Theory and Estimation in the
Economics of Housing Demand
By Stephen K. Mayo
From Journal of Urban
Economics, 1981, p95-116
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 + clnpH ,
Where H is housing;
y is income;
pH 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(êy) = eyVy
Where
Vy=Var(yp)/Var(y)=Var(yp)/[Var(yp)+Var(yt))]<1
yp is permanent income; yt 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
Author
Data
Year
Micro
Aggregated
1.A.10 ; 1.B.19b
Nelson
C-Eu
1970
0.24
1.16
Grouped by census tracts
1.A.13 ; 1.B.22c
Smith/Campbell
CSL
1971
0.51
1.12
Grouped by housing value
1.A.10 ; 1.B.19a
Nelson
C-Eu
1970
0.24
0.36
Grouped randomly
1.A.13 ; 1.B.22a
Smith/Campbell
CSL
1971
0.51
0.59
Grouped randomly
1.A.13 ; 1.B.22b
Smith/Campbell
CSL
1971
0.51
0.68
Grouped by income class
1.A.11 ; 1.B.20
Polinsky/Elwood
FHA
1969
0.38
0.52
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-θQ)a(S-θS)b(Z-θZ)c
(1)
Where a+b+c=1.
Maximize equation (1) with respect to the
budget constraint: y=pzZ+R,
(2)
And, let R=QSm, where 0<m<1
(3)
So, budget constraint is y=pzZ+QSm
(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.