Theory and Estimation in the Economics of Housing Demand By Stephen K. Mayo From Journal of Urban Economics, 1981, p Presented by Yong Li December.4, 2002

Introduction and Purpose A review of theoretical and empirical developments made prior to 1980 on the subject of housing demand. Four main topics: –Income elasticity of demand for housing –Price elasticity of demand for housing –Demographic variation in housing demand –Dynamic aspects of housing demand

Basic Model A log-linear demand equation: lnH = a + blny + clnp H, Where H is housing; y is income; p H is the relative price of housing a, b and c are parameters

Income Elasticity Key issues: –How sensitive is demand to changes in income? –Empirical work uses current income rather than an appropriate measure of permanent, or expected income, to estimate the model. –As a result, to what degree are the estimates of elasticity likely to be biased?

The Bias Current income elasticity will be biased downward in proportion to the ratio of variances of permanent income to current income asymptotic E(ê y ) = e y V y Where V y =Var(y p )/Var(y)=Var(y p )/[Var(y p )+Var(y t ))]<1 y p is permanent income; y t is transitory income

The Bias The smaller the variance of transitory income, the smaller the bias of estimated current income elasticity. Efforts made to deal with the problem of estimating permanent income elasticity. –Grouping –Averaging –IV

Some Discussions Demand Elasticity AuthorDataYearMicroAggregated 1.A.10 ; 1.B.19bNelsonC-Eu Grouped by census tracts 1.A.13 ; 1.B.22cSmith/CampbellCSL Grouped by housing value 1.A.10 ; 1.B.19aNelsonC-Eu Grouped randomly 1.A.13 ; 1.B.22aSmith/CampbellCSL Grouped randomly 1.A.13 ; 1.B.22bSmith/CampbellCSL Grouped by income class 1.A.11 ; 1.B.20Polinsky/ElwoodFHA Grouped by SMSA

Demographic Effects What’s the impact of inclusion of demographic variables on estimated demand elasticity? Difficult to compare the results of previous work. Some general conclusions from analyses using additive specifications of demographic variables. –Race –Sex –Age and household size Alternative methods dealing with demographic variables

Extension Stone-Geary utility function with three goods—housing quality, Q; housing quantity, S; and other goods, Z: U=(Q-θ Q ) a (S-θ S ) b (Z-θ Z ) c (1) Where a+b+c=1. Maximize equation (1) with respect to the budget constraint: y=p z Z+R, (2) And, let R=QS m, where 0<m<1 (3) So, budget constraint is y=p z Z+QS m (4)

Conclusions For a wide range of analyses employing different data bases and methodologies, the permanent income elasticity of demand for housing is estimated to be well below one on average. It’s been shown that not only are aggregation biases serious in affecting demand elasticity estimates, but, fortunately, they are largely avoidable if proper precautions are taken.

Conclusions Demographic variables, which have so far been only poorly integrated into theories of housing demand appear to have significant impacts on demand. It’s been suggested that demand equations explicitly based on appropriate utility functions deserve more attention.