Effects of urban land-use regulations on greenhouse gas emissions

Cities 70 (2017) 135–152

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Effects of urban land-use regulations on greenhouse gas emissions

MARK

Benjamin D. Leibowicz Graduate Program in Operations Research and Industrial Engineering, The University of Texas at Austin, ETC 5.128D, 204 E. Dean Keeton St., C2200, Austin, TX 78712, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Urban form Greenhouse gas emissions Land use Climate change Smart growth Zoning

This article describes a model-based exploration of the greenhouse gas (GHG) emissions impacts of urban landuse regulations. Two forms of regulation are considered: floor area ratio (FAR) restrictions and urban growth boundaries (UGBs). The model is designed so that regulation causes an endogenous adjustment of urban spatial structure, which in turn leads to changes in residential and transportation emissions. A novel aspect of the framework is that it captures regulation-induced inter-city migration. Results indicate that cities with low emission intensities should be cautious about adopting smart growth controls for climate change mitigation purposes. Even if such a regulation reduces per capita emissions everywhere, it can have the unintended consequence of increasing total emissions by pushing households to cities with higher emission intensities. Model variations reveal that this outcome is less likely if migration is costly or all urban areas are subject to some degree of regulation. Reducing emissions through land-use regulation generally carries a high abatement cost because consumers suffer from higher housing prices. Nevertheless, it could be an attractive mitigation option if policies are deployed in the right places, coordinated across cities, or generate substantial co-benefits (e.g., improved air quality, agglomeration economies, avoided infrastructure expansion).

1. Introduction This article describes a model-based exploration of the greenhouse gas (GHG) emissions impacts of urban land-use regulations. Such policies are ubiquitous, and through their effects on urban form, they could strongly influence GHG emissions in an increasingly urbanized world. In addition, given the difficulties of formulating consistent climate policies on national and global levels, environmentally conscious cities could turn to land-use regulations as mitigation instruments governed and operating at the urban scale. The findings of this study shed light on several key research questions with clear policy relevance. Under what circumstances will urban land-use regulations reduce emissions? When they do reduce emissions, what will be the abatement cost borne by consumers due to higher housing prices? What factors do these outcomes most critically depend on? In short, this study advances the literature by developing a modeling framework for analyzing urban land-use regulations, and using it to enhance our understanding of their emissions and welfare impacts. The remainder of this article is organized as follows. Section 2 contains a literature review. The model developed for this study is presented in Section 3. Section 4 describes the numerical simulations and the parameter values used as inputs. Results of the simulations are reported and discussed in Section 5. In Section 6, model variations are constructed to examine whether results are sensitive to different

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.cities.2017.07.016 Received 7 February 2017; Received in revised form 29 June 2017; Accepted 15 July 2017 0264-2751/ © 2017 Elsevier Ltd. All rights reserved.

assumptions or additional model features. Section 7 concludes with a summary of the most salient findings of this study. 2. Literature review 2.1. Urban form and greenhouse gas emissions It is well established that more compact urban forms are associated with lower GHG emissions (Grubler et al., 2012, chap. 18), an important consideration at a time of growing anxiety about climate change (IPCC, 2014). This relationship is based on several pathways related to emissions from the transportation and residential sectors. In transportation, higher population densities tend to shorten commutes as well as encourage investment in, and use of, public transit (Kennedy et al., 2011; Lohrey & Creutzig, 2016; Marshall, 2008). In the residential sector, homes in denser cities are typically smaller and more likely to be part of multifamily buildings, which use energy more efficiently than single-family detached houses (Ewing & Rong, 2008; Kennedy et al., 2011). Myriad empirical studies have analyzed the linkages between urban form and GHG emissions. Glaeser and Kahn (2010) present data that reveal striking heterogeneity in per capita emissions across U.S. cities. Taking as examples the two cities at opposite ends of the range, an average household in Memphis produces 75% more residential and transportation emissions than an average household in San Diego. The

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chap. 56). However, other drivers of urban sprawl are related to negative externalities and policy failures. Sprawling development requires greater public infrastructure expenditures to extend power lines, roads, and sewage systems (Brown & Southworth, 2008; Nechyba & Walsh, 2004). Massive federal spending on highways (in contrast to low investment in public transit) distorts transportation mode decisions in favor of automobiles (Glaeser & Kahn, 2004, chap. 56; Hart & Spivak, 1993). The failures of many central cities to control crime and maintain adequate public schools have driven former central city residents to the suburbs (Berry-Cullen & Levitt, 1999). Land-use regulations which restrict housing supply and raise prices push residents to communities on the urban periphery in search of affordable housing (Bertaud & Brueckner, 2005; Glaeser, Gyourko, & Saks, 2005). Externalities such as climate change are largely unpriced, so the private costs of emitting activities like driving are lower than their social costs. Analysts have increasingly emphasized the potentially significant contributions that efforts to limit urban sprawl could make toward reducing GHG emissions and mitigating climate change. Marshall (2008) suggests that better urban design is an undervalued mitigation strategy that could have long-term impacts similar in magnitude to those of technological innovation. Stone, Mednick, Holloway, and Spak (2009) project that strong urban densification in the Midwestern U.S. would reduce year 2050 transportation emissions by the same amount as full adoption of hybrid-electric vehicles. Hankey and Marshall (2010) estimate that year 2020 U.S. passenger vehicle emissions would be 18% lower than year 2000 emissions under a high densification scenario but 17% higher under a high suburbanization scenario. If urban design is neglected, the increase in vehicle travel could offset improvements in vehicle efficiency and carbon intensity of fuels. Clearly, policies that counteract urban sprawl and lead to more compact urban forms have the potential to significantly reduce GHG emissions. Since urban landuse regulations are implemented by individual cities or urban areas, they can be effective tools for reducing emissions in the absence of political will to address climate change at higher levels of government.

observed heterogeneity has a number of explanations, but the authors find that urban form is a major factor.1 In particular, more compact cities produce less emissions from automobile use and residential electricity consumption. Gasoline consumption decreases with census tract density and increases with distance to downtown. Electricity use and emissions from electricity are lower in denser cities. Marshall (2008) uncovers an inverse relationship between population density and vehicle travel across U.S. cities, with an elasticity of −30%. Ewing and Rong (2008) determine that residents of more sprawling U.S. counties typically live in larger homes and are more likely to reside in single-family detached houses, both of which lead to higher residential energy use. Andrews (2008) shows that residential and transportation emissions decrease with population density across municipalities in New Jersey. Kennedy et al. (2011) study data from ten global cities that exhibit even more dispersion in per capita GHG emissions than the U.S. cities analyzed by Glaeser and Kahn (2010). For example, Denver produces over five times as much emissions as Barcelona does on a per capita basis. The analysis identifies a significant, inverse relationship between urban density and transportation emissions. Three sprawling North American cities – Denver, Los Angeles, and Toronto – feature the highest per capita transportation emissions by a substantial margin. Notably, New York, which is denser than these other cities, has much lower transportation emissions similar to those of the European cities in the sample. All four North American cities consume more fuel for heating and industrial uses than their climates would imply, likely due to larger home sizes. Lohrey and Creutzig (2016) find that transportation emissions decrease with density across a sample of global cities. They show that a threshold density for high public transit use exists around 50 persons per hectare, and that a large public transit mode share reduces emissions significantly. The evidence indicates that more compact urban forms are associated with lower GHG emissions, but many cities around the world are spreading out. This phenomenon, known as urban sprawl, is most evident and acute in the U.S. (Mieszkowski & Mills, 1993). In 1950, 65% of the American urban population lived in central cities and the remaining 35% lived in suburbs. By 1990, these percentages had flipped (Nechyba & Walsh, 2004). Population densities in both central city and suburban areas fell over this period. According to Marshall (2008), the average urban population density in the U.S. fell by 13% per decade from 1960–1990 and 34% from 1990–2000. Data from the two most recent U.S. censuses reveal a further 12% decline from 2000–2010 (U.S. Census Bureau, 2000, 2012). Urban sprawl is a dominant tendency in many other countries. Cities throughout the formerly socialist states of Central and Eastern Europe are undergoing low-density suburban sprawl, often around deteriorating urban cores (Schmidt, Fina, & Siedentop, 2015). Bart (2010) and Siedentop and Fina (2012) document substantial sprawl in Ireland, Portugal, and Spain, where increases in road transport carbon dioxide (CO2) emissions and artificial land cover are outpacing population and economic growth. Chinese cities like Guangzhou and Dongguan are adding urban land at historically unprecedented rates and quickly approaching the expansive forms of U.S. urban areas (Schneider & Woodcock, 2008). On the other hand, there are notable counterexamples to urban sprawl. Supported by consistent policy priorities and investment in public transit, Oslo has become denser while experiencing significant population growth. Urban population densities have increased throughout Norway and Sweden (Næss, Næss, & Strand, 2011). The dominant cause of urban sprawl has been lower transportation costs enabled by the widespread diffusion of cars and trucks. In this sense, sprawl could be viewed as a beneficial process through which consumers are maximizing their well-being (Glaeser & Kahn, 2004,

2.2. Urban land-use regulations Urban land-use regulations have a fascinating history, particularly as they proliferated and evolved over the twentieth century. Rather than provide a lengthy survey of the vast suite of land-use regulations in effect in cities around the world, this subsection focuses on the two forms of regulation analyzed in this study. For a broad overview of urban land-use regulations, see Downs (1994) and Fischel (2004, 2015). 2.2.1. Floor area ratio restriction A floor area ratio (FAR) restriction imposes an upper limit on the ratio of building floor space to lot area. For example, a 60% FAR restriction applied to a lot of 10,000 square feet (ft2) limits the building floor space constructed on it to 6,000 ft2. FAR restrictions less than 100% are in place in many suburbs, as they mandate that a portion of each lot be dedicated to lawns, trees, and other uses apart from physical housing. Dense city centers may be subject to FAR restrictions many times greater than 100%, which effectively limit the number of stories in a building. For example, a 500% FAR restriction limits building height to five stories if the whole lot is covered, or ten stories if half the lot is covered. Therefore, maximum building heights, which are another popular form of urban land-use regulation, function in largely the same manner as these FAR restrictions. FAR restrictions are typically adopted for reasons other than concerns about sprawl or climate change. Proponents of these regulations argue that they prevent excessive densities that would lead to undesirable levels of traffic congestion, noise, and air pollution. They also preserve natural light and aesthetic value (Ewing & Rong, 2008). Austin, Texas uses FAR restrictions extensively for these purposes. Its zoning code specifies permitted uses for each lot, and many uses are subject to FAR restrictions. For example, Austin imposes maximum

1 Other explanations include the climate, as it affects heating and cooling degree days, and the fuel mixes used for electricity generation and home heating.

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as much as it appears (or even reducing them at all). The present study assesses the validity of this concern using a model which allows land-use regulation to induce inter-city migration.

FARs of 75% for medium-density multi-family residence lots, 100% for high-density multi-family residence lots, and 800% for central business district lots (City of Austin, 2016). High densities place greater demands on public infrastructure and services that many cities in the developing world are unable to provide, so FAR restrictions are employed to preclude these untenable densities. This is a primary justification for the FAR restriction in force in Bangalore, India (Bertaud & Brueckner, 2005). Critics contend that residents of some municipalities use FAR restrictions as exclusionary zoning tools to prevent unwanted income or racial groups from moving to their communities. Suburban FAR restrictions make it difficult to build multi-family housing and generally make housing more costly by limiting its supply. A desire by voting homeowners to increase the values of their homes could also motivate adoption of an FAR restriction. Although FAR restrictions are not typically introduced for climate change reasons, they can affect GHG emissions through their influence on urban form. In general, it is not obvious whether an FAR restriction would increase or decrease emissions. On the one hand, an FAR restriction might reduce emissions by prohibiting oversized homes that consume high quantities of energy (Ewing & Rong, 2008). On the other hand, the restriction might cause a spatial redistribution of population within the urban area, and possibly across cities. By limiting housing supply and raising prices, the FAR restriction could cause residents to move to more distant communities or to other cities in search of affordable housing. If these places are more emissions-intensive, the overall effect could be to increase emissions.

2.3. Modeling foundations The quantitative framework developed for this study is based on the classic monocentric city model. This subsection briefly reviews its development, application, and previous extensions. A mathematical presentation of the model is included in the next section. The monocentric city model was originally formulated by Alonso (1964), Muth (1969), and Mills (1967, 1972). It is a highly stylized representation of an urban area, but using only several relationships and assumptions, it explains spatial patterns of population density, housing prices, and building size that are regularly observed in many cities. The model can predict how these variables respond to changes in income, transportation cost, and preferences. Anas, Arnott, and Small (1998) use the monocentric city model with a specific set of assumptions that leads to a negative exponential population density function. They compare the density gradient predicted by the model to the observed average gradient across a sample of U.S. cities and conclude that the model performs quite well. It also reproduces the observed effect of declining transportation costs with reasonable accuracy. Wu and Plantinga (2003) formulate a two-dimensional version of the monocentric city model to analyze the effect of exogenous open space on the spatial distributions of population density and housing prices. Their framework includes two distinct income groups. They determine that open space primarily attracts high-income households and can cause leapfrog development in locations further from the center. The overall effect of open space on the area of developed land is ambiguous. A rare application of the monocentric city model to land-use regulation is the work of Bertaud and Brueckner (2005), who employ it to analyze the effect of an FAR restriction on urban form. Unsurprisingly, they find that the restriction causes the city to expand spatially, and reduces consumer utility. The present analysis goes beyond their study in its representation of an FAR restriction by allowing it to apply to only a portion of the urban area, a formulation which is capable of producing more nuanced outcomes. Some researchers have extended the monocentric city model to include multiple centers, and the resulting frameworks are referred to as polycentric city models (Fujita & Ogawa, 1982; Henderson & Mitra, 1996). Glaeser and Kahn (2004, chap. 56) investigate the determinants of urban sprawl using a polycentric city model with multiple employment centers, which are established endogenously. They find that the fixed cost of establishing a center is an important factor. Since cars and trucks allow centers to be established without rail depots and ports, the authors postulate that they have driven decentralization of employment and housing.

2.2.2. Urban growth boundary An urban growth boundary (UGB) prohibits urban development outside a specified area including the central city, its close-in suburbs, and additional room to accommodate likely future growth. Surrounding land beyond the UGB is set aside for agriculture, forests, open space, and natural ecosystems. A UGB ensures that future development causes the city to become denser rather than expand spatially. To be effective, a UGB requires the commitment of all municipalities in a metropolitan area, not just the central city. This cooperation can be difficult to achieve. Portland, Oregon has had a UGB since 1979, and its effects have been studied extensively through empirical analysis. Judgments about its success are mixed. Jun (2004) finds evidence that the UGB has not successfully contained urban sprawl or reduced automobile use, partly due to spillover effects to nearby counties not covered by the UGB. However, several empirical studies confirm that the UGB causes property values within the boundary to exceed those outside it, indicating that the regulation is a binding constraint on development (Grout, Jaeger, & Plantinga, 2011; Mildner, Dueker, & Rufolo, 1996). While they attest to the influence of the UGB, higher housing prices can be problematic. Portland housing prices are high for a city of its size, which has a disproportionate impact on the poor and could deter people from moving to Portland (Fischel, 2015; Phillips & Goodstein, 2000). Unlike FAR restrictions, UGBs explicitly aim to curb urban sprawl and GHG emissions. In principle, a UGB should reduce both transportation and residential emissions in the city which adopts it. The regulation would force some residents to live closer to the city center, shortening their commutes. By restricting the land available for housing, the UGB would probably raise housing prices and cause people to live in smaller homes. However, higher housing prices induced by a UGB might cause some households to move out of the city, and deter potential residents from moving in. Depending on where those former residents and deterred potential residents end up living, the net effect could theoretically be an increase in emissions. In fact, Glaeser and Kahn (2010) conclude their article by raising this concern, particularly because the U.S. cities with more stringent land-use regulations tend to be places with lower per capita emissions. To the extent that the Portland UGB causes people who might otherwise live there to instead live in less regulated and more emissionsintensive cities like Dallas and Houston, it might not be reducing emissions

3. Model 3.1. Monocentric city model This subsection presents the monocentric city model, which forms the basis of the quantitative framework of this study. For a more detailed treatment of the model, see Brueckner (1987, chap. 20), which this overview more or less follows. Table 1 provides a quick reference guide to the parameters, variables, and functions of the model. Parameter values used as inputs for numerical simulations are discussed in Section 4. All residents in the city commute to the central business district (CBD), which entails cost t per roundtrip mile.2 For simplicity, the CBD is taken to be a point at x = 0, and therefore a resident living at distance x from the CBD pays tx in commuting costs. Every resident has income 2 This cost, as well as other parameters in the model, are valued on a per-period basis, typically annual.

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On the supply side of the housing market, housing is produced according to the concave, constant returns to scale production function H (N,ℓ), where N is capital and ℓ is land. Since consumers rent housing at price p, the revenue generated by producing housing is pH(N,ℓ). Normalizing the constant cost of capital to unity and letting r denote the land rent, profit is pH(N,ℓ) − N − rℓ. Profit can also be written as

Table 1 Quick reference guide to the parameters, variables, and functions of the model. Parameter values used as inputs for numerical simulations are discussed in Section 4. Parameter

Description

Value

t y η ρ L θ a b γ α

Annual household commuting cost per roundtrip mile Annual household income People per household Annual agricultural land rent per acre Population Radians of urban land area dedicated to housing Utility function exponent on composite good Housing production function exponent on capital Housing production function coefficient Annual household transportation CO2 emissions per roundtrip mile Annual household residential CO2 emissions per square foot of housing Description Distance from the CBD Consumption of composite good Consumption of housing Rental price of housing Equilibrium utility level Capital input to housing production Land input to housing production Rental price of land Capital-land input ratio for housing production Population density City radius Annual household CO2 emissions Total annual CO2 emissions Per capita annual CO2 emissions Description Utility function Housing production function Housing production per unit of land

$611 $60,000 2.4 $136 10,000,000 0.8π 0.5 0.75 10 Varies

β Variable x c q p u N ℓ r S D x m M μ Function v H h

ℓ(ph (S ) − S − r ),

where S is the capital-land ratio N/ℓ and h(S) ≡ H(S,1) is floor space of housing per unit of land. The housing producer chooses S to maximize profit as defined in Eq. (4), which yields the first-order condition

ph′ (S ) = 1.

Varies

v (y − tx − pq, q) = u

q

ph (S ) − S = r .

r = ρ,

(7)

where ρ is the exogenous agricultural land rent. In other words, at distances beyond x , it is more profitable to use land for agriculture than for urban housing. The population of the city L is given by

L=

∫0

x

θxDdx,

(8)

where θ/2π is the fraction of land in the city dedicated to housing. Researchers typically solve the monocentric city model in either the closed-city case or the open-city case. The closed-city case represents a scenario with no inter-city migration, and the open-city case assumes costless migration so that residents are no better or worse off than those living elsewhere. In the closed-city case, the population L is fixed while the equilibrium utility level u and city radius x are determined endogenously. Eqs. (7) and (8) simultaneously determine u and x . In the open-city case, u is fixed while L and x are determined endogenously. Eq. (7) determines x , and then Eq. (8) determines L. In this study, the utility function v(c,q) and the housing production function H(N,ℓ) are assumed to be of the Cobb-Douglas forms v(c,q) = caq1 −a and H(N,ℓ) = γNbℓ1 −b. This is a common assumption in the literature; for example, Wu and Plantinga (2003) and Bertaud and Brueckner (2005) also include Cobb-Douglas functions in the monocentric city model.

(1)

3.2. Extension to Two Cities This study extends the model to a context with two monocentric cities by combining elements of the standard closed-city and open-city cases. Let the two cities be denoted A and B. Spatial equilibrium holds within each city individually and across the two, so that the utility level is a constant u at all points in A and B. Migration is allowed between A and B,3 but migration in or out of the two-city system is prohibited. The combined population of A and B is a constant L. In response to a change in parameters, or regulation, some households may relocate within the same city, while others may migrate from one city to the other. Because

(2)

where subscripts denote partial derivatives. Additionally, the optimal consumption bundle must yield utility level u, so that

v (y − tx − pq, q) = u.

(6)

Eqs. (5) and (6) simultaneously determine S and r, which vary with x. As Brueckner (1987, chap. 20) demonstrates, S and r both decrease with x. Lower land rents compensate housing producers for lower housing rents at greater distances. Since land is relatively cheaper further from the CBD, producers shift the mix of inputs from capital to land, resulting in lower housing density. Several other quantities of interest can be computed. The population density D at distance x is equal to ηh(S)/q, where η is the number of people per household. The radius of the city x is the distance at which

The first-order condition corresponding to Eq. (1) is

v2 (y − tx − pq, q) = p, v1 (y − tx − pq, q)

(5)

Constant returns to scale production requires the zero-profit condition,

y. After subtracting commuting costs, each resident has budget y − tx to spend on housing and a composite good. The common utility function for all residents is v(c,q), where c denotes consumption of the composite good and q denotes consumption of housing, in square feet. v(c,q) is assumed to be strictly quasiconcave. The price of the composite good is set to unity, while the rental price of housing in dollars per square foot is denoted p. The key to the monocentric city model is spatial equilibrium in utility, such that the maximum attainable utility is a constant u at any distance x from the CBD. The logic behind spatial equilibrium is that if this condition did not hold, some residents would be inclined to move, and the spatial distribution of households in the city would not be stable. Eq. (1) is the utility maximization condition, which states that residents achieve utility level u by choosing the utility-maximizing division of their non-commuting budget between housing and the composite good.

maximize

(4)

(3)

Eqs. (2) and (3) simultaneously determine q and p, which vary with x. As Brueckner (1987, chap. 20) shows, p decreases with x while q increases with x. Essentially, residents who live further from the CBD are compensated for higher commuting costs by living in larger homes, which they can afford because housing is cheaper at greater distances from the center.

3 Migration is assumed to be costless in the basic model, but costly migration will be considered in one of the model variations covered in Section 6.

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3.4. Urban growth boundary

it incorporates both of these channels, the two-city context is more appropriate for analyzing the emissions effects of urban land-use regulations than the traditional closed-city and open-city cases, which feature only a single urban area. The closed-city case entirely omits regulation-induced inter-city migration. The open-city case implicitly allows inter-city migration, but it cannot account for the GHG emissions of households that leave the city. The open-city case also cannot capture the effect of a regulation on consumer utility, which it treats as constant. In the two-city model, the equilibrium utility level u, the City A radius xA , and the City B radius xB are determined endogenously by solving Eqs. (9)–(11) simultaneously. These equations are analogous to Eqs. (7) and (8). The A and B subscripts reflect the fact that there are now two instances of many of the parameters and variables described in the previous subsection, corresponding to the two cities A and B.4

rA = ρA

(9)

rB = ρB

(10)

L=

∫0

xA

θA xA DA dxA +

∫0

xB

θB xB DB dxB

x , effectively prohibiting A UGB exogenously specifies a city limit ∼ housing development beyond this distance. For the UGB to have any x < x must hold, where x is the unrestricted radius at which effect, ∼ r = ρ. Assuming this is true and the UGB binds, the closed-city case can be solved by omitting Eq. (7) and using Eq. (8) to determine the equilibrium utility level. 3.5. Greenhouse gas emissions Any equilibrium produced by the model has an associated level of GHG emissions. This analysis only considers emissions from the residential and transportation sectors, and therefore omits industrial and commercial sources, as well as emissions from land use change.7 Consequently, it does not provide a full account of urban emissions, but it does include those sources which are most strongly influenced by urban form and land-use regulations. The GHG emissions m generated by a household at distance x are computed as

m = αx + βq.

(11)

(12)

This greatly simplified relationship states that each roundtrip mile of travel generates α units of emissions and each square foot of housing generates β units of emissions. Eq. (12) neglects forces which could cause emissions to be nonlinear, such as heterogeneous transportation modes,8 traffic congestion, and differences in energy efficiency across housing types. The total GHG emissions of the city M can be calculated by integrating.

The subsections that follow explain how urban land-use regulations are incorporated into the monocentric city model in the simpler closedcity case, but extending the implementation to the two-city context is straightforward. The same is true for calculating GHG emissions.

3.3. Floor area ratio restriction An FAR restriction imposes an upper limit on h(S), the housing floor space per unit of land. Bertaud and Brueckner (2005) incorporate such a restriction into the monocentric city model, but the implementation in this study is more general. In their analysis, the regulation defines a maximum FAR of ĥ for the entire city. Since the freely chosen h(S) decreases with x, the FAR restriction is typically a binding constraint close to the CBD, but ceases to bind beyond distance x ̂ where h (S ) = ĥ . Unsurprisingly, the regulation expands the size of the city, with more residents living further from the CBD, and reduces consumer utility. The FAR restriction in this study is more general in that it can be applied to a portion of the city between distances x1 and x2 from the CBD.5 This more general implementation permits consideration of FAR restrictions that apply to only a particular part of the metropolitan area, such as the central city or the suburbs. The outcomes of such policies might be far less obvious than those of a uniform FAR restriction imposed on the entire area. For example, as Fischel (2004) notes, an FAR restriction in the suburbs could push some residents to more distant rural areas but cause other residents to relocate closer to the center. The closed-city case with an FAR restriction can be solved by considering different regions separately. From the city center to x1, housing density takes on its unrestricted value h(S). Assuming that the FAR restriction binds in at least some places ( x ̂ > x1), housing density equals ĥ between x1 and Min (x ,̂ x2) .6 Beyond Min (x ,̂ x2) , housing density is again equal to its unrestricted value h(S). The endogenous variables of the model will now be defined piecewise over these three regions, so the integrals used to compute quantities like population must be decomposed accordingly. It is assumed that x > Min (x ,̂ x2) , so that the urban boundary occurs at a distance where the FAR restriction does not bind.

Numerical simulations are used to explore the effects of three urban land-use regulations. Outcomes under each regulation are compared to results of the no policy scenario, which serves as a baseline. In the main set of numerical simulations, City A is regulated, but City B is not. The presence of City B provides an outlet for inter-city migration induced by regulation in City A. While City B is not subject to land-use regulation in the main set of simulations, the possibility that City B is also regulated will be included as a model variation in Section 6. The FARcc scenario represents a central city FAR restriction in City A. The regulation stipulates that, within 10 miles of the CBD, the

4 It is assumed that the two cities are sufficiently far apart that they do not encroach on one another, and that they are surrounded by land with potentially different agricultural values. 5 The Bertaud and Brueckner (2005) implementation is a special case of the more general one here, with x1 = 0 and x2 = ∞. 6 Note that other endogenous variables, such as p and q, may still vary in this region.

7 Urban development occupies only 3.2% of the U.S. land area (Fischel, 2015), so the small changes in city size that the model generates under regulations would make a negligible contribution to land use change emissions on a national scale. The dominant driver of land use change emissions is land conversion among cropland, pasture, and forests. 8 A model variation considered in Section 6 includes multiple transportation modes.

M=

∫0

x

θxmη−1Ddx

(13)

Per capita emissions μ are simply M/L. 3.6. Model implementation and variations The basic model presented in this section, for the two-city context, is implemented in Mathematica. The main results reported in Section 5 are derived using this version. Later, in Section 6, three model variations will be constructed to assess whether results are sensitive to different assumptions or additional model features. These variations incorporate costly migration, multiple transportation modes, and adoption of landuse regulations in both cities. 4. Numerical simulations 4.1. Regulations

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roundtrip miles, then multiplying it by the number of work days per year and the number of workers per household. To estimate the annual residential CO2 emissions per square foot of housing (β), household data for electricity and natural gas expenditures are obtained from the 2015 ACS (U.S. Census Bureau, 2015) and filtered by MSA. Expenditures are divided by prices to calculate household consumption quantities. City-level electricity price data are taken from Electricity Local (2017) and state-level natural gas price data are taken from the EIA (2016b). Electricity consumption is converted to CO2 emissions using subregional electricity emissions factors published by the EPA (2015). Natural gas consumption is converted to CO2 emissions using the relevant EIA (2016a) coefficient. Annual household residential CO2 emissions is the sum of the contributions from electricity consumption and natural gas consumption.10 This must be divided by average home size in square feet to compute β. Average home size is calculated using the average home price and average home price per square foot reported by the real estate website Zillow (2017) for the MSA. CO2 coefficients computed for each city are plotted in Fig. 1. The horizontal axis is the coefficient for housing (β) and the vertical axis is the coefficient for driving (α). Within the sample, there is a lot more dispersion in β than in α. This is not surprising. While cities could in principle feature different vehicle fleets or traffic conditions that cause differences in the emission intensity of driving, these differences across cities appear to be minor. In contrast, cities exhibit vastly different emission intensities of housing. Climate obviously plays a major role, and the cities at the far right of Fig. 1 all have cold winters that lead to substantial natural gas consumption for heating. The carbon intensity of electricity generation is also an important factor. San Francisco has the least emissions-intensive housing in the sample not only due to its mild climate, but also its relatively clean electricity generation mix. Based on the empirical analysis, three sets of CO2 coefficient values are used to parameterize each city in the numerical simulations. These are Clean, Average, and Dirty, as indicated by the red diamonds in Fig. 1. They span the full range of observations for large U.S. metropolitan areas and allow the emissions impacts of urban land-use regulations to be evaluated in a variety of contexts where the emission intensities of regulated and non-regulated cities vary.

housing square footage per square mile of land area cannot exceed 2,000,000. The FARsb scenario represents a suburban FAR restriction in City A. The regulation demands that, between 10 and 25 miles from the CBD, the housing square footage per square mile of land area cannot exceed 1,000,000. The UGB scenario represents a UGB in City A. The regulation prohibits urban development beyond a radius of 15 miles from the CBD.

4.2. Parameter values Parameter values used as inputs for numerical simulations are reported in Table 1. City A and City B are parameterized identically, with the exceptions of the CO2 coefficients α and β which can differ between the two cities and are varied across simulations. This allows the emissions impacts of the regulations to be assessed in a variety of contexts distinguished by the relative emission intensities of the regulated (City A) and non-regulated (City B) urban areas. Some parameter values are essentially arbitrary for the purposes of this model-based exploration. These include the combined population of the two cities (L), the utility function exponent on the composite good (a), the housing production function exponent on capital (b), and the housing production function coefficient (γ). There is, however, some logic underlying the values chosen. For example, setting a = 0.5 specifies that households spend half their non-commuting budget on housing, and setting γ = 10 makes the simulations yield FARs which are fairly consistent with empirically observed values. Other parameter values reflect averages for the U.S. as a whole. For instance, the average agricultural land rent (ρ) is provided by the U.S. Department of Agriculture through its National Agricultural Statistics Service (2016), and the average number of people per household (η) is reported in the 2015 American Community Survey (ACS) (U.S. Census Bureau, 2015). The annual household commuting cost per roundtrip mile (t) includes both money cost and time cost. Money cost per vehicle mile traveled (VMT) is estimated using the publicly available Motor Vehicle Cost Analyzer tool (Hofstrand & Edwards, 2008) with the U.S. average gasoline price reported by the EIA (2015). Time cost per VMT is estimated using the approach of Wu and Plantinga (2003). Annual household income is divided by the number of workers per household (2015 ACS national average is 1.1) and the number of work hours per year (2015 ACS national average is 2018) to yield the hourly wage. It is assumed that commuting traffic moves at 30 miles per hour and that commuting time is valued at 60% of the wage. To compute t as the model defines it, the commuting cost per VMT is doubled to reflect roundtrip miles, then multiplied by the number of work days per year (2015 ACS national average is 272) and the number of workers per household. As described above, numerical simulations consider a range of possible settings defined by the CO2 coefficients α and β in the two cities. To establish realistic ranges of variation for α and β, these coefficients are empirically calcuated using data for each city in a sample of 23 of the largest U.S. metropolitan areas.9 To estimate the annual household transportation CO2 emissions per roundtrip mile (α), vehicle data from the most recent National Household Travel Survey (Federal Highway Administration, 2009) are filtered by MSA. Total gasoline consumption is divided by total VMT to yield gasoline consumption per VMT, which is converted to CO2 emissions per VMT using the EIA (2016a) carbon dioxide coefficient for gasoline. Following the procedure outlined for t earlier in this subsection, α is computed by doubling the CO2 per VMT value to reflect

5. Urban growth boundary results This section reports numerical simulation results for the UGB. Unlike FAR restrictions, this form of regulation is likely to be adopted in pursuit of sustainability goals such as climate change mitigation. Nevertheless, FAR restrictions represent traditional zoning mechanisms whose adoption is more widespread, so it is instructive to examine their emissions impacts as well. For the purposes of clarity and focus, FAR restriction results are relegated to Appendices A (central city FAR restriction) and B (suburban FAR restriction). From this point forward, the main body of this article will focus on the UGB. 5.1. Urban form Fig. 2 illustrates the effects of a UGB11 in City A on the urban forms of the two cities. The plots exhibit the endogenously computed gradients of key spatial structure variables moving outward from the CBD. Blue lines represent City A and orange lines represent City B. Solid lines denote the no policy baseline and dashed lines denote the regulation 10 This ignores households that use other fuels for heating, such as liquefied petroleum gas or fuel oil, but they are relatively few in number. 11 To make Fig. 2 easier to interpret, one change to the parameter values in Table 1 is made: annual household income is changed to $61,000 in City A and $59,000 in City B. Without introducing this parameter disparity, the gradients of the two cities in Fig. 2 would coincide and be impossible to distinguish. Beyond Fig. 2, which serves an illustrative purpose, the cities are parameterized identically according to Table 1.

9 This sample represents the 25 most populous U.S. metropolitan areas (U.S. Census Bureau, 2016). The list is reduced to 23 because the National Household Travel Survey (Federal Highway Administration, 2009) treats Los Angeles and Riverside as a single metropolitan area, and does the same for Washington and Baltimore.

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Fig. 1. Empirically calculated CO2 coefficients for 23 of the largest U.S. metropolitan areas. The horizontal axis is the CO2 intensity of housing (β) and the vertical axis is the CO2 intensity of driving (α). The three red diamonds visualize the Clean, Average, and Dirty parameterizations used for numerical simulations.

Fig. 2. Illustration of how a UGB in City A affects urban form in the two cities.

outcome. As the dashed blue lines indicate, the UGB restricts City A to a radius of 15 miles. Within the boundary, housing density and population density increase, since residents remaining in City A are confined to a smaller area. Land rents and housing rents also rise, and consumers adjust to the change in relative prices by living in smaller homes. The decrease in home size leads to a reduction in household CO2 emissions

at all City A locations inside the boundary. The results clearly show that the UGB in City A induces migration to City B. Even though the latter urban area is unregulated, the changes that take place there are similar to those observed in the regulated city. Throughout City B, housing density, population density, land rent, and housing rent all increase. Just as in City A, consumers respond to higher housing rents by living in smaller homes, which reduces household emissions at all locations. 141

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Fig. 3. Effects of the UGB in City A on city populations, city per capita CO2 emissions, and total CO2 emissions. Results are reported for different parameter settings with varying assumptions about the CO2 coefficients in the two cities.

show that the UGB reduces per capita emissions in both cities in all three parameterizations. The effect is stronger in regulated City A, but to some extent the decline in per capita emissions spills over to unregulated City B. This spillover occurs because the influx of immigrants to City B raises housing prices, which leads to smaller homes and lower household emissions. The effect of the UGB on total emissions is highly dependent on the CO2 coefficients of the two cities. If both cities have Average emission intensities, the UGB causes total emissions to decrease (Fig. 3c). If City A is Dirty and City B is Clean, the emissions reduction is more drastic because the local and inter-city migration effects of the City A UGB work in the same direction to lower emissions (Fig. 3i). However, if City A is Clean and City B is Dirty, then the UGB actually causes total emissions to increase (Fig. 3f). This outcome is particularly interesting because total emissions increase despite the fact that per capita emissions decline in both cities. Even though the UGB reduces per capita emissions everywhere, it induces enough migration from a relatively cleaner city to a relatively dirtier city to make inter-city migration the dominant driver of the total emissions impact.

However, as the dashed orange lines indicate, an influx of immigrants to City B expands the radius of the city by a few miles. 5.2. Population and CO2 emissions Population and emissions impacts of the UGB are presented graphically in Fig. 3 for three different parameter settings. Across each row, charts compare city populations, city per capita CO2 emissions, and total CO2 emissions under the UGB against the no policy baseline. In the top row, CO2 coefficients are set to Average levels in both cities. In the middle row, they are set to Clean in City A, and Dirty in City B. In the bottom row, they are set to Dirty in City A, and Clean in City B. These parameterizations of the CO2 coefficients refer to those indicated in Fig. 1. Fig. 3a, d, and g are identical because variations in CO2 coefficients do not affect the amount of inter-city migration induced by the UGB. They reveal that the UGB causes a significant redistribution of households from City A to City B, with many former City A residents preferring to move to City B rather than settle for smaller homes in the now denser and more expensive central portion of City A. Fig. 3b, e, and h 142

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imply an average abatement cost in the range $1127–1233 per metric ton of CO2 (tCO2). Relative to mainstream estimates of the social cost of carbon (which measures the benefit of reducing emissions), this average abatement cost is considerably higher.13 This does not mean that the UGB fails the cost-benefit criterion. By increasing urban densities, the UGB likely generates many co-benefits in addition to lower CO2 emissions, such as air quality improvement, agglomeration economies, avoided costs of infrastructure expansion, preservation of open space, and enhanced social interaction. Nevertheless, the average abatement cost estimate suggests that climate change mitigation benefits alone probably do not justify the UGB (unless one prefers extremely high social cost of carbon estimates). Furthermore, it appears to be a far less cost-effective strategy for reducing CO2 emissions than policies which target emissions directly, such as a carbon tax or an emissions trading system. The CO2 abatement cost for the parameter setting where City A is Dirty and City B is Clean comes in lower, in the range $365–399/tCO2. This follows from the results in Fig. 3, since in this setting the local and inter-city migration effects work in the same direction to reduce emissions more dramatically. While this abatement cost still exceeds mainstream social cost of carbon estimates, it at least indicates that climate change mitigation benefits could justify a meaningful portion of the policy cost, making it more plausible that various co-benefits could make up the difference. If City A is Clean and City B is Dirty, utility declines and total emissions increase, so residents effectively pay to produce higher emissions. Abatement cost estimates for different parameter settings, as well as the model variations covered in the next section, are documented in Table 2.

The possibility that a UGB could increase total CO2 emissions, observed here for a parameter setting based on empirically calculated input data, suggests that cities with relatively low emission intensities should be cautious about attempting to reduce emissions through smart growth controls. As the results indicate, if such a regulation raises housing prices enough to cause residents to leave the city or deter potential residents from moving in, and these households locate instead in urban areas with higher emission intensities, the environmentally motivated regulation could have the unintended consequence of increasing total emissions. Glaeser and Kahn (2010) previously raised this suspicion and suggested that it merited future research. The findings of this study thus corroborate their concern, which could be problematic in the U.S. where the cities with strict land-use regulations tend to be places with low emission intensities. Whether the migration flows induced by these regulations are strong enough, and to destinations with sufficiently high emission intensities, to yield an increase in total emissions is very difficult to assess. Nevertheless, it is likely that inter-city migration effects are at the very least partially offsetting emissions reductions achieved through land-use regulations in relatively clean cities. To maximize the effectiveness of UGBs for reducing emissions, they should be deployed in cities with high emission intensities if possible. When deployed in these urban areas, the local and inter-city migration effects will work in the same direction to mitigate climate change. It should be noted that the possibility that a smart growth control has the unintended consequence of raising total emissions is probably more of a concern in the U.S. than in most other countries. The U.S. occupies a tremendous land area with diverse climate zones and regional electricity mixes. Its fragmented policy landscape permits significant differences in local regulatory conditions. The increased emissions outcome requires that the UGB induces considerable intercity migration, and Americans move residences more frequently than citizens of nearly every other nation. A Gallup (2013) survey found that 24% of Americans migrated over a period of five years; the global average was 8%.

6. Model variations A major finding of the main numerical simulations is that the UGB increases total emissions if it is enacted in a Clean city and induces migration to a Dirty city. In this section, three model variations are developed to explore whether this unintended consequence of the UGB persists if model assumptions are altered or additional features are incorporated. The three variations include costly migration, multiple transportation modes, and adoption of land-use regulation in both cities. All graphical results correspond to the City A Clean, City B Dirty parameterization, since this is the context where the unintended consequence arises. They should thus be compared to the middle row of Fig. 3.

5.3. CO2 abatement cost The UGB reduces emissions in most contexts, but at what cost? The regulation raises housing rents and decreases home sizes, resulting in a lower equilibrium utility level. To estimate the average CO2 abatement cost, the decline in utility is converted to monetary terms by calculating the compensating variation (CV) and equivalent variation (EV) per household. The CV is the additional income a household must be given under the UGB to grant it the same maximum utility it would have in the no policy scenario. The EV is the amount of income that must be taken away from a household in the no policy scenario to grant it the same maximum utility it would have under the UGB. Either measure can be multiplied by the number of households, then divided by the reduction in total emissions, to yield an average abatement cost. It is usually true that CV > EV, and it is a well-known result that the change in consumer surplus lies between the two. So, CV and EV can be calculated to estimate a range for the average abatement cost. Consider the parameterization where both cities feature Average emission intensities. The CV and EV for the UGB are $2466 and $2255, respectively, per household. These values are quite high, and indicate that the negative effect on utility of higher housing rents caused by the regulation is meaningful.12 When multiplied by the number of households and divided by the reduction in total emissions, the CV and EV

6.1. Costly migration In the basic model analyzed thus far, inter-city migration is costless. This assumption is standard in the open-city case of the monocentric city model. In reality, however, relocating from one urban area to another entails both monetary and non-monetary costs. Those making such a move often need to find a new home, transport themselves and their belongings, seek employment, buy furniture, establish a social network, and so on. By assuming costless migration, the basic model likely exaggerates the amount of inter-city migration that a land-use regulation induces. This could be relevant to the outcome where a UGB increases emissions, since it relies on strong induced migration. In this variation, migration cost is specified as a percentage of annual household income. This one-time cost is distributed over a ten-year 13 The Interagency Working Group on Social Cost of Carbon (2013) estimates that the social cost of carbon emitted in 2020 is $12/tCO2 for a 5% discount rate, $43/tCO2 for a 3% discount rate, and $65/tCO2 for a 2.5% discount rate. However, there is considerable disagreement in the literature, with some studies suggesting the possibility of much higher values. For example, Moore and Diaz (2015) show that changing damages from a GDP level effect to a persistent growth rate effect raises the social cost of carbon above $200/tCO2. Ackerman and Stanton (2012) suggest that high climate sensitivity, high damages, and a low discount rate imply a social cost of carbon close to $900/tCO2.

Empirical analyses find that land-use regulations have a significant, positive effect on housing prices. For example, Glaeser et al. (2005) conclude that half of the prices of condominiums in Manhattan arises from regulatory constraints on new housing construction. Based on empirical findings like this, the large CV and EV computed here certainly seem plausible. However, they could also be attributed to the form of the utility function, which incorporates housing only through home size and excludes other potentially desirable attributes such as proximity to urban cultural amenities or open space. 12

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Table 2 Average CO2 abatement costs for the UGB, with ranges established by compensating variation and equivalent variation. Values in parentheses denote cases where consumer utility decreases and total emissions increase; in other words, society pays for higher emissions. Results refer to the intermediate parameterization of each model variation. Migration cost is 50% of annual household income; the zero-carbon and low-carbon transportation radii are 10 and 20 miles, respectively; and the City B UGB radius is 30 miles. City A CO2 coefficients

City B CO2 coefficients

Model variation

CO2 abatement cost ($/tCO2)

Average Clean Dirty Average Clean Dirty Average Clean Dirty Average Clean Dirty

Average Dirty Clean Average Dirty Clean Average Dirty Clean Average Dirty Clean

Basic model Basic model Basic model Costly migration (50%) Costly migration (50%) Costly migration (50%) Multiple trans. modes (10,20) Multiple trans. modes (10,20) Multiple trans. modes (10,20) Regulation in both cities (30) Regulation in both cities (30) Regulation in both cities (30)

1127–1233 (1348–1474) 365–399 1072–1187 72,273–79,999 483–535 1036–1133 (1542–1686) 357–390 869–1019 2372–2783 467–548

& Rappaport, 2008). Zero-carbon modes include walking, biking, and transportation powered by renewable electricity. Low-carbon modes include public transit in general, and options like carpooling. These mode categories are incorporated into the model in a simple fashion by assuming that commuting entails zero emissions for households located within a radius rz of the CBD, and entails a CO2 coefficient α/2 for households at distances between x = rz and x = rl. Beyond x = rl, residents continue to drive with CO2 coefficient α. This representation is limited in that it does not alter the uniform transportation cost assumption and does not make mode choice endogenously depend on density. Nevertheless, this model variation could amplify the emissions reduction caused by the UGB. In addition to reducing transportation emissions by shortening car commutes, as in the basic model, the UGB now has the effect of shifting some households to locations where commutes are less emissions-intensive. Fig. 5 illustrates how the population and emissions impacts of the UGB vary with the sizes of the zero-carbon and low-carbon transportation zones. Incorporating multiple transportation modes does not affect UGB outcomes as much as costly migration. The zero-carbon and low-carbon modes are available at relatively central locations, so they replace driving commutes that were short and thus not major contributors to total emissions. They reduce emissions regardless of whether a regulation is in place, so while the UGB can achieve additional emissions reductions by pushing more households into the zero-carbon and low-carbon transportation zones, the no policy emissions benchmark is lower with these modes present. With multiple transportation modes, CO2 abatement costs are quite similar to their values in the basic model (Table 2). Overall, it appears that the effects of the UGB are fairly insensitive to the inclusion of multiple transportation modes.

time horizon, so that if the migration cost is 20% of annual household income, for example, it is implemented as a 2% reduction in y. A household will move from City A to City B if the utility it can achieve in City B after its income is reduced by the migration cost is at least as high as the utility it can achieve by remaining in City A. If migration occurs, there will be two distinct groups of residents in City B: the original residents of City B (who are richer) and immigrants from City A (who are poorer, having paid to migrate). This contradicts the standard assumption of the basic model that all agents have the same equilibrium utility level. Greer and White (1981) confront this issue and solve a model with costly migration by imposing four conditions, which are adapted to this study. Assume that migration flows from City A to City B. First, utility levels for all households remaining in City A and all households that migrate to City B must be equal, so that households are indifferent between remaining and migrating in equilibrium. Second, the population of richer residents in City B must equal the population of this city in the no policy baseline. Third, the population of City A plus the population of poorer residents (immigrants) in City B must equal the population of City A in the no policy baseline. Fourth, in City B, poorer residents live closer to the CBD, richer residents live further away, and at the border between them their bid prices for housing are equal. The rows of Fig. 4 show the population and emissions impacts of the UGB with migration costs equal to 20%, 50%, and 100% of annual income (2%, 5%, and 10% reductions in y). With a 20% migration cost, the UGB still increases total emissions. However, a 50% migration cost dampens migration enough to cause the UGB to just barely reduce emissions. A 100% migration cost virtually extinguishes inter-city migration. In this case, the UGB reduces emissions in City A while leaving City B essentially unchanged, so total emissions decline sharply. Compared to analogous figures for the basic model, with costly migration, average CO2 abatement cost is slightly lower in the setting where both cities have Average emission intensities, and slightly higher in the setting where City A is Dirty and City B is Clean (Table 2). A 50% migration cost is sufficient to undo the increase in emissions caused by the UGB in the City A Clean, City B Dirty parameterization, but abatement cost is exceedingly high. So, while costly migration means that the regulation lowers rather than raises emissions, the regulation is an expensive mitigation strategy in this context.

6.3. Regulation in both cities All numerical simulations presented thus far assume that land-use regulation is only adopted in City A, with City B serving as an unregulated outlet for induced migration. The flow of households from City A to City B should be weaker if the latter is also subject to some degree of regulation. This would be the case if, for example, a broader regional or national land-use policy applies to both urban areas. This model variation considers whether the 15-mile UGB in City A still leads to an increase in emissions if City B also adopts a UGB. The rows of Fig. 6 show how population and emissions outcomes vary with the radius of the City B UGB. Clearly, imposing a UGB in City B to complement the policy in City A has a significant effect on regulation impacts, and results are sensitive to the stringency of the City B boundary. At a radius of 45 miles, the City B UGB is too weak to have a noticeable effect. At a radius of 30 miles, it is strong enough to yield a decline in total emissions. This UGB has little effect on inter-city migration, but it reduces per capita emissions in City B by a large amount.

6.2. Multiple transportation modes The basic model assumes that all residents commute using the same transportation mode (personal automobile), and that the CO2 coefficient for transportation (α) is the same throughout the urban area. In reality, people who reside in more central locations are probably more likely to commute via zero-carbon and low-carbon transportation modes (Bento, Cropper, Mobarak, & Vinha, 2005; Glaeser, Kahn, 144

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Fig. 4. Effects of the UGB in City A on city populations, city per capita CO2 emissions, and total CO2 emissions for different assumptions about the cost of inter-city migration.

Policy impacts were evaluated in a variety of contexts distinguished by the CO2 emission intensities of transportation and housing in each urban area. Model variations were included to investigate whether prominent findings are sensitive to costly migration, multiple transportation modes, and adoption of land-use regulations in multiple cities. The findings of this study have clear policy relevance, as they illustrate the conditions under which urban land-use regulations are likely to reduce emissions, and the range of CO2 abatement costs associated with this mitigation strategy. UGBs reduce CO2 emissions in most settings. They densify the city, which eliminates long commutes and decreases home sizes. The latter effect is a result of higher housing prices, which also induce migration of households to other urban areas. The influx of these immigrants to other cities raises housing prices and decreases home sizes in these other places, a spillover effect of the UGB which further reduces total emissions. However, if the regulated city with the UGB has relatively low emission intensity, and migration pushes households to cities with relatively high emission intensities, the UGB can actually increase total emissions even though it reduces per capita emissions everywhere. Glaeser and Kahn (2010) previously raised the possibility of this

When City B adopts the same UGB as City A (15-mile radius), the cities are identical to each other under the regulations, so no inter-city migration takes place. Eliminating induced migration from the Clean city to the Dirty city causes a sizable drop in total emissions. While adopting regulation in both cities slightly increases the CO2 abatement cost in the City A Dirty, City B Clean setting, it reduces abatement costs in the other contexts (Table 2). These results clearly demonstrate the importance of applying land-use regulation broadly to many urban areas to achieve emissions reductions. This is especially true if the cities which would adopt such policies on their own feature low emission intensities. 7. Conclusion This study has explored the GHG emissions impacts of urban landuse regulations using a model of endogenous urban spatial structure. A novel aspect of the modeling framework is that it captures regulationinduced inter-city migration, which is a potentially important determinant of emissions outcomes. Two forms of regulation were considered: floor area ratio restrictions and urban growth boundaries. 145

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Fig. 5. Effects of the UGB in City A on city populations, city per capita CO2 emissions, and total CO2 emissions for different assumptions about the sizes of zero-carbon and low-carbon transportation zones.

substantial co-benefits such as air quality improvement, agglomeration economies, and avoided costs of infrastructure expansion. More than any model variation, the CO2 emission intensities of cities appear to be the dominant drivers of abatement cost. Land-use regulations reduce emissions more cost-effectively when they are deployed in more emissions-intensive urban areas. Contrary to the current state of affairs in the U.S., the dirtiest cities are the best places to deploy smart growth controls, not the cleanest ones. FAR restrictions are typically adopted for reasons other than climate change mitigation, and results for these regulations are relegated to the appendices. Nevertheless, FAR restrictions are representative of traditional zoning mechanisms whose use is widespread, so it is instructive to briefly summarize their GHG emissions impacts. Similar to UGBs, FAR restrictions raise housing prices and induce migration to other urban areas. The effect that this has on emissions depends on the relative emission intensities of regulated and unregulated cities. FAR restrictions only weakly affect per capita emissions, so their overall emissions impacts are not as significant as those stemming from UGBs. Results suggest that FAR restrictions applied to suburban areas have a

unintended consequence, and the results of this study corroborate it. This effect could be problematic in the U.S. because the urban areas with more stringent land-use regulations tend to have low emission intensities, the fastest growing urban areas generally have high emission intensities, and the population is highly mobile. Whether migration flows and emission intensity differences across cities are strong enough to imply that current regulations are raising emissions is difficult to assess. Nevertheless, the findings of this study indicate that relatively clean cities should be cautious about using smart growth controls for climate change mitigation purposes. Emissions reductions obtained via land-use regulation come at a cost to residents, whose welfare declines due to higher housing prices. CO2 abatement costs were calculated by using compensating variation and equivalent variation to convert the drop in welfare to monetary terms. Results demonstrate that abatement costs of reducing emissions through a UGB are fairly high. While the social cost of carbon is subject to considerable debate and controversy, the computed abatement costs exceed most mainstream social cost of carbon estimates. However, urban land-use regulations might still be justified if they generate 146

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Fig. 6. Effects of regulation on city populations, city per capita CO2 emissions, and total CO2 emissions for different assumptions about the radius of the UGB adopted in City B. The regulation in City A remains a 15 mile UGB.

imperfect, and are based on a combination of empirical analysis, averages, and approximations. The model depicts a static equilibrium and does not address the transition of urban structure from an initial condition toward this equilibrium. While these are all fruitful directions for future research, this study has generated valuable insights about the GHG emissions impacts of urban land-use regulations, and the costs of deploying them as climate change mitigation instruments in various contexts.

slightly less detrimental effect on per capita emissions than restrictions applied to central cities, because the former at least cause some households to relocate closer to the center rather than to more distant neighborhoods. The conclusions of this study are tempered by the limitations of the modeling framework. The model is a stylized and abstract representation of an urban area. In reality, employment is spatially scattered throughout an urban area rather than concentrated exclusively at the center. The model does not account for traffic congestion, and all households in an urban area are assumed to be homogeneous. The linear relationship between home size and residential energy use fails to capture differences in energy efficiency among various home types, such as apartments versus detached houses. The two-city context is a considerable improvement relative to the classic one-city cases, but it does not represent the full range of relocation options available to households in the real world. Parameterizations are obviously

Acknowledgments Financial support for this study was provided by The University of Texas at Austin through a start-up research grant for new faculty. The author received excellent suggestions from the editor and two anonymous reviewers.

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Appendix A. Central city FAR restriction results

Fig. A.1. Illustration of how a central city FAR restriction in City A affects urban form in the two cities.

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Fig. A.2. Effects of the central city FAR restriction in City A on city populations, city per capita CO2 emissions, and total CO2 emissions. Results are reported for different parameter settings with varying assumptions about the CO2 coefficients in the two cities.

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Appendix B. Suburban FAR restriction results

Fig. B.1. Illustration of how a suburban FAR restriction in City A affects urban form in the two cities.

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Fig. B.2. Effects of the suburban FAR restriction in City A on city populations, city per capita CO2 emissions, and total CO2 emissions. Results are reported for different parameter settings with varying assumptions about the CO2 coefficients in the two cities.

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