Estimating housing demand with an application to explaining racial segregation in cities.

We present a three-stage, nonparametric estimation procedure to recover willingness to pay for housing attributes. In the first stage we estimate a nonparametric hedonic home price function. In the second stage we recover each consumer's taste parameters for product characteristics using first-order conditions for utility maximization. Finally, in the third stage we estimate the distribution of household tastes as a function of household demographics. As an application of our methods, we compare alternative explanations for why blacks choose to live in center cities while whites suburbanize.

KEY WORDS: Demand estimation; Hedonics; Heterogeneity; Nonparametrics; Product differentiation; Racial segregation.

1. INTRODUCTION

Housing accounts for a major fraction of consumer spending and wealth. Shelter is the largest of the seven categories that comprise the consumer price index (CPI) market basket, accounting for 32% of the total index. Between 1935 and 1991, shelter's budget share increased by 61%, while food's budget share fell by 59% (Costa 1998). Housing equity represents the largest source of household wealth. Based on the 1998 Survey of Consumer Finances, the value of stocks owned by households was $7.8 trillion, whereas the value of primary residences was $9.4 trillion. About two-thirds of American households own their homes, whereas less than one-half of households own stocks. The majority of those who own both stocks and a home still have more wealth in home equity than in stocks (Di 2001).

Analyzing the demand for housing is a challenging empirical problem. A home is a bundle of three types of characteristics. The first characteristic type comprises the physical attributes of the home, such as the number of rooms, the lot size, and whether or not the unit is attached. The second includes the attributes of the community, such as the mean demographic characteristics of the surrounding neighborhood. A third characteristic is the commute to one's place of work. There is considerable heterogeneity in preferences for housing attributes. These preferences depend on observed demographic characteristics of the household, such as the number of children and marital status. Also, there is considerable heterogeneity in preferences even after accounting for all household demographics.

Recently, there have been major advances in estimating the demand for local public goods that explicitly incorporate heterogeneity into the estimation procedure. Epple and Sieg (1999) presented an equilibrium model in which households who differ with respect to income and local public good preferences sort across Boston communities. Sieg, Smith, Banzhaf, and Walsh (2002) extended this framework to allow for a heterogeneous housing stock and showed how to use hedonic methods to construct price indices. Smith, Sieg, Banzhaf, and Walsh (2004) used a locational equilibrium model to estimate the environmental benefits of Clean Air Act regulation. Bayer, McMillan, and Rueben (2002) also estimated a rich model of the demand for housing attributes using tools similar to those proposed by Berry, Levinsohn, and Pakes (1995). Given their demand estimates, they then simulated an equilibrium model of the housing market.

In this article we present a empirical model of housing demand that explicitly incorporates heterogeneity into the estimation procedure. Our model of housing demand allows preferences to be a flexible function of observed demographics and idiosyncratic taste shocks for housing characteristics. Furthermore, the model accommodates both discrete and continuous characteristics. Finally, our model accounts for the simultaneity of the choice of where to live and where to work. To the best of our knowledge, no previous model of housing demand has these features.