series relative to the business cycle. From these graphs, it turns out that variables reflecting the housing cycle (house prices, sales, household investment, building permits, housing starts) lead the GDP growth cycle with a varying advance. For example, it seems that sales possess a larger advance than prices and household investment. Housing prices cycle is certainly a bit more resilient than the housing sales cycle. Concerning the two variables related to production in volumes (permits and starts), we note that, due to administrative delays, permits cycle obviously leads the housing starts cycle.7 Last we notice that IPI in construction and employment in construction are coincident with economic activity.

Table 2 Maximum cross-correlation coefficients and corresponding leads/lags between housing and other macroeconomic variables (from 1980 Q1 to 2009 Q2)

GDP H. Prices H. Sales Investment Employment Survey Short rate Long rate Permits Starts IPI

GDP Prices 0.64 -2 -3 -2 0 +1 0 +2 -1 +1 0 +3 -8 +3 -4 0 -1 0 0 +2

Sales Invest. Employ. Survey Short Long Permits Starts IPI 0.48 0.80 0.72 0.58 0.68 -0.52 0.58 0.62 0.60 0.36 0.70 0.71 0.50 0.54 0.44 0.61 0.62 0.43 0.60 0.27 0.35 -0.37 -0.49 0.44 0.61 -0.49 +3 0.69 0.53 0.50 0.54 0.63 0.70 0.39 +7 +1 0.55 0.56 0.64 0.52 0.47 0.57 +3 0 -2 0.37 -0.41 0.42 0.44 0.38 0 +1 0 +2 0.59 0.44 0.43 0.62 -1 +3 0 -7 -1 -0.48 -0.47 -0.52 +1 -3 -4 -2 -5 +6 0.69 0.58 +2 -1 -4 -1 -4 +5 +1 0.54 -2 0 0 +2 -1 +8 +4 +3

Note: a negative number indicates that the series in row leads the series in column with an advance equal to this number, and conversely.

7 Figures of building permits and housing starts between 2007 and 2008 should be taken with caution because of an administrative reform that led to a statistical bias in the data collection process.

44

Laurent Ferrara and Olivier Vigna

Turning to financial variables, it appears that long term interest rates movements and the GDP growth cycle are quite coincident, while short term interest rates seem slightly delayed with GDP growth cycle. Moreover, the correlation coefficient between long term interest rates and the GDP growth cycle also posts a negative sign when considering eight quarters earlier. As the cross-correlation is the highest for 8 quarters and negative in that case, it comes out that the lower long term interest rates are, the higher GDP growth rate should be two years later. But an essential finding is that, all in all, variables describing the housing market activity tend to lead the economic cycle.

Invest

0.7

Employ Short

0.6

Prices Starts Permits

IPI Survey

Long

0.5

AbsCorrelation

0.8

0.9

For a more specific interpretation, the highest cross-correlations and their corresponding leads-lags (in quarters) are presented in Table 2. Maximum correlation coefficients are on the upper diagonal while their corresponding lags are on the lower diagonal. A negative value in the lower diagonal indicates that the variable in row leads the variable in column with an advance equal to this figure, and, conversely, a positive value indicates that the variable in row lags the one in column. For example, the correlation between GDP and housing prices is of 0.64, this latter variable being leading with 2 quarters.

0.4

Sales

−10

−8

−6

−4

−2

0

2

Lag

Fig. 1 Leads and lags versus absolute correlation coefficients between GDP and various variables

Cyclical relationships in France

45

First, we note that values are larger than previously when we focused only on contemporaneous correlations, implying thus that taking dynamics into account leads to a more informative analysis. In particular, correlation coefficients are noteworthy between employment in construction and real house prices (0.71), GDP (0.72) and household investment (0.69). It is indeed noticeable that employment is coincident with GDP but lags residential investment with one quarter and housing prices with two quarters. High correlation coefficients also appear between housing starts and both residential investment and building permits (0.70 and 0.69 respectively). We note that the chronology is respected in the sense that permits leads housing starts with a lag of one quarter. Cyclical relationship between residential investment and housing prices is also strong and positive (coefficient equal to 0.70), prices leading with one quarter. This observation suggests that housing investment is accompanied with rising house prices due to supply constraints in the short run. The highest cross-correlation is posted by GDP and residential investment (0.80), the link being contemporaneous. All these results are summarized in Figure 2.2.2 where optimal leads and lags of the various variables with GDP are represented, as well as corresponding correlation coefficients (for the sake of presentation we plot absolute correlation coefficients).

2.2 Turning point analysis Starting from the previously extracted growth cycles, we estimate the dates of peaks and troughs by using a quarterly version of the Bry-Boschan algorithm (BBQ algorithm by Harding and Pagan, 2002). In fact, as the series are extremely smooth, peaks and troughs can be detected unambiguously. We carry out the analysis until Q2 2009, but the last turning points are subject to revision and therefore the analysis over the recent past has to be taken with caution. 2.2.1 Lead/Lag analysis Estimated dates of peaks and troughs are presented in Table 5 (in Appendix) in which leads and lags of the turning points of each variable are also presented in comparison with turning points in the GDP growth cycle. In this part, we use GDP as the reference cycle and we will compare other variables to it. From Table 5 (in Appendix), we first observe that turning points in the GDP growth cycle are shared by the other variables under review.8 In this sense, we point out the existence of a growth cycle which is common to all the variables. The difference lies in the fact that the other variables may present some idiosyncratic extra8

Recall that IPI series only starts in 1990.

46

Laurent Ferrara and Olivier Vigna

cycles not visible in GDP. For example, the short-term and long-term interest rates present two supplementary cycles (in 1991-92 and 1998-99 and in 1987-89 and 2004-05, respectively). A striking feature in Table 5 (in Appendix) is that, on average, almost all turning points in housing-related variables lead turning points in the macroeconomic cycle. Indeed, we observe that housing prices, sales, housing starts and permits are leading the GDP growth cycle. The advance ranges between 4 quarters, for permits, and 2 quarters, for other housing-related variables. It is noteworthy that the advance of prices, sales, residential investment and housing starts is similar, close to two quarters. Moreover, the business survey in construction also possesses a lead of around one quarter over the macroeconomic cycle, with a standard error of 1.4. This result means that this survey could be of great interest to economists for the monitoring and forecasting of short-term economic fluctuations. Employment and IPI in construction are rather lagged over the GDP growth cycle (around one quarter). In fact, IPI is coincident for all turning points, the positive lag being only due to the trough in 2004 Q4, strongly lagged (6 quarters). Thus, IPI in construction should be reasonably caracterized as a contemporaneous variable. Last, short-term and long-term interest rates are the variables among the selected ones whose turning points are on average the closest to the GDP growth cycle turning points, with a coincidence for both interest rates (see Figure 2). However, in addition to the relatively higher volatility for such financial variables compared with real variables, the role of both variables is ambiguous because they can have also a counter-cyclical property as suggested in the previous section.

Table 3 Contemporaneous concordance indexes (from 1980 Q1 to 2009 Q2) GDP H. Prices Sales Invest. Employ. Survey Short Long Permits Starts IPI

GDP 1 0.72 0.64 0.75 0.79 0.80 0.77 0.74 0.70 0.80 0.81

Prices Sales Invest. Employ. Survey Short Long Permits Starts IPI 1 0.56 0.81 0.75 0.80 0.58 0.73 0.72 0.82 0.64

1 0.53 0.54 0.67 0.54 0.44 0.66 0.69 0.40

1 0.79 0.81 0.65 0.69 0.70 0.87 0.72

1 0.71 0.66 0.69 0.63 0.71 0.85

1 0.66 0.59 0.82 0.84 0.72

1 0.66 1 0.54 0.59 0.64 0.67 0.74 0.65

1 0.86 0.56

1 0.63 1

Note: ’Short’ and ’Long’ refer to short term (3 months) and long term (10 years) interest rates, respectively.

Cyclical relationships in France

47

2.2.2 Concordance analysis of turning points In order to assess synchronization among the variables, the concordance index allows to estimate the fraction of time that cycles are in the same phase (ascending or descending)9. Let (Sit )t denotes the binary variable that represents the phase of the cycle (ascending: Sit = 0, descending: Sit = 1) for a given country i. In the bivariate case, for two variables i and j, the concordance index CI can be expressed in this way: 1 T CI = ∑ It , (1) T t=1 where It = Sit S jt + (1 − Sit )(1 − S jt ).

(2)

At each date t, for all (Sit , S jt ) ∈ {0, 1}, It is equal to 1 when Sit = S jt and equal to 0 when Sit = (1 − S jt ). This tool is very interesting in empirical studies to assess the synchronization between two cycles, although it possesses some shortcomings pointed out by Harding and Pagan (2002). Concordance indices are presented in Table 3. We note that the GDP growth cycle is well synchronized (CI ≥ 0.80) with housing starts and IPI in construction, as well as with the business survey in the construction sector. High concordance indexes also appear between GDP and residential investment, employment and interest rates. Strong synchronization also appear among variables of the housing sector such as housing starts and residential investment or permits. In order to get statistical evidence of the relationship between economic and housing cycles, we carry

Table 4 Contemporaneous concordance indexes (CI), maximum cross-concordance indexes (CCI) and t-stat of the Harding-Pagan test (from 1980 Q1 to 2009 Q2) for various variables with GDP cycle

Prices Sales Invest. Employ. Survey Short Long Permits Starts IPI

CI Contemp t-stat CCI Lead/Lag t-stat 0.72 0 3.40 0.77 -2 4.10 0.64 0 1.70 0.71 -4 3.04 0.75 0 4.01 0.77 -1 4.48 0.79 0 4.78 0.83 +1 5.69 0.80 0 5.06 0.85 -2 6.58 0.77 0 4.94 0.77 0 4.94 0.74 0 5.29 0.74 0 5.29 0.70 0 2.84 0.77 -3 4.50 0.80 0 4.61 0.84 -1 5.52 0.81 0 3.60 0.81 0 3.60

Note: optimal leads (-) and lags (+), the Harding-Pagan test is a test for non-synchronisation (H0 = Strong Non-Synchronisation). 9

See Artis et al. (1997), Artis et al. (2004) and Harding and Pagan (2006) for others measures of synchronization.

48

Laurent Ferrara and Olivier Vigna

out the synchronisation test based on concordance index proposed by Harding and Pagan (2006). In this respect, we test the hypothesis that cycles are strongly nonsynchronized (SNS) based on the statistic ρˆ S , namely the estimated correlation coefficient between (Si,t )t and (S j,t )t (see for example Darn´e and Ferrara, 2009, for an application). We use a heteroscedastic and autocorrelation consistent (HACC) standard error version of the test. The results presented in Table 4 enable to reject the null hypothesis of non-synchronisation at the usual 5% level, except for housing sales (t-stat=1.70). As in the correlation analysis, we compute cross-concordance indexes (CCI) with GDP cycle in order to identify optimal leads and lags. That is we compute concordance index as defined in equation (1) between Si,t and S j,t−k for various lags k, positive and negative. Among all lags k, the maximum cross-concordance index is retained and presented in Table 4. First, we note that the values of the crossconcordance indexes increase when including a dynamic relationship, in comparison with the first column of Table 3. Housing-related variables possess clearly a leading pattern, as in the correlation analysis. Moreover, the results of the HardingPagan test based on maximum cross-concordance indexes (see Table 4) enable to reject strongly the null hypothesis of non-synchronisation. Those results confirm the advance of the housing sector over the economic cycle, with a lead ranging from 1 (residential investment and housing starts) to 4 quarters (housing sales). The results of the turning point analysis are presented in Figure 2 where optimal leads and lags of the various variables with GDP are represented, as well as corresponding concordance indexes. In conclusion, the results point out that variables reflecting the housing market are strongly related to the GDP cycle and possess a significant lead. This latter result is robust to both turning point and correlation analysis. Main results are summarized in figures and 2.

3 Structural factors affecting long-term cycles in the housing market In this section, we complete the previous comparative analysis between housing market and macroeconomic cycles by investigating whether some structural variables play a significant role in shaping cyclical developments. The subsequent analytical framework is therefore based on a comparison of supply-demand side, pricequantity considerations and financial-real factors at play. When focusing on euro area countries since 1980, and France in particular, empirical studies identify only two recession phases -defined in the NBER sense-, in addition to the 2008 recession, namely the second oil shock double-dip (1980-81

Cyclical relationships in France

49

and 1982) and a phase in 1992-93 following the US recession in 1991. We refer to the CEPR Dating Committee (2009) or to Eurostat (Anas et al., 2007, Anas et al., 2008) for recession dating chronologies. When looking at real housing prices fluctuations in France (deflated with the HICP, see Figure 3), we observe two complete phases of negative growth: from 1981 Q1 to 1984 Q4 and from 1991 Q2 to 1997 Q1. Those two phases of negative growth roughly correspond to recession periods, except that the troughs in the housing cycle are significantly more protracted events lagging the economic business cycle (around 2 years and 4 years for the first and the second recession, respectively). Regarding the 2008 recession, the peak in housing prices occurs in 2008 Q1, as the peak in GDP, but the trough cannot not yet been recognized with the data available until 2009 Q2. Consequently, it seems that longterm dynamics in French housing prices are quite different from those in GDP and are more persistent. This fact has been also pointed out in Ferrara and Koopman (2010, this volume).

Survey

Starts

Employ

0.80

IPI

0.75

Permits Prices Invest

Short Long

0.70

Sales

0.60

0.65

Concordance

0.85

0.90

We consider now long-term trends of GDP, housing prices, residential investment and sales estimated by a low-pass Hodrick-Prescott filter that enables to drop fluctuations with a period lower than 8 years. We observe in Figure 4 that long-term trends have a quite different pattern for GDP and the three other housing market

−5

−4

−3

−2

−1

0

1

2

Lag

Fig. 2 Leads and lags versus concordance indexes between GDP and various variables

50

Laurent Ferrara and Olivier Vigna

variables. Common fluctuations are present in the three housing variables, although the recent downturn in sales appears more severe, reflecting global housing market evolutions. The fact that long-term trends in housing market and in macroeconomics may have different dynamics leads us to turn more specifically to the determinants of housing market fluctuations in the long-term. Obviously, structural factors have an impact on long-term evolutions of the French housing market. Six considerations are indeed to be taken into account in order to assess structural developments in the French housing market. Such variables enable to partly explain why housing prices did not collapse in France in the recent period at the same pace as they did in other economies like Spain, Ireland or the United Kingdom for example. 1. Among the main euro area countries, France posts the lowest share of new housing loans to households with adjustable rate (see Figure 5). In fact, flexible rates represent in France around 10% of the new housing loans, while this share approximates 15% in Germany on recent years, 40% in the Euro zone as a whole and has exceeded the 50% threshold in 2004-2005. The highest share amongst the main European economies is observed in Spain, where only 10% of the new housing loans to households is granted at fixed rates. 2. The type of financial instruments used for housing financing is also important, notably the extent to which mortgage equity withdrawals instruments exist. In fact, in countries where growing housing prices allow households to get new funds from banks to increase their private consumption or their housing invest2.0

1.8

1.6

1.4

1.2

1.0

0.8

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

Fig. 3 Housing prices (HICP deflated) 1980Q1 - 2009Q2 and the euro area recession phases (shaded)

Cyclical relationships in France

51

ment, the subsequent rise in their leverage ratio may have the opposite effect in a downward-oriented housing market: in such a case, decreasing prices make it quite impossible to extract new financing facilities from an asset whose price is eroding. In France mortgage equity withdrawals have only been introduced in 2006 extending at a very low pace, although no official data exist so far. On the contrary, in countries like the US or the UK, financial institutions are more

gdp

6.08

investment

3.1

6.00 3.0 5.92 5.84

2.9

5.76 2.8

5.68 5.60

2.7 5.52 5.44

1980

1983

1986

1989

1992

1995

1998

2001

2004

2.6

2007

prices

0.7

1980

1983

1986

1989

1995

1998

2001

2004

2007

1998

2001

2004

2007

sales

3.5

0.6

1992

3.4

0.5 3.3 0.4 0.3

3.2

0.2

3.1

0.1 3.0 0.0 2.9

-0.1 -0.2

1980

1983

1986

1989

1992

1995

1998

2001

2004

2.8

2007

1980

1983

1986

1989

1992

1995

Fig. 4 Long-term trends estimated by a low-pass HP filter (1980Q1 - 2009Q2) France

Germany

Italy

Spain

1.00

0.75

0.50

0.25

0.00

2003

2004

2005

2006

2007

2008

2009

Fig. 5 Share of fixed rates in new housing loans (in 1/100 of %, source: European Central Bank)

52

Laurent Ferrara and Olivier Vigna

willing to increase the amount of the initial housing loan when prices go up, as the market value of the guarantee also appreciates. Such a phenomenon contributes to reduce the private saving ratio, as higher housing prices induce consumers to save less, thus potentially amplifying the amplitude of business cycles. Regarding the US, Hatzius (2005), for example, indicates that mortgage equity withdrawals from 1990 to 2004 lowered the personal saving rate from 2 to 5 percentage points. As personal consumption expenditures account for two-thirds of aggregate spending in the US, such an effect would imply an impetus of as much as 0.3 percentage points to average annual real GDP growth over this period. Calza, Monacelli and Stracca (2007) also conclude that the correlation of consumption growth with changes in house prices is higher in economies with more-developed mortgage finance systems. 3. Regarding solvency, French households indebtedness is still quite moderate, at 75% of GDP mid-2009 vs 90% in the Euro area or quite 160% in the US. Taking into account real disposable income as a reference instead of GDP would not change the picture. This means there is some room for further residential investment for French households. 4. On the recent period, there is no sign of overinvestment in France in terms of the share of residential investment in GDP (see Figure 6). Indeed, the share of residential investment in total GDP, despite an increase from 3.4% in 2002 to 4.0% at the end of 2007-early 2008, has then been slightly decreasing -at 3.5% in September 2009- and is currently not going back to its long-term average of 5.8% calculated over the longest period - since 1949 - quarterly national accounts are made available by the INSEE. Far from the peak of 8.4% observed in 1974 Q1, the present situation is therefore not characterized by a need of a significant correction according to this long term comparison. Moreover, in the recent period, residential investment in France in percentage of GDP is still below figures posted in Germany, Italy or Spain, and the US and UK have gone below the figures for France in 2008 for the first time since 1995. 5. A growing part of French people want to become home owner as an economic rational choice to secure their future and invest for their progeny (Mistral et Plagnol, 2009). According to an international comparison (Hilbers et alii, 2008), France is one of the developed countries posting the strongest increases in the share of home owner since 1980, with +8 points in France compared with +3 points in the US, +1 point in Germany but +11 points in the UK. However, in spite of this catching-up process, the percentage of French people being owner of their home according to Eurostat (2009) is among the lowest in the European Union, at 58% in 2007 (47% in 1978), that is below the EU average of 65% and the French neighbours figures (83% in Spain, 72% in Italy, 67% in Belgium and 71% in Luxembourg) except the German one (46%). This factor should consequently also help sustain the demand side in the coming years. Furthermore, housing investment is becoming a crucial element in the strategy ded-

Cyclical relationships in France France

4.0

53 Spain

8.0

3.9

7.5

3.8

7.0

3.7

6.5

3.6

6.0

3.5

5.5

3.4

5.0

UK

7.0

6.5

6.0

5.5

5.0

4.5

3.3

4.0

3.5

4.5 1995

1997

1999

2001

2003

2005

2007

2009

Germany

8.0

3.0 1995

1997

1999

2001

2003

2005

2007

2009

Italy

4.92

1997

1999

2001

2003

2005

2007

2009

US

6.5

6.0

4.80

7.5

1995

5.5

4.68 7.0

5.0 4.56 6.5

4.5 4.44 4.0

6.0 4.32

5.5

3.5

4.20

5.0

3.0

4.08 1995

1997

1999

2001

2003

2005

2007

2009

2.5 1995

1997

1999

2001

2003

2005

2007

2009

1995

1997

1999

2001

2003

2005

2007

2009

Fig. 6 Residential investment in percentage of GDP (Source: National Statistical Institutes)

icated to improve the standard of living in the retirement period. The median age at which French people buy a dwelling (40 years old in Paris in 2007) lost 4 years from 1997 to 2007 as said by notaries data, underlying the willingness to prepare earlier this lifetime. Fiscal incentives (encouraging rental investment in the new property market, for example the Loi Scellier, or enabling grandparents to give a higher lump-sum of money to their grandchildren without any tax) and rational anticipations (such as the expectation to get a profit with a higher probability by selling a dwelling rather than a share or a bond on more volatile financial markets) also contributed to this development. All in all, housing property (including land) accounted in 2007 for 72% of the net total value owned by households or the equivalent of 7.5 years of their gross disposable income vs. an average of 4.4 years on the period 1978-1998. 6. From a demographic point of view, both the current situation and the main projections are also supportive for fuelling the need of housing in the future. First, the size of French households has diminished: according to INSEE data, the share of housings occupied by one person grew from 19.1% in 1954 to 32.5% in 2005, whereas the share of housings occupied by at least six persons diminished from 9.9% to 1.9% on the same period. Eurostat (2008) also concluded that the percentage of single person living in private households was in France in 2007, at 8%, above the figure of some neighboring countries (3.5% in Spain, 6.5% in Italy, 7% in the UK, but 10% in Germany). INSEE forecast the share of households with one person to represent in 2030 between 43.2% and 46.0% of the total number of households depending on the type of scenario (see Jacquot, 2006). In

54

Laurent Ferrara and Olivier Vigna

addition, the average number of people per household may get smaller from 2.31 in 2005 (2.57 in 1990) to a range of 2.04-2.08 in 2030 according to the scenario.

4 Conclusions The analysis of correlations between housing and GDP cycles in France suggests that the former, as a leading variable, may add a significant information to help assess business outlook. In particular, several structural variables impacting the housing market and contributing to shape real estate developments, are vital for better understanding both GDP growth cycles and why the French real estate market so far did not collapse as it did in other developed countries. As further research, it would be worthy to consider other real and financial variables, such as bonds or stock exchange prices (Friggit, 2009), in their correlation with house prices. Moreover, the development of an econometric model to check the empirical results that we found, for both cyclical and long-term components, would be of interest. Acknowledgements We would like to thank O. de Bandt, R. Br¨uggemann, G. Dufr´enot and B. Pluyaud for helpful comments as well as the participants to the conference on Macroeconomics of Housing Markets organized by Banque de France, November 2009. The views expressed herein are those of the authors and do not necessarily reflect those of the Banque de France.

References ` Alvarez, L. J., Bulligan, G., Cabrero, A., Ferrara, L. and Stahl, H. (2010), Housing cycles in the major euro area countries, this volume. ` Alvarez, L. J. and Cabrero, A. (2010), Does housing really lead the business cycle?, this volume. Andr´e, C. (2009), A bird’s eye view of OECD housing markets, OECD, Economics Department Working Papers, No. 746. Anas, J., Billio, M., Ferrara, L. and Mazzi G.-L. (2008), A system for dating and detecting turning points in the euro area, The Manchester School, 76, 5, 549-577. Anas, J., Billio, M., Ferrara, L. and LoDuca, M. (2007), A Turning Point Chronology for the Eurozone Classical and Growth Cycle, in G. L. Mazzi and G. Savio (eds), Growth and Cycle in the Euro-zone, New York, Palgrave Macmillan. Artis, M., Kontolomis, Z.G. and Osborn, D.R. (1997), Business cycles for G7 and European countries, Journal of Business, 70, 249-279. Artis, M., Marcellino, M. and Proietti, T. (2004), Dating business cycles: A methodological contribution with an application to the Euro area, Oxford Bulletin of Economics and Statistics, 66, 537-565. Baxter, M. and King, R.G. (1999), Measuring business cycles: Approximate band-pass filters for economic time series, Review of Economics and Statistics, 81, 575-593. Calza, A., Monacelli, T. and Stracca, L. (2007), Mortgage Markets, Collateral Constraints, and Monetary Policy: Do Institutional Factors Matter?, Center for Financial Studies, Working Paper Series, No. 2007/10.

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Canova, F. (1998), De-trending and business cycle facts, Journal of Monetary Economics, 41,475512. CEPR (2003), Press Release, Euro Area Business Dating Committee, 22 September 2003. Christiano, L. and Fitzgerald, T. (2003), The band pass filter, International Economic Review, 44, 2, 435-465. Darn´e, O. and Ferrara, L. (2009), Identification of slowdowns and accelerations in the Euro area, CEPR, Discussion Paper, No. 7376. Eurostat (2008), Living Conditions in Europe, Eurostat Pocketbooks, 2008 edition. Ferrara, L. and Koopman, S.J. (2010), Common business and housing market cycles in the Euro area from a multivariate decomposition, this volume. Friggit, J. (2009), Le prix des logements sur longue p´eriode, Informations Sociales, forthcoming. Goodhart, C. and Hofmann, B. (2008), House prices, money, credit, and the macroeconomy, Oxford Review of Economic Policy, 24, 180-205. Gouri´eroux, C. and Laferr`ere, A. (2009), Managing hedonic housing price indexes: The French experience, Journal of Housing Economics, forthcoming. Harding, D. and Pagan, A. (2002), Dissecting the cycle: A methodological investigation, Journal of Monetary Economics, 49, 365-381. Harding, D. and Pagan, A. (2006), Synchronization of cycles, Journal of Econometrics, 132, 59-79. Hatzius, J. (2005), Housing holds the key to Fed policy, Goldman Sachs, Global Economics Paper, No. 137. Hilbers P., Hoffmaister, A., Banerji, A. and Shi, H. (2008), House price developments in Europe: A comparison, IMF, Working Paper, No. 08/211. Hodrick, R. and Prescott, E. (1997), Postwar U.S. Business Cycles: An Empirical Investigation, Journal of Money, Credit, and Banking, 29, 1-16. Jacquot, A. (2006), Projection de m´enages pour la France m´etropolitaine l’horizon 2030, Insee, Document de Travail, No. F0605. Leamer, E. (2007), Housing is the business cycle, NBER, Working Paper, No. 13428. Mistral, J. and Plagnol, V. (2009), Loger les classes moyennes : la demande, l’offre et l’´equilibre du march´e du logement, Conseil d’Analyse Economique, Rapport, No. 82. Mullbauer, J. and Murphy, A. (2008), Housing markets and the economy: the assessment, Oxford Review of Economic Policy, 24, 1-33. Vargas-Silva, C. (2007), Monetary policy and the US housing market: A VAR analysis imposing sign restrictions, Journal of Macroeconomics, 30, 997-990.

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Appendix

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

4 2 0 -2 -4 -6 -8 -10

30 20 10 0 -10 -20 -30 -40

6 4 2 0 -2 -4 -6 -8

gdp

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

1996

1998

2000

2002

2004

2006

2008

1996

1998

2000

2002

2004

2006

2008

1998

2000

2002

2004

2006

2008

housing prices

1980

1982

1984

1986

1988

1990

1992

1994

sales

1980

1982

1984

1986

1988

1990

1992

1994

household investment

1980

1982

1984

1986

1988

1990

1992

1994

1996

Fig. 7 Growth cycles for GDP, for housing prices, for housing sales and for household investment, 1980Q1 - 2009Q2, and GDP growth cycle (shaded area)

Cyclical relationships in France

2.4 1.6 0.8 -0.0 -0.8 -1.6 -2.4 -3.2

57

employment

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

survey

40 20 0 -20 -40 -60

40 20 0 -20 -40 -60 -80 -100

15 10 5 0 -5 -10 -15 -20

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

short rate

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

1996

1998

2000

2002

2004

2006

2008

long rate

1980

1982

1984

1986

1988

1990

1992

1994

Fig. 8 Growth cycles for employment in the housing sector, for short and long rates, and survey in housing, 1980Q1 - 2009Q4, and GDP growth cycle (shaded area)

58

Laurent Ferrara and Olivier Vigna

20

permits

15 10 5 0 -5 -10 -15

15 10 5 0 -5 -10 -15 -20 -25 -30

6

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

housing starts

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

ipi building

4 2 0 -2 -4 -6

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Fig. 9 Growth cycles for permits, housing stats and IPI in construction, 1980Q1 - 2009Q2, and GDP growth cycle (shaded area)

Cyclical relationships in France

59

prices

1.00

short

1.00

0.75

0.75

0.50

0.50

0.25

0.25

0.00

0.00

-0.25

-0.25

-0.50

-0.50

-0.75

-0.75

-1.00

-1.00 -10

-5

0

5

10

sales

1.00

-10

-5

1.00

0.75

0.75

0.50

0.50

0.25

0

5

10

0

5

10

5

10

5

10

5

10

long

0.25

0.00

0.00

-0.25

-0.25

-0.50

-0.50

-0.75

-0.75

-1.00

-1.00 -10

-5

0

5

invest

1.00

-10

10

-5

permits

1.00

0.75

0.75

0.50

0.50

0.25

0.25

0.00

0.00

-0.25

-0.25

-0.50

-0.50

-0.75

-0.75

-1.00

-1.00 -10

-5

0

5

10

employment

1.00

-10

-5

1.00

0.75

0.75

0.50

0.50

0.25

0

starts

0.25

0.00

0.00

-0.25

-0.25

-0.50

-0.50

-0.75

-0.75

-1.00

-1.00 -10

-5

0

5

survey

1.00

-10

10

-5

1.00

0.75

0.75

0.50

0.50

0.25

0.25

0.00

0.00

-0.25

-0.25

-0.50

-0.50

-0.75

-0.75

-1.00

0

ipi building

-1.00 -10

-5

0

5

10

-10

-5

Fig. 10 Cross-correlations with GDP growth cycle, 1980Q1 - 2009Q2

0

60

Laurent Ferrara and Olivier Vigna

Table 5 Peaks and troughs dating for growth cycles estimated by using HP2 filter with bandwidth 1.5-8 years. Lead and lags viz the GDP growth cycle turning points are in parenthesis. IPI series only starts in 1990. GDP Prices Sales 81Q1 () Peak 82Q3 81Q2 83Q1 (-5) (+2) Trough 87Q2 84Q4 86Q1 (-10) (-5) Peak Trough

Invest Employ Survey Short 80Q3 () 80Q4 82Q4 81Q4 (-7) (+1) (-3) 85Q2 85Q1 86Q3 (-8) (-9) (-3)

Trough Peak 90Q1 90Q4 89Q4 89Q3 91Q2 (+3) (-1) (-2) (+5) Trough

89Q2 (-3)

Peak Trough 93Q3 93Q1 (-2) Peak 95Q2 94Q3 (-3) Trough 97Q1 98Q2 (+5) Peak

93Q2 93Q4 (-1) (+1) 95Q1 95Q3 (-1) (+1) 98Q1 98Q1 (+4) (+4)

93Q1 (-2) 94Q4 (-2) 96Q3 (-2)

99Q4 01Q1 (-4) (+1) 04Q2 04Q3 (+4) (+5)

00Q4 (0) 03Q3 (+1)

Peak 07Q4 06Q4 07Q1 07Q4 07Q4 (-4) (-3) (0) (0)

07Q3 (-1)

Trough Peak 00Q4 00Q2 (-2) Trough 03Q2 03Q2 (0) Peak

93Q1 (0) 94Q1 (-5) 95Q2 (-7) 99Q1 () 00Q1 ()

Trough

Mean StdErr

(-2.0) (-2.7) (-1.7) 4.4 3.2 4.2

(1.0) 4.2

Long Permits Starts IPI

81Q4 (-3) 86Q3 (-3) 87Q4 () 89Q2 () 90Q1 90Q3 (0) (+2) 91Q2 () 92Q4 () 94Q2 93Q4 (+3) (+1) 95Q2 95Q1 (0) (-1) 96Q4 99Q1 (-1) (+8) 98Q2 () 99Q2 () 00Q4 00Q2 (0) (-2) 04Q1 03Q2 (+3) (0) 04Q2 () 05Q3 () 08Q2 07Q3 (+2) (-1)

82Q4 (+1) 84Q2 (-12)

88Q4 89Q4 (-5) (-2)

93Q1 93Q2 (-2) (-1) 94Q3 94Q4 (-3) (-2) 97Q1 97Q3 (0) (+2)

92Q1 () 93Q3 (0) 95Q2 (0) 97Q1 (0)

98Q4 99Q1 00Q4 (-8) (-7) (0) 03Q1 03Q2 04Q4 (-1) (0) (+6)

06Q4 07Q3 08Q1 (-4) (-1) (+1)

(-1.3) (0.1) (0.1) (-3.8) (-1.6) (1.2) 1.4 2.3 3.4 4.1 2.8 2.4

Does Housing Really Lead the Business Cycle in Spain? ´ Luis J. Alvarez and Alberto Cabrero

Abstract The aim of this paper is to characterize the cyclical properties of Spanish real and nominal housing related variables. Our three main results are: first, housing appears to lead the business cycle. Second, fluctuations in home prices are positively related to those of residential investment, suggesting the dominant role of demand factors over supply ones. Third, there are interesting asymmetries in cyclical fluctuations: contractions in GDP appear to be briefer than expansions.

JEL codes : E32, R21,R32 Keywords : Housing, business cycles, filtering

1 Introduction The protracted period of sharp house price increases and booming investment in residential construction in most advanced economies in the first half of the years 2000, has motivated an explosion of papers analysing the housing market. This interest is even stronger at present, as the boom has come to an end: house prices have rapidly decreased in a number of countries and residential investment is dragging down GDP. Housing markets have multiple interactions with the rest of the economy, so that a number of different issues have been addressed in the literature. For instance, a strand of research has analysed to which extent price levels are consistent with eco´ L.J. Alvarez. Banco de Espa˜na, e-mail: [email protected] A. Cabrero Banco de Espa˜na, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_4, © Springer-Verlag Berlin Heidelberg 2010

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´ Luis J. Alvarez and Alberto Cabrero

nomic fundamentals (Ayuso and Restoy, 2006; Mikhed and Zemcik, 2009). Others authors have stressed the role of home wealth as a driver of household consumption at the aggregate (Poterba, 2000; L’Hotellerie and Sastre, 2006) and on the basis of microeconomic data (Case et al., 2005; Bover, 2005). The role of housing in the monetary transmission mechanism has also received a lot of attention, as reviewed in Mishkin (2007). Finally, there is growing work using estimated Dynamic Stochastic General Equilibrium models in which housing serves as a collateral asset (Iacoviello, 2005; Iacovello and Neri, 2008; Iacoviello, 2010, this volume; AspachsBracons and Rabanal, 2009; Rubio, 2009). Evidence on volume cycles and the earlier warning signal nature of real housing developments is considerably scanter than for price cycles. 1 Recently, Leamer (2007, 2009) stressed the substantial effects on United States activity of volume changes in home building. Indeed, 8 out of the last 10 recessions in the US have been preceded by contractions in residential investment. For European countries, evidence for France, Germany, Italy and Spain has been recently made available in the papers collected in Part II of the book 2 ). The analysis of housing volume cycles in Spain is particularly relevant, given the strong investment in residential construction in the decade prior to 2006, against the background of low interest rates and sizable migration inflows. Real average annual growth of housing investment in this period exceeded 8% and its share in GDP reached record high levels in 2007 (9.3%), almost 5 percentage points above 1996 and substantially above that in the euro area as a whole or the United States. The marked expansion of housing supply did not prevent a period of soaring house prices, but had a highly beneficial impact on employment in the construction sector: its share in total employment reached 13.8% in 2007, almost 5 percentage points above 1996. The aim of this paper is twofold. First, we analyse wheter residential investment fluctuations in Spain lead those of GDP (section 2). With respect to other literature, we consider a much wider set of real and nominal construction variables. Robustness of results is analysed using several different estimation procedures. Second, assymetries in the behaviour of housing related variables in expansions and contractions are analysed (section 3). Concluding remarks are presented in section 4.

2 The leading nature of housing The aim of this section is to determine whether residential investment cycles in Spain tend to precede those in GDP, like in the United States, as well as to charac1

The leading role of residential construction in the United States with respect to GDP has been stressed in Greene (1997), Stock and Watson (1999) and Coulson and Kim (2000) 2 Besides this paper, see Alvarez ´ et al. (2010, this volume); Bulligan (2010, this volume); Ferrara and Koopman (2010, this volume); Ferrara and Vigna (2010, this volume) and Knetsch (2010, this volume.

Does Housing Really Lead the Business Cycle in Spain?

63

terize the cyclical features of housing related variables in Spain. Where possible we make a comparison with available international evidence. We consider a sample period that starts in 1980:Q1 and ends in 2008:Q4, thus including the lastest minimum turning point. Starting in 1980 tries to strike a balance between having the longest available time series and avoiding substantial changes in the definition of the variables. However, seasonally adjusted quarterly national account estimates prior to 1995 are too noisy, reflecting the fact that the National Institute of Statistics used to pay close attention to trend estimates, rather than to seasonally adjusted series. This has led us to pre-filter (the logs of) all data using the methodology in G´omez and Maravall (2001). This procedure has the advantage that it provides a clearer signal that helps improve the dating of turning points. Prior to the pre-filtering stage, we have also extended the series with forecasts to obtain an accurate assessment of the cyclical component at the end of the sample (and minimise revisions). Data sources appear in Appendix 1, year-on-year growth rates of the variables are plotted in Appendix 2.

2.1 Housing and other expenditure side GDP components In this subsection, we focus on the cyclical behaviour of expenditure side GDP components. To that end, we estimate cyclical components mainly using Butterworth and kernel methodologies. We also analyse the robustness of our results by considering alternative estimates of cyclical components. The methodology used is presented in Appendix 3. Results using the Butterworth filter and the Epanichnekov kernel are reported in table 1 and estimates of the cyclical components are plotted in appendix 4. The first column refers to the volatility of the component, as measured by the ratio of the standard deviation of a variable 3 to the standard deviation of GDP. The remaining columns report the cross correlation coefficient 4 (ρ j ) between each variable at time t and GDP at t + j. We say that a variable leads (lags) GDP if (absolute value) cross correlation is highest with respect to future (past) GDP. We say that a variable is pro-cyclical (counter-cyclical) if the maximum cross-correlation is positive (negative). The table shows that residential investment leads GDP, is pro-cyclical and is considerably more variable than total output or consumption (standard errors of estimates are reported in Appendices 5 and 6). Residential investment is linked to a higher extent with future output than with contemporaneous output and thus serves 3 4

For clarity of exposition, we refer to the cyclical component as variable X, simply as variable X. Standard errors of correlation coefficients are reported in appendices 4 and 5.

´ Luis J. Alvarez and Alberto Cabrero

64 Table 1 Cross correlation of demand components with GDP

Butterworthfilter Variable leads GDP Contemp. Variable lags GDP 4 3 2 1 0 1 2 3 4 Private consumption 1.0 0.48 0.60 0.71 0.77 0.74 0.64 0.51 0.41 0.33 Public consumption 0.6 -0.49 -0.44 -0.36 -0.24 -0.08 0.04 0.12 0.17 0.19 Equipment investment 5.0 0.70 0.76 0.82 0.85 0.83 0.76 0.65 0.51 0.35 Residential investment 2.7 0.61 0.69 0.74 0.76 0.75 0.71 0.65 0.57 0.48 Non residential invest. 2.4 0.08 0.16 0.23 0.28 0.31 0.30 0.27 0.24 0.20 Other investment 1.6 0.57 0.64 0.67 0.67 0.61 0.53 0.46 0.39 0.33 Exports 1.9 0.36 0.52 0.65 0.74 0.74 0.69 0.61 0.52 0.42 Imports 3.8 0.70 0.78 0.84 0.87 0.85 0.78 0.68 0.55 0.40 Epanechnikov filter Volatility Variable leads GDP Contemp. Variable lags GDP 4 3 2 1 0 1 2 3 4 Private consumption 1.1 0.53 0.63 0.72 0.78 0.80 0.79 0.76 0.73 0.72 Public consumption 1.0 0.43 0.51 0.58 0.64 0.70 0.75 0.78 0.78 0.76 Equipment investment 5.2 0.79 0.82 0.85 0.86 0.84 0.79 0.71 0.62 0.51 Residential investment 3.8 0.86 0.87 0.87 0.86 0.83 0.79 0.74 0.68 0.61 Non residential invest. 3.4 0.51 0.59 0.66 0.71 0.74 0.75 0.75 0.74 0.72 Other investment 2.5 0.87 0.89 0.90 0.89 0.86 0.81 0.76 0.70 0.64 Exports 2.0 0.08 0.12 0.15 0.16 0.15 0.11 0.05 -0.01 -0.06 Imports 3.9 0.78 0.84 0.88 0.90 0.90 0.86 0.81 0.74 0.66 Variable

Volatility

as a leading indicator, in line with the results in Leamer (2007, 2009). The maximum correlation coefficient of residential investment with GDP is high, but not perfect (0.76 using the Butterworth filter and 0.87 with the Epanichnekov kernel). The estimated lead varies from 1 to 3 quarters. Further robustness analysis is presented in Table 2, in which cross correlations of residential investment with respect to nominal prices and to GDP are reported using Hodrick Prescott, band pass Hodrick Prescott, Baxter and King and Christiano and Fitzgerald filters. 5 Using these alternative filters, residential investment leads GDP by 2 or 3 quarters. Maximum correlations are also high (in the 0.59-0.80 range). Larger quantitative differences are observed in terms of volatility, but the robust finding is that residential investment fluctuates considerably more than GDP. Table 3 presents an international comparison using a Butterworth filter: residential investment is also found to lead GDP in Germany, but not in France or Italy. However, Ferrara and Vigna (2010, this volume) using a band pass Hodrick Prescott filter find that French residential investment also leads GDP as Leamer (2007, 2009) for the US. For advanced economies, IMF (2008) considers deviations from a log-linear trend, finding that housing tends to lead the cycle, although with some exceptions in the euro area (Germany, Italy and Finland) and the Nordic countries (Sweden and Norway). Despite the anticipatory nature of residential investment fluctuations with respect to those in GDP found in the data, attempts of explanations in the existing theoretical literature have had limited success (Gangopadhyay and Hatchondo, 2009). In a standard general equilibrium model with homogeneous agents (Greenwood and 5

The leading nature of housing is also found using year on year growth rates. From a historical perspective, annual data for the 1850-2009 period, also confirm this result.

Does Housing Really Lead the Business Cycle in Spain?

65

Table 2 Cross crorrelation. sensitivity to the filter used. Sample period (1980:Q1-2008:Q4 Housing invest. vs GDP

Vol. * Residential invest. leads GDP Contemp. Residential invest. lags GDP 4 3 2 1 0 1 2 3 4 HP 3 .7 0 .74 0 .76 0 .77 0 .76 0 .72 0 .66 0 .58 0 .50 0 .41 Band pass HP 3 .6 0 .77 0 .80 0 .80 0 .79 0 .76 0 .70 0 .62 0 .53 0 .42 Baxter and King 4 .9 0 .68 0 .69 0 .68 0 .64 0 .61 0 .52 0 .43 0 .35 0 .27 Cristiano and Fitzgerald 3 .9 0 .57 0 .59 0 .58 0 .56 0 .54 0 .45 0 .37 0 .29 0 .23 Butterworth 2 .7 0 .61 0 .69 0 .74 0 .76 0 .75 0 .71 0 .65 0 .57 0 .48 Epanechnikov 3 .8 0 .86 0 .87 0 .87 0 .86 0 .83 0 .79 0 .74 0 .68 0 .61 H. prices vs housing invest. Vol. ** H. prices leads housing invest. Contemp. H. prices lags housing invest. 4 3 2 1 0 1 2 3 4 HP 0 .8 0 .38 0 .46 0 .51 0 .55 0 .58 0 .60 0 .62 0 .62 0 .62 Band pass HP 0 .9 0 .40 0 .47 0 .53 0 .57 0 .60 0 .63 0 .65 0 .65 0 .64 Baxter and King 0 .9 0 .35 0 .43 0 .49 0 .54 0 .58 0 .61 0 .65 0 .68 0 .69 Cristiano and Fitzgerald 0 .8 0 .26 0 .33 0 .38 0 .44 0 .49 0 .52 0 .55 0 .58 0 .57 Butterworth 0 .6 0 .38 0 .50 0 .59 0 .65 0 .70 0 .72 0 .72 0 .70 0 .64 Epanechnikov 1 .0 0 .45 0 .51 0 .57 0 .61 0 .64 0 .68 0 .70 0 .72 0 .74 *Standard deviation of housing investment relative to standard deviation of GDP ** Standard deviation of house prices relative to standard deviation of residential investment

Hercowitz, 1991) representative agents react to a positive technology shock by increasing business investment at the expense of residential investment, thus generating a negative comovement between residential and business investment, at odds with the data. David and Heathcote (2005) obtain a positive comovement between both variables in a model with multiple sectors. In their model, positive technology shocks drive down house prices, allowing consumers to buy more houses. This view of supply driven residential cycles is inconsistent with the positive comovement of house prices and residential investment, typically found in the data. Fisher (2007) succeeds in explaining the leading feature of residential over business investment, but not with respect to GDP. The idea is that, by increasing the size of the house, families increase their labour productivity. As a response to a positive productivity shock in the market sector, households first increase their residential investment at the expense of business investment, which allows them to increase their productivity in periods following the shock. Recently, Yuan (2009) has developed a model in which residential investment leads GDP. In his model, agents face collateral constraints and receive a signal about future productivity one period in advance. A good signal about future productivity makes household spend more to intertemporally smooth consumption. Increased expenditures are financed up to a fraction of the value of the house by borrowing at mortgage interest rates, which are lower that for unsecured consumer loans. As a result, agents buy more housing relative to other goods. Though the model is able to account for the leading nature of housing, the way the financial market is modelled is not completely satisfactory. In particular, households typically do not continuously vary the size of mortgages, according to fluctuations in total spending.

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Table 3 Leading nature of housing. International comparison * Lead of variable with respect to GDP (quarters) Maximum cross correlation France Germany Italy Spain France Germany Italy Spain Residential investment 0 2 0 1 0.53 0.71 0.53 0.76 Building permits 5 5 na 4 0.75 0.59 na 0.75 Housing starts 4 na na 4 0.58 na na 0.75 *Sample: 1980:Q1-2008:Q4. Butterworth filter

2.2 Additional real and nominal construction variables The leading nature of housing is considerably clearer when using some indicators, such as housing starts and building permits, instead of residential investment. Indeed, Butterworth and Epanichnekov kernel procedures show that both variables lead GDP by 4 quarters (see table 4). This is explained by the fact that residential investment in national accounts refers to the value of constructions in progress. There is, thus, a time lag between the start of a house (or the time a building is authorised to start) and the national account magnitude. As expected, indicators constructed on the basis of housing starts or building permits and a time to build hypothesis lead to a smaller lead with respect to GDP. Building permits and housing starts in France and Germany are also found to lead GDP (Table 3), a result also found for France by Ferrara and Vigna (2010, this volume). The leading nature of residential investment with respect to GDP is not shared by Gross Value Added in construction. This variable also includes non-residential construction, which is either synchronous or lags GDP. The maximum GVA-GDP correlation is considerably lower than the maximum residential investment GDP correlation, probably reflecting the discretionary nature of public construction. Even though at present public construction is being used to stabilize the economy through a fiscal stimulus package, this has not been always the case within the sample period. In Spain, public construction by regional governments and city councils typically is more closely linked to the electoral cycle rather than to the business cycle. Labour input in the construction sector, both in terms of number of workers and full time equivalent workers, is pro-cyclical and lags residential investment using both filters: the Butterworth filter shows a lead of 1 quarter and Epanechnikov kernel of three quarters. The lag of the labour input probably reflects the fact that firms face costs in adjusting the size of their workforce. Material input indicators, such as concrete consumption and production, are pro-cyclical and coincident with GDP. Nominal house prices and residential investment are pro-cyclical. The examination of the maximum cross correlation coefficient between residential investment and house prices (0.72 with the Butterworth filter and 0.74 with the Epanechnikov kernel) shows positive comovement. This result is also robust to the use of other filters (Table 2). This suggests that demand factors (e.g. demographics or interest rates) appear to have been more important than supply considerations (e.g. technological progress). This is in line with Gonz´alez and Ortega (2009) who find that

Does Housing Really Lead the Business Cycle in Spain?

67

Table 4 Cross correlation of several building indicators with GDP Butterworth filter Volatility Variable leads GDP Contemp. Variable lags GDP 4 3 2 1 0 1 2 3 4 Residential investment 2.7 0.61 0.69 0.74 0.76 0.75 0.71 0.65 0.57 0.48 Investment in non residential construction 2.4 0.08 0.16 0.23 0.28 0.31 0.30 0.27 0.24 0.20 Gross value added in construction 2.0 0.25 0.31 0.37 0.41 0.41 0.39 0.35 0.31 0.27 Building permits 11.3 0.75 0.73 0.69 0.60 0.47 0.35 0.22 0.09 -0.05 Housing starts 10.4 0.75 0.74 0.72 0.68 0.60 0.50 0.40 0.29 0.15 Housing in progress index (building permits) 10.6 0 .68 0.74 0.77 0.77 0.74 0.69 0.62 0 .53 0.42 Housing in progress index (housing starts) 9.0 0.59 0.65 0.69 0.71 0.71 0.70 0.65 0.59 0.51 Concrete production 4.7 0.45 0.58 0.68 0 .74 0.74 0.70 0.62 0.53 0.42 Concrete consumption 4.0 0.52 0.65 0.76 0 .82 0.84 0.81 0.75 0.66 0.56 Employment in construction (persons ) 3.4 0.64 0 .76 0.84 0.88 0.84 0.77 0.68 0.58 0 .47 Employment in construction sector (FTE) 9.2 0.78 0.82 0.81 0.72 0.57 0.44 0.30 0.15 0.00 Nominal house prices(*) 0.6 0.38 0.50 0.59 0.65 0.70 0.72 0.72 0.70 0.64 Real house prices(*) 0.6 0.50 0.61 0.68 0 .72 0.73 0.72 0.68 0.62 0.54 Residential investment deflator 1.1 0.17 0.16 0.13 0.10 0.06 0.02 -0.04 -0.10 -0.16 Investment in construction deflator 0.8 0.29 0 .40 0.49 0.56 0.57 0.55 0.51 0.46 0 .39 Mortgage credit 2.4 0.64 0.71 0.75 0.77 0.76 0.73 0.68 0.61 0.52 Epanechnikov filter Variable

Variable

Volatility Variable leads GDP Contemp. Variable lags GDP 4 3 2 1 0 1 2 3 4 Residential investment 3.8 0.86 0.87 0.87 0.86 0.83 0.79 0.74 0.68 0.61 Investment in non residential construction 3.4 0.51 0.59 0.66 0.71 0.74 0.75 0.75 0.74 0.72 Gross value added in construction 2.7 0.70 0.76 0.81 0.83 0.84 0.83 0.80 0.77 0.73 Building permits 11.1 0.73 0.70 0.66 0.60 0.52 0.44 0.35 0.26 0.17 Housing starts 9.1 0.64 0.63 0.62 0.59 0.55 0.50 0.44 0.37 0.29 Housing in progress index (building permits) 10.4 0 .76 0.76 0.75 0.73 0.70 0.65 0.59 0 .52 0.44 Housing in progress index (housing starts) 8.5 0.64 0.65 0.65 0.64 0.61 0.59 0.55 0.50 0.43 Concrete production 5.8 0.59 0.65 0.70 0 .74 0.75 0.72 0.68 0.63 0.56 Concrete consumption 6.1 0.77 0.82 0.87 0 .89 0.90 0.88 0.84 0.79 0.73 Employment in construction (persons ) 4.1 0.68 0 .76 0.83 0.88 0.89 0.88 0.86 0.83 0 .78 Employment in construction sector (FTE) 11.6 0.91 0.93 0.92 0.88 0.81 0.73 0.63 0.53 0.43 Nominal house prices(*) 1.0 0.45 0.51 0.57 0.61 0.64 0.68 0.70 0.72 0.74 Real house prices(*) 1.1 0.52 0.58 0.63 0 .67 0.69 0.72 0.73 0.74 0.75 Residential investment deflator 2.0 -0.07 -0.04 0.00 0.03 0.06 0.09 0.11 0.13 0.15 Investment in construction deflator 1.6 -0.11 -0 .05 0.00 0.06 0.10 0.12 0.14 0.15 0 .17 Mortgage credit 3.4 0.19 0.28 0.36 0.43 0.49 0.54 0.57 0.59 0.60 *Cross correlation computed with housing investment

immigration has played a major role in the recent housing market boom in Spain. Our evidence (table 4) also points out that price cycles lag volume cycles (1 quarter with the Butterworth filter and 4 quarters with the Epanechnikov kernel), reflecting price stickiness or investment decisions anticipating future prices changes. Results on real house prices are less clear. Real prices are coincident with residential investment using the Butterworth filter, but lag 4 quarters with the Epanechnikov kernel. For advanced economies, IMF (2008) finds that real house prices tend to lag the business cycle. For Italy, Bulligan (2010, this volume), finds that house prices lag residential investment. In contrast, Ferrara and Vigna (2010, this volume) find that French real house prices lead GDP. Finally, mortgage credit evidence is inconclusive.

68

´ Luis J. Alvarez and Alberto Cabrero

3 Brevity and violence of expansions and contractions A recurring theme in discussions about business cycle fluctuations is their asymmetric nature: are contractions of economic activity briefer than expansions? Are contractions more violent than expansions? A number of authors have developed theoretical models than allow for such asymmetries. For instance, in Hansen and Prescott (2005) asymmetries are due to capacity constraints: production takes place at individual plants that may or may not be operated in a given period. In recessions, some plants simply are not used, whereas in booms firms hit capacity constraints. In Kocherlakota (2000) asymmetric business cycles are the results of credit constraints. In contractions, agents would like to borrow, but are unable to obtain the amount they would like, as they have credit constraints. As a result, they have to cut down production. Other authors, such as McKay and Reis (2008), put the emphasis on the labour market: In contractions, firms can quickly dismiss workers, but in booms they need time to find and train workers. In our empirical analysis, we first determine the turning points of the different variables, so as to segment the sample into periods of expansions and contractions. Specifically, we identify these periods with a binary random variable (St ) that takes the value of unity in expansions and zero in contractions. Then, we consider a number of statistics to characterise the brevity and violence of the cycles. Turning points are dated non-parametrically, using a variant of the Bry and Boschan (1971) methodology proposed by Harding and Pagan (2002). The method first determines peaks (troughs) as the local maxima (minima) in the series. Second, it eliminates some of these preliminary turning points, so as to ensure that expansion (trough to peak) and contraction (peak to trough) phases exceed a pre-specified number of quarters, while completed cycles have a duration of at least a given number of quarters. We consider durations of 5 quarters for expansions and contractions and 10 quarters for full cycles. Third, it ensures that peaks and troughs alternate. Table 5 presents statistics on the number of peaks, troughs, as well as mean durations and amplitudes of full cycles. In our sample period, we detect around 5 peaks and 4 troughs for the majority of variables. The mean duration of a full cycle (i.e. the time from peak to the next peak) is around 6 years, with a quite homogeneous distribution across variables. There are very marked differences, though, in terms of the amplitude of fluctuations. As expected, fluctuations in GDP are less marked than in residential investment, reflecting the smoothness of household consumption. Moreover, fluctuations in short-term indicators, such as housing starts and building permits, are considerably larger than for other variables. Fluctuations in real variables are generally larger than for prices.

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Table 5 Cyclical characterisation and classification of GDP and construction variables. Butterworth and Epanechnikov filters Butterworth filter Mean duration Mean ampl. Steepness Asymmetry Coincidence Median Lead Exp. Cont. Exp. Cont. Exp. Cont. Duration Amplitude Index Exp. Cont. 14.3 9.5 2.8 3.0 0.2 0.3 1.5 1.0 ... ... ... 11.7 13.8 10.2 10.0 0.9 0.7 0.8 1.0 0.8 3 -2 9.3 9.6 10.4 10.1 1.1 1.0 1.0 1.0 0.7 3 -1 7.5 13.0 7.4 6.9 1.0 0.5 0.6 1.1 0.6 4 1 14.3 11.0 48.1 35.9 3.4 3.3 1.3 1.3 0.6 2.5 1 14.0 11.3 39.0 30.8 2.8 2.7 1.2 1.3 0.6 3 7 12.2 11.0 37.2 32.6 3.1 3.0 1.1 1.1 0.7 0.5 4 12.0 12.5 26.1 31.1 2.2 2.5 1.0 0.8 0.6 0.5 5 12.3 11.8 16.0 18.7 1.3 1.6 1.0 0.9 0.7 1 0 13.7 11.3 12.9 14.3 0.9 1.3 1.2 0.9 0.7 2 -2 22.5 12.3 13.4 14.1 0.6 1.1 1.8 1.0 0.7 3 0 12.0 11.5 9.0 10.7 0.8 0.9 1.0 0.8 0.7 1 0 13.3 10.0 5.7 5.2 0.4 0.5 1.3 1.1 0.8 -0.5 0 12.7 12.0 5.6 5.8 0.4 0.5 1.1 1.0 0.8 0.5 0 9.4 9.5 3.2 2.9 0.3 0.3 1.0 1.1 0.6 2 1 13.7 11.3 3.3 3.7 0.2 0.3 1.2 0.9 0.6 1.5 1 11.3 14.5 7.8 7.7 0.7 0.5 0.8 1.0 0.7 0.5 -2 Epanechnikov kernel Turning points Mean duration Mean ampl. Steepness Asymmetry Concordance Median Lead Peaks Troughs Exp. Cont. Exp. Cont. Exp. Cont. Duration Amplitude Index Exp. Cont. GDP 4 4 15.5 8.3 4.0 2.8 0.3 0.3 1.86 1.41 ... ... ... Residential investment 3 3 24.3 11.0 19.7 12.1 0.8 1.1 2.21 1.63 0.6 6 2.5 Investment in non residential construction 5 5 13.6 9.0 13.0 13.7 1 1.5 1.51 0.95 0.7 2 0 Gross value added in construction 2 2 40.0 13.0 20.2 22.1 0.5 1.7 3.08 0.92 0.7 3 2 Building permits 5 5 16.0 9.3 52.6 33.1 3.3 3.6 1.73 1.59 0.6 2 7 Housing starts 4 3 13.8 11.3 39.8 29.2 2.9 2.6 1.21 1.36 0.5 3 3 Housing in progress index (building permits) 6 5 13.2 9.5 40.8 31.8 3.1 3.3 1.39 1.28 0.7 -1 4 Housing in progress index (housing starts) 5 4 14.0 12.3 35.6 29.7 2.5 2.4 1.14 1.20 0.6 2 5 Concrete production 5 5 14.3 10.5 24.3 18.7 1.7 1.8 1.36 1.30 0.6 0 5 Concrete consumption 5 5 14.4 8.8 21.7 16.5 1.5 1.9 1.65 1.31 0.6 0 4 Employment in construction (persons ) 4 4 19.0 10.0 18.6 17.1 1.0 1.7 1.90 1.09 0.7 3 5 Employment in construction sector (FTE) 4 4 19.0 10.0 18.6 17.2 1.0 1.7 1.90 1.08 0.7 1 1 Nominal house prices 2 2 28.0 28.0 24.9 26.9 0.9 1.0 1.00 0.92 0.6 3.5 12.5 Real house prices 2 2 29.0 28.0 25.4 24.8 0.9 0.9 1.04 1.02 0.6 3.5 -8.5 Residential investment deflator 3 2 27.5 31.0 8.3 9.1 0.3 0.3 0.89 0.91 0.5 4.5 13 Investment in construction deflator 5 4 11.0 10.7 4.1 3.3 0.4 0.3 1.03 1.25 0.7 2 1 Mortgage credit 4 3 14.7 19.3 14.8 15.1 1.0 0.8 0.76 0.98 0.7 3 3 Duration: Number of quarters in expansion (exp.)/contraction (cont.) Amplitude: Change in the cyclical component between begining and end of the expansion/contraction Asymmetry: Ratio of median duration (amplitude) of expansions and contractions. Steepness: Ratio between the duration and amplitude. Shows the intensity of the expansions and contractions Concordance Index: Computed according to Harding and Pagan (2002) Median lead: Number of quarters of median lead(+)/lag(-) Sample period: 1980-Q1 - 2008-Q4

Turning points Peaks Troughs GDP 5 4 Residential investment 5 5 Investment in non residential construction 5 6 Gross value added in construction 4 4 Building permits 5 5 Housing starts 5 4 Housing in progress index (building permits) 6 5 Housing in progress index (housing starts) 5 4 Concrete production 5 5 Concrete consumption 5 5 Employment in construction (persons ) 4 4 Employment in construction sector (FTE) 5 5 Nominal house prices 5 5 Real house prices 5 4 Residential investment deflator 6 6 Investment in construction deflator 5 4 Mortgage credit 5 4

To focus on asymmetries, we compute measures of brevity, violence and steepness of variables. Brevity is measured in terms of average duration of expansions (DE ) and contractions (DC ) DE =

T St ∑t=1 ne

DC =

T (1 − St ) ∑t=1 nc

(1)

where ne and nc refer, respectively, to the number of expansions and contractions and T is the sample size. We find that GDP contractions are substantially briefer than GDP expansions. Depending on the filter, contractions tend to last slightly above 2 years, whereas expansions last close to 4 years. 6 Asymmetry is less clear for residential investment: 6

The difference is economically significant. However, given the simple length, point estimates are fairly imprecise. The null hypothesis that the duration of expansions equals that of contractions is not rejected by the data.

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using the Epanechnikov kernel contractions are briefer, but the opposite result is found with the Butterworth filter. In contrast, other real indicators, such as housing starts or building permits share the asymmetric pattern. Employment in construction tends to show higher asymmetry than GDP, as in McKay and Reis (2008): contractions last between 2 or 3 years, but expansions typically last close to 5 years. Asymmetry in terms of nominal and real house prices is found to be much less relevant. Asymmetry may also refer to the violence of the change. Violence of expansions (Ae ) is measured in terms of the change in the series (∆ yt ) from a trough to the next peak and violence of contractions (Ac ) as the change of the series from the peak to the following trough. Formally,

AE =

T St ∆ yt ∑t=1 ne

AC =

T (1 − St )∆ yt − ∑t=1 nc

(2)

Having estimated the cycles for the different variables, a question that arises is whether booms or busts in two series go in tandem. Harding and Pagan (2002) define a coincidence indicator (CI) that measures the fraction of time that two series are in the same (expansionary or contractionary) phase. Formally, T S1t S2t + (1 − S1t )(1 − S2t ) ∑t=1 (3) T where S1t and S2t are binary variables, defined analogously to St , that capture if series 1 and 2 are either in expansion or contraction. This measure provides additional information to the standard linear correlation coefficient.

CI =

GDP does not show a clear asymmetry in terms of violence: troughs do not appear to be of larger absolute magnitude than peaks and the main two filters we use give conflicting signals. Residential investment also does not present a clear pattern: the Epanechnikov kernel shows asymmetry, but this is not shared by the Butterworth filter. There is no consistent evidence of asymmetry for the rest of variables. Statistics of steepness of expansions and contractions which measure the average gain (loss) per unit of time in an expansion (contraction)- also do not show interesting asymmetric patterns for the different variables. Regarding cyclical classification, Table 5 reports the coincidence index for the different construction variables. It seems that there is substantial comovement of these variables with GDP. Around 70% of the time each variable is in the same expansionary or contractionary phase as GDP. The table also reports the median lead of the turning points in each variable with respect to those in GDP. Results of mean lags confirm those of the previous cross-correlation analysis: housing leads GDP. This is particularly true for housing starts and building permits indicators and somewhat less clear for residential investment. Results for nominal and real prices

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71

are not conclusive: the Butterworth filter suggests a coincident role with respect to GDP, but linear kernels show some lead. In section 2 we have emphasized the leading nature of housing with respect to GDP: housing related variables show a higher correlation with future output than with current or past output. An alternative approach is to analyse whether the turning point in a given variable precedes or not that of GDP. Table 5 also reports median lead for all turning points, peaks and troughs. This allows us to check for asymmetries in the lead-lag relationship. We find that the lead of residential investment with respect to GDP in expansions is larger than in contractions.

4 Concluding remarks This paper analyses housing volume and price cycles in Spain. We find that residential investment is linked to a higher extent with future output than with contemporaneous or past output and thus serves as a leading indicator of GDP, in line with evidence found in the US. Earlier signals of future changes in GDP are given by housing starts or building permits. These empirical regularities deserve close attention and more theoretical work is needed to further understand them. The recent experience of the Spanish economy has shown a marked expansion of housing supply that has not prevented a protracted period of sharp house price rises. It is, therefore, not surprising that we find that fluctuations in home prices have been positively linked to those of residential construction. This supports a view of mainly demand driven housing volume cycles, in line with the observed increase in immigrants and the number of single person households, as well as the drop in interest rates. Among supply factors, technological progress in home building is likely to have played a minor role, but land use constraints probably less so. Moreover, price cycles tend to lag volume cycles, reflecting price stickiness or the fact that building firms may anticipate future prices changes. Third, there are interesting asymmetries in cyclical fluctuations: contractions in GDP and housing real variables appear to be briefer than expansions. Further, we find that the lead of residential investment with respect to GDP in expansions is larger than the lead in contractions.

Acknowledgements We wish to thank participants at the Conference ”The macroeconomics of housing markets”, particulary our discussants Ralph Br¨uggemann (Konstanz University) and Gilles Dufr´enot (Aix-Marseille University and Banque de France). We are also grateful to seminar partic´ ipants at Banco de Espa˜na, Banque de France, Jos´e Manuel Gonz´alez, Luis Angel Maza and Juan Pe˜nalosa for their comments and suggestions. We are specially indebted with V´ıctor G´omez for providing his Butterworth filter software (TRACE).

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References ´ Alvarez, L. J., Bulligan, G., Cabrero, A., Ferrara, L. and Stahl, H. (2009) Housing cycles in the major euro area countries, Banque de France, Working Paper, No. 269 ´ Alvarez, L. J and Cabrero, A. (2009) Pitfalls in business cycle estimation with local polynomial regression, Banco de Espa˜na, mimeo Artis, M.J.; M. Marcellino and T. Proietti (2003) Dating the euro area business cycle. CEPR. Discussion Paper, No. 3696 Aspachs-Bracons, O. and P. Rabanal (2009) The Drivers of Housing Cycles in Spain, IMF, Working Paper, 09/203 Ayuso, J. and F. Restoy (2006) House prices and rents: An equilibrium asset pricing approach, Journal of Empirical Finance, 13, 3, 371–388. Baxter, M. and R. G. King (1999) Measuring Business Cycles. Approximate Band-Pass Filters for Economic Time Series, The Review of Economics and Statistics, 81, 4, 575-593 Bry, Gerhard and Charlotte Boschan (1971), Cyclical Analysis of Economic Time Series: Selected Procedures and Computer Programs, NBER, Technical Working Paper, No. 20 Bulligan, G. (2009), Housing and the macroeconomy: The Italian case, Banca d’Italia, mimeo Burns, A. M. and W. C. Mitchell (1946) Measuring Business Cycles, National Bureau of Economic Research Butterworth, S. (1930) On the theory of filter amplifiers, Experimental Wireless and the Wireless Engineer, 7, 536-541 Canova, F. (1998) Detrending and business cycle facts, Journal of Monetary Economics, 41, 475512 Caporello, G., And Maravall, A. (2004) Program TSW: Revised Manual, Banco de Espa˜na, Occasional Paper, No. 0408 Case, K.; J. Quigley and R. Shiller (2005),Comparing Wealth Effects: the Stock Market versus the Housing Market, Advances in Macroeconomics, 5, 1 Christiano, L. J. and Fitzgerald, T. J. (2003), The band pass filter, International Economic Review. 44, 2, 435-465 Coulson, N. E. and M-S. Kim (2000) Residential Investment, Non-residential Investment and GDP, Real Estate Economics, 28, 2, 233-47 Ferrara, L. and O. Vigna (2009) Evidence of relationships between macroeconomic and housing cycles in France, Banque de France, mimeo Ferrara, L. and S. J. Koopman (2009) Common business and housing markets cycles in the euro area: A multivariate component approach, Banque de France, mimeo G´omez. V. (2001) The use of Butterworth filters for trend and cycle estimation in economic time series, Journal of Business and Economic Statistics, 19, 3, 365-373 G´omez, V. and A. Maravall (2001) Seasonal adjustment and signal extraction time series in A Course in Time Series Analysis. Pe˜na, D., G. C. Tiao and R. S. Tsay (eds.) John Wiley and Sons. Gonz´alez, L. and F. Ortega (2009) Immigration and Housing Booms: Evidence from Spain, Universitat Pompeu Fabra, Department of Economics and Business, Economics Working Papers No. 1167 Green, R. K (1999) Follow the Leader: How Changes in Residential and Non-residential Investment Predict Changes in GDP, Real Estate Economics, 25, 2, 253-270 Hansen, G. D. and E. C. Prescott (2005) Capacity constraints, asymmetries, and the business cycle, Review of Economic Dynamics, 8, 4, 850–865 Harding, D. and A. Pagan (2001a) Dissecting the Cycle: A Methodological Investigation, Journal of Monetary Economics, 49, 2, 365-381 Hodrick, R. J. and E. C. Prescott (1997) Postwar U.S. Business Cycles: An Empirical Investigation, Journal of Money, Credit and Banking, 29, 1, 1-16 Iacobucci, A. and A. Noullez (2005) A Frequency Selective Filter for Short-Length Time Series, Computational Economics, 25, 1, 75-102

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Iacoviello, M. (2005) House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle, American Economic Review, 95, 3, 739-764 Iacoviello, M. and S. Neri (2008) Housing market spillovers: Evidence from an estimated DSGE model, Temi di discussione, 659, Banca d’Italia. International Monetary Fund (April 2008), World Economic Outlook : Housing and the business cycle. Knetsch, T. (2009) Trend and cycle features in German residential investment before and after unification, Deutsche Bundebank, mimeo Kocherlakota, N. R. (2000) Creating business cycles through credit constraints, Quarterly Review, Federal Reserve Bank of Minneapolis, Summer, 2-10 Leamer, E. E. (2007) Housing is the business cycle, Proceedings, Federal Reserve Bank of Kansas City, 149-233 Leamer, E. E. (2009) Homes and Cars: Why are the Cycles in Homes and Consumer Durables so Similar?, Advances in Economic Analysis & Policy, Berkeley Electronic Press, 9, 3, article 5 L’Hotellerie, P. and T. Sastre (2006) Demand decisions by households and firms in Servicio de Estudios del Banco de Espa˜na (ed.) The analysis of the Spanish economy. Banco de Espa˜na McKay, A. and R. Reis (2008) The brevity and violence of contractions and expansions, Journal of Monetary Economics, 55, 4, 738-751 Mikhed, V. and P. Zemcik (2009) Do house prices reflect fundamentals? Aggregate and panel data evidence, Journal of Housing Economics, 18, 2, 140-149 Mills, T. C. (2003) Modelling Trends and Cycles in Economic Time Series, Palgrave Macmillan Mishkin, F. S (2007). Housing and the Monetary Transmission Mechanism, NBER Working Papers, No. 13518, National Bureau of Economic Research Poterba, J. M. (2000). Stock Market Wealth and Consumption, Journal of Economic Perspectives, 14 Prescott, E. C. (1986) Theory Ahead of Business Cycle Measurement, Quarterly Review, Federal Reserve of Minneapolis, Fall, 9-22 Rubio, M. (2009) Fixed and variable mortgages, business cycles and monetary cycle. Working Paper, No. 0903, Banco de Espa˜na. Stock, J. and Watson, M. (1999) Business cycle fluctuations in US macroeconomic time series in J. B. Taylor and M. Woodford (eds.), Handbook of Macroeconomics 1. Elsevier.

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Appendix 1: Database description

1 2 3 4 5 6 7 8 9 10 11 12

Variables GDP Private consumption Public consumption Investment in equipment Residential investment Non residential investment Investment in other products Exports of goods and services Imports of goods and serivces Gross value added in construction Building permits Housing starts

Source QNA. INE and own elaboration (*) QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration QNA. INE and own elaboration Architects and own elaboration (**) Ministry of Housing

Comments

Linkage of national accounts bases 1995 since 1980 to 1994:Q4) and 2000 using q-o-q growth rates Index 2000=100

Number of buiildings Number of houses. Includes both subsidized and unsubsidized houses. Architects and own elaboration Index calculated with building permits and an estimated calendar of construction Ministry of Housing and own elab. Index elaborated on housing starts and an estimated calendar of construction

13 Housing in progress index (building permits) 14 Housing in progress index (housing starts) 15 Concrete production 16 Concrete consumption 17 Employment in construction Labour Force Survey (INE) Thousand of people (persons) 18 Employment in construction QNA and own elaboration Full time equivalent sector (FTE) 19 Nominal house prices Ministry of Housing and own elab. 20 Real house prices INE and own elaboration 21 Residential investment deflator QNA 22 Investment in construction deflator QNA 23 Mortgage credit Bank of Spain (*) INE. National Institute of Statitistics INE (**) Architects: Architects and Technical Architects Associations

Does Housing Really Lead the Business Cycle in Spain?

Appendix 2: Seasonally adjusted (or original) series (1980:1 2008:4)

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Appendix 3: Estimating cycles: methodological considerations Decomposing aggregate output into a trend which accounts for long term growth-, a cyclical component which measures deviations from this trend corresponding to business cycle frequencies- and an irregular component -which accounts for very short-term fluctuations- have been made using a large number of procedures, each with different properties (Canova, 1998; or Mills, 2003). In this context, it is crucial to define beforehand the business cycle concept the researcher is interested in, so as to avoid conceptual confusions. We consider procedures that eliminate trend and irregular components, while retaining intermediate (business cycles) components. Our desired filter is what is known in the literature as an ideal band-pass filter. This definition is conceptually different from the one used in other approaches, such as DSGE models, production function approaches or Markov switching models.

1 The ideal band-pass filter The aim of an ideal band-pass filter is to pass through components of a time series belonging to a pre-specified band of frequencies (pass band), while removing components at higher and lower frequencies. The gain function G(p) of a filter determines how the different cyclical fluctuations contribute to the signal. If G(p0 ) = 1 cyclical fluctuations with period p0 are fully passed by the filter, whereas if G(p0 ) = 0 they are fully suppressed. In formal terms, the ideal band-pass filter GBP i (p) has a gain function (Figure 1) given by  i f |p| < p1 0 1 i f p1 ≤ |p| ≤ p2 GBP I (p) =  0 i f |p| > p2

(1)

which means that cyclical fluctuations belonging to the interval [p1 , p2 ] pass through the filter untouched, but all other fluctuations are completely removed.

1.1 Butterworth filters Butterworth filters [Butterworth (1930)] are low-pass or band-pass filters widely used in electrical engineering in their one-sided form. In business cycle analysis, two-sided versions are to be preferred, to avoid phase shifts that would distort the timing of turning points. There are two families of Butterworth filters, which are

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based on the sine function (BFS) and the tangent function (BFT), respectively. Interestingly, the Hodrick Prescott filter is a particular low pass BFS [G´omez (2001)], so that Butterworth filters are more flexible than the HP filter, suggesting that there may be gains from their use. BFT filters fully suppress high frequency fluctuations, in contrast with BFS, so they are more appropriate for cycle estimation.

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Fig. 1 Butterworth and Epanechnikov filters - Gain as a function of period for the Butterworth band pass filter and impact of changing d (left), and for Epanechnikov filter and impact of changing the bandwith (right)

Butterworth band-pass filters in the time domain are symmetric, two sided filters in the lag and forward operator given by

BPL(L, F ) =

(1 − L2 )d (1 − F 2 )d + λ (1 − α L + L2)d (1 − α F + F 2 )d

(1 − L2 )d (1 − F 2 )d

(2)

where d is an integer parameter, α = cos((ω p2 + ω p1 )/2)/ cos((ω p2 − ω p1)/2), ω p1 , and ω p2 are the lower and upper limits of the band-pass, respectively, and λ is a parameter to ensure that the gain of the filter at a pre-specified period equals one-half. Note that larger values of d produce sharper filters, so there is better approximation to the ideal filter (Figure 1). Approximations to the ideal filter are quite good for moderate values of d. G´omez (2001) suggests a model-based two-stage procedure to obtain the cyclical component based on Butterworth filters, which can be shown to be identical to joint estimation of all components. In the first stage, the series is extended with ARIMA forecasts and backcasts to minimise the size of revisions and then a model-based trend-cycle component is obtained following the methodology in G´omez and Mar-

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avall (2001). Second, the band-pass BFT is applied. This method presents several advantages. First, the identification of a model for the first stage decreases the risk of inducing spurious results. For instance, if one tries to obtain a trend from a white noise series, the first stage will lead to the conclusion that no such a trend exists. Second, since optimal forecasts are used, revisions in preliminary estimates are reduced and an earlier detection of turning points is allowed for. Third, use of trends instead of seasonally-adjusted series or raw data leads to less noisy cycles, so the detection of turning points is easier.

1.2 Kernel regressions Kernel regression is a well known method in the statistical literature, which has recently been used by Leamer (2007) for business cycle analysis. The underlying idea of this nonparametric method is that, under suitable regularity conditions, any function can be well approximated by a Taylor series expansion in the neighbourhood of any point. The approach provides a method for obtaining pointwise estimates. That is, an arbitrary point is chosen and then a local polynomial regression provides an estimate of the trend at that point. The procedure is then repeated for all data points, so to obtain an estimate of the entire trend it is required to fit as many regressions as the number of observations. Specifically, to estimate the trend for a given date (t0 ) a linear regression is fit using only the data in an interval around t0 . The width of the interval used the bandwidth is a fixed number (h) chosen by the analyst. As h gets large, the local polynomial fit approaches the polynomial fit using the whole sample. Specifically,

yt = a(to )+b1 (to )(t −to )+...+bk (t0 )(t −to )k + εt

t ∈ [to − h,to + h]t = 1....n (3)

Each of these regressions is fit using weighted least squares (WLS), solving the following minimization problem over a and b. n

∑ K(

t=1

t − to )(yt − a(to) − b1(to )(t − to ) − ... − bk(t0 )(t − to )k )2 h

(4)

The trend estimate is then obtained as the fitted value of the above regression. In our empirical application, we considerer kernel regression using an Epanechnikov kernel. 7 3 K(u) = (1 − u2)I(|u| ≤ 1) 4 7

(5)

Use of alternative kernels, such as biweight, cosine or Gaussian produces very similar results.

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where u is the argument of the kernel function and I(|u| ≤ 1) is an indicator function that takes a value of one if its argument is true, and zero otherwise. The window width (h), which determines the number of points used in each regression. Increasing (decreasing) h involves using a wider (narrower) interval, which tends to increase (decrease) the smoothness of the trend. We have considered a bandwidth equal to 10. ´ Alvarez and Cabrero (2009) provide a frequency domain interpretation of kernel regressions. Figure 1 plots the gain function of a linear Epanechnikov kernel with different bandwidths. It is seen that the kernel method provides a reasonable approximation to the ideal filter, except for short-run fluctuations, where it performs quite badly. To avoid this problem and make comparisons with results of the Butterworth filter easier, we do not employ original series in our empirical application, but rather the trend-cycle component using G´omez and Maravall (2001) procedure. This method eliminates very short-run fluctuations, so kernel results that we present do not suffer from their general limitation.

1.3 Comparisons with other filters In this section, we briefly review some widely used non-parametric procedures to obtain business cycles. This is relevant since other cyclical analyses of the housing sector have employed different procedures. For instance, Ferrara and Vigna (2009) use a band pass Hodrick and Prescott filter and Bulligan (2009) the Baxter and King (1999) filter. Hodrick and Prescott filter The underlying assumptions of the Hodrick and Prescott (1997) filter are that the trend is stochastic and it varies smoothly over time. The original motivation of the procedure is to obtain a trend balancing its smoothness and the fit to the original series. The parameter λ that characterises the filter determines to which extent fit is traded-off by smoothness. Interestingly, the HP estimator of the cycle may be considered as a high-pass filter (Prescott, 1986). The cyclical HP filter damps cyclical fluctuations with high periods and leaves short-run cycles barely untouched. The higher the value of lambda the more attention is paid to long-term cycles (figure 2). Hodrick and Prescott bandpass filter Given the frequency domain interpretation of the Hodrick-Prescott filter, it is natural to design a band pass filter as the difference of two HP filters (Artis et al., 2003), the first working on short run fluctuations (e.g. less than six quarters) and the second one on long run movements (e.g. fluctuations with periods over 8 years). However, as stressed by Iacobucci and Noullez (2005), the bandpass version of the Hodrick Prescott filter cumulates the

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Fig. 2 Alternative filters - Gain as a function of period for the Hodrick-Prescott filte (top left, as well as impact of changing lambda), for the Hodrick-Prescott bandpass filter (top right), for the Baxter-King filter (bottom left, as well as impact of changing the moving average) and for the Christiano-Fitzgeral filter (bottom right)

compression of two standard HP filters and is thus a poor approximation of the ideal bandpass filter (Figure 2). Baxter and King bandpass filter It is well known that the ideal band-pass filter requires an infinite-order moving average. Since series are of finite length in empirical applications, Baxter and King (1999) derive an approximation of the ideal band-pass filter with a symmetric moving average of 2k + 1 terms. The approximation error (Figure 2) diminishes by increasing k, but this leads to a loss of 2k observations (k leads and k lags). In practice, with quarterly data, k is equal to 12, which entails losing information for the first and last 12 quarters, a great loss for policymakers. Moreover, the gain of the BK filter oscillates around the gain of the ideal filter. Christiano and Fitzgerald (2003) filter Christiano and Fitzgerald (2003) provide an alternative band pass filter. Their optimal filter depends on the data generating process, but they find that weights under the assumption that the series is a random walk provide a reasonable approximation. Weights are not symmetric in terms of past and future observations, except in the middle of the data set, so that for each date a different filter is used.

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The asymmetry of the filter causes a nonzero phase, which distorts the timing of the different frequency components and the nonstationarity causes the gain and the phase to depend on time. Iacobucci and Noullez (2005) stress the spurious shifts induced in the signal by the Christiano and Fitzgerald filter and show that distortions can be large: some cyclical fluctuations can be shifted up to plus or minus 5 months. Another limitation of this procedure is that the gain can be negative, so peaks (troughs) associated with some cyclical fluctuations could be turned into troughs (peaks).

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Appendix 4: Cyclical components (1980:1 2008:4) Cyclical components (% ) 0,06

GDP

0,05 0,04 0,03

0,25

Residential investment

0,15

0,15

0,10

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Housing in progress index (building permits) 0,60 0,40 0,20 0,00 -0,20 -0,40

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Housing in progress index (housing starts)

Concrete consumption

0,30

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Solid line: Butterworth filter (d=6) Dotted line: Epanechnikov filter (Bw=10)

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Investment in non residential construction

0,05

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0,20

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Appendix 5: Cross correlation of variables with GDP. Butterworth filter

RES INV

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´ Luis J. Alvarez and Alberto Cabrero

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Appendix 6: Cross correlation of variables with GDP. Epanechnikov filter

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Housing Cycles in the Major Euro Area Countries ´ Luis. J. Alvarez, Guido Bulligan, Alberto Cabrero, Laurent Ferrara and Harald Stahl

Abstract The recent burst of the house price bubble in the United States and its spillover effects on real economies worldwide has rekindled the interest in the role of housing in the business cycle. In this paper, we investigate the relationships between housing cycles among the four major euro area countries (Germany, France, Italy and Spain) over the sample 1980q1-2008q4. Our main findings are that GDP cycles between 1.5 and 8 years show a high degree of comovement across these four countries, reflecting trade linkages. In contrast comovements in housing market cycles between 1.5 and 8 years are much weaker, idiosyncratic factors playing a major role. House prices are even less related across countries than quantities (residential investment, building permits, housing starts . . . ). We find however much stronger relationships since 1999, i.e. in the EMU period.

JEL codes : E32, R21, R32 Keywords : Housing cycles, synchronisation measures, euro area countries

´ L.J. Alvarez Banco de Espa˜na, e-mail: [email protected] G. Bulligan Banca d’Italia, e-mail: [email protected] A. Cabrero Banco de Espa˜na, e-mail: [email protected] L. Ferrara Banque de France, e-mail: [email protected] H. Stahl Deutsche Bundesbank, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_5, © Springer-Verlag Berlin Heidelberg 2010

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1 Introduction The recent burst of the house price bubble in the United States and its spillover effects on real economies worldwide have reinforced the interest in the role of housing in the business cycle. Cross-country analysis for the euro area is particularly needed to determine the relative importance of common versus idiosyncratic factors in housing markets and its interaction with the rest of the economy. Higher commonalities are to be expected in the European Monetary Union (EMU) period, given the existence of a common monetary policy. However, other determinants of housing markets may be more idiosyncratic. For example, the strength of housing wealth effects depends inter alia on differences in mortgage markets, which greatly differ across euro area countries.1 Other factors, such as the degree of home ownership, the availability of land or the regulatory framework, can also have an important impact on housing demand and supply decisions (Muellbauer and Murphy, 2008). Existing empirical literature on housing markets mostly refers to Anglo-Saxon countries (particularly, the United States and the United Kingdom) and has emphasized the effects of house price movements on consumption and GDP through wealth channels. Even though housing market imbalances in Anglo-Saxon countries have been stronger than in European markets, cross country heterogeneity in price and volume developments raises two issues: firstly, the interaction between housing variables and the macroeconomy within each national economy and, secondly, the role of synchronization across countries of housing variables. Regarding the first ´ issue, Ferrara and Vigna (2010, this volume) and Alvarez and Cabrero (2010, this volume) find, respectively for France and Spain, that current housing sector cycles are strongly correlated with future GDP cycles, in line with Leamer (2007) for the US. In contrast, Bulligan (2010, this volume) finds that house prices and residential investment lag Italian GDP. Knetsch (2010, this volume) analyses the impact of German unification on housing cycles and estimates long term relationships between residential investment and a set of variables such as household income, population and housing prices. The second issue is tackled in this paper and also in Ferrara and Koopman (2010, this volume). Existing idiosyncrasies of housing markets suggest adopting a flexible enough methodological approach, capable of dealing with these differences. For this reason, we adopt non-parametric approaches to define the cycle (section 2) and date its turning points (section 3). The paper concentrates on the analysis of housing cycles, defined as deviations of series from their long term trend, in the four largest euro area countries (Germany, Spain, France and Italy). The choice of concentrating on growth cycles rather than classical business cycles (defined as cycles in the level of a series) is dictated by the limited number of cycles in the latter. The nature of the paper is descriptive and its aim is to highlight a set of stylized facts, still missing in the euro area empirical literature. The next logical step is to develop a theoretical 1

See Mercer Oliver Wyman (2003), ECB (2003) and IMF (2008)

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model able to account for these stylised facts. The analysis covers the period 1980q1-2008q4, thus including the last recession. We additionally investigate a shorter sample, covering the EMU period, since the adoption of a common monetary policy may have affected the relationship between housing and the business cycle. Our benchmark cycle is real GDP. In the analysis, we include several construction related GDP components such as households’ investment, investment in construction, non-residential construction investment and value added in construction. This set of variables is extended by considering additional indicators, such as the number of building permits, the number of housing starts and employment in the construction sector. We also analyse real and nominal house prices. We explore relationships between the different variables by analysing crosscountry pair-wise and multivariate comovement measures. Specifically, for each country pair, we compute cross-correlation coefficients and cross-concordance indexes and carry out a lead-lag analysis of turning points. We also consider two multivariate measures: effective dependence and average diffusion, defined in section 3. Our results are consistent with previous empirical analysis supporting a broadly common GDP growth cycle among the four major euro area countries, with the German cycle presenting stronger idiosyncratic features, including those related to the reunification process. In contrast, national housing markets seem to be weakly interconnected across countries. Indeed, both housing volume and price cycles are mainly driven by country specific factors. Nonetheless, the housing volume cycles in Germany and Italy are similar to each other, as are those in France and Spain, but there is no common volume cycle among all four countries. Evidence from housing price cycles confirms the idiosyncratic nature of housing markets. We also find that synchronization has increased since 1999 among business cycles and housing volume cycles, whereas housing price cycles are more heterogeneous. Section 4 concludes.

2 Methodology A large number of procedures have been developed in the literature to carry out decompositions of aggregate output into a trend –which accounts for long term growth– and a cyclical component –which measures short-term deviations from this trend (see e.g. Mills, 2003). Cyclical analyses of the housing sector have also employed a variety of procedures. For instance, Leamer (2007) has used linear kernels, Ferrara and Vigna (2010, this volume) the band-pass Hodrick and Prescott’s (1997) ´ filter, Bulligan (2010, this volume) the Baxter and King’s (1999) filter and Alvarez and Cabrero (2010, this volume) the Butterworth’s (1930) filter.

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This variety of procedures employed to characterise housing cycles suggests the ´ need to discuss their relative theoretical merits. Alvarez and Cabrero (2009) provide a frequency domain interpretation of linear kernels for business cycle analysis and show that they present a certain number of shortcomings. Gains of this filter –which measure to which extent each cyclical fluctuation contributes to the signal– vary with the precise kernel and bandwidth chosen, but the different variants share three qualitative regularities. First, the filters present an oscillatory gain (typically referred to as the Gibbs phenomenon). Second, short cycles (with periods less than six quarters) are almost fully passed through, instead of being suppressed. Third, cyclical fluctuations with long periods (more than 32 quarters) –which should be attributed to the trend are only partially removed. In turn, the Hodrick and Prescott (1997) filter does not have an oscillatory gain, but being a high-pass filter damps cyclical fluctuations with long periods and leaves short-run cycles barely untouched. In contrast, the Baxter and King (1999) is a band-pass filter, so mainly focuses on the cyclical band. However, the fact that it is a finite moving average filter gives rise to a Gibbs phenomenon. Moreover, the procedure involves losing k observations at the beginning and k at the end of the series –probably, the most interesting period to policy-makers. In standard applications, the filter involves the loss of the last twelve quarters. In this paper, in order to minimize the shortcomings of the most common filters, we employ the Butterworth filter. This filter closely approximates the ideal band´ pass filter (see Alvarez and Cabrero, 2009). This method is well known in electrical engineering in its one sided form, but is rarely used for economic time series.2 Butterworth filters can be low-pass or band-pass, one sided or two sided and can be based on the sine function (BFS) or the tangent function (BFT). Interestingly, the Hodrick-Prescott filter is a particular low pass BFS, so that Butterworth filters are more flexible than the HP filter, suggesting that there may be benefits from their use. Here, we consider band pass filters, since our definition of the business cycle is the output of an ideal band-pass filter, i.e. a filter which passes through cyclical fluctuations of a time series belonging to a pre-specified band of frequencies (pass band), while removing components at higher and lower frequencies. In formal terms, the ideal band-pass filter (GBP I ) has a gain function given by  i f |p| < p1 0 GBP 1 i f p1 ≤ |p| ≤ p2 (1) I (p) =  0 i f |p| > p2

which means that cyclical fluctuations with lengths (p) belonging to the interval [p1 , p2 ] pass through the filter untouched, but all other fluctuations are completely removed. Use of a two-sided version of the filter allows avoiding phase shifts – present in one-sided versions– that would distort the timing of turning points. We consider a Butterworth filter of the tangent, since it fully suppresses high frequency fluctuations, in contrast with Butterworth filters of the sine.

2

But see Stock and Watson (1990) or Gmez (2001).

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Butterworth band-pass filters of the tangent3 can be expressed in the time domain as symmetric, two-sided filters in the lag (L) and forward (F) operators given by

BPF(L, F) =

(1 − L2 )d (1 − F 2 )d + λ (1 − α L + L2)d (1 − α F + F 2 )d

(1 − L2 )d (1 − F 2 )d

(2)

where d is an integer parameter, α = cos((ω p2 + ω p1 )/2)/cos((ω p2 − ω p1)/2), ω p1 and ω p2 are the lower and upper limits of the band-pass, respectively and λ is a parameter to ensure that the gain of the filter at a pre-specified period equals one-half. Note that larger values of d produce sharper filters, so they provide a better approximation to the ideal filter. Following G´omez (2001), we first extend series with ARIMA forecasts and backcasts to minimise the size of revisions and then estimate the model-based trend-cycle component using the methodology in G´omez and Maravall (2001). Finally, we apply the band-pass BFT to the trend-cycle component of the series.4 Our use of trends instead of seasonally-adjusted series or raw data leads to less noisy cycles, thus making easier the detection of turning points. Estimated cycles for the four main variables in our analysis are presented in Figure 1.

3 Results In this section, we describe the cyclical comovements across the four major euro area economies. The main focus of the analysis is the housing market and we distinguish between housing related real and nominal variables (see Appendix 1 for a description of the database). Among housing market indicators, our preferred variables are residential investment (household investment in housing) and house prices in nominal and real terms. We additionally consider some quantity related construction indicators: investment in construction, non-residential construction investment, value added, employment in the construction sector, building permits and housing starts.5 3

Alternatively, they can be given a model-based interpretation: the band-pass BFT can be obtained as the best linear estimator, in the mean squared sense, of the signal in a signal-plus-noise model, where the signal follows a particular ARIMA model. 4 Estimates are carried out using programs TRACE (G´ omez, 1999) and TRAMO and SEATS (G´omez and Maravall, 1996) 5 Since the housing sector only represents between 40% and 60% of construction value added, some variables also reflect developments in other activity branches, such as commercial building and infrastructures.

´ L.J. Alvarez, G. Bulligan, A. Cabrero, L. Ferrara and H. Stahl

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Fig. 1 Estimated cycles for GDP, residential investment and nominal and real house prices (BFT filter)

We refer to synchronization as the degree to which two or more variables comove contemporaneously and measure it for every country pair by the contemporaneous correlation coefficient and by the concordance index between their respective cycles. Since leading/lagging relationships may exist between variables we also consider their dynamic relationships, by analysing the maximum cross-correlation coefficient and maximum cross-concordance index over a range of leads (+) and lags (-), between +4 and -4 quarters. Finally, it is worth bearing in mind that those two measures of synchronization complement each other nicely. Indeed, on the one hand, the correlation coefficient measures the degree to which two variables are linearly related, by using the whole information in variables, while, on the other hand, concordance measures focus only on cyclical turning points, so they can deal with linear and non-linear relationships between variables, but at the expense of discarding some information. In addition, we consider a measure of multivariate linear dependence put forward by Pe˜na and Rodriguez (2003) and referred to as ”effective dependence” in the re-

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maining. This measure can be thought of as a generalisation of the standard squared correlation coefficient in the bivariate case. Specifically, this measure is defined as PR = 1 − |R|1/p

(3)

where |R| denotes the determinant of the correlation matrix of the variables of interest and p denotes the number of variables. PR is bounded between 0 and 1 and a higher value means a higher degree of linear dependence. A set of orthogonal variables leads to PR = 0, whereas PR = 1 entails perfect collinearity among variables. An additional property of this measure is that it can be used to compare groups with a different number of variables. The results of our analysis refer to the sample 1980q1-2008q4. We also consider a sample for the common monetary policy period since 1999q1. The choice tries to strike a balance between the need to incorporate enough cycles in order to get meaningful results and the need to assess any likely change in the most recent subsample. Note that detailed results, including tables and figures, are presented in the working ´ paper version of this study (Alvarez et al., 2009).

3.1 Correlation analysis First, we consider aggregate GDP cycles, then housing volumes construction cycles, and, finally housing price cycles. For each variable, Table 1 contains the average of all contemporaneous bivariate correlations among countries, as well as measures of effective dependence. 3.1.1 Aggregate activity cycles Table 1 reports comovement results for GDP and other macro-variables, GDP being taken as a benchmark against which to evaluate results for housing related variables. An extended empirical literature is available pointing out that GDP cycles in the Euro area are strongly synchronized (e.g. de Bandt, Herrmann and Parigi, 2006), and that synchronization has increased since the mid-nineties (e.g. de Haan, Inklaar and Jong-A-Pin, 2008). Our results, confirm such findings: the average contemporaneous correlation coefficient between all cross-country GDP pairs is 0.58, with pairwise contemporaneous correlations ranging between 0.47 (between Germany and Spain, as well as between Germany and France) and 0.66 (between Italy and France, as well as France and Spain). We find an effective dependence coefficient of 0.36, which is the highest among the variables considered. The cross-correlation ´ analysis (see Alvarez et al., 2009, for details) reveals that the bulk of comovement is contemporaneous, with the exception of Spain, which tends to lead the other countries (Germany and Italy by two quarters and France by one quarter). Furthermore,

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pairwise correlation coefficients show that activity in France, Spain and Italy has important common elements, whereas the German cycle is characterized by stronger idiosyncratic features, partly reflecting the reunification process. 3.1.2 Construction cycles Synchronization between residential investment cycles is considerably lower than among GDPs, with correlation and effective dependence of 0.21. This suggests that country-specific factors tend to play a stronger role in domestic housing markets. Indeed, with the exceptions of Italian and German cycles, which are strongly correlated (0.71) the remaining pairwise correlation coefficients are generally low leading to low effective dependence. Cross-correlation analysis confirms this point and also shows that the Spanish housing investment cycle slightly leads the French one. Residential investment, as defined in quarterly national accounts, covers the construction of new buildings as well as the renovating/upgrading of existing buildings. Cyclical developments in these two types of investment may be different, so it is worthwhile to separate them. National Accounts data do not allow this distinction, but the number of housing starts and building permits may proxy for investment in new buildings. Unfortunately, data on housing starts are only available for Spain and France.6 Nonetheless, the correlation between housing starts cycles in France and Spain is much stronger (0.73) than when considering total residential investment, with the French cycle slightly leading the Spanish one. The French building permits cycle also slightly leads the Spanish one, both cycles being strongly crosscorrelated (0.77). These facts suggest that renovation/upgrade cycles in France and Spain should differ. German building permits in general do not appear to be related to Spanish or French ones. Cycles in non-residential construction investment show a moderate correlation between France and the other countries (0.45 with Germany, 0.32 with Spain, 0.26 with Italy). Cross-correlations reveal that the Spanish cycle leads the Italian and French ones, while the German cycle seems unrelated to the Italian and Spanish ones. Synchronization among total investment in construction variables is lower than that observed for household residential investment (pairwise average correlation 0.15 and effective dependence 0.14), probably reflecting that public construction is not related across countries. In particular, values close to zero are found between 6

The time series for the number of building permits is too short for Italy and in Germany several government interventions aimed at the abolishment of subsidies for residential investment provoked each time a strong anticipation of permits. This, in turn, affects significantly the correlation and lead-lag relationships to other housing variables and we prefer to reserve the analysis of public interventions in the housing sector for further research. We refer for example to Antipa and Schalck (2009) for such an analysis for France.

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Table 1 Average of pair-wise contemporaneous correlation coefficients and measures of effective dependence over 1980q1-2008q4 and 1999q1-2008q4 Average correlations

Effective dependence

1980q1-2008q4 1999q1-2008q4 1980q1-2008q4 1999q1-2008q4

GDP Total invest. in construction Residential invest. Non-residential construction invest. Construction value added Employment in construction sector Building permits Housing starts Nominal house prices Real house prices

0.58 0.15 0.21 0.12 0.19 0.27 0.26 0.70 0.09 0.33

0.88 0.23 0.62 0.45 0.51 0.59 0.38 0.80 0.17 0.22

0.36 0.14 0.21 0.17 0.15 0.23 0.24 0.29 0.28 0.18

0.77 0.21 0.40 0.34 0.36 0.48 0.36 0.40 0.35 0.34

Germany and Italy7 , while a positive and high value is found between Spain and France (0.60). Cross-correlation analysis reveals the leading nature of the Spanish cycle with respect to the French and Italian ones and the lagging nature of the latter. German cycles for that variable seem to be uncorrelated at any lead and lag with the remaining countries, showing, thus, highly idiosyncratic dynamics. We also find a weak synchronization of employment in the construction sector (pairwise average correlation 0.27, effective dependence 0.23), with the exception of a strong synchronization between the Spanish employment cycle and the French one (correlation 0.73). Lead-lag analysis confirms these results. Note however that employment is more strongly synchronized than investment. Synchronization among value added in construction variables is low on average (0.19), ranging from negative between Italy and Germany (-0.25) to mildly positive between Italy and France and France and Spain (around 0.4 in both cases). Lead-lag analysis suggests that Spain tends to lead the other countries. 3.1.3 House price cycles The idiosyncratic nature of national housing markets is even clearer for house price cycles. These are even more country-specific (average pairwise correlation 0.09) than volume housing cycles. We find a strong relationship only between Spain and Italy (correlation 0.79) and a negative correlation of the French cycle with the Spanish and Italian ones (-0.41 in both cases). Furthermore, the German cycle is weakly correlated with those of the other countries. Results from cross-correlation analysis suggest that the negative contemporaneous correlation of the French house price cy7

This indicates a negative correlation between German residential and Italian non-residential construction investment and also between German non-residential and Italian residential investment, offsetting the strong correlation between German and Italian residential investment.

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cle with Italy and Spain reflects the mildly leading nature of the French cycle. As the behaviour of nominal house prices might reflect that of the general price level (see, e.g. Tsatsaronis and Zhu, 2004), we have also performed the same analysis for the real house price indexes. It turns out that the high value of comovements observed between nominal indexes of Italy and Spain is mainly driven by the common behaviour of inflation in these two countries, so that the real house price comovement is considerably lower (correlation 0.15). A lead-lag analysis indicates that most of the comovements are contemporaneous, although Spain lags with respect to the remaining countries.

3.2 Concordance analysis After discussing the results based on correlation coefficients, we focus now on measures of concordance based on the sequence of turning points in the cycles previously estimated. That is, we look for dependence and leads/lags between countries by only taking the dates of turning points into account. It is noteworthy that, by construction, concordance indexes and correlation coefficients are not directly comparable. Especially, a correlation coefficient allows not only a positive relationship but also a negative one, while a concordance index treats a negative relationship as unrelated. In fact, the concordance index measures the fraction of time two binary variables are in the same regime. Furthermore, as mentioned above, the two synchronization measures focus on different and complementary aspects of the cycle, so that in the following some results might differ from those commented upon in the correlation analysis. The first step in the concordance analysis is to identify peaks and troughs in the Butterworth band-pass filter cycles estimated above. Several approaches have been put forward in the literature to identify turning points in macroeconomic time series, either based on parametric modelling or on non-parametric methods. Most parametric procedures are based on Markov-Switching approaches. Following the seminal work by Hamilton (1989), several authors have tried to identify turning points in business cycles, including Krolzig (2001), Ferrara (2003), Artis et al. (2004) or Bengoechea et al. (2006). In contrast, non-parametric methods generally rely on pattern recognition algorithms, as in the standard Bry-Boschan (1971) algorithm. In this paper, we implement the quarterly extension of the Bry-Boschan algorithm proposed by Harding and Pagan (2002) to locate peaks and troughs of the series. We argue that in order to date turning points in the past it is preferable to use a simple tool that avoids specification issues. Basically, the heart of the Bry and Boschan (1971) algorithm, for a time series (yt )t , is given by the following rule:

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Peak at t: {yt > yt−k , yt > yt+k , k = 1, . . . , K} Trough at t: {yt < yt−k , yt < yt+k , k = 1, . . . , K} , where K = 2 for quarterly time series and (yt )t is the Butterworth filtered series under review. This approach is based on a variation in growth rates over a bandwidth in comparison with an a priori threshold set to zero. Once turning points have been identified, for each variable of each country i, we compute a binary variable (Sit ), the so called reference cycle, such that Sit is equal to 1 during a descending phase of the cycle (that is, between a peak and a trough) and zero otherwise. Our aim is to evaluate whether, for each variable, there is a common pattern and synchronisation among countries. There are several ways to assess synchronisation. The simplest one is to compute a concordance index, which measures the fraction of time that the reference cycles of different series are in the same phase (Harding and Pagan, 2002, or Artis et al., 2004) and which is bounded between 0 and 1. For two countries i and j, the concordance index is defined as: ( ) T 1 T CI = (4) ∑ Sit S jt + ∑ (1 − Sit )(1 − S jt ) T t=1 t=1 At each date t, this concordance index is equal to 1 when Si = S j and to 0 when Si = 1 − S j . In order to take possible leads and lags into account, we also compute a cross-concordance index (CCI), based on the concordance between Si,t and S j,t−h , for various positive and negative h. For each pair of countries, we focus on the maximum CCI over all various leads and lags. As in the case of the maximum cross-correlation, this lead-lag is taken as an estimate of the relative timing between turning points in the cycles of countries i and j. As in the above correlation analysis, we compute the contemporaneous and the cross-concordance indexes for h such that h ∈ {−4, −2, −1, +1, +2, +4}, and we retain the lead (lag) that maximizes the CCI. In addition, when the concordance is found to be strong between two countries, we carry out a lead-lag analysis that consists in computing the average lead (lag) of turning points in one country by comparison with the other one. Obviously, strongly related countries will share more common turning points. This lead-lag analysis is complementary to that with cross´ concordance indexes. Results are presented in details in Alvarez et al. (2009). 3.2.1 Aggregate activity cycles Since 1980, all four countries have experienced four complete cycles from peak to peak, if we include the last peak that we provisionally place in 2007q4 or 2008q1 de-

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pending on the country.8 The analysis based on concordance indexes confirms that GDP comovements among the four countries are strongly synchronised: this index ranges from 0.61 (between Italy and Spain) to 0.73 (between Italy and France). Regarding lead-lag relationships, we note that the German cycle appears to be lagging with respect to other cycles (one quarter with respect to France and four quarters with respect to Spain). We have carried out a lead-lag analysis on turning points (see Figure 2) and computed average and median distances between turning points. In Figure 2, a positive value between two countries indicates that the first country leads the second one, and conversely. Because of the small number of points (between 5 and 10 points), median values are more robust and are thus useful to avoid an overly strong influence of extreme values. It turns out that the German cycle lags Spanish and French ones by around three quarters, while it is more coincident with the Italian one. As in the case of cross-correlations, we find that Spanish and French GDP cycles tend to lead those of Italy and Germany. 3.2.2 Construction cycles Regarding residential investment cycles, the concordance indexes confirm the results from correlation analysis that synchronization is lower than for GDP cycles. Also in line with previous analysis is the high concordance between France and Spain (0.72) and between Italy and Germany (0.69). The latter is, however, generally poorly synchronized with other countries, possibly due to the intertemporal distortions connected with the German reunification (see also Knetsch, 2010, this volume, on this point). Note that concordance measures show that the Italian residential investment cycle lags the other ones, in contrast with the correlation analysis (see Figure 2). Regarding building permits and housing starts, concordance indexes between France and Spain are high (0.75) with a French lead of two quarters. The lead-lag analysis reveals an average lead of one quarter and a median lead of two quarters for French building permits, while the average and median leads are both two quarters for French housing starts. In line with results from the correlation analysis, developments in the number of building permits in Germany do not appear to be related to those in France and Spain. Regarding non-residential investment in construction, there is a high degree of concordance between France and the other three countries. Note also that Spain tends to lead Germany and Italy. The more significant comovement of non-residential investment, by comparison with residential investment, may be explained by the stronger interconnection of business activities as opposed to the more local nature of housing markets.

8

Note that, due to end-point effects in filtering, the dates of this last peak are still provisional and can be changed in the future when including new data. However, we have decided to include them in our analysis.

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The analysis of the cycles of total investment in construction cycles confirms the highly idiosyncratic nature of German volume cycles. Relationships between the remaining series for investment in construction are characterized by stronger ties (between France and Spain CI of 0.79). Furthermore, Italy lags France (two quarters) and Spain (four quarters), with a high degree of concordance (0.74 and 0.71, respectively), a finding in line with results from the correlation analysis. Employment in construction is weakly related across countries in terms of cyclical concordance, with the exception of the strong link between France and Spain (CCI=0.75), in line with evidence from correlation analysis. This result suggests the relevance of country specific differences in labour market contracts. Value added in construction cycles are related across countries: concordance analysis suggest that Spain leads the remaining countries, in line with correlation analysis, by around two

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quarters. Concordance analysis shows a tighter relation between the countries than correlation analysis. 3.2.3 House price cycles Overall, results for nominal and real house prices reinforce the diagnosis of idiosyncratic behaviour for domestic housing markets, especially in the case of nominal prices. Indeed, we observe that high concordance indexes are not common for nominal prices, with two exceptions: a high concordance value between Spain and Italy (0.78) and a strong relationship between Germany and Spain (CI=0.69), Germany being leading. The rest of CIs are not higher than 0.60. We also find that the Italian cycle seems to be systematically lagging. Synchronisation is slightly higher in terms of real house prices, reflecting commonalities in consumer price inflation developments. The highest concordance indexes correspond to France and Germany (CCI=0.68) and France and Spain (CCI=0.65), France leading in both cases by one quarter. For the rest of country pairs, the degrees of concordance are very weak, but we observe again that the Italian cycle is systematically lagging. To sum up the results on cross-country comovement, we confirm the notion of a broadly common GDP growth cycle among the four countries, despite the German cycle being characterized by stronger idiosyncratic features. Such high level of comovement is not found among national housing markets. Indeed, both housing volume and price cycles are mainly driven by country specific factors. Volume cycles in Germany and Italy share a different cycle from that between France and Spain. Moreover, Spain tends to lead the other countries. Evidence from housing price cycles confirms the idiosyncratic nature of housing markets.

3.3 Increasing comovements in the Monetary Union In this section, we analyse the change in synchronization in the more recent 19992008 subsample, referred to as the EMU sample hereafter. We compare average pairwise contemporaneous cross-correlations and the effective dependence measure over 1980-2008 with that over the EMU sample. We also consider a third multivariate measure of concordance, based on the average classical diffusion index,9 defined at each date by

9

Several measures are available in the literature. For example, Harding and Pagan (2006) have proposed a test for multivariate non-synchronisation and perfect synchronisation. Candelon et al. (2009) have extended this test in order to take a small number of cycles into account.

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DIt =

1 n j ∑ Si,t n i=1

(5)

j

where Si,t is the binary variable for variable j in country i. We put forward a multivariate synchronisation index (SI), that measures the fraction of time the n countries are simultaneously in the same phase of the cycle (i.e.: for i = 1, . . . , n, Si,t = 0 or Si,t = 1). This index is bounded between 0 and 1. Thus, we define SI by SI =

1 T ∑ 1 {(DIt = 1) ∪ (DIt = 0)} , T t=1

(6)

where 1 {.} is the indicator function. SI is thus equal to one if all four countries are in the same phase for each date t. Table 1 and Figure 3 clearly show that synchronization for the different variables has increased, regardless of the way it is measured. Particularly noteworthy is the increase in synchronization measures for GDP comovements, a finding highlighted in much of the existing empirical literature (e.g. Cabrero et al., 2004). Housing volume cycles consistently show an increase in synchronization, particularly strong for residential investment and milder for housing starts, which already showed a very high value.10 Results for house prices are mixed, depending on the measure considered. Regarding real house prices, the average correlation reduces from 0.33 to 0.22 during the EMU period, while the effective comovement measure increases from 0.18 to 0.34. However, regarding real house prices, both measures increase. Furthermore, changes in house prices during the EMU period are smaller than for volume variables.

4 Conclusions Recent years have seen an increase of papers focussing on housing price cycles and, to a much lesser extent, housing volume cycles. In this paper, we contribute to this latter incipient literature by analysing housing cycles in the four major euro area countries. We take a fully non-parametric approach both in the calculation of cyclical components and in the dating of turning points. As a benchmark to which we compare housing cycles, we find that, in the four major euro area countries, GDP cycles show a high degree of comovement, most likely due to trade linkages, although idiosyncratic factors play a larger role, particularly in Germany. Cross-country comovements are mostly contemporaneous, but developments in Spain tend to lead those in Germany, Italy and France by one or two quarters. In contrast, comovements are substantially weaker for housing mar10 This high value only reflects developments in France and Spain, as there is no data on housing starts for Germany with its rather idiosyncratic housing market, while for Italy the available time period is too short.

´ L.J. Alvarez, G. Bulligan, A. Cabrero, L. Ferrara and H. Stahl

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ket cycles, where country-specific or local variables, such as land availability or regulation, play a major role. Again, residential investment developments in Spain precede those in the other countries and Italy seems to be lagging. Nominal prices are weakly related across countries, but developments in France tend lead those in the other countries. The analysis of the European Monetary Union period clearly shows stronger GDP linkages across countries than in the whole sample, probably reflecting the increasing importance of trade flows. Stronger relationships are also seen for residential investment variables in the period with a common monetary policy, probably due to convergence in mortgage interest rates. Against this background, comove-

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ments in the housing sector continue to be much weaker for prices than for real variables.

Acknowledgements The authors would like to thank Victor G´omez for providing his Butterworth filters software (TRACE), seminar participants at Banca d’Italia and participants of the conference on Macroeconomics of Housing Markets organized at the Banque de France, December 2009, as well as C. Andr´e, O. de Bandt, J. Gonz´alez M´ınguez, T. Knetsch, L. A. Maza and G. Perez-Quiros for useful comments on earlier versions of this draft. The views expressed herein are those of the authors and do not necessarily reflect those of their institutions.

References ´ Alvarez, L. J., Bulligan, G., Cabrero, A., Ferrara, L. and Stahl, H. (2010), Housing cycles in the major euro area countries, this volume. ´ Alvarez, L. J. and Cabrero, A. (2010), Does housing really lead the business cycle in Spain?, this volume. ´ Alvarez, L. J. and Cabrero, A. (2009), Pitfalls in business cycle estimation with local polynomial regression, Banco de Espa˜na, mimeo. Antipa, P. and Schalck C. (2010), Impact of fiscal policy on residential investment in France, this volume. Artis, M., Krolzig, H-M. and Toro, J. (2004), The European business cycle, Oxford Economic Papers, 56, 1-44. Cabrero, A., C. Chuli`a, and A. Millaruelo (2004), An assessment of macroeconomic divergences in the euro area, Banco de Espa˜na, Occasional Paper, No. 0304. Candelon, B, Piplack J. and Straetmans S. (2009), Multivariate business cycle synchronization in small samples, Oxford Bulletin of Economics and Statistics, 71, 5, 715-737. Baxter, M. and R. G. King (1999), Measuring Business Cycles. Approximate Band-Pass Filters for Economic Time Series, The Review of Economics and Statistics, 81, 4, 575-593. Bengoechea, P., Camacho M. and Perez-Quiros G. (2006), A useful tool to identify recessions in the Euro-area, International Journal of Forecasting, 22, 735-749. Bulligan, G. (2010), Housing and the macroeconomy: The Italian case, this volume. Butterworth, S. (1930), On the theory of filter amplifiers, Experimental Wireless and the Wireless Engineer, 7, 536-541. de Bandt, O., Herrmann, H. and Parigi, G. (2006), Convergence or Divergence in Europe? Growth and Business Cycles in France, Germany and Italy, Springer. de Haan, J., R. Inklaar and R. Jong-A-Pin (2008), Will business cycles in the Euro area converge? A critical survey of empirical research, Journal of Economic Surveys, 22, 2, 234-273. ECB (2003), Structural factors in the EU housing markets, European Central Bank, Monthly Bulletin, March 2003 Ferrara, L. (2003) A three-regime real-time indicator for the US economy, Economics Letters, 81, 373-378. Ferrara, L. and O. Vigna (2010), Evidence of relationships between macroeconomic and housing cycles in France, this volume. Ferrara, L. and S. J. Koopman (2010), Common business and housing markets cycles in the euro area: A multivariate component approach, this volume. G´omez. V. (1999), Program TRACE (Trend and Cycle Estimation): Instructions for the user, mimeo. G´omez. V. (2001), The use of Butterworth filters for trend and cycle estimation in economic time series, Journal of Business and Economic Statistics, 19, 3, 365-373.

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G´omez, V. and Maravall, A. (1996), Programs TRAMO and SEATS, Banco de Espa˜na, Working Paper, No. 9628. G´omez, V. and Maravall, A. (2001), Seasonal adjustment and signal extraction time series, in A Course in Time Series Analysis, Pe˜na, D., G. C. Tiao and R. S. Tsay (eds.), John Wiley and Sons. Hamilton, J.D. (1989), A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357-384. Harding, D. and Pagan, A. (2002), Dissecting the Cycle: A Methodological Investigation, Journal of Monetary Economics, 49 (2), 365-381. Harding, D., Pagan, A. (2006), Synchronization of cycles, Journal of Econometrics, 132, 59-79. Hodrick, R. J. and E. C. Prescott (1997), Postwar U.S. Business Cycles: An Empirical Investigation, Journal of Money, Credit and Banking, 29, 1, 1-16. Hoeller, P. and Rae D. (2007), Housing markets and adjustment in monetary union, OECD Economics Department, Working Papers, No. 550. Knetsch T. (2010), Trend and cycle features in German residential investment before and after unification, this volume. Krolzig, H.M. (2001), Markov-switching procedures for dating the Euro-zone business cycle, Quarterly Journal of Economic Research, 3, 339-351. IMF (2008), World Economic Outlook, April 2008. Leamer, E. (2007), Housing is the business cycle, NBER, Working Paper Series, No. 13428. Mazzi, G.L. and Savio, G. (2007), Growth and Cycle in the Euro-zone, Palgrave MacMillan. Mercer Oliver Wyman (2003), Study on the integration of European mortgage markets, European Mortgage Federation, Bruxelles Mills, T. C. (2003), Modelling Trends and Cycles in Economic Time Series, Palgrave Macmillan. Pe˜na, D and Rodriguez, J. (2003), Descriptive measures of multivariate scatter and linear dependence, Journal of Multivariate Analysis, 85,361-374 Stock, J. and M. Watson (1990), Business cycle properties of selected U.S. economic time series, NBER, Working Paper Series, No. 3376. Tsatsaronis, K. and Zhu, H. (2004), What drive housing prices dynamics: Cross-country evidence, BIS Quarterly Review, 65-78, March 2004.

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Appendix 1: Description of the 10 variables includes in the dataset

GDP

Germany (DE)

Spain (ES)

France (FR)

Italy (IT)

1980q1-2008q4

1980q1-2008q4

1980q1-2008q4

1980q1-2008q4

Destatis*

INE* and own elaboration

INSEE*

ISTAT*

1980q1-2008q4

1980q1-2008q4

1980q1-2008q4

INSEE*

ISTAT*

index 2000=100

INE* and own elaboration

1980q1-2008q1

1980q1-2008q4

1980q1-2008q4

1980q1-2008q4

Destatis*

INE* and own elaboration

INSEE*

ISTAT*

1980q1-2008q4

1980q2-2008q4

1981q1-2008q4

INE* and own elaboration

INSEE*

ISTAT*

1980q1-2008q4

1980q1-2008q4

1981q1-2008q4

INE* and own elaboration

INSEE*

ISTAT*

Investment 1980q1-2008q4 in construction Destatis*, Residential investment

Non-residential 1980q1-2008q1 construction Destatis* investment Construction 1980q1-2008q1 value added Destatis*

Employment 1980q1-2008q1 1980q1-2008q4 1980q1-2008q4 1980q1-2008q1 in construction Destatis* INE* and INSEE* ISTAT* sector own elaboration Authorizations 1980q1-2008q1 1980q1-2008q4 1980q1-2008q4 (1) (Building Destatis* Architects and Minist`ere de permits) Technical, Architects l’Ecologie, de l’Energie,

Housing starts

House prices

(1)

1980q1-2008q4

Associations and own elaboration

du D´eveloppement durable et de la Mer. Commissariat g´en´eral au D´eveloppement durable

1980q1-2008q4

1980q1-2008q4

Housing Ministry

Minist`ere de l’Ecologie, de l’Energie, du D´eveloppement durable et de la Mer. Commissariat g´en´eral au D´eveloppement durable

1980q1-2008q4

BulwienGesa AG Housing Ministry and own calculations and own elaboration

Real house prices

1980q1-2008q4

(1)

1980q1-2008q4

Index Insee-Notaries Source: Il consulente since 1996 and internal Immobiliare and back-calculation own calculation

1980q1-2008q4

1980q1-2008q4

1980q1-2008q4

11980q1-2008q4

own elaboration

own elaboration

own elaboration

own elaboration

*National Statistical Institute (1) Unavailable or incomplete time range

Common Business and Housing Market Cyles in the Euro Area from a Multivariate Decomposition Laurent Ferrara and Siem Jan Koopman

Abstract The 2007 sub-prime crisis in the United States, prolonged by a severe economic recession spread over many countries around the world, has led many researchers to focus on the recent fluctuations in housing prices and their relationships with macroeconomics and monetary policies. The existence of common housing cycles among the countries of the euro zone could lead the European Central Bank to integrate more specifically the evolution of such asset prices in its assessment. In this paper, we implement a multivariate unobserved component model on housing market variables in order to assess the common euro area housing cycle and to evaluate its relationship with the economic cycle. Among the general class of multivariate unobserved component models, we implement the band-pass filter based on the trend plus cycle decomposition model and we allow the existence of two cycles of different periods. The dataset consists of gross domestic product and real house prices series for four main euro area countries (Germany, France, Italy and Spain). Empirical results show a strong relationship for business cycles in France, Italy and Spain. Moreover, French and Spanish house prices cycles appear to be strongly related, while the German one possesses its own dynamics. Finally, we find that GDP and house prices cycles are related in the medium-term for fluctuations between 4 and 8 years, while the housing market contributes to the long-term economic growth only in Spain and Germany.

JEL codes : C13, C32, E32, R21 Keywords : House prices, Business cycles, Euro area, Unobserved components model L. Ferrara Banque de France, Directorate Business Conditions and Macroeconomic Forecasting, e-mail: [email protected] S. J. Koopman VU University Amsterdam, Department of Econometrics, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_6, © Springer-Verlag Berlin Heidelberg 2010

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1 Introduction According to European treaties, the main objective of the Eurosystem is to maintain price stability through a two pillars strategy. In opposition to the Fed, the ECB has clarified that price stability is measured by inflation rates of below, but close to, 2% over the medium term. To get this target, the first pillar consists in an analysis based on a large set of economic and financial indicators and the second pillar gives a role to the money. In this respect, it is well known that asset prices are variables of great interest in the conduct of monetary policy and will certainly be more and more integrated in the future in the monetary policy decision-making process. Especially, among all asset prices, the monitoring of housing prices is regularly carried out by central banks. Indeed, housing finance has an impact on the transmission of monetary policy to the economy and a better understanding of the housing sector could lead to more accurate inflation forecasts. Recently, some researchers have put forward that central banks should rather target asset prices instead of inflation in their strategy. For example, Leamer (2007) proposes a monetary policy based on housing starts rather than output gap. Since the summer 2007 the evolution of housing prices has raised concern in the wake of the US sub-prime crisis. The economic recession experienced in industrialised countries has shed light on the role of the housing sector and has led researchers and economists to investigate this specific sector. Regarding the aggregate euro area, assessment of house prices is generally carried out by considering the euro area as whole. However, the aggregate level can hide some country-specific fluctuations. Indeed, to our knowledge, there is no evidence that euro area members housing cycles are synchronized, although several papers have shown that the euro area business and growth cycles cycles are meaningful (see, for example, Anas et al., 2008, for a review of various euro area cycles dating). The existence of a common housing cycle among the countries of the zone could lead ECB to integrate more easily the evolution of this specific asset price in its assessment. On the other side, if country-specific cycles were too large, this would complicate the task of the ECB. A wide number of empirical papers have pointed out the existing relationship between housing and business cycles. For example, Leamer (2007) compares the US housing market cycle and the US business cycle as defined by the Dating Committee of the NBER, from 1947 to 2006. By using the contributions to GDP growth during the 8 phases of recession covering the whole period, Leamer points out that the business cycle is in fact a consumer cycle mainly driven by residential investment. Consequently, the author argues that residential investment can be seen as an accurate early warning of an oncoming recession. Ahearne et al. (2005) find that real house prices are pro-cyclical, that is co-moving with real GDP, consumption, investment, CPI, budget, current account balances and output gaps. They note also that house price booms are typically preceded by a period of expansionary monetary policy, but then diminishing slack and rising inflation lead monetary authorities

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to begin tightening policy before the house price peak. We also refer to Iacovello (2005, 2010, this volume), for a theoretical monetary business cycle model that formalizes the interaction between house prices and the business cycle, or to Goodheart and Hofmann (2008) for empirical evidence of a ”significant multidirectional link between house prices, broad money, private credit and the macroeconomy”. Generally, econometric methods involved in empirical comparison of crosscountry housing cycles rely on graphical inspection of peaks and troughs as in Ahearne et al. (2005) or standard non-parametric tools, such as contemporaneous or ´ cross-correlations as proposed by Catte et al. (2004) or Alvarez et al. (2010, this volume). Parametric modelling has been also undertaken in order to estimate housing cycles. For example, probit regressions have been considered by Borio and McGuire (2004), van den Noord (2006) or Cunningham and Kolet (2007) in order to estimate the probability of an upcoming peak in the housing cycle. Terrones (2004) explains house prices fluctuations and co-movements by using a dynamic factor model for house price growth and six other key variables applied to 13 industrial countries. Del Negro and Otrok (2007) estimate also a dynamic factor model for the US states to differentiate a common cycle in house prices from local state-specific cycles. Cer´on and Su´arez (2004) applied various multivariate extensions of the MarkovSwitching model in order to discriminate between a common cyclical component and country-specific component on housing prices. They also include in the models four variables with a potential impact on housing cycle, namely GDP growth, unemployment rate, interest rates and inflation rate. VAR models have been also considered to relate housing prices shocks, monetary policy and macroeconomic variables. For example, Del Negro and Otrok (2007) implement a VAR model to assess to what extent expansionary monetary policy in the US is responsible for the increase in houses prices. Also Vargas-Silva (2008) examines the impact of monetary policy shocks on the US housing market using a restricted VAR model. In the multi-country framework, Goodheart and Hofmann (2008) or Assenmacher-Wesche and Gerlach (2009) estimate a panel VAR model with 17 OECD countries including quarterly variables such as GDP, house prices, consumer price index, interest rates. In this paper, we present an econometric analysis based on unobserved component time series models to capture the house price cycle among the four main euro area countries (Germany, France, Italy and Spain, representing around 80% of the euro area GDP) and to assess its relationship with the economic growth cycle. The class of unobserved component models as introduced by Harvey (1989) can be effective in the signal extraction of business cycles. We refer for example to Azevedo, Koopman and Rua (2006) for a macroeconomic business cycle application in a multivariate setting. We consider the multivariate unobserved component model for modeling housing price fluctuations and business cycles simultaneously. Fadiga and Wang (2009) have also adopted with success an unobserved component model for identifying common movements and dynamics in the house prices of four main U.S. regions. By specifying different multivariate decomposition models, we empirically identify common trends and cycles in GDP and house price series in

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the four euro area countries for the period from 1981 to 2008. Specifically, we find a strong relationship for macroeconomic growth cycles in France, Italy and Spain. Moreover, French and Spanish house price cycles appear to be strongly related, while the German one possesses its own dynamics. Finally, we find that the GDP and house prices cycles are related in the medium-term for fluctuations between 4 and 8 years, while the housing market contributes to the long-term economic growth only in Spain and Germany.

2 Unobserved components time series models Our aim is to show empirical relationships between macroeconomic and housing cycles for Germany, France, Italy and Spain. We focus on the two key variables Gross Domestic Product (GDP) and real house prices (RHP). The unobserved components (UC) time series model provides a valuable methodology for the econometric analysis of time series, see Harvey (1989) for a complete treatment. While an univariate UC model can be regarded as a pure time series model, the multivariate extension allows the establishment of dynamic relations between different time series which may have an economic interpretation. These dynamic interactions can be disentangled into short, medium and long term effects. In this section we introduce our multivariate UC approach for the purpose of analyzing the dynamics of the GDP series and real house prices for the four euro zone countries (France, Germany, Italy and Spain) with the purpose of studying the dynamic relations between the business and housing market cycles. First we briefly introduce the univariate basic form of the model and provide some details of the model which are needed for an understanding of our analysis.

2.1 Univariate unobserved component models In an UC model, the observed time series is disentangled into components that are formulated as stochastic functions of time and are designed to represent dynamic features such as trend, cycle and irregular noise. A basic decomposition for many macroeconomic time series (in logs) can be based on trend, cycle and noise components where the trend is modelled as a slowly evolving process, the cycle is typically based on a stationary autoregressive moving average (ARMA) process and the noise is often taken as a Gaussian white noise process. The cyclical dynamics for the cycle component can be enforced by having complex characteristic roots in the autoregressive polynomial. It is straightforward in a UC model to introduce additional features such as explanatory variables, interventions and seasonal components. This flexibility is due to the fact that the UC model can be regarded as a special case of the state space model. Therefore, parameter estimation and the signal extraction of the components can be based on the Kalman filter and its related

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smoothing algorithms. In the state space framework, we can treat multivariate time series, missing observations, mixed frequencies, unevenly recorded data and other data irregularities as part of the standard methodology. A detailed treatment of state space methods is presented in Durbin and Koopman (2001). We assume that the observed time series {Yt } is routinely transformed into logs, that is yt = logYt , t = 1, . . . , n. (1) The UC model decomposes yt into additive stochastic components as given by yt = µt + ψt + εt ,

εt ∼ NID(0, σε2 ),

t = 1, . . . , n,

(2)

where µt represents the trend, ψt the cycle component and εt the irregular disturbance term. The trend component µt in (2) is specified in our applications by the local linear trend model as given by

µt+1 = µt + βt + ηt , ηt ∼ NID(0, ση2 ), βt+1 = βt + ζt , ζt ∼ NID(0, σζ2 ),

(3)

where βt represents the drift or slope of the trend µt and the disturbances εt , ηt and ζt are mutually uncorrelated at all lags and leads, for t = 1, . . . , n. Some notable limiting cases of this specification include: if σζ → 0 while ση is nonzero the trend is a random walk with drift β1 ; if ση → 0 while σζ is nonzero the trend follows a smooth integrated random walk; when both tend to zero, µt reverts to a deterministic linear trend. In our empirical section we use a smooth trend specification by restricting ση2 to zero. The initial values of µ1 , β1 are generally unknown, and will be represented by non-informative or diffuse initial distributions. Fluctuations in economic time series associated with medium-term frequencies related to periods between 1.5 and 8 years are typically interpreted as the business cycle, see Baxter and King (1999).1 The dynamic effects related to these medium frequencies appear often less pronounced in the observed economic time series and tend to be of a stationary nature. To incorporare the cyclical dynamics in the time series model, we have the stochastic cyclical component ψt with          ψt+1 ψt κt κt cos λ c sin λ c = + , ∼ NID(0, σκ2 I2 ), ρ ∗ ψt+1 − sin λ c cos λ c ψt∗ κt∗ κt∗ (4) where the three unknown coefficients λ c , ρ and σκ2 in the cycle equation (4) represent, respectively, the cyclical frequency, the damping factor and the cycle disturbance variance, respectively. The period of the cycle is given by 2π /λ c. For |ρ | < 1, 0 < λ < π , the cycle ψt and the auxilary process ψt∗ are stationary ARMA(2,1) processes, with variance σκ2 /(1 − ρ 2). The cycle collapses into an AR(1) process when 1

Sometimes this cycle is also referred to as the growth or deviation cycle (Mintz, 1969) by opposition to the business cycle as defined by the NBER which refers to expansion/recession cycle. However, in this paper we keep the business cycle terminology to describe those medium-term fluctuations.

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λ c approaches zero. The cycle process (4) is stationary when |ρ | < 1 and its unconditional distribution provides the properly defined initial conditions for ψt and ψt∗ . The disturbances κt and κt∗ are specified to be uncorrelated with the disturbances of the other components at all lags and leads, and uncorrelated with the initial distributions. In case the variance for a particular component is equal to zero, the component is deterministic (rather than a dynamic stochastic process). In case the cycle variance is zero (and usually with the estimate of ρ close or equal to unity), the cycle component is a fixed sine-cosine wave. In case the period of a cycle is zero or as a very large value, the cycle process reduces to an autoregressive process of order one with its autoregressive coefficient equal to ρ . The UC model can be formulated as a linear state space model specified by the equations yt = Z αt + εt , εt ∼ NID(0, σε2 ), αt+1 = T αt + ηt , ηt ∼ NID(0, H),

t = 1, . . . , n,

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where the first equation relates the observation yt to an unobserved state vector αt , which contains the trend, cyclical and other components required for describing the model. The state vector is modelled by the vector autoregressive process specified in the second equation, together with an initial distribution for α1 . The system variables Z, T , σε2 , H are chosen to represent a particular model, and will usually depend on unknown parameters, which can be estimated by maximising the Gaussian likelihood function of the model. After replacing the parameters by their estimated values, the unobserved components can be estimated using the Kalman filtering and smoothing equations. For a more complete discussion of state space methods and their applications, we refer to Harvey (1989) and Durbin and Koopman (2001). An introductory text for UC models is Commandeur and Koopman (2007).

2.2 Multivariate unobserved component models The UC model for univariate time series can be easily extended to multivariate time series. For example, letting yt denote a N × 1 vector of observations, a multivariate UC model can be applied to the N time series simultaneously. The decomposition model (2) becomes multivariate when its scalar components is replaced by vector components. We then have yt = µt + ψt + εt ,

εt ∼ NID(0, Σε ),

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to come from multivariate normal distributions. Specifically, we have for t = 1, . . . , n

ηt ∼ NID(0, Ση ),

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The cycle specification (4) has become a vector equation but the discounting factor ρ and cycle frequency λ are common to all elements of ψt . These coefficients are therefore kept as scalars. Harvey and Koopman (1997) define this specification as the similar cycle model. To incorporate cycles with different frequencies in the model, different similar cycle components can be included. The multivariate extension of the trend-cycle decomposition model (2) is referred to as the Seemingly Unrelated Time Series Equation (SUTSE) model. The individual slopes in vector βt are only related through the correlations between the individual disturbances in vector ζt as implied by the variance matrix Σζ . The same principle applies to the slope and cycle vector components in the model. The disturbance variance matrices therefore play an important role. In particular, the rank of the variance matrix is of interest. For example, in case Σζ has full rank, all trend disturbances in ζt have their own unique source of variation but may be correlated between each other. In case Σζ has lower rank, the individual trend disturbances in ζt are generated by a smaller set of independent disturbances. This follows straightforwardly since any variance matrix can be expressed via the Choleski decomposition, that is Σζ = Aζ Dζ A′ζ , (7) where Aζ is a lower unity triangular N × rζ matrix and Dζ is a diagonal rζ × rζ matrix with the rank of Σζ given by rζ . In a strict sense, we require a full column rank matrix for Aζ and positive values on the diagonal of Dζ for matrix Σζ to have rank rζ . Consequently, we have

ζt = Aζ ζt∗ , and

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is a fixed vector with N − rζ non-zero values and rζ zero values. In this where way, all slope variables in βt have different initial values. In case rζ < N and as a consequence Σζ has a lower rank, ζt and βt are linear combinations of a smaller set of stochastic processes. The same arguments apply to other disturbances and components in the model. A lower rank of the variance matrix can be imposed but it can also be the result of estimation. Testing procedures for common trends and cycles have been developed recently by Nyblom and Harvey (2001).

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3 Data As our aim is to show empirical relationships between macroeconomics and housing cycles for France, Germany, Italy and Spain, we focus on two types of variables, namely Gross Domestic Product (GDP) and real house prices (RHP). For the GDP series we use official series as released by statistical institutes of each country. GDP series are expressed in volume and are chain-linked. The RHP series are not officially harmonised at the European level, as it is for example the case for inflation measurement through the Harmonized Index of Consumer Prices (HICP). We therefore use the database constructed by the four main National Cen´ tral Banks of the Eurosystem (see Alvarez et al., 2010, this volume, for a detailed presentation of this dataset). Note however that German house prices have been interpolated from an annual frequency by the Deutsche Bundesbank. Last, we use real house prices deflated by using national HICP. Both types of variables are sampled on a quarterly basis, from 1981 Q1 to 2008 Q4. Thus we integrate the latest fluctuations related to the sub-prime and financial crisis that led to the 2008 economic recession in euro area countries. For each country, GDP and RHP are presented in figures 1 and 2, respectively.

Fig. 1 Quarterly time series for period 1981–2008 (28 years) of gross domestic product (GDP) in volumes for countries (i) France, (ii) Germany, (iii) Italy and (iv) Spain.

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4 Empirical findings 4.1 Preliminary analysis To obtain a first indication of the dynamic properties of the gross domestic product (GDP) and real house prices (RHP) for the four countries, we present in Figure 3 the correlogram and the sample spectrum for each of the eight time series in first differences. It shows that the series do not share strong common dynamic features, especially for GDP series. The four correlograms for the GDP series do not reveal strong serial correlation in the differences. For Germany there is almost no lagged dependence with the exception of lag 4 (that is, one year). This may be due to the interpolation carried from annual series. The dynamic properties for the RHP series present more persistence and are somewhat more similar although France also appears to have almost no serial dependence in its first difference. The sample spectra for the time series confirm these findings. Furthermore, they also show that cyclical dynamics in the differenced series are not apparent and do not have many common features. We conclude that the formulation of an unobserved components time series model for the decomposition of the time series into trend, cycle and irregular components requires a parsimonious and somewhat restricted framework. In particular, we refer to parameters that determine the dynamic properties of a time series in an UC time series model. The dynamic and common features in the observed time series may not be sufficiently strong that all parameters of the model can be estimated

Fig. 2 Quarterly time series for period 1981–2008 (28 years) of real house prices (RHP) for countries (i) France, (ii) Germany, (iii) Italy and (iv) Spain.

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on the basis of this data-set. We therefore will impose restrictions in the selection of the models. All restrictions will be justified and we will present diagnostic results to provide some evidence that restrictions are sufficiently supported by the data-set. The spectra of the time series in first differences do not provide much evidence of cyclical dynamics in the data-set. If any, some cyclical activity can be recognised for frequencies associated with longer cycles (the lower frequencies) and with shorter cycles (the high frequencies, say smaller than 0.5 × 2π = π ). It is hard to separate these features from the low frequencies of the trend. We therefore propose to formulate a flexible cycle component in our model to capture all possible cyclical features in the data. By considering a component for the cyclical dynamics with a length of, say, 5 years and another component for cyclical dynamics of, say, 12 years, we allow all possible cyclical characteristics in the data to be captured. Further details of the model specification are given below. Here we emphasize that we opt for this specification to accomodate a wide range of cyclical features in the model. To separate the trend dynamics from the (weak) cyclical dynamics, we can impose a smoothness restriction for the trend component.

Fig. 3 Correlogram and sample spectrum for quarterly growth rate of gross domestic product (GDP) and real house prices (RHP) for (i) France, (ii) Germany, (iii) Italy and (iv) Spain. The sample for each time series covers the years 1981–2008 (28 years). Each time series consist of 112 observations. The x-axes for the spectra is the frequency scaled by 2π so 0.5 is associated with π and 1.0 with 2π .

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4.2 Empirical model specification These preliminary empirical findings has motivated us to base our analysis on univariate and multivariate unobserved components time series models which are discussed in section 2. We include components for trend, cycle and noise. The cycle component is modelled by two separate cyclical processes with different periods, each of them having the parametric form described in equation (4). The first cycle may capture the shorter term dynamics while the second cycle may account for the longer term dynamics in the cycle component. The model for the time series is then given by yt = µt + ψ1t + ψ2t + εt , (9) where yt is the observed variable (GDP or RHP for France, Germany, Italy or Spain) at time t. The unobserved variables trend µt , irregular εt and cycles ψ1t and ψ2t are discussed in section 2. Each unobserved component is driven by stochastic disturbance processes which are not correlated with each other. In case the analysis is for a single time series, the observation yt and the components µt , ψ1t , ψ2t and εt are scalar variables. In case of a multivariate time series analysis and by adopting the notation as used by (7) and (8), we can reformulate model (6) in terms of common factors. Such a decomposition model with trend, two cycles and irregular components together with possible regression effects (Xt ) is given by (1)

∗(1)

yt = µ ∗ + Aη µt∗ + Aκ ψt

(2)

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+ Aκ ψt

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+ Xt δ + Aε εt∗ ,

(10)

(2)

where factor loading matrices Aη , Aζ , Aκ , Aκ and Aε are lower unity triangular N × r matrices (with r ≤ N varying for each loading matrix) and the common ∗(1) ∗(2) components µt∗ , βt∗ , ψt , ψt and εt∗ are associated with disturbances that have diagonal variance matrices. Common components are of interest for studying the dynamic structures and interactions within a set of time series. For example, common trends imply that economic time series are cointegrated, see the discussion by Stock and Watson (1988). The estimation of the unobserved components trend and cycle together with the maximum likelihood estimation of unknown coefficients is based on state space methods which are applicable to both univariate and multivariate models. Some further details are discussed in the next section.

4.3 Parameter estimation and signal extraction Parameter estimation is based on the maximum likelihood method. The likelihood function is routinely evaluated by the Kalman filter for a given value of the parameter vector. A quasi-Newton optimization method is then employed to maximize the likelihood function with respect to the parameter vector. For this purpose, the score function is evaluated numerically using a smoothing algorithm. This approach is

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implemented in the user-friendly software STAMP 8.0 by Koopman et al. (2007). The Kalman filter and related smoothing algorithms also carry out the estimation of the unobserved components that is often referred to as signal extraction. Finally, the Kalman filter also forms the basis for forecasting. This approach applies to univariate and multivariate models. However, the computational effort becomes more involved when the dimension of yt increases. It may also be numerically more difficult to find the maximum of the likelihood function with respect to a large dimensional parameter space.

4.4 Univariate analysis for each series We begin the empirical analysis by analysing the eight time series (the GDP and RHP series for the four countries France, Germany, Italy and Spain) using the univariate UC model as described in section 2.1. The main purpose of the univariate analysis is to verify whether the trend-cycle decomposition based on equation (9) is adequate for each of the eight time serie and whether possible restrictions are appropriate. The estimation results are reported in Table 1. In this Table 1 we indicate this by “–” and it only occurs for the house prices of Spain. All reported variances are relative to the variance of the irregular component of the model. In case, the irregular variance is estimated as zero, the largest variance of a component is chosen as the numeraire. For all eight time series we report in Table 1 the estimated variances of the disturbances associated with the trend, the two cycle processes and the irregular component. For each cycle component, we further report the estimated values for the discounting factor ρ and the period p (in years). The model decompositions appear to apply for the GDP series with France and Italy having short business cycle frequencies. Some of the estimated cycle components have zero variances (Germany for Cycle 1; France, Italy and Spain for Cycle 2). We emphasize that the sum of Cycle 1 and Cycle 2 is a stochastic stationary time series process. For the GDP time series, the estimated cycles represent rather short term dynamics (most cycle lengths are less than 5 years) except for Germany which has an estimated cycle length of 13.5 years. These findings confirm the features of the series reported in Figure 3. In case of the house price series, the trend-cycle decomposition is clearly applicable for house prices in Germany where the cycle lengths are estimated as 4.48 and 2.82 respectively for Cycles 1 and 2 but with Cycle 2 having a low persistence (ρ is estimated as 0.61) such that the cycle process disappears after two or three periods in future. Most dynamical features in the price series are captured by the flexible trend specifications. This is apparent from the relatively high values for the estimated trend variances. It is difficult to capture the stationary dynamics represented by the cycle components in the relatively short time series of 112 quarterly observations which constitute 28 years in the period from 1981 to 2008. Since all series are decomposed according to a similar model structure, it is of interest to compute the correlations between the extracted cycles. These correla-

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Table 1 Estimation results for univariate models for each series France R 0.65 0.03 0.81 0.17 0.94 0.90 3.04 5 0.00 1 1.0 0.95 5.8 12 1 0.0 7.2 11.4 14.5 24.9 0.31 0.24 France RHP R Trend var 0.59 0.03 Cycle 1 var 0.00 0.01 Cycle 1 ρ 1.0 0.90 Cycle 1 p 6.34 5 Cycle 2 var 0.00 2.19 Cycle 2 ρ 1.0 0.95 Cycle 2 p 8.37 12 Irreg var 1 1 N 23.8 0.59 Q 10.6 187 R2 0.61 0.25 GDP Trend var Cycle 1 var Cycle 1 ρ Cycle 1 p Cycle 2 var Cycle 2 ρ Cycle 2 p Irreg var N Q R2

Germany R 0.01 0.03 0.00 0.15 1.0 0.90 5.42 5 1.81 2.86 0.95 0.95 13.5 12 1 1 3.23 5.23 15.1 14.6 0.11 0.02 Germany R 0.34 0.03 0.31 1.51 0.97 0.90 4.48 5 1 19.9 0.61 0.95 2.82 12 0 1 5.89 9.95 55.5 111 0.35 0.15

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Spain

R 0.48 0.03 3.85 5.75 0.87 0.90 2.97 5 0.00 7.79 1.00 0.95 5.50 12 1 1 6.58 11.1 9.26 13.3 0.23 0.12 Italy R 0.00 0.03 0.04 0.02 0.96 0.90 1.11 5 1 49.4 0.99 0.95 13.3 12 0 1 7.03 8.32 13.7 68.4 0.56 0.22

R 0.10 0.03 0.07 0.00 0.95 0.90 3.62 5 0.00 2.31 1.00 0.95 9.11 12 1 1 27.1 34.9 22.1 24.8 0.22 0.12 Spain R 0.39 0.03 1 0.01 0.34 0.90 – 5 0.00 39.5 0.99 0.95 – 12 0 1 36.1 11.9 29.3 127 0.47 0.28

Note: Parameter estimates for each component are reported. var denotes variance of the component relative to the irregular variance (when applicable), ρ is the discount parameter and p is the period of the cycle (in years). Diagnostic test statistics for the standardized one-step ahead prediction residuals are also reported: N is the Jarque-Bera normality test (distributed as a χ 2 variable with two degrees of freedom (df) and 95% critical value 5.99, Q is the Ljung-Box portmanteau test statistic based on the sum of squared sample autocorrelations (from 1st order upto 12th order of the standardized residuals and R2 is the goodness-of-fit statistic that compares the fit of the model with a simple random walk model. Estimation results are presented for all series and for two model specifications: the UC model (10) with unrestricted parameters and with the restrictions trend var σζ2 = 0.03, Cycle 1 ρ = 0.9, Cycle 1 p = 5, Cycle 2 ρ = 0.95 and Cycle 2 p = 12 (in columns labelled with R).

tions are reported in Table 2. We first concentrate on the aggregate cycle, that is the sum of Cycle 1 and Cycle 2. The cycle components for GDP can be interpreted as business cycles. First, for each country, correlations between GDP and house prices range from 0.06 for Italy and 0.76 for Spain. The high correlation for Spain reflects the strong contribution of the housing sector to the economic growth in Spain. The GDP-RHP correlations for France and Germany are close to 0.5. Second, we find that the GDP cycles for the four countries are strongly correlated, the correlations range from 0.52 to 0.89. The GDP correlations are highest between France, Italy and Spain while all correlations with Germany are the lowest but still larger than 0.5. The German business cycle is known to be lagging the business cycles of other

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´ euro area countries, see for example Alvarez et al. (2010, this volume). It may explain the low GDP correlations with Germany. The housing price cycle correlations between countries range from 0.42 to 0.94. The highest correlations are obtained with the house prices of Spain and France and with those of Germany and Italy. Last, the cross-correlation between GDP of one country and the house prices of another country are all relatively low. Particular low values are between France GDP and Germany price (0.23), France GDP and Italy price (0.15) and Italy GDP and German price (0.08). High cross-correlations are obtained between Spanish prices and, on the one hand, French GDP and Italian GDP, on the other hand. Both are larger than 0.6. When we consider the correlations of the cycles separately for Cycle 1 and Cycle 2, we find that generally the correlations for Cycle 2 are similar to those of the combined cycles. The correlations for Cycle 1 are also similar with the exception of all correlations with Italian housing prices being negative. This is most likely due to the short period of Cycle 1 that is estimated as low as 1.1 years. The other periods for Cycle 1 are estimated at 3 years or higher with the exception of the Germany-RHP Cycle 2. To enable a stable and consistent model-based analysis for the eight time series, we design a trend-cycle decomposition by enforcing the following restrictions: (i) the relative trend variance is set equal to the low value of 0.03; (ii) the length of Cycle 1 and Cycle 2 are set to 5 and 12 years respectively; (iii) the persistence parameters ρ are set to 0.9 and 0.95 respectively. These values are chosen after some experimentation but it has been established that the chosen values produce reliable decompositions. Initial justification of these parameter choices is given at the end of section 4.1. With respect to our choice of the cycle lengths 5 and 12 years, we confirm that the standard business cycle length lies between 1.5 and 8 years. However, in Table 1 we have reported estimates of cycle lengths higher than 8 years, in particular, Germany-GDP, Italy-GDP, France-RHP and Italy-RHP. This finding has motivated us to set the long cycle length to 12 years. The short cycle length of 5 years is close to the average of the estimates of Cycle 1 reported in Table 1. It is found that the reported results are not very sensitive to other choices of cycle lengths when they are fixed at values which are sufficiently close to 5 and 12 years. With respect to the choice of the discount factor ρ , the values 0.9 and 0.95 are close to the estimates from univariate models for Cycles 1 and 2, respectively. The relative trend variance is chosen such that trend component is sufficiently smooth. The remaining parameters are estimated. The estimation results are reported in Table 1 where the restricted models are indicated by the letter R in the column headers. For the restricted models, signal extraction is also carried out by Kalman filter and smoother methods. The implied weight and gain functions of the estimated trend and cycle components from a restricted model are presented in Figure 4. The weight functions are sufficiently wide to produce smooth estimates for trend and cycles. The gain functions show that the decomposition is effective since the trend captures the lowest frequencies, the short cycle appears to weight most heavily on the typical business cycle frequencies while the long cycle captures fluctuations of longer period when they exist. Also a sufficient amount of band-pass properties

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can be recognised in this set of gain functions. The estimated irregular component captures the remaining high frequencies in its gain function that is not reported in Figure 4. Although the normality (N) and serial correlation (Q) diagnostics are somewhat better for the unrestricted models and although the goodness-of-fit (R2 ) measures are worse for all restricted models, the models still produce an effective decomposition. The restrictions enforce the same decomposition model to all eight series. The importance of each cycle component to each series is still determined via the estimation of the two cycle variances. The model is rather poor in terms of goodness-of-fit for the Germany GDP series but we regard this as the exception. The other series provide satisfactory decompositions based on our trend-cycle model (10). From the univariate analysis we can conclude that the decomposition model is adequate for our analysis and that the resulting cycles have sufficient features in common to analyze the series further and to search for common dynamic properties.

4.5 Bivariate analysis for each country The model for a bivariate analysis in which we treat GDP and real house prices simultaneously is considered for each country individually. The model is given by

Fig. 4 The weight and gain functions for a restricted univariate decomposition model with the components (i) trend, (ii) 5-years short cycle, (iii) 12-years long cycle and (not reported) irregular. The x-axes for the gain functions is the frequency scaled by 2π so 0.5 is associated with π and 1.0 with 2π .

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Table 2 Correlations between cycles extracted from univariate models for each series Cycle 1 Fra GDP Fra RHP Ger GDP Ger RHP Ita GDP Ita RHP Spa GDP Spa RHP Cycle 2 Fra GDP Fra RHP Ger GDP Ger RHP Ita GDP Ita RHP Spa GDP Spa RHP Cycle 1 + 2 Fra GDP Fra RHP Ger GDP Ger RHP Ita GDP Ita RHP Spa GDP Spa RHP

Fr GDP Fr RHP Ge GDP Ge RHP It GDP It RHP Sp GDP Sp RHP 1.00 0.46 0.40 0.24 0.64 -0.46 0.57 0.42 0.46 1.00 0.29 0.62 0.33 -0.51 0.35 0.39 0.40 0.29 1.00 0.32 0.75 -0.16 0.67 0.58 0.24 0.62 0.32 1.00 0.18 -0.52 0.06 0.13 0.64 0.33 0.75 0.18 1.00 -0.13 0.61 0.65 -0.46 -0.51 -0.16 -0.52 -0.13 1.00 -0.25 -0.19 0.57 0.35 0.67 0.06 0.61 -0.25 1.00 0.75 0.42 0.39 0.58 0.13 0.65 -0.19 0.75 1.00 Fr GDP Fr RHP Ge GDP Ge RHP It GDP It RHP Sp GDP Sp RHP 1.00 0.51 0.53 0.23 0.89 0.16 0.90 0.63 0.51 1.00 0.46 0.44 0.58 0.68 0.68 0.94 0.53 0.46 1.00 0.52 0.44 0.49 0.62 0.46 0.23 0.44 0.52 1.00 0.07 0.82 0.22 0.43 0.89 0.58 0.44 0.07 1.00 0.08 0.90 0.72 0.16 0.68 0.49 0.82 0.08 1.00 0.29 0.64 0.90 0.68 0.62 0.22 0.90 0.29 1.00 0.76 0.63 0.94 0.46 0.43 0.72 0.64 0.76 1.00 Fr GDP Fr RHP Ge GDP Ge RHP It GDP It RHP Sp GDP Sp RHP 1.00 0.51 0.52 0.23 0.83 0.15 0.89 0.61 0.51 1.00 0.44 0.44 0.52 0.68 0.68 0.94 0.52 0.44 1.00 0.50 0.54 0.47 0.61 0.44 0.23 0.44 0.50 1.00 0.08 0.80 0.22 0.42 0.83 0.52 0.54 0.08 1.00 0.06 0.84 0.64 0.15 0.68 0.47 0.80 0.06 1.00 0.29 0.64 0.89 0.68 0.61 0.22 0.84 0.29 1.00 0.76 0.61 0.94 0.44 0.42 0.64 0.64 0.76 1.00

Note: The reported correlations are for the estimated cycles from the unrestricted univariate analysis for each time series. Since our UC model contains two cycles, we report correlations for each cycle (Cycle 1 and Cycle 2) and for the combined cycle (Cycle 1 +2).

yt = µt + ψ1t + ψ2t + εt ,

(11)

where yt is a 2 × 1 vector containing the observations for GDP and real house prices in a given country at time t. The unobservables trend µt , business cycle ψ1t , longer cycle ψ2t and irregular εt are also 2 × 1 vectors. Each unobservable is driven by bivariate stochastic disturbance processes which are correlated. The estimation results for each country are reported in Table 3. In all cases, we obtain for at least one component a high correlation coefficient between GDP and RHP for a specific dynamic process, providing some evidence that the series have common dynamic features. In all countries, except for Italy, the highest correlation between GDP and RHP is found for the estimated business cycle components. For Italy, the highest correlation is recorded for the irregular component. This may be due to the presence of a shift between the two cycles; it may have vanished

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the contemporaneous correlation. For the other countries, when looking separately at both medium-term and long-term cycles the situation is interestingly quite different. Indeed, for France, the highest correlation is between medium-term cycles (with a period estimated at 8 years), while there is no dependence between long-term cycles of period 15.6 years. This means that the housing market may have an impact on conjunctural economic activity, but the determinants of long-term economic and housing market cycles may be different. The finding for Spain is also different. We find that both medium-term (8.2 years) and long-term (14.4 years) cycles are strongly correlated (0.95 and 0.82, respectively). These results point out the strong dependence between the housing market and the Spanish economic activity, at both short and long frequencies. This may reveal that the housing market has a major role in macroeconomic developments for Spain. It turns out that for many years the Spanish economy has taken benefit from the boom in the housing sector, both in terms of growth and employment, at least until the recent downturn. It appears that, for the same reasons, the housing market cycle in Germany is strongly correlated to economic activity. The periods of the two German cycles are estimated as 4.3 and 7 years which are typical business cycle frequencies. The negative correlation of cycles with the lowest period may indicate a phase shift between GDP and RHP. We note that the estimation results indicate that two cycles can be recognised, a short cycle with a period smaller than 8 years and a long cycle with a period larger than 8 years. Germany and Italy appear to possess only shorter cycles while longer cycles are found for France and Spain where the periods are even as high as 15.6 and 14.4 years, respectively. The relationships in housing prices between France and Spain, on one hand, and between Germany and Italy, on the other hand, could stem from the similar dynamics in terms of short and long cycles. These results seem to justify our choices for the restricted univariate model with short and long cycle lengths of 5 and 12 years, respectively, in section 4.4. The restricted model setting can be regarded as the common denominator of the bivariate models that are estimated in this section. We therefore have also considered the estimation of the bivariate model with the restrictions: (i) the relative trend variance is set equal to the low value of 0.03; (ii) the lengths of the cycles 1 and 2 are set to 5 and 12 years respectively; (iii) the persistence parameters ρ are set to 0.9 and 0.95 respectively. The correlation between the trend disturbances for GDP and RHP is set to zero.

4.6 Four-variate analysis for GDP and house prices Next we consider GDP and RHP series for the four countries and model them simultaneously by the similar decomposition model given in equation (11), where yt is now a 4 × 1 vector of observed GDP or RHP variables for France, Germany, Italy and Spain. After a prior analysis we found that an appropriate decomposition can be based on independent trend µt and independent irregular εt components. In other words, we impose diagonal variance matrices for the disturbances driving

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Table 3 Estimation results for the bivariate model for each country Parameter estimates (Restricted) GDP var RHP var corr.coeff period discount ρ FRANCE sqr-trend Cycle 1 Cycle 2 irregular GERMANY sqr-trend Cycle 1 Cycle 2 irregular ITALY sqr-trend Cycle 1 Cycle 2 irregular SPAIN sqr-trend Cycle 1 Cycle 2 irregular

Diagnostics GDP RHP

0.0 (0.03) 3.0 (0.68) 1.0 (1.75) 0.6 (1.00)

0.0 (0.03) 3.3 (0.21) 126 (229) 1.6 (0.00)

0.00 (0.00) – – N 3.25 13.4 0.88 (0.78) 8.0 ( 5) 0.98 (0.90) Q 17.0 17.4 0.07 (0.53) 15.6 (12) 0.99 (0.95) R2 0.38 0.63 -0.2 (0.00) – –

0.0 (0.03) 2.5 (0.66) 3.1 (0.35) 4.3 (1.00)

0.0 (0.03) 5.4 (1.33) 0.5 (0.46) 1.1 (0.00)

0.00 (0.00) – – N 8.52 1.08 -0.6 (-0.3) 4.3 ( 5) 0.90 (0.90) Q 6.86 42.1 1.00 (0.95) 7.0 (12) 0.98 (0.95) R2 0.39 0.29 0.58 (0.90) – –

0.1 (0.03) 4.3 (6.92) 0.0 (5.23) 0.8 (1.00)

0.9 (0.03) 16. (1.08) 8.4 (1654) 1.2 (1.00)

-0.2 (0.00) – – N 4.19 4.57 -0.1 (-0.8) 6.0 ( 5) 0.92 (0.90) Q 10.1 8.60 0.00 (0.00) 1.1 (12) 0.94 (0.95) R2 0.14 0.47 0.96 (1.00) – –

0.0 (0.03) 3.3 (0.00) 0.0 (1.15) 3.9 (1.00)

0.0 (0.03) 12. (0.00) 83. (133) 7.7 (0.00)

0.00 (0.00) – – N 9.05 21.7 0.95 (1.00) 8.2 ( 5) 0.98 (0.90) Q 17.5 43.0 0.82 (0.61) 14.4 (12) 0.99 (0.95) R2 0.45 0.73 -0.4 (0.00) – –

Notes: Periods are expressed in years. The values in parentheses refer to the restricted model specification. Diagnostic test statistics for the standardized one-step ahead prediction residuals are also reported: N is the Jarque-Bera normality test (distributed as a χ 2 variable with two degrees of freedom (df) and 95% critical value 5.99, Q is the Ljung-Box portmanteau test statistic based on the sum of squared sample autocorrelations (from 1st order upto 12th order of the standardized residuals and R2 is the goodness-of-fit statistic that compares the fit of the model with a simple random walk model.

these components. We could also have assumed to include common trends for the four countries. Our preliminary results indicated that imposing independent trends helps in finding country associations for the cycle components. Given our focus on the cycle components, we have opted for independent trend specifications. An important constraint imposed on the four-variate model is that the cycle disturbances have variance matrices with ranks equal to two. It implies that the euro area cycle is represented by two 5-year cycles and two 12-year cycles. We load the pairs of two cycles on France and Germany. The cyclical dynamics in the GDPs of Spain and Italy are obtained as linear functions of these four cyclical factors. The estimated components (µt , ψ1t , ψ2t and εt ) are graphically presented in Figure 5 for each country. The dynamic specification underlying this decomposition is appropriate since the diagnostic statistics are satisfactory. The estimated common dynamics in the cycle components for GDP are reported in Table 4. The business cycles for Germany and France are highly correlated with each other for the long term cycle. The cycles for Italy and Spain are closely connected with the cycle of France although the short-term cycle of Spain is negatively correlated with the one of France. The cy-

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cles of Germany strongly affect the business cycles of the other countries although its marginal longer term influence on Italy and Spain is negative. From the estimated long cycles in Figure 5 (Cycle 2) we learn that the negative correlations with Germany are due to the close-to-recession years 2003 − 2006 in Germany not experienced by Italy and Spain. In Table 4 we notice the negative loading coefficient for Spain on Germany’s GDP Cycle 2 (−0.41) while its corresponding correlation coefficient is positive (0.64). Given the strong correlation of Germany’s GDP Cycle 2 with the one of France (0.79) and the strong positive loading coefficient for Spain on France’s GDP Cycle 2 (1.79), this apparent contradiction can be clarified. The same decomposition model is applied to the RHP series for the four countries (see bottom panel of Table 4) and the resulting decomposition is presented in Figure 6. The decomposition model specification is the same but we have restricted the variance of the trend component to enforce it as a smooth function of time. The evidence for common dynamics in the housing cycle within the euro area is less evident. The housing price cycles in France and Germany have correlations that do not exceed the value of 0.4. The 5-year RHP cycle of Italy is strongly and negatively correlated with the one of France while the 5-year RHP cycle of Spain is strongly and negatively correlated with the one of Germany. The 12-year housing price cycle dynamics appear to have common features with those in Spain while a negative correlation exists between Germany and Italy. From Figure 6 we learn that the longer cycles have the same swings from peaks to throughs over time, the timings of the

Fig. 5 A multivariate trend-cycle(s) decomposition for the GDP of countries (i) France, (ii) Germany, (iii) Italy and (iv) Spain. 13.00 12.75 12.50

LFRA_GDP

Level

13.25 13.00

LGER_GDP

Level

12.6 12.4

LITA_GDP

Level

12.25

LSPA_GDP

Level

12.00 11.75

12.75

11.50 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.02 LITA_GDP−Cycle 1 0.010 LSPA_GDP−Cycle 1 LFRA_GDP−Cycle 1 LGER_GDP−Cycle 1 0.01 0.02 0.01 0.005 0.00 0.00 0.00 0.000 −0.01 −0.005 −0.01 −0.02 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.050 LSPA_GDP−Cycle 2 LFRA_GDP−Cycle 2 LGER_GDP−Cycle 2 LITA_GDP−Cycle 2 0.025 0.025 0.02 0.025 0.000

0.000

−0.025

−0.025

−0.001

−0.01

0.00

0.000

−0.025 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.0050 LITA_GDP−Irregular 0.02 LSPA_GDP−Irregular LFRA_GDP−Irregular LGER_GDP−Irregular 0.001 0.01 0.0025 0.01 0.000 0.00 0.0000 0.00 −0.0025 −0.01 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010

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peaks and throughs are different. Therefore the correlations between the long-term RHP cycles are mixed between the countries. However, the correlation matrix for the 12-year RHP cycle is quite similar to the one for the 12-year GDP cycle with the exception that the two underlying factors for France and Germany are less correlated for housing price (0.79 for GDP and 0.38 for RHP). Note that those results are in line with the comparative analysis carried out by ´ Alvarez et al. (2010, this volume) for both GDP and RHP variables, although the periods of cycles involved in both analysis are not exactly identical. Table 4 Covariances, correlations and factor loadings for the two cycle components in the fourvariate models for GDP and RHP France Germany Italy GDP Cycle 1 (covariances ×10−6 ) France 4.11 0.25∗ 0.77 ∗ Germany 1.77 11.8 0.81∗ Italy 5.65 10.1 13.1 Spain -1.04 3.50 1.27 GDP Cycle 2 (covariances ×10−6 ) France 8.08 0.79∗ 0.48∗ Germany 7.94 12.5 -0.16∗ Italy 3.43 -1.39 6.28 Spain 11.2 9.11 6.73 RHP Cycle 1 (covariances ×10−6 ) France 15.5 0.37 ∗ -0.89∗ Germany 4.73 10.8 0.10∗ Italy -21.0 1.97 36.2 Spain 0.89 -14.6 -14.6 RHP Cycle 2 (covariances ×10−6 ) France 44.5 0.38∗ 0.70∗ Germany 4.43 3.13 -0.40∗ Italy 66.9 -10.3 207.1 Spain 100.4 19.9 88.3

Spain France Germany factor loadings -0.40∗ 1 0 0.78∗ 0 1 0.27 ∗ 1.08 0.69 1.65 -0.41 0.35 0.98∗ 0.64∗ 0.66∗ 16.4

1 0 0 1 1.42 -1.02 1.79 -0.41 factor loadings 0.05∗ 1 0 -0.91∗ 0 1 -0.50∗ -1.64 0.90 23.8 0.55 -1.60 0.93∗ 0.69∗ 0.38∗ 262.8

1 0 2.13 1.89

0 1 -6.30 3.69

Note: CCorrelations are reported in the upper right part and marked with ∗ . The last two columns (i) report the factor loading matrices Aκ in (10) for i = 1, 2. For the RHP model we have restricted 2 2 the variance of the trend (ση / σε = 0.03) to enforce a smooth trend function.

4.7 Multivariate analysis for all eight variables In this section we carry out a multivariate analysis of all eight variables simultaneously. We collect the GDP and RHP time series for France, Germany, Italy and Spain into the 8 × 1 observation vector yt . We consider the multivariate UC model (10) and discussed in section 2.2. Regression effects are not included in the multivariate model. The same restrictions are imposed on the model as those for the

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bivariate and four-variate models considered earlier (two cycles of periods 5 and 12 years, independent trends, cyclical dynamics of Spain and Italy expressed as linear functions of France and Germany). We limit reporting the estimation results by only presenting the correlation coefficients for the two cycle components. The correlations are presented in Table 5 for the short and long cycles (Cycle 1 and Cycle 2, respectively). From Table 5 we note first that we obtain strong correlations for the 5-year cycles of GDP, they range from 0.66 to 0.88 but there is less evidence for strong correlation for the 12-year cycles of GDP. We find low correlations of the GDP Cycle 2 components with the GDP Cycle 2 component of Germany. However, France and Italy share a common long-term economic cycle. Overall, this finding indicates a strong concordance at the business cycles frequencies among the four countries. In other words, common shocks are driving the euro area business cycle fluctuations, while long-term cycles may have a more idiosyncratic behaviour. We observe relatively low correlations for real RHP variables among the four countries. For the 5-year RHP cycle, only France and Germany have a positive correlation value while Germany and Spain are strongly but negatively correlated. The negative correlation indicates a phase shift in cycles. For example, it is found in the ´ study of Alvarez et al. (2010, this volume) that the Spanish RHP cycle leads other RHP cycles of other euro area countries. With respect to the 12-year RHP cycle, we

Fig. 6 A multivariate trend-cycle(s) decomposition for the RHP of countries (i) France, (ii) Germany, (iii) Italy and (iv) Spain.

5.5 5.0 4.5 4.0

LFRA_RHprice

Level

0.3 0.2 0.1

LGER_RHprice

Level

0.25 0.00

LITA_RHprice

Level

3.0

LSPA_RHprice

Level

2.5

2.0 0.0 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.02 LFRA_RHprice−Cycle 1 0.02 LGER_RHprice−Cycle 1 0.04 LSPA_RHprice−Cycle 1 LITA_RHprice−Cycle 1 0.05 0.01 0.02 0.00 0.00 0.00 0.00 −0.01 −0.02 −0.02 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.050 LGER_RHprice−Cycle 2 0.2 LITA_RHprice−Cycle 2 LFRA_RHprice−Cycle 2 LSPA_RHprice−Cycle 2 0.1 0.2 0.1 0.025 0.0 0.0 0.0 0.000 −0.1 −0.1 −0.2 −0.025 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 0.002 LITA_RHprice−Irregular LFRA_RHprice−Irregular LGER_RHprice−Irregular LSPA_RHprice−Irregular 0.01 5e−5 0.01 0.001 0.00

0

−0.01

−5e−5

−0.25

0.000 0.00 −0.001 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010

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find two relatively high correlations, those between France and Spain and between Germany and Italy (0.58 and 0.57, respectively). There is some evidence of relationships between GDP and RHP cycles of specific countries. Some correlations of substance have appeared mainly for the 12-year cycles. An exception is the 5-year cycle for Spain that possesses a positive correlation (0.34) for its GDP and RHP Cycle 1. With respect to Italy, we obtain close to zero correlations between GDP and RHP at the business cycle frequencies. A similar finding is obtained for the estimated Cycle 1 from the bivariate analysis but also, to a lesser extent, for the estimated Cycle 2 (lower frequencies). We further notice the interesting result that a correlation of 0.41 is found for the 12-year cycle in Germany between its GDP and RHP series. This correlation is also obtained for both restricted and unrestricted bivariate models, implying thus a significant contribution of the housing sector to the long-term dynamics of the economy. Table 5 Correlations for the two cycle components in the eight-variate model France

Germany

Italy

Spain

Cycle 1 France

GDP RHP Germany GDP RHP Italy GDP RHP Spain GDP RHP Cycle 2 France

GDP RHP Germany GDP RHP Italy GDP RHP Spain GDP RHP

GDP RHP GDP 1 -0.33 0.67 1 0.075 1

RHP 0.10 0.65 0.17 1

GDP 0.81 -0.35 0.80 0.055 1

RHP -0.59 -0.13 -0.27 -0.26 -0.037 1

GDP 0.77 -0.12 0.88 -0.10 0.66 -0.55 1

RHP 0.13 -0.64 -0.011 -0.95 0.034 -0.040 0.34 1

GDP RHP GDP 1 0.95 0.19 1 0.44 1

RHP 0.043 0.24 0.41 1

GDP 0.72 0.63 -0.31 -0.005 1

RHP 0.41 0.43 0.26 0.57 0.045 1

GDP 0.54 0.57 0.44 0.036 0.12 0.13 1

RHP 0.50 0.58 0.21 0.29 0.37 0.099 0.61 1

Note: For this model we have restricted the variance of the trend (ση2 / σε2 = 0.03) to enforce a smooth trend function.

5 Conclusions In this paper, we have implemented several multivariate unobserved component models in order to assess commonalities in the housing and business cycles of the four main euro area countries (France, Germany, Italy and Spain) and to detect cycli-

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cal relationships between macroeconomy and the housing sector. Specifically, we have allowed two cycles of different periods in the model specification. It turns out that we have shown synchronisation among the business cycles of the four countries, leading thus to the existence of common cycles in the euro area. In contrast, there is overall less evidence concerning real house prices, although results may slightly vary according the various multivariate model specification. Indeed, in spite of the proven relationship between France and Spain and of commonalities in the long-term cycles, there is no strong common housing cycles in the euro area. It turns out that specificities and regulations in each country strongly contribute to the evolution of domestic house prices. Finally, we find that the GDP and real house prices cycles are related in the medium-term for fluctuations between 4 and 8 years, while the housing market contributes to the long-term economic growth only in Spain and Germany. As further research, it would be useful to integrate phase shifts in unobserved components modelling in order to take leads and lags among cycles into account (see for example Ruenstler, 2004). Another useful specification in this framework would be to assess the convergence of housing cycles over recent years by using the approach proposed by Koopman and Azevedo (2008), especially by integrating the last cycle in the analysis. Last we have used real housing prices to evaluate the housing cycle, but other variables could have been considered as for example residential investment, nominal house prices or measures of volume activity (housing starts, buiding permits ...). ´ Acknowledgements We would like to thank L. Alvarez, C. Andr´e, O. de Bandt, T. Knetsch and G. P´erez-Quir´os for useful remarks on a preliminary version of the paper, as well as participants to the conference on Macroeconomics of Housing Markets organized at Banque de France, December 2009. The views expressed in this paper do not necessary reflect those of the Banque de France.

References Ahearne, A., Ammer, J., Doyle, B., Kole, L. and Martin, R. (2005), House prices and monetary policy: A cross-country study, Board of Governors of the Federal Reserve System, Discussion Paper, No. 841. ´ Alvarez, L., Bulligan, G., Cabrero, A., Ferrara, L. and Stahl, H. (2010), Housing and macroeconomic cycles in the major euro area countries, this volume. Anas, J., Billio, M., Ferrara, L. and Mazzi, G. L. (2008), A system for dating and detecting turning points in the euro area, The Manchester School, 76, 5, 549-577. Assenmacher-Wesche, K. and Gerlach, S. (2009), Monetary policy, asset prices and macroeconomic conditions: A panel-VAR study, National Bank of Belgium, Working Paper Research, No. 149. Azevedo, J., Koopman, S. J. and Rua, A. (2006), Tracking the business cycle of the euro area: A multivariate model-based bandpass filter, Journal of Business and Economic Statistics, 24, 3, 278-290. Baxter, M. and King, R. (1999), Measuring business cycles: Approximate band-pass filters for economic time series, Review of Economics and Statistics, 81, 575-593. Borio, C. and McGuire, P. (2004), Twin peaks in equity and housing prices?, Quarterly Review, 79-93, Bank for International Settlements.

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Catte, P., Girouard, N., Price, R. and Andr´e, C. (2004), Housing markets, wealth and the business cycle, Economic Department, OECD, Working Paper, No. 394. Cer´on, J. and Su´arez, J. (2004), Hot and cold housing markets: International evidence, CEPR, Discussion Paper, No. 5411. Commandeur, J. and Koopman, S. J. (2007), An Introduction to State Space Time Series Analysis, Oxford, Oxford University Press. Cunningham, R. and Kolet, I. (2007), Housing market cycles and duration dependence in the united states and canada, Bank of Canada, Working Paper, 2007-2. Del Negro, M. and Otrok, C. (2007), 99 luftballons: Monetary policy and the house prices boom across US states, Journal of Monetary Economics, 54, 1962-1985. Durbin, J. and Koopman, S. J. (2001), Time Series Analysis by State Space Methods, Oxford, Oxford University Press. Fadiga, M. and Wang, Y. (2009), A multivariate unobserved component analysis of US housing market, Journal of Economics and Finance, 33, 13-26. Goodhart, C. and Hofmann, B. (2008), House prices, money, credit and the macroeconomy, Oxford Review of Economic Policy, 24, 180-205. Harvey, A. C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge, Cambridge University Press. Harvey, A. C. and Koopman, S. J. (1997), Multivariate structural time series models, in C. Heij, H. Schumacher, B. Hanzon and C. Praagman (eds), Systematic Dynamics in Economic and Financial Models, John Wiley and Sons, Chichester, 269-298. Iacovello, M. (2005), House prices, borrowing constraints and monetary policy in the business cycle, American Economic Review, 739-764. Iacovello, M. (2010), Housing in DSGE Models: Findings and New Directions, this volume. Koopman, S. J. and Azevedo, J. (2008), Measuring sychronisation and convergence of business cycles for the euro area, UK and US, Oxford Bulletin of Economics and Statistics, 70, 1, 23-51. Koopman, S. J., Harvey, A. C., Doornik, J. A. and Shephard, N. (2007), STAMP 8.0: Structural Time Series Analyser, Modeller and Predictor, Timberlake Consultants, London. Leamer, E. (2007), Housing is the business cycle, NBER, Working Paper, No. 13428. Mintz, I. (1969), Dating post-war business cycles: Methods and their application to Western Germany, 1950-1967, NBER, Occasional Paper, No. 107. Nyblom, J. and Harvey, A. C. (2001), Testing against smooth stochastic trends, Journal of Applied Econometrics, 16, 3, 415-429. Ruenstler, G. (2004), Modelling phase shifts among stochastic cycles, Econometrics Journal, 7, 232-248. Stock, J. H. and Watson, M. (1988), Testing for common trends, Journal of the American Statistical Association, 83, 1097-107. Terrones, M. (2004), The global house price boom, IMF, World Economic Outlook, Chapter 2. van den Noord, P. (2006), Are house prices nearing a peak? A probit analysis for 17 OECD countries, OECD, Economics Department Working Papers, No. 488. Vargas-Silva, C. (2008), Monetary policy and the US housing market: A VAR analysis imposing sign restrictions, Journal of Macroeconomics, 30, 990-997.

The International Transmission of House Price Shocks Olivier de Bandt, Karim Barhoumi and Catherine Bruneau

Abstract In order to assess transmission mechanisms between global and domestic house prices, and possibly contagion effects, we use a large database of macroeconomic variables for OECD countries. We extract common factors to summarize the comovements of the variables and include them in stationary FAVAR models. We mainly focus on the ”pandemic” view of contagion where local shocks, originating from a country or a local housing market, spread out to other domestic housing markets. An interesting finding is that, even allowing for other channels of international transmission (through global interest rates or activity), the US real house prices, which appear to be exogenous in the US dynamics, unidirectionally causes the international house price factor, which in turn causes the domestic real house price growth for several countries. The channels of contagion from the US appears therefore to be either direct, through house prices (in particular in the UK or Spain), or indirect through other variables.

JEL codes : G33, E32, D21, C41 Keywords : housing, factor models, Vevtor Autoregressive models

O. de Bandt Banque de France, e-mail: [email protected] K. Barhoumi Banque de France, e-mail: [email protected] C. Bruneau Banque de France and University of Paris Ouest - Nanterre La D´efense, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_7, © Springer-Verlag Berlin Heidelberg 2010

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1 Introduction The run-up of the housing bubble as well as the housing crisis that erupted in the USA in the summer of 2006, followed by the crisis in the UK and the sharp fall in house prices in Ireland and Spain, have raised questions of possible international transmission of shocks across countries (Terrones and Otrok, 2004). Arguably, price adjustments in housing markets are slower than in financial markets, given the existence of transaction costs and the absence of full comparability across units, which differ in terms of services they offer, notably location. As a consequence, housing markets are generally viewed as ”local” markets, plagued with idiosyncrasies, even if ”local” economic fundamentals (city-based, regional, or national) may also be a key component of it (see, among others, Ortalo-Magne and Prat, 2009, for such a ”spatial” asset pricing point of view). Despite these traditionnal features of housing markets, the recent period provides, at face value, evidence in favour of correlation across markets. Correlation may occur at different horizons. In the long run, quality-corrected house prices should equalize, within a given economic area as a result of population movements. This may imply leads and lags of a few years between markets. Here, we rather focus on short or medium run links across markets. Different explanations are possible of an international transmission of house price shocks. First of all, house prices may be driven by fundamentals that are either real macroeconomic or financial variables (see Goodhart and Hofmann, 2008 for the role of credit variables). If the cycles of fundamentals are correlated, and house prices are driven by fundamentals, then house prices are likely to comove. Second, news on house prices in some countries may lead investors to revise their expectations on house prices in other countries. Third, in an open economy, house prices may be directly affected by international fundamentals (world activity, global liquidity, world interest rates) that affect global investors arbitraging across domestic house markets (see e.g. Kiyotaki, Michaelides and Nikolov, 2008 for a model of domestic house prices determined by the world interest rate). A final possibility, is that the channel of transmission is time varying, leading to possible ”contagion effects” in case of crisis, and notably global crisis : house price changes are more significant under some circumstances, e.g. when prices are decreasing, or during a crisis. Another definition of contagion, closer to the previous explanation, is also, as in the case of a ”pandemic”, the occurrence of a double interaction, i.e. when local prices in one region affect global prices, which in turn influence local prices in other regions. We investigate the existence of such interactions across countries, notably the link between macroeconomic fundamentals and the dynamics of house prices and the relevance of international comovements, using factor analysis.

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The plan of the paper is the following. Section 2 recalls the main principles of the econometric models we have selected to investigate the question of contagion, namely the Factor Augmented Vector Autoregressive (FAVAR) and the Logistic Smooth Transition Autoregressive (LSTAR) models. In section 3, we present the data. The results are discussed in section 4, as well as the main steps of the empirical analysis.

2 Empirical methods Based on the two definitions we have given above for contagion, we rely on two different tools. FAVAR models, as well as methods to assess non linearities in the reaction of house prices, in particular LSTAR models. We now present them successively.

2.1 FAVAR models for the analysis of the international transmission of house prices House prices in many industrial countries have increased unusually rapidly in recent years and in some cases these increases do not seem to be fully explained by economic fundamentals. The dynamics of house prices have indeed been mainly studied at the national level (Tatsanoris and Zhu, 2004), housing markets being viewed as ”local” in nature. Goodhart and Hofmann (2008) stress the need to extend the set of fundamentals to money and credit variables. In that context, the transmission across markets is mainly national, between local and regional markets. However, Del Negro and Otrok (2007) conclude that the early 2000s in the US were different from before, with a much larger contribution of national as opposed to state level components. In contrast, the analysis of international transmission of housing prices is less developed with the exception of Vansteekiste and Hiebert (2009) who use a Global VAR approach to study comovements of house prices in the euro area and conclude to limited spillovers across countries. Earlier, Terrones and Otrok (2004) had developed a systematic analysis of the dynamics of house prices across a larger number of industrial countries. They showed that house prices were highly synchronized and that the house price boom that took place in the early 2005 was unusual in both its strength and duration. Innovative aspects of the analysis was the use of dynamic factor (DFA) models to determine the extent to which house price comovements are explained by global or country-specific factors and of FAVAR models (for Factor Augmented Vector AutoRegressive models), that combine country-specific vari-

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ables with factors in VAR-type frameworks. Terrones and Otrok (2004) investigated the extent to which fundamentals explain the dynamics of house prices. They indeed found empirical evidence in favor of the dependence of house prices on economic fundamentals (real income growth, interest rates), besides a significant contribution of the autoregressive component: house prices appear to be highly persistent with a significant autocorrelation of order one. Their factor analysis consisted in extracting factors from different variables (not only the growth rate of house price, but also real stock returns, per capita output, per capita consumption, per capita residential investment, and changes in the short- and long-term interest rates) for 13 industrial countries, over the period 1980-2004. The methods allowed to identify complementary factors, namely, a global factor, which affects all variables in all countries, capturing the common shocks affecting these variables, a global housing factor, affecting all house prices in all countries, but not other variables, similarly, a global interest rate factor, capturing common shocks to global interest rates but not to other variables, and so on for each type of variable in the data base. Moreover, country-specific factor were estimated, reflecting the common shocks to the country-specific variables. The results were that a large share (about 40 percent on average) of house price movements appears to be due to global factors, which reflect global co-movements in interest rates, economic activity, and other macroeconomic variables, which in turn result from common underlying shocks. The overall global factor affecting all variables explained (on average) about 15 percent of movements in house prices, while the global housing factor –capturing global shocks to housing markets alone– explains –on average– 25 percent of house price movements, with a clear heterogeneity in the contribution of the common. Our aim is to estimate the same type of FAVAR models from our database described hereafter. We use a slightly different database and extend the sample to include the burst of the housing bubble. We implement a more robust approach to assess the additional explanatory power of international house prices : we first estimate country-by-country models of real house prices based on domestic macroeconomic fundamentals, based on the usual view that housing market are ”local” (i. e. respond to regional or national determinants); we then consider whether international house prices, derived from common factors, help provide better models. In the following section we recall briefly how to build a FAVAR model, which may be of two types, and explain how we implement such a methodology in our case.

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2.1.1 FAVAR Model in the lines of Stock and Watson (2005) One considers a set of n vectors X1t , . . . , Xnt with factor dynamics. The matrix Xt may include in our case, house prices as well as other indicators (GDP, short and long interest rates, prices, housing investment, etc) for a large set of countries. Xit = λi (L) ft + εit where cov( ft , εit ) = 0 and cov(εit , ε jt ) = 0 if i 6= j The idiosyncratic components εit may be serially correlated, for example obeying an AR model of order p: ∀i, εit = δi (L)εit−1 + vit Transforming the model as following: (Id − δi (L)L)Xit = (Id − δi (L)L)λi (L) ft + vit fit = e ⇐⇒ X λi (L) ft + vit allows to get white residuals.

⇐⇒ Xit = e λi (L) ft + δi (L)Xit−1 + vit

The R factors ft = ( f1t , . . . , fRt )′ are dynamic factors obeying an AR model too: ft = Γ (L) ft−1 + ηt Finally, e (L) ft + D(L)Xt−1 + vt Xt = Λ   δ1 (L) 0 0 D(L) =  0 . 0  0 0 δn (L) e e Λ (L) = (λ1 (L), . . . , e λn (L))′ vt = (v1t , . . . , vnt )′ ft = Γ (L) ft−1 + ηt

ηt = (η1t , . . . , ηRt )′ ∀i, ∀r, ∀t, ∀s, E(vit ηrs ) = 0 e dimensional If Γ (L) is a polynomial matrix of order q − 1, one can define the Rfactor Ft , R ≤ Re ≤ Rq as: ′ ′ Ft = ( ft′ , ft−1 , . . . , ft−(q−1) )′

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such that: Xt = Λ Ft + D(L)Xt−1 + vt Ft = Φ (L)Ft−1 + Gηt or, equivalently, in a VAR-type framework:        Φ (L) 0 ξ Ft Ft−1 = + Ft Xt Λ Φ (L) D(L) Xt−1 ξXt       ξ I 0 Gηt + where Ft = vt ξXt Λ It is worth emphasizing that the past values of the ith component do not directly influence the dynamics of the jth component ( j 6= i) because the lag operator D(L) is diagonal. The influence of the ith component on the jth component ( j 6= i), if it exists, is indirectly transmitted through the factors. The previous FAVAR model appears to be a constrained VAR model. It is different from the FAVAR models estimated by Bernanke et al (2004), or Del Negro and Otrok (2005) who do not impose constraints on the autoregressive parameters.

2.1.2 The FAVAR model by Bernanke et al. (2004) The idea underlying the FAVAR models estimated by Bernanke et al. (2004) is the following: if a small number of estimated factors effectively summarizes large amounts of information about the economy, then a natural solution to the degreesof-freedom problem in VAR analyses -which have to be of limited dimensions- is to augment standard VARs with estimated factors. One considers a M × 1 vector Yt of observable economic variables of interest, namely in our case, domestic macro variables (GDP, housing prices, short and long interest rates, housing investment, etc.) for a given country. One assumes that additional economic information, not fully captured by the Y series, may also be relevant to modeling the dynamics of these series. More precisely, one assumes that this additional information can be summarized by an K × 1 vector of unobserved factors, F, where K is “small”. The joint dynamics of (Y, F) is given by:     Ft F = Φ (L) t−1 + vt Yt Yt−1

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with vt denoting a white noise process. The previous model provides a way of measuring the contribution of the additional information contained in the factors Ft . Besides, if the true system is a FAVAR, the estimation of a VAR model for Y , with the factors omitted, may lead to biased estimates of the VAR coefficients and the associated impulse response coefficients. The FAVAR model cannot be estimated directly because the factors Ft are unobservable. However, as the factors represent forces that potentially affect many economic variables, one can suppose that it is possible to infer something about the factors from observations on a variety of economic “informational” time series, denoted by a N × 1 vector Xt . This includes house prices in other countries which may affect domestic house prices. The number of informational time series N is “large” generally assumed to be much greater than the number of factors (K + M << N ) and the series Xt are related to the unobservable factors Ft and the observable factors Yt by: Xt′ = Λ f Ft′ + Λ yYt′ + et′ where Λ f is an N × K matrix of factor loadings, Λ y is N × M , and the N × 1 vector of error terms et are mean zero and are assumed either weakly correlated or uncorrelated, depending on whether estimation is obtained by principal components or likelihood methods. Indeed, the model can be estimated in a two-step principal components approach or a single-step Bayesian likelihood approach. In the two-step procedure, (Ft ,Yt ) is estimated using the first K + M principal components of Xt 1 . In the second step, a FAVAR model is estimated by standard methods, with Ft replaced by Fbt . However, to account for the uncertainty in the factor estimation, it is generally recommended to implement a bootstrap procedure, in order to obtain accurate confidence intervals on the impulse response functions deduced from the FAVAR, except if N is large enough relative to T .

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The estimation of the first step does not exploit the fact that Yt is observed. However, as shown in Stock and Watson (2002), when N is large and the number of principal components Ct used is at least as large as the true number of factors, the principal components consistently recover the space spanned by both Ft and Yt . Fbt is obtained as the part of the space covered by the components Ct that are not covered by Yt , tanks to a specific identifying assumption used in the second step.

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2.2 Non linear single equations : the Smooth Transition Autoregressive (STAR) and the LSTAR specifications In order to detect possible regime shifts that can be associated with contagion, we rely on non linear specifications. 2.2.1 The STAR model Such a model is written as: ′

(1)

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(1)

with F(Zt , γ , s) = [1 + exp(−γ (Zt − s))]−1 , the logistic transition function. Y is the endogeneous variable, X denotes (jointly) the lagged endogenous variable and an exogenous variable and Z the transition variable. In what follows, the exogenous variable is also the transition one. Equivalently, the model can be written as: ′

′

Yt = π10 + π1Xt + (π20 + π2 Xt )([1 + exp(−γ (Zt − s))]−1 − 1/2) + εt (1)

′

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with π10 = φ0 , π1 = φ (1) , π20 = φ0 − φ0 , π2 = φ (2) − φ (1) {γ = 0} indicates that Yt is a linear process:

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Yt = π10 + π1 Xt + εt Accordingly, Ter¨asvirta (1994) test the linear model against the non linear model by implementing the test: H0 :{γ = 0} against H1 :{γ > 0} He propose to implement a LM test, after solving out the identification problem due to the fact that the parameters π20 , π2 and s are not identified under the null hypothesis. There are two usual choices of the transition function which lead to the LSTAR and the ESTAR models. 2.2.2 The LSTAR specification The transition function is the logistic one, defined as: F(Zt , γ , s) = [1 + exp(−γ (Zt − s))]−1

(3)

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• If Zt < s and |Zt − s| tends to infinity, the transition function tends to 0 and the process Yt is characterized by: (1)

′

Yt = φ0 + φ (1) Xt + εt which corresponds to the first regime. • If Zt > s and |Zt − s| tends to infinity, the transition function tends to 0 and the process Yt is characterized by: (2)

′

Yt = φ0 + φ (2) Xt + εt which corresponds to the first regime. Intermediate values of the transition variable implies a combination of both ”regimes” in the dynamics of Y. The transition speed depends on the parameter γ . If γ tends to infinity,one finds an AR specification with varying coefficients, depending on the impact of a dummy variable indicating a crisis event. Note that there is another usual specification of the transition function: the exponential one corresponding to the definition:   F(Zt , γ , s) = 1 − exp(−γ (Zt − s))2

(4)

Thus, if |Zt − s| is large, whatever the value of Zt compared to s, F tends to 1 and the dynamics of Yt is described by: (2)

′

Yt = φ0 + φ (2) Xt + εt On the contrary, Zt is near from the threshold s, la fonction F tends to 0 and the dynamics of Yt obeys: (1)

′

Yt = φ0 + φ (1) Xt + εt In what follows, we prefer to validate a LSTAR model, with two regimes - a normal one and a critical one- respectively associated with a low and an high value of the transition function compared to the threshold. Thus the LSTAR specification allows an easier interpretations of the regimes from an economic point of view.

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The statistic procedure is as follows. First, the maximal lag order of the AR model is chosen by using the AIC criterion. Next, linearity is tested against non linearity. At a third step, one has to validate the LSTAR against the ESTAR specification. Finally, one estimates the parameters of the LSTAR model. In the following sections, we build on the FAVAR literature by considering a slightly different set of house prices (for 15 OECD countries). We proceed in two steps. First, we extract common factors. We estimate these common factors from our database including house prices only. Following Stock and Watson (2005), we consider that the factors can be written in a VAR format. In a second step, we include our common factors into VAR systems for each country. These FAVAR models are estimated with real house prices in the country, as well as other domestic macroeconomic variables (interest rates, GDP, inflation, etc) and the common house price factors. We also test whether the relationship is non linear by estimating by estimating, extended AR-type model including dummies indicating crisis events or LSTAR model.

3 Data As indicated before, the analysis concentrates on house prices, but we also used data for the real economy, using OECD quarterly national accounts (households’ investment, consumption prices, 3-month and 10-year interest rates). We exclude non residential investment (i.e commercial real estate, like offices, warehouses, etc.). For house prices, several database are available, either from the OECD or the BIS. In order to consider a larger (i. e. more recent) sample we rely therefore on national data on house price and checked whether are consistent with the data assembled by the OECD. We use data on Australia, Canada, Switzerland, Finland, France, Germany, Ireland, Italy, Japan, Netherlands, Norway, New Zealand, Spain, United Kingdom, United States, hence a total of 15 countries. It turned out that they are very close to the OECD for the period starting in 1980. We concentrate therefore on the period from 1980Q1 to 2008Q4, where the data are the most reliable. Series were seasonally adjusted. Based on the house price data for 15 countries, we constructed common factor using the Stock&Watson (1998)’s approach, after demeaning and standardizing the quarterly growth rates on nominal prices. The common factors are called f ac1,t , f ac2,t , etc for the first two factors. We also computed two world indices of nominal house prices, based on a geometric average of national house prices, the first one being unweighted, the second one weighted by the share of the country in world GDP. As indicated in Figure 1, the first factor is very close to the quarterly growth rate of the unweighted index.

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4 Modelling approach and empirical results To assess the likelihood of contagion effects, we have considered two different definitions as mentioned before. According to the first definition, contagion occurs when the transmission is different, in particular more pronounced, during crisis events. This implies to investigate whether the results are differently affected across subsamples. In the second approach, we investigate whether global shocks, initially originating at the local level, spread out to other domestic housing markets. In both cases, the main objective is to investigate whether common factors have an effect on domestic real house prices. We consider both linear and non linear models and different information sets, depending whether we extract common factors from a database including housing prices only, or whether we use a more complete database, in order to uncover other channels of transmissions of housing shocks. When we refer to the first definition of contagion, we estimate non linear single equations including dummies indicating crisis events or describing a smooth transition process according to a LSTAR specification. Thus, the factor which is included as the transition variable is extracted from the whole data set (excluding the house prices) or is one of the factor extracted from the house prices only. For the second definition, we estimate FAVAR models for the different countries, with the factor extracted from the set of house prices only. In this case the transmis-

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sion channel of contagion is exclusively based on the house prices. We start the analysis by adopting a simple single equation approach, where we explain the real house price growth by lagged values of domestic fundamentals nominal interest rate and inflation rate- and lagged values of factors extracted from international house prices only. The regressions are thus linear; then, we introduce non linearity in two ways: first, by introducing dummies indicating crisis periods, second, by looking for regimes and smooth transition mechanisms from a LSTAR specification.

4.1 Univariate linear models We first estimate univariate models, using the General-to-Specific approach, as available in the Grocer software, by including factors extracted from the house prices only. 4.1.1 Linear single equations for each country We first estimate, for each country, a model with the autoregressive component, as well as domestic fundamentals (inflation, GDP growth with an expected positive impact, interest rates with an expected negative impact). We then add the first two common house prices based factors ( f ac1,t , f ac2,t ) and test whether the factors have additional explanatory power.2 Notice that all time series are stationary in growth rates (real house prices, consumption deflator), as clearly indicated from unit root tests. The only exception is for the US, which is a more borderline case since only KPSS tests do not reject I(0) for the growth rate of real house prices. We have alternatively tested the factor lagged by one quarter or contemporaneously (but do not present the latter results to save space). The results are exhibited in Table 1 in Appendix A. In all cases, it turns our that the best models, as selected by the General-to-Specific approach, include one-period lagged variables, for domestic fundamentals as well as for factors. All models end up including fundamentals (interest rate or inflation) , except for Australia and UK. 2 Note that in order to avoid spurious correlations, when regressing a country house price on the common house price factor, we exclude the country’s price from the database of international house prices. As a result, f ac1 should actually be written as f aci1 for country i when considering the first common factor extracted from the database of all house prices excluding country i′ s house price. f aci1 enters all regressions involving country i, for example, f acusa 1 in the particular case of the USA. Even if it turns out that such a difference is not very significant, as shown in Figure 2. all ( f aci1 ≃ f ac1j ≃ f acall 1 for all i 6= j, with f ac1 the first common factor from the database of all i all house prices), using f ac1 instead of f ac1 provides more robust results.

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Fig. 2 First common factor from databases excluding one country at a time

A positive and significant coefficient associated with f ac1,t−1 means that increases in international house prices have a positive spillover on domestic prices.3 Two groups of countries can be distinguished: • Australia, Spain and the UK, where the first common factor has a significant effect (at the level of 10%); • the other countries, namely USA, Germany, France and Ireland, where real house prices can be explained by domestic fundamentals only. The level of the interest rate (it−1 ) is associated with a significantly negative coefficient for France, Germany, Ireland. However, when measured in first difference (∆ it−1 ), in order to account for its persistence, it is no longer significant .The coefficient of the (lagged) inflation rate is significant only in the case of Germany. As announced before, we introduce dummies to account for crisis periods and we examine the robustness of the previous results to crisis events. 4.1.2 Robustness to crisis events In order to assess the robustness of the previous results to changes in the transmission mechanism of international house prices during specific events, notably crisis, 3

Note that factors are estimated but this is not taken into account for statistical inference on the ground that they are efficiently estimated in the first (factor extraction) step. This is also consistent with Bernanke, Boivin and Eliasz (2004) who show that two-step Favar analysis yields very similar results to one step analysis.

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Fig. 3 Crisis periods in OECD countries

we now test whether the sensitiveness is time varying. This is a measure of contagion of house prices, as we expect domestic prices to react more significantly to international house prices during crisis periods. Here we test therefore

∆ Log(ph,t−1 ) = α 0 + α1 (L)∆ Log(ph,t−1 ) + α 2 f ac1,t−1 + α3 du crisett f ac1,t−1 + εt where du crisett is a dummy variable that takes the value of 1, during a crisis and 0 otherwise. Under such a specification, α3 measures the differential impact of the crisis on domestic house crisis. Testing for contagion implies rejecting the null hypothesis H0 : α3 = 0 vs H1 : α3 > 0. We need therefore to define du crisett . We use for that the definition of crisis in the World Economic Outlook, April 2009 (based on Reinhart and Rogoff, 2008), which provides the recession periods, associated with financial crisis. When at least one OECD country is in recession, the indicator is equal to one. An alternative index, would measure the proportion of countries in recession. We update such an index by introducing a recession period as from 2008Q2. The index appears in Figure 3. It turns out that for 4 countries, namely Australia, Spain, Ireland and United Kingdom, (See Appendix A, Table 2), α2 is not statistically different from zero, while α3 is significantly negative. This should be interpreted (given the normalization of the housing factor) as a stronger positive elasticity of domestic house prices to international house prices during a financial crisis period.

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Next, we extend the linear models by introducing factors extracted from a larger data base including prices, interest rates, GDP among other variables. 4.1.3 Transmission through other macroeconomic variables We now use the full database described in the data section to compute common factors with a view to consider various transmission channels of house price changes. Several alternatives are possible. Either we extract factors from the whole database of housing and macroeconomic variables, or we consider subsamples of the variables. According to the first approach, we get orthogonal factors, and it is possible to constrain them in order to identify these factors4 . However, factors are linear combination of the variables and maybe difficult to interpret. This would argue in favour of the second approach, on which we focus here. We adopt therefore a three steps procedure. First, we extract 3 common factors from a larger database excluding the house prices. Secondly, we identify the factors (Glob1 price, Glob2 price and Glob3 price). Finally, we estimate for each country the appropriate model, by using one of these ”global” factors or a factor extracted from the house prices only as in previous section. It turns out that the factors that we estimate from that extended database have a direct economic interpretation. As shown in Figure 4 to 6, the first factor of the database excluding house prices, denoted Glob1 pricet−1 ,is correlated with interest rates and captures the remaining non-stationarity in the database. The second factor, denoted Glob2 pricet−1 is correlated with GDP growth. The third factor is an activity specific factor as it appears to be quite close to the world Output Gap. In contrast, when the factors are extracted from a complete database with interest rates in first differences, but after exclusion of inflation, the first common factor is closely related both with the common house price factor as well as the Glob2 price common activity factor (see Figure 7). This confirms our choice to concentrate on the common house price factor and Glob2 price in the remainder of the paper.

4

See Kose, Otrok and Whiteman (2003), Del Negro and Otrok (2007).

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Fig. 4 First global factor excluding house prices (Glob1 price) and world interest rates (%)

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In Table 3 in Appendix A, we present the results from the estimation of the same type of univariate regressions as in Table 1 (Appendix A). The first factor is never

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associated with a significant coefficient except in the case of Ireland. The second factor has now a negative impact in Australia but positive in Spain. The housing factor remains significant in Australia and the UK. It now becomes significant in the case of France, as from the new set of candidate regressors, Grocer selects a model with international house factor f ac1,t as the only regressor on top of the autoregressive component. Now we examine whether the dynamics could have different features depending on different regimes, by estimating LSTAR models.

4.2 LSTAR models When estimating the LSTAR models, we limit us to five countries at this step of the analysis, namely France, Germany, Spain, UK and USA. The investigation will be further extended to the other countries. We run through the different steps and find different transition variables, namely Glob1 prices for Spain and UK, Glob2 prices for France and Glob3 prices for the USA. As indicated above, these factors can be interpreted, respectively, as a global interest rate, the growth rate of global GDP in OECD countries, the (inverted) lagged annual growth rate of GDP. In the Table 4 of Appendix A, we summarize the main results about the instantaneous impact (denoted correlation) of the global factor which is also the transition variable. We just focus on the contemporaneous impact of the global factor. Indeed, it has its own dynamics, which cannot be characterized from the single equation which describes the dynamics of the endogenous variable (the house price). The MA type specification obtained by inverting the AR type model including X (and Y ) involves an infinite number of lags of the exogenous variable (that is the global factor). But contrary to standard impulse response analyses, one cannot consider any shock on the lagged values of the global factor as past innovations. The difference comes from the intertemporal correlations between the different lags of the global factor. The first result is that non-linearity is clearly validated only for two countries, Spain and UK. In both cases, the two regimes are defined by the level of world interest rates: high level of interest rates versus low level. One observes a negative correlation between the level of world interest rates and the first differences in log (real) house prices in these 2 countries. The negative coefficient is stronger when interest rates are low. For France and the USA, house prices respond to the world GDP cycle, but the results may be seen as a bit suspicious, since non-linearity is borderline (the loglikelihood of the model with two regimes is not very different from the model with

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one regime only). For the USA, we observe a positive correlation between the output gap and the first difference in log (real) house price with a higher correlation in expansion periods. House prices are therefore more sensitive to the world output gap when the latter is very positive, than when it is negative. For France, we find a positive (respectively negative) correlation between (contemporaneous) world GDP growth rate and the change in Log real house prices, in expansion periods (respectively recession) periods. For both countries, USA and France, house prices would therefore tend to respond more to activity in the upswing than in the downswing. One can conjecture that other factors than activity, notably financial variables, may explain the adjustment of prices in the downswing. In any case, it is not easy to interpret one or the other regime as a crisis regime. For Spain and UK, one could claim that the low level of interest rate is explained by lower risk premia, and accordingly, the corresponding regime could be viewed as a ”critical” state. Thus we could conclude that we have found evidence of contagion, according to our first definition for both countries. Actually we would rather conclude that we have identified a more ”speculative” behavior of housing markets in the second subperiods, with sharper reactions of house prices to interest rates. To summarize, at this stage of the analysis, the LSTAR approach does not provide a clear conclusion in terms of contagion effects. Moreover, the analysis we have proposed up to now should be considered as a simple investigation preceding the multivariate analysis. Indeed, we will observe that the linear specification of the equation describing the dynamics of the real house price growth rate is dramatically changed inside a FAVAR model, which tends to prove that the regressors of the single equations are not exogenous. In what follows, we focus on the multivariate analysis involving all factors extracted previously (including the first factor extracted from international house prices only) except the first global factor, which we drop because of its high persistence. However, as it is strongly related to interest rates, we decide to systematically include a national long term interest rate in the FAVAR models, after differencing this variable to insure its stationarity.

4.3 FAVAR models and causality analysis In this section, we present the results we have obtained for each country of the panel, by estimating a FAVAR model. It is worth emphasizing that we do not have any tool which allows us to choose the best FAVAR model. Our General-to-Specific approach, carried out through the GROCER software, in order to select the best specifications of the single equations for all countries, cannot be used in the VAR context.

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We postulate a special role for the USA and look whether the American housing market can trigger contagion channels to the rest of the world. We check that it is indeed the case using causality tests5 . The numerical results are detailed in Appendix. For the USA, we include three factors, f ac1 , Glob2 price and Glob3 price, on top of the domestic long term interest rate and house price growth rate. This allows to shed light on the maximum number of transmission channels. Indeed, according to our ”pandemic” view of contagion once a factor is influenced by one (or two) of the local variables, it can be associated with a contagion mechanism of a shock originating from the local house market or interest rate. Moreover, it is worth examining whether contagion effects involve the house markets only or more global activity channels. For the other countries we limit the FAVAR model to four components, the interest rate, the real house price growth and two factors, the house price factor f ac1 and Glob2 price or Glob3 price, depending on the country. Due to the limited number of observations, we aim at limiting the order of the FAVAR models. However, the persistence of the factors obviously increases the autoregressive order of the models. We test therefore different types of models, which mainly differ in terms of lags and estimation method and check the consistency of the results.6 More precisely, our strategy is the following: First, as causal links can be measured equation by equation in a VAR model, we estimate FAVAR models with lower orders (see Tables 5 to 9 in Appendix), because it is easier to get white noise residuals from single equations taken separately and for which we test causality. To make sure that the results are not biased by persistence effects, we increase the order of the FAVAR models, when necessary, as proposed by Toda and Yamamoto (1995) and Dolado and L¨utkepohl (1996) for implementing causal analyses in non-stationary VAR models, without preliminary cointegration analyses. But this latter step does not seem to be necessary, as proved by the features of the generalized impulse responses which returns to zero after a sufficient number of periods (about 36). Second, for each country, we estimate a FAVAR model of high order (about 12) in order to obtain residuals which define a vectorial (weakly) white noise. Thus, we deduce from this FAVAR a system of equations, so as to limit the number of parameters to estimate: we just keep the regressors associated with significant coefficients, 5

See Beltratti and Morena (2009) for an analysis of the role of the USA in international house price dynamics. 6 We also computed impulse responses, based on bootstraping using JMulti (see L¨ utkepohl and Kr¨atzig, 2004). The results are quite similar across methods and confirm the positive impact of the common factor on domestic house prices.

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by still checking that the residuals are white noises. This system is reestimated with a Seemingly Unrelated Regression method. Then causal links are measured through the system. As mentioned before, both kinds of analyses provide rather close results about causal links. We decide to keep as ”certain” the causal links jointly identified through both analyses. It is worth emphasizing that the domestic interest rates and house price growth rates are both exogenous in the American model and in this model only. Moreover the house price factor ( f ac1 ) is unidirectionally caused by these two variables. Accordingly, one can imagine ”exogenous” shocks impacting the American interest rates or the (real) house price growth rate and one can be sure that these shocks will affect the (world) house price factor f ac1 . A second main result ,obtained from the FAVAR approach, is that the house price factor causes systematically the local house price growth for 5 of the 7 countries under review at the usual significance level of 5% (See Table 9 in Appendix B, 7% for Australia). The other two countries are Ireland and Germany. In the case of Ireland, the growth rate of real house prices appears to be exogenous in the FAVAR model of limited order estimated for that country (see Table 7 in Appendix B). Moreover, it is worth noticing that, in the case of Germany, causality from the house price factor f ac1 to the domestic house price growth rate is indirectly transmitted by the global factor Glob3 price, for which one cannot reject a causal link from f ac1 (see Table 8 in Appendix B). However when causality is investigated from systems of equations, we find strong evidence of causality from the house price factor to each domestic house price growth rate (See table 8 in Appendix B). Moreover in the second approach, exogeneity of both domestic variables (house price growth and interest rates) is confirmed as well as causality from the domestic variables to the house price factor (See Table 10 in Appendix B). These results tend to prove that contagion may occur from the USA house price market to all other house markets. One can also imagine contagion mechanisms for shocks originating from the American interest rate, which is an interesting finding, if one refers to the recent subprime crisis, which was revealed after the increase in interest rates, which indeed took place in 2006. Accordingly, we could develop a stress test exercise replicating this increase in interest rate in order to examine its impact on all house markets and more generally on the global activity factors.

5 Conclusions We have investigated contagion effects among house prices across industrial countries by extracting factors and including these factors in linear multivariate models or non linear single equations, depending on the definition of contagion we have retained.

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Indeed, we have introduced two different definitions of contagion. According to the first definition, contagion occurs when the transmission is different during crisis events. In the second approach, contagion is viewed as a ”pandemic” transmission mechanism where local shocks, originating from a country or a local housing market, spread out to other domestic housing markets. In both cases, the main objective was to investigate whether common factors have an effect on domestic house prices, through non linear equations for the first definition and FAVAR models or systems of equations derived from them, for the second one. More precisely, referring to the first definition of contagion, we have estimated non linear single equations including dummies indicating crisis events or describing a smooth transition process according to a LSTAR specification. In the latter case, the factor included as the transition variable has been extracted from the large data set, which provides three factors, mainly correlated to interest rates and activity. We have thus observed non-linearity in the dynamics of two countries (Spain and UK). But the results we obtain are not very conclusive at this stage, given the small sample size: the two regimes correspond to two subperiods of high, respectively low interest rates, with the break occurring in the mid-1990’s. It is difficult to interpret them as a ”normal” versus a ”critical” regime. For France and the USA we provide evidence that the sensitiveness to the business cycle is more pronounced in the upswing than in the downswing, although non-linearity is less significant. Thus, results obtained from this approach should be considered as preliminary and further completed. According to the second definition, we have focused on multivariate dynamics. Thus we have included factors, first extracted from international house prices only, second from a larger database, as components of a VAR model, on top of indicators of domestic economic fundamentals (namely, the growth of real house prices and the interest rates). When the factors are only derived from house prices, we provide evidence on the role of the common house price factor in the group made of the UK, Australia, Ireland and Spain, which means that contagion may occur, transmitted by a common component made of house prices. In the broader approach, allowing many channels of global transmission of shocks, including house price specific as well as global factors, an interesting finding is that the US house price, which appears to be ”independent” in the US dynamics –that is, not caused by any other variable-, causes the international house price factor, which in turn causes the domestic house price of many other countries,within the associated model. This tends to prove that a local shock originating from the US housing market can spread out to the other domestic housing markets and that the most direct transmission channel seems to involve house markets only.

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Acknowledgements Many thanks to Jean Ludovic Audret for helping assemble the database. Comments by C. Andr´e and G. Perez-Quiros are gratefully acknowledged. All errors remain ours. The opinions expressed are not necessarily those of the Banque de France or the Eurosystem.

References Ben S. Bernanke, Jean Boivin and Piotr Eliasz (2004), Measuring the effects of monetary policy:a factor augmented vector autoregressive (FAVAR) approach, NBER, Working Paper, No. 10220, and Quarterly Journal of Economics, February 2005. Beltratti, A and C. Morena (2009) International House Prices and macroeconomic fluctuations, Forthcoming Journal of Banking and Finance. Del Negro, M. and C. Otrok (2007), 99 Luftballons: Monetary Policy and the house price boom across US states, Journal of Monetary Economics, 54, 1962-1985. Dolado,J. J. and H. Lutkepohl (1996). Making wald tests work for cointegrated var systems. Econometric Reviews, 15, 369-386. Goodhart, C. and B. Hofmann (2008), House prices, money, credit and the macroeconomy, Oxford Review of Economic Policy, 24, 180-205 James H., Stock and M. W. Watson (1998), Diffusion Indexes, National Bureau of Economic Research, Inc, Working Paper, No. 6702. Kiyotaki, N., Michaelides, A. and Nikolov, K. (2008), Winners and Losers in Housing Markets, mimeo. Kose, A., Otrok, C.and C. Whiteman (2003), International Business Cycles: World, Region, and Country-Specific Factors, American Economic Review, 93, September, 1216-39. Kose, A., Otrok, C.and C. Whiteman (1998), Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa, International Economic Review, 39, 4, 997-1014. L¨utkepohl, H. and M. Kr¨atzig (2004) Applied Time Series Econometrics, Cambridge University Press. Ortalo-Magne, F. and Prat, A. (2009), Spatial asset pricing : a first step, mimeo. Reinhart, C, M. and K. S. Rogoff (2008), This Time is Different: A Panoramic View of Eight Centuries of Financial Crises, NBER, Working Paper, No. 13882, March. Stock, James H and M.W. Watson (2002),Macroeconomic Forecasting Using Diffusion Indexes, American Statistical Association, Journal of Business and Economic Statistics, 20, 2, 147-62, April. Stock, James H. and M.W. Watson (2005), Implications of dynamic factor models for VAR analysis, Working Paper, No. 11467. Tatsaronis, K. and H. Zhu (2004), What drives housing price dynamics: cross-country evidence, BIS, Quarterly Review, March, 65-78. Terasvirta, T. (1994), Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models, Journal of the American Statistical Association, 89, 208-218. Terrones, M. and C. Otrok (2004), The global house price boom, IMF, World Economic Outlook, September. Toda, H. Y. and T. Yamamoto (1995). Statistical inference in vector autoregressions with possibly integrated processes, Journal of Econometrics, 66, 225-250. Vansteenkiste, I. and P. Hiebert (2009), Do house price developments spill over across euro area countries : evidence from a Global VAR, ECB, Working Paper, No. 1026.

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Appendix A: Single equation approach Table 1 Country Single Equations (1983:1-2008:4)

∆ Log(prh,t−1) ∆ it−1 ∆ Log(pc,t−1) 0.54 (5.16) R2 =0.37 Germany 0.65(7.50) 0.001 (0.31) 0.40 (4.01) R2 =0.36 Spain 0.49 (2.71) 0.19 (0.75) R2=0.52 France 0.50 (4.16) 0.001 (0.40) R2 =0.30 Ireland(*) 0.30 (4.09) 0.28 (2.96) R2=0.25 United Kingdom 0.53 (4.85) R2=0.57 United States 0.90 (13.24) −0.01 (-0.91) R2=0.80 Country Australia

fac1,t−1 0.002 (1.86)

0.004 (1.88) 0.001(1.47) 0.000(0.78) 0.004 (2.75) 0.001 (0.13)

(*) we report here the lagged endogenous variable at t-2 and t-3. Student t (exhibited in parenthesis) are based on Newey-West HAC standard errors NB: ∆ Log(phr,t ) is the domestic real house price, it is the domestic short term nominal interest rate, ∆ Log(pc,t) is the quarter-on-quarter domestic inflation rate computed with the consumption deflator. fac1,t is the first common factor from the international house price database.

Table 2 Country Single Equations (1983:1-2008:4) Country ∆ Log(prh,t−1) ∆ Log(prh,t−2) ∆ Log(prh,t−3) du crisist ×fac1,t−1 other Australia 0.59 (5.26) 0.004 (2.64) R2=0.44 Spain 0.67 (5.12) 0.003(1.60) 0.22 (1.39) R2=0.49 (∆ Log(p c,t−1) ) Ireland 0.32 (3.50) 0.21 (2.32) 0.006(1.88) -0.003 (-0.82) R2=0.27 (∆ it−1 ) UK 0.56 (6.55) 0.008 (4.64) R2=0.57 See Table 1 for details

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Table 3 Country Single Equations with global factors (1983:1-2008:4)

∆ Log(p rh,t−1) Glob1 pricet−1 0.55 (4.92) R2=0.46 Germany 0.35 (3.60 ) R2=0.28 Spain 0.53 (4.42 ) R2=0.48 France 0.47 (3.60 ) R2=0.32 Ireland 0.24 (1.57) -0.001 (-2.11) R2=0.13 United Kingdom 0.50 (5.98) R2=0.58 United States 0.94 (14.10) R2=0.84 Country Australia

Glob2 pricet−1 Glob3 pricet−1 fac1,t−1 -0.002 (-2.54) 0.004 (2.84) -0.006 (-2.31 ) 0.0021 (2.42 ) 0.002 (1.94 )

0.001 (1.96)

0.004 (3.39)

-0.001 (-0.52)

Student t (exhibited in parenthesis) are based on Newey-West HAC standard errors

Table 4 Summary of the results obtained from LSTAR models regime 1 Glob1 < −0.08 −0.675 USA Glob3 < 0.11 −0.38 ES

low interest rates (crisis) stronger < 0 corr. with int. r. high Output GAP stronger > 0 corr.with GAP

FR

low contemp. GDP < 0 correlation low interest rates (crisis) stronger < 0 correlation

Glob2 < −0.058 −0.41 UK Glob1 < 0.11 −0.60 ◦

where GDP is quarterly GDP growth

◦

regime 2 Glob1 > −0.08 −0.325 Glob3> 0.11 −0.08

high interest rates < 0 corr. with int. r. low Output GAP (crisis) > 0 corr. with GAP

Glob2 > −0.58 0.29 Glob3 > 0.11 −0.20

high contemp. GDP > 0 correlation high interest rates < 0 correlation

◦

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Appendix B: CAUSALITY in FAVAR models of reduced orders The models include the growth of real house prices, the first difference of the long term nominal interest rate and several common factors : fac1 (housing factor), Glob2 price and Glob3 price. The order is chosen in order to get white noise residuals, equation by equation. In the following tables, the maximum number of lags is given in parenthesis in column 1, row 1. Causality tests are run from the variables in the first column to the variables in the first row. P-values of the Chi-square test statistic are reported. Table 5 USA USA/FAVAR(7) House price growth D(interest rate) Fac1 (house price) Glob2 price House price growth ∗∗∗ 0.4067 0.0186 0.0938 D(interest rate) 0.9345 ∗∗∗ 0.0287 0.6848 Fac1(house price) 0.6717 0.9833 ∗∗∗ 0.0232 Glob2 price 0.5180 0.5070 0.7633 ∗∗∗ Comments: for the USA, real house price growth and the first difference of the interest rate are exogenous; and they unidirectionally cause the house price factor (fac1) and also the global factor Glob2, with a weaker causal link between real house price growth and the Glob2 factor

Table 6 France FRANCE/FAVAR(6) House price growth D(interest rate Fac1(house price) Glob2 price House price growth ∗∗∗ 0.1188 0.0018 0.8883 D(interest rate) 0.0617 ∗∗∗ 0.1169 0.0414 Fac1(house price) 0.2206 0.0109 ∗∗∗ 0.0053 Glob2 price 0.8456 0.0001 0.9766 ∗∗∗ Comments: Evidence of indirect causality from the house price factor fac1 to real house price growth through the interest rate

Table 7 Ireland Ireland/FAVAR(5) House price growth D(interest rate Fac1(house price) Glob2 price House price growth ∗∗∗ 0.1931 0.7275 0.0567 D(interest rate) 0.6136 ∗∗∗ 0.0579 0.1801 Fac1(house price) 0.9709 0.1503 ∗∗∗ 0.0023 Glob2 price 0.9676 0.1723 0.7865 ∗∗∗ Comments: In the case of Ireland, real house price growth is exogenous.

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Table 8 Germany Germany/FAVAR(4) House price growth D(interest rate) Fac1(house price) Glob3 price House price growth ∗∗∗ 0.0010 0.2680 0.0269 D(interest rate) 0.0039 ∗∗∗ 0.7268 0.0002 Fac1(house price) 0.3041 0.1367 ∗∗∗ 0.0001 Glob3 price 0.0038 0.9902 0.0779 ∗∗∗ Comments: Evidence of indirect causality from the house price factor fac1 to real house price growth through the global factor Glob3 price Table 9 Causality in FAVAR models in the case of Australia Australia/FAVAR(3) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.1820 0.0199 0.4273 D(interest rate) 0.0011 ∗∗∗ 0.0585 0.2210 Fac1(house price) 0.0682 0.5095 ∗∗∗ 0.0246 Glob2 price 0.0678 0.3319 0.3862 ∗∗∗ Comments: Direct causality from the house price factor fac1 to real house price growth Table 10 Causality in FAVAR models in the case of UK UK/FAVAR(5) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.0961 0.2631 0.8940 D(interest rate) 0.1533 ∗∗∗ 0.0442 0.3108 Fac1(house price) 0.0010 0.8416 ∗∗∗ 0.0248 Glob2 price 0.4941 0.0566 0.4515 ∗∗∗ Comments: Direct causality from the house price factor fac1 to real house price growth Table 11 Causality in FAVAR models in the case of Spain Spain/FAVAR(6) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.2865 0.8252 0.0441 D(interest rate) 0.0266 ∗∗∗ 0.0005 0.0070 Fac1(house price) 0.0001 0.0435 ∗∗∗ 0.1072 Glob2 price 0.0476 0.0582 0.9217 ∗∗∗ Comments: Direct causality from the house price factor fac1 to the growth rate of the real house price Table 12 Summary Table of Causality from house price factor to real domestic house price in FAVAR models of limited order Countries France Spain UK Australia Ireland Germany Fac1(house price) 0.0042 0.0001 0.0010 0.0682 0.9709 0.3041 Comments: p-values of the chi-square test statistic used to test for causality of the house price factor fac1 to the domestic house price growth rate

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Appendix C: CAUSALITY tested from systems of equations The systems are derived from FAVAR models of high order (12 or 13) including the growth rate of real house prices, the first difference of the long term nominal interest rate and the factors fac1 (house prices), Glob2 price and/or Glob3 price.

Table 13 System of equations for USA USA/system House price growth growth D(interest rate) Fac1

Glob2 price

Glob3 price

equations 1.6E-4+0.90(∗∗∗) *USA IMMO REAL GT(-1) Adjusted R-squared 0.79 -0.09(∗∗∗) +0.22(∗∗∗) *DUSA IRL(-1)-0.20(∗∗∗) *DUSA IRL(−7) Adjusted R-squared 0.11 -0.36(∗∗∗) -0.42(∗∗∗) * DUSA IRL(-10)+29.77(∗∗∗) *USA IMMO REAL GT(-1) +0.50(∗∗∗) *Fac1 USA(-1)+0.32(∗∗∗) *Fac1 USA(-2) +0.24(∗∗∗) *Fac1 USA(-10)-0.32(∗∗∗) *Fac1 USA(-12) +0.19(∗∗∗) *GLOB2 PRICE(-10)+0.27(∗∗∗) * GLOB3 PRICE(-1) Adjusted R-squared 0.88 -0.29+26.10(∗∗∗) *USA IMMO REAL GT(-4)+ 0.76(∗∗∗) * GLOB2 PRICE(-1) + 0.76(∗∗∗) *GLOB3 PRICE(-7)-0.27(∗∗∗) *GLOB3 PRICE(-8) Adjusted R-squared 0.76 -0.16-0.53(∗∗∗) * DUSA IRL(-1)-0.54(∗∗∗) *DUSA IRL(-3) -0.26(∗∗∗) *DUSA IRL(-6)-0.44(∗∗∗) *DUSA IRL(-11) -0.37(∗∗∗) *GLOB2 PRICE(-1)+ 0.17(∗∗∗) GLOB2 PRICE(-7) +0.70(∗∗∗) * GLOB3 PRICE(-1)+ 0.36(∗∗∗) *GLOB3 PRICE(-3) (∗∗∗) -19.34 *USA IMMO REAL GT(-4)+17.01(∗∗∗) *USA IMMO REAL GT(-5) Adjusted R-squared 0.75

USA IMMO REAL GT is the growth rate of real house prices; DUSA IRL is the first difference of the long term interest rate for the USA; Fac1 USA is the first common factor from the database of house prices excluding the USA. The parameters are estimated by using the SUR estimation method, after whitening the residuals of the different equations. (∗∗∗) indicates that the coefficients are statistically significant at a level of 5%. Comments: The growth rate of real house prices rate and the first difference of the interest rate are both exogeneous. They unidirectionnally cause the house price factor (Fac1 USA) .The global factor Glob2 price is caused by the global factor Glob3 price and the growth rate of real house prices. The global factor Glob3 price is caused by the other three variables.

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Appendix D: CAUSALITY tested from FAVAR models of order 12

Table 14 USA USA/FAVAR(12) House price growth D(interest rate) Fac1 (house price) Glob2 price Glob3 price House price growth ∗∗∗ 0.7569 0.0015 0.0004 0.4028 D(interest rate) 0.4283 ∗∗∗ 0.2764 0.0492 0.0226 Fac1(house price) 0.5688 0.7467 ∗∗∗ 0.0364 0.8715 Glob2 price 0.5681 0.1202 0.0610 ∗∗∗ 0.0000 Glob3 price 0.0655 0.4670 0.0419 0.0144 ∗∗∗

Comments: The first difference of the interest rate is exogenous; the house price growth unidirectionnally causes the house price factor (Fac1) and the global factor Glob2; the first difference of the interest rate unidirectionaly causes the global factors Glob2 and Glob3.

Table 15 France FRANCE/FAVAR(12) House price growth D(interest rate Fac1(house price) Glob2 price House price growth ∗∗∗ 0.0880 0.1964 0.9906 D(interest rate) 0.0496 ∗∗∗ 0.0465 0.5334 Fac1(house price) 0.0037 0.1374 ∗∗∗ 0.0054 Glob2 price 0.2324 0.0061 0.8972 ∗∗∗ Comments: Evidence of direct causality from the house price factor fac1 to the growth rate of the real house price

Table 16 Ireland Ireland/FAVAR(12) House price growth D(interest rate Fac1(house price) Glob2 price House price growth ∗∗∗ 0.2492 0.9127 0.3642 D(interest rate) 0.9227 ∗∗∗ 0.0019 0.2139 Fac1(house price) 0.4928 0.2252 ∗∗∗ 0.0034 Glob2 price 0.9242 0.0850 0.8709 ∗∗∗ Comments: In the case of Ireland, the house price growth rate is exogenous.

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Table 17 Causality in FAVAR models in the case of Germany Germany/FAVAR(12) House price growth D(interest rate) Fac1(house price) Glob3 price House price growth ∗∗∗ 0.0685 0.1195 0.5814 D(interest rate) 0.0476 ∗∗∗ 0.5853 0.1145 Fac1(house price) 0.5975 0.2565 ∗∗∗ 0.0512 Glob3 price 0.2147 0.8931 0.4464 ∗∗∗ Comments: Direct causality from the house price factor fac1 to Glob3; direct causality from the interest rate to the house price growth Table 18 Causality in FAVAR models in the case of Australia Australia/FAVAR(12) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.7535 0.1004 0.2255 D(interest rate) 0.0508 ∗∗∗ 0.3988 0.5505 Fac1(house price) 0.0470 0.0946 ∗∗∗ 0.1335 Glob2 price 0.0061 0.0228 0.9634 ∗∗∗ Comments: Direct causality from the house price factor fac1 to the growth rate of the real house price Table 19 Causality in FAVAR models in the case of UK UK/FAVAR(12) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.5049 0.1334 0.1832 D(interest rate) 0.8829 ∗∗∗ 0.0000 0.1000 Fac1(house price) 0.0041 0.6088 ∗∗∗ 0.0074 Glob2 price 0.8142 0.3204 0.5304 ∗∗∗ Comments: Direct causality from the house price factor fac1 to the growth rate of the real house price ; exogeneity of the interest rate Table 20 Causality in FAVAR models in the case of Spain Spain/FAVAR(12) House price growth D(interest rate) Fac1(house price) Glob2 price House price growth ∗∗∗ 0.3428 0.2482 0.7138 D(interest rate) 0.5606 ∗∗∗ 0.0254 0.0902 Fac1(house price) 0.0158 0.0272 ∗∗∗ 0.5404 Glob2 price 0.6813 0.0085 0.8032 ∗∗∗ Comments: Direct causality from the house price factor fac1 to the growth rate of the real house price Table 21 Summary Table of Causality from house price factor to real domestic house price in FAVAR models of higher order Countries France Spain UK Australia Ireland Germany Fac1(house price) 0.0037 0.0158 0.0041 0.0470 0.4928 0.5975 Comments: p-values of the chi-square test statistic used to test for causality of the house price factor fac1 to the domestic house price growth rate

Part III

Macroeconomic Models of Housing

The ’Housing Bubble’ and Financial Factors: Insights from a Structural Model of the French and Spanish Residential Markets Trend and Cycle Features in German Residential Investment Before and After Reunification User Costs of Housing when Households Face a Credit Constraint: Evidence for Germany Causes and Welfare Consequences of Real Estate Price Appreciation

The ’Housing Bubble’ and Financial Factors: Insights from a Structural Model of the French and Spanish Residential Markets Pamfili Antipa and R´emy Lecat

Abstract Over the last decade, France and Spain have experienced property price and residential investment increases which were among the strongest and the lengthiest in the euro area. Although the quality of the underlying data limits the precision of the estimates, the present paper aims at analysing the fundamental factors behind these evolutions. The analysis presented here assesses whether the observed price dynamics may be attributed to a pure expectation bubble phenomenon or to the large changes in financial and demographic factors. This is done by means of a structural model of the demand and supply sides of the housing market with an error-correction process. When taking into account a standard set of macroeconomic variables, our estimates imply that residential property prices in France and Spain were approximately 20% above the level explained by their fundamentals by the end of 2008. When demographic and financial factors such as the borrowing capacity are taken on board, the degree of overvaluation is drastically reduced. The adjustment path to equilibrium is slightly faster in France than in Spain, but both countries display significant downward rigidity in prices.

JEL codes : C32, E22, E27, R21, R31 Keywords : House prices, Housing demand, Borrowing capacity, Residential Investment, Error correction model, Instrumental variables

P. Antipa Banque de France, e-mail: [email protected] R. Lecat Banque de France, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_8, © Springer-Verlag Berlin Heidelberg 2010

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1 Introduction Over the last decade, a number of OECD countries, including the USA and the UK but also continental European countries have experienced housing booms of a sometimes unprecedented scale and length. Among euro area countries, housing prices and residential investment were both particularly dynamic in France and Spain. During the last housing boom for example (1998-2007), the yearly average growth rate of house prices was above 10% in Spain and France, peaking at 18% for Spain and 16% for France in 2004. Since then, yearly growth rates have been declining very rapidly, and have even turned negative towards the end of 2008. The magnitude and volatility of these developments may have dramatic consequences through wealth effects on consumption and residential investment, as well as on business investment through the financial accelerator. Diagnosing the causes of the recent large swings in property prices should in the first place allow forecasting the extent of the downturn lying ahead. In addition, understanding the fundamental factors behind the recent evolutions in housing prices should then help to suggest adequate economic policy measures notably in terms of financial stability. Given the above, a distinction should be drawn between two different approaches to the explanatory factors underlying house prices dynamics. A first line of thought would be that prices are fully determined by their fundamentals. In that case, large and dramatic changes in the latter may explain similar evolutions in housing prices. One may think of the deregulation of mortgage markets in the 1980s and the process of European monetary integration that have substantially softened credit conditions. A second approach would consist in considering that observed house prices can, at least temporarily, depart from the path determined by their fundamentals. In theory, there can be many possible reasons behind such a departure from equilibrium levels. Specific rigidities could, for example, prevent supply from reacting immediately to an increase of demand (Ayuso and Restoy, 2006). Another possibility would be that prices increase based on the sole expectation of further price increases. This is equivalent to the definition of a bubble that may be identified when ’the reason the price is high today is only because investors believe that the selling price will be high tomorrow-when ’fundamental’ factors do not seem to justify such a price’ (Stiglitz, 1990). This is the diagnosis set by R.J. Shiller (2007) on the current crisis, for example. In the present analysis we will focus on the quantification of the degree of overor undervaluation. Attention will also be paid to the adjustment path towards equilibrium. To that end, a structural model of the French and Spanish housing markets is estimated, the theoretical framework being one of an Error Correction Mechanism (ECM). The remainder of the paper is organised as follows: the next section presents the methodological choices leading to the selection of the model. Section 3 will detail the construction and sources of data used for the main variables of the

A structural model of the housing market

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model. In section 4, estimation results for the long-term equations are commented. Section 5 presents the results for the short term equations and section 6 offers some brief concluding remarks.

2 Estimation strategy 2.1 Estimation methodology There are several approaches to account for the fundamental value of residential property prices. A first, financial approach consists in modelling house prices such as any other asset price, valued according to the future discounted flow of revenues or services generated. More precisely, this financial approach implies exploiting the relationship between house prices and rents, as originally proposed by Case and Shiller (1989). Although valuable to assess the investors’ viewpoint, this approach does not allow an explicit modelling of the respective role of fundamental macroeconomic factors, such as households’ disposable income, the residential capital stock or demographics. Structural models of the housing market, accounting for the dynamics of supply and demand of housing, allow identifying the role of the fundamental factors on house price formation. Initially the so-called stock flow models go back to the seminal article of DiPasquale and Wheaton (1994). The authors emphasised the importance of accounting for the very long lags in market clearing due to transactions costs and land supply rigidities. Subsequently, they apply error-correction models to their data, in order to allow for diverging dynamics in the short and the long run. In the present analysis we will follow this macroeconomic approach, in order to explicitly account for the role of fundamental factors of the French1 and Spanish real estate markets respectively. Both the supply and demand equations will be estimated2 by means of ECMs as proposed by Engle and Granger’s two step procedure (1987). In addition, as we will focus on the long-run determinants of housing prices, the simultaneity in the determination of price and supply will be our main concern. McCarthy and Peach (2002) used a vector error correction model (VECM) approach, which allows modelling accurately the interactions between the different variables. 1

This type of model has been adapted to the French housing market by Bessone et al. (2005), who conclude that there is no housing bubble up to 2004. 2 Indirectly we suppose that that the supply of housing is not rigid, since this assumption fits the observed evolutions of the 2000s during which residential investment experienced an important surge. According to our computation, the residential housing stock increased by 17 percent in France and by 55 percent in Spain over the 2000-2008 period.

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This methodology was motivated by the paper’s objective, which was to account for the role of monetary policy in residential investment dynamics. Here, instrumental variables will rather be used to control for the endogeneity of the supply variables in the demand equation and of the demand variables in the supply equation. This type of computation allows isolating more explicitly the exogenous component of the endogenous variables. More specifically, the instruments used here will be the exogenous variables of the supply equation in the demand equation and vice versa. As endogeneity should be less of a problem at this horizon, the short run equations are estimated by OLS with Newey-West standard errors (1987) whenever heteroskedasticity is detected.

2.2 The basic model The aim of the present study is to model the structural demand and supply factors underlying residential property price developments in France and Spain. The methodological framework adopted here is a version of the stock-flow model that is commonly used for the analysis of the housing sector (DiPasquale and Wheaton, 1994). Actual values of the fundamentals are used here rather than ’equilibrium’ values of the fundamentals: one may think that fundamental determinants, such as income, demographic factors or construction costs are themselves over or under-valued. Our assessment of what are the ’fundamental’ determinants is based on standard model of the housing market such as Salo (1994) for the demand side of the market and Poterba (1984) for the supply side of it. Our model is characterized by two long term relationships in which demand and supply factors determine housing prices and residential investment. On the demand side, the long run real price for housing pd is given by the housing stock h, households’ permanent income y, the user cost of housing uc and a demographic factor n. The number of households can be chosen here to account for demographic changes that reach beyond birth and mortality rates and migratory fluctuations. Social changes regarding the composition of family units and population ageing imply that the number of households can grow faster than a country’s population. More precisely, over the 1981-2008 period the number of households grew by an annual average of 1.8% in Spain and 1.3% in France3 against an annual growth rate of only 0.7% for the Spanish population and 0.5% for the French population. However, in France, the number of households is measured by means of population censuses, which were not conducted every year, and is not available until 2008. Hence, popu3

Estimation of the number of households in France for 2008 is based on INSEE premi´ere N 1106 - October 2006 ’Des m´enages toujours plus petits’, Alain Jacquot.

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lation will be used as a proxy in the French case. Note that the number of households may be determined jointly with housing prices: for example, children may tend to stay longer at their parents’ if they cannot find an affordable dwelling. This problem may somewhat extend to population as the decision to have a child may be constrained by housing space. This potential endogeneity problem means that we will have to test the direction of causality of these variables and examine alternative specifications excluding demographic factors. Following the above, the long-term demand equation in logarithms can be expressed as: ptd = α1 ht + α2 yt + α3 uct + α4 nt + εtd

εtd

E[εtd ]

V [εtd ]

(1)

σε2 .

is a white noise for which = 0, = The user cost uct is where computed following Poterba’s definition (1992) and can formally be expressed as uct = pt [(1 − τty )rt + δ − E(πt+1 )]

(2)

• pt is the the price of housing per square meter in real terms • τty the average income tax. This implies taking into account tax deductibility of interest payments for residential mortgages whenever it applies.4 The relevant revenue tax rate would be a marginal one, but as the latter is not available for Spain and France, we use here an effective tax rate • rt the long term interest rate (yield on 10 year government bonds) in real terms • δ the depreciation rate for residential structures: for Spain, it has been fixed at 2%, implying an average life time of 50 years for residential buildings; for France, it is based on INSEE households’ balance sheet accounts. • E(πt+1 ) the anticipated capital gains. These gains were proxied by average residential property prices over the last four quarters, implying that agents form adaptive anticipations. We also test a more ’conservative’ definition where capital gains equal past CPI inflation (Poterba, 1992). Equation (1) has to be understood as an inverted demand curve. The demand price level of homes depends negatively on the residential housing stock: an increase in the housing stock makes the housing supply more abundant and weighs hence on demand prices. Housing demand also declines in line with increasing residential capital user costs, as for that case it becomes less appealing to own a house than to rent it. On the contrary, housing prices should increase parallel to households’ permanent income: as income grows, demanded housing square meters per individual tend 4 In France, the deductibility of interest payments has been suspended from 01/01/1997 for new dwellings and one year later for all dwellings and reintroduced partly in 2007. In Spain, on the contrary income tax relief is offered on the purchase, building, rehabilitation or extension of a primary residence and both principal and interest payments on a mortgage can be deducted (for more details on the tax treatment of housing in Spain see the OECD, 2007b).

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to increase. Demographic factors, such as population growth and ageing but also migratory movements and household formation, should also augment demand pressure and hence prices. On the supply side, residential investment it is supported by real house prices pt . Construction costs cct (encompassing the costs for labour and material inputs) should weigh on residential investment. xt is a vector of quantitative variables such as housing permits and starts that will be used for the supply side of the Spanish housing market. One crucial assumption here is that existing home prices (used here) are in close relationship with new dwelling prices due to households’ arbitrage. In logarithms the supply side equation is given by it = β1 pt + β2cct + β3xt + εts where

εts

is a white noise for which

E[εts ]

=

(3)

0, V [εts ] = σε2 .

There seems to be, however, a large body of evidence that residential property prices and investment adjust slowly to exogenous shocks. At a given point in time, it is therefore possible to observe a difference between the actually observed price for housing and the one determined by fundamentals (DiPascale and Wheaton, 1994). Hence, it seems plausible to introduce equations representing the short-term adjustments in the housing market. These short-run equations for the demand and the supply side of the French and Spanish residential housing market take the classical form of an error correcting process. Demand equation 5

d ∆ pt = α1 εt−1 + ∑ αn+1 ∆ pt−n + α7 ∆ ht + α8 ∆ yt + α9 ∆ nt + α10 ∆ rrt + εt

(4)

n=1

Supply equation 5

s ∆ it = β1 εt−1 + ∑ βn+1 ∆ it−n + β7∆ cct + β8∆ pt + εt

(5)

n=1

εtd and εtd are respectively the error-correction term from the demand equation (1) and the supply equation (3). Additionally, the five following explanatory variables were incorporated in the short run equations: lagged changes in real housing prices (∆ pt ), residential investment (∆ it ), real households’ disposable income (∆ yt ), real interest rates (∆ rrt ) and construction costs (∆ cct ). These ’standard’ short term equations describe the adjustment path towards equilibrium. However, there seems to be a general consensus that there are asymmetries in the short term adjustments. More precisely, the downward movement of a declining housing market will not be as rapid and important as the upward movement in a

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rising market. That is to say that housing markets exhibit downward rigidity. 5 Gao et al. (2009) have conducted this type of analysis for the United States. The authors find evidence that house prices not only exhibit serial correlation, but also downward rigidity. More precisely, although prices tend to overshoot the equilibrium in appreciating markets, they can experience downward rigidity during periods of decline. In order to test this hypothesis for the French and Spanish housing markets, positive and negative values of the error-correction term were separately tested in the short run demand equation. If only the negative residuals prove to be statistically significant in the short-run, we would conclude that indeed house prices exhibit downward rigidity. Analytically this adjusted type of short term equation takes the following form: Adjusted demand equation 5

d pos dneg ∆ pt = α1 εt−1 + α2 εt−1 + ∑ αn+2 ∆ pt−n + α8 ∆ ht + α9 ∆ yt + α10 ∆ nt + α11 ∆ rrt + εt n=1

(6)

Adjusted supply equation 5

spos sneg ∆ it = β1 εt−1 + β2εt−1 + ∑ βn+2 ∆ it−n + β8∆ cct + β9∆ pt + εt

(7)

n=1

ε d pos and ε dneg are the positive and negative error correction terms from the demand equation (1), and ε spos and ε sneg the positive and negative error correction terms from the supply equation (3).

3 Construction and data sources 3.1 France House prices used here are quarterly and seasonally adjusted existing home prices covering France as a whole produced by INSEE, retropolated using a series published by a real estate agents network, the FNAIM, on the basis of its transactions.6 The INSEE hedonic index of house prices is used here, which implies that house 5

From an economic viewpoint this happens because sellers withdraw their houses from a declining market in order to prevent rapid prices declines. 6 An alternative choice would be an extrapolation on INSEE prices for Paris only. However, the evolution of prices between Paris and the rest of France was strongly divergent in the 1980s and beginning the 1990s, which would lead to a bias in the resulting series.

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prices are related to a standard dwelling in terms of quality and size, defined by elementary areas. Hence, part of the increase in demand due to higher income may be reflected in the increasing size and quality of the standard dwelling. According to the estimates, the hedonic correction however does not fully absorb the increase in permanent income, as the average characteristics of existing dwellings may evolve more slowly than the resulting demand. Absent sufficiently long time series of new home prices data, the simplifying assumption has to be made that arbitrage between existing and new dwellings leads to similar evolutions in the two series. The housing stock is computed on the basis of yearly households’ balance sheet accounts, interpolated with the residential investment series and deflated by national accounts’ GFCF prices. The other basic variables of the demand equation are households’ permanent income and the user cost of residential capital. Households’ permanent income is proxied by real disposable income. All series were deflated using the private consumption deflator.

3.2 Spain For Spain, quarterly house prices used are the average price per square metre of all, new and existing dwellings released initially by the Spanish Ministerio de Fomento and currently by the Ministerio de la Vivienda.7 This price index is not quality adjusted, which can be problematic as housing is not a homogenous good varying with its location, size or structure.8 Keeping in mind that the exclusion of quality effects can imply an upward bias in the price data, it can still be expected that the used metric reflects relatively well house price developments over time. As no balance sheet accounts are available for Spain, the residential capital stock was calculated on the basis of the permanent inventory method. The initialisation value was computed using the formula: (GFCFt × µt ) (8) 2 GFCFt equals residential gross fixed capital formation in volumes. The average life span of housing µt is deduced from a depreciation rate of residential structures that 7

According to the OECD, Spain displays the highest home owner rate among OECD countries (82% in 2005). This implies a negligible rental market encompassing less than 12% of all dwellings in 2005, which in turn entails that rents are not taken into account in this study when assessing home prices (OECD, 2007a). 8 When hedonically correcting for location, Bover and Velilla (2001) find indeed that the official house price index for Spain includes an upward bias ranging from 0.75% to 1.2% p.a..

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is fixed at 2% per annum implying that a not maintained residential structure has a life time of 50 years. This computation implies that measurement errors regarding the capital stock can be relatively important at the beginning of the estimation period, but should fade over time in line with capital depreciation. Because of data limitations,9 prices for constructible land are very roughly approximated by agricultural land prices. Note that the approximation is substantial since factors such as zoning rules, but also transport and other infrastructure will affect the premium on land for construction purposes over other types of land use (ECB, 2003). The series for agricultural land prices is provided for by the Spanish ministry of agriculture and is originally deflated by the GDP deflator. With the exception of the standardized ILO unemployment rate provided by Eurostat, the remainder of the series (number of households, households’ disposable income, etc.) is primarily taken from national accounts. If not indicated otherwise, all series were deflated using the private consumption deflator.

3.3 Unit root and causality tests The unit root tests conducted imply that all series in our data set are first order integrated (see Appendix). In addition, the series used for the computation of the demand and supply sides of the French and Spanish housing markets exhibit common trends, indicating the possible presence of a cointegration relationship between them. Finally, preliminary Johansen’s cointegration tests (not reported here) confirm that there is at most one cointegrating relationship among the respective demand and supply data sets.10 We further conduct Granger causality test in order to assess the risk of reverse causality between the endogenous and exogenous variables. For the demand equation, real disposable income, and population in France do Granger-cause house prices, the reverse hypothesis being rejected (see appendix). On the contrary, both hypothesises on the direction of causality are not rejected for user cost and housing stock in France. This is hardly surprising for the housing stock which is considered endogenous. For the user cost, the causality from user cost to housing prices is harder to justify: user cost includes a lagged housing prices growth term as a proxy of expected capital gains and it is difficult to justify the impact of house prices on other user costs terms such as long term interest rates or taxes. For the Spanish data, real disposable income, the user cost, the number of households and the capital stock do Granger-cause real house prices. The reverse sense of causality is rejected 9

The only existing series on constructible land prices in urban areas begins only in 2004. For the demand data set in France, the trace test indicates one or two cointegration relationships depending on the critical value (1 or 5%).

10

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for all of the variables. This is reassuring for the number of households, as household formation can depend on property prices. In the following we maintain that the Spanish capital stock is endogenous as well, since we consider that in the long term it is determined simultaneously with housing prices. On the supply side, it is more difficult to disentangle the direction of causality according to the conducted Granger tests (see Appendix). For France, both directions are possible between residential investment and its two envisaged determinants, housing prices (which are actually supposed to be endogenous) and construction costs. For the Spanish data, all exogenous variables do Granger-cause residential investment. We do not find a reverse causality from residential investment to house prices. Both direction of causality are possible for building starts, implying that instruments for the former will be introduced in the following computations.

4 Equilibrium values from long term equations 4.1 Standard demand factors Equation (1) is estimated by Two Stage Least Squares for France and Spain. Demographic factors (population and the number of households) are introduced in some of the equations. A third regression for Spain includes also the standardized ILO unemployment rate that accounts for precautionary motives of Spanish households (which does not appear significant in France). The estimation results are displayed in Table 1.11 For France and Spain, the housing stock’s coefficient is negative as expected and close to what McCarthy and Peach (2002) find for the United States (-4.2) or Bessone et al. for France (-3.6 with no explicit control fort demographic factors). The coefficient on households’ disposable income is greater than 1 in equations 1, 3, 4 and 5, indicating a high long-run income elasticity. This is consistent with the idea that dwelling service is a superior good whose demand grows faster than 11

The estimation period is 1980-2008 for France and 1982-2007 for Spain. All regressions include a constant that is not reported here. Estimations were computed by Two-Stage Least Squares. Exogenous instruments for the capital stock are construction costs and the long-term interest rate. First-step estimates’ F tests indicate that instruments are strongly significant. Sargan-Hansen tests of instruments over-identification do not reject the null hypothesis of orthogonality of instruments. Wu-Hausman tests of exogeneity reject the null hypothesis of exogeneity of the housing stock. Joint residual skewness / kurtosis tests do not reject the null hypothesis of normality. Breusch-Pagan tests reject the null hypothesis of homoskedasticity. Hence, heteroskedasticity robust variancecovariance matrix estimates are used. Cumby-Huizinga (IV) or Breusch-Godfrey (OLS) reject the null hypothesis of no autocorrelation, which is to be expected when ECMs are estimated in two steps, as it is the case here.

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income. Permanent income also captures general expectations about the state of the economy and housing prices themselves, which reinforces its impact. Although some studies such as Meen (2001) find an elasticity in the region of one, there are no clear cut theoretical reason to think this elasticity has to be of that order. Indeed, developments in the price of an asset may not be parallel to the one of income, even in the long-run, if the structure of consumption changes with growing purchasing power. Subsequently, Mart´ınez-Pag´es and Maza (2003) find a long run house price income elasticity that is with 2.8 equal to the result obtained here. Bessone et al. find a coefficient of 8.3 for France and McCarthy and Peach (2002) of 3.4 for the United States. The user cost has the expected significant negative impact on demand prices for France, but it is not significant for Spain. This is the case for various ways of calculating it, i.e. for different hypothesis regarding anticipated gains. The statistical non-significance of the user cost might be related to the data problems interfering in its calculation (see also part 2 of this study). However, this result is in line with what other studies on the subject find: Pag´es and Maza (2003) for the case of Spain and McCarthy and Peach (2002) for the United States also conclude that the user cost is not significant in their respective calculations. Demographic factors are proxied by population growth for France12 and by the number of households for Spain. As expected, these factors have a significantly positive impact on demand prices. This underlines the large impact household formation and hence socio-demographic factors (geographical mobility, mono-parental family structures, migration etc.) have on housing demand (see also Gonzalez and Ortega, 2009). Also, at first sight, the difference in magnitude between the coefficients on demographic factors between France (+28.9) and Spain (+5.7) is striking. The use of different variables (number of households vs. population) explains this

Table 1 House prices: Long-term demand relationship France Spain Eq.1 Eq.2 Eq.3 Eq.4 Eq.5 Housing stock -2,67*** -6.42*** -1.98*** -4.46*** -4.50*** Gross disposable income 3,80*** 0,54*** 2.91*** 3.43*** 3.52*** User cost -0,38* -0,15** -0.25 Demographics (1) 28,94*** 5.76*** 5.41*** Unemployment rate -0.13* Sargan P-value 0.88 0.57 0.45 0.99 0.99 Wu-Hausman F test P-value 0.00 0.00 0.00 0.00 0.00 0.88 0.98 0.96 0.99 0.99 Adjusted R2 * p¡0.10, ** p¡0.05, *** p¡0.01, according to Engle and Granger (1987). (1)Population for France; number of households for Spain.

12

For France, data on the number of households were available only on a discontinued basis and do not cover the whole estimation period.

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gap. More precisely, as households grow two to three times faster than population, we may expect a higher coefficient for population in France than for households in Spain. It is also noteworthy that the inclusion of demographic factors for Spain is necessary to obtain stationary residuals for the long term equations. The number of households will hence be taken into account for all following computations for the demand side of the Spanish housing market. Regression 5 includes also the standardized ILO unemployment rate whose coefficient is negative and statistically significant. The explicative power of the unemployment rate is, however, limited in comparison to the other explanatory variables, as reflected by the coefficients relative magnitude. It is not a significant determinant for France, as gross disposable income may capture most of the impact of unemployment. In order to determine whether these demand equations can be modelled as an error correcting processes, we test for the residuals’ stationarity. According to the Shin (1994) test, the null hypothesis of cointegration of residuals is not rejected, at the 10% threshold for equations 2, 3, 4 and 5, but only at the 1% threshold for equation 1, which is not fully satisfactory for this test. This may be due to the fact that the cointegration relationship did not work as prices departed strongly from their demand equilibrium value from 2004 onwards. For equations 2, 4 and 5, unit root tests concluded that the residuals were stationary at the 10% threshold. 13 Having established the possibility of modelling the demand side of the Spanish and French housing market as an ECM, we check for the robustness of the above mentioned results by estimating them over several periods. This is particularly important, as the significant imbalances that started building up in the countries’ property market after 2000 may have altered our estimation results. Over the ’pre-bubble period’, coefficients remain significant and have the proper sign (see Appendix). Their magnitudes are close, the main difference being permanent income: this variable grew more rapidly since 2004, contributing more to house price changes over the recent period. The stationarity tests for the residuals are now satisfactory for all equations: the null hypothesis of cointegration of residuals is never rejected at the 10% threshold.

13

’Classical’ unit root tests (ADF and Philllips-Perron) were conducted using the critical values tabulated by Engle and Yoo (1987). In addition, Ng-Perron (2001) unit root tests were also undertaken, as they have two advantages in comparison to more ’classical’ unit root tests: their power is enhanced by local GLS detrending of the data and the use of modified information criteria leads to substantial size improvements. Note that the test results in favour of the residuals’ stationarity are also in line with Granger’s and Newbold’s (1974) rule for spurious regressions. More precisely, as the equations’ Durbin-Watson Statistics (not reported here) are higher than the adjusted R2 , chances are that the equations’ residuals are stationary.

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Part of the recent increase in property prices remains unexplained on the demand side. In 2008, housing prices are about 0-19% above the price explained by the usual long-term determinants for France. In Spain, the overvaluation is of 11-25% by the end of 2007.14 The increase in prices is explained up to 2005 for France and up to 2003 for Spain in particular by the increase in gross disposable income. Afterwards, the increases in the supply of dwellings and, particularly after 2006, in the user cost of housing capital have weighed on long-run prices, leading to a growing overvaluation of prices (note that prices display, however, a certain slowdown in their growth rate). In France, the acceleration of population growth from 2000 onwards explains most of the housing boom. However, the pace of household formation is supposed to have decreased since 2004 from 1.5% to 1.1% p.a. and equation 1 may hence over-estimate equilibrium prices in 2008. Over the 1980s and 1990s, we can see that house prices have often departed from their long-run equilibrium values and remained persistently over- or under- valued. Over the considered period, several boom and bust episodes may be identified for both France and Spain: a boom in the beginning of the 1980s, of the 1990s and middle of the 2000s. A bust phase in the second half of the 1980s and of the 1990s and beginning of the 2000s. This persistence may either be due to the serial correlation of housing prices or could also stem from variables omitted in our specifications. Therefore the following section explores whether financial factors might have contributed to the observed price dynamics.

4.2 Demand side: is the overvaluation a ’pure’ bubble phenomenon or does it reflect changes in financial factors? The overvaluation of housing may reflect several phenomena. Either one or several fundamental variables have been omitted from the equation. Subsequently, the recent house price dynamics could be explained by the evolutions of that omitted variable. Or the recent house price boom is a ’pure’ bubble phenomenon. In that case, the recent important house price increases would stem from investors’ sole expectations of further price increases. Concerning the omitted fundamental variables, one may think of financial variables as there have been major evolutions over the period in consideration. Indeed, financial factors have been pointed as one of the major determinants in differences in national housing market dynamics. For example, Tsatsaronis and Zhu (2004) 14 This is in line with the magnitude of overvaluation (roughly 20%) that the IMF (2009) finds. In addition, the given equation reproduces well the results that Pags and Maza (2003) found for the Spanish housing market in 2002.

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have emphasised how different characteristics of mortgage markets regarding loan to value ratios, mortgage rate references, valuation methods or securitisation practises may affect the interactions between housing prices and other macroeconomic variables (GDP, interest rates, bank credit). Over the horizon of this analysis, major regulatory changes intervened in both the French and Spanish mortgage markets. In 1987, the end of administrative control of credit (’encadrement du cr´edit’) triggered a period of fast increases in loans and housing prices as banks competed for market shares. No such a major regulatory change can be observed in the recent period. Although securitisation regulation has been softened in the 1990s, its development in France for housing credit has not been of such a large scale as in the US. In Spain, the liberalisation of the mortgage market goes back to the year 1981. It is from that date onwards that universal banks and other specialised credit institutions are allowed to enter the market and to compete with public mortgage banks and savings banks, which before then were the only mortgage lenders. This increase in competition, coupled with the low prevailing interest rates, has triggered an important expansion in housing mortgages (OECD, 2000). According to the Asociacion Hipotecaria Espaola, total outstanding mortgage lending has accelerated strongly from 12,921 million to around 900 billion over the past two decades. Over the same period, the number of new mortgages subscribed each year rose from 135,000 to close to 1,700,000. 15 Apart from these important regulatory changes, a series of other factors has had an impact on banks’ pricing policy for mortgages. In the first place, the process of European monetary integration has contributed to a decline in interest rates, a development of which banks and consumers have benefited from in both countries. In addition, banks’ pricing and margin behaviour has very much evolved over the period in consideration. Especially in France, mortgages credits have become a product that banks use to attract and secure loyalty of their clients. Consequently, rates on mortgage credits have been very much reduced: for an average over the 1990-2008 period of 7.6% (11.5% in 1990), fixed rates on mortgage credits (the dominant type of credit) have decreased to 4.5% in 2005 and 5.5% on average in the 2000s. The Spanish market has experienced a similar evolution: while the average mortgage rate stood at roughly 11% over the 1990-2000 period rates fell to an average of 4.7% for the 2000-2008 period. Simultaneously, the average duration of new mortgage credits has substantially increased in France: from 11.8 years on average in 1989, it increased to 14.3 years in 1999 and accelerated to 19.2 years in 2008 (Modele Fanie, Observatoire du cr´edit immobilier). There is evidence that credit duration has substantially increased in 15

These figures include both residential and commercial lending.

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Spain as well, although data are scarcer than for France. According to l’Estadistica Registral Immobiliara, average credit duration was of around 15 years over the 1990s and stands at approximately 26 years in 2007 (see also Girard-Vasseur and Quignon, 2006). While the rise in the average duration of mortgages has increased households’ borrowing capacity, overall credit conditions may have softened as well. However, only very short time series are available by means of the bank lending survey to support that trend. Given the above, we propose to construct an indicator of maximum indebtedness that synthesises some of the indications on financial factors mentioned in the preceding paragraphs. This indicator should be understood as the maximum amount of money a household is able to borrow for the purchase of a house given his income, the average duration of mortgages and interest rates for newly contracted mortgages. A household may borrow up to a monthly payment equal to a third of its income. It is thus possible to compute a maximum average amount of indebtedness per households (Kt ) as: Kt =

T 1 1 × yct × ∑ t 3 t=1 (1 + rt )

(9)

where yct equals gross disposable income in value per household, T is average mortgage duration and rt the average interest rate on mortgages. Average mortgage duration could be caused by housing prices: the duration of a mortgage could be set so that the purchase becomes affordable. This may reflect common expectations for housing prices by lenders and borrowers. This reverse causation is however not the main direction of causality according to Granger causality tests (see Appendix). We would rather attribute the increase in the average duration of mortgages to a strengthening of banking competition. As customers became less faithful towards their banks in the 1990s, mortgages were used as a way to establish a long-term relationship with clients. The results for the computation including households’ borrowing capacity are presented in table 216 . Permanent income and user costs have been removed from the regressions as borrowing capacity already includes a gross disposable income 16

Estimation period: 1990-2008 for France, 1993-2007 for Spain. All regressions include a constant that is not reported here. Estimations by Two-Stage Least Squares for France, OLS for Spain. Exogenous instruments for the capital stock are construction costs and the long-term interest rate. First-step estimates’ F tests indicate that instruments are strongly significant.Sargan-Hansen tests of instruments over-identification do not reject the null hypothesis of orthogonality of instruments. Wu-Hausman test of exogeneity does not reject the null hypothesis of exogeneity of the housing stock for the demand price equation, but is close to the 10% significance threshold. Joint residual skewness / kurtosis tests do not reject the null hypothesis of normality for eq.1. Breusch Pagan tests do not reject the null hypothesis of homoskedasticity for Spain but reject it for France. Hence, robust standard errors are used. According to the Shin (1994) test, the null hypothesis of cointegration of residuals is not rejected at the 10% threshold for France and Spain. Cumby-Huizinga (IV)

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term and takes into account changes in interest rates. As can be seen from the results, the borrowing capacity has the expected positive impact on house prices in France and Spain. The Spanish housing stock is statistically not significant we hence present directly the equation excluding it. For both countries the inclusion of the borrowing capacity explains practically all of the overvaluation period in housing prices observed in the previous equations. Note that the borrowing capacity’s computation relies on credit duration data that is only directly observed over the recent years of the estimation period, inducing hence some uncertainty around this metric. Nonetheless, this set of results implies that the overvaluation found in the previous parts of the analysis is not a bubble phenomenon. On the contrary, much of the observed fluctuations can be explained when taking into account financial factors that are not part of the usual macroeconomic approach to house price dynamics. This is all the more striking as many of the changes in financial factors, such as credit condition softening, are not taken into account in the here calculated borrowing capacity indicator. Although financial factors may be considered as ’fundamental’ factors, they can be subject to a greater degree of volatility than other fundamentals, inducing hence volatility of housing prices themselves, as the current financial crisis has emphasised. For Spain, Ayuso and Restoy (2006) also conclude that the recent market boom is not due to speculative behaviour.

Table 2 House prices: financial factors France Spain Housing stock -11.8*** Borrowing capacity 3.17*** 0.07*** Demographics 27.6*** 8.67*** Unemployment rate -0.12*** Sargan P-value 0.20 Wu-Hausman F test 0.13 0.97 0.99 Adjusted R2 * p¡0.10, ** p¡0.05, *** p¡0.01 according to Engle and Granger (1987)

or Breusch-Godfrey (OLS) reject the null hypothesis of no autocorrelation, which is to be expected when ECM are estimated in two steps, as it is the case here.

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4.3 Supply Equation (3) is run for France and Spain; the results are displayed in table 3.17 As expected, housing prices tend to support residential investment as suppliers of residential dwellings may benefit from the increased price of their production. Construction costs weigh on residential investment in the case of France, but are not significant in the Spanish case. We replace construction costs by another cost factor, namely real long term interest rates. In addition, as in Sastre and Fern´andez-S´anchez (2005), we introduce a quantity variable (as opposed to the prices variables already used), namely building starts.18 According to the Shin test (1994), the null hypothesis of cointegration of residuals is not rejected at the 10% threshold for the French and Spanish equation. The increase in housing prices explains practically all of the acceleration in residential investment in the 2000s, while some limited over investment appears by the end of the estimation period in France as prices declined. For the Spanish housing market we find that actual investment is somewhat beneath the path projected by the theoretical relationship. However, this result hinges

Table 3 Residential investment: Long-term supply relationship France Spain Eq.1 Eq.2 Eq.3 House prices 0,80*** 0.27*** 0.28*** Construction costs -0,63*** -0.08 Interest rate -0.06*** -0.06*** Building starts (-2) 0.46*** 0.46*** Sargan P-value 0.77 0.27 0.27 Wu-Hausman F test 0.01 0.00 0.01 0.76 0.97 0.97 Adjusted R2 * p¡0.10, ** p¡0.05, *** p¡0.01 according to Engle and Granger (1987)

17

The estimation period is 1980-2008 for France and 1982-2007 for Spain. All regressions include a constant that is not reported here. Estimations were computed by Two-Stage Least Squares. For France, exogenous instruments for housing prices are user cost and population; for Spain instruments are population, land prices and construction costs. First-step estimates’ F tests indicate that instruments are strongly significant. Sargan-Hansen tests of instruments over-identification do not reject the null hypothesis of orthogonality of instruments. Wu-Hausman tests of exogeneity reject the null hypothesis of exogeneity of the housing prices. Joint residual skewness / kurtosis tests do not reject the null hypothesis of normality. Breusch Pagan tests do not reject the null hypothesis of homoskedasticity. 18 The production process of housing units implies that even at steady state there is a delay between the building start and the moment the housing unit is put on the market, the latter being the moment at which the unit is taken into account as residential investment. For that reason, building starts are introduced in the long term relationship with two lags.

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also on the inclusion of property prices for which we had found a certain degree of overvaluation. This introduces an upward bias in our estimations for the fundamental value of investment.

5 Short-term equations: which adjustment path to equilibrium? 5.1 Demand The results for the different short run demand equations are presented in table 4.19 The equations were estimated using OLS with Newey-West standard errors (1987) whenever heteroskedasticity was detected. For France and Spain,20 the error correction terms are significant, meaning that house prices do converge to their fundamental value. The point estimate of the error correction term is about -0.10 for France and -0.07 for Spain, indicating that half of

Table 4 House prices: Short-term demand relationship France Eq.1 Eq.2 -0,10*** -0,07

Spain Eq.3 Eq.4 -0.07** 0.09

Error correction term (-1) Error correction term (-1) positive values Error correction term (-1) -0,12*** -0.23*** negative values ∆ log House prices (-1) 0,44*** 0,43*** ∆ log House prices (-2) 0,25** 0,26*** ∆ log House prices (-3) 0.14** 0.12* ∆ log House prices (-4) 0.47*** 0.47*** ∆ log House prices (-5) 0.16* 0.16* ∆ log Interest rates (lagged) (1) -0,07* -0,07* -0.03* -0.04** ∆ log Land prices (-2) 0.36** 0.42*** Adjusted R2 0.50 0.50 0.33 0.39 * p¡0.10, ** p¡0.05, *** p¡0.01 (1)ES: Short-term interest rates; FR: housing credit interest rates

19

Estimation period: 1980-2008 for France, 1982-2007 for Spain. Estimations by OLS with Newey-West standard errors. All regressions include a constant that is not reported here. BreuschGodfrey test as well does not reject the null hypothesis of no autocorrelation. Joint residual skewness / kurtosis tests do not reject the null hypothesis of normality of residuals. Breusch-Pagan tests reject the null hypothesis of homoskedasticity. Hence, Newey-West standard errors are used for both equations. 20 The residual used for the French short term equation is the one deduced from the demand equation including financial factors. For Spain, it is the residual from equation 3 of table 1.

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the gap between house prices and their fundamental value is bridged over the course of two years for France and roughly 2.5 years for Spain.21 None of the ’basic’ explanatory variables (household’s disposable income, capital stock, demographics) are statistically significant for Spain and France. For Spain, the short term interest rate is significant, while it is housing credit interest rates that are significant for France. This is consistent with the predominance of variable rates credit in Spain and fixed rates in France. Both interest rates are lagged (by a year and a half for Spain and a half-year for France), as changes in market rates are not immediately passed through into credit rates. This can be explained by the lag between the decision to grant a credit and the purchase itself. In addition, past variations of residential prices (including land prices for the case of Spain) are highly significant (and displaying a positive sign). This indicates that property prices in the short term are mostly explained by their own developments in the recent past. This finding is in line with the perception that house prices often exhibit serial correlation in the short term, as Case and Shiller (1987) and Capozza et al. (2004) show for local markets in the United States. In France and Spain property price formation in the short run is determined by past price dynamics. In other words, when prices are engaged in a rising trajectory, they will continue to increase in the short term, only because they did so in the very recent past. Only interest rates are significant, entailing that financing conditions play a role for property price formation in the short run. Columns 2 and 4 present the results when positive and negative values of the error correction term are introduced separately. Only the coefficient on negative residual values is highly significant. This underlines a downward rigidity of housing prices in France and Spain.

5.2 Supply Results for the supply equation are presented in Table 5. The error correction terms are significant, supporting for the French market a correction of half the gap between equilibrium and current residential investment in 4 years. The point estimate of the error correction term for the Spanish equation implies that the wedge between the actual and fundamental levels of residential investment is closed in a little more than a year. This is particularly fast given the production process of housing.

21

For the US, McCarthy and Peach (2002) find a rate of price adjustment of 18% per year; according to DiPasquale and Wheaton (1994) the adjustment could account for 16% -29% a year.

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Table 5 Residential investment: Short-term supply relationship France Eq.1 Error correction term (-1) -0.04** ∆ Residential investment (-1) 0.57*** ∆ Residential investment (-2) 0.20* ∆ Residential investment (-3) ∆ Residential investment (-4) ∆ Construction cost (-1) -0.11* ∆ Real house prices (-1) 0.06 ∆ Real house prices (-1) (new dwellings) Adjusted R2 0.48 * p¡0.10, ** p¡0.05, *** p¡0.01

Spain Eq.2 -0.21*** -0.20** -1.76*** 0.32*** 0.22

Lagged changes in residential investment are significant, reflecting some inertia in this variable. For Spain, lagged investment bears a negative coefficient, entailing that the series displays mean reversion which can be expected for the growth rate of a stationary variable. Among the fundamental determinants, construction costs weigh, even in the short run, on residential investment. House prices are not significant in the French case. They are significant in the Spanish equation, but we chose here to include prices for new dwellings as there is a more direct nexus between this series and residential investment efficient is statistically significant and bears the expected positive sign22 .

6 Conclusion Taking into account a standard set of fundamentals, this study highlights some overvaluation both on the French and Spanish market, reaching approximately 20% by end-2008. When enriching fundamentals with a measure of households’ borrowing capacity, most of this overvaluation, however, disappears as credit duration increased substantially in both countries since the 1990s. This emphasises that the analysis of house prices should include banking practises much beyond interest rates. This could be extended in particular to credit standards applied to the approval of loans, when long enough time series is available. Although this study points to the role of fundamentals rather than speculation in the recent run-up of housing prices, this does not entail that large movements in housing prices may not be taking place. Indeed, as emphasised by the current crisis, credit conditions may be more volatile than other fundamentals and may give rise to 22

Replacing total property prices by prices for new dwellings improves the equation’s fit substantially.

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large changes in equilibrium house prices. As they display downward rigidity, house price movements may moreover take time to adjust to their equilibrium in time of overvaluation. Hence, monetary policy has limited power to control house price dynamics. First, housing prices displays strong inertia which makes an accurate control of their movements through interest rates difficult. Second, housing prices may be sensitive to different segments of the interest rate curve within the euro area (e.g. short-term segment in Spain or long term one in France), leading to highly heterogeneous reactions of European housing markets. Finally, banking practises such as credit duration are important determinants of housing price changes. In the debate on the need of monetary policy to control potentially damaging housing booms, this pleads for the use of a wider set of policy tools. A first direction in that sense could structural reforms rendering the supply of housing units flexible enough to curb down lasting house prices appreciation.

Acknowledgements The authors gratefully acknowledge comments by Olivier de Bandt, Andrew Benito, Olivier Darn´e, Maria-Teresa Sastre, the participants of the conference on Macroeconomics of Housing Markets organized by Banque de France, November 2009, as well as Jean Pierre Villetelle and Lionel Potier for the series provided. All errors remain ours. The views expressed herein are those of the authors and do not necessarily reflect those of the Banque de France.

References ` Alvarez, L. J., Bulligan, G., Cabrero, A., Ferrara, L. and Stahl, H. (2009), Housing cycles in the major euro area countries, Banque de France, Working Paper, No. 269. Ayuso F. and Restoy, J. (2007), House prices and rents in Spain, Does the discount factor matter?’, Journal of housing economics, No. 16, Bessone, A.-J., Heitz, B. and Boissinot, J.(2005), March´e Immobilier : voit-on une Bulle ?, INSEE note de conjoncture, No. 16, Bover, O. and Velilla, P. (2001), Hedonic house prices without characteristics: the case of new multiunit housing, Banco de Espaa, Working Paper, No. 73. Capozza, D.R., Hendershott, C.H. and Mack,P. (2004), An Anatomy of Price Dynamics in Illiquid Markets: Analysis and Evidence from Local Housing Markets, Real Estate Economics, 32, 1-32. Case K.E. and Shiller, R.J. (1987), Prices of single-family homes since 1970: new indexes for four cities’, New England Economic Review. Case K.E. and Shiller, R.J. (1989), The efficiency of the market for single-family homes’, American Economic Review, 79, 125-137. DiPasquale D. and Wheaton, W.C. (1994), Housing Market Dynamics and the Future of Housing Prices, Journal of Urban economics, 35, 1-27. ECB, (2003) Structural factors in the EU housing markets. Engle R.F. and Granger, C. (1987) Co-integration and Error Correction: Representation, Estimation, and Testing, Econometrica, 55, 2, 251-76.

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Engle R.F. and Yoo, B.S. (1987) Forecasting and Testing in Cointegrated Systems, Journal of Econometrics. Gao, A., Lin, Z. and Na, C. (2009) Housing market dynamics: evidence of mean reversion and downward rigidity, Journal of Housing Economics, Special Issue, 18, 256-266. Girard-Vasseur, M. and Quignon, L. (2006) Quel sc´enario pour l’immobilier r´esidentiel en Espagne ?, BNP Paribas conjoncture flash. Gonzalez, L. and Ortega, F. (2009) Immigration and Housing Booms: Evidence from Spain, IZA working paper, No. 4333. Granger, C. and Newbold, P. (1974) Spurious regression in econometrics, Journal of econometrics(2), 111-120. IMF (2008) World Economic Outlook: Housing Finance and Spillovers from Housing. Koenker, R. (1981) A Note on Studentizing a Test for Heteroskedasticity, Journal of Econometrics, 17, 107-112. Lanne, M. and Lutkepohl, H. (2002) Unit root tests for time series with level shifts: a comparison of different proposals, Economics Letters, 75, 1. Mart´ınez-Pag´es, J. and Maza, L.A. (2003) Analysis of house prices in Spain, Banco de Espana, Working paper series, No. 0307. McCarthy, J. and Peach, R.W. (2002) Monetary Policy Transmission to Residential Investment, FRBNY, Economic Policy Review. Meen, G. (2001) Modelling Spatial Housing Markets, Kluwer Academic. Newey, W.K. and West, K.D. (1987) A Simple Positive Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 55. Ng, S. and Perron, P. (2001) LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power’ Econometrica, 69, 6. OECD (2000) Economic Surveys: Spain. OECD (2007a) Economic Surveys: Spain. OECD (2007b) Taxing Wages 2006-2007. Poterba, J. (1984) Tax subsidies to owner-occupied housing: an asset market approach Quarterly Journal of Economics, 99. Poterba, J. (1994) Taxation and Housing: Old Questions, New Answers, American Economic Review, 82. Salo, S. (1994) Modelling the Finnish housing market, Economic Modelling, 11. Sastre, M.T. and Fern´andez-S´anchez, J.L. (2005) Un modelo emprico de la decisiones de gasto de las familias espa¨nolas, Banco de Espana, Working paper, No. 0529. Shin, Y. (1994) A residual based test of the null in cointegration against the alternative of noncointegration, Econometric theory, 10. Shiller, R.J. (2007) Understanding recent trends in house prices and home ownership, Cowles Foundation Discussion Paper, No. 1630. Stiglitz, J.E.,(1990) Symposium on Bubbles, Journal of Economic Perspectives, No. 2. Tsatsaronis, K. and Zhu, H. (2004) What drives housing price dynamics: cross country evidence, BIS Quarterly review.

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Appendix

Table 6 Unit Root tests for main variables, France Ng-Perron - Ho: series has a unit root I (0) I (1) Real house prices 0.98 -7.11* Housing stock 0.46 -16.43* Real disposable income 1.84 -13.99** Population 2.29 -7.50* Construction costs 2.73 -16.01*** Residential investment -2.77 -17.92*** Series including structural breaks User cost -2.42 -4.76*** Borrowing capacity 2.88 -4.49*** * p¡0.10, ** p¡0.05, *** p¡0.01 Ng and Perron (2001) For the series with structural breaks, Lanne and Ltkepohl (2002)

Table 7 Unit Root tests for main variables, Spain Ng-Perron - Ho: series has a unit root I (0) I (1) House prices -0.44 -76.6*** House prices (new dwellings) 1.44 -27.5*** Construction costs -4.04 -13.9*** Capital stock 1.70 -5.01 Residential investment 2.24 -34.8*** Building starts 1.88 -17.2* Disposable income 0.91 -29.1*** Population 1.80 -9.28 Number of households 0.30 -47.6*** Unemployment rate -4.52 -32.8*** Series including structural breaks Long term interest rates -0.63 -5.48*** Mortgage interest rates -0.65 -4.75*** Short term interest rates -2.02 -7.57*** User cost -2.30 -8.94*** Borrowing capacity -0.49 -2.60* Agricultural land prices -2.01 -2.67* * p¡0.10, ** p¡0.05, *** p¡0.01 Ng and Perron (2001) For the series with structural breaks, Lanne and Ltkepohl (2002)

Note that critical values can vary depending on whether a trend is included or not. In the case of Spain, population and the capital stock are I(2) according to the conducted unit root tests. For the capital stock this stems from the fact that our initialisation value induces an upward bias at the beginning of the series. In light of

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the latter fact and the theoretical relationship assumed for the two given variables, it will be considered that they are I(1).

Table 8 Granger causality tests, France Demand side Real disposable income does not Granger cause house prices House prices does not Granger cause real disposable income User costs does not Granger cause house prices House prices does not Granger cause user costs Population does not Granger cause house prices House prices does not Granger cause population Housing stock does not Granger cause house prices House prices does not Granger cause housing stock Borrowing capacity does not Granger cause house prices House prices does not Granger cause borrowing capacity

Observations F-Statistic Probability 121 2.43757 0.0918

114

122

122

73

0.75202

0.4737

7.65918

0.0008

8.13631

0.0005

4.46939

0.0135

1.83388

0.1644

5.59351

0.0048

2.75562

0.0677

4.66646

0.0023

2.33621

0.0648

Table 9 Granger causality tests, France Supply side Construction costs does not Granger cause residential investment Residential investment does not Granger cause construction costs House prices does not Granger cause residential investment Residential investment does not Granger cause house prices

Observations F-Statistic Probability 115 15.2270 0.0002

115

25.0033

0.0000

11.4688

0.0010

1.38725

0.2414

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Table 10 Granger causality tests, Spain Demand side User cost does not Granger cause house prices House prices does not Granger cause user cost Number of households does not Granger cause house prices House prices does not Granger cause number of households Population does not Granger cause house prices House prices does not Granger cause population Unemployment rate does not Granger cause house prices House prices does not Granger cause unemployment rate Disposable income does not Granger cause house prices House prices does not Granger cause disposable income Borrowing capacity does not Granger cause house prices House prices does not Granger cause borrowing capacity Capital stock does not Granger cause house prices House prices does not Granger cause capital stock

Observations F-Statistic Probability 103 13.1 0.00 0.90 0.35 107 4.78 0.03 0.81 0.37 107 4.85 0.03 33.6 0.00 105 2.55 0.06 3.81 0.01 100 1.94 0.06 2.52 0.02 94 3.58 0.03 0.95 0.39 100 2.09 0.05 2.27 0.02

Table 11 Granger causality tests, Spain Supply side Building starts not Granger cause residential investment Residential investment does not Granger cause building starts Interest rate (lt) does not Granger cause residential investment Residential investment does not Granger cause interest rate (lt) Construction costs does not Granger cause residential investment Residential investment does not Granger cause construction costs House prices does not Granger Cause residential investment Residential investment does not Granger cause house prices

Observations F-Statistic Probability 107 5.76 0.02

103

107

99

23.2

0.00

4.08

0.05

1.78

0.19

2.53

0.12

3.53

0.06

2.00

0.05

1.20

0.31

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Table 12 House prices: Long-term demand relationship up to the bubble period France Spain Eq.1 Eq.2 Eq.3 Eq.4 Housing stock - 7.36 *** -0.95*** -5.23*** -4.47*** Gross disposable income 0.47** 1.64*** 3.89*** 3.70*** User cost -0.34** -0.46*** Demographics 33.5*** 6.31*** 4.17*** Unemployment rate 0.16* Sargan P-value 0.66 0.17 0.54 0.99 Wu-Hausman F test 0.00 0.00 0.00 0.00 0.88 0.89 0.98 0.98 Adjusted R2 * p¡0.10, ** p¡0.05, *** p¡0.01, according to Engle and Granger (1987).

Notes: The estimation period is 1980-2003 for France and 1982-2000 for Spain. These dates were chosen as they marked the end of the ’pre-bubble period, i.e. residential property prices started growing at two digit rates afterwards. All regressions include a constant that is not reported here. Estimations were computed by TwoStage Least Squares. Exogenous instruments for the capital stock are construction costs and the long-term interest rate. First-step estimates’ F tests indicate that instruments are strongly significant. Sargan-Hansen tests of instruments over-identification do not reject the null hypothesis of orthogonality of instruments. Wu-Hausman tests of exogeneity reject the null hypothesis of exogeneity of the housing stock. Joint residual skewness / kurtosis tests do not reject the null hypothesis of normality. Breusch-Pagan tests reject the null hypothesis of homoskedasticity for equations 1 and 2; heteroskedasticity robust variance-covariance matrix estimates are hence used for those equations.

Trend and Cycle Features in German Residential Investment Before and After Reunification Thomas A. Knetsch

Abstract Real residential investment in Germany is found to be cointegrated with population, real national income per capita and real house prices. This evidence is consistent with a model where the trend in housing demand is determined by demographic factors and economic well-being to which supply adjusts so slowly that real house prices are affected persistently. Reunification seems to have induced two structural changes in the empirical housing market model. First, the speed of equilibrium adjustment via residential investment slowed down substantially and real house prices lost the capacity to contribute to the adjustment process. Second, the degree of persistence in the error correction term increased a lot. The changing features are key to explain significant differences in alternative trend-cycle decompositions of residential investment.

JEL codes : E22, C32 Keywords : Residential investment, vector autoregression, trend-cycle decomposition, Germany

1 Introduction The evolution of the German housing market has differed from that in many other industrialized countries for quite some time. While house prices recently underwent a pronounced up-and-down movement in the U.S. and some western European countries, they remained flat in Germany. Furthermore, weak residential investment has steadily weighed on economic growth in Germany since the mid-1990s, whereas the construction of new dwellings had been a major stimulus for economic growth Thomas A. Knetsch Deutsche Bundesbank, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_9, © Springer-Verlag Berlin Heidelberg 2010

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elsewhere until the house price bubbles, which had often emerged simultaneously, ultimately burst. A boom-bust movement in residential construction happened in Germany about ten years earlier.1 After the fall of the iron curtain, strong immigration into western Germany and the need to improve the overall run-down housing stock in Eastern Germany triggered a steep upswing in housing investment which was additionally bolstered by exuberant government promotion. Towards the end of the 1990s, market conditions not only relaxed but also turned, at least in part, into a situation of misallocation and over-investment (Deutsche Bundesbank, 2002, for instance). As a consequence, the government gradually curtailed the quite advantageous depreciation allowances for investors as well as the subsidies and grants offered to homebuyers. Against the backdrop of a stagnant population trend and gloomy income growth prospects, demand for new dwellings then declined for several years. Until recently, residential investment has been rather weak, with some stimuli created by modernization activity in the existing housing stock. In applied macroeconomic research in Germany, residential investment has attracted little interest in recent years. One reason for the lack of attention might be the fact that, in this series, the post-reunification period did not end until the middle of the past decade, making it difficult to separate the time series properties of “normal” phases from the special pattern induced by the circumstances in the early 1990s. Looking at the complete boom-bust movement, this paper identifies what has remained unchanged since the West German era and what has changed since then. On the one hand, the changes are temporary insofar as they are attributed to this seminal event, which caused a big shock and triggered adjustment processes thereafter. On the other hand, reunification might also have brought the housing market to a new long-run equilibrium. The boom-bust movement which appeared in the housing market after reunification changed the time series properties of residential investment which had been manifest in the West German era. In general, simple statistical trend-cycle filter techniques are not able to identify the post-reunification movement as a cycle of different duration and amplitude but tend to assign it to the trend component. This paper, however, suggests a model which comes out with a rather smooth trend in residential investment driven by economic fundamentals such as demographics, economic well-being and house price developments. In addition, it figures out that the forces of equilibrium correction have weakened substantively in the German housing market since reunification. The speed of adjustment in residential investment has slowed down significantly and house prices seem to have lost the capacity to equilibrate demand and supply in this market. Moreover, the evidence suggests a marked increase in the degree of persistence in the cyclical component of residential investment. It is as yet an open question whether, or to what extent, the changed features will return to the initial patterns in the future. The paper aims at presenting facts on ag1

It is worth mentioning that the boom-bust cycle in Germany was first and foremost a quantity phenomenon. In the boom phase between 1990 and 1995,house prices in western Germany rose less strongly compared with the corresponding episodes in other countries. Thereafter, they remained more or less flat instead of falling significantly.

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gregate housing market developments in Germany over the last 35 years, including a big shock approximately in the middle of this time period. However, it will not address the implications these observations may have on forecasting and structural analysis. In the first part of the paper, a cointegration analysis yields an overall stable longrun economic relationship between residential investment, population, real national income per capita and real house prices. It is worth mentioning that this structure deviates from the consumption good hypothesis, which is the theoretical concept guiding the modelling of residential investment in many macroeconometric models.2 The second part is devoted to the major structural change of the early 1990s, namely a substantial deceleration in the speed of adjustment to the long-run equilibrium relationship, suggesting that residential investment displays a Gonzalo and Granger (1995) cycle component of higher persistence and amplitude.3 The pitfalls this structural change implies for the application of standard statistical trend-cycle filters are highlighted in addition. In the final section, some conclusions are drawn and the limitations of the present analysis are mentioned.

2 Long-run determinants of residential investment In the first part, the theoretical foundations of residential investment are discussed. As a microeconomic approach based on utility theory suffers from the fact that representative behavior is virtually indetectable in the aggregate housing market owing to various forms of segmentation, the macroeconomic factors influencing the trend in dwellings construction are derived in a less rigorous way. As shown in the second part, however, a cointegration analysis provides evidence which supports the claim that residential investment, population, per-capita real national income and real house prices form a long-run equilibrium relationship.

2.1 Some theoretical considerations In contrast with the other private uses of GDP such as private consumption, business fixed investment and changes in inventories, macroeconomic theory has not established a leading hypothesis underpinning the econometric modelling of residential investment. This shortcoming might, in part, be explained by the ambiguous character of housing as a consumption and investment good. 2 Carnot et al. (2005) give a brief overview of the general modelling principles of residential investment in macroeconometric models. See Heilemann (2004) for an implementation in a leading macroeconometric model for the German economy. 3 Strictly speaking, Gonzalo and Granger (1995)have suggested a permanent-transitory decomposition which is, in the understanding of this paper, a variant of trend-cycle measurement amongst a wide range of methods including statistical filters.

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From a utility perspective, private households consume the flow of services generated by a dwelling which they either own or rent. Whereas many consumption goods are exclusively used at the time of their purchase, dwellings possess an extremely long service life, suggesting that residential construction is a rather weak proxy for the use of housing services. Assuming that the services generated by an asset are proportionate to its value, this theory can be applied to the housing stock (net of depreciation), suggesting a positive correlation with income and wealth and a negative dependence on user costs. However, the inference for residential investment need not be straightforward, as comparatively long adjustment lags, non-negligible transaction costs, credit constraints and binding supply restrictions such as insufficient designation of building land and high market segmentation are factors to be considered. While some side conditions could generally be integrated in a model of housing demand, it is the heterogeneity of the dwellings market which makes it difficult to recover hypotheses derived from consumption theory in aggregate data. Regional segmentation is one aspect worth mentioning in this regard. Perhaps equally important, in particular when residential construction is of primary concern, is the fact that the supply of housing is divided into owner-occupied and tenant-occupied dwellings.4 Under real circumstances, the household’s decision to build a house for its own use follows substantively different rules compared with an investor’s decision to build, say, an apartment block with a number of rental units. Arbitrage mechanisms between house prices and rents are supposed to be present but work rather slowly owing to significant frictions. These include government interventions promoting either form of activity in residential construction. Given the numerous difficulties in transferring the implications of a rigorous preference-based model of housing demand to a specification valid for a macroeconometric modelling exercise, let us opt for a more modest approach to discover the economic fundamentals explaining the trend in residential investment. In this context, the basic observation is that, apart from cyclical fluctuations, real dwellings construction has been increasing moderately over time, suggesting that there has been an ongoing capital formation process, given that the depreciation rate of residential buildings has remained more or less unchanged. The rising demand for housing services might be explained mainly by demographic factors and mounting economic prosperity. The diverse trends in the size and structure of population including ageing have a complex impact on housing demand. It seems a priori unclear whether the number of residents or the number of households is the better proxy in this respect. The number of households is directly connected with the number of occupied housing units but are neither all units equivalent in terms of investment costs nor does every household require the same unit. The living space increases with household size, albeit not in a one-to-one relationship owing to synergies in spatial use. While the square meters reserved for each household member and the creation of an own 4

In 2003, 43 percent of private households lived in their own house or apartment. The ownership ratio had increased during the 1990s, with the ratio being significantly higher in western Germany. See Statistisches Bundesamt (2006) for details.

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household are choices which follow economic principles based on preferences (relative to other consumption goods) and the budget constraint, housing is understood as a fundamental need of each individual regardless of her specific income position, justifying ascribing to demographic developments (measured in terms of the population size) a primary impact on the demand for housing. Investments in new buildings and home improvements are expected as a consequence of rising economic prosperity. This is partly because individual households are then generally faced with laxer budget constraints and housing services tend to make up a larger share in their consumption bundles owing to the nature of housing as a superior good. Another reason is that the more prosperous a society is, the wider is generally the government’s room for manoeuvre to assist poor households in terms of accommodation allowances and to provide enough subsidized public housing. Apart from demographic trends, the demand for housing is therefore assumed to be positively affected by the well-being of the society, which is approximated by a measure of economy-wide real income. In this context, an appropriate statistical concept is the gross national income adjusted for price and terms-of-trade effects. Separating the effects of population and real national income on housing demand may be difficult because population and income are related to each other by a pure scale effect. While maintaining the primary importance of population, the scale effect in real national income can be removed by considering per-capita figures. As a consequence, the sensitivity of housing demand to changes in (absolute) income is reflected by the sensitivity to population provided that per-capita income remains unaltered. In turn, the impact of population on housing demand results from the income effect and an additional (thereof independent) influence of demographic factors.5 When population grows more than aggregate income, housing demand is, apart from the scale effect, negatively affected by the reduction in per-capita income. It is assumed that the latter does not completely outweigh the former owing to public policies in favour of social housing. The demand for housing is supposed to be a downward-sloping function of the real house price, where population and real national income per capita are regarded as location parameters shifting the function in a permanent manner. As determinants of a nonstationary nature, in a long-term perspective, they tend to dominate any other influences stemming from more cyclical factors such as user costs, lending conditions and credit availability. In formal terms, the demand for housing can be written as : H D = H D (PHR; POP, NIR/POP, X) with

H1D < 0, H2D > 0, H3D > 0,

(1)

where PHR is the real house price, POP population and NIR gross national income adjusted for price and terms-of-trade effects. The vector X comprises the additional

5

Under the simplifying assumption that the income elasticity of housing demand is unaffected by the level of income, the elasticity attributed to population is the sum of the income elasticity and the own elasticity of population.

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(short-term) impact factors; H1D , H2D and H3D denote the partial derivatives with respect to the argument and the first two location parameters of the function. The supply of housing is assumed to be proportionate to the existing residential stock which evolves over time according to the accumulation identity:

∆ H S = RI − δ H S

(2)

where ∆ is the difference operator, RI (gross) real residential investment and δ the depreciation rate, which is assumed to be constant over time. The stock of dwellings is expected to react rather slowly to variations in housing demand. This is due not only to the time it takes to construct buildings but also to many other factors holding up residential investments. These include the time households need to prepare and take the decision as well as delays owing to administrative aspects such as the designation of new building land and the grant of building permits. The comparatively sluggish reaction of residential investment implies that, in the housing market equilibrium, house prices move as a result of tensions between demand and supply. As illustrated in Figure 1, an (unexpected) increase in housing demand which is triggered by, say, positive net migration immediately lifts house prices. So, the delayed adjustment of dwellings supply through positive (net) residential investment takes place amid elevated house prices. The reverse argument can be made for a negative demand shock. Under real circumstances, the equilibrating tendencies may be quite persistent and are, thus, perceived as a medium-term to longer-term phenomenon. Apart from the slow pace of adjustment due to administrative obstacles and construction time, an ongoing price movement may automatically be reinforced by expectation mechanisms and speculation, occasionally leading to price bubbles in extreme cases. Rising house prices not only fuel residential construction to the extent that supply ultimately equilibrates demand but often also tend to induce over-investment owing to the expectation of high returns. By contrast, private households and investors abstain from constructing new dwellings when house prices are on a downward trend because expected capital losses reduce expected returns, making alternative uses of their funds more profitable. Regardless of whether or not the reinforcing speculative component is present, the assumed sluggish adjustment of housing supply to changes in demand suggests a long-run positive comovement between residential investment and real house prices, with population and real income per capita playing a role as shifters of housing demand. Solved for residential investment, the long-run equilibrium relationship may be written as : RI∗ = f (POP∗ , NIR∗ /POP∗ , PHR∗ ) with

f1 ≥ 0, f2 ≥ 0, f3 ≥ 0,

(3)

where the superscript “∗” indicates that the figures are equilibrium values and f1 , f2 and f3 denote the partial derivatives with respect to the arguments. In the remainder of this paper, the pure population effect is referred to as the quantitative aspect of housing demand while per-capita real income is named as the qualitative component. As regards the measurement of house prices in real terms, it

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193

110 housing demand

105

0

5

10

15

housing supply

20

2 residential investment

1

0

5

10

15

20

15

20

107.5 105.0 house price

102.5 0

5

10

Fig. 1 Stylized time profile of housing market movements following an unexpected demand shock

is worth mentioning that (nominal) house prices are deflated by the aggregate price index of all domestically produced goods except dwellings. This choice follows the idea of evaluating the price of new dwellings vis-`a-vis the prices of any alternative uses in consumption and investment.

2.2 Cointegration analysis Unit root tests provide evidence (see Appendix) that the quarterly time series of residential investment, population, real national income per capita and real house prices, all series transformed into natural logarithms, are integrated of order 1, abbreviated by I(1),6 in the sample between the first quarter of 1975 and the fourth quarter of 2009. In the full sample, a statistical break in the first quarter of 1991 has to be taken into account, as the territorial basis changed at that date. For comparison, the overwhelming part of the empirical analysis is replicated in the West German subsample ending in the fourth quarter of 1991.7 The existence of a long-run economic relationship of the form (3) can therefore be examined using cointegration analysis on the basis of a log-linearized version. In particular, it is tested whether cointegration can be established between the four series under consideration. More precisely, data 6

In general, the order of integration d is henceforth denoted by I(d). In this subsample, the data for the year 1991 refers to western Germany while it refers to Germany as a whole in the full sample. 7

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should support the existence of exactly one cointegrating relation, with the coefficients taking the theoretically hypothesized signs. The variables of interest are jointly modelled by a vector autoregression (VAR) of lag order p including deterministic regressors. If the full sample is considered, the system comprises a constant, a linear trend and a step dummy variable S(91:1), which is unity since the first quarter of 1991 and otherwise zero. The latter variable is absent when the analysis is restricted to the west German subsample, suggesting that the standard likelihood ratio (LR) cointegration tests proposed by Johansen (1991) can be applied. In the full sample, however, it is necessary to account for the existence of a structural break in the first quarter of 1991. An appropriate handling of this element in the set framework is to use the cointegration test proposed by Saikkonen and L¨utkepohl (2000), henceforth abbreviated by SL. The basic idea of this approach is to remove the deterministic components prior to testing for cointegration using a standard LR test a` la Johansen (1991). The linear trend is supposed to be absent in the cointegrating relation, as (3) does not suggest any role for it in the long-run equilibrium relationship. This hypothesis in turn implies that, in a Kdimensional system, the cointegration rank r is K − 1 at maximum, given that the involved time series are trending over time. When cointegration is established, the resulting cointegrating relation represents (3) in log-linearized form. It may be written as : rit − b1popt − b2 inct − b3 phrt + c = ect

∼

I(0),

(4)

where rit , popt , inct and phrt are the logs of RIt , POPt , NIt∗ /POPt∗ and PHRt∗ respectively. Theory suggests b1 , b2 , b3 to be positive or nil. The error correction term or long-run residual series is denoted by ect , with the constant c ensuring that this series possesses a zero mean. Cointegration testing follows the specific-to-general rule, implementing the logic that there is no role for any further I(1) variable in a single cointegrating relation if cointegration has already been established between some I(1) variables (L¨utkepohl,2007). Given the primary importance of population for residential investment, this means that the smallest system is two-dimensional, modelling only the quantitative element of housing demand without a persistent relative price effect. If cointegration between residential investment and population cannot be established, there are two alternatives for a three-dimensional system. The first is {ri, pop, inc}, meaning that the trend in residential investment is represented by the quantitative and the qualitative determinants of housing demand, and the second is {ri, pop, phr}, implying the existence of the relative price effect in a long-run equilibrium where housing demand is restricted to the quantitative aspect only. The full model contains all variables; thus, ultimately, an attempt is made to establish cointegration in a four-dimensional system. Table 1, Panel (a), shows the results of the SL cointegration tests carried out in the whole sample for the different systems under review. They are performed in VARs of lag orders 2 and 5, with the parsimonious lag length representing the choices of the consistent information criteria HQ and SC while the long order results from

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Table 1 Cointegration tests lag order p = 2 (HQ, SC) null hypothesis r=0 r≤1 r≤2 (a) Germany (1975 – 2009) {ri, pop} 7.47 [0.134]

{ri, pop, inc}

16.23

{ri, pop, phr}

27.02 [0.006]

[0.706]

{ri, pop, inc, phr}

39.99

12.96

[0.195]

[0.016]

2.55

26.09

[0.394]

3.94

[0.478]

5.00

[0.009]

[0.337]

32.89

16.12

[0.030]

[0.200]

5.06

[0.329]

[0.204]

[0.297]

6.72

[0.616]

21.70

{ri, pop, phr}

21.34 [0.347]

8.75

[0.396]

21.33

{ri, pop, inc, phr}

52.80

26.96

[0.015]

4.99

[0.338]

11.17

[0.213]

22.19

5.22

13.18

[0.411]

p = 5 (AIC) r≤1 r≤2

[0.311]

5.50

[0.282]

(b) western Germany (1975 – 1991) {ri, pop} 11.04 {ri, pop, inc}

r=0

[0.105]

[0.326]

10.67 [0.237]

10.20 [0.270]

8.87

[0.348]

[0.385]

54.71

26.98

[0.009]

[0.105]

10.39 [0.256]

Cointegration tests are performed in VARs of lag order p. The full-sample specifications include a step dummy and a (contemporaneous) impulse dummy capturing the statistical break in the first quarter of 1991. The p-values of the LR trace tests taken from the software JMulti 4 are reported in brackets.

AIC selection (L¨utkepohl, 2005).8 It is evident that the trend in residential investment cannot be modelled by relying solely on the factors of housing demand. It is necessary to include real house prices in order to establish cointegration. As this variable is understood as a proxy for the tensions between supply and demand, its presence in the cointegrating relation implies that the forces equilibrating the quantities on the housing market work rather slowly. Hence, price movements in either direction are persistent enough to be empirically modelled by a unit root process. Furthermore, the cointegration analysis for the full sample indicates that the qualitative aspect of housing demand is rather weak, as cointegration is already present in the three-dimensional system {ri, pop, phr}. By contrast, the quality aspect plays a crucial role in explaining the trend in housing demand when only the West German subsample is considered. As displayed in Table 1, Panel (b), Johansen’s (1991) standard LR test procedure finds evidence for the existence of exactly one cointegrating relation between the four variables at conventional significance levels, whereas cointegration is absent in all two-dimensional or three-dimensional subsystems under consideration. However, the results from the reduced sample should be interpreted with caution because, with only 68 observations, cointegration rank tests are less reliable than the full-sample analysis, in particular when the systems are of higher dimension. 8

All cases are chosen out of a set of VARs whose lag orders take the integers from 1 to 10.

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Table 2 Cointegrating relations

estimation method rit popt

Germany (1975 – 2009) OLS DOLS 1 1 −1.56 −1.61

western Germany (1975 – 1991) OLS DOLS 1 1 −2.58 −2.37 (0.43)

(0.51)

inct

−0.26 −0.26

−0.38

−0.38

phrt

−0.76 −0.83

−0.64

−0.66

const

− 7.4 − 8.0

11.3

10.5

adj. R2 DW

0.92 0.28

0.77 0.84

0.77 0.81

sample

(0.06) (0.08) (0.13) (0.7)

(0.06) (0.08) (0.13) (0.7)

0.92 0.25

(0.05) (0.08)

(1.7)

(0.08) (0.09)

(2.1)

Standard errors are reported in parentheses. Auxiliary regressors in DOLS estimates are omitted.

The long-run relationship between residential investment, the trend determinants of housing demand and real house prices is established by estimating the static regression choosing residential investment as the left-hand side variable. Apart from using ordinary least squares (OLS), the dynamic OLS (DOLS) approach is additionally applied in order to come closer to estimation efficiency (Saikkonen, 1991). Starting from a model including the first differences of the (exogenous) regressors together with their first two leads and lags, specification search using standard information criteria suggests maintaining the contemporaneous differences only.9 Regardless of whether the full sample or the West German subsample is considered, the coefficients of the cointegrating relation show the expected signs. The estimates do not differ much depending on whether the OLS or the DOLS approach is used. While cointegration testing in the full sample has not suggested that percapita real income is necessarily present in the long-run equilibrium relationship, the estimates of the cointegrating vector point to a rather small but not statistically negligible impact. The essential role of per-capita real income in the cointegrating relation for the west German era is confirmed by a higher coefficient (in absolute value). The regression results also suggest that the impact of population on residential investment is more than a pure scale effect, as the estimated coefficient clearly exceeds unity (in absolute value). Hence, the trend in residential investment seems to be quite sensitive to demographic developments. While a population elasticity which exceeds unity may be difficult to be theoretically reconciled with households’ budget constraints in an economy possessing a high fertility rate, it may be sustainable in the German context where, apart from some pronounced waves of immigration, 9

A maximum likelihood estimation of the full system, however, yields less reliable results because the number of coefficients to be estimated is high compared with the number of observations available, in particular as far as the west German subsample is concerned.

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Fig. 2 Long-run residuals of residential investment

the population has been more or less stable for the last 35 years and the qualitative aspect of housing demand turns out to be of rather limited magnitude. The significance of real house prices in the cointegrating relation confirms the view that persistent tensions between housing demand and supply are reflected in the price of new dwellings, with the sign of the coefficient signalling that supply tends to adjust slowly to variations in demand. Here, too, the empirical results are consistent with the suggestions developed in the theoretical part of the paper. As displayed in Figure 2, what is striking in the long-run residual series (taken from the DOLS estimates) is that the degree of persistence changed substantially at reunification. Whereas fluctuations of a standard business cycle length are apparent in the west German era, the residual series thereafter describes a pronounced cycle lasting from 1991 to 2005 followed by a mild recovery. The prolonged cycle duration is also reflected by the fact that serial correlation is distinctly higher in the full-sample residual series compared with its subsample counterpart, which is reflected by a substantially lower Durbin-Watson (DW) statistic. In sum, the cointegration analysis has provided two main results. First, the trend in residential investment cannot be explained solely by fundamental factors of housing demand such as population growth and permanent gains in per-capita real national income. To establish cointegration, it is necessary to additionally consider real house price developments as a measure of persistent tensions between housing demand and supply. Second, while this pattern is generally maintained over the whole sample under investigation, reunification led to a change in the degree of persistence of the error correction term.

3 Cycle features of residential investment The analysis of this section is based on the observation that the residual series of the cointegrating relation established between residential investment, population and

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real national income per capita and real house prices has changed the degree of persistence in the course of reunification. This fact matters for the measurement of activity cycles in the housing market. The in-depth study of cyclical features in residential investment generally uses the framework of a vector error correction model (VECM). However, central results can be derived from a specification which is substantively simplified owing to the observation that population, per-capita real income and real house prices are weakly exogenous. The preferred model structure also makes it possible to form the trendcycle decomposition suggested by Gonzalo and Granger (1995) with observable variables and the estimated cointegrating vector only. In particular, the GonzaloGranger (GG) cycle component of residential investment is defined by the residual series of the cointegrating relation. The final part of this section shows that the GG cycle deviates substantively from the results of standard univariate trend-cycle filters, which gives rise to a discussion on the pitfalls of simple filter techniques in a situation where the properties of the time series to be filtered change.

3.1 Adjustment to the housing market equilibrium The study of adjustment processes towards the long-run housing market equilibrium requires a complete econometric specification of the time series under review. Accounting for cointegration, the VAR(p) representing the data generating process of the four variables stacked in yt = (rit , popt , inct , phrt )′ can be rewritten as the following VECM :

∆ yt = α ect−1 +

p−1

∑ Γj ∆ yt− j + Φ Dt + εt ,

(5)

j=1

where α is the four-dimensional vector of adjustment parameters correcting nonzero realizations of the (scalar) long-run residual series. It is taken from (4), which is compactly written as ect = β ′ yt + c with β = (1, −b1 , −b2 , −b3 )′ . In addition, Γ1 , ..., Γp−1 are (4 × 4) parameter matrices, Φ is the parameter matrix attached to the deterministic components collected by Dt which includes const and impulse dummy variables related to S(91:1). The residual term εt is assumed to follow a Gaussian vector white noise process with zero mean and the variance-covariance matrix Ω . A variable may contribute to the convergence of the system towards its long-run equilibrium if the coefficient attached to the error correction term in the respective system equation is significantly different from zero. A time series which does not fulfill this requirement is said to be weakly exogenous (with respect to the cointegrating space). A LR test for weak exogeneity, provided that cointegrating vectors are given or estimated, is suggested by Johansen (1996). For a variable to contribute to the error correction process, however, it is sufficient that the adjustment parameter and the coefficient attached to this variable in the cointegrating vector possess

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Table 3 Adjustment parameter estimates and weak exogeneity tests sample

Germany (1975 – 2009) OLS DOLS

estimation method (a) adjustment parameters ∆ rit −0.108 −0.109 (0.039)

(0.039)

∆ popt

0.002

0.002

∆ inct

−0.002

0.001

∆ phrt

0.003

0.004

(b) weak exogeneity {popt , inct , phrt } {popt , inct }

(0.002)

(0.013)

(0.008)

2.61

[0.456]

2.46

[0.292]

(0.002) (0.013) (0.008)

2.73

[0.436]

2.42

[0.298]

Western Germany (1975 – 1991) OLS DOLS −0.390 −0.380 (0.121)

(0.122)

0.001

0.001

(0.002)

(0.002)

−0.065 −0.059 (0.040)

(0.040)

0.061

0.063

(0.026)

8.35

[0.039]

2.83

[0.243]

(0.026)

8.35

[0.039]

2.50

[0.287]

Panel (a) presents the estimates of the vector α in (5); standard errors are reported in parentheses. Panel (b) reports the LR test statistics of the weak exogeneity hypothesis. The statistics are asymptotically χ 2 distributed, with the degrees of freedom equalling the number of variables tested to be weakly exogenous. The p-values of these tests are reported in brackets. In both cases, results are subject to prior OLS/DOLS estimation of the cointegrating vector.

opposite signs. The speed of the adjustment process is reflected in the magnitude of the parameter in absolute value. Table 3 reports the estimates of the adjustment parameter vector and the results of weak exogeneity tests based on the super-consistent estimates of the cointegrating vector. While the results do not vary with the estimation methods, the properties of the model alter considerably depending on whether the full sample or the west German subsample is considered. In the full sample, the error correction term only loads on ∆ rit , while the adjustment parameters in the other system equations are not significantly different from zero at conventional significance levels. Hence, it comes as no surprise that the null hypothesis of weak exogeneity of {popt , inct , phrt } is not rejected by a formal test. If the analysis is restricted to the West German subsample, results change qualitatively, as deviations from the long-run equilibrium relationship are, apart from residential investment, also corrected via real house prices. The equilibrium-correcting force of the price variable is less strong (in absolute value). However, the adjustment parameter in the system equation of ∆ phrt is significantly different from zero and weak exogeneity of {popt , inct , phrt } is clearly rejected, too. By contrast, the joint hypothesis that population and per-capita income are weakly exogenous cannot be rejected by a statistical test. Thus, in the years between 1970 and 1991, residen-

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tial construction and house prices helped “correct” disequilibria between housing demand and supply. Since reunification the endogeneity of house prices has been lost and the speed of the error correction mechanism via residential investment has slowed down considerably. The adjustment parameter attached to ∆ rit is about four times lower in the full-sample estimate than in the estimate on the basis of the west German subsample. More precise evidence on this issue can be obtained by specifying a conditional error correction model in residential investment for the full sample, letting the adjustment parameter switch at the date of reunification. According to Johansen (1992), this setup provides efficient estimates of the parameters of interest, as population, per-capita real national income and real house prices can be assumed to be weakly exogenous. Without loss of generality, the (full) VECM in (5), rewritten in the form : 

          p−1 ∆ y1t α1 Γ1 j Φ1 j ε1t Ω Ω = ect−1 + ∑ Dt + , Ω = 11 12 , (5′ ) ∆ yt− j + Ω21 Ω22 ∆ y2t α2 Φ2 j ε2t j=1 Γ2 j

can be decomposed into the conditional model :

∆ y1t = α c ect−1 + ω∆ y2t +

p−1

∑ Γjc ∆ yt− j + Φ c Dt + εtc

(6)

j=1

and the marginal model :

∆ y2t = α2 ect−1 +

p−1

∑ Γ2 j ∆ yt− j + Φ2Dt + ε2t ,

(7)

j=1

−1 where ω = Ω12 Ω22 , α c = α1 − ωα2 , Γjc = Γ1 j − ωΓ2 j , Φ c = Φ1 − ωΦ2 , and εtc = c =Ω − ε1t − ωε2t is a white noise process with the variance-covariance matrix Ω11 11 ωΩ21 . Under weak exogeneity of the variables stacked in y2t (i.e. α2 = 0), it is α c = α1 and statistical inference on α1 can be based on (6) only. Following the results of the weak exogeneity tests, let y1t = rit and y2t = ( popt , inct , phrt )′ . In addition, α1 is allowed to switch at reunification. Assuming lag order p = 2 but subsequently dropping nonsignificant coefficients in ω , Γ1c and Φ c , an OLS regression of this specification using the DOLS estimate of the cointegrating relation (4) yields (standard errors in parentheses) :

∆ rit = − 0.250 ect−1 + 0.184 [ ect−1 S(91:1) ] + 4.32 ∆ popt + 0.86 ∆ inct + (0.075)

(0.081)

(1.65)

(0.18)

+ 0.52 ∆ phrt − 0.75 ∆ S(91:1) − 0.029ice1t − 0.013ice4t + (0.26)

(0.38)

(0.006)

(0.007)

+ 0.021ice1t−1 + 0.012ice4t−2 + εtc , (0.006)

(0.007)

R2 = 0.56,

DW = 2.01,

(8)

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201

where ice1t and ice4t measure the number of days with a maximum temperature below freezing in the first and the fourth quarter respectively as a percentage of the seasonal mean and are zero in the remaining quarters. The estimate highlights the significant drop in the adjustment parameter in absolute value, from 0.250 in the West German era to 0.066 afterwards.10 The built-in forces for equilibrium correction in the housing market via residential investment have therefore weakened substantively since reunification. In addition, residential investment is instantaneously affected by changes in population and per-capita real national income. The short-term elasticity of residential investment to demographic variations is particularly high. Construction activity is hampered (favoured) by an unusually severe (mild) winter.11 The weather effect is revealed to be roughly twice as strong when it appears in the first quarter rather than the fourth quarter. The significantly positive coefficients attached to ice1t−1 and ice4t−2 point to the existence of countereffects in the following spring. The estimates of the coefficients are plausible also in their (absolute) magnitude, as the positive lagged effects more or less compensate for the initial negative effects.

3.2 A trend-cycle decomposition of residential investment The VECM in (5) implies a permanent-transitory decomposition of the Gonzalo and Granger (1995) type. It is interpreted as an approach to trend-cycle measurement where the identification follows the rule that, in the long-run (i.e. for horizons approaching infinity), conditional predictions of yt are exclusively affected by shocks to trend factors while shocks to cycle components only possess a temporary impact. For the formal description, let us denote by α⊥ and β⊥ the orthogonal complements of α and β respectively, satisfying α⊥′ α = 0 and β⊥′ β = 0. The GG trendcycle decomposition is then given by yt = y0 + yb0 S(91:1) + Aτt + Bct

with

τt = α⊥′ yt

and ct = β ′ yt ,

(9)

where y0 and yb0 are some initial values, the three-dimensional vector process τt represents the trend factors and ct is the time series of the single cyclical factor in this system. The (4 × 3) matrix A = β⊥ (α⊥′ β⊥ )−1 collects the loadings attached to the trend factors while the loadings attached to the cyclical factor are stacked in B = α (β ′ α )−1 , which is a four-dimensional vector in the case of a single cointegrating relation. 10

Although the resulting estimate of the adjustment parameter is rather low for the pan-German era, it turns out to be statistically significant from zero, as a Wald-type coefficient test for equal but reversely signed coefficients attached to ect−1 and ect−1S(91:1) yields the statistic 4.45, which suggests that the null hypothesis is rejected at the 5% level. 11 Recall that the analysis considers residential investment in seasonally and working-day adjusted form, implying that the dampening effect of a “usual” winter on residential construction is removed by seasonal adjustment.

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Thomas A. Knetsch

Fig. 3 Gonzalo-Granger trend component of residential investment Actual residential investment is displayed by the solid line and the GG trend component by the dashed line.

Under weak exogeneity of popt , inct and phrt , i.e. α = (a1 , 0, 0, 0)′ with a1 < 0, (9) simplifies substantively. First, the weakly exogenous variables directly represent the three independent stochastic trend factors driving residential investment because, in this case, α⊥ = [o : I3 ]′ where I3 denotes an identity matrix of order 3 and o is a three-dimensional vector of zeros. The trend component of residential investment is the weighted average of the weakly exogenous variables where the weighting scheme is given by the coefficients in the cointegrating vector attached to them with reverse sign. Second, the cyclical factor only loads on rit because B = (1, 0, 0, 0)′ . Hence, the cycle component of residential investment is represented by the error correction term. In sum, (9) can be written as          rit b1 b2 b3  c ect pop t popt  0  1 0 0   0           (9′ )  inct  = 0 +  0 1 0  inct +  0  . hprt 0 0 0 1 0 hprt

In this framework, the GG trend-cycle decomposition is informative for residential investment only, while population, per-capita real national income and real house prices do not possess a meaningful cycle component. It is worth stressing that the latter set of variables may nonetheless include transitory dynamics; however, these fluctuations lie in the space spanned by α⊥ and, thus, fail to possess the capacity to bring about equilibrium correction (Proietti, 1997). The fact that the speed of convergence via residential investment has slowed down since reunification does not affect the trend-cycle decomposition in a formal sense because neither α⊥ nor B depend on α in this special case. Instead, it is the time series structure of the error correction term which causes the increase in the degree of persistence characterizing the cycle component of residential investment since 1991. Figure 3 shows residential investment vis-`a-vis its GG trend component, resulting from the estimates in the full sample and the west German subsample. Overall, the

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trend is smooth but fluctuates visibly as a result of cycling behavior in fundamental factors. Most prominent in this respect are the waves of immigration into western Germany at the end of the 1980s as well as into Germany in the early 1990s. In the west German era, phases of economic weakness as in the mid-1970s and in the early 1980s were associated with gaps in residential construction. While departing from a more or less balanced cyclical position in 1990 despite rather strong trend growth just before that, the reunification-induced shift in the fundamentals of housing demand, in particular the increase in residents, required a considerably higher trend level of dwellings construction only half of which could be promptly served by existing capacities. Consequently, the construction sector expanded rapidly, lifting residential investment not only to its trend but far beyond it. The excessive formation of residential capital during the 1990s called for an adjustment which, in turn, materialized in the form of a long period of below-trend construction activity. This pattern prevailed throughout the past decade though the distance to the trend level has reduced significantly since 2005. The GG trend of residential investment is virtually flat between 1991 and 2009. Relying on the econometric description in (9′ ) informed by the development of economic fundamentals, this observation is ascribed to anemic demand for housing, as the population stagnated virtually and real national income per capita evolved less dynamically. With an exception towards the end of the 1990s, real house prices also declined steadily in this period.

3.3 Pitfalls for univariate statistical filtering The change in the cyclical features of residential investment makes it difficult for univariate statistical filter techniques to come out with a trend-cycle decomposition resembling the one that was derived in the previous section. The reason is that univariate filters lack flexibility in the sense that they extract the trend component on the basis of a time-invariant statistical criterion. For instance, the Hodrick-Prescott (HP) filter imposes a constant variance ratio λ between trend innovations and shocks to the cycle, whereas the Baxter-King (BK) filter defines a fixed frequency limit below which oscillations are ascribed to the trend component. Figure 4 shows the trend component of residential investment resulting from the HP filter with λ = 1, 600 (as usual for quarterly data) and from the BK high-pass filter assigning to the trend those oscillations whose duration surpasses eight years. The reunification shift is incorporated in the HP procedure by including S(91:1) in the measurement equation of the underlying state-space model. The BK trend component results from applying the high-pass filter to the residuals of the OLS regression of residential investment on const and S(91:1). While the outcomes of the statistical filtering techniques are virtually the same, they differ markedly from the GG trend component. In general, the HP and BK trends follow more closely the actual movements in residential investment, making the corresponding cyclical fluctuations less pronounced. This feature is most

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Fig. 4 Trend extraction with univariate statistical filters The HP and BK trend components of residential investment are displayed by the thick solid line in the respective charts. Actual residential investment (thin solid line) and the GG trend component (dashed line) are shown as reference series.

Fig. 5 GG and HP cycle components of residential investment The cycle components are measured as percentage deviation from the trend.

striking after reunification, as the boom-bust movement in dwellings construction is attributed to the HP and BK trends, whereas the GG trend is flat. In addition, the cointegration analysis shows that the economic fundamentals of housing demand would have implied a substantially bigger mean shift in residential investment than the one that actually happened at reunification. By contrast, the removal of the structural break incorporated in the HP filtering exercise brings about a mean shift in the resulting trend components which closely resembles the observed change in residential investment between the west German level of the fourth quarter of 1990 and the pan-German level of the first quarter of 1991.12 The marked discrepancy between the GG trend-cycle decomposition and the results of the univariate statistical filter techniques can be further highlighted by study12

The mean shift in the BK trend is virtually equal to the mean shift in the actual series.

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ing the time series characteristics of the corresponding cycle components. Owing to the strong similarity of the HP and BK results, the comparative analysis is restricted to the HP cycle.13 Figure 5 plots the GG and HP cycle components of residential investment, which differ from the gap between the actual series and the respective trend components in that, in order to reduce erratic variations, the impact of unusual weather conditions in the winter term including the counter effects in the following spring are eliminated by a regression approach.14 The two cycle components differ in terms of duration and amplitude. In addition, the time series characteristics of the HP cycle component seem to be stable over time while, in the GG cycle component, a switch is recognizable in the course of reunification. In order to confirm the visual impression with statistical evidence, spectral analysis is used. The idea is to find significant differences in shape between the fullsample spectrum and the spectra of the west-German and pan-German subsamples respectively. As the full-sample spectrum serves as a reference, its point estimate is surrounded by 95 percent confidence bands which are constructed using the bootstrap procedure suggested by Franke and H¨azdle (1992). With this technique, kernel spectral estimates are bootstrapped by resampling from the periodogram of the data. The bootstrap is based on 2,000 replications. As shown in the upper panel of Figure 6, the full-sample spectrum of the GG cycle component peaks in a frequency range which is consistent with a cycle duration of about eight years. The observation that the peak in the spectrum of the west German subsample is located to the right while the pan-German counterpart is located to the left of the eight-years frequency implies that the cycle length of the dominating oscillation increased at reunification, confirming the visual impression taken from the time series plot. In addition, the spectra of the west German and pan-German subsamples also differ with respect to the height of peak. This observation means that the spectral mass attached to the dominating oscillation is much more concentrated in the GG cycle component after reunification than in the spectrum of the west German subsample, suggesting that fluctuations in the range of major business cycles (and beyond it) shape the cyclical behavior of residential investment after reunification to a higher degree than before. Considering the confidence bands of the full-sample estimates, the evidence is significant from a statistical point of view, as the peak in the spectrum of the pan-German subsample clearly surpasses the upper limit of the confidence interval while the peak in the spectrum of the west-German subsample drops below the lower limit. The frequency-domain analysis of the HP cycle component reveals a number of differences in comparison with the GG cycle component. First, the HP cycle spectrum peaks visibly within the range of business cycle frequencies. In particular, the duration of the oscillation to which most spectral mass is assigned is about five years. Second, the HP spectrum is generally flatter than the GG spectrum, suggest13

The HP filter has been chosen for simplicity, namely because of the fact that, in contrast to the BK filter, it provides results for the full sample without any further treatment of data or techniques. 14 The regressors are ice1 and ice4 including the countereffect in the forthcoming spring, which t t have been shown to possess a significant effect on the quarter-on-quarter changes in residential investment.

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Fig. 6 Spectra of cycle components The charts depict the spectrum of the subsample mentioned in the respective headline as a thick solid line. The point estimate of the full-sample spectrum is drawn by the thin solid line, with the limits of the 95 percent confidence interval represented in the dashed format. The abscissa scale is frequency divided by 2π . The dashed vertical lines limit the frequency band attributed to periodicities of two and eight years (“business cycle frequencies”).

ing that, in the HP cycle component, fluctuations at business cycle frequencies are less dominant relative to erratic variations. Third, the subsample spectra of HP cycle component do not exhibit striking differences in the placement and the height of the peak. In the frequency range around the peak, the spectrum of the pan-German subsample lies within the confidence interval of the full-sample spectrum while the spectrum of the west-German subsample slightly exceeds the upper limit. A substantive break in the cyclical properties of the HP cycle component cannot be concluded from this evidence. In sum, the changing cyclical pattern in residential investment, which is a key result of the econometric analysis using a cointegrated VAR framework and which can be represented in terms of a GG trend-cycle decomposition, cannot be replicated by standard univariate filter techniques such as the HP and BK filter. Taking for granted the conclusions from the cointegration analysis, which incorporates a great deal of theoretical considerations, this can be seen as a deficiency and, thus, caution

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is advised when interpreting and using results which are derived from HP or BK filtered time series in this context.

4 Conclusion Real residential investment in Germany is modelled in a cointegrated vector autoregression with population, per-capita real national income and real house prices. Regarding the estimates of the cointegrating relation, demographic factors affect dwellings construction through more than a pure scale effect, while real income per capita turns out to have a small but statistically non-negligible impact. Tensions between housing demand and supply seem to be persistent, assigning real house prices a significant role in the long-run equilibrium relationship. The long-run residual series which is implied by the cointegrating vector is subject to a marked increase in the degree of persistence at reunification. The specification and estimation of the full vector error correction model have given rise to the belief that, during the German reunification episode, the speed of equilibrium adjustment via residential investment slowed down and real house prices lost the capacity to contribute to the adjustment process. If the analysis is based on the full sample including West German data from 1970 to 1990 and panGerman data from 1991 onward, population, real income per capita and real house prices are weakly exogenous. This result implies that the full time series properties of residential investment can be described by a single-equation error correction model conditioned on instantaneous changes in the weakly exogenous variables. The existence of a single cointegrating relation where population, per-capita real income and real house prices are weakly exogenous also means that the long-run residual series constitutes the cycle component of residential investment in the trend-cycle decomposition proposed by Gonzalo and Granger (1995). The corresponding trend component, which is a linear combination of movements in population, per-capita income and real house prices, has been shown to be smoother than the trends which have been extracted by standard univariate filtering techniques. In particular, the boom-bust movement in residential construction after reunification is part to the Gonzalo-Granger cycle component while the Hodrick-Prescott and the Baxter-King filters assign it largely to the trend component. A corollary of the approach to modelling residential investment within a vector error correction model is that the short-term dynamics of dwellings construction have been explained only insofar as they are governed by the adjustment process towards the long-run equilibrium. Together with government interference in the various segments of the housing market, this turns out to be a dominant feature in residential investment throughout the 1990s and the first half of the 2000s. The influence of other economic factors such as user cost of housing capital, lending conditions and the degree of affordability might be concealed. In any case, the integration of these elements in the specification of housing demand and, thus, residential investment was beyond the focus of this paper.

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The outcomes of alternative trend-cycle decompositions can be assessed in terms of economic plausibility. However, the ultimate proof which variant comes closest to reality can never be offered as there are no direct observations of trend and cycle components. As a consequence, the critical statements on simple statistical filtering techniques are not meant to deny their practical relevance, in particular when the intention is to conduct a comparative analysis on a unique methodological basis ´ (Alvarez et al., this volume, for instance). The example should rather remind users to be cautious in dealing with trend-adjusted figures in this context. ´ Acknowledgements Valuable comments by Luis Alvarez, Andrew Benito, Laurent Ferrara and Karl-Heinz T¨odter are gratefully acknowledged. The paper expresses the author’s personal opinion which does not necessarily reflect the views of the Deutsche Bundesbank.

References Carnot, N., Koen, V. and Tissot, B. (2005), Economic Forecasting, Hampshire and New York, Palgrave Macmillan. Deutsche Bundesbank (2002), The housing market during the nineties, Monthly Report January 2002, 27-37. Engle, R. F. and Granger, C. W. J. (1987), Co-integration and error correction: Representation, estimation, and testing, Econometrica, 55, 2, 251-276. Franke, J. and H¨ardle, W. (1992), On bootstrapping kernel spectral estimates, Annals of Statistics 20, 1, 121-145. Gonzalo, J. and Granger, C. W. J. (1995), Estimation of common long-memory components in cointegrated systems, Journal of Business and Economic Statistics, 13, 1, 27-35. ¨ Heilemann, U. (2004), Das RWI-Konjunkturmodell – Ein Uberblick, in W. Gaab, U. Heilemann and J. Wolters (eds), Arbeiten mit o¨ konometrischen Modellen, Heidelberg: Physica, 161-212. Johansen, S. (1991), Estimation and testing of cointegration vectors in Gaussian vector autoregressive models, Econometrica, 59, 6, 1551-1580. Johansen, S. (1992), Cointegration in partial systems and the efficiency of single-equation analysis, Journal of Econometrics, 52, 389-402. Johansen, S. (1996), Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford and New York, Oxford University Press. Johansen, S., Mosconi, R. and Nielsen, B. (2000), Cointegration analysis in the presence of structural breaks in the deterministic trend, Econometrics Journal 3, 216-249. Kurozumi, E. (2002), Testing for stationarity with a break, Journal of Econometrics, 108, 63-99. Kwiatkowski, D. A., Phillips, P. C. B., Schmidt, P. and Shin, Y. (1992), Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, 54, 154-178. L¨utkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Berlin, Springer. L¨utkepohl, H. (2007), General-to-specific or specific-to-general modelling? An opinion on current econometric terminology, Journal of Econometrics, 136, 319-324. MacKinnon, J. G. (1991), Critical values for cointegration tests, in R. F. Engle and C. W.J. Granger (eds), Long-Run Economic Relationships: Readings in Cointegration, Oxford, Oxford University Press, 267-276. Perron, P. (1989), The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 6, 1361-1401. Proietti, T. (1997), Short-run dynamics in cointegrated systems, Oxford Bulletin of Economics and Statistics, 59, 3, 405-422.

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Saikkonen, P. (1991), Asymptotically efficient estimation of cointegration regressions, Econometric Theory, 7, 1-21. Saikkonen, P. and L¨utkepohl, H. (2000), Testing for the cointegrating rank of a VAR process with structural shifts, Journal of Business and Economic Statistics, 18, 4, 451-464. Statistisches Bundesamt (2006), Immobilienwirtschaft in Deutschland 2006: Entwicklungen und Ergebnisse, Wiesbaden.

Appendix The time series of real residential investment, population and national income are taken from quarterly national accounts, adjusted for seasonal and working-day variations. The quarterly data on (nominal) house prices are produced by interpolating the annual price series for new dwellings, specifically terraced houses and flats, which is constructed by the Deutsche Bundesbank on the basis of primary data collected by BulwienGesa. The deflators needed to calculate real national income and real house prices are computed using national accounts data. The time series refer to Germany as a whole from 1991 onward. They are chained with the corresponding series for western Germany starting in 1975 and with an overlap in 1991. Real quantities and price indices refer to 1991 as the reference year. This choice ensures comparability between the west German and the pan-German subsamples. The time series are transformed in natural logarithms. Table 4 Unit root tests time series rit popt inct phrt

deterministic terms c, t, S(91:1) c, t, S(91:1) c, t, S(91:1) c, t, S(91:1)

(0) (0) (0) (1)

ADF −3.28 −3.60(∗) −2.21 −2.92

(3) (1) (5) (8)

PP −3.29 −3.69(∗) −2.36 −2.54

KPSS (4) 0.211∗∗ (4) 0.205∗∗ (4) 0.115(∗) (4) 0.190∗

The numbers in parentheses indicate the lag length in the ADF procedure and the bandwidth parameter in the PP and KPSS procedures. The ADF and the PP tests are performed following Perron (1989), as a structural break has to be considered in the specification. Critical values are taken from Table IV.B of this paper which are −4.32, −3.76 and −3.46 in the given setup. The KPSS test is performed according to Kurozumi (2002); critical values are found in Table 1b: 0.204, 0.134 and 0.106.∗∗ ,∗ ,(∗) mean rejection of the null hypothesis at the 1%, 5% and 10% level respectively.

Real residential investment, population, real national income per capita and real house prices are plotted in Figures 7(a) to (d). Visual inspection shows them to be nonstationary even if the drifts are only slightly positive in the case of residential investment and population. While per-capita income tends upward over the whole sample with a setback at reunification, real house prices have fluctuated substantially around an overall negative trend. The order of integration is checked by standard unit root tests, namely the augmented Dickey-Fuller (ADF) test, the Phillips-Perron

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Fig. 7 Time series The vertical line indicates the date from which data for Germany as a whole are available. As regards Figures (a) to (d), note that data for western Germany and Germany as a whole are available for a short overlapping period, namely the year 1991.

(PP) test and the KPSS test proposed by Kwiatkowski et al. (1992). The ADF and the PP procedures test for a unit root under the null hypothesis. In the present setup, the null hypothesis of the KPSS test is trend-stationarity including a mean shift in the first quarter of 1991. As Perron (1989) has suggested for the ADF and PP tests, the structural break is taken into account by a prior removal of the mean shift and by applying the crit-

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ical values reported in this paper for TB /T = 0.5 where TB is the date of the break and T the length of the sample. Against the alternative of trend stationarity with a change in mean in the first quarter of 1991, the null hypothesis of a unit root cannot be rejected for any series at the 5% level. The evidence seems clear-cut except for population, where both the ADF and the PP procedures signal rejection of the unit root hypothesis at the 10% level. The mean shift in the KPSS test procedure is captured by the test structure proposed by Kurozumi (2002). For all series under consideration, the null hypothesis of stationarity is rejected at conventional significance levels, confirming the I(1) assumption for residential investment, population, real national income per capita and real house prices. Figures 7(e) and (f) display the time series plots of the variables ice1t and ice4t which measure the effects of unusual weather conditions in the first and the fourth quarter. The time series are constructed on the basis of information about the number of days with a maximum temperature below freezing in the respective quarters. As the average impact of production impediments due to weather conditions in the first and fourth quarters is removed by seasonal adjustment, the variables are defined in relation to the long-run seasonal means; to be precise, as a percentage of the longrun average of days with a maximum temperature below freezing in the respective quarters.

User Costs of Housing when Households Face a Credit Constraint: Evidence for Germany Tobias Duemmler and Stephan Kienle

Abstract We develop a formula for user costs of housing on the basis of a neoclassical approach to housing investment which does not impose a perfect capital market assumption. We suggest that the definition for the user costs of housing should be extended by an additional term which mirrors the credit constraints a household would be faced with. This extension term consists of the inflation gap between consumer and house price inflation multiplied by an average loan-to-value ratio and the real house prices. The empirical relevance of our finding is confirmed by a VECM. We provide evidence that the dynamics of residential investment in Germany are significantly influenced by the extended user costs (i.e. basic user costs plus the extension term) as well as by net financial wealth. A time series for the user costs of housing is calculated using this extended definition.

JEL codes : C32, E13, E22 Keywords : Housing investment, user cost of housing, cointegration

1 Introduction The housing market plays an important role in an economy in several respects. In accordance with the ECB (2003), three key reasons can be mentioned. First, housing is one of the main parts of the private sector’s net wealth. Households’ behavior may have serious impacts on aggregate demand. In the literature - see Bundesbank (2007) or Campbell and Cocco (2005), for instance - effects of aggregate housing T. Duemmler Deutsche Bundesbank, e-mail: [email protected] S. Kienle Deutsche Bundesbank, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_10, © Springer-Verlag Berlin Heidelberg 2010

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on aggregate consumption are supposed to exist especially when wealth effects are permanent. Strong correlations between the two variables, as are found by Case et al. (2001), support these findings. Second, house price bubbles, as have occurred in some countries, play a major role in financial stability and monetary transmission. Third, the housing market with its high transaction costs and non-portable housingrelated benefits has an implication for labor mobility, and thus for the supply side of an economy. Moreover, the IMF (2008) postulates that monetary policy should take developments in the housing market explicitly into account, since, due to innovations, the influence of the housing sector on the economy has increased. We focus on a key concept - the user costs of housing - to gain further insights. The concept of the user costs is crucial for modeling investment behavior. A classical derivation can be found in Jorgenson (1963). Dougherty and Van Order (1982) applied the concept to housing investment decisions and derived a measure of user costs of housing in a neoclassical environment. Nevertheless, this approach can be enlarged by lifting the perfect capital market assumption. Hence, in our approach a household can only partly finance housing investment by a mortgage; the remainder has to be financed by other liquid funds. This change in assumption is reflected by an extended definition of the user costs of housing. The resulting expression consists partly of a term which is equal to the user costs of housing measure derived by Dougherty and Van Order (1982) - it will be denoted below as the classical definition of user costs - but is also enlarged by an additional term. This additional term consists of the real house prices, an average loan-to-value-ratio, and an inflation gap defined as the difference between the changes in consumer prices and house prices respectively. Since explicit account has to be taken of country-specific peculiarities, we focus on Germany. The sample starts in the first quarter of 1980 and ends in the fourth quarter of 2007. Using the Johansen procedure, we find one cointegrating relationship between the variables under consideration, i.e. households’ investments in housing, disposable income, net financial wealth, and user costs of housing including the extension term. The estimation of the cointegrating relationship can be interpreted as a long-run equilibrium relationship of housing investment due to a credit constraint. Estimating a full Vector Error Correction Model (VECM), we find that user costs are weakly exogenous. In addition, a likelihood-ratio (LR) test suggests that the extension is present in the user costs expression. An average loan-tovalue ratio for German households can be derived from VECM estimates. Using this estimated value, we calculate and show time series for the German user costs of housing. The remainder of the paper is organized as follows. In Section 2 we set up a theoretical model within a neoclassical framework in order to derive user costs of housing. In Section 3 econometric analyses are carried out in order to evaluate the relevance of our theoretical derivation. Section 4 gives a summary of the key find-

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ings and some final conclusions. The dataset for the empirical part is described in the Annex.

2 Theoretical model Extending the neoclassical approach of Dougherty and Van Order (1982), a theoretical framework is derived containing a credit constraint relevant to the representative household’s decision between non-durable consumption and residential investment. This results in an extended version of the user costs of housing which includes in addition to the basic expression - a term depending on the inflation gap between consumer prices and house prices, real house prices, and an average loan-to-value ratio.

2.1 The set up of the model Suppose that the preferences of the representative household are reflected by the instantaneous utility function u(ct , ht ) with u′ > 0, u′′ < 0 where ct is the consumption of non-durable goods and ht is the use of housing services in period t. The use of housing services can be restrained to a quality-adjusted stock of housing. That means that housing services can be seen as proportional to the housing stock. The household receives a nominal income flow Yt and can raise nominal liquid funds through debt expansion −St . Both can be spent on consumption goods Ct , gross housing investment Xt affecting housing stock Ht , or interest payments on debt Zt . In general, the household faces the budget constraint: Yt − St = Ct + Xt + Zt . The nominal housing stock can be financed either by a mortgage loan Mt or by an unsecured credit Bt . The household has to pay a nominal interest rate ih,t = ir,t + πh,t or it = ir,t + πt respectively, with a real interest rate ir,t . We assume that the consumer price inflation πt is larger than the house price inflation πh,t , i.e. πt > πh,t . A mortgage is covered by housing stock, so that only the share of the nominal housing stock η , with 0 ≤ η ≤ 1, can be financed by this kind of credit. Since the mortgage is cheaper, the household always takes the maximum available share. Thus we have Mt = η Ht and Bt = (1 − η )Ht . In this context, η can be interpreted as a loan-to-value ratio for real estate mortgages. In analogy with Iacoviello and Minetti (2008), we expect the ratio to be in a range between 60 and 100 percent.

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Hence, for the nominal debt expansion we obtain: −St = Mt−1 − Mt + Bt−1 − Bt = Ht+1 − Ht . According to this, the nominal interest expenditures are given by Zt = jt Ht where jt = [(ir,t + πh,t )η + (ir,t + πt )(1 − η )] = it − η (πt − πh,t )

(1)

is the effective nominal interest rate on household debt as a weighted average of the mortgage rate and the credit rate it . An increasing share of mortgage credit implies a decrease in interest expenditures since πt > πh,t . In real terms, with a price ratio qt = ph,t /pt , i.e. the real house prices, we obtain the real housing accumulation, equation (2), and the real debt expansion, equation (3): ht+1 = (1 − δt )ht + xt −st = ht+1 (1 + πh,t ) − ht

(2) (3)

where δt is the economic depreciation rate of the housing stock. Economic depreciation consists of technical decay δ˜t as well as capital gains or losses:

δt = δ˜t − [πh,t − πt ]. We can express the real budget constraint, i.e. the budget constraint in units of consumer prices as Yt ph,t Ct ph,t ph,t Ht − st = + xt + jt pt pt pt pt ph,t pt which can be written more compactly as yt − qt st = ct + qt xt + jt qt ht .

(4)

2.2 The maximization problem of the household Let us assume that the household maximizes life-time utility represented by a timeseparable function, i.e.

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217 T

∑ ρtt u(ct , ht ) ct ,ht+1 max

t=0

with the discount rate ρt = (1 + it − πt )−1 and subject to equations (2), (3), and (4). We rewrite the budget constraint as a function of consumer goods and the stock of housing in the current and the next period:

ψ (ct , ht , ht+1 ) = yt − ct − qt [xt + st + jt ht ] = 0. The dynamic Lagrange function L=

∞

∞

t=0

t=0

∑ ρtt u(ct , ht ) + λ ∑ ρtt ψ (ct , ht , ht+1 )

(5)

yields the following first-order conditions:

∂L ∂u ∂ψ = ρtt + λ ρtt =0 ∂ ct ∂ ct ∂ ct ∂L ∂u ∂ψ ∂ψ = ρtt+1 + λ ρtt+1 + λ ρtt =0 ∂ ht+1 ∂ ht ∂ ht ∂ ht+1 which may be written more compactly as uc + λ ψc,t = 0

ψh,t+1 uh + λ ψh,t + λ =0. ρt

(6) (7)

Optimization implies that consumption of non-durable goods must be extended up to the point where the marginal rate of utility of consuming goods is equal to the marginal costs of financing consumption. By analogy, consumption of housing services must be extended until the marginal utility of housing services matches the marginal costs of buying an extra unit of housing stock which is the discounted sum of the current and the following period. Combining equations (6) and (7) leads to: uh ψh,t ψh,t−1 = + . uc ψc,t ψc,t ρt With the partial derivatives of the budget constraint

ψc,t = −1 ψh,t ψh,t+1

"

# ∂ xt ∂ st = −qt + + jt = −qt [ jt + δt ] ∂ ht ∂ ht " # ∂ xt ∂ st = −qt [−πt ] = −qt + ∂ ht+1 ∂ ht+1

(8)

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we obtain the following expression for the real user costs of housing: " # − qt [ jt + δt ] − qt [−πh,t ] πh,t uh + . = = qt jt + δt − uc −1 −ρt ρt

(9)

2.3 Defining basic and extended versions of the user costs Using equation (1) and the approximation πh,t /ρt = πh,t (1 + it − πt ) ≈ πh,t , we can write the equilibrium optimality condition as: uh = qt [it − πt + δt + (1 − η )(πt − πh,t )]. uc

(10)

Depending on the share of mortgage loans, i.e. η , user costs of housing range between qt [it − πt + δt ]η =1 and qt [it − πh,t + δt ]η =0 . For η = 1, which means that the full stock of housing can be financed by a mortgage, the user costs of housing collapse to the version presented by Dougherty and Van Order (1982).1 Therefore, we define the basic user costs UCtB relevant to households without a binding credit constraint as: UCtB = qt (it − πt + δt ). (11) In equilibrium, the marginal rate of substitution between consumption of housing services and consumption of the non-durable good is equal to the basic user costs of capital expanded by an extension term. This wedge between the marginal rate of substitution and the basic user costs consists of three factors: The differential between consumer price inflation and house price inflation (inflation gap), the price ratio q, and the average loan-to-value ratio. We define these extended user costs UCt as: UCt = (1 − η )qt (πt − πh,t ) + qt (it − πt + δt ).

1

(12)

For simplicity, the taxation factor included by Dougherty and Van Order (1982) is omitted. For user costs following classical references, see, for example, Jorgenson (1963).

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3 Empirical analysis The theoretical analysis suggests the presence of an extension term in the expression of the user costs of housing that mirrors the credit constraint a household may be faced with. First, we check the general relevance of the extension term by analyzing basic time series properties of the inflation gap between house prices and consumer prices, which is the main time-varying component. Since its mean is shown to be significantly different from zero, the wedge may principally have an effect on housing demand. The second part of this section is therefore devoted to specifying and estimating an econometric model representing residential investment as a function of user costs and other determinants where the impact of the additional term can be tested statistically.

3.1 The relevance of the inflation gap in the user costs of housing

inflation gap

q

.05

1.35

.04

1.30

.03

1.25

.02

1.20

.01

1.15

.00

1.10

-.01

1.05

-.02

1.00

-.03 -.04

80 82 84 86 88 90 92 94 96 98 00 02 04 06

0.95

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Source: Author’s own calculations. Fig. 1 Inflation gap (π − πh ) (left graph) and real house prices (q) (right graph)

In the theoretical part, two versions of user costs of housing have been described: the basic one UCtB and the extended one UCt as in equations (11) and (12). The difference between the two expressions is the product of the inflation gap (πt − πh,t ), the real house prices qt , and the average loan-to-value ratio η . The latter is taken as a constant parameter depending, for instance, on the institutional framework of

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bank lending to homebuyers. As shown in Figure 1, however, the inflation gap is a rather volatile variable fulfilling the properties of a covariance-stationary series. If the inflation gap has a zero mean, i.e. E(π − πh ) = 0, the extended version degenerates to the basic version in the long run. As this case means that the additional term is irrelevant in a long-run perspective even if a credit constraint is binding, it is worth checking in advance whether or not the inflation gap has a non-zero mean. In the sample at hand, mean and median are both 0.9%. In addition, the null hypothesis of zero mean can be rejected at the 1% level. Using Newey-West HAC standard errors and covariance, a t-statistic of 2.70 and a probability of 0.008 are obtained.2 The real house prices qt , as a further component of the extension term, have a negative trend in the sample at hand. The actual magnitude of the inflation gap’s influence on user costs also depends on η . This ratio is expected to be strictly positive since a loan-to-value ratio of zero implies that, irrespective of housing stock pledged as collateral, no loan is available. German banks usually accept a loan-to-value ratio up to 80 percent in standard mortgage contracts.

3.2 A long-run equilibrium relationship for housing demand We estimate a long-run equilibrium relationship for housing demand. The components of the extended user costs are considered separately. This means that basic user costs and extension term are included as single variables in the model. The key variable in the empirical model is residential investment because the credit constraint is likely to be present when a new dwelling should be financed by mortgages. Under these circumstances, banks usually evaluate the income and wealth position of the household which suggests that the household’s disposable income and the value of wealth used as collateral are relevant factors affecting creditworthiness. As a consequence of focusing on residential investment which measures dwellings construction only, the value of assets does not include the building land and other real estate property. Instead, the empirical analysis uses households’ financial assets and financial liabilities which are not netted as a precondition. In sum, we define a vector zt consisting of six variables. Private residential investment (hit ), disposable income (dit ), financial assets ( f at ), and liabilities ( f lt ) are divided by the number of households and transformed into logs. In addition, the vector include the extension term qt (π − πh )t and the basic user costs of housing   (UCtB ). In sum, zt ′ = hit dit f at f lt qt (π − πh )t UCtB . The econometric analysis is carried out for the German economy. The sample starts in the first quarter of 1980 and terminates in the fourth quarter of 2007. Graphical inspection points to a 2 The sample for our empirical analysis starts in 1980 and ends in 2007. We decided on a sample of 27 years owing to a lack of data as we use expected inflation rates in our empirical analysis derived using the ARIMA approach (see the Annex for details).

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mean shift in some series in the first quarter of 1991 due to Germany’s reunification, which is captured by a dummy variable. A detailed description of all time series is found in the Annex. Standard unit root tests indicate that series for hi, di, f a, f l, q(π − πh ), UCB can be regarded as I(1) processes.3 These findings are supported by the plots of the series.4

3.2.1 Econometric setup The variables under consideration are modeled jointly, taking them as endogenous in general. Hence, the basic framework is a vector autoregression (VAR). Since the time series are nonstationary, we apply the concept of cointegration and use a vector error correction model (VECM) to reveal the long-run relationships between the variables.5 The model can be written as

∆ zt = Π zt−1 +

µ −1

∑ Γω ∆ zt−ω + κ Dt + εt

ω =1

where zt is a set of k time series, µ is the lag order of the underlying VAR, Γω are short-run parameter matrices. Under cointegration, the matrix Π has reduced rank r, 0 < r < k, and can be written as Π = αβ ′ , where α and β are (k x r) matrices. The residual εt is a zero mean white noise process with time-invariant positive definite covariance matrix, κ is a parameter matrix attached to the intercept term and an impulse dummy variable I(91 : 1) to control for German reunification in the first quarter of 1991; i.e. Dt = [c, I(91 : 1)]. I(91 : 1) is unity in the first quarter of 1991 and zero otherwise. The matrix β collects the cointegrating vectors of the system. Thus β ′ zt ∼ I(0) can be interpreted as long-run equilibrium relationships.6 For specifying the VECM, the lag order µ and the cointegration rank r have to be determined first.

3

The results are reported in the Annex. For an overview of non-stationary time series, see Stock and Watson (1988), for instance. 4 See Figures 3 and 5. 5 The concept of cointegration accounts for the observation that I(1) series may be interrelated in a way that linear combinations between them are stationary. The reason for this is that cointegrated series share common (stochastic) trend factors. These processes were introduced by Granger (1981) and Engle and Granger (1987). 6 For a more detailed discussion of VECMs as well as proofs etc., see, for example, L¨ utkepohl (2007).

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3.2.2 Determining the lag order

Table 1 VAR lag order selection Lag 0 1 2 3 4 5 6 7 8 ∗

AIC -22.553 -39.663 -40.537 -40.571∗ -40.469 -40.355 -40.261 -40.158 -40.255

SC -22.248 -38.442∗ -38.402 -37.520 -36.502 -35.473 -34.464 -33.445 -32.627

HQ -22.429 -39.169 -39.672∗ -39.335 -38.862 -38.377 -37.913 -37.438 -37.165

indicates lag order selected by the criterion.

Table 2 VAR(µ ) residual serial correlation LM tests Lag order µ = 1 (SC) µ = 2 (HQ) µ = 3 (AIC) µ =4 λ LM-Stat. Prob. LM-Stat. Prob. LM-Stat. Prob. LM-Stat. Prob. 1 110.66 0.00 87.66 0.00 38.39 0.36 41.90 0.23 2 75.57 0.00 64.35 0.00 46.62 0.11 41.83 0.23 3 42.39 0.21 44.97 0.15 42.06 0.23 29.51 0.77 4 41.72 0.24 35.60 0.49 41.99 0.23 38.41 0.36 5 52.99 0.03 47.26 0.10 48.78 0.08 40.22 0.29 6 42.86 0.20 41.17 0.25 34.08 0.56 31.06 0.70 H0 : no serial correlation at lag order λ . Probabilities from χ 2 (36).

We follow the conventional practice of choosing the lag order µ by fitting unrestricted VAR(µ ) models in levels for the set of lag orders µ =0,1,2,...,µmax, where µmax =8 in this application. The estimator selected is of the order µ , which minimizes standard information criteria AIC, SC and HQ, following Akaike (1969,1971) (AIC), Schwarz (1978) (SC), and Hannan and Quinn (1979) (HQ). The results are presented in Table (1). Unfortunately, the three criteria do not come up with a unique suggestion. Instead, the chosen lag orders range from µ =3 (AIC) to µ =1 (SC). As a further check, we perform residual autocorrelation tests in the VAR(µ ), µ =1 to 4. Results are reported in Table (2). The hypotheses of no serial correlation of order λ = 1, 2, ..., 6 for the VAR models with µ = 1, 2 are mostly rejected at the 5% level. Due to the autocorrelation properties of residuals, we therefore disregard the choices of the SC (µ = 1) and HQ (µ = 2) information criteria. By contrast, the residual autocorrelation properties from the VAR(3) and especially from the VAR(4) model are much better: The absence of serial autocorrelation cannot be rejected at all orders

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λ = 1, 2, ..., 6. As the lag orders µ = 3 and µ = 4 (in levels) have adequate autocorrelation properties, we show all further steps for both lag orders, which implies considering VECMs with two and three lags of the variables in first differences in the analysis that follows. 3.2.3 Determining the cointegration rank Conditional on µ = 3 and 4, we test for the cointegration rank using the procedure proposed by Johansen (1995). As we do not assume the inclusion of a deterministic trend restricted to the cointegrating space, the maximum number of cointegrating equations to be tested is 4. According to the results of the Johansen test, we conclude that there is exactly one cointegrating relation between the I(1) variables.

Table 3 Test for the cointegration rank Johansen Trace Test Cointegration LR-statistic LR-statistic 0.10 0.05 0.01 rank r µ=3 µ = 4 critical value critical value critical value r=0 107.58∗∗ 106.55∗∗ 89.48 94.15 103.18 r≤1 63.58 64.49 64.84 68.52 76.07 r≤2 35.28 37.33 43.95 47.21 54.46 r≤3 16.63 20.06 26.79 29.68 35.65 r≤4 3.88 3.76 13.33 15.41 20.04 Johansen trace test indicates 1 cointegrating equation at the 0.01 level. ∗∗ denotes rejection of the hypothesis at the 0.01 level. Critical values are drawn from Osterwald-Lenum (1992). We correct the Johansen LR-statistic to avoid over-rejection of the null hypothesis, as suggested in Banerjee et al. (1993).

The resulting reduced rank regression of the VECM(3), without imposing restrictions on the cointegrating space, yields the cointegrating relation7

βˆ ′ zt = hit −0.305 dit −0.483 f at +0.750 f lt +4.585 qt (π − πh )t +12.235 UCtB (2.187)

(0.929)

(0.564)

(2.297)

(2.282)

and for the VECM(4) the relation

βˆ ′ zt = hit −0.476 dit −0.564 f at +0.925 f lt +3.969 qt (π − πh)t +13.371 UCtB . (1.991)

(0.881)

(0.546)

(2.137)

(2.167)

The vectors of adjustment parameters are given by 7 Standard errors are given in parentheses. To the right of the estimated adjustment parameter matrix, we indicate to which left-hand-side variable the corresponding row of αˆ belongs. For the procedure computing standard errors for the cointegrating vector, see Boswijk (1995).

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

−0.009



 (0.012)   0.006     (0.003)   0.012     (0.004)  αˆ V ECM(3) =    0.019   (0.003)     −0.004   (0.002)    −0.004 (0.001)



−0.014



 (0.013)   0.010     (0.003)   0.014     (0.004)  αˆ V ECM(4) =    0.021   (0.002)     −0.003   (0.002)    −0.003

hit dit f at f lt qt (π − πh )t UCtB .

(0.002)

In general, we define βˆ ′ zt = b0 hit + b1 dit + b2 f at + b3 f lt + b4 qt (π − πh )t + b5UCtB and αˆ ′ = a0 a1 a2 a3 a4 a5 accordingly.

Standard errors of estimated coefficients of the cointegrating vector are relatively high in some cases. In particular, this applies to disposable income, financial assets and financial liabilities which are variables included to capture the presence of a credit constraint. On the one hand, the exclusion of this set of variables cannot be rejected on the basis of an LR test as the corresponding statistic is 1.44 for the VECM(3) and 4.04 for the VECM(4), which implies marginal significance levels of 0.258 and 0.697, respectively, taken from asymptotic χ 2 (3) distribution. On the other hand, a test for cointegration in the reduced system does not provide evidence for the presence of cointegration between the remaining variables hit , qt (π − πh )t and UCtB (Table 4 for the results of the corresponding Johansen test). We therefore proceed with the analysis in the full model, taking the sometimes large standard errors as an indication of a great deal of estimation imprecision which might be due to the relatively low degrees of freedom. This problem can be resolved, at least to some extent, by imposing restrictions and thus reducing the set of parameters to be estimated. The theoretical analysis gives us some hints on how to follow these strategies. Table 4 Test for the cointegration rank II between the variables hit , qt (π − πh )t and UCtB Johansen Trace Test Cointegration LR-statistic LR-statistic 0.10 0.05 0.01 rank r µ=3 µ = 4 critical value critical value critical value r=0 25.93 21.46 26.79 29.69 35.65 r≤1 4.25 4.02 13.33 15.41 20.04 Johansen trace test indicates no cointegrating equation at the 0.10 level. Deterministic assumptions and lag order remained unchanged. Critical values for the Johansen trace test are drawn from Osterwald-Lenum (1992). We correct the Johansen LR-statistic to avoid over-rejection of the null hypothesis, as suggested in Banerjee et al. (1993).

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3.2.4 Hypothesis tests Let us now reconsider the full model. Regarding possible restrictions imposed on the cointegrating space, we first check the net wealth condition. Because net financial wealth is computed as the difference between financial assets and liabilities, the estimated coefficient should be equal in absolute value. A LR test of this hypothesis H0 : b2 = −b3 is not rejected by the data. Furthermore, we assume that extended user costs are weakly exogenous.8 An LR test of the hypothesis H0 : a5 = a6 = 0 indicates that the restriction is not rejected. The hypothesis H0 : b2 = −b3; a5 = a6 = 0, i.e. testing for joint restrictions on β and α , is not rejected by a LR test either. Table 5 LR Tests for binding restrictions on β and α Test description Restriction imposed on β and α Net wealth condition; b2 = −b3 Weak exogenity of UC; a5 = a6 = 0 Joint restriction; b2 = −b3 ; a5 = a6 = 0 No long-run impact of q(π − πh ); b4 = 0 No long-run impact of UCB ; b5 = 0 No long-run impact of UC; b4 = b5 = 0

df 1 2 3 1 1 2

VECM(3) χ 2 (d f ) Prob. 0.054 0.816 5.004 0.082 5.053 0.168 3.910 0.048∗ 11.972 0.001∗ 16.935 0.000∗

VECM(4) χ 2 (d f ) Prob. 0.119 0.730 3.848 0.146 4.215 0.239 4.963 0.026∗ 17.779 0.000∗ 22.353 0.000∗

∗

denotes rejection of the hypothesis at the 0.05 level. d f : degree of freedom.

As the extension term q(π − πh ) in the definition for the user costs of housing is the new additional element, we test for the relevance of this term within the estimated VECMs. The hypothesis is H0 : b4 = 0. We also test the hypotheses H0 : b5 = 0 and H0 : b4 = b5 = 0 within our model, i.e. testing the relevance of the basic user costs term UCB (and the extended user costs UC, respectively) within the VECMs. We can reject all hypotheses of no impact of user costs variables at the 5% level. According to these results, the impact of the extension term on household investment cannot be denied.

3.2.5 Estimating the parameters of the cointegrating space As mentioned, the vector to be modeled ′ is defined so that  zt = hit dit f at f lt qt (π − πh)t UCtB . The identification scheme for the cointegrating matrix β was described above, which is also true of the zero restrictions imposed on the adjustment parameter matrix α .

8

See Johansen (1995) for the definition and implications of weak exogenity.

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The cointegrating relation of the VECM(3) is given by9

βˆ ′ zt = hit −0.214 dit −0.410 f at +0.410 f lt +2.319 qt (π − πh)t +4.941 UCtB (0.204)

(0.323)

(0.323)

(1.188)

(1.198)

and for the VECM(4) by

βˆ ′ zt = hit −0.080 dit −0.548 f at +0.548 f lt +2.211 (π − πh)t +6.590 UCtB . (0.228)

(0.378)

(0.378)

(1.330)

(1.380)

The vectors of adjustment parameters are given by 

      αˆ V ECM(3) =      

−0.029 (0.019)

0.005 (0.005)

0.022 (0.007)

0.036 (0.004)

0.000 0.000

            



      αˆ V ECM(4) =      

−0.032 (0.020)

0.013 (0.005)

0.025 (0.007)

0.037 (0.004)

0.000 0.000

            

hit dit f at f lt qt (π − πh )t UCtB .

3.2.6 Insights from estimated cointegrating vector β Using nwt = f at − f lt and rearranging terms with regard to the user cost expression yields the following long-run equilibrium relationships: 10 VECM(3) household investments hit - 0.21 disposable income dit - 0.41 net wealth nwt + 4.94 ∗ [0.47 ∗ qt (π − πh )t +UCtB ] ∼ I(0)

VECM(4) household investments hit - 0.08 disposable income dit - 0.55 net wealth nwt + 6.59 ∗ [0.34 ∗ qt (π − πh )t +UCtB ] ∼ I(0)

Since the extended user costs are defined in equation (12) as UCt = (1 − η ) ∗ qt (π − πh)t + UCtB 9 Standard errors are given in parentheses. To the right of the estimated adjustment parameter matrix, we indicate to which left-hand-side variable the corresponding row of αˆ belongs. For the procedure computing standard errors for the cointegrating vector, see Boswijk (1995). 10 See also Johansen (2002) for remarks on the interpretation of the cointegrating vector.

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the loan-to-value ratio is estimated to be ηˆ = 0.53 in the VECM(3) and ηˆ = 0.66 in the VECM(4), respectively. The estimate is roughly in line with our prior value in the range between 60% and 100% that is usually required by German banks in housing finance. Looking at the partial effects of income, wealth and extended user costs, it can be seen that they are consistent with intuition:

∂ hi ∂ hi ∂ hi ∂ hi > 0, > 0, < 0. < 0 and B ∂ di ∂ nw ∂ UC ∂ UC In Figure 2, the long-run residual series resulting from the estimated cointegrating relations are plotted. Over the last 27 years, investment in housing stock deviates from the long-run equilibrium reflecting the income and wealth conditions from German households. These developments might be explained by changes in the nature and strength of government interventions in the housing market. For instance, after German reunification in 1991, there was a boom in some segments, and substantially so in residential construction, which was driven by strong stimuli created by economic policy. The stepwise reduction of the rather expansionary fiscal policy stance in this market segment has led to less investment in housing compared with the equilibrium, especially in view of the fact that the exaggerations in dwellings construction in the first half of the 1990s resulted in an excess supply in many regions, especially in eastern Germany. VECM(3)

VECM(4)

.4

.6

.3

.4

.2 .2

.1 .0

.0

-.1

-.2

-.2 -.4

-.3 -.4

82 84 86 88 90 92 94 96 98 00 02 04 06

-.6

82 84 86 88 90 92 94 96 98 00 02 04 06

Source: Own calculation. Fig. 2 Cointegrating relations

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3.2.7 Diagnostic checks - break tests and residual checks The estimated systems are checked for a possible mean shift of the cointegrating relations in the first quarter of 1991 due to German reunification. Therefore, a shift dummy is included in the cointegration vectors, and a LR test for binding restriction is used to decide whether the dummy is to be included or not. From χ 2 (1) distribution, a value of 0.058 is obtained for the VECM(3), i.e. the probability of this result under the null is 0.810. For the VECM(4) a value of 0.002 is obtained and, thus, the probability under the null is 0.964. The hypotheses of no level shift in the first quarter of 1991 cannot be rejected at a 5% level, i.e. no break in mean has to be included in the VECMs. To substantiate that the models are well-specified, some diagnostic checks on the VECMs residuals are performed. In the following tables, standard diagnostic checks on residual series are reported. These include serial correlation LM tests, normality tests, and White heteroskedasticity tests.11 Table 6 VEC residual serial correlation LM tests VECM(3) VECM(4) Lag order LM-Statistic Probability LM-Statistic Probability 1 59.965 0.007 42.433 0.213 2 38.331 0.364 45.122 0.142 3 37.900 0.383 38.229 0.369 4 45.528 0.133 29.130 0.785 5 39.505 0.316 35.917 0.473 6 32.318 0.644 24.439 0.928 H0 : no serial correlation at lag order h. Probabilities from χ 2 (36). Table 7 VEC residual heteroscedasticity and normality tests VECM(3) VECM(4) χ 2 (d f ) Probability χ 2 (d f ) Probability Heteroscedasticity test 535.791 0.822 752.840 0.952 Normality tests Skewness 5.717 0.456 4.884 0.559 Kurtosis 1.226 0.976 8.537 0.201 Jarque-Bera 6.943 0.861 13.421 0.339 heteroscedasticity test: H0 : no heteroscedasticity normality tests: H0 : residuals are multivariate normal

Serial correlation is absent in the residual series of the VECM(4). For the VECM(3) we cannot reject autocorrelation of residuals. Normality tests for both 11

Jarque-Bera residual normality test using a Cholesky orthogonalization, see L¨utkepohl (2007) for details. Ordering of variables: hit , dit , f at , f lt , qt (π − πh )t ,UCtB .

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VECMs show that residuals can be regarded as being drawn from a normal distribution. Heteroskedasticity tests do not indicate problems either. On the basis of the results of the VECM serial correlation tests of residuals, we decide to use the VECM(4) as our preferred model. Section 3.3 therefore refers only to the results from VECM(4).

3.3 An extended measure of the user costs of housing The econometric analysis has provided evidence that variables which are related to the presence of a credit constraint have to be considered in the modeling of residential investment. This includes an extension term in the formula of user costs which is dependent on the inflation and an average loan-to-value ratio. As the ultimate VECM estimate points to ηˆ = 66%, we are now able to compute and analyze the extended measure of user costs which is given by UCt = (1 − 0.66) ∗ qt (πt − πh,t ) + UCtB . In Figure 3, a comparison of both series - basic user costs and extended user costs of housing - is shown. All time series included in the user costs definition are described in the Annex. Both measures of user costs behave rather similarly with regard to trend properties, which comes as no surprise against the backdrop that the inflation gap is stationary. However, it substantively affects the cyclical properties of user costs. In particular, the extension term increases the volatility, which is also confirmed by the descriptive statistics shown in Table 8.

.14 .12 .10 .08

extended user costs basic user costs

.06 .04 .02 .00

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Source: Own calculation. Fig. 3 Extended and basic user costs of housing

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Table 8 Descriptive statistics for user costs series Mean Maximum Minimum Std.dev.

Extended user costs Basic user costs 0.085 0.081 0.142 0.126 0.012 0.023 0.023 0.019

In order to obtain more insights into the driving forces of extended user costs, let us further investigate its components UCt = qt (ir,t + δ˜t + [πt − πh,t ]) + (1 − η )qt (πt − πh,t )

(13)

with the real interest rate ir,t defined as ir,t = it − πt and δ˜t as the technical depreciation rate of residential capital (see the Annex for details).

real interest rate

depreciation rate (technical)

.08

.08

.07

.07

.06

.06

.05

.05

.04

.04

.03

.03

.02

.02 80 82 84 86 88 90 92 94 96 98 00 02 04 06

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Source: Author’s own calculations (see the Annex for details). Fig. 4 Comparison of time series with impact on user costs - Real interest rate (left graph) and Depreciation rate (technical) (right graph)

Among its components, the inflation gap and the real interest rate exhibit no clear trending behavior over time and may, in particular, contribute to cyclical effects. Technical depreciation increases steadily, but with a more or less marginal impact owing to its relatively small overall magnitude. The key driver for trending behavior of the basic user costs UCB is thus the relative price ratio q.

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4 Conclusions Due to the overall importance of the housing market, this paper presents some theoretical and empirical considerations in order to obtain further insights in the investment decision of private households. We modify the basic neoclassical approach of user costs of housing introducing a credit constraint with which an arbitrary household is faced when purchasing an owner-occupied dwelling. This constraint should be important as residential investment is usually financed by credit to a large extent. Compared with the basic neoclassical approach to housing investment, the implementation of this credit constraint leads to an additional term in the first-order condition. The extension could be interpreted as a wedge between the marginal rate of substitution and the basic user costs. The wedge is determined by the inflation gap between consumer prices and house prices multiplied by the real house prices and the loan-to-value-ratio. The relevance of the theoretical findings are checked in the empirical part of the paper by specifying and estimating a time-series model for housing demand incorporating elements related to the presence of a binding credit constraint. The analysis is based on German data. The sample starts in the first quarter of 1980 and ends in the fourth quarter of 2007. The model comprises household investment in housing, disposable income, financial assets, financial liabilities, the extension term and basic user costs of housing as endogenous variables. As the time series under consideration can be regarded as I(1) processes and we are interested in a long-run equilibrium relationship between these variables, a VECM is used to model household investments in housing. Carrying out cointegration tests indicates one cointegrating relation between variables. Estimating the model also leads to an estimate of the average loan-to-value ratio. Equipped with this, we have computed a time series of extended user costs showing the diminishing importance of the standard user costs. This is due to the fact that the real price of housing has exhibited a negative trend in the sample under review. The empirical results also provide evidence that the dynamics of residential investment in Germany are significantly influenced by the extended user costs (i.e. basic user costs plus extension term) as well as by net financial wealth. We close with brief caveats. Firstly, the analysis has focused on German data exclusively. The more general relevance of the model framework needs to be verified, for instance, by considering other countries. Secondly, the estimation results have to be interpreted cautiously. This is due to measurement issues - in particular, concerning financial assets and financial liabilities as well as inflation expectations.

Acknowledgements The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Deutsche Bundesbank. The authors wish to thank Timo Wollmersh¨auser for discussing the paper at the JRP conference in Paris, Karl-Heinz T¨odter, Ger-

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hard Ziebarth and, especially, Thomas A. Knetsch for their outstanding support, comments and suggestions. Any remaining shortcomings in the paper are entirely the responsibility of the authors.

References Akaike, H. (1969), Autoregressive model fitting for control, Annals of the Institute of Statistical Mathematics, 21, 1, 243-247. Akaike, H. (1971), Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics, 23, 1, 163-180. Banerjee, A., Dolado, J.J., Galbraith, J.W. and Hendry, D.F. (1993), Co-integration, error correction, and the econometric analysis of non-stationary data, Oxford, 1993. Boswijk, H.P. (1995), Identifiability of Cointegrated Systems, Discussion Paper, University of Amsterdam, 1995. Campbell, J.Y. and Cocco, J.F. (2005), How do House Prices affect Consumption? Evidence from Microdata, NBER Working Paper, No.11534, 2005. Case, K.E., Quiggley, J. and Shiller, R.J. (2001), Comparing Wealth Effects: The Stock Market versus Housing Market, NBER Working Paper, No.8606, 2001. Deutsche Bundesbank (2007), Private consumption in Germany since reunification, Monthly Report, September 2007, 41-56. Dougherty, A. and Van Order, R. (1982), Inflation, Housing Costs, and the Consumer Price Index, The American Economic Review, 72, 1, 154-164. Durbin, J. and Koopman, S.J. (2001), Time series analysis by state space methods, Oxford, 2001. ECB (2003), Structural factors in the EU housing markets, Frankfurt, 2003. Engle, R.F. and Granger, C.W.J. (1987), Co-integration and error correction: Representation, estimation and testing, Econometrica, 55, 251-276. Granger, C.W.J. (1981), Some properties of time series data and their use in econometric model specification, Journal of Econometrics, 16, 121-130. Greene, W.H. (2008), Econometric Analysis, New Jersey, 2008. Guiso, L., Haliassos, M. and Japelli, T. (2002), Household Portfolios, MIT, 2002. Hamilton, J.D. (1994), Time Series Analysis, Princeton, 1994. Hannan, E.J. and Quinn, B.G. (1979), The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society, 41, 2, 190-195. Iacoviello, M. and Minetti, R. (2008), The credit channel of monetary policy: Evidence from the housing market, Journal of Macroeconomics, 30, 1, 69-96. IMF (2008), The Changing housing cycle and the implications for monetary policy, World Economic Outlook, April 2008, 103-132. Johansen, S. (1995), Likelihood-based Inference in Cointegrated Vector Autoregressive Models, Oxford, 1995. Johansen, S. (2002), Interpretation of Cointegrating Coefficients in the Cointegrated Vector Autoregressive Model, Working Paper, University of Copenhagen, 2002. Jorgenson, D.W. (1963), Capital theory and investment behaviour, The American Economic Review, 53, 2, 247-259. Junttila, J. (2001), Structural breaks, ARIMA model and Finish inflation forecasts, International Journal of Forecasting, 17, 203-230. Kurozumi, E. (2002), Testing for stationarity with a break, Journal of Econometrics, 108, 63-99. Kwiatkowski, D.A., Phillips, P., Schmidt, P. and Shin, Y. (1992), Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics, 54, 159-178. L¨utkepohl, H. (2007), New introduction to multiple time series analysis, Berlin, 2007.

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MacKinnon, J.G. (1996), Numerical distribution functions for unit root and cointegration tests, Journal of Applied Econometrics, 11, 601-618. Newey, W.K. and West, K.D. (1994), Automatic Lag Selection in Covariance Matrix Estimation, Review of Economic Studies, 61, 631-653. Osterwald-Lenum, M. (1992), A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics, Oxford Bulletin of Economics and Statistics, 54, 3, 461-471. Perron, P. (1989), The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 6, 1361-1401. Schwarz, G. (1978), Estimating the dimension of a model, The Annals of Statistics, 6, 2, 461-464. Stock, J.H. and Watson, M.W. (1988), Variable Trends in Economic Time Series, Journal of Economic Perspectives, 2, 3, 147-174.

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Appendix 1: Time series used for variables f a, f l, di and hi As discussed in section 3.2, households investments’ in housing hit depends inter alia on (disposable) income dit and the difference between financial assets f at and liabilities f lt , i.e. net financial wealth nwt . Therefore, time series for these variables are needed. Real disposable income per household 9.2

Gross financial assets per household 11.8 11.6

9.1 11.4 9.0

11.2 11.0

8.9 10.8 8.8

80 82 84 86 88 90 92 94 96 98 00 02 04 06

10.6

Gross financial liabilities per household

Households' investments in housing

10.8

6.9

10.6

6.8

10.4

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10.2

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80 82 84 86 88 90 92 94 96 98 00 02 04 06

80 82 84 86 88 90 92 94 96 98 00 02 04 06

6.4

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Source: Bundesbank (disposable income and households’ investments); Author’s own calculations (financial assets and liabilities). Fig. 5 Disposable income, financial assets and liabilities, households’ investments in housing

Disposable income dit and households’ investments in housing hit are taken from the Deutsche Bundesbank. Financial assets f at and liabilities f lt are well-known series from Germany’s financial account. We decided to use per household series (see section 3.2). The transformation was done using number of total households. Series for real disposable income, gross financial assets and gross financial liabilities are

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price-adjusted with house price index ph . These series used in our empirical model are seasonally and working-day adjusted and in real terms (i.e. in 2000 euro). The series are taken in natural logarithm. The sample starts in the first quarter of 1980 and ends in the fourth quarter of 2007. The sample size is T = 112. Graphs reported show the per household series used. Appendix 2: Time series used for calculating user cost series Our extended user costs are defined in equation (12) as UCt = (1 − η )qt (πt − πh,t ) + qt (it − πt + δt ), and basic user costs in equation (11) as ph,t UCtB = qt (it − πt + δt ), i.e. excluding the wedge (1 − η )qt (πt − πh,t ). Using qt = pt and δt = δ˜t − [πh,t − πt ] we can write our extended version also as UCt =

ph,t [it − πt + δ˜t − (πh,t − πt ) + (1 − η )(πt − πh,t )]. pt

(14)

To derive our extended user costs series we need a time series for all variables used in equation (14). η is estimated within our econometric model and value is set to 66%. 120

1.35

110

1.30

100

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90

1.20

80

1.15

70

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60

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50

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0.95

house price index (left scale) consumer price index (left scale) price ratio q (right scale)

Source: Bundesbank (ph and p), Author’s own calculations (q). Fig. 6 Consumer price index p, house price index ph , and ratio q

We use a house price index for the variable ph,t , a consumer price index for pt . it is represented by a nominal interest rate paid by household series. For πh,t and πt we calculate a series for expected house price inflation rate and expected consumer price inflation rate, respectively. δ˜t is our technical depreciation rate of residential housing. All series used are seasonally and working-day adjusted. The sample starts

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in the first quarter of 1980 and ends in the fourth quarter of 2007. The sample size is T = 112. Below, all series mentioned are plotted and the derivation is briefly discussed, wherever needed.

.07

.10

.06

.08

.05

.06

.04

.04

.03 .02

.02

.00

.01

-.02

.00 -.01

80 82 84 86 88 90 92 94 96 98 00 02 04 06 consumer price inflation expected consumer price inflation

-.04

80 82 84 86 88 90 92 94 96 98 00 02 04 06 house price inflation expected house price inflation

Source: Bundesbank (π n , πhn ), Author’s own calculations (π , πh ). Fig. 7 (Expected) house price inflation (πh ), πhn , and (expected) consumer price inflation (π ), π n

In Figure 7, consumer price inflation πtn and expected consumer price inflation πt are plotted. Values for πt from consensus forecasts are available only from fourth quarter of 1989 onwards, so we do have to calculate our own series. The expectations formation of future consumer price inflation is modeled using the ARIMA approach. We use an ARIMA (5,1,0) model of the type:12 log(pt ) − log(pt−1 ) = θ0 + θ1 [log(pt−1 ) − log(pt−2 )] + ... + θ5 [log(pt−5 ) − log(pt−6 )] + εt . The εt are independent, identically distributed random variables. Starting with the period from 1970 to 1979, this model is used to forecast the development of consumer price inflation over the next five years. Our starting point (1970Q1) remained fixed. By adding one observation at a time to the end, but keeping the starting point the same, the whole sample is reestimated until 2007Q4, and the forecasts for the following 20 months from each estimation are obtained.13 Calculating the mean of each estimated series leads to our expected quarterly consumer price inflation series. The year-on-year increase πt is the sum of the last four expected values. Figure 7 also n shows house price inflation πh,t and expected house price inflation πh,t . To forecast the development of house price inflation, we use the same approach as before with consumer price inflation. Slightly different is the ARIMA (4,1,0) model we use. It has the type: log(ph,t ) − log(ph,t−1 ) = θ0 + θ1 [log(ph,t−1 ) − log(ph,t−2 )] + ... + 12 13

The model was specified by minimizing SC for each sample periods’ estimations. For a similar procedure, see Junttila (2001).

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θ4 [log(ph,t−4 ) − log(ph,t−5 )] + εt . Also different is our starting period, which is now 1975 to 1979. All other steps of the procedure are executed in the same way. In Figure 8, economic depreciation rate δt , technical depreciation rate δ˜t , and the difference between expected house price inflation and expected consumer price inflation as a measure for capital gains or losses are plotted. In this context, δ˜t was derived using the value for real depreciation of residential housing drawn from the Deutsche Bundesbank and the series for residential housing stock.

.06

.13 .12

.04

.11

.02

.10 .09

.00

.08

-.02

.07 .06

-.04 -.06

.05 80 82 84 86 88 90 92 94 96 98 00 02 04 06 delta (economic) delta (technical) expected inflation differential

.04

80 82 84 86 88 90 92 94 96 98 00 02 04 06

interest rates i

Source: Author’s own calculations (left graph), Bundesbank (right graph). Fig. 8 Left side: Economic and technical depreciation rates of residential housing (δ and δ˜ ) and capital gains or losses. Right side: Nominal interest rates paid by households

The residential stock of housing in billions of 2000 euro (see Figure 9) was calculated using the available series from the Deutsche Bundesbank between 1991 and 2007. Values between 1980 and 1991 have been derived using cumulative private investments in residential housing drawn from the Deutsche Bundesbank. Resulting series have a yearly frequency. Quarterly values have been derived using a Kalman filter.14

14

For a discussion of the Kalman filter technique, see, for example, Durbin and Koopman (2001).

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8.5

11.70

8.4

11.65 11.60

8.3

11.55

8.2

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80 82 84 86 88 90 92 94 96 98 00 02 04 06

residential stock of housing

11.30

80 82 84 86 88 90 92 94 96 98 00 02 04 06

residential stock of housing per household

Source: Author’s own calculations. Fig. 9 Residential stock of housing

Appendix 3: Unit root tests We performed unit root tests in order to obtain more information on the trending behavior of the time series. Due to German reunification, a statistical break in the first quarter 1991 (TB ) has to be taken into account. This is visible in the series for the variables dit , f at , f lt . The trending setup for these series includes a constant c and a deterministic trend t. To control for the statistical break, we therefore include a dummy variable SM (91 : 1). SM (91 : 1) is unity from the first quarter of 1991 onwards, and zero otherwise. For households’ investments in housing series hit graphical inspection indicates that we may have to include breaks in trend. In 1987, the German government introduced Article 10e EStG subsidies; in 1996 the Eigenheimzulage [grant to homebuyers] was introduced; in 2004 the Eigenheimzulage was abolished. But it is not possible to attribute the effect of these changes in law to a specific date. Due to this fact, and also because of the short sample, we do not control for these possible structural breaks in 1987, 1996, and 2004. The trending setup for the hit series includes a constant c and a deterministic trend t. It is unclear whether the series for the basic user costs of housing UCtB , the price ratio qt , and the inflation gap (π − πh)t appear to be non-stationary or not. After graphical inspection, we decided that a statistical break should not to be included. The trending setup for these both series includes a constant c. In Table 9, results for series used in our VECM are reported for augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests and the test proposed by Kwiatkowski et al (1992) (KPSS).15 ADF and PP procedures test for a unit root in the series; KPSS assumes stationarity under the null hypothesis. The numbers in brackets indicate the lag length in the ADF procedure and the bandwidth parameter in the PP and KPSS procedures. Lag length was selected by minimizing the Schwarz (1978) criterion (SC) (calculated up to lag length 12), bandwidth parameter was chosen by the automatic procedure suggested 15

For details on the ADF and the PP test, see, for instance, Greene (2008) or Hamilton (1994).

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by Newey and West (1994). For KPSS we also display values for a shorter bandwidth p parameter value of 4 which results from applying the rule of thumb integer 4 ∗ 4 T /100, also used by Kwiatkowski et al (1992), for example. Critical values for the ADF and the PP tests, including a structural break, are tabulated in Perron (1989), Table IV.B, which are -4.34, -3.72, -3.44 for series with a break in mean in the given setup with TB /T = 0.4. For the KPSS testing the hypothesis of trendstationarity, the asymptotic critical values are tabulated in Kurozumi (2002), Table 1b, which are 0.143, 0.103 and 0.086 for series with a break in mean in the given setup. For series without breaks we took the MacKinnon (1996) critical values for the ADF and the PP tests. For series including a constant c, these are -3.49, -2.89 and -2.58. Including a constant c and deterministic trend t the values are -4.05, -3.45, -3.15 in the given setup. For the KPSS testing, the asymptotic critical values for series without breaks are tabulated in Kwiatkowski et al (1992). For series including a constant c, these are 0.739, 0.463 and 0.347. Including a constant c and deterministic trend t, the values are 0.216, 0.146, 0.119. ∗∗ , ∗ , (∗ ) mean rejection of the null hypothesis at the 1%, 5% and 10% level, respectively. Table 9 Unit root tests Series Deterministic terms hit c, t dit c, t, SM (91 : 1) f at c, t, SM (91 : 1) f lt c, t, SM (91 : 1) (π − πh )t c qt c qt (π − πh )t c UCtB c

ADF −1.81(1) −4.53(2)∗∗ −5.89(0)∗∗ −1.58(0) −3.06(4)∗ −1.94(4) −3.18(4)∗ −2.80(1)(∗)

PP −2.08(2) −4.61(4)∗∗ −5.73(6)∗∗ −2.30(6) −2.87(5)(∗) −0.89(8) −2.99(4)∗ −3.07(4)∗

KPSS 0.33(4)∗∗ 0.18(9)∗∗ 0.30(4)∗∗ 0.19(8)∗∗ 0.21(4)∗∗ 0.13(9)∗ 0.22(4)∗∗ 0.14(9)∗ 0.14(4) 0.10(8) 1.82(4)∗∗ 0.99(9)∗∗ 0.12(4) 0.09(8) 0.56(4)∗ 0.38(8)(∗)

For any trending series except the series for the inflation gap (π − πh )t nonstationarity is confirmed by the KPSS test results. The existence of a unit root cannot be rejected by either the ADF or the PP test for hit , f lt and qt series. For UCtB , dit and f at series we obtain no clear results. ADF and PP test results indicate that we can reject the null hypothesis of a unit root, whereas both KPSS versions reject the stationarity hypothesis. We think it is fair to skip the ADF and PP results and use only the KPSS ones for our decision on stationarity or nonstationarity and, thus, to conclude that these three series contain a unit root. As a working hypothesis for the analysis they will be taken as I(1) series. For the (π − πh )t series, ADF and PP tests indicate that we can reject the existence of a unit root, and the two KPSS versions accept the stationarity hypothesis. For the qt (π − πh )t series, unit root tests indicate stationarity. But as the tests clearly confirm nonstationarity for the price ratio qt , which is a component of the expression qt (π − πh )t , we disregard the test results in this case and take the series as I(1).

Causes and Welfare Consequences of Real Estate Price Appreciation Filippo Scoccianti

Abstract This paper studies quantitatively the welfare consequences of the increase in housing prices observed in Italy over the last decade. It develops a general equilibrium, overlapping generations model with financial and housing assets, where mortgage debt is collateralized. The model generates an endogenous increase in housing prices through an unexpected decrease in the interest rate and down-payment requirement. There is a redistribution of welfare from renters towards young homeowners. Middle-aged home-owners lose from lower capital gains on their financial assets more than they benefit from the reevaluation of their housing assets.

JEL codes : C30, C50, E50 Keywords : Housing prices, general equilibrium, overlapping generations

1 Introduction This paper studies the causes and welfare consequences of the 30 percent’s increase in housing prices that has taken place in Italy over the last decade. It investigates how much of the observed house price dynamics can be attributed to changes in the real interest rate and the tightness of borrowing constraints and quantify the welfare consequences of these changes across different age-groups, income levels and housing tenure status. I construct an overlapping generations model with uninsurable labor income risk and two assets: a liquid, risk-free financial asset and a housing asset that can be rented or bought. In the model, households save for retirement, to self-insure against labor income shocks, for bequests reasons, and to buy a house. Each households will have a different history of income shocks which in equilibFilippo Scoccianti Banca d’Italia, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_11, © Springer-Verlag Berlin Heidelberg 2010

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rium will give rise, in the spirit of Aiyagari (1994), to a wealth distribution. I find that an exogenous decrease in the real interest rate for house purchases generates the observed increase in housing prices. There is a redistribution of welfare away from renters and towards young home-owners. Renters suffer from an increase in their rental rates and loose 5 percent of equivalent life-time consumption. Young homeowners benefit from lower mortgage rates on their debt and gain around 5 percent of equivalent life-time consumption. Middle-aged home-owners lose from the unexpected shocks through the decrease in capital income return on their accumulated liquid financial assets. The transition analysis shows how financial and housing assets converge asymmetrically towards the new steady-state. While financial assets demand rapidly converges to its final steady-state level, it takes longer for households to increase their housing demand towards its new optimal stationary level. This paper is related to a growing literature on heterogenous-agents general equilibrium models with two assets, see Nakajima (2005 and 2008), and to the literature on financial integration and consumption smoothing (see, for the Italian case, Jappelli and Pistaferri, 2008)). The most closely related paper is Kiyotaki et al.(2008), where the authors study the welfare consequences of an increase in housing prices in a general equilibrium model. They include an housing supply sector with land as a limited factor of production and find that the larger the share of land in housing’s production, the greater the movement in prices and welfare. The rest of the paper is organized as follows. Section 2 presents the facts, Section 3 the model and equilibrium definition. Section 4 gives details on the calibration of the model’s parameters. In Section 5 results are presented and explained. Section 6 concludes.

2 Facts House prices in Italy have increased by 30 percent in real terms in between 1995 and 2005, see Figure11. At the same time Bartiloro et al. (2008) show that Italian households’ net worth rose from 6.14 times income in 1995 to 7.94 times disposable income in 20052, and that for the lower three deciles of the income distribution, most of the increase in the wealth-to-income ratio came from real assets appreciation. Over the same period, there has been a substantial decrease in the real interest rate, see Figure 2, from an average of 5 percent in the period 1988 to 1997, to an average of 1 percent in the period 1998 to 2005. Furthermore, since the early 1990s, but especially in the late 1990s, important changes in the Italian mortgage market have taken place: among others, the introduction of new scoring techniques, longer terms for mortgage repayments, and higher loan-to-value ratios for house purchases. In particular, while the average loan-to-value ratio in 2006 was 70 percent, with 50 percent of loans-to-value ratios higher than 80 percent, see Rossi (2008), back in 1

I thank Antonio Bassanetti and Francesco Zollino for providing the data The wealth-to-income ratio increased across the income distribution, most markedly for those at the bottom and those at the top of the income distribution (by 60 percent and 30 percent, respectively) see Paiella (2007).

2

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1990 the average maximum loan to value ratio was around 60 percent. To the increase availability of credit has corresponded an increased willingness to borrow: the stock of bank loans-lending to Italian households for the purchase of a house, rose from 3.62 per cent of GDP in 1990 to 13.7 per cent in 2004.

Fig. 1 Real House Prices

Fig. 2 Real Interest rates

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3 The Model 3.1 Environment I consider an overlapping generations model in which agents face uninsurable idiosyncratic earnings shocks and uncertain lifespans. When agents die, transmit after tax liquidated assets and the first earning shock to their immediate successor. I explicitly model housing. Housing has a dual role in the model: it directly provides utility and can be used as a collateral for borrowing. While housing can be at least characterized by tenure, location, size and quality, I consider tenure and size directly, location is indirectly considered through adjustment costs on housing transaction, quality is left out of the picture. Several frictions are present in the model: lack of annuity markets to insure against uncertain lifespan, different specifications of borrowing constraints, transaction costs for trading in housing stock as well as a minimum house purchasing size. The last two features make it possible to talk with sufficient realism of houses, their implied cost being that the resulting non-convexities will complicate the computational task. Households are indifferent between renting or owning a house, but in equilibrium we will have a fraction of the population in home-ownership and a fraction living in renting units because of three factors: (1) borrowing constraints, which will make it impossible for some earnings poor agents, especially the young, to provide the down-payment requirement necessary for housing purchases (2) a higher depreciation rate for renting units which, everything else equal, will discourage renting and (3) adjustment costs in housing transactions coupled with exogenous minimum house size requirements which, everything else equal, will tend to discourage home-ownership.

3.2 Demographics There is a continuum of individuals of measure one at each point in time. Each individual lives at most J periods. In each period j ≤ J of his life the conditional probability of surviving and living in period j + 1 is denoted by α j ∈ (0, 1). Define α0 = 1 and αJ = 0. The probability of survival, assumed to be equal across individuals of the same cohort, is beyond the control of the individual and independent of other characteristics of the individual (such as income or wealth). We assume that α j is not only the probability of survival for a particular individual, but also the (deterministic) fraction of agents that, having survived until age j, will survive to age j + 1. Annuity markets are assumed to be absent. After death, the individual is replaced by a descendant who inherits its after-tax financial and (liquidated) housing wealth, and part of its permanent productivity according to a stochastic earnings −1  j transmission Markov matrix. In each period a number µ1 = 1 + ∑J−1 Π α i j=1 i=1 of newborns enter the economy, and the fraction of people in the economy of age

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j is defined recursively as µ j+1 = α j µ j , with µ j+1 = αJ = 0. Let J = {0, 1, ..., J} denotes the set of possible ages of an individual.

3.3 Technology 3.3.1 The Firm’s Problem There is one good produced according to the aggregate production function Y (Kt , Lt ) where Kt is the aggregate capital stock and Lt is the aggregate labor input. I assume that Y is strictly increasing in both inputs, strictly concave, has decreasing marginal products which obey the Inada conditions and is homogeneous of degree one. As usual with constant returns to scale production technologies, in equilibrium the number of firms is indeterminate and without loss of generality we assume that there is a single representative firm. The representative firm solves the following static problem max Y (Kt , Lt ) − (r + δ k )Kt − wLt Kt ,Lt

where r is the rental price of capital net of depreciation and w is the wage per efficiency unit of labor. 3.3.2 The Financial Institution’s Problem There is a representative financial institution that in each period receives deposits A′ from households, rents residential services F to households and rents capital K to the representative firm. We allow rental units to have a different depreciation rate δ f than owner occupied housing δ h . The perfectly competitive financial institution solves the following problem   1 ′ f ′ A − (1 + r)A + rK + (i − δ )F + Ψ (A) = max Ψ (A ) 1+r A′ ,K,F s.t. K +F ≤ A where F is the stock of rental units and i is their rental price. The financial institution rents capital and houses in the same period in which it acquires them.

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3.4 Preferences and Endowments Individuals are endowed with one unit of time in each period that they supply inelastically in the labor market. Individuals differ in their labor productivity due to differences in age and realizations of idiosyncratic uncertainty. The labor produc J tivity of an individual of age j is given by ε j η , where ε j j=1 denotes the age profile of average labor productivity. The stochastic component of labor productivity, η , follows a finite state Markov chain with state space η ∈ E = {η1 , ...ηN } and transition probabilities given by the matrix π (η ′ |η ). Let Π denote the unique invariant measure associated with π . I assume that all agents, independent of age and other characteristics face the same Markov transition probabilities and that the fraction of the population experiencing a transition from η to η ′ is also given by π . This law of large numbers and the model demographic structure assure that the aggregate labor input is constant. As with lifetime uncertainty we assume that individuals cannot insure against idiosyncratic labor productivity by trading contingent claims. Moral hazard problems may be invoked to justify the absence of these markets. After its death the individual is replaced by a direct descendant who inherits its after-tax financial and (liquidated) housing wealth, if any, and receive its first idiosyncratic shock according to the intergenerational earnings transmission matrix Γ which shares the same states η ∈ E = {η1 , ...ηN } of the stochastic component of labor productivity. Bequests are accidental in that parents derive no utility from them. Individuals derive utility from consumption of the nondurable good, c, and from the housing services acquired either trough the rental market, g( f ), or trough homeownership g(h′ ). Housing services are a function g(·) of the housing stock purchased or rented. The choice between home-ownership and renting is exclusive at each period, and represented by the indicator function I ∈ {0, 1} . Individuals  J value streams of consumption and housing/renting services c j , g(s) j j=1 , where s = (1 − I) f + Ih′ , according to E0

(

J

∑β

j=1

j−1

)

u(c j , g(s) j )

where β is the time discount factor and E0 is the expectation operator, conditional on information available at time 0. The per period utility function u(c, g(s)) is assumed to be strictly increasing in both arguments and obeying the Inada conditions with respect to nondurable consumption. The instantaneous utility from being dead is normalized to zero and expectations are taken with respect to the stochastic processes governing survival and labor productivity. I assume that the per period utility function is of the CRRA form

u(c, g(s)) =

(cγ g(s)1−γ )σ − 1 1−σ

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where σ is the coefficient of relative risk aversion and cγ g(s)1−γ is the CobbDouglas aggregator between non-durable consumption and housing services.

3.5 Timing and Information The timing of events in a given period is as follows. Households observe their idiosyncratic labor productivity shock η and, in their first life period, receive net transfers from bequests and their first period labor productivity shock η according to the intergenerational earnings transmission process. Then labor is supplied to the firm and financial assets are supplied to the financial institution. Capital is rented to the firm by the financial institution. Production takes place. Next households receive wages from the firm and interest on their deposits form the financial institution and choose nondurable consumption c, housing h′ or rental consumption f services and next period asset position a′ . A unit of rental housing f yields consumption services ′ today. A unit of housing stock for tomorrow h yields consumption services today. Finally uncertainty about early death is revealed.

3.6 Consumer’s Problem Individuals are assumed to be price takers in the goods and factor markets they participate in. At each moment of time individuals are characterized by their position of assets and holdings of housing stock, as well as their age and labor productivity status (a, h, η , j). Let by Φt (a, h, η , j) denote the measure of agents of type (a, h, η , j), at time t. We normalize the price of the final good to one. The price of renting units is denoted by i ≡ rt + δ f , where δ f is the depreciation rate for renting units. Let rt , rtm ,wt and pth denote the risk-free interest rate, the mortgage rate, the wage rate per efficiency unit of labor, and the relative price of a house, respectively. The consumer’s problem at time t can now be formulated recursively as Vt (a, h, η , j) =

max

ct ,at+1 ,ht+1 ,It

u(ct , st ) + β Vt+1 (at+1 , ht+1 , ηt+1 , j + 1)

Vt+1 (at+1 , ht+1 , ηt+1 , j + 1) = α j

∑ π (ηt+1|η )Vt+1 (at+1 , ht+1 , ηt+1 , j + 1)

ηt+1

s.t.

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ct + it ft + pthht+1 + τ (h, ht+1 , pth ) + at+1 = (1 − τl )wt ηε j + (1 + rt )a +(1 − δ h)pth h + ϒ P, i f a ≥ 0

ct + it ft + pth ht+1 + τ (h, ht+1 , pth ) + at+1 = (1 − τl )wt ηε j + (1 + rtm)a +(1 − δ h)pth h + ϒ P, otherwise

st = (1 − It ) ft + It ht+1 at+1 ≥ b(pth , ht+1 , η , j) a1 = 0, b1 = 0

ϒ=



1 0

if j ≥ 10 otherwise



i h max ct ≥ 0, ht+1 ∈ {0} ∪ hmin , It ∈ {0, 1} , h j

Where P stands for households pension income (which is enjoyed from age 56 on, i.e. when j ≥ 10) which is assumed to be independent of households income history3 . We define hmin as the minimum house purchasing size while τ (h, ht+1 , pth ) stands for non-convex housing stock’s adjustment costs

τ (h, ht+1 , pth )

=



  0 if h′ ∈ (1 − µ ) pth h, (1 + µ ) pth h ρ1 pth h + ρ2 pth ht+1 otherwise

This formulation of transaction costs allows households to change their level of housing consumption by undertaking housing renovation up to a fraction of µ the value of the house or by allowing depreciation up to a fraction of µ the value of the 3 A more realistic assumption is that social security benefit is a concave function of the accumulated contributions. Under this assumption, the total contributions become an additional state variables, which increases the computation time dramatically.

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house as an alternative to moving. If the house depreciates by more that a fraction µ of the value, or if the value of the stock increases by more that a fraction µ of the value, we assume that the stock has been sold. In those cases, the household has to pay the transaction costs as a fraction ρ1 of its selling value and ρ2 of its buying value. Borrowing constraints b(pth , ht+1 , η , j) are specified as being an exogenous fixed fraction of the value of owner-occupied housing services, where households can only borrow up to (1 − θ ) of their desired housing stock’s value at+1 ≥ −(1 − θ )pthht+1 , θ ∈ [0, 1]

4 Calibration I calibrate a first steady-state economy to 1995 Italian data. A second one is calibrated to 2005 data. I will work under the assumption of a small open economy4, where the difference between the two steady-states economies is represented by a lower real interest rate and looser collateral constraints. I will then compute the whole transition from the initial to the final equilibrium, under the assumption that the two once-and-for-all exogenous shocks - i.e. a lower real interest rate and a looser borrowing constraints - are both unexpected. Table1 shows the annualized5 benchmark parameters for the economy, which are chosen partly on the basis of microeconomic evidence and partly so that the stationary equilibrium for the economy matches selected long-run averages of Italian data.

4.1 Demographics The model’s period is five years. Households enter the labor market at age 25. I set the retirement age at 60. Workers die with certainty at age 95. Survival rates are taken from ISTAT and refer to females in the year 2000.

4

I am assuming here that the observed change in the real interest rate and financial market liberalization are linked to the introduction of the Euro, and are thus exogenous to the model. 5 I report the annualized parameters’ value for ease of exposition. In the model I use their five-year counterparts.

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4.2 Discount factor and interest rate I set the discount factor β to match the 1995 Italian’s aggregate wealth to income ratio of 6.26 . The interest rate r is set at an annual rate of 5 percent in the 1995economy. In the 2005-economy the interest rate is exogenously lowered to 1 percent. Interest rates on mortgages are set equal to the respective risk-free interest rates plus a 2 percent markup in both economies.

4.3 Income process The logarithm of the income process zit is specified as an AR(1): zit = ρ zit−1 + ηit with persistency parameter ρ , where ηit ∼ N(0, ση2 ). εit is an i.i.d. normal with zero mean and σε2 . I calibrate the deterministic age profile for the income process using data from the SHIW. The stochastic components ηit and εit are both estimated using panel data from the SHIW. Using Tauchen (1986)’s method, I approximate the continuous AR(1) processes with a six-states Markov chain 7 . Below are the supports for the AR(1) discretized earnings shocks: E AR(1) = {0.074, 0.1848, 0.4580, 1.1349, 2.8121, 6.9678}

(1)

where mean earnings are normalized to 1. In the Table below we show how well the chosen earnings process approximates the Italian earnings distribution: Earnings Gini (2000) 1st 2nd 3rd 4th 5th Italian data 0.557 -0.001 1.34 12.47 27.58 58.60 Model 0.555 0.00 3.49 11.59 23.96 60.94

4.4 Preferences and Technology The utility function is of the constant relative risk aversion class with a CobbDouglas aggregator between housing services and non-housing consumption. Hous6

Italian net wealth to disposable income ratio have been increasing from 6.14 in 1995 to 7.94 in 2005, see Bartiloro et al. (2008). 7 Further increasing the number of income states does significantly affect results

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ing services are assumed to be proportional to the housing stock, i.e. g(s) = s. The coefficient of risk aversion σ is set to 2, within the range of commonly used values.

u(c, s) =

(cγ s1−γ )σ − 1 1−σ

(2)

The Cobb-Douglas aggregator can be considered as a special case of the constant elasticity of substitution (CES) function when the elasticity of substitution parameter is equal to zero. Villaverde and Krueger (2004) report that according to the literature that estimates the degree of elasticity of substitution between housing and non-housing consumption, zero is an empirically reasonable choice. I select a Cobb-Douglas production function Y (Kt , Lt ) = NKtα Ltα as a representation of the technology that produces the final good. I normalize N = 1. I follow the construction of measures of output, capital and stock of houses from D´ıaz and Luengo-Prado (2006). I define capital as the sum of non-residential private fixed assets plus the stock of inventories plus consumer durables. Investment in capital is defined accordingly. H is private residential stock. Finally I need a measure of output. Output is defined as GDP minus housing services. I proceed as Cooley and Prescott (1995) to calculate the capital share of the economy. I do not make any imputation to output for government owned capital since our focus is on privately held wealth. The implied share of capital in output α is 0.26.

4.5 Market Arrangements The average replacement rate in the economy is fixed to 0.58, meaning that on average, retired households’ income is 58 percent of their working-age earnings. There are transaction costs attached to housing assets’s purchases. I consider non-convex costs of adjustment in the housing market, which results in infrequent adjustment of the housing stock. Transactions costs on housing sales and purchases are set equal to respectively 6 percent and 17 percent, see Global Property Guide (2007). If the change in the housing asset is smaller or equal than the depreciated part of it, no adjustment cost will be charged on the household. The down-payment requirement θ (i.e. the share of the value of a house that cannot be borrowed and must be paid upfront by the buyer) was on average 40 percent in 1995 and 20 percent in 2005. Those two numbers will be fed exogenously into the model. The depreciation rate of owner occupied housing δ h is set to match the housing investment to housing stock ratio of 6.43 percent; the renting depreciation rate δ f is set equal to δ h , while the minimum house size is set to match an aggregate home-ownership rate of 80 percent. I set the depreciation rate of capital δ to match an investment-capital ratio of 10 percent. The parameter γ - the share of non-housing consumption in the utility function - was set at 0.65, in order to match the initial 1995 steady-state housing to disposable income ratio. This value is also consistent with housing expenditures being about 30 percent in the SHIW. The rental rate in the initial steady state econ-

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Filippo Scoccianti

omy is fixed according to the no-arbitrage condition outlined in Section 3.3.2; once the two unexpected shocks take place, the rental rate evolution is exogenously fixed to the house price increase so as to maintain fixed the housing price-rent ratio at its initial value. Table 1 Calibration Parameters PARAMETERS Demographics α j survival probability Technology α capital share in National Income δ depreciation rate of capital δ h housing depreciation δ f renting depreciation Government policy τ social security tax P social security replacement rate τe estate tax rate Housing market θ 1995 down payment ρ1 housing selling transaction cost ρ2 housing buying transaction cost hmin minimum house size Preferences σ risk aversion coefficient γ weight of non-housing β discount factor

VALUE Istat 0.28 0.10 0.0327 0.0327 0.195 0.58 100% 40% 6% 17% 10% of E(w) 2 0.65 0.9635

5 Results In order to properly account for the welfare change associated to an unexpected policy shock I will compute the whole transition dynamic of the economy. Welfare changes are expressed in terms of consumption-equivalent variations. I follow Floden (2001) and decompose the total welfare change in two components: the welfare gain (or loss) of increased consumption levels, i.e. percentage increase in average consumption between the two economies, and welfare gain (or loss) of reduced uncertainty, i.e. the fraction of average consumption that an individual would be willing to give up to avoid all the risk associated to earnings shock fluctuations. Welfare changes are conditional on the initial (age 25) earnings shock, age and housing tenure choice.

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253

5.1 Aggregates and Real Housing Prices The model is able to account for the 30 percent increase in housing prices observed in Italy over the 1995-2005 period. Housing prices adjust at any time during the transition in order to let real housing demand in that period equate its 1995 benchmark level.8 Table 2 shows aggregate statistics, where the 1995 model-economy matches its data counterpart by construction. Financial assets accumulation in the final 2005 steady state is smaller than its data counterpart: under the small open economy framework, the quantity of financial assets needed to clear markets is assumed to flow into the economy from the rest of the world. Figure 6 in the Appendix shows the wealth accumulation profiles in the initial steady state economy versus the transition. The transition economy shows a much higher accumulation of housing assets trough collateralized borrowing at young ages. Households tenure choices are reported in Table 3 below, where households have been divided by age group and productivity levels: ”low” refers to households who have entered the economy at age 25 with the lowest earnings shocks, ”high” refers to households endowed with the highest shocks. In the next subsection I turn the attention to the welfare consequences of those changes.

Fig. 3 Transitional Dynamics

8

I am assuming that housing supply is fixed between 1995 and 2005.

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Filippo Scoccianti

Table 2 Aggregates Statistic ph ∗ H/Y K/Y ph

Data-1995 4 2.2 1

Model-1995 4 2.2 1

Data-2005 5 3 1.3

Model-2005 5.9 1.7 1.3

Table 3 Tenure Choice AGE/Earn Low Medium High 25 Renter Renter Owner 35 45

Renter Renter

Renter Owner

Owner Owner

55 65

Renter Renter

Owner Owner

Owner Owner

75

Renter

Owner

Owner

5.2 Welfare I change the parameters unexpectedly and solve for the path of prices and quantities that lead the economy to the new steady state. The transition lasts for 15 periods, where each period is equivalent to 5 years and the whole transition to the final steady state takes 75 years. Welfare changes are calculated by age, initial shock level9 and home tenure choice. Table 4 and 5 show welfare changes for renters and homeowners, where CEV refers to the consumption equivalent variation, C to the welfare gain (or loss) of increased consumption levels, i.e. the percentage increase in average consumption between the two economies, and C2 to welfare gain (or loss) of reduced uncertainty. The sum of the welfare changes due to consumption, C, and due to the variability of consumption C2 , equals the total consumption equivalent welfare change CEV . Earnings-poor households are all renters in equilibrium and lose from the increase in their rental rates that follow the housing price’s increase. Young renters who start the transition at age 25 experience a welfare loss of around five percent of life-time equivalent consumption. The decrease in consumption volatility is not enough to compensate the loss of consumption due to the higher rental rates. The lower volatility of the optimal consumption path along the transition comes from easier inter-temporal consumption smoothing linked to lower real interest rates. Intuitively, a lower interest rate makes it cheaper to smooth consumption through self-insurance across time, as the price of tomorrow’s consumption in terms of today’s decreases. Against this effect works the increase in the wage rate caused by the decrease in the real interest rate. A higher wage rate scales up the part of the consumer’s income that is stochastic (i.e. earnings) and scales down the part that is 9 At each age I consider the mass of agents that have reached that age by starting their life-cycle at age 25 with the specified income shock. Hence ”low-earnings households” at any age refer to households of that age who have started their life cycle with low earnings.

Causes and Welfare Consequences of Real Estate Price Appreciation

Fig. 4 Welfare changes

Fig. 5 Housing Prices Transition

255

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Filippo Scoccianti

deterministic (capital income), causing the amount of risk the consumer is exposed to, to be higher. Given that the economy has incomplete markets and there is no direct insurance for labor income risk, this amounts to a decrease in consumption smoothing’s opportunities. Which of the two effect dominates depends on the specification of the earnings process. With the high persistency and low volatility of the estimated Italian’s earnings process (see Rodano and Scoccianti (2009)), the first (positive) effect dominates and overall we observe an increase in consumption ”insurance” for renters. Furthermore, gains deriving from lower consumption volatility are decreasing with the age at which the household is hit by the unexpected shocks and starts the transition, since the older the household the smaller the time horizon left out to smooth any earnings shocks. On the other hand, consumption levels decrease as renters suffer from both higher rental rates and lower real interest rates on their accumulated financial assets. These losses are increasing with the age at which the household starts the transition period since older households have accumulated more financial assets and thus suffer more from the lower real return on their liquid assets.

Table 4 Welfare: Renters AGE 25 35 45 55 65 75

CEV - 5% -5% -7% -14% -50 % -25%

C -10% -13% -17 % -20% -17% -8%

C2 5% 8% 10% 6% -33% -17

AGE 25 35 45 55 65 75

CEV 5% 0% -5% -11% -9% 0%

C -8% -15% -12% -20% -14% 0%

C2 13% 15% 7% 9% 5% 0%

Table 5 Welfare: Home-owners

High earnings households are in majority home-owners and gain five percent of equivalent life-time consumption when hit by the shocks at age 25. Indeed, the combined effect of smaller down-payment requirements and lower interest rates increase the affordability of housing purchases and benefit the young, who are most often

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257

borrowing constrained. As in the case of young renters, average consumption levels decrease following the increase in housing prices while consumption volatility decreases thanks to easier housing consumption smoothing. For young home-owners the negative effect of lower consumption is outweighted by the positive effect on consumption smoothing and overall they register positive welfare gains. The difference between young home-owners and young renters is worth noting: quantitatively, the two groups loose the same in terms of consumption levels. They differ in the volatility of their consumption paths though, owing to the different borrowing constraints they are facing. In equilibrium, young renters are poorer than young home-owners in terms of earnings and they are not allowed to borrow, since all borrowing is collateralized by the housing asset. They thus cannot benefit from looser borrowing constraints and lower mortgage rates. The welfare effect of an increase in housing prices is negative when the home-owner is hit by the policy shocks at middle-age. Home-owners are high earnings households and by middle-age, they have already accumulated a considerable amount of wealth, both housing and financial assets. While housing wealth increases in value due to the reevaluation of housing assets along the transition, financial assets returns decrease together with a lower interest rate. Overall the second effect dominates the first and middle-aged home-owners register a negative welfare change.

6 Conclusion I have built an heterogeneous agents, overlapping generations model with a housing and a financial asset, where mortgage debt is collateralized. I have studied the welfare effect of an endogenous increase in housing prices caused by an unexpected, once-and-for-all exogenous decrease in the real interest rate and down-payment requirements. To this end, I have simulated the whole equilibrium path from the first steady state economy through the transition periods towards the final steady state. The model is able to account for the increase in Italian housing prices over the last decade. There are sizeable welfare losses for earnings-poor renters who suffer from an increase in rental rates while young high-earnings home-owners benefit overall from the changes: their consumption levels decrease in the wake of higher real housing prices but the volatility of their consumption paths benefits proportionally more from the easier access to mortgage debt represented by both smaller down-payment requirements and lower interest rates. Middle-aged home-owners start the transition period with a relatively high level of accumulated risk-free financial assets: the decrease in capital income due to lower real returns on their saving outweight the capital gains on their housing assets and overall they register negative welfare changes. The model, due to computational constraints, has a simple asset markets structure, lacking investment in risky assets. In this respect it possibly underestimates the welfare changes experienced by high-income households. Including a more realistic portfolio choice is left for future research.

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Fig. 6 Wealth Accumulation Profiles

Acknowledgements I would like to thank Antonia Diaz, Matteo Iacoviello, Alexander Michaelides and John Muellbauer for useful comments as well as the participants to the conference on Macroeconomics of Housing Markets organized by Banque de France, November 2009. The views expressed herein are those of the author and do not necessarily reflect those of the Bank of Italy.

References Aiyagari, S.R. (1994), Uninsured Idiosyncratic Risk, and Aggregate Saving, Quaterly Journal of Economics, 109, 659-684. Bartiloro, L. and Coletta, M. and De Bonis, R. (2008), Italian Household Wealth in a Cross-Country Perspective, Banca d’Italia, Household Wealth in Italy, 31-53. Cannari, L. and Faiella, I. (2008), House Prices and Housing Wealth in Italy, Banca d’Italia, Household Wealth in Italy, 91-109. Cooley, T.F. and Prescott, E.C. (1995), Economic Growth and Business Cycle, Frontiers of Business Cycle Research, Princeton university Press. De Nardi, M. (2004), Wealth Inequality and Intergenerational Links, Review of Economic Studies, 71, 743-768. D´ıaz, A. and Luengo-Prado, M.-J. (2006), The Wealth Distribution with Durable Goods, Working Paper Floden, M. (2001), The Effectiveness of Government Debt and Transfers as Insurance, Journal of Monetary Economics, 48, 1, 81-108. Jappelli, T. and Pistaferri, L. (2000), The Dynamics of Household Wealth Accumulation in Italy, Fiscal Studies, 21, 27, 269-295. Jappelli, T. and Pistaferri, L. (2008), Financial Integration and Consumption Smoothing, CSEF Working Paper, 200.

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Kiyotaki, N. and Michaelides, A. and Nikolov, K. 2008, Winners and Losers in Housing Markets, Working Paper. Nakajima, M., (2005) Rising Earnings Instability, Portfolio Choice, Working Paper. Nakajima, M., (2008) Optimal Capital Income Taxation with Housing,Working Paper. Paiella, M., (2007) Does wealth affect consumption? Evidence for Italy, Journal of Macroeconomics, 29, 189-205. Rodano, G. and Scoccianti, F. (2009), An Empirical Investigation of Earnings Processes in Italy, Working Paper. Rossi, P., L’Offerta di Mutui alle Famiglie: Caratteristiche, Evoluzione e Differenze Territoriali. I risultati di un’indagine Campionaria (2008), Bank of Italy, Occasional Paper. Skinner, J., (1996) The Dynamic Efficiency Cost of Not Taxing Housing, Journal of Public Economics, 59, 397-417. Tauchen, G., (1986) Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions, Economic Letters, 20, 177-181. Fernandez-Villaverde, J. and Krueger, D. (2004), Consumption over the life cycle: Facts from consumer expenditure survey data, Working Paper. Fernandez-Villaverde, J. and Krueger, D. (2004), Consumption and Saving over the Life Cycle: How Important are Consumer Durables?, Meeting Papers 357b of the SED. Bassanetti, A. and Zollino, F. (2008), The Effects of Housing and Financial Wealth on Personal Consumption: Aggregate Evidence for Italian Households, Bank of Italy, Temi di Discussione.

Part IV

Wealth Effects

Wealth Effects on Private Consumption: the French Case An Assessment of Housing and Financial Wealth Effects in Spain: Aggregate Evidence on Durable and Non-durable Consumption The Effects of Housing and Financial Wealth on Personal Consumption: Aggregate Evidence for Italian Households Housing and Portfolio Choices in France

Wealth Effects on Private Consumption: the French Case Valerie Chauvin and Olivier Damette

Abstract This paper studies the relationship between consumption and wealth based on the concept of cointegration. The analysis focuses on French data over the 1987 - 2006 period. This relationship is expressed in two ways: in terms of Marginal Propensity to Consume out of wealth (MPC) and in terms of Elasticity of consumption to wealth. Three concepts of consumption are investigated: total households consumption expenditure, consumption excluding financial services and consumption excluding durable goods. Different estimators are also considered. Based on the MPC approach, when considered as permanent by households, an increase (decrease) in total wealth of one euro would lead to an increase (decrease) of 1 cent in total consumption. In terms of elasticity, an increase (decrease) of 10% in wealth would imply also a relatively small impact of 0.8 to 1.1% on consumption depending on the concept of consumption considered. In most cases, the effect of a change in financial wealth is bigger than of a change in housing wealth. The results indicate that the wealth effects in France are smaller than in the UK and US but close to what is observed in Italy. In addition, any deviation of the variables from their common trends is corrected at first by adjustments in disposable income in line with what has been uncovered by studies on Germany and consistent with the ”saving for the rainy days” approach of Campbell (1987). But our results contrast with the seminal study of Lettau and Ludvigson (2004) in the US where asset prices make the bulk of the adjustment.

JEL codes : E21, E32, C22, G12, G20 Keywords : consumption, wealth effect, France

Valerie Chauvin Banque de France, e-mail: [email protected] Olivier Damette University Paris12, ERUDITE e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_12, © Springer-Verlag Berlin Heidelberg 2010

263

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1 Introduction Following the subprime crisis, asset prices lost more than half their value between June 2007 and April 2009. At the same time, activity and both business and consumer sentiment surveys plummeted. Hence a crucial question for monetary policy: is the impact of the financial crisis on activity permanent and what is its magnitude? Asset prices may impact economic activity via different channels. In this paper, we will focus on the wealth effect in France, restricted to the link between asset prices and households’ consumption. Using cointegration techniques, we estimate the relationship between households’ consumption, disposable income and wealth. Aggregated and disaggregated (financial and housing) measures of wealth are considered and several concepts of consumption are analyzed. Furthermore, two different functional forms (marginal propensity to consume and elasticity) are tested here, contrary to other studies on this topic, especially considering the French case. Besides, a comparison of several estimators is derived. Following several papers in the literature (e.g. Lettau and Ludvigson, 2004) we try to assess how much of the wealth movements are considered as permanent and thus may influence consumption. All in all, there is some evidence of a small but robust wealth effect in France, whatever the approaches considered. The remainder of this article is organized as follows. In the first part, we present the theoretical models underlying our approach. The second part describes the existing results concerning the French case. Our results are derived and analyzed in the third part.

2 Theoretical background The theoretical models developed in order to assess the impact of asset prices on consumption can be divided in two main categories.

2.1 Models based on budget constraint Following Campbell and Mankiw (1989), Lettau and Ludvigson (2001) derived from the household budget constraint the existence of a cointegrating relationship between consumption, income and the components of wealth. As long as consumers are forward-looking, the gap between the observed variables and their long term equilibrium may convey information on the future development of consumption but also asset prices and income (Lettau and Ludvigson, 2004). Campbell and Mankiw (1989), by rearranging the log-linearized budget constraint for total wealth which is defined as the sum of observable assets and human capital, found the following relationship:

Wealth Effects on Private Consumption: the French Case

(ct − wt ) ≈ Et

∞

w − ∆ ct+k ) ∑ ρwk (rt+k

265

(1)

k=1

where ct , wt and rt denote the log of consumption, total wealth and gross return on total wealth, and ρw ≡ 1 − exp(c − w). The ratio of consumption to total wealth on the left hand side of the equation gives information on the future developments of consumption and asset prices on the right hand side of the equation. Moreover, if the term on the right hand side of equation (1) is stationary, then consumption and wealth (broadly defined) should be cointegrated. The problem is that, with the inclusion of human wealth, total wealth is not observable, so that the link cannot be tested empirically. Lettau and Ludvigson (2001) modified equation (1) by making assumptions about the unobserved human wealth. They first assume that the share ω of observable asset value at in total wealth is approximately constant and that the average return of overall wealth is a weighted sum of return on assets. They also assume that the nonstationary component of human wealth can be captured by aggregate labour income Yt . So that they obtain the following equation linking observable data: cayt ≡ ct − ω at − (1 − ω )yt ≈ Et

∞

a h + (1 − ω )rt+k − ∆ ct+k ] + (1 − ω )zt ∑ ρwk [ω rt+k

k=1

(2) where zt is a stationary zero-mean variable. One of the pitfalls of this approach is that ω cannot be observed. However, if the return on wealth and expected consumption growth are assumed to be stationary, cayt is stationary as well. This implies a cointegration relationship between log consumption, assets and labor income. ω can then be estimated superconsistently by cointegration methods. Lettau and Ludvigson (2004) estimate the parameters of cayt following Stock and Watson (1993). In a VECM (Vector Error Correction Model) framework, they find that departures of cayt from its long run value in the US help forecast the returns on SP 500 stock index rather than consumption.

2.2 Models based on the consumption function The approach developed above is very parsimonious, which makes it attractive. However, as it uses only the information contained in the budget constraint, it obviously misses some characteristics of the consumer behaviour that can be assessed for instance via the complete analysis of the consumer’s program at the aggregate level. Moreover, the analytical resolution of the consumer’s program may lead to a different functional link between consumption and wealth. Three features seem important in that respect. Firstly, if the consumer utility function is quadratic or isoelastic, her consumption is equal to her permanent income and thus proportional to her total wealth, which can be separated in assets and human wealth. Considering that human wealth is

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determined by the current non property income, then: Ct =

Wt At + W ht At Yt = = + κ κ κ κh

(3)

where Ct , Wt , At , W ht and Yt denote respectively consumption, total wealth, assets, human wealth and non property income. According to Altissimo et alii (2005), theoretical models would set potential values of κ1 between 3 and 10.1 Secondly, households consume housing services whereas they do not consume services from their non housing assets. In the extreme case of autarky, households are either renters or owners. If housing prices rise, owners are better off, whereas renters (or future owners) are worse off, preferring that housing prices fall. Thus housing prices play a role in the distribution of wealth, but not necessarily on aggregate consumption, if all consumers have the same utility function for example. The only potential source of wealth effect is a bubble in the housing market. In the recent literature, both Muellbauer (2008)2 and Buiter (2008)3 stress the difference between both kind of assets. The results above are partly due to the fact that the financial markets are assumed to be perfect. Credit constraints may change the role of housing prices on consumption in two opposite ways. Credit constraints for the first time buyers, who must save for the minimum deposit required to get onto the owner-occupied housing ladder, oblige the young to save all the more as prices are high. Thus, these constraints reinforce the negative impact of housing prices on consumption, compared to the results of the theoretical models developed above, but consumption smoothing is not affected. On the contrary, higher housing prices boost home equity loans and consumption in some countries such as the US, where housing wealth may be used as collateral to buy consumer goods. Thirdly, Carroll, Otsuka, Slacalek (2006) remind that taxes4 , demographics, productivity growth, financial structure and regulation, interest rates, social insurance among others have changed, so that the cointegrating vector between consumption, income and wealth may not be stable. Indeed, Rudd and Whelan (2006) do not find any cointegrating vector for the US. Muellbauer (2008) and Barrell and Davis (2007) insist on the fact that the estimation of wealth effects may be biased by omit1 More precisely, in the case of a constant risk aversion, 1 tend to ra as the horizon of the conκ 1+ra sumer tends towards infinity, where Ra = 1 + ra denotes the average return of non human wealth. In the case of an isoelastic utility function and Blanchard’s(1985) finitely living overlapping generations model, κ1 ≈ σ · ρ + (1 − σ ) · ra + π where ρ , σ and π respectively denote the subjective discount rate, the intertemporal elasticity of substitution (the inverse of risk aversion) and the constant probability of death. Usual values of these parameters lead to the range mentioned before. 2 In a life-cycle permanent income model for a single representative agent where the future relative price of housing is expected to be constant. 3 In a more developed framework, such as the general equilibrium model where there is no lifecycle-related effects on the demand for housing service (the Yaari-Blanchard overlapping generations model). 4 In France, owner occupiers do not pay taxes on their housing and can even deduct part of the interests paid for housing loans from income taxes. On the other hand, transactions on housing are taxed.

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ted variables. These previous studies lead us to carefully assess the robustness of our results, both over time and by controlling for omitted variables.

3 Wealth effect approach debate and empirical estimations for France We first discuss the respective merits of consumption elasticities and marginal propensity to consume out of wealth as measures of wealth effect and then, in the light of the previous debate, the existing literature for France.

3.1 Elasticities versus marginal propensity to consume As seen in section 2, the effect of wealth on consumption may be measured via two methods, which have been independently developed by various authors. One measure is the elasticity of consumption to wealth (section 2.1), which is the percentage change of consumption to be expected after a 10 percentage point change in wealth. The other measure (section 2.2) is the marginal propensity to consume (mpc) out of wealth, which is the marginal increase in consumption in euro due to a marginal increase in wealth of 1 euro. Formally, these measures, elasticity and mpc, are respectively defined by:

εC/A =

∂C C ∂A A

and mpc =

∂A ∂C

If asset prices are unchanged relative to consumer prices, the elasticity may be deduced from mpc by: εC/A = mpc · CA The two different measures are equivalent as far as the ratio of assets to consumption to ( CA ) is stable. But this is not the case: the ratio of net wealth or housing wealth over consumption in France varied from respectively 3.9 and 2.6 in 1980 to 8.2 and 5.9 in 2007. Therefore, the specification choice is not without consequences on the results. From a technical point of view, there are pros and cons for each approach. • Elasticities are preferred by econometricians because estimations in log are less subject to heteroscedasticity problems. There is a long term log-linear equilibrium (ie consumption, income and wealth grow at the same rate), provided that the sum of the two elasticities of consumption to wealth and to income is equal to 1, as shown by Chauvin and Damette (2010), which can be tested. One disadvantage is, the equilibrium cannot be derived in an analytical way. Muellbauer and Lattimore (1995) and Altissimo et alii (2005) show that the log-linear specification leads to problems, especially when we try to estimate the impact of different kinds of wealth on consumption. • The marginal propensity to consume is preferred by modelers because the long term equilibrium can be derived analytically, see Chauvin and Damette (2010).

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3.2 Empirical results for France Empirical work on the wealth effect in France has only been conducted on macrodata, because there is no common source of micro-data on households consumption, income and wealth. The estimations for the long term impact are presented in table 1. The various methodologies used across studies, as well as the sample chosen, may impact the results and are pointed out hereafter. Table 1 Long term impact of wealth on consumption in France Sample MPC Studies Wealth Aviat et alii (2007) Barrell and Davis (2007) Barrell and Davis (2007) Slacalek (2006) Slacalek (2006) Catte et alii (2004) IMF country report (2004) Fraisse (2004) Beffy and Monfort (2003) Byrne et alii (2003) Bertaut (2002) Boone et alii (2001)

Elasticity

total financial housing 1985q1-2006q1 0.4 1980q1-2001q4 3.1 1980q1-2001q4 3.6 1970q2-2003q2 3.2 1970q2-2003q2 4.6* 1979q2-2002q1 1982q1-2003q4 1971q4-2003q2 1.6 1978q1-2000q4 2.5 1972q2-1998q4 1978q1-1998q4 1970q1-1996q2 2.5

2.6 2.9 1.4 2.5

2.0* 2.3* 0.0 0.5

total financial housing 2.3 17.8 20.8 18.5 26.6 9.2 14.0

3* 4.7 6.8

4.2

12.3

5.5 6.1 3.0 5.3

7.3 8.4 0.0 1.9

16.3 10.0 12.0

13.1

Note : According to Aviat et alii, an increase in wealth by 100% implies an increase in consumption by 2.3%. Taking into account the average ratio of wealth over consumption during 1995-2005, this means that an increase by 1 euro of financial wealth induces an increase by 0.4 cents in annual consumption. Estimation results stated directly by the authors are in bold the others are computed using the wealth to consumption ratio. * estimates are not significant.

Many papers estimate wealth effect for France in a context of international comparison by estimating a consumption function for each country separately, without taking into account the cross-country dispersion. To our knowledge, Boone et alii (2001) were among the first ones. However, they estimate the cointegration vector between consumption, wealth and income without taking into account the potential endogeneity of the variables, which is also the case of Fraisse (2004). Bertaut (2002), Beffy and Monfort (2003), IMF (2004), Catte et alii (2004), Slacalek (2006) and Aviat et alii (2007) take into account this problem by using dynamic ordinary least squares (DOLS). In some cases, the sum of the parameters is constrained to one as in Beffy and Monfort (2003) and Aviat et alii (2007). Barrell and Davis (2007) and Byrne et alii (2003) use unrestricted Error Correction Models (ECM) estimated via non linear least squares. Barrell and Davis used dummy variables to account for the impact of financial liberalisation. However, if they do consider the increasing oustanding amount of credit in the second half of the eighties, they do not take into account the reversal that came in 1991-1992, when banks restricted housing credits after having liberalised too much. Byrne et alii also test the impact of illiquid versus liquid wealth.

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All these studies estimate only the impact of permanent change in wealth on consumption. Most of the authors find a significant impact of wealth on consumption in France, albeit smaller than in the United States. The lack of robustness of the results is highlighted in Bertaut (2002) and Byrne and Davis (2003). This may be due to the fact that these papers were among the first ones and the dataset they used stops at the end of the nineties. None of the studies have analysed the sensitivity of the results to different approaches. Most of them make use of univariate methods and they never quantify how much of the adjustment to the long run equilibrium may come not from a change in consumption, but in wealth, as it is suggested by Lettau and Ludvigson (2001) and Whelan (2008), or in income.

4 Econometric results Our empirical framework starts from the now well-known concept of cointegration. Two or more variables which are integrated to the same order and drift randomly are said to be cointegrated if there exists a linear combination between them which is stationary; in this case the series can deviate from the equilibrium in the short run but will return to it in the long run. Concerning the data we used in this analysis (see appendix, tables 7 and 8), most of them come from financial and non financial quarterly national accounts. As developed in the first section, income is the flow of human wealth and thus is measured here by disposable income net of property and housing (imputed rents) income. Three concepts of consumption are of interest. Total households expenditure is the most popular one.5 However, as income is net of property income and in particular net of FISIM (Financial Intermediation Services Indirectly Measured), we considered also consumption excluding financial services.6 Finally, textbooks usually stress that simple consumer models consider a separable consumption utility function and exclude liquidity constraints so that they are more adapted to describe non durable consumption than overall consumption. We then tested consumption excluding durables, although wealth was not adjusted for the stock of durables.7 As explained above, the link between consumption and wealth may be expressed in two manners: marginal propensity to consume (MPC hereafter) and elasticities. 5

Results for households expenditures excluding housing services were also computed, as housing services might not be well measured. They are also available on request; they are very close to that of total households consumption expenditure as long as a trend is added to estimations. The estimates for this trend are in line with the relative evolution of rents compared to overall deflator. 6 These FISIM behave erratically particularly since 2000 in line with the difference between long term and short term interest rates, which may not be relevant for consumption behavior. Financial services represent only 5 to 7.5% of total consumption. 7 It is difficult to assess the impact of this lack of adjustment on the estimated mpc and elasticity, as the dynamics of the stock of durables is different from that of wealth.

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While only the second approach is analyzed in most empirical studies, we test and estimate both in the following sections.

4.1 Empirical MPC model investigation We first investigate the existence of a long run relationship along the MPC pattern over 1987-2006. Although the data set starts in 1978, the estimation period starts in 1987, to avoid the financial liberalisation episode (lifting of credit controls...). In this case, based on the equation (3), the following relationship is analyzed:

Ct At−1 Ht−1 Ft−1 Ct = α +β + ε1t or = α +β +γ + ε2t Yt Yt Yt Yt Yt

(4)

where α is a constant and β the marginal propensity to consume out of wealth. In the first step, we use At as the aggregate non human wealth, in a second step, we test its disaggregation in two different components: housing Ht and financial wealth Ft . Before testing the existence of one or more cointegration relationship(s), we need to investigate the order of integration of the 6 series. They are respectively the ratio of consumption to income net of property income, computed for total consumption, non durable consumption, consumption net of financial services consumption, financial wealth and housing wealth, total wealth. Usual unit root tests - Augmented Dickey-Fuller (ADF, 1979) and DF-GLS from Elliot Rothenberg Stock (ERS, 1996) are performed using the usual selection criteria (LR, AIC, SIC, HQ).8 Note that the last one is the most powerful and has been found to dominate the others under certain conditions. Table 9 (see Appendix) outlines the usual unit root statistics results for consumption and wealth ratios. Following the usual unit root tests, we do not reject the null hypothesis of unit root at 1% apart from the housing wealth/income ratio.9 In the wealth income ratio series (in level and difference), one or two structural breaks seem nevertheless present. To avoid problems of bias rejections and to take account potential structural breaks, we performed the endogenous two-break LM unit root test derived in Lee and Strazicich (2003). This test is an extension of the LM unit root test developed by Schmidt and Phillips (1992). As compared with the Zivot and Andrews (1992) test assuming no break under the null, the Lee and Strazicich one allows for breaks both under the null and the alternative hypothesis. The results of the LM unit root test with two structural breaks are reported in Table 10. 8

It is well known that the determination of the number of lags is very important because unit root tests are sensitive to it. The number of lags is determined by comparing the different criteria. 9 Only non durable consumption and excluding financial services consumption specifications are presented in Table 9 because the total consumption expenditure ratio is stationary. Therefore, no long run relationship in the equation (3) is possible considering the total consumption concept.

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According to it, the unit root of the housing wealth/income ratio is rejected at the 5% level. Hence, the unit root test of Lee and Strazicich (2003) provides evidence in favor of the stationarity of the housing wealth ratio in difference. All of the series are therefore I(1) and cointegration methods are warranted in our view. Note finally that considering the other series (consumption and financial wealth ratios), the conclusions are similar when the unit root with breaks tests are used. Using the Johansen (1988) methodology, we test the existence of the exact number of cointegrating relationships in a multivariate VAR (Vector AutoRegressive) model by performing the Johansen and Juselius Trace and Maximum Eigenvalue Statistics. Considering both nondurable consumption and net of financial services consumption ratios during 1987-2006, we find strong evidence of the existence of a cointegrating vector among the ratio of consumption and the aggregate wealth ratio.We also find strong evidence of a single cointegrating vector among the consumption ratio and the disaggregated wealth ratio. On both data sets, one can reject indeed the null hypothesis of no cointegration at the 1% level. (In addition, these conclusions are robust to the cointegration recursive test we performed. The tests are not reported here but available upon request). We can consequently estimate this cointegrating vector in order to evaluate the marginal propensity to consume. There are two main cointegration approaches to estimate the long-run model (3): single equation approaches and multivariate VAR approaches. The oldest single equation approach is the Engle and Granger’s (1987) 2 step method which consists in using OLS to obtain a cointegrating vector (or a long-run estimate) and then testing for cointegration using ECM cointegration tests. Indeed, OLS provide superconsistent estimates when the data seem to support the assumption of a single cointegration vector. However, we have to assume that all regressors are exogenous, which is not the case as the dynamics of wealth and income depends on that of consumption. An estimation method taking into account the possible endogeneity of the regressors (wealth, income) and improving the Engle and Granger single equation approach is thus needed. We consequently performed the DOLS method proposed by Stock and Watson (1993) via a dynamic OLS (DOLS) regression and the VECM Johansen approach by ML (Maximum Likelihood) estimation in line with Johansen (1995). Note that in small sample, the DOLS estimator is more precise, as it has a smaller mean squared-error than the MLE, see Stock and Watson (1993). In order to test the stability of the long term results, a Generalized Least Squares (GLS) system approach is also proposed for comparison.10 Table 2 summarizes the estimated cointegrating vectors. Our results seem rather robust to the estimator used. We describe our methodology for the elasticity approach before concluding for both sets of results.

10

Bruggemann and L¨utkepohl (2005) have indeed shown that GLS system estimator has better properties than the dominant Johansen MLE in small samples and/or in situations where the MLE produces extreme estimates. The convergence between the results of the two different estimators is thus a robustness indicator.

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Table 2 Estimates of long run MPC (equation (4)) Total Wealth Wealth 1 Wealth 2

OLS

DOLS

VECM-ML VECM-GLS

1.83 (0.73) 1.73* (0.69) 1.79* (0.72) 0.437* (0.17) 3.06 (1.22) 3.45* (1.38) 3.27* (1.31) 1.329 (0.53)

Disagr. Wealth

OLS

DOLS

Housing wealth 1 Housing wealth 2 Financial wealth 1 Financial wealth 2

0.83 (0.33) 0.79 (0.32) 4.55 (1.82) 11.93 (4.77)

4.33* (1.73) 1.74* (0.70) 4.43* (1.77) 9.71* (3.88)

VECM-ML VECM-GLS 2.76* (1.10) 0.96 (0.38) 4.40* (1.76) 9.51* (3.80)

2.73* (1.09) 0.85 (0.34) 4.58* (1.83) 9.8* (3.92)

Note: 1=nondurable consumption ratio 2= ratio of consumption excluding financial; MPC cannot be computed for total consumption in the same way, since the total consumption / wealth ratio is stationary - see footnote 9. 3 or 6 lags for disaggregate, 1 or 2 lags for aggregate. We do not introduce any deterministic term in the VECM model. *, ** and *** indicate significance at 1%, 5% and 10% level respectively and (.) indicate the annualized results that is the increase in cents in annual consumption induced by an increase by one euro in wealth.

4.2 Logarithm or elasticity approach Following the Lettau and Ludvingson (2001) approach presented in 2.1, we estimate here: ct = α + β1at−1 + β2yt + ε1t or ct = α + β1 ft−1 + β2 ht−1 + β3 yt + ε2t

(5)

where c, a , f , h, y are the log of the consumption, aggregate non human wealth, financial wealth, housing wealth and disposable income.11 The time series properties of the log variables are first tested. The study of the non stationary properties of the variables is crucial in the investigation of cointegration relationships. We find evidence in favour of a single unit root test in the stochastic process of most log variables (see Table 9). Nevertheless, the housing wealth seems to be integrated of order two while the other variables are integrated of order one, whatever the deflator considered. As in the previous section, the Lee and Strazicich unit root test (2003) test was performed to check this conclusion. The results of table 10 show that the log of the real housing wealth considering the non durable consumption concept is difference stationary at 10% level. However, the housing wealth deflated by consumption excluding financial services is still I(2). Thereafter we will test the existence of a cointegrating relationship between consumption, disposable income, financial wealth and housing wealth in a ”disaggregated” analysis. As in the previous approach, Johansen and Juselius Trace and Maximum Eigenvalue statistics are performed. Some evidence of two cointegrating relationships 11

a, f , h, y are computed as the value deflated by the deflator coherent with the concept of consumption used.

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arises in aggregate and disaggregate analysis (statistic values are not reproduced here). More over, the sum of the elasticity of income and wealth is far from one in most cases, which shows the weakness of this approach. It is indeed particularly true for our estimations concerning consumption excluding durable goods, but this variable is integrated with total consumption with an elasticity of 0.9, which explains why elasticities with income and wealth are so low in that case. Tables 3 to 5 show the cointegration vectors. Table 3 Estimates of the long run elasticity of total consumption Total Wealth DOLS VECM-ML VECM-GLS Wealth Income Disagr. Wealth Housing Financial Income

0.13* 0.69*

0.10* 0.75*

0.11* 0.75*

0.08* 0.08* 0.63*

0.08* 0.09* 0.62*

0.08* 0.09* 0.60*

*, ** and *** indicate significance at 1%, 5% and 10% level respectively 2 lags for disaggregate (results no sensitive), 2 lags for aggregate

Table 4 Estimates of the long run elasticity of non-durables consumption Total Wealth DOLS VECM-ML VECM-GLS Wealth Income

0.08** 0.90*

0.08* 0.58*

0.09 0.53*

0.05* 0.11* 0.73*

0.06* 0.10* 0.63*

0.06* 0.12* 0.62*

Disagr. Wealth Housing Financial Income

*, ** and *** indicate significance at 1%, 5% and 10% level respectively 6 or 1 lags for disaggregate (results no sensitive), 5 lags for aggregate

Considering long term relationship between log of total/non durable consumption, wealth (total and disaggregated) and income, it is possible to outline the joint dynamics of these variables by a vector error correction model. The vector of estimated adjustments (or loading) coefficients associated with the long run relationship, which are also the coefficients on the lagged cointegrating residuals, is the most interesting feature of the dynamics analysis (that is the reason why all the coefficients of the lagged variables are not reproduced here). Results suggest that any deviations of the variables from their common trends are corrected at first by adjustments in disposable income. The coefficient of adjustment for wealth is only slightly significant in one case (elasticity of non durable consumption) and always smaller

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Table 5 Estimates of the long run elasticity of total consumption excluding financial services Total Wealth DOLS VECM-ML VECM-GLS Wealth Income

0.08* 0.92*

0.07* 0.67*

0.08* 0.65*

0.08* 0.11* 0.65*

0.06* 0.12* 0.66*

0.06* 0.13* 0.64*

Disagr. Wealth Housing Financial Income

*, ** and *** indicate significance at 1%, 5% and 10% level respectively 2 lags for disaggregate and aggregate wealth

than that of income. This is in line with the study for Germany conducted by Hamburg et al. (2006) but in contrast with the seminal study of Lettau and Ludvigson (2001, 2004) for the US, where asset prices adjusted. Table 6 Coefficients of the lagged cointegrating residuals MPC Consumption to income ratio Wealth to income ratio 1 2

-0.19* -0.38*

0.001 -0.0007

Elasticity

Consumption

Wealth Income

1 2 3

-0.24* -0.24* -0.07

0.56*** 0.66*** 0.25 0.66* 0.27 0.72*

*, ** and *** indicate significance at 1%, 5% and 10% level respectively 1=nondurable consumption ratio 2=excluding financial consumption ratio 3=total consumption ratio

4.3 Main conclusions of both approaches Overall, estimates are in general statistically significant and economically plausible in terms of sign and magnitude of estimated coefficients given the level of interest rates (Altissimo et alii, 2005). Robustness tests and stability analysis are performed for both approaches. First, eigenvalue recursive and CUSUM tests suggest that the estimated relationship between consumption and wealth (disaggregated or not) is rather stable over the sample period (see Chauvin and Damette, 2010). Second, Portmanteau and LM test for

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residual autocorrelation, Heteroskedasticity ARCH test and Jarque Bera normality test show that models seem to be robust to various departures from the standard linear model assumptions (see table 10 in appendix). Third, the vector of regressors has been extended by adding unemployment rate, change in unemployment rate, real interest rate and delinquency rates (considering these variables as strictly exogenous and consequently out of the VECM cointegrating space estimated) without any significant change in the estimated coefficients of the cointegrating vector (ie the long run link between consumption, income and wealth).12 Fourth, all the computations have been made on the sample extended to include preliminary data for 2007 and 2008. The Lee and Strazicich results concerning the stationarity of housing wealth (not reproduced here) are still more significant. The estimation results are also robust to this change. In addition, the estimates of wealth effect are very similar with a given specification, whatever the estimating method, DOLS, Maximum Likelihood and Generalize Least Squares. In particular, Maximum Likelihood and Generalize Least Squares estimates are very close: this is an indicator of robustness in accordance to Bruggemann and L¨utkepohl (2005).13 However, DOLS results seem to draw a more realistic picture than the ML and GLS ones in the elasticity approach. The sum of elasticity coefficients is indeed closer to one, especially when analysing the impact of total wealth on total consumption or on non durables. It may be due to the satisfactory small sample properties of the DOLS estimator - we worked with only 80 observations. As pointed out by Stock and Watson (1993), the Johansen estimators exhibit more dispersion than the DOLS one in small samples.14 Estimates for disaggregated wealth are somewhat less robust than the ones for aggregated wealth and need to be cautiously interpreted, although they pass many tests. In particular, the elasticity approach may be weaker than the mpc approach, for two reasons. On the one hand, the cointegration tests imply the existence of two rather than one cointegrating vector. On the other hand, the sum of the elasticity of consumption to wealth and to income is not equal to one except in two DOLS regressions (see tables 4 and 5), which is the condition of long-term equilibrium. It may be so because elasticity is not the best approach with disaggregated wealth or because the housing wealth is not clearly integrated of order one. 12

Concerning the change in unemployment rate, it appeared significantly with the expected negative signs in most of the estimations for the elasticity approach (values stated in chauvin and Damette, 2010). Results are more mixed in the MPC approach, with instability and/or the wrong sign of the coefficient. This does not mean that the change in unemployment rate is not a significant determinant of consumption. However, it does not appear significant in our framework where we favoured wealth effects and with a very short sample which does not encourage a large number of exogenous variables. 13 They have indeed shown that GLS system estimator has better properties than the dominant Johansen MLE in small samples and/or in situations where the MLE produces extreme estimates. The convergence between the results of the two different estimators is thus a robustness indicator. 14 It is well known that the Johansen estimates are somewhat sensitive to the sample and to the lag length choice and that the small sample properties of the MLE are not very good.

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Finally, considering both approaches, there is some evidence that the estimated long run relation between financial wealth, housing wealth and aggregate consumption is significantly positive but small. Based on the MPC estimates, an increase (decrease) in one euro in total asset wealth considered as permanent by households would lead to an increase (decrease) of about 1 cent in annual consumption, which is equivalent to an 5 to 8 % elasticity, given the average wealth to consumption ratio over the period 1995-2005. The estimated long run elasticity of consumption with respect to the total wealth is somewhat higher, about 8-11% (which means a MPC of about 2 cents); the estimated long run elasticity of consumption with respect to the housing effect is very small (at most 6%, that is a MPC of 2 cents) and the estimated long run elasticity of consumption with respect to the financial wealth is about 10%, which is a MPC of 4 cents. This order of magnitude is coherent with theory, according to which consumption is equal to permanent income. Also consistently with economic theory, the financial effect is bigger than the housing effect whatever the approaches and the concepts of consumption used. This dampens the overall impact of wealth on consumption as housing wealth is a bigger component of non human wealth than financial wealth. All these estimates are smaller than in the US and the UK, but close to the Italian ones. With the greatest importance of wealth in the US and the UK, this dissimilarity is likely to explain the fact that the saving rate is higher in France than in the US. On the whole, our result is not surprising as the financing system in France is more based on banks, as in Italy, than on the market, as in the US and the UK. Ludwig and Slok (2004) indeed showed that wealth effects were less important in countries where finance was bank-based. Moreover, the retirement system is nearly only based on pay-as-you-go schemes.15 Concerning the impact of housing wealth, ECB(2009) showed that in the euro area and in France, non interest loan conditions were tighter and mortgage equity withdrawal less common than in the US and the UK, although some financial innovations took place in the recent past. Finally, our results are near the theoretical values (Altissimo et alii, 2005) and near the average of the results of earlier studies for the French case reported in Table 1.

5 Conclusions The paper focus on estimating the impact of permanent change in change on private consumption, trying different specifications to check the robustness of the results. Based on the elasticity approach, an increase (decrease) of 10% in wealth would imply a relatively small impact, of 0.8 to 1.1% on households consumption, according to the concept of consumption considered. Considering the MPC estimates, an increase (decrease) in one euro in total asset wealth would lead to an increase (decrease) of about 1 cent in consumption. Therefore, there is somewhat convergence 15

The comparison with Germany is more difficult as estimates may differ widely: Barrell and Davis (2007), Catte et alii (2004) and Byrne and Davis (1998) find results similar to ours, whereas Slacalek (2006) and Hamburg et alii (2008) find much higher estimates.

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between the different specifications we tested here (MPC and elasticity) in the sense that the wealth effects are quite weak. In most cases, the financial effect is bigger than the housing one. Nevertheless, this result should be considered very cautiously. Firstly, we only analysed the impact of a change in wealth considered as permanent by the consumers. Secondly, the results are somewhat sensitive to the econometric framework, especially when the total wealth effect is considered. In addition, MPC results are more robust than elasticity results in our case (especially, the housing wealth ratio is clearly I(1)). All in all, this analysis extends the existing papers about the wealth effect in European countries by focusing on the special case of France. This is the first paper to compare different specifications for France, using the latest and an original dataset and confronting several cointegration approaches and estimators. Moreover, this is the first attempt to evaluate the dynamics of the wealth effects in France. And income seems to adjust in the short term rather than non human wealth of consumption. At this stage, an interesting further research direction would be to address a variance decomposition analysis in order to identify permanent and transitory components in the consumption dynamics.

Appendix Data Most of the data come from the national accounts (see tables 7 and 8). Interest rates are those agreed for new housing loans, as most housing loans have fixed interest rates in France. Current series of MFI interest rates starting in 2003 have been backdated by different vintages of data, see Boutillier and Rousseaux (2005) in particular. Table 7 Data sources (1) Series name

Full denomination

Consumption Households consumption expenditures Household income Households disposable income (B6) excluding net property income (d40) and imputed rents (part of b2) Consumption deflator Households consumption expenditures deflator Net financial wealth Households financial assets net of debts Housing wealth Households’ tangible assets: land and housing Interests paid for housing loans Interest paid for housing loans Interest rates paid for housing loans Interest rates paid for housing loans Default rate for households Write-offs over total households loans Unemployment rate Unemployment rate

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Table 8 Data sources (2) Series name

Treatment if any

Consumption Quarterly national accounts, INSEE Household income Quarterly national accounts, INSEE Consumption deflator Quarterly national accounts, INSEE Net financial wealth Quarterly financial accounts, Banque de France Housing wealth Wealth account, converted to quarterly data with a housing price index as a guide Interest paid for housing loans Bank accounts annual data converted to quarterly data without guide(*) Interests rates paid for housing loans Monetary data from Banque de France Default rate for households Monetary data from Banque de France Unemployment rate INSEE

(*)see Demuynck et alii (2008), Kierzenkowski and Oung (2007), Wilhelm (2005).

Unit root tests and specifications tests

Table 9 Usual unit root tests Variables

ADF Intercept Intercept/Trend

Consumption/Income 1 Consumption/Income 2 Aggregate Wealth/Income Housing Wealth/Income Financial Wealth/Income Log Real Financial Wealth 1 Log Real Financial Wealth 2 Log Real Housing Wealth Log Real Housing Wealth 1 Log Real Housing Wealth 2 Log Aggregate Wealth Log Aggregate Wealth 1 Log Aggregate Wealth 2 Log Real Income Log Real Income 1 Log Real Income 2 Log Aggregate Real Income

-2.36 (-12.25) -2.25 (-13.37) 3.74 (-3.13) -2.48 (-2.65) -1.44 (-8.17) -1.69 (-8.38) -1.47 (-8.12) 0.52 (-1.65) -0.23 (-0.99) 1.61 (-1.44) 0.96 (-5.83) 2.54 (-2.43) 1.96 (-6.21) -1.38 (-12.39) 0.60 (-4.11) 0.53 (-11.04) -1.38 (-12.40)

-3.16 (-12.24) -3.21 (-13.37) 1.49 (-7.42) 0.68 (-2.20) 2.02 (-8.16) -2.58 (-8.43) -2.53 (-8.16) -1.57 (-2.10) -0.08 (-1.50) -1.67 (-1.66) -0.27 (-5.93) 0.87 (-8.19) 0.45 (-6.59) -1.87 (-12.43) -1.96 (-4.18) -1.22 (-11.05) -1.87 (-12.42)

DF-GLS Intercept Intercept/Trend 0.21 (-4.54) -1.72 (-4.79) -2.43 (-12.95) -0.45 (-12.22) 5.77 (-2.82) -1.14 (-7.51) 0.34 (-2.04) -2.12 799(-2.65) 0.62 (-8.20) -1.84 (-8.20) -1.71 (-8.50) 1.80 (-8.22) -1.85 (-8.02) 1.84 (-7.98) -2.05 (-1.79) 0.43 (-1.63) -1.75 (-1.67) -2.13 (-1.70) -2.09 (-1.68) -0.13 (-0.96) 1.37 (-5.87) -1.43 (-5.97) 6.36 (-2.45) -1.41 (-2.73) 3.32 (-2.26) -0.92 (-6.44) 1.93 (-10.96) -1.34 (-12.31) -2.02 (-2.11) -2.20 (-3.00) 3.37 (-2.43) -1.35 (-10.33) -1.33 (-12.31) 1.93 (-10.96)

(.) are unit root statistics (Augmented Dickey Fuller and DF-GLS) referring to variables in difference. Bold results denotes I(2) variables. 1=non durable consumption used 2=excluding financial services consumption used.

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Table 10 Lee and Strazicich LM unit root test with two breaks Variables

k

TbB

Statistics

Housing Wealth/Income 0 1997:01, 2004:04 -9.39*** Log Real Housing Wealth 1 6 1996:01, 2003:02 -5.76** Log Real Housing Wealth 2 3 1991:02, 1997:04 -5.12 Statistics refer to variables in first difference. k is the number of lagged first-differenced terms included to correct the serial correlation and TbB denotes the estimated break points. 1=non durable consumption used 2=excluding financial services consumption used.

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Table 11 Specification tests Disaggregated

Elasticity 1

Elasticity 2

DOLS ML GLS DOLS ML GLS Portmanteau LM JB

0.00 0.00 0.53 0,02 0,98 0,05 0,80 0,00 0,15

0,00 0,14 0,00 0,01 0,36 0,00 0,32 0,01 0,49

Aggregated

Elasticity 1

Elasticity 2

DOLS ML GLS DOLS ML GLS Portmanteau LM JB Disaggregated

0.00 0.01 0.21 0.00 0.42 0.01 0.99 0.02 0.79 MPC 1

0.00 0.06 0.22 0.00 0.14 0.03 0.36 0.13 0.74 MPC 2

DOLS ML GLS DOLS ML GLS Portmanteau LM JB Aggregated

0.00 0.00 0.01 0.09 0.00 0.00 0.85 0.01 0.45 MPC 1

0.00 0.00 0.01 0.01 0.26 0.00 0.32 0.01 0.50 MPC 2

DOLS ML GLS DOLS ML GLS Portmanteau LM JB

0.00 0.00 0.99 0.00 0.48 0.00 0.08 0.15 0.04

0.00 0.00 0.99 0.00 0.47 0.22 0.26 0.37 0.01

Portmanteau and LM refer to Portmanteau and Breush-Godfrey Lagrange Multiplier test for residual autocorrelation and JB refers to the Jarque-Bera statistic of the test for normal residuals. All results are p-values. Note that the LM test is more suitable to test for low order autocorrelation, contrary to the Portmanteau test (see for instance L¨utkepohl, 2008). 1=nondurable consumption 2= excluding financial consumption.

Acknowledgements All views expressed in the paper are only those of the authors and are not necessarily those of the Banque de France. We wish to thank warmly Franc¸oise Charpin, Pierre Morin, John Muellbauer as well as participants of the AFSE conference (2009) for helpful comments.

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281

References Altissimo, F., Georgiou, E., Sastre, T. , Valderrama, M. T., Sterne, G., Stocker, M., Weth, M., Whelan, K., Willam, A. (2005), Wealth and asset price effects on economic activity, ECB, Occasional paper series, 29. Aviat, A., Bricongne, J-C., Pionnier, P-A. (2007), Richesse patrimoniale et consommation : un lien tenu en France, fort aux Etats-Unis, Note de conjoncture INSEE, 208. Barrell, R., Davis, E. P. (2007), Financial liberalisation, consumption and wealth effects in seven OECD countries, Scottish Journal of Political Economy, 54, 2, 254-267. Beffy, P.O., Montfort, B. (2003), Patrimoine des menages, dynamique d allocation et comportement de consommation, Document de travail INSEE, G2003/08. Bertaut, C. (2002), Equity prices, household wealth, and consumption growth in foreign industrial countries: wealth effects in the 1990s, Board of Governors of the Federal Reserve System, International Finance Discussion Papers, 2002-724. Blanchard, O.J. (1985), Debt, deficits, and finite horizons, Journal of Political Economy, 93, 223247. Boone, L., Giono, C., Richardson, P. (1998), Stock market fluctuations and consumption behaviour: some recent evidence, OECD, Economics Department Working Papers, No. 208. Boutillier, M., Rousseaux, P. (2005), Loan Interest Rates: a Spread Analysis using French data from 1993 to 2004, colloque du GdR “Economie Mon´etaire et Financi`ere”, Strasbourg, June 2005; European Economic Association, Econometric Society European Meetings (EEA-ESEM), Vienna, August 2006. Bruggemann, R., L¨utkepohl, H. (2005), Practical Problems with Reduced-rank ML Estimators for Cointegration Parameters and a Simple Alternative, Oxford Bulletin of Economics and Statistics, 67, 5, 673-690. Buiter, W.H. (2008), Housing wealth isn’t wealth, CEPR Discussion paper, No. 6920. Byrne, J. P., Davis, E. P. (2003), Disaggregate wealth and aggregate consumption: an investigation of empirical relationships for the G7, Oxford Bulletin of Economics and Statistics, 65, 2, 197220. Campbell, J. Y., Mankiw, N. G. (1989), Consumption, income and interest rates: reinterpreting the time series evidence, NBER macroeconomics annual, 25, 2, 185-216. Carroll, C., Otsuka, M., Slacalek, J. (2006), How large is the housing wealth effect? A new approach, NBER Working Paper, No. 12746. Catte, P., Girouard, N., Price, R., Andre, C. (2004), Housing markets, wealth and the business cycle, OECD Economics Department Working Papers, No. 394. Chauvin, V., Damette, O. (2010), Wealth effects, the French case, Banque de France working papers, No. 276. Demuynck, J., Mosquera-Yon, T., Duquerroy, A. (2008), Evolutions recentes du credit aux mnages en France, Bulletin de la Banque de France, janvier 2008 Dickey, D.A., Fuller, W.A. (1979), Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427431 ECB, (2009), Housing finance in the euro area, ECB, Occasional paper, March 2009 Elliott, G., Rothenberg, T. J, Stock, J. H, (1996), Efficient Tests for an Autoregressive Unit Root, Econometrica, Econometric Society, vol. 64(4), 813-36, July Engle, R., Granger, C, Co-integration and error correction: Representation, estimation and testing, (1987), Econometrica, Econometric Society, vol.55(2), 251-276. Fraisse, H. (2004), Du nouveau sur le taux d’epargne des menages francais ?, Banque de France, Bulletin mensuel, 130, 33-56. Gregory, A., Hansen, B. (1996), Residual-based tests for cointegration in models with regimeshifts, Journal of Econometrics, 70, 99-126. Hamburg, B., Hoffmann, M., Keller, J. (2008), Consumption, wealth and business cycles in Germany, Empirical Economics, 34, 3, 451-476. IMF, W.H. (2004), Modelling consumption behavior, IMF country report, Selected issues, 04/346, 6-18.

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Johansen, S. (1995), Likelihood-based Inference in Cointegrating Vector Autoregressive Models, Oxford University Press, Oxford. Kierzenkowski, R., Oung, V. (2007), L evolution des credits a l habitat en France : une grille d analyse en termes de cycles, Banque de France, NER, No. 172, Juillet 2007. Lee, J., Strazicich, M.C. (2003), Minimum LM unit root test with two structural breaks, Review of Economics and Statistics No. 85, 1082-1089. Lee, J., Strazicich, M.C. (2004), Minimum LM unit root test with one structural break, Department of Economics, Working Paper, Applachian State University. Lettau, M., Ludvigson, S. (2001), Consumption, aggregate wealth, and expected stock returns, Journal of Finance, 56, 815-849. Lettau, M., Ludvigson, S. (2004), Understanding trend and cycle in asset values: reevaluating the wealth effect on consumption, American Economic Review, 94, 1, 276-299. Ludwig, A., Slok, T. (2004), The relationship between stock prices, house prices and consumption in OECD countries, Mannheim university working paper. L¨utkepohl, H., Krazig,H. (2008), “Vector autoregressive and vector error correction models”, in Applied Time Series Econometrics, L¨utkepohl and Krazig ed., Cambridge University Press, Cambridge, pp. 86-158. Muellbauer, J. (2008), Housing, credit and consumption expenditure, CEPR, Discussion paper, No. 6782. Muellbauer, J., Lattimore, R. (1995), The consumption function: a theoretical and empirical overview, in Handbook of applied econometrics: macroeconomics, Pesaran M. H. and Wickens M. ed., Blackwell, Oxford, 221-311. Rudd, J., Whelan, K. (2006), Empirical proxies for the consumption wealth ratio, Review of economic dynamics, 9, 34-51. Schmidt, P., Phillips,P.C.B. (1992), LM tests for a unit root in the presence of deterministic trends, Oxford Bulletin of Economic and Statistics, 54, 257-287. Slacalek, J. (2006), What drives personal consumption? The role of housing and financial wealth, DIW working paper, No. 647. Stock, J. H., Watson,M. W. (1993), A simple estimator of cointegrating vectors in higher order integrated systems, Econometrica, 61, 783-820. Whelan, K. (2008), Consumption and expected asset returns without assumptions about unobservables, Journal of monetary economics, 55, 1209-1221. Wilhelm, F. (2005), L evolution actuelle du credit a` l habitat en France est-elle soutenable ?, Bulletin de la Banque de France, aoˆut 2005 Zivot, E., Andrews,D. W.K. (1992), Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis, Journal of Business and Economic Statistics, 10, 3, 251-270.

An Assessment of Housing and Financial Wealth Effects in Spain: Aggregate Evidence on Durable and Non-durable Consumption Teresa Sastre and Jos´e Luis Fern´andez

Abstract Recent developments in housing and financial markets have led to fresh interest in the empirical evidence on wealth effects on consumption. This paper aims at providing up-to-date estimates of wealth effects by using a vector error correction model (VECM) approach to account for endogeneity and allow for the possibility of more than one variable equilibrating the system, in the same vein as previous work by Lettau and Ludvigson in the US. The breakdown of wealth into its housing and financial components leads to additional possibilities of adjustment to reach the long run equilibrium. In addition, the model accounts for potentially different values of the parameters linking consumption and wealth when distinguishing between durable and nondurable goods.

JEL codes : E21, C32 Keywords : Consumption, consumption of durables, housing wealth, financial wealth, cointegration

1 Introduction Recent developments in housing and financial markets have led to fresh interest in the empirical evidence on wealth effects on consumption. The varied and controversial results in the empirical literature, as well as the doubts on whether residential assets may really affect consumption in a similar way as financial wealth does, have maintained a debate over the actual magnitude of wealth effects and the relative size of its housing and financial components.

T. Sastre Banco de Espa˜na, e-mail: [email protected] J.L. Fern´andez-S´anchez Banco de Espa˜na, e-mail: [email protected] O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_13, © Springer-Verlag Berlin Heidelberg 2010

283

284

Teresa Sastre and Jos´e Luis Fern´andez

This paper aims at providing up-to-date estimates of wealth effects in Spain by using a vector error correction model (VECM) approach to account for the endogeneity of several variables. This also makes it possible to incorporate not only a self-correction mechanism in consumption -as empirical consumption functions with an error correction term do- but also the possibility of other variables equilibrating the system, in the same vein as previous work by Lettau and Ludvigson in the US. The analysis follows the same approach of Sastre and Fern´andez-S´anchez (2005), who distinguished between durable and non-durable consumption to better describe aggregate consumption in Spain. In the current analysis a more recent sample and new definitions of some variables have been incorporated. This paper is organized as follows. Section 2 describes some stylized facts about recent developments in Spanish private consumption and household savings rate. Section 3 provides the theoretical background which is the basis for using the cointegration analysis as our empirical approach. This methodology is briefly explained in section 4 together with a short description of the data set. The main empirical results are reported and interpreted in section 5 and the last section presents some brief conclusions.

2 Stylised facts of wealth effects in Spain Up to 2008 the savings ratio of Spanish households fluctuated within a range of 10 to 15 % of gross disposable income (Fig. 1). To a large extent, these fluctuations are associated to cyclical movements, which have an impact on income expectations and thereby on the propensity to save. Thus, in the crisis of the first half of the nineties the savings rate increased, although with an erratic pattern, and decreased during the booming period of the second half of that decade. In the mild downturn experienced in the early years of this century the ratio of savings to income increased slightly to drop again until 2007. In the last two years this ratio has risen again. This time in a very sharp way, as a consequence of the deterioration in economic perspectives and the increased uncertainty derived both from the financial crisis and the growth of unemployment. Household net worth seems to have also contributed to these developments as it can be seen in Fig. 1. During the second half of the nineties the unprecedented fall in real interest rates experienced by the Spanish economy and the subsequent increase of financial wealth boosted household spending above income growth, thus pushing down the savings rate and raising the ratio of net financial wealth to consumption (Fig. 2). After the reversal of equity prices, financial wealth decelerated in the early years of this century, but total wealth still provided an important support for consumption due to the contribution of housing wealth.

An assessment of housing and financial wealth effects in Spain

285 %

11

Net total wealth/Disposable Income (l)

Savings rate (r)

16

10

15

9

14

8

13

7

12

6

11

5

10

4

9

3

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

8

Fig. 1 Household wealth and savings rate 3.0

Net financial wealth/Private consumption (l) Housing wealth/Private consumption (r)

2.5

12 10

2.0

8

1.5

6

1.0

4

0.5

2

0.0

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

0

Fig. 2 Household wealth breakdown

When considering the response of consumption to wealth, differences may arise as regards the durability of expenditure and the type of assets.1 This debate has not settled down yet and seems to be country-dependent. In the case of Spain, a key feature is the fact that residential assets, mainly the primary residence, are very homogenously distributed across income groups. Not only the home ownership rate is very high -more than 80%-, but also about 70% of households in the lowest income quintile are owners of their homes, as compared to 41% in the US and 44% in Italy (see Table 1). This suggests that the response of consumption to housing wealth might be fairly high in Spain. On the other hand, the fact that housing is rarely used as collateral for consumption loans –home equity withdrawal- would imply a housing wealth effect on consumption lower than in other countries where this is a more common practice. The distinction between consumption of durable and non-durables goods may prove to be useful to better understand the relationship between spending decisions, savings and wealth accumulation. Expenditures on durables share similar charac1

See a summary of this debate in section 2.1.4 in Altissimo et al. (2005).

286

Teresa Sastre and Jos´e Luis Fern´andez

Table 1 Household holdings of primary residence % of households Percentile of income

Spain

USA

Italy

1st quintile 2st quintile 3st quintile 4st quintile 80 - 90 90 - 100

70.7 78.6 81.0 85.8 87.8 92.9

41.4 55.2 69.3 83.9 92.6 94.3

44.3 59.8 73.2 79.1 87.1*

All families

81.3

68.6

68.7

(*) 5th quintile Source: Encuesta financiera de las Familias 2005 (ES) Survey of Consumer Finances 2007 (USA) Survey of Household Income and Wealth 2006 (IT)

teristics to investment in capital goods and also participate of some similarity to savings. As in the case of capital goods, the acquisition of durable goods entails the allocation of a big amount of resources to a good which will produce returns or consumption services for several periods in the future. The variability and pro-cyclical pattern of durable consumption is fairly high, as it also happens with capital goods, and larger than the variability of non-durable spending. These differences, which are quite evident for Spanish durable and non-durable consumption data (Fig.3), suggest that the link between spending on durables and lifetime wealth may differ considerably from the one linking non-durables to their long-run fundamentals. For instance, most developments in Spanish private consumption on non-durables have closely tracked labour income growth, giving rise to a fairly stable pattern in the consumption to income ratio since the economic crisis of the early nineties (Fig. 3). In the previous years, the process of convergence of the Spanish economy to the European standards had gradually reduced consumer spending rate out of labour income. On the other hand, the ratio of durable expenditure to labour income showed a lower average level in the early nineties than in the following years, as well as relatively wide swings in the whole period 1987-2008, due to fairly large differences in the average growth of these two variables during prolonged periods of time (lower panel of Fig. 3). To give account of the behaviour of durable consumption in those periods, other variables than labour income appear to be needed.

An assessment of housing and financial wealth effects in Spain

25

287

annual rate (%)

Non durables

20

Durables

25 20

15

15

10

10

5

5

0

0

-5

-5

-10

-10

-15 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

-15

128

Private consumption (l) Non durables average (1993-2008)

124

116 Non durables (r) 112

120

108

116

104

112

100

108

96

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

14

%

Durables 13 12 11 10 9 8 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Fig. 3 Durables and non durables consumption annual change (top) - Consumption-Labour Income Ratio (middle) - Durable consumption-Labour Income Ratio (bottom)

Household net worth, which kept a rather stable ratio to income up to the midnineties and progressively increased since then, is the main candidate but not the only one. The fact that the acquisition of durable goods entails a big-ticket purchase implies a need for financing for many households, which suggests that financing conditions -interest rate, availability of loans- may also play a significant role. Credit availability for durable purchases remained quite subdued since 1990 until 1997 (Fig. 4), which might help to explain the fall in the ratio of durables to labour income in those years. The increasing profile of the spending rate on durables since the mid-nineties might be associated to the big fall in real interest rates or, perhaps, to developments in the relative price of durable goods, which has shown a declining trend over the last twenty five years. A negative relationship between this last variable and expenditure on durables can also be observed in the short to medium run (lower panel of Fig. 4).

288

Teresa Sastre and Jos´e Luis Fern´andez

40

annual rate (%)

Loans for durables purchasing (cdur)

40

30

30

20

20

10

10

0

0

-10

-10

-20 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

-20

30 20

annual rate (%)

Durables spending (l) Durables deflator/consumption deflator (r)

6 4

10

2

0

0

-10

-2

-20

-4

-30 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

-6

Fig. 4 Loans for durables purchasing in real terms (top) - Durables and relative price(bottom)

In previous empirical studies on aggregate consumption in Spain which model separately spending in durable and non-durable goods similar variables have been considered. In Estrada (1992) expenditure on durables in the long-run is related to disposable income and the relative price of energy, which captures one of the components of durables user cost. This study also stressed the need of considering other variables than income to explain the long-run behaviour of durables, especially those related to credit market conditions. In this same vein, Bover and Estrada (1994) found a significantly direct effect of purchase of the main residence on durable expenditure, at least in the late eighties. In Estrada and Buis´an (1999) three main spending decisions of households were analysed: non-durable spending, durable consumption and residential investment, using two definitions of income -labour and disposable income- and two types of wealth -financial and residential-. These authors found that financial wealth was a significant long-run determinant of both durables and non-durables, when labour income was used, 2 and that the relative price of energy was also needed to explain the long-run path of durable spending. Sastre and Fern´andez-S´anchez (2005) estimated a model for those same decision 2

With disposable income, financial wealth was only relevant in the case of non-durable spending.

An assessment of housing and financial wealth effects in Spain

289

variables -non-durable spending, durable consumption and residential investmentby using a multivariate framework (VECM). They found that both durable and non-durable expenditure tended to move closely together with both components of wealth -financial and residential- and labour income in the long run, and in the case of spending on non-durable goods, together with the real interest rate. Lastly, Bover (2005) obtained estimates of the wealth effect by using micro-data (the Survey of Spanish Household Finances). She found that the largest effects were for owner occupied housing, with financial wealth effects being smaller.

3 Theoretical background The empirical analysis described in the next sections is based on the approach initiated by Lettau and Ludvigson (2001), who derived the implications of the intertemporal budget constraint to the long-run cointegration relationship between consumption, income and wealth. Their work resorted to that of Campbell and Mankiw (1989), who obtained an expression for the log consumption-total wealth ratio by taking a first-order Taylor expansion of the budget constraint, solving forward the resulting difference equation and imposing a transversality condition. The resulting expression is:

ct − wt ≈ Et

∞

∑ ρwi (rw,t+i − ∆ ct+i )

(1)

t=1

where lower case letters denote log variables, rw = log (1 + Rw ) is the average net return of total wealth (W), and ρw is the steady-state ratio of new investment to total wealth, (W - C)/W. This expression makes it clear that the consumption-total wealth ratio embodies household expectations of both future wealth returns and consumption growth. Total wealth includes assets (A) –real and financial- and human wealth (H), which is not observable. However, an approximate expression with only observable variables on the left hand side can be obtained by assuming that labour income (yL ) can be thought of as the dividend of human capital and by using an approximation to log total wealth, i.e. wt ≈ θ at + (1- θ ) ht (θ is the steady state share of non-human wealth in total wealth). The expression in observable variables is: ∞

L ct − αa at − αy ytL ≈ Et ∑ ρwi (θ ra,t+i + (1 − θ )∆ yt+1+i − ∆ ct+1 )

(2)

t=1

The net return of total wealth, rw , is the average of returns on non-human wealth, ra , which may vary over time, and labour income growth. If wealth returns and con-

290

Teresa Sastre and Jos´e Luis Fern´andez

sumption growth are assumed to be stationary, then consumption, labour income and assets must be tied together by a cointegrating relationship. Thus, the expression on the left hand side represents deviations from their common trend which, according to the right hand side, may reflect expectations of future returns to assets, future changes to labour income, planned growth of consumption or some combination of the three. Likewise, the existence of a cointegration relationship implies that the system (c, a, yL ) can be represented as a Vector Error Correction Model (VECM) with at least one of the three variables adjusting in case of deviations from their common trend. 3

4 Data and econometric methodology The cointegration relationship among consumption, wealth and labour income, all measured in logarithms, implied by the lifetime budget constraint is analysed in a VECM framework, where consumption is broken down into durable and nondurable spending. Then, at least two cointegrating relationships are expected. A priori assumptions about the set of variables that are weakly exogenous are not required under this framework, they can rather be easily tested through t-ratios of certain parameters. The variables used in the empirical analysis (Fig.5) were taken from quarterly national accounts in most cases. Other data sources also used are quarterly financial accounts, censuses of houses and house price data released by the Housing Ministry. Quarterly data of durable and nondurable consumption were obtained from the yearly consumption breakdown by type of goods and function (COICOP classification) which were interpolated by using appropriate quarterly short-run indicators. Labour income is defined as disposable non-property income, which differs from the definition used in Sastre and Fern´andez-S´anchez (2005). 4 Nominal variables are expressed in real terms by using the consumption deflator. A more detailed description of data is summarised in Appendix 1. Cointegration relationships are analyzed by adopting the Johansen approach, as outlined in Johansen (1995), which produces maximum likelihood estimates of long-run parameters. The first step under this approach is to estimate an unrestricted VAR model such as: Zt = ∑ Γj Zt− j + ξt

(3)

j

3

See Engle and Granger (1987). Sastre and Fern´andez-S´anchez (2009) offers a comparison of several alternative definitions of labour income in Spain.

4

An assessment of housing and financial wealth effects in Spain 11.6

Non durables (cnd)

11.5

291

9.6

Durables (cd)

9.4

11.4 9.2

11.3 11.2

9.0

11.1 8.8

11.0 10.9 1987

1993

1999

11.7

2005

Labor income (yl)

11.6

8.6 1987

1993

1999

15.6

2005

Housing wealth (hw)

15.2

11.5 11.4

14.8

11.3 11.2

14.4

11.1 11.0

14.0

10.9 10.8 1987

1993

1999

2005

13.7

Net financial wealth (nfw)

13.6

1999

2005

5 Real interest rates (r)

3

13.4 13.3

2

13.2

1

13.1 13.0

0

12.9

1987

1993

4

13.5

12.8

13.6 1987

1993

0.3

1999

2005

Relative price of durables (pdur)

0.2

-1 1987

1993

17.6

1999

2005

Loans for durables purchasing (cdur)

17.2

0.1

16.8

0.0 16.4

-0.1

16.0

-0.2 -0.3 1987

1993

1999

2005

15.6 1987

1993

1999

2005

Fig. 5 Variables of VAR Systems (log level)

where Z is the vector of n endogenous variables and ξ a vector of white noise error terms. The VAR system can also be expressed in vector error correction form:

∆ Zt = ∑ Γj ∆ Zt− j + Π Zt−1 + ξt

(4)

j

Π is the (n x n) trend-cycle decomposition parameters of the dynamic system. The cointegration test is based on the rank of this matrix, r, which indicates the number of long-run relationships among the endogenous variables in the VAR. If 0 < r < n, then Π can be decomposed as Π = α β ′ , where β ′ is a (r x n) matrix which describes the r linear combinations of the variables which are stationary and α is a (n x r) matrix of coefficients which define the adjustment path of each endogenous variable to deviations from the long-run relationships given by β ′ Z. To identify α

292

Teresa Sastre and Jos´e Luis Fern´andez

and ß several identifying restrictions are needed to be imposed on these matrices. The number of restrictions necessary to identify the long-run is k, such that k ≥ r2 . In general, if k = r2 the system is exactly identified and when k > r2 , the system is overidentified and these overidentifying restrictions may be tested by conducting likelihood ratio tests.

5 Econometric results 5.1 The basic empirical model A VAR is specified over the period 1987.Q1 to 2007.Q4 for the following endogenous variables: nondurable consumption (cnd), durable consumption (cd), labour income (yl), housing wealth (hw), net financial wealth (nfw) and real interest rate (r). The assumption that all variables included in the system are integrated of order one -I(1) processes- appears to be validated by the sample data (see Table 2). The null hypothesis of one unit root cannot be rejected for all the variables except for the real interest rate, which seems to be borderline stationary in this period of time. 5 In the case of housing wealth, the null hypothesis cannot be rejected at the 10% significance level. The lag order of the VAR was chosen so as to obtain well behaved residuals. In the Appendix 2, several diagnostics for this VAR system are reported, which suggest there is no evidence of serial correlation, heteroskedasticity or non-normality in the residuals. The tests proposed by Johansen for the number of cointegrating relationships (Trace and Maximum-Eigenvalue statistics) are reported in Table 3 together with tests on the weak exogeneity of the variables under several hypothesis about the number of cointegrating relationships. In VAR systems with a large dimension the reduction of the size of the system becomes very important to improve the performance of cointegration tests in small samples. 6 Therefore, weak exogeneity tests are conducted in order to reduce the number of endogenous variables by imposing exogeneity restrictions accepted by the data. According to the Chi2 tests, the hypothesis that net financial wealth is weakly exogenous (with rank (Π ) = 2 or 3) cannot be rejected. In this smaller VAR, with financial wealth being considered weakly exogenous, the Johansen tests for the number of cointegrating relations are not clear cut but point to three cointegrating relationships, although a lower rank could also be possible, as suggested by the maximum eigenvalue test with small sample cor5

In previous studies with Spanish data it was found that the real interest rate was integrated of order one. The fact that the sample used in this paper includes more years of the EMU period, may help to understand why this variable is closer to be stationary, which is the usual assumption in theoretical models and in section 3. The real interest rate can be included in the VAR even under that assumption, since a stationary variable may be included together with others which cointegrate among themselves. 6 See Greenslade et al. (2002).

An assessment of housing and financial wealth effects in Spain

293

Table 2 Unit root test p (H0 : p =1 en ∆ Xt = α + (ρ − 1)Xt−1 + Σ∆ Xt−p + εt i =1 Level

p ADF

∆

p ADF

∆2

p ADF

cnd cd yl nfw hw nw r pcd pdur cdur

1 5 1 2 2 2 1 2 1 2

∆ cnd ∆ cd ∆ yl ∆ nfw ∆ hw (b) ∆ nw ∆r ∆ pcd ∆ pdur ∆ cdur

2 4 1 2 1 1 1 1 2 1

∆ 2 cnd ∆ 2 cd ∆ 2 yl ∆ 2 nfwr ∆ 2 hwr ∆ 2 nwr ∆ 2r ∆ 2 pcd ∆ 2 pdur ∆ 2 cdur

2 -9.4827** -

0.32 -0.81 -0.87 -1.82 -0.98 -0.83 -2.46 -1.20 1.78 -1.92

-3.7352** -3.9140** -4.4903** -3.8013** -1.9501* -3.4678* -12.953** -5.5223** -6.1014** -4.3694**

(a) All variables are in logs except the real interest rate and the consumption deflator. Sample period: 1981 (3) to 2008 (4) (b) The value of ADF test refers to a regression without constant. which was not significant. cnd: Real non-durable consumption cd: Real durable consumption yl: Real labor income nfw: Real net financial wealth hw: Real estate wealth nw: Real total wealth r: Real interest rate for house purchasing pcd: Private consumption deflator pdur: Relative price of consumer durable goods with respect to the private consumption deflator cdur: Credit for durable purchasing in real terms ** Significant at 1% (critical value for T = 100 and constant -3.51. without constant -2.58) * Significant at 5% (critical value for T = 100 and constant -2.89. without constant -1.94)

rection.7 Some ambiguity also arose in Sastre and Fern´andez-S´anchez (2005) who presented results for both cases, r = 2 and r = 3. Cointegrating relationships were normalized in non-durable and durable consumption variables, in the case of r = 2, while under r = 3, the third relationship was normalised in labour income. To identify the cointegrating relationships one needs to impose some identifying restrictions on the value of long-run coefficients. In order to do so it is helpful to incorporate prior information from economic theory or other analyses, especially in VAR systems with small samples as it is our case. Therefore, the dynamic ordinary least square (DOLS) method proposed by Stock & Watson (1993) is used to obtain a robust range of values for long-run parameters. This method takes into account the possible endogeneity of regressors in a single equation framework and it seems to be more precise in small samples than several system estimators. Table 4 offers these estimates for two equations: non-durable spending and durable consumption. According to them the elasticity of non-durables to income lies in the range (0.5 - 0.6) across several specifications and the elasticity to aggregate wealth could be about 0.1 - 0.2, depending on whether an aggregate definition of wealth is used or

7

See Reimers (1992).

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Table 3 Johansen Cointegration Tests Unrestricted VAR Endogenous variables: [cnd. cd. yl. nfw. hw. r] Conditioning variables in cointegrating relationships:[] Critical H0: M´ax value Eigenvalue (95%) Eigenvalue rank (r)

Trace

Critical value (95%)

(a) (a) 0.556 =0 68.1** 48.6** 39.4 149.4** 106.7** 94.2 =1 32.1 22.9 33.5 81.3** 58.1 68.5 0.318 =2 29.0* 20.7 27.1 49.2* 35.1 47.2 0.292 =3 12.5 8.9 21.0 20.2 14.5 29.7 0.138 =4 7.4 5.3 14.1 7.8 5.6 15.4 0.085 =5 0.3 0.2 3.8 0.3 0.2 3.8 0.004 Weak exogeneity tests (Chi2) cnd cd hl nfw hw r r=2 2.1 [0.3] 5.8 [0.0] 19.4 [0.0]** 0.9 [0.6] 11.1 [0.0]** 8.6 [0.0]* r=3 14.7 [0.0]** 19.3 [0.0]** 29.5 [0.0]** 0.9 [0.8] 11.6 [0.0]** 16.8 [0.0]** VAR with financial wealth weakly exogenous Endogenous variables: [cnd. cd. yl. hw. r] Conditioning variables in cointegrating relationships:[nfw] Critical H0: M´ax value Eigenvalue (95%) Eigenvalue rank (r)

Trace

Critical value (95%)

(a) (a) 0.553 =0 67.7** 51.6** 33.5 141.8** 108.1** 68.5 =1 31.7* 24.1 27.1 74.1** 56.5** 47.2 0.314 =2 28.9** 22.1* 21.0 42.4** 32.3* 29.7 0.291 =3 8.8 6.7 14.1 13.5 10.3 15.4 0.100 =4 4.7* 3.5 3.8 4.7* 3.5 3.8 0.054 Weak exogeneity tests (Chi2) cnd cd hl hw r r=2 1.8 [0.4] 5.8 [0.0] 19 [0.0]** 10.6 [0.0]** 8.8 [0.0]* r=3 17.6 [0.0]** 23.4 [0.0]** 29.2 [0.0]** 11.1 [0.0]* 17.4 [0.0]** (a) Correction for sample size. Reimers (1992). In the Chi2 tests the significance level is in brackets

the breakdown in its housing and financial components. 8 The real interest rate appears as non significant, in contrast to previous studies. The estimated equation for durable consumption is less informative, since the coefficient of labour income and interest rate are poorly determined, in terms of magnitude and sign. The high correlation of wealth with income and also with the real interest rate appears to pose serious difficulties to obtain precise estimates of the separate effect of each of them. Wealth parameters seem somewhat more robust, at least its sign and relative size, being the elasticity of the financial component the largest. The parameters of the cointegration relationships were estimated in a multivariate framework by applying the Johansen method (Table 5). These relationships were 8

The restriction that the long run elasticities of income and wealth should add-up to one is understood as a constraint on the whole household demand –private consumption and housing investment-. Such an assumption is imposed in the quarterly econometric model of Bank of Spain. See Ortega et al. (2007).

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295

normalised and identified so as to define the long-run paths of non-durable spending, durable consumption and the inverse of the ratio of non-durables to income, a kind of ”savings from non-durables” (yl − cnd). The elasticity of non-durables to income has been fixed at a value close to 0.5, similar to that used in the study by Sastre and Fern´andez-S´anchez and in accordance with the estimates obtained from Stock-Watson procedure. In comparing the current estimates with the results of that study, the elasticity to total wealth, which was 0.22 there, is very similar when using disaggregated wealth since the sum of the elasticity to housing and financial wealth also adds up to 0.22. On the other hand, interest rate semi-elasticity becomes almost unsignificant, with a wrong sign. The collinearity between each component of wealth and the real interest rate, and the fact that this variable seems to be borderline stationary suggest to remove it from the VAR, at least to estimate the long-run co-movements among the other variables. Then, a new VAR is estimated with the following variables: non-durables, durables, labour income and housing wealth, together with net financial wealth, which is treated as a weakly exogenous variable. In this case the values of the parameters of non-durable spending are similar to the ones seen before while those of durable consumption appear somewhat undetermined due to the collinearity between income and wealth. Thus, two alternatives are presented in Table 6: the first one with the elasticity of durables to labour income fixed at 0.5 and a high value for the coefficient of financial wealth, and the second one, with unit elasticity to income and a lower parameter of financial wealth, while housing wealth becomes non-significant. The restrictions implied by both specifications are not rejected at conventional significance levels thus pointing out the difficulty of disentangling the link between durable spending, income and wealth, at least with these data. Nonetheless, the relationship between non-durable expenditures and wealth is well determined and fairly robust to several specifications. The recursive estimation of these coefficients also behaves fairly stable (see Fig. 6 9 ).

Table 4 Stock and Watson Estimates of long-run relationships (*) Non durable consumption Durable consumption (A) (B) (C) (A) (B) (C) (D) Labour income (yl) 0.64 0.57 0.51 0.91 -0.18 -0.4 (0.03) (0.05) (0.05) (0.26) (0.29) (0.24) Total wealth (nw) 0.12 0.07 (0.01) (0.09) Housing wealth (hw) 0.11 0.13 0.29 0.34 0.23 (0.01) (0.01) (0.07) (0.06) (0.02) 0.07 0.09 0.72 0.76 0.59 Net financial wealth (nfw) (0.02) (0.02) (0.13) (0.11) (0.04) -0.54 -0.05 -5.46 1.74 Real interest rate (r) (0.44) (0.57) (3.37) (3.63) (*) Standard errors in brackets

9

In this figure a positive relationship between wealth and consumption appears with a negative sign.

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Table 5 Durable and non-durable consumption VECM with interest rate (a) Endogenous variables: cnd. cd. yl. hw. r Conditioning variables:nfw Sample period: 1987 (1) to 2007 (4) cnd*

cd*

yl*

cnd 0.00 [ - ] cd 0.00 [ - ] yl 0.50 [ - ] 0.50 [ - ] hw 0.13 [0.01] 0.11 [0.04] nfw 0.09 [0.02] 0.68 [0.07] r 0.84 [0.35] 0.00 [ - ]

1.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.00 [ - ]

Long run (ß-coeff.) non-durable durable labor income housing wealth net financial wealth real interest rate

Error correction (α -coeff.) (cnd -cnd*)

∆ cnd ∆ cd ∆ yl ∆ hw ∆r

(cd -cd*)

(yl -yl*)

0.03 [0.11] 0.03 [0.02] -1.32 [0.48] -0.46 [0.1] 0.25 [0.09] 0.02 [0.02] 0.18 [0.07] 0.02 [0.01] 0.72 [0.24] 0.1 [0.05]

0.07 [0.05] -0.89 [0.20] -0.05 [0.04] 0.02 [0.03] 0.11 [0.10]

LR-test. rank=3: Chi2 (4) = 26.938 [0.0000] ** (α ) Standard errors in brackets. In the likelihood ratio test. the significance level is in brackets.

-0.105

-0.080 housing wealth1

-0.110

financial wealth1

-0.090 -0.100

-0.115

-0.110

-0.120

-0.120 -0.130

-0.125

-0.140 -0.130 -0.135

-0.150 2006

2007

2008

0.000

2009

housing.

-0.050

-0.160

2006

2007

2008

0.000

2009

financial.

-0.100 -0.200 -0.300

-0.100

-0.400 -0.150

-0.500 -0.600

-0.200

-0.700 -0.250

2006

2007

2008

2009

-0.800

2006

2007

2008

2009

Fig. 6 Recursive estimation of long-run parameters for non-durable consumption (top) and durable consumption (bottom).

From these results, one can get an approximate idea of the magnitude of wealth effects on consumption, since non-durables stand for about 90 % share of total consumption. The elasticity of non-durables to housing wealth is very similar to the one corresponding to financial wealth (Table 6) -leaving aside the possibility that the portion of transitory changes may be larger in financial wealth-. Because of very different ratio of consumption to wealth, the marginal propensity to consume non-

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297

Table 6 Durable and non durable consumption VECM: basic model Basic model (a) Endogenous variables: cnd. cd. yl. hw Conditioning variables:nfw Sample period: 1988 (1) to 2007 (4) cnd*

cd*

yl*

cnd 0.00 [ - ] cd 0.00 [ - ] yl 0.50 [ - ] 0.50 [ - ] hw 0.13 [0.00] 0.14 [0.03] nfw 0.12 [0.01] 0.52 [0.06]

1.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.00 [ - ]

Long run (ß-coeff.) non-durable durable labor income housing wealth net financial wealth

Error correction (α -coeff.) (cnd -cnd*)

∆ cnd ∆ cd ∆ yl ∆ hw

-0.35 [0.14] -1.84 [0.68] 0.34 [0.13] 0.57 [0.33]

(cd -cd*)

(yl -yl*)

0.02 [0.02] -0.45 [0.09] 0.01 [0.02] 0.08 [0.05]

0.01 [0.05] -0.90 [0.24] 0.01 [0.04] 0.26 [0.12]

LR-test. rank=3: Chi2 (2) = 3.7007 [0.1572] Marginal propensity to consume cnd

cd

0.020 0.012

0.002 0.002

0.066 0.064

0.031 0.034

cnd*

cd*

yl*

- 0.00 [ - ] 0.00 [ - ] 0.50 [ - ] 1.00 [ - ] 0.13 [0.00] 0.01 [0.04] 0.12 [0.01] 0.40 [0.07]

1.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.00 [ - ]

Housing wealth (average) (2007) Net financial wealth (average) (2007) Endogenous variables: cnd. cd. yl. hw Conditioning variables:nfw Sample period: 1988 (1) to 2007 (4) Long run (ß-coeff.) non-durable durable labor income housing wealth net financial wealth

cnd cd yl hw nfw

Error correction (α -coeff.) (cnd -cnd*)

∆ cnd ∆ cd ∆ yl ∆ hw

-0.34 [0.15] -2.30 [0.73] 0.35 [0.13] 0.65 [0.35]

(cd -cd*)

(yl -yl*)

0.02 [0.02] -0.45 [0.09] 0.01 [0.02] 0.08 [0.05]

0.02 [0.06] -1.36 [0.32] 0.02 [0.06] 0.34 [0.16]

LR-test. rank=3: Chi2 (2) = 3.7007 [0.1572] Marginal propensity to consume cnd

cd

(average) (2007)

0.020 0.012

0.000 0.000

(average) (2007)

0.066 0.064

0.024 0.026

Housing wealth Net financial wealth

(α ) Standard errors in brackets. In the likelihood ratio test. the significance level is in brackets.

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durables (mpc) out of financial wealth is however far larger, about 6 cents, than the mpc out of housing wealth, between 1 and 2 cents.10 On the other hand, a one euro rise in financial wealth would be associated with an increase of about 2.5-3.5 cents in durables, while a one euro rise in housing equity would have a negligible effect. Thus, total consumption would increase between 1 and 2 cents with a one euro rise in housing wealth and about 9-10 cents with a one euro rise in net financial wealth.11 These results are in line with the estimates obtained for other European countries, like France or Italy, for which housing wealth is associated with smaller changes in consumption than non-housing assets. The main difference is the effect of financial wealth, which appears somewhat larger in Spain than in these two countries, although the estimates with more recent data point to a lower effect of net financial wealth on durable consumption(see Fig. 6). In this restricted VAR the third cointegration relation involves labour income and non-durable consumption with a unit coefficient (yl – cnd), and captures the stable behaviour of the ratio of non-durable spending to labour income in Spain since the early nineties, as described in section 2 12 . This relationship together with the cointegrating vector linking non-durable spending, wealth and labour income implies that there are other stationary relationships linking wealth components and income. In addition to the parameters of the ß matrix, the long run properties of the endogenous variables in the VAR also depend on the adjusting mechanisms which allow equilibrating the system when there are deviations from the long run paths, i.e. the α -coefficients or loadings. These coefficients indicate the reaction of each endogenous variable in the VAR to departures from the estimated long run paths. This makes it clear why these systems are called Vector Error Correction Models (VECM). In cases of multi-cointegration –several cointegrating relations-, as is our case, the equilibrating mechanisms may become varied and complex. In the two systems shown in Table 6, the deviations of non-durable spending from its long-run path (cnd*) -given by income, housing and financial wealth and the ß-coefficients- are closed by changes in three variables: a self-correction in nondurables given by the negative coefficient of ∆ cnd to (cnd – cnd*), and a reaction in labour income and housing wealth, both with a positive sign. If consumption expenditures are above their long-term trend, as made it clear in section 3.1, that must be either because of expectations of higher future returns to assets, or expected increases of labour income, or because of a lower planned consumption growth, or a combination of them. Since consumers take into account relevant information to form their expectations it happens that, in practice, these expectations end up being 10

Bover (2005) reports a mpc out of housing wealth of about 2 cents with Spanish household data. These estimates should be viewed as a first approximation to the link between consumption and wealth since no distinction has been made between permanent and transitory movements in the variables. 12 Sastre and Fern´ andez-S´anchez (2005) also obtained this same stationary relationship when they considered that the cointegration rank was 3. 11

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299

self-fulfilled to a certain extent, i.e. labour income and housing wealth returns react as consumers expected to do. 13 In the case of departures of durable consumption from its long-run path (cd - cd*), these are adjusted via a self-correction in durables. These expenditures do not only react to this gap, but also to those situations in which the non-durables deviate from its long-run path (cnd – cnd*), i.e. durables are used as an adjusting mechanism when there is an ”excessive” consumption in non-durables. Likewise, when the ratio of non-durable spending to labour income is above or below its long-run level –the inverse of the third cointegrating relationthere is also a response of spending on durables. The interpretation of this is as follows. If this ratio is above its long-term value, that implies that savings (yl – cnd) are below its long-run value, and -according to Campbell (1987)- this may be seen as reflecting consumers expectations of higher future income growth which make consumers react by increasing their holdings of durables. This kind of reaction fits well with the stylized fact that durable consumption tends to anticipate business cycle movements. The last adjusting mechanism captured in these VECMs is an endogenous reaction of housing wealth to changes in that ratio of non-durables to income. When this ratio is below its long-run level, these savings (yl – cnd) are above it, feeding through housing wealth increases, which push up non-durables to reach its log-run equilibrium. The equilibrating mechanisms either through income or asset returns (or both) were firstly described in Lettau & Ludvigson (2001) and have also been found in previous studies for several European countries 14 . The adjustment through durables when non-durables deviates from its shared trend with labour income and wealth and the quick response implied by the coefficient of its own error correction term both point to durable acquisitions as one of the main mechanisms used to smooth non-durable consumption. This interpretation fits well with the larger variability shown by durables as compared to non-durable spending which was pointed out in section 2. The three cointegrating relations already described are shown in Fig. 7. While the fitted long-run path of non-durables and labour income track very closely the observed variables, the fitted path of durables deviates from the observed data in a persistent way, mainly during the first ten years of the sample period. This suggests that there might be some missing variable in the estimated long-run relationship. This possibility is explored in the next section.

13

According to Lettau and Ludvigson (2001) study, deviations from the common trend of consumption, labour income and asset wealth contain predictive elements for stock market returns in the US. 14 See the studies by Fern´ andez-Corugedo et al. (2003) for the UK, Chauvin and Damette (2010, this volume) for France, Bassanetti and Zollino (2010, this volume) for Italy and Sastre and Fern´andez-S´anchez (2005) for Spain. In all of them income was found to adjust to restore the long-run equilibrium. In the case of Italy, housing wealth was also an adjusting mechanism.

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Teresa Sastre and Jos´e Luis Fern´andez 11.6

0.03 cnd-cnd* 0.02

Fitted

11.4

0.01

11.3

0.00

11.2

-0.01

11.1

-0.02 -0.03 1987

Non durables (cnd)

11.5

11.0 1993

1999

0.25

2005

cd-cd*

0.20

10.9 1987

1993

9.6

1999

2005

Durables (cd)

Fitted

9.4

0.15 9.2

0.10 0.05

9.0

0.00

8.8

-0.05 8.6

-0.10 -0.15 1987

1993

1999

0.04

2005

yl-yl*

0.02

1993

1999

11.7

2005

Labor income (yl)

11.6

Fitted

11.5

0.00

11.4 11.3

-0.02

11.2

-0.04

11.1 11.0

-0.06 -0.08 1987

8.4 1987

10.9 1993

1999

2005

10.8 1987

1993

1999

2005

Fig. 7 Cointegrating relationships (basic model)

5.2 Extensions of the basic model The main candidates to account for the departure of observed durables from its estimated long-term path are credit availability and the relative price of durables, as suggested in section 2. The decision to purchase a durable good implies an up-front payment, since the services obtained from that good extend over several periods. Then it may appear sensible to also differ the funding of that purchase over time by resorting to external finance and periodic payments of that debt instead of doing it through income saved from non-durable consumption at the time of purchasing durable goods. Another alternative to acquire durables is to liquidate financial assets. The empirical relevance of credit to understand consumption developments has been highlighted in several studies, some of them analysing the impact of financial liberalisation on aggregate consumption. 15 In order to explore the ability of credit to help understand developments in the acquisition of durables, a new VECM was formulated by adding the stock of loans for 15

See, for instance, Japelli and Pagano (1994), Bacchetta and Gerlach (1997) and Aron et al. (2007).

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the purchase of durables to the basic empirical model of the previous section. This variable -which is first order integrated- experienced a strong growth in the second half of the eighties and stabilized, or even decreased, in the first half of the nineties, showing a profile quite similar to developments in durables acquisition (Fig. 5). The results of this estimation are reported in Table 7. According to it loans enter the long-run relation which determines the shared common trend of durables, income and wealth with a positive coefficient, though borderline significant. It also enters the third relationship between non-durable consumption and labour income with a negative sign. This can be interpreted as a substitution effect between savings from non–durable spending and credit, two variables embedded in the consumer budget constraint at each period of time. This substitution is also channelled through a negative response of loans for purchasing durables to an increase in savings above its long-run -captured by the third cointegrating relation-, which is given by the α – coefficient of ∆ cdur to deviations from that relationship. The other features of the basic model remain fairly similar except for the fact that net financial wealth enters now the relationship between labour income and non-durable consumption. This last relation becomes now a kind of linear combination of the second and third relationships of the basic model and results more difficult to interpret. Though the over-identifying restrictions implicit in this VECM are easily accepted, the introduction of credit transforms the third cointegrating relationship in a kind of approximation to a consumer budget constraint. Besides of consumption and labour income, this would include net property income, credit and financial assets. Under this set-up the mean-reverting behaviour of the non-durable to labour income ratio has implications over the long-run profile of the other variables of the budget constraint. Thus, some combination of them must also exhibit a stationary behaviour. 16 To determine which specific combination is an empirical matter which is beyond the scope of this paper and may be addressed in future research. Another aspect to be considered is that credit is more likely to be linked to durables, income and wealth in the short to medium run than in the long-run. Then it should not appear in the cointegrating relationships and it would be better incorporated as an explanatory variable once the dynamics of the vector error correction is fully specified. Another factor which is thought to have some explanatory power of the observed swings in the profile of durables over time is its relative price. A VAR system was estimated by adding the change in durables relative price to the basic empirical model of the previous section (Table 7). Although this variable is of a lower order of integration than the other endogenous variables, nothing precludes the possibility that a stationary variable appear in a relationship among other variables which cointegrate. In general, the relative price of durables was found to affect the long-run of durables with a negative sign. However, the best specifications in terms of not rejection of the identifying restrictions were those in which the relative price appears in 16

One possibility is that the ratio of investment in durable goods and in financial assets to an aggregation of net property income and new loans for durables purchasing is stationary.

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Table 7 Durable and non durable consumption VECM: extensions Basic model and credit (a) Endogenous variables: cnd. cd. yl. hw. cdur Conditioning variables:nfw Sample period: 1987 (1) to 2007 (4) cnd*

cd*

yl*

cnd cd 0.00 [ - ] yl 0.50 [ - ] hw 0.13 [0.01] nfw 0.10 [0.01] cdur 0.00 [ - ]

0.00 [ - ] 0.50 [ - ] 0.13 [0.04] 0.19 [0.07] 0.11 [0.06]

1.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.17 [0.02] -0.04 [0.01]

Error correction (α -coeff.) (cnd -cnd*)

(cd -cd*)

(yl -yl*)

-0.21 [0.11] 0.04 [0.02] -1.80 [0.55] -0.53 [0.10] 0.30 [0.10] 0.03 [0.02] 0.66 [0.24] 0.11 [0.05] -0.85 [0.63] -0.04 [0.12]

-0.06 [0.06] -0.86 [0.30] -0.03 [0.05] 0.08 [0.14] -1.54 [0.35]

Long run (ß-coeff.) non-durable durable labor income housing wealth net financial wealth durable credit

∆ cnd ∆ cd ∆ yl ∆ hw ∆ cdur

LR-test. rank=3: Ch2 (2)= 0.84828 [0.6543] Basic model and relative price of durables (a) Endogenous variables: cnd. cd. yl. hw. ∆ pdur Conditioning variables:nfw Sample period: 1988 (1) to 2007 (4) cnd*

cd*

yl*

non-durable cnd durable cd 0.00 [ - ] labor income yl 0.45 [ - ] housing wealth hw 0.14 [0.00] net financial wealth nfw 0.11 [0.01] ∆ durable price ∆ pdur 0.00 [ - ]

0.00 [ - ] 0.45 [ - ] 0.12 [0.01] 0.50 [ - ] 0.00 [ - ]

1.00 [ - ] 0.00 [ - ] 0.00 [ - ] 0.00 [ - ] -9.38 [1.49]

Error correction (α -coeff.) (cnd -cnd*)

(cd -cd*)

(yl -yl*)

-0.28 [0.12] 0.04 [0.02] -1.21 [0.60] -0.55 [0.11] 0.37 [0.11] 0.01 [0.02] 0.58 [0.27] 0.11 [0.05] 0.06 [0.12] -0.03 [0.02]

0.05 [0.03] -0.35 [0.13] -0.05 [0.02] 0.12 [0.06] -0.09 [0.03]

Long run (ß-coeff.)

∆ cnd ∆ cd ∆ yl ∆ hw 2 ∆ pdur

LR-test. rank=3: Ch2 (5) = 9.8531 [0.0795] (α ) Standard errors in brackets. In the likelihood ratio test. the significance level is in brackets.

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the relation between income and non-durables. This may suggest that changes in the ratio of non-durables to labour income are related to changes in the relative price of durables. Thus, a lower relative price of durables will make those goods more attractive and consumers will tend to adjust down the ratio of non-durable spending to labour income, hence increasing their savings.

6 Conclusions This paper offers an updated assessment of the magnitude of wealth effects on Spanish consumption by distinguishing the consumption of durables from that of nondurables. This breakdown makes it possible to uncover several differences in wealth effects: housing equity affects non-durable consumption with a marginal propensity to consume of 1-2 cents, while the mpc out of financial wealth is about 6 cents. In the case of the spending on durables the mpc out of financial wealth is lower while that of housing wealth is negligible. Thus, the strongest wealth effects concentrate on non-durable consumption which stands for 90% of total private consumption. These values are in line with those obtained in other studies, though the effect of financial wealth estimated in this paper may be somewhat higher and more comparable to the effect of non-equity net financial wealth. 17 Furthermore, the distinction between non-durable and durable expenditures enriches the analysis by providing a better understanding of the adjustments in consumer’s decision variables. According to our empirical model durable consumption plays an important role as an adjustment variable to smooth consumption over time, as it reacts to situations of ”excessive” or ”scarce” expenditure on non-durables and also appears to anticipate future changes in labour income. On the other hand, the historical stability of the ratio of non-durables to income suggests that the aggregate of durables and “savings’ –whose definition depends on the assumed consumer budget constraint- should also have been fairly stable, exhibiting a long-term substitution between them. Lastly, there is also evidence that labour income and housing wealth adjust in the short run to achieve long-run equilibrium of non-durable spending, similarly to the findings of Chauvin & Damette (2010, this volume) and Bassanetti & Zollino (2010, this volume) for France and Italy, respectively. In the US the main adjusting mechanism comes instead from returns to financial wealth, as shown in Lettau & Ludvigson (2001, 2004).

17

See Altissimo et al. (2005).

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Teresa Sastre and Jos´e Luis Fern´andez

Acknowledgements We wish to thank our discussants Val´erie Chauvin (Banque de France) and Jean-Pierre Villetelle (Banque de France). We are also grateful to seminar participants at Banca d’Italia, Alberto Cabrero, Jos´e Manuel Gonz´alez and Juan Pe˜nalosa for their comments and suggestions.

References Altissimo, F., E. Georgiou, T. Sastre, M.T. Valderrama, G. Sterne, M. Stocker, M. Weth, K. Whelan and A. Willman (2005), Wealth and Asset Price Effects on Economic Activity,European Central Bank, Occasional Paper, No. 29, June. Aron, J., J. Muellbauer and A. Murphy (2007), Housing Wealth, Credit Conditions and Consumption, mimeo. Bacchetta, P. and S. Gerlach (1997), Consumption and Credit Constraints: International Evidence, Journal of Monetary Economics 40, 207-238. Bover, O. and A. Estrada (1994), Durable Consumption and House Purchases: Evidence from Spanish Panel Data, Banco de Espa˜na, Working Paper, No. 9411. Bover, O. (2005), Wealth effects on consumption: Micro-econometric Estimates from the Spanish Survey of Household Finances, Banco de Espa˜na, Documento de Trabajo, No. 0522. Campbell, J. (1987), Does Saving Anticipate Declining Labour Income? An Aternative Test of the Permanent Income Hypothesis, Econometrica, vol. 55, No. 6, 1249-1273. Campbell, J. and G. Mankiw (1989),Consumption, Income and Interest Rates: Reinterpreting the time Series Evidence, in O. Blanchard and S. fischer (eds.), Cambridge, MIT Press, NBER Macroeconomics Annual, 185-216. Engle, R.F. and C. W. Granger (1987),Cointegration and Error Correction: Representation, Estimation and Testing, Econometrica, vol. 55, 251-276. Estrada, A. (1992), Una funci`on de consumo de bienes duraderos, Banco de Espa˜na, Working Paper, No. 9228. Estrada, A. and A. Buis`an (1999), Banco de Espa˜na, El gasto de las familias en Espa˜na, Estudios Econ`omicos, No. 65. Greenslade, J.V., S.G. Hall and S.G. Brian Henry (2002), On the Identification of Cointegrated Systems in Small Samples: A Modelling Strategy with an Application to UK Wages and Prices, Journal of Economic Dynamics & Control, 26, 1517-1537. Japelli, T. and M. Pagano (1994), Saving, Growth and Liquidity Constraints, Quarterly Journal of Economics, 83-109. Lettau, M. and S. Ludvigson (2001), Consumption, Aggregate Wealth and Expected Stock Returns, Journal of Finance, June 2001, 56 (3), 815-849. Lettau, M. and S. Ludvigson (2004), Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption, American Economic Review, 94, 1, 276-299. Ortega, E., P. Burriel, J.L. Fern´andez and S. Hurtado (2007), Update of the quarterly model of the Bank of Spain, Banco de Espa˜na, Working Paper, No. 0717. Reimers, H. E. (1992), Comparisons of Tests for Multivariate Cointegration, Journal of Finance, June 2001, 56 (3), 815-849. Sastre, T. and J. L. Fern´andez-S´anchez (2005), Un modelo emp´ırico de las decisiones de gasto de las familias espa˜nolas,Banco de Espa˜na, Working Paper, No. 0529. Sastre, T. and J. L. Fern´andez-S´anchez (2009), Mediciones alternativas de las rentas del autoempleo: implicaciones sobre la renta laboral, Julio-Agosto, Banco de Espa˜na, Bolet`ın Econ`omico. Stock, J. H. and M. W. Watson (1993), A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems, Econometrica, vol. 61, No. 4, 783-820.

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Appendix Appendix1. Data sources

Non-durable National Accounts. Breakdown by expenditure function and conjuntural consumption indicators. INE and Banco de Espa˜na Durable National Accounts. Breakdown by expenditure function and conjuntural consumption indicators. Banco de Espa˜na and INE Labour Income Disposable non-property income with household surplus net of fixed capital consumption and imputed residential rents. National Accounts and own calculations. INE and Sastre and Fernandez-Sanchez (2009) Housing wealth Census of houses and house price. Housing Ministry Net financial Household financial assets minus liabilities. Quarterly Financial Accounts wealth Banco de Espa˜na Real interest rate Nominal interest rate for house purchasing minus inflation as measured by private consumption deflator. Banco de Espa˜na and INE Relative price of Durables deflator relative to private consumption deflator. National Accounts. durables Breakdownby expenditure function and conjuntural indicators. INE Credit for durable Nominal credit for durable purchasing of banks and savings banks divided purchasing by private consumption deflator. Banco de Espa˜na and INE

Appendix2. Diagnostic tests for consumption VARs Tests on residuals: (1987.I - 2007.IV; lag order = 4) Endogenous variables: cnd. cd. hl. nfw. hw. r Conditioning variables in cointegrating relationships: Dummys: constant. I922. I923. d92I B-P(9)

LM(1-5) NORM Chi2(2)

non-durable consumption (cnd) 3.707 0.69 [0.63] durable consumption (cd) 7.054 0.89 [0.49] labor income (yl) 3.297 0.43 [0.83] net financial wealth (nfw) 14.888 2.30 [0.06] housing wealth (hw) 3.836 0.88 [0.50] real interest rate (r) 3.931 0.52 [0.76]

ARCH4

1.77 [0.41] 2.31 [0.31] 3.48 [0.18] 0.78 [0.68] 4.58 [0.10] 0.18 [0.92]

0.59 [0.67] 0.39 [0.81] 0.23 [0.92] 1.98 [0.11] 0.73 [0.58] 2.32 [0.07]

LM(1-5) NORM Chi2(2)

ARCH4

Endogenous variables: cnd. cd. hl. hw Conditioning variables in cointegrating relationships: nfw Dummys: constant. I922. I923. d92I B-P(9) non-durable consumption (cnd) 3.206 durable consumption (cd) 5.950 labor income (yl) 4.382 housing wealth (hw) 16.472

0.86 [0.51] 1.05 [0.40] 0.37 [0.86] 2.34 [0.05]

0.63 [0.73] 1.41 [0.49] 3.13 [0.21] 0.79 [0.67]

0.42 [0.79] 0.69 [0.60] 0.07 [0.99] 1.77 [0.15]

The Effects of Housing and Financial Wealth on Personal Consumption: Aggregate Evidence for Italian Households Antonio Bassanetti and Francesco Zollino

Abstract In this paper we focus on Italian aggregate quarterly time series covering the 1980-2008 sample period and test the presence and size of wealth effects on consumption, taking separately account of financial assets and residential property on the basis of new stock measures. We find sound evidence in favour of a cointegrating relation, in which both wealth components display the expected, positive effect on households’ consumption. In particular, our results point to a lower marginal propensity to consume out of housing than out of non housing net worth, with a respective size laying in the range of 1.5-2 and 4-6 cents. Following the estimate of a vector error correction model, we discuss the role played by transitory and permanent shocks in driving changes in the variables we consider. We have found that both consumption and wealth respond almost exclusively to permanent shocks, which are the sole determinants of the common stochastic trend in our theoretical set-up. As a result, we are confident that our estimates of wealth coefficients in the cointegrating vector match very closely the true long run marginal propensity to consume for Italian households.

JEL codes : E21, C32 Keywords : wealth effects, consumption, housing

A. Bassanetti Bank of Italy, e-mail: [email protected] F. Zollino Bank of Italy, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_14, © Springer-Verlag Berlin Heidelberg 2010

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1 Introduction The sizeable rise in house prices that started during the nineties in all main industrial countries - with the important exceptions of Germany and Japan - and in the largest emerging economies (IMF, 2009) has led to fresh interest in the empirics of wealth effects on consumption amid rapid innovation in financial markets. Differently from received theoretical literature, the debate is centred on the different channels through which housing as opposed to financial assets may affect consumer spending and, combined with residential investment, aggregate demand as a whole. Interest in this issue has gained further momentum recently, given the financial turmoil that show up in August 2007 in the US subprime mortgage market that trigged liquidity distress in financial markets at a global level. The wide implications for monetary policy are also revealing, as ”the uncertainty around housing-related monetary transmission mechanism provides one further reason why monetary policy will continue to be an art, albeit one that makes use of science” (Mishkin, 2007). Indeed the question is not simple as certified by the controversial results in the available empirical literature, despite the recently prevailing view in favour of a significant and large housing wealth effect whose size, compared with financial assets, seems to depend on country specific factors. In this paper we focus on the recent experience of the Italian economy, where wealth accumulation seems to outperform international comparison. At the same time, the research effort aimed at the possible link with consumer spending has not been as intense as in other advanced economies. We contribute to the debate by looking at the Italian aggregate time series to estimate the link between consumption, financial and housing wealth over a 29-year sample period (1980-2008), controlling for the role of income and common exogenous drivers, such as the brisk drop in interest rates on the eve of European Monetary Union. For this purpose, we have exploited cointegration analysis to study the long run relationships between the variables involved. The empirical literature often interprets the coefficients of such relationships as long run elasticities of consumption with respect to income and wealth. Though this practice is quite convenient, these parameters summarize the correlation between the permanent movements in the aggregates, because they are based on the existence of a common stochastic trend. On the contrary, they are not indicative at all of the link between households spending and transitory fluctuations in income and wealth. As a consequence, as first suggested by Lettau and Ludvigson (2004), once we have estimated the long run correlation among the variables of the system, we need to assess whether there exists (transitory) movements in income and wealth that are not associated with

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(permanent) changes in consumption. This will allow a correct reading of the cointegrating vector. Given the increasing relevance of this issue in recent literature, we have adopted the variance decomposition approach put forward by Gonzalo and Ng (2001) to assess the share of quarterly fluctuations which are due, respectively, to permanent and transitory shocks. This can be done easily by exploiting the information directly available from the estimated VECM for Italy. Among the main results we find a long run marginal propensity to consume in the range, respectively, of 1.5-2 and 4-6 cents out of each one euro increase in housing and financial wealth. This paper is organized as follows. Section 2 describes some stylized facts about recent developments in the Italian economy, with a particular focus on the household propensity to save and on the housing market. Section 3 delivers a summary of the theoretical predictions about wealth effects, followed in Section 4 by a review of empirical evidence available for Italy. After sketching the theoretical set-up adopted for our analysis (Section 5), we describe the data set and report upon the preliminary analysis (Section 6). Main empirical results are presented in Section 7, followed by a variance decomposition exercise (Section 8). The final section presents a brief conclusion. The propensity of Italian households to save, or the saving ratio, had long been particularly high among industrial countries, being still on the rise in the early eighties (Figure 1). Since then, it has shown a brisk deterioration that, apart from a temporary break between 1995 and 1997, has gradually brought the saving rate down to a low of 10% by the end of the nineties. At the beginning of the current decade, private savings first showed a partial recovery, then resumed their negative trend until the eve of the financial crisis, and as the latter deepened they partially recovered. In the years 2008-2009, the saving ratio in Italy averaged slightly above 11%.

2 Searching for macroeconomic facts for consumption in Italy Looking for explanations of developments prior to the ongoing crisis, a first candidate is a trend reversal in key factors that had previously sustained high personal savings, namely the high productivity performance that drove up income expectations and lagging capital markets which prevented the scope for consumption smoothing (Guiso, Jappelli and Terlizzese, 1994). On the one hand, since the middle of the nineties the productivity trend has turned negative (Bassanetti et al., 2004), plausibly curbing consumer spending in the medium term; on the other, the development of the capital markets accelerated with progress in financial liberalization at domestic level and European integration, peaking at the start of monetary union in 1999, and plausibly alleviated liquidity constraints for Italian households.

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Fig. 1 Saving ratio and wealth income ratio in Italy (Source: Authors’ own computations based on data from Istat and Bank of Italy)

These forces might have offset the demand for precautionary saving that probably originated from increased economic uncertainty amid a sequel of reforms in social security and labour markets, that began in the early nineties. In this framework the deep financial crisis largely added on uncertainty, driving up saving formation. The drop in personal saving prior to the crisis went in association with a brisk acceleration in real and financial wealth held by consumer households. Following a broad stability throughout the eighties, the ratio of total wealth (including durables) to annual income soared from around 5.5 at the start of the recession in 1992 up to 7 between 2000 and 2001, peaking at 7.8 at the end of 2007; it went slightly back at the end of 2008 (Figure 1).1 Based on a tentative exercise in which we have disentangled the main contributors to changes in financial and housing wealth, it seems that in the first half of the years 2000s new savings explained a major part of the increasing stock of financial assets held by households in Italy. This result occurred in spite of the negative performance in asset prices between 2001 and 2003, which caused a huge devaluation in financial wealth. After 2008 asset devaluation became more severe, driving negative changes in total stock amid a negligible share of savings channelled into the financial market (Figure 2). At the same time, savings channelled to the residential market gained gradually momentum prior to 2008, even if they played a minor role in driving the fast growth in housing wealth, as long as the positive trend in house prices markedly accelerated. In 2008 the positive change in total stock almost halved due to both lower saving and revaluation. As a whole, these pieces of preliminary evidence imply that the traditional arguments for a positive direct wealth effect may play a less important role in explaining 1 If durable stock is not included, over the whole period, total wealth climbed from 4.8 to 7 as a ratio of disposable income of consumer households.

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Fig. 2 Changes in stock and real prices in Italy (Source: Authors’ own computations based on data from Istat and Bank of Italy)

the medium term drop of Italian personal saving than implied by the negative correlation between the saving ratio and wealth, as shown in Figure 1. Anyway the size of wealth effects needs to be tested more carefully against a long lasting period of rapid changes in the market value of assets, with particular reference to real estate. Since the start of the current decade, the average annual growth in house prices in Italy has been around 4.5%, net of consumer price variation, or by half a percentage point higher than in the euro area as a whole. Differently from previous business cycles, the performance of house prices, prior to the crisis, had not been affected by the state of economy, with a continuous increase in house prices, while domestic activity virtually stagnated (Figure 3). House prices have gradually slowed down, with a virtual stagnation as the financial crisis deepened and conditions on the credit markets worsened.

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The upward trend in prices had entailed a strong increase in the value of the real estate wealth of Italian households, which at the end of 2008 accounted for almost 60% of total wealth, or 20 percentage points more than financial assets (in 2000 the gap was below 4 points, with the share of housing around 51% of total wealth). The home ownership rate now stands at 72 % among Italian households, or some 10 points higher than the estimated value for the euro area as a whole; among the main industrial countries, Italy is 5 points above the level reached in the UK and USA, around 15 and 30 points above France and Germany, respectively.

3 The theory of wealth effects According to the life cycle model, households smooth over time their consumption spending on the basis of intertemporal budget constraint, given by the sum of the discounted flow of future expected income and the current endowment in wealth. Smoothing is achieved by borrowing when young against higher expected future income, then repaying the debt when income actually raises and consuming out of accumulated wealth when retired. It turns out that consumption expenditure depends on permanent income and initial wealth, besides life expectancy and time preference. In this framework, an unexpected and permanent increase in wealth entails a roughly equal rise in consumption in every future period that households expect to live. According to the theory, therefore, the marginal propensity to consume out of wealth is significantly positive and increases with age. Since the standard model is mostly aimed at explaining long run changes in consumption, an additional prediction that has exerted a long lasting impact on macromodelling is that wealth composition does not matter: households instantaneously adjust their spending by the same amount against either financial or real additional wealth. This is partly related to the key theoretical assumption that capital markets are perfect and complete, which rules out liquidity constraints as well as transaction and borrowing costs due to imperfect information. As a consequence most ingredients of the current debate regarding housing prices, housing finance and consumer spending are simply missed in the standard model. For this purpose, following Deaton and Muellbauer (1980) and Poterba (1984) we rearrange the intertemporal budget constraint to take account of two different wealth components: housing and financial assets. This allows one to take into account that while financial assets are mainly a liquid store of value whose holding implies negligible costs, dwellings may be considered both a consumption good, specifically providing housing services, and an investment good that requires maintenance costs to keep the structure from depreciating.2 Omitting the time subscript for simplicity, the budget constraint becomes: 2

These add to insurance costs and fiscal burden, such as property taxes.

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Fig. 3 House prices and business cycles in Italy (Source: Authors’ own computations based on data from Istat and Bank of Italy. Index 2005=100)

C + p(R + δ )WH = Y p + R(W FI0 + pW H0 ) where C is non-housing consumption, p is the relative price of housing compared to a non-housing basket of goods, R is the real interest rate and δ is the depreciation rate, Y p is a measure of permanent real income, W FI0 and W H0 are the initial endowments of financial and housing wealth. Thus p(R + δ )W H is the cost of housing services, with p(R + δ ) being the real user cost. The effect of a permanent increase in relative house prices on non-housing consumption is given by:

∂C = RW H0 − (R + δ )WH + (R + δ )ε W H = RW H − 0 − WH(R + δ )(1 + ε ) ∂p where ε is the elasticity of housing demand to its own price. Three transmission channels are at work: 1. a positive direct wealth effect, since housing endowment is now worth more: RW H0 ; 2. a negative income effect, due to higher costs of housing services: (R + ε )W H; 3. a positive substitution effect, depending on the own price elasticity of housing: (R + δ )ε W H. Extending consumer expenditure to include imputed consumption of housing services, namely CH = (R + δ )W H, the effect on total consumption CT = C + CH is given by: ∂ CT = RW H0 − (R + δ )WH ∂p

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with the substitution effect now collapsed compared with the previous result. It turns out that the size and sign of the residential wealth effect depend mostly on the following two factors: i) the accurate measurement of the cost of housing services. If consumption of housing services is imputed on the basis of the real cost (R + δ ), the housing wealth effect is likely to be negative on total consumption (CT ), turning positive on nonhousing consumption (C) since ε is plausibly lower but close to unity. If the real interest is instead omitted, the sign on total consumption would depend on (R − δ ), while confirming positive on non-housing consumption. In any case, however, this standard model predicts that housing wealth effects, proxied by R − δ (1 + ε ), would be lower than financial ones, proxied by R; ii) the rate of home ownership, as proxied by the distance between W H and W H0 . In fact, while a positive shock to financial wealth has no effect on consumption for households that do not own financial assets (apart from a possible impact on confidence climate and expected future income), a permanent increase in relative house prices may affect both renters’ and owners’ optimal choice. Both would suffer from a negative income effect, but for owners this would be somewhat offset by a positive wealth effect. At the aggregate level, the balance between the two conflicting impacts is thus expected to turn positive to the extent that the rate of home ownership increases over time. A third factor, though not modelled in the framework above, refers to differences in the processes that generate prices of financial and housing assets. Indeed, available international evidence points to much less volatility in the latter, with signs of stronger serial correlation (Leamer, 2007; OECD, 2005). This implies that, given an observed common shock in both asset prices, households may assign a greater importance to the higher permanent component for housing than for financial net worth. The argument would dampen the gap between the effects on consumption from the two different components, otherwise expected in a life cycle approach. Finally, there is another important feature by which wealth effects may differ, namely that dwelling purchases are usually highly leveraged and imply transaction costs, related to the indivisibility and uncertainty regarding the true asset value which are much higher than for investments in financial stocks. As testified by the current debate about the housing finance revolution, this raises important implications for consumer spending that are missed by the standard theory, due to its simplifying assumption of complete capital markets. When information asymmetries are considered, the size of housing wealth effects proves to be increasing with the rate of innovation in mortgages and, more generally, with financial liberalization. As it is stressed in Mishkin (2007) and Muellbauer (2007), in the long run the main reason is that well developed financial markets make housing wealth very liquid, with two important implications: i) reducing the negative income effects on poten-

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tial first buyers, especially when young, as far as the requirement for down-payment is relaxed and the savings to be channelled in a housing deposit shrink; ii) increasing wealth effects of owners, as far as they are available to downsize their dwellings, especially when old, without incurring high transaction costs. An additional effect, the equity withdrawal from housing or the supply of higher loans to households due to an increased value in collateral, is likely to play a minor role in the long run, when consumption remains anchored to the fundamental of total resources the households command, net of fiscal and financial costs. Anyway equity withdrawal might play an important role in the short run, since it increases the ability of households, otherwise credit constrained under asymmetric information, to smooth consumption over time. In summary, the predictions of the standard life cycle model extended to include the main features by which housing and financial wealth may differ implies that the first may exert a lower effect on long run consumption under complete capital markets; the effect would become larger as the rate of home ownership increases and, under a more realistic world of asymmetric information, as financial liberalization deepens. This helps explain why housing wealth effects may differ across countries and why they outperform financial assets where the housing finance revolution has proceeded most. These predictions have recently been subject to increasing criticism as to the significance of the wealth effect itself when the adjustment of stocks is made endogenous too, or when we move from a partial to a general equilibrium analysis (Lettau and Ludvingson, 2004). At the same time, wealth might only exert an indirect effect, for example when a strong stock market performance proves to be a leading indicator of better general economic perspectives, which drive up both asset prices and households’ expenditure.3 These arguments enrich the reasons for ambiguities in the theoretical analysis of wealth effects, which are passed to the validation of empirical tests.

4 Empirical evidence: an overview for Italy We might think that on balance theoretical literature suggests that the wealth effect plays some role in affecting consumption but it is not precise enough to point to either the size of the overall effect or the relative impact of housing versus financial wealth. Many efforts have thus been made on the empirical side within a large variety of countries, starting from the first macro-estimate for the US economy during the sixties. At the applied level results do not deliver a sound solution either, as 3

Further criticism points to non-linearities in the utility function and different mental accounts that may limit the willingness to spend out of saving accumulated for specific reasons, such as long term retirement or bequest motives. For a survey of main recent contributions on these issues, see Ludwig and Sløk (2002) and Belsky and Prakken (2004).

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evidence proves dependent on the estimation strategy, such as variable choice and measurement, the time period covered, the statistical model, the kind of data, the within or cross country approach. Among the main controversies, the recent debates have increasingly focused on the role of the different components of wealth, since the wave of innovation in housing finance seems to have made the link between booming house prices and consumer spending more uncertain and country-specific. Overall, it seems that housing wealth plays quite a strong role in the US, with the marginal propensity to consume (MPC) ranging between 5 and 10 cents out of a one dollar increase in dwellings against 3 to 6 cents for financial stock (Case, Quigley and Shiller, 2005, Carroll, Otsuka and Slacalek, 2006; CBO, 2007). For the rest of industrial countries evidence is more mixed (Altissimo et al., 2005), with results for continental Europe broadly pointing to a more active role for financial assets than housing wealth in the long run (Ludwig and Sløk, 2002). When focusing on the Italian economy, there is not a long empirical tradition regarding the consumption effect of financial versus housing wealth. In a cointegration analysis covering the long sample between 1951 and 1992 and controlling for pension wealth, Rossi and Visco (1995) finds the MPC out of financial and real wealth as a whole at around 3 cents in the long run. Updated evidence, based on years up to 1998, shows that the same propensity has increased to around 5 cents in the long run, against a lower MPC for pension wealth (at around 2 cents) as important social security reforms in 1992 and 1995 added uncertainty about future benefits (Zollino, 2001). In a set of recent contributions, which confirm a size of total (non-pension) wealth effect of between 3 and 5 cents in the long run despite a shorter time period, financial assets prove to exert a stronger role than housing wealth on long run consumption. An exception is provided in Catte, Girouard and Price (2004), where evidence covering the period 1975-2002 points to MPC as small as 1 cent out of one euro increase in either financial or housing wealth. More generally the coefficient of the latter proves surprisingly negative, showing occasionally no statistical significance (Kennedy and Andersen, 1994). In a cointegration analysis covering the period 1980-1996, Girouard and Bl¨ondal (2001) found a negative MPC out of housing at around 3 cents in the long run, compared with the positive propensity of 5 cents estimated for financial assets. 4 By adopting the new methodology proposed by Carroll, Otsuka and Slacalek (2006) which is mainly base on estimated slugginess in aggregate consumption, Slacalek (2009) finds evidence for Italy of a particularly strong MPC out of financial assets, at around 10 cents or the second highest value among the main industrial countries; on the contrary, the propensity 4

By adopting the same data set, time period and methodology but a different deterministic control (in order to take account of main financial innovation events), Boone, Girouard and Wanner (2001) find a similarly negative propensity for housing, but a bit higher positive propensity for financial assets, at around 6 cents in the long run.

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for housing proves the lowest, resulting negative at 1 cent. At household level, based on repeated cross-sections retrieved from the Bank of Italy’s biannual Survey on Household Income and Wealth (SHIW) over the period 1991-2002, Guiso, Paiella and Visco (2005) estimate a marginal propensity to consume out of housing wealth of about 1.6 cents, which is barely one half of what they found for financial assets. By splitting the sample, they find that homeowner propensity to consume out of housing wealth is close to 3.5 cents, in line with evidence for US and UK, with signs of a negative effect on renters’ consumption. By adopting almost the same data set, in the full sample Paiella (2004) finds a somewhat lower MPC out of the housing wealth effect and a much higher one for the financial wealth; in the latter case, however, the coefficient risks to be biased upward due to under-reporting on the part of the wealthiest. Grant and Peltonen (2005), based on the panel section in the SHIW over the period 1989-2002, found that the housing wealth effect on consumption is not statistically significant, with a MPC size far lower in comparison with the value of 5-6 cents estimated for financial wealth.

5 The modelling framework We restate the intertemporal budget constraint of a representative consumer according to the formulation given by Campbell and Mankiw (1989): Wt+1 = (1 + RW,t+1)(Wt − CTt )

(1)

where CTt is total consumption and Wt is total wealth, made of the human (HUt ) and non-human (At ) components; RW,t is the net return on aggregate wealth. 5 Solving forward, log-linearizing and defining r ≡ log(1 + R) yields: 6 ctt − wt =

∞

∑ ρwj (rw,t+ j − ∆ ctt+ j )

(2)

j=1

which is a log-linear version of the infinite horizon budget constraint. 7 Extending the approach of Lettau and Ludvigson (2004), we then disaggregate non-human wealth into two different components, housing (W Ht ) and non-housing (W NHt ) wealth, yielding:8

5 Labour income does not appear explicitly because tradable human capital is included in aggregate wealth. 6 In the equations of this section we will always neglect the constant component of a linearization process. 7 rho ≡ 1 − exp(ct − w); where ct and w are at their steady state value. w 8 Lettau and Ludivigson’s main focus is just on human and non-human wealth.

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Wt = HUt + At = HUt + W NHt + W Ht

(3)

with non housing wealth given by the sum of financial (W FIt ) and valuables (WVAt ) net worth. Simple algebraic manipulation lead us to: wt ∼ = γhu + γwnh wnht + (1 − γhu − γwnh)wht

(4)

where γi is the steady state share of asset i in total wealth. Substituting in (2) gives: ct − γhu hut − γwnhwnht − (1 − γhu − γwnh)wht =

∞

∑ ρwj (rw,t+ j − ∆ ctt+ j )

(5)

j=1

The non observability of human capital hut prevents the empirical application of this equation. Once again, we follow Lettau and Ludvigson (2001) to face the issue and assume that income Yt is the annuity value of human wealth: Yt = R( h,t +1)HUt . Some additional manipulation leads to: (6)

hut = yt + zt

where zt is a mean zero stationary random variable. Substituting and taking expectations of both sides yields: ct − ωhu yt − ωwnhwnht − (1 − ωhu − ωwnh)wht = Et

∞

∑ ρwj (ϖt+ j − ∆ ctt+ j ) + ωhuzt

j=1

where

(7)

ϖt+ j = ωhu ruh,t+ j + ωwnh rwnh,t+ j + (1 − ωhu − ωwnh)rwh,t+ j

All the variables on the left hand side of equation (7) are now observable. Moreover, if we assume that those on the right hand side are stationary, then consumption, income, housing and non-housing wealth should be tied together by some cointegrating relation, upon which we next concentrate in the empirics of the second part of the paper.

6 Data and preliminary analysis In this section we briefly describe the dataset and the definition of variables, then we summarize the results of a preliminary analysis and the kind of deterministic control we consider in the VECM estimation.

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6.1 The dataset The empirical analysis focuses on the time range 1980q1-2008q4 exploiting several data sources. Total households’consumption (CTt ) is readily available from quarterly national accounts and includes spending on non durables, durables and services. Households’gross disposable income is published within national statistics only at annual frequency; in this paper we resort to a quarterly disaggregation of this series (Yt ) which is regularly estimated by the Bank of Italy. Households’ wealth is taken from a new database provided by the Bank of Italy whose aggregate series are employed for the first time in this paper.9 The new housing wealth series (W Ht ) are at annual frequency and span from 1990 onwards. Consistently with the methodology that led to their estimation, we extend the data backwards exploiting, for the decade 1980-1989, the dynamics of time series on new dwellings and on house prices.10 Once yearly data span the whole sample, quarterly disaggregation is achieved through the dynamics of residential investment published in national accounts. Wealth effects will be estimated also for a measure of housing assets net of mortgages W H At . Official data for net financial wealth (W FIt ) are supplied within financial accounts from 1995 onwards; backward estimation is obtained resorting to older versions of the same data, although conformed to previous accounting standards. When W H At is used; the value of financial assets is corrected accordingly (i.e. gross of mortgage debt; W FI At ). The stock of valuables (WVAt ) is evaluated on the basis of information gathered within the Survey of Household Income and Wealth (SHIW) run by the Bank of Italy; annual data are disaggregated at quarterly frequency through linear interpolation. Finally, interest rates (Rt ) are given by the returns on Treasury bonds with maturity longer than one year and deflated according to expected inflation, and public consumption (CCt ) is directly available from quarterly national accounts.

9

For details, Bank of Italy (2008). For details, see Bassanetti and Zollino (2008). Data on new dwellings are provided by Cresme which is a research institute focused on the Italian construction industry; house prices for the eighties are estimated based on new dwellings in provincial capitals (Muzzicato, Sabbatini and Zollino, 2008). 10

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6.2 Preliminary analysis As reported at the end of section 4, equation (7) suggests the possible existence of a cointegrating relation among consumption, income, housing and non housing wealth. According to a variety of tests, we find evidence in favour of a single unit root in the data generating processes of each of these variables (see Appendix I). We also applied the same tests to the proxy of the expected flow of real interest, namely Rt , and the hypothesis of a unit root cannot be rejected.11 We have done so also for real public consumption (CCt ), with similar findings. The latter results allow us to explore the possibility of testing if Rt and/or CCt may play as common exogenous drivers for the long-run equilibrium.12 Before estimating a VECM and testing the existence of cointegration, it is important to consider the consequences of two major economic events that happened within the sample period. In 1992-93 the Italian economy witnessed a severe currency crisis and a deep recession, with GDP falling for six quarters in a row. Following a 4.3 percent drop in 1993 as a whole, households’ real disposable income took some six years to recover to the same level as before the recession. The slump was initially less dramatic for consumer spending, that during the nineties recovered more rapidly from the annual 3.1% fall of 1993; in the following years households’ expenditure tracked very closely income developments (Figure 4). The deep nature of these effects put under pressures the productive and institutional setting of our economy as a whole, calling for urgent and permanent revisions in key fields of economic policies; they were actually implemented as for restrictions in social security provisions and public employment, plausibly curbing permanent income on the side of Italian households (Miniaci and Weber, 1999). The second event happened some years later when, after significant fiscal effort achieved in 1997 and 1998 to meet the convergence requirements, Italy joined the single currency area. The institutional changes that followed, including new exchange rates and monetary policy regimes, plausibly represent a permanent innovation in the data generating processes. In particular, the mortgage interest rate almost halved between 1997 and 1999, thus easing the access to the credit market for consumers and giving a huge support to house transactions (Figure 5). For these reasons we have considered two dummy variables in 1992q3 and 1999q1, restricted to lying in the cointegrating relationship to control for the possi11

The nominal interest rate Rt has been turned into real terms through a measure of inflation expectations. Results do not change if relative prices are computed with the households’ consumption deflator. As discussed in the text, our aim is not to test the stationarity of variables on the right hand side of equation (7), namely the weighted average return on different kind of wealth, whose calculation is much more cumbersome. 12 We also tested the effects of other forcing variables, such as public consumption and changes in the unemployment rate, with the cointegration analysis remaining broadly unchanged, though with a worse diagnostic check.

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Fig. 4 Italian households disposable income and consumption (Sources: Authors’ own computations based on data from Istat and Bank of Italy. Index 1980=100; chain linked values.)

Fig. 5 House transactions and costs of mortgages in Italy(Sources: Authors’ own computations based on data from Istat, Bank of Italy and Agenzia del Territorio.)

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bility of level shift in the long-run equilibrium; as reported in the next section, we have found that only the second one shows statistical significance while unrestricted intervention dummy variables better control for the unprecedented policy changes at the beginning of the nineties.13 Alternatively, we have tested the effects of two forcing variables, namely public consumption and real interest rate, which we think better summarize the economic changes driving level shifts in cointegrating relation; confirming the first evidence about the pivotal effect of the monetary union, we found a significant role for the interest rate only.

7 Econometric results ′

We estimate the VECM ∆ Xt = µ + αβ Xt−1 + ∑k Γk ∆ Xt−k + εt for the vector Xt = (ctt , yt , wht , wnht , rt )′ , where variables are in real terms and lower case letters indicate logs; non housing wealth is W NHt = W FIt + WVAt . In the first instance, we do not introduce any deterministic control in the VAR, whose length has been set equal to five.14

7.1 Rank of cointegration Results for the rank test are reported in Table 1 1; standard critical values appear alongside those to be considered when including the Bartlett correction in the statistics, in order to take into account the relatively small dimension of our sample. The hypothesis of one cointegrating relation (r = 1) and four common trends (n − r = 4) is accepted; the diagnostics of the system do not reveal major specification problems, apart from some violation of the normality assumption that will be easily fixed with the introduction of the unrestricted dummies mentioned previously. The choice r = 1 is robust across different VAR length specifications and independent from the presence of outlier controls; the same rank is assigned also when 13

Indeed in a preliminary version of the paper, that covered the period only up to 2006 we found statistical significance also for the 1992q3 dummy in the cointegrating relation (Bassanetti-Zollino, 2008); revisions in data and a larger time horizon have plausibly added momentum to the effects of the monetary union, making more difficult a clear identification of the sole fiscal regime shift we dated at the beginning of the nineties. 14 Information criteria pointed to a slightly more parsimonious specification, but we preferred to maintain a richer dynamic structure. The main results presented in the following of the section do not depend on the order of the VAR. Details of the lag length determination procedure are available on request.

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Table 1 Cointegration trace test Common trends Rank Trace test Trace test* Standard critical values n−r r 5 4 3 2 1

0 1 2 3 4

84.208 44.406 21.485 8.6 2.183

70.808 37.441 17.033 6.849 1.8

p-value 0.002 0.101 0.338 0.411 0.14

p-value* 0.04 0.331 0.646 0.601 0.18

Note. Critical values refer to a model with an unrestricted constant term. (*) Bartlett corrected statistics.

the system is reduced to contain a single measure of total wealth (wtott ), instead of the two distinct forms wht and wnht . Some evidence in favour of r = 2 arises when we introduce the deterministic control for the two candidate level shifts, mainly depending on the precise timing at which we date the effect of the 1992 recession. Nonetheless, considering the overall outcomes and the economic a priori based on our theoretical set-up, we set the rank r = 1.15 16

7.2 Long run relationships In the upper panel of Table 2 we report the estimates of the cointegrating vector β for the different model specifications obtained controlling for deterministic shift in 1999q1. Results were always statistically different from introducing a dummy variable controlling for the fiscal policy changes since the early nineties. Interestingly, as we comment later on, the statistical significance of deterministic control vanishes at all when we consider the interest rate as a forcing variable. Overall, estimates look statistically significant and economically plausible both in terms of sign and magnitude; further they are quite robust across different VAR specifications. Forward and backward recursive tests do not reject the hypothesis of 15

Results are available on request. Simulated critical values have been considered with standard ones, in order to take into account the dependency of asymptotic distribution on deterministic components, in particular on structural breaks. The CATS software, which was used for estimations, includes procedures both for simulating critical values for non standard models and for applying the Bartlett small sample correction. 16 The choice seems corroborated by inspecting the graph of the second possible cointegrating relation, which exhibits signs of persistency and thus suggests that the equilibrium error might be non-stationary. Further, the recursively calculated trace test for r = 2 lies under the 5% critical value for most of the sample.

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constancy over the time range under analysis (Appendix II). While the cointegrating relationship summarizes the correlation between the permanent movements in consumption, income and wealth over the sample period, the empirical literature often interprets the estimated parameters in terms of elasticities or MPC. As in Lettau and Ludvigson (2004), this is a reasonable practice as they come out from a regression of consumption on wealth, controlling for income and real interest rates. The estimated parameters are also super-consistent and thus robust to regressors endogeneity. Based on our estimates of the cointegrating vector, one percentage point increase in housing (wht ) and non housing (wnht ) wealth would be associated with an increase of, respectively, 0.08 and 0.11 percentage points in total consumer spending (column C in Table 2). These elasticities remain statistically unchanged when we correct for mortgage debts in both kinds of wealth (column E). In terms of marginal propensity to consume, the outcomes state that a one euro rise in housing and non housing wealth would be associated with an increase of about, respectively, 2 and 4 cents in consumption.17 If we concentrate on a single measure of total net worth (wtott ; column A), the elasticity of consumption amounts to 0.17 and the marginal propensity to consume to 2.6 cents for a one euro wealth increase. Finally the MPC out of disposable income is in the order of 70 cents. It is worth noting that these results are confirmed when we test for common external drivers leading the system of variables we considered, implying evidence in favour of a direct wealth effect. In this regard, in Table 2 we report estimates obtained by controlling for changes in the long-term real interest rate. This variable proves to be weakly exogenous under the different specifications we tested, and leaves the cointegrating vector substantially unchanged and largely significant. 18 Additionally, we tested for the role of real public consumption as a proxy for fiscal discipline: like Rt , CCt proves weakly exogenous to our cointegrating system. Moreover, comparison of columns E and F shows that when the two variables are jointly modelled as common drivers, the case for deterministic controls drops. The result delivers an interesting economic content of the two regime switches that statistically show up in the dummies 1999q3 and 1998q1. On one side, the stringent curbing of public deficit over the nineties may have provided support to the households’ spending plans in the long run much in line with a Ricardian neutrality mechanism; on the other, the fall in real long-term yields was presumably perceived by households as permanent too, and this contributed to shift their plans from saving to consumption. According to this specification, the marginal propensity to consume amounts to about 60 cents out of one euro increase in income, and about 6 and 1.5 17 Marginal propensities are obtained by dividing the elasticities by the average ratio of the corresponding variable to consumption over the full sample period. 18 Weak exogeneity implies that the interest rate enters the cointegrating vector, but it does not contribute to the correction towards the long run equilibrium (namely, the loading coefficient αr is not statistically different from zero). It also turns out that the coefficient in the cointegrating vector is not significant, as shown in the table.

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Table 2 Cointegration coefficients Model specification (A)

(B)

(C)

(D)

(E)

(F)

Cointegration coefficents (β - vectors) Total wealth (wtott )

-0.187 (-6.0)

Housing wealth (wht )

-0.166 (-5.3) -0.076 (-3.896) -0.109 (-2.680)

Non housing wealth (wnht )

-0.074 (-4.056) -0.118 (-2.937)

Housing wealth net of mortgages (wh at )

-0.076 -0.047 (-3.723) (-3.879)

Non housing wealth gross of mortgages (wnh at ) Disposable income (yt )

-0.94 -0.791 -0.845 (-10.7) (-9.2) (-8.067) Interest rate (rt ) 0.031 (2.9) Deterministic control 1999q1 -0.033 -0.044 (-2.9) (-3.803)

-0.871 (-8.046) 0.009 (-0.901) -0.05 (-3.654)

-0.093 (-2.004) -0.959 (-7.929) 0.014 (-1.211) -0.058 (-3.781)

-0.191 (-8.463) -0.755 (-9.008) 0.045 (6.162)

Error correction loading (α ) Total consumption (ctt ) Total wealth (wtott ) Housing wealth (wht ) Non housing wealth (wnht ) Housing wealth net of mortgages (wh at ) Non housing wealth gross of mortgages (wnh at ) Disposable income (yt )

0.033 (-1.19) 0.38 (-4.009)

0.054 0.028 0.02 0.03 -0.16 (-2.283) (-0.84) (-0.567) (-0.968) (-2.427) 0.265 (-3.343) 0.641 0.57 (-4.355) (-3.681) 0.176 0.216 (-1.172) (-1.374) 0.482 0.774 (-3.426) (-3.064)

0.171 -1.288 0.206 0.178 0.26 0.285 0.255 (-6.774) (-6.848) (-6.731) (-6.993) (-7.157)

-0.091 (-0.339) 0.308 (-4.055)

Note. Values normalized on the coefficient of total consumption c: t. t-statistics in parenthesis.

cents out of similar changes in financial and housing wealth, respectively. 19 19

If pension wealth is included in the cointegrating system, its impact on consumption is negligible in the considered period, contrary to the positive effect found over a much longer time horizon (Zollino, 2001). It appears that the repeated changes in social security rules since 1992 have made benefits and retirement dates more uncertain, reducing the responsiveness of consumption plans to pension wealth.

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7.3 Equilibrium correction In the upper panel of Table 2 we report the coefficients α = (αct , αy , αwh , αwnh )′ of the error correction term β ′ Xt−1 that give a measure of the reaction of each variable, at time t, to the disequilibrium of the system in period t − 1. Consumption smoothness is confirmed by the fact that αct is not statistically significant; it turns out that the adjustment process towards the long-run equilibrium is mainly achieved via housing wealth, while non-housing net worth does not show significant error correction movements. This comes as no surprise, given the widespread diffusion of house ownership among Italian households, as shown by the particularly high rate of home ownership. Also disposable income contributes to smooth household spending, although to a much lesser extent.

8 Permanent - transitory decomposition The cointegrating coefficients of the previous section are based on the existence of a common trend that ties together the long run movements of consumption, income and wealth. Thus, as already noted, they reveal the degree of correlation among the permanent components of the variables in the system, whereas they are completely useless for inference regarding the relationship between consumption and transitory changes in income and wealth. If a large degree of quarterly fluctuations of income and wealth was to be actually due to transitory events, then cointegrating coefficients would be poorly informative about their relation with households spending and should be cautiously interpreted. Consequently, as suggested by Lettau and Ludvigson (2004), once we have determined the long run correlation among the variables in the system, we need to assess whether there exist (transitory) movements in income and wealth unassociated to (permanent) changes in consumption. We apply to our system Xt of I(1) variables the econometric framework proetP ) and transitory ( η etT ) posed by Gonzalo and Ng (2001) to isolate the permanent (η shocks, as defined by the following two conditions: limh→∞

∂ Et (Xt+1 ) etP′ ∂η

6= 0 and limh→∞

∂ Et (Xt+1 ) etT ′ ∂η

=0

Hinging on Gonzalo and Granger (1995), it can be shown that these shocks can be readily recovered with a two step procedure exploiting the information available in the VECM.

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Starting from the multivariate moving average representation ∆ Xt = δ +C(L)et ,20 in the first step the vector ut of unorthogonalized permanent and transitory shocks is given by the following simple transformation of innovations (residuals) et : ut = where



utP utT

α⊥′ α

(n−r)×1 r×1

=



  ′ r×n α⊥ α⊥′ et = Ge with G = ′ t β ′ et β (n−r)×n

= 0.

et is achieved exploiting the Choleski deIn the second step, orthogonality of η 21 composition of cov(u):   E ut uti = HH −1 et = H −1 ut η

We end up, therefore, with the Wold representation: e η et ∆ Xt = δ + C(L)et = δ + C(L)G−1 HH −1 Get = δ + D(L)HH −1 ut = δ + D(L) that allows one to bring back the growth of each variable in the system to a function of the permanent and transitory shocks. Specifically, on the basis of our results, a cointegration rank equal to one implies the existence of three common stochastic trends (permanent shocks) and one transitory innovation. Gonzalo and Ng’s decomposition enables the assessment of their role in the movements of consumption, disposable income, housing and non-housing wealth. For brevity, in Table 3 we concentrate on a system with deterministic controls and report the share of the variance in the h-step forecast error attributable to the two kinds of shock. 22 In the top panel, we used the estimates discussed in the previous section; in the bottom part, the statistically insignificant error correction coefficients, αc and αwnh , have been set to zero, as suggested by Gonzalo and Ng. In both cases the three permanent shocks dominate the variance of consumption growth; this implies, in accordance with the prediction of the life-cycle model, that 20

C(L) is a distributed lag opetator and et is a (nxI) vector with E(et ) and E [et es ] = 0 i f t 6= Ω otherwise. 21 Gonzalo and Ng (2001) outline that the Choleski decomposition is one of the many available et alternatives for choosing H, which need to be lower block triangular. As a consequence, the η we found are not unique. Further, the Choleski decomposition, although being quite convenient, entails that the order matters; however it can be easily shown that in this setting a variable Xi, j can e Pj,t even if j > i, thus mitigating the effects of the recursive structure of the system. react to η 22 See the system in column C, Table 2. s;

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Table 3 Forecast error variance decomposition - disaggregated wealth

∆ ctt+h − Et ∆ ctt+h ∆ yt+h − Et ∆ yt+h ∆ wht+h − Et ∆ wht+h ∆ wnht+h − Et ∆ wnht+h Horizon Perm.

Trans.

Perm.

Trans.

Perm.

Trans.

Perm.

Trans.

0 .978 0 .985 0 .989 0 .992 0 .993 0 .995 0 .995 0 .996 0 .996 0 .997 0 .997 0 .997 0 .999 0 .999

0 .022 0 .015 0 .011 0 .008 0 .007 0 .005 0 .005 0 .004 0 .004 0 .003 0 .003 0 .003 0 .001 0 .001

1 1 0.996 0.995 0.996 0.996 0.996 0.997 0.997 0.997 0.998 0.998 0.999 0.999

0 0 0.004 0.005 0.004 0.004 0.004 0.003 0.003 0.003 0.002 0.002 0.001 0.001

Setting ac and ae to their estimated values 1 2 3 4 5 6 7 8 9 10 11 12 24 36

0 .988 0 .983 0 .983 0 .987 0 .99 0 .993 0 .994 0 .995 0 .996 0 .996 0 .997 0 .997 0 .999 0 .999

0 .012 0 .017 0 .017 0 .013 0 .01 0 .007 0 .006 0 .005 0 .004 0 .004 0 .003 0 .003 0 .001 0 .001

0 .275 0 .359 0 .388 0 .451 0 .518 0 .594 0 .666 0 .727 0 .777 0 .816 0 .846 0 .869 0 .958 0 .975

0 .725 0 .641 0 .612 0 .549 0 .482 0 .406 0 .334 0 .273 0 .223 0 .184 0 .154 0 .131 0 .044 0 .025

0 .696 0 .778 0 .855 0 .896 0 .921 0 .936 0 .947 0 .954 0 .96 0 .964 0 .967 0 .97 0 .984 0 .989

0 .304 0 .222 0 .145 0 .104 0 .079 0 .064 0 .053 0 .046 0 .04 0 .036 0 .033 0 .03 0 .016 0 .011

Setting ac = a( wnh) = 0 1 2 3 4 5 6 7 8 9 10 11 12 24 36

1 0.999 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 1 1 1 1

0 0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0 0 0 0

0.331 0.429 0.449 0.503 0.561 0.628 0.691 0.746 0.79 0.825 0.852 0.873 0.956 0.973

0.669 0.571 0.551 0.497 0.439 0.372 0.309 0.254 0.21 0.175 0.148 0.127 0.044 0.027

0.704 0.775 0.848 0.89 0.917 0.934 0.945 0.953 0.959 0.964 0.967 0.97 0.985 0.99

0.296 0.225 0.152 0.11 0.083 0.066 0.055 0.047 0.041 0.036 0.033 0.03 0.015 0.01

Note. Orthogonalized VAR residuals. Shares might not sum to unity because of their rounding.

households’ spending responds exclusively to changes in the permanent component of wealth and income. Actually from Table 3 it emerges that permanent shocks are responsible for almost the entire variance in non-housing net worth of Italian households at all horizons, the picture being not much different for residential wealth, apart from the very etT is not negligible. Transitory innovation effects take time to first quarters when η elapse for disposable income, driving three fifths of its variability on the average of the first year and one fourth after eight quarters, with overwhelming permanent shocks in the longer run.

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Table 4 Forecast error variance decomposition - total wealth

∆ ctt+h − Et ∆ ctt+h ∆ yt+h − Et ∆ yt+h ∆ wtott+h − Et ∆ wtott+h Horizon Perm.

Trans.

Perm.

Trans.

Perm.

Trans.

Setting ac and ae to their estimated values 1 2 3 4 5 6 7 8 9 10 11 12 24 36

0.974 0.973 0.975 0.978 0.981 0.984 0.987 0.988 0.99 0.991 0.992 0.993 0.997 0.998

0.026 0.027 0.025 0.022 0.019 0.016 0.013 0.012 0.01 0.009 0.008 0.007 0.003 0.002

0.187 0.195 0.224 0.277 0.351 0.441 0.53 0.608 0.672 0.724 0.765 0.797 0.934 0.963

0.813 0.805 0.776 0.723 0.649 0.559 0.47 0.392 0.328 0.276 0.235 0.203 0.066 0.037

0.715 0.792 0.85 0.883 0.904 0.918 0.928 0.936 0.943 0.948 0.952 0.956 0.978 0.985

0.285 0.208 0.15 0.117 0.096 0.082 0.072 0.064 0.057 0.052 0.048 0.044 0.022 0.015

0.713 0.789 0.849 0.885 0.907 0.923 0.934 0.942 0.949 0.954 0.958 0.962 0.981 0.987

0.287 0.211 0.151 0.115 0.093 0.077 0.066 0.058 0.051 0.046 0.042 0.038 0.019 0.013

Setting ac = 0 1 2 3 4 5 6 7 8 9 10 11 12 24 36

1 0.999 0.997 0.996 0.997 0.997 0.997 0.998 0.998 0.998 0.998 0.998 0.999 1

0 0.001 0.003 0.004 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.001 0

0.207 0.235 0.259 0.319 0.397 0.488 0.574 0.646 0.703 0.748 0.783 0.811 0.932 0.959

0.793 0.765 0.741 0.681 0.603 0.512 0.426 0.354 0.297 0.252 0.217 0.189 0.068 0.041

Note. Orthogonalized VAR residuals. Shares might not sum to unity because of their rounding.

These overall features hold substantially true also when we focus on a single measure of total wealth, for which transitory innovation effects almost fully disappear after a few quarters (Table 4). It turns out that the cointegrating coefficients reported in Tables 2 and 3 are very informative as to the relation between Italian households’ spending and wealth, both their movements being soon dominated by the common trend they share. Some more caution should be used when reading the coefficient of income, whose reaction to transitory innovation is not trivial. Let’s consider, for instance, the average variance decomposition of the first eight quarters: since 51% of the

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movements in income are transitory, then only the remaining 49% will be associated with the marginal propensity to consume of 70 cents estimated in section 7.3. In the longer run, however, the overwhelming role played by permanent shocks confirms that we can consider the income MPC as actually informative. Decomposition results are broadly in line with those already available in the international applied literature, the major difference being the bigger role played by permanent innovations in the dynamics of Italian non-housing net worth. In particular, Lettau and Ludvigson (2004) find that in the US stock market wealth - just a component of the broader financial aggregate we used for Italy - is dominated by transitory shocks, which explain half of the variance of US financial assets also in Kundan Kishor (2006). According to Pichette and Tremblay (2003), this share declines to about 30 per cent for Canadian stock wealth. The heterogeneity of results can be brought back to the composition of Italian households’ financial wealth, in which money and deposits - presumably particularly sensitive to permanent shocks - have traditionally played a relevant role in families’ portfolios, while stocks have represented a minor share.

9 Conclusions Since the strong upsurge of real estate prices in the late nineties, renewed interest has emerged on the linkage between households’ consumption, income and wealth. More specifically, analysts and economists frequently ask questions about the significance and magnitude of the marginal propensities to consume out of financial and, above all, housing wealth. Despite the increasing interest, the aggregate evidence on this issue was virtually nil for the Italian economy. Based on fresh estimates on households’ wealth, we find sound evidence in favour of the existence of a cointegrating relation between consumer spending and different stock components, with a positive wealth effect in the long run. In the vein of Lettau and Ludvigson (2004), we enriched the research by investigating the role of transitory and permanent shocks in the variables considered. We found that consumption, housing and non housing wealth respond almost exclusively to permanent shocks; the same shocks play an overwhelming role also for disposable income over a long horizon, whereas in the short run the effects of transitory shocks are not negligible. As a result, we estimate a marginal propensity to consume out of housing and non housing wealth in the range of, respectively, 1.5-2 and 4-6 cents, which we may consider to closely match the true values in the long run equilibrium.

Acknowledgements We would like to thank the participants to seminars in the Bank of Italy, Universit`a di Torino and to the conference on Macroeconomics of Housing Markets organized by Banque de France, November 2009. The views expressed herein are those of the authors and do not necessarily reflect those of the Bank of Italy.

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References Altissimo, F., Georgiou, E., Sastre, T., Valderrama, M.T., Sterne, G., Stocker, M., Weth, M., Whelan, K. and A. Willman (2005), Wealth and Asset Price Effects on Economic Activity , European Central Bank, Occasional Paper Series, No. 29. Banca d’Italia (2008), Household wealth in Italy, Rome. Bassanetti, A., and Zollino, F. (2008), Appendix. Measuring the Annual Housing Wealth of Italian Households, in Banca d’Italia Household wealth in Italy, Rome. Belsky, E. and J. Prakken (2004), Housing Wealth Effects: Housing’s Impact on Wealth Accumulation, Wealth Distribution and Consumer Spending , Harvard University. Joint Center for Housing Studies, W04-13. Boone, L., Girouard, N. and I. Wanner (2001) Financial Market Liberalisation, Wealth and Consumption , OECD, Economic Department, Working Paper No. 308. Campbell, J.Y. and G. Mankiw (1989), Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence , in O. Blanchard and S. Fischer (eds.), NBER Macroeconomics Annual: 1989, Cambridge MA, MIT Press, 185-216. Carroll, C.D., Otsuka, M. and J. Slacalek (2006), How Large is the Housing Wealth Effect? A New Approach , NBER, Working Paper No. 12746. Case, K., Quigley, J. and R. Shiller (2005), Comparing Wealth Effects: The Stock Market Versus the Housing Market , Advances in Macroeconomics, 5, 1, 1. Catte, P., Girouard, N. and R. Price (2004), Housing Markets, Wealth and the Business Cycle , OECD,Economics Department Working Paper No. 394. Congressional Budget Office (2007), Housing Wealth and Consumer Spending, CBO Background Paper. Deaton, A. and J. Muellbauer (1980), Economics and Consumer Behavior, Cambridge, Cambridge University Press. Girouard, N. and S. Bl¨ondal (2001), House Prices and Economic Activity , OECD, Economics Department Working Paper No. 279. Gonzalo, J. and C. Granger (1995), Estimation of Common Long Memory Components in Cointegrated Systems , Journal of Business and Economic Statistics, 13, 27-35. Gonzalo, J. and S. Ng (2001), A Systematic Framework for Analyzing the Dynamic Effects of Permanent and Transitory Shocks , Journal of Economic Dynamics and Control, 25, 10, 15271546. Grant, C. and Peltonen, T. (2005) Housing and Equity Wealth Effects of Italian Households, DNB Working Paper No. 43. Guiso, L., Jappelli, T. and D. Terlizzese (1994) Why is Italy’s Saving Rate so high?, in A. Ando, L.Guiso and I. Visco (eds.), Savings and the Accumulation of Wealth. Essays on Italian Household and Government Saving Behaviour, Cambridge, Cambridge University Press. Guiso, L., Paiella, M. and I. Visco (2005), Do Capital Gains Affect Consumption? Estimates of Wealth Effects from Italian Households’ Behavior, Banca d’Italia, Temi di discussione, No. 555. IMF (2009), The World Economic Outlook, October Volume, Washington D.C. Kennedy, N. and P. Andersen (1994) Household Saving and Real House Prices: an International Perspective , BIS Working Paper No. 20. Kishor, N.K. (2006), Does Consumption Respond More to Housing Wealth Than to Financial Wealth? If So, Why? , Texas Tech University, mimeo. Leamer, E.E. (2007) Housing is the Business Cycle , NBER Working Paper No. 13428. Lettau, M. and S. Ludvigson (2001), Consumption, Aggregate Wealth and Expected Stock Returns , Journal of Finance, 56, 3, 815-849. Lettau, M. and S. Ludvigson (2004), Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption , American Economic Review, 94, 1, 276-299. Ludwig, A. and T. Sløk (2002), The Impact of Changes in Stock Prices and House Prices on Consumption in OECD Countries , IMF, Working Paper No, 02/1.

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Miniaci, R. and G. Weber (1999), The Italian Recession of 1993: Aggregate Implications of Microeconomic Evidence , Review of Economics and Statistics, 81, 2, 237-249. Mishkin, F.S. (2007), Housing and the Monetary Transmission Mechanism , Federal Reserve Board, Division of Research, Statistics and Monetary Affairs, Finance and Economics Discussion Series, No. 2007-40 Muellbauer, J. (2007), Housing, Credit and Consumer Expenditure , Federal Reserve Bank of Kansas City, Jackson Hole Symposium. OECD (2005), Economic Outlook, 2005/2, No. 78, Paris. Paiella, M. (2004), Does Wealth Affect Consumption? Evidence for Italy , Banca d’Italia, Temi di discussione, No. 510. Pichette, L. and D. Tremblay (2003), Are Wealth Effects Important for Canada? , Bank of Canada, Working Paper No. 2003-30. Poterba, J.M. (1984), Tax Subsidies to Owner-Occupied Housing: an Asset Market Approach , Quarterly Journal of Economics, 99, 729-745. Rossi, N. and I. Visco (1995), National Saving and Social Security in Italy , Ricerche Economiche, 49, 4, 329-356. Slacalek, J. (2009), What Drives Personal Consumption? The Role of Housing and Financial Wealth , The BE Journal of Macroeconomics 9,1, 37. Zollino, F. (2001), Personal Saving and Social Security in Italy: Fresh Evidence from a Time Series Analysis , Banca d’Italia, Temi di discussione, No. 417.

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Appendix I - Unit root test results

Table 5 Unit root test results

Levels 1st differences

Levels 1st differences

Levels 1st differences Levels 1st differences

Non Housing housing Non wealth net wealth Total Housing housing of gross of Total Disposable consumption wealth wealth mortgages mortgages wealth income (ct ) (wht ) (wnht ) (wh at ) (wnh at ) (wtott ) (yt ) Augmented Dickey-Fuller Test - H0 : series with unit root -1.800* -0.638* -1.344* 0.095* -1.176* -1.489* -1.7818* (0.38) (0.86) (0.61) (0.96) (0.68) (0.536) (0.39) -3.560 -4.13 -9.023 -0.348 -8.689 -6.410 -3.773 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.000) Phillips.Perron Test - H0 : series with unit root -1.456* -1.297* -1.322* -1.435* -1.149* -1.302* -3.763 (0.55) (0.63) (0.62) (0.56) (0.69) (0.63) (0.004) -7.09 -5.232 -9.547 -5.310 -9.485 -6.51 -7.489 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) ERS1 - H0 : series with unit root 1045* 57.47* 351.7* 52.49* 407.0* 477.0* 454.2* 1.35 2.16 0.49 2.17 0.49 1.02 2.69 KPSS2 - H0 : series stationary 1.142 1.065 1.141 1.045 1.148 1.171 0.982 0.239* 0.072* 0.20* 0.07* 0.16* 0.10* 0.61

Interest rate (rt ) -0.958* (0.77) -5.99 (0.00) -0.798* (0.82) -6.05 (0.00) 122.40* 0.68 1.142 0.086*

Note. Variables in logs and real terms. When reported, p-values in brakets. (*) H0 accepted at 95% confidence level. (1) Elliot, Rothenberg and Stock point optimal test. (2) Kwiatkowski, Phillips, Schmidt and Shin test.

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Appendix II - Recursive tests of parameter constancy The recursive tests are based on the concentrated version of the VECM: R0,t= αβ ′ R1,t + vt is the cointegrating vector, α contains the loadings of the EC term and the rank of cointegration is set equal to one. 23 The advantage of this approach is that it averages out the short-run structure of the VECM, leaving the sole adjustment towards the long-run equilibrium. It is precisely on the parameters involved by this equilibrium (i.e. α and β ) that we focus the testing procedure. We run both forward and backward recursive estimations in order to test the parameters constancy at the end and at the beginning of the sample. As for forward recursions, the baseline sample we chose is 1980q1-1990q1, whereas for the backward exercise it is 1998q4-2006q4.

Fig. 6 Test for constancy of the log-likelihood; H0 : constant parameters

Statistic scaled by the 95% quantile of the appropriate asymptotic distribution:a value below 1 implies acceptance of H0 The concentrated version is obtained starting from the VECM ∆ Xt = αβ ′ Xt−1 + ∑k Γk Xt−k + Φ Dt + εt and rewriting it more compactly: Z0,t= αβ ′ Z1,t +Ψ Z2,t + εt , with Z0,t= = ∆ Xt , Z1,t = Xt−1 , Z2,t = [∆ Xt−1 , ∆ Xt−2 , ..., ∆ Xt−k, Dt ] and Ψ = [Γ1 , Γ2 , ..., Γk , Φ ]. Then define the auxiliary regres−1 −1 and B′2 = M1,2 M22 , sions: Z0,t= = B′1 Z2,t + R0,t and Z1,t = B′2 Z2,t + R1,t , with B′1 = M0,2 M22 ′ Mi, j = ∑t (Zi,t Z j,t )/T . It follows that the concentrated model is R0,t= αβ R1,t + vt 23

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Fig. 7 Recursively calculated eigenvalue λ

Dotted lines correspond to the 95% confidence bands.

Fig. 8 Eigenvalue fluctuation test. H0 : constant eigenvalue λ

Statistic scaled by the 95% quantile of the appropriate asymptotic distribution: a value below 1 implies acceptance of H0 . This test checks for constancy of α and β .

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Fig. 9 Test for β constancy. H0 : constant cointegration coefficents

Statistic scaled by the 95% quantile of the appropriate asymptotic distribution: value below 1 implies acceptance of H0 .

Housing and Portfolio Choices in France Luc Arrondel and Fr´ed´erique Savignac

Abstract In this paper, we focus on the interactions between housing wealth and the composition of households’ financial portfolio. We use a very survey among French households (Enquˆete Patrimoine, Insee) to describe the composition of housing and financial wealth of French households. We estimate the main determinants of housing wealth (as primary, secondary residences as well as investments in real estate). We study the impact of the exposure to real estate risk on stock demand. We find that, besides information and transaction costs and risk aversion, housing wealth is a key determinant of stockownership: households facing real estate risk tend to moderate their investments in stocks. This behaviour, called ”temperance”, may thus contribute to explain why people own so few stocks, in particular in France (stock participation puzzle).

JEL codes : D91, G11, R22, E21 Keywords : Portfolio choice, background risks, housing demand, life-cycle model

1 Introduction The recent financial crisis sheds light on the interactions between housing and financial markets. In France, households faced a decrease of 40% in stock market prices, of 7% in housing price (see Figure 1 below) and simultaneously overindebtedness impacted an increasing number of households (+16% between January 2009 and March 2009, according to the Secretariat of the Household Debt CommisL. Arrondel CNRS-PSE and Banque de France, e-mail: [email protected] F. Savignac Banque de France, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_15, © Springer-Verlag Berlin Heidelberg 2010

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sions (Banque de France). However, most of the empirical literature about portfolio choices does not take into account simultaneously housing and financial wealth. In this chapter, we propose to study the interactions between the composition of financial portfolios and the exposure to real estate risk. Housing is the main assets in households’ portfolios. In France, 55% of households own their main residence and housing wealth represents more than 50% of their wealth. Housing wealth differs in various characteristics from the financial components of households’ portfolios. First, it is relatively indivisible and illiquid. Transaction costs are very high in time and in money, even when selling. Imperfections in the housing credit market, institutional constraints, uncertainty about quality, and the fact that every unit is unique can explain these transaction costs. Second, households’ decisions about housing are the result of a dual behavior that more concerns durable goods: as a generator of housing services, housing satisfies consumption needs; as an asset, housing is taken into consideration in investment decisions. Finally, housing contributes to portfolio risks. This ”housing risk” can also be reinforced by the fact that real estate goods are often acquired by highly leveraging. Due to these specificities, housing can constrain households to rebalance their financial portfolio. Thus, to understand households financial behaviour, it seems crucial to consider the interactions between housing and financial wealth at the households’ level. The households financial behaviour (wealth accumulation, portfolio diversification, real estate investments etc.) varies a lot within the population and may also be particularly impacted in the current context characterized by economic and financial difficulties, aging of the population and high uncertainty concerning the evolution of housing and financial prices. The portfolio choice literature shows that unavoidable risks (background risks) such as unemployment risk, uncertainty about future incomes or exposure to real estate risk may lead households to moderate their global exposure to risk by reducing their investment in stocks (Kimball, 1993). This behaviour, called temperance, may then contribute to explain why so few people invest in stocks compared to the predictions of the standard portfolio literature. For example, only 20% of French households own financial risky assets (directly or indirectly via mutual funds) while Merton’s model predicts that households’ wealth is fully diversified. This low stockmarket participation is known as the stockholding puzzle (Haliassos and Bertaut, 1995; Haliassos, 2003). It is also related to the equity premium puzzle (Mehra and Prescott, 1985) that points out that the observed longterm difference in expected returns between equity and bonds requires implausibly high risk aversion by investors. Our analysis aims at contributing to the empirical literature about this stockholding puzzle by focusing on the role that housing risk can have on financial portfolio decisions. We rely on high quality data on households (Enquˆete Patrimoine, 2004) so that we are able to account for risk aversion as well as various background risks faced by households (housing, job market, business risk, health). This chapter is organized as follows: the French households’ portfolio composition as well as the determinants of homeownership and stockholding are presented in section 2. Then we provide an empirical analysis of the impact of the exposure to real estate risk on stockholding in section 3, and we conclude in section 4.

Housing and Portfolio Choices in France 7000

339

CAC40

Housing Price

6000

250

200

5000 150 4000 100 3000 50

2000

0 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09

19 96 19 97 19 98 19 99 20 00

1000

Fig. 1 Evolution of stock prices index (CAC40) and the housing price index in France (Source: Insee)

2 Households’ portfolios in France In this section, we rely on the French wealth survey (Insee, Enquˆete Patrimoine 2004) to give a picture of the composition of housing and financial portfolios at the household level in France.

2.1 Data This descriptive analysis relies on the wealth survey conducted by the French National Statistical Institute (Insee) every 6 years. This survey named “Enquˆete Patrimoine” is a cross-section. We use the latest available wave (2004) run on a nationally representative sample of 9,692 households, for whom detailed information on wealth is available. In particular, it provides: - detailed information on the socioeconomic and demographic situation of the household (education, occupational group, marital status, information concerning the children...), as well as on the biographical and professional evolutions of each husband and wife (youth, career, unemployment or other interruptions of professional activity); - detailed data on household’s income, on the amount and the composition of wealth (including liabilities and professional assets); - brief information on the inter-generational transfers received and bequeathed (financial helping out, gifts and inheritance) and more generally on the ”history” of household’s wealth.

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2.2 Portfolio composition The households’ portfolio composition in France is reported in Table 1. On average, households’ wealth amounts to 172,500 euros in 2004. Residential housing is the most widespread type of assets (after saving and current accounts held by the quasitotality of households in France) and it represents 54.9% of total wealth. About 58% of households own residential housing and 55% are owner of their main residence. This homeownership rate is lower than in other countries : more than 80% in Spain, 69% in Italy, and about 68% in the U.S, according to Bover (2005). Table 1 Households’ portfolio composition in France (Source: Patrimoine 2004, Insee) Asset classification

Proportion holding Mean asset Percentage the asset (%) holding (e) of total wealth Saving & current accounts 99.4 13,600 7.9 Employer sponsored saving plan 16.7 1,350 0.8 Housing saving schemes 41.3 4,950 2.9 Life insurance 25.8 7,850 4.5 Annuities 11.6 1,593 0.9 Residential housing 57.8 94,650 54.9 Equities (shares, bonds, mutual funds) 25.8 6,650 3.8 Dwelling for renting out, investment in lands & business 18.4 26,674 11.2 asset (non exploited by the owner) Business asset (exploited by the owner) Other assets

16.9 5.8

21,250 1,300

12.3 0.8

Total

100.0

172,500

100.0

Equities represent about 3.8% of total wealth, only 15.4 % of households hold directly stocks (see Table 2): around 7 percent have listed shares, 1.4 percent hold non-listed shares and 10.2 percent own shares via a a stocks’ saving account (Plan d’´epargne en actions, PEA). The proportion of households with indirect stockholding -mainly through mutual funds- is around 6.7 percent. It follows that the upper bound of (direct or indirect) stock ownership in France is estimated to be around 20 percent of the population. The average amount invested in (direct) stocks is about 4,350 euros (28,000 euros among direct stockholders) and households invest on average 1,146 euros in mutual funds (65,600 euros among mutual funds owners). Compared to the U.S., stock market participation remains limited in France. For the same surveyed year (2004), using the Survey of Consumer Finances, Bucks et al. (2009) report that the fraction of households holding directly or indirectly publicly traded stocks is about 50% in the U.S. This lower participation in stock markets is more generally observed in Europe, except in Sweden and in the U.K. (See Guiso et al., 2003).

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Table 2 Households’ portfolio composition in France (Source: Patrimoine 2004, Insee) Ownership Average Average amount Amount by stockowner (%) (e) (e) Direct holding Stocks: - Listed stocks - Unlisted stocks - Listed or unlisted stocks via PEA

15.4 7.2 1.4 10.2

4,348 1,594 766 1,988

28,169 132,408 200,388 39,312

1,146

65,584

Indirect stockholding Mutual funds (excluding money market funds)

6.7

Concerning the evolution of stockownership along the life-cycle, one can notice the increase in the participation in stock markets until age 54 and the decrease after age 64 (see Graph 2). The proportion of owner-occupiers varies a lot according to age: very few young households own their main residence (about 20% of the 25-29 years old), then this rate increases until age 70. Our cross-section dataset does not allow us to disentangle the life-cycle effects from the generation effects behind this pattern. Indeed, the age effect can be due to heterogeneity in the access to credit market, a down-payment constraints for young households or to the size of family (and children’ age), etc., while at the same time, each generation of households encounters specific economic conditions especially as regards employment, growth, credit conditions and housing policies for a given age. Table 3 reports some sample statistics calculated by age group for homeowners. As expected, we observe a decrease in both the ratios of house value and housing debt to net wealth with age. Before 40 years old, the ratio of housing to net worth is greater than one, reflecting the households’ leverage position (housing debt represents about 42% of households net wealth). Then, the housing debt becomes to be reimbursed and the real estate risk exposure decreases. At the end of life, the housing debt is fully reimbursed while house value represents more than 70% of net wealth for homeowners.

2.3 Determinants of housing portfolio and stockholding We start by analysing the determinants of stockholding and homeownership at the household level in France before studying the interactions between households’ investment in stocks and their exposure to real estate risk in the next section.

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% 80

% of stockholders (direct or indirect) % of stockholders (direct only) % of homeowners

70 60 50 40 30 20 10

> 75

4 70-7

9

4

65-6

60-6

9

4

55-5

50-5

9 45-4

4 40-4

9 35-3

4 30-3

9 25-2

< 25

0

Fig. 2 Homeownership and stockholding along the life-cycle (Source: Insee, Patrimoine 2004). Table 3 Housing wealth and debt by age groups (sample of homeowners, source: Patrimoine 2004, Insee)

Age

< 30 30-40 40-50 50-60 60-70 70-80 > 80

Nber of house housing households value/net debt/net (%) worth wealth 0.81 8.57 17.14 23.99 22.43 20.49 6.58

1.437 1.217 0.875 0.742 0.747 0.715 0.728

0.595 0.425 0.225 0.104 0.044 0.022 0.004

2.3.1 Housing portfolio We consider the following variables to explain the probability to own real estate: - the size of the family (measured by the number of children and the marital status) is used as a proxy for the housing consumption motive; - the financial net wealth, income and income risk take into account households’ financial resources and risk; - the age and education of the head of household; - the heterogeneity in local housing prices (measured by the size of the urban area); - individual preferences (risk aversion and time preference).

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As dependent variable, we alternatively consider the probability to own the main residence, to own other properties and to invest in real estate as the investment and consumption motives may differ according to the different type of properties (Henderson and Ioannides, 1983; Arrondel and Lefebvre (2001) for an application on French data). In general, we find similar determinants of the probability to own the main residence or other residences while the motivations for owning rented housing seem to be different (see table 4). The consumption motive is emphasized by the positive significant effect of the number of children on the probability to be owner of the main and/or secondary residences (while it decreases the likelihood to invest in real estate, see column 3). Intergenerational transfers as well as the household income increase the probability to hold a real estate whatever its nature (main, secondary residences or rented housing). Households with secondary residences are also those with larger financial wealth. Homeownership is positively related with age (for the three types of housing assets): we observe an increasing impact until age 70 for the main residence (and until age 60 for rented real estate) and a lower effect after. The education of households and the localization have large significant effects on the main or secondary residences. Living outside from Paris, in particular in a rural area favor the ownership of the main residence and decreases the probability to own other residences. Moreover, the probability to be owner of the main residence is significantly lower in Paris than in all other areas (urban as well as rural): this heterogeneity reflects differences in the local housing prices.

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Table 4 Determinants of homeownership (Probit) Explanatory variables

Main residence Other residences Rented Coeff. Std. Err Coeff. Std. Err Coeff. Std. Err -0.55 0.06*** -0.20 0.09** -0.11 0.08 0.10 0.02*** 0.01 0.02 -0.04 0.02** 0.38 0.06*** 0.47 0.08*** 0.52 0.07*** -0.01 0.25 0.70 0.27*** 0.35 0.19* 0.18 0.03*** 0.17 0.06*** 0.21 0.05***

Spouse(yes=1) Number of children Past Inheritance Financial wealth (E+6) Income Age less than 30 ref. 30-40 0.90 40-50 1.40 50-60 1.59 60-70 1.91 70-80 1.82 more than 80 1.64 Education No diploma ref. Primary level 0.02 Primary level (vocational) 0.31 Secondary level 0.33 Baccalaureate 0.49 Graduate studies 0.44 Post graduate studies 0.51 Grandes Ecoles 0.33 Heterogeneity in housing prices Rural area 1.18 Urban (< 20, 000 inhabitants) 0.83 Urban(20,000-100,000 inhabitants) 0.49 Urban (> 100, 000 inhabitants) 0.63 Paris area (except Paris itself) 0.39 Paris ref. Relative risk aversion No response -0.29 CRRA ≥ 3.76 ref. 2 ≤ CRRA < 3.76 0.02 1 ≤ CRRA < 2 -0.06 CRRA < 1 -0.05 Time preference scale No response -0.09 First quartile ref. Second quartile -0.04 Third quartile -0.05 Fourth quartile -0.153 Constant

0.13*** 0.14*** 0.14*** 0.15*** 0.15*** 0.18***

ref. 0.42 0.83 1.26 1.37 1.41 1.44

0.31 0.30*** 0.30*** 0.30*** 0.30*** 0.32***

ref. 0.28 0.63 0.63 0.38 0.35 0.34

0.19 0.18*** 0.18*** 0.19** 0.20* 0.23

0.11 0.11*** 0.15** 0.16*** 0.14*** 0.13*** 0.12***

ref. 0.03 -0.06 0.41 0.25 0.52 0.50 0.44

0.17 0.17 0.19** 0.21 0.17*** 0.17*** 0.16***

-0.12 -0.04 -0.06 -0.06 0.15 0.02 0.25

0.14 0.13 0.17 0.18 0.15 0.15 0.14*

0.14*** 0.14*** 0.14*** 0.12*** 0.14***

-0.72 -0.61 -0.34 -0.22 0.16 ref.

0.17*** 0.18*** 0.18* 0.15 0.16

0.14 -0.21 0.13 -0.10 -0.30 ref.

0.15 0.16 0.16 0.14 0.16**

0.11***

-0.24 ref. -0.04 -0.01 0.13

0.14*

-0.08 ref. 0.01 0.05 0.02

0.13

0.08 0.10 0.15 0.16 0.09 0.08 0.080**

0.14 ref. -0.10 -0.04 -0.13

0.09 0.13 0.19 0.19 0.11 0.10 0.10

-3.454 0.371*** -4.20 0.68***

-0.41 ref. -0.12 -0.11 -0.10

0.08 0.11 0.17 0.20** 0.09 0.09 0.09

-3.84 0.56***

log likelihood -1241.9 -758.8 -1033.9 Number of observations 2660 2660 2660 % of owners 70.1 10.7 15.3 Source: Patrimoine 2004 (Insee survey) The dependent variable in the probit model is a dichotomous variable which equals to one if households owns respectively its main residence, other residences and rented real assets. */**/*** indicates that the variable is statistically significant at respectively 10%-5%-1%.

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Table 5 Determinants of stockholding (Probit) Explanatory Variables Spouse(yes=1) Number of children Past Inheritance Financial wealth (E+6) Income

Direct Indirect & direct stockownership stockownership Coeff. Std. Err Coeff. Std. Err. 0.01 0.07 0.01 0.06 0.01 0.01 0.01 0.01 0.21 0.06*** 0.29 0.06*** 0.23 0.13*** 0.19 0.02*** 0.34 0.05*** 0.27 0.04***

Age less than 30 30-40 40-50 50-60 60-70 70-80 more than 80

ref. 0.30 0.34 0.50 0.69 0.67 0.74

0.15** 0.15** 0.15*** 0.15*** 0.16*** 0.19***

ref. 0.45 0.45 0.58 0.75 0.78 0.72

0.14*** 0.14*** 0.14*** 0.15*** 0.15*** 0.18***

Education No diploma Primary level Primary level (vocational) Secondary level Baccalaureate Graduate studies Post graduate studies Grandes Ecoles

ref. 0.12 0.14 0.23 0.35 0.51 0.46 0.60

0.14 0.13 0.16 0.17** 0.14*** 0.14*** 0.13***

ref. 0.09 0.14 0.44 0.43 0.49 0.53 0.75

0.13 0.12 0.15*** 0.16*** 0.14*** 0.13*** 0.12***

Parents own stocks (yes=1)

0.43 0.08***

Relative risk aversion No response γ ≥ 3.76 2 < γ ≤ 3.76 1<γ ≤2 γ ≤1 Time preference scale No response First quartile Second quartile Third quartile Fourth quartile

-0.04 ref. 0.11 0.09 -0.01

Constant

-5.35 0.55***

-0.12 ref. 0.21 0.39 0.43

0.12 0.07*** 0.10*** 0.15*** 0.17 0.08 0.08 0.08

0.40 0.08*** -0.11 ref. 0.24 0.42 0.35 -0.10 ref. 0.05 0.07 0.08

0.11 0.07*** 0.09*** 0.14** 0.16 0.08 0.08 0.08

-4.64 0.47***

log likelihood -1274.6 -1373.8 Number of observations 2660 2660 % of owners 26.6 33.2 Source: Patrimoine 2004 (Insee survey). The dependent variable in the probit model is a dichotomous variable which equals to one if the household is stockowner. */**/*** indicates that the variable is statistically significant at respectively 10%-5%-1%.

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2.3.2 Stockholding Following the literature about portfolio choices, we consider as determinants of stockownership: - the existence of transactions costs (proxied by income and financial wealth); - the stock of financial information (proxied by age, education, parents’ wealth composition); - risk aversion - and time preference.1 As dependent variables, we consider direct stockholding (first column of table 5) as well as total stockholding (direct and indirect, second column) and we estimate the probability to own stocks with a probit model. We obtain similar results for direct and total (i.e. including indirect) stockownership. The significant effect of income reflects the existence of transaction costs.2 The probability to be stockowner is also driven by the households’ financial knowledge: it increases with age, education and the fact that the parents were also stockowners. As predicted by the theoretical literature, our dataset allows us to emphasize risk aversion as a key determinant of stocks investments.

3 The impact of housing risk on stockholding On top of transaction costs and liquidity constraints, the existence of other risks may explain the low stockmarket investment (Kimball, 1993). Indeed, it has been shown that unavoidable risks such as unemployment risk, or uncertainty about future income lead households to mitigate their global exposure to risk by reducing the share of financial wealth invested in stocks (Heaton and Lucas, 2000). This behaviour, called temperance, may thus contributes to the equity premium puzzle (Arrondel et al., 2010). Recently, housing, which is associated with various constraints and risks (housing price evolution, illiquidity, indebledness), has been considered as another background risk. In this section, we study the link between financial and housing wealth by investigating whether the exposure to real estate risk affects households financial portfolio in France.

3.1 Housing as a background risk in the literature Previous empirical investigations show that housing wealth crowds out stockholding due to liquidity constraints and to the risk associated with owning real estate 1

The definitions of the variables are presented in the appendix. As financial wealth is clearly endogenous in this regression, the associated coefficient is likely to be biased. An instrumental approach is used in the following section to account for this problem.

2

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(Fratantoni (2001), Flavin and Yamashita (2002), Cocco (2004), Yao and Zhang (2005)). These papers underline that the heterogeneity over the life cycle in households’ portfolio composition (in particular, the increase in stockholding with age) may be explained by changes in housing wealth. In most of the microeconomic literature about the impact of housing on portfolio compositions, housing ownership is considered as an unavoidable, exogenous and independent risk. In this case, Fratantoni (2001) shows that homeownership (and especially the risk associated with the committed expenditure due to mortgage payments) induces an additional temperance to that caused by labor income uncertainty. This temperance behaviour leads household to reduce their exposure to stockmarket risk.3 In this section, we aim at testing the correlation between stockholding and housing wealth by relying on similar models as those cited above. Compared to these previous papers, our empirical analysis fully takes into account risk aversion as well as various background risks faced by households (housing, job market, business risk, health).

3.2 Empirical analysis The empirical strategy consists in introducing additional explanatory variables reflecting the exposure to real estate risk in the standard portfolio choice model (Yamashita (2003), Saarimaa (2009)). More precisely, the share of the financial wealth invested in stocks is estimated by taking into account the traditional determinants (income, risk aversion, time preference, information costs, etc.) as well as the impact of other risks (exposure to housing risk, income risk, business risk).4 From the econometric point of view, the selection bias arising from the fact that a significant proportion of households does not own stocks is handled by estimating a Tobit model. Moreover, as the determinants of stockhownership may differ for renters and homeowners (this is obviously the case for housing wealth), the regression is done separately for homeowners and for renters.5 Table 6 reports probit and tobit estimates for homeowners6. The marginal effects of variables on the likelihood to be stockholder and on the ratio of stocks to financial wealth are computed both for homeowners and renters in Tables 7 and 8. For both subsamples, our results emphasize the significant role played by transaction 3

More recently, Pelizzon and Weber (2008) extend the analysis by considering the case where returns are correlated and thus where housing may hedge financial market risk. 4 See the definitions of the variables in the appendix 5 The endogeneous sample splitting is corrected by adding the inverse Mills ratio of the probit regression for the tenure choice (renting versus owning) estimated in section 2.3. We also account for the endogenous nature of the financial wealth variable: we add in the tobit model the first stage residuals of an equation describing households financial wealth (see Rivers and Vuong (1988)). As instruments, we include: the size of the family (number of children living at home, living outside). 6 The detailed results for renters are available from the authors.

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and information costs, the attitude toward risk and the exposition to various risks in explaining the share of stocks in the financial portfolio. These results are obtained by considering direct stockownership.7 The impact of the exposure to real estate risk According to our results, exposure to real estate risk is one of the main determinants of households’ investments in stocks and contribute to understand why the traditional portfolio choice models fail to explain the equity premium puzzle. Indeed, the ratio of housing to net wealth has a crucial negative impact on stockholding for a given financial wealth. In other words, homeowners moderate their total exposure to risk by reducing their equity investment. When reimbursing their mortgages, homeowners increase their net wealth (which lowers the housing to net wealth ratio) and become more prone to invest in stocks. For instance, a homeowner, moving from the last decile of the distribution of the housing to net wealth ratio to the first one (i.e. from a ratio greater than 1.3 to a ratio smaller than 0.3) increases the probability to own stocks by 12.8 percentage point and the share of financial wealth invested in stocks from 4.1% to 7.6%. Other determinants of the share of financial wealth invested in stocks: homeowners versus renters Concerning the other explanatory variables, we obtain similar effects for homeowners and for renters. The significant positive effect of financial wealth and income model is consistent with the presence of fixed transaction costs both for homeowners and renters when they decide to own stocks : moving a homeowners from the 10th to the 90th percentile of the labor income distribution increases the probability of being a stockholder by 17.4 percentage points. Income is also a main determinant of the share of financial wealth invested in stocks which increases from 3.7% to 8.5% (respectively from 0.7% to 3.4%) when moving a homeowner (respectively a renter) from the first decile to the last decile of the income distribution of the subsample (and holding the other variables constant at their means). The stock of information inherited from parents proxied by the ownership of the same assets in parents’ wealth increases also the investment in stocks. Households (both renters and homeowners) whose parents owned stocks are about 10 percentage points more likely to hold stocks directly, again keeping the other regression variables constant at their means. Moreover, education has a strong positive effect on stockholding, especially for homeowners: with graduate studies stockownership increases by 12.1 percentage points compared to without diploma and the share of financial wealth invested in stocks increases from 4.0 to 7.2%. This regression confirms the large impact of risk aversion on portfolio choices both for renters and homeowners. For instance, homeowners classified in the group of high risk averters are, ceteris paribus, about 15.7 percentage points less likely to hold stocks directly (relatively to the group of low risk averters), and the share of financial wealth invested in stocks is twice as less (5.1% versus 9.9%). 7

We also run similar regression taking into account both direct and indirect stockholding that confirm these findings.

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In addition to the exposure to real estate risk, our results emphasize that stocks investments is also limited by other background risks such as the labour market risk. We find a significant negative effect of unemployment and income risks: households whose future income is more risky are also those who invest less in risky assets. However, the size of the effect is limited (homeowners without any unemployment risk on their labour income were, ceteris paribus, about 1.7 percentage points less likely to hold stocks directly compared to households who are in the highest risky income decile).

4 Conclusion In this paper, we focus on the link between housing wealth and stock-markets participation. Housing represents the main assets in the households’ wealth and is associated with various constraints and risks (housing price evolution, illiquidity, indebtedness over a long period) that may lead households to limit their investment in risky financial assets by temperance. This question is linked to the so-called ”equity premium puzzle”: how can be explained the low participation of households in stock-markets, and when they do participate, why do they under-invest compared to the main results of the theoretical models? We use the French wealth survey (“Enquˆete Patrimoine 2004”, Insee) that gives us detailed information on households’ portfolio composition (housing and financial wealth, mortgages), socio-demographic variables, and several measures of attitudes (risk aversion, scales on time preference) and exposition to various risks (income, unemployment, health, business). We start by analyzing the microeconomic determinants of homeownership and stockholding. The ownership of the main residence is explained by consumption motives. As expected it varies with age (increasing positive effect until age 70) and is determined by the local housing market. Concerning the demand for risky financial assets, we find that stockholding depends on transaction and information costs (measured by financial wealth, income and education) and on risk aversion. Then we study the link between the composition of the financial portfolio and housing wealth. Our results emphasize the large impact of the exposure to real estate risk on the share of financial wealth invested in stocks: an increase in the housing to net wealth ratio crowds out stock market investment for a given total financial wealth. It means that households tend to moderate their global exposure to risk by limiting the share of their financial wealth invested in risky assets. To conclude, this analysis may help to evaluate the impact of the current economic crisis that reinforces household’s exposure to risks and which is associated with large uncertainty about the effect of housing prices on households’ wealth allocation.

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Table 6 Estimates of direct stockholding (discrete and continuous choice) Variables

Probit Coeff. Std. Err

Tobit Coeff. Std. Err.

Financial wealth (E-5)

0.675 0.179***

0.134 0.050***

Housing wealth/net wealth -0.296 0.100*** -0.124 0.030*** Business wealth/net wealth -0.037 0.156 -0.068 0.050 Other Real estate/net wealth 0.260 0.193 0.065 0.057 Income 0.330 0.077*** 0.109 0.022*** Unemployment risk (E-10) -0.165 0.041*** -0.346 0.114*** Age less than 30 ref. ref. 30-40 0.294 0.448 0.031 0.130 40-50 0.174 0.465 0.008 0.135 50-60 0.272 0.469 0.060 0.136 60-70 0.326 0.497 0.168 0.144 70-80 0.301 0.502 0.162 0.145 more than 80 0.097 0.513 0.075 0.149 Self-employed -0.041 0.153 0.007 0.044 Retired self-employed 0.226 0.214 0.012 0.060 Retired employed -0.095 0.166 -0.094 0.048** Employed ref. ref. Health (past diseases=1) Education No diploma Primary level Primary level (vocational) Secondary level Baccalaureate Graduate studies Post graduate studies Grandes Ecoles Parents own stocks (yes) Relative risk aversion No response γ ≥ 3.76 2< γ ≤ 3.76 1< γ ≤ 2 γ ≤1

-0.350 0.253 ref. 0.080 0.068 0.116 0.425 0.222 0.333 0.176

0.170 0.164 0.201 0.219** 0.197 0.190* 0.213

0.254 0.110** -0.160 ref. 0.141 0.388 0.412

0.142

-0.106 0.077 ref. 0.016 0.026 0.076 0.098 0.071 0.119 0.083

0.051 0.049 0.060 0.065 0.058 0.057** 0.062

0.086 0.030***

-0.016 ref. 0.097 0.053 0.135*** 0.097 0.225* 0.141

0.041 0.028** 0.038** 0.062**

λˆ hi 0.326 0.179** 0.117 0.053** εˆFi 0.326 0.179** 0.117 0.053** Constant -4.782 1.026*** -1.498 0.301*** Number of observations 1442 1442 Number of stockholders 458 458 Log likelihood -727.9 -535.5 Sample:Homeowners. The dependent variable in the probit model is a dichotomous variable equals to one if households hold directly stocks. The dependent variables in the tobit model is the ratio of direct stockholding on financial assets. */**/*** indicates that the variable is statistically significant at the 10-5-1 percent level.

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Table 7 Estimated probabilities and amount (stocks/financial assets) of stock demand for homeowners. Variables Housing wealth/net wealth (d1) Housing wealth/net wealth (d9)

Estimated Probabilities Estimated (stock/financial assets) of stockholding (%) 0.348 7.6 0.220 4.1

Financial wealth (d1) Financial wealth (d9)

0.193 0.401

3.5 9.3

Income (d1) Income (d9)

0.204 0.378

3.7 8.5

Risk aversion (γ > 3.76) Risk aversion (γ < 1)

0.417 0.260

9.9 5.1

Unemployment risk (d1) Unemployment risk (d9)

0.284 0.267

5.8 5.3

Parents own stocks (yes) Parents own stocks (no)

0.346 0.255

7.5 5.0

No diploma High school

0.215 0.336

4.0 7.2

Mean values 0.291 6.1 Estimated value (average household) 0.283 5.7 Source: Patrimoine 2004 (Insee survey). Note: This table is computed using the tobit estimates. d1/d9 indicate the value computed respectively for the first decile/last decile of the variable.

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Table 8 Estimated probabilities and amount (stocks/financial assets) of stock demand for renters. Variables Financial wealth (d1) Financial wealth (d9)

Estimated Probabilities Estimated (stock/financial assets) of stockholding (%) 0.068 1.0 0.169 3.1

Income (d1) Income (d9)

0.046 0.178

0.7 3.4

Risk aversion (γ > 3.76) Risk aversion (γ < 1)

0.255 0.150

5.3 2.7

Unemployment risk∗ (d1) Unemployment risk (d9)

0.179 0.164

3.4 3.0

Retired self-employed Employed (ref)

0.408 0.153

10.2 2.8

Parents own stocks (yes) Parents own stocks (no)

0.299 0.159

6.6 2.9

Mean values 0.140 2.9 Estimated value (average household) 0.104 1.7 Source: Patrimoine 2004 (Insee survey) Note: This table is computed using the tobit estimates. d1/d9 indicate the value computed respectively for the first decile/last decile of the variable.

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Acknowledgements We thank Gilbert Cette, St´ephane Gr´egoir, Anne Laferr`ere, Andr´e Masson, Philippe Trainar, Guglielmo Weber, Francesco Zollino and participants of workshops and conferences at Banca d’Italia and Banque de France (”Macroeconomics of Housing Markets”) for their comments and suggestions. This paper represents the views of the authors and should not be interpreted as reflecting those of Banque de France.

References Arrondel, L., Calvo Pardo H., and Xisco O. (2010), Temperance in Stock Market Participation: Evidence from France, Economica, 77, 306, 314-333. Arrondel L., Lefebvre B. (2001), Consumption and Investment Motives in Housing Wealth Accumulation : a French Study, Journal of Urban Economics , 50,112-137. Arrondel L., Savignac F. (2009), Stockholding: Does Housing wealth matter? , Banque de France, Working paper N◦ 266. Barsky R. Juster T., Kimball M., Shapiro M. (1997)., Preference Parameters and Behavioral Heterogeneity : an Experimental Approach in the Health and Retirement Study, Quarterly Journal of Economics CXII, 537-580. Bover O., (2005), The wealth of the Spanish Households: a Microeconomic comparison with the United States, Italy and the United Kingdom, Banco De Espana, Economic Bulletin j. Bucks B. Kennickell A., Mach T., Moore K. (2009), Changes in U.S. Family Finances from 2004 to 2007: Evidence from the Survey of Consumer Finances, Federal Reserve Bulletin , No. 95. Cocco J. (2004), Portfolio Choice in the Presence of Housing, Review of Financial Studies 18-2 . Flavin M., Yamashita T. (2002), Owner-Occupied Housing and the Composition of the Household Portfolio, American Economic Review, 92,1, 345-362. Fratantoni M. (2001), Homeownership, committed expenditure risk, and the stockholding puzzle, Oxford Economic Papers No. 53 , 241-259. Guiso L., Jappelli T., Terlizzese D. (1996), Income Risk, Borrowing Constraints and Portfolio Choice, American Economic Review, 86,1, 158-172. Guiso L., Haliassos M., Jappelli T. (2003), Stockholding in Europe, (Palgrave, Hampshire). Haliassos M. (2003), Stockholding: Recent Lessons from Theory and Computations , Stockholding in Europe, Edited by Luigi Guiso, Michael Haliassos and Tullio Jappelli, Palgrave Macmillan Publishers. Haliassos M., Bertaut C. (1995), Why Do So Few Hold Stocks?, Economic Journal, 105, 432, 1110-1129. Heaton J., Lucas D. (2000), Portfolio Choice in the Presence of Background Risk, Economic Journal, 110 , 1-26. Henderson V., Ioannides Y. (1983), A Model of Housing Tenure Choice, American Economic Review, 73, 98-111. Kimball, M. S. (1993), Standard Risk Aversion, Econometrica, 61, 589-611 Mehra, R, Prescott E.C. (1985), The Equity Premium: A Puzzle, Journal of Monetary Economics, 15, 145-161 Merton R. (1969), Lifetime Portfolio Selection under Uncertainty: the Continuous Time Case , Review of Economic Studies, 51,3, 247-257. Merton R. (1971), Optimal Consumption and Portfolio Rules in a continuous-Time Model, Journal of Economic Theory , 3, 4, 373-413. Pelizzon L., Weber G. (2008), Are Household Portfolios Efficient? An Analysis Conditional on Housing, Journal of Financial and Quantitative Analysis, 43,2, 401-432. Pelizzon L., Weber G. (2009), Efficient portfolios when housing needs change over the life cycle, Journal of Banking and Finance, 33,11, 2110-2121. Rivers D., Vuong Q (1988), Limited Information Estimators and Exogeneity Tests for Simultaneous Probit Models, Journal of Econometrics , 39, 3, 347-366.

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Saarimaa T. (2009), Owner-occupied Housing and Demand for Risky Financial Assets: Some Finnish Evidence, Finnish Economic Papers , 21,1, 22-38. Yamashita T. (2003), Owner-occupied Housing and Investment in Stocks: an Empirical Test, Journal of Urban Economics, 53,2, 220-237. Yao R., Zhang H. (2005), Optimal Consumption and Portfolio Choices with Risky Housing and Borrowing Constraints, Review of Financial Studies, 18,1,197-239.

Appendix The data: Econometric sample In addition to the composition of households’ wealth and to socio-demographic information, a part of the Insee questionnaire gives us a general idea of individuals’ degree of exposure and aversion to risk, as subjectively perceived and assessed by respondents. It consists of a recto-verso questionnaire which was distributed to the interviewees at the end of the first interview. This page submitted to the whole sample must be filled in individually by the interviewee and his/her spouse (if applicable) and returned by post to Insee. Only 4,262 individuals answered to this questionnaire (corresponding to 3,872 households). The content is slightly different for employed persons than for unemployed or non working persons: it asks the former to assess their short and long-term risks of unemployment, as well as the likely change in their future income over the next 5 years. In addition, a simple two-stage lottery game enables us to divide the individuals into four groups according to their degree of relative risk aversion following the methodology initiated by Barsky et al. (1997). Descriptive statistics are reported in table A1 in the annexes for the whole sample of 9,692 households which is representative of French households and for the subsample of the 3,872 respondents to the additional questions about risk attitude. In order to be able to use the information about risk aversion, time preferences and expectations, we select the households for whom the reference person answer the additional questionnaire. Thus, we are left with 2,452 households. Their descriptive statistics are very similar to those reported for the whole sub-sample of respondents.

Variables definition Income risk : proxy for the subjective variance of household income. It is computed following Guiso et al. (1996): each income recipient was asked to attribute probability weights (100 points) to given intervals of real income increases 5 years ahead of the interview.

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Unemployment risk : Each respondent has to evaluate the chances to lose his/her job in the five next years. The question is as follows: ”How do you imagine your future employment within the next 5 years: 1) There is little or no risk that you will lose your job; 2) There is a possibility that you may lose your job (small risk); 3) It is probable that you will lose your job (considerably high risk); 4) It is certain, or almost certain, that you will lose your job”. By making simple assumptions, this information can be used to compute a measure of income variance (see Arrondel and Savignac, 2009). Exposure to real estate risk : The homeowners’ exposure to real estate risk is measured by the ratio of housing wealth to net worth. Housing wealth is the value of the main residence8 , as usually done, the net worth is total wealth less total debt (mortgages for main residence and other properties, consumption loans, professional loans). Exposure to business risk :the exposure to business risk is proxied by a dummy variable identifying self-employed heads of households and the ratio of business wealth to net wealth. Measure of risk aversion: As in Barsky et al. (1997), a measure of risk aversion is obtained by asking respondents about their willingness to gamble on lifetime income, say R. The subject is offered various job contracts in the form of a lottery, with one chance out of two to earn twice more and one chance out of two to earn only λ R (with λ a parameter inferior to one). In the standard framework assuming expected utility, the subject with indirect utility V will prefer the contract to the sure gain R only and only if : 1 1 V (2R) + V (λ R) ≥ V (R) (1) 2 2 with V assumed to be isoelastic of parameter γ . A range of variation for relative risk aversion γ can be determined by varying the value of λ . The outcome is a range measure (in four brackets) for the relative risk aversion coefficient (γ ) under the assumption that preferences are strictly risk averse and of the CRRA type (see table A1 for the results). Time preferences : This indicator is obtained by asking households to give their subjective position on the following scale of time preference :”On a scale of zero to ten, where would you place yourself between the following two ”extreme” descriptions? 0 : persons who live day by day and take life as it comes, who don’t think too much about tomorrow nor worry about the future; 10: persons who are preoccupied by their future (even their distant future) and whose mind is well set on what they want to be or do later in on life.”.

8

The value of other residences is introduced as another explanatory variable.

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Table 9 Samples characteristics

Number of households Wealth Total gross wealth (mean in euros) Median gross wealth Financial wealth (mean in euros) Housing wealth (mean in euros) Household income (mean in euros) Percent. holding directly risky assets Percent. holding directly or indirectly risky assets Percent. holding housing wealth (%) Age of head (%) Less than 30 30-40 40-50 50-60 60-70 More than 70 Social Status of head (%) Farmer Self-employed (small production unit) Self-employed (large production unit) Liberal profession Executive High qualified employee Low qualified employee High qualified workers Low qualified workers Retired or other not working Education of head (%) No diploma Primary level Secondary level Baccalaureate Graduate Post-graduate Family structure (%) Single Couple, no child Couple, one child Couple, two children Couple, three children or more Single, children Other cases Relative risk aversion (CRRA, see definition below) 3.76 ≤ CRRA 2 ≤ CRRA < 3.76 1 ≤ CRRA < 2 CRRA < 1

Sub-sample Full sample of respondents 3,872 9,692 190,000 131,500 38,000 100,000 32,500 19.6 24.9 62.3

170,000 100,000 32,500 87,000 29,000 15.4 19.8 55.7

10.5 19.3 19.7 19.0 13.7 17.9

10.2 18.5 19.8 17.9 13.1 20.5

4.2 6.4 1.1 1.2 17.5 22.2 17.5 20.5 7.5 2.0

4.6 7.7 1.1 1.3 13.6 19.5 19.3 22.0 9.0 2.0

14.9 16.0 32.2 13.6 10.0 13.3

20.6 16.9 30.9 12.6 8.0 11.1

26.8 30.0 13.8 14.4 6.1 6.2 2.7

30.1 27.6 12.6 12.7 6.5 7.7 2.8

58.3 39.4 11.2 4.8

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Part V

Housing, Economic Policy and Financial Stability

House Price Boom/Bust Cycles: Identification Issues and Macro-prudential Implications Impact of Fiscal Policy on Residential Investment in France

House price Boom/Bust Cycles: Identification Issues and Macro-prudential Implications Vladimir Borgy, Laurent Clerc and Jean-Paul Renne

Abstract Over the recent months, several initiatives have taken place to develop macro-prudential regulation in order to prevent systemic risk and the build-up of financial imbalances. These discussions took place in the aftermath of the recent financial crisis that is the consequence of the bust of an house price bubble that took place in the US and spread out to most developed countries. Crucial to the success of such policy is the ability of the macro-prudential authority to identify in due time such imbalances, generally featured by asset price boom-bust cycles. In this paper, we investigate the possibility of detecting house price booms according to alternative identification strategies and assess their robustness. In addition, we try to disentangle costless or low-cost from costly house price booms. Resorting both to a non-parametric approach and a discrete-choice (logit) model, we analyze the ability of a set of indicators to robustly explain costly house price booms. According to our results, real long term interest rates, total investment, real credit and real stock prices tend to increase the probability of a costly house price boom.

JEL codes : E37, E44, E51 Keywords : Early Warning Indicators, Discrete-Choice Model, Asset Price Booms and Busts, Macro-prudential Regulation, Leaning Against the Wind Policies

1 Introduction The recent financial crisis has triggered an impressive amount of policy initiatives and recommendations. Most of these proposals aim at developing macro-prudential V. Borgy Banque de France, e-mail: [email protected] L. Clerc Banque de France, e-mail: [email protected] J.P. Renne Banque de France, e-mail: [email protected] O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_16, © Springer-Verlag Berlin Heidelberg 2010

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regulations intended to address both pro-cyclicality and systemic risks in financial systems. An even more challenging objective is sometimes assigned to macroprudential policies: avoiding asset price bubbles (see Landau, 2009 for example). Indeed, there are compelling evidence that the current financial crisis is the consequence of the bust of an housing-price bubble that took place in the US and spread out to most developed countries. The possible factors that have contributed to the build-up of this housing bubble are: a context of financial deregulation; a wave of financial innovations in the securitization process; bad incentives in the financial industry; regulatory arbitrage; too lax internal and external controls, in particular from supervisors only focused on individual institutions and missing systemic linkages; and eventually too accommodative monetary policies. In this chapter, we focus specifically on the identification issues of house price booms and bust cycles and on the ability of empirical model to identify their potential determinants: indeed, several recent studies have highlighted that house price booms/bust cycles could be costly, noticeably when we compare their features with stock price cycles.1 Goodhart and Hofmann (2008) show evidence of a significant multidirectional link between house prices, money, private credit and macroeconomic variables. This result could illustrate the specific role played by the housing sector on the macroeconomy. Empirical evidence also show that house price growth is positively impacted by real income growth and credit availability and negatively by interest rates (see for instance Terrones and Otrok, 2004). As a consequence, residential investment and house price dynamics could be affected by monetary policy decisions and credit policies by financial intermediaries. However, even if such empirical relationships between these variables could be identified, their precise role in the build-up of a house price bubble is far from being straightforward (and not easily quantified). House price dynamics can affect the macroeconomy through wealth effect and the collateral channel, that is the fact that house can be used as collateral in borrowing operations by households: numerous papers report that private consumption is related to housing wealth.2 In addition, in countries like the United States and the United Kingdom, consumer spending has been sustained through mortgage refinancing operations (see Canner et al., 2002): increasing house prices rose the value of the collateral that households used during refinancing operations, increasing in the end private consumption. These macro-linkages could explain why house prices are procyclical (rising during expansion and falling during recessions). This could also explain why a bust in house price could be ”costly” from a macroeconomic 1

See IMF (2009), Chapter 3. There is an extensive litterature on this issue: see Muellbauer (2008) for a survey and papers in Part IV in this volume. There is also a growing litterature focusing on the role played by the housing sector on the macroeconomy in general equilibrium frameworks (see Iacoviello, 2005 and 2010, this volume).

2

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point of view (leading to a noticeable decrease of output growth). In this chapter, we focus on the following questions: is it possible to detect, in a robust way, house price booms? What is the probability that an house price boom turns into an house price bust? Is it possible to disentangle ”good” - that is to say costless or low-cost booms - from ”bad” - i.e. costly - house price booms? What are the main determinants of costly house price booms and do they differ from those explaining costless or low-cost house price booms? What is the scope of macroprudential regulation and is there a case for state-contingent policies? In a first step, we analyse the main empirical features of house price boom/bust cycles and the methodological issues related to the identification scheme. We find that the different identification methodologies seem to deliver quantitatively similar but qualitatively different results: they spot more or less the same episodes but their duration and main features (such as the degree of asymmetry for instance) differ significantly. In a second step, we analyze the ability of a set of indicators to robustly explain costly house price booms by resorting both to a non-parametric approach and a discrete-choice (logit) model. According to our results, real long term interest rates, total investment, real credit and real stock prices tend to increase the probability of a costly house price boom. The rest of the chapter is organized as follows. Section 2 provides an overview of the identification methods used in the literature. In section 3, we implement some of these methods to identify ”costly house price booms” and assess the extent to which the results are consistent across methods. In section 4, we implement nonparametric tests to disentangle, amongst the set of ”usual suspects”, the variables which are more suited to explain costly house price booms with respect to costless or low-cost ones. We develop a ”performance indicator” which helps us to detect the best indicator variables that are robust to the identification methods. Section 5 provides the estimations results from a discrete-choice (logit) model. Section 6 concludes.

2 The methodologies used to detect house price booms and busts Bubbles are hard to detect and economists disagree on their exact definition.3 To overcome these difficulties, the literature has rather focused on asset price ”booms” and ”busts”. The general idea of the methodologies implemented in this literature is to identify periods in which the value of an asset price exceeds a pre-determined threshold. The computation of the threshold can be based on deviations from a trend series. Then, several parameters have to be specified in order to identify relevant

3

See Gurkaynak (2008) for a recent survey on econometric tests of asset price bubbles.

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episodes: the choice of the filtering procedure, the smoothing parameters, the level of the threshold values, whether filters have to be computed in real time or not. There is no commonly accepted methodology concerning the proper way to identify asset price boom/bust episodes. For this reason, several methodologies (or variants) have been developed in the literature. Here, we apply four different methodologies in order to identify house price booms and busts. We assess the extent to which they deliver consistent results regarding the identification of boom/bust episodes and their main features.4

2.1 Extended Hodrick-Prescott (EHP) method This method consists in extracting a trend from the considered series using the HP filter. Boom episodes (respectively bust episodes) are defined as periods during which the gap is larger than δ times its standard deviation (lower than −δ times). Instead of keeping the entire period (denoted with P) for which the gap is above (below) the threshold, the quarters that follow the maximum (the minimum) of the gap on period P are removed from the boom (the bust) period. Furthermore, in order not to capture only the end of the episode (boom or bust), the periods are extended by adding N quarters before the date at which the series breach the pre-determined threshold (however, the quarters are not added if these are already part of the precedent episode). By implementing this method we arbitrarily include the 12 quarters ahead of each identified episode.

2.2 Recursive Hodrick-Prescott (RHP) method This method differs from the previous one with respect to the use of the Hodrick Prescott filter, which is recursive in this case. Specifically, for each period t1 , one computes the HP-filtered series over the sample [t0 ,t1 ]. The last value of the obtained filtered series (corresponding to period t1 ) is allotted to the recursive-HP-filtered series (for period t1 ). Boom and bust episodes are detected when the gap between the price series and the recursive-HP-filtered series is above or below a given threshold. The threshold can either be constant over the sample or be recursive (based on the standard deviation of the recursive gaps that are computed for each new period). We detect boom and bust episodes when house price deviations from trend is over +/1.3 times the standard deviation. This threshold is equal to the one considered in Bordo and Jeanne (2002). The trend is computed using a one-sided HP filter with a smoothing coefficient of 100.000 as in Alessi and Detken (2009). To the extent that the recursive-HP filter is one-sided, this filter can be seen as a real-time one. 4

See Borgy et al., 2009 for a detailed presentation of the features of the different methodologies and a comparison of the results between house price and stock price booms/busts cycles.

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Papers by Alessi and Detken (2009), Adalid and Detken (2007) and Detken and Smets (2004) rely on such methodology.

2.3 Band-pass filter (BP) method In this method, the gap is obtained by applying the Christiano-Fitzgerald band-pass filter to the house price series. To the extent that high frequencies are removed from it, the resulting gap is smoother, which makes it possible to clearly distinguish peaks and troughs. Amongst the gap optima - that are defined as maxima or minima over a given window of W quarters -, only those that are sufficiently far from the zero line (the threshold being expressed as a multiple of the gap standard deviation) are retained. Having identified these optima, the boom and bust episodes are defined in the following manner: the booms (busts) are the longest possible periods that are bounded by 0 on the left and a gap maximum (minimum) on the right; in addition, the gap is never negative (positive) over the period. The use of a band-pass filter that excludes high-frequency variability makes it easier to detect optima, which may be seen as a way of using peaks and trough detection as in Agnello and Schuknecht (2009) at the quarterly frequency (while they use yearly data). An asset price boom (bust) is defined in our study as a period when the band-pass filter exceeds (falls below) zero by more than one standard deviation. The gap optima are defined as maxima or minima over a given window of 5 quarters as in Agnello and Schuknecht (2009). The filter is calibrated so as to filter out cycles below 2 years and above 30 years.

2.4 Moving Average (MA) method In this case, one computes the moving average (including M lags) of the year-onyear growth of the considered series. Those periods for which the moving average is larger (respectively lower) than a threshold are identified as boom (bust) periods. This method is a real-time one in the sense that the diagnostic in period t only depends on information that is known in t. Contrary to previous ones, the MA method may detect a boom (bust) episode even in a context where the price series is below (respectively above) its trend. This potential pitfall may be avoided by conditioning the detection to the position in the cycle (which would naturally require the computation of a cycle indicator). Bordo and Jeanne (2002), Fatas et al. (2009) and Barajas et al.(2008) rely on that method to select their episodes.5 We define a house price boom (bust) as a period when the 8-quarter trailing moving average of the annual growth rate of the considered asset price exceeds (falls below) a given threshold, 5

Gerdesmeier, Reimers and Roffia (2009) implement similar method - however based on a recursive average - to an asset price composite indicator which incorporates developments in both stock and house price and focus on bust episodes.

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i.e. when: 1/8 ∑7i=0 gt−i > x, where g is the growth rate of the asset price and x the threshold. In this exercise, x is set equal to 5% (-5% for a bust) for housing prices. The duration of an episode is measured as the amount of time the 8-quarter moving average of the growth rate of the asset price exceeds (falls below) the threshold. When the above condition holds, the periods t − 7 through t are labeled as a boom (bust). Consequently, the minimum duration of all episodes is of two years.

3 Identification of house price booms We implement these different methodologies on real housing price quarterly indices provided by the BIS, from 1970Q1 to 2008Q3, collected on a set of 18 OECD countries: Australia, Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, the Netherlands, New-Zealand, Norway, Spain, Sweden, Switzerland, the United-Kingdom and the United-States. The different methods seem to deliver quantitatively similar but qualitatively different results: they spot more or less the same episodes but their duration and main features (such as the degree of asymmetry for instance) differ significantly. Then, we differentiate between the identified house price booms those which have a significantly negative impact and those which have a mild or even negligible impact on the economic activity. We use the same definition as in Alessi and Detken (2009): we define a ”costly” house price boom as a boom which is followed by a three-year period in which overall real GDP growth has been at least three percentage points lower than potential growth. Put another way, a costly boom results in a cumulated loss amounting to at least three percentage points of potential output in the three-year period following the peak in the house price or a widening of the output gap by 3 percentage points. In order to identify costly and low-cost house price boom for the recent years, we complete the GDP data with forecasts published by the OECD (Economic Outlook, July 2009). The main features of the identified episodes are summarized in Table 1. A first striking result stemming from Table 1 is that there are huge differences across methodologies. It is also likely that changes in the parameter and threshold values may lead to subtsantial changes in the set of identified episodes. Consequently, identifying house price booms is certainly easier than identifying house price bubbles, but it is not necessarily as robust and as easy as usually expected. The moving average and the ”extended” HP filter methods on the one hand, the recursive HP and the Band-pass filters on the other, tend to display close results. Second, the number of episodes varies a lot depending on the method implemented: in our sample, we identify between 50 and 30 booms and busts, 20 to 30 being qualified as costly episodes. Depending on the identification methodology, ”costly” house price booms represents between 50% and 79% of all the booms.

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Regarding the robustness of the identification methods, one can check whether methods, confronted two-by-two, display coherent and synchronized results. Table 2 displays the percentage of periods in which two alternative methods give a similar diagnostic or signal regarding the state of house price developments (i.e. whether there is a booming or a busting phase). It follows, from Table 2 that the extended-HP and the band-pass filters display the closest results (75% of coherent signals between the two methods). Moving average with both extended HP filter and the band-pass filter display the lowest synchronisation (53% of coherent signals between these methods). Another perspective on the episode-classification results is provided in Figures 1 which displays ”diffusion

Table 1 Summary statistics on house price booms and busts.(* Implementing this method, 4 additional booms were identified but could not be qualified)

Booms costly costless/low-cost Busts

Booms costly costless/low-cost Busts

Booms costly costless/low-cost Busts

Booms costly costless/low-cost Busts

House prices Moving-Average-based detection method* Nb of episodes Avg length 51 19 25 19 22 18 40 17 Recursive-HP-based detection method Nb of episodes Avg length 45 9 23 10 22 8 40 11 Extended-HP-based detection method Nb of episodes Avg length 37 16 23 15 14 18 34 16 Band-pass-filter-based detection method Nb of episodes Avg length 42 14 33 14 9 14 33 14

Table 2 Method synchronization House prices Moving Average Recursive HP Filter Extended HP Filter Moving Average — — — Recursive HP Filter 59% — — Extended HP Filter 53% 64% — Band-pass filter 53% 64% 75%

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indices” according to the different methodologies implemented. These indices are obtained, for a given method and at a given date, by summing up across our set of 18 countries an indicator variable of the state of the house price development. This indicator variable takes the value 1 when the house price is in a booming phase, zero when the phase is unclassified, and -1 when it is a busting period. It corresponds to a crude measure of correlation in house prices in the sense that if boom/bust cycles are local and/or uncorrelated phenomena, this summation should lead to a small number with respect to the total number of countries in the sample, a boom in a place being eventually compensated by a bust in another.

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Depending on the method, one can identify three major waves of house price booms (which peaked around 1979, 1989 and 2006) since 1970. The main result is that the number of countries experiencing simultaneously a boom or a bust being rather limited (between 5 and 10 out of 18). One must notes that the results are highly dependent upon the method implemented: for instance, in 2005, only 5 coutries were experiencing a house price boom according to the HP extended identification method, half the number identified with the band-pass and the moving average methodologies. In addition, we can consider the proportion of costly booms amongst all house price booms (see Figure 2). This figure strinkingly illustrates the fact that the great bulk of house price booms belongs to the category ”costly booms”.

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Based on our results, we are now in position to measure the probability that a house price boom turns into a house price bust. Specifically, we consider that a boom turns into a bust if a bust begins in the two years following the end of this boom. The results are displayed in Table 3. First, there is clear evidence that a house price boom is not systematically followed by a house price bust. Roughly speaking, it is broadly the case for about half of them. However, Table 3 displays huge differences across methods. Second, there is a case to distinguish costly and non-costly booms as, irrespective the method, a boom qualified as costly turns more systematically into a bust than a ”non-costly” one. The only exception is related to the Extended HP filter method for which the probability that a non-costly boom is followed by a bust is slightly higher (50%) than a costly boom (45%). It follows also that a house price bust may have mild effects on the economy and may not necessarily require a policy response. Finally, if one would like to identify costly house price booms with the highest probability, he would have to resort to the moving-average to identify costly house price booms. Overall, it seems that designing systematic or mechanistic macro-prudential rules is not necessarily a panacea. These rules should therefore be designed in order to address and prevent costly house price booms only. Otherwise, they may bear some deadweight welfare losses and from this view point would neither be desirable nor justified.

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Table 3 Probabilities that an asset price boom is followed by a bust (with respect to the detection method) Moving Average whatever kind of boom 67% - if the boom is not costly 60% - if the boom is costly 74% Recursive Hodrick Prescott filter whatever kind of boom 23% - if the boom is not costly 18% - if the boom is costly 28% Extended Hodrick Prescott Filter whatever kind of boom 47% - if the boom is not costly 50% - if the boom is costly 45% Band-pass filter whatever kind of boom 35% - if the boom is not costly 22% - if the boom is costly 41%

The questions we are now confronted with are the following: are we able, amongst the set of usual early warning indicators, to distinguish those which will signal costly house price booms only? Are they different from those leading or signalling booms with mild or even without any consequences on the real economy? This is the scope of the next section.

4 The determinants of house price booms: a

non-parametric approach 4.1 The ”usual suspects” There is a long standing literature focusing on past asset market booms from which we can spot a set of relevant early warning indicators (see Bordo and Wheelock, 2004; Schularick and Taylor, 2009). The list is not exhaustive but usually contains: • several macro-economic variables illustrative of a ”regime” or ”paradigm” shift (”new economy”) such as: above-trend growth, below trend inflation, current account deterioration (capital flows), falling private sector savings; • credit and monetary indicators such as: faster real money supply growth, M2-toreserve expansion, above trend domestic credit, rising foreign reserves;

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Table 4 List of indicator variables House prices Stock prices Real GDP Residential investment Residential-investment-to-GDP ratio Investment Total-investment-to-GDP ratio Credit (real) Credit Credit-to-GDP ratio Money (real) Money Money-to-GDP ratio Nominal long term rate Nominal short term rate Real long term rate Real short term rate Spread Current-account-to-GDP ratio

• global factors such as: global commodity price collapse, global liquidity. One can add very accommodative financing conditions featured by historically low interest rates. Due to data availability and working on a set of 18 countries from 1970 to 2008 on a quarterly basis, we restrict our attention to the 19 indicators listed in Table 4. Moreover, we consider up to 3 different transformations of these variables in addition to the original data (deviation from a HP trend, deviation from a linear trend and annual growth rate or annual change) and up to 5 different lags (from contemporaneous to 4-quarter lagged observations). Therefore, we overall test the information content of 380 indicators. Real GDP, Investment, Residential investment - both in level and as GDP ratios - aim at capturing the potential effects of real activity on house markets’ developments. Real credit variables tend to capture the ”credit view”, which states that the quantity of bank credit matters, above and beyond the level of bank money. Put another way, proponents of that view consider that the entire banks’ balance sheet, leverage and composition may have macroeconomic implications. Propagation occurs through a financial accelerator mechanism (as in Bernanke and Blinder, 1988) or through collateral constraints (as in Bernanke, Gertler and Gilchrist, 1999). Recent research carried out at the ECB indeed shows that credit variables seem to be pretty good early warning indicators of asset price busts (Gerdesmeier et al., 2009) or of costly asset price booms (Alessi and Detken, 2009), thereby confirming earlier find-

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ings by Borio and Lowe (2002). Monetary aggregates (we focus here on broad aggregates such as M3) intend to capture the ”money view”, which states that the level of money supply strongly influences output in the short term and as such might also feeds house price booms. It reflects the importance of aggregate liquidity in fuelling asset markets’ development and emphasizes the role of aggregate banks liabilities (or funding liquidity) beyond the role of monetary and financial institutions in credit creation. Current account variables intend both to capture the role of capital inflows and more generally of global imbalances in the formation and the developments of house price bubbles and to explain eventually the discrepancy between broad monetary aggregates and credit developments (corresponding to the external counterpart of broad monetary aggregates). Interest rates (real, nominal and spread) reflect the behavior of central banks or monetary authorities. We use them to assess the extent to which historically low level of interest rates may be prone to asset price bubbles. This stems from the fact that a lower level of interest rates tends first to increase the level of future expected dividends, in the case of stocks, or rents, in the case of housing, while at the same time decreasing the values of discount factors, thereby resulting in an increase in asset prices. In addition, it should be borne in mind that during an asset price boom, one would expect that an interest rate increase may trigger a bust or signal a costly boom as it may exacerbate both adverse selection and moral hazard problems and increase defaults of overindebted households. Finally, we investigate the information content of stock price to account for house prices developments. This may eventually capture the impact of financial wealth on other asset prices, resulting either from portfolio rebalancing or diversification.

4.2 A non-parametric analysis A first assessment of the links between the above-mentioned variables and the occurrences of specific episodes, say boom (vs. no boom) or costly boom (vs. non-costly / low cost boom), is obtained by resorting to non-parametric tests. By definition, these tests are immune to specification errors. In addition, they do not require satisfying particular assumption regarding the distribution of the variables. Their straightforward implementation makes it possible to quickly look for potentially relevant determinants of some episodes amongst a large set of variables. Indeed, the number of variables to test dramatically increases when different lags and transformations of the variable are considered in the analysis. Intuitively, if one suspects a given variable to be a determinant of a kind of episode, say a boom, one should expect this variable to have different character-

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istics before and during the boom. The approach that is developed in the following is aimed both at testing the significance of such qualitative observations and at finding the relevant lags and transformations to apply to the set of potential determinants in the second approach (see Section 5). Our approach is based on an extensive use of the Kruskall-Wallis tests (see Sheshkin, 1997 and for some applications, see e.g. Musard-Gies, 2006 or Clare and Courtenay, 2001), whose null hypothesis is the equality of medians of different sets of observations.6 More generally, assume that a set of observations is split into two. If one subgroup tends to contain the higher observations, the KW test statistics is high and the null hypothesis of equal medians is rejected. Conversely, if the ranking of the observations is relatively even over the two subgroups, the test statistics is low and the null hypothesis is not rejected. This functioning of the KW test statistics is exploited in order to rank the potentially explicative variables. Our approach is also designed so as to accommodate our objective of finding variables whose relationship with given episodes is robust across the four detection methods: a single performance measure pX - based on the computation of the KW test statistics for each of the four detection methods - is indeed attributed to each variable X , transformation and lag. More precisely, the sequencing of the approach is the following: 1. For each variable X, transformation T , lag k and detection method d: a. The observations of the - transformed-and-lagged - variables are ranked and divided in two subgroups - denoted by A and B -, depending on the type of episodes they correspond to. X b. Based on this decomposition, the KW test statistic - denoted by KWd,T,k - is

B,X computed, as well as the medians mA,X d,T,k and md,T,k of the two subgroups. The relative position of the medians reflects the direction of the potential effect of the considered variable on the type of episode (for the considered lag, transformation and detection method).

2. For each variable, transformation and lag, if the direction of the effect is different across the four detection methods, a zero performance is attributed to this transformed-and-lagged variable (pXT,k = 0). Otherwise, the minimum of the four test statistics (corresponding to the four detection methods) is taken as the performance metrics for this transformed-and-lagged variable. 3. For each variable, one looks for the transformation and lag that results in the best performance metrics.7 The test statistic is KW = 12/(N(N + 1)) ∑Kk R2k /nk − 3(N + 1) where K is the number of groups, nk nk is the number of observations in group k, and Rk = ∑i=1 ri,k is the rank sum for group k (ri,k being th the rank of the i observation of group k) and N is the total number of observations (N = ∑Ki=1 nk ). Under the null hypothesis of equal medians, the KW statistics is distributed χ 2 (K − 1). Specifically, in our case, K is equal to 2 (boom vs. no-boom in a first analysis and costly-boom periods vs. noncostly-boom periods in a second one). 7 As a result, steps 2 and 3 constitute a MaxMin approach: after having selected the smallest value of the KW statistics with respect to the detection method (for each variable, lag and transformation), we maximize with respect to the different lags and transformations. 6

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Formally, steps 2 and 3 read pX = Max pXT,k T,k

where pXT,k =

(

B,X A,X B,X X if, ∀d mA,X d,T,k > md,T,k or ∀d md,T,k < md,T,k then Min KWd,T,k

0 otherwise.

d

Since all the performance metrics pX originally were computations of KW test statistics - following χ 2 (1) distributions under the null hypothesis -, they can be compared to the associated critical values. Accordingly, a performance pX which lies below the 5% critical value of the KW test points to a weak relationship between this variable and the types of considered episodes. More precisely, if a variable falls in this category, it means that for any lag and transformation applied to it, either the detection methods never agree on the sign of the relationship or there is at least one detection method for which the relationship was not statistically significant. While Table 5 is aimed at analyzing the potential determinants of booms for house prices , Tables 6 presents the results when looking for the determinants of the ”costly” booms. In both tables, the variables are ranked with respect to their performance metrics pX . Considering house price booms versus the absence of boom, macroeconomic variables expressed as deviations from trend (Real GDP, Investment, Residential and total investment) tend to be the most relevant and robust across methods determinants with the expected positive signs, followed by the year-on-year growth rate of credit variables, which tend to dominate broad monetary aggregate indicators (see Table 5). Low nominal, rather than real, long term interest rate also explain house price booms quite significantly but with a lag. We now consider the ability of our set of indicator variables to explain costly house price booms versus low-cost or costless booms. Table 6 confirms previous intuitions regarding house price developments. First, in a booming phase, an increase in the real interest rate will tend to increase the cost of an housing boom: this may stem from the fact that highly leveraged households will tend to see the real service of their debt increasing, raising the probability of their default and, as argued earlier, such an increase in interest rates will tend in addition to exacerbate both adverse selection and moral hazard problems on credit markets. Real indicators continue to play a significant role while credit still tends to dominate significantly monetary indicators. Overall, non-parametric tests tend to confirm the significant role of real economic activity and credit variables in shaping house price booms. These variables also tend to be the most relevant and robust in explaining costly asset price booms. Interestingly the role of interest rate tends to be asymmetric and dependent upon the state of the economy: there is some evidence that low interest rates may contribute to trigger house price booms and that, once a boom has started, interest rates’ hikes may increase the cost of this house price boom.

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5 The determinants of house price booms: a

discrete-choice (logit) model

We complement the non-parametric analysis by considering now the output of a logit-type approach. Such an approach will provide us with further information, in particular the marginal impact of a given variable to the probability of being in a boom or is a costly boom. One advantage of this approach compared to the signalling approach widely used in the early warning indicator literature is that is allows for statistical inference and tests. In order to carry out our estimations, we will rely on the results of the KW procedure (presented in Section 4.2). For instance, regarding house prices (see Table 6), the variables with the higher performances are real GDP and the investment variables (total and residential capital expenditures). The transformations selected by our procedures for these variables are deviation from the HP trend without any lag. The different variables computed on the basis of the credit series rank next (computed on the basis of annual growth). The annual change of the current-account-toGDP ratio (without lag) rank next and the KW is highly significant.8 The lower part

Table 5 Non-parametric analysis of potential determinants of house price booms. Lag House prices Real GDP Investment Residential investment Residential investment-to-GDP ratio Total investment-to-GDP ratio Credit (real) Credit Credit-to-GDP ratio Current account-to-GDP ratio Money (real) Nominal long term rate Money Stock prices Money-to-GDP ratio Nominal short term rate Real long term rate Real short term rate Spread

Transformation Performance Direction

0 Annual growth 0 Gap (HP trend) 0 Gap (HP trend) 0 Gap (HP trend) 0 Gap (HP trend) 0 Gap (HP trend) 0 Annual growth 2 Annual growth 1 Annual growth 0 Annual change 0 Gap (linear trend) 4 Gap (HP trend) 3 Annual growth 3 Gap (HP trend) 4 Annual growth 4 Gap (HP trend) 0 No transf. 4 Gap (linear trend) 4 Gap (HP trend)

488,1 252,8 187,5 157,8 133,5 96,5 95,3 77,8 67,5 57,3 50,1 36,5 33,7 33,6 29,4 26,9 8,2 6,8 5,4

+ + + + + + + + + − + − + + + − − − +

Note: The performance metrics is based on the Kruskall-Wallis test. Heuristically, the larger this metrics, the more dependent on the type of episodes (boom vs. non boom) the behavior of the considered variable; the last column indicates the direction of the relationship (a + sign means that the considered variable tends to have larger values during booms). Recall that under the null hypothesis of the KW test, the test statistics follows a χ 2 (1) distribution, implying 1% and 5% critical values of, respectively, 10.8 and 3.84.

8

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of Table 5 includes mainly the variables related to monetary aggregates and shortand long term interest rates. As a consequence, we select total investment, real credit, current account (in percentage of GDP) and long term interest rate with the appropriate lags and transformation in order to run the logit estimation. Formally, let us denote with yit a binary variable that is equal to 1 when country i is experiencing a boom in period t (and 0 otherwise).9 The logit model postulates that the probability distribution of yit conditional on vector xit is defined by: P(yit = 1|xit ) = P(xit β + νi ) where P(z) = (1 + exp(−z))−1 .10 The estimations are performed by including random effects. The results of the boom-vs-no-boom logit analysis for the four identification methodologies are presented in Table 7. The coefficients represent the marginal increase in the probability of a boom evaluated at the mean level of the other variables. These coefficients are normalized so as to facilitate the reading of the results. For instance, an increase of one

Table 6 Non-parametric analysis of potential determinants of the type of house price booms (costly vs. costless or low-cost). Lag Real long term rate Real short term rate Stock prices Residential investment-to-GDP ratio Investment Total investment-to-GDP ratio Credit (real) Money (real) Residential investment Credit-to-GDP ratio Money-to-GDP ratio Housing prices Real GDP Spread Nominal long term rate Credit Current account-to-GDP ratio

Transformation Performance Direction

4 No transf. 4 No transf. 0 Gap (HP trend) 4 Annual growth 1 Annual growth 3 Gap (HP trend) 1 Annual growth 0 Annual growth 3 Gap (HP trend) 2 Annual growth 1 Annual growth 0 Annual growth 0 Annual growth 0 Annual change 4 Gap (linear trend) 4 Annual growth 0 Gap (linear trend)

52,0 46,0 33,8 30,7 24,8 20,8 19,9 9,6 9,1 6,6 5,7 2,4 1,5 1,0 0,2 0,1 0,0

+ + + + + + + + + + + + + − + + −

Note: The performance metrics is based on the Kruskall Wallis test. Heuristically, the larger this metrics, the more dependent on the type of episodes (costly boom vs. non-costly boom) the behavior of the considered variable; the last column indicates the direction of the relationship (a + sign means that the considered variable tends to have larger values during costly booms). 9

In this estimation, we do not made distinction between costly and non-costly booms. Underlying this model is the variance component model yit = 1 ⇐⇒ xit β + νi + εit > 0, where εit are i.i.d. logistic distributed with mean zero and variance σε2 = π 2 /3. 10

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Table 7 House price boom vs. no boom Variable

Transform - Lag Marg. Effect Std. Err.

Detection method: Extended HP Real GDP Gap (HP trend) - 0 Total Investment Gap (HP trend) - 0 Credit (real) Annual growth - 0 Current Account (% GDP) Annual change - 0 long term interest rate Gap (HP trend) - 4 Detection method: Recursive HP Real GDP Gap (HP trend) - 0 Total Investment Gap (HP trend) - 0 Credit (real) Annual growth - 0 Current Account (% GDP) Annual change - 0 long term interest rate Gap (HP trend) - 4 Detection method: Moving average Real GDP Gap (HP trend) - 0 Total Investment Gap (HP trend) - 0 Credit (real) Annual growth - 0 Current Account (% GDP) Annual change - 0 long term interest rate Gap (HP trend) - 4 Detection method: Band-pass filter Real GDP Gap (HP trend) - 0 Total Investment Gap (HP trend) - 0 Credit (real) Annual growth - 0 Current Account (% GDP) Annual change - 0 long term interest rate Gap (HP trend) - 4

z

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0.1082 -0.0060 0.0234 -0.0229 -0.0235

.0161 .0123 .0080 .0075 .0078

6.70 -0.49 2.93 -3.04 -2.99

0.000 0.621 0.003 0.002 0.003

0.0660 0.0399 0.00907 -0.0130 -0.0160

.0158 .0114 .0060 .0057 .0058

4.16 3.50 1.51 -2.27 -2.72

0.000 0.000 0.131 0.023 0.006

0.1857 0.0112 0.0584 -0.0266 -0.0812

.0229 .0212 .0142 .01271 .0131

8.08 0.53 4.09 -2.10 -6.20

0.000 0.598 0.000 0.036 0.000

0.1015 0.0393 0.0221 -0.0143 -0.04136

.016 .0135 .0086 .0075 .0083

6.35 2.91 2.57 -1.89 -4.95

0.000 0.004 0.010 0.059 0.000

Note: (a) The model is P(yit = 1|xit ) = P(xit β + νi ) where, for any period t and country i, yit is equal to 0 (no boom) or 1 (boom) and P(z) = (1 + exp (−z))−1 ; (b) The marginal effect corresponds to the impact off a 1st.dev. of the considered variable on P(yit = 1).

standard deviation in real credit raises the probability of a house price boom by 5.8 percentage points in the case of the moving average identification scheme. The most striking results are the following: above trend real activity, as captured by real GDP or total investment, and long term interest rate variables are significant for the four identification methodologies; above trend real credit is significant for 3 identification methodologies out of 4 and its marginal contribution to the probability of a house price boom ranks between 2.2 and 5.8 percentage points. According to our estimates, the increase in the probability of a house price boom induced by a rise of 1 standard deviation of real GDP ranks between 6.6 and 18.5 percentage points according to the different identification methodologies. The annual change of the current account (as a % of GDP) is significant at the 1% level only in the case of the ”Extended HP” methodology. In this case, a decrease (i.e. deterioration) of the current account to GDP ratio by 1 standard deviation over one year increases the probability of a house price boom by 2.3%.

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Table 8 House price costly boom vs. non-costly boom

Variable

Transform - Lag Marg. Effect Std. Err.

Detection method: Extended HP Real long term interest rate No transf. - 4 Total investment Annual growth - 1 Real credit Annual growth - 1 Real stock prices Gap (HP trend) - 0 Detection method: Recursive HP Real long term interest rate No transf. - 4 Total investment Annual growth - 1 Real credit Annual growth - 1 Real stock prices Gap (HP trend) - 0 Detection method: Moving average Real long term interest rate No transf. - 4 Total investment Annual growth - 1 Real credit Annual growth - 1 Real stock prices Gap (HP trend) - 0 Detection method: Band-pass filter Real long term interest rate No transf. - 4 Total investment Annual growth - 1 Real credit Annual growth - 1 Real stock prices Gap (HP trend) - 0

z

p-value

0.259 0.06941 3.74 0.292 0.08253 3.54 -0.105 0.0592 -1.78 0.2805 0.0821 3.42

0.000 0.000 0.075 0.001

0.2582 0.0699 3.69 0.0548 0.05103 1.07 0.3492 0.0759 4.60 0.0608 0.0561 1.09

0.000 0.282 0.000 0.278

0.2771 0.0214 0.0553 0.1599

0.0368 0.0289 0.0262 0.0308

7.51 0.74 2.11 5.18

0.000 0.457 0.035 0.000

0.1020 0.0197 -0.0049 0.0167

0.0411 0.0176 0.0122 0.0126

2.48 1.12 -0.41 1.32

0.013 0.263 0.685 0.187

Note: (a) The model is P(yit = 1|xit ) = P(xit β + νi ) where, for any period t and country i, yit is equal to 0 (non-costly boom) or 1 ( costless or low-cost boom) and P(z) = (1 + exp (−z))−1 (b) The marginal effect corresponds to the impact off a 1st.dev. of the considered variable on P(yit = 1).

The estimated probability of a housing boom by country according to the different identification schemes are presented in Figures 3 to 6 in the Appendix. The charts provide an illustration for each country of how well the logit model perform in order to predict a house price boom for each identification methodologies. We analyze now the determinants of the probability of a costly house price boom conditional upon the fact the economy is already in a booming phase. This means that, to carry out our logit regressions, we exclude those observations that do not correspond to booms. Formally, in the logit equation, the binary variable yit is set equal to 1 (respectively to 0) when country i is experiencing a costly (respectively a costless or low-cost) boom in period t. Table 8 displays the results. The most robust results are found for the real long term interest rates in level and the above trend stock price index which all contribute positively to the probability of a house price boom. The marginal impact is however quite volatile depending on the methodology, ranging from 10 to 27 percentage points for long term interest rates and 1 to 28 percentage points for stock prices. The rate of growth of credit is positively signed in 2 cases out of 4. The marginal impact of total investment, which is positively signed irrespective of the identification method, is not always statistically significant.

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6 Conclusion In this paper, we try to assess the robustness of several asset price boom/bust identification procedures applied to house price for a set of 18 OECD countries. We find that: 1) the identification of an house price boom or bust remains challenging ex ante and ex post despite the fact that the methodologies implemented in the literature differ sometimes only marginally. There remain critical choices regarding the determination of key parameters (method and degree of smoothing, real time data, magnitude of deviation from trend etc.). Implementing four of the most popular methods used in the literature, we find that these methods robustly identify between 53% and 75% of house price boom episodes. 2) Regarding the main features of the identified episodes, we find that most house price booms tend to turn into costly recessions. Looking at diffusion indices, we find that a limited proportion of house price boom and bust episodes tend to occur simultaneously across our set of 18 countries: in several cases, around 10 out of 18 countries are experiencing simultaneously a boom or a bust. 3) There is a case to distinguish costly asset price booms from other booms, which would implies to rely on state-contingent macro-prudential policies rather than on mechanistic or systematic instrument rules. Indeed, it would be detrimental to long term growth to consider that all credit or all house price expansions are dangerous. However, such an identification cannot be performed ex ante. 4) Looking at the main determinants, by relying on a limited set of (mostly) macroeconomic variables, our empirical analysis displays results that could be seen as useful from a macro-prudential perspective: we find that credit variables play indeed a significant role in shaping house price booms, and in particular costly ones. We find also evidence that interest rates play an asymmetric role: their low level is likely to trigger an house price boom and an interest rate hike in the booming phase is conducive to a bust or a costly boom. From these results, we can draw the following policy implications: 1) If the scope of macro-prudential regulation is to prevent asset price bubbles or booms, it is not clear why macro-prudential authorities will be better equipped than central banks, unless they rely on a different set of information variables (eventually individual data on banks’ balance sheets) to identify these episodes ex ante. This has still to be clearly assessed. Therefore, the ex ante identification of a bubble remains a challenging task. 2) We find some evidence that credit developments are a major and significant determinant of house price booms meaning that overall bank balance sheets, composition and leverage matter. Second, we also confirm that house price booms are likely to

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turn into severe economic contractions. This may relates to the facts that, consistent with the ”credit view”, most house price busts or costly house price booms can been seen as ”credit booms gone wrong” as put forward by economists like Minsky (1977) or Kindleberger (1978). This view would also be consistent with recent declarations by Mishkin (2009) arguing that not all asset bubbles are alike and distinguishing between (costly) credit bubbles and (costless or low-cost) speculative bubbles. House price booms, as long as they are generated by credit developments, are clearly in the scope of macro-prudential policies. In addition, they can be adressed by other stabilisation policies: legislation which can for instance impose loan to value ratios or taxation which can reduce incentives to housing investment or foster housing supply. Acknowledgements This chapter is an excerpt from Borgy et al. (2009). We are very grateful to B´eatrice Saes-Escorbiac and Aur´elie Touchais for excellent research assistance. We thank participants at the conference The Macroeconomics of Housing Markets (held in Paris on 3-4 December 2009) and at the ECB expert meeting on Tools for detecting asset price imbalances, the role of money and credit and the impact on consumer-price inflation (held at Frankfurt on 15 December 2009). In particular, we thank our discussants Timo Wollmershauser, Giovanni Ferri and Nicola Doyle for helpful comments. We are also grateful to the BIS for having kindly provided us with asset price data. The views expressed in this paper do not necessarily reflect those of the Banque de France.

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Impact of Fiscal Policy on Residential Investment in France Pamfili Antipa and Christophe Schalck

Abstract The present paper assesses the impact of fiscal policy on residential investment in France. The analysis is conducted in the framework of a VECM, since this allows accounting for endogeneity between the variables. Our results imply that a long term relationship between investment and subsidies exists, making subsidies an adequate tool to influence residential investment and hence the business cycle. In addition, a disaggregated approach taking into account several different types of fiscal measures highlights that tax and interest rate subsidies are the most efficient fiscal tools for influencing residential investment. When accounting for financial factors by means of households’ borrowing capacity, we find that the latter also impacts residential investment positively. Moreover, this alternative specification underlines the robustness of the above mentioned results, as it confirms subsidies as the most efficient measure to influence residential investment.

JEL codes : E62, R21, C22 Keywords : Fiscal policy, residential investment, VECM

1 Introduction Recent evolutions on European housing markets have been marked by an important degree of volatility and several studies have attempted to explain these movements P. Antipa Banque de France, e-mail: [email protected] C. Schalck ESG Management School, e-mail: [email protected]

O. de Bandt et al. (eds.), Housing Markets in Europe: A Macroeconomic Perspective, DOI 10.1007/978-3-642-15340-2_17, © Springer-Verlag Berlin Heidelberg 2010

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by the emergence of bubbles (Ball, 2005; Norris and Shiels, 2007; Bessonne and al, 2005). Whatever the reasons (fundamentals vs. bubbles) behind these developments, the role of housing markets in the economic cycles of advanced economies has been well established (IMF 2008; Muellbauer and Murphy, 2008). Developments in real housing prices have been correlated with the business cycle; residential investment has driven the business cycle in several countries and seems to be a good predictor of economic recessions. In the US, Leamer (2008) has shown for instance that residential investment accounted for 10% of the weakness in GDP growth a year before a recession. Moreover, some authors point out that residential investment not only leads the cycle, but that it actually has become a destabilising factor in most advanced economies due to the volatility it induces (Davis and Heathcote, 2005; Ball and Wood, 1999). 1 Consequently, residential investment is a key variable to control when the aim is to stabilise the business cycle. The aforementioned issues explain easily the attention that has been paid to the evolutions of residential investment. Several studies have identified macroeconomic variables influencing residential investment such as household income and housing prices (Henderson and Ioannides, 1983; Lin and Lin, 1999; Arrondel and Lefebfre, 2001). Other studies have analysed the impact of mortgage market structures on investment and consumption spending (Campbell and Hercowitz, 2005). Although it seems very plausible that structural fiscal factors may contribute to determining residential investment (ECB, 2003), studies in that domain are scarce. Among the few existing ones, most studies have investigated the impact of fiscal policy on asset prices. Alfonso and Sousa (2009) have for example shown that fiscal policy shocks play a minor role in the asset markets of the U.S. and Germany. However, fiscal policy measures substantially increase the volatility of housing and stock prices in the U.K and Italy. In the same way, van den Noord (2003) has suggested that the tax systems in smaller euro area countries are conducive to volatile house prices and have been interacting with generally higher inflation rates. In the present study we propose to close the gap by modelling French residential investment, taking explicitly into account fiscal policy measures (taxes and subsidies alike). We assess the possibility that fiscal policy influences residential investment and therefore the business cycle. To that purpose, we build a model where residential investment is explained by a number of macroeconomic (permanent income, house prices, interest rates) and fiscal variables. This will be done in the framework of a Vector Error Correction Model (VECM). The remainder of the paper is organised as follows: Section 2 presents a short overview of housing taxes and subsidies in France. Section 3 outlines the VECM methodology utilised. Section 4 then presents the empirical results obtained. The final section 5 offers some brief concluding remarks.

1

In the same way, Bisping and Patron (2008) found that shocks to residential investment have a large impact on US GDP.

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2 Overview of fiscal intervention on residential investment in France This section examines the evolution of residential investment and the various types of housing subsidies and taxes. Data on the different types of subsidies and taxes were provided by the French Ministry of Housing. The data on residential investment are taken from national accounts. Our dataset covers the period from 1984 to 2006 (the availability of fiscal data constrains the sample period). The share of residential investment in GDP exhibits a decline from 1984 to 1992, but is relatively stable around 4.3% since 1993. Residential investment’s growth rate in real terms, however, displays strong cyclical movements inducing the aforementioned instability on the business cycle (Figure 1).

2.1 Subsidies on residential investment Residential investment in France is characterised by an important, although slightly decreasing, degree of policy intervention for the period under review. In 2006, the various subsidies amounted to e 11.2 bn in real terms which is to be compared to e14 bn in 1984. For 2006, this corresponds to 1.5% of residential investment. The growth rate of subsidies in real terms displays strong fluctuations in line with residential investment developments. Subsidies on residential investment have de-

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creased over the period under review: their share in GDP declined from 0.14% in 1984 to 0.06% in 2006. This evolution covers sometimes opposite trajectories for the different sub-categories of subsidies, reflecting mainly legislative changes (Figure 2). Total subsidies can be further subdivided into three categories (financial, interest rate and tax subsidies) for which the French Ministry of Housing provides data (Table 1).

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Table 1 Subsidies on residential investment in 2006 ( e bn) Amount Financial subsidies 1.3 Interest rate subsidies 2.2 Of which general loans to households 1.5 Of which loans for social housing 1.5 Of which ’1% housing framework 0.4 Tax subsidies 7.7 Total 11.2 Source: French Ministry of Housing

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Financial subsidies amounted to e1.3 bn in 2006 and accounted for approximately 12% of total housing subsidies.2 This type of subsidies has been relatively stable over time: financial subsidies decreased somewhat in line with the decline in subsidies related to the construction of social housing around 1995, but increased again when the National Housing Agency (NAH) extended its activities from 2002 onwards. Interest rate subsidies consist in loans at preferential rates. The amount of subsidy is estimated by difference between the amount of a loan (capital and interest) contracted at market rate and a credit contracted at a preferential rate. This type of subsidy amounted to e2.2 bn in 2006 and represented 20% of total investment subsidies. Interest rate subsidies decreased by around 25% over the period, mainly due to the decline in market interest rates. Interest rate subsidies can further be divided into three categories: • General loans for households take the form of either i) housing saving plans or ii) the so-called ’zero rate loan’ that were introduced in 1995. i) A housing saving plan is very much a bank account on which the household in question has accumulated monetary holdings for at least 4 and up 10 years. It is the existence of the latter that allows a household to access preferential interest rates. ii) The zero rate loan is a supplementary loan for households planning their first home purchase, its amount being limited to 20% of total investment. The share of these loans in the total of interest rate subsidies has increased from 28% in 1986 to 66% in 2006. • Loans for social housing. The aim of these loans is to promote the purchase and improvements of social housing by low income households. The part of loans for social housing has decreased from 55% in 1986 to 16% in 2006. • Loans that are part of the ’1% housing’ framework. These loans consist in supplementary loans for main home purchases, financed by companies’ contributions to a common fund. The ’1% housing’ scheme represents a stable part of 18% in interest rate subsidies. Tax subsidies amounted to e7.7 bn or 68% of total subsidies in 2006. This last category of subsidies has doubled over the period, increasing particularly since 1999. These subsidies mainly concern housing improvements that benefit from a reduced VAT rate (5.5%) and, since 1999, tax credits. The remainder of tax subsidies takes the form of income tax reductions (’Perissol’, ’Robien’ and ’Borlo’ plans).

2

Financial subsidies have to be understood as actual cash flows between economic agents and the state.

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2.2 Taxes on residential investment In 2006, taxes on residential investment amounted to e22.7 bn in real terms, correspondong to 3.1% of total residential investment. As for subsidies, the growth rate of taxes in real terms displays strong fluctuations in line with residential investment. Over the period under consideration, taxes have increased as a share of GDP (0.09% in 1984 to 0.13% in 2006. Taxes on residential investment can be divided into indirect taxes and property taxes. Out of the two, the main component is property taxes. Their evolution exhibits a linear increasing trend since their computation is based on a stable tax base (the cadastral value) and local tax rates. On the contrary, the evolution of indirect taxes exhibits strong fluctuations and their trajectory was in particular affected by the 1995 tax cuts and a number of fiscal measures over the 1999-2001 period (see Appendix).

3 The VECM methodology Subsidies and taxes (our explanatory variables) are of course linked to the amounts finally spent on residential investment (the endogenous variable). Therefore, comovements and endogeneity may occur within the given set of variables. The VECM methodology outlined in the following allows to deal with these issues, uncovering truly exogenous fiscal shocks and assessing their effect on residential investment.

3.1 The data Residential investment (INV ) is commonly thought to depend on households’ permanent income (Y ). For our study, we chose to proxy permanent income by households’ consumption in non-durables goods and services. According to the theory of permanent income, households consume a constant fraction of their permanent income at every period, implying that a household’s consumption is proportional to its permanent income. As consumption in durable goods is rather an investment than a consumption decision, consumption in non-durables and services seems therefore to be a good proxy for permanent income. Since the aim of this study is to analyze the impact of public interventions on residential investment, we include subsidies (G) and taxes (T ) in the set of explanatory variables.

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Note that in our specification interest rates an exogenous. The long term interest rate (IRL) that we use for our specification is the 10 year government bond. This variable is clearly not determined by any of the series used in our data sample, but rather by monetary and fiscal policy actions and inflationary expectations. Using the interest rate as an exogenous variable, allows us therefore to focus on fiscal factors, disregarding financing conditions in the standard specification of the present analysis. In addition, the series of government bonds has the advantage of exhibiting the same trajectory as mortgage rates. Indeed, the margin on mortgage rates over government bonds is stable over time and small in levels as mortgages are often cross subsidized and used by banks to attract customers while banks’ profits are made in other segments of their activity. Housing prices (HP) correspond to the housing index for existing dwellings and are also held exogenous as their impact on residential investment is far from clearcut. As illustrated in Salo (1994), housing is an ’ordinary good’ (its demand is negatively related to prices) in markets where credit is not restricted. In an economy with binding quantitative restrictions imposed on borrowers, housing is no longer necessarily a decreasing function of prices and income and interest rates can have perverse effects on the stock of housing (see also Miles, 1994, and Kenny, 1999). The impact on prices will hence depend on the financing conditions of the economy. However, this subject is beyond the scope of our analysis that concentrates on fiscal measures’ impact on the business cycle. The dataset encompasses data from 1984 to 2006. National account data on residential investment are denominated in chained volumes. The fiscal series are given in current prices; in order to obtain volume indices data were deflated by the CPI. This was also done for the price series used. All variables are expressed in logarithms and real terms. According to statistical tests, data present neither seasonal patterns nor level shifts, the latter being important for the subsequent unit-root and cointegration testing procedure.

3.2 Testing procedure 3.2.1 Unit root analysis We follow the testing and estimation procedure outlined in L¨utkepohl (2004). As mentioned above, none of the series used exhibit structural breaks or shifts. It is therefore possible to conduct standard unit root tests. We conduct the type of unit root test proposed by Ng and Perron (2001). The Ng-Perron tests have two advantages in comparison to other unit root tests: their power is enhanced by local GLS detrending of the data and the use of modified information criteria leads to substantial size improvements. Unit root tests indicate that all series are first order integrated

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(see appendix). In that respect, it was particularly important to deflate the fiscal series, since otherwise they were found to have two unit roots, as often the case for data defined in current prices.

3.2.2 Determining the cointegration rank The model set up takes the following form: the data generating process (DGP) of a given K−dimensional vector of time series yt can be decomposed into a deterministic part θt and a stochastic part xt . yt = θt + xt

(1)

The deterministic part is here only of secondary interest, containing for example a constant, a polynomial trend or seasonal and other dummy variables. The stochastic part is a first order integrated process generated by a VECM of the following form:

∆ xe,t = αβ ′ xe,t−1 + Γ1∆ xe,t−1 + ... + Γp−1∆ xt−p+1 + εe,t

(2)

εe,t is a K-dimensional unobservable zero mean white noise process with positive definite covariance matrix E(ut ut′ ) = Σu . xt is a K-dimensional vector of observable variables and α and β are (Kxr) matrices of rank r. They specify the long-run part of the model where β contains the cointegration matrix, r is the cointegrating rank of the process, and α represents the loading coefficients. Thus, αβ ′ x can be referred to as the error correction term. The Γi ′ (i = 1, ..., p − 1) are (KxK) short-run parameter matrices. Given the model set-up, it is in practice necessary to determine the number of lags to take into account for the cointegration tests. This can either be done by sequential testing procedures or be based on model selection criteria. For this study the lag order was determined based on AIC criterion (L¨utkepohl and Saikonnen, 1999). Cointegration tests for the model were conducted taking into account the so-determined lag order. As the dimension of a system can have an important impact on the test results (Gonzalo and Pitarakis, 1999), cointegration tests are also undertaken for all possible sub-systems, i.e. pairs of variables. 3 Johansen’s trace test detects one cointegration relationship for residential investment (see appendix). The results of the pair wise tests (not reported here) are consistent with those for the higher dimensional systems.

3 The consistency check in a system of variables can best be explained by an example: in a system of three first-order integrated variables, all pairs of variables are found to be cointegrated. Consequently, there has to be two cointegration relationships in the whole system.

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For a given cointegration rank and lag order the VECM can be estimated by a reduced rank regression, as shown in Johansen (1991, 1995). To that purpose, restrictions have to be imposed to identify matrices α and β in (2). For one cointegration relation (r = 1) this amounts to normalising the coefficient of the first variable to one. Note that the normalisation of one or more variables requires adequate ordering of the variables in the VECM. In that sense it is particularly useful to know the cointegration ranks of all subsystems. Economically, applying restrictions on matrices α and β allows us to identify cointegration relations and by that means to replicate economic relations. We chose to normalize the coefficient of investment, since it is the dynamics of this variable that we seek to explain.

3.3 Impulse response functions and variance decomposition The relationship between variables might be highlighted by impulse response functions, these functions presenting the reactions of one variable to various shocks. However, due to the presence of unit roots (all series are first order integrated) it is not possible to invert the VAR in levels into a MA representation (i.e. the Wold representation does not exist). In order to address this issue, L¨utkepohl and Reimers (1992) suggest an algorithm that allows obtaining impulse responses recursively in a cointegrated system. To that end, the reduced form VECM is rewritten as a VAR representation in levels using the following relations: p

xe,t = ∑ Ae,p xe,t−p + εe,t

(3)

i=1

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i

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where Φo = Ik . Confidence intervals for impulse responses were constructed by bootstrap, since the latter have certain advantages over asymptotic confidence intervals. In particular, they were found to be more reliable for small samples (L¨utkepohl, 2004). The confidence intervals surrounding the following impulse response functions were obtained by the standard percentile interval as in Efron and Tibshirani (1993) with 2000 replications.

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Forecast error variance decompositions are alternative tools for analysing the dynamic interactions between the variables. Denoting by ωk j (h) the percentage contribution of variable j to the h-step forecast error variance of variable k it can be shown that:

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(θk2j,0 + ... + θk2j,h−1) ∑Kj=1 (θk2j,0 + ... + θk2j,h−1)

(5)

Where θk j,1 is the k j-th element of Φ . This method allows to decompose the total variance into different sources of variation.

4 Empirical results 4.1 Regression results for the baseline scenario The tables below report the estimation results for residential investment in France over the 1984-2006 period. Table 2 presents the results for the cointegration vector for the long-term relationship. As can be seen, income (Y ) is the main driving factor behind residential investment. The coefficient on households’ disposable income is slightly greater than unity, indicating that the share of households’ investment in GDP is constant. More precisely, this result implies a high long-run elasticity that is in line with the idea that a housing service is a superior good whose demand grows faster than income. The coefficient on subsidies (G) has the expected positive sign and is statistically significant. Results suggest a long-run elasticity of investment with respect to subsidies equal to 0.31. Thus, a rise in subsidies increases residential investment in the long run but the multiplier is below unity. This result confirms the influence of fiscal policy on residential investment. No long-run relationship is found between taxes (T ) and residential investment as the coefficient is not statistically significant. It may seem surprising that only subsidies can influence residential investment in the long run. This may be related to the fact that subsidies are a crucial variable affecting households’ investment decisions while taxes determine both consumption and investment choice.

Table 2 Baseline: cointegrating vector INV Y G T Constant 1.000 -1.095 -0.306 0.093 -2.169 [-3.618] [-3.085] [0.522] [-0.623] t-stat in brackets

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Interestingly enough, the pairwise cointegration tests conducted on the subsystems of the variables, did not indicate that a cointegration relationship exists between housing taxes and subsidies. This is in line with the budgetary principle of non-appropriation which prevents that specific fiscal revenues be earmarked to specific expenditures. More precisely, this entails that subsidies for residential investment are not financed by the revenues that taxes on residential investment generate. In addition, property taxes are levied on local levels of government and the way they are fixed is surrounded by a high degree of uncertainty. The tax base on which property taxes are levied on is the cadastral value of the property as calculated by the state. This value, although public, is little known by home buyers, since it can differ from the actual purchasing price of a housing unity. In addition, the overall tax rate is the aggregation of taxes levied at different layers of local governments (city, department, region) which fix their own tax rate each year depending on their financing needs. Therefore, the level and the evolution of property taxes are hardly foreseeable for home buyers or builders. The little information agents have on taxes ex-ante may explain that property taxes are not considered when the decision to buy or construct a house is made, and this in turn may explain that they are not significant in our estimation.

Table 3 Baseline: short term dynamics Variable ∆ INV ∆Y ∆G ECT (−1) -0.103 0.040 0.138 [-3.307] [3.117] [1.912] ∆ IRL(−2) -0.054 0.014 -0.008 [-2.882] [1.775] [-0.174] ∆ HP 0.036 0.033 0.248 [1.544] [1.220] [1.629] constant -0.010 0.008 0.012 [-2.107] [4.485] [1.100] R2 0.57 0.61 0.54 t-stat in brackets

∆T 0.008 [0.276] -0.011 [-0.635] 0.024 [0.397] 0.001 [0.187] 0.35

Table 3 summarises the results for the short-term dynamics. The short-term relationship is satisfactory in the sense that the error correction term related to the cointegration vector (ECT) is significant and exhibits the expected negative sign. The change in long-term interest rate has a negative impact on the growth rate of residential investment with a lag of 2 quarters. This is consistent with standard economic theory, since an increase in interest rates involves a bigger debt burden for households, weighing on their borrowing capacity, hence lowering investment volumes. The coefficient of housing prices is not statistically significant. This result might be explained by the fact that house prices can have mixed effects on residential investment. If housing is considered as an ’ordinary good’ an increase in prices will dampen investment. If housing is viewed as an investment in the strict sense, an increase in prices can augment residential investment. This distinction hinges also

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on whether one considers that residential investment is undertaken by households or construction firms, the former having to comply with costs while the latter can pass them on to consumers (see also Kenny, 1999).4

4.2 Impulse response analysis and variance decomposition In order to analyse the relationship between variables, impulse responses functions were computed for the model. The impulse responses are measured here as the response of residential investment to a one Cholesky standard deviation shock to each variable. As expected, the impact of revenue on residential investment is positive, even if its effect appears to be relatively weak: 0.8% after 3 years (Figure 3). The impact of subsidies is positive as expected and about 1% after 10 years. As already for the cointegration analysis, the impact of taxes on residential investment is not significant.

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The variance decomposition allows determining which of the explanatory variables is the most prominent for the dynamics of residential investment. The main explanatory variable is residential investment itself, implying some inertia in the series. This result can hint at the existence of autocorrelation which can be expected for a I(1) series. Revenue explains only 6% of investment’s variance. On the con4

This result is also broadly consistent with Girouard and Bl¨ondal (2001), as the authors find that the nexus between residential investment and the price-cost ratio appears to be weak in France.

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trary, the impact of fiscal measures is highly significant: taxes explain up to 13% of the variance after 15 quarters. The explicative power of subsidies even increases over the period under consideration and attains 25%. Subsequently, fiscal policy has a significant impact on residential investment both in the long and short run. Therefore, fiscal variables should be part of the set of explanatory variables, when analysing the factors affecting investment. It seems, however, that housing subsidies have more of an impact than taxes, making the former a more accurate tool to stabilise investment and hence the business cycle.

4.3 Specification tests Specification tests were performed for the baseline and two other specifications (see Appendix). LM tests conclude that residuals were not correlated, Jarque-Bera tests (using Urzua’s method of orthogonalization) imply their normality, and the models seem to be robust to various departures from standard linear model assumptions. The ordering of the variables may have an impact on the results. This possibility was checked by reversing the ordering of the variables and results show that this has only a negligible effect.

4.4 Alternative specifications 4.4.1 Net subsidies We consider an alternative specification for residential investment using net subsidies (subsidies minus taxes) as the only fiscal variable. This second set of results underlines the relative robustness of our results (Tables 4 and 5): long-run elasticities of investment with respect to permanent income and to net subsidies (NG) are positive and statistically significant. In addition, short-term dynamics exhibit the expected trajectories. The change in long-term interest rate has a negative impact on the growth rate of residential investment with a lag of 2 quarters; the change in housing prices is again statistically not significant. Finally, impulse responses functions display the same expected paths, as was already the case for the benchmark model (Figure 4).

Table 4 VECM with net subsidies: cointegrating vector INV Y NG Constant 1.000 -1.587 -0.316 -1.361 [-5.902] [-3.444] [-0.121] t-stat in brackets

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Table 5 VECM with net subsidies: short term dynamics Variable ∆ INV ∆Y ECT (−1) -0.062 0.031 [-2.345] [3.095] ∆ IRL(−2) -0.052 0.014 [-2.694] [1.823] ∆ HP 0.005 0.046 [0.079] [1.756] constant -0.005 0.007 [-1.190] [4.490] R2 0.50 0.34 t-stat in brackets

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Fig. 4 Alternative specifications: net subsidies

4.4.2 Financial factors Financial factors have been highlighted as one of the major determinants in differences in national housing market dynamics. For example, Tsatsaronis and Zhu (2004) have emphasised how different characteristics of mortgage markets regarding loan to value ratios, mortgage rate references, valuation methods or securitisation practises may affect the interactions between housing prices and other macroe-

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conomic variables (GDP, interest rates, bank credit). Over the period under review, major regulatory changes intervened in the French mortgage market. In 1987, the end of the administrative control of credit (’encadrement du cr´edit’) triggered a period of fast increases in loans and housing prices as banks competed for market shares. Apart from these important regulatory changes, a series of other factors had an impact on banks’ pricing strategies for mortgages. In the first place, the process of European Monetary integration contributed to a decline in interest rates, a development of which banks and consumers have benefited from in all countries. In addition, banks’ pricing and margin behaviour has very much evolved over the period in consideration: mortgages credits have become a product that banks use to attract and secure loyalty of their clients. Simultaneously, the average duration of new mortgage credits has substantially increased in France: from 11.8 years in average in 1989, it increased to 14.3 years in 1999 and accelerated to 19.2 years in 2008 (Modele Fanie, Observatoire du cr´edit immobilier). Given the above, we propose to construct an indicator of maximum indebtedness that summarizes the impact of the change in financial factors as mentioned in the preceding paragraphs. This indicator should be understood as the maximum amount of money a household can borrow for the purchase of a house given his income, the average duration of mortgages and interest rates for newly contracted mortgages.5 A household may borrow up to a monthly payment equal to a third of its income. It is thus possible to compute a maximum average amount of indebtedness per households (Kt ) as: Kt =

T 1 1 × yct × ∑ 3 (1 + rt )t t=1

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Where yct equals gross disposable income in value per household, T is average mortgage duration and rt the average interest rate on mortgages. The results for that specification are presented in tables 6 and 7. Permanent income and interest rates have been removed from the regressions as borrowing capacity already includes a gross disposable income term and takes into account changes in interest rates. The borrowing capacity has the expected positive impact on residential investment. The coefficient’s magnitude is particularly important, underlining the important influence of the above mentioned financial factors on investment. In addition, this alternative specification does not change the results obtained in former parts of the analysis: subsidies continue to be highly significant, while taxes and property prices are not. Impulse reaction functions are also consistent with the 5

This indicator has also been used by Antipa and Lecat (2010, this volume)

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ones for the benchmark model (Figure 5).

Table 6 VECM with financial factors: cointegrating vector INV K G T Constant 1.000 -0.517 -0.240 0.151 -7.736 [-5.931] [-2.476] [1.516] [-3.866] t-stat in brackets

Table 7 VECM with financial factors: short term dynamics

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The obtained results imply that fiscal tools and financial factors have a large impact on residential investment. When both of these factors are taken into account,

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property prices cease to influence residential investment. On the one hand, this entails that taxes can obviously distort price signals. On the other hand, it underlines the important role fiscal policy can play for the stabilisation of the business cycle.

4.5 A disaggregated approach While the previous sections assessed the impact of subsidies and taxes on residential investment as a whole, this section attempts to exploit the disaggregated data on the different types of taxes and subsidies described in section 2. The methodological framework remains the same (VECM, income as part of the endogenous variables, prices and interest rates as exogenous variables) while we replace the aggregate fiscal variable (subsidies or taxes) by a specific fiscal variable. The fiscal items available of are the following: financial subsidies, interest rate subsidies, tax subsidies, indirect taxes, and property taxes.6 The long term specification exhibits the same properties as the originally estimated VECM. Income is statistically significant and bears a positive sign; the same is true for all subsidies apart from the financial ones (the latter being the smallest item might explain why there impact is statistically not significant). None of the taxes considered is statistically significant. These disaggregated results confirm therefore our first set of estimations. Concerning the short-term dynamics, the error correction term is always negative and significant, and the change of interest rates has a remaining negative impact on investment growth. The change in house prices is still not significant. Figure 6 displays impulse response functions of residential investment for a positive shock of the fiscal items mentioned above. The reaction of an increase in subsidies is always positive but the magnitude is volatile depending on the fiscal item. The impact of financial subsidies is not significant, which might be due to the relatively low amounts these subsidies account for (see section 2). On the contrary, tax subsidies appear to be the type of subsidy that has the greatest impact on investment. Interest rate subsidies have a significant positive impact and this although they only represent 20% of total subsidies. Concerning taxes, indirect taxes are the only ones that exhibit the expected negative impact on investment, but their significance level decreases rapidly. The impact of a property tax shock on investment is somewhat counterintuitive, as it exhibits a positive sign which might be related to changes in the tax base that are not correlated 6

The number of lags chosen for specifications related to financial subsidies and indirect taxes is smaller (3 lags) than the one in the baseline (4 lags), reflecting the fact that these measures are paid out /levied directly. In contrast, the number of lags chosen for the specification related to tax subsidies is higher (6 lags) as households benefit from the latter only upon reception of their income tax return.

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to the evolutions of residential investment itself. The mixed effect of the disaggregated tax sub-categories explains the non-significance of taxes as an aggregate item.

4.6 Changes in fiscal activism over time The structure of public intervention on residential investment in France has strongly changed since the 1980s and this is especially the case regarding subsidies. These changes could have modified the impact each fiscal item has on residential investment. To detect possible changes of fiscal measures’ impact over time, we propose a recursive analysis of subsidies on data windows of 11 years. For each type of subsidy, we estimate the VAR over [t1 , t44 ] and compute the associated impulse response functions. In the following, we move ahead by one period and reestimate over the sample [t1 , t45 ]. This procedure is repeated up to the last available data point of the sample[t1, tT ]. The impact of financial subsidies is relatively low over the period. Moreover, although the first impulse on investment is positive, the effect decreases rapidly. When the 1996-1997 period is included, the estimated impact is strongly negative and may reflect the impact of subsidy cuts. Conversely, the extension of the scope of the National Housing Agency in 2002 appears to have a more persistent positive effect. Interest rate subsidies have a positive impact that is relatively stable over the

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period in consideration. Finally, tax subsidies’ impact is always strongly positive, but seems to have declined somewhat over the period. The results for the dynamic assessment underline that the positive impact subsidies can have on residential investment is also stable over time. Our results would thus imply that by far the most effective policy to influence residential investment is one that relies on tax and interest subsidies. Interestingly, the actual measures taken since 2006 seem consistent with the results of this study. The deductibility of loan interest rates for instance is a tax subsidy that should have a significant effect on housing market dynamics. Similarly, the green ’zero rate loans’ instituted in the 2009 budget should enhance the fiscal stimulus for residential investment and should therefore help cushion turbulences in the French housing market.

5 Concluding remarks The present study models French residential investment by means of a VECM that explicitly takes into account fiscal variables. Our analysis has shown that fiscal variables (subsidies and taxes) should be included in the analysis of residential investment. Analytically, a long term relationship between investment and subsidies exists, making subsidies an adequate measure to influence residential investment and hence the business cycle. A disaggregated approach for several different fiscal measures confirms that subsides rather than taxes should be used in order to effectively impact residential investment. More precisely, tax and interest rate subsidies have the most significant positive impact on investment. When accounting for financial factors by means of households’ borrowing capacity, we find that the latter also influences residential investment positively. In addition, this alternative specification underlines the robustness of our baseline specification, as it confirms subsidies as the most efficient measure to influence investment. It is also noteworthy that for none of our specifications residential property prices have a statistically significant impact on investment. This result probably hinges on the dual character of housing (investment versus consumption good). While this entails that taxes can distort price signals, it underlines as well the important role fiscal policy can play for the stabilisation of the business cycle.7

7 Measures taken since 2006 seem consistent with the results of this study. The deductibility of loan interest ,for instance, is a tax subsidy that can have significant effects on housing market dynamics and might help cushion the ongoing decline in house prices.

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References Alfonso A., Sousa T. (2009), Fiscal policy, housing and stock prices, ECB, Working Paper, No.990. Antipa P., Lecat R. (2010), Impact of fiscal policy on residential investment in France, this volume. Arrondel L., Lefebfre B. (2001), Consumption and investment motives in housing wealth accumulation: a french study, Journal of Urban Economics, No.50. Ball M. (2005), RICS European Housing Review, RICS, London. Ball M., Wood A. (1999), Housing investment: long run international trends and volatility, Housing Studies, No.14. Bisping T., Patron H. (2008), Residential investment and business cycles in an open economy: a generalized impulse response approach, Journal of Real Estate Finance and Economics,, 37, 1. Beffy P-O., Montfort B. (2003), Patrimoine des m´enages, dynamique d’allocation et comportement de consommation, INSEE, Working Paper, No.G2003/08. Bessonne A-J., Boissinot J., Heitz B. (2005), Are we seeing a bubble on the French housing market ?, INSEE Conjoncture. Campbell, J., Hercowitz, Z. (2005), The role of collateralized household debt in macroeconomic stabilization, NBER, Working Paper No.11330. Davis M., Heathcote J. (2005), Housing and the Business Cycle, International Economic Review, 46,3. ECB (2003), Structural factors in the EU housing markets, ECB, Monthly Bulletin, 46, 3. Efron, B., Tibshirani, R.J. (1993), An introduction to the bootstrap, Chapman & Hall, London. Girouard N., Bl¨ondal S. (2001), House prices and economic activity, OECD, Working Paper, No. 279. Gonzalo J., and Pitarakis, J-Y (1999), Dimensionality effect in cointegration analysis, in R. Engle and H. White (eds), Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger, Oxford University Press, Oxford. Henderson J., Ioannides Y. (1983), A model of housing tenure choice, American Economic Review, No.73. IMF (2008), The changing housing cycle and the implications for monetary policy, World Economic Outlook. Leamer (2008), What’s a recession, anyway?, NBER, Working Paper, No. 14221. Lin C-C, Lin S-J. (1999), An estimation of elasticities of consumption demand and investment demand for Owner-Occupied housing in taiwan: a two-period model, International Real Estate Review, No. 2, 1. L¨utkepohl, H. (2004), Recent advances in cointegration analysis, European University Institute Working Paper L¨utkepohl, H., Reimers H-E. (1992), Impulse response analysis of cointegrated systems, Journal of Economic Dynamics and Control, No.16. L¨utkepohl, H. and Saikkonnen, P. (1999), Order selection in testing for the cointegration rank of a VAR process in R. Engle and H. White (eds), Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger, Oxford University Press, Oxford. Miles, D. (1993), House price, personal sector wealth and consumption: some conceptual and empirical issues, The Manchester School of Economics and Social Studies, 61, 0. Muellbauer J., Murphy A. (2008), Housing markets and the economy: the assessment, Oxford Review of Economic Policy, 24, 1. Ng S., Perron (2001), Lag length selection and the construction of unit root tests with good size and power, Econometrica, 69, 6. Norris M., Shiels P. (2007), Housing inequalities in an enlarged European Union: patterns, drivers, implications, Journal of European Social Policy, 17, 1. Van den Noord P. (2003), Tax incentives and house price volatility in the euro area: theory and evidence, OECD, Working Paper, No.356.

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Appendix

Table 8 Ng-Perron unit root tests: variables in levels Variable Exogeneous INV C+T 5% critical values Y C+T 5% critical values G C 5% critical values T C+T 5% critical values HP C+T 5% critical values IRL C+T 5% critical values

Lag MZa MZt 1 -4.084 -1.191 -17.300 -2.910 1 -2.275 -1.034 -17.300 -2.910 5 -2.505 -1.112 -8.100 -1.980 1 -4.036 -1.371 -17.300 -2.910 2 -3.275 -0.971 -17.300 -2.910 1 -12.548 -2.525 -17.300 -2.910

MSP 0.292 0.168 0.454 0.168 0.444 0.233 0.339 0.168 0.297 0.168 0.198 0.168

MPT 19.878 5.480 38.509 5.480 9.738 3.170 22.013 5.480 22.106 5.480 3.839 5.480

MSP 0.228 0.233 0.636 0.233 0.193 0.233 0.188 0.233 0.188 0.168 0.112 0.233

MPT 2.602 3.170 22.364 3.170 1.975 3.170 1.915 3.170 1.915 5.480 0.622 3.170

Table 9 Ng-Perron unit root tests: variables in first differences Variable Exogeneous ∆ INV C 5% critical values ∆Y C 5% critical values ∆G C 5% critical values ∆T C 5% critical values ∆ HP C+T 5% critical values ∆ IRL C 5% critical values

Lag MZa MZt 3 -8.536 -2.175 -13.800 -1.980 10 -0.783 -0.498 -13.800 -1.980 5 -13.153 -2.536 -13.800 -1.980 9 -13.153 -2.589 -13.800 -1.980 2 -19.766 -2.589 -17.300 -2.910 0 -39.511 -4.444 -13.800 -1.980

The Ng-Perron test fails to reject the null hypothesis of a unit root the first difference of the permanent income series. However, as the graphical analysis of the series in first differences showed there is no reason to believe that the series for permanent income contains a unit root. ADF and Phillips Peron unit root tests (not reported here) confirmed in addition that the series is stationnary once differentiated. Note that for seasonally adjusted series the null hypothesis of a unit root is less often rejected than it should be (Davidson et al., 1992).

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Table 10 Johansen cointegration tests Series included: INV, Y, G, T Lags: 1 to 4 rank Eigenvalue Trace Stat. 5% Critical value Max. Eigenv. Stat. 5% critical value r=0 0.301 58.831 47.856 31.138 27.584 r=1 0.176 27.684 29.797 16.887 21.132 r=2 0.072 10.807 15.494 6.471 14.265 r=3 0.049 4.335 3.841 4.335 3.841

Table 11 Residual tests Test Portemanteau Portemanteau adj. LM-Type Jarque-Bera

t-stat 37.590 37.361 25.601 17.160

p-value 0.003 0.002 0.096 0.029

Table 12 Chronology of fiscal measures Date 1984 1993 1995 1996 1998 1999

2001 2002 2003 2005 2006

Category Tax subsidy Interest rate subsidy Interest rate subsidy Indirect tax Financial subsidy Interest rate subsidy Tax subsidy Indirect tax Interest rate subsidy Interest rate subsidy Tax subsidy Tax subsidy Indirect tax Tax subsidy Financial subsidy Tax subsidiy Interest rate subsidy Tax subsidy

Measure Mehaignerie Plan Social renting loan (’PLS’) Instauration of the zero interest rate loan Reduction of the regional tax rate Rate reduction Modification of taxation for housing saving plans Perissol Plan Abolition of regional tax rate Abolition of subsidies for renting loans (’PLA’) Introduction of a social renting loans (’PLUS’) Besson Plan Income tax credit for small housing works VAT reduction for housing sector Extension of income tax credit Extension of intervention field of NAH Robien Plan Extension of zero interest rate loan Borloo Plan