An Empirical Analysis of Determinants of Multi-Dimensional Urban Sprawl

Transcription

1 An Empirical Analysis of Determinants of Multi-Dimensional Urban Sprawl Qing Su Department of Marketing, Economics, and Sports Business Northern Kentucky University Nunn Drive, BC 338 Highland Heights, KY Phone: (859) Joseph DeSalvo Department of Economics University of South Florida 4202 E. Fowler Ave. CMC 207E Tampa, FL Phone: (813) Abstract: This paper applies a simultaneous equation model to examine the impact of a variety of factors on four dimensions of urban sprawl: spatial size, sprawl index, and daily vehicle miles traveled per capita. The regression results indicate that the transportation cost has a negative impact on urban sprawl in terms of spatial size, land consumption per capita and daily VMT. The impact of household income on spatial size, land consumption per capita and daily vehicle miles traveled per capita are U-shaped. The impact of number of household is mixed: it has a positive impact on spatial size and daily VMT, but a negative impact on land consumption per capita. Urban growth boundary has a negative and statistically significant impact while minimum lot size has a positive impact on two dimensions of urban sprawl (spatial size and land consumption per capita). Regression results also indicate that among the variables that capture the political, social and geographic characteristics of an area, the amount of intergovernmental transfers as a percentage of local revenue has a positive and statistically impact on all four dimensions of urban sprawl while the percentage of urban fringe area overlying aquifers has such an impact on three dimensions (spatial size of an area, sprawl index, and land consumption per capita). The violent crime rate in the central cities has a positive and statistically significant impact on two dimensions of urban sprawl (spatial size and land consumption per capita). Key words: multi-dimensional urban sprawl; simultaneous equation model; urban growth boundary; minimum lot size; violent urban crime rate in central city; JEL classification: R10 1

2 An Empirical Analysis of Determinants of Multi-Dimensional Urban Sprawl 1. Introduction Urban sprawl or suburbanization is a topic that has generated much debate in the past twenty years and has become an important policy issue in the United States. Much of our understanding of urban growth stems from the monocentric urban model, earlier developers of which include Alonso (1964), Mills (1967), and Muth (1969). Many recent studies were extensions of this model to incorporate more contributors of urban expansion (Brueckner 2000, 2003, 2005), Glaeser and Kahn (2003), Song and Zenou (2006), Su and DeSalvo (2008), Geshkov and DeSalvo (2012)). Polycentric urban model was developed to reflect the reality that many urban areas have more than one employment centers (Anas and Kim, 1996; Anas and Xu, 1999). While polycentric urban model incorporates more realistic factors, Anas (2007) leaves the empirical application of his theory as an extension. On the other hand, many existing empirical estimations are based on the monocentric model using samples in different size ranging from relatively small urbanized areas (Brueckner and Fansler, 1983; Su and DeSalvo, 2008; Geshkov and DeSalvo, 2012) or multi-year dataset of very large urbanized areas (McGrath, 2005) to those including almost all urbanized areas (Song and Zenou, 2006; Spivey, 2008) or all metropolitan areas (Paulson, 2012). It is generally agreed that the monocentric model lends itself easily to empirical estimation and has proved robust. Different variables have been used in the literature to measure urban sprawl. Given the comparative static results from the monocentric model, the spatial size of an urbanized area is a natural choice for many scholars (Brueckner and Fansler, 1983; McGrath, 2005; Song and Zenou, 2006; Su and DeSalvo, 2008; Spivey, 2008; Geshkov and 2

3 DeSalvo, 2012). The spatial size of an urban area, however, captures only one dimension of urban sprawl: the total land consumption. It cannot capture the inter-area variations in land consumption per capita that are better reflected by density, another popular measure of urban sprawl (Galster et al., 2001; Malpezzi and Guo, 2001; Hess et al., 2001). Density, as a descriptor of compactness, omits some other important attributes of urban growth such as the degree of fragmentation (Burchfield et al., 2006) and accessibility (caused by massive use of private vehicles and normally measured by travel time of households and/or average daily vehicle miles traveled (DVMT)). There is no doubt that a single measure of urban growth cannot capture different aspects of sprawl well. While most of existing empirical analyses focus on one dimension of urban sprawl, it is also important to recognize the fact that the same area considered much sprawled in terms of one measure could be considered very compact in another measure. This can be better illustrated by a few examples. Based on the sample selected for this paper, Austin, Texas, is ranked as the 4 th most sprawled area in terms of spatial size, 130 th sprawled in terms of land consumption per capita, 103 th in Burchfield et al. s sprawl index and 43 th in daily vehicle miles traveled per capita. Charlottesville, Virginia, is ranked as the second most sprawled in Burchfield et al. s sprawl index, but 120 th sprawled in spatial size, 93 th in land consumption per capita, and 72 th in DMVT per capita (for detailed information on the list of 152 urban areas and their ranks in various measures, see Table A1). Urban sprawl, therefore, is multi-dimensional. The multi-dimensional nature of urban growth naturally raises an important question: whether there are common factors contributing to those different dimensions of urban sprawl and what are their impact on those measures of urban sprawl. Despite the difference in ranks (for an urban area) depending on the measures of urban sprawl, it is likely that some unobserved or 3

4 uncontrolled factors may be correlated to all these measures. In other words, these different measures of urban sprawl are jointly determined. This paper examines the impact of a wide variety of factors on urban sprawl. It adds to a sizable empirical literature, contributing three improvements. First, urban sprawl is measured by four simultaneously determined variables: total spatial size, land consumption per capita, sprawl index measured as an average percentage of undeveloped land surrounding a typical dwelling in an urban areas (the measure of urban sprawl used by Burchfield et al., 2006), and daily vehicle miles traveled per capita. Second, in addition to standard monocentric variables, land use policies (e.g. urban growth boundary, minimum lot size regulation, maximum lot size regulation), urban violent crime rate in the central city, and political and geographic characteristics used in Burchfield et al. (2006) are also included to capture their impact on multi-dimensional sprawl. Third, since an area s degree of fragmentation (measured by sprawl index from Burchfield et al) may affect land consumption per capita, this paper allows the interdependence of these endogenous variables. The major findings from this paper may help us better understanding the causes of urban sprawl and look for relevant policy tools to reduce sprawl. 2. Literature Review Both monocentric and polycentric urban models have been developed to explain spatial expansion of cities during the past thirty years. The monocentric model has a predetermined center, the central business district (CBD), to which all travel is made for work and other activities. Travel is along radial and dense transportation routes between the household s residential location and the CBD. These clearly untrue assumptions are the foundation, at the same time, the most obvious shortcoming of the monocentric urban model. Polycentric urban model was developed to incorporate the reality that most urban areas have more than one 4

5 employment centers. The polycentric urban theory provided by Anas and Kim (1996) and Anas and Xu (1999) both address most of the criticisms involving the monocentric model pretty well. Although polycentric urban model incorporate more realistic factors, Anas (2007) leaves the empirical application of his theory as an extension. On the other hand, the monocentric model lends itself easily to empirical estimation and has proved robust. Estimated coefficients are mostly statistically significant and have the theoretically predicted signs in samples ranging from relatively small urbanized areas (Brueckner and Fansler, 1983; Su and DeSalvo, 2008; Geshkov and DeSalvo, 2012) to those including almost all urbanized areas (Song and Zenou, 2006; Spivey, 2008) and multi-year pooled cross-section data set of very large urbanized areas (McGrath, 2005). This review of literature review, therefore, focuses on the monocentric urban model and the major empirical works on urban sprawl. Brueckner (1987) provides a comparative static analysis of the monocentric urban model, which is considered a canonical monocentric theory and has been used as a standard model for extensions. This comparative static analysis indicates that an increase in population and household income as well as a decrease in transportation cost and rural land rent result in urban expansion. Empirical research on the general equilibrium monocentric urban model was initiated by Brueckner and Fansler (1983). McGrath (2005) provides the most recent empirical analysis of the model. Song and Zenou (2006) extend the model to include the property tax, and Su and DeSalvo (2008) extend it to include two modes of transportation and transportation subsidies. Geshkov and DeSalvo (2012) test the model extended to include various land-use controls. Brueckner and Fansler (1983) use 1970 census data for a sample of 40 urbanized areas, each contained within a single, relatively small county. They find that urban area population and 5

6 household income have a statistically significantly positive effect on the spatial size of urban areas while agricultural land value has a significantly negative effect, all consistent with the theoretical predictions. McGrath (2005) uses a panel dataset obtained from census data for 1950 through 1990 to create a sample of 153 urbanized areas contained within the thirty-three largest U.S. metropolitan areas. The regression results indicate that population, income, and agricultural land values are all statistically significant and have signs consistent with expectations. Song and Zenou (2006) conduct both theoretical and empirical analysis by incorporating property tax in urban expansion model based on a linear, not circular, urban area. Their sample consists of data on 448 urbanized areas in Their findings on population and income and transportation cost are consistent with the monocentric model. Their coefficient on agricultural land value, however, is positive, contrary to theory, and statistically insignificant. Finally, they also find the coefficient on the property-tax variable to be negative and statistically significant, suggesting that an increase in the property tax would cause the urbanized area to contract, as their theoretical model predicts. Su and DeSalvo (2008) investigate the effect of transportation subsidies on urban sprawl. Their theoretical model has two transport modes (bus and auto) and incorporates subsidies for both modes to reflect the fact that users for both modes don t pay the full cost of their travel. A subsample of 93 urbanized areas from the 2000 census is selected so that there is a single central city in a single county to conform better to the monocentric model. Their findings on the impact of population, income, and property tax rate are consistent with the theoretical prediction. The effect of agricultural land value is negative, as predicted, but not statistically significant. They also find that the spatial size of the urban areas increases as transit subsidies decline while increases at decreasing rate with respect to highway subsidy. 6

7 Spivey (2008) uses 452 urbanized areas in 2000 and eighty-five urbanized areas for which data on commuting time and cost are available. Her findings on the monocentric model s exogenous variables are consistent with theory. She also finds that the number of subcenters negatively affects the spatial size of urbanized areas, implying that urban areas with more subcenters are smaller spatially. In addition to the studies based on one-year, cross-sectional data, empirical evidence based on panel data sets and panel data approach also proved the robustness of the monocentric urban model. Paulsen (2012) applies fixed effect model based on a sample of 328 metropolitan areas over period. He finds that an increase in population and income in an area leads to urban expansion. In addition to the four standard monocenric exogenous varaibles, land use controls are identified as factors affecting urban growth. Minimum lot-size zoning (Pasha 1996), maximum floor-area-ratio (Bertaud and Brueckner 2005), maximum building heights (Bertaud and Brueckner 2005) are found to have a direct impact on the spatial size of an area. Maximum lotsize zoning (Pasha 1992), urban growth boundaries (Quigley and Swoboda 2007), minimum square-footage limitations and minimum number of persons per room (Bertaud and Brueckner 2005) are found to have an inverse effect. Geshkov and DeSalvo (2012) estimate the effect of various land-use controls on the spatial size of an urban area. They select a subsample of 182 urbanized areas located within a single county and with a single central city. For the eight land-use controls (minimum lot-size zoning, maximum lot-size zoning, urban growth boundaries, maximum floor-area restrictions, minimum square-footage limitations, maximum building permits, minimum number of persons per room, and impact fees), all have the expected sign and all but the urban growth boundary and 7

8 minimum square-footage limitations are statistically significant. Their OLS regression results on population, income, agricultural land rent are consistent with theoretical prediction. Differing from the above mentioned studies, Burchfield et al (2006) use a sprawl index defined as the percentage of open space in the square kilometer surrounding an average dwelling in a metropolitan area as measure of sprawl. They find that sprawl is positively related to higher population growth, decentralized employment, and reliance on automobile over public transportation. They incorporate various geographic measures and find the positive relationship between sprawl and ease of well drilling, rugged terrains, absence of barriers such as high mountains, percentage of land in the urban fringe not subject to municipal planning regulations, and intergovernmental fund transfers. Our literature review certainly cannot exhaust the literature, but they represent the major focus and results of such studies that are most relevant to our topic. 3. Data and Variables Most variables used in this paper are from four major sources: US Bureau of Census, Census 2000; Burchfield, et al (2006); Highway Statistics 2000, and Geshkov and DeSalvo (2012). Supplementary variables are from Annual Urban Mobility Report and National Agricultural Statistics Service, and Federal Bureau of Investigation Crime Report. Measures of urban sprawl We have four endogenous variables to measure different dimensions of urban sprawl. The first variable is the spatial size of an urban area obtained from Census The spatial size of urbanized areas in square kilometers for total area, water area, and land area is provided by Table GCTPH1. The land area in square miles is used to measure the spatial size of an urban area. The second variable is sprawl index, which is obtained from Burchfield, et al (2006). This 8

9 variable measures sprawl as the percentage of open space in the square kilometer surrounding an average dwelling in To obtain their measure, for each meter cell of residential development in a metropolitan area, they calculate the percentage of undeveloped land in the immediate square kilometer. The index is constructed by averaging the above-mentioned percentage for each cell in a metropolitan area. The third variable is land consumption per capita, derived from Census It is derived by dividing total land area by total population in an urban area. The last variable is daily vehicle miles traveled per capita in an urban area, identified by Burchfield, et al (2006, pp. 587) as another measure of urban sprawl. This variable is obtained from the Highway Statistics 2000, Table HM 72. The summary of statistics is reported in Table 1 and the correlation matrix of these endogenous variables is reported in Table 2. Explanatory variables are categorized in four groups: standard variables from monocentric urban model, land use control variables, political, economic, and geographic characteristics, and other variables used to explain DVMT. Standard variables from monocentric urban model There are four variables from monocentric urban model: number of household, mean household income, transportation cost, as well as rural rent at the urban fringe. The number of households in an urbanized area is obtained from Census 2000, SF3, Table P15. The mean household income 2 in an urbanized area is reported by Census 2000 for 1999 in SF3, Table P54. For rural land rent, the mean estimated market value of farm land per acre for the county in which the urbanized area is located is used as a proxy. This variable is available from the 1 They derive their measures from the 1992 National Land Cover Data, the most recent dataset available. 2 We also experimented with median household income, the major results remain unchanged. 9

10 National Agricultural Statistics Service. Since the Census of Agriculture is conducted every five years and in different years from the decennial census, this variable is the mean of the means reported for 1997 and 2002 assuming this mean land value approximates that for the year An alternative proxy is obtained from National Agricultural Statistics Service s report on annual agricultural land values. The variable measures the average farm land value per acre at the state level. Both proxies have been used and the major results of this paper remain unchanged. Accurate measurement of transportation cost at the urban area level is not available. As a proxy, highway expenditures per user at the state level are used. This measure is derived by dividing the total annual highway expenditures by the state in which a sample urbanized area is located by the number of users. The users include those using cars and transit, those using bicycles, and pedestrians. The data on state governmental expenditures and users are obtained from Census 2000 SF3, Table P58. Considering the fact that highway expenditures at the state level are financed from state gasoline tax and motor related taxes, this measure is expected to be positively related to transportation cost (for detailed description of complicated highway financing in the US, see Su (2006), Table 4.1). A correlation analysis indicates that it is positively correlated to state average gasoline price. Based on the monocentric urban model, the impact of this variable on urban spatial expansion should be negative. The proxy variable for transportation cost is used as an explanatory variable for three endogenous variables except the last equation of per capita DVMT. Following the most recent studies on travel demand measured by VMT based on the area level data (Small and Van Dender 2007, Hymel et al. 2010, Su 2011), per mile fuel price at the state level is used as explanatory variable to measure travel cost per mile. Fuel cost per mile is derived by dividing the product of state gasoline price and total gallons of gasoline consumed by total VMT. 10

11 Land use control variables The land-use control variables are from Geshkov and DeSalvo (2012). They use eight land use regulation variables: (1) minimum lot-size zoning; (2) maximum lot-size zoning; (3) urban growth boundaries; (4) maximum floor-area-ratio restrictions; (5) minimum squarefootage limitations; (6) maximum building permits; (7) minimum number of persons per room; and (8) impact fees. These land use control variables are dummy variables indicating whether the central city of and county in which the urbanized area is located have such land use regulation in place. These variables are pretty self-explanatory and definitions are thus not provided. Political, economic, and geographic characteristics of an area Eight variables describing an area s political, economic, and geographic characteristics used by Burchfield, et al. are also used in this paper as control variables (for detailed description, see Burchfield, et al (2006) pp ). The hypotheses proposed by Burchfield et al are briefly summarized as follows. Their first hypothesis is that cities will be more compact if they are specializing in sectors where employment tends to be more concentrated. The proxy variable is the centralized sector employment in The second hypothesis is the same as the monocentric urban model with respect to transportation cost. Their proxy for transportation cost is streetcar passenger per capita in1902. Their third hypothesis is that cities with higher population growth rate tend to be more compact. Their proxy for this variable is mean decennial percentage population growth from 1920 to The fourth hypothesis is related to leapfrogging. They expect that leapfrogging is positively related to the uncertainty of future urban growth. The proxy for uncertainty of future urban growth is the standard deviation of decennial population growth from 1920 to

12 Their fifth hypothesis is that the presence of aquifers may allow households to sink their own water wells, thereby avoiding the necessity of connecting to a public water system, which may induce sprawl. Their proxy for this variable is the percentage of urban fringe area that overlies aquifers. Their sixth hypothesis relates to physical barriers of an area, such as mountains and hilly terrain. They expect that rugged terrain contributes to scattered development while high mountains at the urban fringe work as a barrier to make urban development more compact (pp ). Their proxy variables are the range in elevation at the urban fringe and a terrain ruggedness index in the urban fringe. They also pay attention to the impact of climatic factor and note that those cities with a pleasant temperate climate experience more sprawl (pp. 613). They provide two proxies: mean cooling degree-days and mean heating degree-days. They have two more hypotheses related to the impact of political geography. They expect that when developers can escape municipal regulations by building outside municipal boundaries, urban development becomes more scattered. Their proxy for this variable is the percentage of urban fringe land that was incorporated in Their final hypothesis is related to inter-government fund transfer. They expect that sprawl would be more prevalent where local taxpayers pay a smaller share of local government expenses to provide public services. Their proxy for this variable is the amount of intergovernmental transfers as a percentage of local revenues in Public finance model also identifies some factors that may contribute to urban sprawl. The push side of public finance model focuses on inner city problems. People, in particular high income earners are more likely to move to suburbs to avoid inner city problems such as high crime rate. To capture the inner city problems, violent crime rate of the central city of an urban area is used. This variable is obtained from FBI s annual crime report by city. Considering the 12

13 fact that household location change may not be immediate response to higher crime rate in the central city, the average crime rate between 1990 and 2000 is used. It is expected that those areas with higher violent crime rate in the central city experience more sprawl. Table 1: Summary of Data Statistics Variable Unit Mean Standard Deviation Minimum Maximum Spatial Size Sq. mile Sprawl_1992 Percentage Land Consumption per capita Sq mile/person DVMT Per Capita Mile Standard Monocentric Variables Households Mean Household Income $ Rural Rent $/acre Highway Exp. Per User $ Other Variables Fuel Cost per Mile $ Number of Vehicle per capita Number of Bus per capita Number of Violent Crimes in the Central City Road Milers per 1000 Residents Mile Land Use Variables (proportion) Minimum Lot Size Zoning Maximum Lot Size Zoning Urban Growth Boundary Maximum Floor-Area-Ratio Restrictions Minimum Square-footage Limitations Maximum Building Permits Minimum Number of Persons Per Room Impact Fees N

14 Table 2: Correlation Matrix Spatial size Land consumption per capita Spatial size Sprawl index Daily VMT Land consumption per capita Sprawl index Daily VMT Other variables Since this paper uses daily VMT per capita as one dimension of urban sprawl, we also draw variables from the literature investigating traveler s behavior. Following Small and Van Dender (2007), we use road lane miles per 1000 residents to capture the impact of road density in an area. Those areas with higher road density are expected to experience more sprawl. To reflect the inter-area difference in vehicle ownership 3, the number of automobile per capita at the state level is used. The number of bus per capita is also used as a proxy to control for the impact of public transit. Both variables are obtained from Highway Statistics 2000 (Table MV-1). 4. Methodology and Empirical Specification Our empirical specification is based on a model that determines spatial size, population density, average percentage of open space surrounding a typical urban dwelling, and daily vehicle miles traveled per capita in an urban area jointly. We assume that households in each urban area choose the size and location of their residence given their income. Their choices are also subject to land use regulations, geographic conditions of an area, as well as public services 3 Number of drivers per capita is also experimented and the coefficient of this variable is statistically insignificant (z-value ranges between and 0.005), therefore, dropped from regressions. 14

15 in an area. The aggregation of household choices jointly determines spatial size, and population density, and average percentage of open space surrounding a typical residence in an urban area. Households in an area choose how much to travel accounting for per mile fuel cost of driving subject to road network density, population, and other factors affecting people s travel needs. Based on these assumptions, the structural model is as follows: Size = f ( X s tan dard SprawlIndex =, X f ( X DVMTPerCapita = landuse, PoliticalEconomicGeographic LandConsumptionPerCapita = f ( P m X, X PoliticalEconomicGeographic f ( X s tan dard, X, X s tan dard dvmt ), X ) LandUse ) landuse, X PoliticalEconomicGeographic, SprawlIndex) (1) X s tan dard represents the variables from the monocentric urban model; X landuse represents the land use control variables; X PoliticalEconomicGeographic represents the political, economic and geographic characteristics of an area; Pm is the fuel price per mile; X dvmt represents other variables discussed in last section. The three-stage estimation of system of simultaneous equations is used to run the regression. 5. Regression Results 5.1 Structural Equations The model specification selection process is guided by two principles. First, given the theoretical foundation, the standard monocentric variables are included in three equations except the sprawl index equation 4. Second, the inclusion and exclusion of all the other variables discussed previously start with OLS regressions. For those variables that are not individually statistically significant, various joint significance tests are conducted. Those variables are not 4 None of the standard monocentric variables are included in Burchfield et al (2006). We exclude the monocentric variables in the sprawl index equation to make our results more comparable and to avoid the potential bias from the case when variables are measured at different time spots (sprawl index in 1992, while monocentric variables at 2000). 15

16 jointly significant are removed from all equations except the sprawl index equation. All the variables used by Burchfield et al are included in the sprawl index equation to make the results more comparable to theirs. The regression results of estimating the structural system are reported in Tables 3-6. Each table presents the results for two different estimation methods: three-stage least squares (3SLS) and OLS. The spatial size equation (Table 3) explains the total land area of an urbanized area. The regression results indicate that that an urban area expands with an increase in the number of households, as predicted by the monocentric model. The proxy measure of transportation cost in an area has a statistically significant negative impact on spatial size of an area, which is also consistent with monocentric model. Its effect, however, is small. A possible explanation could be that this proxy does not capture the all transportation costs paid by household. The coefficient of rural land rent is not statistically significant and but the sign is consistent with the model prediction. A possible explanation may be that the measure used does not accurately capture the land value right on the urban fringe. The impact of income, as shown by the quadratic terms, is not linear. Among the political and geographic variables used by Burchfield et al. (2006), the percentage of urban fringe area overlying aquifers and the amount of intergovernmental transfers as a percentage of local revenue both have a positive and statistically significant effect on the spatial size of urban areas while the centralized sector employment has a statistically significant negative impact. These results provide evidence to support Burchfield et al hypotheses: (1) that the presences of aquifers enables households to avoid the necessity of connecting to a public water system and induce sprawl; (2) that sprawl will be more prevalent where local taxpayers 16

17 pay a smaller share of local government expenses to provide public services; (3) urban areas with higher degree of employment concentration is more compact in land areas. Table 3: Spatial Size Equation Variable 3SLS a,b OLS a,c ln(household Income) *** (5.00) ** (4.66) (ln(household Income)) *** (4.37) 0.098*** (3.89) ln(number of Households) 0.920*** (26.66) 0.883*** (23.47) ln(highway Expenditure Per User) ** (2.41) *** (2.95) ln(rural Rent) (0.21) (0.25) Minimum Lot Size Zoning 0.113*** (2.95) 0.120*** (2.88) Urban Growth Boundary * (1.90) * (2.04) Minimum Number of Persons Per Room (0.47) * (1.70) Percentage of Urban Fringe Area Overlying Aquifers ** ( ** (2.24) Intergovernmental Transfers as a Percentage of Local Revenues in *** (5.50) 0.008*** (4.83) Centralized Sector Employment in ** (2.20) ** (2.05) ln(violent Crime in the Central City) 0.091** (3.51) 0.079*** (2.83) Constant 8.512*** (2.98) 9.751*** (3.06) R a dependent variable: ln(spatial Size of Urban Areas). b absolute value of z-statistics in parentheses. ). c absolute value of t-statistics in parentheses *2-tail significance at α = **.2-tail significance at α = ***2-tail significance at α = The regression results also indicate that land use policies play a role in urban growth. The minimize lot size zoning policies has a statistically significant and positive impact while urban growth boundary has a statistically significant and negative on the spatial size of urban area. The number of violent crime per 100,000 residents in the central city of an urban area has a 17

18 statistically positive effect. This finding suggests that residents may be pushed out of central city because of inner city problems, which contributes to urban spatial expansion. Table 4: Sprawl Index Equation Variable 3SLS a,b OLS a,c Centralized-sector Employment (0.53) Streetcar Passenger Per Capita *** (3.39) Mean Decennial Percentage Population Growth *** (2.68) St. Dev. Decennial Percentage Population Growth 0.101* (1.79) Percentage of Urban Fringe Area 0.060*** Overlying Aquifers (2.94) Elevation Range in Urban Fringe (0.52) Terrain Ruggedness Index in Urban Fringe (1.40) Mean Cooling Degree Days *** (2.68) Mean Heating Degree Days *** (2.96) Percentage of Urban Fringe Incorporated (0.92) Intergovernmental Transfers as a Percentage of 0.227*** Local Revenues in 1967 Minimum Number of Persons Per Room Urban Growth Boundary (3.26) ** (1.98) (1.52) (0.36) *** (3.54) *** (2.90) 0.169** (2.57) 0.056** (2.57) (0.72) (1.24) *** (2.76) *** (3.06) (0.91) 0.182** (2.34) -3.22** (2.05) (1.36) 72.20*** (3.93) Constant 64.30*** (3.83) R a dependent variable: Sprawl index. b absolute value of z-statistics in parentheses. ). c absolute value of t-statistics in parentheses *2-tail significance at α = **.2- tail significance at α = ***2-tail significance at α = 0.01 In the sprawl index equation (Table 4), among the 11 variables used by Burchfield et al, all the coefficients have the same sign as reported in their paper, but the coefficients of four variables (centralized employment, elevation range in urban fringe, terrain ruggedness index in urban fringe, and percentage of urban fringe incorporated) are not statistically significant. 18

19 Only one land use variable has a statistically significant impact of the sprawl index. The minimum number of persons per room requirements has a statistically significant and negative impact on the sprawl index, suggesting this land use policy may reduce the amount of undeveloped land around a typical urban dwelling, which increases an urban area s compactness. Table 5: Land Consumption Per Capita Equation Variable 3SLS a,b OLS a,c ln(household Income) *** (5.22) *** (5.04) (ln(household Income)) *** (4.53) 0.108*** (4.46) ln(highway Expenditure Per User) ln(number of Household) *** (2.57) *** (2.57) ** (2.17) * (1.73) ln(rural Rent) Minimum Lot Size Zoning Maximum Lot Size Zoning 19 (0.15) 0.116*** (3.07) (1.14) Urban Growth Boundary * (1.88) Impact Fees (0.48) Percentage of Urban Fringe Area *** Overlying Aquifers (2.25) Intergovernmental Transfers as a Percentage of *** Local Revenues in 1967 (5.12) Centralized Sector Employment in ** (2.20) ln(violent Crime in the Central City) 0.087*** (3.42) Sprawl_ *** (2.67) (0.68) 0.111*** (2.76) (1.13) (1.33) (0.93) * (1.70) 0.007*** (3.75) ** (2.12) 0.093*** (3.41) 0.008*** (3.97) Constant 9.212*** (3.17) 8.970*** (2.91) R a dependent variable: ln(land per capita). b absolute value of z-statistics in parentheses. ). c absolute value of t-statistics in parentheses *2-tail significance at α = **.2-tail significance at α = ***2-tail significance at α = 0.01 In the land consumption per capital equation (Table 5), the regression results indicate that the number of household in an area and transportation cost have a statistically significant and

20 negative impact on land consumption per capita. While the coefficient of rural land rent is also negative, it is not statistically significant. The impact of income is not linear. Among the four land use policy dummies, the minimum lot size zoning has a statistically significant and positive impact while urban growth boundary has a statistically significant and negatively impact on land consumption per capita in an urban area. The sprawl index is used as right-side variable. It has a statistically positive impact on per capita land consumption, indicating that those areas with a higher percentage of undeveloped land around a typical urban dwelling in 1992 tend to have higher land consumption per capita in The percentage of urban fringe area overlying aquifers and the amount of intergovernmental transfers as a percentage of local revenue both have a positive and statistically significant effect on the land consumption per capita while the centralized sector employment has a statistically significant and negative impact. Combined with the findings on the spatial size of an area, these results indicate that urban sprawl in terms of spatial size and land consumption per capita is more prevalent when aquifers are available at urban fringe, local taxpayers pay a smaller share of local government expenses to provide public services, and employments are less concentrated. In the per capita daily vehicle miles traveled equation (Table 6), the coefficient of per mile fuel cost is negative and statistically significant at the level of at least 0.1. The coefficient is , indicating daily travel demand per capita is price inelastic. The road density in an area has a positive and statistically significant impact on per capita daily VMT, which provide additional evidence to support the hypothesis of induced travel. Bus per capita is used as a proxy 5 As a robustness test, sprawl index is dropped from this regression, and the major findings of this equation and the paper remain unchanged. 20

21 to control for the impact of transit. It has a statistically significant and negative impact on daily VMT, although its impact is relatively small. The number of household in an area has a statistically significant and positive impact on daily VMT while the impact of income, once again, is not linear. Among all the land use variables and those variables used by Burchfield et al, only intergovernmental transfers as a percentage of local revenues in 1967 has a statistically significant and positive impact. The number of vehicle per capita is used as a control variable and it has a statistically significant and negative impact on daily VMT. Table 6: Daily VMT Per Capita Equation Variable 3SLS a,b OLS a,c ln(fuel Cost Per Mile) * (1.80) ln(road Mile Per1000 Residents) 0.262*** (4.27) ln(rural Rent) (1.40) Number of Vehicle Per Capita ** (2.40) ln(number of Household) 0.07* (1.90) ln(household Income) ** (2.94) (ln(household Income)) *** (3.21) ln(violent Crime in the Central City) (1.03) ln(bus per capita) * (1.79) Intergovernmental Transfers as a Percentage 0.004** of Local Revenues in 1967 (2.21) Constant 9.087** * (1.74) 0.263*** (4.12) (1.47) ** (2.33) 0.066* (1.72) *** (2.84) 0.090*** (3.08) (0.95) * (1.69) 0.004** (2.09) 9.182** (2.41) (2.43) R a dependent variable: ln(daily VMT per capita). b absolute value of z-statistics in parentheses. ). c absolute value of t-statistics in parentheses *2-tail significance at α = **.2-tail significance at α = ***2-tail significance at α =

22 5.2 Robustness Check and Caveats Given our sample is restricted to only those urban areas with one central city and relatively small, robustness check is conducted to test the sensitivity of the results to variable measurements and selections. Limitations of this empirical analysis are also discussed in this section. The first robustness check concerns measures of household income, transportation cost, and rural land rent. As discussed in the literature review, the monocentric urban model assumes that households are identical, which implies their income are the same. In addition, the measures of rural land rent (should be measured at the immediate urban fringe) and transportation costs (at area level) that match the definitions of variables from the monocentric model are not available. In the robustness check, alternative measures of the three variables including median household income, average farm land value at the state level, and average gasoline price per gallon at the state level are used to check the sensitivity of the results. The second robustness check is to test whether the major findings of this paper are sensitive to exclusion of variables that are dropped due to joint insignificance based on the OLS results. This robustness check is conducted using the same method by Barslund et al. (2007). The core variables are those used and reported in Tables 3-6. The testing variables include the land use variables and geographic and political variables excluded. The robustness check is conducted to run different regressions, including all the core variables and different combinations of testing variables. A summary of this robustness check is reported in Table 7. Only those variables that are statistically significant for at least one dimension of urban sprawl are included. The third robustness check is motivated by the fact that the sprawl index used by Burchfield et al. is measured based on data in 1992, which is the most recent data on National 22

23 Land Cover (Burchfield et al., 2006, pp. 588). It may be true that the same unobserved and/or uncontrolled factors (buried in error terms) could also affect the other dimensions of urban sprawl (the reasoning for the 3SLS simultaneous equation model). When variables are not measured at the same time spots, however, potential bias resulting from it cannot be ruled out. To reduce the impact of this potential bias, regressions are also run to treat sprawl index as an explanatory variable for other three jointly determined equations as another robustness check. The results from all those robustness check indicate that the major findings of this paper remain unchanged. While it is clear that the robustness of the results of this paper is encouraging, a few major caveats remain. The first major limitation involves the measure of daily vehicle miles traveled per capita. The method that is used to collect data on vehicle miles traveled at the state and urban area levels has been long criticized for its inaccuracy since some states rely on direct although sporadic vehicle count while some others rely on indirect imputation. This may be the reason that the variables of interest have a relative lower explanatory power on daily vehicle miles traveled. A better approach to at least reduce the impact of imperfect data is to use panel data estimates accounting for state fixed effect, which may be a focus for future research. The second caveat stems from inaccuracy or potential measurement errors from the explanatory variables used in this paper. Rural land rent is not measured at the immediate urban fringe while transportation cost is measured at the state level. In addition, land use policy variables are only controlled by dummy variables, which cannot capture the impact of regulation details (e.g. minimum size is 0.4, or 0.6, or 1 acre). The potential measurement errors may bias the result given the small sample size. It will be ideal to have multiple year data on all urbanized areas with better measurement of variables, which again could be a direction for future research. 23

24 Table 7: Summary of Robustness Check Results a Variable Spatial Size Sprawl Index Land Consumption per capita Monocentric Standard Variables ln(number of Household) range [0.85, 0.96] [-.090, mean ln(household Income) b range [-2.64, -1.18] [-2.47, -2.38] mean (ln(household Income)) 2 range [0.02, 0.11] [0.098, 0.121] mean ln(highway Expenditure per range [-0.10, -0.05] [-.083, -.062] user)/ln(fuel Cost per mile) mean Land Use Control Variables Minimum Lot Size Zoning range [0.083, 0.12] [.085,.119] mean Urban Growth Boundary range [-.089, -.068] [-.076, -.068] mean Minimum Number of Persons range [-5.00, -2.88] Per Room mean Political, Economic, and Geographic Characteristics of an Area Centralized Sector range [-.038, -.035] [-.038, -.032] Employment in 1977 mean Percentage of Urban Fringe range [.0012,.0015] [.044, 0.67] [.0008,.0014] Area Overlying Aquifers mean Intergovernmental Transfers as range [.0083,.0094] [.179,.229] [.0067,.0084] a Percentage of Local Revenues in 1967 mean ln(violent Crime Rate in Range [.088,.126] [.087,.121] Central City) mean Daily VMT per capita [0.063, 0.072].067 [-1.74, -1.29] [.072,.010].082 [-.90, -.61] -.72 [.0041,.0043] a only those variables that are statistically significant for the dimension of urban sprawl are reported. b. this range is based on the results when both median and mean household income are used 6. Conclusion.0042 This paper applies a simultaneous equation model to examine the impact of various factors on four dimensions of urban sprawl: spatial size, sprawl index, land consumption per capita, and daily vehicle miles traveled per capita. Among the standard monocentric model variables, the regression results indicate that the transportation cost has a negative impact on 24

25 urban sprawl in terms of spatial size, land consumption per capita and daily VMT. The impact of household income on spatial size, land consumption per capita and daily vehicle miles traveled per capita are U-shaped. The impact of number of household is mixed: it has a positive impact on spatial size and daily VMT, but a negative impact on land consumption per capita. The impact of rural land rent is not statistically significant on any dimension of urban sprawl. Among the land use controls, urban growth boundary has a negative and statistically significant impact while minimum lot size has a positive impact on two dimensions of urban sprawl (spatial size and land consumption per capita). The minimum number of persons per room has a negative and statistically significant impact on one dimension of urban sprawl: sprawl index. Regression results also indicate that among the variables that capture the political, social and geographic characteristics of an area, the amount of intergovernmental transfers as a percentage of local revenue has a positive and statistically impact on all four dimensions of urban sprawl while the percentage of urban fringe area overlying aquifers has such an impact on three dimensions (spatial size of an area, sprawl index, and land consumption per capita). The violent crime rate in the central cities has a positive and statistically significant impact on two dimensions of urban sprawl (spatial size and land consumption per capita). The major findings of this paper may have important policy implications if curbing urban sprawl is desirable. First, given the multi-dimensional nature of urban sprawl, it is important for us to recognize that which dimension to target and identify potential tools accordingly. For example, if the policy goal is to increase the compactness of an area or reduce urban fragmentation, land use policies such as urban growth boundary and minimum number of persons per room may be included in the list of potential policy tools. Second, given 25

26 transportation cost has a negative impact on urban sprawl; policy tools that can increase variable travel cost should also be considered. Considering the impact of violent crime rates in the central cities also contribute to urban sprawl, policy tools to reduce violent crime rates in central cities may also help curb the expansion of urban fringe in the suburb areas. 26

27 Table A1: List of Urbanized Areas in the Sample and Their Ranks in Various Measure of Urban Sprawl Rank Land Consumption per AREA Spatial Size capita Sprawl Index DVMT per capita Abilene, TX Albany, GA Alexandria, LA Altoona, PA Anderson, IN Anderson, SC Anniston, AL Atlantic city, NJ Austin, TX Bakersfield, CA Bangor, ME Battle Creek, MI Bay City, MI Beaumont, TX Bellingham, WA Bismarck, ND Bloomington, IN Bloomington-Normal, IL Brownsville, TX Burlington, NC Burlington, VT Canton, OH Cedar Rapids, IA Champaign, IL Charlottesville, VA Cheyenne, WY Chico, CA College Station, TX Colorado Springs, CO Columbia, MO Corvallis, OR Davis, CA Dayton, OH Decatur, AL Decatur, IL Des Moines, IA Dothan, AL Dover, DE Elmira, NY Erie, PA Eugene, OR Fairfield, CA Fayetteville, NC Flint, MI Florence, SC Fort Collins, CO Fort Wayne, IN Frederick, MD Fresno, CA Gadsden, AL Gainesville, FL Goldsboro, NC Grand Junction, CO Great Falls, MT Greeley, CO Green Bay, WI Greenville, NC Hickory, NC Huntsville, AL Iowa City, IA Jackson, MI Jackson, TN Jacksonville, NC