Uncertain Economic Growth And Sprawl: Evidence From A .

Uncertain Economic Growth and Sprawl:Evidence from a Stochastic Growth Approach*Belal Fallah1Mark Partridge2Rose Olfert3June 26, 2011Acknowledgement: We thank Infrastructure Canada for their support in funding part of thisresearch under a grant titled. "Mapping the Rural-Urban Interface: Partnerships for SustainableInfrastructure Development." We also thank the Canada Rural Revitalization Foundation and theFederation of Canadian Municipalities for their support of this project, in particular RobertGreenwood. An earlier version of this paper was presented at the Canadian AgricultureEconomics Society Meeting. We thank Elena Irwin for her helpful comments and suggestions.1College of Administrative Sciences and Informatics, Palestine Polytechnic University.bfallah2000@yahoo.com.2Swank Professor of Rural-Urban Policy and Professor, Department of Agricultural, Environmental, andDevelopment Economics, Ohio State University. Partridge.27@osu.edu (contact).3Johnson-Shoyama Graduate School of Public Policy, University of Saskatchewan. rose.olfert@usask.ca* The final publication is available at springerlink.com

1Uncertain Economic Growth and Sprawl: Evidence from a Stochastic Growth ApproachAbstract: This paper examines how the volatility of local economies, represented by uncertaintyover future land rents, affects urban sprawl. We develop a theoretical model that links sprawl toshocks to expected rent from future land development, among other factors. The econometricanalysis draws upon panel data from U.S. metropolitan areas. To measure urban sprawl, weconstruct a distinctive measure that captures the distribution of population density withinmetropolitan areas. Using a proxy for uncertainty over future land rents, we confirm thetheoretical prediction that across U.S. metropolitan areas, higher levels of uncertainty areassociated with lower levels of sprawl.Keywords: Economic Growth; Sprawl1. IntroductionThe emergence of urban sprawl in North America in the mid-20th Century has spawned aliterature investigating its forms and effects, as well as aimed at understanding its underlyingcauses. Understanding the causes of urban sprawl is important because it represents an importantshift in population distribution and land-use as it reshapes the rural-urban interface, pushingdevelopment well out into what were historically rural communities, changing the distribution ofeconomic activities across urban areas. These in turn potentially affect productivity (Fallah et al.,forthcoming) and potentially foster environmental degradation (Carruthers and Vias 2005;Glaeser and Kahn 2004). Sprawl can also affect the quality of life through impacts on the cost ofinfrastructure provision and the work-commute relationship (Carruthers and Ulfarsson 2008; Wu2010). Because attempts to mitigate greenhouse gas emissions will likely entail more planningand zoning to reduce energy usage, the need to understand the causes of sprawl will likelyintensify.Urban economists have traditionally used the theory of the static monocentric city to explain theforces underlying urban sprawl and the implied decrease in population density farther from thecentral business district (CBD). In the absence of a single precise definition of urban sprawl, weuse the term objectively to mean low density development with the expansion of urbandevelopment into (previously) undeveloped rural areas and interior urban areas (e.g., Nechybaand Walsh, 2004). Thus, we assess the key feature of most discussion of sprawl, namely the

2relatively low land-use intensity of development, leaving the impacts on efficiency to furtherempirical investigation.The expansion of the urban structure hinges on the tradeoff between land rent and commutingcosts. In equilibrium, this requires lower land rent at the urban fringe to offset the highercommuting cost to the CBD. The declining rent gradient leads to a decline in the density gradient(often modeled as a constant decline) as distance increases from CBD to the urban fringe (Alonso1964; Muth 1969; Mills 1967). Research on sprawl has typically used this model as a startingpoint to propose a variety of causes of sprawl. 1Despite its success in reproducing general aspects of the urban spatial structure, the staticmonocentric model has been criticized by many urban economists. For example, Anas (1978)suggests that the monotonic decline of density away from the CBD occurs only under specialconditions, such as rising income levels. Moreover, in dynamic models with durable housing andmyopic landowners, Anas (1978), Harrison and Kain (1974), and McFarlane (1999) argue thatresidential development around the employment center is an incremental process and that densitydepends on the economic conditions at the time of development.Dynamic models have conventionally assumed that a risk-neutral developer will choose to investwhen the present value of expected cash flows exceeds the cost of development. However, if thefuture cash flow is uncertain and the investment is durable and irreversible, as in landdevelopment, this principle must be modified. For example, as in our model, consider an openurban area experiencing shocks in labor demand.2 The resulting shocks in population growth andhousing demand lead to an uncertain future land/housing rent to be earned from developing newlots. Titman (1985), McDonald and Siegel (1985, 1986), and others suggest that under1For example, past research has proposed many causes of sprawl such as rising income (Margo 1992),declining transportation costs (Glaeser and Kahn 2004), fragmented local governance (Carruthers 2003),and improved infrastructure such as improved highways (Baum-Snow 2007).2The shock could be to households—changes in labor supply—perhaps due to amenities. However, it ismore likely due to be a labor demand shock.

3uncertainty and illiquid durable investment, developers may choose to delay investment. Theability to delay investment decisions has economic value, i.e., a real option (Pindyck 1991).Cappoza and Helsley (1990) were among the first to explore the relationship between urbanspatial structure and uncertainty. Assuming that future rent follows a stochastic pattern, theyfound that in cities with a higher level of uncertainty, developers would delay land developmentuntil the expected future rent (usually referred to as reservation or hurdle rent) compensates notonly for the agricultural land value and conversion cost, as in the case of a certain future, but alsofor the real option value. In their model, the real option value reflects the ability to delay landdevelopment while awaiting more information on future land prices. As a result of thedevelopment delay, Cappoza and Helsley (1990) suggest that the expected city size decreases, allelse constant.3In examining the effect of uncertainty on city size, Capozza and Helsley (1990) assume that thelot size is fixed across urban areas. Capozza and Li (1994) extend this work by investigating theinteraction between uncertainty and the ability to vary residential capital intensity. Assuming thatdevelopers choose the optimum capital intensity and time of development, they find thatuncertainty raises the reservation rent and delays the development decision.To date, urban economists have done little to empirically test the implications of models thatrelate uncertainty about future land rent to urban spatial structure. 4 The objective of this paper isto address this gap. Specifically, we investigate how variations in uncertainty over future rentexplain differences in the extent of U.S. metropolitan sprawl. The importance of this questderives from policymakers' and urban planners' need to understand how an expanding and volatile3Bar-Ilan and Strange (1996) extend the Capozza and Helsley (1990) model to allow for lags between thedecision to develop a project and its completion. In this scenario, development lags may lead to a leap frogpattern where more distant land is developed prior to that closer to the city center. Mills (1981) alsomodeled scenarios in which a leap frog development pattern occurs under uncertainty and perfect foresightassumption.4Most of the related literature on uncertainty (real options) has focused on capital investment (e.g,Caballero and Pindyck 1996; Paddock et al. 1988; Moel and Tufano 2002). Fewer studies have exploredlinkages between uncertainty and real estate. For example, Holland et al. (2000) examined the effect ofprice uncertainty on changes in property size.

4urban economy can influence urban sprawl so that they can better address its impacts on thelivability of the urban environment, residence-work commute relationships, and the provision ofphysical infrastructure (roads, schools, sewers, and other public facilities).We depart from the work of Capozza and Helsley (1990) and Capozza and Li (1994) as follows:Capozza and Li‘s (1994) model is site-specific, predicting the irregular intra-metropolitan densityprofile rather than the overall density distribution. The latter is the emphasis of this paper. Inaddition, Capozza and Helsley (1990), focusing on the relationship between uncertainty andurban size, assume that each household consumes one unit of a fixed-sized lot, leading to constantdensity across urban areas. We relax the fixed-size assumption by allowing householdpreferences to determine lot size. Note that 'the lot' remains the unit of new land developmentwith implications for how uncertainty in population growth is represented, namely in terms ofabsolute growth and how much land is developed.In this paper, we also seek a theoretically consistent measure of sprawl that links metropolitanpopulation density to uncertainty, differing from previous work in two ways. First, our modeldoes not include structural capital. Instead, the variation in the density (sprawl) across urban areasarises from variations in lot size. Second, unlike Capozza and Li (1994), we assume that therepresentative household chooses the optimal lot size through utility maximization behavior (seeWu 2010), while a representative developer takes the optimal lot size as given and chooses theoptimal time to convert agricultural land into residential use. In practice, this is akin to assumingthe construction industry is relatively competitive, allowing household preferences to determinelot size (perhaps through the political process and zoning), which is more realistic than a fixed lotsize across the entire urban area. To account for varying density across an urban area, we assumethere is a composition effect where new lot development in the interior of the city is denser thandevelopment at the urban periphery, while the elasticity of lot size also plays a differential rolebetween the periphery and interior.