HOUSING OVER TIME AND OVER THE LIFE CYCLE: A STRUCTURAL ESTIMATION

• DOI: http://doi.org/10.1111/iere.12196
• Published date: 01 November 2016
• Date: 01 November 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

HOUSING OVER TIME AND OVER THE LIFE CYCLE:

A STRUCTURAL ESTIMATION∗

BYWENLI LI,HAIYONG LIU,FANG YANG,AND RUI YAO1

Federal Reserve Bank of Philadelphia,U.S.A.; East Carolina University,U.S.A.; Louisiana State

University, U.S.A.; Baruch College, U.S.A.

We construct a model of optimal life-cycle housing and nonhousing consumption and estimate the elasticity between

the two goods to be 0.487. The estimate is robust to different assumptions of housing adjustment cost, but sensitive

to the choice of sample period and the degree of aggregation of data moments. We then conduct experiments in

which house prices and household income fluctuate. Compared with the benchmark, the impact of the shocks on

homeownership rates is reduced, but the impact on nonhousing consumption is magnified when housing service and

nonhousing consumption are highly substitutable or when the house selling cost is sizable.

1. INTRODUCTION

The U.S. housing market has experienced dramatic price movements in recent years. These

movements, accompanied by substantial changes in household indebtedness, have drawn the

attention of policymakers and academicians. Calibrated housing models are now increasingly

deployed in studying the effects of housing on consumption and savings, stock market partic-

ipation and asset allocation, asset pricing, and the transmission channel and effectiveness of

monetary policies.2Despite this growing interest in housing models in an intertemporal setting,

econometric research aimed at identifying the relevant housing preference parameters has been

lacking. As a consequence, theoretical models are often calibrated with little empirical guidance

regarding the key model input parameters.3

One such key parameter is the intratemporal elasticity of substitution between housing and

nonhousing consumption, which governs to a large extent the impact of changes in house prices

and income and, hence, policies that affect these changes, on household consumption and wel-

fare. Among the few econometric studies of housing preferences, there has been little consensus

∗Manuscript received November 2011; revised June 2015.

1We thank Andra Ghent, Christopher Carroll, Juan Contreras, Alex Michaelides, Jesus Fernandez-Villaverde, three

anonymous referees, and participants at various seminars and conferences for their comments. The views expressed in

this article are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Philadelphia,

or the Federal Reserve System. This article is available free of charge at http://www.philadelphiafed.org/research-and-

data/publications/working-papers/.Please address correspondence to: Wenli L i, Research Department, Federal Reserve

Bank of Philadelphia, Philadelphia, PA 19106. E-mail: wenli.li@phil.frb.org.

2See Campbell and Cocco (2007), Fernandez-Villaverde and Krueger (2011), Li and Yao (2007), Stokey (2009),

Kiyotaki et al. (2011), and Yang (2009) for consumption and savings; Cocco (2005), Flavin and Yamashita (2002), and

Yao and Zhang (2005) for stock market participation and asset allocation; Piazzesi et al. (2007), Siegel (2008), Lustig

and Van Nieuwerburgh (2005), and Flavin and Nakagawa (2008) for asset pricing; and Iacoviello (2005) for monetary

policy effects.

3Many theoretical studies using numerical calibrations adopt the Cobb–Douglas utility function for its simplicity

and often abstract from housing adjustment costs. A direct implication of the Cobb–Douglas utility function is that

housing expenditure share is constant over time and across regions. The aggregate housing expenditure as a share of

total expenditure, however, has fluctuated over time with a sharp rise, leading to the Great Depression followed by a

prolonged decline. The share started to recover at the end of World War II and has since fluctuated more mildly than

before (Figure A1 in the online appendix). At the micro level, the Consumer Expenditure Survey also indicates that

expenditure shares at the metropolitan statistical area (MSA) level have fluctuated over time, with many experiencing

upward movement until the recent housing crisis (Figure A2). See Stokey (2009) and Kahn (2008) for additional

evidence against Cobb–Douglas utility specification.

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(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1238 LI ET AL.

on the magnitude of this coefficient. Studies based on macro level aggregate consumption or

asset price data frequently suggest a value larger than 1—implying that households reduce

expenditure share on housing when house prices move up relative to prices of nonhousing con-

sumption (Piazzesi et al., 2007; Davis and Martin, 2009). These studies have typically assumed

the existence of a representative agent and abstracted from market incompleteness and infor-

mational frictions, despite strong evidence of household heterogeneity and housing adjustment

cost documented in the literature (Carroll and Dunn, 1997; Attanasio, 2000).

In contrast, investigations using household-level data recover much lower values for the elas-

ticity parameter, often in the range of 0.15 and 0.60 (for example, Hanushek and Quigley, 1980;

Flavin and Nakagawa, 2008; Siegel, 2008; Stokey, 2009). These studies, however, suffer from se-

lection bias because households endogenously make decisions on both house tenure (renting vs.

owning and moving vs. staying) and the quantity of housing service flows. Furthermore, the iden-

tification in many of the studies is predicated on households having unlimited access to credit,

which contradicts the practice in reality. The lack of robustness to market friction and incom-

pleteness, therefore, complicates the interpretation of the empirical estimates in these studies.

This article structurally estimates a stochastic life-cycle model of consumption, savings, and

housing choices and jointly identifies the intratemporal as well as intertemporal preference

parameters by matching average wealth and housing profiles generated by the model with the

profiles from micro data. We postulate constant elasticity of substitution (CES) preferences

over housing and nonhousing consumption and allow households to make housing decisions

along both the extensive margin of homeownership and the intensive margin of housing service

flows and house value. The model explicitly admits a housing transaction cost and a collat-

eral borrowing constraint, as well as labor income and house price uncertainties. Our model,

therefore, builds on a growing literature examining household house tenure and housing con-

sumption choices in a life-cycle framework (Gervais, 2002; Ortalo-Magn´

e and Rady, 2005; Yao

and Zhang, 2005; Campbell and Cocco, 2007; Li and Yao, 2007; Chambers et al., 2009; Yang,

2009; Fernandez-Villaverde and Krueger, 2011; Dotsey et al., 2014).

Our estimation of the structural parameters is achieved through the method of simulated

moments (MSM). We first construct the average wealth, homeownership rates, moving rates,

house value-to-income ratio, and rent-to-income ratio profiles from the Panel Study of Income

Dynamics (PSID) data set across three age groups between 1984 and 2005. For homeownership

rates, house values, and rent values, we further group households according to the levels of

house prices in their state of residence and construct additional moments. We then numerically

solve the model for optimal household behavior and simulate the model to generate paths of

life-cycle housing and wealth profiles in the same manner as the data moments to eliminate

potential bias caused by cohort and time effects as well as selection bias. By minimizing the

weighted difference between the simulated model profiles and their empirical counterparts, we

identify the parameters of our structural model.

Our simulated wealth and housing profiles match important features in the data over the sam-

ple period. Our estimation also reveals that after explicitly accounting for housing adjustment

cost, the intratemporal elasticity of substitution between housing services and nondurables is

around 0.487, a value that is on the high end of microempirical estimates but smaller than those

assumed in macro models. The estimate is not very sensitive to different parameterizations of

housing transaction cost. When we double our exogenously imposed housing transaction cost

from 8% of the house value to 16%, the parameter comes down slightly to 0.485. The low

elasticity estimate, however, is largely driven by moments conditional on state house prices

and moments in the latter half of the sample period. When we focus on a sample period with

little house price movement (1984–93) and drop moments conditional on state house prices, the

elasticity estimate more than tripled, increasing to 1.690.

To illustrate the importance of the different estimations of the elasticity parameter, we con-

duct several policy experiments. Specifically, we investigate how households respond to changes

in house prices and income as those observed between 2005 and 2011. We find that large and per-

sistent house price depreciation coupled with declines in income leads to significant decreases