Property tax and urban sprawl: Theory and implications for US cities

Transcription

1 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.1 (1-16) Journal of Urban Economics ( ) Property tax and urban sprawl: Theory and implications for US cities Yan Song a, Yves Zenou b,c,d, a Department of City and Regional Planning, University of North Carolina at Chapel Hill, NC , USA b Research Institute of Industrial Economics, Box 55665, Stockholm, Sweden c GAINS, Université du Maine d CEPR Received 31 October 2005; revised 12 May 2006 Abstract We develop a model that adopts a log-linear utility function with a variable elasticity of substitution greater than one and show that increasing the property tax reduces city size unambiguously. We then test this result using a dataset of effective property tax rates we developed using GIS methods for 448 urbanized areas. The empirical analysis estimates a regression equation relating an urbanized area s size to the property tax rate measure and other control variables such as population, income, agricultural rent, and transportation expenditure. We find that higher property taxes indeed result in smaller cities Elsevier Inc. All rights reserved. JEL classification: H3; H71; R14 Keywords: Urban sprawl; Urban economics; Property tax; Instrumental variables 1. Introduction Urban Sprawl is characterized by scattered and poorly planned low-density development beyond the edge of urbanized areas. Over the past century, US cities have expanded and density per capita has declined drastically. Here are some facts: Nationwide, land consumed for building far outpaces population growth. According to the American Farmland Trust, between 1960 and 1990, the amount of developed land in metropolitan * Corresponding author. addresses: ys@ .unc.edu (Y. Song), yves.zenou@industrialeconomics.se (Y. Zenou) /$ see front matter 2006 Elsevier Inc. All rights reserved. doi: /j.jue

2 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.2 (1-16) 2 Y. Song, Y. Zenou / Journal of Urban Economics ( ) areas more than doubled, while population grew by less than half. For example, between 1970 and 1990, greater Cleveland lost 11 percent of its population, yet developed land grew by 33 percent; the population of greater Chicago increased by 4 percent compared with a 46 percent rise in residential land; Los Angeles population grew by 45 percent while its developed land increased by 300 percent. Between 1982 and 1997, Upstate New York gained 2.6 percent in population but witnessed a 30 percent expansion in urbanized land. Census Bureau figures show that in 1920, the average density of urbanized areas (which includes cities, suburbs, and towns) was 6160 persons per square mile. In 1990, that number had fallen to Urban sprawl is a major concern in many US cities and is associated with a host of economic, social, and environmental consequences. Sprawling development wastes resources by increasing public expenditures to provide infrastructure and services. Urban sprawl increases travel distance and commuting time and low-density development reduces the feasibility of mass transit, thus increasing reliance on private automobile usage. This automobile excess increases pollution, congestion, alienation, and the use of scarce energy resources. Sprawl is also associated with excessive loss of farmland (for overviews on urban sprawl issues, see Brueckner [3], Nechyba and Walsh [14], and Glaeser and Kahn [10]). Urban sprawl cannot be attributed to a single cause. In a recent study by Burchfield et al. [6], ground water availability, temperate climate, rugged terrain, decentralized employment, early public transport infrastructure, uncertainty about metropolitan growth, and unincorporated land in the urban fringe are found to increase sprawl. In addition, the long-standing debate on land taxation and its virtues (George [9], Skaburskis and Tomalty [17]) reveals that the property tax might be one of the potential causes of urban sprawl. The property tax can be viewed as a tax levied at equal rates on both the land and capital embodied in structures while, in a pure land tax, the tax on capital (i.e., improvements) is set to zero. The literature for example, Arnott and MacKinnon [1], Case and Grant [7], Oates and Schwab [15], Mills [13], and Brueckner and Kim [5] provides an abundance of arguments for how property tax may influence land development. Brueckner and Kim [5] provide the only theoretical analysis that incorporates a land market to investigate the connection between urban spatial expansion and the property tax. Specifically, as Brueckner and Kim [5] assert, there are two countervailing effects of the property tax on the spatial sizes of cities. The improvement effect refers to the impact of the property tax in lowering the equilibrium level of improvements chosen by the developer. The lower level of improvements per acre implies a reduction in the intensity of land development and this lower density associated with property tax appears to encourage urban sprawl. On the other hand, the dwelling size effect operates through the property tax s impact on the consumer s choice of dwelling sizes. As the tax on land and structures is partly shifted forward to consumers, dwelling size decreases due to a higher cost of housing floor space. The reduction in dwelling size implies an increase in population density and thus, a decrease in the city s size or spatial extent. In Brueckner and Kim s full analysis, the net effect of the property tax on the spatial extent of a city is ambiguous. A review of the literature indicates that there has been no empirical study that formulates a regression equation relating a city s spatial extent to a property tax measure and other relevant variables. This paper seeks to fill this gap by first proposing a theoretical model of the net effect of the property tax on the spatial extent of cities and then testing it using data collected from a set of urbanized areas in the United States. We first develop a theoretical model that investigates the property tax s effects on urban sprawl. As stated above, the main paper in this literature is that of Brueckner and Kim [5], which shows that for Constant Elasticity of Substitution (CES) preferences with an elasticity of

3 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.3 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 3 substitution greater or equal to one, the relationship between the property tax and urban sprawl is always negative. Here, we use a log-linear utility function, which exhibits variable, rather than constant, elasticity of substitution but where the elasticity also exceeds one. The main feature of our utility function is that it has a zero income elasticity of housing demand but it allows us (contrary to the CES case) to have explicit closed-form solutions. We unambiguously show that increasing the property tax reduces the size of the city and thus, urban sprawl. Our result combined with that of Brueckner and Kim [5] may suggest that, any utility function with elasticity of substitution greater than 1, whether constant or variable, implies the above result. This is pure conjecture but more realistically, our analysis offers one more reason to doubt that the property tax causes sprawl, beyond the results in the previous paper. We then undertake an empirical analysis to test our main theoretical result, namely the negative impact of the property tax on the spatial size of cities. We collect data on effective property tax rates from various taxing jurisdictions and develop a sample of effective tax rates for 448 urbanized areas in the US. In the regression analysis, we also control for the effects of population, income, agricultural rent and commuting costs on the city size. In identifying the impact of the property tax on the spatial size of cities, we use a two-stage least squares (2SLS) regression to correct for the simultaneity problem between the city size and the property tax. Our empirical results confirm the main prediction of the theoretical model: an increase in the property tax reduces the spatial extent of urbanized areas. Section 2 of the paper outlines the theoretical model and Section 3 describes the steps we take to develop a national sample of effective tax rates for urbanized areas in the US. Section 4 describes the data and the empirical test on the impact of property taxes on the spatial extent of cities. The conclusion is presented in Section Theory We now develop our theoretical model in order to examine the connection between the property tax and urban sprawl The model City The city is monocentric, closed and linear where the Central Business District (CBD hereafter) is located as the origin (zero). All land is own by absentee landlords. Firms (land developers) There is a housing industry that has the following production function 1 : Q = H(K,L)= 2 KL (1) where Q is the housing output and L and K are respectively land and capital (or nonland input). This function is increasing and concave in each of its arguments and has constant returns to scale, which implies that the production function can be written as: h(s) = Q L = 2 S (2) 1 Observe that the housing capital K is assumed to be perfectly malleable. This strongly simplifies the analysis since it implies that producers are able to costlessly adjust both their capital and land inputs, and, as a result, the issue of durability of structures is not analyzed here.

4 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.4 (1-16) 4 Y. Song, Y. Zenou / Journal of Urban Economics ( ) where S K/L represents the capital per acre of land or improvements per acre and thus h(s) is the housing output per acre of land. S is also referred to as structural density (Brueckner [2]) and is an index of the height of buildings. The function h(s) defined by (2) is housing output per acre of land, with h (S) > 0 and h (S) < 0. Denote by θ, the property tax rate. Then, each profit maximizing housing developer solves 2 : { max π = RH 2 S (1 + θ)(r + rs) } at each x [0,x f ] (3) S where π is the profit per acre of land, R H is the rental price per unit of housing service q, R is the rent per unit of land (land cost per acre) and r the price of capital (or the cost per unit of S). The city fringe is denoted by x f and x is the distance to the CBD. Consumers/Workers Each household contains one person. Each individual chooses z and q that maximize his/her utility function under the budget constraint, i.e. max z,q s.t. z + R H q = y tx (4) where z and q are, respectively, the consumption of the composite good (whose price is taken as the numeraire) and the dwelling size, y, the common income, and t the pecuniary commuting cost per unit of distance. We assume a quasi-linear utility function, that is: U(z,q)= z + log q. (5) In that case, solving (4) leads to: q = 1 R H (6) z(x,y) = y tx 1. (7) The indirect utility function can thus be written as: u = y tx 1 log R H (8) where u is the utility level obtained in the city, and the bid rent function is given by: R H (x, u) = exp(y tx 1 u). (9) Plugging this value R H (x, u) in q = q(x) gives finally 1 q(x,u) = exp(y tx 1 u). (10) It is important to observe that, even though the housing consumption q is not directly affected by income y (see (6)), 3 it is indirectly affected by income through the land rent (see (10)). Indeed, when income increases, the bid rent increases (see (9)) since people are richer. As a result, because housing is more costly, they consume less land and thus reduce their dwelling size. This seemingly counterintuitive result is due to the fact that we analyze the effect of y on q(x,u) holding u constant. 2 Observe that it does not matter whether the developer or the urban resident pays the property tax θ. The same results would emerge if the residents pay at a rate θ, so that the gross-of-tax rent price is written R H (1 + θ). Then, the developer profit will just be R H h(s) (R + rs), with no tax term showing up. 3 This is because of the log-linear nature of the utility function, which is defined in (5).

5 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.5 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) The equilibrium Plugging (9) in (3), the housing developer s program becomes { } max π = 2 S exp(y tx 1 u) (1 + θ)(r + rs) at each x [0,x f ]. S The first order condition yields: S = and thus exp[2(y tx 1 u)] (1 + θ) 2 r 2 (11) exp(y tx 1 u) h(s) = 2. (12) (1 + θ)r We can now define the population density as D h(s) q(x,u) = 2 (1 + θ)r which is the ratio between square feet of floor space per acre of land and square feet of floor space per dwelling (person). This is a different concept than the structural density or improvements defined by S. As noted above, the improvements (i.e. the intensity of land development) are a measure of building height so a higher S means that developers construct higher buildings, containing more housing floor space per acre of land. On the other hand, a higher population density means that either the housing floor space is higher or the dwelling size is lower. Since H( ) has constant returns to scale, in equilibrium, the housing industry is such that all firms make zero profit at each x, that is exp[2(y tx 1 u)] R(x,u,θ) = (1 + θ) 2. (13) r This equation gives the bid-rent function for land and is found by solving for R in the zero-profit condition, using (11) and (12). We can now formally define the equilibrium. Definition 1. An urban land-use equilibrium in a linear and closed city with absentee landlords is a vector (u, x f ) such that: R(x f,u,θ)= R A x f 0 h(s) q(x,u) dx = N where R(x f,u,θ), h(s), q(x,u) are defined by (13), (12), and (10), respectively. (14) (15) Equation (14) says that the bid rent of the individuals must be equal to the agricultural land at the city fringe. Equation (15) gives the population constraint. Solving the first equation (14) using (13) yields tx f = y 1 u log(1 + θ) log rr A (16)

6 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.6 (1-16) 6 Y. Song, Y. Zenou / Journal of Urban Economics ( ) and the second equation (15) leads to tx f = y 1 u 1 2 log{ exp [ 2(y 1 u) ] (1 + θ)rtn }. (17) By combining these two equations, we finally obtain: xf = 1 ] [1 2t log tn + (1 + θ)r A (18) u = y log{ (1 + θ)r [ (1 + θ)r A + tn ]}. (19) Proposition 1. Assume that the city is closed and landlords are absentee. Then, if the utility function is quasi-linear and defined as in (5) and the production function h(s) is Cobb Douglas as in (1), we have: x f θ < 0, Moreover, we have u θ < 0. (20) x f t < 0, x f N > 0, x f R A < 0. (21) An increase in the property tax unambiguously decreases both urban sprawl and utility. By remembering our discussion about structural versus population density, the intuition of this result is easy to understand. There are two countervailing effects of an increase of the property tax θ on urban sprawl x f. On the one hand, an increase in θ has a direct negative effect on the profit of developers, which accordingly reduces the level of improvements (or structural density). 4 As a result, for a given size of dwellings, buildings are shorter and thus the population density is lower. Because population is fixed (closed city), it has to be that the city increases in size (this is referred to as the building height effect). On the other hand, an increase in θ has an indirect negative effect on households housing consumption because the tax on land and improvements is partly shifted forward to consumers, which yields a higher price of housing and thus a lower dwelling size. Smaller dwellings imply an increase in population density D and thus less urban sprawl (this is referred to as the dwelling size effect). The net effect is not ambiguous here (contrary to the case of a general utility function; see Brueckner and Kim [5]) because consumptions of z (composite good) and q (housing) are highly substitutable since the elasticity of substitution is greater than one. Thus, the dwelling-size effect becomes more important and the net effect is such that an increase in θ decreases urban sprawl. Observe that our utility function is not a special case of the CES utility function proposed by Brueckner and Kim [5]. In their model the elasticity of substitution σ = 1/(1 + β) is a constant that depends only on the parameter β whereas here it is given by: σ = 1 + 1/z, which, in equilibrium and using (7) is equal to: σ = 1 + 1/(y tx 1), and thus depends on distance to the CBD. As noted by Brueckner and Kim [5], one could go further by relaxing the assumption that landlords are absentee and thus consider the fully closed city, where urban land is rented from 4 Another way to see this is to center on the fact that the land component of the property tax θ is partly capitalized into the price of land, so that the property tax raises the price of improvements relative to land, causing the developers to substitute land for capital.

7 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.7 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 7 absentee landlords at a price equaling the agricultural rent (for a standard analysis of a fulled closed city, see Pines and Sadka [16], and Fujita [8, Chapter 3]). To be more precise, the city residents are now assumed to form a government, which rents the land for the city from rural landlords at agricultural rent R A. The city government, in turn, subleases the land to city residents at the competitive rent R(x,u,θ) at each location x. We can define the total differential rent (TDR) from the city as: TDR = x f 0 [ R(x,u,θ) RA ] dx. (22) The only thing that changes in the analysis is the fact that the income of each individual is now given by y + TDR/N instead of y. As a result, replacing y by y + TDR/N in (16) and (17), and solving these two equations gives the new values of xf and u. It is easy to verify that xf = x f and u = u + TDR/N, so that the negative relationship between the city size xf and the property tax θ is exactly the same as before. Indeed, the inclusion of TDR as income has no effect on urban sprawl because of the zero income elasticity of housing demand. 3. Developing a national sample of effective tax rates We would like now to test the main result of our theoretical model, i.e. the fact that increasing the property tax reduces the spatial extent of urbanized areas. We begin our analysis by presenting the steps involved in developing our sample of effective tax rates Data sources The unit of analysis for this study is the urbanized area. Urbanized areas are defined as cities with 50,000 or more inhabitants and their surrounding densely settled urban fringe, incorporated or unincorporated. 5 Generally in an urbanized area, there are various taxing entities such as county, township, city, town, school, and special taxing districts. We thus need to construct the aggregated effective tax rate for each urbanized area. To do so, we first collect effective tax rates imposed at different levels of taxing jurisdictions in an urbanized area counties, cities, townships, and school districts. We do not collect effective tax rates from special districts such as fire, water, sewer, etc., as those tax rates are generally not reported by the state agencies. Since special districts are formed to provide services to the inhabitants of a limited area, we argue that the omission of the tax rates from special districts would not have a significant impact on the results of this study. Data on the effective tax rates from counties, cities, townships and schools can be collected either from states or local government units. Many state level units, such as the Department of Taxation and Association of County Commissioners, conduct tax rate surveys to collect effective tax rates from various localities and have made effective tax rates available on their web- 5 Urbanized areas differ in concept from metropolitan areas. In general, metropolitan areas are defined as cities with 50,000 or more inhabitants, their counties, and surrounding counties that have a high degree of social and economic integration with the core. Metropolitan areas thus include urban population not contiguous to the core as well as rural population. Therefore, as suggested by Brueckner and Kim [5], the urbanized area corresponds to the requirements of the theory in a better way than other census-defined units.

8 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.8 (1-16) 8 Y. Song, Y. Zenou / Journal of Urban Economics ( ) sites. 6 As one of the main purposes of collecting tax rates by the state is to offer a common standard for the comparison of tax rates among taxing jurisdictions, these rates are thus comparable across areas and states. Generally, the effective tax rates are obtained by adjusting the nominal tax rate with the sales/assessment ratio, which is estimated and determined by the state agencies. For those states without available information online, we directly contact the local government units to obtain data on the effective rates imposed by the local jurisdictions such as the counties, cities and school districts. To construct the aggregated effective tax rate for each urbanized area, we also collect spatial datasets that contain the boundaries of various taxing jurisdictions such as counties, cities, townships, and school districts Geographic Information System (GIS) methods To distill a single value for an urbanized area from the tax rates imposed by various taxing entities, we then create a weighted average of tax rates by coalescing input tax rates from various jurisdictions based on the localities spatial relationships within the urbanized area. Next, we describe the steps involved in constructing the aggregated tax rate for each urbanized area. As an example of our approach, Fig. 1 presents three levels of tax rates levied in the Salem, OR urbanized area: county, city, and school district. First, we use GIS techniques to intersect the boundaries of different taxing jurisdictions with the boundary of the urbanized area and obtain the proportion of the urbanized area within any given county, city, or school district. Second, we calculate the property tax rates by each of the three taxing jurisdictions: county, city, and school district. Specifically, we show that the Salem urbanized area falls into two counties: Marion and Polk with 84.6% of the urbanized area in Marion County and the rest in Polk County. These two counties impose different tax rates and tax assessment ratios. To obtain the effective tax rate for the urbanized area at the county level, we sum the effective tax rates (which are the product of tax rates and ratios) from the two counties adjusted by their area proportions. 8 We also show that the Salem urbanized area also contains three cities, Salem, Keizer, and Turner, and that 60.2% of the urbanized area is in Salem, 10.4% is in Keizer and the rest is located in Turner. To calculate the effective tax rate at the city level, we also need to find out which county the city is located in since we also need to apply the county tax assessment ratio in the calculation. For example, the city of Salem is in both Marion and Polk counties while the cities of Keizer and Turner are only in Marion County. Thus for the city of Salem, GIS techniques are employed to obtain the proportion of the urbanized area that is in the city of Salem, but in different counties. We show that for the 60.2% of the urbanized area that is in Salem, 52.7% is in Marion County and 7.5% is in Polk County. To obtain the effective tax rate for the urbanized area at the city level, we sum the effective tax rates (which are the product of city tax rates and county 6 Examples of these web sites include: North Carolina: Illinois: New York: 7 These data are available from the US Census, or can be purchased from GeoCommunity (a GIS data depot). 8 The aggregate tax rate at the county level is obtained by: Marion County Tax rate Marion County Tax ratio Proportion of urbanized area in Marion County + Polk County Tax rate Polk County Tax ratio Proportion of urbanized area in Polk County = % % =

9 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.9 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 9 Fig. 1. Levels of taxation in the urbanized area of Salem, OR.

10 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.10 (1-16) 10 Y. Song, Y. Zenou / Journal of Urban Economics ( ) tax assessment ratios) from the three cities, adjusted by their area proportions. 9 The strategy of computing the effective tax rate at the city level applies to the calculation of the effective tax rate at the school district level. The calculations indicate that the effective tax millage rates levied by the county, city, and school district are 4.184, 5.483, and respectively. 10 Finally, we sum up these three effective tax rates at different levels to obtain the aggregated effective tax millage rate for the Salem urbanized area, which is Table 1 Effective tax millage rates of selected 54 urbanized areas Urbanized area Effective Urbanized area Effective tax rate tax rate Akron, OH urbanized area Miami, FL urbanized area Albuquerque, NM urbanized area 8.31 Minneapolis St. Paul, MN urbanized area Altoona, PA urbanized area Muncie, IN urbanized area Barnstable Town, MA urbanized area New Bedford, MA urbanized area Benton Harbor St. Joseph, New Haven, CT urbanized area MI urbanized area Boise City, ID urbanized area Olympia Lacey, WA urbanized area Cape Coral, FL urbanized area Parkersburg, WV OH urbanized area 8.23 Casper, WY urbanized area 8.19 Pocatello, ID urbanized area Champaign, IL urbanized area Pueblo, CO urbanized area 9.26 Chico, CA urbanized area Reno, NV urbanized area 8.74 Columbia, SC urbanized area 7.69 San Luis Obispo, CA urbanized area 8.33 Deltona, FL urbanized area Santa Fe, NM urbanized area 6.20 El Centro, CA urbanized area Santa Maria, CA urbanized area 9.56 Elkhart, IN MI urbanized area 9.68 Savannah, GA urbanized area Fort Wayne, IN urbanized area Spokane, WA ID urbanized area Gainesville, GA urbanized area 7.99 Springfield, OH urbanized area Gilroy Morgan Hill, CA urbanized area 8.39 St. Cloud, MN urbanized area Idaho Falls, ID urbanized area State College, PA urbanized area Janesville, WI urbanized area Stockton, CA urbanized area 9.41 Kailua (Honolulu County) Kaneohe, 4.91 Sumter, SC urbanized area 6.94 HI urbanized area Kennewick Richland, WA urbanized area Tallahassee, FL urbanized area Kingston, NY urbanized area Titusville, FL urbanized area Lake Charles, LA urbanized area 3.85 Trenton, NJ urbanized area Livermore, CA urbanized area Warner Robins, GA urbanized area 9.22 Madison, WI urbanized area Winchester, VA urbanized area 7.76 McKinney, TX urbanized area Winter Haven, FL urbanized area Akron, OH urbanized area York, PA urbanized area The aggregated tax rate at the city level is obtained by: [(Salem Tax rate Marion County Tax ratio Proportion of urbanized area in Salem and in Marion County + Salem Tax rate Polk County Tax ratio Proportion of urbanized area in Salem and in Polk County) + (Keizer Tax rate Marion County Tax ratio Proportion of urbanized area in Keizer) + (Turner Tax rate Marion County Tax ratio Proportion of urbanized area in Turner)] = [( % %) + ( %) + ( %)] = A millage is a unit equal to one thousandth. Thus, a tax millage rate of equals %.

11 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.11 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 11 Using this approach, we constructed the effective tax rates for 448 urbanized areas in the US. 11 Table 1 shows the effective tax millage rates for a collection of 54 randomly selected urbanized areas. 4. Data and empirical test 4.1. Variables and data An empirical test based on the above theoretical analysis is extremely useful to facilitate the debate on the relationship between the property tax and urban development. We therefore rely on an analytical framework that includes a variety of interacting factors in a regional land market that affect city size. In particular, Eq. (18) shows that, in addition to the property tax θ, the spatial extent of urban sizes xf is also determined by the commuting cost t, the agricultural land rent R A, and the total population N. We thus include these variables in the empirical analysis but we also add the income y. Mills [13] provides justification for including all these variables to determine urban spatial extent. The intuition of including these variables is also stated in Brueckner and Fansler s [4] study. A recent study by McGrath [11] confirms the validity of this set of variables. An increase in the urban population would increase the urban spatial extent since more people would require more housing. An increase in agricultural land rent would lead to a higher opportunity cost of urban land and thus make the city more compact. A higher level of income would imply an increase in housing demand and thereby lead to a larger city. Finally, an increase in commuting cost would lower disposal income at all locations and thus reduce city size. Given the confluence of an expanding population, rising incomes, and falling commuting costs, it is not surprising that most US cities have expanded rapidly in recent decades. We then perform a regression analysis to examine the effect of the property tax on the spatial extent of cities. This analysis allows us to isolate the effects of property tax on city size while controlling for other factors. We describe the data used to construct the variables here. In the regression model, the dependent variable is the size of the urbanized area and is measured by the size, in acres, of the urbanized area in the year The population variable represents the 2000 urbanized area population. The income variable is a measure of the 2000 median household income adjusted by the ACCRA Cost of Living Index. 12 The Cost of Living Index provides a measure of living cost differences among urban areas. Items on which the Index is based include: grocery items, housing, utilities, transportation, health care, and miscellaneous goods and services. Note that the Cost of Living Index includes the item of housing as a component and the inclusion of housing in normalizing our income variable can be inconsistent with the theory. Realizing this limitation, we nonetheless decided to make use of the Index to normalize our income variable for two reasons. First, in addition to the housing item, five other important items also appear in the Index. Second, the Index serves our purpose fairly well since it measures differences in living costs among different areas at a single point in time We excluded those urbanized areas with a population size larger than five million as they contain too many localities, which complicate the calculations. 12 The Cost of Living Index is produced by ACCRA and can be purchased from 13 Many other indices (such as Consumer Price Index produced by the Bureau of Labor Statistics) measure how much costs have changed over a specific period in that particular area and thus do not show whether living costs are higher or lower in that area relative to another.

12 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.12 (1-16) 12 Y. Song, Y. Zenou / Journal of Urban Economics ( ) Table 2 Dependent and independent variables and measurements Variables (variable name) Measurements (data source) Dependent variable Size of urbanized area (UA) The spatial extent of land area in the urbanized area in acres in 2000 (US Census). Independent variables Population (POP) Income (INCOME) Agricultural land rent (AGVAL) Government expenditure on transportation (TRANS) Property tax (TAXRT) 2000 Urbanized area population (US Census) Median household income adjusted by the ACCRA Cost of Living Index (US Census & ACCRA) Median agricultural land value per acre for the county containing the urbanized area (US Census of Agriculture/National Agricultural Statistics Service and GIS operation) Transportation expenditure per person who drives to work (US Census of Governments and GIS operation). A weighted average property tax millage rate for each urbanized area in 1997 (US Census, Web survey, Secondary Data sources and GIS operation). Table 3 Descriptive statistics of the variables Variable (unit) Minimum Maximum Mean Std. dev. UA (acres) ,256,051 90, ,797 POP 49,776 4,918, , ,474 INCOME (dollars) 16,362 86,246 48,522 11,206 (standardized by cost of living index) AGVALUE (dollars) 0 224, ,954 TRANS (dollars) TAXRT (millage rate) Sample size: 448. To construct the commuting cost variable, government expenditure on transportation per person driving to work in 1997 is used as a proxy. Other things being equal, a higher value of government expenditure on transportation would be associated with ease of transportation system usage and a lower level of commuting costs. As data on government expenditure on transportation is available at the county level, we construct a weighted average of government expenditure on transportation for each urbanized area based on the area proportions of counties in relation to the urbanized area using GIS techniques. Similarly, as data on agricultural land rent is only available at county level, we construct a weighted average of median agricultural land value per acre for each urbanized area. Finally, as mentioned above, the 1997 effective tax rate for the urbanized area is constructed according to the steps described in Section 3. Note that we lag the property tax θ by three years because the effect of θ on the size of an urbanized area is not instantaneous, but rather takes time. Data sources and measurements of the dependent and independent variables are summarized in Table 2. Summary statistics of these variables are presented in Table Endogeneity and Instrumental Variables (IVs) There is one potential problem in assuming the exogeneity of the property tax. From our theoretical model, we see that the property tax leads to two countervailing effects, which lead to a

13 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.13 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 13 reduction in the size of cities. On the other hand, urban sprawl will have an effect on the property tax. For example, as demand for supporting infrastructure such as sewer-lines, waterlines, gas lines, phone lines, streets, and gutters increases, some jurisdictions located far away from existing centers of infrastructure may raise the property tax rates to generate revenues in an attempt to cover service costs. McGuire and Sjoquist [12] suggest that the spatial size of the city helps to determine the magnitude of the tax base that would in turn affect the chosen property tax rate. If this reverse channel of causation is active, the OLS estimate of the coefficient of the effective tax rate is biased. The challenge here in estimating a causal impact of the property tax on city size is to overcome the simultaneity bias. Instrumental variable estimation is one method to reduce the endogeneity bias. In order to isolate the impact of the property tax on the spatial extent of cities using instrumental variables, we need an instrument that predicts changes in the property tax rates across urbanized areas, but is unrelated to changes in the city size (after controlling for other relevant factors). An appropriate instrument for the property tax rate is the magnitude of state aid to schools, since this variable is correlated with the property tax rate but not with the urban size. The underlying idea is that school districts generating lots of tax revenue per student receive relatively small amounts of state aid. While a large tax base per student is one cause, higher revenue can also be generated by a high tax rate. Thus, one might expect an inverse association between state aid and the tax rate. Therefore, we use state aid to schools per school age child as an instrument. Data on state aid to schools per school age child are available from the National Center for Education Statistics (NCES). In this context, the impact of the property tax on the city size is estimated using two-stage least squares (2SLS), treating the property tax variable as endogenous, the other right-hand side variables as exogenous, and using the state aid to schools per school age child variable as an instrument. To be valid, the instrument must be correlated with the property tax rate but also exogenous to the city size. The F -test for the significance of the instrument is and statistically significant. Furthermore, the first stage results (not shown for brevity) show that the coefficient associated with the instrument exhibits a negative sign, which is consistent with our expectation. These results suggest that the requirements for instrument validity are satisfied. For diagnostics of the potential endogeneity, we also perform a Hausman endogeneity test. We find that the Hausman statistic is significant at the level. The small p-value indicates that there is a significant difference between the IV and OLS coefficients, and that the OLS model is not consistent Empirical results Given that the theory provides no guidance as to the functional form of the estimating equation, the empirical work makes use of the Box Cox transformation. The optimal value of the functional form parameter λ equals 0.46, indicating that a square-root transformation of the variables is appropriate. 14 Regression results using OLS and 2SLS are respectively presented in columns two and three of Table 4. Both regressions have high R 2 values. Results indicate that in both estimations the signs of most estimated coefficients conform to the predictions of the theory. The population and income variables have positive and significant coefficients, indicating that the spatial size 14 Note that the Box Cox transformation was derived for the OLS regression and then used for 2SLS. We have also tried the linear function form (without the Box Cox transformation) and all results sustain.

14 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.14 (1-16) 14 Y. Song, Y. Zenou / Journal of Urban Economics ( ) Table 4 Regression results OLS IV constant *** *** (8.63) (6.31) POP *** *** (17.35) (6.31) INCOME *** *** (6.37) (4.21) AGVAL (0.41) (0.25) TRANS *** *** (5.57) (8.96) TAXRT *** ** (5.36) (2.41) R SQUARE Notes. Absolute values of robust t-statistics are in parentheses. * Significant at the 10% level. ** Idem, 5%. *** Idem, 1%. Table 5 Elasticities estimated from the 2SLS Population Income Transportation Property tax expenditure millage rate Elasticities of urbanized areas is an increasing function of population and income. The results also show that the expenditure on transportation variable has a positive and significant coefficient. Indeed, a higher spending level on transportation is designed to improve local transportation and thus to lower commuting costs. Thus, since the government expenditure on transportation variable is used as a proxy for commuting costs, the result confirms the predicted negative relationship between urban size and commuting costs. The estimated coefficient of agricultural rent variable is not significant. The poor performance of the agricultural rent variable may be a sign that the constructed weighted average of agricultural land rent for the urbanized area is not reflective of the actual agricultural land rent at the periphery of the urbanized area. The influence of the property tax rate on the spatial extent of urban areas is of primary interest to this research. The coefficient of the property tax rate is negative and statistically significant, but OLS underestimates the negative effect of the property tax rate: the coefficient of the variable is in the OLS regression and in the 2SLS regression. This result supports what has been predicted by the theory: the spatial size of cities is a decreasing function of the property tax rate. To provide a sense of the implications of the estimated magnitudes of the coefficients, we present the elasticities of urban size with respect to the significant variables in Table 5 (the elasticities are evaluated at sample means). The elasticities show that a 1% increase in population leads to a 0.519% increase in urban spatial extent, a 1% increase in income leads to a 0.724% increase in urban spatial extent, and that a 1% increase in government spending in transportation

15 JID:YJUEC AID:2517 /FLA [m1+; v 1.65; Prn:31/08/2006; 13:42] P.15 (1-16) Y. Song, Y. Zenou / Journal of Urban Economics ( ) 15 leads to a 0.288% increase in urban spatial extent. Finally, the elasticity shows that a 1% increase in the effective property tax rate reduces the urban spatial extent by 0.401%. 5. Conclusion This paper has examined the relationship between the property tax and urban sprawl through both theoretical and empirical analyses. The theoretical model incorporates two countervailing effects: (i) the property tax suppresses improvements, which in turn reduces population density and (ii) the tax reduces dwelling sizes, which raises population density. The theoretical model adopts a log-linear utility function that exhibits a variable elasticity of substitution greater than one. The model shows that increasing the property tax reduces the city size and thus, urban sprawl. Based on a dataset of the effective property tax rates and using GIS methods for 448 urbanized areas, the empirical analysis estimates a regression equation relating an urbanized area s size to a property tax rate measure and other control variables, such as population, income, agricultural rent, and transportation expenditure. Results from the empirical analysis are consistent with findings from the theoretical reasoning, suggesting that higher property tax can make cities smaller: city size would decrease by 0.4% if the property tax increases by 1%. Acknowledgments We thank the Lincoln Institute of Land Policy for financial support. We would also like to thank Jan Brueckner, two anonymous referees, and the participants of the 2005 David C. Lincoln fellowship seminar for very helpful comments. Any shortcomings in the paper, however, are our responsibility. References [1] R.J. Arnott, J.G. MacKinnon, The effects of the property tax: A general equilibrium simulation, Journal of Urban Economics 4 (1977) [2] J.K. Brueckner, The structure of urban equilibria: A unified treatment of the Muth Mills model, in: E.S. Mills (Ed.), Handbook of Regional and Urban Economics, vol. 2, North-Holland, Amsterdam, 1987, pp [3] J.K. Brueckner, Urban sprawl: Diagnosis and remedies, International Regional Science Review 23 (2000) [4] J.K. Brueckner, D.A. Fansler, The economics of urban sprawl: Theory and evidence on the spatial sizes of cities, Review of Economics and Statistics 65 (1983) [5] J.K. Brueckner, H. Kim, Urban sprawl and the property tax, International Tax and Public Finance 10 (2003) [6] M. Burchfield, H.G. Overman, D. Puga, M.A. Turner, Causes of sprawl: A portrait from space, Quarterly Journal of Economics 121 (2006) [7] K.E. Case, J.H. Grant, Property tax incidence in a multijurisdictional neoclassical model, Public Finance Quarterly 19 (1991) [8] M. Fujita, Urban Economic Theory, Cambridge Univ. Press, Cambridge, [9] H. George, Progress and Poverty: An Inquiry into the Cause of Industrial Depressions and of Increase of Want with Increase of Wealth, Robert Schalkenbach, New York, [10] E.L. Glaeser, M.E. Kahn, Sprawl and urban growth, in: J.V. Henderson, J.-F. Thisse (Eds.), Handbook of Regional and Urban Economics, vol. 4, North-Holland, Amsterdam, 2004, pp [11] D.T. McGrath, More evidence on the spatial scale of cities, Journal of Urban Economics 58 (2005) [12] T.J. McGuire, D.L. Sjoquist, Urban sprawl and the finances of state and local governments, in: D.L. Sjoquist (Ed.), State and Local Finances under Pressure, Edward Elgar, London, [13] E.S. Mills, The economic consequences of a land tax, in: D. Netzer (Ed.), Land Value Taxation: Can It and Will It Work Today? Lincoln Institute of Land Policy, Cambridge, MA, 1998, pp [14] T.J. Nechyba, R.P. Walsh, Urban sprawl, Journal of Economic Perspectives 18 (2004)

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