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The effect of land-use on urban sprawl

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Title:
The effect of land-use on urban sprawl
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English
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Geshkov, Marin
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University of South Florida
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Land-use controls
Urban sprawl
Decentralization
Zoning
Urban model
Dissertations, Academic -- Economics -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Chapter 1 provides a discussion of definitions, criticisms, and measurements of urban sprawl. Land-use controls are surveyed in Chapter 2. In Chapter 3, we present the monocentric urban model, followed by a discussion of extensions of that model to include land-use controls. Chapter 4 is a survey of previous empirical analysis of the monocentric model, while Chapters 5 and 6 present our own empirical work. In general, our empirical results support the theoretical predictions as well as providing support for policies to control sprawl. In particular, the results support the use of maximum lot-size zoning, urban growth boundaries, and density restrictions in the form of minimum building heights, minimum square-footage limits, maximum building permits, and minimum persons per room. The importance of this dissertation lies in the fact that it presents the first empirical analysis of the effects of land-use controls on urban sprawl. For this reason, the findings should be of interest to urban planners in their efforts to control urban sprawl. Because we test theoretical hypotheses found in the urban economics literature, the results should also be of interest to academic economists. Finally, the data on land-use controls gathered for the empirical analysis should be of importance to researchers in urban economics
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2010.
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Includes bibliographical references.
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by Marin Geshkov.
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Includes vita.

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The Effect of Land-Use Controls on Urban Sprawl by Marin V. Geshkov A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Economics College of Arts and Sciences University of South Florida Major Professor: Jose ph S. DeSalvo, Ph.D. Kwabena Gyimah-Brempong, Ph.D. Gabriel A. Picone, Ph.D. Kenneth F. Wieand, Ph.D. Date of Approval: March 19, 2010 Keywords: land-use controls, urban spra wl, decentralization, zoning, urban model Copyright 2010, Marin V. Geshkov

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ACKNOWLEDGMENTS I welcome this opportunity to pay my re spects to all whose encouragement and support I received from the preliminary to th e concluding stage of th is dissertation. Specifically, I would like to extend my gratitude to my major professor, Professor Joseph S. Desalvo, for his supervision, a dvice, and guidance at every st ep of my work. He provided me with an unflinching faith in my inne r resources and ability to complete my dissertation. His high standards and passion for scie ntific research were an inspiration to me that enriched my work and nouris hed my intellectual maturity. I would like to thank my other committee members, Professors Kwabena GyimahBrempong, Gabriel A. Picone, and Kenneth F. Wieand, for their assistance and insightful comments on my work and for the wisdom they possess on which they graciously allowed me to draw. I would also like to thank the faculty and staff of the Department of Economics, and particularly Professors Kwabena Gy imah-Brempong, Don Bellante, and Michael Loewy, for their continuous support and unde rstanding during the entire period I was working on my dissertation. Last but not least, I would like to thank my family and friends; without them, my journey toward a PhD would have never begun, much less successfully completed.

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i TABLE OF CONTENTS LIST OF TABLES ..................................................................................................... iv ABSTRACT ............................................................................................................... v 1. INTRODUCTION ............................................................................................... 1 Definition, Criticism, and Meas urement of Urban Sprawl ............................ 2 Definition ........................................................................................... 2 Criticism ............................................................................................. 2 Measurement ...................................................................................... 5 Causes of Urban Sprawl................................................................................. 5 Conclusion and Plan of Dissertation .............................................................. 11 2. DESCRIPTION OF LA ND-USE CONTROLS .................................................. 12 Zoning ............................................................................................................ 12 History of Zoning ........................................................................................... 14 Land-Use Controls: Their Purpose, De scription, and Effect on Sprawl ....... 17 Minimum Lot-Size Zoning ................................................................ 17 Maximum Lot-Size Zoning ................................................................ 18 Building-Height Limitations .............................................................. 18 Population-Density Restrictions ........................................................ 19 Impact Fees and In-Kind Exactions ................................................... 20 Urban Growth Boundary .................................................................... 22 Population-Growth Limitations ......................................................... 22 Square-Footage Limitations ............................................................... 23 Rent Control ....................................................................................... 24 Conclusion ..................................................................................................... 26

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ii 3. THEORIES OF URBAN FORM WITH LAND-USE CONTROLS .................. 27 Development of the Monocentric Urban Model ............................................ 27 Rationale for Using the Monocentric Urban Model to Study Sprawl ........... 31 The Monocentric Urban Spatial Model ......................................................... 32 The Household Sector ........................................................................ 32 The Housing Production Sector ......................................................... 33 Boundary and Population Conditions ................................................ 34 Closed City and Open City Solutions of the Model .......................... 35 Comparative Static Analysis: Closed City Model ............................ 37 Comparative Static Analysis: Open City Model ............................... 39 Other Variants of the M onocentric Urban Model .............................. 40 Extensions of the Model to Include Land-Use Controls ................................ 41 Minimum Lot-Size Zoning ................................................................ 41 Maximum Lot-Size Zoning ................................................................ 46 Urban Growth Boundaries and Similar Land-Use Restrictions ......... 50 Density Controls ................................................................................ 54 Impact Fees ........................................................................................ 59 Conclusion ..................................................................................................... 65 4. A REVIEW OF EMPIRICAL ANALYS IS OF THE GENERAL EQUILIBRIUM MONOCENTRIC URB AN SPATIAL MODEL ......................................... 66 Introduction .................................................................................................... 66 Brueckner and Fansler ................................................................................... 67 McGrath ......................................................................................................... 69 Song and Zenou ............................................................................................. 72 Su and DeSalvo .............................................................................................. 75 Conclusions .................................................................................................... 78 5. DATA DESCRIPTION ....................................................................................... 79 Introduction .................................................................................................... 79 The Urban Area.............................................................................................. 80

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iii Theoretical Variables, Their Proxies, and Data Sources ............................... 81 Non Land-Use Control Variables ...................................................... 81 Land-Use Controls ............................................................................. 85 Summary ........................................................................................................ 88 6. ESTIMATION ..................................................................................................... 89 Preliminary Analysis: Correlation Matrices ................................................. 90 Regression Results ......................................................................................... 92 The Effect of Land-Use Controls on the Size of the Urbanized Area 94 The Effect of Other Variables on the Size of the Urbanized Area .... 98 Summary of the Effect of Land-Use Controls on the Size of the Urbanized Area ................................................................................................................ 99 7. SUMMARY, CONCLUSIONS, LIMITA TIONS, AND SUGGESTIONS FOR FURTHER RESEARCH ..................................................................................... 101 Summary ........................................................................................................ 102 Conclusions .................................................................................................... 104 Limitations of the Study and Sugge stions for Further Research ................... 106 LIST OF REFERENCES ........................................................................................... 109 APPENDICES ........................................................................................................... 117 Appendix: Data Sources for City and County Land-Use Controls ............... 118 ABOUT THE AUTHOR ..................................................................................... End Page

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iv LIST OF TABLES Table 3.1 Summary of Reduced Form Equations .................................................... 37 Table 3.2 Summary of Comparative Static s: Closed City Model, Brueckner (1987) ....................................................................................................... 38 Table 3.3 Summary of Comparative Statics: Open City Model, Brueckner (1987) 39 Table 3.4 Minimum Lot-Size Compar ative Statics, Pasha (1996) .......................... 44 Table 3.5 Maximum Lot-Size Compar ative Statics, Pasha (1992b) ........................ 49 Table 3.6 Comparative Statics of LandUse Restrictions, Quigley and Swoboda (2007) ....................................................................................................... 52 Table 3.7 Maximum FAR Comparative Statics, Bert aud and Brueckner (2005) .... 57 Table 3.8 Property-Tax Comparative Statics, Song and Zenou (2006) ................... 64 Table 3.9 Effects of Land-Use Controls on the Spatial Size of Urban Areas .......... 65 Table 4.1 Box-Cox Non-Linear Estimation ( = 0.53), Brueckner and Fansler (1983) ....................................................................................................... 68 Table 4.2 Box-Cox Linear Estimation ( = 1), Brueckner and Fansler (1983) ....... 68 Table 4.3 OLS Estimation, McGrath (2005)............................................................ 72 Table 4.4 OLS and 2SLS Estimation, Song and Zenou (2006) ............................... 74 Table 4.5 OLS Estimation, Su and DeSalvo (2008) ................................................ 77 Table 5.1 Theoretical Variables, Pr oxy Variables, and Data Sources ..................... 81 Table 5.2 Descriptive Statis tics of Non Land-Use Contro l Variables, U.S. Urbanized Areas, 2000 ....................................................................................... 85 Table 5.3 Descriptive Statistics of LandUse Control Variables, Central Cities and Counties of U.S. Urbanized Areas, 2000 ................................................. 86 Table 6.1 Correlation Matrix for Ce ntral City Land-Use Controls.......................... 90 Table 6.2 Correlation Matrix fo r County Land-Use Controls ................................. 91 Table 6.3 Correlation Matrix for CountyCentral City Land-U se Controls ............ 92 Table 6.4 Regression Results ................................................................................... 93 Table 6.5 Summary of Results ................................................................................. 99 Table 7.1 Change in Mean Urbanized Ar ea Size in the Presence of County LandUse Controls............................................................................................. 105

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v THE EFFECT OF LAND-USE CONTROLS ON URBAN SPRAWL Marin Geshkov ABSTRACT Chapter 1 provides a discussion of definitions, criticisms, and measurements of urban sprawl. Land-use controls are surveyed in Chapter 2. In Chapter 3, we present the monocentric urban model, followed by a discus sion of extensions of that model to include land-use controls. Chapter 4 is a survey of previous empirical analysis of the monocentric model, while Chapters 5 a nd 6 present our own empirical work. In general, our empirical results support th e theoretical predicti ons as well as providing support for policies to control sprawl. In particular, the resu lts support the use of maximum lot-size zoning, urban growth boundaries and density restrictions in the form of minimum building heights, minimum s quare-footage limits, maximum building permits, and minimum persons per room. The importance of this dissertation lies in the fact that it presents the first empirical analysis of the effects of land-use contro ls on urban sprawl. For this reason, the findings should be of interest to urban planners in their efforts to cont rol urban sprawl. Because we test theoretical hypotheses found in the urban economics literature, the results should also be of interest to academic econom ists. Finally, the data on land-use controls gathered for the empirical analysis should be of importance to researchers in urban economics

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1 CHAPTER 1: INTRODUCTION Urban sprawl is a contentious issue, involving various and conflicting views on such fundamental matters as its definition, measurement, and causes. Economists’ contributions to this literature emphasize the theo retical and empirical analysis of the causes of urban sprawl. This dissertation follows in that tradition with an empirical analysis of the effect of land-use controls on urban sp rawl, drawing on testable hypotheses found in the theoretical literature. As will be discussed later, many empirical studies have been performed on the effect of land-use controls on housing prices but no study has examined their effect on urban sprawl. This dissertati on therefore makes a unique cont ribution to the literature on urban sprawl by documenting the effect of landuse controls on the spatial size of the urban area. Such information should be useful to urban planners w ho are trying to curb sprawl. In addition, this dissertation tests theore tical hypotheses on the effect of land-use controls on the spatial size of urban areas. These theoretical hypotheses have not previously been empirically tested. As such, th is dissertation adds to the positive literature on urban economics.

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2 DEFINITION, CRITICISM, AND ME ASUREMENT OF URBAN SPRAWL Definition In general, economists distinguish two types of statements. Positive statements are descriptive. They describe the world the way it is. Normative statements are prescriptive. They make a claim about the wa y the world ought to be. In the urban economics literature, we find both positive and normative definitions of urban sprawl. According to the normative definiti on, urban sprawl is the excessive decentralization of population and employment from the central city to the suburbs (Mills, 1999; Brueckner, 2000). According to the positive definition, urban sp rawl is simply the decentralization of population and employment from the central city to the suburbs. This pr ocess is also called decentralization and suburbanization (Mills and Hamilton, 1994, p. 81). There are other definitions of urban spra wl in the urban econ omics literature as well. Glaser and Kahn (2004) view urban spra wl as relatively lowpopulated residential and employment areas combined with low-de nsity suburbanization in the urban fringe. Nechyba and Walsh (2004) interpret urban spra wl as planned communities that have their own downtowns near a lake or a park, or as interspersed reside nts among rural areas. In this dissertation, we use the positive definition, except that, since our data are for population only, we define urban sprawl as the decentralization of population from the central city to the suburbs. Criticism Over the years, urban sprawl has genera ted a great deal of criticism from economists and planners. According to British urban planning advocate, John Osborn, as dis-

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3 cussed in Williams, Burton, and Jenks (2000), urban sprawl has two downsides: it is economically wasteful and socially disadvantag eous. It is economica lly wasteful because transportation improvements have allowed city residents to move farther from the city center, at the expense of long and costly da ily commutes, as opposed to the situation in more compact cities. Economists argue that this problem is cau sed by congestion externalities and subsidization of the auto (for a review of au to externalities, see Parry, Walls and Harrington, 2007). Urban sprawl is socia lly disadvantageous because movement of city residents to the suburbs worsens local community life by making access to the countryside more difficult for those people who are left in the central city (see also Nechyba and Walsh, 2004). Others criticize sprawl on different grounds. For example, Brueckner (2000) names three major drawbacks of urban spraw l: loss of open space, traffic congestion, and racial segregation. As a result of sprawl, open space is gradually replaced by urban structure. Recent studies in urban economics (Geoghegan, Wainger, and Bockstael, 1997; O’Sullivan, 2006) find that the market price of a house increases at a decreasing rate with the amount of open space. Therefore, open spac e is most valued in direct proximity to the house and less valued farther from the hous e. Acharyi and Bennett (2001) show theoretically that in suburban residential areas, th e price of housing increases as the amount of open space surrounding the house increases. Th erefore, households value open space, and the loss of open space is a negati ve consequence of urban sprawl. Another consequence of urban sprawl is that people live farther out and drive more often and for longer distances. By using their au tomobiles more frequently, residents of the urban area create traffic congestion (Kahn, 2000).

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4 Finally, sprawl exacerbates income segr egation because different income groups cannot travel equal distances. Low income groups live in areas closer to downtown which is served by public transportation. Hi gher income groups live in areas farther from downtown which are only accessible by the automobile. This income segregation exacerbates racial segregation because lower income groups are predominately black. Bertaud (2004) claims that urban sprawl is a reason for inad equate transportation systems. He examines the issue of providing mass transit in low density cities. Bertaud compares Barcelona, Spain, to Atlanta, Geor gia—two cities almost equal in population but highly different in their concentration of people (Barcelona has a population density of 171 people per hectare compared to 6 peopl e per hectare for Atlanta). According to him, “to duplicate the accessibility and riders hip of the Barcelona system, Atlanta would have to build an additional 3,400 kilometers of metro tracks and 2,800 stations,” while “in contrast, the Barcelona system has just 99 kilometers of tracks and 136 stations” (O’Sullivan, 2006, p. 149). Bertaud’s conviction is that urban sprawl makes it impossible to create a well functioning ma ss transportation system. A local example confirms Bertaud’s conclusions. The Hartline bus system in Tampa is much less effective than the Metro rail system in Washington, DC. Har tline covers only certain parts of the Tampa area, and its buses arrive every 30 minutes to an hour (www.hartline.org). The Washington Metro system trains arrive almost ev ery three minutes, and the Metro system in Washington covers almost the entire area of Washington, DC, and surrounding communities (www.wmata.com).

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5 Measurement Urban sprawl is often measured by the de nsity gradient, which represents the percentage decrease of population density w ith distance from the urban area center Over time or cross-sectionally, a smaller density gradient means greater decentralization Mills (1972, p. 35) finds that the density gradients of U.S. urban areas in his sample decreased significantly from 1880 to 1963, which indicates th at urban sprawl has been occurring for many years. Another measure of urban sprawl is the sp atial size of the urban area: other things equal, the bigger the urban area, the lower the average population density, and the greater the sprawl. Regarding spatial size, O’ Sullivan (2006, p. 145) notes, “between 1950 and 1990 the amount of urbanized land in the Un ited States increased by 254 percent while the urban population has incr eased by only 92 percent.” CAUSES OF URBAN SPRAWL The first general equilibrium analytical model of urban structure is Wheaton (1974). Wheaton derives many properties of hi s model, among which is that the spatial size of the urban area is direc tly related to the urban area ’s mean income and population and inversely related to the cost of travel within the urban ar ea and to the value of rural land adjacent to the urban-rural boundary. Wheaton’s model does not contain a housing sector, but Brueckner (1987) synthesizes the simulation models of Mills (1972) and Muth (1975), which do contain a housing sector, wi th the theoretical model of Wheaton, and obtains the same results.

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6 Population growth and rising real inco me increase the demand for housing, and a greater quantity of housing is a better buy fart her out. The land price decreases with distance from the center of the urban area because of the demand for accessibility to the central business district (CBD). For a give n quantity of housing, th en, housing price also falls with distance from the CBD. People choos e where to live in an urban area by trading off the decrease in housing expenditure against the increase in commuting cost with distance. As long as the decrease in housi ng expenditure (the marg inal benefit of distance) is greater than the increase in commu ting cost (the marginal cost of distance), households will move farther from the CBD. When these quantities are equal, the household has found the optimal distance. Increa sed demand for housing upsets this equilibrium because it induces the household to purchase more housing, which, since housing price falls with distance, is a better buy fart her out. This causes the urban area to expand spatially. Lower real transportation cost allows people to commute longe r distances at the same total cost, which also encourages s uburban living. According to Glaser and Kahn (2004), automobiles have been the primary r eason for urban sprawl throughout much of the twentieth century. Nechyba and Wals h (2004) show that, for the period 1910–1920, the number of car registrations increased dramatically, from half a million to more that eight million. Glaser and Kahn (2004) point out that by 1952 a majority of U.S. residents had at least one car. From 1964 to 2000 th e number of people commuting to work increased by 24 percentage points, from 64 pe rcent in 1964 to 88 per cent in year 2000. Undoubtedly, the rise of automobile transpor tation is an important reason for sprawl.

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7 Finally, higher rural land values impe de urban development because urban land use must command a higher value to allow buyer s to outbid rural la nd users. These predictions have empirical support (Bruec kner and Fansler, 1983; McGrath, 2005). In addition to the fundamental causes discussed above, economists identify market and government failures as contributing s ources of urban sprawl. The following is a brief discussion of them. Failure to Account for the Social Costs of Road Congestion (Brueckner, 2001). Auto commuters pay the private cost of ope rating and maintaining their cars, and they pay partial costs of road use through taxes. They do not, however, pay the full cost of congestion. That induces households to occ upy residences farther from the CBD than they would if they paid the full costs of co mmuting, which leads to excessive spatial expansion of urban areas. Failure to Account for the Social Value of Open Space (Brueckner, 2001). As already noted, households value open space, but open space, such as parks within urban areas and rural land outside of urban areas, is a public good, and, as such, exhibits the free-rider problem. Thus, a household chooses to live at the urban fringe, causing a conversion of open space to urban use, and does not consider the effect s of its action. Consequently, too much open space is converted to urban use. Failure to Account Fully for the Infr astructure Costs of New Development (Brueckner, 2001). When a new residential area is developed, the cost of public infrastructure, such as roads, sewer systems, schools, and recreation centers, is mostly paid through the property tax. This results in a government failure be cause developers and home buyers do not bear the full cost of converting the open space into land available for urban

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8 use. The infrastructure cost imposed on home owners by local governments through the property tax generally does not cover the marginal infrastructure cost but the average, which is generally less than the marginal. Homeowners with equal assessed values pay the same tax regardless of whether the house is located in newly de veloped areas or in already developed areas. As a result, devel opers would bid higher prices for undeveloped land than normally, which lead s to converting more rural la nd into urban use. Thus, people living in high density, already devel oped areas subsidize re sidents living in lowdensity, suburban areas. This is an argumen t for impact fees, which have become more prevalent as well as higher in recent years (Brueckner, 1997). Transportation Subsidies (Brueckner, 2005a). Bruec kner points out that for transportation and location decisions to be effi cient, residents should pay the full cost of transportation. In reality, however, individuals do not bear the full cost of transportation because of transportation subsidie s. The fact that residents un derpay the cost of traveling allows residents to commute longe r distances and seek living in city suburbs, thus contributing to sprawl. Su and Desalvo (2008) empi rically test the effect of transportation subsidies on urban sprawl, showing that the urban area contracts with public transit subsidies and expands with auto-subsidies. Mortgage Subsidies Mortgage interest is deductible from income for the purpose of federal and state income taxes, which lo wers the cost of home ownership, and which, for reasons discussed above, encourages people to locate in the suburbs of urban areas. Williams, Burton, and Jenks (2000) argues that through their generous mortgage insurance and loan programs, both the Federal H ousing Administration (FHA) and the Veterans Administration (VA) create incentives fo r urban sprawl. For example, the FHA pro-

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9 vides federal guarantees to private mortga ge lenders by loweri ng the minimum down payment to just 10 percent and extending the pay-back period from 20 to 30 years. The VA offers low-interest mortgages without down payment to all qualified veterans. The Property Tax Brueckner and Kim (2003) adva nce the idea that the property tax is a source of sprawl. Pr operty taxes are usually lower in the suburbs than in their central cities. Therefore, land in the suburbs is developed less intensively than land in the central city, which contributes to the spatial expansion of the city. Brueckner and Kim provide numerical examples that confirm th e suggestion that the property tax may encourage urban sprawl. O’Sullivan (1985) analyzes the spatial e ffect of property taxes using a model including both bus iness and residential property, finding that an increase in property taxes reduces employ ment in both central and s uburban sectors causing the urban area to shrink in size. Arnott and MacK innon (1997) use general equilibrium simulation of the spatial effects of the property ta x and find that an incr ease in the property tax shrinks the size of the urban area. The resu lts are disputed by Pasha and Ghaus (1995) who note that they might not hold in a more general model. Most recently Song and Zenou (2006) and Su and DeSalvo (2008) find empi rically that property taxes contracts the urban area. Federal Spending Persky and Kurban (2003) contend that spatially dispersed federal spending could lead to urban sprawl In Chicago, they find that government spending to alleviate poverty and support the elderly affect s residential location decisions. In fact, they show that land use in the outer fringe of Ch icago increased by 20 percent because of federal spending.

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10 Land-Use Controls Cities and counties employ a variety of land-use controls, including minimum lot-size zoning, maximu m lot-size zoning, popul ation density controls, rent control, buildi ng height restrictions, urban land-use boundaries, land-use management districts, watershed protection po licies, land-purchase programs, differential property tax assessments, transferable property rights, etc. These land-use controls are intended to achieve various, and sometimes c onflicting, goals, such as reducing or eliminating urban sprawl (e.g., urban land-use boundaries, maximum lot-size zoning, population density controls), ensuri ng adequate housing for the poor (e.g., rent control), aesthetics (e.g., building height rest rictions), environmental im provement (e.g., watershed protection), etc. As will be discussed later, many empirical studies have been performed on the effect of land-use controls on housing prices, but no study has examined their effect on urban sprawl. This dissertati on therefore makes a unique cont ribution to the literature on urban sprawl by documenting the effect of landuse policies on the spatial size of the urban area. Such information should be useful to urban planners w ho are trying to curb sprawl. In addition, this dissertation tests theore tical hypotheses on the effect of land-use controls on the spatial size of urban areas. These theoretical hypotheses have not previously been empirically tested. As such, th is dissertation adds to the positive literature on urban economics. Finally, the data set on land-use controls should be of great use to urban researchers.

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11 CONCLUSION AND PLAN OF THE DISSERTATION This chapter familiarizes the reader with the nature of urban sprawl and analyses some of its causes. Since urban sprawl is widely believed to be a problem for a large number of U.S. cities, local governments develop measures inte nded to restrict the spatial size of the urban area. Chapter 2 provides a description of land-use controls. Chapter 3 surveys papers that provide empirically testab le hypotheses on the e ffect of land-use controls on urban sprawl. Chapter 4 surveys em pirical analyses of the monocentric urban spatial model. Chapter 5 discusses the data we use in our empirical analysis. Chapter 6 supplies an empirical analysis of the effect of land-use controls on urban sprawl. Chapter 7 provides a summary and conclusions.

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12 CHAPTER 2: DESCRIPTIO N OF LAND-USE CONTROLS As a response to urban sprawl and for the other reasons, local governments adopt various kinds of land-use controls. The theore tical urban literature argues that some of these land-use controls prevent or restrain urban sprawl while some facilitate urban sprawl. There have been virtually no empi rical tests of these theoretical predictions, however. This dissertation estimates the magn itude and direction of the effect of landuse controls on urban sprawl. The next chap ter reviews the basic model of urban structure without land-use controls and incorporates theoretical ex tensions of that model to include land-use controls. Theoretical hypothe ses about the effect of land-use controls on urban sprawl are drawn from the literature. This chapter, however, provides a description of the various land-use controls. ZONING1 The urban regulation used most by local governments is zoning. Fischel (1985, p. 21) defines zoning as “the divi sion of a community into dist ricts or zones in which certain land-use activities are prohibited and othe rs are permitted.” There are two types of zoning: cumulative and prescriptive. Cumula tive zoning assigns a hierarchy of land-use restrictions to zones within the city, starti ng with the least restricted zones and moving toward the most restricted zones. This hi erarchy is usually justified by a negative exter1 This section draws heavily on O’Flaherty (2005, pp. 170–197), Bogart (1998, pp. 207–223), and Fischel (1985, pp. 21–37).

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13 nality that some buildings or activities could impose on the surrounding environment. Prescriptive zoning determines the allowable use of land for each parcel of property. A special permit must then be requested to use land in areas of the city not zoned for that activity, even when the desired use is ranked higher in the hierarchy. A zoning code specifies the kind of buildi ngs permitted or prohibited in different districts of the city. For example, resident ial zoning permits the pr esence of residential buildings; commercial zoning permits commer cial and entertainment buildings; and industrial zoning permits factories and other indus trial buildings. What was just described may be called “traditional” zoning. More recently, however, zoning codes have expanded to cover many other kinds of restrictions. The zoning code may also set limits on building size, location, lot size, maximum height, and even color. It may also restrict the number and size of off-street parking spaces and even the number and size of trees. Zoning may also determine the number of buildings in particular zones and the amount of land they occupy. Some of these land-use controls are discussed more fully later. Even though zoning codes are very strict, some exceptions are possible. For example, local government might allow one buildin g to be higher than the maximum height restriction in a zone. The local government issues special permits to some activities that generally are not allowed in any zone. Drugsto res, fast food restaura nts, and gas stations are examples of activities that require a local government perm it in order to be located in particular city zones. A zoning term frequently encountered is “nonconforming land use.” The term refers to the situation in which activities loca ted in conformity to a zoning code become

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14 nonconforming under a new zoning code. In such cases, local governme nt allows the affected buildings to continue their existence, usually with the proviso that they are not to expand nor change dramatically. Finally, local government has the right to change the boundaries of the zones and the rules that apply to them. In order to obtain variances or special permits, individuals and businesses must apply to a zoning or plan ning board. The board usually consists of people appointed by the local government and is empowered to approve or disapprove a submitted application. The board is not usua lly required to provide reasons for its approval or disapproval. Adversely affected fi rms and individuals may object to the board decisions in a special hearing. In most cases, the board acts in the in terest of those citizens who live near the land unde r consideration for a variance. If the neighbors do not object, then the board usually approves the reque st; if there are objections, then the board usually does not a pprove the request. HISTORY OF ZONING2 Today, many U.S. cities have adopted zoning as a common measure of land-use control. The initial purpose of zoning, as not ed earlier, was to put different enterprises into different zones to reduce transmission of smoke, dust, noise, etc., from one sector to another. The second decade of the twentieth centur y marked the beginning of U.S. zoning. The first comprehensive zoning plan was de veloped in New York City in 1916. Eight other cities adopted zoning in the same year Before introduction of comprehensive zoning, many cities used ordinances to monitor a nd exercise land-use control in specific 2 This section draws heavily on O’Sullivan (2006, pp. 185–204) and Fischel (2004, pp. 317–340).

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15 areas of the city. For example, cities regulated the height of tall buildings in response to concerns that tall buildings could block the view of shorter buildings. After 1916, more and more cities started to adopt zoning as a measure of land-use control. By 1936, zoning had been introduced by more than 1,300 cities. The state of urban transp ortation technology in the la te 19th and the early 20th century is viewed as the main cause for not implementing zoning before 1916. Back then, manufacturers transported their output on horse-drawn wagons, which was a slow and expensive mode that required firms to be located near a port or railroad terminal, which were generally at or near the city center. At that time, the main form of public transportation was the hub-and–spoke street ca r system. Low income households lived in apartments close to the city center or along th e spokes of a street-car system. Almost all commercial activities and apartm ents were located along the r oute of the street-car system, a locational pattern that generated ne ighborhoods of mixed land use. Single-family homeowners, on the other hand, lived a few bloc ks from the street-car route and away from industry, commerce, and apartments. Ho meowners valued their quiet, convenient, low-density neighborhoods off th e street-car route and made efforts to prevent extension of the street-car route toward their communities, since possible extension would have disturbed their peace. Introduction of intercity truc k transportation in 1910 allo wed firms to move away from the city’s central export node and closer to their suburban work ers. Before introduction of the intercity truck, the externalities generated fr om industrial firms were confined to the central part of the city where such firms were predominately located. With the existence of intercity truc k transportation, firms moved away from the central part of

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16 the city, thus spreading pollution, noise, dust, etc., into residential areas. That provided the city government with a reason to introduce industrial zoning. The primary goal of industrial zoning was to separa te business, industrial, and commercial activities from residential areas. At the same time, the innovation of mass transit increased mobility of workers. The motorized passenger bus, invented in 1920, allowed workers to live away from the factory and inhabit apartments closer to the homeowners. Local governments responded with the introduction of resident ial zoning. The role of residential zoning was to keep apartments out of homeowners’ neighborhoods. In time, U.S. city and, later, county governments gradually developed a large number of other types of la nd-use controls, such as popula tion land-use limitations, minimum lot-size zoning, maximum lot-size zoning, urban land-use boundaries, buildingheight limitations, square-footag e limitations, impact fees, and density controls. The main reason for these land-use controls was to limit expansion of th e urban area. There were also other reasons for implementation of land-use controls by local governments. For example, minimum lot-size zoning require s more space between houses, which protects one building from nega tive externalities pr oduced by neighboring houses. Maximum density controls prevented overpopulation in certain areas of the city. Buildingheight limitations generated a smoother skylin e and ensured that taller buildings would not block either the view or the sunlight of shorter ones. Fire and occupancy codes were also used for these purposes. Lastly, rent control was designed to ensure that the poor could afford housing in the city.

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17 LAND-USE CONTROLS: THEIR PURPOSE, DESCRIPTION, AND EFFECT ON SPRAWL Minimum Lot-Size Zoning As Bates and Santerre (1994, pp. 253–254) note, “there are two contrasting theories regarding why communities adopt zoning re quirements. According to the public interest theory, zoning laws are implemented to reduce or eliminate th e impact of negative externalities.... Alternativel y, the special interest group th eory argues that zoning laws are designed to promote the fiscal and exclusi onary objectives of the entrenched residents of a community.” By the public-interest th eory, minimum lot-size zoning would reduce population density, thereby mitigating negative ex ternalities thought to be associated with high density, such as disease, fire, crime, a nd traffic congestion. By the special-interest theory, minimum lot-size zoni ng, as well as other population-de nsity restrictions, as Mills (2005, p. 572) puts it, “may be intended to ex clude low-income and/or minority people from high-income suburbs.” Both of these views imply that the urban area expands under minimum lot-size zoning, but th at is an empirical question. Pasha (1992a) discusses minimum lot-size zoning as a type of land-use control and analyzes two cases. In the first case, the central city is regulat ed, but the suburbs are not. In the second case, the central city is not regulated, but the suburbs are. This theoretical paper, to be discussed t horoughly in the next chapter, pr oduces mixed results. In one version of his model, Pasha finds that th e urban area expands under minimum lot-size zoning. In another version, the result is am biguous. In a later paper, in which minimum lot-size zoning was binding on the rich but not on the poor, Pasha (1996) finds that minimum lot-size zoning expands the urban area. According to Pasha, this finding indicates

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18 that implementing minimum lot-size controls in suburbs might be a major factor contributing to urban sprawl. Maximum Lot-Size Zoning Maximum lot-size zoning is used to mini mize the amount of land used for urban infrastructure in the city (Pasha, 1992b). Developing countries use maximum lot-size zoning to keep the price of land low in certain areas of the city so that the poor can afford to live there. If binding, maxi mum lot-size zoning makes lots smaller than otherwise, and a smaller lot, other things equal, is a cheap er lot. Pasha (1992b) studies maximum lotsize zoning in a model in which maximum lotsize restrictions are not binding on the poor but are binding on the rich. Under these conditions, he finds that no matter whether the rich live in the suburbs a nd the poor live in the central city, which is the case in most developed countries, or the rich live in the central city and the poor live in the suburbs, which is the case in most developing countri es, applying maximum lot-size restrictions leads to a contraction of the spatial size of the urban area. Building-Height Limitations Local governments introduce building-height limitations for several reasons. One reason is to achieve a smooth and aesthetic sk yline. Another reason is to prevent tall buildings from blocking the view of shorte r buildings and the s unlight from reaching them. Thus, building-height restrictions pr otect shorter bu ildings from being overshadowed by taller buildings. Like minimum lot-si ze restrictions, building-height limitations may lower population density, which could lead to expansion of the urban area. On the

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19 other hand, as noted by Brueckner and Kim (2003) in discussing the effect of the property tax on the spatial size of urban areas, building-height lim itations may reduce the size of dwelling units in a building, possibl y increasing population density. The first theoretical work on building-height limitations is that of Arnott and MacKinnon (1997). The authors use a model de signed to simulate Toronto. They demonstrate that, in the presence of building-height limitations, the reside ntial land-rent function is higher than it would be without those restrictions. It therefore equals rural land rent farther from the CBD. Thus, building-heig ht restrictions increase the spatial size of the urban area. The major draw back of Arnott and MacKinnon’s analysis is the use of a simulation model with specific functional fo rms and parameters, which limit the model’s generality. Recently, Bertaud and Brueckner (2005) obtain the same results as those of Arnott and MacKinnon in a more general model. Instead of building-height limitations, Bertaud and Brueckner use the fl oor-area ratio, which is the ratio of the floor area of the building to the land area on which building is located. Generally, the greater the floorarea ratio, the taller the build ing. In other words, a bindi ng restriction on the floor-area ratio means a restriction on building height. Population-Density Restrictions Another form of land-use control is popul ation density restri ctions. Maximum population density restrictions may be used to avoid the negative ex ternalities discussed above in the context of minimum lot-size zonin g. Also, as noted there, they may also be used as exclusionary devices. Although not necessarily the purpose, maximum popula-

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20 tion density restrictions might cause an urba n area to expand relative to an urban area without density controls. Minimum population density restrictions, on the other hand, are intended to avoid excessive spread of population over the urban area. As already discussed, most urban econ omists working on the relation between density controls and sprawl have modeled popul ation density indirectly in terms of lotsize and building-height restrictions in general equilibrium models. Peiser (1989) and Heikkila and Peiser (1992) e xplicate the differences in population density resulting from continuous vs. discontinuous (o r leapfrogging) development Peiser (1989) concludes that policies that restrict di scontinuous development may reduce efficiency in the land market and lead to lower, rather than highe r, urban density. Hei kkila and Peiser (1992) find that if the planner opts for a continuous rather than discontinuous, development pattern, the result is lower densities but higher property values. The researchers conclude that planning efforts to limit sprawl are more consistent with tax-base considerations than with concerns over density. These articles show how population density may be affected by continuous vs. discontinuous development, but they do not explicitly address the effect of population density restrictions on urban sprawl. Impact Fees and In-Kind Exactions When an urban area expands in both sp atial and population size and when a new development takes place within the urban ar ea, local governments provide public services, such as roads, rights of way to electri city and telephone companies, water mains, sewers, etc. Historically, local governments ma ke capital expenditures that are usually supported by bond sales. The carrying cost of the bonds is covered by property taxes im-

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21 posed on existing and future residents. In othe r words, old residents contribute to the cost of development for new residents. Considering this policy inequitable, so me local governments place the additional capital cost on developers. This additional co st may be in the form of in-kind exactions on the developers, who are expected to provide parks, roads, and schools, along with other necessary local infrastructure. This additi onal cost may also be in the form of impact fees on developers to pay for additio nal infrastructure (Brueckner, 1997). In-kind exactions and impact fees raise the direct cost of development, which may postpone development and slow the spatial a nd population growth of the urban area. Brueckner (1997) claims this to be an impor tant reason for the incr easing use of in-kind exactions and impact fees by lo cal governments. In a theore tical model, Brueckner finds that the effect of impact fees on new deve lopment depends strongly on the time needed to implement the impact fees and on how devel opment costs and infrastructure costs vary with the urban area population. Brueckner s hows that under usually assumed cost conditions the timing of the shift from bond financi ng to impact fees affects the timing of development and the rate of growth of the spat ial size and population of the urban area. In some cases, the urban area will continue to de velop the same way with or without impact fees, but impact fees cause urban expansion gr adually to slow down. In other cases, the imposition of impact fees causes an immediat e slow-down of devel opment in the areas that are affected by impact fees. Brueckner’ s conclusion is that impact fees on balance cause a slowdown in the expansion of ur ban spatial size and of urban population. Although Brueckner’s article is insightful and informative, it does not provide the kind of comparative static model we seek. In fact, we have been unable to find such a

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22 model. For this reason, in Chapter 2, we will present the model of Song and Zenou (2006). Although a model of the property tax, it is nevertheless useful for our purpose. Urban Growth Boundary Local government imposes an urban gr owth boundary (UGB) by establishing a radius around the city and outlawing any de velopment beyond the radius. The urban growth boundary was first implemented in 1958 in Kentucky. Since then the use of urban growth boundaries has grow n rapidly. By its nature, the urban growth boundary restricts the spatial size of the urbanized area. In a theoretic al model, to be discussed more fully in the next chapter, Quigley (2007) and Quigley and Swoboda (2007) show that, in the presence of a binding urban growth bounda ry, the spatial size of the urban area is lower than otherwise. In reality, however, cities with UGB’s may expand the radius of the UGB to accommodate development, so it is unclear what effect UGB’s have on urban sprawl empirically. Population-Growth Limitations Another type of land-use control used by local governments is the populationgrowth limitation. Population-growth limita tions include direct population caps, building-permit limitations, and maximum density restrictions. The purpose of populationgrowth limitations is to prevent growth, which is associated with overcrowding and sprawl. Maximum population dens ity restrictions were discu ssed earlier, and their likely effect to slow population growth was noted. So far, no U.S. city has adopted direct population caps although some California cities ar e considering them (Groening, 2008). Most

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23 U.S. cities use building-permit limitations to control population growth. Local governments issue a fixed number of building permits per year. If the number of permits issued is less than the number demanded, the result may be to restrict the amount of new development that would otherwise take place. Th e restriction on the number of new buildings may therefore retard growth in the spatial si ze of the urban area. On the other hand, if building permits do not impose a minimum lot-si ze, it is conceivable that the urban area could expand spatially. No theoretical or em pirical research showi ng the effect of building-permit limitations on the spatial size of the urban area has as yet been done. Square-Footage Limitations Local governments adopt both minimum and maximum square-footage limitations on the size of offices and apartment in urban areas. In urba n areas, population density (say, in persons per square mile), housing density (say, in square feet of floor space per acre), and structural dens ity (say, in number of floors per acre), and land rent all decrease at decreasing numerical rates with dist ance from the CBD. Hence, when a binding maximum square-footage limitation is establis hed, buildings near the CBD are required to have a smaller square foot age per acre than would otherwis e be chosen, while at some distance from the CBD, beyond which the limita tion is no longer binding, buildings will have square footage per acre equal to or lower than the maximum. For a given population, this lowers density near the center ca using higher density away from the center, which raises land rent and expands th e spatial size of the urban area.

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24 For a minimum square-footage limitation, th e reverse is the case. Near the CBD, where the limitation is not binding, densities wi ll be equal to or gr eater than the minimum, while farther out, where the limitati on is binding, the desire d densities will be smaller than the required minimum. This cau ses those living farther out to live at higher densities than they would pr efer and, given population, woul d cause the urban area to contract. In a theoretical paper, to be discussed thoroughly in the next chapter, Bertaud and Brueckner (2005) investigate the effect of square-footage limitati ons on the size of an urban area and show that they have the eff ects described above. No empirical studies have been performed to test these theoretical predictions. Rent Control3 Rent control is another land-use control adopted by local governments. Rent control is a price ceiling established on apartment rents. The main purpose of rent control is to ensure affordable housing for the poor, but it may also induce low-income households to live in the city, which might limit spatial expansion of the urban area. On the other hand, it might contribute to sprawl if rich and middle-income households move to the suburbs to avoid the poor. Rent control was imposed in the United States just after the U.S. entered World War II, the first city with rent control being New York. The war required massive relocation of labor, with consequent pressure on many local housing markets. The type of rent control imposed at that time wa s called first-generation rent c ontrol. First-generation rent 3 This subsection draws heavily on Roistacher (1992), Arnott (1995), and Ho (1992).

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25 control was a rent freeze. Later, local gove rnments allowed some provisions in the mechanism of setting rents, which led to second-generati on rent control. Second-generation rent contro l was more flexible than first-generation rent control. For example, second-generation rent control commonly permitted the landlord to increase rent each year, with the percentage increase equal to the annual inflation rate. The local government could also allow the landl ord to justify rent increases based on cost increases other than inflation. An example is a cost-through provision, which permits the landlord to apply for a rent increase above the inflation rate when th e landlord has a justifiable cost increase associated with the apartm ent. Another type of allowable increase is called a hardship provision, which allows discre tionary increases to assure that the landlord does not have a cash-flow problem. Fi nally, there is a rate -of-return provision, which permits discretionary increases in rent to ensure that the landlord receives a reasonable return. In some jurisdictions, s econd-generation rent control permits vacancy decontrol, i.e., the unit beco mes decontrolled once it is va cated. Other local governments apply inter-tenancy decontrol, in which rent control is imposed during a given tenancy with an allowable rent increase during th e inter-tenancy period. Another type of secondgeneration rent control is rent-l evel-decontrol. In this case the apartment is decontrolled but becomes re-controlled if re nt exceeds a certain level. Although much theoretical and empirical re search has been performed on rent control (for a summary, s ee Roistacher, 1992; Arnott, 1995, and Ho 1992), only one study deals with the effect of rent contro l on urban sprawl (Skelly, 1998), which finds that the imposition of rent c ontrol contracts the urban area. Pasha (1995) develops a

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26 model of rent control but draws no conclusion as to its effect on the spatial size of the urban area. CONCLUSION This chapter has discussed various kinds of land-use controls that have been applied by local governments. “Traditional” zo ning is clearly the most commonly used kind of land-use control, but many others ha ve arisen over time. Several land-use controls have been incorporated into theoretical urban models. Little or no empirical research has been performed that tests the pred ictions of these models regarding the effect of land-use controls on urban sprawl. In the next chapter, we review the th eoretical models, drawing out their implications for the effect of land-us e controls on urban sprawl. With this task completed, we then turn to empirical tests of the theoretical predictions. The urban areas in our data set do not employ all of the land-use controls di scussed above, and all have “standard” zoning and building permits. Consequently, in the next chapter, we concentrate on only those kinds of land-use contro ls whose effects we can estimate in our sample of urban areas.

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27 CHAPTER 3: THEORIES OF URBAN FORM WITH LAND-USE CONTROLS The purpose of this chapter is to expos it the standard monoc entric urban model (Brueckner, 1987) and the extensi ons of it that urban economists have made to derive the effect of land-use controls on urban form, in particular, for our purpose, on the size of the urban area. From the extensions, we draw empirically testable hypotheses concerning the effect of land-use controls on urban form, whic h form the basis for the empirical work to follow. Some papers in the area of land-us e controls do not use the static monocentric model. We shall discuss these papers if they shed light on the size of the urban area. We begin, however, with a review of the devel opment of the monocentric urban model and a justification for our use of it to study urban sprawl. DEVELOPMENT OF THE MONOCENTRIC URBAN MODEL The beginnings of the monocentric urban model occurred in the 1960’s, starting with Alonso (1964). Alonso adapted von T hnen’s (1966 [1826]) agricultural land-use model to urban areas. He applied the c oncept of bid-rents, whereby land users bid against one another to obtain land for urban use. Under the assumption that all employment occurs in the CBD and that commuting cost rises with distance from the CBD, the demand for land near the CBD is great but atte nuates with distance. The bidding for land results in high land rent near the CBD and d eclining land rent with distance from the CBD. Because of the ability of households to substitute land for other non-commuting

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28 expenditures, land rent falls at a decreasing numerical rate with di stance from the CBD. A spatial equilibrium is established when all land users are unwilling to relocate within the urban area because those located close to the CBD are “penalized” for their low commuting cost by high land rents, while t hose living farther away from the CBD are “compensated” for their high commuting costs with low land rents. Alonso tested his prediction that residen tial land rent falls wi th distance from the CBD by regressing land expenditures per family (the product of land price per square foot and the number of square feet per fa mily) on family median income and distance from the CBD, using data for Philadelphi a for 1950. Based on the regression results, Alonso concluded that the value of land per fa mily increased with income and decreased with distance from the CBD (Alonso, 1964, pp. 168–172). Although Alonso recognized that a complete model of an urban area had to involve a housing market with households and housing producers as well as a residential land market and that it require d conditions ensuring that a ll households were housed in the urban area, he never deve loped a successful general equi librium model. That came with Wheaton (1974). In addition, the comparativ e static results of Alonso’s partial equilibrium theory of urban consumer choice were all ambiguous. The ambiguity of the model’s comparative static results was due to Alonso’s inclusion of distance from the CBD as an ar gument of the household utility function, assuming that the marginal utility of distance wa s negative. Alonso’s ra tionale for this assumption was to capture the time cost of commuting. Muth (1969) dropped that assumption, arguing that it was unclear empirically wh ether utility increased or decreased with distance from the CBD. Consequently, Muth a ssumed that distance did not enter the util-

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29 ity function but affected location by opera ting through the cost of commuting in the budget constraint. This slight change of a ssumption allowed Muth to obtain a number of empirically testable hypotheses. DeSalvo ( 1977) provided the complete set of comparative static results of Muth’s model. Like Alonso, Muth started his research by defining and deriving the conditions for household equilibrium in urban space. Next Muth added housing producers to the model and obtained equilibrium conditions for housin g producers, but, as with Alonso, he did not successfully develop a general equilibrium model of a monocentric urban area. He nevertheless did provide much empirical evidence on urban areas. Muth found that housing price (the flow price per unit of housing space) fell at slightly less than 2 percent per mile in some cities (Muth, 1969, p. 192) but at 1 percent per mile in a more detailed study of Chi cago (Muth, 1969, p. 309). Subsequently, others generally confirmed the finding that housing pr ice falls at a numerically decreasing rate with distance from the CBD (e.g., Evans, 1973; Wieand, 1973; Coulson, 1991). As will be seen later, this pattern of housing prices produces a dec line in population density also at a decreasing numerical rate Muth confirmed this hypothesis by estimating negative exponential population density functions for forty-six urban areas in 1950 (Muth, 1969, pp. 141–145). By regressing the natural log of population density on distance from the CBD, he produced estimates of the paramete rs, central density (i.e., population density extrapolated to the CBD) and the density gradie nt (i.e., the percentage decline of density with distance). A decrease in the density gradient unambiguously means decentralization of population, while an increase means centraliza tion. To investigate the determinants of population density, Muth regres sed his estimated density gr adients on characteristics of

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30 households, finding that the de nsity gradient falls with income and population, meaning that urban areas decentralize as income rise s, but rises with commuting cost (Muth, 1969, pp. 153–158). In the U.S., the real income of urban residents and urban population have risen over time, while real transport costs have fallen, which are the major factors explaining decentralization of population. Although the early work of Alonso and Muth was extremely important, it did not succeed in producing a general equilibrium mode l. A few years later, however, Mills (1972, pp. 96–108) developed the first general equilibrium urban monocentric simulation model; working independently, Muth (1975) did so as well. Altmann and DeSalvo (1981) showed that these two models were e ssentially identical, prov ided some tests of the Mills-Muth model, and extended it in directio ns that resulted in more accurate predictions of urban development. Wheaton (1974) produced the first general equilibrium analytical urban monocentric model and deri ved a number of comparative results. In addition to developing his simulati on model, Mills (1972, pp. 34–58) also estimated population and employment density fu nctions and, as did Muth, estimated the determinants of density gradients. Mills used a different approach from regression analysis which allowed him to use data further back in time than others had heretofore done. His main finding on population density was th at population had been decentralizing at least since 1880. To investigat e the determinants of densit y, he regressed his estimated population and employment density gradient s on population, income, and transportation costs, with results similar to those of Muth. Wheaton (1974) produced an analytic gene ral equilibrium model, but without a production sector. Finally, Brueckner (1987) combined the work of Muth, Mills, and

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31 Wheaton into an analytic general equilibrium monocentric urban model with a production sector. From here on, when we refer to the monocentric urban model, we are referring to Brueckner’s synthesis. RATIONALE FOR USING THE MONOCENTRIC URBA N MODEL TO STUDY SPRAWL As will be fully exposited later, the monocentric urban model explains urban structure in terms of housing consumption, hous ing price, population density, structural density (housing capital per uni t of land), housing density (t he amount of housing per unit of land), land rent, and the spatial size of the urban area. All of these, except for the spatial size of the urban area, are functions of distance from the CBD. In one variant of the model, called the closed city model, it also determines the spatial equilibrium household utility level, given population, while in anothe r variant, called the ope n city model, it determines the urban population, given the spatia l equilibrium utility level. These endogenous urban structure variables are determ ined by the exogenous variables, population (in the closed city model), the spatial equili brium utility level (in the open city model), rural land rent, household income, and commuting cost. The closed city version of the monocentric urban model, which is the version used most in both theoretical and empirical analysis explains sprawl as the growth in the spatial size of the urban area under change s in population, household income, commuting costs, and rural land rent. Although the ope n city model can e xplain migration among urban areas, while the closed city model canno t, for reasons given in the next paragraph, we use the closed city model in our study of urban sprawl.

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32 In the open city model, the assumption is that households will migrate from urban areas providing lower utility to urban areas pr oviding higher utility unti l utility levels are equalized. If urban areas are homogeneous in the sense that there is no comparative advantage to living in one versus another, then urban areas in the open city model will have equal populations, land-rent functions, housing-pr ice functions, transpor tation costs, etc. When land-use controls differ across urban ar eas in the open city model, however, one would observe differences in sprawl among ur ban areas even allowing for migration to equalize utility. In this case, each urban ar ea in the open city model can be treated as closed with respect to the variation of land-use controls across urban areas. Hence, the closed and open city models may be expected to produce similar results when studying the impacts of land-use cont rols if the urban areas are “imperfect competitors” because of differing land-use controls. (In our sample of urban areas, imperfect competition is further ensured by differences in climate, topography, water access, etc.) Because the open and closed city models will produce similar results with respect to land-use controls, we remain with in the existing literature on sprawl and employ the closed city model.4 THE MONOCENTRIC URBAN SPATIAL MODEL The Household Sector The monocentric model has as a predetermi ned 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 th e household’s residential location and the 4 We thank Professor Kenneth F. Wieand for providing th is justification for the use of the closed city model.

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33 CBD. A household’s quasiconcave utility function, v ( c q ), is defined over housing consumption, q which is a normal good, and non-housi ng, non-transportation expenditures, c The household spends its exogenous income, y on housing; non-housing, nontransportation goods; and transportation. Round-tr ip transportation cost is determined by distance between home and CBD, x and the round-trip cost per mile of travel, t Thus, the problem of the household is to maximize v ( c q ) subject to y = c + pq + tx where p is the price per unit of housing. Upon eliminating c this problem gives rise to the familiar first-order condition (,) (,)q cvytxpqq p vytxpqq (3.1) where the price of the numra ire good is normalized to unity. All urban households are assumed identical with respect to utility function and income. Consequently, for them to be in spatial equilibrium in which no one wa nts to move, it is necessary for the following condition to hold (,) uvytxpqq (3.2) where u is the urban-area-wide spatial equilibri um utility level. The, numraire good, c plays no role in the analysis and is therefore ignored. The Housing Production Sector Housing is produced via a constant-retu rns-to-scale concave production function defined over land, l and non-land inputs, N as follows (,) HHlN (3.3) but because of constant returns to scale, this may be rewritten as

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34 ,1(,1)(), or () HN HHShSHlhS ll (3.4) where S is the nonland-to-land ratio, called struct ural density. Profit per unit of land is given by () p hSiSr (3.5) where p is housing price, as before, i is the rental rate of the nonland input, and r is the rental rate of the land input. Setting equal to zero, solving for r and maximizing rent per unit of land produces the following first-order condition () p hSi (3.6) which is the familiar result that marginal reve nue product equals factor price at the profitmaximizing S Finally, the spatial equilibrium condition for housing producers is that land rent absorbs profit, so all housing pr oducers are equally well off at any location () rphSiS (3.7) Boundary and Population Conditions To complete the model requires an ur ban-area boundary condition and an urban population condition. The urban boundary condition is Arxr (3.8) where x is the distance from the CBD at which th e urban area ends and the rural area begins and Ar is rural land rent (or the opportunity cost of land). Urban households outbid rural land users between the CBD and x while rural land users outbid urban land users beyond x The urban population condition is

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35 0()xhS x dxP q (3.9) where is the number of radians in a circle available for urban residential use and P is the urban population, which is assumed to be the same as the number of urban households. The quotient is population density sin ce it is the total quant ity of housing per unit of land at any given x divided by per-household cons umption of housing at that x. Integrating population density times residential land over all urban land gives total population. This condition ensures th at the population of the urban area exactly fits inside the boundary of the urban area. Closed City and Open City Solutions of the Model5 At this point in the development of the model, it is necessary to distinguish between the “open city” and “closed city” versio ns of the model because some authors use the open city version and others use the clos ed city version while conducting their theoretical analysis. In an open city, utility is exogenous while population is endogenous. The idea behind this is that if utility is higher in one urban area than in another, people will migrate to the first urban area from the second. This raises population and lowers utility in the first urban area while lowering population and raising util ity in the second. Eventually, the utility level is the same in both urban areas and migration stops. In the closed city model, the revers e is the case. An exogenous increase in population lowers utility in the urban area, but no out-migration occu rs. It is sometimes said that the closed city model is a “short-run” model, while th e open city model is a “long-run” model. Since both versions are used, we sh all present the solutions for both. 5 This subsection draws on DeSalvo (2008).

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36 In both versions of the model, Equations. (3.1) and (3.2) are solved simultaneously for p and q, producing the reduced form equations ,,,qqxuty (3.10) and ,,, ppxuty (3.11) Also, in both versions of the model, Equati ons (3.6) and (3.7) are solved simultaneously for S and r, producing the reduced form equations SSpi and rrpi or, using Equations (10) and (11) ,,,, SSpxutyi (3.12) and ,,,, rrpxutyi (3.13) In the open city model, setting ,,,,Arrpxutyi and solving for x produces the reduced form urban-rural boundary equation ,,,,A x xutyir (3.14) Finally, using the above solutions for S q and p the reduced form population equation may be obtained from Equation (3.9) as ,,,,, PPxutyi (3.15)

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37 The recursive solution for the urban -rural boundary and population in the open city model is possible because the spatial eq uilibrium utility is exogenous. In the closed city model, however, this is not the case, and Equations (3.8) and (3.9) must be solved simultaneously, producing ,,,,,AxxPtyir (3.16) and ,,,,,AuuPtyir (3.17) Table 3.1 summarizes these results. TABLE 3.1: Summary of Reduced Form Equations Closed City Open City ,,, qqxuty ,,, ppxuty ,,,, SSpxutyi ,,,, rrpxutyi ,,,,,AxxPtyir ,,,,A x xutyir ,,,,,AuuPtyir ,,,,, PPxutyi Comparative Static Analysis: Closed City Model Comparative static analysis of this mode l is quite complicated and has been provided by Brueckner (1987). We summarize his re sults in Table 3.2. Because our interest is in the effect of exogenous variab les on the size of the urban area, x we only discuss the results for this variable, but see DeSal vo (2008) for a thorough discussion. Following Brueckner (1987), we suppress the variables fo r the radians of available residential land, and the price of th e non-land input, i Suppression of thes e variables has become

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38 common practice although it is not clear why. The reasoning for suppressing the nonland input price is probably the assumption that it varies little among urban areas, for the interest rate, which is its primary componen t, is determined on a national market. Perhaps authors suppress the radians of available residential land, thinking that this is more an empirical than theoretical issue. These are simply speculations as no one to our knowledge has explained the suppression of these variables in comparative static analysis. These remarks apply also to open city mode ls. In both models, equilibrium housing price and land rent are functions of distance from the CBD, i.e., p = p ( x ) and r = r ( x ). In the closed city model, both of these functions shift due to changes in population and rural land rent, but they also pivot due to change s in income and transportation cost; all functions of x only shift in the open city model. Therefore, in Table 3.2, x is the distance at which the pivot occurs. TABLE 3.2: Summary Comparative Statics: Closed City Model, Brueckner (1987) Exogenous Variables Endogenous Variables q p S r x u x + – – – NC NC P – + + + + – r A – + + + – – y x < x + – – – + + x > x ? + + + + t x < x ? + + + – – x > x + – – – – Note : Effects due to and i are omitted. NC means “no change.” The effect of exogenous variab les on the size of the city, x may be seen from Table 3.2. Since x is a specific value of x there is no compara tive static effect of x on x An increase in population incr eases the demand for housing, which drives up housing

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39 price and land rent. At the urban-rural boundary, urban households now outbid rural households and the urban area expands. In contra st, a rise in rural land rent allows rural households to outbid urban households for la nd at the urban fringe and the urban area contracts. If household income increases, ho useholds choose to locate farther from the CBD. An increase in income causes an incr ease in the demand for housing, and since housing price and land rent fall with distance from the CBD more housing is a better buy farther out. Moving farther out raises housi ng price and land rent there and lowers them closer in. That is why these functions pivot at x The increase in land rent farther out allows urban households to outbid rural hou seholds at the urban fringe, thereby expanding the urban area. An increase in transport cost has effects opposite those of an income increase because an increase in transport cost lowers income available for all nontransportation expenditures, including housing. Comparative Static Analysis: Open City Model As for the previous version, comparative st atic analysis of this variant of the model is quite complicated and has been provid ed by Brueckner (1987). We summarize his results in Table 3.3. TABLE 3.3: Summary Comparative Statics: Open City Model, Brueckner (1987) Exogenous Variables Endogenous Variables q p S r x P x + – – – NC NC rA NC NC NC NC – y – + + + + + t + – – – – Notes : Effects due to i and u are omitted. NC means "no change."

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40 Because our interest is only in the effect of exogenous variables on the size of the urban area, x we only discuss the results for this variable, but see DeSalvo (2008) for a thorough discussion. Table 3.3 shows that there is no effect of a change in x on x since x is a specific value of x If rural land rent increases, th is would allow rural households to outbid urban households for land at the ur ban fringe, which would contract the size of the urban area. An increase in household income causes the demand for housing to increase which increases housing price and land rent allowing the ur ban area to expand. An increase in transpor tation cost has effects opposite those of an increase in income. In this variant of the model, the land rent a nd housing price functions do not pivot because of inand out-migration. Other Variants of the Monocentric Urban Model Although we refer to the preceding mode l as the “standard” monocentric urban model, others have presented variants of it th at we feel should be mentioned here. Some researchers have used the indirect, rather than the direct, utility func tion, which leads to a slightly different solution process. Some have included two income classes as well as two modes of transportation. In the closed c ity version of models with either two income classes or two modes, some authors have designated the model as “semi-closed,” meaning that the population, while fixed in total, may migrate within the area thereby changing the boundary between land occupied by hi gher and lower income households or by household using different transportation mode s. Finally, in some cases, the housing production sector has been omitted to simplify th e model if nothing substantive is thereby lost.

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41 EXTENSIONS OF THE MODEL TO INCLUDE LAND-USE CONTROLS Many urban economists have extended th e standard monocentric urban model to incorporate land-use controls, deriving the effect of such controls on the size of the urban area. We survey those models here. Minimum Lot-Size Zoning Pasha (1996) analyzes the effect of minimu m-lot size zoning on the size of the urban area, as well as on other urban variables. He uses the semi-closed version of the standard monocentric urban model with tw o income groups and no housing production sector. Pasha divides the city into two zones, central city and suburbs. He assumes that the rich, denoted by the subscript 2 on releva nt variables, live in the suburbs and face a binding minimum lot-size constraint. The poo r, denoted by the subscript 1, on the other hand, live in the central city and do not face a minimum lot-size constraint.6 The author also assumes that all land is available for residential use, or 2 The author starts his analysis with the suburbs, followed by the centr al city, and we shall follow his approach. Suburbs The utility function of suburban residents is defined as 222,vvcl, where 2ll and l is the minimum lot size, so the minimum lot size is exactly the amount each rich household consumes. (Pasha assumes all households, those residing in both the suburbs and the central city, have the same utility function, so we have omitted 6 In general, the determination of which income class lives in the suburbs and which in the central city depends on the relative magnitudes of the income elasticity of the demand for housing (or land) and the income elasticity of marginal transportation cost. It is not in general the case that the rich live in the suburbs either theoretically or empirically. The first person to recognize this point was Muth (1969, pp. 29–34). In Pasha’s model, the income elasticity of marginal trans portation cost is zero since it is not a function of income. Consequently, for any positive income elasticity of demand for housing (or land), higher income households will live farther from the CBD than will lowe r income households. Therefore, Pasha does not need to assume the pattern he wants.

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42 the subscript on the functional operator, v. ) Residents living in the suburbs face the following budget constraint 222crlz (3.18) where 22zytx. The spatial equilibrium condition for suburban households is 22,uvcl (3.19) where 2u is the spatial equilibrium level of utility. Since, 2vu and ll, 2c is determined by Equation (3.19). Then given 2y and t 2ris determined by Equation (3.18). The suburban population condition is 22x xx dxP l (3.20) where x is the boundary between the ce ntral city and the suburbs and 2Pis the suburban population. (Previously, x stood for the distance from the CBD at which the land rent and housing price functions pivot.) Equation (3.2 0) assumes, as noted earlier, that all rich households consume the minimum lot size. The urban-rural boundary, x is given by 222,, A rzulr (3.21) where x t y z 2 2. Central City In contrast to suburban resident s, central city households do not face a minimum lot-size restriction. Ther efore, these households choose values of 11 and cl in the standard budget-constrai ned utility maximization problem 1111111max, s.t. vvclcrlz (3.22) where 11zytx. Solution of the first-order conditions generates the demand functions 1111,cczr (3.23)

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43 1111,llzr (3.24) The indirect utility function,) (1 1 1r z V V and the spatial equilibrium condition,1u V combine to provide the solution for 1r 1111, rrzu (3.25) Substituting Equation (3.25) into Equa tion (3.24) gives the solution for l1 1111, llzu (3.26) The population condition for the central city is then 1 0 12xx dxP l (3.27) where 1P is the central city popul ation. The boundary between the central city and the suburbs, x is determined endogenously from ) ( ) (1 1 1 2 2 2u z r l u z r (3.28) where x t y zi i = 1,2. Comparative Static Analysis Equations (3.20), (3.21), (3.27), and (3.28) represent a four-equation system that may be solved for the values of the main endogenous variables, x x 2u, and 1u, given the exogenous variables, l, 2P, 2y, 1P, 1y, t and A r. Once these endogenous variables are known, then 2c may be obtained from Equation (3.19), 2r from Equation (3.18), 1r from Equation (3.25), 1c from Equation (3.23), and 1l from Equation (3.24). Note that while l2 is fixed at l, l1 is determined endogenously, so, given A r, x is determined endogenously as well. Pasha conducts comparative static analysis of the effect of minimum lot-size zoning on the main endogenous variables. Since th e mathematics is fairly complicated and is

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44 available in the article, we si mply summarize the results in Table 3.4. The important conclusion for us is that an increase in a mi nimum lot-size constraint that is binding on suburban households expands the size of the city. Presumably this occurs because the binding minimum is greater than the lot size th at would be chosen in the absence of the constraint although this is not st ated explicitly by Pasha. Thus, the rich suburbanites consume more land than they ot herwise would, which expands the urban area, and which also accounts for their becoming worse off. It is interesting to note th at the central city boundary also expands, which, in this model, means that the poor also consume more land and become better off. The reduction in land rent paid by the poor produces these results. TABLE 3.4: Minimum Lot-Size Comparative Statics, Pasha (1996) Exogenous Variable Endogenous Variables 1u2u1r2r x x l + – – ? + + Other Research on Mini mum Lot-Size Zoning Turnbull (1991) examines the effect of minimum lot-size zoning on development in a dynamic monocentric open city model. There is no urban area size variable in his model. For comparison with the zoned urban area, Turnbull first discusses the unzone d urban area. The unz oned urban area may develop away from the CBD or toward the CBD depending on how developer profit changes over time with lot size. If profit in creases or remains unchanged with lot size over time, development proceeds outward from the CBD with decreasing density at greater distances. If profit falls with lot size over time, development proceeds outward from the CBD at increasing, decreasing, or c onstant density. This case also includes the possibility that development proceeds inward toward the CBD with density decreasing

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45 with distance from the CBD. Under minimu m lot-size zoning, development may proceed outward from the CBD, be postponed for a time, produce leapfrogging development, or even produce reverse leapfrogging development. Although this is a ri ch and interesting model, it provides no empirically testable implications on the effect of minimum lot-size zoning on the size of the urban area. Bucovetsky (1984) finds that increasing a minimum lotsize restriction increases the price per unit of housing se rvice and decreases the unit price of land. Although he does not deal directly with the size of the urban area, the preceding finding implies the urban area contracts with increa ses in minimum lot size. Th is follows because a decrease in urban land rent allows rural households to outbid th e given number of urban households for land at the urban-rural fringe. This result is our conjecture since it is not derived explicitly in th e model, nor, for that matter, is the number of households included in the model. If correct, this resu lt contradicts that of Pasha. In an unpublished paper by Henderson ( 1983), Bucovetsky notes, however, that his result depends on the assumption that the ur ban area is small and open, such that the interurban spatial equilibrium utility level is parametric. In the open city model, any land-use restriction will lower utility, in which case population will decline and the urban area will contract. Pasha’s paper assumes a clos ed urban area, that is one with fixed total population, and an endogenous spatial equilibrium utility level. In our opinion, Pasha’s result is the more convincing. Miceli (1992) and Bates and Santerre (1994) examine the fiscal advantages to local government of enacting minimum lot-si ze zoning. Gyourko a nd Voith (1997) show that minimum lot-size zoning results in sorti ng by income within th e urban area with an

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46 increasing concentration of the poor in the ce ntral city. Lichtenberg, Tra, and Hardie (2007) showed that minimum lot-size restric tions induce developers to substitute private space for public open space in urban areas. Although exploring interesting topics, these papers say nothing about the effect of mini mum lot-size zoning on the size of the urban area. Maximum Lot-Size Zoning Pasha (1992b) incorporates maximum lotsize zoning into the standard monocentric model. He assumes a monocentric city with two income classe s as well as two modes of transportation, the auto for the rich and public transportation for the poor. In his analysis Pasha uses subscript 1 for the poor and subscript 2 fo r the rich. He also assumes that all land is available fo r residential use; therefore 2 The Poor Pasha begins his analysis with th e poor, who are assumed not to face a maximum lot-size constraint. The poor thus face the standard budge t-constrained utility maximization problem max 1 1 1, l c v v s.t. 1 1 1 1z l r c (3.29) wherex t y z1 1 1 Pasha assumes both rich and poor have the same utility function. Thus there is no subscript on th e utility function operator. So lution of the first-order conditions generates the demand functions 1 1 1 1, r z c c (3.30) 1 1l l 1 1, r z (3.31) The indirect utility function, ) (1 1 1r z V V and the spatial equilibrium condition,1 1u V combine to provide a solution for 1r

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47 1 1r r 1 1, u z (3.32) Substituting Equation (3.32) into Equa tion (3.31) gives the solution for l1 for the poor as follows 1 1l l 1 1, u z (3.33) The Rich. Pasha assumes that the maximum lot-size constraint is operative for the rich. Hence the rich f ace the budget constraint 2 2 2z l r c (3.34) where x t y z2 2 2 and where l is the maximum lot size. The spatial equilibrium condition is l c v u ,2 2 (3.35) where 2u is the spatial equilibrium level of utility. Since 2u v and l l, 2c is determined by Equation (3.35). Then given 2y and 2t, 2r is determined by Equation (3.34). As in the model discussed in the preceding subsection, Pasha assumes that the rich consume exactly the maximum lot size. To complete the model requires population and boundary conditions. We postpone stating these conditions because in this m odel, in contrast to his previous one, Pasha considers two cases, and the population a nd boundary conditions differ depending on which case is being considered. Case I The poor live in the cen tral city and the rich live in the suburbs. The population condition for poor households is 1 0 12xx dxP l (3.36)

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48 wherexis the boundary between the centr al city and the suburbs and 1P is number of poor households. Similarly 22x xx dxP l (3.37) where x is the boundary between ru ral and urban area and 2P is the population of rich households. The boundary between poor and rich is given by l z u r u z r ) (2 2 2 1 1 1 (3.38) where x t y zi i i 2 1 i. Given fixed rural land value Ar, the urban-rural boundary, x is found where Ar l z u r ,2 2 2 (3.39) where x t y z2 2 2 In Case I, Equations (3.36) to (3.39) re present a four-equation system that may be solved for the endogenous variables, 1u, 2u, x and x Once these variables are known, 1z ,2z, 1z, and 2z are known, and the remaining variables—1c, 2c, 1l,1r and 2r—may be obtained from Equations (3.30)–(3.34), given l, 1P, 1y,2P,2y,1t,2t, and Ar. Case II. The rich live in th e central city, while the poor reside in the suburbs. In this case, the population conditi on for rich households is 2 02xx dxP l (3.40) The population condition for the poor is 1 12x xx dxP l (3.41) The boundary between rich and poor, x is given by

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49 ) , ( ) (2 2 2 1 1 1l z u r u z r (3.42) where x t y zi i i 2 1 i Finally, the urban-rural boundary is given by Ar z u r 1 1 1, (3.43) where x t y z1 1 1 For Case II, Equations (3.40)–( 3.43) may be solved simultaneously for 2 1, u u,x and x Then the remaining endogenous variables—1c ,1l,1r ,2c, and 2r—may be obtained from Equations (3.30) and (3.32)–(3.35). Comparative Static Analysis Next Pasha conducts a co mparative static analysis of the effect of maximum lot-size zoning on the main endogenous variables. The comparative static analysis is done separately for each case. We summarize the results in Table 3.5. Comparative static results show that in both Case I and Case II, reducing the maximum lot size binding on the rich, i.e. reduc ing the amount of land that the rich may occupy, leads to contraction of the urban area. (We speak in terms of decreasing maximum lot size because this policy is usually intende d to control the spread of the urban area.) Although this result seems intuitively acceptable, some of the other results are more difficult to explain, and some are puzzling. TABLE 3.5: Maximum Lot-Size Comparative Statics, Pasha (1992b) Exogenous Variable l Endogenous Variables 1u2u x x 1r2r1l Case I – ? – – + ? – Case II + ? – – – ? + Note : Signs represent a decrease in maximum lot size. In Case I, reducing a binding maximum lotsize constraint on the rich, who live in the suburbs, raises land rent for the poor, w ho live in the central c ity, and reduces their

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50 consumption of land, which explains why they are worse off and why the area they occupy contracts. The effects on the rich, who live in the suburbs, are ambiguous, however. A given number of rich now o ccupies less land, so one woul d expect that land rent for them would rise because land supply falls, which would make them worse off, but, instead, the results are ambiguous. In Case II, reducing a binding maximum lo t-size constraint on the rich, who now live in the central city, contracts the urban area as well as the size of the central city. This would seem to raise land rent for the rich becau se the same number of rich households now occupies a smaller area, which might be expected to lower their utility, but both of these result are ambiguous. For the poor, la nd rent falls and land consumption rises, which explains why they become better off. Land rent for the poor may fall because, although the urban area contracts, the area occupi ed by the rich also contracts, so the supply of land to the poor may increase. Other Research on Maximum Lot-Size Zoning Despite a diligent search, we have found no theoretical treatment of maximum lotsize zoning, other than that of Pasha (1992b), discussed at length above. Urban Growth Boundaries and Similar Land-Use Restrictions Urban areas often place some amount of la nd off-limits to development, for example, parks, wetlands, conserva tion areas, and so forth. The most severe form of landuse restrictions is the urban growth boundary (UGB), which defines an area from the downtown out to a given distance in which urban development is permitted and beyond which no urban development may occur. The UGB may also take the form of a “green-

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51 belt,” which consists of a belt of land surr ounding the unrestricted area. Portland, Oregon, is the best known and most stud ied city in the U.S. with a UGB. Much empirical work but little theoretical work has been performed on UGB’s. Quigley (2007) and Quigley and Swoboda (2007) provide the best theo retical treatment. We follow the development in Quigley and Swoboda, as it is more thorough. The authors start with the standard monocentric m odel, Equations (3.1)–(3.9) above, but modify it to incorporate land-use restrictions and the UGB. Quigley and Swoboda define unrestricted or urbanized land as that land within the urban area th at may be developed. They define the restricted area as the land that cannot be develope d for urban use. Quigley and Swoboda also assume that there is no l eapfrogging development beyond the restricted area. Quigley and Swoboda assume that the restrictions affect k radian of an annulus of width ˆ x at the distance x from the CBD. The urban-rural boundary is, as before, x so ˆ x xx Land use is unrestricted in the rest of the circular urban area. To incorporate land-use restrictions into the standard monocentric model, Quigley and Swoboda modify the population condi tion, Equation (3.9), as follows 0(())(()) 22 ()()xx xhSxhSx x dxkxdxP qxqx (3.44) where k 2 are the radians of unrestricted land, and the remaining variables have the definitions noted above. Equations (3.1)–(3.8 ) and (3.44) represent the complete model with land-use restrictions. Comparative Static Analysis We summarize comparative static results Table 3.6. An increase in the radians of restricted land, k at a given distance from the CBD, x *, limits the supply of land available for developmen t. Given a fixed population, this drives up

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52 the price of housing, p and reduces its consumption, q Although the increase in housing price reduces housing consumption, it increases structural density, S as developers build taller buildings on the reduced supply of land. This drives up land rent, r which expands the urban area not subjec t to the restriction, x Finally, the spatial equilibrium utility level, u falls because of both the increase in housi ng prices and its reduced consumption. Decreasing the distance from the CBD at which the restriction takes effect, x *, holding k constant, reproduces the qualitati ve effects of an increase in k TABLE 3.6: Comparative Statics of Land-Use Restrictions, Quigley and Swoboda (2007) Exogenous Variable Endogenous Variables p q S r x u k + – + + + – x + – + + + – Note : Results for x represent a decrease in distance from the CBD at which the restriction takes effect. In addition to the preceding limited la nd-use restrictions, Quigley and Swoboda examine the more restrictive case where 2 k In this case, we have a UGB that outlaws any development beyond its inner boundary which limits the size of the urban area to a circle with radius x =* x. Under the UGB, the urban-ru ral boundary is determined exogenously by the local government, and the mo del reduces to Equations (3.1), (3.2), (3.5), (3.6), and (3.7) above. The comparativ e static results are qualitatively the same as those given in the second row of Table 3.5, i.e., for a decrease in x, holding k constant at 2 except for the effect on x which decreases along with x *. Other Research on Urban Growth Boundarie s and Similar Land-Use Restrictions The UGB has been widely studied. Researcher s have investigated the effects of a UGB on urban development and the conversion of fa rm land to urban use (Cho, et al., 2007; Cunningham, 2007; Cho, et al., 2006; Jun, 2004 ; Turnbull, 2004; Abbott, 2002; Kline and

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53 Alig, 1999); the effect of a UGB on agricultu ral land values (Marin, 2007); whether or not a UGB is a preferable substitute for a congestion toll (Anas and Rhee, 2006; Anas and Rhee, 2007; Brueckner, 2005b); the distribut ional effects of alte rnative anti-sprawl policies, including the UGB (Bento, Franco, and Kaffine, 2006); the effects of a UGB on urban housing and land prices (Downs, 2002; Lang, 2002; Ne lson, 2002; Fischel, 2002; Phillips and Goodstein, 2000); and amenity a nd disamenity effects either caused by or mitigated by a UGB (Knaap and Nelson, 1988; Cho, 1997). Although many aspects of the urban land-use boundary have been studied, only the work of Quigley and Quigley and Swoboda, discussed at length above, deals directly with the effect of a UGB on the size of the urban area. Cho (1997) and Knapp and Nelson (1998) di scuss the effects of a UGB on land rent when the UGB produces an amenity or disamenity. Cho considers the case of an amenity effect on both sides of the UGB due to the desirability of residential location near a wooded area. Accord ing to Cho, a UGB causes la nd rent to rise throughout the urban area, except in the gree nbelt created by the UGB, where it falls. This implies that the urban area expands. In addition, because of the amenity, land rent rises as one approaches the UGB from either side. Knapp and Nelson assume that the UGB confers an amenity near the inside of th e greenbelt, that is, toward th e CBD, but a disamenity on the outside. Their reason for the amenity is the same as Cho’s. The reason for the disamenity is that Knapp and Nelson assume the land outside the UGB is agricultural and suffers adversely from closeness to the urban area. In this case, they argue that land rent falls from the CBD, rises as one approaches th e UGB, drops discontinuously at the UGB, rises away from the UGB, and eventually begins to fall at some distance away from the UGB.

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54 Since land is rural outside th e UGB, urban development presum ably stops at the inside boundary of the UGB although they do not discuss this. Neither Cho nor Knaap and Nelson present a fully articulated model, nor do these authors derive their results mathematically wi thin such a model. They nevertheless call attention to the importance of the kind of land use on the outside of a UGB. Quigley and Swoboda do provide a fully articu lated model and perform a co mparative static analysis of the effect of an land-use boundary. Mor eover, the Quigley-Swoboda model can be interpreted in ways that make its results consistent with those of Cho and Knaap and Nelson. In the Quigley-Swoboda model, if ur ban land use is permitted beyond the radius at which the UGB begins, then the urban area expa nds. On the other hand, if rural land use begins on the outside of the UGB, then the UGB contracts the urba n area over what it would otherwise have been. For our purpose, the presence or absence of amenity and disamenity effects are not of importa nce; the size of the urban area is. Density Controls Introduction High urban population density cont ributes to traffic congestion, noise, and pollution as well as producing le ss aesthetic skylines, and local governments have used various techniques to control it. In addition, dens ity controls, as Mills (2005, p. 572) noted, “may be intended to exclude low-income and/or minority people from high-income suburbs.” On the other hand, governments have sought to increase density to encourage use of transit, as opposed to the auto, incr ease neighborhood interactions, and reduce infrastructure cost.

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55 We divide density controls into tw o categories, direct and indirect.7 Direct density controls set a maximum or minimum number of people per unit of land. Indirect density controls can be grouped into two classes, housing densit y restrictions and structural density restrictions. Housing density rest rictions set an upper or lower bound on the amount of housing per unit of land. Structural density re fers to the amount of non-land inputs per unit of land and is reflected in bui lding height restrictions and setback requirements. To relate these ideas to the model of Sec tion 1 of this chapter, recall the constantreturns-to-scale housing production function, given in Equation (3.3) above HHlN and its intensive form, given in Equation (3.4) above H hS l where H is the amount of housing at a given di stance from the CBD, which is produced by land, l and non-land, N and where S = N / l The quotient, h / q is the total amount of housing per unit of land at any given dist ance from the CBD divided by per-household consumption of housing at that distance. Assuming single-person households, this is population density, D The three density measures—housing density, h ; structural density, S ; and population density, D —are all directly related. Also, as seen from Table 3.2, S falls with distance from the CBD. Since 0 hS then h also falls with distance. Although not discussed in Section 1, population density also falls with distance. This may most easily be seen by rewriting h / q as ( H / l )/ q Then, since H / l falls and q rises, popula7 In this, we partially follow Mills (2005), who related de nsity controls directly or indirectly to structural density.

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56 tion density falls with distance from the CBD. Because of these relationships, we shall use the model of Bertaud and Brueckner (2005) which deals with housing density in the form of a maximum floor-area ratio ( FAR ). Although we have not found studies dealing directly with structural dens ity and population density rest rictions, we assume Bertaud and Brueckner’s findings can be applied to th ese kinds of restrictions. Some additional comments on this will be made later. The Model Bertaud and Brueckner provide an analysis of the effect of a FAR restriction on the spatial size of the urban area, urban residents’ welf are, housing price, housing consumption, and land-rent. The FAR restriction is repres ented by the following expression hSh (3.45) where h is the maximum FAR set by the local government. To incorporate this FAR restriction into the basic model requires that the following equation replace Equation (3.9) ˆ ˆ 0 xx xhS h x dxxdxP qq (3.46) The first integral in Equati on (3.46) represents the ur ban area population where the FAR is binding, called the restricted area, and th e second integral represents the urban area population where the FAR is not binding, called the unrestr icted area. Integrating both populations gives the total popula tion of the urban area. Except for this change, this model is identical to that of the basic model. Comparative Statics Bertaud and Brueckner obtai n the results summarized in Table 3.7.

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57 TABLE 3.7: Maximum FAR Comparative Statics, Bertaud and Brueckner (2005) Exogenous Variable Endogenous Variablesa u x h p qr h –+ ++– NC aResults for x and u are general; the rest are obtained by simulation and are evaluated at x If the urban area has a binding maximum FAR then from the CBD out to some distance at which the restrict ion is no longer binding, th e urban area will have lower population, housing, and structural densities inside the restricted area than it would have had in the absence of the FAR restriction. This lowers the utility of those living in the restricted area because the restriction is binding on them, i.e., they are forced to live at a lower density than they would prefer. Given an exogenous total population, the FAR restriction leads to population outflow from th e restricted area to the unrestricted area, which expands the urban area and raises housi ng density in the unrestricted area. The increased population in the unrestricted ar ea increases the demand for housing there, which raises housing price and reduces quantity demanded, which, in turn, reduces utility. Finally, at the urban bounda ry, land rent will be the same for an urban area with and without a FAR restriction because, in either case, ur ban land rent is equal to agricultural land rent, Ar, at the urban-rural boundary. Becau se of their direct relation to h these results also apply to caps on structural density, S and population density, D We found no theoretical anal ysis of minimum density re strictions, but we did find such restrictions in our data. Consequently we interpret the results of Bertaud and Brueckner in terms of minimum density restricti ons. Their argument for a positive effect of a maximum FAR on urban spatial size is that the urban population is constrained by the FAR up to the distance at which it ceases to be a binding co nstraint (since FAR will fall

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58 with distance in the uncons trained model). This causes households to seek locations beyond the distance at which the constraint is binding, whic h raises land rents beyond that distance, which, in turn, causes the urban area to expand. Applying this logic to a minimum FAR means that the constraint will be nonbinding up to some distance from the CBD. Beyond that distance and up to the urbanrural boundary, however, the unconstrained FAR would be lower than allowed by the minimum FAR i.e., people are being required to live at a higher density than they would prefer. For a given populati on, this would reduce the spa tial size of the urban area. Again, because of the direct relation among population, structural, and housing density, we conclude that minimum density restrictions, which we denote h S and D will all reduce the spatial size of the urban area. Other Research on Density Restrictions Arnott and MacKinnon (1977) are the first to examine structural dens ity restrictions, in the form of building-height restrictions, in a general equilibrium simulation model. Although their purpose is to measure the costs of such restrictions, not to determined the effect of a buildin g-height restriction on the urban-rural bounda ry, their results may nevertheless be interpreted as supportive of the results of Bertaud and Brueckner. Pash a (1992a, 1995) treats dens ity restrictions as minimum lot-size restrictions, which we have analyzed earlier. Fu and Somerville’s (2001) objective is to determin e how variation in density re strictions within an urban area, due to different intere sts between different levels of government, affects the outcome of site-specific urban redevelopment. To accomplish this objective, they derive a relationship between land price per unit of buildable space and the building-height restriction. Estimating this relationship for Sh anghai, China, they find, “concerns for con-

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59 gestion raise the restriction on redevelopment densities. However, higher resettlement cost and greater inefficiency in the existing land use tend to lower the restriction” (Fu and Somerville, 2001, p. 421).” This analysis, whil e interesting, does not shed light on our concern with the effect of dens ity restrictions on the decentr alization of urban areas. In an empirical study of Mumbai, India, similar to that of Fu and Somerville, Nallathiga (2006, p. 132) finds, “the impact of density regulation is highes t on the already highly demanded space in the CBD; also, the impact is significant in the suburbs.” Again, this type of analysis does not shed light on our concerns. Impact Fees Introduction When new development occurs in an urban area, the local government (municipality or county) must provide infrastructure (roads, water mains, sewer lines, parks, schools, police and fi re protection, etc.) to support that development. To pay for the infrastructure, local governments collect property taxe s, which are the main source of local governmental revenues, but exactions, that is, non pr operty-tax revenues, are also used. Only about 10 percent of localities in the U.S. used exactions before 1960, but by the mid 1980’s, in contrast, 90-percent of local ities were using exacti ons. Prior to 1960, most exactions were levied in-kind, such as the developer’s provision of land for a park, but by the mid 1980’s, about 60 percent of local ities were using both in-cash and in-kind exactions (Altshuler and Gmez-Ibez, 1993) Such exactions are known as development or impact fees, and incl ude, in addition to those noted above, fees in lieu of developer land contributions for parks and schools, an d development excise taxes, also called privilege or facilities taxes (Mullen, 2003).

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60 As discussed further below, most research on impact fees deal s with their effect on housing and land prices and on their efficien cy aspects. We have found no research on the effect of impact fees on the size of th e urban area. For our purpose, we would like a model similar to those discu ssed above, that is, a static monocentric model, but apparently there is none. Instead, we present Song and Zenou’s (2006) model of the property tax. Although the property tax is levied a nnually, whereas the imp act fee is a one-time exaction, both are imposed on real property (i.e., land and improvements), and we assume that both should have the same qualitative effect. As Song and Zenou note, Brueckner and Ki m (2003) “provide the only theoretical analysis that incorporates a land market to investigate the connection between urban spatial expansion and the prope rty tax” (Song and Zenou, 2006, p. 520). Unfortunately, however, Brueckner and Kim’s finding regardin g this effect is ambiguous. The ambiguity arises from two effects of the property tax and, we assume, impacts fees on the spatial size of the urban area. The firs t is called the “building height effect.” Since the property tax, as well as the impact fee, is imposed on both land and structures, it s effect is to lower developers’ profits per unit of land, resulting in a lower building height per unit of land (a lower structural density). Given population, this effect would, by itself, lead to an expansion of the urban area. The other effect is called the “dwelling size” effect. Since some of the property tax or impact fee is shifte d forward to households when levied on landlords or imposed directly on homeowners, then housing prices increase and households choose smaller dwelling units on smaller sites. For a given population, smaller dwellings and smaller sites imply increas ed population density and a sp atially smaller urban area.

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61 To get around this ambiguity, Song and Ze nou use a model with specific, rather than general, functional forms. Their mode l yields an unambiguous decrease in the spatial size of the urban area due to the propert y tax, and their empiri cal analysis supports that finding. We should note that Su and DeSalvo (2008) ha ve presented a model with a property tax, which is more general than that of Song and Zenou. We choose not to present that model because its main emphasis is on the effect of tr ansportation subsidies on the spatial size of the urba n area. Also, it contains tw o transportation modes, which would complicate the analysis n eedlessly. Finally, it contains no explicit housing market, which, given that impact fees are levied on housing developers, renders the model unsuitable for our use. Nevertheless, Su and DeSa lvo’s empirical analysis supports the negative effect of the property tax on th e spatial size of an urban area. The Model For the household sector, Song and Zenou assume a quasi-linear utility function ,ln vcqcq (3.47) where the variables have the same definitions as before. Maximizing this subject to the budget constraint ycpqtx (3.48) and solving the first-order condition given by Equation (3.1) above produces the closed form demand functions 1 and 1 qcytx p (3.49) Substituting these into the utility functi on produces the indirect utility function 1ln Vytxp (3.50)

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62 where V is taken as the urban-area spatial equili brium level of utility, analogous to Equation (3.2) above. Then the housing pr ice function may be solved as 1 ytsVpe (3.51) and the housing demand function as 11ytxVq e (3.52) For the housing production sector, Song and Zenou assume the housing production function 0.5,2 HHlNlN (3.53) analogous to Equation (3.3) above. Dividing through by l gives 0.52 H hSS l (3.54) analogous to Equation (3.4) above, where S = N / l It is at this poi nt that Song and Zenou introduce the property tax, Hence, profit per unit of land is 0.5121 phSriSpSriS (3.55) which is analogous to Equation (3.5) above a nd where the variables are as previously defined. Song and Zenou argue that imposing the property tax on developers produces the same effect as imposing it on households. In fact this formulation is better for our purpose because impact fees are imposed on developers. At this point, the methodology diverges from that of the basic m odel. Instead of setting equal to zero, solving Equation (3.55) for r and maximizing r with respect to S getting the first-order cond ition analogous to Equation (3.6 ) above, Son and Zenou substitute the previously derived housing price function, Equation (3.51), into Equation

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63 (3.55), then maximize the modified Equation (3.55) with respect to S Given the functional forms assumed allows them to solve the first-order condition for S getting 21 2 21ytxVe S i (3.56) Substituting this into h ( S ) yields 12 1ytxVe hS i (3.57) To get the land rent function, substitute Equations (3.56) a nd (3.57) into Equation (3.55), set 0 and solve for r getting 21 21 1ytxVphS e riS i (3.58) which is analogous to Equation (3.7) above. The boundary condition, analogous to Equation (3.8) above, is 21 21ytxV A e r i (3.59) while the population condition, anal ogous to Equation (3.9) above, is 21 002 1ytxV xxhS e dxdxP qi (3.60) Note that the term preceding the in tegrand in Equati on (3.9), namely x is missing from Equation (3.60). This is so because Song a nd Zenou assume a linear, not circular, urban area. These two equations may be so lved for the equilibrium values of and x V, giving 1 ln1 21 A tP x tr (3.61)

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64 and 0.5ln11AVytirtP (3.62) This completes the model, and from here it is easy to obtain the comparative static effects of the property tax on endogenous variabl es, shown in Table 3. 8. An increase in the property tax raises housi ng price and land rent, which reduces the demand for housing and causes developers to produce smaller dwelli ng units per unit of land. These effects contract the urban ar ea spatially and lower household utility. TABLE 3.8: Property-Tax Comparative Statics, Song and Zenou (2006) Exogenous Variable Endogenous Variables p r q h x V + + – – – – Other Research on Impact Fees. As noted above, most of the research on impact fees has been on their effect on housing and la nd prices (for a survey, see Fischel, 1985). The general conclusion is that impact fees raise housing and land prices (Ihlanfeldt and Shaughnessy, 2004; Skaburskis, 1992; Dela ney and Smith, 1989; Baden, Coursey, and Harris, 2000; Evans-Cowley and Lawhon, 2003; Mathur, Waddell, and Blanco, 2004). Gyourko (1991) examines the relationship betwee n impact fees and exclusionary zoning. He finds that impact fees reduce the incentive for communities to engage in exclusionary zoning, which leads to an increase in the optim al density of new development. Brueckner (1997) finds that impact fees retard urban land-use, limiting both population and spatial size of urban areas. Jeong and Feiock ( 2006) explored the economic consequences of impact fees on local economic development and job growth. They use time-series crosssection data for sixty-six Florid a counties and find that, in c ontrast to other research re-

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65 sults, impact fees enhance economic performan ce and lead to job gr owth. Finally, Skaburskis (1990) examines the incidence of deve lopment impact fees. His analysis shows that, in competitive markets, the burden of impact fees is pa ssed forward to households. Skaburskis also finds that changing impact fees in response to changing market conditions increases housing prices by increasing uncertainty. CONCLUSION The purpose of this chapter is to familiarize the reader with the theory of the standard monocentric model as well as with the theore tical extensions of th is model that include land-use controls. Table 3.9 summarizes the effect of land-use controls on the size of the urban area as given in the urban literatur e, including the behavi or of density restrictions that we presented above. TABLE 3.9: Effects of Land-Use Controls on the Spatial Size of Urban Areas Land-Use Control Effect Minimum Lot Size, l (Pasha, 1996) + Maximum Lot Size, l (Pasha, 1992a) – Urban Growth Boundary, x *, k (Quigley and Swoboda, 2007) – Maximum Density Restriction (B ertaud and Brueckner, 2005) Housing Density (FAR), h Building-Height, S Population Density, D + Minimum Density Restriction (Bertaud and Brueckner, 2005) Housing Density (FAR), h Building-Height, S Population Density, D – Impact Fee, (Song and Zenou, 2006) – Note : Signs represent effects from incr eased stringency of the control.

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66 CHAPTER 4: A REVIEW OF EMPIRICAL ANALYSIS OF THE GENERAL EQUILIBRIUM MONOCENTRI C URBAN SPATIAL MODEL INTRODUCTION Empirical research on the general equilib rium monocentric urban model was initiated by Brueckner and Fansler (1983).8 McGrath (2005) provides the most recent empirical analysis of the model. Both of these articles report tests of the basic, unextended, closed city model described in Chapter 3, pp. 27–34. Song and Zenou (2006) extend the model to include the property tax, and Su and DeSalvo (2008) ex tend it to include two modes of transportation, transp ortation subsidies, and the prop erty tax. Both of these latter articles include empirical testing. Becau se we shall use similar empirical analysis, we provide a brief review of the a bove articles in this chapter. All of these articles test the closed ci ty model. To our knowledge, no one has tested the open city model. Table 3.2, p. 33, summarizes the comparative statics of the closed city model. The spatial size of the urban area, repres ented by its radius, x which is also the urban-rural boundary is found to be directly rela ted to urban area population, P ; directly related to urban area income, y assumed equal for all urban households; inversely related to marginal = average transportation cost per round-trip mile, t also assumed to be equal for all urban households; and inversely related to ru ral land rent at the urban-rural boundary, rA. 8 In Chapter 3, we reviewed relevant theoretical and empirical work prior to the development of the general equilibrium model.

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67 BRUECKNER AND FANSLER Brueckner and Fansler (1983) use 1970 censu s data for a sample of 40 urbanized areas, each contained within a si ngle, relatively small county. The dependent variable is the size of the urbanized area in square miles, a proxy for x P is urbanized area population. Brueckner and Fansler (1983, n. 11, p. 481) describe their procedure for estimating income, y as follows: “The population of the city not living in group quarters (e.g., prisons and fraternities) was multiplied by per capita income, and the resulting figure was divided by the number of households in th e urban area (shown by the census as the number of occupied housing units).” Brueckner and Fansler (1983, p. 481) claim this is “a measure of average household income similar to median income.” It is unclear what they mean by this because it is unclear if they u se “city” to mean “central city” or as a synonym for “urbanized area.” If the former, it is not clear to us that this approximates median household income for the urbanized area. If the latter, then it estimates urbanized area mean household income. We interpret thei r income variable as the latter. The authors use two proxy-variabl es for transportation cost, t The first is called TRANSIT, which is equal to the percentage of commuters using public transit. They argue that this variable should be directly related to t because bus, which is the most widely used form of transit in their urbanized areas, is co stly in terms of time. The second is AUTOS, which is equal to the percentage of house holds owning one or more automobiles. The authors argue that this proxy s hould be inversely related to t because a high value of AUTO would imply ease of auto u sage due to less congestion. Finally, Brueckner and Fansler proxy rural land rent, rA, by the 1969 median agricultura l land value per acre for the county containing the urbanized area. They believe that rural la nd value in small coun-

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68 ties better approximates the theoretical variab le than would rural land value in larger counties, which is why they restrict ed their sample to small counties. Because the theory does not dictate a part icular functional form, Brueckner and Fansler use two Box-Cox specifications, a nonlinear flexible form and a linear form. The authors estimate two equations for each form, one using TRANSIT and the other using AUTOS as the transportation cost proxy. The r esults are presented in Table 4.1, for the non-linear form, and Table 4.2, for the linear form. TABLE 4.1: Box-Cox N on-Linear Estimation ( = 0.53), Brueckner and Fansler (1983) Variable With TRANSIT With AUTOS Coefficient t Coefficient t P 0.015449.0430.15399.158 y 0.079083.2330.079053.230 TRANSIT ( t )–0.046790.1979 r A –0.071502.856–0.079052.736 AUTOS ( t ) 0.111680.1573 Constant –16.71153.046–18.716651.309 R2 0.7760 0.7760 N 40 40 TABLE 4.2: Box-Cox Linear Estimation ( = 1), Brueckner and Fansler (1983) Variable With TRANSIT With AUTOS Coefficient t Coefficient t P 0.0004110.0300.000409.876 y 0.006203.0330.006243.050 t ( TRANSIT )–0.244400.406 r A –0.030283.090–0.028882.888 t ( AUTOS ) 0.247460.4604 Constant –41.072322.277–63.469131.244 R2 0.7982 0.7985 N 40 40 These tables show that urban area population has a st atistically significantly positive effect, agricultural land value has a signi ficantly negative effect, and income has a

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69 significantly positive effect on the spatial size of the urbanized area, all consistent with the theoretical predictions. The authors find both proxy vari ables for transportation cost to have the right signs but to be statistically insignificant. Brueckner and Fansler conjecture that the proxies may fail to capture actu al commuting cost differences and that, although they may be correlated with commuti ng cost, their small range of variation within the sample may prevent precise estimation results. The coefficients of determination, R2, are high for all estimates, i ndicating that the few exogenous variables capture most of the variation in spatial size. The reason for using both a non-linear and a linear form is that they could not reject th e hypothesis that the form was linear. In the non-linear version, = 0.53, indicating an approximately square root transformation, while in the linear version, was set equal to one. MC GRATH McGrath (2005) uses census data for 1950 through 1990 to create a sample of 153 urbanized areas contained with in the thirty-three largest U.S. metropolitan areas, which would give him a potential sample size of 165, but several urbanized areas were missing data on land area and CPI, reducing the sample to 153 complete observations. Since the spatial size of a circ ular urban area is A = x 2, McGrath estimates the radius of the urban area, as x = ( A / )0.5, which he calls XBAR, where A is the area of the urbanized area in square miles. Population, P called MSAPOP, is measured as the population in thousands for the metropolitan area. Income, y called RPINC, is real per capita personal income for the metropolitan area in 1990 dollars. Rural land rent, rA, called RAGVAL, is proxied by the nominal agricultural land value per ac re for the state in which the metropolitan

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70 area is located. The data are from the USDA Economics and Statis tics Office and were converted to 1990 dollars. As a proxy for transportation cost, t McGrath creates a variable called APTCPI, which is the regionally adju sted private transpor tation consumer price index in 1990 dollars for the metropolitan ar ea, where APTCPI = 100 for Atlanta. This variable was created by scaling CPI data by re gionally comparative private transportation cost data for 1990, available from the Ameri can Chamber of Commerce. The author also creates a time variable, ca lled DECADE (also called ) which he uses to capture the increasing polycentricity of urban areas, fiscal and social disparities, and market failures, all of which he contends contribute to th e spatial expansion of urban areas over time. We are troubled by the mixing of data for urbanized areas, metropolitan areas, and states, for these areas may di ffer significantly with respect to all variables in the estimated equations. We would have preferred th at all variables related to urbanized areas. Despite these concerns, McGr ath’s results are statistica lly good, as we shall see. McGrath estimates two regression models. In Model 1, the author does not use the time trend variable, DECADE. In this model, the author regresses LNXBAR (the natural logarithm of x ) on LNPOP (the natural logarithm of P ), RPINC ( y ), RAGVAL ( rA), and APTCPI ( t ), using OLS in an equation of the form 01234lnlntiiiAi x Pyrt (4.1) where i represents the metropolitan region and represents time. McGrath argues that the functional form “i s consistent with logarithmic functional forms identified for metropolitan density grad ients....(McGrath, 2005, p. 4)” Although he provides no further justification, his rationale apparently follows from the fact that population density functions are usually estimated in the negative exponential functional form

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71 10 DxDxDe (4.2) which under natural log transform becomes 01lnln D xDDx (4.3) where D ( x ) is population density at distance x from the CBD, D0 is the level parameter, and D1 is the density gradient (Mills, 1972). Since densit y is population, P divided by area, A at distance x from the CBD, then ln D ( x ) is ln P ( x ) – ln A ( x ), and, with a little algebra, Equation (4.3) becomes 01lnlnln A xPxDDx (4.4) Since A proxies x this gives the relation between x and P that McGrath wants. This is, however, not really the same as his estimati ng equation, Equation (4 .1). Equation (4.4) has A and P varying with x as well as including x as a regressor, while McGrath’s A and P are metropolitan area totals and x is not a regressor. Nevertheless, his estimating equation produces good results. Both OLS estimations are presented in Ta ble 4.3. The results for Model 1 show that the coefficients on populat ion, real personal income, a nd real agricultural land values are all statistically significant and have signs consistent with expect ations. However, the coefficient on the transportation cost index is not statistically si gnificant although its sign is consistent with the theory. The R2 indicates that over 87 percen t of the variation in urbanized area size is explained by the variable in the regression. In Model 2, which includes the time trend variable, all the coefficients on the independent variables are statis tically significant. The coe fficient on the transport cost proxy variable is statistically significantly ne gative, which is in accord with theory. The time variable is positive and statistically si gnificant, which means that urbanized areas

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72 tend to grow spatially over time for reasons other than those proposed by the theory. As McGrath points out, the coefficient on the time -trend variable implies that the spatial size of urbanized areas on average grows 2.3 percen t larger per year than implied by changes in the other regressors, but the explanator y power of the model improves only slightly, indicating that these variabl es still are the predominant forces at work explaining urban growth. TABLE 4.3: OLS Estimation, McGrath (2005) Variable Model 1 Model 2 Coefficient t Coefficient t P 0.37624.340.38224.39 y 0.00003655.830.00001531.74 r A –0.00004672.01–0.00005472.42 t –0.0001690.240.002552.58 0.1163.33 Constant –0.6416.25–0.6726.33 R2 0.871 0.879 N 153 153 SONG AND ZENOU The primary purpose of Song and Zenou (2006) is to estimate the effect of the property tax on the spatial size of the urban area. Their th eoretical model, discussed in Ch. 3, differs from those underlying the preceding estimations in that it assumes a linear, not circular, urban area. Ne vertheless, Song and Zenou use th e variables of the standard model in addition to the property tax as regressors. Their sample consists of data on 448 urbanized areas in 2000. Data on urbanized area size, population, and income are from the 2000 Census. The dependent variable is the size of the urbanized areas in acres, a proxy for x For income, y they use median household income adjusted by the 2000 ACCRA Cost of Living Index, which permits

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73 cost-of-living comparisons among urbanized area From the U.S. Census of Agriculture, they obtain 1997 median agricu ltural land value pe r acre for the c ounty containing the urbanized area, a proxy for rA. As a proxy for t they create a vari able called TRANS, which is 1997 governmental transportation e xpenditures per person who drives to work, obtained from the U.S. Census of Governments. Song and Zenou argue that, other things equal, a higher value of TRANS would be asso ciated with ease of transportation system usage and a lower level of commuting cost. An urbanized area may contain within its geographical boundaries many different taxing jurisdictions, such as, c ounties, cities, townships, and school districts. For consistency with their theoretical model, Song and Zenou need a property tax rate for each urbanized area in their sample. They were able to obtain an effective property tax rate (that is, the property tax rate times the ratio of assessed value to market value) for each geographical area within their sam ple urbanized areas from public sources as well as conversations with officials of the various taxing authorities. Ne xt, using GIS techniques, they determine the proportion of each taxing jurisdic tion’s spatial size to th at of the urbanized area. Their weighted-average property tax rate, called TAXRT, is the sum of each taxing jurisdiction’s effective property tax rate multip lied by its proportionate size. Because of the proliferation of taxing ju risdictions in large urbanize d areas, Song and Zenou exclude from their sample urbanized areas with populations larger than five million. Song and Zenou are concerned that includi ng their property tax variable as a regressor might give rise to simultaneity between that variable and the size of the urban area. On one hand, a higher property tax c ould decrease the size of the urban area. On the other hand, as an urban area expands spat ially, it might increase property tax rates to

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74 pay for infrastructure required by the expans ion. Of course, whethe r or not property tax rates rise depends on how average infrastru cture costs change as population increases. They could rise, fall, or remain unchanged if the marginal infrastructure costs were greater than, less than, or equal to the average.9 To handle this potential problem, Song and Zenou use two-stage least squares (2SLS). As an instrumental variable (IV) for th e property tax rate, they choose the magnitude of state aid to schools, obtained from the National Cent er for Education Statistics. This variable is negatively correlated with th e property tax (richer school districts get less state aid) but uncorrelated with urba nized area size. Their IV passes the F -test, and the first stage of their 2SLS estimation produces a negative sign on the IV, as expected. The authors also perform a Hausman endogeneity test, which shows a significant difference between the 2SLS and OLS estimates. TABLE 4.4: OLS and 2SLS Estimations, Song and Zenou (2006) Variable OLS 2SLS Coefficient t Coefficient t P 0.002017.350.00206.31 y 0.001826.370.001934.21 r A 0.000090.410.000050.25 t 0.144175.570.142868.96 TAXRT –3.484795.36–4.236212.41 Constant 117.492608.63120.09746.31 R2 0.8536 0.8520 N 448 448 The empirical results are presented in Table 4.4. The income and population coefficients are positive and st atistically significant. The co efficient on the transportation cost proxy variable is positive and statistically significant, meaning that an increase in governmental expenditures on ro ads and highways lowers tr ansportation cost and in9 We thank Professor Kenneth F. Wieand for this point.

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75 creases urban size. The coefficient on agricu ltural land value is positive, contrary to theory, and statistically insigni ficant. This poor result coul d be explained by the difficulty of capturing the exact value of agricultural land at the ur ban-rural fringe. Finally, the authors find the coefficient on the property-tax variable to be nega tive and statistically significant, meaning that an increase in th e property tax would cau se the urbanized area to contract, as their theoretical model predicts. SU AND DE SALVO The primary purpose of Su and DeSalvo ( 2008) is to investig ate the effect of transportation subsidies on urban sprawl. Th e authors use a sample of 201 urbanized areas from the 2000 census, selected so that ther e is a single central city in a single county to conform better to the monocentric mode l (the sample size ultimately falls to 93 because of data unavailability). The theoretical model, not presented here indicates that the following variables are directly related to urban area spatial si ze: households, income, fixed and variable transit costs, and auto subsidy. Those invers ely related to urban ar ea size are: rural land rent, the property tax rate, fixe d and variable auto costs, and the transit subsidy. Intergovernmental grants have no effect on urban area size. To test these theore tical predictions, Su and DeSal vo regress the spa tial size of the urbanized area on the number of households, P ; mean value of agricultural land, rA; mean household income, y ; and two sets of variables repr esenting fixed transportation cost, fi, and marginal transportation cost, ti, and transportation subsidy, i, where i = 1 for auto and i = 2 for transit. Transportation cost is represented by the follo wing variables: the

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76 percentage of the working age population using transit; auto insuran ce premium, registration fee, license fee, and motor vehicle tax pe r household by urbanized area; bus fare cost per passenger mile traveled; and fuel tax payment per vehicle-mile traveled. Transportation subsidy is represented by the following variables: the su bsidy to bus service per passenger–mile, county subsidies to auto use pe r vehicle-mile traveled, and intergovernmental transfers from state to local gov ernments for transportation purposes, G To capture taxes, Su and DeSalvo incl ude the property tax rate, estimated as the percentage of average household income paid as property taxes. A state dummy variable, S is used to partially account for the age of the urbani zed area and underlying differences in state planning laws and other factors that might influence urban sp atial size. Because of some non-linearities in the data, Su and DeSalvo ente r the income and transit subsidy variables in linear and squared form. The other variables enter linearly. Data on spatial size, population, income percentage of working age population, county subsidies to auto use, intergovernm ental grants, and property tax payments are from the Census. Agricultural land value is from the National Agricultural Statistics Service. The fixed auto costs, bus fares, and va riable auto costs are from the Federal Highway Administration, while the bus subsidies ar e from the Federal Transit Administration. Even though, theoretically, a ll the independent variabl es in the equation are exogenous, Su and DeSalvo consider the possibility that one or more of the explanatory variables may be endogenous econom etrically. In particular, th ey think the transportation cost and subsidy variables may be simultaneously determined with urbanized area spatial size, specifically, working age population using transit, bus marginal cost, bus subsidies, auto marginal cost, auto subsidies. In additi on, they think this might be so for the proper-

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77 ty tax rate as well. To deal with these po ssibilities, Su and DeSalvo use three IV’s for auto marginal cost: state gasoline tax per gallon, urbanized area fr eeway lane–miles, and the number of interstate highway rays in 1970 (a ray is a highway passing through downtown). The authors also use three IV’s for the three potenti al endogenous bus-related variables: the crime rate per 1,000 bus users, adult single-trip base fare, and the federal Urban Area Formula Program funds per passen ger-mile. Finally, Su and DeSalvo use state school aid per student as an IV for the property tax. An F -test reveals that the suspected variables do not signifi cantly bias the OLS results. Consequently, only the OLS results are presented in Table 4.5. TABLE 4.5: OLS Estimation, Su and DeSalvo (2008) VariableCoefficientp-value P 0.00730.000 y 0.13560.000 2y -0.00120.000 r A –0.02690.440 –0.11020.076 G –1.94 e – 70.844 f1 –0.10550.000 t1 0.00930.020 1 –0.00120.016 f2 –0.39570.008 t2 –0.03960.314 2 0.90000.014 2 2 –0.77790.007 Constant 0.8992– R2 0.8365 N 93 The authors find the spatial size of the urbanized area increases with income, as predicted, but at a decreasi ng rate. The coefficient on popul ation, is positive, as predicted, and statistically significant. The coe fficient on agricultural land value is negative,

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78 as predicted, but not statistically significant. The coefficient on the property tax rate is negative, as predicted, and st atistically significant. The coefficient on the proxy for bus fixed cost is negative, as predic ted, and statistically significant. This result indicates that as the percentage of people using transit incr eases, the spatial size of urbanized area decreases. The coefficient on bus marginal cost is positive, as predicted, and statistically significant. That means that an increase in the bus subsidy per passenger-mile reduces urban area size. The coefficient on auto margin al cost is negative, as predicted, but not statistically significant. The coefficient on au to subsidy is positive, as predicted, and statistically significant, while that on auto subs idy squared is negative and statistically significant. These results indicate that the spatial size of the urbanized area is increasing at decreasing rate with resp ect to highway subsidy. CONCLUSIONS The theory of urban spatial structure has b een shown to be robust to specification of estimating equation, proxies for theoretica l variables, sample si ze, and population of urbanized areas included in the database. Th ere appears to be little or no econometric endogeneity of theoretically exogenous variab les, except possible fo r the property tax, although Song and Zenou’s finding differ from t hose of Su and DeSalvo on this point. Extensions of the basic model to include prope rty taxes and transportation subsidies have also held up well to estimation.

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79 CHAPTER 5: DATA DESCRIPTION INTRODUCTION In our empirical analysis, we intend to use an approach similar to that used in studies reviewed in Chapter 4, but with the in clusion of land-use controls as regressors, in addition to population, income, transportation cost, and agricultural land value. The empirical work will test the theo retical predictions of the effects of land-use controls on an urban area’s spatial size, which we presented in Chapter 3. As discussed in Chapter 3, theoretical m odels predict certain effects of land-use controls on sprawl, but none di stinguishes city and county controls. In the U.S. the county is a unit of government and, as such, may impose its own land-use controls. Some of the theoretical work (e.g., Pasha, 1992a, 1996) does include the geographical extent of controls within the urban area, specifically, cont rols in the central city and not in the suburbs and vice versa, but it is implicitly assu med that there is one entity governing the entire urban area encompassing central city and suburbs. No one, to our knowledge, has modeled an urban area with cont rols in both the central city and in the county while recognizing that these are different governments. Despite the theoretical predictions, therefore, it is not obvious what effect such cont rols have on sprawl. For example, land-use controls instituted by the city may, in f act, increase urban spra wl by inducing population to locate in the surrounding c ounty area. On the other hand, the controls in the city and

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80 the county may reinforce each other and redu ce sprawl. For these reasons, we collect land-use control information on both the central city and its surrounding county. THE URBAN AREA We selected a subsample of 182 urbanized areas from the complete set of 465. A subsample is used for three reasons. First, for conformity with th e standard monocentric model, the subsample consists of those urba nized areas located with in a single county and with a single central city. Second, the fact that the outlying portions of our urbanized areas lie within one county considerably simp lifies the gathering of data on county landuse controls. Finally, the analysis should bett er isolate the effect of a land-use control if there is a single city and county imposing the control than if there were several cities and counties doing so. The urbanized area as defined by the U.S. Bureau of the Census is a densely settled core of census block groups and surroundi ng census blocks that meet minimum population density requirements of 1,000 people pe r square mile for the core block and 500 people per square mile for th e surrounding blocks. Together the core block groups and surrounding blocks comprising the urbanized area must encompass a population of at least 50,000 people. The urbani zed area is considered by ur ban economists to best approximate the theoretical urba n area because the urbanized ar ea includes interrelated urban activities without including much rural land (Mills and Hamilton, 1994, p. 6), which is why we shall use it, as have all of th e empirical studies reviewed in Chapter 4.

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81 THEORETICAL VARIABLES, THEIR PROXIES, AND DATA SOURCES An important part of our research is to obtain the data on land-use controls for our sample of urbanized areas. In addition to da ta on land-use controls, we need data on the other variables included in th e theoretical models, namely, the boundary of the urbanized area, x ; population, P ; income, y ; the rental value of rural land at the urban-rural boundary, rA; and transportation cost, t Table 5.1 presents the proxies used for these variables and their sources. The text provides more de tailed discussion. In the text, we split the discussion between the non landuse control variables and the land-use control variables. Tables 5.2 and 5.3 provide descriptiv e statistics for these variables. TABLE 5.1: Theoretical Variables, Proxy Variables, and Data Sources Theoretical Variable Proxy Variable Data Source x Size of the UA sq. mi. Census 2000 P UA households, number Census 2000 y Median UA household income, $ Census 2000 r A Farm land price, county of UA $/acre Census of Agr. 1997, 2002 t Highway expenditures per UA user, $ Census 2000 l Minimum lot-size dummy Planning agency website l Maximum lot-size dummy Planning agency website x* k Urban growth boundary ( UGB ) dummyPlanning agency website S Maximum building-height dummy Planning agency website h Minimum square-footage dummy Planning agency website D D Maximum building permits dummy Minimum persons/room dummy Planning agency website Planning agency website Impact fee dummy Planning agency website Note : UA = urbanized area. Non Land-Use Control Variables Spatial Size of the Urbanized Area ( x ). In the theoretical models, the spatial size of an urban area is the radial distance from the CBD to the urban-rural boundary, symbolized by x Except for McGrath (2005), all of th e studies summarized in Chapter 4 used

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82 use the area, A of the urbanized area in square miles as a proxy for x McGrath calculated the radius, x from the area, A We use the area, A of the urbanized area in square miles as a proxy for x United States Census 2000 Summary File 3 ( SF3), Table P3 (http://www.census.gov), provides the spatial size of urbanized areas in squa re kilometers, which we have converted to square miles. In our sample, the mean size is about 80 square mil es. This is approximately the size of the Athens -Clarke County, GA, urbanized area. The smallest urbanized area in our sample is Davis, CA, with an area of 13.6 square miles, while the largest is Pittsburgh, PA, with an area of 852.4 square miles. Population ( P ). Brueckner and Fansler (1983) McGrath (2005), and Song and Zenou (2006) used population, while Su and DeSalvo (2008) used number of households. We think that number of households is more consistent with the theory since not all households are single-person, as assumed by the theoretical models. In any event, all of these proxies perform very well in the regressions. We use the number of urbanized area households to measure P This variable is found in U.S. Census 2000, SF3, Table P15. In our sample, the mean number of households is around 70,000, which is approximately the size of the Hickory, NC, urbanized area. The smallest urbanized area in our sample, with 15,286 households, is Hinesville, GA, while the largest, with 729,000 households, is Pittsburgh, PA. Income ( y ). Brueckner and Fansler (1983) used a construct that they claim is similar to median income. McGrath (2005) used per-capita personal income for the metropolitan area, not the urbanized area. S ong and Zenou (2006) used median household in-

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83 come adjusted by the 2000 ACCRA Cost of Li ving Index. Su and DeSalvo used mean household income. All of these alternative proxies perform ve ry well in the regressions. We use urbanized area median household income, which is reported by U.S. Census 2000 for 1999 in SF3, Table P54. In our sample, the median household income is about $40,750, which is approximately the me dian income of the Beloit, WI-IL, urbanized area. The standard de viation and range are large, however, with incomes ranging from $22,330, in the Blacksburg, VA, urbani zed area, to about $74,300 in the San Luis Obispo, CA, urbanized area. Rural Land Rent, rA. In the theoretical models, rural land rent, rA, is the rental value of the land per unit area immediately adjacent to the built-up part of the urban area. Since this value of land is not reported by the Census or any other published source, researchers have used alternatives. Bruec kner and Fansler (1983) and Song and Zenou (2006) used median agricultura l land value per ac re for the county containing the urbanized area. McGrath (2005) u sed agricultural land value per acre for the state in which the metropolitan area was located. Su and De Salvo (2008) used mean agricultural land value per acre of the county in which the urbanized area was located. The rural landvalue variable has had mixed success in the empirical studies, being statistically significant only in Brueckner and Fans ler (1983) and McGrath (2005). We use the mean estimated market value of farm land per acre for the county in which the urbanized area is located. This variable is available from the Census of Agriculture (National Agricultural Statistics Service, 1999 and 2004). Since the Census of Agriculture is conducted every five years and in different years from the decennial census, our variable is the mean of the mean s reported for 1997 and 2002. We assume this

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84 mean land value approximates that for the year 2000. In our sample, the mean value of agricultural land is about $5,500 per acre, which is approxim ately the value for San Joaquin County in which the Stockt on, CA, urbanized area is locat ed. It ranges from nearly $150 per acre in Ector County in which the Odessa, TX, urbanized area is located, to about $45,000 in Frederick County in which the Frederick, MD, ur banized area is located. Transportation cost, t In the theoretical models, t is the round-trip cost of travel per unit distance. This variable is unavaila ble, so researchers ha ve used a number of proxies for it, with mixed results. Bruec kner and Fansler (1983) used two proxy variables for transportation cost, TRANSIT and AUTO, where the former is the percentage of commuters using transit and the latter is the percentage of households owning one or more autos. Neither of these was statistically sign ificant in their regressions. McGrath (2005) created a regionally adju sted private transportation co nsumer price index, which was statistically significant in his Model 2 but not in his Model 1. Song and Zenou (2006) calculated the transpor tation expenditures per person who drives to work. This variable was statistically signi ficant. Su and DeSalvo used proxies for both fixed and variable transportation costs for both transit and auto travel. Three of the four such variables were statistically significant. As a proxy for transportation cost in the theoretical models, we use total annual highway expenditures for the state in which a sample urbanized area is located divided by the number of users. The term “users” includ es those using cars and transit vehicles on streets and highways, those using bicycles on stre ets, as well as pedestrians on sidewalks. The data on expenditures and users are obtaine d from U.S. Census 2000 SF3, Table P58.

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85 Song and Zenou (2006) used a similar variable a nd found it to be statistically significant. In our sample, highway expend itures per user average $0.26, which is about the amount for the State of Oregon, in which the Bend, OR urbanized area is lo cated. It ranges from about $0.0015 in the State of Virginia, in which the Winchester, VA, urbanized area is located, to $1.87 in the State of California, in which the San Luis Obispo, CA, urbanized area is located. Descriptive Statistics of N on Land-Use Control Variables The descriptive statistics for these variables are presented in Table 5.2. TABLE 5.2: Descriptive Statistics of Non Land-Use C ontrol Variables, U.S. Urbanized Areas, 2000 VariableUnit Mean St. DevMinimumMaximum Range A Sq. Mi. 79.76 90.38 13.63852.40 838.77 P Households68,68792,94015,286728,884 713,598 y $ 40,74863,97522,33074,335 52,002 r A $/acre 5,51724,24514745,100 44,953 t $ 0.260.19 0.0015 1.87 1.87 Land-Use Control Variables Introduction Unfortunately, data on land-use controls are not available in the census or in any other published source. Consequently, we conducted an extensive search for data on land-use controls reported at the websites of local government agencies. To our regret, we could not collect values of these controls because most governmental agencies do not report this information on their websites. For example, we could rarely find the actual minimum or maximum size of a lot in those jurisdictions with minimum or maximum lot-size zoning, the maximu m building height in those jurisdictions with building-height limitations, etc. Therefore, we use 0-1 dummy variables to represent the absence or presence of land-use controls. (Although we only cite cities, we

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86 found that it was always the cas e that the city website would lead us to the appropriate county information.) The land-use controls for which we have central-city and county data are: (1) minimum lot-size zoning, l; (2) maximum lot-size zoning, l; (3) urban growth boundaries, UGB (Quigley and Swoboda (2007) used two variables to capture UGB ’s, x and k so we are simply naming the dummy variable UGB ); (4) maximum building-height restrictions, S; (5) minimum square-footage limitations, h; (6) maximum population density controls, as proxi ed by building permits, D ; (7) minimum population density controls, as proxied by minimum nu mber of persons per room, D ; and (8) impact fees, We turn now to a brief discussion of the na ture of the various controls in our sample central cities and counties. Table 5.3 provides some descriptive statistics. TABLE 5.3: Descriptive Statisti cs of Land-Use Control Variables, Central Cities and Counties of U.S. Urbanized Areas, 2000 Land-Use Control Central Cities Counties Mean St. Dev Mean St. Dev. l 0.50 0.50 0.68 0.37 l 0.24 0.43 0.33 0.35 UGB 0.19 0.39 0.26 0.48 S 0.77 0.42 0.83 0.44 h 0.48 0.50 0.54 0.47 D 0.49 0.50 0.57 0.45 D 0.50 0.50 0.57 0.43 0.55 0.50 0.63 0.42 None of the central cities and counties in our sample uses rent control and all of them use “traditional” zoning, so those land-use controls have been eliminated from the following discussion and from the analysis repor ted in Chapter 6. Chapter 2 provides a thorough discussion of the various kinds of landuse controls, so here we simply note the specific measures found in our sample.

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87 Since the number of counties and the nu mber of cities are both equal to our sample size, a higher proportion in Table 5.3 also means a higher number. A notable observation is that more counties than cities empl oy controls, which holds for every control. In addition, except for urban growth boundaries and building height limits, there is less variation in the number of controls imposed by counties than by central cities. The table reveals that maximum building height is the most commonly used control for both counties and ci ties, with 151 cities and 140 count ies using it. The least popular control is the urban gr owth boundary, with only 35 cities and 47 counties using it. Among the remaining controls, the rank order is almost the same for cities and counties, with slight variation in ra nk order of minimum lot-size zoning, minimum population density restrictions, and impact fees. Although, as noted earlier, we were able to obtain values for few land-use controls, it might nevertheless be instructive to cite a few examples of the values we did obtain. These may be found in the web sites of city and county agencies. The Bellingham, WA, urbanized area imposes a minimum residen tial lot size of 9,500 square feet, while Canton County, OH, imposes a minimum residen tial lot size of 20,000 square feet. Oshkosh, WI, imposes a maximum lot size of 75,000 square feet on businesses and 30,000 square feet on residences. Although it seems contradictory, 22 percent of our sample urbanized areas impose both minimum and maximu m lot-sizes. Cleveland, TN, has an urban growth boundary with a radius of about fi ve miles from the center of the city beyond which no development may occur. Frederic k, MD, imposes a maximum building height 30 feet. In Macon, GA, the minimum size of an office is 500 square feet, and the minimum size for a one-bedroom dwelling unit is 400 square feet. Some urbanized areas and

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88 counties limit new construction by requiring builders to obtain building permits. For example, Austin, TX, set the maximum number of building permits at 12,500 in 2000. Minimum density controls are usually impo sed as the minimum number of people per room. For example, some resi dential districts in Huntsville, AL, require at least three people for three-bedroom apartments and at least two persons for two-bedroom apartments. Finally, Las Vegas, NV, imposes an im pact fee of $0.36 per square foot of habitable area for residential cons truction to support the construc tion of parks in the city. SUMMARY Chapter 5 describes the theoretical vari ables of our models and their empirical proxies, which are to be used in the analysis of Chapter 6. Chap ter 5 also provides descriptive statistics. To give the reader a bett er idea of the central cities and counties that comprise our sample of urban areas, we repor t ranges for values of the non land-use variables. For the land-use variables, we ar e forced to use dummy variables because few central cities or counties provi de actual values of these variables. Proportions and standard deviations are reported for these dummy va riables. We find, in general, that cities and counties use the same set of controls a lthough more counties em ploy controls than do cities. We also find that the rank order of controls is almost the same for cities and counties. Again to give the reader a sense of how these controls are used, we have included some of the actual values of land-use controls for those entities that report them. Chapter 6 reports our empirical analysis of the effect of land-use controls on the spatial size of urbanized areas

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89 CHAPTER 6: ESTIMATION The purpose of this chapter is to estimate the effect of land-use controls on the spatial size of the urbanized area. This is an attempt to see how effective land-use controls are in restricting the spat ial size of urban areas, that is, in controlling urban sprawl. As discussed in Chapter 5, we have collect ed data on land-use controls, coded as 0-1 dummy variables, for both central cities and counties in our sample of urbanized areas, along with other variable s dictated by urban theory. We begin with a preliminary analysis of correlations among the land-use controls for central cities and for counties. We then proceed to an analysis of correlation am ong central city land-u se controls and those of their surrounding counties. We tentativel y conclude from these analyses that county land-use controls are likely to explain the sp atial size of the urbanized area better than would central city controls. We also conclude that there is likely to be little strategic interaction between central citi es and their surroundi ng counties in the choice of land-use controls. From these preliminary analyses, we proceed to regression analysis of the effect of land-use controls on the spatial size of urbanized areas. We find that, as suspected, the county regression is better than the centr al city regression. In the country regression, all land-use controls except buildi ng permits have the theoretically correct signs, but two, urban growth boundaries and minimum square footage limits, are not statistically significant at the 10-percent level or better.

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90 PRELIMINARY ANALYSIS: CORRELATION MATRICES Since we intend to use land-use control dummy variables as regressors, a natural question arises as to their correlation within th e sample of central cities as well as within the sample of counties. Correlation between any two variables will cloud the effect of any one variable on the spatial size of the urba nized area. In additi on, the size and statistical significance of the correlation coefficients should provide a hint as to which entity— the central city or the county—is likely to provide the better estim ated regression. We adopt the criterion that a “high” correlation is one that is at least 0.5 in absolute value and in which the p -value is at most 0.10. For the central cities in our sample, Table 6.1 reveals eight “hi gh” correlations out of the twenty-eight correlation coefficients in the table. These correlations may hint of possible multicollinearity in the central-city regression. TABLE 6.1: Correlation Matrix for Central City Land-Use Controls l l UGB S h D D l 1.0000 l 0.5133 (0.2203) 1.0000 UGB –0.0034 (0.9635) 0.00586 (0.4319) 1.0000 S –0.1043 (0.2350) 0.0961 (0.1970) 0.1287 (0.0834) 1.0000 h 0.6710* (<0.0001) 0.1019 (0.1710) 0.02101 (0.7775) –0.0241 (0.7468) 1.0000 D –0.5166* (< 0.0001) 0.0638 (0.3925) –0.0177 (0.8129) –0.0383 (0.6093) –0.5401* (<0.0001) 1.0000 D 0.6044* (<0.0001) 0.0770 (0.3015) 0.02812 (0.7056) 0.0261 (0.7267) 0.6710* (<.0001) –0.4946* (<0.0001) 1.0000 0.3534 (<0.0001) 0.0471 (0.5282) –0.0193 (0.7959) –0.0142 (0.7458) 0.2697 (0.0002) –0.5501* (<0.0001) 0.5742* (<.0001) 1.000 *“High” correlation = greater that 0.5 in absolute value and statistically significant at the 0.10 level or better. In contrast, for the counties in our samp le, Table 6.2 shows no “high” correlation coefficients. This leads us to hypothesize that the county regression is likely better to re-

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91 veal the effect of land-use controls on the si ze of the urbanized area. Since the urbanized area spreads beyond its central ci ty into the county, it appear s likely that the county controls have the greater effect on urbanized area size. TABLE 6.2: Correlation Matrix for County Land-Use Controls l l UGB S h D D l 1.0000 l –0.0445 (0.5505) 1.0000 UGB –0.2158 (0.7931) 0.0350 (0.6393) 1.0000 S 0.3731 (0.0034) 0.4760 (0.5235) –0.2519 (0.0006) 1.0000 h –0.2809 (<.0001) 0.7643 (0.3051) 0.2485 (0.0007) –0.2077 (0.0049) 1.0000 D –0.4680 (<.0001) 0.1055 (0.1565) 0.2582 (0.0004) –0.3960 (<.0001) 0.2560 (<.0005) 1.0000 D –0.0954 (0.2003) –0.0941 (0.2065) 0.0592 (0.4277) –0.0272 (0.7158) 0.0140 (0.5789) 0.0600 (0.4214) 1.0000 –0.6122 (0.4116) 0.0445 (0.5505) 0.1377 (0.0639) 0.1086 (0.1447) 0.1618 (0.0292) –0.0683 (<.3594) –0.0052 (0.9444) 1.000 Another issue we want to address in this preliminary analysis is the possible strategic interaction betw een the central city and its surrounding county. Brueckner (1998) found that for a sample of California cities ther e existed strategic inte raction in the choice of land-use controls. It is po ssible, therefore, that such interaction exists between the central cities and their surr ounding counties in our sample of urbanized areas. Some indication of the existence of central city and county inter action may be revealed by the correlation coefficients between a central city contro l and its county’s control. The correlation matrix is present in Table 6.3. Of the 64 correlation coefficients, only four are “high.” Nearly 50 percent of central cities and 57 percent of counties use building permits, D so it is not surprising to find the high correlation of 0.91 between central cities and coun ties for this variable. It probably does not represent a stra tegic interaction. The existence of building permits in

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92 counties is highly correlated with the existence in central cities of square footage limitations, h (–0.65) and minimum numb er of persons per room, D (–0.60). A country’s imposition of, or reduction in, a ma ximum number of building permits is theoretically expected to expand the urban area. Central cities coul d be reacting to this by imposing, or increasing, minimum square footage limits and minimum number of persons per room limits, which are theoretically e xpected to contract the urban area. If this supposition is accurate, it would represent a case of strategic interaction. Otherwise, the correlation analysis seems to support th e hypothesis that there is no st rategic intera ction between central cities and th eir surrounding counties. TABLE 6.3: Correlation Matrix for C ounty-Central City Land-Use Controls CO \ CC l l UGB S h D D l 0.3747 (<.0001) –0.0436 (0.5593) 0.0196 (0.7931) 0.0684 (0.3588) 0.3785 <.0001 –0.5716* (<.0001) 0.3968 (<.0001) 0.4021 (0.0001) l –0.1332 (0.0730) -0.3927 (<.0001) –0.1872 (0.0114) 0.0000 1.0000 –0.0953 (0.2008) 0.4021 (0.0001) –0.0888 (0.2331) 0.0255 (0.7325) UGB –0.3194 (<.0001) –0.0656 (0.3791) 0.2012 (0.0065) 0.1206 (0.1047) –0.2341 (0.0014) 0.3180 (<.0001) –01432 (0.0538) –0.1926 (0.0092) S 0.3407 (<.0001) –0.0656 (0.3791) 0.0177 (0.8129) 0.1164 (0.1176) 0.3200 (<0.0001) –0.4943 (<.0001) 0.3407 (<.0001) 0.4838 (<0.0001) h –0.1434 (0.0534) 0.0241 (0.7471) –0.0143 (0.8480) –0.0222 (0.7666) –0.1033 (0.1654) 0.3621 (<.0001) –0.0331 (0.6574) –0.1908 (0.0099) D –0.0193 (<.0001) 0.0429 (0.5652) –0.0268 (0.7191) 0.0121 (0.8709) –0.6481* <0.0001 0.9053* (<.0001) –0.5978* (<.0001) –0.4441 (<0.0001) D 0.1793 (0.0152) –0.0156 (0.8347) 0.1571 (0.0341) –0.0164 (0.8259) –0.0131 (0.8607) 0.1398 (0.602) 0.1798 (0.0152) 0.1126 (0.0912) –0.0441 (0.5546) 0.1109 (0.1361) 0.1044 (0.1607) –0.0362 (0.6274) 0.0255 (0.7330) 0.0237 (0.7504) 0.1383 (0.0073) 0.3578 (<.0001) Note : CO = county; CC = central city. *“High” correlati on = greater that 0.5 in absolute value and statistically significant at the 0.10 level or better. REGRESSION RESULTS For both the central city and county data we estimate the following regression 01234567 89101112 A A PyrtllUBG ShDD (6.1)

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93 We use a linear functional form because, as discussed in Chapter 4, various forms have been used and none is superior. The OLS regr ession results are given in table 6.4. Before discussing the results, we note that the regressions buttress our conjecture that the county regression would be better. For th e land-use controls, the county regression has only one “wrong” sign, while th e city regression reports four Also, the country regression finds six land-use control variables to be statistically significant at the 0.10 level or better, while the city regression finds five. We turn now to a discussion of the results for the land-use control variables first, as those are our main interest. TABLE 6.4: Regression Results Variable Central City County Coefficient p Coefficient p l, Min. Lot Size 85.27 <0.01b 18.60 0.07 d l, Max. Lot Size 1.45a 0.87 –20.37 0.02 c UGB Urban Growth Boundaries 12.11 a 0.22 –3.32 0.72 S, Max. Bldg. Ht. Limits 4.16 0.64 19.66 0.05c h, Min. Sq. Ft. Limits 28.67 a 0.02 c –8.24 0.38 D, Max. Bldg. Permits –57.05 a <0.01 b –21.75 a 0.04 c D, Min. Persons/Room –47.94 0.01 b –22.98 0.01 b Impact Fees –77.71 <0.01 b –21.98 0.02 c P No. of UA Households 0.41 10–4 <0.01 b 0.54 10–4 <0.01 b y Median Household Income 0.12 10–4 0.07d 0.20 10–4 0.01 b rA,Median Farm Land Price –0.96 10–5 0.01 b 0.10 10–4 a 0.02 c t Hwy. Exp./User 34.22 0.08 d 28.71 0.21 Constant 73.26 <0.01b 60.13 0.01 b R2 0.73 0.73 N 182 a “wrong” sign. b0.01 p c 0.010.05 p d 0.050.10 p

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94 The Effect of Land-Use Controls on the Size of the Urbanized Area Minimum Lot Size The coefficient on minimum lot-size, l, is positive in both the central city and county regressions, which is consistent with theory, but it is statistically significant at only the 7-pe rcent level for the county, while it is highly statistically significant for the central city. The impositi on of a minimum lot-si ze restriction by the county would increase the urbanized area by 19 s quare miles, on average, while a central city minimum lot-size restriction would in crease the urbanized area by over 85 square miles. Although counties use minimum lot-size zoning to a greater degree than do central cities, the introduction of minimum lot si zes into the central city would have more impact, probably because of the greater numbe r of households in the central city. Since lot size rises with distance from the CBD, a minimum lot-si ze restriction would be binding on those households near the CBD, but beyond some distance, the minimum would not be binding. This woul d cause those households for which the limit is binding to occupy larger lots which would expand the urban area. If central citi es impose this control, it will be binding on more households than if counties impose the control and should therefore have a greater effect on the size of the urban area. Maximum Lot Size In the county regression, the co efficient on maximum lot size, l, is negative, as expected in theory, and stat istically significant at the 2-percent level. On the other hand, the coefficient is positive and not statistically significant in the central city regression. Adopting a maximum lotsize restriction by the county would cause the urbanized area to contract by sligh tly over 20 square miles on average. Urban Growth Boundary For the county regression, we find the coefficient on the urban growth boundary, UGB to be negative, which is anticipated by urban theory,

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95 but not statistically significant, while for the centr al city regression, it is positive, contrary to theory, as well as not statis tically significant. Only 19 pe rcent of central cities and 26 percent of counties in our sample have ur ban growth boundaries, which may explain the poor statistical results. It may also be the case that, while these cen tral cities and counties have urban growth boundaries, th ey may not yet be binding. Maximum Building Height The coefficient on maximum building height, S, is positive, as predicted by urban theory, and sta tistically significant at slightly over the 5percent level in the county regression, while being positive but not statistically significant in the central city regression. The presen ce of a maximum building height in the county would increase the urbanized area by nearly 20 square miles on average. Minimum Square Footage In the central ci ty regression, the coefficient on minimum square footage, h, is positive, contrary to theory, and statistically significant, while it is negative, consistent with theory, but not stat istically significant in the county regression. As noted in Chapter 3, we found no theore tical analysis of a minimum square footage limit. Therefore, the expected sign on its coefficient is based on the relationship between urban spatial size and a maximum floor-area ratio ( FAR ) obtained by Bertaud and Brueckner (2005). Their argument for a positive effect of a maximum FAR on urban spatial size is that the urban population is constrained by the FAR up to the distance at which it ceases to be a binding constraint (since FAR will fall with distance in the unconstrained model). This causes households to seek lo cations beyond the distance at which the constraint is binding, which raises land rents beyond that distance, which, in turn, causes the urban area to expand.

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96 Applying this logic to a minimum FAR means that the constraint will be nonbinding up to some distance from the CBD. Beyond that distance and up to the urbanrural boundary, however, the constrained FAR would be larger than preferred. This would cause the given urban population to live at higher densities th an preferred, which would reduce the spatial size of the urban area. Maximum Building Permits The coefficient on maximum building permits, D is negative, contrary to theory and statistically significant for both the central city and the county, but the statistical signi ficance is better for the count y, and the effect of building permits on the size of the urban area is gr eater in the county. Introducing maximum building permits in the county reduces the size of the urban area by 57 square mile, while introducing them in the central city re duces its size by only about 22 square mile. As was the case for a minimum FAR we found no theoretical treatment of a maximum density constraint and again used the logic of Bertaud and Br ueckner (2005) to justify a negative relationship between the sp atial size of the ur ban area and maximum building permits. The fact that for both cen tral cities and counti es the relationship is found to be negative empirically cases doubt on this explanation. Maximum building permits do not work exactly as the theory for maximum densities argues because densities fall with dist ance from the CBD while a maximum number of building permits is independent of distance. Nevertheless, if th e central city imposes a binding maximum number of building permits and the county does not, then those who want to live in the urban area will locate in the county, rather than the city, and will expand the urban area. On the other hand, if the county imposes a binding maximum num-

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97 ber of building permits while the city does not, then the reverse is the case, and the urban area will contract. These results would be consistent with the theory. In our data, however, neither of these conditions holds. As can be seen from Table 6.3, the correlation betw een central city and county building permits is 0.91 ( p < 0.0001). Therefore, in the great majority of urbanized areas in our sample, both the central city and its county have building permits. Thus, if the number of building permits is binding in both the city and county, there is no place for households to locate in the urban area to avoid the cap. In this case, a nega tive coefficient on the variable seems reasonable. The problem is with the theory, which assumes an area in which restrictions are not binding, which is apparently not the case in reality, at least for our sample. Minimum Number of Persons per Room The coefficient on minimum number of persons per room, D, is negative, consistent with theo ry, and statistically significant in both regressions, but the impact on the size of the urbanized area is much greater for the central city restriction. Us ing this restriction by the centr al city would decrease the size of the urbanized area by nearly 48 square m iles, on average, while its use by the county would expand the urbanized are by nearly 23 squa re miles, on average. This is another example of our using the logic of Bertaud and Brueckner (20 05) to justify the expected sign, for we found no theoretica l treatment of this variable. Impact Fee The coefficient on the impact fee, is negative, as predicted by urban theory, and statistically si gnificant in both the central city and county regressions. The magnitude of the contracti onary effect on the urbanized area is much greater if the central city imposes the impact f ee, a contraction of almost 78 square miles, than if the county imposes the fee, a contrac tion of only 22 square miles.

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98 The Effect of Other Variables on the Size of the Urbanized Area Households The coefficient on number of households, P is positive, as is consistent with urban theory, and highly statistically significant in both the central city and county regressions, as is usually the case in analyses of this ki nd. In our case, increasing the number of households by 10,000 would incr ease the urbanized area by from 4.1 to 5.4 square miles. Income The coefficient on median household income, y is positive, in conformity to urban theory, and statistically significan t in both the central ci ty and county regressions, as is usually the case in these kinds of regressions. In our case, a $10,000 increase in median income leads to an increase of urbanized area by from 1.2 to 2.0 square miles, on average. Agricultural Land Value The coefficient on the mean value of agricultural land, rA, is negative in the central city regression, which is consistent with urban theory, but positive in the county regression, while both ar e statistically significant. As noted in Chapter 5, this variable has not performed we ll in most analyses. A possible explanation for the sign discrepancy is that rural land va lues rise in anticipation of conversion to urban use. In rapidly growing urban areas, the larger radius, adjusted for income and population may reflect speculation of continued grow th. One way to check this conjecture is to add a variable measuring urban growth from 1990 to 2000. This variable might be change in population, change in the size of the urban area, or change in the number of households.10 Increasing the value of agricultura l land surrounding th e urbanized area by $1,000 per acre would shrink the urbanized ar ea by about 1 square mile, on average. 10 We thank Professor Kenneth F. Wieand for this explanation and suggestion for future research.

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99 Highway Expenditure per User The coefficient on highway expenditures per user, t is positive, which is consistent with ur ban theory because higher expenditures are presumed to lower transportation costs, and st atistically insignificant. The theoretical variable has proved difficult to proxy, and, as a result, few studies have found the “right” sign and statistical significance for this variab le. Our choice of vari able was based on a similar variable’s successful use by Song and Zenou (2006). SUMMARY OF THE EFFECT OF LAND-USE CONTROLS ON THE SIZE OF THE URBANIZED AREA In this section, we summarize the results of the empirical analysis by comparing the theoretically predicted effects of land-u se controls with the empirically estimated counterparts. As already not ed, the county regression perfor ms better than the central city regression, so we only discuss that one. Table 6.5 presents the results. TABLE 6.5: Summary of Results Land-Use Control Sign ( County Only ) p TheoreticalEmpirical Minimum Lot Size l + + 0.07 Maximum Lot Size l – – 0.02 Urban Growth Boundary UGB – – 0.72 Maximum Building Height S + + 0.05 Minimum Sq. Ft. h – – 0.38 Maximum Building Permits D + – 0.04 Minimum Persons/ Room D – – 0.01 Impact Fees – – 0.02 In all but one case, the empirically obtained sign is consistent with the theoretical prediction. The one “incorrect” sign is for maximum building permits. Five of eight estimated coefficients are statistica lly significant at the 5-percent level or

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100 better, while one more is statistically signi ficant at the 10-percent level or better. Only two remain not statistica lly significant at these levels.

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101 CHAPTER 7: SUMMARY, CONCLUSI ONS, LIMITATIONS, AND SUGGESTIONS FOR FURTHER RESEARCH As stated in Chapter 1, urban sprawl is a contentious issue, involving various and conflicting views on such fundamental matters as its definition, measurement, and causes. Economists’ contributions to this literature emphasize the theoretica l and empirical analysis of the causes of urban sprawl. This disse rtation follows in that tradition with an empirical analysis of the effect of land-use c ontrols on urban sprawl drawing on testable hypotheses found in the theoretical literature. As was noted earlier, many empirical studi es have been performed on the effect of land-use controls on housing prices, but no st udy has examined their effect on urban sprawl. This dissertation th erefore makes a unique contribu tion to the literature on urban sprawl by documenting the effect of land-u se controls on the spatial size of the urban area. Such information should be useful to urban planners who are trying to curb sprawl. In addition, this dissertation tests theo retical hypotheses on the effect of land-use controls on the spatial size of urban areas. These theoretical hypotheses have not previously been empirically tested. As such, th is dissertation adds to the positive literature on urban economics.

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102 SUMMARY Chapter 1 provides a discussion of defi nitions, criticisms, and measurements of urban sprawl. From this discussion, we a dopt a non-normative defi nition, namely, that urban sprawl is the decentra lization of population and employm ent from the central city to the suburbs. In our empirical work, however, we have data only on population. In the monocentric models of urban stru cture, this decentral ization of population is characterized by increased sp atial size of the urban area. In their theoretical analyses, Wheaton (1974) and Brueckner (19 87) found that the spatial si ze of an urban area is directly related to real househol d income and population and inve rsely related to transportation costs and rural land rent. Increasing real income, in creasing population, decrea sing real transportation costs, although expanding the urban area spatia lly, are not causes of sprawl in its normative sense, which is that sprawl is the excessive decentralization of population and employment. Sprawl in this normative sense h as been explained by the failure to account for the social costs of road congestion, the failure to account for th e social value of open space, the failure to account fully for the in frastructure costs of new development (Brueckner, 2001), transportation subsidies (B rueckner, 2005), the property tax (Brueckner and Kim, 2003), federal spending (Persky and Kurban, 2003), and land-use controls (Brueckner, 1998). Of these, this dissertation addresses the latter. Controls on land use abound in urban areas. We find traditional zoning, which is designed to separate incompatible land uses a nd which has a long history that we survey in Chapter 2. More recent forms of land-use control, discussed in detail in Chapter 2, include minimum lot-size zoning; maximum lot-size zoning; maximum building heights;

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103 various kinds of density r estrictions, including maximu m floor-area ratios, minimum square-footage limits, maximum building permits, and minimum persons per room; impact fees and in-kind exactions; urban growth boundaries; and rent control. With the discussions in Chapters 1 and 2 as background, we then turn in Chapter 3 to theories of urban form, starting with the history of th e development of the monocentric urban model and proceeding to a detailed exposition of that model in both its closed city and open city versions. We then turn to a discussion of extensions of the monocentric urban model that include land-use cont rols. Here we find analyses of minimum lotsize zoning (Pasha, 1996), maximum lot-si ze zoning (Pasha, 1992b), urban growth boundaries and similar land-use restrictions (Quigley a nd Swoboda, 2007), the maximum floor-area ratio (Bertaud and Brueckner, 2005), and the property tax (Song and Zenou, 2006). We did not find extensions of the monocentric urban model that included analyses of impact fees and density restrictions, othe r than the maximum floor-area ratio. Since central cities and counties in our sample impose impact fees, we argued that the results of the property-tax model of Song and Zenou (2006) could be interpreted as applying to impact fees. Also, since cent ral cities and counties in our sample impose maximum building heights, minimum square-footage limits maximum building permits, and minimum persons per room, we argued that these various density restricti ons could be related to the results of Bertaud and Brueckner (2005). The reasons for this is the theoretically direct relation between structural density, housing density, and po pulation density. Maximum building-height limits are related to maximum structural density limits; minimum squarefootage limits are related to minimum hous ing density; maximum housing permits are

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104 related to maximum population density; and minimum persons per room are related to minimum population density. Given these theoretical results, we turned in Chapters 4 to a survey of previous empirical analysis of the monocentric model, emphasizing their results on spatial size. Specifically, we surveyed the work of Br ueckner and Fansler ( 1983), McGrath (2005), Song and Zenou (2006), and Su and DeSalvo (20 08). In all of these cases, the findings supported the theoretical predictions of the mono centric urban model. With this as background, we turned, in Chapters 5 and 6, to our own empirical work. Chapter 5 discussed our data, and Chapter 6 presented our regression results. CONCLUSIONS Our findings are summarized in Table 6.5. Recall that these are the results from the county regression, as we c oncluded that it better repre sented the effect of land-use controls on urban spatial size. The interpretation of the city regression would be similar to that of the county regression. The city regr ession, however, appears to us to be better for reasons given earlier. Our empirical analysis may be viewed in two ways. First, it may be seen as tests of the theoretical predictions of extensions of the monocentric urba n models that encompass land-use controls. Second, it may provi de guidance to urban governments in the efficacy of policies to contain urban sprawl. Regarding our empirical findi ngs as tests of the extended models of urban structure, it is clear that our findings support the theoretical prediction of these models. Based on the county regression, all but one of the theoretical predic tions regarding the direction

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105 of the effect of land-use cont rols on urban spatial size are upheld. They are not, however, all statistically significant, in particular, those involv ing urban growth boundaries and minimum square-footage limitations. In sum, we find evidence of the importance of land-use controls on the spatia l size of urban areas, a findi ng that heretofore had only theoretical support. To provide a sense of the magnitude of th e impacts of land-use controls on urban spatial size, Table 7.1 provides the percentage change in the size of the average urban area in our sample, approximately 80 square miles, of the presence of each control. TABLE 7.1: Change in Mean Urbanized Area Size in the Presence of County Land-Use Controls Land-Use Control % Change ( sq. mi. ) Min. Lot Size +23.3 Max. Lot Size –25.5 UGBa Max. Bldg. Height +24.6 Min. Sq. Ft.a Max. Bldg. Permits –27.3 Min. Persons/Room –28.8 Impact Fees –27.6 aStatistically insignificant coefficient. Regarding our empirical fi ndings as providing policy guidance on containing urban sprawl, it is first necessar y to recognized that land-use controls are not necessarily implemented primarily to control urban spra wl. For example, Bertaud and Brueckner (2005) point out that the apar theid policies formerly used in South Africa caused black households’ residences to be located far from urban centers, as did the policies of the former Soviet Union. Minimum lot-size zo ning limits suburban development densities,

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106 while, Mills (2005) has charged, excluding low-income and minority households from high-income suburbs. Similarly building-hei ght limits, found in the central areas of U.S. cities as well as in cities such as Washington, D.C., and Paris, while controlling the density of development, may be primarily for aest hetic purposes. Also, efforts to increase central density, such as through maximum floor-area ratios, may be intended to reduce population and employment densiti es in the hope of protecting environmental quality, reducing traffic congestion, and reduci ng demands on urban infrastructure. Nevertheless, these and other land-use contro ls have an effect on the spatial size of urban areas and, as such, may be implemen ted as policies to contai n urban sprawl. In any event, to contain urban sprawl, our empirical analysis supports the use of maximum lot-size zoning, maximum building permits, minimum persons per room, and impact fees. According to our results, these would have pow erfully reduced the size of our mean urbanized area by 25.5, 27.3, 28.8, and 27.6 pe rcent, respectively. Clearly, minimum lotsize and maximum building-hei ght restrictions expand the urbanized area, by 23.3 and 24.6 percent, respectively. In the interest in controlling sprawl, these policies should be avoided. In the case of building heights, urban areas could mandate taller, rather than shorter, buildings. LIMITATIONS OF THE STUDY AND SUGGESTIONS FOR FURTHER RESEARCH In this section, we discuss both theoretic al and empirical limitations of the present study, which lead to suggestions for future research. As already previously noted, we found no theoretical extensions of the mono centric urban model to include minimum square-footage and minimum persons-per-room restrictions. Neither did we find exten-

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107 sions to include maximum building-permit rest rictions. We did, however, find such restrictions being used by cities and counties in our sample. To circumvent this lacuna in the theory, we drew on the theoretical relationship among population, structural, and housing density, which allowed us to interpret the work of Bertaud and Bruckner (2005) in terms restrictions on minimum square f ootage, minimum persons per room, and maximum building permits. Similarly, we found no theoretical work extending the urban structure model to include impact fees but, again, found evidence of urban areas’ use of impact fees. As a consequence, we used the property-tax model of Song and Zenou (2006). We would have preferre d to have had fully worked out extensions to the basic urban structure model, such as those discussed in Chapter 3, for all four of these land-use controls. We propose to develop such extensions in future research. Another potentially useful ar ea of research would be th e theoretical treatment of the central city and its surrounding county as separate govern mental entities, which is, of course, what they are in the U.S. None of th e theoretical models reviewed in this dissertation did this. The one who came closest was Pasha (1996 and 1992b). He divided his urban area into two parts, the central city a nd the suburbs, but he im plicitly treated them as parts of the same governmental entity. Alth ough in some countries, such as the U.K., the city (“local authority” in the U.K.) is administered in large part by the national government, this is not the case in the U.S. Given that cities and counties do not follow a unitary policy with respect to land-use controls, as was seen by the mostly lack of correlation between city and county pol icies in the correlation matrix of Table 6.3, it is highly likely that results of models without this specification will generate incorrect comparative static results. We intend to pursue this line of research.

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108 Turning to empirical limitations of our r esearch, surely the most important is our inability to obtain actual m easures of land-use controls. Unable to find such measures led us to use dummy variables representing the pr esence or absence of controls. Unfortunately, we do not have high expectations of finding such data in easily accessible form. Even collecting the information on the presence or absence of controls was a laborious process. While we realize dummy variables ar e a week measure of land-use controls, we were constrained to use them since obtaining actual values of land-u se controls would an arduous and extremely time-consuming process. Nevertheless, in future research, we intend to survey planning agencies of each ci ty and county in our sample requesting the actual value of each land-use c ontrol they employ. Obtaini ng the actual values of landuse controls will serve two purposes. First, it will make our empirical estimation more precise. Second, we could draw conclusions regarding the strength of each land-use control in affecting the spatial size of the urban area. The latter will give us an opportunity to provide planning agencies with valuable guidance on how to control urban sprawl.

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109 LIST OF REFERENCES Abbott, Carl. 2002. “Planning a Sustainabl e City: The Promise and Performance of Portland’s Urban Growth Boundary,” in D. Gregory (ed.), Urban Sprawl: Causes, Consequences, and Policy Responses Washington, D.C.: Urban Institute Press, pp. 207–235. Alonso, William. 1964. Location and Land Use: Toward a General Theory of Land Rent Cambridge, MA: Harvard University Press. Altmann, James L. and Joseph S. DeSalvo. 1981. “Tests and Extensions of the MillsMuth Simulation Model of Urban Residential Land Use,” Journal of Regional Science 21, 1–21. Altshuler, Alan A., Jos A. Gmez-Ib ez, and Arnold M. Howitt. 1993. Regulation for Revenue: The Political Economy of Land-Use Exactions Washington, DC: Brookings Institution Press. Anas, Alex and Hyok-Joo Rhee. 2007. “Curbing Excess Sprawl with Congestion Tolls and Urban Growth Boundaries,” Regional Science and Urban Economics 36, 510– 541. ______. 2006. “When Are Urban Growth B oundaries Not Second-Best Policies to Congestion Tolls?,” Journal of Urban Economics 61, 263–286. Acharyi, Gayatri and Lynne Lewis Bennett. 2001. “Valuing Open Space and Land-Use Patterns in Urban Watershed,” Journal of Real Estate Finance and Economics 22 221–237. Arnott, Richard J. 1995. “Time fo r Revisionism on Rent Control?,” Journal of Economic Perspectives 9, 99–120. ______ and James G. MacKinnon. 1977. “Measuri ng the Costs of Height Restrictions with a General Equilibrium Model,” Regional Science and Urban Economics 7, 359– 375. Bates, Laurie J. and Rexford E. Santerre. 1994. “The Determinants of Restri ctive Residential Zoning: Some Empirical Findings,” Journal of Regional Science 34, 253– 263.

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110 Baden, Brett M., Don L. Coursey, and Irving B. Harris. 2000. “An Examination of the Effects of Impact Fees on Chicago’s Suburbs,” Worki ng Paper, Series N 99.25, Department of Public Policy, University of Chicago. Bento, Antonio M., Sofia F. Fr anco, and Daniel Kaffi ne. 2006. “The Efficiency and Distributional Impacts of Alternative Anti-Sprawl Policies,” Journal of Urban Economics 59, 121–141. Bertaud, Alain. 2004. “The Spatial Organi zation of Cities: Delib erate Outcome or Unforeseen Consequence?,” Working Paper, Institute of Urban and Regional Development, University of California Berkeley. ______ and Jan K. Brueckner. 2005. “Analyzi ng Building Height Restrictions: Predicted Impacts, Welfare Costs, a nd a Case Study of Bangalore, India,” Regional Science and Urban Economics 35, 109–125. Bogart, William. 1998. The Economics of Cities and Suburbs Upper Saddle River, NJ: Prentice-Hall. Brueckner, Jan K. 1987. “The Structure of Urban Equilibria: A United Treatment of the Muth-Mills Model,” in Edwin S. Mills (ed.), Handbook of Regional and Urban Economics Vol. 2, “Urban Economics.” Amsterdam: Elsevier, pp. 821–845. ______. 1997. “Infrastructure Financing a nd Urban Development: The Economics of Impact Fees,” Journal of Public Economics 66, 383–407. ______. 1998. “Testing for Strate gic Interaction Among Local Governments: The Case of Growth Controls ” Journal of Urban Economics, 44, 438-467. ______. 2000. “Urban Sprawl: Diagnosis and Remedies,” International Regional Science Review 23, 160–171. ______. 2001. “Urban Sprawl: Lessons from Urban Economics,” Brookings-Wharton Papers on Urban Affairs Washington, D.C.: Brooki ngs Institution Press, 65–97. ______. 2005a. “Transport Subsidies, Sy stem Choice, and Urban Sprawl,” Regional Science and Urban Economics 35, 715–733. ______. 2005b. “Urban Growth Boundaries: An Effective Second-Best Remedy for Unpriced Traffic Congestion?,” Journal of Housing Economics 16, 263–273. ______ and David A. Fansler. 1983. “The Econo mics of Urban Sprawl: Theory and Evidence on the Spatial Size of Cities,” Review of Economics and Statistics 65, 479– 482.

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111 ______ and Hyun-A Kim 2003. “Urban Sprawl and the Property Tax,” International Tax and Public Finance 10, 5–23. Bucovetsky, Sam. 1984. “On the E ffects of Minimum Lot-Size Zoning,” Economics Letters 15, 189–193. Cho, Man. 1997. “Congestion Effects of Sp atial Growth Restrict ions: A Model and Empirical Analysis,” Real Estate Economics 25, 409–438. Cho, Seong-Hoon, Zhuo Chen, Steven T. Yen, and David B. Eastwood. 2006. “Estimating Effects of an Urban Growth Boundary on Land Development,” Journal of Agricultural and A pplied Economics 38, 287–298. ______, Olufemi A. Omitaomu, Neelam C. Poudyal, and David B. Eastwood. 2007. “The Impact of an Urban Growth Boundary on Land Development in Knox County, Tennessee: A Comparison of Two-Stage Prob it Least Squares and Multilayer Neural Network Models,” Journal of Agricultural and Applied Economics 39, 701–717. Coulson, N. Edward. 1991. “Really U seful Tests of the Monocentric Model,” Land Economics 67, 299–307. Cunningham, Christopher R. 2007. “Growt h Controls, Real Options, and Land Development,” Review of Econom ics and Statistics 89, 343–358. Delaney, Charles J. and Marc T. Smith. 1989. “Impact Fees and the Price of New Housing: An Empirical Study,” Real Estate Economics 17, 41–54. DeSalvo, Joseph S. 1977. “Urban Househol d Behavior in a Mode l of Completely Centralized Employment,” Journal of Urban Economics 4, 1–14. ______. 2008. Urban Spatial Economic Th eory: A Provisional ( and Incomplete ) Text Tampa, FL: ProCopy. Downs, Anthony. 2002. “Have Housing Pr ices Risen Faster in Portland Than Elsewhere?,” Housing Policy Debate 13, 7–31. Evans, A. W. 1973. The Economics of Residential Location London: Macmillan Press. Evans-Cowley, Jenifer and Larry L. Lawhon. 2003. “The Effects of Impact Fees on the Price of Housing and Land: A Literature Review,” Journal of Planning Literature 17, 351–359. Fischel, William. 1985. The Economics of Zoning Laws Baltimore, MD: Johns Hopkins University.

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115 Persky, Joseph and Kurban Haydar. 2003. “Do Federal Spending and Tax Policies Build Cities or Promote Sprawl?,” Regional Science and Urban Economics 33, 361–378. Phillips, Justin and Eban Goodstein. 2000. “Growth Management and Housing Prices: The Case of Portland, Oregon,” Contemporary Economic Policy 18, 334–344. Quigley, John M. 2007. “Regulation and Property Values in the United States: The High Cost of Monopoly,” in Gregory K. Ingram and Yu-Hung Hong (eds.), Land Policies and Their Outcomes Cambridge, MA: Lincoln Institute of Land Policy, pp. 46–65. ______ and Aaron Swoboda. 2007. “A General Equilibrium Analysis of Land Use Restrictions and Residential Welfare,” pape r presented at the International Conference on Sustainable Urban Areas, Rotterdam. Roistacher, Elizabeth. 1992. “Rent Control in New York City: Simulating Decontrol Options,” Journal of Housing Economics 2, 107–138. Sang, Lok, Ho. 1992. “Rent Control: Its Rationale and Effects,” Urban Studies 29, 1182–1190. Skaburskis, Andrejs. 1992. “An Empirical Estimation of the Price Effects of Development Impact Fees,” Urban Studies 29, 653 – 667. ______. 1990. “The Burden of Development Impact Fees,” Journal of Property Research 6, 173–185. Skelley, Chris. 1998. “Rent Control and Complete Contract Equilibria,” Regional Science and Urban Economics 28 711 – 743. Song, Yan and Yves Zenou. 2006. “Property Tax and Urban Sprawl: Theory and Implications for U.S. Cities,” Journal of Urban Economics, 60, 519–534. Stull, William J. 1974. “Land Use and Zoning in an Urban Economy,” American Economic Review 64, 337–347. Su, Qing and Joseph S. DeSalvo. 2008. “The Effect of Transportation Subsidies on Urban Sprawl,” Journal of Re gional Science 48, 567–594. Turnbull, Geoffrey K. 1991. “A Compara tive Dynamic Analysis of Zoning in a Growing City,” Journal of Urban Economics 29, 235–248. ______. 2004. “Urban Growth Controls: Transitional Dynamics of Development Fees and Growth Boundaries,” Journal of Urban Economics 55, 215–237. U.S. Bureau of the Census. http://www.census.gov/, accessed on 11/23/09.

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117 APPENDICES

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118 APPENDIX: DATA SOURCES FOR CI TY AND COUNTY LAND-USE CONTROLS City of Abilene, TX. http://www.abilenetx.com/ons/, accessed on 9/11/09. City of Albany, GA. http://www.alba ny.ga.us/pd/pd_plan_zoning.htm, accessed on 9/11/09. City of Alexandria, LA. www.sos.louisi ana.gov/comm/fss/fss-index.htm, accessed on 9/11/09. City of Altoona, PA. http://www.huntingdoncou nty.net/altoona/site /default.asp, accessed on 9/11/09. City of Ames, IA. www.city.a mes.ia.us, accessed on 9/11/09. City of Anderson, IN. http://www.ci tyofanderson.com/, accessed on 9/11/09. City of Anderson, SC. www.cityofandersonsc.com, accessed on 9/11/09. City of Anniston, AL. http://www. ci.anniston.al.us/, accessed on 9/11/09. City of Antioch, CA. http://www.ci .antioch.ca.us/, accessed on 9/11/09. City of Athens-Clarke County, GA. www.at hensclarkecounty.com/~planningdept/acorts/, accessed on 9/11/09. City of Atlantic City, NJ http://www.aclink.org/Pl anning/, accessed on 9/12/09. City of Austin, TX. www.ar.utexas.e du/Planning/links.html, accessed on 9/12/09. City of Bakersfield, CA. http://www. bakersfieldcity.us/, accessed on 9/12/09. City of Bangor, ME. http://www. bangormaine.gov/, accessed on 9/12/09. City of Bay City, MI. http://www. baycitymi.org/, accessed on 9/12/09. City of Battle Creek, MI. http:// www.battlecreek.org/, accessed on 9/12/09. City of Beaumont, TX. http://www.cityofbeaumont.com/, accessed on 9/12/09. City of Bellingham, MT. http:// www.bellingham.org/, accessed on 9/12/09. City of Bend, OR. http://www. ci.bend.or.us/, accessed on 9/15/09.

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119 APPENDIX (CONTINUED) City of Billings, MT. http://ci.billings.mt.us/, accessed on 9/15/09. City of Bismarck, ND. http://www.bismarck.org/, accessed on 9/15/09. City of Blacksburg, VA. http://www.blacksburg.va.us/, accessed on 9/15/09. City of Bloomington–Normal, IL. http://www.normal.org/, accessed on 9/15/09. City of Bowling Green, KY. h ttp://www.bgky.org/, accessed on 9/15/09. City of Brownsville, TX. http ://www.cob.us/, accessed on 9/15/09. City of Brunswick, GA. http://www. brunswickga.org/, accessed on 9/15/09. City of Burlington, NC. http://www.ci .burlington.nc.us/, accessed on 9/17/09. City of Burlington, VT. http://www.ci .burlington.vt.us/, accessed on 9/17/09. City of Canton, OH. http://www. cantonohio.gov/, accessed on 9/17/09. City of Cedar Rapids, IA. http://www. cedar-rapids.org/, accessed on 9/17/09. City of Champaign, IL. http://ci. champaign.il.us/, accessed on 9/17/09. City of Charlottesville, VA. http://www. charlottesville.org/, accessed on 9/17/09. City of Cheyenne, WY. http://www.ch eyennecity.org/, accessed on 9/17/09. City of Chico, CA. http://www.chico.ca.us/, accessed on 9/22/09. City of Cleveland, TN. http://www.c ityofclevelandtn.com/ accessed on 9/22/09. City of Coeur d'Alene, ID. http ://www.cdaid.org/, accessed on 9/22/09. City of College Station–Bryan, TX. http://www.cstx.gov/, accessed on 9/22/09. City of Colorado Springs, CO. h ttp://www.springsgov.com/, accessed on 9/22/09. City of Columbia, MO. http:// www.gocolumbiamo.com/, accessed on 9/22/09. City of Columbus, IN. http://www.cit yofcolumbus.org/, accessed on 9/22/09. City of Corvallis, OR. http://www. ci.corvallis.or.us/, accessed on 9/25/09.

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120 APPENDIX (CONTINUED) City of Dalton, GA. http://www.cit yofdalton-ga.gov/, accessed on 9/25/09. City of Danville, IL. http://www.ci tyofdanville.org/, accessed on 9/25/09. City of Danville, VA. http:// www.danville-va.gov/, accessed on 9/25/09. City of Davis, CA. http://cit yofdavis.org/, accessed on 9/25/09. City of Dayton, OH. http://www.cityof dayton.org/Pages/default.aspx, accessed on 9/25/09. City of Decatur, AL. http://www.di gitaldecatur.com/, accessed on 9/25/09. City of Des Moines, IA. http://www.dmgov.or g/, accessed on 9/30/09. City of Dothan, AL. http://www. dothan.org/, accessed on 9/30/09. City of Dover, DE. http://www.c ityofdover.com/, accessed on 9/30/09. City of Elmira, NY. http://www.cityofel mira.net/index/index.html, accessed on 9/30/09. City of Erie, PA. http://www. erie.pa.us/, accessed on 9/30/09. City of Eugene, OR. http://www.eugene-o r.gov/portal/server.pt accessed on 9/30/09. City of Fairfield, CA. http://www. ci.fairfield.ca.us/, accessed on 9/30/09. City of Fayetteville, NC. http://www. ci.fayetteville.nc.us/, accessed on 9/30/09. City of Flint, MI. http://www.c ityofflint.com/ /, accessed on 9/30/09. City of Florence, SC. http://www. cityofflorence.com/, accessed on 10/3/09. City of Fort Collins, CO. http ://www.fcgov.com/, accessed on 10/3/09. City of Frederick, MD. http://www.co.f rederick.md.us/index. asp?NID=100, accessed on 10/3/09. City of Fresno, CA. http://www.fresno.gov/ Government/DepartmentDirectory/PlanningandDevelopment/Default.htm, accessed on 10/3/09. City of Gadsden, AL. http://www. cityofgadsden.com/, accessed on 10/3/09. City of Gainesville, GA. http://www.c ityofgainesville.org/ accessed on 10/3/09.

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121 APPENDIX (CONTINUED) City of Gainesville, FL. http://www.c ityofgainesville.org/ accessed on 10/3/09. City of Goldsboro, NC. http://www.ci.gol dsboro.nc.us/city_hall/ planning.aspx, accessed on 10/7/09. City of Grand Junction, CO. http://www. gjcity.org/CityDeptWebPages/CommunityDevelopment/DevelopmentServices/ZoningCode.htm, accessed on 10/7/09. City of Great Falls, MT. http://www.great fallsmt.net/people_o ffices/planning/current.php, accessed on 10/7/09. City of Greely, CO. http://greeleygov.com/CommunityDevelopment/default.aspx, accessed on 10/7/09. City of Green Bay, WI. http://www.ci.g reen-bay.wi.us/geninfo/planning_development/planning_development.html, accessed on 10/7/09. City of Greenville, NC. http://www.gr eenvillenc.gov/departme nts/community_development/information/default.aspx?id=1067, accessed on 10/7/09. City of Harrisonburg, VA. http://ci. harrisonburg.va.us/, accessed on 10/7/09. City of Hickory, NC. http://www.ci.hic kory.nc.us/department /?fDD=15-0, accessed on 10/7/09. City of Hinesville, GA. www.cityofhinesville.org/ accessed on 10/10/09. City of Huntsville, AL. http://www.hs vcity.com/Planning/zon ing/building_permit_info.php, accessed on 10/10/09. City of Idaho Falls, ID. http://www.ci.a mmon.id.us/departments/planningzoning/zoningcommisision-members.asp, accessed on 10/10/09. City of Iowa City, IA. http://www.ic gov.org/default/?id=147 8, accessed on 10/10/09. City of Jackson, TN. http ://www.cityofjackson.net/departm ents/planning/index.html, accessed on 10/10/09. City of Jackson, MI. http://www.cityofjack son.org/departments/communitydevelopment/planreview.asp, accessed on 10/15/09. City of Jacksonville, FL. http://www. coj.net/default.htm, accessed on 10/15/09.

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122 APPENDIX (CONTINUED) City of Jacksonville, NC. http://www.ci.jacksonville.nc.u s/opencms/opencms/residents/Zoning, accessed on 10/15/09. City of Janesville, WI. http://www.ci.j anesville.wi.us/citysite /, accessed on 10/15/09. City of Jefferson City, MO. http:/ /www.jeffcitymo.org/, accessed on 10/15/09. City of Johnstown, PA. http://www.cit yofjohnstownpa.net/cod es/zoning.htm, accessed on 10/15/09. City of Jonesboro, AR. http://www.j onesboro.org/Planning /Planning.htm, accessed on 10/15/09. City of Kalamazoo, MI. http://www.ka lamazoocity.org/portal/government.php?page_id=440, accessed on 10/15/09. City of Kankakee, IL. http://ci.kank akee.il.us/citydept.htm, accessed on 10/15/09. City of Kenosha, WI. http://www.kenosha .org/departments/development/index.html, accessed on 10/15/09. City of Kingston, NY. http://www.ci.kings ton.ny.us/content/76/78/default.aspx, accessed on 10/15/09. City of Kokomo, IN. http://www.cityof kokomo.org/department/index.asp?fDD=14-0, accessed on 10/15/09. City of Lafayette, LA. http://www.lafa yettela.gov/pzc/dpt90 00Index.asp, accessed on 10/15/09. City of Laredo, TX. http://www.ci.lare do.tx.us/city-planning/about/index.htm, accessed on 10/18/09. City of Las Cruces, NM. http://lcm poweb.las-cruces.org/, accessed on 10/18/09. City of Las Vegas, NV. http://www.c ityofnorthlasvegas.com/ accessed on 10/18/09. City of Lawrence, KS. http://www.la wrenceks.org/pds/, accessed on 10/18/09. City of Lee’s Summit, MO. http:// www.lees-summit.mo.us/content/department_planning.cfm, accessed on 10/18/09. City of Lewiston, ME. www.ci.lewiston.me.us/development/planningcode.htm accessed on 10/18/09.

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123 APPENDIX (CONTINUED) City of Lexington-Fayette, KY. www.poli ce.lfucg.com/index.aspx?page=17&recordid=498, accessed on 10/18/09. City of Lima, OH. www.cityhall.lima.oh.us/dept/community/cpc.asp, accessed on 10/18/09. City of Lincoln, NE. www.lincoln.ne.gov/City/plan/index.htm, accessed on 10/18/09. City of Livermore, CA. http://www.ci.l ivermore.ca.us/econdev/index.html, accessed on 10/22/09. City of Logan, UT. www.loganutah.o rg/Community%20Development/Planning%20and%20Zoning/index.cfm, accessed on 10/22/09. City of Lompoc, CA. http://www.cityoflompoc.com/departments/comdev/planning.htm, accessed on 10/22/09. City of Longview, TX. http://www.ci.l ongview.tx.us/services/planning_and_zoning.html, accessed on 10/22/09. City of Macon, GA. http://www.mbpz.org/, accessed on 10/22/09. City of Madison, WI. www.cityofmadi son.com/planning/, accessed on 10/22/09. City of Mansfield, OH. www.ci.man sfield.oh.us/, accessed on 10/22/09. City of McAllen, TX. www.mcallen.net/d evservices/planning/def ault.aspx, accessed on 10/22/09. City of Medford, OR. www.ci.medford .or.us/SectionIndex.asp?SectionID=, accessed on 10/22/09. City of Merced, CA. http://www.cityofmer ced.org/depts/cd/planning/default.asp, accessed on 10/22/09. City of Missoula, MT. http://www. co.missoula.mt.us/, accessed on 10/22/09. City of Mobile, AL. http://www.cityofm obile.org/services2.php, accessed on 10/22/09. City of Modesto, CA. www.modestogov.co m/development/zoning/gis.asp, accessed on 10/22/09. City of Monroe, LA. www.ci.m onroe.la.us/pud_inspections2.php accessed on 10/22/09.

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124 APPENDIX (CONTINUED) City of Montgomery, AL. www.montgom eryal.gov/?page=20&r ecordid=676&returnURL=%2Findex.aspx, accessed on 10/22/09. City of Morgantown, WV. http:// www.morgantown.com/planner.htm, accessed on 10/22/09. City of Mount Vernon, WA. www.ci.mount-vernon.wa.us/default.asp accessed on 10/24/10. City of Muncie, IN. http://www.co.delaw are.in.us/department/index.asp?fDD=20-0, accessed on 10/24/10. City of Myrtle Beach, SC http://www.nmb.us/Page.aspx?ID=2&LinkID=55&SubID=55, accessed on 10/24/10. City of Napa, CA. http://www.co.napa.ca.us/Gov/Departments/DeptDefault.asp?DID=29000, accessed on 10/24/10. City of Newark, OH. http://www.ci.newark.oh.us/city/citydepartments/departments2.asp?method=dept&dept_id=43, accessed on 10/24/10. City of Ocala, FL. http://www.ocalaf l.org/planning.aspx, accessed on 10/24/10. City of Odessa, TX. http://www.odessa-tx. gov/public/departmen ts.asp, accessed on 10/24/10. City of Olympia–Lacey, WA. bullsheet .wordpress.com/2009/02/20/lacey-washingtoncommission-oks-tent-cities accessed on 10/27/09. City of Oshkosh, WI. http://www.ci.o shkosh.wi.us/community_development/Extraterritorial_Zoning.htm#, accessed on 10/27/09. City of Panama City, FL. http://www. panamacityfl.gov/planning_zoning_information.htm, accessed on 10/27/09. City of Pine Bluff, AR. http://www.cit yofpinebluff.com/inspection/index.htm, accessed on 11/3/09. City of Pittsfield, MA. http://www.pittsfield-ma.org/s ubpage.asp?ID=547, accessed on 11/3/09. City of Pocatello, ID. http://www.pocatello.us/, accessed on 11/3/09. City of Port Arthur, TX. http:// www.portarthurtexas.com/, accessed on 11/5/09.

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125 APPENDIX (CONTINUED) City of Port Huron, MI. http://www.por thuron.org/content.aspx? Pageid=28, accessed on 11/5/09. City of Provo–Orem, UT. http://www.pr ovo.org/comdev.zoning_enforcement_request.html, accessed on 11/5/09. City of Pueblo, CO. http://www.pueblo.us/cgibin/gt/tpl_page.html.template=35&content=87&nav1=1&, accessed on 11/5/09. City of Racine, WI. h ttp://www.cityofracine .org/Depts/develop ment/, accessed on 11/9/09. City of Raleigh, NC. http://www.ralei ghnc.gov/portal/server.pt/gateway/PTARGS_0_2_306_204_0_43/http%3B/pt03/DIG_Web_Content /dept/public/Dept-AboutUsPlanning.html, accessed on 11/9/09. City of Rapid City, SD. http://www. co.pennington.sd.us/, accessed on 11/9/09. City of Redding, CA. http://www.ci.re dding.ca.us/devserv/pl anning/index.html, accessed on 11/9/09. City of Reno, NV. http://www.cityofreno.com/Index.aspx?page=348, accessed on 11/9/09. City of Rochester, MN. http://www.ro chestermn.gov/departments/planning_zoning/index.asp, accessed on 11/12/09. City of Rochester, NY. http://www.ci.rochester.ny.us/dcd/Buildings_Zoning/Buildings_Zoning_Zoning_Why. cfm, accessed on 11/12/09. City of Rome, GA. http://www.romega.u s/faq.asp?searchTerm s=&TID=32, accessed on 11/12/09. City of Saginaw, MI. http://www.saginawmi.com/Government/Departments/Development/Zoning/, accessed on 11/12/09. City of Salem, OR. http://www.cityofsalem.net/Departments/CommunityDevelopment/Planning/Zoning/ZoningMaps/Pages/Nor thSalem.aspx, accessed on 11/12/09. City of Salt Lake City, UT. http://www.murray.ut ah.gov/, accessed on 11/12/09. City of San Angelo, TX. http://www. sanangelotexas.org/, accessed on 11/12/09. City of San Antonio, TX. http:// www.sanantonio.gov/dsd/, accessed on 11/12/09.

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126 APPENDIX (CONTINUED) City of San Jose, CA. http://www.sanjosec a.gov/planning/zoning/, accessed on 11/14/09. City of San Luis Obispo, CA. http:// www.slocounty.ca.gov/planni ng.htm, accessed on 11/14/09. City of San Rafael–Novato, CA. www.c ityofsanrafael.org/Gove rnment/Community_Development/Contact_Us.htm accessed on 11/14/09. City of Santa Barbara, CA. http:/ /www.santabarbaraca.gov/Business/Records_and_Property_Information/Planning_and _Zoning_Maps/, accessed on 11/14/09. City of Santa Clarita, CA. planning .lacounty.gov/view/major_accomplishments_2007, accessed on 11/14/09. City of Santa Fe, NM. http://www.santafenm.gov/index.asp?NID=332, accessed on 11/14/09. City of Savannah, GA. http://www.ci .savannah.ga.us/cityweb/CommServ.nsf/E2781A18CF37107C85256DB7004D721B/E 68E883EA6FCEF1685256DE20057DF 5C?OpenDocument, accessed on 11/14/09. City of Sheboygan, WI. http://ci.sh eboygan.wi.us/Development/DevelopmentHome.html, accessed on 11/14/09. City of Sherman, TX. http://www.cityof sherman.org/code_pz.asp, accessed on 11/14/09. City of Simi Valley, CA. www.ci.simi-valley.ca.us accessed on 11/14/09. City of Sioux Falls, SD. http:// www.siouxfalls.org/, accessed on 11/14/09. City of Spartanburg, SC. http://www.c ityofspartanburg.org/C ity_Government/City_Departments/Development%20Ser vices.html, accessed on 11/14/09. City of Springfield, IL. http://www.springfield.il.us/City_Gov/ComServ/zoning.htm, accessed on 11/14/09. City of Springfield, MO. http://www.sp ringfieldmo.gov/egov/planning_development/zoning/howto/htrezone.html, accessed on 11/15/09. City of St. Charles, MD. http://www. charlescounty.org/, accessed on 11/15/09. City of St. George, UT. http: //www.sgcity.org/, accessed on 11/15/09. City of State College, PA. http://www.zoningmatters.org/issues, accessed on 11/15/09.

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127 APPENDIX (CONTINUED) City of Stockton, CA. http://www.st ocktongov.com/CD/PlanningDivision.cfm, accessed on 11/15/09. City of Sumter, SC. http://www.sumter sc.gov/Departments/P lanning.asp, accessed on 11/15/09. City of Tallahassee, FL. http://www. talgov.com/planning/index.cfm, accessed on 11/15/09. City of Terre Haute, IN. http:// www.terrehaute.in.gov/, accessed on 11/15/09. City of Topeka, KS. http://www.topeka.o rg/planning/index.sh tml, accessed on 11/16/09. City of Tucson, AZ. http://www.tucs onaz.gov/planning/maps/zoning/, accessed on 11/16/09. City of Tulsa, OK. http://www.cityoftu lsa.org/Community/Planning/Index.asp, accessed on 11/16/09. City of Tuscaloosa, AL. http://www.ci .tuscaloosa.al.us/, accessed on 11/16/09. City of Tyler, TX. http://www.cityoftyler.org/Admin/Tabs/tabid/97/Default.aspx, accessed on 11/16/09. City of Utica, NY. http://www.city ofutica.com/EconomicDevelopment/Planning/Zoning+Board+of+Appeals.htm, accessed on 11/16/09. City of Valdosta, GA. http://www.val dostacity.com/Index.aspx?page=72, accessed on 11/16/09. City of Victoria, TX. http://www.vict oriatx.org/planning/index.asp, accessed on 11/16/09. City of Visalia, CA. http://www.ci.v isalia.ca.us/, accessed on 11/16/09. City of Waco, TX. http: //www.waco-texas.com/city_depts/ planningservices/planning.htm, accessed on 11/16/09. City of Waterloo, IA. h ttp://www.wplwloo.lib.ia.us/wat erloo/zoning.html, accessed on 11/16/09.

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ABOUT THE AUTHOR Marin Vesselinov Geshkov w as born December 25, 1972, in Sofia, Bulgaria. He earned a master’s degree in engineering from the Technical Univer sity–Sofia in 1996 and a master’s degree in economics from the Univ ersity of National and World Economics in Sofia in 2000, while also working as a speci alist in urban gasification for OVERGAS INC., for which he successfully designed inve stment projects in sever al Bulgarian cities. Mr. Geshkov earned a master’s degree in economics from the University of South Florida in 2002 and entered th e doctoral program that year During his PhD studies, he taught principles of microeconomics, princi ples of macroeconomics, and urban economics. On January 5, 2010, he presented “The Effect of Land-Use Controls on The Spatial Size of U.S. Urbanized Areas,” co-authored with Joseph S. DeSalvo, at the Annual Conference of the American Real Estate and Urban Economics A ssociation in Atlanta, GA.


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ABSTRACT: Chapter 1 provides a discussion of definitions, criticisms, and measurements of urban sprawl. Land-use controls are surveyed in Chapter 2. In Chapter 3, we present the monocentric urban model, followed by a discussion of extensions of that model to include land-use controls. Chapter 4 is a survey of previous empirical analysis of the monocentric model, while Chapters 5 and 6 present our own empirical work. In general, our empirical results support the theoretical predictions as well as providing support for policies to control sprawl. In particular, the results support the use of maximum lot-size zoning, urban growth boundaries, and density restrictions in the form of minimum building heights, minimum square-footage limits, maximum building permits, and minimum persons per room. The importance of this dissertation lies in the fact that it presents the first empirical analysis of the effects of land-use controls on urban sprawl. For this reason, the findings should be of interest to urban planners in their efforts to control urban sprawl. Because we test theoretical hypotheses found in the urban economics literature, the results should also be of interest to academic economists. Finally, the data on land-use controls gathered for the empirical analysis should be of importance to researchers in urban economics
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