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Econ 6301 Applied Microeconomic Theory
READING ASSIGNMENT #2
Ch 3 Demand
Reading: “What is the Price Elasticity of Housing Demand?”
Eric A. Hanushek and John M. Quigley
The Review of Economics and Statistics
Vol. 62, No. 3 (Aug., 1980), pp. 449-454
Read the above article and answer the following questions.
1. Describe the paper’s conceptual framework. Do you agree
with this framework? What are some of its limitations?
2. Describe the model used to estimate housing demand.
3. Work through the math described in the paper to make sure
that you know how the authors obtained equations (4) and (5).
What are the main differences between equations (4) and (5)?
4. Briefly describe the data from the Housing Allowance
Demand Experiment. Why are these data good for this study?
What are some of the limitations of the data? How do you think
these issues might affect the results?
5. Describe the empirical results. Why do the long-run and
short-run price elasticities differ?
6. How do the results in this paper differ from results found by
previous studies? Why?
7. Would the results from this study hold in today’s market?
Discuss.
ABGB 302: Week 3 Case Study Assignment
Describe the source of the dispute and the results of the case in
WTO (40 points)—U.S.-E.U Beef Hormone case study.
Note: 250 words each for the source of dispute and the results
rendered by WTO—500 words total.
This week's case study is about U.S.-EU Beef hormone. The
dispute was argued in the WTO.
The question is: Describe the source of the dispute and the
results of the case in WTO—U.S.-E.U Beef Hormone case
study.
Note 250 words each for the source of dispute and the results
rendered by WTO. That will be 500 words in total.
This is a very easy case study. Here I'm asking you to describe
the source of the dispute and the results rendered by the WTO
in this case.
The content component will be writing what was the source and
the decision rendered by the WTO.
The application component is expanding on the case--like
putting meat on the bones. The source of the dispute (250
words)--talk about the issue, countries involved, background
why this case came to WTO, what is WTO, why it was created,
who were the parties to the dispute, why hormone-fed beef is
good in the US and bad in the EU. What is EU (the composition
of EU countries) their trade policy in beef?
Next part is that the WTO gave the decision, what was the
decision and how it affects beef trade. Has the EU allowed the
US to export hormone-fed beef? Include all these points in your
application (200 words).
Organization and grammar (4 points)... usual stuff as mentioned
in the rubric.
AGB 302 Grading Rubric – Case Studies Fall B – 2018
Evaluation Criteria Excellent Very Good Adequate Needs
Improvement No Credit
Content
(18 points)
Complete and
organized
submissions that
adhere to all
assignment
instructions.
Submission is missing
minor elements
and/or is not well-
organized and/or
missed an
assignment
instructions.
Submission is missing
minor elements
and/or is not well-
organized and/or
missed an assignment
instructions.
Submission is missing
elements and/or is
not well-organized
and/or did not adhere
to assignment
instructions.
Did not submit or
submission
unacceptable.
18 13.5 9 4.5 0
Application
(18 points)
High quality
submissions that
clearly demonstrate
understanding of
course materials.
Thorough
explanation of source
of dispute in US-EU
beef hormone case;
result or decision
rendered by WTO,
knowledge of
international trade,
workings of WTO.
Good submissions
with some
connections to
course materials.
Occasionally
contributes ideas,
relevant personal
experience, materials
and/or comments.
Moderate
explanation of source
of dispute in US-EU
beef hormone case;
result or decision
rendered by WTO,
knowledge of
international trade,
workings of WTO.
Good submissions
with some
connections to course
materials.
Occasionally
contributes ideas,
relevant personal
experience, materials
and/or comments.
Adequate explanation
of source of dispute in
US-EU beef hormone
case; result or
decision rendered by
WTO, knowledge of
international trade,
workings of WTO.
Little to no evidence
that course materials
are understood or
incorporated into
submissions. Poor
explanation of source
of dispute in US-EU
beef hormone case;
result or decision
rendered by WTO,
knowledge of
international trade,
workings of WTO.
Did not submit or
submission
unacceptable.
18 13.5 9 4.5 0
AGB 302 Grading Rubric – Case Studies Spring B – 2018
Organization and
Grammar
(4 points)
Properly formatted
submissions
demonstrating
professional, college-
level tone, no
spelling or grammar
errors and well-
documented sources
(when applicable).
Submission may be
lacking proper
formatting or
professional tone or
may contain minor
spelling/ grammar
errors or is not well-
supported (when
applicable).
Submission may be
lacking proper
formatting or
professional tone or
may contain minor
spelling/ grammar
errors or is not well-
supported (when
applicable).
Submission may be
lacking proper
formatting and/or
professional tone
and/or may contain
multiple
spelling/grammar
errors and/or is not
well-supported (when
applicable).
Did not submit or
submission
unacceptable.
4 3 2 1 0
WHAT IS THE PRICE ELASTICITY OF HOUSING DEMAND?
Eric A. Hanushek and John M. Quigley*
I. Conceptual Framework
DISAGREEMENT about the responsiveness
of housing demand to variations in relative
prices persists, despite extensive empirical anal-
yses. Two factors underlie this disagreement: the
multidimensional character of housing makes di-
rect observation of prices (as distinct from ex-
penditures) impossible; and, the significant
search, transactions, and moving costs asso-
ciated with changing dwellings imply that, at any
instant, a given household's consumption may
deviate significantly from its utility maximizing
level in a static equilibrium. While a number of
ingenious attempts have been made to circum-
vent these problems, each is quite indirect and
relies upon strong, and untestable, assumptions
(cf. Mayo (1978)). This paper provides direct
estimates of price elasticities, based upon an
explicit model of housing consumption dynamics
and utilizing the experimental manipulations of
housing prices incorporated in the Housing Al-
lowance Demand Experiments.1 While the data
are limited to two years of longitudinal data and
pertain only to low income renters, they never-
theless permit the direct estimation of this key
parameter of housing demand.
This analysis focuses on the price responsive-
ness of households, but clearly other changes in
household circumstances (such as in income or
family size) affect desired housing consumption.
In fact, given the limited longitudinal data, in-
formation about other demand adjustments pro-
vides valuable insights into consumption dynam-
ics. Price changes can be viewed as but one of a
variety of exogenous influences on housing de-
mand.
A complete structural model of housing de-
mand would consider the joint influence of
household preferences, relocation costs, and
prices on search and moving behavior and, con-
ditional on this, their subsequent influence on
housing consumption. However, both household
preferences and relocation costs are generally
unobserved, and estimation of such a complete
model is simply beyond our current capabilities.
We concentrate upon the more modest goal of
modelling the reduced form relationship between
housing consumption and housing stock dis-
equilibrium (defined below).
Consumption dynamics are represented by
variants of a linearized stock adjustment process .
This formulation is based on the simple observa-
tion that adjustments will generally be a
monotonic function of the magnitude of dis-
equilibrium in housing consumption. As indi-
cated by past work (Hanushek and Quigley,
1979), this is both a convenient and powerful
characterization of short run dynamics.
Two basic formulations of consumption
dynamics are considered. Let Htd represent the
"desired," or static equilibrium, quantity of
housing demanded by a given household, and let
Ht be the actual (observed) housing consumption
at time t. In the simplest form, households are
assumed, on average, to close the gap between
desired and equilibrium housing consumption at
a constant rate a, so that
Ht+ = a[Ht+Id -Ht ] + 4Ht (1)
where + is one plus the rate of relative price
increase during the interval.2 This formulation, Received for
publication August 15, 1978. Revision ac-
cepted for publication February 22, 1980.
* University of Rochester and University of California,
Berkeley, respectively.
This is a substantially shortened version of "What is the
Price Elasticity of Housing Demand?", Discussion Paper No.
7803, Public Policy Analysis Program, University of Roches-
ter, August 1978. Copies of the more complete paper are
available from the authors. Support for this research was
provided by Abt Associates and a grant from the Alfred Sloan
Foundation. The research assistance of Robbe Burnstine is
gratefully acknowledged.
1 Alternative approaches to this problem can also be found
in Friedman and Weinberg (1978).
2 While the H's refer to quantities, only consumption ex-
penditures measured in current prices can be measured. Unit
prices in the initial period are arbitrarily normalized to one,
and 0 indicates changes in relative prices over time.
Given the large fixed cost component to searching and
moving, individual households would not be expected to
make a series of marginal adjustments to equilibrium but
instead would be more likely, given a decision to adjust, to
close substantially the gap. Thus, this relationship is best
thought of as the reduced form consumption relationship that
incorporates both adjustment decisions (searching and mov-
[ 449 ]
450 THE REVIEW OF ECONOMICS AND STATISTICS
however, does not allow for differences in behav-
ioral responses occasioned by different patterns
of equilibrium changes. Since the principal
method of changing housing consumption is
through searching and moving, households may
be more responsive in any period to contem-
poraneous changes in equilibrium demand than
to initial disequilibrium. This possibility is con-
sidered by decomposing the level of disequilib-
rium into its time components with the hypothe-
sis that y > f3:3
Ht+ = f[Htd -H] + y[Ht+ld- Htd]
+ Ht- (2)
Now consider a household for which housing
prices are exogenously reduced by some propor-
tion -j (O ? -r < 1). The new equilibrium housing
demand, Htt+d, resulting from the price change
is, by definition,
Ht+ I = Ht+?d(1 + E6) (3)
where E is the price elasticity of demand for resi-
dential housing. Substitution into (1) and (2)
yields
Ht+j= a[Ht+ld - H] + aEqHt+Id + Ht, (4)
and
Ht+= /3[Htd- H] + y[Ht+ld- Htd]
+ 13E71Htd + yEq[Ht+ld - Htd]
+ OHt * (5)
Both formulations explicitly recognize lagged
responses to exogenous stimuli. From equation
(4), the long run response to a price change is the
price elasticity times the price change, En-, but on
average only 100a per cent of this response will
be observed in the first period. In equation (5)
the observed response to an experimental change
in housing prices is yE-q after one period and (y +
,/ - 83Y) Eij after two periods, even though the
long run response is again El).
Estimation of this model requires longitudinal
information on the actual housing consumption
of households (Ht), their equilibrium demands
for given incomes, preferences and initial prices
(Htd), and the price reduction (-r).
II. Empirical Analysis
Data from the Housing Allowance Demand
Experiment, which provided housing subsidies
to a sample of low income, renter households in
Phoenix and Pittsburgh, allow estimation of the
housing adjustment models in equations (4) and
(5). This analysis concentrates upon 586 house-
holds in Phoenix and 799 households in
Pittsburgh. Of these, 302 in Phoenix and 424 in
Pittsburgh were randomly assigned to treatment
groups receiving experimental reductions in
rental payments (-q) that ranged from 0.2 to 0.6
(i.e., rent subsidies of 20% to 60%); the remain-
der were assigned to control groups that received
no subsidy.4 Detailed longitudinal information
about household characteristics and housing
consumption was collected at the beginning of
the experiment and annually for two subsequent
years.
The empirical implementation involves spec-
ifying the equilibrium demands of individual
households (HI) in each period and then estimat-
ing the dynamic responses and price elasticity
parameters. Direct estimation of equilibrium de-
mands was used instead of more common sub-
stitution of exogenous demand determinants into
the dynamic relationships for two reasons: prac-
tical limitations imposed by the complicated ad-
justments in equation (5) (particularly given the
limited longitudinal data); and the lack of sepa-
rate identification of changes in relative prices
(k) with substitution.5
ing) and actual consumption choices. For present purposes,
the focus on expected aggregate behavioral responses is
sufficient, although information about the distribution of out-
comes across individual households requires more detailed
analysis of structural moving relationships (see Hanushek
and Quigley (1978)).
3 Note that [H,+ Id - H,] [Htd - H,] + [H,t+d - H,d].
4 Receipt of subsidy did not depend upon any specific hous-
ing consumption choices. The experimental payments were
actually received for one full year after the period examined
here, and experimental households knew that they would
receive assistance in obtaining other subsidies after comple-
tion of the experiment-thus minimizing effects of the limited
duration of the experiment. (Other treatment groups receiv-
ing income subsidies similar to a negative income tax are not
analyzed here.) Sample median incomes were 0.5-0.6 of each
SMSA's median income.
Since the experimental group is small relative to the entire
housing market, there would be no perceptible supply re-
sponses, and the price elasticity is therefore identified.
I Errors in estimating equilibrium demands may affect the
subsequent estimation of the demand relationships. How-
ever, in the simplest model (equation (4)) the problems with
using instruments for equilibrium demands are the same as
those encountered in direct substitution when equilibrium
demands are stochastically related to the exogenous vari-
ables. Moreover, as discussed below, it is possible to assess
PRICE ELASTICITY OF HOUSING DEMAND 451
In competitive markets where households face
the same prices, contract rents (standardized for
landlord provision of utilities and appliances)
provide an unambiguous measure of the quantity
of housing services actually consumed.6 Assum-
ing that households recently making relocation
decisions consume their utility maximizing quan-
tity of housing services (Hd), equilibrium de-
mand functions at initial housing prices for each
housing market are then estimated by regressing
expenditures on income, assets, family size, po-
sition in the life cycle, and other demographic
characteristics for recent mover households.7
These estimates, presented and discussed else-
where (Hanushek and Quigley, 1979), are consis-
tent with expectations and prior research esti-
mates, but, importantly, they indicate systematic
differences between the two housing markets.
All previous investigations of price elasticities
that utilized price variations across housing mar-
kets have assumed that the demand relationships
are the same across areas-an assumption that
does not appear warranted.
By substituting relevant household income and
demographic characteristics for each time pe-
riod, household and time specific instruments for
desired consumption (i.e., Hod, H d, and H2d) are
constructed from the equilibrium demand func-
tions. These estimates, combined with actual
rent expenditures in each period adjusted for
tenure discounts, allow direct estimation of the
price elasticity of housing demand-estimation
that is free from the most stringent assumptions
and data problems encountered by indirect
methods.8
HI. Empirical Results-Adjustment and Price
Elasticity Estimates
Table 1 presents coefficient estimates for
households in the Phoenix and Pittsburgh hous-
ing markets, replicated in two successive one-
year intervals for the same sample of households.
Assuming that the errors are normally distrib-
uted, the estimates are obtained by maximum
likelihood techniques incorporating the non-
linear constraints on parameters.
Standard covariance tests suggest little differ-
ence in the estimated parameters in the two time
periods and that the basic adjustment behavior of
those households receiving experimental housing
price reductions is no different from the behavior
of control households who are unaffected by the
experiment.9 The simple adjustment coefficient
(a) indicates that, on average, 19% of the gap
between desired housing consumption and ob-
served initial consumption is closed in each
one-year period in Pittsburgh. In Phoenix, where
the average mobility rate of households is higher,
the results suggest that 35% of the gap is closed
in any year. In both housing markets, (A is sig-
nificantly greater than one, indicating modest in-
creases in relative prices. The rate of inflation in
housing prices is consistently greater in Phoenix
than in Pittsburgh.
Based upon the simple adjustment model,
equation (4), the estimated price elasticity of
demand is -0.64 in Pittsburgh and -0.45 in
Phoenix. These are estimates of the long run
the importance of such problems in the extended models
(equation (5)). Some attempts at using self-reported "satis-
faction" indexes as instruments for housing disequilibrium
were also made, but these crude instruments yielded unsatis-
factory results.
6 A significant housing price gradient would imply that
households face differing prices, but this does not appear to
be a problem in the cities analyzed here. For Phoenix and
Pittsburgh, Merrill (1977) tests for equality of coefficients
between central city and suburbs in hedonic price equations.
In Pittsburgh, coefficient equality cannot be rejected; in
Phoenix, the hypothesis can be rejected, although the esti-
mated prices are very similar and the standard error of esti-
mate changes only slightly with stratification. Independent
analysis of Pittsburgh for the NBER Urban Simulation Model
(reported in private correspondence by Gregory Ingram)
provides no evidence of price gradients. Finally, Muth (1969)
found estimated population gradients for Pittsburgh to be
insignificantly different from zero at the 0.10 level (and to
have the third smallest point estimate for the 46 areas he
analyzed).
7 All households, regardless of subsequent assignments to
treatment groups, that moved within 12 months of enrollment
(t = 0) are assumed to be in equilibrium and included in the
estimation. This is consistent with the assumed micro-
behavior in footnote 2.
8 Landlord cost savings from long term occupancy (result-
ing from both reduced redecorating costs and lower vacancy
rates) would be expected to be reflected, at least partially, in
reduced rents. (See, for example, previous estimates by Kain
and Quigley (1975) and Schafer (1979).) Here, measured ex-
penditures are normalized to new occupants (consistent with
the estimated equilibrium demands) by using the estimated
tenure coefficients from the Phoenix and Pittsburgh hedonic
price equations of Merrill (1977). These tenure discounts
grow to 10% in Pittsburgh and 19% in Phoenix for more than
10 years of occupancy.
9 For Phoenix, the hypothesis of coefficient equality across
time periods is rejected in the simpler model at the 5% level.
However, in the more complex model, time period equality of
coefficient is not rejected. Since -1 = 0 for the control house-
holds, the relevant test is for equality of a's, a's, y's and O's
across samples in each time period. This simply confirms the
random assignment of households to treatment groups.
452 THE REVIEW OF ECONOMICS AND STATISTICS
TABLE 1.-ESTIMATES OF STOCK ADJUSTMENT MODELS
OF HOUSING CONSUMPTION
FOR EXPERIMENTAL AND CONTROL HOUSEHOLDSa
Pittsburgh Phoenix
Pooled Pooled
Coefficient 01 1 >2 Time Periods 0l 1- 2 Time Periods
a ~~~~~0.223 0.155 0.185 0.407 0.273 0.352
(7.65) (6.23) (9.79) (10.01) (7.61) (13.02)
p8 0.213 0.145 0.181 0.402 0.259 0.330
(7.24) (5.80) (9.56) (9.02) (7.09) (11.87)
y 0.466 0.444 0.376 0.462 0.534 0.512
(4.23) (3.46) (4.86) (4.26) (3.77) 6.38)
-0.573 -0.278 -0.689 -0.693 -0.642 -0.359 -0.484 -0.427 -0.385
-0.374 -0.453 -0.409
(3.07) (2.75) (2.71) (2.68) (4.13) (3.36) (2.90) (2.49) (1.80)
(1.71) (3.53) (3.65)
4 1.028 1.022 1.036 1.030 1.033 1.032 1.085 1.084 1.058 1.053
1.074 1.067
(27 I1)b (2.06)b (3.77)b (3.12)b (4.70)b (4.79)b (5.02)b (4.95)b
(3.75)b (3.43)b (6.39)b (5.94)b
R 2 0.582 0.585 0.700 0.702 0.648 0.649 0.535 0.535 0.695
0.697 0.610 0.613
Sample Size
Control 375 375 361 361 736 736 284 284 243 243 527 527
Experimental 424 424 407 407 831 831 302 302 265 265 567
567
Parameter Equality
Experimental
& Control 0.292t 0.893c 0.043c l.796c 0.863c 0.571c 1.039c
0.977c
Time Periods 1.278c 2.031c 4.l14c 2.399c
/ = y 5.240d 5.493d 6.434d 0.297d 3.770d 6.214d
a t-statistics are in parentheses.
bt-statistics are calculated on null hypothesis that parameter
equals one; i.e., that there were no changes in the relative prices
of housing and other goods.
c F-statistics.
d t-statistics.
responsiveness of housing consumption to exog-
enous price changes; i.e., the responses ob-
served after all households had fully adjusted to
the changed housing prices. The short run
elasticities-those which would be observed
after one year of altered prices-are, however,
considerably less. While a 10% reduction in
housing prices would lead eventually to a 6.4%
increase in housing consumption in Pittsburgh,
only a 1.2% increase is actually observed after
one year. Similarly, in Phoenix only a 1.6% in-
crease in housing consumption (from a 10% rent
reduction) is observed after the first year, even
though a 4.5% increase is expected in the long
run.
Table 1 also presents the maximum likelihood
estimates of the expanded adjustment model,
equation (5), which distinguishes between initial
levels of disequilibrium in housing consumption
and changes in equilibrium demands. Again the
model is replicated in two successive one-year
intervals for the same sample of households in
each market.10 Covariance tests indicate no dif-
ferences in adjustment behavior for experimental
and control households and no differences be-
tween time intervals.
The estimated price elasticities in the more
general formulation of equation (5) are -0.36 in
Pittsburgh and -0.41 in Phoenix. These esti-
mates imply a somewhat less elastic response
than found in the simpler models (and implicitly
that achieving housing consumption goals
through rent subsidies could be quite expensive).
The estimates of equation (5) also strongly sug-
gest significant differences in the short run re-
sponsiveness of housing consumption to current
changes in equilibrium demands and to initial
levels of disequilibrium.
One concern throughout this estimation is the
potential for biases arising from the inaccuracy in
estimation of equilibrium demands and problems
in distinguishing adjustment lags from serial cor-
relation in housing demands. Measured house-
hold characteristics explain roughly 40% of the
variation in equilibrium demands. If unmeasured
factors determining demand are uncorrelated
with the observed exogenous variables, the pa-
rameters of the equilibrium demand functions
are, of course, unbiased, but the estimated
equilibrium demand for individual households
will contain errors. The expanded adjustment
model (equation (5)) provides some insight into
the importance of this problem. A portion of the
residual variation undoubtedly reflects system-
atic, but unmeasured, differences in household
10 In estimating equation (5), it must be recognized that 'q
= 0 for all households at the beginning of the experiment.
Thus, for the first interval (O -+1) the estimated model is
(N- 1) H1 = , [Hod - Ho] + y [Hid-H0d] + 7yciH1d
+ bHo
and for the second interval (1 -- 2), the estimated model is
(N - 2) H2 = 8 [Hld - H1] + y [H2d - Hld] + yE71 [H2d
- Hld] + .CP1 Hld + 4H1.
PRICE ELASTICITY OF HOUSING DEMAND 453
tastes and other factors that remain stable over
time. When changes in equilibrium demands are
considered, any time invariant household factors
will be eliminated, and, in the extreme, the error
variance for this term will be zero. Thus, it is
logical to expect biases in y to be less severe than
those in p, and this may partially explain why
estimates of /8 are smaller than those for y. How-
ever, since the price discount was not in effect at
enrollment, Xhe form of the estimation (as ex-
plained in footnote 10) differs across the two
periods, and any biases from inaccurate mea-
surement and serial correlation of demands
would differ across the two intervals. The finding
of coefficient equality for the two periods thus
offers considerable support for this explicit
model of household dynamics.
For the simple models of stock adjustment, the
95% confidence interval for the price elasticity of
housing demand is (-0.33 to -0.95) for
Pittsburgh households and is (-0.20 to -0.71)
for Phoenix households. For the expanded mod-
els the confidence intervals are (-0.22 to -0.54)
and (-0. 19 to -0.63) in Pittsburgh and Phoenix,
respectively. Although the long run elasticity es-
timates obtained from the expanded models are
smaller, the latter models suggest a more rapid
temporal response to price variation.
By way of comparison, Muth (1971) estimates
the price elasticity from the production function
for new housing and reports three estimates of
the price elasticity with 95% confidence intervals
of (-0.51 to -0.99). Polinsky and Ellwood
(1977), using an identical methodology, report
two estimates, with a confidence interval of
(-0.56 to -0.86). Again, these studies are for
national samples of households and are confined
to the purchasers of new single detached, FHA
insured housing. This more direct analysis sug-
gests that renters are somewhat less responsive
to price variation and that responses do vary
across housing markets.
The evolution of consumption responses to
price changes depends not only upon the demand
elasticity and adjustment parameters but also
upon the supply elasticity. As shown in table 2,
which describes the interaction of these factors,
the response to a price reduction will be smaller
with less elastic supply. For example, with a
supply elasticity of 1.0, a 10% price reduction
will elicit only a 3% to 4% increase in housing
consumption over the long run, and, at the end of
five years, only 60% to 90% of this eventual
increase will be realized. The estimates thus sug-
gest inelastic responses to price reductions and
ones that evolve rather slowly over time.
TAbLE 2.-PERCENTAGE CHANGE IN HOUSING
CONSUMPTION FROM A 10% REDUCTION IN HOUSING
PRICES AS A FUNCTION
OF DEMAND AND SUPPLY PRICE ELASTICITIESa
Demand Elasticity
Pittsburgh Phoenix
Simple Expanded Simple Expanded
Adjustment Period/ Adjustment Adjustment Adjustment
Adjustment
Supply Elasticity (8) E=-.642 e=-.359 e=-.453 e=-.409
A. After one year
supply elasticity 0.2 0.75% 0.81% 0.89% 1.02%
0.4 0.92% 1.01% 1.14% 1.38%
0.6 0.99% 1.10%10 1.26% 1.55%
1.0 1.06% 1.19% 1.33% 1.73%
00 1.19% 1.35% 1.60% 2.09%
B. After five years
supply elasticity 0.2 1.35% 1.13% 1.34% 1.30%
0.4 2.03% 1.57% 2.00% 1.92%
0.6 2.44% 1.81% 2.40% 2.28%
1.0 2.91% 2.05% 2.86% 2.69%
00 4.11% 2.58% 4.01% 3.69%
C. After full adjustment
supply elasticity 0.2 1.53% 1.28% 1.39% 1.34%
0.4 2.46% 1.89% 2.12% 2.02%
0.6 3.10% 2.25% 2.58% 2.43%
1.0 3.91% 2.64% 3.12% 2.90%
00 6.42% 3.59% 4.53% 4.09%
Calculations based upon estimated adjustment models of
demand in table 1, assuming constant supply elasticities. Entries
are obtained by substitution along the
uncompensated demand curve, i.e., entries in the table are U,/8 -
f, where 8 is the supply elasticity and f, is the responsiveness of
demand to price change after period T
(i, = ae, io. = e).
454 THE REVIEW OF ECONOMICS AND STATISTICS
REFERENCES
Friedman, Joseph, and Daniel Weinberg, Draft Report on the
Demand for Rental Housing: Evidence from a Percent
of Rent Housing Allowance, Abt Associates, Sept.
1978 (processed).
Hanushek, Eric A., and John M. Quigley, "The Dynamics of
the Housing Market: A Stock Adjustment Model of
Housing Consumption," Journal of Urban Economics
6 (Jan. 1979), 90-1i1.
,"An Explicit Model of Residential Mobility," Land
Economics 54 (Nov. 1978), 411-429.
Kain, John F., and John M. Quigley, Housing Markets and
Racial Discrimination, National Bureau of Economic
Research, 1975.
Mayo, Stephen K., "Theory and Estimation in the Econom-
ics of Housing Demand," paper presented at the North
American Meetings of the Econometric Society,
Chicago, IL, Aug. 1978.
Merrill, Sally R., Draft Report on Hedonic Indices as a
Measure of Housing Quality, Abt Associates, Dec.
1977 (processed).
Muth, Richard F., "The Derived Demand for Urban Residen-
tial Land," Urban Studies 8 (Oct. 1971), 243-254.
, Cities and Housing (Chicago: University of Chicago
Press, 1969).
Polinsky, A. Mitchell, and David T. Ellwood, "An Empirical
Reconciliation of Micro and Grouped Estimates of the
Demand for Housing," this REVIEW 61 (May 1979),
199-205.
Schafer, Robert, "Racial Discrimination in the Boston Hous-
ing Market," Journal of Urban Economics 6 (Apr.
1979), 176-196.
Article Contentsp. 449p. 450p. 451p. 452p. 453p. 454Issue
Table of ContentsThe Review of Economics and Statistics, Vol.
62, No. 3 (Aug., 1980), pp. 329-489Front MatterOffset and
Growth Coefficients for Five Industrial Countries: 1960-1970
[pp. 329-338]A Model of FHLBB Advances: Rationing or
Market Clearing? [pp. 339-347]Inventory Demand and Cost of
Capital Effects [pp. 348-356]Autonomous Expenditures, Interest
Rate Stabilization, and the St. Louis Equation [pp. 357-
363]Local Fiscal Response to Intergovernmental Transfers [pp.
364-370]Specific Training and Inter-Industry Wage
Differentials in U.S. Manufacturing [pp. 371-378]The Effect of
Economic Conditions on the Success of Equal Employment
Opportunity Laws: An Application to the Sex Differential in
Earnings [pp. 379-387]Sex Differences in Worker Quitting [pp.
388-398]Vintage Effects in the Earnings of White American
Men [pp. 399-407]Home Production--A Forgotten Industry [pp.
408-416]A Time Series--Cross Section Analysis of International
Variation in Crime and Punishment [pp. 417-423]Does
Reporting Deter Burglars?--An Empirical Analysis of Risk and
Return in Crime [pp. 424-431]A Derived Demand Function for
Freight Transportation [pp. 432-441]Alternative Techniques for
Developing Real Estate Price Indexes [pp. 442-448]What is the
Price Elasticity of Housing Demand? [pp. 449-454]NotesThe
Stability of the Demand for Money: Evidence from the Post-
1973 Period [pp. 455-459]The Real Wage Rate Over the
Business Cycle [pp. 459-461]The Poverty Line--A Pilot Survey
in Europe [pp. 461-465]Determinants of Family Participation in
the AFDC-Unemployed Fathers Program [pp. 466-470]Vertical
Integration and Technological Innovation [pp. 470-
474]Diversification, Strategic Groups and the Structure-
Conduct- Performance Relationship: A Synthesis [pp. 475-
477]Flexible Cost Functions for Multiproduct Firms [pp. 477-
481]A Note on the Relationship of Minimum Expected Loss
(MELO) and Other Structural Coefficient Estimates [pp. 482-
484]Autocorrelation and Trended Explanatory Variables: A
Comment [pp. 484-487]Autocorrelation and Trended
Explanatory Variables: A Reply [pp. 487-489]Back Matter

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Econ 6301 Applied Microeconomic TheoryREADING ASSIGNMENT #2Ch .docx

  • 1. Econ 6301 Applied Microeconomic Theory READING ASSIGNMENT #2 Ch 3 Demand Reading: “What is the Price Elasticity of Housing Demand?” Eric A. Hanushek and John M. Quigley The Review of Economics and Statistics Vol. 62, No. 3 (Aug., 1980), pp. 449-454 Read the above article and answer the following questions. 1. Describe the paper’s conceptual framework. Do you agree with this framework? What are some of its limitations? 2. Describe the model used to estimate housing demand. 3. Work through the math described in the paper to make sure that you know how the authors obtained equations (4) and (5). What are the main differences between equations (4) and (5)? 4. Briefly describe the data from the Housing Allowance Demand Experiment. Why are these data good for this study? What are some of the limitations of the data? How do you think these issues might affect the results? 5. Describe the empirical results. Why do the long-run and short-run price elasticities differ? 6. How do the results in this paper differ from results found by previous studies? Why? 7. Would the results from this study hold in today’s market? Discuss. ABGB 302: Week 3 Case Study Assignment Describe the source of the dispute and the results of the case in WTO (40 points)—U.S.-E.U Beef Hormone case study. Note: 250 words each for the source of dispute and the results
  • 2. rendered by WTO—500 words total. This week's case study is about U.S.-EU Beef hormone. The dispute was argued in the WTO. The question is: Describe the source of the dispute and the results of the case in WTO—U.S.-E.U Beef Hormone case study. Note 250 words each for the source of dispute and the results rendered by WTO. That will be 500 words in total. This is a very easy case study. Here I'm asking you to describe the source of the dispute and the results rendered by the WTO in this case. The content component will be writing what was the source and the decision rendered by the WTO. The application component is expanding on the case--like putting meat on the bones. The source of the dispute (250 words)--talk about the issue, countries involved, background why this case came to WTO, what is WTO, why it was created, who were the parties to the dispute, why hormone-fed beef is good in the US and bad in the EU. What is EU (the composition of EU countries) their trade policy in beef? Next part is that the WTO gave the decision, what was the decision and how it affects beef trade. Has the EU allowed the US to export hormone-fed beef? Include all these points in your application (200 words). Organization and grammar (4 points)... usual stuff as mentioned in the rubric.
  • 3. AGB 302 Grading Rubric – Case Studies Fall B – 2018 Evaluation Criteria Excellent Very Good Adequate Needs Improvement No Credit Content (18 points) Complete and organized submissions that adhere to all assignment instructions. Submission is missing minor elements and/or is not well- organized and/or missed an assignment instructions. Submission is missing minor elements and/or is not well- organized and/or
  • 4. missed an assignment instructions. Submission is missing elements and/or is not well-organized and/or did not adhere to assignment instructions. Did not submit or submission unacceptable. 18 13.5 9 4.5 0 Application (18 points) High quality submissions that clearly demonstrate understanding of course materials. Thorough explanation of source of dispute in US-EU beef hormone case; result or decision rendered by WTO,
  • 5. knowledge of international trade, workings of WTO. Good submissions with some connections to course materials. Occasionally contributes ideas, relevant personal experience, materials and/or comments. Moderate explanation of source of dispute in US-EU beef hormone case; result or decision rendered by WTO, knowledge of international trade, workings of WTO. Good submissions with some connections to course materials.
  • 6. Occasionally contributes ideas, relevant personal experience, materials and/or comments. Adequate explanation of source of dispute in US-EU beef hormone case; result or decision rendered by WTO, knowledge of international trade, workings of WTO. Little to no evidence that course materials are understood or incorporated into submissions. Poor explanation of source of dispute in US-EU beef hormone case; result or decision rendered by WTO, knowledge of international trade, workings of WTO.
  • 7. Did not submit or submission unacceptable. 18 13.5 9 4.5 0 AGB 302 Grading Rubric – Case Studies Spring B – 2018 Organization and Grammar (4 points) Properly formatted submissions demonstrating professional, college- level tone, no spelling or grammar errors and well- documented sources (when applicable). Submission may be lacking proper formatting or professional tone or may contain minor spelling/ grammar
  • 8. errors or is not well- supported (when applicable). Submission may be lacking proper formatting or professional tone or may contain minor spelling/ grammar errors or is not well- supported (when applicable). Submission may be lacking proper formatting and/or professional tone and/or may contain multiple spelling/grammar errors and/or is not well-supported (when applicable). Did not submit or submission
  • 9. unacceptable. 4 3 2 1 0 WHAT IS THE PRICE ELASTICITY OF HOUSING DEMAND? Eric A. Hanushek and John M. Quigley* I. Conceptual Framework DISAGREEMENT about the responsiveness of housing demand to variations in relative prices persists, despite extensive empirical anal- yses. Two factors underlie this disagreement: the multidimensional character of housing makes di- rect observation of prices (as distinct from ex- penditures) impossible; and, the significant search, transactions, and moving costs asso- ciated with changing dwellings imply that, at any instant, a given household's consumption may deviate significantly from its utility maximizing level in a static equilibrium. While a number of ingenious attempts have been made to circum- vent these problems, each is quite indirect and relies upon strong, and untestable, assumptions (cf. Mayo (1978)). This paper provides direct estimates of price elasticities, based upon an explicit model of housing consumption dynamics and utilizing the experimental manipulations of housing prices incorporated in the Housing Al-
  • 10. lowance Demand Experiments.1 While the data are limited to two years of longitudinal data and pertain only to low income renters, they never- theless permit the direct estimation of this key parameter of housing demand. This analysis focuses on the price responsive- ness of households, but clearly other changes in household circumstances (such as in income or family size) affect desired housing consumption. In fact, given the limited longitudinal data, in- formation about other demand adjustments pro- vides valuable insights into consumption dynam- ics. Price changes can be viewed as but one of a variety of exogenous influences on housing de- mand. A complete structural model of housing de- mand would consider the joint influence of household preferences, relocation costs, and prices on search and moving behavior and, con- ditional on this, their subsequent influence on housing consumption. However, both household preferences and relocation costs are generally unobserved, and estimation of such a complete model is simply beyond our current capabilities. We concentrate upon the more modest goal of modelling the reduced form relationship between housing consumption and housing stock dis- equilibrium (defined below). Consumption dynamics are represented by variants of a linearized stock adjustment process . This formulation is based on the simple observa- tion that adjustments will generally be a
  • 11. monotonic function of the magnitude of dis- equilibrium in housing consumption. As indi- cated by past work (Hanushek and Quigley, 1979), this is both a convenient and powerful characterization of short run dynamics. Two basic formulations of consumption dynamics are considered. Let Htd represent the "desired," or static equilibrium, quantity of housing demanded by a given household, and let Ht be the actual (observed) housing consumption at time t. In the simplest form, households are assumed, on average, to close the gap between desired and equilibrium housing consumption at a constant rate a, so that Ht+ = a[Ht+Id -Ht ] + 4Ht (1) where + is one plus the rate of relative price increase during the interval.2 This formulation, Received for publication August 15, 1978. Revision ac- cepted for publication February 22, 1980. * University of Rochester and University of California, Berkeley, respectively. This is a substantially shortened version of "What is the Price Elasticity of Housing Demand?", Discussion Paper No. 7803, Public Policy Analysis Program, University of Roches- ter, August 1978. Copies of the more complete paper are available from the authors. Support for this research was provided by Abt Associates and a grant from the Alfred Sloan Foundation. The research assistance of Robbe Burnstine is gratefully acknowledged.
  • 12. 1 Alternative approaches to this problem can also be found in Friedman and Weinberg (1978). 2 While the H's refer to quantities, only consumption ex- penditures measured in current prices can be measured. Unit prices in the initial period are arbitrarily normalized to one, and 0 indicates changes in relative prices over time. Given the large fixed cost component to searching and moving, individual households would not be expected to make a series of marginal adjustments to equilibrium but instead would be more likely, given a decision to adjust, to close substantially the gap. Thus, this relationship is best thought of as the reduced form consumption relationship that incorporates both adjustment decisions (searching and mov- [ 449 ] 450 THE REVIEW OF ECONOMICS AND STATISTICS however, does not allow for differences in behav- ioral responses occasioned by different patterns of equilibrium changes. Since the principal method of changing housing consumption is through searching and moving, households may be more responsive in any period to contem- poraneous changes in equilibrium demand than to initial disequilibrium. This possibility is con- sidered by decomposing the level of disequilib- rium into its time components with the hypothe- sis that y > f3:3 Ht+ = f[Htd -H] + y[Ht+ld- Htd] + Ht- (2)
  • 13. Now consider a household for which housing prices are exogenously reduced by some propor- tion -j (O ? -r < 1). The new equilibrium housing demand, Htt+d, resulting from the price change is, by definition, Ht+ I = Ht+?d(1 + E6) (3) where E is the price elasticity of demand for resi- dential housing. Substitution into (1) and (2) yields Ht+j= a[Ht+ld - H] + aEqHt+Id + Ht, (4) and Ht+= /3[Htd- H] + y[Ht+ld- Htd] + 13E71Htd + yEq[Ht+ld - Htd] + OHt * (5) Both formulations explicitly recognize lagged responses to exogenous stimuli. From equation (4), the long run response to a price change is the price elasticity times the price change, En-, but on average only 100a per cent of this response will be observed in the first period. In equation (5) the observed response to an experimental change in housing prices is yE-q after one period and (y + ,/ - 83Y) Eij after two periods, even though the long run response is again El). Estimation of this model requires longitudinal information on the actual housing consumption of households (Ht), their equilibrium demands
  • 14. for given incomes, preferences and initial prices (Htd), and the price reduction (-r). II. Empirical Analysis Data from the Housing Allowance Demand Experiment, which provided housing subsidies to a sample of low income, renter households in Phoenix and Pittsburgh, allow estimation of the housing adjustment models in equations (4) and (5). This analysis concentrates upon 586 house- holds in Phoenix and 799 households in Pittsburgh. Of these, 302 in Phoenix and 424 in Pittsburgh were randomly assigned to treatment groups receiving experimental reductions in rental payments (-q) that ranged from 0.2 to 0.6 (i.e., rent subsidies of 20% to 60%); the remain- der were assigned to control groups that received no subsidy.4 Detailed longitudinal information about household characteristics and housing consumption was collected at the beginning of the experiment and annually for two subsequent years. The empirical implementation involves spec- ifying the equilibrium demands of individual households (HI) in each period and then estimat- ing the dynamic responses and price elasticity parameters. Direct estimation of equilibrium de- mands was used instead of more common sub- stitution of exogenous demand determinants into the dynamic relationships for two reasons: prac- tical limitations imposed by the complicated ad- justments in equation (5) (particularly given the limited longitudinal data); and the lack of sepa-
  • 15. rate identification of changes in relative prices (k) with substitution.5 ing) and actual consumption choices. For present purposes, the focus on expected aggregate behavioral responses is sufficient, although information about the distribution of out- comes across individual households requires more detailed analysis of structural moving relationships (see Hanushek and Quigley (1978)). 3 Note that [H,+ Id - H,] [Htd - H,] + [H,t+d - H,d]. 4 Receipt of subsidy did not depend upon any specific hous- ing consumption choices. The experimental payments were actually received for one full year after the period examined here, and experimental households knew that they would receive assistance in obtaining other subsidies after comple- tion of the experiment-thus minimizing effects of the limited duration of the experiment. (Other treatment groups receiv- ing income subsidies similar to a negative income tax are not analyzed here.) Sample median incomes were 0.5-0.6 of each SMSA's median income. Since the experimental group is small relative to the entire housing market, there would be no perceptible supply re- sponses, and the price elasticity is therefore identified. I Errors in estimating equilibrium demands may affect the subsequent estimation of the demand relationships. How- ever, in the simplest model (equation (4)) the problems with using instruments for equilibrium demands are the same as those encountered in direct substitution when equilibrium demands are stochastically related to the exogenous vari- ables. Moreover, as discussed below, it is possible to assess
  • 16. PRICE ELASTICITY OF HOUSING DEMAND 451 In competitive markets where households face the same prices, contract rents (standardized for landlord provision of utilities and appliances) provide an unambiguous measure of the quantity of housing services actually consumed.6 Assum- ing that households recently making relocation decisions consume their utility maximizing quan- tity of housing services (Hd), equilibrium de- mand functions at initial housing prices for each housing market are then estimated by regressing expenditures on income, assets, family size, po- sition in the life cycle, and other demographic characteristics for recent mover households.7 These estimates, presented and discussed else- where (Hanushek and Quigley, 1979), are consis- tent with expectations and prior research esti- mates, but, importantly, they indicate systematic differences between the two housing markets. All previous investigations of price elasticities that utilized price variations across housing mar- kets have assumed that the demand relationships are the same across areas-an assumption that does not appear warranted. By substituting relevant household income and demographic characteristics for each time pe- riod, household and time specific instruments for desired consumption (i.e., Hod, H d, and H2d) are constructed from the equilibrium demand func- tions. These estimates, combined with actual rent expenditures in each period adjusted for tenure discounts, allow direct estimation of the
  • 17. price elasticity of housing demand-estimation that is free from the most stringent assumptions and data problems encountered by indirect methods.8 HI. Empirical Results-Adjustment and Price Elasticity Estimates Table 1 presents coefficient estimates for households in the Phoenix and Pittsburgh hous- ing markets, replicated in two successive one- year intervals for the same sample of households. Assuming that the errors are normally distrib- uted, the estimates are obtained by maximum likelihood techniques incorporating the non- linear constraints on parameters. Standard covariance tests suggest little differ- ence in the estimated parameters in the two time periods and that the basic adjustment behavior of those households receiving experimental housing price reductions is no different from the behavior of control households who are unaffected by the experiment.9 The simple adjustment coefficient (a) indicates that, on average, 19% of the gap between desired housing consumption and ob- served initial consumption is closed in each one-year period in Pittsburgh. In Phoenix, where the average mobility rate of households is higher, the results suggest that 35% of the gap is closed in any year. In both housing markets, (A is sig- nificantly greater than one, indicating modest in- creases in relative prices. The rate of inflation in housing prices is consistently greater in Phoenix than in Pittsburgh.
  • 18. Based upon the simple adjustment model, equation (4), the estimated price elasticity of demand is -0.64 in Pittsburgh and -0.45 in Phoenix. These are estimates of the long run the importance of such problems in the extended models (equation (5)). Some attempts at using self-reported "satis- faction" indexes as instruments for housing disequilibrium were also made, but these crude instruments yielded unsatis- factory results. 6 A significant housing price gradient would imply that households face differing prices, but this does not appear to be a problem in the cities analyzed here. For Phoenix and Pittsburgh, Merrill (1977) tests for equality of coefficients between central city and suburbs in hedonic price equations. In Pittsburgh, coefficient equality cannot be rejected; in Phoenix, the hypothesis can be rejected, although the esti- mated prices are very similar and the standard error of esti- mate changes only slightly with stratification. Independent analysis of Pittsburgh for the NBER Urban Simulation Model (reported in private correspondence by Gregory Ingram) provides no evidence of price gradients. Finally, Muth (1969) found estimated population gradients for Pittsburgh to be insignificantly different from zero at the 0.10 level (and to have the third smallest point estimate for the 46 areas he analyzed). 7 All households, regardless of subsequent assignments to treatment groups, that moved within 12 months of enrollment (t = 0) are assumed to be in equilibrium and included in the estimation. This is consistent with the assumed micro- behavior in footnote 2. 8 Landlord cost savings from long term occupancy (result- ing from both reduced redecorating costs and lower vacancy
  • 19. rates) would be expected to be reflected, at least partially, in reduced rents. (See, for example, previous estimates by Kain and Quigley (1975) and Schafer (1979).) Here, measured ex- penditures are normalized to new occupants (consistent with the estimated equilibrium demands) by using the estimated tenure coefficients from the Phoenix and Pittsburgh hedonic price equations of Merrill (1977). These tenure discounts grow to 10% in Pittsburgh and 19% in Phoenix for more than 10 years of occupancy. 9 For Phoenix, the hypothesis of coefficient equality across time periods is rejected in the simpler model at the 5% level. However, in the more complex model, time period equality of coefficient is not rejected. Since -1 = 0 for the control house- holds, the relevant test is for equality of a's, a's, y's and O's across samples in each time period. This simply confirms the random assignment of households to treatment groups. 452 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 1.-ESTIMATES OF STOCK ADJUSTMENT MODELS OF HOUSING CONSUMPTION FOR EXPERIMENTAL AND CONTROL HOUSEHOLDSa Pittsburgh Phoenix Pooled Pooled Coefficient 01 1 >2 Time Periods 0l 1- 2 Time Periods a ~~~~~0.223 0.155 0.185 0.407 0.273 0.352 (7.65) (6.23) (9.79) (10.01) (7.61) (13.02) p8 0.213 0.145 0.181 0.402 0.259 0.330
  • 20. (7.24) (5.80) (9.56) (9.02) (7.09) (11.87) y 0.466 0.444 0.376 0.462 0.534 0.512 (4.23) (3.46) (4.86) (4.26) (3.77) 6.38) -0.573 -0.278 -0.689 -0.693 -0.642 -0.359 -0.484 -0.427 -0.385 -0.374 -0.453 -0.409 (3.07) (2.75) (2.71) (2.68) (4.13) (3.36) (2.90) (2.49) (1.80) (1.71) (3.53) (3.65) 4 1.028 1.022 1.036 1.030 1.033 1.032 1.085 1.084 1.058 1.053 1.074 1.067 (27 I1)b (2.06)b (3.77)b (3.12)b (4.70)b (4.79)b (5.02)b (4.95)b (3.75)b (3.43)b (6.39)b (5.94)b R 2 0.582 0.585 0.700 0.702 0.648 0.649 0.535 0.535 0.695 0.697 0.610 0.613 Sample Size Control 375 375 361 361 736 736 284 284 243 243 527 527 Experimental 424 424 407 407 831 831 302 302 265 265 567 567 Parameter Equality Experimental & Control 0.292t 0.893c 0.043c l.796c 0.863c 0.571c 1.039c 0.977c Time Periods 1.278c 2.031c 4.l14c 2.399c / = y 5.240d 5.493d 6.434d 0.297d 3.770d 6.214d a t-statistics are in parentheses. bt-statistics are calculated on null hypothesis that parameter equals one; i.e., that there were no changes in the relative prices of housing and other goods.
  • 21. c F-statistics. d t-statistics. responsiveness of housing consumption to exog- enous price changes; i.e., the responses ob- served after all households had fully adjusted to the changed housing prices. The short run elasticities-those which would be observed after one year of altered prices-are, however, considerably less. While a 10% reduction in housing prices would lead eventually to a 6.4% increase in housing consumption in Pittsburgh, only a 1.2% increase is actually observed after one year. Similarly, in Phoenix only a 1.6% in- crease in housing consumption (from a 10% rent reduction) is observed after the first year, even though a 4.5% increase is expected in the long run. Table 1 also presents the maximum likelihood estimates of the expanded adjustment model, equation (5), which distinguishes between initial levels of disequilibrium in housing consumption and changes in equilibrium demands. Again the model is replicated in two successive one-year intervals for the same sample of households in each market.10 Covariance tests indicate no dif- ferences in adjustment behavior for experimental and control households and no differences be- tween time intervals. The estimated price elasticities in the more general formulation of equation (5) are -0.36 in Pittsburgh and -0.41 in Phoenix. These esti- mates imply a somewhat less elastic response
  • 22. than found in the simpler models (and implicitly that achieving housing consumption goals through rent subsidies could be quite expensive). The estimates of equation (5) also strongly sug- gest significant differences in the short run re- sponsiveness of housing consumption to current changes in equilibrium demands and to initial levels of disequilibrium. One concern throughout this estimation is the potential for biases arising from the inaccuracy in estimation of equilibrium demands and problems in distinguishing adjustment lags from serial cor- relation in housing demands. Measured house- hold characteristics explain roughly 40% of the variation in equilibrium demands. If unmeasured factors determining demand are uncorrelated with the observed exogenous variables, the pa- rameters of the equilibrium demand functions are, of course, unbiased, but the estimated equilibrium demand for individual households will contain errors. The expanded adjustment model (equation (5)) provides some insight into the importance of this problem. A portion of the residual variation undoubtedly reflects system- atic, but unmeasured, differences in household 10 In estimating equation (5), it must be recognized that 'q = 0 for all households at the beginning of the experiment. Thus, for the first interval (O -+1) the estimated model is (N- 1) H1 = , [Hod - Ho] + y [Hid-H0d] + 7yciH1d + bHo and for the second interval (1 -- 2), the estimated model is
  • 23. (N - 2) H2 = 8 [Hld - H1] + y [H2d - Hld] + yE71 [H2d - Hld] + .CP1 Hld + 4H1. PRICE ELASTICITY OF HOUSING DEMAND 453 tastes and other factors that remain stable over time. When changes in equilibrium demands are considered, any time invariant household factors will be eliminated, and, in the extreme, the error variance for this term will be zero. Thus, it is logical to expect biases in y to be less severe than those in p, and this may partially explain why estimates of /8 are smaller than those for y. How- ever, since the price discount was not in effect at enrollment, Xhe form of the estimation (as ex- plained in footnote 10) differs across the two periods, and any biases from inaccurate mea- surement and serial correlation of demands would differ across the two intervals. The finding of coefficient equality for the two periods thus offers considerable support for this explicit model of household dynamics. For the simple models of stock adjustment, the 95% confidence interval for the price elasticity of housing demand is (-0.33 to -0.95) for Pittsburgh households and is (-0.20 to -0.71) for Phoenix households. For the expanded mod- els the confidence intervals are (-0.22 to -0.54) and (-0. 19 to -0.63) in Pittsburgh and Phoenix, respectively. Although the long run elasticity es- timates obtained from the expanded models are smaller, the latter models suggest a more rapid temporal response to price variation.
  • 24. By way of comparison, Muth (1971) estimates the price elasticity from the production function for new housing and reports three estimates of the price elasticity with 95% confidence intervals of (-0.51 to -0.99). Polinsky and Ellwood (1977), using an identical methodology, report two estimates, with a confidence interval of (-0.56 to -0.86). Again, these studies are for national samples of households and are confined to the purchasers of new single detached, FHA insured housing. This more direct analysis sug- gests that renters are somewhat less responsive to price variation and that responses do vary across housing markets. The evolution of consumption responses to price changes depends not only upon the demand elasticity and adjustment parameters but also upon the supply elasticity. As shown in table 2, which describes the interaction of these factors, the response to a price reduction will be smaller with less elastic supply. For example, with a supply elasticity of 1.0, a 10% price reduction will elicit only a 3% to 4% increase in housing consumption over the long run, and, at the end of five years, only 60% to 90% of this eventual increase will be realized. The estimates thus sug- gest inelastic responses to price reductions and ones that evolve rather slowly over time. TAbLE 2.-PERCENTAGE CHANGE IN HOUSING CONSUMPTION FROM A 10% REDUCTION IN HOUSING PRICES AS A FUNCTION OF DEMAND AND SUPPLY PRICE ELASTICITIESa
  • 25. Demand Elasticity Pittsburgh Phoenix Simple Expanded Simple Expanded Adjustment Period/ Adjustment Adjustment Adjustment Adjustment Supply Elasticity (8) E=-.642 e=-.359 e=-.453 e=-.409 A. After one year supply elasticity 0.2 0.75% 0.81% 0.89% 1.02% 0.4 0.92% 1.01% 1.14% 1.38% 0.6 0.99% 1.10%10 1.26% 1.55% 1.0 1.06% 1.19% 1.33% 1.73% 00 1.19% 1.35% 1.60% 2.09% B. After five years supply elasticity 0.2 1.35% 1.13% 1.34% 1.30% 0.4 2.03% 1.57% 2.00% 1.92% 0.6 2.44% 1.81% 2.40% 2.28% 1.0 2.91% 2.05% 2.86% 2.69% 00 4.11% 2.58% 4.01% 3.69% C. After full adjustment supply elasticity 0.2 1.53% 1.28% 1.39% 1.34% 0.4 2.46% 1.89% 2.12% 2.02% 0.6 3.10% 2.25% 2.58% 2.43% 1.0 3.91% 2.64% 3.12% 2.90% 00 6.42% 3.59% 4.53% 4.09% Calculations based upon estimated adjustment models of demand in table 1, assuming constant supply elasticities. Entries are obtained by substitution along the
  • 26. uncompensated demand curve, i.e., entries in the table are U,/8 - f, where 8 is the supply elasticity and f, is the responsiveness of demand to price change after period T (i, = ae, io. = e). 454 THE REVIEW OF ECONOMICS AND STATISTICS REFERENCES Friedman, Joseph, and Daniel Weinberg, Draft Report on the Demand for Rental Housing: Evidence from a Percent of Rent Housing Allowance, Abt Associates, Sept. 1978 (processed). Hanushek, Eric A., and John M. Quigley, "The Dynamics of the Housing Market: A Stock Adjustment Model of Housing Consumption," Journal of Urban Economics 6 (Jan. 1979), 90-1i1. ,"An Explicit Model of Residential Mobility," Land Economics 54 (Nov. 1978), 411-429. Kain, John F., and John M. Quigley, Housing Markets and Racial Discrimination, National Bureau of Economic Research, 1975. Mayo, Stephen K., "Theory and Estimation in the Econom- ics of Housing Demand," paper presented at the North American Meetings of the Econometric Society, Chicago, IL, Aug. 1978. Merrill, Sally R., Draft Report on Hedonic Indices as a Measure of Housing Quality, Abt Associates, Dec. 1977 (processed).
  • 27. Muth, Richard F., "The Derived Demand for Urban Residen- tial Land," Urban Studies 8 (Oct. 1971), 243-254. , Cities and Housing (Chicago: University of Chicago Press, 1969). Polinsky, A. Mitchell, and David T. Ellwood, "An Empirical Reconciliation of Micro and Grouped Estimates of the Demand for Housing," this REVIEW 61 (May 1979), 199-205. Schafer, Robert, "Racial Discrimination in the Boston Hous- ing Market," Journal of Urban Economics 6 (Apr. 1979), 176-196. Article Contentsp. 449p. 450p. 451p. 452p. 453p. 454Issue Table of ContentsThe Review of Economics and Statistics, Vol. 62, No. 3 (Aug., 1980), pp. 329-489Front MatterOffset and Growth Coefficients for Five Industrial Countries: 1960-1970 [pp. 329-338]A Model of FHLBB Advances: Rationing or Market Clearing? [pp. 339-347]Inventory Demand and Cost of Capital Effects [pp. 348-356]Autonomous Expenditures, Interest Rate Stabilization, and the St. Louis Equation [pp. 357- 363]Local Fiscal Response to Intergovernmental Transfers [pp. 364-370]Specific Training and Inter-Industry Wage Differentials in U.S. Manufacturing [pp. 371-378]The Effect of Economic Conditions on the Success of Equal Employment Opportunity Laws: An Application to the Sex Differential in Earnings [pp. 379-387]Sex Differences in Worker Quitting [pp. 388-398]Vintage Effects in the Earnings of White American Men [pp. 399-407]Home Production--A Forgotten Industry [pp. 408-416]A Time Series--Cross Section Analysis of International Variation in Crime and Punishment [pp. 417-423]Does Reporting Deter Burglars?--An Empirical Analysis of Risk and Return in Crime [pp. 424-431]A Derived Demand Function for Freight Transportation [pp. 432-441]Alternative Techniques for Developing Real Estate Price Indexes [pp. 442-448]What is the
  • 28. Price Elasticity of Housing Demand? [pp. 449-454]NotesThe Stability of the Demand for Money: Evidence from the Post- 1973 Period [pp. 455-459]The Real Wage Rate Over the Business Cycle [pp. 459-461]The Poverty Line--A Pilot Survey in Europe [pp. 461-465]Determinants of Family Participation in the AFDC-Unemployed Fathers Program [pp. 466-470]Vertical Integration and Technological Innovation [pp. 470- 474]Diversification, Strategic Groups and the Structure- Conduct- Performance Relationship: A Synthesis [pp. 475- 477]Flexible Cost Functions for Multiproduct Firms [pp. 477- 481]A Note on the Relationship of Minimum Expected Loss (MELO) and Other Structural Coefficient Estimates [pp. 482- 484]Autocorrelation and Trended Explanatory Variables: A Comment [pp. 484-487]Autocorrelation and Trended Explanatory Variables: A Reply [pp. 487-489]Back Matter