An economic analysis of the homeownership decision

JOURNAL

OF URBAN

ECONOhlICS

17,230-246(1985)

An Economic Analysis of the Homeownership Decision PETERLINNEMAN’ Wharion School, University of Pennsylvania, Philadelphia, Pennsylvania I91 04 Received March 9,1983; revised May 19,1983

I. INTRODUCTION Analysts of the homeownership decision have traditionally asserted that “owning makes much greater sensethan renting” ([16], p. 359) for families in high tax brackets. However, empirical studies of homeownership propensities indicate that not all high-income families own nor do all low-income families rent. For example, Li ([8], p. 1081) notes that “a large number of studies” find that a variety of variables, such as “family size, age of the head, and race are generally found to be.. . determinants of homeownership” even when income or the marginal tax bracket are held constant. Previous attempts to explain why the marginal tax bracket is not a sufficient statistic for homeownership argue that people differ in their preferences for homeownership either because owning and renting are not perfect substitutes in consumption (see, for example [13, 141)or because of differences “in liquidity, mobility, ability at home repairs and home management, and simply peculiar circumstances” ([4], p. 14). This paper develops a general model of the homeownership decision and explores two alternative explanations of why the marginal tax bracket is not a sufficient statistic. This is accomplished by incorporating both transaction costs and housing market quality sorting into the model. Section II derives a simple parametric statement of the homeownership decision. The third section examines the special case which yields a homeownership decision rule which is comparable to existing models. An alternative special case is presented in the fourth section which incorporates consumer sorting across quality markets. It is demonstrated that the housing market may adjust until

‘Helpful comments and suggestions were provided by Douglas Diamond, Mark Flannery, Patric Henderschott, Shelly Lundberg, Jay Ritter, Jeremy Siegel, Pablo Spiller, Dick Star%, and George Tolley. Helpful reactions to earlier drafts were obtained from the participants of the Transaction Cost Workshop at the University of Pennsylvania, the Urban Economics Workshop at the University of Chicago, and a presentation at Ohio State University. 230 0094-1190/85 Copyright All rights

$3.00

(0 1985 by Academx Press. Inc. of reproduction in any form reserved

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all consumers are indifferent with respect to their ownership status. Section V uses the 1973 AMU~ Housing Survey for Chicago and New York City to parameterize the homeownership decision and to evaluate the relevance of these special cases.The data fail to support either special case and indicate that tax effects, quality market sorting, and transaction costs are all important determinants of homeownership. II. GENERAL MODEL OF HOMEOWNERSHIP Consumers face the problem of choosing both the optimal level of housing quality and whether to purchase or rent their optimal residence. If it is assumed that consumers derive no direct utility from owning their optimal quality residence a consumer decides to own if NET = TOTALR - TOTAL’ 2 0

0)

where TOTAL’ is the full total cost of tenure mode i where i = R refers to renting and i = 0 indicates homeownership.2 The total cost of renting a residence equals the rental payments for the residence. When the expected present value of capital gain taxes is zero,3 the competitive rental price of a residence (RENT) is4 RENT = COSTL + CLOSEL + DOWNL -

(TACC -t GAINL) l--T

(2)

where COSTL is the landlord’s production cost, CLOSEL is the landlord’s transaction and closing costs, DOWNL is the opportunity cost of the landlord’s equity in the residence, GAINL is the landlord’s capital gain on this equity, ACC is the value of accelerated depreciation over economic depreciation, and 7 is the landlord’s marginal tax bracket. *This section develops a simple model of the homeownership decision for an individual resident. Since all critical results can be derived using a single period-certainty framework, the model is specified without explicit use of expected value operators and present value notation. Also, the marginal tax bracket of landlords is assumed to be exogenous. 3Although actual capital gains taxes are nonzero, the expected present value of these taxes on a property with an expected holding period of 10 to 15 years is small. This is particularly true in view of the possibility of trading properties to avoid capital gains taxes. This assumption can be relaxed without changing major implications of the model. 4Proftt for the landlord, IT,is equal to his rent minus landlord production costs, COSTL, plus capital gains realized on the equity, GAINL, minus the contracting costs associated with finding a tenant, CLOSEL, plus any tax advantages from accelerated depreciation over true depreciation, ACC, minus the opportunity cost of the equity, DOWNL, and minus federal corporate income taxes levied on adjusted net income at a rate of 7 n = RENT - COSTL - CLOSEL - (1 - 7) DOWNL + GAINL - T(RENT - COSTL -CLOSEL - ACC).

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The total cost of owning one’s residence can be similarly expressedas the sum of the self-production costs, COSTO, the opportunity cost of owner equity, DOWN’, closing and other transaction costs, CLOSEO, minus the expected capital gain on one’s equity, GAIN’, and the tax subsidies which are given to homeowners, SUB, TOTAL0 = COST’ + (1 - ot) CLOSE’ + (1 - t) DOWN’ -GAIN’

- SUB

(3)

where u is the proportion of the owner’s transaction costs which are deductible at a personal marginal tax rate of t. Substituting (2) and (3) into (1) yields a general statement of the net total cost advantage associated with purchasing one’s optimal residence NET = [COSTL - COST’] + [CLOSEL - (1 - at) CLOSE’] + [DOWNY - (1 - t) + GAIN’-

e]

DowNO]

(4)

+[SUB - e].

This formulation of the homeownership decision indicates that the view that homeownership provides an equity interest unavailable through rental housing is technically correct but economically misleading. This is because the equity available to the consumer via homeownership is available to the landlord which is reflected in lower rents. Thus, renters experience the advantages of landlord expected capital gains on equity indirectly through reduced rents which allow renters to obtain investment returns on altemative assets. In order to obtain more detailed insights into the determinants of homeownership it is useful to introduce simple proportional parameterizations of the economic concepts represented in (4). Since similar derivations have appeared elsewhere (see, for example, Diamond and Tolley [4]), the derivation of the proportional parameterization is developed in the Appendix. It is demonstrated there that the net advantage of homeownership can be expressed as:

NET= V (1 -a)(8+m~+p)++h~~(1 t ++#+p)

+o -f)(lr

--at)] -*

1-T

- *))

where V is unit’s value; a is the relative production efficiency versus

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self-production of housing (a > 1 indicates landlords are relatively efficient while a < 1 implies landlords are relatively inefficient); 6 is the economic depreciation rate of the unit; p is the property tax rate; mf is the product of the mortgage interest rate (m) and the loan-to-value ratio (f ); y represents the value of accelerated depreciation (net of recapture) relative to economic depreciation (y > 0 indicates landlords receive an accelerated allowance); t is the pretax opportunity rate of return on equity; g is the unit’s expected rate of capital gain; B expressesclosing and other transaction costs as a fraction of the unit’s value; N is the expected tenancy period of the resident; and p is the period the landlord expects to hold the unik5 The most important feature of this formulation of the net advantage of homeownership relative to the literature is the introduction of relative landlord production efficiency (a). It is intuitively obvious that as relative landlord production efficiency rises, the attractiveness of homeownership declines because competition incorporates this efficiency in the form of lower rents. Relative landlord efficiency may derive from superior credit ratings, greater political influence which yield lower tax assessments,maintenance cost efficiencies, or economiesassociatedwith processing a landlord’s credit application versus that for a homeowner. Particularly in multifamily structures and dense neighborhoods landlord production costs may be substantially lower than those of homeowners due to the fact that landlords can solve a number of free-rider problems. For example, the landlord solves the free-rider problem faced by the resident of a high rise with respect to common facility maintenance. Similarly, when residencesare densely located the probability of serious externalities increases. Landlords facilitate the internalization of these externalities by reducing the bargaining costs associated with dealing with neighbors (both within and outside the structure). Offsetting these advantages, particularly in nondense residential settings, is the fact that the landlord and tenant enter into a bilateral agreement which encourages what Williamson 1241describes as “opportunistic behavior.” That is, once a lease is signed, both the landlord and tenant have incentives to violate its terms. For example, the landlord may not provide adequate heating or maintenance while the tenant may let children draw on the wall, burn the carpet, or “skip out.” Since monitoring contracts between landlords and tenants is expensive, there is an incentive to economize on these costs by vertical integration, that is by shifting to homeownership. ‘This formulation incorporates several simplifying assumptions. First, it is assumedthat the relative landlord efficiency applies equally to closing costs, mortgage interest payments, depreciation, and property taxes. In fact, all differences between landlords and homeowners in these costs are assumed to be captured by this single parameter. Landlords and owners are also assumed to have the same: proportional transaction costs, pretax opportunity rate of return, and expected capital gain rate. It is also assumed that neither landlords or homeowners can borrow on the margin. Relaxing this last assumption simply induces neutrality of NET with respect to the loan-to-value ratio.

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This discussion suggests that different types of housing markets have differing degrees of relative landlord efficiency and hence differing degrees of homeownership even when other factors are held constant. In fact, the impacts of depreciation, mortgage interest rates, property taxes, loan-to-value ratio, and the value of the unit are all ambiguous and depend on the degree of relative landlord production efficiency. For example, if landlords are relatively inefficient (a < 1) then increases in property tax rates favor homeownership via tax considerations. However, if landlords are sufficiently more efficient (in a maner proportional to costs) then any further cost increase favors renting as landlords can more effectively minimize the burden of tax increase. The relative production efficiency aspect of the homeownership decision has been ignored in previous studies in spite of the fact that it is capable of explaining why some low-income residents own while some high-income residents rent. For example, low-income families who desire relatively nondense residences (for example, due to large family sizes increasing their demand for lot space) tend to own because the costs of monitoring “opportunism” are high relative to the gains from the landlord’s dealing with free-riding problems. Similarly, high-income families desiring a center city residence (possibly due to a high demand for “night life”) rent if the gains from landlord’s solving free-riding problems outweigh the costs of monitoring “opportunistic behavior” and the tax benefits of homeownership. Alternatively stated, the inclusion of the relative production efficiency parameter indicates that one’s marginal tax bracket is not a sufficient statistic for identifying homeownership propensities. One must also consider the production efficiency of the particular type of housing desired by the consumer. consumer. Another noteworthy aspect of (5) is the explicit modeling of the transaction costs associated with homeownership. Simply stated, the advantages of homeownership rise nonlinearly with respect to the tenant’s expected tenancy period and fall nonlinearly with the landlord’s expected holding period. If these periods are identical then the advantages to homeownership are positive if homeowners can deduct closing costs from their tax liabilities and landlord relative efficiency is not too large. However, since landlord holding periods tend to be longer than resident tenancy durations, increases in closing costs favor renting. This is particularly true for families in relatively low tax brackets and for families residing in quality markets with large relative landlord production advantages. In sum, this section argues that in addition to the commonly stressedtax considerations, both relative landlord production efficiency and closing costs are key determinants of the homeownership decision. Further, these generally ignored considerations can explain why income is not a sufilcient statistic for the homeownership propensity without relying upon ad hoc

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variations in tastes. To further highlight the importance of these new factors, two extremum special casesof the general model are contrasted in the next two sections. III. SPECIAL CASE l-THE MUNICIPAL BOND ANALOGY Traditional analyses of the homeownership decision indicate that only a trivial number of consumers are indifferent with respect to their tenure status in equilibrium. Since a similar type of equilibrium is generally used to describe municipal bond purchases, this special case of the homeownership decision is referred to here as the municipal bond analogy of homeownership (MBAH).6 To understand this special case it is helpful to summarize the municipal bond purchase model. This model argues that the favorable tax status of municipal bonds makes the after-tax return exceed that of alternative assets if all assetshave the same pre-tax return. Since investors are heterogeneous with respect to their marginal tax rates and the risk characteristics of all investment instruments are the same (via portfolio diversification), arbitrage occurs until the marginal investor is indifferent between holding a municipal bond and an alternative asset. In equilibrium investors in high tax brackets (relative to the tax bracket of the marginal investor) hold municipal bonds as they provide higher expected after-tax returns than alternative assets while investors in low tax brackets do not hold municipal bonds becauseof their low after-tax return. Previous models of homeownership have noted that homeownership, like municipal bonds, represents an investment instrument with diversifiable investment risk and an after-tax yield dependent on one’s marginal tax bracket. They argue implicitly or explicitly that the heterogeneous population bids for these homogeneous investment instruments (in terms of risk) and that arbitrage occurs until the marginal bidder is indifferent between homeownership and renting. Since only a small fraction of the total population are marginal bidders, most of the population is not indifferent between owning and renting.7 In this special case the critical marginal tax rate, tc, at which homeownership is as attractive as renting is obtained by solving (5) for the marginal tax rate which yeilds NET = 0. These models further implicitly assume that landlords and homeowners have equal production efficiencies (a = 1) and that there are no closing costs (B = O).8 For this special case the homeownership decision is expressedas OWNi = 1 if t, 2 tC

(6)

%ee Miller [ll] for a descripttion of the market equilibrium for municipal bonds. ‘In this case renting refers to using alternative investment instruments to build one’s portfolio with the funds that could be used for purchasing equity in one’s residence. *See Shelton [17] for a notable exception to the zero transaction cost assumption.

236

PETER LINNEMAN TABLE 1 MBAH Critical Tax Bracket for Alternative Parameter Sets

___ (1) [T = 0.4,6 = 0.05, f= 0.8, g = 0.1, p = 0.02, y = 1, m = 0.12, r = 0.101: fc = 0.313 (2) [T = 0.4,6 = 0.05, f = 0.8, g = 0.1, p = 0.02, y = 3, m = 0.12, r = 0.101: I' = 0.764 (3) [T = 0.4,6 = 0.05, f-

0.8, g = 0.1, p = 0.02, y = 1, m = 0.18, r = O.lO]: fc = 0.237

where OWN, indexes the jth household’s tenure status and

4 +(l -rh tC = (1 - r)[(mf+p)

+(1 -f)r]

.

The decision rule for this special case depends only upon exogenous parameters (7, y, 8, f, g, m, p, and r). Given these parameters the household’s tax bracket is a sufficient statistic for predicting homeownership propensities. Table 1 displays the critical tax brackets for three alternative sets of exogenous parameters. The second row indicates that an increase in accelerated depreciation raises tC while the third row shows that a higher mortgage interest rate reduces tC.This latter result is usually used to explain why homeownership (often via the conversion of apartments into condominiums) rates rose when inflation during the 1970s pushed mortgage interest rates upward. Similarly, the dramatic increase in the accelerated depreciation allowance which was introduced in 1981 is often suggestedas a key factor in the recent slowdown in the growth of homeownership. Contrary to the implications of this special case, empirical studies indicate that not all families with the same tax bracket choose the same ownership status. This result has been explained by appealing to variations in the taste for homeownership among families.’ The next section specifies another special case of the general model which does not rely on taste variations to explain this outcome. IV. SPECIAL CASE 2-THE EFFICIENT MARKET MODEL Contrary to the assumption underlying MBAH, urban economics asserts that in equilibrium the housing market is characterized as a series of quality markets with each quality market composed of homogeneous consumers bidding for a homogeneous housing quality. This section demonstrates that if this fully sorted equilibrium occurs, the equilibrium homeownership outcome will not be represented by MBAH. 9Diamo~d and Tolley [4] utilize preferences for ownership to explain the data while Rosen and Rosen [14] use a random utility specification with respect to tenure status. Most other studies appear to use, generally implicitly, one or both of these variations to explain the failure of the MBAH.

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A simple example is useful in demonstrating the equilibrium associated with this special case. Assume that income is the sole determinant of the demand for housing quality and that there are three high and three low income consumers. Let the housing stock be composed of three high-quality and three low-quality units. In order to maximize their utility the three high-income families consume the high-quality units while the three lowquality units are consumed by the low-income families. Thus, the heterogeneous population sorts into two internally homogeneous quality markets. Initially the rental offer price for the low-quality units reflects the lowest rent consistent with a competitive profit realization by the least efficient landlord. If the tax advantages associated with homeownership for lowincome residents make the net-of-tax homeownership cost less than this rent then there is an incentive for the residents to buy out the least efficient landlord. With an upward sloping supply curve of landlord-supplied housing (for any given quality), the remaining two developers are more efficient landlords (higher a) and can earn competitive profits at lower rents. If the new marginal landlord is sufficiently efficient, the full cost of homeownership is equal to the rental cost. Equilibrium then occurs where all low-quality units have the same full cost irrespective of whether they are owned or rented. In this simple example, l/3 of the low-quality units are owned and 2/3 are rented. All three low-income residents are indifferent as to whether they own or rent if competition eliminates the inefficient landlord. The three high-income residents would realize higher tax advantages than the low-income residents from consuming low-quality housing. However, they obtain greater utility from consuming high-quality units. Since tax advantages associated with homeownership are greater for high-income residents, more landlords are eliminated (for any distribution of a) before the high-quality market achieves equilibrium, as only the most efficient landlords of high-quality housing are able to reduce rents sufficiently to compete with the tax advantages of owing high-quality housing. Rents fall as inefficient landlords are eliminated until rents equal the full cost of ownership and all high-income consumers are indifferent to tenure status. This example demonstrates a special case in which all consumers are indifferent with respect to their homeownership status in equilibrium. This special case assumes(1) complete sorting of the heterogeneous population into homogeneous housing quality markets; and, (2) an upward sloping landlord supply curve. This special case, referred to there as the efficient market proposition (EMP), implies that the percentage of the relevant quality market which is owned is a sufficient statistic for predicting any individual’s homeownership decision. That is, if EMP is correct then one’s best guess of any individual’s homeownership propensity is the percentage of their quality market which is owned becausein equilibrium all individuals are indifferent with respect to tenure status in their quality market.

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The special case of EMP can be expressedin terms of the general model by noting that due to the sorting of individuals into homogeneous housing quality markets, the marginal tax bracket (t) and the expected tenancy period (N) are exogenous parameters for any given quality market. The unknowns in this case (for any quality market) are the equilibrium relative landlord efficiency parameter (CY)and the equilibrium percentage of homeownership. Solving (5) for the (Y value with NET = 0 provides the equilibrium relative landlord efficiency parameter, CX’,as a function of the exogenous parameters

a!c=[fs+mf+p+$-f$ +(1-r+ - p-J] .[a + $1

- at) +(1 - r)(mf+p)]-l.

Once the equilibrium value of relative landlord efficiency is known for any quality market, the percentage of homeownership in that market equals one minus the percentage of the market which is supplied by landlords with relative efficiency parameters greater than or equal to (Y’ %OWNED(Q = Q,) = 1 - @a)

do

(9)

where %OWNED(Q = Qi) is the percentage of quality market Qi which is owned in equilibrium, fi((~) is the distribution of the relative efficiency parameter in quality market i, and (u; is the equilibrium relative landlord efficiency in quality market i. Since all individuals in quality market i are identical in this special case and inefficient landlords are eliminated from market i until the net full cost of owning and renting are equal, all families residing in the i th market are indifferent between owning and renting. Thus, the probability of family j, which resides in market i, owning their residence is equal to the percentage of the units in market i which are owned in equilibrium Pr(OWNj = 1 given j resides in market i) = %OWNED(Q = Qi). (10) Stated differently, in the special caseof EMP all families are indifferent with respect to their ownership status if: (1) they reside in their optimal quality market; and (2) their quality market has achieved an equilibrium which has eliminated all landlords who are not efficient enough to compete successfully with homeownership.

239

ECONOMIC ANALYSIS OF HOMEOWNERSHIP TABLE 2 Critical Relative Landlord Efikiencies

(1) (2) (3) (4) (5)

(6)

Base case: [T = 0.4,6 = 0.05,f = 0.8, g = 0.1, p = 0.02, r = 0.1, B = 0.1, (J = 0.5, R = 15, n = 0.12,~ = 1, N = 3, t = 0.31: AI1 parameters the same as base case except t = 0.10: All parameters the same as base caseexcept r = 0.50: AI1 parameters the same as base case except m = 0.18: AI1 parameters the same as base caseexcept y = 3: AI1 parameters the same as base caseexcept N = 9:

01' = ac = (Xc= a' =

0.827 0.688 1.02 0.932

UC= 0.410 a’ = 0.939

Not all households have the same homeownership propensities since they reside in different housing quality markets. Different quality markets achieve different equilibrium ownership propensities in this model as the result of differences across markets in (1) the distribution of the relative landlord efficiency parameter; (2) different marginal tax brackets; and (3) different expected tenancy periods. Table 2 displays critical landlord efficiency values for a set of parameter values. Any increase in the critical relative efficiency parameter, for a given distribution of (Y,means that the equilibrium homeownership propensity increasesbecausefewer landlords are efficient enough to compete with homeownership. In the base case(row 1) any landlord who is more than 83% as efficient as the marginal resident can offer consumers an attractive alternative to ownership. This critical value moves inversely with the tax bracket and expected tenancy duration of the households in the relevant quality market. Also, as expected, the percentage of homeowners falls when accelerated depreciation allowances are increased. However, only if the relative efficiency parameter is such that all landlords are more (less) efficient than the critical value are all units in the relevant quality market rented (owned) in equilibrium. In sum, this section has developed a special case of the general model of homeownership, referred to as EMP, which yeilds an equilibrium where (absent comer solutions) all consumers are indifferent with respect to their housing tenure status. This result occurs because a heterogeneousconsumer population sorts into a number of internally homogeneous housing markets and competition forces rents down until consumers are indifferent between ownership and renting and marginal landlords earn a competitive profit. V. AN EMPIRICAL TEST OF MBAH AND EMP It was demonstrated in the last two sections that depending upon the economic assumptions one makes, the general model of the homeownership developed in Section II can yield different equilibria. Specifically, the MBAH assumes that (1) landlords and homeowners are equally efficient at housing production; (2) all households bid for the same quality housing;

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and (3) no closing costs are associatedwith homeownership. As the result of these extreme assumptions the equilibrium homeowner decision rule implies that (1) all households with the same potential tax bracket make the same tenure decision; and (2) a household’s homeownership propensity is explained by its tax bracket. However, when the extreme assumptions associated with the EMP are imposed, the general model yields an equilibrium which implies that (1) not all identical households make the same tenure decision; and (2) a household’s homeownership propensity equals the percentage of the units in the quality market in which they reside are owned. The extreme assumptions which generate the EMP equilibrium are that (1) landlord relative production efficiency varies across quality markets; (2) the population sorts into a series of internally homogeneous quality markets; and (3) equilibrium market rents are endogenously determined through a competitive process which eliminates landlords which are not efficient enough to compete with homeownership. The relevance of either of these extreme casesof the general model is an empirical matter. Further, many alternative equilibria can be generated through other restrictions on the general model. However, because of their simplicity both the MBAH and EMP are attractive versions of the general model. This reason, plus the fact that the MBAH is the model underlying most policy discussions, makes it particularly interesting to ask if observed homeownership patterns refute either or both extreme cases. A simple test of the empirical relevance of these special casesis available because they both have sufficient statistics in terms of the individual household’s homeownership propensity. In the case of the MBAH this sufficient statistic is the household’s marginal tax bracket while for the EMP it is the homeowner percentage for the quality market in which the household resides. Thus, to test these special cases one can simply regress the individual homeowner decision (1 if they own their residence, 0 if they rent) on proxies for the household’s potential tax bracket, a variable measuring the proportion of their quality market which is owned, and a set of household traits unrelated to the tax bracket. If the only significant variable in this regression is the ownership proportion then the EMP is not rejectable but the MBAH is rejected. Similarly, the EMP is rejected and the MBAH is not rejected if the only significant regressors are the proxies for the household’s tax bracket. If both the homeownership proportion and tax bracket proxy variables are found to be significant determinants of the probability of homeownership then both EMP MBAH are rejected. Of course, this is also the case if none of these variables are significant regressors. Finally, if other household traits are significant regressorsor the tax proxy variables do not display the correct signs then one can reject both the EMP and the MBAH.

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ANALYSIS

OF HOMEOWNERSHIP

241

Following previous work on this topic three household characteristics are used as proxies for the household’s tax bracket. These proxies are gross family income, family size, and age of the head. The household’s potential tax bracket increases with increasesin income, reductions in family size, and reductions in the age of the head. The positive income effect is due to the progressive structure of our tax system while the negative family size effect reflects exemptions and the standard deduction. The age of the head effect on the tax bracket is attributable to both a “learning effect” with respect to minimizing one’s taxes as well as the fact that medical deductions tend to be larger for older households. The race and sex of the head, and whether there are two adults in the household are also included in the homeownership equation. There are no obvious channels through which these traits should atIe& the household’s tax bracket. If these characteristics are significant explanatory variables in the homeownership regression it indicates that factors other than the family’s tax bracket (prehaps discrimination or tastes) enter into the homeownership decision. Such a result is contrary to the implications of the MBAH and will cause the rejection of this special case. In order to measure the homeownership proportion in the household’s quality market the observations must first be grouped into meaningful housing quality cells. This is accomplished by defining a series of quality markets on the basis of the unit’s structural and neighborhood characteristics. For example, all 15year-old units with two bedrooms and one bathroom in a neighborhood with good schools, etc. might be assigned to quality market 1 while all such units with two bathrooms are assigned to quality market 2, and all such units which have four baths are assigned to a third quality market. This method is used to define a large number of “quality” markets to which the data can be assigned.The quality market homeownership proportion for any household is then the percentage of the units assigned to the same quality market which are owned. Unfortunately, a statistical trade-off exists in defining these housing quality markets. If one defines many detailed quality cells the measurement error associated with quality declines. However, the sampling error of the market homeownership proportion (MARKET) rises due to the reduced number of observations in any cell. For example, if one allocates 1000 observations to 800 detailed quality cells it is unlikely that any cell contains more than one true quality level. However, since few housing quality cells would contain more than a few observations the sampling error associated with MARKET is large. In order to minimize these problems, samples from the two largest cities (New York City and Chicago) in the 1973 Annual Housing Survey (AHS) are used in this study. The Chicago sample is allocated to 17 quality cells while the New York City data are divided to 39 cells. These quality cells each contain approximately 40 observations and are defined by the number of bathrooms, the number of rooms, the number

242

PETER LINNEMAN TABLE 3 Summary Statistics

-Income Age of head Family size White head Male head Two-adult family Percentagehome ownership Observations

Chicago

New York

$9,621 48.2 2.7 0.65 0.61 0.51 0.39 707

$10,680 48.8 2.6 0.19 0.68 0.52 0.26 1,774

of units in the structure, age of the structure, elevator availability, and whether the unit is furnished.‘0 Table 3 displays sample means for each city for the variables used in this study. The first and third columns of Table 4 report the mean partial derivatives of the probability of homeownership for Chicago and New York, respectively, when only the tax bracket proxies and other family traits are included and the market homeownership proportion variable (MARKET) is excluded in the logit model.I* The results for both cities are generally significant at standard confidence levels and are consistent with previous empirical work. Contrary to MBAH the impacts of both family size and age of the head are strongly positive in both cities. MBAH, the most commonly used model, is further repudiated by the importance of the non-tax-related regressors. Specifically, white households and families with two adults are significantly more likely to own their residences in both cities. Also, maleheaded households are significantly more likely to be homeowners in Chicago. Although similar inconsistencies between the data and MBAH have been found in previous empirical studies, previous analysts have failed to appreciate that the data reject the special assumptions implicit in the traditional model. This study indicates that this failure to reject the MBAH is unwarranted. The second and fourth columns of Table 4 display the mean estimated partial derivatives of the probability of homeownership when the market homeowner&p proportion (MARKET) is also included in the logit equations for Chicago and New York. In both samples, MARKET is significant at standard confidence levels and substantially improves the fit of the regression. i°Complete quality cell definitions are available upon request. “Complete logit results are available upon request. Following Li [S], interactive variable specifications were also estimated. However, the results reported in the text are robust with respect to these alternatives.

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ECONOMIC ANALYSIS OF HOMEOWNERSHIP TABLE 4 Estimated Mean Impacts on Individual Homeownership Probabilities (1) Chicago Income (per $1000) Age of head (per 10 years) Family size White head (1 if yes) Male head (1 if yes) Two-adult family (1 if yes) Market

0.017’ 0.159* 0.080* 0.102* 0.110* 0.158;

(2) Chicago 0.009’ 0.145* 0.026 0.128 0.130 0.088 1.258*

(3) New York

(4) New York

0.104s 0.075; 0.034* 0.063; - 0.061 0.162*

0.003 0.064* - 0.029’ 0.058 - 0.009 0.108; 1.144’

*Significantly different from zero at the 95% level.

When the market ownership proportion is included as a regressor, the importance of personal characteristics significantly diminishes for both cities. For example, in the New York sample, family income has an insignificant impact on individual homeownership probabilities when (MARKET) is included (Table 4). This suggeststhat once it is known that a family resides in a quality market where in equilibrium 60% of the residences are owner occupied, knowing the family’s income does not tell us if they tend to own or rent. This result is consistent with EMP and is further evidence of the inappropriateness of MBAH. Similarly, the introduction of MARKET eliminates the previously significant impacts of both the race and sex of the household head in both cities, and the impacts of family size and two adult families in the Chicago sample. In fact, only 5 of the 12 personal characteristic parameters (6 for each city) continue to exhibit significant impacts on the individual homeowner probability when MARKET is included in the regression. Further, the magnitudes (in absolute value) of all 5 of these remaining significant (and 5 of the 7 nonsignificant) personal characteristic parameters are reduced when MARKET is included in these regressions. All of these factores are supportive of EMP and reject MBAH equilibrium. However, the continued signi6cance of a number of the personal characteristics when MARKET is a regressor also leads one to reject an EMP equilibrium. Thus, the data reject both extreme special casesof the general model. It should be noted that this rejection of EMP indicates either that the EMP is (1) inappropriate; or (2) relevant but measurement errors in the quality market cells incorrectly cause its rejection. For example, if different quality markets are incorrectly categorized as a single quality market, personal characteristics remain significant determinants of homeownership even when the proportion of homeownership is included as a regressor.This is because the personal characteristics capture the different equilibrium

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homeownership rates in the true markets. Unfortunately, these samples are too small to distinguish whether the rejection of EMP is due to measurement errors or the irrelevance of this special case. It is clear, however, that these data demonstrate the presence of some market sorting and reject MBAH. This suggests that future research should concentrate on other variations of the general model of homeowner&p. VI. SUMMARY AND CONCLUSIONS This paper has developed a simplified general model of the homeownership decision. It was shown that the net full cost advantage of homeownership increases with one’s marginal tax bracket and relative expected tenancy period. It was also noted that the relative production efficiency of landlords is an important determinant of the net full cost advantage of homeownership. Two polar special casesof the general model were specified. The municipal bond analogy model of homeownership assumedthat consumers do not sort into homogeneous markets and hence only a small fraction of the population will be indifferent with respect to tenure status. This special case was contrasted with the efficient market proposition equilibrium where the heterogeneous population completely sorts into a series of internally homogeneous housing quality markets. Both of these special caseswere rejected by an analysis of 1973 data for Chicago and New York City. However, the presence of measurement error may incorrectly cause the EMP to be rejected. The data do indicate that some degree of the market sorting phenomena developed in this paper is present. In conclusion, the general model presented in this paper, and in particular the special case of EMP, does suggest a new and different approach to the homeownership decision. Further, the results here clearly demonstrate the inappropriateness of the traditional model at both theoretical and empirical levels. Since the impacts of a wide range of policy decisions depend upon the workings of the housing market, this approach should prove useful in evaluating these policies. Hopefully this paper represents a significant step toward obtaining a more complete understanding of the housing market and the housing tenure decision. APPENDIX: DERIVATION

OF EQUATION 5

The production costs associatedwith a unit of given quality are assumed to be the sum of: (1) mortgage interest payments (M); (2) property tax payments (P); and (3) economic depreciation (D). If it is assumed that relative landlord efficiency takes on a proportional relationship then COST0 = aCOSTL = a(M + P + D),

a > 0.

(Al)

ECONOMIC ANALYSIS OF HOMEOWNERSHIP

245

Mortgage interest payments can be expressed as the product of the mortgage interest rate (m), the loan-to-value ratio (f), and the unit’s value (V) M = mfV.

W)

If economic depreciation is 6 percent of the unit’s value and the local property tax rate is p then COST’ = aCOSTL = aV(mf + p + 6).

(A3)

The closing costs for a landlord are expressed as a proportion, B, of the annualized value of the unit for the time period the landlord expects to hold the unit (m) B > 0.

CLOSEL = z N’

(A4

For a homeowner the closing costs are expressedas a proportion, aB, of the annualized unit value over the owner’s expected tenancy period (N) CLOSE’ = $!, where a reflects relative landlord production efficiency. The primary tax advantage for landlords is that they receive depreciation allowances in excess of economic depreciation. This advantage (net of recapture) is expressed as y of economic depreciation ACC = yW,

y > 0.

W)

For a homeowner the tax subsidies are the deductability of mortgage interest and property tax payments. The value of these deductions depends upon the family’s marginal tax bracket. If landlord relative efficiency applies equally to all elements of the production costs then this tax subsidy is simply SUB = taV(mf + p).

647)

If it is assumed that the pretax opportunity rate of equity return (r) is the same for both landlords and owners the before-tax opportunity cost of equity is DOWNL = DOWN0 = r(1 - f)V.

648)

Finally, the expected capital gain is assumed the same for both landlords and homeowners with an expected rate of capital gain of g, GAINL = GAIN’

= gV(l - f ).

649)

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PETER LINNEMAN

Substituting these expressionsinto (4) yields the parametric the net cost advantage of homeownership shown in (5).

expression

of

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