URBAN SPRAWL, JOB DECENTRALIZATION, AND CONGESTION: THE WELFARE EFFECTS OF CONGESTION TOLLS AND URBAN GROWTH BOUNDARIES

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1 URBAN SPRAWL, JOB DECENTRALIZATION, AND CONGESTION: THE WELFARE EFFECTS OF CONGESTION TOLLS AND URBAN GROWTH BOUNDARIES Wenjia Zhang City and Regional Planning Program School of Architecture The University of Texas at Austin Kara M. Kockelman Professor and William J. Murray Jr. Fellow Department of Civil, Architectural and Environmental Engineering The University of Texas at Austin 6.9 E. Cockrell Jr. Hall Austin, TX Phone: Under review for Presentation at the 93 rd Annual Meeting of the Transportation Research Board, August 2013, Under review for Publication in the Journal of Regional Science, August 2013 Abstract: This paper develops a spatial general equilibrium model to explore the endogenous relations between urban sprawl, job decentralization, and traffic congestion, and then compare the efficiency and welfare impacts of anti-congestion policies. Results suggest that congestion spurs firms to decentralize and agglomerate away from the urban center, with households living more centrally. A congestion-toll policy brings more compact urban form and serves as the most effective strategy to reduce congestion and correct congestion externalities, by maximally improving social welfare. But such tolls may induce different job losses due to firms labor compensation needs. Urban growth boundary (UGB) strategies tested here alleviate congestion externalities and lower travel times, vehicle-miles traveled, and travel costs, but they also tend to bring some side effects, like worsened congestion, social welfare loss, land rent escalation, fewer job opportunities by residents. Key Words: urban economics, sprawl, congestion pricing, job decentralization, Urban Growth Boundaries (UGBs) INTRODUCTION Urban sprawl connotes an excessive and uncoordinated urban expansion, with low-density development, auto-dominated designs, and decentralization of population, firms and infrastructure to the edge of cities. Such settings are regularly believed to be at the root of many urban and suburban woes, such as auto-dependent lifestyles, residential segregation, loss of open space amenities, and insufficient public infrastructure, facilitating urban decay (Gottlieb,1999; Brueckner, 2000; Nechyba and Walsh, 2004; Knaap, 2007). Many of these issues link to traffic congestion, of which urban sprawl can be both cause and effect. For example, workers living in sprawling suburbs may commute to the urban core by automobile, resulting in heavier traffic on the roads, air pollution, accidents, and rising reliance on fossil fuels, especially in monocentric 1

2 regions. On the other hand, sprawl can be an effective response for those seeking to escape high land prices and congestion in the core, due to over-centralization. The relationship between urban growth and traffic congestion in a polycentric region, where sprawl is associated with both job and housing decentralization, is even more complex. Population of many US cities central cores may be falling and employment decentralizing (Glaeser and Kahn, 2001; Kim, 2007; Kneebone, 2009). Job decentralization changes the nature of urban sprawl: by re-agglomerating households and firms in city edges or sub-centers (McMillen and Smith, 2003; Gilli, 2009). The strategies for coping with congestion-related issues in non-monocentric regions can be quite different (e.g., Giuliano and Small, 1991; Crane and Chatman, 2004); but empirical findings remain inconclusive, and understanding how clustering versus decentralization affects congestion requires deeper theoretical investigation. This paper explores the connection between urban sprawl, job decentralization, and traffic congestion in a relatively flexible setting via application of a spatial general equilibrium framework. It integrates production externalities that agglomerate firms in some locations and congestion externalities that tend to decentralize firms while attracting people to their workplaces. Using this theoretical framework, we examine the efficiency and welfare effects of congestion tolls, labor subsidies, and UGB regulations on congestion costs. The paper is organized as follows: Section 2 reviews existing urban equilibrium models and their findings; Section 3 describes this new model s assumptions and equilibrium conditions, in Section 4; Section 4 compares simulation results for land use and congestion and evaluates different policy scenarios; Section 5 concludes the paper. LITERATURE REVIEW Several existing models of urban economies incorporate congestion externalities. Early works by Solow (1972), Henderson (1975), Arnott (1979), and Pines and Sadka (1985) considered congestion cost to be endogenous. With congested travel in a circular monocentric city, for example, the cost per mile at distance x away from the urban center is proportional to a power of the traffic flow across the ring at x relative to the road width at x. By differentiating congestion costs with respect to traffic flows, the congestion externality across the ring at x can be calculated as the marginal cost of adding another traveler to the traffic flow at location x. A congestion toll pricing on the difference between social marginal cost and private marginal cost of using a road is the first-best instrument to correct congestion losses. Some of these early studies also suggest that a properly chosen UGB may be an effective second-best substitute for first-best tolling, since the shadow value of land is less than its market value at the region s edge in a monocentric equilibrium (Arnott,1979; Pines and Sadka, 1985). Wheaton (1998) compared the population density of a market equilibrium without endogenous congestion and an optimum with endogenous congestion. Regardless of whether transportation capacity is endogenously provided, the optimal solution with priced congestion is found to be more compact (and thus denser) than the equilibrium solution without priced congestion. Urban sprawl can be caused by the market failure associated with congestion, and increasing central densities can generate an equal improvement in welfare that would arise from first-best tolling. This findings are often used to support UGB regulation as an effective second-best policy, since a UGB increases densities. However, Brueckner (2007) argues that UGBs achieve a much lower 2

3 welfare improvements than first-best tolling strategies. His monocentric spatial equilibrium model found that the best UGB offered just 0.8% of the welfare gain from levying congestion tolls. Presumably, the UGB could not foster strong central densification. Similar results can be found in Kono et al.(2012), who discovered that a UGB policy alone is a poor substitute for first-best tolling, best that optimal regulation of building size for higher central densities plus a suitable UGB is an effective second-best remedy. It seems that welfare gains from a restrictive UGB are largely offset by welfare loss from its negative side effects, such as land rent escalation and reduced areas for development. Unfortunately, all the above models were developed within a traditional monocentric framework. They conflict with the polycentric context of most of the US cities. Decreasing transportation costs, rising incomes, and better suburban amenities propel decentralization of both population and jobs (Crane and Chatman, 2004; Kim, 2007; Kneebone, 2009). This mismatch between theory and reality makes planners and practitioners less interested in using policy instruments developed by economic theories (Gottlieb, 1999). Fortunately, there are some sophisticated polycentric and multi-city models to better reflect the real world. Anas and colleagues (1996, 1999, 2006, 2007, 2008) have established such general equilibrium models in non-monocentric settings to reflect congestion endogenously. Anas and Kim (1996) presented a comprehensive CGE model integrating the decisions of consumers and firms, alongside congestion and agglomeration externalities. The agglomeration externalities in their model are on the consumption side, in which consumers are assumed to make more shopping trips to larger shopping centers with retail-job agglomeration. Simulation findings from a linear city with discrete parcels suggest that congestion externalities bring a dispersive urban form, with more shopping centers, while shopping agglomeration tendencies bring a more compact form, with fewer and bigger centers. Anas and Xu (1999) examined the effectiveness of congestion pricing and the relationship between congestion and urban form, using the Anas-Kim model but without considering shopping agglomeration. Their simulations suggest that levying congestion tolls generated job decentralization as well as residential centralization. Although firm agglomeration economies were discussed as important, Anas and Xu (1999) excluded them, which may make these findings implausible, because positive production externalities may surpass negative congestion externalities, and bring job centralization rather than decentralization. Anas and Rhee (2006) extended Anas and Xu s (1999) model to examine the efficiency of anti-sprawl policies, while including the value of open space at the urban edge in consumers utility functions. They concluded that policy efficiency of depends on open space values are specified. If open space offers no consumer value, the consumer welfare falls as greenbelt spaces expand. Only when the utility of open space reaches some thresholds can a UGB policy add to consumer surplus. They concluded that a restrictive UGB is not a second-best substitute for first-best tolling, and other policies, such as gasoline taxes and parking fees, are more efficient. Anas and Rhee (2007) and Anas and Pines (2008) explored UGBs as a second-best policy in a city-suburb system and a two-city system, respectively. When jobs are pre-set to locate at the region s core, they found that congestion tolls can cause jobs to relocate to the suburbs or another city, in order to shorten average commuting distances. They found that an effective UGB should be expansive rather than restrictive, forming a more sprawling structure through a process of jobs 3

4 decentralization. As before, these papers neglect of productive externalities of firms. In reality, agglomeration economies for firms have been important in shaping regions. Firms benefit from locating close to each another through access to intermediate inputs and labor, and knowledge spillovers (Fujita and Thisse, 2002; Glaeser, 2008). Firm agglomeration also changes the location choices of workers, who wish to moderate their commutes. Such agglomeration effects may be not necessary for reinforcing existing urban centers but rather shaping some new suburban centers, thanks to lower commute costs and land rents outside the urban core. Suitable sprawl or decentralization may be the welfare-maximizing choice of residents and firms, and serves as a solution for various urban issues (Anas, 2012a). Several studies have explicitly recognized the importance of production externalities and polycentric structures in their economic assessments of land use policies and/or fiscal policies (e.g., Fujita and Ogawa, 1982; Anas and Kim, 1996; Lucas and Rossi-Hansberg, 2002; Berliant et al., 2002; Wheaton, 2004; Arnott et al., 2007; Borck et al., 2010). Fujita and Ogawa (1982) were among the first to explore the economics of non-monocentric urban growth with production externalities, using a continuous linear city form. Production externalities, or location potential function (as defined in their paper), are reflected in firm profits, which include not only the net profit earned by production but also profits through spatial clustering of economic activities. Their simulation results demonstrate how agglomeration economies and transportation costs can determine moncentric, polycentric, and mixed equilibrium structures. Berliant et al. (2002) extended the Fujita-Ogawa model to consider the agglomeration effects of knowledge spillover, and concluded, somewhat differently, different conclusion that a polycentric configuration is never an equilibrium of urban structure. Their appraoch found that high commuting costs are associated with complete mixing of jobs and housing, while low enough commuting costs lead to a monocentric urban form. Two papers closely related to our study are those by Lucas and Rossi-Hansberg (LRH, 2002) and Wheaton (2004). LRH s model established an elegant spatial general equilibrium for firms and worker location choice within a circular region that fully endogenizes production externalities, and allows for non-monocentric urban structure. They found that Mills s monocentric form exists when commute costs are low enough. When these travel costs rise, a polycentric equilibrium may exist, and then everything becoming a mixed land use patterns when commuting costs are high enough. Rossi-Hansberg (2004) used the LRH model to evaluate labor subsides, land taxes, zoning restrictions, and other policies. He found that a location-specific labor subsidy is better than a zoning instrument to pursue an efficient allocation of residential and employment land use. Wheaton s (2004) paper combined a congestion externality and center-agglomeration forces. His numerical analysis compared market outcomes and socially optimal outcomes on the basis of land use mixing. He made some strong assumptions, such as inward-only radial commuting, exogenous land consumption levels of households and firms, roads provision without any of land, and production externalities determined by distances to the CBD. His simulation suggest that longer commuting distances and worse congestion are associated with more centralized firm agglomeration, while employment decentralization brings shorter commuting distance and low congestion levels. Our paper differs from the LRH and Wheaton s papers in several ways. First, we build a CGE 4

5 model that fully endogenizes both production and congestion externalities. Congestion externalities can be simply introduced as a negative component of production, as suggested by Rossi-Hansberg (2004); but we believe that congestion externalities should be fully considered, as an influence on people s daily travel. Second, there is a latent assumption in all the above non-monocentric models; the city/metropolitan boundary is fixed. We relax this strong assumption and replace it with fixed agricultural land rents at the region edge. It appears that for any fixed boundary there is a corresponding edge rents that yields the same equilibrium. But a fixed-boundary assumption is not equivalent an assumption of fixed edge rent, since the latter also constrains land availability for firms and housing. Third, our approach relaxes several assumptions used in Wheaton s and LRH s models, by acknowledging the difference between value of commute time and wage, and land use share for transportation infrastructures. Our model also relaxes the assumption of fixed population scale, allowing for population changes to capture possible effects of alternative policies on both land use. Finally, this new spatial general equilibrium model can be used to evaluate the welfare and land-use influence of a list of anti-congestion policies. ANALYTICAL FRAMEWORK City Endowments The model applied here assumes a continuous symmetric circular region with a radius,. The assumption of symmetry essentially implies that people need travel only towards or away from the center along radial street networks. Two agents, households and firms, exist and can reside at the same location inside the region. For any location x, and represent the fractions of land area used by firms and households, respectively. They satisfy: 1 where, is transportation infrastructure s land use share. Household Choices Each household chooses its home location x to maximize its Cobb-Douglas utility function involving goods and residential lot size. Households are assuming identical and their maximization problem is,,,, 0 1 subject to the budget constraint: (1) where is land rent at location, is the total money budget of a household living at x, is wage income for households living in location x, and reflects a potential lump-sum redistribution of overall land rents to address the gains in land rents while landlords are absent. If is the maximized utility level of each household in the region, constant over locations (for equilibrium), solving the relevant first-order conditions of utility maximization for and yields their optimal solutions: 1 (2) (3) 5

6 Characterizing Firms and Production Externalities Each firm is a price taker in the output and input markets, and decides how much labor and land to use for production, at each location x. The first part of a firm s two-part production function is an ordinary, constant-returns production technology that relates land and labor. If is production per unit of land and is employment density, then constant-returns production appears as follows (LRH, 2002): 0, 0 1 The second part of the production function is a positive technological externality from firm agglomeration. Many existing studies have tested and proven the existence of such agglomeration effects (see, e.g., Dekle and Eaton, 1999; Rosenthal and Strange, 2004; Melo et al., 2009; and Puga, 2010). Such external effects rise with the density of economic activities and proximity to other firms, typically at the region s center (e.g., Fujita and Ogwa, 1982; Lucas and Rossi-Hansberg, 2002; Ng, 2012; Glaeser and Kahn, 2001; Wheaton, 2004). Here, production externalities are defined proportional to local jobs density (at x) and the integral of exponentially distance-weighted job counts within a pre-existing cluster around the region s center point, up to an (exogenously set) boundary distance of. Following LRH (2002), the production externality at each location x is set as,, (4) where is the polar angle around the center (ranging from 0 to 2 ) and,, is the straight-line distance between a firm at location x and any firm lying within miles of the center (at a counter-clockwise angel of from the first firm). Thus,,, 2 cos Total production per unit of land at location x can be calculated as follows (LRH, 2002): The firms then maximize this profit function with respect to each of the three input quantities (density of workers, wages, and location: n, w, x), while the price of firm output is set as the numeraire ($1) without loss of generality: Max Π,, From the first-order condition of profit maximization with respect to, one can obtain an optimal wage, as offered by firms at location x: (5) Thus, optimal employment density at location x is as follows: / Given perfectly competitive input and output markets, all firms make zero (excess) profit, with land rents rising to ensure this, as follows: (6) Combining this equation with Eq. (6), land rent of a firm in location x will thus be: 1 / / / (7) 6

7 Recognizing Transport Technology and Congestion Externalities In a symmetric city, worker travel will take place in just the two, radial directions: inward (toward the city center) and outward. Here, represents marginal travel time (i.e., instantaneous travel pace in hours per mile, for example) at location x, with negative values representing inward travel and positive values representing outward travel. Since only one travel mode or transport technology (e.g., the private car) is included in this model, the magnitude of the marginal travel time in an uncongestible network will equal a constant, (in hours per mile), representing the inverse of free-flow travel speed by that mode. A lower value represents more advanced transport technology, with higher (free-flow) speeds. Since transportation systems are congestible, the true marginal travel time contains an additional component to reflect congestion. Here, this second component is assumed proportional to a power of the ratio of travel demand to supply or transport capacity at location x (as used, for example, by Solow, 1972; Wheaton, 1998, 2004; and Brueckner, 2007). Here, represents total travel demand passing location x. When 0, travel flow is inward; when 0, commute travel is outward; and, when 0, no travel demand crosses location x. Under these three potential travel settings, the marginal travel time is as follows: 0 0 (8) 0 where and are positive parameters and reflect network congestibility. Such behaviors imply that congestion externalities exist in the city, thanks to the added travel-time impacts of higher travel demand (versus a constant background capacity). Using workers value of travel time (VOTT, i.e., with representing the ratio of VOTT to wage) to quantify this congestion externality, and simply multiplying marginal travel pace (per traveler passing location x) by total demand at that location, one has the following cost of delay at each location in the region: 0 (9) 0 where also represents the congestion toll (per mile) at location x that charges commuters for the damage from the congestion externalities at x. The Land Market s Equilibrium Conditions Since both firms and households can exist in the same location, a competitive market requires they bid for the land via their willingness to pay (or maximized rents). Given the optimal solutions,,, from the partial equilibrium of households and firms at each location x (as shown in Eqs. (2), (3), (6) and (7)), the land market equilibrium requires that land rents satisfy the following equations: (1) max,,. 7

8 (2) 0. (3) 0. (4). From these equilibrium conditions, one can derive the optimal shares of land use for firms and households, and. If both and are less than, both and will equal zero. If equals, a mixed land use pattern will emerge at location x, and the number of firm workers will equal the number of households (or resident workers) at that location in an equilibrium (LRH, 2002). In other words: 1 if Given that both and will exceed (except at the developed region s edge), the land use shares for firms and households at each location x are as follows: 1 / (10) 0 1 (11) Moreover, thanks to households budget constraint, the lump-sum redistribution of land rent to each resident,, in a spatial equilibrium satisfies the following: 2 (12) where N is the region s equilibrium population. The Labor Market s Equilibrium Conditions Wage Equilibrium under Congestion In a spatial equilibrium, the locations chosen by each household and firm should be fixed and stable. Thus, households living at location x can freely chose different work and home locations, but they cannot improve their utility by changing their workplaces or residences. Similarly, no worker can achieve a higher net wage (net of commute costs) by changing his or her job location, which is labeled a wage no arbitrage condition in LRH s (2002) model. Here, each worker is assumed to allocate one unit of time to work plus two-way commute time. For residents who live and work in the same location, commute time is zero, so the worker s net wage income equals to the wage provided by firms at this location. Consider first the wage gradients over x of a laissez-faire equilibrium setting, when traffic congestion is un-priced. At location x, where commuting is outward ( 0 and 0), the number of workers within the annulus [0, ) exceeds the number of jobs there. Since workplaces within [x, ] are indifference to the worker when reaching a spatial equilibrium, all alternative firms within [x, ] must yield the workers living at x identical net income. Suppose workers living at location x-dx commute a distance of dx to work at location ; then, their wage condition will be as follows:

9 where is the ratio of VOTT to wage and is the ratio of value of working time (VOWT) to wage. The second component in the right-hand side of the equation, often overlooked in urban economic models (e.g., Wheaton, 1998; LRH, 2002; Brueckner, 2007), represents the cost of commute and the opportunity benefit of not working during commute. The VOWT typically equals to the wage because the employer will be willing to pay for working when compensating for other activities or travel (Jara-Diaz et al., Small, et al., 1993), so is often set as 1. In this case, the above equation can be rewritten as: 1 2 Thus, a worker commuting from x-dx outward to can earn a higher wage from firms in location than those that do not commute any distance, in order to compensate such workers for their efforts and thus sustain the spatial equilibrium among the region s homogeneous workers. Similarly, in locations where 0 and 0, workers at location find jobs inward, in the annulus [0,x], so wage at location satisfies the following: 1 2 Combining the above equations, the wage gradient at location x in the laissez-faire equilibrium is as follows: 2 (13) Notably, when =0, the marginal wage at location x may be positive or negative, with two possible values, as having two values in Eq. (8). This is because since wages are falling on either side of such points, as worker households approach living in such no-commute locations. Similarly, if a congestion toll is applied for all travel, workers commuting across location x will pay a toll that equals to the marginal cost of delay on other road users, as defined in Eq. (9). Thus, the wage gradient at location x in an equilibrium under marginal-cost road pricing is 2 2 (14) Clearing the Labor Market A spatial equilibrium requires that travel demand at the city edge,, and in the city centerpoint, 0, equals zero (since there are no jobs or workers beyond this boundary, to attract or generate such trips). In between these two locations, travel demand can and regularly does vary greatly. For 0, represents the added or reduced amount of travelers passing the infinitesimal interval dx from location x outward to location range [x+dx, ) and it involves two components: one is the net number of travelers generated in the interval dx, or number of workers residing in the interval, minus number of workers needed by firms in the interval: 2 ; the other is the number of travelers hired in the interval dx (and stop commuting across dx) to compensate for lost work hours when x workers pass the interval dx, i.e., 2. The change in travel demand (regardless of the sign of ) is thus given by: 2 2 (15) 9

10 As noted above, the two boundary conditions for demand are: (16) Spatial General Equilibrium Given the transportation parameters described above, one can combine the households and firms partial equilibria with equilibrium conditions for labor and land markets, thereby creating a spatial general equilibrium model for the region. Three types of spatial equilibrium are discussed in this paper, including the laissez-faire city -- without road pricing, the congestion-toll equilibrium, and equilibrium under two restrictive UGBs. In order to identify rent, land use, and traffic solutions, each household s or worker s utility level,, is fixed here, along with transportation infrastructure s land use share,, the production parameter,,and the background agricultural land rent,. These same parameters are regularly given/pre-set in these types of equilibrium problems (LRH, 2002; Wheaton, 1998; Brueckner, 2007). Under, for example, the laissez-faire setting, competition drives households to determine optimal bid rents,, and housing lot sizes,, by minimizing expenditures given the target utility level, while driving firms to choose optimal rent bids,, and employment densities,, in order to maximize their profits. At the same time, available land or properties are assigned to agents offering the highest bid rents, while city edge rents equal the background (agricultural) land rent, jobs and housing are balanced, consistent with Eq. (15), and each worker s net wage (after considering commute costs) is constant across locations, as shown in Eq. (13). A more rigorous definition of this laissez-faire equilibrium is provided as Definition A of Appendix I. As shown in Appendix I, the sufficient and necessary conditions for the other two equilibrium policy scenarios are quite similar to the laissez-faire spatial equilibrium setup (Definition A). For example, in the UGB case (Definition B), the condition of a fixed land rent at the city edge is replaced by the assumption of a fixed metropolitan boundary: (17) In the congestion-toll equilibrium (Definition C), the money budget of each household change since a lump-sum congestion toll,, is redistributed back to each household, and the wage difference between two locations for a worker should cover not only the difference of commuting costs but also the difference of congestion externalities, due to sustain the condition of wage equilibrium. In this case, the marginal wage distribution thus should satisfy Eq. (14), instead of Eq.(13), and the money budget,, and the congestion toll,, are given by (18) and (19) Given,,,,, and from one of three equilibriums, social welfare can be calculated as the net surplus, NS, including the producer surplus and consumer 10

11 surplus: 2 (20) All of the above equilibrium allocations are Pareto-optimal, as proven in Appendix II. Social welfare is maximized when a city reaches any spatial general equilibrium defined in Appendix I. NUMERICAL SIMULATIONS Parameter Values and Algorithm Table 1 shows the parameter values calibrated using data from Texas metropolitans such as Houston and Austin, and values found in the existing literature (e.g., LRH, 2002; Wheaton, 1998; Brueckner, 2007)). Some parameters are held constant across scenarios. For example, the Cobb-Douglas utility function s parameter reflects a household s expenditure shares on goods and services, versus rents (relative to a household s or worker s net income). Here, we rely on LRH s (2002) data-based value of 0.9, with 1- = 0.1 as the share of net income going to housing rent. The consumption expenditure on daily goods after spending housing and transportation in the Houston metropolitans in 2009 is around $30,000 1, and the median lot size for Houston households in 2007 is about 1950 square feet per unit 2. From the utility function, the utility level is estimated as The farmland at the city edge of Austin sells for about $50,000 per acre 3 and is amortized over 40 years at a discount rate of 5%, rural land rent is over $4,000,000 per square mile per year (which also equal to Wheaton (1998) s setting). Thus the agricultural land rent, R A, is set to $4,000,000 per square mile, i.e., cents per square foot per year in this work s numerical simulations. Table 1 Parameter value assumptions R A 0.9 4,000 $4,000,000 per sq. mi (14.35 SF) per year , miles to to 6E Key parameters for firm behaviors also refer to LRH s paper, where 0.95 and The parameter of production externality,, will affect urban from in different values (LRH, 2002). Since this paper focus on the congestion effects, is fixed as 5. Total factor productivity,, is set at 30,000, by calibrating Eq. (6) assuming Austin s 2011 per capita money income (of $31,000 4 ) and an average employment density of over 100 persons per acre (in Austin s year-2010 downtown 5 ). Following Wheaton s (1998) study, roadways or transportation s share of land is assumed to be 30%. Commuting s VOTT is assumed to be 50 percent of hourly wage, and the developed region s boundary is set to 3 miles, the area with employment density 6 in Austin. 1 See p. 448 of 2 See p. 4 of 3 Estimated using data at CAMPO, 6 CAMPO, 11

12 The congestion-related parameters were calibrated using the City of Austin as a prototype, with other parameters are fixed. When (representing a free-flow travel speed of 25 mile/hour), 1 10, and 1.2, the city area and job count in a laissez-faire equilibrium were miles (or square miles) and 513,000 workers, and thus close to Austin s actual context (over 300 square miles and more than 500,000 workers in 2010). In order to get a sense of transport and congestion impacts, the congestion-related parameters were varied across scenarios. For example, the transport technology indicator varied from to 0.01, 0.005, and 0.002, corresponding to free-flow travel speeds of 5, 12.5, 25 and 62.5 mile/hour, respectively, if one unit time represents 8 hours in reality. The congestion indicator changed from 0 to , , and , with fixed at 1.2. The results of these variations are discussed in the next section. The spatial equilibria were solved for using MATLAB, following LRH s two-step fixed-point algorithm (2002). The first step computes equilibrium of land use and labor distribution, given a production externality function,, while the second step calculates a new based on Eq. (4). The simulation has converged when reached a fixed point, after several interations 7. Since our model differs from LRH s model, by virtue of including congestion effects, allowing for a relaxed city boundary, and enabling redistribution of rents and toll revenues to residents, the algorithm in the first step differs from that in LRH s work. For example, given an initial wage 0 at the city centerpoint (x = 0), wages and land uses at other locations can be derived via a recursive process based on Eq. (13) (the laissez-faire case) or Eq. (14) (the congestion-toll case) and Eq. (15). The process of finding an equilibrium corresponds to seeking an equilibrium initial wage 0 to clear all land and labor markets. This process involves two processes: The first uses a grid-search algorithm to find a 0 given an initial edge rent,. The second calculates a new edge rent based on Eq. (12) and goes back to the first procedure until reaching a fixed point for (i.e., ). The run time for finding such spatial equilibria on a standard personal computer ranges from 10 minutes to 1 hour, depending on parameter assumptions used. Relating Congestion and Sprawl The relationships between transport technology (in the form of assumed free-flow travel pace, ), congestion levels (via the parameter), and urban sprawl (reflected in a region s form, size and land use pattern) are explored here under a laissez-faire equilibrium. 7 The algorithm s convergence is proven in LRH s model when congestion effects are absent. Although the lemma that a convergence can be reached by the algorithm introduced in this paper are not rigidly proven in theory, the results presented in this paper are all convergent in practice. 12

13 Figure 1 Effects of transport technology (or free-flow speed) on urban form: equilibrium rents (left) by use type and equilibrium residential density (right) over space, without congestion ( 0), and as travel pace, phi varies from to (time units per mile). First, we examine the effects of transport technology on urban form and sprawl, when congestion effects are absent ( 0. Figure 1 shows how different parameter assumptions ( changes 13

14 from to 0.025) generate different styles of urban forms, including (1) the traditional monocentric structure, where a great many firms are able to occupy the urban core with higher bid rents than households (and job rents and densities peak close to this core), while worker households sort themselves outside the core (Figures 1a3 and 1a4); (2) the non-monocentric annulus structure, where worker households form the urban core and firms agglomerate at the edge of this core (Figure 1a2); and (3) the partially-mixed land use structure, where speeds are slow, households and firms share the region s center, and job densities peak at the edge of this core (Figure 1a1). In general, a higher-speed (and lower marginal-cost) transport technology settings (with lower ) tend toward a more monocentric and far-flung urban form, by enabling many firms to enjoy agglomeration benefits in the urban center while residents locate at lower rents, often far (in distance, but not time, terms) from the center. In contrast, lower-speed travel (with higher marginal travel costs) tend toward a mixed urban form. These findings generally appear consistent with those of Fujita and Ogawa (1982) and Lucas and Rossi-Hansberg (2002). However, in replacing the fixed-boundary assumption with the more realistic constraint of a known edge rent, the fully mixed-use form as a spatial equilibrium in previous models (Fujita and Ogawa,1982; Lucas and Rossi-Hansberg, 2002; Berliant et al., 2002) does not emerge as an equilibrium condition here, since wages and land rents lay flat and so cannot satisfy the edge-rent constraint. Moreover, firms may agglomerate in a single annulus, producing a type of polycentric landscape, but will not agglomerate in two or more annuli (as found in F-O and LRH models). This finding actually is consistent with the results of a revised LHR model form, as provided in Ross and Dong (2012). If simply using the region s radius or area and density to measure urban sprawl, faster transport technologies (from lower φ) are associated with more urban sprawl, as expected. As travel speeds rise from 5 to 62.5 mi/hr (as travel pace ( ) falls, from to 0.002), the region s radius rises from 5.34 to 10.23, 16.92, and finally miles (Figure 1); the numbers of workers (or jobs) increases from 0.1 to 0.42, 1.2 and 4.13 million; and thus, the residential density drops from 2044 to 2040, 1988, and 1892 persons per square miles. When transport technology improves, more people will move to the city and this city thus will expand more with relative low-density development. In addition, residential use reacts more strongly to higher speeds than commercial use. As illustrated in Figure 1c1-1c4, when transport technology improves the region s jobs clusters move just a bit closer to the urban center: from 2.81 mile to 1.85 mile, a net centralization of just 0.96 mile, while the limit of firm locations expands from 3.17 to 3.81 mile, a net decentralization of just 0.64mile. The residents, however, extend their limiting location from 5.34 to miles, a dramatic edge shift of nearly 26.4 miles. Next, we examine these relationships when congestion is present. The simulated equilibria suggest that higher levels of congestion result in more centralization of households and a more decentralized agglomeration of firms, while less congestion results in a more monocentric urban form. For example, assuming speeds of 25 mile/hour ( 0.005), as shown in Figure 2, the laissez-faire equilibria under light congestion ( 1 10 or 1 10 ) produce monocentric urban structures with larger city boundaries and population, while heavy-level congestion ( 5 10 or 1 10 ) produces an annulus structure with smaller city areas and population. As the congestion level increases and generates more travel costs, workers will live closer to their workplace, while firms will move away from the urban core for avoiding the excessive labor costs due to compensate congestion costs (or firms cannot bid higher rents 14

15 for the core s land than households after paying high wages to their workers). Figure 2 Effects of network congestibility on urban form: equilibrium densities when the congestion indicator varies from to (and = 0.005) Network congestibility is another important determinant of equilibrium city size and land use patterns. In the Figure 2 scenario, higher congestion levels are estimated to make the city/region more compact mile defines the region s limiting radius under the less congestible case ( 1 10 ), falling to 7.44 mile in the high congestion case ( This finding is consistent with Wheaton s (1998) more compact result in a monocentric equilibrium when congestion effects were recognized, versus neglected. However, we also find several differences in density distribution between the traditional monocentric model and our findings. For example, when firm behaviors are ignored in the monocentric model, the central residential density in an optimum with congestion is much higher than in an equilibrium without congestion (more than twice, e.g. see Wheaton, 1998). In our models allowing for job decentralization and non-monocentric equilibrium, the central residential density (or the whole density distribution) decrease slightly, rather than increase (Figure 2). Facing congestion effects, the market may have two potential adjustments by itself. The first one is to raise population density, and the second is 15

16 to decentralize firms or jobs. The latter strategy is difficult to detect in a monocentric model, since firm locations are pre-set/fixed at the centerpoint; but it appears common in practice/reality. As expected, regulating densities does not appear equivalent to tolling congestion in a city, when the model permits job decentralization. Therefore, in the following section, two policies are evaluated using our model allowing for job decentralization: one is congestion tolls and the other one is UGB regulation (often labeled density regulation, although Brueckner (2007) and Kono et al. (2012) have suspected the effects of UGBs on central density rise in a monocentric model).? I can t understand this last statement. Just b/c someone mistakenly calls it density regulation (which is different, and is acre by acre, not just defining an edge limit) doesn t lead to the B&K citations, and & I can t understand what they have suspected ; please overhaul or remove. Policy Scenarios In this section, two distinct policies efficiency and welfare effects vis-a-vis traffic congestion (and its associated negative externalities) are examined. The policies are application of congestion tolls and imposition of two different UGB regulations (where the region s laissez-faire radius is reduced 10% and then 20%). All three sets of results are compared to the laissez-faire equilibrium, where congestion externalities are un-priced. In these policy scenarios, the transport technology indicator is fixed at 0.005, while the congestion indicator changes from = to , and , as part of a sensitivity analysis. Table 2 provides various aggregate travel attributes of different congestion levels. These attributes are average commuting time, distance and costs. One common benefit of all three policy scenarios is that they reduce (average) travel times, distance and costs as compared to the laissez-faire case even though tolls are applied and/or traffic densities rise. The UGB regulations reduce average travel distance more than the congestion-toll policy. One important reason is that UGB regulations often bring more compact urban form (smaller boundary and higher residential densities) than the congestion-toll policies. In the case of high congestibility ( = ), the average commute distance of round trips in a congestion-toll case is 5.99 miles, smaller than 6.84 miles in the laissez-faire case, but larger than 5.82 miles in the 10% area-reduction UGB regulation and 4.76 miles in the 20% area-reduction UGB regulation. As shown in Figure 3, both equilibrium boundaries of the congestion-toll case (8.35 mile) and the 20% UGB case (6.82 mile) are smaller than the laissez-faire case (8.53 mile), and the residential density of the 20% UGB equilibrium (2904 hhs/sq mi) is 44% larger than the congestion-toll equilibrium (2013 hhs /sq mi), and 55% larger than the laissez-faire equilibrium (1869 hhs/sq mi). Meanwhile, the peak of job density in the congestion-toll equilibrium slightly move outward to 2.69 mile from 2.56 mile in the laissez-faire case, and 2.54 in the 20% UGB equilibrium. If reducing travel distances and thus vehicle-miles traveled (VMT) is a key community objective, an appropriate UGB policy may be effective (as noted in Zhou et al. s (2009) simulations of Austin, Texas land use and travel patterns). 16

17 Table 2 Simulation Results of Travel Attributes and Welfare Effects under Different Policy Scenarios and Different Network Congestibility ( 0.005, σ 1.2) Policy Scenarios Boundary Pop Travel Time Travel Distance Travel Cost Cost of Externality Net Surplus Total Welfare Avg. Welfare Avg. HH Rents (mi) (1000 hhs) (min/day) (mi/day) $/yr (%) ($ mil/yr) ($ mil/yr) ($ mil/yr) (%) ($) ($ mil) (%) Very High congestible Laissez-Faire Toll UGB (10%) UGB (20%) High congestible Laissez-Faire Toll UGB (10%) UGB (20%) Medium congestible Laissez-Faire Toll UGB (10%) UGB (20%) Low congestible Laissez-Faire Toll UGB (10%) UGB (20%) Notes: Travel time and distance are round-trip-based. Travel time is calculated based on 1 unit of time=8 hours. Percentage changes (% s, in bold) are relative to the Laissez-Faire equilibrium. Total welfare=net surplus - cost of congestion externality + potential tolls/tax 17

18 (a) Laissez-Faire versus Congestion-Toll (b) Laissez-Faire versus UGB (20%) Figure 3 Equilibrium rents and land use patterns under three policy settings (with & 5 10 ) In addition, the congestion-toll policies may bring significant reduction on travel costs when the network congestibility is high enough, e.g., 17% lower costs than the laissez-faire equilibrium when = and 30% lower when = ). 10% of boundary reduction by the UGB regulation may bring about 10%-14% reduction of travel costs; while 20% of boundary reduction may bring above 20% reduction of costs. In the cases of low congestibility, the effectiveness of reducing travel costs by the UGB regulations tend to be larger than the congestion-toll policies. Although better travel outcomes can be gained by suitable UGB regulations, the UGB policies cause much lower total/per capita social welfare in the region than the congestion-toll policies, and even than the laissez-faire case (Table 3). Here, social welfare is calculated by adding the net surplus as in Eq. (12) and potential total congestion tolls after eliminating the amount paying for social costs of congestion externality. Only in the congestion-toll cases, congestion externality is priced and compensated by the tolls levied from residents with commuting behaviors; thus, its total social welfare equals to the net surplus. From Table 2, the more severe a region s/network s congestibility, the more effective a toll-related policy will be, in terms of welfare improves. For very high congestible network ( ρ= ), above 49% of social welfare is improved by levying a congestion toll. For relative light congestible network ( ρ= ), only 7% increases of social welfare is gained by the congestion-toll strategy. In contrast, the UGB policies result in nearly 20% and 40% declines in the community s overall welfare or net surplus (for the 10% and 20% area-reduction cases), vs. the laissez faire case. For example, for = , the less restrictive UGB policy (10%) brings about 27% loss of total welfare (or above 27% loss of average welfare), while the more restrictive UGB (20%) brings about 40% loss of social welfare (or 36% loss of average welfare). 18

19 Several factors may explain the reason why UGB policies cause welfare losses rather than gains in our models allowing for job decentralization. First, the UGBs may limit the market to adjust itself towards an optimum through jobs decentralization when facing congestion. Levying a congestion toll is associated with some jobs decentralization, with the employment peaks shifting slightly outward for about 0.2 mile, for example, from a radius of 2.5 mile to 2.69 mile as shown in Figure 3a. On contrast, the 20% UGB makes jobs relatively centralized, for example, from a radius of 2.5 mile to 2.48 mile. Although the changes seems to be small, this finding still reveals a difference between the first-best congestion tolling and the UGB regulation: the optimum by congestion tolling seeks for a more decentralized jobs distribution while the UGB equilibrium tend to become more centralized with higher density. Second, the UGBs cause the edge rents to escalate, versus the background agriculture-use rent. While such policy saves land for other uses, and is estimated to lower commute costs here, less land overall means more competition for land (even with population endogenous here), resulting in higher rents and smaller parcels per household or worker, and thus lowered household utilities and lowered economies of production. In a real setting, lower-income households and lower-paying jobs may be unable to remain in the region, creating other issues (in equity and industrial balance, for a fully functioning economy, for example). As shown in Table 2, the increases of households average bid-rents by the UGB regulations are much higher than by the congestion-toll policies. With relatively high network congestibility ( = ), the households average bid-rent is significantly increased by 69% in the 20% UGB equilibrium, and by 12% in the congestion-toll equilibrium. For the light congestible case ( = ), the corresponding increased percentages of households bid-rent are 45% of the 20% UGB policy and as low as 0.6% of the congestion-toll policy. For further sensitivity analysis, we examine policy scenarios of a UGB with the same boundary to that of the congestion-toll equilibrium and a 5% UGB and 15% UGB. Relative results are basically consistent with the above analyses. All UGB regulations can raise residential density and land rents for households, centralize jobs, and make the regions more compact, but cannot bring social welfare improves after compensating congestion externality. The welfare effects of three policy scenarios are also evaluated when the transport technology indicator is set as 0.01 and The larger the is, the more effective the congestion-toll policies tend to be, and the more losses of social welfare the UGB regulations cause. These sensitivity analyses reconfirms the relationship seen in Table 2, suggesting that a seemingly robust conclusion: UGB strategies tend to alleviate congestion externalities and lower VMT and travel costs, but it is not an effective substitute for the first-best congestion-toll policy especially when job decentralization occurs in a non-monocentric urban setting, since they bring large losses of social/community welfare through escalating land rent and limiting job decentralization. CONCLUSION AND DISCUSSION This paper develops and then applies a new spatial general equilibrium model in order to explore the impacts of tolling and growth-boundary policies on region size, population, land use patterns, job decentralization, travel costs, land rents, and traffic congestion. Results of many parameter and policy scenarios allow one to evaluate the welfare and commuting effects of such anti-sprawl policies. This new model differs from many existing studies (e.g., Fujita and Ogwa,1982; Anas and Kim,1996; Lucas and Rossi-Hansberg, 2002; Wheaton, 2004) by allowing for job decentralization in non-monocentric structures, endogenous population/jobs counts, and relaxed city boundaries, along with both congestion and production externalities. 19