WORKING PAPER NO

Transcription

1 FEDERALRESERVE BANK OF PHILADELPHIA Ten Independene Mall Philadelphia, Pennsylvania (215) , Working Papers Researh Department WORKING PAPER NO Does the U.S. Tax Treatment of Housing Promote Suburbanization and Central City Deline? Joseph Gyourko and Rihard Voith Latest Draft: September 17, 1997

2 WORKING PAPER NO Does the U.S. Tax Treatment of Housing Promote Suburbanization and Central City Deline? a b Joseph Gyourko and Rihard Voith Latest Draft: September 17, 1997 a Real Estate and Finane Departments, The Wharton Shool, University of Pennsylvania b Researh Department, Federal Reserve Bank of Philadelphia The views expressed in this paper do not neessarily reflet those of the of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System.

3 ABSTRACT This paper examines the role of U.S. housing-related tax expenditures in reating inentives for deentralization and enouraging residential sorting by inome and entral ity deline. Tax expenditures assoiated with the dedutibility of mortgage interest and property taxes make housing less expensive relative to other goods and, hene, inrease the quantity of housing and residential land purhased and lower the density of urban areas. Beause the tax expenditures inrease with inome and the onsumption of housing servies, they lower the ost of geographi sorting by inome typially assoiated with exlusionary zoning and other landmarket imperfetions. A diret onsequene of this sorting proess is that housing-related tax expenditures are onentrated on ommunities with the highest inomes and house values. These effets do not arise simply beause of housing-tax poliies alone, but rather from the interation of these poliies and other fators that affet loal real estate markets, suh as zoning or fixed housing apital stoks. Three models are developed to formally analyze these issues. In our base ase model in whih there are no land-use onstraints and loal amenities are fixed, tax dedutions related to home ownership result in population deentralization within the metropolitan area and a less dense entral ity, but do not indue sorting by inome. Moreover, land pries in the ity inrease beause the subsidy inreases the aggregate demand for housing in all ommunities. Thus, the mere presene of the federal housing tax expenditures inreases deentralization, but annot generate Ameria s patterns of inome sorting and entral ity deline. These onlusions hange in an important way in our seond model in whih a land-use onstraint, suh as the type of minimum lot size zoning prevalent in the suburbs, is introdued. In this ase, the housing subsidies foster the separation of the rih from the poor. Inome sorting results, and onsequently, there is an inreasing onentration of the poor in the entral ity. However, there still is no weakening of pries in ity land markets in this model. Our third and final model endogenizes the prodution of loal amenities in the sense that they are made an inreasing funtion of ommunity inome. In this ase, three harateristis ommon to Amerian urban form result: population deentralization within the metropolitan area, inreased onentration of the poor in the urban ore, and weak ity land markets. These results indiate that Ameria s urrent urban form reflets, at least in part, inentives arising from the interation of the national tax and loal zoning systems, rather than unique Amerian tastes for low-density living environments.

4 I. Introdution Compared with their ounterparts in the developed world, U.S. metropolitan areas are haraterized by greater population deentralization, less dense entral ities, and more extreme residential sorting by inome aross the metropolitan area. The latter feature in partiular is assoiated with the soioeonomi deline of many of Ameria s larger entral ities (Mills and Lubuele (1997). The traditional Mills-Muth-Alonzo (MMA) monoentri urban model offers a ompelling argument that the proess of deentralization is driven by inreasing household inome and delining transportation osts. The MMA model does not, however, offer a similarly ompelling explanation for residential stratifiation by inome or entral ity deline. Often, researhers laim that Amerians show unique preferenes for low density living to explain the 1 spatial sorting by inome that so haraterizes Ameria s urban form. 1 The reliane on preferenes an be seen in the following passage from Mieszkowski and Mills (1993):...The older, smaller, entrally loated units, built when average real inomes were lower, filter down to lower inome groups. This natural working of the housing market leads to inome stratified neighborhoods, and there is a tendeny for low inome groups to live in entral loations and for affluent households to reside in outlying suburban areas. The majority of the middle lass apparently prefers larger single family lots in the suburbs to denser multi-family residenes in the entral ity." (emphasis added) (p.136). Note that in the absene of this exogenous preferene assumption, sorting by inome in the traditional monoentri model would not our beause pries of more entrally loated houses would simply fall until higher-inome residents were indifferent aross loations. [This assumes that the housing stok an be adjusted to math the demands of the higher-inome residents.] While loal zoning powers and Tiebout-type differenes in demand for loally provided publi goods an aount for sorting (see Cassidy and Epple (1994, for example)), the belief that the typial Amerian is fundamentally different from her foreign ounterparts in terms of preferenes for housing and living arrangements is widespread. Arhitet and urbanologist Witold Rybzynski begins his reent book City Life by quoting a friend who asks why Amerian ities are not like European ities (Paris, to be exat). While proeeding to provide a history 1

5 Rather than making an appeal to unique Amerian preferenes, this paper presents a series of models showing how publi poliy, through its interation with ommon features of the housing market suh as minimum lot-size zoning, an reate inentives for deentralization, residential sorting by inome, and entral ity deline. The fous is on the role of U.S. tax oderelated subsidies to housing, but the models apply to any poliy that an materially affet the spatial prie pattern differentially aross households by inome. Tax expenditures assoiated with the dedutibility of mortgage interest and property taxes 2 are extremely large, almost $70 billion in 1996 alone, and there is good reason to suspet they have helped the proess of deentralization. The dedution of mortgage interest and property taxes makes housing less expensive relative to other goods and, hene, inreases the quantity of housing purhased (Mills (1987), Feldstein (1982), Hendershott (1982)). If residential land use is an inreasing funtion of quantity of housing servies demanded, an inrease in suh subsidies will result in more land onsumed per household and less densely developed urban areas. Thus, these tax expenditures reinfore the basi eonomi fores for deentralization suggested by the MMA model. The potential effets of housing-related tax expenditures extend beyond reinforing the proess of deentralization. A key aspet of these impliit subsidies is that they vary aross households along inome lines. Beause the tax expenditures inrease with inome and the onsumption of housing servies, they lower the ost of geographi sorting by inome typially ontrasting ity development in the Old and New Worlds, Rybzynski s answer to his friend s query essentially boils down to the different preferenes of Amerians in these regards. 2 Soure: Statistial Abstrat of the United States, 1996, Table No. 518: Tax Expenditures, by Funtion 1994 to 1997." 2

6 assoiated with exlusionary zoning and other land-market imperfetions. The tax expenditures not only allow high-inome individuals to onsume more housing in exlusive ommunities, but they also redue ommunities osts of setting large minimum lot size requirements to more effetively sort. A diret onsequene of this sorting proess is that housing-related tax expenditures are onentrated on ommunities with the highest inomes and house values. To the extent that loal amenities are assoiated with ommunity inome levels, housing subsidies not only finane sorting by inome level but also foster delining land values in ommunities with a disproportionately high number of low inome residents. These onsequenes are amplified by an inome effet assoiated with the fat that the bulk of the housing-related tax expenditures is reaped in areas with high inomes and high house pries. These sorting effets arise, not from inentives in the tax treatment of housing alone, but rather from the interation of these inentives with other features of the housing market. For example, in our base ase model in whih there are no land-use onstraints (suh as zoning or fixed housing apital stoks) and loal amenities are fixed, tax dedutions related to home ownership result in population deentralization within the metropolitan area and a less dense entral ity, but do not indue sorting by inome. Moreover, land pries in the ity inrease beause the subsidy inreases the aggregate demand for housing in all ommunities. Thus, the mere presene of the federal housing tax expenditures inreases deentralization, but annot generate Ameria s patterns of inome sorting and entral ity deline. These onlusions hange in an important way in our seond model in whih a land-use onstraint, suh as minimum lot size zoning that is prevalent in the suburbs, is introdued. In 3

7 this ase, the housing subsidies foster the separation of the rih from the poor. Inome sorting results with an inreasing onentration of the poor in the entral ity. However, there still is no weakening of pries in ity land markets in this model. Our third and final model endogenizes the prodution of loal amenities in the sense that 3 they are made an inreasing funtion of ommunity inome. In this ase, three harateristis ommon to Amerian urban form result--population deentralization within the metropolitan area, inreased onentration of the poor in the urban ore, and weak ity land markets. Essentially, the amenity differential between ommunities widens one inome sorting begins, leading to more extreme inome sorting and, under reasonable onditions, depressed ity land markets. These results indiate that Ameria s urrent urban form reflets, at least in part, inentives arising from the interation of the national tax and loal zoning systems, rather than unique Amerian tastes for low-density living environments. As an empirial matter, the extent to whih tax-related housing subsidies ontribute signifiantly to deentralization, sorting by inome, and entral ity deline depends on the magnitude of the subsidy, the extent to whih the housing subsidies lower residential land pries (instead of being apitalized into land pries), and the elastiity of residential land onsumption with respet to the prie of land. As is shown in setion two, housing-related tax expenditures are large, espeially for upper-inome households. With respet to the issue of how muh of the subsidy is passed forward to landowners via apitalization, it is well known that housing markets an adjust along both quantity and prie margins in response to hanging subsidy levels. If the 3 This assumption is onsistent with Yinger s (1986) interesting model in whih sorting by inome has fisal effets that adversely affet the land values and utility in the ommunity that has a larger share of low inome people. 4

8 supply of housing is perfetly inelasti, any housing subsidy will be passed on diretly to the land owner. In this ase, the after-subsidy prie of land would be unhanged, and subsidies would have no effet on the urban form. While there are good reasons to expet housing supply to be relatively inelasti in ities, housing supply should be relatively elasti on the urban fringe (Voith (1996)). Siani (1997) finds relatively small apitalization of federal inome tax hanges into house values. Assuming a disount rate of 9 perent, Siani (1997) alulates that 13 perent of 4 the present disounted value of a permanent tax hange is refleted in the asset prie of housing. The prie elastiity of the residential demand for land is an issue in urgent need of researh so that the effets of the housing-related tax expenditures on urban form an be omputed. The remainder of the paper is organized as follows. Setion two presents evidene on the extent of deentralization, the degree of sorting by inome aross suburbs and entral ities, the magnitudes of housing subsidies for individuals of various inomes and rates of housing onsumption, and the aggregate distribution of housing-related tax expenditures aross suburbs and entral ities. This setion also addresses the roles of pries and preferenes in the proesses of deentralization and sorting. Setion three presents the basi analytial framework for evaluating the spatial and distributional onsequenes of the housing-related tax poliies. Setion four presents the omparative statis of the model, delineating the onditions under whih the tax expenditures essentially finane deentralization, sorting, and entral ity deline. Setion five onludes and raises issues requiring additional theoretial and empirial work. 4 Siani s (1997) result reflets an average aross ity and suburban markets. 5

9 II. Deentralization and Inome Sorting: Pries or Preferenes? With the exeption of those in Australia, U.S. metropolitan areas and their entral ities tend to be less densely populated than their ounterparts in the rest of the developed world. Table 1 shows an international omparison of the density of metropolitan areas and their entral 5 ities. Columns 1 and 2 of Table 1 show metropolitan areas and their densities sorted by metropolitan area density. Columns 3 and 4 show the ities and their densities, this time sorted by ity density. These data learly show that U.S. and Australian metropolitan areas and entral ities are far less dense than their European and Asian ounterparts. Population in metropolitan areas throughout the developed world has been deentralizing th 6 in the seond half of the 20 entury. Many entral ities have experiened not only population delines relative to their suburbs but also absolute population delines as well. This trend has been very strong in the U.S. despite the relatively low initial density of U.S. entral ities. Table 2 douments the hanges in population and relative ity/suburban population shares for the 20 largest U.S. ities that have had no hange in their land area. Beause we have hosen ities whose land area has not hanged over time, hanges in density are the same as hanges in population. With the exeption of Los Angeles, Miami, and Oakland, all of the ities lost population from , resulting in lower densities. Over half of the ities experiened population and density delines of more than 20 perent. The share of metropolitan-area 5 Metropolitan area definitions differ aross ountries, and the underlying definitions of entral ities and metropolitan areas are not always omparable. Newman and Kenworthy (1989) have assembled data on large metropolitan areas and their entral ities that are intended to have broadly omparable definitions for the metropolitan areas and their entral ities. 6 There has been a great deal of researh doumenting the proess of deentralization internationally. See Meiszkowski and Mills (1993) for review of these studies. 6

10 population living in the entral ity delined in every metropolitan area. In all but three areas, the ity s share of population fell more than 20 perent. Not only have most U.S. ities lost population, but all of the entral ities examined systematially lost higher inome residents. Table 3 shows the ratio of ity per apita inome to suburban per apita inome in 1960 and in 1990, as well as the hange in that share from In 1960, ity per apita inomes averaged 93.2 perent of suburban inomes and eight of the 20 ities had higher average per apita inomes than their suburban ounterparts. By 1990, ity per apita inomes averaged only 75.3 perent of suburban per apita inomes and only two ities had average inomes that were greater than or equal to those of their suburban neighbors. City inome relative to suburban inome fell in all 20 ities from As a purely statistial matter apart from the ausal fores investigated in the models below, the population deentralization and sorting by inome aross ity and suburbs evident in Tables 2 and 3 has strong impliations for the distribution of housing-related tax expenditures aross ommunities. Sorting by inome auses differential inidene of housing tax expenditures beause tax-ode-related housing subsidies are muh larger for high-inome households than for lower-inome households. Tax-ode-related housing subsidies are larger for higher-inome households for three reasons: 1) higher-inome households purhase more expensive houses; 2) higher-inome households have higher marginal tax rates; and 3) lower-inome households seldom find it advantageous to use itemized dedutions, whih eliminates the possibility of reeiving the subsidy. To the extent that high- and low-inome households sort into separate ommunities, housing tax expenditures will be skewed towards ommunities with higher-inome residents. 7

11 Table 4 shows the estimated values of mortgage and property tax dedutions for various 7 house values. For a married ouple purhasing a residene worth over $225,000, in just the first year, the value of the dedutions of mortgage interest and property taxes in exess of the standard dedution is estimated to be over 2 perent of home prie. Given that 30-year mortgages amortize slowly, the subsidy rate falls only slightly in the near term even in the absene of releveraging. Hene, the present value of the subsidy stream amounts to a very signifiant fration of purhase prie for owners of relatively expensive housing. The onverse is true for purhasers of relatively inexpensive units. Under reasonable onditions, the sum of ownership-related dedutions on a $75,000 house does not exeed the standard dedution for a married ouple. Thus, there is no effetive subsidy to housing onsumption for married owners of these units. The impliations for the spatial distribution of these subsidies within the metropolitan area are outlined in Tables 5 and 6. Table 5 reports data from the 1990 Census publiation General Housing Charateristis (CH-1-1). Information on the distribution of homes aross the prie distribution is presented for owner-oupied homes inside and outside the entral ities of 8 government-defined metropolitan areas. In 1990, the Census reports that there were 44,045,859 owner-oupied units within metropolitan areas. Of that total, only 14,588,932, or 33 perent, were loated inside the entral ity (or ities) of those metropolitan areas. It is also evident that the majority of the owner-oupied units inside entral ities have values below the $85,000 7 See the Appendix for the details behind these alulations. 8 By restriting the analysis to metropolitan areas, most rural housing units are ignored, making possible a more sensible entral ity-suburban omparison. 8

12 utoff point at whih ownership-related dedutions exeed the standard dedution for a married ouple. Outside entral ities, only 37 perent of the owned units have values below $80,000. Thus, two-thirds of suburban owners reeive some subsidy to housing while less than one-half of ity owners do. Table 6 then reports the aggregate housing subsidies/tax expenditures aruing to entral ity and suburban residents of metropolitan areas given our assumptions for leverage, interest rates, taxpayer status, and marginal tax braket (i.e., those underlying Table 4). Sine the value of annual ownership-related dedutions does not exeed the standard dedution for a married ouple for owners of homes valued at $75,000 or below, the aggregate subsidy to those owners is zero. From Table 4 we know that for an $85,000 home, the value of ownership-related dedutions in exess of the standard dedution is $141 in the first year for a married ouple in the 28% braket. Multipling $141 by the 921,292 entral ity owners and 2,097,099 suburban owners of suh homes yields tax expenditures/housing subsidies of $130,270,689 and $296,529,799, respetively. These subsidies/tax expenditures pale in omparison to those reaped by owners of expensive housing--the bulk of whih arue to suburban property owners. For example, the 11.3 perent of suburban owners of units valued at $250,000 or more reeive $40.4 billion in subsidy--69 perent of the total reeived by all owners in the suburbs. In the ity, the 7.7 perent of owners who reside in units valued at more than $250,000 reeive $13.5 billion in subsidies to housing onsumption--71 perent of all subsidies reeived by entral ity homeowners. The ex post differenes in housing-related tax expenditures aross ommunities is an indiation of the magnitude of poliy-generated finanial support underlying the urrent spatial 9

13 distribution of population and inome. Housing subsidies of this magnitude that have differential inidene aross ommunities suggest that the deentralized, stratified urban form of Ameria s ities ould be the result of people reating to a prie system profoundly affeted by tax poliy as opposed to a refletion of intrinsi Amerian preferenes for low density, stratified ommunities. The extent to whih differenes in urban form aross nations reflet preferenes as opposed to priing differentials is an extremely important question beause the answer largely determines whether and how the government should at to shape urban development. For example, Meiszkowski and Mills (1993) write that "...if households prefer to live in low density suburbs, and to use automobiles as their primary means of intra-urban transportation, the publi setor should validate these preferenes with the appropriate highway and infrastruture investments." (p.144). However, they go on to note that fisal distortions affeting loation deisions ould lead to a very different onlusion. Hene, it is important to understand whether publi poliy ould have led to distortions that helped generate the urban form we see in Ameria s metropolitan areas. III. The Analytial Framework The models presented below are in the Tiebout tradition in the sense that distane as represented by aess to the urban ore plays little or no role. While simple, the models apture the entral features of the individual s loation hoie under alternative assumptions regarding the nature of land-use onstraints, the prodution of publi amenities, and urban agglomeration eonomies. The onlusions still hold in a world in whih distane to a entral employment loation is relevant, but they are muh easier to show in a framework without spae. 10

14 Charaterization of the Metropolitan Area There is a single metropolitan area onsisting of two jurisditions indexed by j = (,s), with denoting the entral ity and s denoting the suburban jurisdition. Central ity boundaries are exogenously given and annot be hanged so that the entral ity s land area is fixed in size. In ontrast, unimproved land is assumed to be perfetly elastially supplied in the suburban region. Beause suburban land is perfetly elastially supplied, its prie is equal to the prie of agriultural land plus the value of publi amenities, whih are available only where agriultural land has been onverted to residential use. The two jurisditions are haraterized by their presubsidy house pries, r j, as well as loation-speifi attributes for eah jurisdition, A j. In addition, two types of workers indexed by i=(h,l), with h denoting high skill and l denoting low skill, live in the metropolitan area. Eah group is fixed in size, and high-skill h l workers earn wage w and low-skill workers earn wage w. The distribution of these two groups aross the metropolitan area depends on preferenes, equilibrium pries and amenities, and housing subsidies. Charaterization of the Housing Subsidy The mortgage interest and property tax dedutions lower the after-tax prie of housing. The value of the dedution for any individual depends on whether the individual finds it advantageous to use itemized dedutions, on her marginal tax rate, and on her level of housing onsumption. Generally, the dedution is of higher value for higher-inome individuals. For i simpliity, we speify the mortgage interest and property tax dedutions as a subsidy,, defined as the fration of the house prie paid by the government. It is also presumed that the level of the standard dedution and the progressivity of the tax ode ombine to funtion so that the housing 11

15 h l subsidy is available only to high-skill workers. Thus, 0< < 1, with = 0. Preferenes Individuals onsume a market good, x, (whose prie is the numeraire) and housing servies, h j. In addition, utility is derived from loation-speifi amenities, A j. An individual onsumer, k, maximizes utility by hoosing residential loation and optimal quantities of x and i i h given r,, A, and w. More formally, j j j ik i i (1) Max U ( x, h j; A j ) Subjet to: x + (1 - ) r j h j = w. Individuals of a given type are assumed to have idential preferenes over x, h j, and A j, but they differ in their preferenes for ity or suburban loation. The utility funtion is defined suh that ik the indiret utility funtion, V, takes the following form (2) hk h h hk High skill: V = V(r j,, w ; A j) + j lk l lk Low skill: V = V(r j, w ; A j) + j, where V(.) is the systemati omponent of utility and ik j is the inrement to indiret utility assoiated with the hoie of loation j. Note that ik j is normalized suh that it represents the inremental utility assoiated with an individual hoosing a suburban loation. Speifially, let = define the relative idiosynrati preferene for loations and s. ik ik - ik s Loation Choie Beause all onsumers have idential tastes exept for idiosynrati preferenes for ity or suburban living, the marginal onsumer is defined (separately for rih and poor individuals) by that, k i*, satisfying 12

16 i* i i (3) = V - V. s More formally, for eah worker type the marginal onsumer is defined suh that (3 ) h* h h h h = V(r s,, w ; A s) - V(r,, w ; A j) l* l l = V(r s, w ; A s) - V(r, w ; A j). i i* By speifying a density funtion,, for, the fration of rih or poor individuals hoosing ity i i residenes, n, an be determined as a funtion of r, w, and A. j j One further simplifiation is to fous on the differene in amenities, A, rather than the absolute levels of amenities in ity and suburbs. Thus, let A=As-A, with the population distributed as in (4)-(5) n = ( r s, r, A), for i = h, l. Housing Demand i i 9 Given an indiret utility funtion, Roy s identity provides the demand for housing by eah 9 Beause the signs of the first partials of these funtions will be important later, it is helpful to determine them now. Downward-sloping demand implies that the fration of people i hoosing a ity residene delines as ity rents inrease, so that M /Mr = r <0 ; similarly i i M /Mr s= r s >0. Inreases in ity amenities or a redution in suburban amenities should inrease the number of people who hoose ity residenes. Beause A represents suburban i amenities relative to ity amenities, M /MA = A <0. Note also that the fration of either high- or low-skill people living in the entral ity or suburban portion of the metropolitan area is h assumed not to be diretly affeted by beause the housing subsidy applies equally (on a i perentage basis) to any given ity or suburban housing unit. Similarly, w does not affet the population distribution beause wages for individuals of a given type within the single metropolitan area labor market are assumed to be the same in both jurisditions. i 13 i

17 individual. Given the hoies of jurisditions, the aggregate housing demand is a funtion of r, j h h h l l, w, and n j for high-skill individuals and r j, w and n jfor low-skill individuals as shown in equations (6)-(9). h h h h h (6)-(7) H j = H ( r j,, w ; n j), for j=,s ; l l l l 10 (8)-(9) H j = H (r j, w ; n j), for j=,s. Housing Supply Housing servies are assumed to be proportional to developed land. Further, there is no 11 vaant land in the ity beause of another assumption that all land there is developed. Thus, the total supply of housing servies in the ity, H, is fixed. Consequently, the following onstraint applies for the ity portion of the metropolitan area 10 One again, the signs of a variety of marginal effets on housing demand will prove of interest for the omparative stati analysis below. First, the amount of housing onsumed by both high and low skilled workers obviously dereases with inreases in the prie of housing i servies, so that MH /Mr = H i >0 H i r <0 (with the analogous result holding for suburban region). For high skilled individuals who are able to use the mortgage interest dedution, the subsidy to housing onsumption inreases their demand for housing in the entral ity, so that h MH /M =. Finally, ity housing demand is inreasing in wages and in the number of people hoosing to live in the ity, with MH /Mw = >0 and MH /Mn = H w i n >0. i i i H i i i 11 In this model, when population falls in the ity, the remaining ity residents onsume more ity housing servies. Impliitly, we assume that the housing stok adjusts in terms of size of housing to math demand. This is obviously unrealisti in the short run, as housing that does not math onsumer demands is often left vaant. It should be noted, however, that this sort of fixity of ity housing stok will only reinfore the types of results we show later with regard to sorting by inome. 14

18 h (10) H = H + H l IV. Comparative Statis Case 1: Fixed Amenities and Wages, No Lot-Size Constraints The first ase onsidered is the simplest. Wages and amenities are exogenously given i and no land-use onstraints of any type are present. With w and A j exogenously fixed, equations h l h l (4), (5), (6), (8), and (10) form a system of five equations in five variables r, n, n, H, H. Note that r does not adjust in this ase beause agriultural land is perfetly elastially supplied s and amenities are fixed by assumption. To examine the effets of hanging the mortgage interest dedution on loation hoies and housing onsumption by high- and low-skill workers, as well as ity land pries, these equations an be totally differentiated as follows, (11) dn h ' h r dr (12) dn l ' l r dr (13) dh h ' H h d % H h r dr % H h h n dn h 15

19 (14) dh l ' H l r dr % H l dn l l n (15) dh h '&dh l. h l h l Equations (11)-(15) then an be solved for dr /d, dn /d, dn /d, dh /d, and dh /d. [Hereafter, we drop the supersript on, sine it is assumed relevant only for high-skill workers.] Consider first the effets of a hange in subsidies on the prie of housing servies in the ity whih is given by equation (16), (16) dr d '& H l r %H l n l l r H h %H h r %H h n h >0. h r The numerator is learly positive sine the demand for housing inreases with the level of the housing subsidy. With respet to the denominator, beause the demand for housing by eah skill type falls as prie inreases, the first and third terms are negative. The seond and fourth terms are also negative beause housing demand is inreasing in the number of people hoosing the ity, but the number hoosing the ity is dereasing in ity pries. Thus, equation (16) is stritly positive. This is not surprising sine an inrease in housing subsidies inreases the overall demand for housing, whih, in turn, inreases ity pries beause housing in this part of the metropolitan area is inelastily supplied. 16

20 Solving for the effet of housing subsidies on the distribution of high- and low- skill people yields equations (17) and (18), (17)-(18) dn i d ' r dr d < 0 i'h,l. Reall that i r <0 beause fewer people hoose to live in the ity as ity rents inrease. And, equation (16) just showed that inreases in the federal tax subsidy raise ity rents. Thus, a higher housing subsidy redues the number of high- and low-skill workers hoosing to live in the ity. Essentially, the housing subsidy auses everyone to substitute housing for other goods. Beause ity land is in fixed supply, the rising ity pries ause both skill types to shift demand to the suburbs where housing is elastially supplied. However, beause the housing subsidies are usable only by high-skill workers, they have differential effets on housing onsumption aross worker types. For high-skill workers, the effet on ity housing demand is given by equation (19) (19) dh l d ' H l r dr d % H l n l dn l d < 0. Sine the amount of ity housing purhased by a low-skill person falls with inreases in prie l l l (i.e., MH /Mr <0), and inreases with the number of low-skill people in the ity (i.e., MH /Mn >0), both terms of equation (19) are negative. Some low-skill workers end up in the suburbs beause 17

21 the housing subsidy to high-skill workers is driving up ity rents. This leaves aggregate demand by the low skill types lower in the ity. For high-skill workers, the housing subsidy has the opposite effet. From equation (10), (20) dh h d '& dh l d > 0. Even though the housing subsidy redues the number of high-skill people hoosing to live in the ity, housing onsumption by the remaining high-skill workers inreases. This ours beause the after-subsidy prie of housing in the ity falls for this group (even though the market prie of ity housing rises). For this type, fewer people onsume more housing in the ity. In summary, population deentralization within the metropolitan area and a less dense entral ity result from the mortgage interest dedution. However, the federal tax poliy indues no sorting. Not only is there no soioeonomi deline assoiated with an inreasing onentration of the poor in the ity, but high-skill workers end up onsuming more of the ity housing stok as a result of the tax-ode-related housing subsidies. Case 2: Fixed Amenities and Wages, With Lot-Size Constraints The seond ase introdues a ommon suburban land-use restrition in the form of a minimum lot-size requirement for residential development. To help simplify the analysis here, it is assumed that lot-size onstraints exist suh that no low-skill people hoose to live in the 12 suburbs, but the onstraints are not binding for high-skill workers. In other words, high-skill 12 The model would generate the same qualitative results with a weaker assumption. The only requirement is that zoning prelude some low skill workers from hoosing a suburban 18

22 workers earn suffiiently high wages that they always hoose lots at least as large as the onstraint whenever they hoose a suburban site. Low-skill workers, on the other hand, have suffiiently low wages that they never hoose to purhase a lot as large as the minimum in the suburbs. These simplifying assumptions onerning lot size imply the following modifiations to the omparative statis analyzed in Case 1. Equation (12) is no longer relevant, sine low-skill workers never hoose to live in the suburbs, and equation (14) simplifies to: (21) dh l ' H l r dr. Although the signs of the omparative statis are unhanged from those of Case 1, the effets of a housing subsidy on ity rents are greater as shown in equation (22) (22) dr d '& H l r H h %H h r %H h n h > & h r H l r %H l n l l r H h %H h r %H h n h >0. h r The right-most expression in equation (22) is simply that from equation (16) for Case 1. The intuition behind why ity rents are higher in this ase with binding lot size onstraints in the suburbs is that beause low-skill workers annot adjust by hanging loation, the overall demand for ity housing drops less. The larger impat on rent, however, means that more high-skill loation. 19

23 people hoose to leave the ity than otherwise would have ourred (the omparative stati is the same equation as equation (15)). Thus, in the presene of lot-size onstraints, housing subsidies suh as those arising from the mortgage interest dedution to higher inome people foster the separation of the rih from the poor. The rate of loss of ity population is somewhat lower, however, as the ity does not lose the poor. This ase leads to less deentralization, but the predition of sorting by inome aross jurisditions is onsistent with the inreasing onentration of the poor in many entral ities. However, the even higher pries in the ity land market predited by this model are not onsistent with the data in many urban areas. Case 3: Endogenous Amenities, Fixed Wages, with Lot-Size Constraints The prodution of loal publi amenities is endogenous in this ase. Amenities in a jurisdition are assumed to depend on the number of high-skill workers residing in the jurisdition. This is onsistent with amenities being normal goods whose demand inreases with ommunity inome and with the existene of peer group effets in whih high-skill workers positively affet the utility of high- and low-skill workers alike. To examine the effets of endogenously produed amenities, the basi model must be augmented with two additional equations: one that determines the effet of amenities on rent and another that determines the level of amenities. Reall that the prie of suburban residential land is simply the value of agriultural land plus the value of amenities. Suburban residential land pries vary with A as in equation (23) (23) r s ' r(a). 20

24 The level of relative amenities depends on the number of high skilled workers hoosing to live in the ity so that (24) A ' A(n h ). Beause equations (23) and (24) do not arise expliitly from the maximization problem outlined above, some restritions are needed to ensure sensible outomes. In partiular, we assume that inreases in amenities resulting from a greater onentration of high-skill workers do not raise pries so fast as to more than offset the utility from the additional amenities. In other words, the positive effet of A on the fration of people hoosing suburban residenes is always assumed to be greater than or equal to the negative effet on suburban residential hoie resulting from A s positive effet on suburban pries. Mathematially, this an be stated as as $ rs R A A h n. A A n h Totally differentiating equations (4), (6), (8), (10), (23), and (24) results in a system of six l h l equations and six unknowns: r, r s, n, H, H, A. The differential equations for housing demand and supply (equations (13)-(15)) are unhanged but equation (11) now must take into aount hanges in suburban pries and relative amenities as shown in equation (25) (25) dn h ' h r dr % h r s dr % A da. In addition, the total differentials for equations (23) and (24) are given by 21

25 (26) dr s ' R A da (27) da ' A n h dn h. Equations (13), (14), (15), (25), (26), and (27) an be solved for the effets of hanges in housing subsidies on the number of high-skill people hoosing to work in the ity, rents in the ity, relative suburban/ity amenities, and housing onsumption in the ity by high- and low-skill workers. Consider first the effets of housing subsidies on the fration of high-skill workers hoosing to live in the ity. Algebrai manipulation yields: (28) dn h d ' (1 & rs R A A n h & r H h A A h n )(&H h r &H l r ) & r H h n h < 0 The numerator is always negative for reasons disussed in the previous ases. Given the assumptions regarding the relationship among amenities, suburban pries and hoie of residential loation (i.e., as A A n h $ rs R A A n h ), the denominator is always positive. Thus, making amenities a funtion of the per apita wealth of the ommunity does not hange the diretion of this effet. Rather, endogenizing amenities reinfores the effets of the housing 22

26 subsidy beause suburban ommunities beome more attrative while ity ommunities beome less attrative in terms of amenities. Mathematially, (29) da d dn i ' A i n d > 0. Beause the relative position of the suburbs and ity in regard to amenities is endogenous, the effet of housing subsidies on ity pries may be positive or negative. The effet of housing subsidies on ity pries is shown in equation (30) (30) dr d ' H h &H h r &H l r % H h n h &H h r &H l r dn h d < > 0. In the previous two ases, housing pries in the ity unambiguously rose beause overall demand for housing both in the ity and the suburbs rose. In this ase, the inreased exodus of high-skill workers from the ity indued by the housing subsidies lowers the relative attrativeness of the ity s amenities. Thus, the housing subsidy has ountervailing effets on ity pries as represented by the two terms in equation (30). If amenities are strongly sensitive to the omposition of the population, it is possible that the housing subsidy an ause a deline in residential pries in the ity. In sum, this ase predits a number of empirial phenomena ommon in U.S. metropolitan areas: deentralization aompanied by sorting by inome with inreased 23

27 onentrations of the poor in the ity, low amenities in the ity, and relatively low residential pries in the ity. That is, deentralization within the metropolitan area is aompanied by soioeonomi deline and weak ity land markets. V. Conlusions While some stratifiation by inome is predited by the traditional urban eonomi theory of metropolitan area development, the soioeonomi distress of many of our larger ities is not. Deentralization and deline are distint phenomena. The former is assoiated with a loss of population share by the entral ity. The latter is assoiated with inreasing onentrations of poverty and depressed land markets in the entral ity. A primary goal of our models has been to asertain the onditions under whih subsidies to housing onsumption that vary aross households might have helped generate these onditions. This was aomplished by modeling the impat of federal tax poliy as expressed through housing-related dedutions as they interat with suburban zoning onstraints on lot size and loal amenity pakages that are endogenously determined with ommunity demographis. In the absene of effetive lot-size zoning rules, the mortgage interest dedution leads to inreased deentralization but no soioeonomi deline assoiated with sorting by inome and inreased poverty onentrations in the ity. In fat, the pre-subsidy prie of ity housing rises, with housing onsumption in the ity by itemizers also rising beause their after-subsidy housing 13 prie is lower. 13 This may help explain why ity representatives did not vigorously oppose the introdution of the mortgage interest dedution. In the absene of large lot zoning rules in the suburbs (whih did not beome extensive and binding until the late 1960s), this partiular housing subsidy may not have been viewed as espeially harmful to entral ities. Loss of 24

28 The interation of federal tax poliy regarding housing with large-lot zoning in the suburbs was found to be partiularly interesting. The subsidy effetively inreases the net benefits of sorting--beyond those implied by standard motivations to engage in fisally exlusionary zoning. The two poliies ombine to produe deentralization and inreased onentration of the less well off in the ity. If the prodution of amenities is endogenous so that they are a funtion of the loal population, ity land pries an also deline. The more sensitive amenities are to the makeup of the loal population, the greater potential for ollapsing ity land pries. Our theoretial models do not take into aount the likelihood that the housing tax expenditures make it less ostly to introdue exlusionary zoning that would augment the negative onsequenes of the interation between housing tax expenditures and exlusionary zoning. Population deentralization within the metro area, soioeonomi deline in the ity, and weakening ity land markets result from publi poliy that affets pries and the onstraints households fae when making loation and onsumption deisions. Determining the empirial importane of these poliy effets is an important area for future researh. population share should have been antiipated, but with the benefit of greater housing onsumption by the better off remaining in the ity. 25

29 Bibliography Cassidy, Glenn and Dennis Epple, Property Ownership and Tax Struture, Mimeo, July Feldstein, Martin, Inflation, Tax Rules and the Aumulation of Residential and Non- Residential Capital, Sandinavian Journal of Eonomis, vol. 84, No. 2 (1982) pp Hendershott, Patri H., Government Poliies and the Alloation of Capital between Residential and Industrial Uses, National Bureau of Eonomi Researh, Working Paper No. 1036, De Meiszkowski, Peter and Edwin Mills, The Causes of Metropolitan Suburbanization, Journal of Eonomi Perspetives, Vol. 7, no. 3 (Summer 1993): Mills, Edwin, Dividing Up the Investment Pie: Have We Overinvested in Housing? Business Review, Federal Reserve Bank of Philadelphia, Marh-April, Mills, Edwin, and Luan Sende Lubuele, Inner Cities, Journal of Eonomi Literature, Vol. 35, June, 1997, pp Newman, Peter and Jeffrey Kenworthy, Cities and Automobile Dependene: An International Sourebook, Brookfield: Gower Tehnial (1989). Rybzynski, Witold, City Life, Siani, Todd. "Are Tax Reforms Capitalized into House Pries?" in The Effet of Tax Reform on the Owner-Oupied Housing Market, MIT Ph.D thesis, May Voith, Rihard, The Suburban Housing Market: Effets of City and Suburban Employment Growth, Federal Reserve Bank of Philadelphia Working Paper No , Yinger, John, On Fisal Disparities aross Cities, Journal of Urban Eonomis, Vol. 19, May, 1986, pp

30 Appendix Table A1 provides the details of the bak-of-the-envelope-type estimates of the value of ownership-related dedutions for households oupying homes of varying pries. While the alulations are rude, they ably highlight the key onlusion of the table: that the subsidy to housing onsumption, whih must be alulated net of the standard dedution that would apply in any ase, is zero or very small for owners of inexpensive homes and is very large for owners of the most ostly homes. That said, five key assumptions drive the results reported in the table: (1) mortgage size, whih is determined by an assumed 80 perent loan-to-value (LTV) ratio, is reported in olumn two; this probably is a fairly aurate representation of the leverage only on a reently purhased home; (2) mortgage interest rate, whih is assumed to be 8.5 perent on an annual basis; this reflets urrent market onditions, but not those of the past; the interest due during the first year on an 80 perent loan-to-value (LTV) mortgage is reported in olumn three; (3) the effetive property tax rate, whih is assumed to be 1.5 perent, is reported in olumn four; (4) the size of the standard dedution whih varies by taxpayer status in reality; for simpliity in Table 1, all owners are presumed to be married ouples so that the standard dedution of $6550 that applied in 1995 is available; olumn six reports the differene between the sum of the two ownership-related dedutions and $6550; unless this differene is positive, there is no real 14 subsidy to ownership, as the standard dedution will be taken in lieu of the taxpayer itemizing; (5) marginal tax rates, whih range from a low of 15 perent to a high of 39.6 perent, per the 14 A household ould have other dedutions, suh as large medial expenses or a loal wage tax, that lead it to itemize. In suh a ase, the mortgage interest and property taxes would be valued to the extent that the sum of itemized expenses exeeded the standard dedution. That possibility is not modeled in our tables. 27

31 15 urrent tax ode; beause mortgage interest and loal property taxes are dedutible expenses, not tax redits, their value is a funtion of the taxpaying unit s marginal tax rate. Column 8 reports the produt of multiplying the presumed marginal tax rate times the amount of ownership-related dedutions in exess of the standard dedution. For those owners of less expensive homes below $85,000 for whih the sum of ownership-related dedutions is less than the standard dedution, the value is set to zero, indiating that they reeive no subsidy 16 from ownership. For owners of more expensive homes, the value of ownership-related exess dedutions ranges from a low of $141 to $13,840 during the first year of ownership. Column 9 of Table 1 illustrates the size of the subsidy in terms of home prie. Speifially, the value of ownership-related exess dedutions as a perentage of house value are reported. For the owner of an $85,000 home, the first year subsidy amounts to only 0.2 perent of prie ($141/$85,000). However, the first year value of ownership-related dedutions for owners of homes at least $225,000 in value is above 2 perent of home prie. Given the very low initial prinipal paydowns on fully amortizing, 30-year mortgages, these subsidies remain roughly onstant in the first few years of oupany. Unless releveraging ours after that, the value of the subsidy will deline. While the present value of the subsidy stream is diffiult to pin down, there is no doubt that the subsidy is zero for owners of the least expensive homes, is of small to moderate size for those owning the median-pried home, and is quite large for oupiers of relatively expensive housing pried above $150, With various phase-out provisions and the unapping of the Mediare tax, the top marginal rate is higher than 39.6 perent. The analysis abstrats from these details of the tax ode. Suffie it to say that the value of being able to itemize housing-related dedutions inreases with the marginal tax rate. 16 Aording to data from the National Assoiation of Realtors, the median home prie for existing homes in 1995 was $112,

32 Table 1 Central City and Metropolitan Area Density Population per Square Mile (1980) City City Density City Metro Density Perth Phoenix Brisbane Houston Adelaide Brisbane Phoenix Perth Denver Denver Houston Boston Melbourne Adelaide Los Angeles Washington Sydney Detroit Washington San Franiso Boston Melbourne Detroit Chiago Chiago Sydney Toronto Los Angeles Stokholm New York San Franiso Toronto Copenhagen Hamburg Frankfurt Paris Zurih Amsterdam Amsterdam Stokholm West Berlin Zurih Hamburg Frankfurt Brussels Munih Paris West Berlin New York Brussels Vienna Copenhagen Tokyo Vienna Munih Singapore Singapore Tokyo Hong Kong Hong Kong Soure: Newman and Kenworthy (1989). 29