Essays on housing and real economy

It increases household’sexposure to risk and shifts the conditional distribution of consumption growth.Using the United States data, I …nd that the ‡uctuation of housing-…nancial wealthr

I owe an enormous debt of gratitude to my supervisor, Associate Professor SingTien Foo for his support, guidance and encouragement throughout the Ph.D.program His gentle personality and meticulous attitude to research will bene…t

my career as well as personal life

Special thanks to Dr Liao Wen-chi, who gives me a lot of help on my research,especially for Chapter 3

Great thankfulness is expressed to Associate Professor Fu Yuming, AssociateProfessor Yu Shi Ming, Associate Professor Tu Yong, Professor Ong Seow Eng,Professor Deng Yongheng, Dr Lee Nai Jia, Dr Li Nan, Dr Seah Kiat Ying,

Dr Li Pei, Dr Qian Wenlan, Professor James D Shilling, Dr Chu Yongqiangfor their helpful comments, suggestions and discussions on my thesis and generalacademic career

I am grateful for helpful comments from the participants at the Asian RealEstate Society annual conference 2010, Paci…c Rim Real Estate Society annualconference 2012, and Global Chinese Real Estate Congress annual conference 2012

I would like to thank all of my postgraduate peers I enjoyed sharing ideasand developing my research by conversing with them They are included butnot limited: Wong Woei Chyuan, Omokolade Ayodeji Akinsomi, Liu Bo, ShenHuaisheng, Li Mu, Wei Yuan, Liang Lanfeng, Xu Yiqin, Zhang Huiming, Shen

i

Yinjie, Liu Jingran, Peng Siyuan, Jiang Yuxi, Chen Wei, Wang Yourong, GuoYan, Li Qing, Radheshyam Chamarajanagara Gopinath, and etc.

I would also like to thank the administrative sta¤ members, Zainab Bte AbdulGhani, Zheng Huiming, Nor’aini Bte Ali, Wong Mei Yin, Ko Chen, who were soinstrumental in helping me get things done smoothly

Generous …nancial support from National University of Singapore is highlyappreciated

Finally, I thank my family, particularly my wife, Qiu Leiju, who has beenunconditional supportive and encouraging during the course of my study

Acknowledgements i

1.1 Research Background 1

1.2 Overview of the Research 4

1.3 Signi…cance of the Research 6

1.4 Organization of the Thesis 7

2 Housing, Wealth Composition and Expected Stock Return 9 2.1 Introduction 9

2.2 Related Literature 16

2.3 Model 19

2.3.1 Environment and Preferences 19

2.3.2 Housing Market 21

2.3.3 Pricing Kernel 23

2.4 Data and Measurement 25

2.4.1 Measurement of Housing-Financial Wealth Ratio 26

2.4.2 Consumption Data 30

iii

2.4.3 Financial Data 32

2.5 Long-horizon Forecasts 33

2.6 Cross-Sectional Test of the Linear Factor Model 37

2.6.1 The Linear Factor Model and Fama-MacBeth Procedure 37

2.6.2 Results from Fama-MacBeth Procedure 39

2.6.3 Sensitivity Analysis 45

2.6.4 Time-varying Consumption Betas 47

2.7 Micro Evidence from Subprime Crisis 52

2.7.1 Time-varying Stock Market Participation 53

2.7.2 Determinants of Distress 55

2.7.3 Consequence of Distress 58

2.8 Conclusion 60

2.9 Appendix: Panel Study of Income Dynamics (PSID) Data 61

3 Risk Attitude and Housing Wealth E¤ect 65 3.1 Introduction 65

3.2 Model 69

3.3 Data 76

3.4 Empirical Tests and Results 80

3.4.1 Estimate Risk Attitude 81

3.4.2 Estimate HWE by Risk Attitude 87

3.5 Conclusion 94

3.6 Appendix 97

3.6.1 Descriptive Statistics of Risky Assets Holding 97

3.6.2 First Step Probit Model of Heckman Correction 97

4 Consumption and Wealth Accumulation over the Life Cycle: Does

4.2 Stylized Facts 105

4.3 Model 109

4.3.1 Demographics 109

4.3.2 Technology 109

4.3.3 Preferences 110

4.3.4 Endowments 111

4.3.5 Markets 111

4.3.6 Timing 113

4.3.7 The Household’s Problem 113

4.3.8 Equilibrium 115

4.4 Calibration 116

4.5 Results 118

4.6 Conclusion 123

4.7 Appendix 123

4.7.1 Life-cycle Wealth and Non-housing Consumption 123

4.7.2 Numerical Computation Algorithm 125

5 Conclusion 127 5.1 Summary of Main Findings 127

5.2 Policy Implication 130

5.3 Limitation and Future Work 131

This thesis focuses on issues related to the roles of housing in real economy ing is the single most important consumption good, and the dominate wealth forhouseholds The unique characteristic in‡uences the behavior of households interms of consumption, saving, mortgage issuance, and asset return This thesis iscomposed of three main chapters

Hous-Chapter 2 considers a consumption-based asset pricing model where housing isexplicitly modelled both as an asset and a consumption good As a consumptiongood, housing expenditure share is modelled as a novel risk factor As an asset,

it is the major component of wealth other than …nancial assets The ‡uctuation

of aggregate housing-…nancial wealth ratio, as a consequence of irrational housingmarket, impacts the budget constraints of households It increases household’sexposure to risk and shifts the conditional distribution of consumption growth.Using the United States data, I …nd that the ‡uctuation of housing-…nancial wealthratio is a strong predictor for the expected stock return Conditional on thisfactor, the covariances of the returns with the aggregate risk factors explain alarge ratio of the cross-sectional variations in annual returns of size and book-to-market portfolio The micro mechanism of this asset pricing model is alsosupported by the micro data during subprime crisis

Chapter 3 examines the housing wealth e¤ect— the positive consumption change

vi

a negative relationship between the wealth e¤ect and risk aversion This chapterempirically tests this negative relationship, using data from the U.S ConsumerExpenditure Survey (CEX) The investigation involves two steps In the …rst step,

I make use of households’demographic and their risky and liquid asset holdings

to estimate risk aversion The Heckman correction model is applied to addressthe issue of limited stock market participation In the second step, I constructpseudo panel data through grouping households by their birth years and theirpredicted values of risk aversion, and then, I estimate the responses of households’consumption changes to house price ‡uctuations by di¤erent risk-attitude groups.Consistent with the prediction of the theoretical model, the estimation resultssuggest a signi…cant negative relationship between the housing wealth e¤ect andhouseholds’risk attitude Households, who are less risk averse, experience greaterconsumption changes in response to house price appreciation

Chapter 4 explains the in‡uences of mortgage down payment requirement

in both the housing and the credit markets The rapid expansion of mortgagecredit market since the mid-1990s reduces the mortgage down payment require-ment for the U.S households Micro data over the life cycle show that the pat-terns of consumption and wealth accumulation changed after the credit expansion:non-housing consumption for older household increases signi…cantly, but youngerhouseholds own less wealth This chapter develops a dynamic general equilibriummodel with constant housing supply, which …nds that decreases in down paymentrequirement account for changes in the pro…les of consumption and wealth accu-mulation for households This model also implies that decreases in down paymentrequirement cannot explain increases in homeownership rate since the mid-1990s

List of Tables

2.1 List of Variables 26

2.2 Summary Statistics of Hostorical Data 31

2.3 Long-Horizon Predictability Regressions 36

2.4 Fama-Macbeth Regression Results 40

2.5 Comparison of Asset Pricing Models 42

2.6 Cross-Sectional Results with Lagged Consumption 46

2.7 Cross-Sectional Results with Lagged Housing-Financial Wealth Ratio 48 2.8 Cross-Sectional Results with Overlapped Return 49

2.9 Consumption Beta 51

2.10 Time-varying Stock Market Participation and Foreclosure 53

2.11 Logit Regression on Determinants of Distress 56

2.12 Stock Market Participation by Di¤erent Types Families 58

2.13 Test of Consumption Insurance 59

2.14 Descriptive Statistics of PSID Data 64

3.1 Benchmark Values of Parameters 74

3.2 Regression of Risky Asset Composition on Demographics 84

3.3 Cohort Regression of Consumption Change by Risk Attitude 93

3.4 Comparison of The Housing Wealth E¤ect across Risk Attitude Groups 94

viii

3.6 Descriptive Statistics of Risky Assets Holding 98

3.7 First Step Probit Model of Heckman Correction 99

4.1 Parameters of Benchmark Model 116

4.2 Aggregate Variables in Two States 119

4.3 Household Equivalence Scales 125

List of Figures

2.1 Housing Wealth and Financial Wealth Growth: 1929-2009 282.2 Comparison of Housing-Financial Wealth Ratio Meaurements 292.3 The Housing-Financial Wealth Ratio and 10-yrs Cumulative ExcessReturn 342.4 Realized versus Predicted Returns for the Fama-French Portfolios 44

3.1 Housing Wealth E¤ect by Relative Risk Aversion 753.2 Housing Wealth E¤ect by Initial LTV and Weight in Terminal Wealth 773.3 Structure of Consumer Expenditure Survey (CEX) data 793.4 Reconstruction of Consumer Expenditure Survey (CEX) data 813.5 Consumption and Income over Life Cycle 90

4.1 Consumption of Household over Life-cycle in U.S 1997 and 2005 1064.2 Wealth of Household over Life-cycle in U.S 1994 and 2005 1084.3 Consumption over Life-cycle under 20% and 10% Downpayment 1214.4 Wealth over Life-cycle under 20% and 10% Downpayment 122

x

Housing, that provides necessary shelter, is the largest consumer expenditure inU.S In 2009, personal housing consumption expenditures were about 1.5 trilliondollars, or 15.8% of household budgets1 It is also the dominant wealth compo-sition in household’s portfolio Bertaut and Starr-McCluer (2002) show that res-idential property accounted for about one quarter of aggregate household wealth

in the US in the late 1990s, while Banks and Tanner (2002) report that real estateaccounted for 35% of aggregate household wealth in UK in the mid-1990s

With the development of economy, housing is not just a consumption andinvestment good It also in‡uences modern economic system through the …nancemarket The expansion of property backed …nancial derivatives integrate housingmarket closely with other economic sectors In 2009, the total mortgage relatedsecurity is about 9.18 trillion U.S dollar compared with 34.74 trillion U.S dollartotal value in US bond market2 The recent subprime mortgage crisis highlights

1 Data is from National Income and Product Account (NPIA) Table 2.4.5 “personal tion expenditures by types”.

consump-2 Data source: Securities Industry and Financial Markets Association (SIFMA)

1

the pervasive in‡uences of housing in the economy Studies show that this crisis

is triggered by declines in housing market, which consequently causes a dramaticrise in mortgage delinquencies and foreclosures in the US, The adverse e¤ects spillover to the …nancial markets around the world

There is a substantial, mostly older literature on the modelling of housing inreal economy This stream of literature takes the overall economic environment

as given and explores the e¤ects of income and interest rates on residential vestment, housing price and other related real estate issues (e.g Alberts 1962,Fair, 1972; Ketchum 1954; de Leeuw and Gramlich, 1969) By including interestrate and income as explanatory variables, the literature explicitly explores thelink from economic environment to housing market However, the feedback e¤ectfrom the housing market is widely neglected by most of the previous literatures.Since the substantial weight of housing wealth in the real economy, changes inhousing market impact the whole economic system The previous literature fails

in-to consider endogeneity issues between the housing market and the real economy.Built on this stream of literature, the housing researches now expand to awider scope The frontier research on housing covers three aspects Firstly, theperformance of housing market can be taken as a sensitive indicator of economy

As Leamer (2007) said “housing is the business cycle”, economic statistics showstrong correlations between the housing variables (e.g residential investment,housing consumption, housing price) and the macroeconomic variables (e.g inter-est rate, unemployment, in‡ation)3 This linkages o¤er a clear sign of economic

‡uctuation One of implementations is asset pricing model Cochrane (1991, 1996)tests his production-based asset pricing model with both common and residential

http://www.sifma.org/uploadedFiles/Research/Statistics/SIFMA_USBondMarketOutstanding.pdf

3 The related research can refer to Green (1997), Gauger and Snyder (2003), Leamer (2007), etc.

variables into the asset pricing framework (e.g Piazzesi, Scheider and Tuzel, 2007;Lustig and Nieuwerburgh, 2006; Chu, 2010) has been published.

The ‡uctuations in housing market also provide feedback e¤ects into the realeconomy The most important feedback e¤ect in the housing market is known asthe "housing wealth e¤ect" This research pioneers by Case, Quigley and Shiller(2005) Their most widely cited paper …nds signi…cant housing e¤ects, which islarger than the wealth e¤ects from the stock market However a number of subse-quent empirical researches examining the housing wealth e¤ect from both microand aggregate level show mixed results The strength of housing wealth e¤ectsvaries depending on the dataset and methodology4 Theoretically, the di¢ culty

of housing wealth e¤ect is the completely di¤erent impacts of housing price onhomeowners and renters It is easy to understand that homeowners feel rich based

on their home’s appreciation and therefore consume more The problem with thisline of thought is that increasing housing price means increasing housing cost forrenters, who experience the boom of housing market as a decrease in real wage Inorder to avoid this problem, housing wealth e¤ect is generally modelled in the con-texts of life cycle, tenure choice and credit constraint These models (e.g Buiter,2008; Campbell and Cocco, 2007) show that housing wealth will be of second or-der importance for non-housing consumption Housing value increases result in

4 Carroll and Slacalek (2006) reports larger and signi…cant housing wealth e¤ect in US market based on aggregate data Campbell and Cocco (2007) …nd housing wealth e¤ect in UK with individual data Gabriel, Bostic and Painter(2009) link CEX and SCF two micro datasets and show positive housing wealth e¤ect in US However, Attansio, Blow, Hamilton and Leicester (2009) employ UK micro level dataset and …nd no housing wealth e¤ect They argue that correlation between housing wealth and consumption may arise from the same response to third factors Calomiris, Longhofer and Miles (2009) question the methodology in Case, Quigley and Shiller (2005) and Carroll and Slacalek (2006)’s paper They claim housing wealth e¤ect is mythical after handling the endogeneity issues Following this idea, Sousa (2009) reports housing wealth e¤ect is virtually nil in European countries.

higher collateral value and therefore relax borrowing constraints5 Housing wealthindirectly a¤ects non-housing consumption through the collateral channel.

Since housing wealth and consumption have considerable weight in real omy, housing can play a role of media during economic cycle Business downturndeteriorate asset values, reduce debt capacity and depress investment, which willcollectively amplify the magnitude of declines in the downturn (Bernake and Gerl-ter, 1989) Recent empirical evidences are reported by Chaney, Sraer and Thesmar(forthcoming) for US and France, and Gan (2007a, 2007b) for Japan The recentsubprime crisis shows the need for researches not to neglect the importance ofhousing in the macroeconomic models Household leverage, mortgage issuance,and foreclosure are closely linked with asset price, investment and consumptionthrough housing market during and after this recession (e.g Mian and Su…, 2010;Mian, Su…, and Trebbi, 2011)

In line with above cutting-edge researches, I discuss the linkage between housingand real economy in this dissertation In my study, housing is modeled into theutility function of household; and also considered in the budget constraint at thesame time Housing plays a dual-role in my research, and I propose a consumptionbased asset pricing model, a typical household consumption model and a generalequilibrium model in the following three main chapters respectively They describedi¤erent impacts of housing on real economy

Chapter 2 extends the consumption-based asset pricing model, where housing isconsidered as both consumption and wealth composition As consumption goods,

5 This is called "collateral e¤ect" in the research on corporate real estate Higher real estate asset value can increase …rms’debt capacity e.g Benmelech, Garmaise and Moskowitz, 2005; Chaney, Sraer and Thesmar, forthcoming; Gan, 2007a, 2007b.

in housing will in‡uence household’s consumption when the market declines The

‡uctuations of irrational housing market can add volatility into the stock market.The micro data from subprime crisis shows a clear linkage between over-investment

in housing and distress in consumption Using the U.S market data, the housingwealth composition factor is found to be a strong predictor of the expected stockreturn

Chapter 3 studies the consumption behaviors of heterogeneous households responding to changes in housing prices, which is also known as "housing wealthe¤ect" The researches on housing wealth e¤ect ‡ourish recently, but the resultsare still controversial In my study, housing wealth e¤ect is linked to household’srisk attitude Through both the theoretical analysis and empirical testing usingConsumer Expenditure Survey (CEX), I …nd that housing wealth e¤ect variesacross households with di¤erent risk attitudes Households, who are less riskaverse, experience greater consumption changes in response to house price appre-ciation

cor-Chapter 4 shows the patterns of consumption and wealth accumulation over lifecycle changed with the rapid mortgage credit expansion Micro-data reports thatthe non-housing consumption for older households increase signi…cantly, whereasthe wealth accumulates slowly for younger households after the mortgage creditexpansion in U.S An overlapping generation model is proposed and calibrated,which explicitly shows that lower down payment requirement can impact bothhousing and credit market It accounts for the changes of consumption and wealthaccumulation pro…les

1.3 Signi…cance of the Research

This research emphasizes the linkage between housing and real economy and siders the dual-role of housing— both consumption and investment goods — intoconsumption sector A consumption based asset pricing model, a typical house-hold consumption model and a general equilibrium model are proposed in thisdissertation respectively to describe the impacts of housing on real economy Itpotentially contributes to the current …nance, macroeconomic and real estate lit-erature

con-To …nance literature, it adds the ‡uctuation from housing market into set pricing model and mitigates the poor empirical performance of consumptionasset pricing model (see Breedem, Gibbons and Litzenberger, 1989; Mehra andPrescott, 1985) This dissertation also discusses the impacts of credit expan-sion on both housing market and credit market It enriches the studies on therecent severe mortgage credit expansion since 1990s (see Chomsosengphet andPennington-Cross, 2006; Mayer and Pence, 2008; Greenspan and Kennedy, 2008)

as-To macroeconomic literature, it considers that the households’ consumptionbehavior over life cycle and how they response to the shock from housing marketand credit market It is related to a growing literature on how durable goods a¤ectthe households’consumption over life cycle (See Cho and Sane 2006; Fernandez-Villaverde and Krueger, 2011)

To real estate literature, this dissertation enhances the understanding on threestreams literature Firstly, it is the part of literature that studies the linkage be-tween real estate returns and stock returns (see Kullman, 2003; Chu, 2010); sec-ondly, the results in this dissertation indicate a new angle for previous researches

on housing wealth e¤ects Previous literature have presented encouraging ical evidences (see Case, Quigley and Shiller, 2005; Benjamin, Chinloy and Jud,

empir-Thirdly, it is also a complement of the researches on house ownership decision ofborrowing constrained households (see Zorn, 1989; Linneman and Wachter, 1989;Brueckner and Follain, 1990).

More speci…cally, the signi…cance of each main chapter is presented as follows.This thesis proposes a housing asset pricing model (Chapter 2) which includes bothhousing consumption and housing wealth risk factors The empirical test …nds thatthis model can mitigate the poor performance of consumption based asset pricingmodel (CCAPM) The housing pricing factors show higher explanatory power incross section and time serially

Housing wealth e¤ects on consumption are examined by the risk attitudes ofhouseholds in the thesis (Chapter 3) This study …nds that housing wealth e¤ectsvary among households with heterogeneous risk attitudes It adds a new angle inunderstanding the cross-sectional variation in housing wealth e¤ects in previousliterature

The thesis investigates the in‡uence of changes in down payment requirement

on consumption and savings behaviors of households in a general equilibrium ture (Chapter 4) Unlike prior studies, variables in the …nancial market and thehousing market are all endogenous Households are impacted by changes in downpayment requirement through these two markets at the same time

The remaining part of the thesis is organized as follows: Chapter 2 presents the

…rst story, entitled “Housing, Wealth Composition and Expected Stock Return” It

explores the in‡uences of the housing market on the stock market The impacts ofincreasing housing prices on non-housing consumption are examined in Chapter 3,entitled “Risk Attitude and Housing Wealth E¤ect” Chapter 4 presents the thirdstory, entitled “Consumption and Wealth Accumulation over the Life Cycle: DoesDown Payment Matters? ” This chapter investigates the consumption and savingbehaviors of households over the cycle corresponding di¤erent down payment re-quirements The …nal chapter concludes the thesis, highlights the limitations ofthe study, and provides recommendations for further research.

Housing, Wealth Composition

and Expected Stock Return

Housing is widely accepted having a dual-role in real economy It is the singlemost important consumption good supplying amenity for households, and, at thesame time, the dominant asset in their portfolios This research explicitly modelsthis characteristic in the utility function to explain the variations in both expectedreturns across stocks and equity risk premium over time

My research starts with Flavin and Yamashita (2002)’s point that housing isone asset in household’s portfolio In an uncertain environment, wealth composi-tion should satisfy the mean-variance e¢ ciency structure(Flavin and Nakagawa,2008) If the stock market is e¢ cient, as in the Fama’s (1970) hypothesis, the

‡uctuation of wealth composition, measured by housing-…nancial wealth ratio, istriggered by irrational housing market The ‡uctuation of wealth compositionin‡uences the budget constraints of households, and changes the distribution of

9

consumption growth This is a possible channel through that irrational housingmarket impacts the expected stock return.

This research use U.S equity returns data to test the predictability Themodel …nds a signi…cant relationship between irrational housing market and riskpremia Risk premia of consumption growth in a hot housing market is higher.The consumption betas are time-varying Conditional on the wealth composition,the covariances of returns with aggregate risk factors explain 80% of the cross-sectional variation in annual size and book-to-market portfolio returns

Housing plays a dual-role in my asset pricing model As a consumption good,

it is separated from the common consumption and modeled as an independentargument in the utility function In Piazzesi, Schneider and Tuzel’s (2007) generalequilibrium model, housing consumption introduces a novel risk factor: shock ofthe non housing expenditure share This new argument in stochastic discountfactor (SDF) is derived from the non separable utility function, and represents theconsumption composition risk

As an investment good, housing is an asset in the households’wealth portfolio.The change in wealth composition re‡ects the change in the expected risk premiafor individual asset If housing market is irrational, a high housing-…nancial wealthratio implies that housing market is hot Investors expect housing to have highrisk premium in future, and they will increase housing investment in their portfo-lio On the other hand, when their expectations are broken, some of the investorswill be su¤ered from tight budget constraints Considering a full consumption in-surance here: "If markets are complete or if there is some other mechanism or set

of institutions that implement a full-information Pareto-optimal allocation, then

an individual’s consumption should not respond to idiosyncratic income or wealthshocks."(Cochrane,1991) Consumption growth is determined by the systematic

fore, tight budget constraint will change households’consumption growth, whichintroduces a new factor to asset pricing model This mechanism bridges the wealthcomposition and expected stock return.

The above describes the mechanism of how macroeconomic factors predict theexpected stock returns Four key elements play the key roles in this process Theyare listed as follows:

Irrational Housing Market The stock market e¢ ciency is a widely cussed topic, and Fama (1970) concludes that the e¢ cient market hypothesis isnot neglected after reviewing a large number of articles on market e¢ ciency re-search This hypothesis asserts that …nancial markets are "informationally e¢ -cient", in other word, rational Although the hypothesis is still controversial bysome empirical results and behavior …nance theory, economists will still acceptthis hypothesis in their models’assumption1 However, housing market is known

dis-to be less e¢ cient and driven by irrational behavior of households because of thespecial characteristics of housing, such as high transaction cost, indivisibility, andlack of short sell This is supported by empirical evidence2

Portfolio "Modern portfolio theory is a theory of investment, which attempts

to maximize portfolio expected return for a given amount of portfolio risk, orequivalently minimize risk for a given level of expected return, by carefully choos-ing the proportions of various assets"3 It is so called "mean-variance e¢ ciency

1 The continuous discussion on e¢ cient market hypothesis can be found in Fama’s(1998) other survey paper.

2 The most important paper testing e¢ ciency in housing market is published by Cash and Shiller(1989,1990) They build repeated sale housing price index for four metropolitan areas, and …nd very strong serial correlation They conclude U.S market for homes appears not to

be e¢ cient Recently Shilling and Sing (2009) point out the irrational term in commercial real market can explain 4 percent of the variations among total 19 to 27 percent.

3 http://en.wikipedia.org/wiki/Modern_portfolio_theory

framework" This leads to the development of the synthetic risk model known as

"CAPM theory" (Sharpe,1964; Lintner,1965), widely used in the stock market.Flavin and Yamashita (2002) include housing as one of the assets in household’sportfolio, and explain the owner-occupied housing decision based on this theoret-ical framework4 In the mean-variance e¢ ciency framework, the composition ofportfolio is determined by the expected return, volatility of assets, and the riskattitude of consumer In a general equilibrium structure, the expected return andthe volatility of assets both source from the uncertain environment The portfoliocomposition is …xed if the risk attitude of consumer is constant The composition

of portfolio re‡ects the expected returns of asset in an uncertain environment.Consumption Insurance This idea came from the permanent income hy-pothesis in macroeconomic area Modigliani and Brumberg (1954) and Friedman(1957) note in their permanent income hypothesis and life cycle model that in-dividuals tend to smooth their consumption over states of nature in order tomaximum their utility functions over the life cycle The consumption insurance inasset pricing model is viewed as a cross-sectional counterpart to the life cycle the-ory5 The full consumption insurance implies that heterogeneous consumers areable to equalize, state by state, their marginal rates of substitution Therefore, theequilibrium in a heterogeneous-consumer economy is isomorphic in its pricing im-plications to the equilibrium of a representative-consumer economy (Wilson, 1968;Constantinides, 1982) This theoretical fundamental underlies most of macroeco-nomic asset pricing models, and thus the aggregate data can link with pricingmodels with representative agent The primary testable implications of equilib-

4 The researches on portfolio choice with exogenous returns in the presence of housing also can be found in Yamashita (2003), Cocco (2005), and Flavin and Nakagawa (2008).

5 There is an extensive literature on the hypothesis of complete consumption insurance; see Cochrane (1991), Mace (1991), Altonji, Hayashi, and Kotliko¤ (1992), and Attanasio and Davis (1996).

security prices Mehra and Prescott (1985) point out that the model predicts amean equity premium that is too low and a mean interest rate that is too highgiven the observed low variability of aggregate consumption growth in U.S mar-ket, and they call this phenomenon "equity premium puzzle" Modi…cations aresuggested to mitigate the poor empirical performance of the model Some startfrom the assumption of full consumption insurance, and this research is one ofthem.

Heterogeneous consumers and Limited Participation If consumptioninsurance is incomplete, representative agent makes no sense in asset pricingmodel The earlier studies suggest that the potential enrichment of the jointassumption — heterogeneous consumers and incompletely consumption insurance

on asset pricing is illusory6 Constantinides and Du¢ e (1996) argue that theprevious models with heterogeneous consumers, that have failed to improve theperformance, have a common feature, that the individual income to aggregateincome is time series stationary They relax this assumption by adding a factor,consumption growth distribution, in the SDF This theory is empirical supported

by U.S Consumer Expenditure Survey (CEX) data (Brav, Constantinides andGeczy, 2002) Their idea is adopted by most of models with heterogeneous con-sumers7 That is, to de…ne a non-stationary individual endowment to aggregate

6 For example, Mankiw (1986), Lucas (1994) and Telmer (1993) calibrate economies in which consumers face uninsurable income risk and borrowing or short-selling constraints, and conclude that consumers are able to come close to the complete-markets rule of complete risk sharing, even though consumers are allowed to trade in just one security in a frictionless market Aiyagari and Gertler (1991) and Heaton and Lucas (1992, 1995, 1996) added transaction costs or borrowing costs in economies with uninsurable income risk and concluded that consumers are still able to come close to the complete-markets rule of complete risk sharing, unless the ratio of the net supply of bonds to aggregate income is restricted to an unrealistically low level.

7 For example, Jouini and Clotilde (2007) discuss the heterogeneous belief; Chien and Lustig (2010) focuse on distribution of wealth; Gomes and Michaelides (2008) combine the idiosyncratic

data ratio …rstly, and then derive a distribution factor in the SDF The tail of thedistribution can be truncated, which implies limited participation in asset pricingmarket Empirical data support this assumption Based on the 1984 Panel Study

of Income Dynamics (PSID) data, Mankiw and Zeldes (1991) …nd that only about30% households own stocks in the U.S Despite the tremendous growth of U.S.stock markets during 1990s, such limited market participation still exists The

1998 Survey of Consumer Finances (SCF) shows that less than 50% of the U.S.households own stocks and/or stock mutual funds (including holding in their re-tirement accounts) (Cao, Wang and Zhang, 2005) In my model, all agents areheterogeneous and some of their participations on stock market are restricted byunexpected declines in housing price

My model is built on the consumption based asset pricing model (CCAPM)(Breeden, 1979; Breeden and Litzenberger, 1978; Campbell, 2003) The fourkey elements incorporate the irrational housing market risk into asset pricing.The irrational housing market introduces new source of risk; and portfolio theorypoints out that wealth composition can measure the irrational market I assumefull consumption insurance only happens for households without bound budgetconstraints Heterogeneous consumers and limited participation is added to correctbias generated from the aggregate data

The recent …nance crisis is a natural incentive of this research It is believedthat a crisis starting from irrational market and the risk in housing market is fullylaid on the …nancial market As the press describes:

Housing peaked in 2005 By early 2006 it was widely recognized theboom was likely over, and by mid-2006 it was beyond question In June

2006, sales of existing single-family homes were 9% below their

year-shocks and borrowing constraints and imply incomplete risk sharing among investors add risk

to the pricing factor.

shares had fallen 41% from its July 2005 peak.

— WSJ, 24/12/2007, “Egg Cracks Di¤er In Housing, Finance Shells”

If we take a close look at the U.S macroeconomic statistic, we …nd a puzzle

on the link between consumption growth and equity premium Before the cial crisis, in 2007, the equity premium in U.S market was around 7%, and wasconsumption growth 1.5% During the crisis, the market return was -49%, andthe consumption growth was only about -1% That implies a huge change in riskaversion coe¢ cient; it is impossible

…nan-My model includes a new risk factor, deriving from the consumption growthdistribution and limited participation, as a wedge between the di¤erent consump-tion "betas" before and after crisis The declines in housing price change somehouseholds’ budget constraints, because of the losses in expected These house-holds must change their consumption growth and withdraw their equity from thestock market The following are reported in the press:

At the start of 2008, with the U.S economy weakening and joblosses multiplying, the defaults began to spread as millions of Ameri-cans with plain-vanilla prime mortgages also ran into trouble makingtheir payments In some cases, borrowers found they had paid in‡atedprices for homes they could no longer a¤ord Others got into trouble

by or borrowing against the equity in their homes According to theFederal Reserve, Americans withdrew more than $1.1 trillion of equityfrom homes in 2006 and 2007

— WSJ, 29/12/2010, “Faces of the Home-Foreclosure Crisis”

To verify the claims of the business reports, this chapter also presents microevidence from the subprime crisis based on a rigorous dataset to illustrate themechanism proposed by this model 2009 Panel Study of Income Dynamics (PSID)survey includes questions on households’…nancial distress information during thecrisis The households’ responses before (2007) and after (2009) the subprimecrisis support the linkage between micro fundamentals and macro environmentproduced by the model The data show that the nondurable goods consumptiongrowth (indicated by food expenditure) and the participation in stock markethave clear heterogeneous patterns between the unconstrained households and thehouseholds in distress The micro data imply that the heterogeneity is embedded

in the risk of housing wealth

This chapter proceeds as follows Section 2 discusses the past related work.Section 3 presents the model and pricing kernel Sections 4 to 6 show the empiricalevidences of asset pricing model Section 7 analyzes the micro evidence to verify

my model The paper is concluded in section 8

and Shapiro,1986).

Reconginizing the limitations of the model in …tting the empirical results, anumber of generalizations have been suggested to mitigate the poor empirical per-formance of the model In a general equilibrium framework, two modi…cations forthe utility function are suggested to add more volatility of consumption growth tothe model One is to use recursive function in utility representation (Epstein andZin, 1989, 1991), which allows for the separation of the elasticity of intertemporalsubstitution (EIS) from the risk aversion The second one is to add habit per-sistence in the preference(Boldrin, Christiano and Fisher, 2001; Constantinides,1990), which has potential to account for the equity premium puzzle by implyingonly a modest degree of risk aversion on the part of households

Besides focusing on the utility function, researchers also try to …nd more riskfactors in the real economy to improve the performance of CCAPM Consider-ing heterogeneous consumers instead of representative agent, Cogley (2002) andBrav, Constantinides and Geczy (2002) …nd that the factor from distribution ofconsumption growth, such as the standard deviation and the skewness, reducesthe size of the Euler equation errors for the stock return Lettau and Ludvigson(2001a, b) empirically show that the ratio of consumption to wealth predicts theasset returns and conditional versions of CCAPM conditioning on the ratio of con-sumption to wealth perform much better than the unconditional versions Santosand Veronesi (2006) incorporate the ‡uctuation of consumption to income ratiointo asset pricing model and show it can forecast the stock return Yogo (2006)shows that, conditional on high risk aversion, a model with consuming durablescan account for time variations in the equity premium, as well as the size and

value premia.

My work is related closely to the work of Piazzesi, Scheider and Tuzel (2007),and Lustig and Nieuwerburgh (2006) Piazzesi, Schneider, and Tuzel (2007) con-struct an equilibrium asset pricing model with housing and show that the compo-sition of the consumption bundle appears in the pricing kernel, and matters forasset pricing The housing expenditure share predicts stock returns Lustig andNieuwerburgh (2006) …nd that the ratio of housing wealth to human capital isrelated to the market price of risk and thus has asset pricing implications Theymodel this mechanism as collateral channel; where the collateral ratio in‡uencesasset pricing through the consumption growth distribution

This research is also part of a small but growing literature that incorporatesreal estate into the asset pricing framework Stambaugh (1982) tests CAPM withseveral market portfolios, constructed as a combination of asset classes, and some

of them include proxies for residential real estate Cochrane (1991, 1996) exploresthe explanatory power of residential and non-residential investment on the equityreturns in the context of his production-based asset pricing framework Cocco(2005), Flavin and Yamashita (2002), and Flavin and Nakagawa (2008) considerportfolio choice with exogenous returns in the presence of housing Kullmann(2003) includes measures of both residential real estate returns and commercialreal estate returns (as measured from REITs) in the market portfolio Chu (2010)models the ratio of consumption to housing as a pricing factor in his intertemporal-CAPM Tuzel (2010) explores the linkage between corporate real estate holdingand stock return controlling for asymmetric adjustment cost of di¤erent capital

The model includes a continuous of in…nitely lived heterogeneous households whoconsume nondurable consumption and housing service Housing plays a dual-role

in the model as both a consumption good and an investment good The irrationalactivity of housing market breaks the assumption of full consumption insuranceand changes the distribution of consumption growth in the cross-section, whichcreates a wedge between the market valuation of payo¤s and the representativeagent’s intertemporal marginal rate of substitution (IMRS)

In an uncertain environment, each households faces two types of uncertainty: one

is the idiosyncratic component y 2 Y ; the other is the aggregate component z 2 Z.The household in time t lives in an environment (yt; zt)2 Y Z This set follows

a Markov process with transition probabilities that obeys:

(z0jz) = X

y 0 2Y

(y0; z0jy; z) 8y 2 Y; z 2 Z (2.1)

where y0 and z0 the state in next period of y and z, respectively

The economy has only two types of commodities: a nondurable consumptiongood, c and housing service, h Preferences are standard We use fxg to represent

where is the time discount factor, and the utility function kernel is de…ned

as constant elasticity of substitution (CES) function over composite consumption

goods (Eichenbaum and Hansen,1990) :

u(ct; ht) = 1

1

hc

is separable when " 1" = 1 ; and if " = 1 it is a Cobb-Douglas function

When constraints are not bound, IMRS, ma

t;t+1 of the representative agent isde…ned as

mat;t+1 = u1(c

a t+1; ha t+1)

u1(ca

t; ha

t) =

ca t+1

ca t

0B

@

1 + h

a t+1

c a t+1

" 1

"

1 + hat

c a t

" 1

"

1CA

ca t

t+1 t

" 1

1 (" 1)

(2.7)

an investment good In each period, he/she can rent out the housing unit toearn rental income If each household is endowed with a labor income stream

be rented out ho denotes housing owned by the household; and h denotes thehousing services enjoyed by the household If the household does not own house,

ho equates to 0 is the depreciation rate of housing

The …nancial asset return rt;t+1a and housing return rht;t+1 are de…ned as

rt;t+1a = vt+1+ dt+1

rt;t+1h = (1 )p

h t+1+ t+1

ph t

In the economy, a household can only accept the price and dividend of …nancialasset, and the price and rental of housing the stream of them are determined bysystematic shocks zt As zt is a Markov process, the excess returns of both the

…nancial asset and the housing are assumed as Brownian motion processes with

a variance-covariance matrix as in Flavin and Nakagawa (2008) Housing and

…nancial assets that make up the wealth portfolio of the household is represented

as fa; ho

g Given that the markets are perfect and frictionless, the composition of

optimal portfolio in the mean-variance e¢ ciency framework is a constant vector

M fMa; Mhg, where Ma and Mh denote the market value of …nancial asset andhouse8 I use the housing-…nancial wealth ratio ha to represent the composition

of household’s portfolio:

hat= htp

h t

The irrational housing market changes the conditional distribution of tion across households and asset pricing Equation (2.8) is the household budgetconstraint at time t Suppose that in the previous hot housing market householdallocates higher weight of housing wealth; hat 1 is higher The return of hous-ing investment is lower than the household’s expectation in next period somehouseholds will face a tight budget constraint because misallocation of wealthportfolio In the next part, I will discuss how the irrational behavior impacts theasset pricing

consump-8 The details of proof can refer to Flavin and Nakagawa (2008)’s paper.

is independent of idiosyncratic shock, and its growth follows a simple pattern cept it is bound by a tight budget constraint When household enters a state oftight constraint, e.g negative net wealth, the idiosyncratic shock is a determinantfactor for consumption growth The consumption growth rate with a tight con-straint is lower than that under the full consumption insurance These householdsare likely to withdraw investment from …nancial assets to satisfy their consump-tion requirement As a result, some households will not invest on the …nancialassets The tight constraint breaks the full consumption insurance hypothesis andthe fraction of households with tight constraints depends on the housing-…nancialwealth ratio In a hot housing market, marked as high housing-…nancial wealthratio, more households will be a¤ected by losses in housing investment As a re-sult, the ‡uctuations of the housing-…nancial wealth ratio change the conditionaldistribution of consumption across households and asset prices.

ex-I use a set of consumption weights fwg to characterize a household’s tion in the aggregate data at time t, the consumption of household i is

both individual and aggregate shock; and the growth rate is ~(yt+1; zt+1)

3

5 ca

where households marked from 0 to ~I are not bound; households marked from ~I

to I are bound I de…ne

a t+1=

As ~(yit+1; zt+1) < (zt+1), at+1 increases with the fraction of households with atight constraint By linking housing-…nancial wealth ratio hat with the fractionchange, at+1can be predicted by hat From equations (2.13), (2.14) and (2.15),theset of consumption weights at time t + 1 can be written as:

; :::; ~(yi

t+1; zt+1)wi

t a

t+1

;~(yi+1 t+1; zt+1)wti+1

a t+1

Over-mt;t+1 = mat;t+1gt+1 (2.18)

where ma

t+1 is the IMRS of a representative agent, which can be calculated byaggregate data as in Hansen and Jagannathan (1991) Following Lustig and VanNieuwerburgh (2005), gt+1 is a liquidity factor contributed by the budget con-straints In stationary equilibrium, only households without tight constraints canparticipate in the asset market So the fraction of households without tight con-straints in‡uences the liquidity factor in pricing kernel In the model, the liquidityfactor depends on the housing-…nancial wealth ratio When the ratio is high, theconstraints are tight because housing return is lower than the expectation Manyhouseholds are highly constrained, the liquidity factor enhances the risk of con-sumption change The risk-free rate is low, inducing households to decrease assets

at a high rate When this ratio is low enough in a cold housing market, none ofthe households are constrained and interest rates are high

In the next part, I show that housing wealth composition can explain some ofthe variations in U.S stock returns over time and in the cross-section

In order to test the model, I use the total housing-…nancial wealth ratio ha topredict the stock market return Next I discuss the data used in the estimationand the construction of ha The de…nitions of related variables are shown in Table2.1

Table 2.1: List of Variables

hvf a total housing wealth from

Fixed Asset account

Fixed Asset Tables

hvrw total housing wealth from Flow

ha is de…ned as the total housing wealth hv divided by total …nancial wealth av

in certain time In the model, this ratio is constant if the market is perfect The

‡uctuation of housing-…nancial wealth ratio indicates that the irrational housingmarket is either hot or cold The housing wealth is generated from Fixed AssetTables (Bureau of Economic Analysis) The net stock current value of owner-occupied and tenant-occupied residential …xed assets for 1929–2009 is de…ned asthe total housing wealth hvf a, as reported in line 1 of the Table 5.1 in FixedAsset Tables "current-cost net stock of residential …xed assets" I use the marketresidential real estate wealth hvrw from the Flow of Funds data (Federal Board

of Governors) from 1945–2009 as robust test This series is reported in line 3,

"the balance sheet of households, and nonpro…t organizations (B.100)" The total

…nancial wealth data from 1929 to 2009 comes from two sources For 1945–2009,

data are not available NBER macro-history database (series 14145) gives thedata on total deposits I assume that the ratio of deposits to total …nancial wealthdecreases slowly from 0.205 in 1929 to 0.198, its level in 1945 (FoF deposits series).

Figure 2.1(a) plots the growth rates of housing wealth and …nancial wealthduring 1929-2009 The housing wealth is based on hvf a The …nancial wealthgrowth is procyclical, peaking during booms and hitting lows during recessions

It is therefore a good indicator for the business cycle The housing wealth growth

is also procyclical, but is smoother than the …nancial wealth The housing market

is illiquid and irrational, adjusted at a slower rate to the shocks Figure 2.1(b) is

a time-series plot of housing wealth growth minus …nancial wealth growth The

…nancial wealth growth is generally exceeds that of housing wealth, except duringthe long recession period, for example 1929-1933, which is a long recession de…ned

by NBER, and the recent crisis 2007-2008 Figure 2.1 shows the time-varyingtrends of housing and …nancial wealth This chapter will test how the ‡uctuations

of their ratio in‡uence expected stock return

As the model’s de…nition, I use hv and av to calculate the housing-…nancialwealth ratio ha I de…ne haf a = hvf a=av; and harw = hvrw=av The …xed timee¤ect on the wealth composition is controlled I run an OLS regression withtime t as independent variable, and hat as dependent variable The coe¢ cient oftime is signi…cant (p value is less than 0.001, not reported) The residual of thisregression is used to represent the housing-…nancial wealth ratio excluding timee¤ect, which are de…ned asha~f aandha~rw Figure 2.2 shows the trend of these fourdi¤erent measurements Figure 2.2(a) shows haf a and the estimated ha~f a from

Figure 2.1: Housing Wealth and Financial Wealth Growth: 1929-2009 This …gureshows the trend of housing wealth and …nancial wealth growth from 1929 to 2009.The housing wealth data is from Fixed Asset Tables; and …nancial wealth data isfrom Flow of Funds data and NBER macro-history database (a) plots the growthrates of housing wealth and …nancial wealth during 1929-2009; (b) plots housingwealth growth minus …nancial wealth growth.