Filtering and housing markets: An empirical analysis

JOURNAL

OF URBAN

Filtering

ECONOMICS

=,21-40

and Housing JOHNC.WEICHER*

(1988)

Markets:

An Empirical

Analysis’

AND THOMASG.THIBODEAU~

‘F. K. Weyerhaeuser Scholar in Public Policy Research, American Enterprise Institute for Public Policy Research, Washington, D.C. 20036, and fAssistant Professor of Real Estate and Regional Science, Southern Methodist University, Dallas, Texas 75275 Received July 2,198s; revised December 16,1985

INTRODUCTION This paper investigates empirically whether filtering occurs in housing markets. We first review briefly the history of the concept, concluding that the most controversial and most policy-relevant question about filtering is whether price declines for a given quality of housing provided by the existing stock when demand for that quality declines, particularly in response to new construction. We then test for this phenomenon by looking at the change in occupancy of low-quality housing in response to private housing construction. We employ an unusual econometric technique, because we are interested in the relationship between two endogenous variables in our model- the quantities of private new construction and substandard housing-and we lack the information necessary to estimate the full model. Our analysis also provides insight into the factors which affect the incidence of low-quality housing, in particular the effect of various government housing subsidy programs. This is the first systematic empirical study of filtering. The Concept of Filtering Analysts have offered many definitions of filtering. A general description illustrates why such diversity exists and serves as a convenient basis for cataloging the literature. Filtering begins when some exogenous factor, such as an increase in income or a reduction in construction costs, generates construction of new housing.* Families moving into the new units leave their former housing vacant. This lowers the demand for the housing that they occupied formerly, ‘The authors thank Thomas Muench for his comments on an earlier draft. The usual disclaimer applies. 2This description assumes that there is no increase in the number of households within the metropolitan area. The new construction occurs solely to enable current residents to live in different, presumably better, housing. Empirically, we treat new construction to satisfy the demand of additional household formation as having no effect on the incidence of low-quality housing. A model with different implications is Sweeney [24]. 21 0094-1190/88 $3.00 Copyright 0 1988 by Academic Press. Ix All rights of reproduction in any form reserved

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reducing its price and permitting families with somewhat lower incomes to buy or rent it. In turn, these families vacate housing of somewhat lower quality. At the bottom of the quality distribution, some households move out of the worst housing, which then drops out of the stock. Various analysts have focused on different aspects of this process. Ratcliff’s [21] original description and subsequent empirical studies of “chains of moves” such as that of Lansing et al. [12] have examined the extent to which households have moved into better housing. Second, individual housing units deteriorate over time. Vintage models of the housing stock, such as that of Muth [16], incorporate this fact as an assumption and trace out its implications. Third, housing units become relatively less desirable as they age. Thus a given unit is likely to be occupied by successivelylower income households over time, This has particular relevance to the study of urban neighborhood dynamics, including racial succession (for example, Leven et al. [13]; Brueckner [4]; Vandell [28]).3 Fourth, prices of existing units may decline, holding quality constant. This is the sensein which we use the term filtering. We believe it is the most important sense of the term for formulating housing policy. If the price of standard quality housing falls when new homes are built, then low-income households benefit from subsidies directed at the well to do; but if not, then the poor benefit only from subsidies targeted to them. Literature Review There has been controversy as to whether filtering can ever occur in the long run. (There is agreement that filtering is possible in the short run.) In a widely cited paper, Lowry [14] argued that the price for a given quality could not fall, because landlords would reduce their maintenance expenditures until the return on their investment was restored to its initial, market-determined level. The same conclusion was reached by Olsen [19], who argued that the “price per unit of housing services” provided by any dwelling would be driven to the minimum long-run average cost of production in a perfectly competitive market, and that this price would be constant over all quality levels. More recently, several formal housing market models have been developed in which filtering is possible. The first and most important of these models was constructed by Sweeney [24, 251; others are from Ohls [18], Braid [2, 31, and Schall [22]. They can be classified as either short-run or long-run models, depending on whether new construction is exogenous. 3Elxtemalities are also likely to be an important phenomenon in these neighborhood changes, in addition to the homogeneity of the housing stock. Since our focus is on individual housing units, we ignore externalities.

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Sweeney’s [24] and Braid’s [2] are short-run models; the other models, including Sweeney [25] and Braid [3], are concerned with the long run. These differ in methodology and in the details of their conclusions, but for our purposes they have certain similarities which are much more fundamental than their differences. In most of them, construction of high-quality housing increases the welfare of low-income households and reduces both the price and the quantity of low-quality housing.4 In the long-run models of Sweeney [25] and Braid [3], these implications are deduced rigorously only for specific construction subsidy programs, not for a general reduction in construction costs. Sweeney considers it likely that the same qualitative conclusions would hold.5 Braid does not discuss the situation. Most of these models have been used to analyze the impact of housing subsidies on low-income households. We also investigate two programs: (1) public housing, built for the poor and made available at below-market rents, and (2) mortgage subsidies for moderate-income households.6 The models have diverse conclusions about the effects of public housing. Olsen argues that benefits accrue only to the households that live in it; all other low-income households have the same incomes and face the same price for housing as they did initially. Ultimately, as many units are withdrawn from the private housing stock as there are households occupying public housing. Sweeney[24, pp. 312-3131, however, concludes that all low-income households benefit from public housing, because the rent for private low-quality units declines; the number of households occupying the lowest quality of housing also declines. Schall’s model appears to have the same implications, although he mentions public housing only briefly. But Ohls simulates public housing and finds that quality declines on balance for unassisted low-income households.7

41t should be made clear that the relationship between new construction and prices for the existing stock of housing is not the only, or in some caseseven the central, issue addressed in this literature. “‘A subsidy that is independent of new construction quality can be expected also to decrease all prices. However, this result has not been rigorously demonstrated for the lower quality levels” (Sweeney [24, p. 3101).The next paragraph indicates that this applies to “any influence which changes new construction costs.” ‘The theoretical literature has also extensively studied housing allowances, which provide cash or vouchers to low-income households to help them rent private housing. We are unable to study these programs empirically. The Section 8 Existing Housing program, the first close approximation to a housing allowance to be enacted, became operational just at the end of our survey period. For the same reason, we omit Section 8 New Construction. ‘Ohls does not attempt to explain this result, but it may occur because public housing construction reduces unassisted private construction, leading in the long run to a smaller, lower-quality private stock.

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Few analysts have attempted to model actual moderate-income subsidy programs, but several have analyzed similar programs, and it is possible to infer the impacts in some cases. Sweeney comes closest to analyzing an actual program; he concludes that the lowest-income households are harmed by moderate-income subsidies, paying higher rents and living in lower-quality housing then they would otherwise.8 Schall, by contrast, finds that the number of low-quality units should be reduced to a lesser extent than by public housing, but by more than the construction of high-quality units.9 In Olsen’s model, only the subsidized households benefit; the poor do not. These studies have been purely theoretical. There has been virtually no systematic empirical investigation of filtering. More than 20 years ago, Grigsby [7, Chap. 41 found an inverse relationship between changes in rents and values for existing units and the volume of new construction, but he used only a simple correlation analysis with a small sample of SMSAs. The computer simulation models of Ohls and the Urban Institute [6] conclude that filtering occurs. Most recent econometric studies of low-quality housing, such as those of Davis et al. [5] and Hirsch and Law [lo], omit private construction entirely. Only Vitaliano [29] includes it, finding no relationship to the incidence of low-quality housing 5 to 15 years later. There is more evidence, though hardly conclusive, on the effect of subsidized housing on quality in the private stock. Both Davis et al. and Hirsch and Law find that new low-rent units, a proxy for subsidized production, are unrelated to the change in the incidence of low-quality housing, defined consistently over time. Vitaliano uses actual public housing construction, finding that it increases substandard housing, an implausible result at variance with all the theoretical models. The Model The model contains three interrelated housing markets, or submarkets: new housing, existing standard quality units, and existing substandard units. Quality is assumed to be uniform within each market, highest in the ‘Sweeney studied a subsidy program in which households in about the second quarter of the income distribution received subsidies to live in units above the minimum quality for new construction. He concluded that the lowest-income households live in lower-quality housing than they would otherwise. Moderate-income subsidy programs were targeted for these households, but units generally were of lower quality than those being built privately at the same time. Sweeney’s analysis thus is not exactly relevant to actual moderate-income programs, but it is close. ‘This result must be qualified. The effects depend on the relative supply and demand elasticities as well as the quality level of the new construction; if, for example, supply is less elastic in the quality range represented by moderate-income subsidy programs, then less filtering could occur. This is apart from the subsidy to the occupying households. Schall analyzes not the effects of subsidies to low-income households, but only those of subsidies to build additional housing.

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new construction market, and lowest in the substandard market.” Each market is characterized by aggregate demand and supply functions for the number of private dwelling units as a share of the total housing stock. Three quality levels are far fewer than those used by theoretical models, but are enough to capture the central implications of filtering and permit empirical testing. Aggregate housing demand in each market is a function of the price in that market and in the adjacent quality market. In the existing standard quality market, demand therefore is a function of all three prices. Demand is also a function of consumers’ permanent incomes and tastes, both exogenous, and the availability of substitutes for private housing at that quality level. The supply functions express price as a function of the number of units in each market. In the new construction market, supply also depends on the cost of producing new units; in the existing standard quality housing market, it depends on the cost of operating a unit at that quality level; in the substandard market, it depends on the number of substandard units at the beginning of the period, the cost of continuing to provide housing at all, and the returns from employing the land or structure in some alternative use. Formally, the model can be written as follows: Market for new units: QN = a, + b,,P,

+ b,,PG + clS, + d,D, + e,

P, = a2 + bzlQN + czX, + e2.

(1) (2)

lo We assume that new housing is categorically better than either existing standard housing or substandard housing. The latter is clear from published data. Less than one-half of 1% of new units built during the 1960sin metropolitan areas were classified as either dilapidated or lacking complete plumbing in the 1970 Components of Inventory Change; no new homes built during the early 1970s were substandard on the basis of definitions developed by the Department of Housing and Urban Development or the Congressional Budget Office (Weicher [30]). For new and existing housing, comparison is more complicated; we choose rents and values as the simplest measure. As of 1970, median rents for new units were 45% higher than those for existing units, and the median new house price was 33% higher than was the median existing house price. During the mid-1970s, median rents and values were, on average, more than one-third higher. There is some overlap between the value and rent distributions for new and existing housing. About 24% of new homes built during the 1960s had values below the median existing home in 1970; about 14% of new rental units had rents below the median existing rent. For the mid-1970s, about 22% of homes built since 1970 had values below the typical existing home (Weicher and Hartzell [31]); about 20% of new rental units had rents below those for decent existing units, as calculated by Ozanne and Thibodeau [20]. In four metropolitan areas-Miami, Orlando, Honolulu, and Springfield (MA)-new homes or apartments were smaller than the typical existing unit, producing a much greater overlap. We believe that the distributions are sufficiently distinct to justify our assumption.

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Market for existing standard quality housing: QG = a3 + b,,P,

+ b34PG + b,,P, + ~$3 + d,D, +

PC = a4 + bd3QG + c4X4 + e4.

e3

(3) (4)

Market for existing substandard housing: QB = a, + b,,P, + bsaP, + c,S, + dsDs + e5

(5)

P, = a6 + bh5QB + csXs + e6-

(6)

In this notation, Q symbolizes the number of housing units as a share of all units within a metropolitan area, P the price of a unit, and the subscripts N, G, and B the three markets (new, good, and bad, respectively). The vectors of income and taste variables affecting demand are symbolized by D, the substitute sources of housing by S, and the vectors of factors affecting supply by X. The possibility of filtering in this model depends on the magnitudes of two parameters: b,, and b43, the coefficients of the quantity variables in the supply functions for new construction and existing standard housing. If the latter is zero, then filtering cannot occur. If only the former is zero, then a factor which shifts demand from the existing standard quality market to the new construction market, such as a rise in income, may reduce substandard housing. Hence the key independent variables are those specific to the first three equations of the model. Either coefficient may be different in the long run than in the short run; we investigate this possibility. We utilize this model to study one aspect of filtering: whether private high-quality housing production reduces the incidence of substandard housing. Our focus thus is different from that of the theoretical models, which have been used primarily to investigate changes in the prices of various qualities of housing, including substandard housing. In making new construction endogenous to our model, we increase its complexity substantially. If new construction is exogenous, then it becomes simply an argument in the demand function for existing standard housing; the model has only two markets and can be reduced to two equations. Treating new construction as endogenous is consistent with the long-run dynamic housing market models of Sweeney[25] and Braid [3], in contrast to their short-run comparative static models; Schall [22] also treats new construction as exogenous. Our model is closest conceptually to Sweeney’s[25] long-run model, but is sufficiently general to test for the existence of filtering, and to distinguish between the class of theoretical models in which filtering occurs and the earlier analyses by Lowry and Olsen which concluded that it is impossible.

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Econometric Technique

The matrix representation of our model is B*Y+G*X+E=O,

(7)

where Y is a 6 * T matrix of observations on endogenous variables, T is the sample size, B is a 6*6 matrix of endogenous variable coefficients, X is a K * T matrix of observations on exogenous variables, G is a 6 * K matrix of exogenous variable coefficients, and E is a 6 * T matrix of residuals. We assume that b{ E } = 0 and c?{E * E’} = s * I, where I is the identity matrix. To test for filtering, we examine the relationship between substandard housing and both private and public new construction. This relationship is embedded in our structural model. We can observe the impact of a change in private new construction on substandard housing by estimating the parameters of the model and then tracing changes occurring through cross-price and supply elasticities from the new construction market to the substandard housing market. However, we lack information on market prices and must purge them from the equation that we eventually estimate. A full reduced-form equation will not suffice because one component of new construction-private construction-is endogenous. We therefore estimate a transformed model that expressesthe incidence of substandard housing as a function of the rate of private construction, exogenously subsidized housing, and remaining exogenous variables. We transform our model by premultiplying (7) by a matrix, A, such that A * B is a matrix having unity along the diagonal, a nonzero value in the fifth row and first column, and zeros elsewhere. Hence our transformed model is A*B*Y+A*G*X+A*E=O.

(8)

This model produces reduced forms for (l)-(4) and (6) and a semireduced form expression for (5). The A matrix with the desired properties was obtained by inverting B using Gaussian elimination on all elements of B except the one in position ($1). The fifth row of (8) is

QB= 0 * QN+ 5 T;X,+ u,

(9)

i=l

where @= -b54b43b32b21/[(b36b65b54b43 - (b,b6~- l)(bA, that

- 111.Note

0 < 0 if b,,b,,b,,b,, > (b,,b,, - l)( b,,b,, - 1) and 0 = 0 if b,,b,,b,,b,, = 0. This means that 0 = 0 if either of the two key filtering

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parameters-b,, or b,,--is zero; but it will also be zero if either of two cross-elasticities of demand is zero. Thus our empirical work tests simultaneously for the existence of filtering and for the responsivenessof demand for a given quality to the price of the next higher quality. A statistically significant coefficient for 0 is necessary to support the filtering hypothesis but an insignificant coefficient is not sufficient to refute it. The relationship between the reduced-form parameters and their semireduced-form counterparts can be established on a case by case basis. For example, it can be shown that the coefficient of public housing in the semireduced-form equation has the same sign as that in the structural equation, but that the sign in the reduced form is indeterminate. However, the semireduced-form coefficient equals the coefficient in the reduced form only if one of the own-price supply elasticities or cross-price demand elasticities is zero. Variables and Data

Two data sets are used to test the model. The first is taken primarily from the 1960 and 1970 decennial Censuses, and comprises 59 large standard metropolitan statistical areas (SMSAs). The decade of the 1960sis the most recent period of more than a few years for which there is a consistent measure of substandard housing, namely the traditional definition of “dilapidated and/or lacking complete plumbing.” This information was reported in the decennial Censusesfrom 1940 to 1970; after 1970, the Census Bureau stopped enumerating dilapidated units. The rate of new private housing construction is expressed as the difference between the rates of new construction and net household formation during the decade. New units that meet the demands of new households only are not likely to generate filtering. Other housing production variables enter the demand functions as substitutes for privately produced housing. New housing demand is expected to depend positively on the availability of recently built units. This variable also measures the extent of disequilibrium in the new housing market, prior to the period of analysis. Alternatives to existing standard-quality housing are units built for middle- or moderate-income households that receive mortgage interest subsidies from the federal government under Section 221 BMIR (below-market interest rate) program. The alternative for substandard housing is public housing. The subsidized production variables are expressed as percentages of the change in the housing stock. Factors affecting the supply of new units include the costs of and restraints on production. Two cost components are measured directly: construction (the change in the Boeckh index for brick single-family homes from 1961 to 1971) and land (the change in the price per acre of agricultural land within the SMSA from 1959 to 1969, reported by the U.S. Department

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of Agriculture). We also include the extent of local governmental fragmentation in the market area, in the expectation that efforts to restrict the availability of land for new housing through “exclusionary zoning” and similar devices are more likely the greater the territorial extent of a jurisdiction (see Hamilton [9]). This is measured as the ratio of governments to population, according to the 1962 Census of Governments. The same income and demographic variables appear in all three demand functions: changes in median family income, the proportion of households with an elderly head, the proportion that are married couples, and the proportion that are black or Hispanic. The demographic variables measure differences in tastes; the minority variable may also reflect the effects of discrimination. The supply of substandard housing is assumed to be affected by the incidence of old housing at the beginning of the decade, in the expectation that such housing is the main source of low-quality units. The supply also depends on the opportunity cost of using the land for nonresidential use, measured by the growth in manufacturing employment in the central city. Our second data source is the Annual Housing Survey (AHS). It contains information for either 5000 or 15,000 households in the same 59 SMSAs, surveyed over a 3-year cycle. We use the first cycle, from 1974 to 1976. The AHS is the only source for quality data since 1970. It reports 30 separate deficiencies, many more than in the decennial Census. It has been used, primarily by government agencies, to construct several measures of low-quality housing. We use one developed at the U.S. Department of Housing and Urban Development (HUD) [27]; it has been used in other research (for example, Weicher et al. [32]). This measure is described in the Appendix. Because this measure is available only for the survey year, we analyze the intermetropolitan differences in the incidence of inadequate housing as of the mid-1970s. To allow for differences at the beginning of the survey period, we include the incidence of substandard housing in 1970, according to the Census definition, as an independent variable. There are a few other differences. Two new middle-income subsidy programs were enacted in 1968: Section 235 for home buyers and Section 236 for renters. They replaced Section 221 BMIR. The cost of providing existing standard quality housing is measured by an index of operating costs for a rental apartment, combining janitors’ wages,accountants’ salaries, and utilities. Another factor affecting demand is the cost of other goods and services, measured by the nonhousing component of the Bureau of Labor Statistics’ intermediate budget for a family of four. Its effect is ambiguous: A change produces both income and substitution effects, with opposite signs. We include median household income in the SMSA in the survey year to measure permanent income. The annual rate of change measures cross-

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sectional differences between permanent and current income. Otherwise, most of the variables are the same.” Because the AHS surveyed SMSAs in different years, all income and cost variables have been adjusted to 1975, and housing construction variables are expressed as annual rates for the period from 1970 to the survey year. For both periods, we experimented with two sources of data on subsidized production. One is the AHS, which relies on the tenant; the other is HUD program data. The AHS asks whether people live in public housing or whether their rent is subsidized, and also when the structure was built. National AHS estimates of total subsidized units nearly equal HUD program records, but the AHS overstates the number of public housing units and understates the number of moderate-income programs. HUD reports the year built only for public housing, but most of the other programs were short-lived and their lives correspond to our survey periods. Most Section 221 BMIR units were built during the 196Os,and nearly all Section 236 units were built between 1970 and 1974. However, the HUD data do not identify units subsidized under the Section 221 Rent Supplement program, which served very-low-income households during the 1960s. It was a small program nationally, with 28,000 completed units by the end of 1969 (Aaron [l, Table D-91). This is about 5% of the total number of subsidized units over the decade. Our reported empirical work uses the AHS data, along with HUD data on the Section 235 homeownership program, which is not available in the AHS. We prefer the AHS regressions partly because of the problem with the Rent Supplement program, and partly on the basis of the identification test statistic first introduced by Koopmans and Hood [ll] and Haavelmo [8]. The test, as we implement it, estimates (9) using 2SLS with Qa as the dependent variable and then reestimates the equation using QN as the dependent variable. We then examine the percentage change in the estimated coefficient for the new construction variable between these two specifications. The changes are very close for the 196Os, and the AHS regressions consistently show a smaller change for the 1970s. Empirical Results Our estimating procedure is two-stage least squares. In the first stage, we regress the rate of new private housing construction on dummies for region and (for the AHS data) survey year, government production, the disequi“Our empirical work initially included both the current proportions of various household types and their growth rata during the 1970s to control for lags in the housing consumption adjustment to demographic changes. However, the growth rates consistently were insignificant and were excluded from the final regressions.

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librium variable, and the growth rate for households with children.12 The regional and survey year dummy variables are consistently the most significant. Our second-stage results for the 1960s are shown in the first regression in Table 1. The most important result is the significance and magnitude of the new construction variable. The theoretical maximum effect of new construction is elimination of one substandard unit for each new unit, implying a coefficient of unity. The estimated coefficient of - 1.41 is larger than, but is not statistically different from, unity. The coefficient of the disequilibrium variable is also significant but much smaller. It implies that the filtering process continues to generate improved housing for more than a decade,but that most of the short-run effect-more than 80%-is dissipated in the course of 10 to 20 years. The other variables from the new construction demand and supply functions are not significant. The zoning variable is the only one with a coefficient larger than its standard error; it has the expected negative sign. The two subsidized production variables are also insignificant. There is no quality improvement for the poor as a result of either public housing or subsidies for moderate-income households. We experimented further with the subsidy variables. First we disaggregated by 5-year periods within the decade to see whether either program had a measurable short-run effect, but neither did. Then we added subsidized production for earlier periods, but these variables were almost always insignificant and the survey-period coefficients for subsidized production were unaffected. One demographic variable is conventionally significant, and one is significant at the 10% level, with the expected signs: An increase in married couples leads to a greater reduction in substandard housing, and an increase in minorities leads to a smaller reduction. Unexpectedly, a change in income has no effect; the demographic variables may incorporate its effect. Second-stage results for the 1970s data, shown in the first regression in Table 2, generally are consistent with those for the 1960s. The new construction variable again is significant, but the magnitude implies less than half as large an impact. For every 100 housing units built annually during the 5-year period, or 500 in all, there are 192 fewer substandard units at the end. The disequilibrium variable is not significant; the coefficient is barely larger than its standard error. The other variables from the new construction demand and supply functions and the subsidized produc“Alternatively, we substituted the level and change in household income for the growth rate of households with children in the first-stage regressions, but we prefer the latter because it performs better on the econometric criteria mentioned previously. The first-stage results are available from the authors.

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WEICHER AND THIBODEAU TABLE 1 Low-Quality Housing, 1960-1970 Variable

Two-stage least-squaresresults

Reduced form

Intercept

0.06 (0.41) - 1.41 (- 2.95) - 0.23 (- 1.96) -0.00 (-0.31) - 0.01 ( - 0.29) - 0.09 (-1.24) 0.02 (0.18) 0.66 (1.74) - 0.05 ( - 0.35) -0.32 (- 2.25) - 0.05 (-1.44) - 0.02 (-0.13) - 8.97 ( - 0.71) 17.86 (0.78)

- 0.01 (-0.13) a

New Construction Diseq60 Land Boeckh Index Govts Income Minorities Elderly Husband-Wife Households Built before 1940 Manufacturing Public Housing Government Subsidies R2

-0.13 (-1.49) - 0.00 (-0.14) 0.02 (0.76) - 0.07 (- 1.26) - 0.04 ( - 0.56) 0.91 (3.07) -0.12 (-1.05) - 0.29 (- 2.57) 0.00 (0.06) 0.00 (0.01) - 18.61 (-1.92) - 25.24 (-1.79) 0.53

Variable

Definition

New Construction

Difference between rate of new private housing construction and rate of net new household formation, 1960-1970 Proportion of 1960 residential stock built between 1950 and 1960 left unoccupied in 1960 Change in average value of farm land per acre between 1959 and 1969 for the county within the SMSA having the lowest value Change in the price of constructing residential frame house 1960-1970, measured by the Boeckh index Number of municipal governments (per 100,000 residents) in the SMSA in 1962 Rate of change in median family income 1960-1970 Change in proportion of nonwhite households 1960-1970

Diseq60 Land Boeckh Index Govts Income Minorities

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TABLE 1 -Continued Variable Elderly Husband-Wife Households Built before 1940 Manufacturing Public Housing Government Subsidies

Definition Change in proportion of elderly-headed (65 years or over) households 1960-1970 Change in proportion of husband-wife households 1960-1970 Proportion of the 1960 residential stock built before 1940 Change in proportion of manufacturing employees in the central city from 1958 to 1967 Proportion of 1970 residential stock that was govemment built between 1960 and 1970, measured by AHS Proportion of 1970 residential stock that was subsidized under Section 221 between 1960 and 1970, measured by AHS

Note: Figures in parentheses are t ratios. uThe rate of endogenously determined private new construction was omitted from the reduced-form equation.

tion variables again are insignificant. The same two demographic variables are significant. Regressions using the HUD program data on subsidized housing are quite similar. For the 1960s the new construction and disequilibrium variables have slightly smaller but more significant coefficients. For the 197Os, the disequilibrium variable is significant at the 20% level, public housing construction is significant at the 10% level, and the incidence of elderly households becomes significant. Other results are unchanged. Both data sets offer evidence that filtering occurs in the short run-measured as 5 to 10 years-but they differ on whether there is a long-run, more or less permanent quality improvement. If there is, it clearly is smaller than the short-run impact. The relative magnitudes of the new construction coefficients seem inconsistent; the effect on substandard housing is larger over the longer period, and the long-term effect is greater 10 to 20 years later than it is after 5 to 15 years. We are inclined to attribute this to differences in the definition of low-quality housing. The traditional criterion represents a smaller share of the housing stock. The HUD measure counts many units as inadequate if they suffer from maintenance problems, such as leaky roofs and peeling paint. More units are likely to be temporarily inadequate under the HUD definition; there is more noise in the data.13 t3We also used a different definition of inadequate housing for the 1970s developed by the Congressional Budget Office [26, p. 81.The results are omitted to conserve space. They show almost the same relationship between new construction and inadequate housing as do those reported in the text, and show a larger coefficient for the disequilibrium variable that is almost significant at the 10% level. We prefer the results using the HUD measure on the basis of the econometric test described in the text.

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TABLE 2 Low-Quality

Housing, 1970s

Variable

Two-stage least-squares results”

Reduced form”

Intercept

- 9.76 (- 0.94) - 1.92 (-3.25) - 0.70 (-1.00) - 0.46 (-0.66) 0.21 (0.08) 0.03 (0.81) -0.00 ( - 0.01) - 0.14 (-0.83) 0.07 (2.73) 0.16 (1.56) 0.16 (2.39) 0.97 (0.98) 0.38 (0.24) - 0.01 (-0.55) 0.33 (2.05) - 1.62 (-0.59) - 2.43 (-0.48) -0.15 (-0.10)

- 13.10 (- 1.31) h

New Construction Diseq70 Land Boeckh Index Govts Income Income Growth Minorities Elderly Unmarried BLS Opcosts Manufacturing Substandard (1970) Public Housing Rent Subsidies Section 235

-0.87 (-1.32) - 0.00 ( - 0.44) 2.07 (0.81) 0.01 (0.25) - 0.04 (-0.23) -0.10 (-0.51) 0.05 (2.01) 0.14 (1.45) 0.16 (2.49) 0.00 (0.81) - 0.32 (-0.22) -0.00 (-0.25) 0.40 (2.64) -2.53 (- 0.96) - 1.48 (- 0.31) 0.52 (0.36) 0.58

R2

Variable New Construction Diseq70

Definition Difference between rate of new private housing construction and rate of net new household formation, 1970 to survey year Difference between rate of new private housing construction and rate of net new household formation, 1960-1970

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TABLE 2-Continued Variable Land Boeckh Index Govts Income Income Growth Minorities Elderly Unmarried BLS Opcosts Manufacturing

Substandard (1970) Public Housing

Rent Subsidies

Section 235

Definition Value of farms (including land and buildings) per acre in the state containing the SMSA as of 1974 Boeckh building cost modifier for brick single-family residences for survey year (measured in 1975 dollars) Number of municipal governments per 100,000 residents of SMSA, in 1972 Median household income in survey year (measured in 1975 dollars) Average annual rate of change in median household income 1970 to survey year (survey year measured in 1975 dollars) Percentage of households with black or Hispanic head, survey year Percentage of households with elderly head, survey year Percentage of households not headed by married couple, survey year Nonhousing, nontax component of intermediate budget for four-person family, survey year Index of operating costs for rental housing (utility costs, janitors’ wages, and accountants’ wages) Percantage change in the number of manufacturing establishments with 20 or more employees in the central city, 1967-1972 Percentage of housing stock substandard, 1970 Average annual number of public housing units built, 1970 to survey year, as percentage of average housing stock during the same period Average annual number of units built under federal rent subsidy programs (primarily Section 236), 1970 to survey year, as percentage of average housing stock during the same period Average annual number of units built under Section 235 homeownership program, 1970 to survey year, as percentage of average housing stock during the same period

Note: Figures in parentheses are t ratios. “See Appendix for the definition of low-quality housing. “The rate of private new construction was omitted from the reduced-form model.

Reduced-Form Results We also estimated the reduced-form regression for the quantity of substandard housing, derived from the entire six-equation model. These results are shown as the second regressions in Tables 1 and 2. The results for the 1960s differ in two important ways from the semireduced-form estimates. Both subsidized production variables have much larger and

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nearly significant coefficients, with the expected negative signs. In addition, the disequilibrium variable is less significant. The results for the 1970s don’t change. In other respects, the reduced-form results for both periods are not very different from the semireduced-form estimates. But they therefore have quite different implications. For both data sets, the semireduced form supports the filtering hypothesis much more strongly; in the 1970s it provides the only support. When the new construction variable is omitted, there is not much evidence that filtering occurs.14 The Effect of Subsidized Production Our results for subsidized production are only partly consistent with the theoretical literature. Moderate-income programs seldom had any effect on substandard housing. These results are consistent with those of Olsen’s model if all of the assisted households were originally living in standard quality housing, as seemslikely, but not with those of Sweeney’sor Schall’s models. The only equations providing evidence that public housing reduces substandard housing are the semireduced-form equation using HUD data for the 1970s (not reported in the tables) and the reduced-form equation, omitting new construction, for the 1960s. These surprising results may be explained partially by three factors. First, empirical studies by Swan [23] and Murray [15] have found that subsidized production substantially substitutes for private housing that otherwise would have been built. The substitution is not complete for public housing, however, according to Murray, who separated subsidized housing by program. Over approximately our period (1961-1977), he found that about one-third of public housing construction was a net addition to the housing stock. Second, the public housing program originally was intended to promote slum clearance as well as to build new housing. Demolition of substandard units, in substantially equivalent numbers, was required as a precondition of new construction. In 1967 the National Commission on Urban Problems (the Douglas Commision) [17] estimated-it thought, conservatively-that about half as many units had been removed as built during the previous 30 years. The effect of demolitions is not given much attention in most models, but Braid [3] and Schall [22] conclude that households in low-quality housing are harmed if higher-quality units are tom down. The Douglas Commision 14There is slightly more support for the existence of filtering in the regressions using the HUD data on subsidized production. As in the semireduced form, the disequilibrium variable has a coefficient that is significant at the 20% level in the regression using the HUD measure of inadequacy.

FILTERING

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HOUSING

MARKETS

37

thought that most of the units actually demolished were substandard, but Congress disagreed and repealed the requirement. Third, unlike the assumption in most theoretical models, public housing occupancy is not restricted to those who lived in substandard housing previously. Program data show that fewer than half of new residents during the early 1970s moved out of substandard housing. This combination of factors may help to explain our findings, but it is at best a partial explanation, even if we assume that only standard units were razed. Demolitions were more common in the 196Os,but our public housing coefficients are insignificant in both regressions. (National policy changes occur before-sometimes well before-the actions of local housing authorities, but our impression is that demolitions were much less frequent after 1968.) Further, even with complete substitution between private and public construction, Swan’s and Murray’s findings imply that the coefficient of public housing should be about the same as that of private construction. A large effect from demolitions would be required to make our results fully consistent with theirs. It seemsclear that further research is warranted. Conclusion

The empirical results for our semireduced forms are consistent with those for the formal commodity hierarchy and chain models developed by Sweeney, Braid, and Schall, rather than the earlier conclusions of Lowry and Olsen. Filtering does occur in housing markets, and it is important quantitatively. As higher-income households vacate existing standard quality housing to occupy new units, lower-income households can afford better-quality housing, and ultimately there is less substandard housing. The magnitude of the filtering effect is large: about one less substandard unit is occupied in 1970 for each new housing unit built during the 1960s and one less is occupied during the mid-1970s for every three new housing units built since 1970, beyond those needed for new households. Our estimating technique is needed to show that filtering exists; it does not appear in a reduced-form regression. We also have some evidence that filtering reduces the incidence of low-quality housing in the long run, although the short-run impact is much greater. The coefficient of the disequilibrium variable indicates that there is about one less substandard unit in 1970 for every four units built during the 1950s. However, the relationship is much less significant between units built during the 1960s and the stock of inadequate housing as of the mid-1970s. The impact of new private construction is the most consistent and usually the strongest finding in our empirical work. Other results, not all reported here, vary with the definition of substandard housing and with the study period. The married couple and minority household variables are significant

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for both periods. l5 We find very little evidence that subsidized production directly for the poor reduces the incidence of substandard housing. Our conclusions with respect to filtering-but not with respect to subsidized production-depend on our unusual estimating procedure. Ideally, we would prefer to estimate the full three-market model as a system of simultaneous equations. We have chosen not to do so because of the absence of reliable data on prices for different qualities of housing. Further research may make it possible to estimate the relevant elasticities in the full structural model. APPENDIX Definition of Inadequate Housing for Mid-1970s Model16 A housing unit is inadequate if one or more of the following conditions holds: Plumbing. Unit lacks or shares complete plumbing (hot and cold running water, flush toilet, and bathtub or shower inside the structure). Kitchen. Unit lacks or shares a complete kitchen (installed sink with piped water, range or cookstove, and mechanical refrigerator). Sewage. Absence of a public sewer, septic tank, cesspool, or chemical toilet. Heating. There are no means of heating; or unit is heated by unvented room heaters burning gas, oil, or kerosene; or unit is heated by fireplace, stove, or portable room heater (does not apply in South Census region). Maintenance. Unit suffers from any two of the following defects: leaking roof, open cracks or holes in interior walls or ceilings, holes in the interior floor, broken plaster or peeling paint (over 1 square foot) on interior walls of ceilings. Public hull. Unit suffers from any two of the following defects: public halls lack light fixtures; loose, broken, or missing steps on common stairways; stair railings loose or missing. Toilet access.Access to sole flush toilet is through one of two or more bedrooms used for sleeping (applies only to households with children under 18 years old). Electrical. Unit has exposed wiring, fuses blew or circuit breakers tripped three or more times in last 90 days, and unit lacks working wall outlet in one or more rooms. ‘5Income and some other demographic variables are insignificant for the results reported here but are significant in some regressionsusing the HUD data on subsidized production or the CBO definition of substandard housing. 16U.S. Department of Housing and Urban Development [27].

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REFERENCES 1. H. Aaron, “Shelter and Subsidies,” Brook@ Institution, Washington, DC (1972). 2. R. Braid, The short-run comparative statics of a rental housing market, J. &bun Econom., 10, 286-310 (1981). 3. R. Braid, The effects of government housing policies in a vintage filtering model, J. Urban Econom., 16, 272-296 (1984).

4. .I. Brueckner, A dynamic model of housing production, J. Urban Econom., 10, l-14 (1981). 5. 0. Davis, C. Eastman, and C. Hua, The shrinkage in the stock of low-quality housing in the central city: An empirical study of the U.S. experience over the last ten years, Urban Stud., 11,13-26

(1974).

6. F. deLeeuw and R. Struyk, “The Web of Urban Housing,” The Urban Institute, Washington, DC (1975). 7. W. Grigsby, “Housing Markets and Public Policy,” Univ. of Penusylvania Press, Philadelphia (1963). 8. T. Haavelmo, Methods of measuring the marginal propensity to consume, in “Studies in Econometric Methods” (W. Hood and T. Koopmans, Eds.), Wiley, New York (1953). 9. B. Hamilton, Zoning and the exercise of monopoly power, J. Urban Econom., 5, 116-130 (1978). 10. W. Hirsch and C. Law, Habitability laws and the shrinkage of substandard rental housing stock, Urban Stud., 16, 19-28 (1979). 11. T. Koopmans and W. Hood, The estimation of simultaneous linear economic relationships, in “Studies in Econometric Methods” (W. Hood and T. Koopmans, Eds.), Wiley, New York (1953). 12. J. Lansing, C. Clifton, and J. Morgan, “New Homes and Poor People: A Study of Chains of Moves,” University of Michigan Institute for Social Science Research, Ann Arbor (1969). 13. C. Leven, J. Little, H. Nourse, and R. Read, “Neighborhood Change,” Praeger, New York (1976). 14. I. Lowry, Filtering and housing standards: A conceptual analysis, L.und Econom., 36, 362-370 (1960).

15. M. Murray, Subsidized and unsubsidized housing starts: 1961-1977, Rev. Econom. Stutist., 65, 590-597 (1983). 16. R. Muth, A vintage model of the housing stock, Papers Region. Sci. Assoc., 30, 141-156 (1973). 17. National Commission on Urban Problems, “Building the American City,” Praeger, New York (1968). 18. J. Ohls, Public policy toward low income housing and filtering in housing markets, J. Urban Econom., 2, 144-171 (1975). 19. E. Olsen, A competitive theory of the housing market, Amer. Econom. Rev., 59, 612-621 (1969). 20. L. Ozanne and T. Thibodeau, FMRs for existing dwellings: An evaluation through

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hedonic index methods, Working Paper No. 1367-04, Urban Institute, Washington, DC (1981). R. Ratcliff, “Urban Land Economics,” McGraw-Hill, New York (1949). L. Schall, Commodity hierarchy chain systemsand the housing market, J. Urban Econom., 10, 141-163 (1981). C. Swan, Housing subsidies and housing starts, Amer. Real Estate Urban Econom. J., 1, 119-140 (1973). J. Sweeney, A commodity hierarchy model of the rental housing market, J. Urban Econom., 1, 288-323 (1974).

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25. J. Sweeney, Quality, commodity hierarchies, and housing markets, Econometrica, 42, 147-167 (1974). 26. U.S. Congressional Budget Office, Human Resources and Community Development Division, “Measures of Housing Need: Findings from the AHS,” Washington, DC (1978). 27. U.S. Department of Housing and Urban Development, “How Well Are We Housed?” Office of Policy Development and Research, Govt. Printing Office, Washington, DC (1978). 28. K. Vandell, The effects of racial composition on neighborhood succession,Urban S&d., 18, 315-333 (1981). 29. D. Vitaliano, Public housing and slums: Cure or cause? Urban Stud., 20, 173-183 (1983). 30. J. Weicher, Product quality and value in the new home market: Implications for consumer protection regulation, J. Law Econom., 24, 365-397 (1981). 31. J. Weicher and D. Hartzell, Hedonic analysis of home prices: Results for 59 metropolitan areas, Rex Real Estate, 2, 267-291 (1982). 32. J. Weicher, L. Yap, and M. Jones, “Metropolitan Housing Needs for the 1980s” Urban Institute, Washington, DC (1982).