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Estimation and policy implications of rental housing demand
JOURNAL
OF URBAN
ECONOMICS
Estimation
16, 76-90 (1984)
and Policy Implications Housing Demand’
of Rental
ALLENC. GOODMANANDMASAHIROKAWAI Department of Political Economy, The Johns Ilbpkins Uniuersity, Baltimore, Maylahd 21218 Received August 23, 1982; revised January 28,1983 The demand for rental housing using the Annual Housing Survey SMSA sample for 1977 is estimated. The principal determinants of rental housing demand, namely housing price and permanent/transitory income, are computed through spatially varying hedonic price techniques and instrumental variables methods (relating to human and nonhuman capital), respectively. Based on the demand estimation results, impacts of hypothetical cash and rent subsidy programs are analyzed in terms of “housing” and “welfare” effects. It is found that a rent subsidy achieves considerably larger effects than does a cash subsidy.
I. INTRODUCTION The past decade has brought about major improvements in the methods used to estimate housing demand. Due largely to the availability of housing price data, most earlier studies have concentrated on owner-occupied units. Although monthly rent is a better measure of expenditures for the flow of housing services than is house value, data limitations have prevented researchers from performing the same extensive analyses that have characterized the market for owner-occupied units. Recently, rental data have become more widely available and, consequently, can be used for estimation as more “pure” measures of housing service flows. This paper attempts to estimate rental housing demand for 19 metropolitan areas by focusing on three specific aspects of the rental housing market. First, as the principal determinant of rental housing demand, we compute the “permanent” and “ transitory” incomes by separating “measured” income into the two components (as in Goodman and Kawai [7]). A proper separation ensures consistent estimation of the permanent income elasticity. Second, as another important determinant of demand, we estimate hedonic prices for each of the 19 metropolitan areas using Box-Cox flexible functional forms (as in Goodman [6]). Third, rental housing demand is estimated by placing the computed permanent income (as well as transitory income) and the hedonic price on the right-hand side of the regression. Based on the demand estimation results, impacts of cash (or income) and rent (or price) ‘This study was supported in part by the Department of Housing and Urban Development’s Annual Housing Survey Grant H-8402SG. which is gratefully acknowledged. 76 0094-1190/84 Copyright All rights
$3.00
e’l984 by Academic Press. Inc. of reproduction in any form reserved.
RENTAL
HOUSING
DEMAND
77
subsidy programs are considered in terms of “housing” and “welfare” effects. Housing effects measure the increment to rental housing consumed in response to a subsidy, and welfare effects measure the change in the rent/income burden ratio. The next section discussestheoretical issues of housing demand estimation, particularly concerning income, price and quantity variables. Possible estimation biases arising from improper specification will be emphasized. Section III reports estimation results, including the computation of permanent/transitory income and hedonic rental prices and the estimation of housing demand. Section IV analyzes the housing and welfare effects of hypothetical income and price subsidies. The final section summarizes policy implications and suggestions for future research. II. ESTIMATION
METHOD
Rental housing demand can be specified as
Q = Q(W’,Z), where Q P Y Z
= flow of housing services demanded, =price of the flow of housing services (relative to a numeraire good), = real income (in terms of the numeraire good), = other variables affecting housing demand such as tastes and household characteristics.
Within a single metropolitan area the numeraire price is assumed to be constant, so that nondeflated price of housing and nominal income represent P and Y in the absence of inflationary expectations. In considering intermetropolitan housing demand, however, it is desirable to deflate the regional housing prices and incomes by cost-of-living indices representing nonhousing items. One difficulty in housing demand analysis is that we do not observe directly several key variables, such as housing quantity, housing price and relevant income variables. First, what is observed in the market is the value S of housing services to be consumed, i.e., the product of quantity and price (S = PQ). We estimate housing prices (and hence quantities) through hedonic price techniques to reflect variations both within and across metropolitan areas. Second, it is generally accepted that permanent income is one of the principal determinants of housing demand, reflecting the fact that households look beyond the current period’s income in making demand decisions. In addition to permanent income, we postulate that transitory income is also important in rental housing demand. However, what is observed is not the individual components but the sum of the two. We
78
GOODMAN
AND
KAWAI
compute both permanent and transitory incomes using instrumental variables related to human and nonhuman wealth. The importance of hedonic prices and permanent/transitory incomes is emphasized elsewhere (Goodman and Kawai [7]) in the context of owneroccupied housing demand, and this study is its extension to rental housing. Since fundamental arguments are found in Goodman and Kawai [7], we summarize the basic points and discuss those issues not mentioned therein. A. Hedonic Prices
There are literally hundreds of variables that could be used in a hedonic price regression, and the list might vary from area to area.2 For reasons of comparability, we use the list developed by Follain and Malpezzi [4] in their Annual Housing Survey studies for 1974 and 1975. Their variables, with only a few exceptions, are used as they formulated them. Personal characteristics which might influence the rent of a unit are also included. Blacks or Spanish-surnamed people may be forced to pay higher prices if discrimination is a problem, for example. Also, the price variation arising from long-time-tenant discounts should be permitted in any estimation procedure; several studies have documented the finding that long-time tenants receive considerable discounts on their rents, compared to new tenants. (See, for example, Merrill [14], Downs [3], and Lowry [12].) Inclusion of tenant characteristics is usually thought to be inappropriate in the first stage of hedonic estimation. Here, however, we include these variables in the first-stage regression rather than as determinants of housing demand, in order to estimate discounts or premia charged to certain residents. This allows unbiased estimates of the housing structure and neighborhood hedonic prices, and permits computation of premia or discounts specific to the renter for a standardized bundle. It is not unlike including a distance term to account for a falling land price gradient within a metropolitan area, allowing a falling house price gradient in accordance with theory. We use the following specific functional form: s? - 1 L= A
vg + &Jmi m
+ &J&.i
+ y,
k
where S is the observed rent, t refers to tenant characteristics, c refers to 2Two basic methods have been used to derive unit pric& of housing, housing cost computation (e.g., Polinsky and Ellwood [16]) and hedonic price estimation (e.g., Kain and Quigley [lo] and Straszheim [19]). We employ the hedonic price estimation technique by allowing the equations to vary spatially.
RENTAL HOUSING DEMAND
79
housing unit and neighborhood characteristics, and h, v, and 6 are the coefficients to be estimated.3Although this Box-Cox flexible form has often been used for owner-occupied housing (see Goodman [6], Linneman [ll], and Halvorsen and Pollakowski [8]), only Linneman [ll] has applied it to rental housing prices. The “price” of a unit of rental housing, P, is determined by evaluating a “standardized unit” according to the area’s hedonic price regression. Within a metropolitan area this price can vary by location, time period, or certain tenant-specific characteristics, such as race or household crowding. The quantity of housing Q, then, is obtained by dividing the gross rent by P, i.e., Q = S/P. B. Permanent and Transitory Income
We postulate that both permanent and transitory components of actual income have substantially positive, separate effects on rental housing consumed. This implies not only that households look beyond the current period’s income in their rental-housing consumption decisions, but also that random variations in actual income have impacts on the quantity demanded. With perfect capital markets, consumers might borrow against future incomes in order to spread out housing consumption over their horizons in ways consistent with their permanent incomes. As a result random income should be expected to have little (life-cycle model) or no (permanent-income model) effects on the amount of the good purchased.4 However, in a more realistic world of imperfect capital markets, consumers cannot generally borrow against their anticipated life time earnings and, hence, the transitory component of actual income may be used to fulfill housing flow demand that could not otherwise be met from permanent income. Thus, the proper demand function should include permanent and transitory incomes separately (or at least permanent income) to estimate the permanent income elasticity consistently.5 Failure to do so can lead to 31t is well known that this form, developed by Box and Cox [2], reduces to linear form when X = 1 and to logarithmic form when A = 0. 4See Friedman [5], Reid [17] and Mayer [13] for summaries and discussionsof such models. Using savings survey data, Attfield [l] concludes that transitory income has a positively significant impact on consumption. He uses a slightly different definition of transitory income, however, than we do. ‘For owner-occupied housing, transitory income is more important because of the savings motivation of housing demand. That is, the purchase of a house, on the one hand, is an investment in a durable good from which the purchaser can enjoy a flow of services; on the other hand, it is an investment in a portfolio from which he can withdraw his equity at the time he sells the property. If transitory income in a given year is to be saved as a source of future consumption, one of many assetsinto which it might go is the buyer’s house. This will lead to a positive effect on stock demand with respect to transitory income. This suggeststhat differences in transitory income coeficients between owners and renters may give some indication as to the magnitude of this “savings-investment demand” for housing.
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GOODMAN AND KAWAI
estimation biases. Goodman and Kawai [7] prove that, if measured income (the sum of permanent and transitory incomes) is used as a proxy for permanent income, then the OLS estimate of the income coefficient underestimates the permanent income coefficient and overestimates the transitory income coefficients. Using the method developed by Goodman and Kawai [7], the following regression equation is estimated to construct the permanent and transitory components of measured income:
where ( Ei) represents education, Ai refers to age, Z$. indicate other human and nonhuman wealth variables for the iti individual. Age is entered quadratically to capture its expected nonlinear effect on permanent income. Education is entered either linearly or in a stepwise manner. In the linear case t#~ is a scalar term; in the stepwise case, where a series of dummy variables indicate educational levels, +i is a vector of coefficients.6 W; is the disturbance term uncorrelated with the explanatory variables so that the OLS procedure provides consistent and efficient estimates. Coefficient signs are expected to be
The predicted value of Y and the predicted value of y can be interpreted as the estimates for permanent and transitory incomes, respectively. C. Rental Housing Demand Function
The above arguments suggest that the rental housing demand regression should include as explanatory variables at least the computed hedonic prices (P) and the permanent (Y ‘) and transitory (Y r) components of measured income. To the extent that P is correlated with Y (= YP + Y r), the price variable should not be left out in consistently estimating the income elasticity.7 If permanent income is assumed to be uncorrelated with transitory income, omission of transitory income will not bias the permanent 6The education variable E, could be expanded to include quadratic and higher level polynomials, similarly to age. Preliminary work settled on the stepwise procedure as being preferable. ‘Possible estimation biases caused by the omission of P are discussedby Polinsky [15], who claims that since house price P systematically falls with distance from a central place and the more affluent (higher Y) are likely to move further out, the income elasticity is underestimated.
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RENTAL HOUSING DEMAND
income coefficient, but its inclusion in the regression equation should enhance the predictive power. The housing-demand equation (1) in its fullest form, therefore, should be specified as: Q,
=
(Y
+
j3pyp
+
PTqT
+
VP,
+
Csjzj;
+
Vi,
(4)
where (Y,fip, &, y, 6’s are the coefficients to be obtained, Zji are relevant explanatory variables other than income and price, and the i’s denote cross-sectional individual households.* III. ESTIMATION
RESULTS
A. Data The data are from the Annual Housing Survey SMSA sample for 1977. For 15 “small” SMSAs (metropolitan areas for which samples of 5000 dwelling units were drawn), a 30% sample of renters was extracted. For four “large” SMSAs (with samples of 15,000 dwelling units) a 10% sample of renters was drawn. Sample sizes vary from 347 observations in Albany and Detroit, to 652 observations in Washington, D.C.9 There is substantial variation for selected variables among areas. Apartment size varies from 3.64 rooms in Los Angeles to 4.66 rooms in Albany. Mean gross rent varies from $155 in Memphis to $273 in Anaheim, and mean income varies from $8770 in Spokane to $13,704 in Washington, D.C. Pittsburgh has the highest mean age (45.7 years per household head), while Salt Lake City (34.7 years) has the lowest. Most SMSAs provide a good city/suburbs mix, and most also provide a balanced racial makeup and good distribution of male and female household heads.” One serious shortcoming in the AHS data set in general is the paucity of geographic and neighborhood detail. The confidentiality requirements that enable the acquisition of such excellent income and other personal data lead to suppression of most of the geographic identifiers that make up neighborhood data. Researchersmay know if a housing unit is in the central city, for example, but it is impossible to determine the distance from the Central Business District, the racial nature of the neighborhood, or the quality of “One might argue that since (4) is the demand function there exists a simultaneity bias if the OLS is applied. Our procedure solves the possible simultaneity bias on two grounds. First, it is quite legitimate to regard (4) as a microeconomic demand function and hence to use the microeconomic data for estimation. Second,both our method of constructing the housing price index, and its use in the demand function have a two-stage least-squares interpretation. ‘The “small SMSAs” are Albany, Anaheim, Dallas, Fort Worth, Madison, Memphis, Minneapolis, Newark, Orlando, Phoenix, Pittsburgh, Salt Lake City, Spokane, Tacoma and Wichita. The “large SMSAs” are Boston, Detroit, Los Angeles and Washington, D.C. “A detailed area-by-area breakdown is available from the authors on request, as are regression results for each of the analyses reported.
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GOODMAN AND KAWAI
the public schools. The data set does include variables concerning residents’ attitudes on some neighborhood characteristics ranging from school quality to street noise. Follain and Malpezzi [4] test these variables as indicators of neighborhood quality and find them wanting. We use them for lack of suitable alternatives, but the results mirror theirs. B. Hedonic Price Estimation
Separate hedonic regressions are estimated for each of the 19 metropolitan areas. Particular attention is directed toward estimating the suitable functional form for a given area by using (2). Most published studies of rental hedonic price formulations have used log-linear forms; theory, such as Rosen [18], suggeststhat these may be overly restrictive. Tests for functional form show that reliance solely on linear or semilogarithmic forms may constitute a serious misspecification. As noted in Table 1, the best functional forms, with the exception of Los Angeles, have X greater than zero but less than 1. Significance tests reject the semilog form (X equal to 0) for all cities but Los Angeles. Unit housing price P is determined by evaluating the systematic part of (2) for a standardized unit. That is, P is the price of the standardized unit adjusted for length of tenancy, race, location in the SMSA and crowding of TABLE 1 Best Functional Forms for Hedonic Price Regressions City
x
x2
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington Wichita
0.6 0.2 0.6 0.6 0.1 0.7 0.0 0.4 0.7 0.8 0.8 0.7 0.4 0.4 0.4 0.5 0.9 0.6 0.2
0.6020 0.6396 0.5651 0.5878 0.6612 0.6593 0.5713 0.5060 0.7411 0.5194 0.5770 0.5993 0.6050 0.5235 0.4409 0.6145 0.4972 0.6499 0.6537
Note: 7i2 = the coefficient of multiple correlation adjusted for the degrees of freedom.
83
RENTAL HOUSING DEMAND TABLE 2 Mean Quantities and Prices by Metropolitan Area City
Quantity
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington, D.C. Wichita
0.963 (0.373) 1.187(0.403) 1.330 (0.583) 1.030(0.445) 1.006 (0.360) 1.149 (0.471) 0.953 (0.473) 1.035(0.351) 1.076(0.445) 0.966 (0.344) 0.912 (0.319) 0.825 (0.308) 1.102 (0.505) 1.037 (0.419) 1.138 (0.505) 1.095 (0.454) 1.099(0.370) 1.036(0.441) 1.095 (0.409)
Price
190.16(18.31) 233.28(19.96) 167.05(19.51) 191.17(21.10) 197.14(17.89) 156.58(17.12) 226.80(27.56) 195.60(11.59) 145.40(13.85) 210.29(15.17) 252.32(27.78) 233.41(38.61) 189.99(20.70) 170.34(22.52) 165.84 (5.78) 153.09(14.76) 169.10(11.36) 217.12(24.14) 167.20(12.20)
Note: Standard errors are reported in parentheses.
the unit. Housing quantity Q is computed by dividing gross rent by P. Table 2 details the mean quantities and the mean prices of “housing” by metropolitan area. The lowest mean quantity is 0.82 units in Orlando; the highest, 1.33 units in Boston. The lowest mean price is $145 in Memphis; the highest, $252 in Newark.
C. Permanent Income Estimation Permanent income is estimated for each of the 19 metropolitan areas. Measured income is regressed on employment status, age, race, Spanish surname, sex of head of household, marital status, education, household size, prior housing tenure, and prior house value if the house was owned. The first eight variables indicate human capital components of permanent income; the latter two indicate nonhuman capital components. In general, the regressions predict fairly well. In Table 3, using a linear form, x2 varies from 0.21 in Anaheim to 0.44 in Pittsburgh, and clusters between 0.30 and 0.40. Standard errors of the regression (SER) vary from $4901 in Spokane to $7901 in Anaheim, although these are not strictly comparable due to cost of living differentials.
84
GOODMAN AND KAWAI TABLE 3 Summary of Permanent Income Regressions City
R2
R2
SER
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington Wichita
0.3353 0.2309 0.4403 0.4080 0.4082 0.3516 0.3006 0.2462 0.3920 0.3514 0.4320 0.3378 0.3135 0.4585 0.2570 0.4072 0.3242 0.3636 0.3192
0.3195 0.2068 0.4265 0.3943 0.3923 0.3292 0.2847 0.2286 0.3748 0.3355 0.4180 0.3235 0.2879 0.4388 0.2328 0.3861 0.3036 0.3506 0.2989
6017 7901 7098 6381 7030 6698 7300 6905 6352 6695 6713 6444 7636 5091 6997 4901 6225 7489 6180
Note: R* = the coefficient of multiple correlation. R2 = the coefficient of multiple correlation adjusted for the de grees of freedom. SER = the standard error of regression.
D. Rental Housing Demand We now consider the estimation results for rental housing demand using both computed hedonic prices and measured or permanent/transitory income. Housing demand was initially estimated for each SMSA. However, due to insufficient geographic variations within an SMSA, price elasticities were generally disappointing. In order to generate enough price variation within the data set, the 19 metropolitan areas are pooled. We report here only the’pooled regression results. To control the interarea price differentials, the Bureau of Labor Statistics family budget is used with its component housing portions deleted. Income and housing price variables are deflated by these nonhousing CPIs. Since the BLS budget is not computed for every city in the sample, several substitutions are made.” In preliminary work, estimated income elasticities were not sensitive to the inclusion or exclusion of the overall price level, so the substitutions do not appear to be serious. Fort Albany: Buffalo (substituted) “The following substitutions have been made: Anaheim: Los AngelesMemphis: Nashville (substituted) Worth: Dallas (substituted) Madison: Milwaukee Tacoma, Spokane: Seattle (substituted) Long Beach (substituted) Salt Lake City, Phoenix: Denver (substituted). (substituted)
85
RENTAL HOUSING DEMAND TABLE 4 Demand Regressions: Pooled Sample Recent movers
All renters Measured Y YP YT P
PER RACE SEX CONST E2 SER 9V 1,
Permanent
- ___-
-
0.00228 (42.21) -
0.00379 (36.17) 0.00174 (28.10) - 0.2535 (21.65) 0.0463 (15.60) -0.1176 (10.34) -0.1378 (13.66) 1.1255 0.2648 0.3809 0.393 - 0.458
- 0.2185 (18.67) 0.0538 (18.03) - 0.1502 (13.21) - 0.0631 (6.80) 1.1655 0.2415 0.3869 0.238 - 0.395
Measured 0.00245 (27.03)
- 0.2625 (13.06) 0.0750 (14.36) -0.1599 (7.50) - 0.0909 (5.71) 1.2744 0.2904 0.3757 0.241 - 0.474
0.00381 (22.04) 0.00195 (18.65) - 0.3001 (14.83) 0.0681 (13.08) - 0.1293 (6.07) - 0.1559 (9.05) 1.2533 0.3103 0.3704 0.381 - 0.542
-
Note: (1) r statistics are shown in parentheses. (2) Y, Yp, Y’, and P are all measured relative to the price level for other goods and services.
Table 4 reports the pooled regression results for housing demand estimation using measured or permanent/transitory income, for both all renters (8608 observations) and recent movers (2845 observations). The regressions are estimated with the income and price terms, household size (PER), race (RACE), and sex of household head (SEX). In the all renter sample, measured income elasticity is 0.238; price elasticity is -0.395. Inclusion of permanent and transitory income not only enhances the predictive power (from 0.2415 to 0.2648 for Iii* and from 0.3869 to 0.3809 for SER) but also raises the income and price elasticities to 0.393 and - 0.458, respectively. It might be suggested that recent movers are closer to equilibrium than long-term tenants, because of moving and other transactions costs. Estimating these regressions for renters who have moved in the past year shows measured (0.241) and permanent (0.381) income elasticities that are quite similar to those estimated for the entire sample. However, estimated price elasticity increases (in absolute value), from - 0.458 to -0.542 in the permanent income regressions, and from -0.395 to -0.474 in the measured income regressions.‘* 12We are currently examining the nature of the differential price elasticities in separate research.
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GOODMAN AND KAWAI
The transitory income coefficients are significant and substantial in both all-renters and recent-movers regressions. For all renters the propensity to spend out of transitory income is approximately 46% of the propensity to spend out of permanent income. For recent movers, this percentage rises to 51%. Since permanent and transitory incomes are orthogonal, omission of transitory income does not bias the estimated permanent income elasticity but, taking the all-renters permanent income regression as an example, R* falls from 0.2648 to 0.1974. The other coefficients behave about as expected. Increased household size leads to higher demand, and black and/or female-headed households purchase less. These coefficients should be interpreted carefully since they represent the second stage of the estimating process. In the sample, on average, male-headed households earn about $2160 more permanent income than do female-headed households. As a result, for a given measured income, the household purchases 21.6 X (fiP - &.) more housing (where 21.6 is the incremental income divided by the average price deflator of 100). Male-headed households, then, purchase 0.094 fewer units (rather than 0.138 fewer units, calculated from the second stage alone) than do femaleheaded households, holding household size constant. This is a difference of about 9%. Similar adjustments are also necessary for race and household size variables.13 IV. HOUSING AND WELFARE EFFECTS OF SUBSIDY During the 1970’s the federal government contracted for two major experiments on market outcomes of housing subsidy and grant programs. One aim of both the Housing Assistance Supply and Demand Experiments (HASE and HADE) was to demonstrate the impacts of cash grant programs on housing demand. These impacts were generally measured either as income elasticities, or as changes in rent burdens (rent as a fraction of income). Most of the estimated permanent income elasticities were in the 0.25 to 0.40 range, and there was some question about whether the limited experiment durations and/or the cash grant methods led to downward biases in the estimates.14 This section discusses a conceptual experiment with a cash assistance program, derived from the regressions displayed in Table 4. It considers a household of three with measured income of $6000 per year, paying the mean price for rental housing. In this experiment, the household is given an unrestricted cash grant of ten percent of income, i.e., $600 per year. This 13Raceis always included in the permanent income regression; household size is included if it improves the standard error of the regression. 14Hanushek and Quigley [9] present an excellent summary and evaluation of the experimental findings.
87
RENTAL HOUSING DEMAND TABLE 5 Housing/Welfare Effects of Income and Rent Subsidies Housing effects Income subsidy
All Renters Recent Movers
Q
P
T
A4
Price subsidy
0.9825
+ 2.29% + 2.22%
+ 1.05% + 1.14%
+ 1.35% + 1.43%
+ 13.0% + 14.2%
1.0321
Welfare effects Income subsidy
AI1 Renters Recent Movers
W
P
T
0.378 0.410
- 7.01% - 7.10%
- 8.14% - 8.05%
M
- 7.86% - 1.19%
Price subsidy - 16.7% - 13.7%
analysis considers the impacts of this grant, depending on whether the household considers it as permanent, transitory or simply measured income. As noted in Table 5, measured income of $6000 leads to 0.9825 units purchased, in the all-renters regression, and to 1.0325 units (approximately 5% more) in the recent-movers regression. The rent burden W is 0.378 in the all-renters regression, and 0.410 in the recent-movers regression. (Estimates of W at the individual SMSA level vary from 0.267 in Memphis to 0.452 in Newark, using the all-renters regressions.) Housing and welfare effects are directly related. Defining housing quantity Q as a function of price P and income Y, the rent burden, W, is W = P - Q( P, Y)/Y.
(5)
Differentiating with respect to Y, for given housing price, we obtain
where 9, refers to the income elasticity of the rent burden, and q, to the income elasticity of housing demand. Thus, income-elastic behavior in housing demand leads to an increasing rent burden, and a trade-off exists between housing and welfare effects. This can be seen in Table 5. Numbers below P, T, and M indicate percentage changes (in housing demand Q or the rent/income burden ratio W) when the household regards the income increment as permanent, transitory or measured, respectively. For the all-renters regression, for example, if renters view the 10% increase as permanent, it results in a 2.29%
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GOODMAN AND KAWAI
increase in Q; if, on the other hand, they view it as only transitory, the resulting increase is only 1.05%. The measured income increase of 1.35% might reflect a program of limited duration. The welfare effect is interpreted similarly. The fall in rent burden is 7.01, 8.14, or 7.86%, depending on whether the perceived income increase is permanent, transitory, or measured. Given the relatively small housing effects of an income subsidy, it is interesting to compare them to the effect of a price subsidy of comparable cost. Using both the all-renters and recent-movers results from Table 4, Table 5 also shows the increase in housing quantity and the decline in the rent/income ratio, if the $600 in aid is used as a rent subsidy rather than as an income transfer. These effects are calculated by dividing the $50 per month by the number of units of housing being purchased, Q. This represents a subsidy of 26.4% for all renters (24.4% for movers only), and results in a 13.0% increase in housing for all renters (14.2% for movers). The relative cost of achieving the same effect through a price subsidy as the permanent income housing effect can also be computed. For example, the 2.29% increase in housing quantity brought about by a $600 income transfer could be achieved at 17.9% of this cost (approximately $90) through a price subsidy. If policymakers are intent on increasing rental housing consumption, price subsidies are a much less expensive instrument, even though they may distort the price of housing relative to other goods. The linkage between price elasticity and welfare effects can be captured by looking at how W is affected. From (5), it can be shown that the two are directly related, that is, 9 wp= 1 -(-v&J The table indicates that the welfare effect of a price subsidy is much greater than that of an income subsidy; the price subsidy reduces the rent/income burden ratio by 16.7% for all renters and 13.7% for recent movers. Since the price elasticity for the recent-movers equation is higher (in absolute value) than that for the all-renters equation, the smaller welfare effects follow. V. CONCLUSION This paper has applied a method of housing demand estimation, originally developed by Goodman and Kawai [7] for owner-occupied housing, to rental housing markets for 1977. Hedonic rental functions are generally nonlinear. The linear hypothesis is rejected in 17 of 19 submarkets; the semilog caseis rejected in 18 of 19 cases.This suggeststhat future work with rental hedonic functions should examine the underlying assumptions concerning functional form. In particular, marginal valuations of specific housing attributes may be quite sensitive to the form used.
RENTAL HOUSING DEMAND
89
The permanent income model as a function of human and nonhuman capital also performs well across metropolitan areas. Most variables have their expected signs with plausible magnitudes. The primary finding is that permanent income derived through instrumental variables methods provides better prediction (in terms of SER and R2) as well as substantially higher income elasticities. Measured income elasticities are generally clustered between +0.2 and +0.3, and permanent income elasticities are clustered between + 0.4 and + 0.5. Transitory income, which is quite plausibly related to housing purchase because of capital market imperfections, also has considerable impact. The transitory income coefficient is generally half the size of the permanent income coefficient. These coefficients provide upper and lower bounds for measuring the impacts of cash transfers to households. Price elasticities vary from approximately -0.46 to -0.54 for a pooled sample. These also fall within the range of conventional estimates. As anticipated recent movers indicate a higher price elasticity by 20% than all renters; income elasticities are similar for the two groups of renters. The last section of the paper examines a conceptual experiment similar to HADE and HASE, where households are “given” income transfers, which are not necessarily tied to housing purchases. In general, the elasticities in this experiment are about the same as the HADE and HASE numbers, and considerably lower than the elasticities calculated at the means of quantity and income. This suggests that the HADE and HASE definitions of permanent income performed similarly to the ones that we postulate. It also suggests that income elasticities calculated with a low income population and linear demand functions should probably be routinely adjusted upward for attribution to the more general population. Our result provides verification that the demand response to income transfers is likely to be fairly small, that is, a small “housing” effect and a correspondingly large “welfare” effect. A price subsidy of comparable cost turns out to achieve a considerably greater housing effect with a simultaneous, substantial reduction in the rent/income ratio. If policymakers desire larger housing effects, specific housing price subsidies to renters or landlords should be seriously considered. REFERENCES 1. C. L. F. Attfield, Testing the assumptions of the permanent-income model, J. Amer. Sfatist. Assoc., 75, 32-38 (1980). 2. G. E. P. Box and D. R. Cox, An analysis of transformations, J. Roy. Statist. Sot., B26, 211-243 (1964). 3. A. Downs, Some aspects of the future of rental housing, in “Rental Housing: Is There a Crisis?” (John C. Weicher, et al., Eds.) Urban Institute Press,Washington, D.C. (1981). 4. James R. Follain and Stephen Malpezzi, “ Dissecting Housing Value and Rent Estimates of Hedonic Indexes for Thirty-nine Large SMSAs,” The Urban Institute, Washington, DC. (1980).
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5. M. Friedman, “A Theory of the Consumption Function,” Princeton Univ. Press,Princeton, N.J. (1957). 6. A. C. Goodman, Hedonic prices, price indices and housing markets, J. [/rhun Econ.. 5. 471-484 (1978). 7. A. C. Goodman and M. Kawai, Permanent income, hedonic prices and demand for housing: New evidence, J. Urbun &on., 12, 214-237 (1982). 8. R. HaIvorsen and H. 0. Pollakowski, Choice of functional form for hedonic price equations, J. Urban Econ., 10, 37-49 (1981). 9. E. A. Hanushek and J. M. Quigley, Complex public subsidies and complex household behavior: Consumption aspects of housing allowances, in “Do Housing Allowances Work?’ (K. L. Bradbury and A. Downs, Eds.), Brookings Institution, Washington, D.C. (1981). 10. J. F. Kain and J. M. Quigley, “Housing Markets and Racial Discrimination,” Columbia Univ. Press,New York (1975). 11. P. Linneman, Some empirical results on the nature of the hedonic price function for the urban housing market, J. Urban Con., 8, 47-68 (1980). 12. I. S. Lowry, Rental Housing in the 1970s: Searching for the crisis, in “Rental Housing: Is There a Crisis?” (John C. Weicher, et al. Eds.), Urban Institute Press, Washington, D.C. (1981). 13. T. Mayer, “Permanent Income, Wealth and Consumption: A Critique of the Permanent Income Theory, the Life-Cycle Hypothesis and Related Theories,” Univ. of California Press, Berkeley, Cal. (1972). 14. S. Merrill, “Draft Report on Hedonic Indices as a Measure of Housing Quality,” Abt Associates, Cambridge, Mass. (1977). 15. A. M. Polinsky, The demand for housing: A study in specification and grouping, Econometrica, 45, 447-461 (1977). 16. A. M. Polinsky and D. T. Ellwood, An empirical reconciliation of micro and grouped estimates of the demand for housing, Reu. Econ. Statist., 61, 199-205 (1979). 17. M. G. Reid, “Housing and Income,” Univ. of Chicago Press, Chicago (1962). 18. S. Rosen, Hedonic prices and implicit markets: Product differentiation in pure competition, J. Pol. Econ., 82, 34-55 (1974). 19. M. Straszheim, “An Econometric Analysis of the Urban Housing Market,” Columbia Univ. Press, New York (1975).
OF URBAN
ECONOMICS
Estimation
16, 76-90 (1984)
and Policy Implications Housing Demand’
of Rental
ALLENC. GOODMANANDMASAHIROKAWAI Department of Political Economy, The Johns Ilbpkins Uniuersity, Baltimore, Maylahd 21218 Received August 23, 1982; revised January 28,1983 The demand for rental housing using the Annual Housing Survey SMSA sample for 1977 is estimated. The principal determinants of rental housing demand, namely housing price and permanent/transitory income, are computed through spatially varying hedonic price techniques and instrumental variables methods (relating to human and nonhuman capital), respectively. Based on the demand estimation results, impacts of hypothetical cash and rent subsidy programs are analyzed in terms of “housing” and “welfare” effects. It is found that a rent subsidy achieves considerably larger effects than does a cash subsidy.
I. INTRODUCTION The past decade has brought about major improvements in the methods used to estimate housing demand. Due largely to the availability of housing price data, most earlier studies have concentrated on owner-occupied units. Although monthly rent is a better measure of expenditures for the flow of housing services than is house value, data limitations have prevented researchers from performing the same extensive analyses that have characterized the market for owner-occupied units. Recently, rental data have become more widely available and, consequently, can be used for estimation as more “pure” measures of housing service flows. This paper attempts to estimate rental housing demand for 19 metropolitan areas by focusing on three specific aspects of the rental housing market. First, as the principal determinant of rental housing demand, we compute the “permanent” and “ transitory” incomes by separating “measured” income into the two components (as in Goodman and Kawai [7]). A proper separation ensures consistent estimation of the permanent income elasticity. Second, as another important determinant of demand, we estimate hedonic prices for each of the 19 metropolitan areas using Box-Cox flexible functional forms (as in Goodman [6]). Third, rental housing demand is estimated by placing the computed permanent income (as well as transitory income) and the hedonic price on the right-hand side of the regression. Based on the demand estimation results, impacts of cash (or income) and rent (or price) ‘This study was supported in part by the Department of Housing and Urban Development’s Annual Housing Survey Grant H-8402SG. which is gratefully acknowledged. 76 0094-1190/84 Copyright All rights
$3.00
e’l984 by Academic Press. Inc. of reproduction in any form reserved.
RENTAL
HOUSING
DEMAND
77
subsidy programs are considered in terms of “housing” and “welfare” effects. Housing effects measure the increment to rental housing consumed in response to a subsidy, and welfare effects measure the change in the rent/income burden ratio. The next section discussestheoretical issues of housing demand estimation, particularly concerning income, price and quantity variables. Possible estimation biases arising from improper specification will be emphasized. Section III reports estimation results, including the computation of permanent/transitory income and hedonic rental prices and the estimation of housing demand. Section IV analyzes the housing and welfare effects of hypothetical income and price subsidies. The final section summarizes policy implications and suggestions for future research. II. ESTIMATION
METHOD
Rental housing demand can be specified as
Q = Q(W’,Z), where Q P Y Z
= flow of housing services demanded, =price of the flow of housing services (relative to a numeraire good), = real income (in terms of the numeraire good), = other variables affecting housing demand such as tastes and household characteristics.
Within a single metropolitan area the numeraire price is assumed to be constant, so that nondeflated price of housing and nominal income represent P and Y in the absence of inflationary expectations. In considering intermetropolitan housing demand, however, it is desirable to deflate the regional housing prices and incomes by cost-of-living indices representing nonhousing items. One difficulty in housing demand analysis is that we do not observe directly several key variables, such as housing quantity, housing price and relevant income variables. First, what is observed in the market is the value S of housing services to be consumed, i.e., the product of quantity and price (S = PQ). We estimate housing prices (and hence quantities) through hedonic price techniques to reflect variations both within and across metropolitan areas. Second, it is generally accepted that permanent income is one of the principal determinants of housing demand, reflecting the fact that households look beyond the current period’s income in making demand decisions. In addition to permanent income, we postulate that transitory income is also important in rental housing demand. However, what is observed is not the individual components but the sum of the two. We
78
GOODMAN
AND
KAWAI
compute both permanent and transitory incomes using instrumental variables related to human and nonhuman wealth. The importance of hedonic prices and permanent/transitory incomes is emphasized elsewhere (Goodman and Kawai [7]) in the context of owneroccupied housing demand, and this study is its extension to rental housing. Since fundamental arguments are found in Goodman and Kawai [7], we summarize the basic points and discuss those issues not mentioned therein. A. Hedonic Prices
There are literally hundreds of variables that could be used in a hedonic price regression, and the list might vary from area to area.2 For reasons of comparability, we use the list developed by Follain and Malpezzi [4] in their Annual Housing Survey studies for 1974 and 1975. Their variables, with only a few exceptions, are used as they formulated them. Personal characteristics which might influence the rent of a unit are also included. Blacks or Spanish-surnamed people may be forced to pay higher prices if discrimination is a problem, for example. Also, the price variation arising from long-time-tenant discounts should be permitted in any estimation procedure; several studies have documented the finding that long-time tenants receive considerable discounts on their rents, compared to new tenants. (See, for example, Merrill [14], Downs [3], and Lowry [12].) Inclusion of tenant characteristics is usually thought to be inappropriate in the first stage of hedonic estimation. Here, however, we include these variables in the first-stage regression rather than as determinants of housing demand, in order to estimate discounts or premia charged to certain residents. This allows unbiased estimates of the housing structure and neighborhood hedonic prices, and permits computation of premia or discounts specific to the renter for a standardized bundle. It is not unlike including a distance term to account for a falling land price gradient within a metropolitan area, allowing a falling house price gradient in accordance with theory. We use the following specific functional form: s? - 1 L= A
vg + &Jmi m
+ &J&.i
+ y,
k
where S is the observed rent, t refers to tenant characteristics, c refers to 2Two basic methods have been used to derive unit pric& of housing, housing cost computation (e.g., Polinsky and Ellwood [16]) and hedonic price estimation (e.g., Kain and Quigley [lo] and Straszheim [19]). We employ the hedonic price estimation technique by allowing the equations to vary spatially.
RENTAL HOUSING DEMAND
79
housing unit and neighborhood characteristics, and h, v, and 6 are the coefficients to be estimated.3Although this Box-Cox flexible form has often been used for owner-occupied housing (see Goodman [6], Linneman [ll], and Halvorsen and Pollakowski [8]), only Linneman [ll] has applied it to rental housing prices. The “price” of a unit of rental housing, P, is determined by evaluating a “standardized unit” according to the area’s hedonic price regression. Within a metropolitan area this price can vary by location, time period, or certain tenant-specific characteristics, such as race or household crowding. The quantity of housing Q, then, is obtained by dividing the gross rent by P, i.e., Q = S/P. B. Permanent and Transitory Income
We postulate that both permanent and transitory components of actual income have substantially positive, separate effects on rental housing consumed. This implies not only that households look beyond the current period’s income in their rental-housing consumption decisions, but also that random variations in actual income have impacts on the quantity demanded. With perfect capital markets, consumers might borrow against future incomes in order to spread out housing consumption over their horizons in ways consistent with their permanent incomes. As a result random income should be expected to have little (life-cycle model) or no (permanent-income model) effects on the amount of the good purchased.4 However, in a more realistic world of imperfect capital markets, consumers cannot generally borrow against their anticipated life time earnings and, hence, the transitory component of actual income may be used to fulfill housing flow demand that could not otherwise be met from permanent income. Thus, the proper demand function should include permanent and transitory incomes separately (or at least permanent income) to estimate the permanent income elasticity consistently.5 Failure to do so can lead to 31t is well known that this form, developed by Box and Cox [2], reduces to linear form when X = 1 and to logarithmic form when A = 0. 4See Friedman [5], Reid [17] and Mayer [13] for summaries and discussionsof such models. Using savings survey data, Attfield [l] concludes that transitory income has a positively significant impact on consumption. He uses a slightly different definition of transitory income, however, than we do. ‘For owner-occupied housing, transitory income is more important because of the savings motivation of housing demand. That is, the purchase of a house, on the one hand, is an investment in a durable good from which the purchaser can enjoy a flow of services; on the other hand, it is an investment in a portfolio from which he can withdraw his equity at the time he sells the property. If transitory income in a given year is to be saved as a source of future consumption, one of many assetsinto which it might go is the buyer’s house. This will lead to a positive effect on stock demand with respect to transitory income. This suggeststhat differences in transitory income coeficients between owners and renters may give some indication as to the magnitude of this “savings-investment demand” for housing.
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GOODMAN AND KAWAI
estimation biases. Goodman and Kawai [7] prove that, if measured income (the sum of permanent and transitory incomes) is used as a proxy for permanent income, then the OLS estimate of the income coefficient underestimates the permanent income coefficient and overestimates the transitory income coefficients. Using the method developed by Goodman and Kawai [7], the following regression equation is estimated to construct the permanent and transitory components of measured income:
where ( Ei) represents education, Ai refers to age, Z$. indicate other human and nonhuman wealth variables for the iti individual. Age is entered quadratically to capture its expected nonlinear effect on permanent income. Education is entered either linearly or in a stepwise manner. In the linear case t#~ is a scalar term; in the stepwise case, where a series of dummy variables indicate educational levels, +i is a vector of coefficients.6 W; is the disturbance term uncorrelated with the explanatory variables so that the OLS procedure provides consistent and efficient estimates. Coefficient signs are expected to be
The predicted value of Y and the predicted value of y can be interpreted as the estimates for permanent and transitory incomes, respectively. C. Rental Housing Demand Function
The above arguments suggest that the rental housing demand regression should include as explanatory variables at least the computed hedonic prices (P) and the permanent (Y ‘) and transitory (Y r) components of measured income. To the extent that P is correlated with Y (= YP + Y r), the price variable should not be left out in consistently estimating the income elasticity.7 If permanent income is assumed to be uncorrelated with transitory income, omission of transitory income will not bias the permanent 6The education variable E, could be expanded to include quadratic and higher level polynomials, similarly to age. Preliminary work settled on the stepwise procedure as being preferable. ‘Possible estimation biases caused by the omission of P are discussedby Polinsky [15], who claims that since house price P systematically falls with distance from a central place and the more affluent (higher Y) are likely to move further out, the income elasticity is underestimated.
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RENTAL HOUSING DEMAND
income coefficient, but its inclusion in the regression equation should enhance the predictive power. The housing-demand equation (1) in its fullest form, therefore, should be specified as: Q,
=
(Y
+
j3pyp
+
PTqT
+
VP,
+
Csjzj;
+
Vi,
(4)
where (Y,fip, &, y, 6’s are the coefficients to be obtained, Zji are relevant explanatory variables other than income and price, and the i’s denote cross-sectional individual households.* III. ESTIMATION
RESULTS
A. Data The data are from the Annual Housing Survey SMSA sample for 1977. For 15 “small” SMSAs (metropolitan areas for which samples of 5000 dwelling units were drawn), a 30% sample of renters was extracted. For four “large” SMSAs (with samples of 15,000 dwelling units) a 10% sample of renters was drawn. Sample sizes vary from 347 observations in Albany and Detroit, to 652 observations in Washington, D.C.9 There is substantial variation for selected variables among areas. Apartment size varies from 3.64 rooms in Los Angeles to 4.66 rooms in Albany. Mean gross rent varies from $155 in Memphis to $273 in Anaheim, and mean income varies from $8770 in Spokane to $13,704 in Washington, D.C. Pittsburgh has the highest mean age (45.7 years per household head), while Salt Lake City (34.7 years) has the lowest. Most SMSAs provide a good city/suburbs mix, and most also provide a balanced racial makeup and good distribution of male and female household heads.” One serious shortcoming in the AHS data set in general is the paucity of geographic and neighborhood detail. The confidentiality requirements that enable the acquisition of such excellent income and other personal data lead to suppression of most of the geographic identifiers that make up neighborhood data. Researchersmay know if a housing unit is in the central city, for example, but it is impossible to determine the distance from the Central Business District, the racial nature of the neighborhood, or the quality of “One might argue that since (4) is the demand function there exists a simultaneity bias if the OLS is applied. Our procedure solves the possible simultaneity bias on two grounds. First, it is quite legitimate to regard (4) as a microeconomic demand function and hence to use the microeconomic data for estimation. Second,both our method of constructing the housing price index, and its use in the demand function have a two-stage least-squares interpretation. ‘The “small SMSAs” are Albany, Anaheim, Dallas, Fort Worth, Madison, Memphis, Minneapolis, Newark, Orlando, Phoenix, Pittsburgh, Salt Lake City, Spokane, Tacoma and Wichita. The “large SMSAs” are Boston, Detroit, Los Angeles and Washington, D.C. “A detailed area-by-area breakdown is available from the authors on request, as are regression results for each of the analyses reported.
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GOODMAN AND KAWAI
the public schools. The data set does include variables concerning residents’ attitudes on some neighborhood characteristics ranging from school quality to street noise. Follain and Malpezzi [4] test these variables as indicators of neighborhood quality and find them wanting. We use them for lack of suitable alternatives, but the results mirror theirs. B. Hedonic Price Estimation
Separate hedonic regressions are estimated for each of the 19 metropolitan areas. Particular attention is directed toward estimating the suitable functional form for a given area by using (2). Most published studies of rental hedonic price formulations have used log-linear forms; theory, such as Rosen [18], suggeststhat these may be overly restrictive. Tests for functional form show that reliance solely on linear or semilogarithmic forms may constitute a serious misspecification. As noted in Table 1, the best functional forms, with the exception of Los Angeles, have X greater than zero but less than 1. Significance tests reject the semilog form (X equal to 0) for all cities but Los Angeles. Unit housing price P is determined by evaluating the systematic part of (2) for a standardized unit. That is, P is the price of the standardized unit adjusted for length of tenancy, race, location in the SMSA and crowding of TABLE 1 Best Functional Forms for Hedonic Price Regressions City
x
x2
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington Wichita
0.6 0.2 0.6 0.6 0.1 0.7 0.0 0.4 0.7 0.8 0.8 0.7 0.4 0.4 0.4 0.5 0.9 0.6 0.2
0.6020 0.6396 0.5651 0.5878 0.6612 0.6593 0.5713 0.5060 0.7411 0.5194 0.5770 0.5993 0.6050 0.5235 0.4409 0.6145 0.4972 0.6499 0.6537
Note: 7i2 = the coefficient of multiple correlation adjusted for the degrees of freedom.
83
RENTAL HOUSING DEMAND TABLE 2 Mean Quantities and Prices by Metropolitan Area City
Quantity
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington, D.C. Wichita
0.963 (0.373) 1.187(0.403) 1.330 (0.583) 1.030(0.445) 1.006 (0.360) 1.149 (0.471) 0.953 (0.473) 1.035(0.351) 1.076(0.445) 0.966 (0.344) 0.912 (0.319) 0.825 (0.308) 1.102 (0.505) 1.037 (0.419) 1.138 (0.505) 1.095 (0.454) 1.099(0.370) 1.036(0.441) 1.095 (0.409)
Price
190.16(18.31) 233.28(19.96) 167.05(19.51) 191.17(21.10) 197.14(17.89) 156.58(17.12) 226.80(27.56) 195.60(11.59) 145.40(13.85) 210.29(15.17) 252.32(27.78) 233.41(38.61) 189.99(20.70) 170.34(22.52) 165.84 (5.78) 153.09(14.76) 169.10(11.36) 217.12(24.14) 167.20(12.20)
Note: Standard errors are reported in parentheses.
the unit. Housing quantity Q is computed by dividing gross rent by P. Table 2 details the mean quantities and the mean prices of “housing” by metropolitan area. The lowest mean quantity is 0.82 units in Orlando; the highest, 1.33 units in Boston. The lowest mean price is $145 in Memphis; the highest, $252 in Newark.
C. Permanent Income Estimation Permanent income is estimated for each of the 19 metropolitan areas. Measured income is regressed on employment status, age, race, Spanish surname, sex of head of household, marital status, education, household size, prior housing tenure, and prior house value if the house was owned. The first eight variables indicate human capital components of permanent income; the latter two indicate nonhuman capital components. In general, the regressions predict fairly well. In Table 3, using a linear form, x2 varies from 0.21 in Anaheim to 0.44 in Pittsburgh, and clusters between 0.30 and 0.40. Standard errors of the regression (SER) vary from $4901 in Spokane to $7901 in Anaheim, although these are not strictly comparable due to cost of living differentials.
84
GOODMAN AND KAWAI TABLE 3 Summary of Permanent Income Regressions City
R2
R2
SER
Albany Anaheim Boston Dallas Detroit Fort Worth Los Angeles Madison Memphis Minneapolis Newark Orlando Phoenix Pittsburgh Salt Lake City Spokane Tacoma Washington Wichita
0.3353 0.2309 0.4403 0.4080 0.4082 0.3516 0.3006 0.2462 0.3920 0.3514 0.4320 0.3378 0.3135 0.4585 0.2570 0.4072 0.3242 0.3636 0.3192
0.3195 0.2068 0.4265 0.3943 0.3923 0.3292 0.2847 0.2286 0.3748 0.3355 0.4180 0.3235 0.2879 0.4388 0.2328 0.3861 0.3036 0.3506 0.2989
6017 7901 7098 6381 7030 6698 7300 6905 6352 6695 6713 6444 7636 5091 6997 4901 6225 7489 6180
Note: R* = the coefficient of multiple correlation. R2 = the coefficient of multiple correlation adjusted for the de grees of freedom. SER = the standard error of regression.
D. Rental Housing Demand We now consider the estimation results for rental housing demand using both computed hedonic prices and measured or permanent/transitory income. Housing demand was initially estimated for each SMSA. However, due to insufficient geographic variations within an SMSA, price elasticities were generally disappointing. In order to generate enough price variation within the data set, the 19 metropolitan areas are pooled. We report here only the’pooled regression results. To control the interarea price differentials, the Bureau of Labor Statistics family budget is used with its component housing portions deleted. Income and housing price variables are deflated by these nonhousing CPIs. Since the BLS budget is not computed for every city in the sample, several substitutions are made.” In preliminary work, estimated income elasticities were not sensitive to the inclusion or exclusion of the overall price level, so the substitutions do not appear to be serious. Fort Albany: Buffalo (substituted) “The following substitutions have been made: Anaheim: Los AngelesMemphis: Nashville (substituted) Worth: Dallas (substituted) Madison: Milwaukee Tacoma, Spokane: Seattle (substituted) Long Beach (substituted) Salt Lake City, Phoenix: Denver (substituted). (substituted)
85
RENTAL HOUSING DEMAND TABLE 4 Demand Regressions: Pooled Sample Recent movers
All renters Measured Y YP YT P
PER RACE SEX CONST E2 SER 9V 1,
Permanent
- ___-
-
0.00228 (42.21) -
0.00379 (36.17) 0.00174 (28.10) - 0.2535 (21.65) 0.0463 (15.60) -0.1176 (10.34) -0.1378 (13.66) 1.1255 0.2648 0.3809 0.393 - 0.458
- 0.2185 (18.67) 0.0538 (18.03) - 0.1502 (13.21) - 0.0631 (6.80) 1.1655 0.2415 0.3869 0.238 - 0.395
Measured 0.00245 (27.03)
- 0.2625 (13.06) 0.0750 (14.36) -0.1599 (7.50) - 0.0909 (5.71) 1.2744 0.2904 0.3757 0.241 - 0.474
0.00381 (22.04) 0.00195 (18.65) - 0.3001 (14.83) 0.0681 (13.08) - 0.1293 (6.07) - 0.1559 (9.05) 1.2533 0.3103 0.3704 0.381 - 0.542
-
Note: (1) r statistics are shown in parentheses. (2) Y, Yp, Y’, and P are all measured relative to the price level for other goods and services.
Table 4 reports the pooled regression results for housing demand estimation using measured or permanent/transitory income, for both all renters (8608 observations) and recent movers (2845 observations). The regressions are estimated with the income and price terms, household size (PER), race (RACE), and sex of household head (SEX). In the all renter sample, measured income elasticity is 0.238; price elasticity is -0.395. Inclusion of permanent and transitory income not only enhances the predictive power (from 0.2415 to 0.2648 for Iii* and from 0.3869 to 0.3809 for SER) but also raises the income and price elasticities to 0.393 and - 0.458, respectively. It might be suggested that recent movers are closer to equilibrium than long-term tenants, because of moving and other transactions costs. Estimating these regressions for renters who have moved in the past year shows measured (0.241) and permanent (0.381) income elasticities that are quite similar to those estimated for the entire sample. However, estimated price elasticity increases (in absolute value), from - 0.458 to -0.542 in the permanent income regressions, and from -0.395 to -0.474 in the measured income regressions.‘* 12We are currently examining the nature of the differential price elasticities in separate research.
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GOODMAN AND KAWAI
The transitory income coefficients are significant and substantial in both all-renters and recent-movers regressions. For all renters the propensity to spend out of transitory income is approximately 46% of the propensity to spend out of permanent income. For recent movers, this percentage rises to 51%. Since permanent and transitory incomes are orthogonal, omission of transitory income does not bias the estimated permanent income elasticity but, taking the all-renters permanent income regression as an example, R* falls from 0.2648 to 0.1974. The other coefficients behave about as expected. Increased household size leads to higher demand, and black and/or female-headed households purchase less. These coefficients should be interpreted carefully since they represent the second stage of the estimating process. In the sample, on average, male-headed households earn about $2160 more permanent income than do female-headed households. As a result, for a given measured income, the household purchases 21.6 X (fiP - &.) more housing (where 21.6 is the incremental income divided by the average price deflator of 100). Male-headed households, then, purchase 0.094 fewer units (rather than 0.138 fewer units, calculated from the second stage alone) than do femaleheaded households, holding household size constant. This is a difference of about 9%. Similar adjustments are also necessary for race and household size variables.13 IV. HOUSING AND WELFARE EFFECTS OF SUBSIDY During the 1970’s the federal government contracted for two major experiments on market outcomes of housing subsidy and grant programs. One aim of both the Housing Assistance Supply and Demand Experiments (HASE and HADE) was to demonstrate the impacts of cash grant programs on housing demand. These impacts were generally measured either as income elasticities, or as changes in rent burdens (rent as a fraction of income). Most of the estimated permanent income elasticities were in the 0.25 to 0.40 range, and there was some question about whether the limited experiment durations and/or the cash grant methods led to downward biases in the estimates.14 This section discusses a conceptual experiment with a cash assistance program, derived from the regressions displayed in Table 4. It considers a household of three with measured income of $6000 per year, paying the mean price for rental housing. In this experiment, the household is given an unrestricted cash grant of ten percent of income, i.e., $600 per year. This 13Raceis always included in the permanent income regression; household size is included if it improves the standard error of the regression. 14Hanushek and Quigley [9] present an excellent summary and evaluation of the experimental findings.
87
RENTAL HOUSING DEMAND TABLE 5 Housing/Welfare Effects of Income and Rent Subsidies Housing effects Income subsidy
All Renters Recent Movers
Q
P
T
A4
Price subsidy
0.9825
+ 2.29% + 2.22%
+ 1.05% + 1.14%
+ 1.35% + 1.43%
+ 13.0% + 14.2%
1.0321
Welfare effects Income subsidy
AI1 Renters Recent Movers
W
P
T
0.378 0.410
- 7.01% - 7.10%
- 8.14% - 8.05%
M
- 7.86% - 1.19%
Price subsidy - 16.7% - 13.7%
analysis considers the impacts of this grant, depending on whether the household considers it as permanent, transitory or simply measured income. As noted in Table 5, measured income of $6000 leads to 0.9825 units purchased, in the all-renters regression, and to 1.0325 units (approximately 5% more) in the recent-movers regression. The rent burden W is 0.378 in the all-renters regression, and 0.410 in the recent-movers regression. (Estimates of W at the individual SMSA level vary from 0.267 in Memphis to 0.452 in Newark, using the all-renters regressions.) Housing and welfare effects are directly related. Defining housing quantity Q as a function of price P and income Y, the rent burden, W, is W = P - Q( P, Y)/Y.
(5)
Differentiating with respect to Y, for given housing price, we obtain
where 9, refers to the income elasticity of the rent burden, and q, to the income elasticity of housing demand. Thus, income-elastic behavior in housing demand leads to an increasing rent burden, and a trade-off exists between housing and welfare effects. This can be seen in Table 5. Numbers below P, T, and M indicate percentage changes (in housing demand Q or the rent/income burden ratio W) when the household regards the income increment as permanent, transitory or measured, respectively. For the all-renters regression, for example, if renters view the 10% increase as permanent, it results in a 2.29%
88
GOODMAN AND KAWAI
increase in Q; if, on the other hand, they view it as only transitory, the resulting increase is only 1.05%. The measured income increase of 1.35% might reflect a program of limited duration. The welfare effect is interpreted similarly. The fall in rent burden is 7.01, 8.14, or 7.86%, depending on whether the perceived income increase is permanent, transitory, or measured. Given the relatively small housing effects of an income subsidy, it is interesting to compare them to the effect of a price subsidy of comparable cost. Using both the all-renters and recent-movers results from Table 4, Table 5 also shows the increase in housing quantity and the decline in the rent/income ratio, if the $600 in aid is used as a rent subsidy rather than as an income transfer. These effects are calculated by dividing the $50 per month by the number of units of housing being purchased, Q. This represents a subsidy of 26.4% for all renters (24.4% for movers only), and results in a 13.0% increase in housing for all renters (14.2% for movers). The relative cost of achieving the same effect through a price subsidy as the permanent income housing effect can also be computed. For example, the 2.29% increase in housing quantity brought about by a $600 income transfer could be achieved at 17.9% of this cost (approximately $90) through a price subsidy. If policymakers are intent on increasing rental housing consumption, price subsidies are a much less expensive instrument, even though they may distort the price of housing relative to other goods. The linkage between price elasticity and welfare effects can be captured by looking at how W is affected. From (5), it can be shown that the two are directly related, that is, 9 wp= 1 -(-v&J The table indicates that the welfare effect of a price subsidy is much greater than that of an income subsidy; the price subsidy reduces the rent/income burden ratio by 16.7% for all renters and 13.7% for recent movers. Since the price elasticity for the recent-movers equation is higher (in absolute value) than that for the all-renters equation, the smaller welfare effects follow. V. CONCLUSION This paper has applied a method of housing demand estimation, originally developed by Goodman and Kawai [7] for owner-occupied housing, to rental housing markets for 1977. Hedonic rental functions are generally nonlinear. The linear hypothesis is rejected in 17 of 19 submarkets; the semilog caseis rejected in 18 of 19 cases.This suggeststhat future work with rental hedonic functions should examine the underlying assumptions concerning functional form. In particular, marginal valuations of specific housing attributes may be quite sensitive to the form used.
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The permanent income model as a function of human and nonhuman capital also performs well across metropolitan areas. Most variables have their expected signs with plausible magnitudes. The primary finding is that permanent income derived through instrumental variables methods provides better prediction (in terms of SER and R2) as well as substantially higher income elasticities. Measured income elasticities are generally clustered between +0.2 and +0.3, and permanent income elasticities are clustered between + 0.4 and + 0.5. Transitory income, which is quite plausibly related to housing purchase because of capital market imperfections, also has considerable impact. The transitory income coefficient is generally half the size of the permanent income coefficient. These coefficients provide upper and lower bounds for measuring the impacts of cash transfers to households. Price elasticities vary from approximately -0.46 to -0.54 for a pooled sample. These also fall within the range of conventional estimates. As anticipated recent movers indicate a higher price elasticity by 20% than all renters; income elasticities are similar for the two groups of renters. The last section of the paper examines a conceptual experiment similar to HADE and HASE, where households are “given” income transfers, which are not necessarily tied to housing purchases. In general, the elasticities in this experiment are about the same as the HADE and HASE numbers, and considerably lower than the elasticities calculated at the means of quantity and income. This suggests that the HADE and HASE definitions of permanent income performed similarly to the ones that we postulate. It also suggests that income elasticities calculated with a low income population and linear demand functions should probably be routinely adjusted upward for attribution to the more general population. Our result provides verification that the demand response to income transfers is likely to be fairly small, that is, a small “housing” effect and a correspondingly large “welfare” effect. A price subsidy of comparable cost turns out to achieve a considerably greater housing effect with a simultaneous, substantial reduction in the rent/income ratio. If policymakers desire larger housing effects, specific housing price subsidies to renters or landlords should be seriously considered. REFERENCES 1. C. L. F. Attfield, Testing the assumptions of the permanent-income model, J. Amer. Sfatist. Assoc., 75, 32-38 (1980). 2. G. E. P. Box and D. R. Cox, An analysis of transformations, J. Roy. Statist. Sot., B26, 211-243 (1964). 3. A. Downs, Some aspects of the future of rental housing, in “Rental Housing: Is There a Crisis?” (John C. Weicher, et al., Eds.) Urban Institute Press,Washington, D.C. (1981). 4. James R. Follain and Stephen Malpezzi, “ Dissecting Housing Value and Rent Estimates of Hedonic Indexes for Thirty-nine Large SMSAs,” The Urban Institute, Washington, DC. (1980).
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5. M. Friedman, “A Theory of the Consumption Function,” Princeton Univ. Press,Princeton, N.J. (1957). 6. A. C. Goodman, Hedonic prices, price indices and housing markets, J. [/rhun Econ.. 5. 471-484 (1978). 7. A. C. Goodman and M. Kawai, Permanent income, hedonic prices and demand for housing: New evidence, J. Urbun &on., 12, 214-237 (1982). 8. R. HaIvorsen and H. 0. Pollakowski, Choice of functional form for hedonic price equations, J. Urban Econ., 10, 37-49 (1981). 9. E. A. Hanushek and J. M. Quigley, Complex public subsidies and complex household behavior: Consumption aspects of housing allowances, in “Do Housing Allowances Work?’ (K. L. Bradbury and A. Downs, Eds.), Brookings Institution, Washington, D.C. (1981). 10. J. F. Kain and J. M. Quigley, “Housing Markets and Racial Discrimination,” Columbia Univ. Press,New York (1975). 11. P. Linneman, Some empirical results on the nature of the hedonic price function for the urban housing market, J. Urban Con., 8, 47-68 (1980). 12. I. S. Lowry, Rental Housing in the 1970s: Searching for the crisis, in “Rental Housing: Is There a Crisis?” (John C. Weicher, et al. Eds.), Urban Institute Press, Washington, D.C. (1981). 13. T. Mayer, “Permanent Income, Wealth and Consumption: A Critique of the Permanent Income Theory, the Life-Cycle Hypothesis and Related Theories,” Univ. of California Press, Berkeley, Cal. (1972). 14. S. Merrill, “Draft Report on Hedonic Indices as a Measure of Housing Quality,” Abt Associates, Cambridge, Mass. (1977). 15. A. M. Polinsky, The demand for housing: A study in specification and grouping, Econometrica, 45, 447-461 (1977). 16. A. M. Polinsky and D. T. Ellwood, An empirical reconciliation of micro and grouped estimates of the demand for housing, Reu. Econ. Statist., 61, 199-205 (1979). 17. M. G. Reid, “Housing and Income,” Univ. of Chicago Press, Chicago (1962). 18. S. Rosen, Hedonic prices and implicit markets: Product differentiation in pure competition, J. Pol. Econ., 82, 34-55 (1974). 19. M. Straszheim, “An Econometric Analysis of the Urban Housing Market,” Columbia Univ. Press, New York (1975).