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Capitalization of interjurisdictional fiscal differentials: An alternative approach
JOURNAL
OF URBAN
ECONOMICS
15,
317-326 (1984)
Capitalization of Interjurisdictional Fiscal Differentials: An Alternative Approach’ BRIAN J. CUSHING Depariment of Economics, West Virginia Universiiy, Morgantown,
West Virginia 26.506
Received August 2,1982; revised October 26,1982 In virtually every study concerning capitalization of fiscal differentials into property values, the unit of observation has been a local jurisdiction or an individual house sale within a jurisdiction. Urban economic theory suggeststhat capitalization of fiscal differentials should be most obvious at the border of two jurisdictions. Housing price differentials between adjacent blocks at the border of two jurisdictions will be used to study capitalization. Such an approach reduces problems associated with measurement of (dishamenities and public services, and with the use of a distance variable in urban areas with multiple employment or recreation centers.
I It has long been recognized that differences in tax burdens and public service provision among local jurisdictions may be capitalized into differences in property values. Since Oates’ [lo] classic article on this topic, there has been a great deal of interest regarding capitalization of interjurisdictional fiscal differentials. An increased understanding of capitalization is important for several reasons. First, the extent of capitalization may provide information regarding the incidence of property taxes: significant capitalization may indicate that property owners bear much of the burden. Second, the extent of public service-tax capitalization is an indicator of the degree to which residential and business location decisions are influenced by local public service and tax levels; this information is critical in the formation of local public policy, particularly in declining central cities. Finally, the existence or nonexistence of capitalization under a variety of circumstances may serve as a test of some of the basic concepts of the bid-rent model of household and business location used by many urban economists. Empirical results regarding the extent of capitalization of interjurisdictional fiscal differentials have been diverse. Using a sample of New Jersey cities, Oates (10, 111 found significant capitalization of educational and noneducational public services as well as nearly complete capitalization of property tax rate differentials. In a recent work using a sample of 39 SMSAs, Follain and Malpezzi [4] found that fiscal surplus (public service expenditures minus taxes per capita) differentials were not capitalized. Of ‘I thank Steven Culler and a referee for comments on earlier drafts. 317 0094~1190/84$3.00 Copyright 0 1984 by Academic Press, Inc. All rights of reproduction in any form reserved.
318
BRIAN J. CUSHING
the many other studies regarding capitalization, some support Oates, some support Follain and Malpezzi, and many fall in between. (See Bloom et al., [l], Edel and Sclar [2], Edelstein [3], Grether and Mieszkowski [5], Hyman and Pasour [7], Ring [8], Noto [9], Rosen and Fullerton [13], Smith [14], Sonstelie and Portney [15], and Wales and Wiens [16]). The purpose of this paper is to explore a different approach to the study of capitalization. In virtually every study of capitalization thus far, the unit of observation has been a local jurisdiction or an individual sale within a jurisdiction. Urban economic theory of residential and business location suggeststhat if capitalization of interjurisdictional fiscal differentials occurs, it should be most obvious at the border of two jurisdictions. Thus, consideration of housing price differentials between adjacent blocks at the border of two jurisdictions will be used to study capitalization. Besides its usefulness as an additional test of the existence and extent of capitalization, this approach has important advantages. First, accessto the central business district (CBD) is not of critical importance using this approach: houses on either side of the border have virtually the same access. This avoids problems of measuring accessto the CBD and accounting for the importance of noncentral employment and recreation locations. Second, this approach reduces the need to measure amenity and public service differentials. For a particular border area, disamenities such as pollution and crime should not vary for houses on opposite sides of the border. Similarly, there should be little difference in the availability of some public services such as police protection and transportation. Due to externalities or measurement problems, it is difficult to quantify differences in provision of these types of public services and disamenities for use in traditional capitalization studies. The relevant urban economic theory for this study is outlined in the next section. Empirical results are presented and discussed in Section III. II Consider a metropolitan area on a flat, featureless plain, consisting of a circular central city of fixed spatial area surrounded by a suburban ring.* All employment is in the CBD which is at a point in the center of the city. Residents occupy all land in the central city and the surrounding ring and commute to the center for employment. All households are identical with respect to income and preferences and are perfectly mobile. Initially, assume that there is no local government sector. In this urban area, the spatial distribution of residents and equilibrium in the housing market are determined by bidding for housing. Bids for housing reflect not only the value of housing services but also the amenities or *The theoretical model is derived from Henderson [6].
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CAPITALIZATION
disamenities associated with particular locations. In the present case, the only location-specific amenity is assumed to be leisure time; leisure time is directly related to accessto the CBD, which affects commuting time. The closer a household is to the CBD, the more leisure time is enjoyed by the household; this results in higher bids for housing as one approaches the CBD. Residents are assumed to work a fixed number of hours. Leisure time is the ftxed number of nonworking hours, T, less time spent commuting, tu, where t is the commuting time per unit distance (there and back) and u is the distance from the CBD; t is constant (there is no congestion). Time cost is the only cost of commuting in the model. The household’s optimization problem can be formally demonstrated. Households maximize utility,
subject to a budget constraint,
Y - PA4 -Pb)W
= 07
(2)
and a time constraint, T - e(u) - tu = 0.
(3)
V(U), e(u), h(u), X(U), and p(u) are, respectively, utility, consumption of leisure, consumption of housing, consumption of other goods, and the price of housing, all at a distance u from the CBD. y is income, and p, is the price of other goods; it is assumed that y and p, do not vary with distance. Demand equations for leisure, housing, and other goods may be derived by maximizing (1) subject to (2) and (3) with respect to x, h, and e. Demands for all three goods vary with distance from the center. Household locational choice is determined by maximizin g (1) subject to (2) and (3) with respect to e(u) and u to obtain the following first-order conditions: -- f3V &=(u)
and
‘=O
[ 1 JP(U) a(u)
-Ah(u)
- yt = 0.
y and h are Lagrange multipliers and are, respectively, the marginal utility of leisure and the marginal utility of income. Combining to solve out y yields the locational equilibrium condition: /+)W
a(u)
= -p (u)t
e
’
320
BRIAN J. CUSHING
where
p,(u) is the monetized value of the marginal utility of leisure and measures the opportunity cost of commuting time. In equilibrium, if a household movesan infinitesimal distance farther from the CBD, the value of the lost leisure, p,(u)t, is exactly offset by a reduction in housing costs, h(u) aP(u)/a(u). The slope of a rent gradient, describing housing prices as a function of distance from the CBD, with utility constant, is obtained by rearranging (4) to get -JPW = -[h(u)]-‘p,(u)t (%4
< 0.
(44
Since an increase in distance from the CBD increasescommuting costs, housing prices decreasewith distance. The height of the equilibrium rent gradient and the location of the outer border of the ring are determined by the price of land in its alternative use (agriculture) as well as by demand and supply conditions in the housing market. In this simple model, equilibrium requires equalization of housing prices at the border of the central city and ring. If housing prices at the border are higher (lower) in the central city than in the ring, residents of the central city (ring) have an incentive to relocate in the ring (central city) by outbidding residents of the ring (central city) for the housing. Equilibrium can be attained only when prices are equal at the border, in which case utility is equalized among households so that no household wants to relocate. Now, suppose that the urban area is divided into local government jurisdictions. The central city is a singlejurisdiction while the ring is divided into many smallerjurisdictions. Each jurisdiction provides a single level of public servicesto its residents and imposesa uniform property tax rate on all housing to finance the public services.All jurisdictions are assumedto have the sametechnology for providing public services. Like housing, leisure, and other goods, demand for public servicesvaries with distance from the CBD. The slope of the public service demand gradient depends on the elasticities of demand for housing and public servicesas well as the slope of the rent gradient. In the relatively large central city, there is a relatively wide range of demandsfor public services. Since a single level of public servicesis provided to all householdsin the central city, most residentsof the central city consumea public servicelevel
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321
different from the one desired. If jurisdictions in the ring are relatively small and provide a diverse set of public service offerings, alI residents of the ring are able to obtain a public service level relatively close to the one desired. Thus, at the border of the central city and ring, residents of the ring have a public service level relatively close to the one desired while residents of the central city have a level that is quite different from the one desired. All else equal, including taxes, residents on the ring side of the border must have a greater level of utility than those on the central city side. As a result, bids for housing in the central city decreasewhile bids for housing in the ring increase. In equilibrium, there will be a housing price differential at the border that assuresequalization of utility among residents. The housing price differential must equal the monetized value of the differences in utility resulting from the consumption of different public service levels (and the resulting differences in consumption of housing and other goods). Likewise, all else equal, including the level of public services, if residents on the central city side of the border pay higher taxes than those on the ring side, then residents of the ring must have a greater level of utility than those on the central city side. In equilibrium, bids for housing on the ring side of the border should exceed those on the central city side by the monetized value of the differences in utility resulting from payment of different tax levels. Since taxes directly affect the budget constraint rather than the utility function, this difference in housing bids is the present value of the differences in expected future tax payments. Allowing for differences in household income and preferences, as well as for location of firms throughout the urban area, complicates the spatial anaiysis; but, it does not alter the conclusion.3 For housing of a given type, the price of housing on the central city side of the border must differ from that on the ring side by the monetized value of the differences in utility resulting from consumption of different public service tax packages.4 Although the current spatial analysis has been restricted to the border of the central city and ring, it should be equally applicable to the borders of other jurisdictions. As long as at least one household or firm in one jurisdiction prefers to be located in another jurisdiction (would have a 31ncomeand preference differences andmetropolitan-wide firm locationarelikely to affect capitalization throughtheireffecton thequalityof the public services demanded and received, aswell ason thetax burdenborne by various groups of households and firms. 4Where two or more households with different preferences and/or incomes bid for the same type of house, the price ditlerential will be the monetized value of the utility differential for the central city household with the greatest preference for the house in the ring. As households with stronger preferences are able to relocate, the value of the remaining differential should decrease. This is consistent with Eklel and S&r’s [2] observation that capitalization should decrease as an urban area approaches equilibrium.
322
BRIAN J. CUSHING
greater level of utility or profit in the other jurisdiction) in the absence of capitalization, then capitalization will occur (see Pauly [12]). III The model discussed above may be tested by regressing the housing price differential at the border of two jurisdictions on housing and neighborhood characteristics, public service differentials, and tax differentials. The dependent variable is the difference in the mean value of owner-occupied units between adjacent central city and ring blocks (VHOUSE). The housing and neighborhood characteristics used are for adjacent central city and ring blocks. They are PLUMBING-the difference in the percentage of owner-occupied units lacking some or all plumbing facilities (a measure of housing quality); ROOMS-the difference in the average number of rooms per owner-occupied unit (a measure of house size); UNIT -the difference in the percentage of total year-round housing units in one unit structures (a proxy for average lot size and for amenities associated with low-density development); BIGUNIT-the difference in the percentage of total year-round housing units in structures of 10 or more units (a proxy for the disamenities associatedwith very high density development); GROUP- the difference in the percentage of the population living in group quarters (a proxy for the disamenities associated with the presence of group facilities); BLACK- ]percentage of the central city block’s population that is black - c] minus ]percentage of the ring block’s population that is black - c] , where c is a constant to be determined by the regression. The form of the BLACK variable is employed to capture two different effects of a larger black population. Taking a neighborhood with few or no blacks, an increase in the black population may depress housing values due to racial prejudice or due to poverty and related externalities that some people associate with the presence of blacks. However, as the black population continues to increase, housing values may eventually increase due to a preference of black people to live with other blacks or due to the necessity of blacks to live with other blacks (as a result of discriminatory zoning). If both of these explanations are valid, then there exists some value for the percentage of the population that is black, c, for which housing values are minimized. The value of c chosen for this study is that which minimizes the sum of squared errors of the regression.’ As suggested above, one advantage of the use of adjacent blocks is that distance, as well as some amenity and public service variables, becomes relatively unimportant. In comparing adjacent blocks, the most important 5c = 0 with a negative estimated coefficient of BLACK would be consistent with the standard hypothesis of only a depressing effect of a larger black population.
CAPITALIZATION
323
public service variable may be the quality of educational services. Adjacent public school systems may provide services of very different quality; and school expenditures make up a large portion of local public expenditures. The quality of library services provided by adjacent library systems may also be quite different; although some sharing may occur near the border. The quality of fire protection may vary for adjacent jurisdictions; factors such as the number of hydrants and water pumping capacity are critical regardless of whether adjacent jurisdictions provide extra equipment and manpower. Also, a city’s fire insurance rating affects premiums for homeowner’s insurance. The public service and tax variables used are for the local jurisdictions governing the adjacent central city and ring blocks. They include TAX-the difference in the natural log of the average of the property tax rates per $1000 of state-equalized valuations for 1967 and 1969; EDUCATION-difference in the natural log of current school expenditures per pupil; LIBRARY-difference in the natural log of library operating expenditures per person served; FIRE-difference in the natural log of fire insurance ratings.6 Significant estimated coefficients for any of the public sector variables will be taken as evidence of capitalization. Consistent public sector data, particularly regarding property tax rates, are difficult to find. Data on average property taxes per $1000 of stateequalized valuations is available for all cities in Michigan. Eighty-six observations from the Detroit, Michigan SMSA are used for this study. Border blocks separated by a geographic feature, such as a river, are excluded. Blocks are also excluded if a feature, such as the presence of a country club, might affect one block more than it would the other. Effects of nearby business and industry locations could not be accounted for; however, blocks with fewer than 10 housing units are excluded. The central city-ring border area approximates the inelastic supply of housing necessary for significant capitalization to occur (a fixed border with virtually no land available for new construction). Data for the housing and neighborhood characteristics, including VHOUSE, are from the U.S. Censusof Housing, Block Statistics, 1970. Data for property tax rates are from the Michigan Statistical Abstract, 1968 and 1970. Education data come from the U.S. Census of Governments, 1967. Library data are from the American Library Directory, 1970. Fire insurance ratings are taken from the Municipal Yearbook, 1969, 1971, and 1976; since
(‘Oates [lo] pointed out that as tax rates increase, further increases should have smaller effects on property values. Likewise, as the quality of public services increases, one might expect diminishing marginal benefits. Thus, the use of natural logs is appropriate for the public-sector variables.
324
BRIAN J. CUSHING TABLE 1 Determinants of Housing Value Differentials Dependent Variable: VHOUSE Explanatory variable CONSTANT BLACK PLUMBING ROOMS UNIT BIGUNIT GROUP TAX EDUCATION LIBRARY FIRE
Expected sign
Estimated coefficient
t Statistic
+ + + + + +
4.02 0.11 0.37 3.57 0.06 0.05 0.10 - 10.04 8.96 2.18 - 4.66
1.46 1.406 0.48 4.45O 2.36“ 1.66 1.30 - 1.346 1.43b 1.63’ - 1.77
Fstatistic = 9.08 “significant at the 0.01 level. bsignificant at the 0.10 level.
fire insurance ratings are conducted infrequently, the rating closest to 1970 is used.’ The equation considered in this paper is just one of a system of simultaneous equations. Right-side endogenous variables include BLACK and the four public-sector variables. Since these variables are likely to be correlated with the disturbance term, two-stage least squares is used for estimation.8 The equation is iterated for the 101 values of c between 0 and 100 inclusive to find the form of BLACK that minimizes the sum of squared errors. The empirical results are presented in Table 1. Most of the estimated coefficients are significant at least at the 10% level, with the expected sign. The sum of squared errors is minimized when c equals 41. This indicates that a larger black population does initially depress property values; however, after reaching about 41% of the population, further increases tend to increase property values. Of the remaining housing and neighborhood characteristics, the estimated coefficients of ROOMS and UNIT are signiticant with the correct signs; this indicates that house size and low-density development significantly increase “‘1” is the best fire insurance rating and “10” the lowest. To fit this study, ratings were transposed as FIRE = 11 - fire insurance rating. ‘A list of instruments is available from the author upon request.
CAPITALIZATION
325
property values. The estimated coefficients of BIGUNIT and GROUP do not have the expected signs. Of greatest interest are the public-sector variables. Since values of the central city public-sector variables are constant for all 86 observations, the estimated coefficients reflect the effect of differences among suburban jurisdictions on the property value differential. The coefficient of TAX indicates that an increase in the average property tax rate from the ring average of 5.1% up to 6.1% would increase VHOUSE (central city property value less ring property value) by about $1798. Given a discount rate of 5% and a 40-year mortgage, full capitalization for a house of average value in the ring ($19,239 for this sample) would yield a change of $1616; the model shows more than full capitalization of tax rate differentials.’ In 1967, education expenditures accounted for 50% of local government expenditures in the Detroit SMSA. Expenditures per pupil amounted to $769 for the 86 ring observations with about one student per household. Given this, a 1% increase in the property tax rate would be expected to increase expenditures per pupil by $96. The estimated coefficient of EDUCATION implies that this would result in a $1054 decrease in VHOUSE (gross of the property tax effect). If library expenditures continued to be about 0.9% of local expenditures with about 3.3 persons per household, the 1% increase in ring property tax rates would increase average library expenditures per person from $3.8 to $4.3; the resulting decrease in VHOUSE is estimated to be $269 (gross of the property tax effect). Together, the increases in educational expenditures and library expenditures offset about 76% of the property tax rate’s effect on property values. The differential in fire insurance rates apparently is not important. The large t statistic with the wrong sign suggeststhat the variable may be picking up effects that have not been captured by the model. The results of the estimation and the calculations above are sensitive to model specification and the assumptions used in the calculations. Also, the statistical results are not as strong as one would like them to be. Some variables, most notably, FIRE, have coefficients with incorrect signs. Several other variables, including the public-sector variables used in the above calculations, have coefficients that are significant only at the 10% level. Therefore, the results must be interpreted with care. Regardless of the exact specification and assumptions used, the model does demonstrate significant capitalization of tax rate, education service, and library service differentials. IV The purpose of this paper was to develop and test an alternative approach to the study of capitalization of fiscal differentials. The urban model ‘For the methodology used, see Oates [lo, pp. 963-9661.
326
BRIAN J. CUSHING
employed may reduce the problems associatedwith measuring public services and amenities; it may also eliminate the problems involved with using a distance variable when there are multiple employment or recreation centers. The empirical results are very plausible and are comparable to those obtained in other studies. While the results are somewhat sensitive to model specification and not quite as robust as they could be, they do indicate roughly full capitalization of tax rates, as well as significant capitalization of education and library services. Further refinement and application of this approach may be fruitful. REFERENCES 1. H. Bloom, H. Brown, and J. Jackson, Residential location and public services, in “Public Needs and Private Behavior in Metropolitan Areas” (J. Jackson, Ed.), Ballinger, Cambridge, Mass. (1975). 2. M. Edel and E. S&r, Taxes, spending and property values: Supply adjustment in a Tiebout-Oates model, J. Pd. Econ., 82, 941-954 (1974). 3. R. Edelstein, The determinants of value in the Philadelphia housing market: A case study of the main line 1967-1969, Rev. Econ. Star., 56, 319-328 (1974). 4. J. Follain, Jr., and S. Malpezzi, The flight to the suburbs: Insights gained from an analysis of central city vs. suburban housing costs, J. Urban Econ., 9, 381-398 (1981). 5. D. M. Grether and P. Mieszkowski, Determinants of real estate values, J. Urban &on., 1, 127-146 (1974). 6. J. V. Henderson, “Economic Theory and the Cities,” Academic Press, New York (1977). 7. D. Hyman and E. C. Pasour, Jr., Real property taxes, local public services, and residential property values, Southern Econ. J., 39, 601-611 (1973). 8. A. J. Ring, Estimating property tax capitalization: A critical comment, J. Pal. Econ., 85, 425-431 (1977). 9. N. A. Noto, The impact of the local public sector on residential property values, 69th P. Ann. C. Tax Nat., 192-200 (1976). 10. W. Oates, The effect of property taxes and local public spending on property values: An empirical study of tax capitalization and the Tiebout hypothesis, J. Pal. Econ., 77, 957-971 (1969). 11. W. Oates, The effect of property taxes and local public spending on property values: A reply and yet further results, J. Pal. Econ., 81, 1004-1008 (1973). 12. M. Pauly, A model of local government expenditure and tax capitalization, J. Pub. Econ., 6, 231-242 (1976). 13. H. Rosen and D. Fullerton, A note on local property tax rates, public benefit levels, and property values, J. Pal. Econ., 85, 433-440 (1977). 14. R. S. Smith, Property tax capitalization in San Francisco, Nat. Tax J., 23,177-191 (1970). 15. J. Sonstelie and P. Portney, Gross rents and market values: Testing the implications of the Tiebout hypothesis, J. Urban Econ., 7, 102-118 (1980). 16. T. J. Wales and E. G. Wiens, Capitalization of residential property taxes: An empirical study, Rev. Econ. Statist., 56, 329-333 (1974).
OF URBAN
ECONOMICS
15,
317-326 (1984)
Capitalization of Interjurisdictional Fiscal Differentials: An Alternative Approach’ BRIAN J. CUSHING Depariment of Economics, West Virginia Universiiy, Morgantown,
West Virginia 26.506
Received August 2,1982; revised October 26,1982 In virtually every study concerning capitalization of fiscal differentials into property values, the unit of observation has been a local jurisdiction or an individual house sale within a jurisdiction. Urban economic theory suggeststhat capitalization of fiscal differentials should be most obvious at the border of two jurisdictions. Housing price differentials between adjacent blocks at the border of two jurisdictions will be used to study capitalization. Such an approach reduces problems associated with measurement of (dishamenities and public services, and with the use of a distance variable in urban areas with multiple employment or recreation centers.
I It has long been recognized that differences in tax burdens and public service provision among local jurisdictions may be capitalized into differences in property values. Since Oates’ [lo] classic article on this topic, there has been a great deal of interest regarding capitalization of interjurisdictional fiscal differentials. An increased understanding of capitalization is important for several reasons. First, the extent of capitalization may provide information regarding the incidence of property taxes: significant capitalization may indicate that property owners bear much of the burden. Second, the extent of public service-tax capitalization is an indicator of the degree to which residential and business location decisions are influenced by local public service and tax levels; this information is critical in the formation of local public policy, particularly in declining central cities. Finally, the existence or nonexistence of capitalization under a variety of circumstances may serve as a test of some of the basic concepts of the bid-rent model of household and business location used by many urban economists. Empirical results regarding the extent of capitalization of interjurisdictional fiscal differentials have been diverse. Using a sample of New Jersey cities, Oates (10, 111 found significant capitalization of educational and noneducational public services as well as nearly complete capitalization of property tax rate differentials. In a recent work using a sample of 39 SMSAs, Follain and Malpezzi [4] found that fiscal surplus (public service expenditures minus taxes per capita) differentials were not capitalized. Of ‘I thank Steven Culler and a referee for comments on earlier drafts. 317 0094~1190/84$3.00 Copyright 0 1984 by Academic Press, Inc. All rights of reproduction in any form reserved.
318
BRIAN J. CUSHING
the many other studies regarding capitalization, some support Oates, some support Follain and Malpezzi, and many fall in between. (See Bloom et al., [l], Edel and Sclar [2], Edelstein [3], Grether and Mieszkowski [5], Hyman and Pasour [7], Ring [8], Noto [9], Rosen and Fullerton [13], Smith [14], Sonstelie and Portney [15], and Wales and Wiens [16]). The purpose of this paper is to explore a different approach to the study of capitalization. In virtually every study of capitalization thus far, the unit of observation has been a local jurisdiction or an individual sale within a jurisdiction. Urban economic theory of residential and business location suggeststhat if capitalization of interjurisdictional fiscal differentials occurs, it should be most obvious at the border of two jurisdictions. Thus, consideration of housing price differentials between adjacent blocks at the border of two jurisdictions will be used to study capitalization. Besides its usefulness as an additional test of the existence and extent of capitalization, this approach has important advantages. First, accessto the central business district (CBD) is not of critical importance using this approach: houses on either side of the border have virtually the same access. This avoids problems of measuring accessto the CBD and accounting for the importance of noncentral employment and recreation locations. Second, this approach reduces the need to measure amenity and public service differentials. For a particular border area, disamenities such as pollution and crime should not vary for houses on opposite sides of the border. Similarly, there should be little difference in the availability of some public services such as police protection and transportation. Due to externalities or measurement problems, it is difficult to quantify differences in provision of these types of public services and disamenities for use in traditional capitalization studies. The relevant urban economic theory for this study is outlined in the next section. Empirical results are presented and discussed in Section III. II Consider a metropolitan area on a flat, featureless plain, consisting of a circular central city of fixed spatial area surrounded by a suburban ring.* All employment is in the CBD which is at a point in the center of the city. Residents occupy all land in the central city and the surrounding ring and commute to the center for employment. All households are identical with respect to income and preferences and are perfectly mobile. Initially, assume that there is no local government sector. In this urban area, the spatial distribution of residents and equilibrium in the housing market are determined by bidding for housing. Bids for housing reflect not only the value of housing services but also the amenities or *The theoretical model is derived from Henderson [6].
319
CAPITALIZATION
disamenities associated with particular locations. In the present case, the only location-specific amenity is assumed to be leisure time; leisure time is directly related to accessto the CBD, which affects commuting time. The closer a household is to the CBD, the more leisure time is enjoyed by the household; this results in higher bids for housing as one approaches the CBD. Residents are assumed to work a fixed number of hours. Leisure time is the ftxed number of nonworking hours, T, less time spent commuting, tu, where t is the commuting time per unit distance (there and back) and u is the distance from the CBD; t is constant (there is no congestion). Time cost is the only cost of commuting in the model. The household’s optimization problem can be formally demonstrated. Households maximize utility,
subject to a budget constraint,
Y - PA4 -Pb)W
= 07
(2)
and a time constraint, T - e(u) - tu = 0.
(3)
V(U), e(u), h(u), X(U), and p(u) are, respectively, utility, consumption of leisure, consumption of housing, consumption of other goods, and the price of housing, all at a distance u from the CBD. y is income, and p, is the price of other goods; it is assumed that y and p, do not vary with distance. Demand equations for leisure, housing, and other goods may be derived by maximizing (1) subject to (2) and (3) with respect to x, h, and e. Demands for all three goods vary with distance from the center. Household locational choice is determined by maximizin g (1) subject to (2) and (3) with respect to e(u) and u to obtain the following first-order conditions: -- f3V &=(u)
and
‘=O
[ 1 JP(U) a(u)
-Ah(u)
- yt = 0.
y and h are Lagrange multipliers and are, respectively, the marginal utility of leisure and the marginal utility of income. Combining to solve out y yields the locational equilibrium condition: /+)W
a(u)
= -p (u)t
e
’
320
BRIAN J. CUSHING
where
p,(u) is the monetized value of the marginal utility of leisure and measures the opportunity cost of commuting time. In equilibrium, if a household movesan infinitesimal distance farther from the CBD, the value of the lost leisure, p,(u)t, is exactly offset by a reduction in housing costs, h(u) aP(u)/a(u). The slope of a rent gradient, describing housing prices as a function of distance from the CBD, with utility constant, is obtained by rearranging (4) to get -JPW = -[h(u)]-‘p,(u)t (%4
< 0.
(44
Since an increase in distance from the CBD increasescommuting costs, housing prices decreasewith distance. The height of the equilibrium rent gradient and the location of the outer border of the ring are determined by the price of land in its alternative use (agriculture) as well as by demand and supply conditions in the housing market. In this simple model, equilibrium requires equalization of housing prices at the border of the central city and ring. If housing prices at the border are higher (lower) in the central city than in the ring, residents of the central city (ring) have an incentive to relocate in the ring (central city) by outbidding residents of the ring (central city) for the housing. Equilibrium can be attained only when prices are equal at the border, in which case utility is equalized among households so that no household wants to relocate. Now, suppose that the urban area is divided into local government jurisdictions. The central city is a singlejurisdiction while the ring is divided into many smallerjurisdictions. Each jurisdiction provides a single level of public servicesto its residents and imposesa uniform property tax rate on all housing to finance the public services.All jurisdictions are assumedto have the sametechnology for providing public services. Like housing, leisure, and other goods, demand for public servicesvaries with distance from the CBD. The slope of the public service demand gradient depends on the elasticities of demand for housing and public servicesas well as the slope of the rent gradient. In the relatively large central city, there is a relatively wide range of demandsfor public services. Since a single level of public servicesis provided to all householdsin the central city, most residentsof the central city consumea public servicelevel
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different from the one desired. If jurisdictions in the ring are relatively small and provide a diverse set of public service offerings, alI residents of the ring are able to obtain a public service level relatively close to the one desired. Thus, at the border of the central city and ring, residents of the ring have a public service level relatively close to the one desired while residents of the central city have a level that is quite different from the one desired. All else equal, including taxes, residents on the ring side of the border must have a greater level of utility than those on the central city side. As a result, bids for housing in the central city decreasewhile bids for housing in the ring increase. In equilibrium, there will be a housing price differential at the border that assuresequalization of utility among residents. The housing price differential must equal the monetized value of the differences in utility resulting from the consumption of different public service levels (and the resulting differences in consumption of housing and other goods). Likewise, all else equal, including the level of public services, if residents on the central city side of the border pay higher taxes than those on the ring side, then residents of the ring must have a greater level of utility than those on the central city side. In equilibrium, bids for housing on the ring side of the border should exceed those on the central city side by the monetized value of the differences in utility resulting from payment of different tax levels. Since taxes directly affect the budget constraint rather than the utility function, this difference in housing bids is the present value of the differences in expected future tax payments. Allowing for differences in household income and preferences, as well as for location of firms throughout the urban area, complicates the spatial anaiysis; but, it does not alter the conclusion.3 For housing of a given type, the price of housing on the central city side of the border must differ from that on the ring side by the monetized value of the differences in utility resulting from consumption of different public service tax packages.4 Although the current spatial analysis has been restricted to the border of the central city and ring, it should be equally applicable to the borders of other jurisdictions. As long as at least one household or firm in one jurisdiction prefers to be located in another jurisdiction (would have a 31ncomeand preference differences andmetropolitan-wide firm locationarelikely to affect capitalization throughtheireffecton thequalityof the public services demanded and received, aswell ason thetax burdenborne by various groups of households and firms. 4Where two or more households with different preferences and/or incomes bid for the same type of house, the price ditlerential will be the monetized value of the utility differential for the central city household with the greatest preference for the house in the ring. As households with stronger preferences are able to relocate, the value of the remaining differential should decrease. This is consistent with Eklel and S&r’s [2] observation that capitalization should decrease as an urban area approaches equilibrium.
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greater level of utility or profit in the other jurisdiction) in the absence of capitalization, then capitalization will occur (see Pauly [12]). III The model discussed above may be tested by regressing the housing price differential at the border of two jurisdictions on housing and neighborhood characteristics, public service differentials, and tax differentials. The dependent variable is the difference in the mean value of owner-occupied units between adjacent central city and ring blocks (VHOUSE). The housing and neighborhood characteristics used are for adjacent central city and ring blocks. They are PLUMBING-the difference in the percentage of owner-occupied units lacking some or all plumbing facilities (a measure of housing quality); ROOMS-the difference in the average number of rooms per owner-occupied unit (a measure of house size); UNIT -the difference in the percentage of total year-round housing units in one unit structures (a proxy for average lot size and for amenities associated with low-density development); BIGUNIT-the difference in the percentage of total year-round housing units in structures of 10 or more units (a proxy for the disamenities associatedwith very high density development); GROUP- the difference in the percentage of the population living in group quarters (a proxy for the disamenities associated with the presence of group facilities); BLACK- ]percentage of the central city block’s population that is black - c] minus ]percentage of the ring block’s population that is black - c] , where c is a constant to be determined by the regression. The form of the BLACK variable is employed to capture two different effects of a larger black population. Taking a neighborhood with few or no blacks, an increase in the black population may depress housing values due to racial prejudice or due to poverty and related externalities that some people associate with the presence of blacks. However, as the black population continues to increase, housing values may eventually increase due to a preference of black people to live with other blacks or due to the necessity of blacks to live with other blacks (as a result of discriminatory zoning). If both of these explanations are valid, then there exists some value for the percentage of the population that is black, c, for which housing values are minimized. The value of c chosen for this study is that which minimizes the sum of squared errors of the regression.’ As suggested above, one advantage of the use of adjacent blocks is that distance, as well as some amenity and public service variables, becomes relatively unimportant. In comparing adjacent blocks, the most important 5c = 0 with a negative estimated coefficient of BLACK would be consistent with the standard hypothesis of only a depressing effect of a larger black population.
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public service variable may be the quality of educational services. Adjacent public school systems may provide services of very different quality; and school expenditures make up a large portion of local public expenditures. The quality of library services provided by adjacent library systems may also be quite different; although some sharing may occur near the border. The quality of fire protection may vary for adjacent jurisdictions; factors such as the number of hydrants and water pumping capacity are critical regardless of whether adjacent jurisdictions provide extra equipment and manpower. Also, a city’s fire insurance rating affects premiums for homeowner’s insurance. The public service and tax variables used are for the local jurisdictions governing the adjacent central city and ring blocks. They include TAX-the difference in the natural log of the average of the property tax rates per $1000 of state-equalized valuations for 1967 and 1969; EDUCATION-difference in the natural log of current school expenditures per pupil; LIBRARY-difference in the natural log of library operating expenditures per person served; FIRE-difference in the natural log of fire insurance ratings.6 Significant estimated coefficients for any of the public sector variables will be taken as evidence of capitalization. Consistent public sector data, particularly regarding property tax rates, are difficult to find. Data on average property taxes per $1000 of stateequalized valuations is available for all cities in Michigan. Eighty-six observations from the Detroit, Michigan SMSA are used for this study. Border blocks separated by a geographic feature, such as a river, are excluded. Blocks are also excluded if a feature, such as the presence of a country club, might affect one block more than it would the other. Effects of nearby business and industry locations could not be accounted for; however, blocks with fewer than 10 housing units are excluded. The central city-ring border area approximates the inelastic supply of housing necessary for significant capitalization to occur (a fixed border with virtually no land available for new construction). Data for the housing and neighborhood characteristics, including VHOUSE, are from the U.S. Censusof Housing, Block Statistics, 1970. Data for property tax rates are from the Michigan Statistical Abstract, 1968 and 1970. Education data come from the U.S. Census of Governments, 1967. Library data are from the American Library Directory, 1970. Fire insurance ratings are taken from the Municipal Yearbook, 1969, 1971, and 1976; since
(‘Oates [lo] pointed out that as tax rates increase, further increases should have smaller effects on property values. Likewise, as the quality of public services increases, one might expect diminishing marginal benefits. Thus, the use of natural logs is appropriate for the public-sector variables.
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BRIAN J. CUSHING TABLE 1 Determinants of Housing Value Differentials Dependent Variable: VHOUSE Explanatory variable CONSTANT BLACK PLUMBING ROOMS UNIT BIGUNIT GROUP TAX EDUCATION LIBRARY FIRE
Expected sign
Estimated coefficient
t Statistic
+ + + + + +
4.02 0.11 0.37 3.57 0.06 0.05 0.10 - 10.04 8.96 2.18 - 4.66
1.46 1.406 0.48 4.45O 2.36“ 1.66 1.30 - 1.346 1.43b 1.63’ - 1.77
Fstatistic = 9.08 “significant at the 0.01 level. bsignificant at the 0.10 level.
fire insurance ratings are conducted infrequently, the rating closest to 1970 is used.’ The equation considered in this paper is just one of a system of simultaneous equations. Right-side endogenous variables include BLACK and the four public-sector variables. Since these variables are likely to be correlated with the disturbance term, two-stage least squares is used for estimation.8 The equation is iterated for the 101 values of c between 0 and 100 inclusive to find the form of BLACK that minimizes the sum of squared errors. The empirical results are presented in Table 1. Most of the estimated coefficients are significant at least at the 10% level, with the expected sign. The sum of squared errors is minimized when c equals 41. This indicates that a larger black population does initially depress property values; however, after reaching about 41% of the population, further increases tend to increase property values. Of the remaining housing and neighborhood characteristics, the estimated coefficients of ROOMS and UNIT are signiticant with the correct signs; this indicates that house size and low-density development significantly increase “‘1” is the best fire insurance rating and “10” the lowest. To fit this study, ratings were transposed as FIRE = 11 - fire insurance rating. ‘A list of instruments is available from the author upon request.
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property values. The estimated coefficients of BIGUNIT and GROUP do not have the expected signs. Of greatest interest are the public-sector variables. Since values of the central city public-sector variables are constant for all 86 observations, the estimated coefficients reflect the effect of differences among suburban jurisdictions on the property value differential. The coefficient of TAX indicates that an increase in the average property tax rate from the ring average of 5.1% up to 6.1% would increase VHOUSE (central city property value less ring property value) by about $1798. Given a discount rate of 5% and a 40-year mortgage, full capitalization for a house of average value in the ring ($19,239 for this sample) would yield a change of $1616; the model shows more than full capitalization of tax rate differentials.’ In 1967, education expenditures accounted for 50% of local government expenditures in the Detroit SMSA. Expenditures per pupil amounted to $769 for the 86 ring observations with about one student per household. Given this, a 1% increase in the property tax rate would be expected to increase expenditures per pupil by $96. The estimated coefficient of EDUCATION implies that this would result in a $1054 decrease in VHOUSE (gross of the property tax effect). If library expenditures continued to be about 0.9% of local expenditures with about 3.3 persons per household, the 1% increase in ring property tax rates would increase average library expenditures per person from $3.8 to $4.3; the resulting decrease in VHOUSE is estimated to be $269 (gross of the property tax effect). Together, the increases in educational expenditures and library expenditures offset about 76% of the property tax rate’s effect on property values. The differential in fire insurance rates apparently is not important. The large t statistic with the wrong sign suggeststhat the variable may be picking up effects that have not been captured by the model. The results of the estimation and the calculations above are sensitive to model specification and the assumptions used in the calculations. Also, the statistical results are not as strong as one would like them to be. Some variables, most notably, FIRE, have coefficients with incorrect signs. Several other variables, including the public-sector variables used in the above calculations, have coefficients that are significant only at the 10% level. Therefore, the results must be interpreted with care. Regardless of the exact specification and assumptions used, the model does demonstrate significant capitalization of tax rate, education service, and library service differentials. IV The purpose of this paper was to develop and test an alternative approach to the study of capitalization of fiscal differentials. The urban model ‘For the methodology used, see Oates [lo, pp. 963-9661.
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employed may reduce the problems associatedwith measuring public services and amenities; it may also eliminate the problems involved with using a distance variable when there are multiple employment or recreation centers. The empirical results are very plausible and are comparable to those obtained in other studies. While the results are somewhat sensitive to model specification and not quite as robust as they could be, they do indicate roughly full capitalization of tax rates, as well as significant capitalization of education and library services. Further refinement and application of this approach may be fruitful. REFERENCES 1. H. Bloom, H. Brown, and J. Jackson, Residential location and public services, in “Public Needs and Private Behavior in Metropolitan Areas” (J. Jackson, Ed.), Ballinger, Cambridge, Mass. (1975). 2. M. Edel and E. S&r, Taxes, spending and property values: Supply adjustment in a Tiebout-Oates model, J. Pd. Econ., 82, 941-954 (1974). 3. R. Edelstein, The determinants of value in the Philadelphia housing market: A case study of the main line 1967-1969, Rev. Econ. Star., 56, 319-328 (1974). 4. J. Follain, Jr., and S. Malpezzi, The flight to the suburbs: Insights gained from an analysis of central city vs. suburban housing costs, J. Urban Econ., 9, 381-398 (1981). 5. D. M. Grether and P. Mieszkowski, Determinants of real estate values, J. Urban &on., 1, 127-146 (1974). 6. J. V. Henderson, “Economic Theory and the Cities,” Academic Press, New York (1977). 7. D. Hyman and E. C. Pasour, Jr., Real property taxes, local public services, and residential property values, Southern Econ. J., 39, 601-611 (1973). 8. A. J. Ring, Estimating property tax capitalization: A critical comment, J. Pal. Econ., 85, 425-431 (1977). 9. N. A. Noto, The impact of the local public sector on residential property values, 69th P. Ann. C. Tax Nat., 192-200 (1976). 10. W. Oates, The effect of property taxes and local public spending on property values: An empirical study of tax capitalization and the Tiebout hypothesis, J. Pal. Econ., 77, 957-971 (1969). 11. W. Oates, The effect of property taxes and local public spending on property values: A reply and yet further results, J. Pal. Econ., 81, 1004-1008 (1973). 12. M. Pauly, A model of local government expenditure and tax capitalization, J. Pub. Econ., 6, 231-242 (1976). 13. H. Rosen and D. Fullerton, A note on local property tax rates, public benefit levels, and property values, J. Pal. Econ., 85, 433-440 (1977). 14. R. S. Smith, Property tax capitalization in San Francisco, Nat. Tax J., 23,177-191 (1970). 15. J. Sonstelie and P. Portney, Gross rents and market values: Testing the implications of the Tiebout hypothesis, J. Urban Econ., 7, 102-118 (1980). 16. T. J. Wales and E. G. Wiens, Capitalization of residential property taxes: An empirical study, Rev. Econ. Statist., 56, 329-333 (1974).