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The interaction between urban form and transit travel

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Title:
The interaction between urban form and transit travel
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English
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Concas, Sisinnio
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Urban economics
Residential location
Travel behavior
Activity-based modeling
Transportation
Dissertations, Academic -- Dean's Office -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Abstract:
ABSTRACT: This study presents an analytical model of the interaction between urban form and the demand for transit travel, in which residential location, transit demand, and the spatial dispersion of non-work activities are endogenously determined. In this model, travel demand is considered a derived demand brought about by the necessity to engage in out-of-home activities whose geographical extent is affected by urban form. In a departure from the urban monocentric model, residential location is defined as a job-residence pair in an urban area in which jobs, residences, and non-work activities are dispersed. Transit demand is then determined by residential location, work trips, non-work trip chains, and goods consumption. Theoretically derived hypotheses are empirically tested using a dataset that integrates travel and land-use data. There is evidence of a significant influence of land-use patterns on transit patronage. In turn, transit demand affects consumption and non-work travel. Although much reliance has been placed on population density as a determinant of transit demand, it is found here that population density does not have a large impact on transit demand and, moreover, that the effect decreases when residential location is endogenous. To increase transit use, urban planners have advocated a mix of residential and commercial uses in proximity to transit stations. In this study, it is found that the importance of transit-station proximity is weakened by idiosyncratic preferences for residential location. In addition, when population density and residential location are jointly endogenous, the elasticity of transit demand with respect to walking distance to a transit station decreases by about 33 percent over the case in which these variables are treated an exogenous. The research reported here is the first empirical work that explicitly relates residential location to trip chaining in a context in which individuals jointly decide residential location and the trip chain. If is found that households living farther from work use less transit and that trip-chaining behavior explains this finding. Households living far from work engage in complex trip chains and have, on average, a more dispersed activity space, which requires reliance on more flexible modes of transportation. Therefore, reducing the spatial allocation of non-work activities and improving transit accessibility at and around subcenters would increase transit demand. Similar effects can be obtained by increasing the presence of retail locations in proximity to transit-oriented households. Although focused on transit demand, the framework can be easily generalized to study other forms of travel.
Thesis:
Dissertation (PHD)--University of South Florida, 2010.
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by Sisinnio Concas.
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The Interaction Between Urban Form and Transit Travel by Sisinnio Concas A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Economics College of Arts and Sciences University of South Florida Major Professor: Jose ph S. DeSalvo, Ph.D. Brad Kamp, Ph.D. Ram M. Pendyala, Ph.D. Gabriel A. Picone, Ph.D. Date of Approval: November 8, 2010 Keywords: urban economics, residential location, travel behavior, activity-based modeling Copyright 2010, Sisinnio Concas

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Dedication I dedicate this dissertation to my wife Martha and to our daughters Isabella and Alessia. Thank you, Amore, for being part of this journey, for your understanding, and for always being there for me. I dedicate th is work to you, Isabella and Alessia, hoping you will grow fond of learning, and to wish you to achieve this and much more.

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Acknowledgements I would like to extend my gr atitude to my major profe ssor, Dr. Joseph S. DeSalvo, for his supervision, advice, and guidance. Thank you, Dr. DeSalvo, for all our conversations held throughout this effort, which at times spanned far beyond the scope of this work to embrace other aspects of research a nd practical life. Thank you Dr. Brad Kamp, Dr. Ramp Pendyala, and Dr. Gabriel A. Picone for agreeing to serve on my committee and for your assistance and insightful comments. Special thanks go to Dr. Josefina Ramoni and Prof. Gianpaolo Orla ndoni for their review and f eedback on the empirical models. Finally, I would like to thank Stephen L. Reich, my program director at the Center for Urban Transportation Research. Thank you, Steve, for your support and for allowing me flexibility in my schedule to a ccommodate for both work and study.

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iv Table of Contents List of Tables ................................................................................................................ ... viiList of Figures ............................................................................................................... ... viiiAbstract .................................................................................................................... i xChapter 1: Introduction ...................................................................................................... .1Motivation ................................................................................................................1Critique of Previous Work on Transit Travel Behavior and Urban Form ...............2Research Objectives .................................................................................................4Outline of Remaining Chapters ...............................................................................4Chapter 2: Urban Form and Transit Travel Behavior, A Review of the Literature ............6Introduction ..............................................................................................................6The Demand for Travel and Urban Form ..............................................................10Existing Critical Literature Reviews ......................................................................11Studies Analyzing the Influence of Urban Form on Transit Patronage .................12Studies Analyzing the Influen ce of Transit on Urban Form ..................................15Studies Analyzing the Contemporane ous Relationship between Transit and Urban Form ...............................................................................................17Inherent Complexity: Accessibilit y, Urban Design, and Self-Selection ...............22Measuring Accessibility .........................................................................................28Urban Form Measures and Polycentric Cities .......................................................30From Trip Generation to Activity-Travel Behavior...............................................34Summary and Implications for Integr ated Models of Transportation and Land Use ..........................................................................................................36

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v Chapter 3: Methodology ...................................................................................................39Introduction ............................................................................................................39Model I: Exogenous Residential Location and Density ........................................41Residential Location, RL, and Transit Station Proximity, WD ..............................43Activity Space: Spatial Disper sion of Non-Work Activities .................................45Trip Chaining, TC ..................................................................................................45Travel Demand, TD ...............................................................................................47Comparative Static Analysis ..................................................................................48Effects of an Increase in Density, D ......................................................... 48Change in Residential Location, RL ......................................................... 49Change in Walking Dist ance to Nearest Station, WD ............................... 50Model II: Endogenous Residential Location, Exogenous Density .......................50Comparative Static Analysis ..................................................................................51Effects of an Increase in Density, D ......................................................... 51Change in Walking Dist ance to Nearest Station, WD ............................... 52Model III: Endogenous Resident ial Location, Endogenous Density ....................52Comparative Static Analysis ..................................................................................53Conclusions ............................................................................................................54Chapter 4: Empirical Analysis ..........................................................................................56Introduction ............................................................................................................56Data Sources ..........................................................................................................56Dependent Variables De scriptive St atistics ...........................................................58Measures of Activity Space, AS ................................................................ 59Measures of Residential Location, RL ...................................................... 61Measures of Transit Station Proximity, WD ............................................. 62Measures of Density, D ............................................................................. 62Explanatory Variables De scriptive St atistics .........................................................63Socio-Demographic Variables .................................................................. 63Travel Behavior Variables ........................................................................ 66Urban Form Variables ............................................................................... 67

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vi Transit Supply Variables........................................................................... 72Method of Analysis ................................................................................................78Model I Results ......................................................................................................79Model II Results .....................................................................................................84Model III Results ...................................................................................................88Post Estimation Analysis .......................................................................................92Dataset Issues .........................................................................................................93Measurement Problems ............................................................................. 93Scaling Issues ............................................................................................ 95Modeling Issues .....................................................................................................96Post Estimation Tests ................................................................................ 96Tests of Endogeneity and Overidentification ........................................... 97Other Issues ............................................................................................... 99Transit-Station Proximity........................................................................ 101Implications..........................................................................................................103Chapter 5: Conclusions ...................................................................................................104Summary of Findings ...........................................................................................104Empirically Estimable Model of Transit and Urban Form ..................................105Research Contributions ........................................................................................108Directions for Further Research ...........................................................................109References ..................................................................................................................11 1Appendices ..................................................................................................................12 3Appendix A: Comparativ e Static Analysis .........................................................124Appendix B: Equation Identification ...................................................................138About the Author ................................................................................................... End Page

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vii List of Tables TABLE 3.1 Comparative Static Results ....................................................................... 54TABLE 4.1 Descriptive Statisti cs: Overall Sample Means .......................................... 64TABLE 4.2 Descriptive Statistics: Samp le Means of Dependent Variables and Selected Trip Measures ............................................................................. 65TABLE 4.4 Urban Form Variables ............................................................................... 69TABLE 4.5 Urban Form Variables by Household Type .............................................. 73TABLE 4.6 Housing and Demographi c Variables by Household Type....................... 73TABLE 4.7 Urban Form Variables by Transit-Station Proximity ................................ 74TABLE 4.8 Urban Form Variables by Transit-Station Proximity ................................ 74TABLE 4.9 List of Variables for Model Estimation .................................................... 77TABLE 4.10 3SLS Regression Results—Model I ......................................................... 82TABLE 4.11 Elasticity Estimates—Model I .................................................................. 83TABLE 4.12 3SLS Regression Results—Model II ........................................................ 86TABLE 4.13 Elasticity Estimates—Model II ................................................................. 87TABLE 4.14 3SLS Regression Results—Model III ....................................................... 91TABLE 4.15 Elasticity Estimates—Model III ............................................................... 92TABLE 4.16 Land-Area Geogr aphic Measures ............................................................. 96TABLE 4.17 Endogeneity and Ov eridentification Tests .............................................. 100TABLE 5.1 Relevant Land-Use and Tran sit-Supply Elasticities of Transit Demand ................................................................................................... 106

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viii List of Figures FIGURE 3.1 Conceptual Model of Urba n Form and Travel Behavior .......................... 40FIGURE 4.1 Standard Distance Circle and Standard Distance Ellipse ......................... 61FIGURE 4.2 Poverty and Tran sit-Station Proximity ................................................... 102

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ix The interaction Between Urba n Form and Transit Travel Sisinnio Concas Abstract This study presents an analytical model of the interaction between urban form and the demand for transit travel, in which reside ntial location, transit de mand, and the spatial dispersion of non-work activities are endogenously determined. In this model, travel demand is considered a derived demand brought ab out by the necessity to engage in out-ofhome activities whose geographica l extent is affected by urba n form. In a departure from the urban monocentric model, residential locati on is defined as a job-residence pair in an urban area in which jobs, residences, and nonwork activities are di spersed. Transit demand is then determined by residential locati on, work trips, non-work trip chains, and goods consumption. Theoretically derived hypotheses are empiri cally tested using a dataset that integrates travel and land-use data. There is ev idence of a significant influence of land-use patterns on transit patronage. In turn, tr ansit demand affects consumption and non-work travel. Although much reliance has been pl aced on population density as a determinant of transit demand, it is found he re that population density does not have a large impact on transit demand and, moreover, that the effect decreases when reside ntial location is endogenous. To increase transit use, urban planne rs have advocated a mix of residential and commercial uses in proximity to transit stations. In this study, it is found that the impor-

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x tance of transit-station proximity is weakened by idiosyncratic preferences for residential location. In addition, when population density and residential location are jointly endogenous, the elasticity of trans it demand with respect to walk ing distance to a transit station decreases by about 33 percent over the cas e in which these variables are treated an exogenous. The research reported here is the first empirical work that explicitly relates residential location to trip chaining in a context in which individuals jo intly decide residential location and the trip chain. If is found that households living farther from work use less transit and that trip-chain ing behavior explains this finding. Households living far from work engage in complex trip chains a nd have, on average, a more dispersed activity space, which requires reliance on more flexible modes of transporta tion. Therefore, reducing the spatial allocation of non-work activities and improving transit accessibility at and around subcenters would in crease transit demand. Simila r effects can be obtained by increasing the presence of retail locations in proximity to transit-oriented households. Although focused on transit demand, the framewor k can be easily generalized to study other forms of travel.

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1 Chapter 1: Introduction Motivation Among the challenges posed by evolving tre nds in transport and land-use is providing a better explanation of the role of non-wo rk travel in residen tial location decisions. Greater mobility and a shift from monocentric to polycentric urban forms have substantially increased non-work travel, further weak ening the relevance of the classical commuting-based theory of residential lo cation (Anas, Arnott, and Small 1998). Although the transportation literature on non-work travel has grown in recent years, it has largely done so without providing a generally accepted behavioral framework. Recent attempts to unify the economic theory of urban residential location and transportation highlight the relevance of nonwork travel to residential location (Anas 2007; Ben-Akiva and Bowman 1998). Central to this endeavor is the notion that in choosing a residential location, the household considers the pa ttern of non-work trips that its members are likely to make from that re sidential location. Accessibility to non-work opportunities is likely to be important and, for many households, perhaps more important than accessibility to jobs. In addition, the extent to which households self-select into communities that support their preferences for transportation and other amenities complicates the effort to uncover causality be tween urban form and travel behavior. In recent years, urban policies intended to reduce presumed negative externalities associated with suburbanization have focu sed on reducing auto travel by manipulating

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2 urban form to reduce trip frequencies and tr avel distances. Specifically, locating residences in proximity to businesses should, it is hypothesized, reduce travel distances because nearby destinations will be preferred to more distant ones. In addition, it is assumed that shorter distances provide added opportunities to link more destinations in a single trip chain (Noland and Thomas 2007). The empirical work on the efficacy of such policies provides mixed evidence. This is so because the res earch is based on ad-hoc empi rical specifications, lacking a formal behavioral framework that considers tr avel the result of activities planned and executed through space and time. It is the purpose of this dissertation to provide such a behavioral framework and test its implications empirically. Critique of Previous Wo rk on Transit Travel Behavior and Urban Form The policies discussed above form what is currently defined as transit-oriented development (TOD). The underlying assumption of TOD is that increased public transportation will reduce auto travel. The eff ectiveness of TOD, how ever, depends importantly on individual self-selec tion to residential location. Thus, ignoring such idiosyncratic preferences toward residential locati on may lead to over-reliance on TOD by urban planners as well as to overes timation of its impact on trav el behavior by empirical researchers. Despite a significant amount of academic and practitioner-oriented research, the practice of choosing the right transit service to support desi red development and the right development to support transit ridership relies on findings that no longer apply to the current urban landscape. Early studies estimated the housing and job densities necessary to support different transit modes (Pushkarev a nd Zupan 1977). Such studies did not con-

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3 sider changes in urban structure, such as tran sit-oriented development, that have recently emerged. At the same time, the urban lands cape has evolved from monocentricity, where the CBD is the predominant employment cente r, to polycentricity, where multiple employment centers characterize an urban ar ea and where households can locate anywhere in an increasingly suburban environment. Employment decentraliz ation, coupled with the increased relevance of non-work travel, has had a profound impact on the way transit responds to urban form, making the earlier studies obsolete. Debate has shifted from the need to determine minimum density thresholds that support transit to the need to provide reliable information to guide decision makers about what mix of land-use policies would better promote transit use. In most previous work, density is treated as exogenous and is assu med not to be impacted by transportation system changes. It is now rec ognized that this approach is inadequate and that what is needed is an empirically estimable behavior al model conducive to generalization and applicability. The bulk of previous research is empirical ly oriented. It uses multivariate techniques to estimate the effect of measures of travel behavior (c ommute length, vehiclemiles of travel, mode choice) on measures of residential and employment density, while controlling for travelers’ demogr aphic characteristics. These studies report the statistical significance, sign, and magnitude of the estimate d coefficients. A sta tistically significant negative coefficient leads one to conclude that an inverse relationshi p exists between travel and density, that is, higher density leads to shorter commutes, fe wer vehicle-miles of travel (VMT), or a shift from auto transporta tion to alternative modes, such as transit. The abundance of such studies has led to the conclusion that policy interventions to in-

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4 crease density would reduce automobile use. These studies have undergone systematic criticism, however, mainly of their ad hoc specifications and failure to recognize that the relationship between urban form and travel mi ght entail simultaneity and endogeneity. Research Objectives The objectives of this dissertation are to (1) define a theoretical model of the interaction between urban form and the demand fo r transit, in which residential location, transit demand, and the spatial dispersion of non-work activities ar e endogenously determined, and (2) to test the hypotheses of that model. The research: 1. Controls for idiosyncratic preferences to ward residential location to test the hypothesis that land-use characteristic s affect non-work travel behavior. 2. Shifts the focus from monocentric meas ures of urban form to polycentric ones. 3. Utilizes a framework that better account s for the influence of space on travel patterns, by shifting the focus from a single-purpose trip-g eneration analysis to one that accounts for scheduli ng and trip-chaini ng effects. 4. Accounts for the trade-off between co mmute time and non-work activities. Outline of Remaining Chapters Chapter 2 reviews the literature on the rela tionship between transit travel behavior and urban form. An analytical framework in which residential location and travel behavior are simultaneously determined is presente d in Chapter 3. First, Chapter 4 describes the development of the dataset used in the empirical research. Then, the dataset is used to

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5 test the relationships hypothesized in Chapter 3. This chapter also discusses the validity of the empirical work and identifies issues that might potentially affect a generalization of the findings. Chapter 5 concludes and provides direction for further research.

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6 Chapter 2: Urban Form and Transit Trave l Behavior, A Review of the Literature Introduction Non-work travel is the result of enga ging in activities, other than commuting, through time and space. Consisting of travel for shopping, social and recreational activities, and family and personal errands, non-work travel accounts for almost 85 percent of all daily trips undertaken at the household level (BTS 2001). The latest statistics from the U.S. Department of Transportation Nationa l Household Travel Survey (NHTS) report that non-work travel now constitutes 56 percent of trips during the AM peak and 69 percent of trips during the PM peak, with a tenyear growth of 100 a nd 35 percent, respectively (NHTS 2007). These trends in non-work travel follow cl osely the pattern of urban growth in the United States, consisting of residential a nd employment decentralization. Policy responses to the potential negative externalities associated with decentr alization and its effects on land-use and travel behavior now in clude attempts to limit urban growth or to change its form. In particular, proponents of neo-traditional or transit-oriented development (TOD) advocate the idea that land us e can be manipulated to serve congestion management, air quality, or othe r related transportation objectiv es (Cervero et al. 2004). The policies most often associated with re duced automobile dependence are mixed-landuse, high-density environments that reduce the distance between residence and non-work travel activities.

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7 In the last decade, more than 50 empirical studies have examined the linkages between urban form and travel behavior. Cr ane (2000), Badoe and Miller (2000), and Ewing and Cervero (2001)summarize the most rele vant empirical work published in the literature of transportation research. The bulk of this research is empirically oriented and based on the application of multivariate techniques that regress various measures of travel behavior (commute length, vehi cle miles of travel, mode c hoice) on measures of residential and employment density, while controlli ng for the demographic characteristics of travelers. The abundance of these types of st udies has led to the conclusion that policy interventions to increase density are capable of reducing automobile use (Burchell et al. 1998; Cao, Mokhtarian, and Handy 2006; Ewi ng 1997). These studies have undergone systematic criticism, however, due to their ad-hoc specifications and omitted variable bias problems, the latter due to the possibility that the relationship between urban form and travel might entail simultaneity and e ndogeneity (Badoe and Miller 2000; Crane 2000). In this chapter, we review studies that look at the influen ce of transit on urban form, the influence of urban form on trans it patronage, and the simultaneous relationship between transit and urban form. The intent is to provide a critical a ssessment of the various methodologies employed in these studies, th eir control for relevant factors associated with transit patronage, and the genera l validity of their findings. We uncovered the following issues that to -date have been addressed but not completely resolved. In particular it is widely recognized that we lack a behavioral framework that can be applied to empirical work and that is conducive to generalization of findings and applicability (Badoe and Mill er 2000; Crane 2000; Ewing and Cervero 2001). Studies that related population and employment densit y to travel behavior are

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8 monocentric-based and fail to account for th e employment and residential decentralization now characterizing the urban landscape. We found that there has been a shift from the study of density threshold levels that make transit cost-feasible to an analysis of the role of urban design and land-use mix on transit usage, after control ling for density levels. The i ssue is no longer at what density threshold it makes sense to supply transit. Instead, the issue is the set of policies affecting urban design and land-use mix that be st influences the spatial arrangements of activity locations so that individuals are more lik ely to utilize transit. This shift is reflected in a growing number of studies that are dedicated to studying the relevance of transit oriented development (TOD) policies in a co ntext where households or individuals tend to prefer certain urban settings to others. Not accounting fo r these inherent idiosyncratic preferences prevents the unraveling of the true impact of TOD. There is a lack of empirical work that examines the relationship between urban form and travel behavior within an activity -based framework and th at takes into account the complexity of travel (i.e., that accounts fo r trip-chaining). Thos e studies that have employed activity-based modeling have faile d properly to account for endogeneity and have disregarded spatial mismatch effects (Dong et al. 2006). Activity-based modeling, a relatively new and growing field of research, is characterized by the recognition that travel is a derived demand, a focus on constraine d patterns or sequences of behavior instead of discrete trips and the in terdependence of decisions us ually made within a household context (Jones, Koppelman, and Orfeuil 1990). This framework is better suited than those previously used to analyze the impact of land-use on travel patterns, as it fully acknowledges the presence of trip-chaini ng behavior. In this context, a trip chain is defined

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9 as a sequence of trips that star ts from home and/or ends at home. Sometimes called stopmaking behavior, trip-chaining behavior in activity-based modeling describes the importance of multi-purpose trip-making rather than single-purpose trip-making. Numerous studies have examined trip-chaining or stopmaking models using the frequency of stops on the way home and/or on the way to work as dependent variables (Bhat 1999; Chu 2003; Concas and Winters 2007; Shiftman 1998). To date, no empirical work has been done that explicitly relate s location to tripchaining behavior in a context where individuals jointly decide location, the optimal trip chain, and the area of non-work activities, based on the optimal trade-off between commute time and non-work travel activities. Boarnet and Crane (2001) recognize that ther e is no best way of organizing a literature survey of this subject area. We or ganize our survey around the alternative ways of viewing the relationship between transit and urban form: (1) studies that have examined the influence of urban form on travel behavior (2) studies that have examined the influence of transit use on urban form, and (3) st udies that have examined the simultaneous nature of the relationship betw een transit and urban form. This literature review is not comprehens ive because it ignores empirical work involving only anecdotal accounts or descriptive analyses withou t an analytical framework of any sort. Descriptive studies have the be nefit of assessing actual behavior without the need to establish causal links. Such studies are limited, however, in providing any useful perspective or guidance in the de velopment of a theoretical or analytical model. As such, these studies are not deemed relevant to the obj ectives of this research effort. An assessment and review of recent anecdotal studies has been informally conducted by Taylor and

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10 Miller (2003). For the same reason, we do not summarize Transit Cooperative Research Program (TCRP) reports that discuss the imp act of the built environment on physical activity (Committee on Physical Activity 2005) or report successful case studies of TOD projects (Evans et al. 2007). The Demand for Travel and Urban Form The demand for travel is a derived dema nd generated by the necessity to engage in activities that are located outside one’s place of residence (Dom encich and McFadden 1975; McFadden 1973). This recognition require s studying the determinants of the demand for out-of-home activities as well as the characteristics of the environment affecting the choice of one mode of transport over another. In this context, urban form affects the demand for travel in two ways. First, the lo cation of employment a ffects the probability that an individual will choose a given mode, gi ven its supply. Second, the spatial extent of goods, services, and activities affects mode use for non-work travel purposes. The influence of urban form on travel beha vior is complicated by the evolution of the built environment itself. Since the de velopment of the monocentric urban model (Alonso 1964; Mills 1972; Muth 1969), the urban landscape has evolved into one where multiple employment centers characterize an urban area and where households can locate anywhere in an increasingly s uburban environment. The empirical fact of polycentricity complicates the development of a theoretical model of the re lationship of transit and urban form. Nevertheless, as we shall see, tran sit patronage is still assumed to be largely dependent on the presence of a major employ ment center although the literature is evolving in the direction of how best to supply transit services in a polycentric urban landscape (Casello 2007; Modarres 2003).

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11 Throughout this review, the term urban form refers to various measures of landuse density and urban design. Land-use de nsity encompasses both residential and employment densities, while the term urban design refers to both the characteristics and arrangements of land-uses that a ffect accessibility to both tran sit services and activity locations. Existing Critical Literature Reviews Crane (2000), Boarnet and Crane (2001) Badoe and Miller (2000), and Ewing and Cervero (2001)summarize empirical work on the relationship between transportation and urban form. Crane (2000) describes research methods, data, and results by dividing empirical work into two main categories: ad-hoc st udies and theoretically-oriented studies. His review focuses only on studies that use statistical technique s to uncover the relationship between travel behavior and urban form. Most studies he reviews find that higher density patterns are correlated with less car travel. Crane concludes, however, that these ad-hoc studies are typically difficult to generalize and lack sufficien t robustness to be used as a basis for policy. Crane uses these findings to justify the development of a behavioral framework consistent with the microeconomic theory of demand for travel, as discussed in detail in the next sect ion of this chapter. Badoe and Miller (2000) re view the empirical litera ture up to 2000 with the objective of pinpointing the shortc omings that lead to what ar e considered questionable and contradictory results. The analysis deals with studies of the relati onship between land use and travel behavior at the macro (density) and micro (design) levels. In conformity with Crane’s findings, Badoe and Mill er uncover weaknesses either in the data used or the me-

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12 thodology employed. For example, some studies work with variable s aggregated into zones that are not homogeneous with resp ect to neighborhood design, land use, and socioeconomic characteristics; this increases da ta measurement errors. Other studies ignore relevant variables, such as measures of tr ansit supply, thereby contributing to omitted variable bias. Ewing and Cervero (2001) summarize more than 50 empirical studies up to the year 2000 that examine the linkage between urban form and travel behavior. They focus on presenting findings that, at a minimum, “make some effort to control for other influences on travel behavior (p. 870) .” Their review does not c over papers that explicitly treat trip-chaining behavior because of a lack of empirical work rela ting trip chaining to land-use and design variables. They find that while trip frequencies are primarily a function of socioeconomic characteri stics rather than a function of urban form, trip lengths are primarily a function of the built environment. Studies Analyzing the Influence of Urban Form on Transit Patronage The most relevant early work under this heading is Pushkarev and Zupan (1977). This publication presented “land-use thresholds ” at which different types of transit become feasible. The methodology used singleequation ordinary least square (OLS) regression analysis. The choice of this method was dictated by th e paucity of data available at the time as well as the desire to present results as nomograms. A nomogram is a graph with which one can find the va lue of a dependent variable given the values of two or more independent variables, with only the use of a straightedge The nomograms were designed to facilitate a planner’ s choice of a feasible transit alternative, given values of current or expected density levels and other relevant variables.

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13 The determinants of transit demand used by Pushkarev and Zupan were the size of the central business distri ct (CBD), measured in non-re sidential floor space; the distance of a site from the CBD; and residentia l density. The study also accounted for socio-demographic characteristics affecting tran sit patronage, such as vehicle ownership levels, household size and income. In an update of their 1977 st udy, Pushkarev and Zupan (1982) examine the feasibility of fixed guide-way transit under the assumption that all work travel was to the CBD. This assu mption would be quite restrictive today, given the multi-centered character of many metropolitan regions. In a report for the Transit Cooperative Research Program (TCRP), Zupan et al. (1996) provide guidance on the land-use character istics that could co st-efficiently support new fixed-guideway transit services. The aut hors find that, in a transport corridor, ridership rises exponentially with both CBD empl oyment and employment density. They present separate models for light rail and commuter rail. For both models, the dependent variable is a natural log tran sformation of total daily transi t boardings for 261 stations across 19 rail lines loca ted in 11 cities. Multicollinearity impairs the reliability of these estimates, as recognized by the authors. Determination of causality is also a problem, for the estimated elasticities merely support a direct relationship between tran sit patronage and populat ion density. This causality problem, which affects most findings in this research field, is discussed in a later section of this study. Fi nally, the authors do not employ a model that accounts for inherent, unobserved region-specific characteristic s that might affect th e reliability of estimates.

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14 Following Zupan et al. (1996), Kuby et al (2004) examine the determinants of light rail transit ridership with a multiple regression model using weekday boardings for 268 stations in nine cities. For each city, five categories of independent variables accounting for land use and other factors are us ed. The authors assume that employment within walking distance of each station is the most important factor for work trips. The model also controls for the relevance of n earby airports and for city-specific unobserved effects that might affect weekly boarding, such as the presence of an international airport. The study finds that an increase of 100 persons employed within walking distance of a station increases boardings by 2.3 passengers per day while an increase of 100 persons residing within walking distance of a stat ion increases boardings by 9.2 passengers per day. The study also finds higher residential population to be asso ciated with higher weekly boardings and that the CBD variable is not statistically signi ficant, indicating that centrality is no longer relevant in determini ng light rail ridership. This result could, however, be due to faulty test statistics pr oduced by the high correlation between the model’s measures of centrality and the CBD dummy. Kuby et al. (2004) make some important improvements to the methodology of Zupan et al. (1996). First, instead of examin ing ridership at non-CBD stations, they capture the effect of the CBD on boardings by introducing a dummy variable for CBD location. Second, Kuby et al. include employment near non-CBD stations instead of just employment within the CBD. Third, they includ e accessibility to nonCBD stations. Zupan et al. (1996) compute distances from the sta tions to the CBD but ignore stations’ accessibility to other stations. Finally, Kuby et al use residential population in the CBD as an independent variable.

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15 While the studies so far discussed use a ggregate data, the increasing availability of disaggregate (or micro) da ta after about 1995 provides th e opportunity to study travel behavior at the individual or household level. The availa bility of disaggregate data brought about a paradigm shift in travel behavior analysis. Reilly and Landis (2002) provide an early use of micro data to study the relationship between urban form and travel. In a study of the 1996 San Francisco Bay Area Travel Survey (BATS96), they test the relati onship between measures of urban form and mode choice. Using geographic informati on system (GIS) methods, they obtain small scale measurements of land-use diversity, inte rsection density, and average lot size. To obtain these measurements, they generate a map of the study area, subdivided into a set of 10,000 grid-cells of one square meter each, called rasters. Th en they proceed to obtain land-use measurements, such as the number of transit stops within a grid-cell. The authors fit gross population density and the amount of residential land area at the census block level into the grid-unit level to compute density values. The results of a multinomial logit mode-choice model show that an increase in average density of 10 persons per hectare (about four persons per acre) within one mile of an individual’s residence is associated with a 7 percent increase in the probab ility of walking or taki ng transit (p. 24). As in most of the studies reviewed, this study does not determine cau sality between urban form and travel behavior. Studies Analyzing the Influence of Transit on Urban Form Other research examines the influence that transit has on urban form. In this context, the vast majority study impacts on urban form in terms of changes in land values at the station-area level (Baum-Snow and Ka hn 2000; Bollinger 1997; Bowes and Ihlanfeldt

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16 2001; Cervero and Landis 1997; McDonald a nd Osuji 1995; Nelson et al. 2007; Zheng and Kahn 2008; Kahn 2007). Most of these stud ies also examine the economic benefits of rail systems at the regional and local le vel. Economic benefits may accrue because transit improves productivity, which increases regional product and income because of accessibility improvement. TCRP Report 16 (TCRP 1995) finds that tran sit raises residen tial property values near stations. Furthermore, there is support that both CBD’s and subcenters benefit from transit development at the station-area level. In the case of CBD’s, transit development helps centers retain their domi nance. In the case of subcenters, regional rail systems contribute to the decentralization of both populat ion and employment. This evidence is provided by way of anecdotal case studies, not empirical investigations based on quantitative analysis. In an in-depth analysis of the Bay Area Rapid Transit (BART) system, Cervero and Landis (1997) find that transit investment had localized impacts on land use that were limited to downtown San Francisco, Oakland, an d a few subcenters. Some studies looked at gentrification effects associated with tr ansit systems. For example, Kahn (2007), shows that access to transit in the form of “Walk and Ride” positively impacts the gentrification trend. Gentrificati on is a phenomenon where old, deteriorated neighborhoods go through a process of renovation leading to land-value apprecia tion. This is brought about by population cohorts sorting themselv es out in residential clusters. Bollinger and Ihlanfeldt (1997) provide a more sophisticat ed analysis of the impact of rail transit on economic developmen t. They present a simultaneous equation model that accounts for the simultaneity be tween population and employment density in

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17 proximity to rail stations in the area cove red by the Metropolitan Atlanta Rapid Transit Authority (MARTA). Results indicate that MARTA has had no discernible impact on total employment and population around stations. Studies Analyzing the Contemporaneous Re lationship between Transit and Urban Form Apart from the instances outlined above, the vast majority of empirical work on the relationship between transit and urban fo rm considers this relationship as one in which the urban landscape influences, in a uni directional fashion, tr ansit supply levels. Existing critical literature revi ews identify the shortcoming of this assumption, the results of which fail to account for any underlying unobserved endogeneity between urban form and travel. There are a few empirical efforts that pr ovide an explicit analytical framework based on clearly defined behavioral assump tions (Badoe and Miller 2000; Boarnet and Crane 2001; Boarnet and Crane 2001, 2001; Bo arnet and Sarmiento 1996; Boarnet and Sarmiento 1998; Crane and Crepeau 1998b, 1998a ; Moshe and Bowman 1998; Schimek 1996; Voith 1991, 1997). These analyses use either multiple regression analysis or discrete choice models, technique s that better account for the interrelationship between the built environment and travel behavior than th e approaches of previous research. Next, we summarize those studies most relevant to our research. Using the 1990 Nationwide Personal Travel Survey (NPTS), Schimek (1996) applies a multiple regression model that accounts for simultaneity between a household’s pick of neighborhood density and the amount of travel. The model is specified as (2.1)

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18 (2.2) where V is the number of vehicles per household, D represents vehicle use (measured by VMT or trips) per household, X is a vector of demographi c and geographic characteristics, and is a column vector of parameters to be estimated. Schimek substitutes (2.1) into (2.2) to obtai n a reduced form equation of (2.2) that he estimates by linear regression. Endogeneity arises between urban form variables and vehicle usage variables because these variable s affect vehicle ownership levels and, in turn, vehicle ownership affects residential location. Endogeneity is controlled by using an instrumental variable (IV) regression with the following in struments: race (white and Hispanic), location of household within the New York City standard metropolitan statistical area (SMSA), a dichotomous variable indi cating if a household is located within an SMSA of three million or more, and a dichot omous variable indicating if a household is located within an SMSA of one million or more. Schimek ju stifies race as an IV by arguing that race and urban form variables in X are linked by spatial and housing market discrimination. He acknowledges that these va riables might violate the basic IV assumption of no correlation with the exogenous vari ables of the reduced form equation. He does not, however, perform any tests for exoge neity or over-identific ation restrictions. The results are indeed impaired by the choice of weak instruments, as these are correlated with the other exogenous variables. The mode l’s results show that a 10-percent increase in density leads only to a 0.7 percent reducti on in household automobile travel. By comparison, a 10-percent increase in household income leads to a 3-percent increase in automobile travel. The results are similar when vehicle trips are used as the dependent variable.

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19 Boarnet and Sarmiento (1998) provide a mo re robust analytical framework, which has been adapted by Boarnet and Crane (2001) and Crane and Crepeau (1998b). Boarnet and Sarmiento address some of the shortcomi ngs of previous work, namely the a priori specification of a behavioral model from whic h a series of hypotheses is tested. They specify a non work-trip demand function in reduced form, where tr ip frequencies and VMT are a function of a set of socio-economic characteristics, land-use factors, and costs of travel (2.3) (2.4) where N is the number of non-work auto trips, p is trip cost, y is income, S is a vector of socio-demographic variables, and L is a vector of land-use characteristics. The authors argue that the cost of travel is itself affected by land-use and that land-use is endogenous because individuals tend to cluster in residential areas based on idiosyncratic preferences for residential locati on. They formalize this assertion by adding two equations that relate land use, L to residential location (2.5) (2.6) where indicates individual residential location; represents individual sociodemographic characteristics (essentially the same as S ); and represents characteristics of residential locations, such as amenities. In particular, is a vector of IV’s for L in a two-stage least squares (2SLS) regression of Equation (2.3). Boarnet and Sarmiento expect the qualitativ e effect of each of the independent variables to be indeterminate. A set of neighbor hood amenity variables is used as IV’s: the

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20 proportion of block-group or cen sus-tract population that is black, the proportion Hispanic, the proportion of housing stock built before 1940, and the proportion built between 1940 and 1960. The authors justify their choi ce of these IV’s based on evidence that neighborhood demographic composition and age of housing are determinants of residential location choice. They argue that these IV’s are good inst ruments since they are correlated with land use but not with transport (VMT or trips) and are, thus, exogenous to the error term. Boarnet and Sarmient o conclude that there is limite d evidence of an effect of land use on transportation behavior; the most important result is that land use is endogenous to transportation behavior. Several issues, related to th e IV’s being employed, impair the validity of these results. In this kind of analys is, good IV’s must be correlated with land use, but they must not be correlated with transpor tation. It is easy to show th at race or minority status affects both location and transportation demand (A rnott 1998). Race is correlated with location because minorities’ choice set is more constrained than that of whites. The same argument applies to minorities’ transportati on choice set as, for example, when race and income are determinants of auto ownershi p and, therefore, impact both trips and VMT (the dependent variable employed by the author s). We conclude that the IV’s chosen by the authors are poor, even if they pass a te st for exogeneity based on over-identification, as outlined in Wooldridge (2002). Crane and Crepeau (1998b) introduce a set of trip-demand functions (they report the demand for auto trips) as a function of travel time and income derived from a CobbDouglas specification (2.7)

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21 where represents a taste parameter; y represents income; represents land-use features, which serve as proxies for the cost of travel (time and distance); and indicates the price of a trip. Travel time is equal to the ra tio of trip length to travel speed (which are themselves choice variables). The authors conduct the analysis at a disa ggregated level with respect to travel choice and land use. Land-use data from the Ce nsus Bureau are merged with travel-diary data using Geographic Information System (GIS ) techniques to match residential location with land-use data at the tract level. GI S visual inspection of the network within 0.5 miles of the household allows measuring the ch aracteristics of street grids and the presence of cul-de-sacs (measures of design). Land-use characteristics enter the demand function as shift parameters. The empirical analysis examines the impact of crosssectional changes of The problem with this approach is that tr avel distance and speed are both affected by land use and urban design, but the functi ons specified by the authors dismiss endogeneity between land use and travel demand. Fo r example, the vector of time prices is a function of speed and trip length, but trip lengt h is also a function of location and street design. The authors acknowledge the problem and run a 2SLS regression using instruments for the price variables, although without "satisfaction with th e variables available in the data (p. 233)." Greenwald and Boarnet (2001) use the preced ing model with minor variations to assess the impact of land use on non-work walking trips, and Zegras ( 2004) applies it to the relationship between land-use and travel behavior in Santiago, Chile.

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22 Voith (1991) analyzes transi t-ridership response to fare levels. He models transit demand and transit supply in a context where ch anges in transit service affect residential location. In this model, the author assumes that changes in service affect location decisions around transit stations, which, in turn, affect transit demand and, recursively, transit supply. In an update of his earlier work, how ever, Voith (1997) concludes that, after controlling for prices and servi ce attributes, demographic eff ects on transit are minimal. Methodological faults affect other research that attemp ts to model transit demand and transit supply simultaneously. For exam ple, although Taylor and Miller (2003) recognize the need to model demand and supply jointly to avoid mi sspecification issues, they provide a poorly specified model. Inherent Complexity: A ccessibility, Urban Design, and Self-Selection In recent years, urban policies to reduce externalities associated with employment and residential decentralizati on have relied on influencing the choice and amount of auto travel by manipulating urban form. The rationa le behind these policies is that car-travel reductions can be achieved by reducing trip freq uencies and travel distances. Mixing residential and employment locations expands the choice set by cluste ring amenities, which reduces average travel distances because nearby destinations are preferred to more distant ones. Furthermore, offering increased public transportation choices further reduces auto travel. Such policies drive the so-called transit oriented development (TOD) (Cervero et al. 2004) approach to land-use planning. An issue at the heart of TOD effectiveness, which has attracted the attention of transportation researchers, is individual self-selection to residential location. In othe r words, individual preferences for location if not explicitly

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23 accounted for during empirical research, might lead to overestimation of the impact of TOD policies on travel behavior. Researchers have tested the effectiveness of TOD by examining aspects of the built-environment, such as the relationship between mixed landuses (where residential and commercial land-us es are in close proxi mity) and accessibility measures to residential locations. There is a recent vast and fast growing literature addressing wh ether or not urban form affects travel behavior and, if it does, th en what is the structural formation of the linkage. Within this field of research, a t opic that has been incr easingly studied and debated is that of residential so rting or self-selection. This refers to the phenomenon that leads individuals or households to prefer a cer tain residential location due to idiosyncratic preferences for travel. In applied work, if residential self-sorting is not accounted for, findings tend to overstate the relevance of po licies to impact travel behavior by changing the built environment. Mokhtarian and Cao (2008) provide a comp rehensive review of empirical work on residential self-selection. While this gr owing body of literature recognizes that unobserved idiosyncratic preferences for travel a ffect residential location decisions, there is still disagreement on how best to treat the most common consequence of not controlling for this problem, namely, the resulting omitted variable bias. The empirical treatment of omitted variable bias in the context of se lf-selection ranges from nested logit models Cervero,(2007) to sophisticated error-correlati on models (Bhat and Guo 2004; Pinjari et al. 2007). Cervero (2007) estimates the degree to which residential self-selection affects transit mode choice by using conditional proba bility estimates that control for idiosyn-

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24 cratic preferences for location. He specifies a decision nest requi ring the parameterization of two indirect utility functions, one f unction expressing reside ntial location choice (specifically, residence within a mile of a rail stop) and one func tion expressing transit mode choice. Workplace proximity to a ra il station, job-accessibility, and household and personal attributes are among the factors aff ecting location choice. He specifies the mode-choice indirect utility function to include a travel-time ratio (transit vs. auto), vehicle stock, personal attributes, and neighborhood density. The results of his analysis show significantly higher transit ridership shares associated with transit-oriented living, but that residential self-selection might accoun t for about 40 percent of such shares. Two issues related to the modeling tec hnique and the choice of the observational unit cast doubt on the po ssibility of generalizing these findi ngs. First the residential location utility function, although cont rolling for accessibility a nd socio-demographics, does not include any controls for neighborhood and housing characteristics. Second, it is not clear if the observational unit of analysis is the household or the individual (the subscript n in equation 1 on page 2,077 refers to the individual, but page 2,078 refers to a household). The implications of modeling household versus individual residential choice are non-trivial. For example, in a two-member household, even after controlling for household characteristics, the first pe rson might have a transit stop near his or her work location, while the second person might not. This re sults in a different travel-time ratio (a control in the lower level mode-choice utility function). When estimating the nested logit regression, the predicted probabilities of resi dential location might differ, assigning the first person to the predicted choice of “near tr ansit station” and the second person to the

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25 predicted choice of “far.” Th is results in having two indi viduals within the same household living at different locations. Following the latest applications of di screte mode-choice modeling developed by Bhat and Guo (2004), Pinjari et al. (2007) propos e a model of joint determination of residential location and mode choice where both choices influence each other by accounting for observed and unobserved individual taste he terogeneity. Findings suggest that, after accounting for self-selection, the built envi ronment has an impact on commute modechoice behavior. The authors present two indirect utility functions, one describing mode choice and one defining residential location. The two f unctions are related by way of an error-term specification. They capture self-selection endogeneity by control ling for both observed and unobserved factors impacting residential location and commu ting-mode choice. First the mode-choice indirect utility function ( indirect here means that the function depicts a realized choice that reflects the primitive object ive function; it is not the indirect utility function of economic theory) includes a term indicating observed socio-demographic factors influencing the mode-choice decision. Th en, an unobserved term is added to capture taste heterogeneity linked to the location deci sion but affecting mode -choice. This takes the form of an error te rm that is correlated to the second indirect utility function related to location choice. A final independent and identi cally distributed error term is added to the equation. The second indirect utility equati on works the same way, with an error term correlated with the mode-choice utility function. The main issue with this methodology is related to the claim of simultaneously determining mode-choice and location. This approach prompts the question “is the

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26 mode-choice decision really simultaneously dete rmined with the location decision?” The authors seem at first to state this hypothesis, then, later, to refute it (p. 564) by admitting that, “The model structure assumes a causal influence of the resi dential location choice (and hence the built environment) on commute mode choice.” This apparent contradiction is probably justified by the specific econometric approach that they take. Specifically, they assume that individuals simulta neously maximize two different, although interdependent, utility functions, subject to somewhat different constraints. As in the case of Cervero (2007), this problem is the result of ad -hoc specifications of indirect utility functions without knowledge of the primitive obj ective functions, as discussed by Jara-Daz and Martinez (1999). Another problem in the study of self-selec tion arises when residential choice is modeled as a discrete variable. The treatme nt of the location decision as a dichotomous variable inherently presents a problem that is at the very he art of residential self-selection research. When using discrete choice modeli ng, one must assume that all individuals can choose among all possible locations within an urban area. The treatment of mode choice and residential location in more sophisticated frameworks does not eliminate the need to determine ad hoc the residential choice set. For example, both Pinj ari et al. (2007) and Bhat and Guo (2004), who adopt the more sophi sticated multinomial logit-ordered structure that explicitly considers the correlati on of unobserved factors simultaneously affecting both choices, must determine a priori the location choice set (in that case, any individual is assumed to be able to choose am ong 223 different locations). This assumption does not explicitly acknowledge that, subject to income and vehicle availability, some individuals have more constr ained mode choices and reside ntial location sets, with the

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27 undesirable effects described by spatial mismat ch theory (Kain 1968). The result is not being able to fully discern the influence of idiosyncratic preferences for location on residential choice from issues rela ted to spatial mismatch. An alternative to treating residential locat ion as a discrete choice is instrumental variable regression that uses a set of properly tailo red instruments, with leading examples discussed earlier (Boarnet and Sarmiento 1998; Crane 2000). Other researchers advocate the use of simultaneous equation modeling (S EM), where additional equations are added to account for simultaneity between urban form, attitudes toward travel, and other factors. Researchers justify preference for the latter ap proach on the basis of its capability to uncover causality between tr avel and urban form. In many instances, research efforts that claim to uncover causality between urban design, travel behavior, and i ndividual self-selection do not make appropriate use of the econometric techniques therein employed. Data constraints al so affect the usefulness of this statistical technique. For example, wh ile Bagley and Mokhtarian (2002), Handy et al. (2005), and Cao et al. (2007) discuss the advantages of SE M, assuming the availability of longitudinal data, they all use the same cr oss sectional dataset that employs a mix of secondary data and primary data from a travel attitude survey (the authors define this dataset as quasi-longitudinal ). Furthermore, in the contex t of simultaneous equation modeling or instrumental variable regression, the validity of results hinges on the determination of the exclusion restrictions. That is, the researcher must determine a priori what explanatory variables are to be included and ex cluded from a given equation. The determination of the exclusion restricti ons determines a model that is correctly specified in the sense that the matrix of the reduced form para meters to be estimated is unique in its re-

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28 presentation of the more primitive structural matrix. Exclusion restrictions need to be drawn outside of the variables a researcher has available from a given dataset, i.e., they should be based on sound behavioral theory (Wooldridge 2002). In all studies of residential self-sel ection employing SEM techniques previously reviewed, including the work of Bagley and Mokhtarian ( 2002), Handy et al. (2005), and Cao et al. (2007, 2006), there is no explicit treatment of the exclusion restrictions that can be traced back to a forma lized theoretical framework. An alternative approach is presented by Vance and Hedel (2007), who employ a two-part model consisting of probit and OLS estimation, using the German Mobility Panel survey (MOP 2006). In the first part of the model, a probit model that controls for socio-demographic factors (income, age, dr iving license) and urban form (commercial density, street density, commer cial diversity) estimates the probability of owning a vehicle. The second stage, a regular OLS model, conditional on the first-stage predicted vehicle ownership, regresses vehicle use (distance traveled) on a vector of sociodemographic and urban form variables. The model is further enhanced by instrumenting the urban form variable using the set of in struments suggested by Boarnet and Sarmiento (1998). Although instrument validity is checked against exogeneity by applying selected diagnostic tests, the choice of instruments is limited to a se t of controls for housing characteristics without the incl usion of neighborhood characteri stics controls to capture a broader set of factors affecti ng residential location choice. Measuring Accessibility Accessibility measures are widely used in transportation plan ning to relate the pattern of land use and the nature of the tr ansportation system. Various measures have

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29 been employed when analyzing the efficacy of mixed land use or transit-oriented policies. A problem related to the use of accessibility is that its measurability is inherent in its definition and quantification. For example, one definition is “the ease and convenience of access to spatially dist ributed opportunities with a choice of travel” (DOE 1996). Obviously, the main difficulty is to quantify the ease of accessibility. We now turn to a discussion of the most widely us ed measures of accessibility. As recently summarized by Dong et al. ( 2006), there are essentially three measures of accessibility that have been employe d to date: isochrones, gravity-based measures, and utility-based measures. The most widely employed are the gravity-based measures, which have the following generic form (2.8) where Acci means accessibility to zone i ; j indexes the available destination zones that can be reached from zone i ; measures the activity opportunities in zone j ; and represents an impedance, or deca y, function of traveling from zone i to zone j This tripbased measure has been used in the recent work of Maat and Ti mmermans (2006), one of the few studies examining the influence of land use on activity-based travel. As pointed out by Dong et al. (2006), this m easure is limited in that it neglects heterogeneity of preferences acr oss individuals, which can lead to absurd conclusions, e.g., “a gravity measure of this type says that a retired grandf ather and his college student grandson who live together have identical valu es of accessibility (p.165).” Furthermore, this measure is highly sensitive to th e specification of the decay function. All of the models showing a relationship between increased transit usage and improvement in accessibility rely on one of the above measures. We think that analyzing

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30 the complexity of accessibility and travel beha vior requires the use of accessibility measures that are strictly linked to the way activit ies are organized. These measures should be selected based on the relationship wi th the observed act ivity pattern. Some attempts are now appearing in the l iterature, although not di rectly related to the field of transportation research, that take into account indivi dual heterogeneity and preferences. For example, utility-based m easures of accessibility, which are based on the random utility theory as originally exposited by Domencich and McFadden (1975), provide ways of relating accessibility measures to the characteristics of the alternative and the characteristics of the individual. The activity-based accessibil ity measure introduced by Dong et al.(2006), for example, is a utility-ba sed measure. This measure is capable of capturing taste heterogeneity acro ss individuals, combining diffe rent types of trips into a unified measure of accessibility, and of qua ntifying differing accessibility impacts on diverse segments of the population. Urban Form Measures and Polycentric Cities As discussed in the introduction to this ch apter, another proble m of empirical analyses of the relationship between travel and la nd use is the adoption of measures of urban form that are monocentric. Monocentric mode ls only consider measures of the strength of the relationship between central business district (CBD) employ ment (and other activities located at the CBD) and trav el behavior. For example, in their seminal work, Pushkarev and Zupan consider the relationship betw een transit service and density in a context where the CBD is the main determinant of tr ansit trips. More recently, Bento et al. (2005) examine the effects of population centr ality, jobs-housing bala nce, city shape, road density, and public transit supply on the commute-mode choices and annual vehicle-

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31 miles of travel of households living in 114 urban areas in 1990. They found that the probability of driving to work is lower the higher the population centrality and rail miles supplied and the lower the road density. Road density, in this model, is defined as miles of road multiplied by road width (for different categories of road) and divided by the size of the urbanized area. In recent decades the process of decent ralization has taken a more polycentric form, with a number of clustered employment centers affecting both employment and population distributions. The majority of thes e centers is subsidiary to an older CBD. Such centers are usually called subcenters or sub-regional centers. McMillen (2001) suggests a more formal definition by defining a subcenter as a “site w ith (1) significantly larger employment density than nearby locati ons that has (2) a significant effect on the overall employment dens ity function (pp.448–449).“ The transportation literature has seldom examined the influence of subcenters on travel behavior. An exception is Cerver o and Wu (1998), who study the influence of subcenters on commute distances in the San Fr ancisco Bay area. They conclude that employment decentralization has led to increased vehicle travel. These studies generally consider subcenters as exogenously determined either by assumption or by an empirical determination that makes use of specific density thresholds. More recent developments in travel de mand behavior and geographical science provide some insight on how better to capture the relationship between urban form and travel in a highly decentralized context. For example, Modarres (2003) proposes the use of GIS to determine subcenters using spatial clustering techniques to cluster patterns of major employers. He then considers the releva nce of transit accessibility within the iden-

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32 tified subcenters (accessibility is defined as the level of service provided by existing routes in each census tract) a nd concludes that spatial accessibility is high within these subcenters. Casello (2007) di scusses the potential to increase and the impacts of increasing transit modal split in the polycentric metropolitan area of Philadelphia. By identifying “activity centers,” i.e., areas where transit use is likely, he models transit competitiveness and system performance. Kuby et al. (2004) update and im prove previous research and find that the same factors affecting CBD board ings also influence non-CBD (subcenter based) transit ridership. The decreasing relevance of the CBD with respect to transit patronage is illustrated by its statistical insignificance in determining transit usage in the recent work of Brown and Neog (2007) and Thompson and Br own (2006). In particular, Brown and Neog examine aggregate transit ridership in 82 U.S. metropolitan statistical areas (MSA) using data from the National Transit Database as provided by the Fl orida Department of Transportation Transit Information System (FTIS). The authors use employment in the CBD and total metropolitan employment as proxi es for urban form explanatory variables in a series of multivariate regression models. They find that transit ridership is not affected by the strength of a CBD, suggesting that improveme nt in ridership can be obtained by better serving d ecentralized urban areas. These findings are supported by Brown and Thompson (2008), who employ a time series analysis of aggregate ridership da ta of the Metropolitan Atlanta Rapid Transit Authority (MARTA) in Atlanta, Georgia. The authors define two employment decentralization measures: number of employees within the MARTA service area located outside the Atlanta CBD (variable EMPMARTA) and the ratio of employment outside the

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33 MARTA service area to employment inside the MARTA service area (variable RATIO_EMP). They specify a first difference autoregressive model with annual linked passenger trips per capita as the dependent variab le as a function of tr ansit supply measures and the above-mentioned decentralization vari ables. Results show that model performance is affected by inclusion of a time tre nd variable, as reflected by the standard error estimates of the variable RATIO-EMP acro ss the two models’ specifications. Notwithstanding these econometric issues, the authors conclude that there exists a positive association between decentralized employment grow th (served by transit) and transit patronage. Although these conclusions favor policies ge ared at servicing employment rather than population concentrations, a generalization of these findings to other spatial context is not warranted. The lack of relevance of th e Atlanta CBD is due to the peculiar spatial characteristics that make it unique with respec t to the rest of the U.S., and the world, as argued by Bertaud (2003). By comparing At lanta’s spatial arrangement of population and employment to other U.S. and world citi es, Bertaud shows that the uniqueness of Atlanta (being highly polycentric) makes a supply-si de policy cost-infeasib le. In particular, Bertaud shows that with only 2 percent of th e total jobs located at the CBD and only 8 percent within 5 kilometers of the city cente r, Atlanta’s dispersion of employment would require the addition of about 3,400 kilometers of metro tracks and about 2,800 new metro stations to provide the same transit accessi bility to a comparab le, although monocentricbased, city, requiring only 99 kilometers of tr acks and 136 stations. Bertaud uses these findings to justify congestion to lling and the provision of sma ll, niche-type transit services to control the negative externalitie s usually associated with sprawl.

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34 In summary, the literature provides contrasting results on the relevance of the CBD to the demand and supply of transit servi ces. The strength of the CBD is conditional on the spatial characteristics of the neighboring suburban areas. From Trip Generation to Activity-Travel Behavior In examining the relationship between trav el behavior and urban form, the literature reviewed above rarely accounts for the fact that the demand for travel is an indirect demand, which arises from the necessity to enga ge in activities requiring travel. The recognition that travel patterns are complex and th at trips are the result of a decision-making process in which activities are organized and prioritized through space and time has led to what is generally considered a paradigm shif t in the study of urban travel behavior (Pass 1985). This paradigm shift has paved the wa y for a new field of research, defined as activity-based modeling Activity-based modeling is char acterized by the recognition that travel is a derived demand, a recognition that sh ifts the research focu s from single trips to trip chains and from indivi dual decision making to househol d members’ interdependent decision making (Jones, Koppelman, and Orfeu il 1990). Activity-bas ed approaches are currently used to describe the activities indi viduals pursue, at what locations, at what times, and how these activities are scheduled within a transportation network characterized by opportunity and constrai nts (Bhat and Koppelman 1999). Essentially, a trip chain may be defined as a sequence of trips that starts from home and/or ends at home. Different ta xonomies defining trip-chaining complexity are possible depending on the purpose or mode of the trip for different classes of travelers. Sometimes called stop-making behavior, trip-c haining behavior in activity-based model-

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35 ing describes the importance of multi-purpose tr ip-making rather than single-purpose trip making. Numerous studies have examined trip-c haining or stop-making models using the frequency of stops on the way home and/or on the way to work as dependent variables (Bhat 1999; Chu 2003; Concas and Winters 2007; Shiftman 1998). In these studies, stopmaking behavior describes stopping behavior made by a traveler, in particular a commuter, on the way to home or work. Under th e assumption that a commuter follows a regular route, then stopping at a location other than home or work during the commute is treated as a deviation from the commute trip. In prior resear ch, stop-making models were usually applied to trips linki ng non-work activities with wo rk activities, including the morning commute, midday trips, evening co mmute, and trips before or after the commute. The analysis of travel behavior within th is context allows the recognition that trips are interrelated as opposed to the current transportation planning modeling assumptions of separation and independence of trips by purpose. Models based on microeconomic theory that explicitly treat the trade-offs i nvolved in the choice of multiple-stop chains (i.e., the linking of several out -of-home activities and related tr ips into one tour) first appeared in the 1970’s (Adler and Ben-Akiva 1979 ). In addition to work trips, non-work trips have also been investigated, where non-wo rkers’ trip-chaining is a series of out-ofhome activity episodes (or stops) of different types interspersed with periods of in-home stays (Misra and Bhat 2002; Misr a, Bhat, and Srinivasan 2003). Although travel-demand forecasting models are now starting to incorporate tripchaining behavior, only a limited number of studies exists th at link the different aspects

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36 of trip-chaining behavior (t rip-tour frequency, complexity, duration) and urban form. There are some studies that relate trip chai ning to regional accessibi lity or that compare trip-chaining behavior across regional subareas, for exampl e, city versus suburbs, as summarized by Ewing and Cervero(2001). Ma at and Timmermans (2006) represent a recent effort to examine the influence of land-use on trip-chaining behavior (by way of analyzing tour complexity). There is some research attempting to integrate activities and residential location by using discrete choice models of household re sidential location and travel schedules (Ben-Akiva and Bowman 1998). We find to date no empirical work explic itly relating location to trip-chaining behavior in a context in which individuals jointly decide locat ion, the optimal trip chain, and the area of non-work activities, based on the optimal trade-off between commute time and non-work travel activities. We thi nk that better insight on the relationship between urban form and travel behavior would be gained by testing the hypothesis that an individual’s residential location is based on util ity maximizing behavior. Summary and Implications for Integrated Models of Transportation and Land Use The bulk of research reviewed in this ch apter is empirically oriented and based on the application of multivariate techniques that regress various measures of travel behavior (commute length, vehicle-miles of travel, m ode choice) on measures of residential and employment density, while controlling for the de mographic characterist ics of travelers. These studies examine the statistical signifi cance, sign, and magnitude of the estimated coefficient on residential popul ation density or employment density. A statistically significant negative coefficient leads one to conc lude that a negative relationship exists between travel and density. For example, hi gher density leads to shorter commutes, fewer

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37 vehicle-miles of travel (VMT), or a shift from auto trans portation to alternative modes, such as transit. The abundance of these t ypes of studies has led to the conclusion that policy interventions directed to influence density are capable of reducing automobile use. The literature review uncovered the following issues that, to date, have been addressed but not completely resolv ed. In particular, it is wide ly recognized that there is a lack of a behavioral framework that can be applied to empirical work and is conducive to generalization of findings and applicability. Studies that relate density (population and employment) measures to travel behavior ar e monocentric and, therefore, fail to account for the employment and residential decentral ization now characterizing the urban landscape. In most of this work, density is tr eated as exogenous and is not assumed to be impacted by transportation system changes. Th ese studies have undergone systematic criticism due to their ad-hoc specifications and because of omitted variable bias problems due to the possibility that the relationship between urban form and travel might entail simultaneity and endogeneity. In a ddition, most of the work that jointly estimate transit demand, transit supply, and factors affecting bo th supply and demand are affected by methodological faults, ranging from misuse of simultaneous equation modeling methods to improper functional specifications. More recent developments in travel de mand behavior and geographical science provide some insight on how better to capture the relationship between urban form and travel in a highly decentralized context. The significance of the CBD in determining transit ridership levels has been revisited and more rele vance is now attr ibuted to decentralized employment by examining the influenc e of subcenters in an increasingly polycentric urban landscape.

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38 While early work sought to provide a gene ralized analytical framework that made use of aggregate data, the more recent literatu re consists of papers that model the simultaneous decision of location and travel (as an application of improved discrete-choice modeling techniques) in a cont ext where individuals choose locations based on specific travel preferences (for example, a preferen ce about a specific mode ) at the disaggregate level. Location decisions based on idiosyncra tic preferences for trav el define the term “residential self-selection beha vior” to indicate how individu als with similar tastes and preferences tend to cluster t ogether in given locations. Finally, there is a lack of empirical work that studies the relationship between urban form and travel behavior within an act ivity-based framework, which takes into account the complexity of travel (i.e., that acc ounts for trip chaining). Those studies that have employed activity-based modeling have failed to properly account for endogeneity and have disregarded spatial mismatch effect s. In examining the relationship between urban form and travel, it is cruc ial to distinguish the effects of land use from the effects of systematic socio-demographic differences of individuals. It is the purpose of this dissertation to provide an estimable model for these failings of previous research.

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39 Chapter 3: Methodology Introduction The objective of this chapter is to develop an empirically testable model of the relationship between transit travel behavior and urban form. Following the methodological issues highlighted by the literature review, the proposed framework seeks to address unresolved issues as follows: It controls for individual idiosyncratic preferences for residential location It shifts the focus from monocentric-based measures of urban form to polycentric ones It utilizes a framework that better account s for the spatial influence on travel patterns, by shifting the focus from a singlepurpose trip-generati on analysis to one that accounts for trip chaining It accounts for the trade-off between commute time and non-work activities In this model, travel demand is consid ered a derived demand brought about by the necessity to engage in out-of -home activities whose geographical extent is affected by urban form. Furthermore, budget-constrained utility-maximizing behavior leads to an optimization of the spatiotemporal allocation of these activities and an optimal number of chained trips. Socio-demogr aphic factors directly influe nce residential location, consumption, and travel behavior. To date, no empi rical work has been done that explicitly

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40 relates location to trip chaini ng behavior in a context where individuals jointly decide location, the optimal trip chain, and the area of non-work activities, based on the optimal trade-off between commute time, leisure, a nd non-work travel ac tivities and accounts for the other methodological problems noted above. FIGURE 3.1 Conceptual Model of Ur ban Form and Travel Behavior In this model, residential location, trav el behavior, the activity space, and urban form are all endogenously determined. Followi ng urban residential location theory, the location decision is assumed to be the result of a trade-off between housing expenditures and transportation costs, given income and th e mode-choice set. In a departure from the monocentric model, the definition of resident ial location is taken from the polycentric model of Anas and his associates (Anas and Kim 1996; Anas and Xu 1999). In this work, residential location is defined as the optimal job-residence pair in an urban area in Residential Location (Home-work commute pair; station proximity) Travel Behavior ( Trip chaining, total linked trips, trip shares) Urban Form (Density, urban design, land-use mix) Activity Space (Spatiotemporal allocation of non-work activities) Socio-demographics (Income, family size, occupation, etc.)

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41 which jobs and residences are dispersed. Following Anas (Anas 2007), the location decision is also based on idiosyncratic preferences for location and travel. In addition to determining optimal residential location, this approach also determines the optimal sequence of non-work trip chains, goods consumpt ion, and transit patrona ge. It is within this framework that questions related to the interrelation between ur ban form, residential location, and transit trav el demand are addressed. How do location decisions affect travel behavior? How does urban form relate to tr avel behavior? Do re sidential location and urban form affect travel beha vior? What is the impact of higher density on travel behavior? To address these questions, we first introduce a basic travel demand model treating residential location and density as exogenous (Model I). We then consider subsequent extensions (Model II and Mode l III) that relax these assumptions to discuss what expected behavioral conclusions can be reached. This chapter presents the most relevant results of the comparative static analysis, while the complete derivation of the comparative statics and the necessary assumptions to ca rry them out are detailed in Appendix A. Model I: Exogenous Residential Location and Density In this specification, reside ntial location, transit station proximity, and density are exogenous. Given these variables, the mode l jointly defines the activity space and the optimal trip chain. The joint determination of activity space and trip chain determines a travel demand function, given consumption a nd location decisions. The household (rather than the individual) is the unit of anal ysis because these decisions take place at the household level. Empirical studies on the rele vance of transit station proximity to transit patronage show a strong relati onship between transit use and station proximity (Cervero

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42 2007; Cervero and Wu 1998). Therefore, this model includes this possibility. To include these considerations, Model I takes the following specific form (3.1) (3.2) (3.3) where TC = the number of non-work trip stops per commute-chain or chain length AS = the activity space (measured as the geographic area surroundi ng the residence in which non-work trips are made) = the demand for transit trips (measured as the number of transit trips) = residential locati on (measured as the job-residence pair distance) = a vector of residential a nd employment density controls WD = transit station proximity (measured as wa lking distance to the nearest transit station) XTC = a vector of controls specific to the TC function; XAS = a vector controls specific to the AS function = a vector of controls specific to the function This model permits testing the hypothesis th at individuals living farther from the workplace engage in more complex tours ch aracterized by a higher number of non-work trips linked to the commute tour. As in Kondo and Kitamura (1987), the number of nonwork trip stops, TC determines the length of the trip chain. In addition, TC as it relates to transit patronage, is directly affected by transit station proximity and by other factors summarized by the vector of controls, XTC. This vector, as explained in more detail in

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43 Chapter 4, includes vehicle availability a nd the presence of young children among other factors likely to affect trip-chaining formation. Trip-chaining behavior defines an activity space, AS which is assumed to represent the optimized spatiotemporal allocation of nonwork activities as affected by the built environment, summarized by the exogenous vector, For example, more densely populated urban areas have more densely cluste red activity locations, which shrink the size of the activity space relative to less densely populated areas. A smaller activity space reduces trip chaining, TC ultimately affecting the demand for travel, TD As we shall see, AS captures the characteristics of activ ity locations as well as the spatiotemporal constraints linked to trip-chaining behavior. This model is suited to either describe a situation where residential location is considered as predetermined, such as a short run time frame or can be used to cross compare decision making among house holds at any point in time. The model may be used to test the effect of urban design policies directly affecting trav el distances an d the land-use mix. Specifically, it may be used to test if higher density e nvironments entail shorter travel distances, which in turn should affect th e composition and complexity of trip chains and the overall amount of travel. Residential Location, RL, and Transit Station Proximity, WD The definitions of residentia l location and transit station proximity used here differ from those used in the current literature. For example, in studies of residential selfselection, the location de cision is often presented as a di chotomous choice, i.e., whether to live near or far away from a transit station. Proximity is measured by a circular buffer around a station, often with a half-mile radius. The extent of this buffer is usually justi-

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44 fied on empirical grounds. Cervero (2007), for example, used a half-mile radius in estimating a nested logit model of the joint dete rmination of mode and location. This measure of transit proximity fails to account for ba rriers that prevent access to a station that lies within the half-mile radius. Some resear chers have considered residential location as a choice to reside within a geographical unit, such as a traffic assignment zone (Bhat and Guo 2004; Pinjari et al. 2007). The use of transit proximity as a proxy fo r residential location, while dictated by the need to sort out the influence of the built environment from self-selection, is not based on any other theoretical underpinnings ab out the decision-making process that is at the heart of urban residential location theory. That is, it doe s not take into consideration the trade-off between housing and transporta tion costs that, at the margin, determine where an individual decides to locate. For example, the standard theory of location shows that individuals choose an optimal di stance between work and home given housing and transportation costs. In a monocentric m odel that only looks at travel between home and the CBD, individuals locate at a distance wh ere the marginal cost of transportation is equal to the marginal housing cost savings obtained by a move farther from the CBD (Alonso 1964; Muth 1969). Recent departures from this view consider that individuals can locate anywhere in an urban area, choos ing an optimal home-w ork distance that optimizes also the amount of non-work travel and non-work activities (Anas and Kim 1996; Anas and Xu 1999). Further expl orations also consider the ro le of trip chaining behavior (Anas 2007).

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45 Activity Space: Spatial Disp ersion of Non-Work Activities The concept of activity space, although not new to behavioral sciences, is novel in terms of its application to travel behavior. The relationship between urban form and geographical patterns of activities has been studied only recently, due to the availability of specialized travel diary data and increasingly sophisticated geospatial tools. A growing field of research that looks at the relations hip between urban form and the spatiotemporal allocation of activities and travel provides additional insight on the impact of the built environment. Recent research describing trav el behavior and the influence of urban morphology and entire patterns of daily househol d activities and travel demonstrates how households residing in decentralized, lower de nsity, urban areas tend to have a more dispersed activity-travel pattern then their c ounterpart residing in centralized, high density urban areas (Buliung and Kanarogl ou 2006; Maoh and Kanaroglou 2007). This study explicitly accounts for the influe nce of the built environment in affecting the spatial dispersion of activities and how spatial di spersion affects the demand for travel and location decisions. This effect is accounted for by introducing the variable activity space AS, into the model. The extent of the activity space is assumed to be affected by the built environment. Densely populated ur ban areas tend to clus ter activity locations together thus shrinking the size of the activity space. This affects the spatial allocation of activities, thus affecting the demand for travel. As seen in the next chapter, there exist several ways empirically to measure the spatial dispersion of activities. Trip Chaining, TC According to activity-based modeling pract ice, trip chaining describes how travelers link trips between locations around an activity pa ttern. In this context, a trip from

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46 home to work with an intermediate stop to dr op children off at day care is an example of a trip chain. In the literature th ere is not a formal definition of trip chain, and different terms and expectations exist as to what kind of trips should be cons idered as part of a chain (McGuckin and Murakami 1999). Sometimes, the term trip chain is used interchangeably with the term tour to indicate a series of trips that start and end at home. In this study, we hypothesize that trip chaining occurring on the home-job commuting pair saves time. These time savings in turn can be either al located to additional non-work travel, thus increasing the overall demand for travel (e.g., total number of trips), or be used to determine a longer co mmute (i.e., a home-job co mmuting pair farther apart). The hypothesis of increased discretionary travel due to trip-c haining has recently been theoretically demonstrated (Anas 2007) The hypothesis of a positive relationship between more complex trip chains and the home-work commute is confirmed by empirical work. For example, in an analysis of trip chaining involving home-to-work and workto-home trips using data from the 1995 na tionwide personal transportation survey (NPTS), McGucking and Murakami (1999) found that people are more likely to stop on their way home from work, rath er than on their way to wor k. About 33 percent of women linked trips on their way to work compar ed with 19 percent of men, while 61 percent of women and 46 percent of men linked trips on their way home from work. Using the 1991 Boston Household Travel Survey, Bhat (1 997) found that about 38 percent of individuals made stops during the commute trip. Davidson (1991) found similar results from her analysis of commute behavi or in a suburban setting, showi ng that traveler s rely heavily on trip chaining in an ur ban context characterized by hi gher spatial dispersion of nonwork activities. Other studies also provide empirical evidence of increased stop-making

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47 during the commute periods (Bhat 2001) or how the ability to link trips is enhanced by the flexibility inherent in auto mobile use (Strathman 1995). Travel Demand, TD Travel demand is herein treated as a de rived demand brought about by the need to purchase goods and services. Travel demand, TD measures the number of work and nonwork transit trips at the household level. The decision process behind the choice of the number of trips, as formalized by this fram ework, considers trip generation as a function of trip chaining and exogenous residential lo cation and socio-demographic factors. The constrained maximization problem of the join t determination of activity space and tripchaining defines an optimal vector of non-work trips, given residential location and urban form characteristics (e.g., reside ntial and employment density levels, land-use mix). This treatment of travel demand as derived from th e desire to engage in out-of-home activities departs in terms of behavioral sophistication from the treatment of trip generation as developed by Boarnet and Crane (2001) in their analysis of travel demand and urban design. In Boarnet and Crane (2001) trip demand functions are either directly affected by land use or indirectly (by infl uencing the cost of travel). In contrast, in this model land use (i.e., ur ban form) directly affects the spatial allocation of activities. As shown by Anas, (2007), it is the budget-constrained utilitymaximization behavior that defines optimal trav el patterns. The complexity of this mechanism is better shown in the ensuing comparative static analysis, which allows ascertaining the effect that urban form exerts on the demand for travel.

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48 Comparative Static Analysis The basic theoretical implications of Model I can be explored by employing comparative static analysis. Th is section considers the impact of changes in exogenous density, and exogenous re sidential location, on travel demand, TD Basically, starting from an equilibrium state, the impacts of an increase in density and residential location on the initial equilibrium are determined. The objective is to see what happens to transit demand as density levels change (for additi onal details on assumpti ons and derivation of the comparative statics, see Appendix A). Effects of an Increase in Density, D The effect of an increase in densit y on travel demand is obtained as (3.4) where subscripts denote a partial differentiati on of the subscripted variable with respect to the variable abbreviated by the subscript. The product gives the increase in transit demand caused by a contracti on in the activity space as a result of increased density. The product gives the increase in transit demand caused by decreasing trip chaining as a result of increased density Based on an assumed relationship between sp atial dispersion of activities and trip chaining, the result of this an alysis shows that changes in density levels exert two contrasting effects on the demand for transit trips.

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49 This explanation is inherent in the dete rminants of trip chaining behavior. In higher density environments, as the spatial extent of non-work activities reduces, trip chaining needs decrease, but indi vidual trips increase and in dividuals prefer to make nonchained trips. First, increased density redu ces the activity space, which directly increases the demand for non-chained trips. Second, incr eased density reduces the activity space, which reduces the need to chain trips (as ti me-saving opportunities decrease) and thus the demand for transit trips. Change in Residential Location, RL Next, we derive the comparative statics of an increase in residential location, RL Note that RL is considered as predetermined in Mode l I. The question to be answered is: “What happens to transit demand as the jobresidence pair changes?” Using cross sectional data, this question can be translated as: “How does transit demand differ for those households facing long comm utes from those making short commutes?” The comparative static result describing the impact of a change in residential location on the demand for transit trips is (3.5) As previously discussed, an increase in re sidential location incr eases trip chaining ( ), which in turn positively affects both the size of the activity space, AS and the demand for transit services. The overall effect on transit demand hinges on the sign of To the extent that an urban area is we ll served by transit, then the relationship between transit demand and residential locati on is positive. A positive relationship is ob-

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50 served in older, more monocen tric cities, where existing tr ansit services support commuting. On the other hand, if s upply constraints exist, trans it demand declines as the jobresidence distance increases. Therefore, the overall effe ct on transit demand due to a change in location depends on both the sign and magnitude of Change in Walking Distance to Nearest Station, WD A change in transit station proximity cause s a change in transit demand equivalent to (3.6) The overall effect of an increase in walk ing distance is ambiguous. An increase in distance to the nearest stati on directly reduces transit demand ). At the same time, reduced accessibility impacts and th e ability to engage in trip chaining using transit, producing an ambiguous effect on tr ansit demand. The sign hinges on the relationship between trip chaining and dist ance to the nearest transit station, which is undetermined. On the other hand, th e empirical literature provides unequivocal evidence of a negative relationship between distance to transit stops and the demand for transit services (Cervero 2007; Cervero and Ko ckelman 1997). The debate is mostly centered on the magnitude of this relationship, as high-lighted by the growing body of literature on residential self-selection. Model II: Endogenous Residentia l Location, Exogenous Density In this model, we relax the assumption of exogenous residential location. Treated as a choice variable, residentia l location is the outcome of a trade-off between transporta-

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51 tion and housing costs. Taking into account idiosyncratic pref erences for location, households choose an optimal home-work commute pair, while at the same time optimizing goods consumption and the ensuing non-work travel behavior (optimal non-work trip chaining and activity space). This model is specified as (3.8) (3.9) (3.10) (3.11) where is a vector of contro ls specific to the equation and all other variables are as defined earlier. Comparative Static Analysis The complete comparative statics are pres ented in Appendix B. A discussion of the findings is presented below. Note that the inclusion of th e endogenous residential location equation, RL complicates the computation of th e total partial derivatives. Effects of an Increase in Density, D The effect of an increase in densit y on travel demand is obtained as (3.12) In the long run, the activity sp ace, transit demand, trip chai ning and residential location are all jointly determined. Exogenous changes in density levels theref ore affect all these variables. An increase in density directly contracts the activity space, whereas it indirectly reduces trip chaining and ambiguously a ffects transit demand through its effect on the

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52 activity space. The effect on residential location operates through the effect on transit demand, but that effect is ambiguous. This re nders the effect of density on transit demand ambiguous as well. Comparing equation (3.12) to equation (3.4), we see that the complexity of the relationship between tran sit demand and density increases substantially. Change in Walking Distance to Nearest Station, WD The comparative static effect of a change in transit station proximity on transit demand is (3.12) With endogenous residential location, th e sign, as well as the magnitude of depends on both the sign and magnitude of and all of which are unknown. As in Model I, the effect of WD is ambiguous. Model III: Endogenous Residentia l Location, Endogenous Density In this last extension to Model I, the assumption of exogenous density is relaxed. This model translates the conceptual fram ework of Figure 3.1 into the following analytical model (3.13) (3.12) (3.13) (3.14) (3.15)

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53 In the long run, the simultaneous choice of location and travel decisions is assumed to affect density levels across a give n urban area. This model best describes a long-run equilibrium, in which both location and travel decisions are optimized under constraint. Urban form is tr eated as endogenous to the proces s and is itself affected by household travel decisions and location behavior Aspects of this relationship and its influences on transit patronage have been previ ously considered in th e literature. For example, while modeling long-run transit demand responses to fare changes, Voith (1997) treats density as endogenous and being affected directly by tr ansit patronage levels. In the long run, these levels are affected by supply-side changes. Voith (1997) assumes that as transit services improve, more people tend to live in proximity to transit stations, thus increasing the demand for transit services. Ideally, empirical testing of this model w ould rely on panel data of individual travel diaries. Generally, howeve r, panel data are unavailable and cross-section data are relied on. With cross section data, we can study changes in behavior by controlling for individual heterogeneity. Comparative Static Analysis Given the endogenous treatment of density, we can use this model to test the effects of policies geared at di rectly affecting density, such as policy interventions intended to increase density around transit stat ions. Assuming an exogenous shock, positively affecting density, comparative statics can be obtained. The inclusion of two more equations complicates the calculati ons to derive the relevant co mparative static results. The results are basically the same as Model II, although the expected magnitudes of impacts differ. To avoid cluttering the text, Appendi x A reports the comparative statics results,

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54 which we will use in the empirical work of Chapter 4. Table 3.1 reports a summary of the comparative statics highlighting the expected signs from changes in the most relevant variables affecting trip chaining, TC activity space, AS and transit demand, TD TABLE 3.1 Comparative Static Results Exogenous Variable D RL AS *TC WD Effect on Trip Chaining, TC + + + +/Effect on Activity Space, AS + + +/Effect on Transit Demand, TD + +/+/*Shift parameters affecting AS and TC Conclusions The analytical framework we presented in this chapter seeks to strike a balance between the complexity of activity-based modeling and the more traditional discretechoice frameworks. The added complexity of the models introduced here is intrinsic to the explicit consideration of non-work travel behavior and its interrelationship with the spatial extent of nonwork activities. These analytical models are general and can be applied to data from any urban area. Empirical testing of the hypotheses of these models requires detailed travel behavior data at the individual le vel. The increased level of sophistication of activity-based travel diaries allows collecting information on activities conducted at home and out of home, as well as their spatial location. As we shall see, the cont ribution of geographic information system (GIS) modeling permits the measurement of the geographic dimension of both activities and trav el and relating them to th e surrounding urban landscape.

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55 Coupling GIS with econometric modeling allo ws conducting empirical tests of the relationships generated by the models of this chapter.

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56 Chapter 4: Empirical Analysis Introduction In this chapter, we test all relevant hypotheses about the re lationship between urban form and transit patronage introdu ced in Chapter 3. The objectives are: 1. to test the signs summarized by Table 3.1; 2. to assess the presence of endogeneity in th e relationship between transit and urban form; and, 3. to assess the magnitude of this relationship. The aim is to ascertain to what extent density matters in shaping the demand for transit, after accounting for any endogeneity or simultaneity that might be present. To test these hypotheses, we rely on a dataset that provides travel behavior information at the disaggregate level. First, we provide descriptive statistics for the models’ dependent and independent variables. Then, we proceed to specify Model I through Model III and choose the appropriate multivariate regression method. We finally present the results of regression at the end of the chapter. Data Sources To test the models presented in the previ ous chapter, we must rely on travel-diary data. Travel diaries ask respondents to compile a log of activities and travel made during a selected time frame, usually one or tw o days, encompassing both weekday and weekend travel. In these survey s, respondents log in info rmation on activities by purpose

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57 (work, recreation, shopping, etc.). The new gene ration of activity-based travel surveys is characterized by travel diaries that provide a high level of activity detail, both at home and out-of-home, to obtain a comprehensive pict ure of all behavioral aspects at the individual and household levels affecting travel decisions. The main advantage of these new type of surveys, as highlighted by Davidson et al. (2007), is that th ey are based on tour structure of travel, with travel derived with in a general framework of the daily activities undertaken by households and persons. In this study, we use trav el-diary data from the 2000 Bay Area Travel Survey (BATS2000). BATS2000 is a large-scale regi onal household travel survey conducted in the nine-county San Francisco Bay Area of California by the Metropo litan Transportation Commission (MTC). Completed in the spring of 2001, BATS2000 pr ovides consistent and rich information on travel behavior of 15,064 households with 2,504 households that make regular use of transit.1 BATS2000 used the latest app lications of activity and timebased survey instruments to study travel be havior. The data from BATS2000 are accessible online and maintained as a set of relational data files and are available as commaseparated value (CSV) and American Standa rd Code for Information Interchange (ASCII) text files (MTC 2008). Each data file ha s a corresponding statistical analysis system (SAS) script to read the data file and act as the data dictionary for the data file (MTC 2007). In the dataset, 99.9 percent of home addresses and 80 percent of out-of-home activities were geocoded using geographic inform ation systems (GIS) to the street address or street intersection level (99.5 percent to th e street address level). This permits a precise geographic determination of non-work act ivities, job, and residential unit locations. 1MTC defines a transit household as one where one or more members used transit at least once during the two-day surveying period.

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58 The choice of this dataset goes beyond its qua lity. Most of the relevant academic and practitioner work on the re lationship between transit and urban form, research on the issue of residential self-sel ection, and the efficacy of tran sit-oriented development policies (TOD) made use of BATS2000. Most of the work we reviewed in Chapter 2 used this dataset. MTC also compiles a list of research papers that made use of the data (Gossen 2005). Our dataset combines BATS2000 travel be havior data with geographical data from the Census Bureau. Census data are from Summary File 3, which consists of detailed tables of social, economic, and housi ng characteristics compiled from a sample of approximately 19 million housing units (about 1 in 6 households) that received the Census 2000 long-form questionnaire ("Census 2000 Summary File 3" 2007). We obtained these data at the Census block-group leve l. Thus, we measur e housing and neighborhood characteristics at the bloc k-group level where the reside ntial unit is located. The unit of observation is the household to reflect the higher hierarchical decision making process of both residen tial location and travel needs. Referring to MTC work on transit use and station proxim ity (MTC 2006), a transit household is defined as one where one or more members used transit at leas t once during the two-day surveying period. Dependent Variables Des criptive Statistics While in Chapter 3 we defined activity space, AS residential location, RL trip chaining, TC walking distance to the nearest station (i.e., station proximity), WD and density, D we now provide some additional explanation on their measurement.

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59 Measures of Activity Space, AS Activity space measures the spatial disp ersion of non-work activity locations. Non-work activities consist of shopping, recr eational activities (e.g. visiting friends or dining out), and non-recreational activities (doctor visits, child rear ing, recurring activities). These activities can be located in proximity to the hous ehold residential unit or be located away from it. To measure the spatia l extent of these activities across the urban landscape, we employ area-based geometric m easures developed in transportation geography. Different metrics that describe the spatial extent of activity locations can be employed. The simplest measure is represented by the standard distan ce circle (SDC) (or standard distance deviation), which is essent ially a bivariate extension of the standard deviation of a univariate distri bution. It measures the standa rd distance deviation from a mean geographic center and is computed as (4.1) where and represent the spatial co ordinates of the mean cen ter of non-work activities at the household level, and the i subscript indicates the coor dinates of each non-work activity. The mean activity center is analogous to the sample mean of a dataset, and it represents the sample mean of the x and y coordinates of non-work activities contained in each household activity set. The coordinate s represent longitude and latitude measurement of each activity and are reported in me ters following the Universal Transverse Mercator (UTM) coordinate system Household activity locations are those visited by surveyed household members during a specified time interval, in this ca se two representative weekdays. Thus, the standard distance of a household’s activity pattern is estimated as the standard deviation (in meters or kilome ters) of each activity location from the mean

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60 center of the complete daily activity pattern. Interpretation is relatively straightforward, with a larger standard distance indicating gr eater spatial dispersion of activity locations. The area of the SDC is the area of a circle with a radius equal to the standard distance. The SDC provides a summary dispersion measure that can be used to explore systematic variations of activities subject to socio-demographic, travel patterns, and patterns of landuse. As pointed out by Ebdon (1977), this measur e is affected by the presence of outliers or activities that are located farthest from the mean center. As a result of the squaring of all the distances from the mean center, the extreme points have a disproportionate influence on the value of the standard distance. To elim inate dependency from spatial outliers, another measure of dispersion, called the standard deviati onal ellipse (SDE) is usually employed, which uses an ellipse instead of a circle. The advantages of the SDE with respect to the SDC have been discusse d in the literature (Ebdon 1977). In addition to control for outliers, the SDE also allows accounting for directiona l bias of activities with respect to their mean center. The ellips e is centered on the mean center with the major axis in the direction of maximum activity dispersion and its minor axis in the direction of minimum dispersion (See Figure 4.1). In this study, we employ the standard distance ellipse ( SDE ), using the formula described in Levine (2005) (4.2) where and represent the length of the major a nd minor axes of the ellipse.

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61 FIGURE 4.1 Standard Distance Circle and Standard Distance Ellipse Measures of Residential Location, RL We define residential location as the average distance of household employment activities to the household residential unit (4.3) where is the Euclidean distance to the residential unit located at j from a household member work location m and k is the total number of employed household members. An alternative specification only considers the distance between the household head’s work location and the residential unit. This assumes that the residential location choice puts more relevance to the location of the household “breadwinner,” as discussed in detail later in this chapter. Activities Mean Center SD Minor Axis Major Axis SDE Y X Y X

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62 Measures of Transit Station Proximity, WD In this study, we treat tr ansit proximity as a continuous variable measuring distance to the nearest transit station from the household re sidential unit. A 2006 publication from MTC made use of BATS2000 data to look at the relations hip between transit use, population density, and characteristics of individuals living n ear transit stations (MTC 2006). An appendix to this study was recently published on the MTC website which reports an updated version of the house hold file containing an additional variable measuring network walking distance from each household residential unit to the nearest transit station (Purvis 2008). Using this file, we measure wa lking distance as actual distance based on network characteristics to take into consideration the existence of accessibility impediments. Measures of Density, D We measure the dependent variable density, D as gross population density of the Census block group in which the household re sidential unit is located. The Census block-group area is measured in square miles. As discussed in Chapter 2, other studies on transit and urban form tend to utilize numbe r of dwelling units per square mile. We also consider additional urban form measures, initially treated as exogenous to the model, which we describe under the exogenous variable section of this chapter. Table 4.1 presents basic descriptive statis tics of the dependent variables, split by different gross population density levels corresponding to th e classification adopted by MTC to differentiate between urbanized and non-urbanized areas. As documented in Chapter 2, there exists an underlying correlati on between density levels and travel behavior. This table shows how the activity space is sli ghtly larger for transit households than

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63 for non-transit households (19.1 versus 17.2 squa re miles) and contracts as density increases, while trip chaining does not follow th is linear relationship. Walking distance to the nearest station noticeably de creases at higher density leve ls. To highlight the relevance of transit patronage, Table 4.2 compares sa mple transit trip aver ages to auto, walk and other trips. This table shows marked di fferences in terms of trip making and trip chaining behavior between tran sit and non-transit households, as well as in average travel times between home and work between tran sit and non-transit hous eholds (51.9 minutes versus 37.4 minutes). Explanatory Variables De scriptive Statistics Socio-Demographic Variables We treat the following socio-demographic variables as exoge nous explanatory variables: Household characteristics Householder gender Householder race Number of children of school age Number of persons employed full-time Household income Number of vehicles Number of licensed individuals Tenure (own versus rent) These variables are available from the BA TS2000 person file. Some of these socio-demographic variables have been included in the studies reviewed in Chapter 3 dealing with the influence of land use on transit patronage, while the most current literature

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64 TABLE 4.1 Descriptive Statisti cs: Overall Sample Means Density (persons/mile2) Activity Space (mile2) Residential Location, RL (miles) Residential Location, RL (min) Trip Chaining, TC (number) Transit Trips (number) Auto Trips (number) Walk Trips (number) Walking Distance, WD (mile) 0 to 499 27.84 14.12 43.40 2.96 0.14 9.00 0.50 2.33 500 to 5,999 19.31 11.82 40.97 3.04 0.27 8.78 0.72 0.45 6,000 to 9,999 15.69 10.02 38.70 2.98 0.29 8.40 0.80 0.23 >=10,000 13.70 8.56 39.41 3.01 0.73 5.98 1.33 0.14 Data Source: 2000 Bay Area Travel Survey (BATS2000) and 2000 Census Summary File 3, Census Bureau

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65 TABLE 4.2 Descriptive Statis tics: Sample Means of Dependent Vari ables and Selected Trip Measures Transit Household Gross Population Density (persons/mile2) Household Activity Space (mile2) Residential Location, RL (miles) Residential Location, RL (min) Trip Chaining, TC (number) Transit Trips (number) Auto Trips (number) Walk Trips (number) Walking Distance, WD (mile) No Mea n 7,910.51 17.16 10.33 37.36 2.87 8.32 0.73 0.49 SD 8,752.95 38.40 10.07 33.32 1.77 6.14 1.62 1.44 N 12,260 10,548 9,128 8,353 11,242 12,260 12,260 12,260 12,260 Yes Mea n 15,172.65 19.14 11.58 51.92 3.65 2.32 5.96 1.70 0.22 SD 17,193.12 37.84 9.76 35.35 1.73 1.29 5.77 2.38 0.38 N 2,503 2,176 2,138 1,918 2,446 2,503 2,503 2,503 2,503 Overall Sample Mea n 9,141.78 17.50 10.57 40.08 3.01 0.39 7.92 0.89 0.45 SD 11,006.88 38.31 10.03 34.18 1.79 1.02 6.14 1.81 1.33 N 14,763 12,724 11,266 10,271 13,688 14,763 14,763 14,763 14,763 Data Source: 2000 Bay Area Travel Survey (BATS2000) and 2000 Census Summary File 3, Census Bureau

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66 on self-selection considers al l of them. Table 4.3 provides a summary of these variables for the overall sample. As with the vast majority of travel survey, the white population is overly represented, as well as the higher income groups. Travel Behavior Variables We also created additional explanatory variables at the household level to control for factors affecting both the sp atial extent of nonwork activities and the ensuing travel behavior: Activity travel time o mean travel time to shopping trips starting at home o mean travel time to recreational trips starting at home o mean travel time to school trips starting at home o mean travel time to other trips not starting at home o mean travel time across all non-work activities Activity duration o mean time duration acro ss all non-work activities These variables are commonly used in th e activity-based literature in modeling activity duration and schedu ling (Bhat 1997, 1999, 2001) and ac tivity travel patterns (Kuppam and Pendyala 2001). Transit households spend less time shopping compared to non-transit households (28.9.0 ve rsus 30.3 minutes), they also spend less time on recreational activities (161.9 versus 175.9 minutes) and at home (181.8 versus 210.1 minutes). The time spent travelling to reach out-of-home activities also differs, with transit households spending an average of 15.7 minutes on the road versus 12.9 minutes for nontransit households. The trade-off between leis ure and work is also reflected in less time spent sleeping (243.6 versus 249.6 minutes for non-transit households). These time-use

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67 variations and the comparison between tran sit and non-transit hous eholds provided in Table 4.2 are indicative of the trade-offs inherent to total time available, residential location, and trip-chaining behavior discussed in Chapter 3. Urban Form Variables Although BATS2000 does not include land-us e variables, it provides exact geographical information about the location of each of the 15,064 households. GIS coordinates permit a precise allocation of each hous ehold residential unit within each Census Bureau geographical unit of reference usi ng GIS techniques. By linking each households’ residential unit x and y geographic coordinates to GI S Census block-group maps of the San Francisco Bay area, we merged a co mprehensive set of la nd-use variables with the travel diary dataset.2 We obtained other variables re lated to non-residential land use from the 2000 U.S. Census Bureau County Busi ness Patterns (CBP) data file. Table 4.4 describes these variables and data sources. We intend to use the last two variables of Table 4.4 as proxy measures of centrality (CBD distance) and polycentricity (dista nce from the nearest subcenter). As mentioned in Chapter 3, monocentric models only co nsider measures of the strength of the relationship between CBD empl oyment (and other activities located at the CBD) and travel behavior. 2 Detailed GIS maps and other geographical data are available online at the MTC website .

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68 TABLE 4.3 Summary of Select ed Demographic Variables Variables Frequency % Share Householder Gender Male 6,901 45.8% Female 8,163 54.2% Householder Race Asian 1,223 8.1% Black 442 2.9% Hispanic 647 4.3% Other 674 4.5% White 12,078 80.2% Children, by age group < 6 year 1,539 10.2% 6 to 11 year 1,973 13.1% 12 to 18 year 2,202 14.6% Employed, Full Time (persons) 0 876 7.0% 1 7,214 57.8% 2 4,063 32.5% >=3 335 2.7% Household Income ($) Less than 10,000 225 1.7% 10,000 to 14,999 230 1.7% 15,000 to 19,999 322 2.4% 20,000 to 24,999 368 2.8% 25,000 to 29,999 464 3.5% 30,000 to 34,999 424 3.2% 35,000 to 39,999 514 3.9% 40,000 to 44,999 756 5.7% 45,000 to 49,999 833 6.3% 50,000 to 59,999 1,352 10.2% 60,000 to 74,999 1,660 12.6% 75,000 to 99,999 2,359 17.9% 100,000 to 124,999 1,620 12.3% 125,000 to 149,999 804 6.1% >= 150,000 1,260 9.6% Vehicles 0 610 4.0% 1 4,938 32.8% 2 6,542 43.4% 3 2,238 14.9% >=4 736 4.9% Tenure Own 10,415 69.4% Rent 4,597 30.6%

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69 TABLE 4.4 Urban Form Variables Variable Definition Source Gross population density Number of persons/Census block group area size (square miles) U.S Census Bureau Summary File 3 Dwelling units Number of owner occupied units U.S Census Bureau Summary File 3 Dwelling density Number of owner occupied units/ Census block group area size (square miles) U.S Census Bureau Summary File 3 Number of retail establishments Total number of retail establishments within a zip code U.S Census County Business Patterns: 2000 Retail establishment density Total number of retail establishments/zip code area U.S Census County Business Patterns: 2000 Number of wholesale establishments Total number of retail establishments within a zip code U.S Census County Business Patterns: 2000 Wholesale establishment density Total number of wholesale establishments/zip code area U.S Census County Business Patterns: 2000 Distance from CBD Distance from CBD BATS2000-GIS derived Distance from subcenter Distance from the nearest subcenter BATS2000-GIS derived Through decades of decentralization, the urban landscape has ta ken a polycentric form, with a number of clustered employment centers affecting both employment and population distributions. The majority of thes e centers is subsidiary to an older CBD. Such centers are usually called subcenters or sub-regional centers (a more formal definition of subcenter is a set of contiguous tracts with signi ficantly higher employment densities than surrounding areas). The transportati on includes few studies of the influence of subcenters on travel behavior. One such study is Cervero and Wu (1998), who have examined the influence of subcenters in th e San Francisco Bay Area on commute distances

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70 to conclude that employment decentralization ha s lead to increased travel. Studies treating subcenters generally take subcenters as exogenously determined either by assumption or by an empirical determination that makes us e of specific density th resholds. There are no established methods to determine the number of subcenters present in any urban area. Existing methods rely on rules of thumb based on knowledge about specific geographic areas (Giuliano and Small 1991), while others account for an endogenous determination based on their impact on agglomerati on and employment (McMillen 2001). To account for urban decentralization and its effect on transit use, we adopt the Census definition of cities and designated pl aces to first identify subcenters and then produce a distance measure between a household residential unit and th e nearest subcenter.3 In addition to the above variables, we obtaine d a set of explanatory variables to control for household idiosyncratic preferences for loca tion. The literature provides some insight on the choice of land-use variables as contro ls or instrumental variables (Boarnet and Crane 2001; Boarnet and Sarmiento 1998; Crane 2000; Crane and Crepeau 1998b). Using the Summary 3 Census Bureau file we obtained the following variables at the block-group level: 1. Stock of housing built before 1945 (number of housing units) 2. Housing median value (dolla rs; owner-occupied units) 3. Housing median age (years; non-rent units) 4. Housing size (median number of rooms; owner-occupied units) 5. House median monthly cost (owner-occupied units) 3 According to the U.S. Census, a city is a type of incorporated place. A census designated place is a statistical entity consisting of a densely settled con centration of population that is not within an incorporated place, but is locally defined by a name.

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71 6. Percent of household li ving below poverty line 7. Diversity index (0 = homogeneous ; 1 = heterogeneous neighborhood) The first variable has been used before as an instrumental variable in multivariate regression studies that consider ed travel behavior as endogen ous to urban form (Boarnet and Crane 2001; Boarnet and Sarmiento 1998; Crane 2000; Crane and Crepeau 1998b), while the remaining ones are unique to this study. Additional cont rols for neighborhood characteristics have also been used elsewh ere. For example, the proportion of blockgroup or census-tract population that is Bl ack and the proportion Hispanic have been used as instruments by Boarnet and Sarmient o (1998) and the percen t of foreigners by Vance and Hedel (2007). In this study we use variables one through five to control for idiosyncratic preferences for housing characteristic s not directly affecting travel behavior but directly affecting the residential choice decision at the house hold level. We use variables six and seven as controls for neighborhood characteristics. In particular, the per centage of households living below poverty levels (henceforth defined as poverty) serves as a proxy for crime, while the diversity index (henceforth called di versity) is used as a proxy for ethnic preferences (i.e., moving into a nei ghborhood with similar ethnic charac teristics). The latter is an index of ethnic heterogeneity that varies from zero (only one race living in the neighborhood) to one (no race is prevalent), sim ilar to Shannon’s diversity index (Begon and Towsend 1996).4 As discussed in further detail in Chapter 5, poverty and diversity serve 4 The Shannon Index is a measurement used to compare diversity between habitat samples. The comparison is made by taking into account the proportion of individuals of a given species to the total number of individuals in the set.

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72 a dual role as instrumental variables wh en we treat transit station proximity, WD endogenous to the model. Table 4.5 and Table 4.6 present relevant sa mple mean values split by households by mode choice. Transit households tend to live in highly populated areas characterized by higher than average poverty levels, as well as sma ller and older housing units. We also generated one-way analysis of variance tables (not repor ted here) that include an interaction term between transi t household and the transit sta tion dummy variable. All variables exhibit a significant difference in means, indicating that housing price, housing age, room size, neighborhood diversity and poverty levels differ across households according to their location and m ode choice. To gain additiona l insight on the trade-off between residential loca tion and preference for transit, Table 4.7 a nd Table 4.8 report the same measures of Table 4.5 and Table 4.6, but differentiate between households living in proximity to a transit stati on. We measure proximity using a Euclidean half-mile buffer around a transit rail line in existence when the BATS2000 travel survey was being conducted. Transit Supply Variables We include the following m easures of transit supply: Presence of a transit stop at workplace Supply of park-and-ride within a half-mile of transit stop Presence of a transit-oriented developm ent (TOD) stop within a half-mile of residential unit

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73 TABLE 4.5 Urban Form Variables by Household Type Transit Household Gross Population Density (persons/mile2) Dwelling density (dwellings/mile2) Retail Establishments Density (number/mile2) Wholesale Establishment Density (number/mile2) No 7,911 3,313 18.4 6.9 Yes 15,173 7,198 43.1 12.6 Overall 9,144 3,974 22.5 7.9 TABLE 4.6 Housing and Demographi c Variables by Household Type Transit Household House Median Value ($) House Median Age (years) Housing Stock (% built before 1949) Housing Size (rooms) Households Median Income Households Below Poverty Diversity Index No 399,819 34.18 0.20 5.97 74,189.52 0.06 0.57 Yes 399,374 41.77 0.36 5.92 67,140.84 0.08 0.62 Overall 399,591 35.47 0.23 5.92 72,994.44 0.06 0.58

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74 TABLE 4.7 Urban Form Variables by Transit-Station Proximity Within 1/2 mile of Transit Station Gross Population Density Dwelling density (dwellings/mile2) Retail Establishments Density (number/mile2) Wholesale Establishment Density (number/mile2) No 7,313.8 2,939.2 14.8 5.7 Yes 19,871.4 10,039.7 67.6 20.8 Overall 9,144.4 3,974.3 22.5 7.9 TABLE 4.8 Urban Form Variables by Transit-Station Proximity Within 1/2 mile of Transit Station House Median Value ($) House Median Age (years) Housing Stock (% built before 1949) Housing Size (rooms) Households Median Income Households Below Poverty Diversity Index No 396,509.6 33.6 18.6% 6.0 75,050.4 5.4% 0.57 Yes 417,647.7 46.3 46.4% 5.2 60,501.5 8.9% 0.64 Overall 399,591.1 35.5 22.6% 5.9 72,994.4 5.9% 0.58

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75 The relevance of transit station proximity to the workplace is confirmed by the literature, as seen in Chapte r 3. For example, using BATS2000, Cervero (2007) showed that the presence of a stati on within one mile of a wo rkplace (with good accessibility) strongly influences both reside ntial choice decisions and tran sit use. The relationship gets stronger as distance to the station declines. The presence of park-and-ride lots nearby transit stops also positively influences transit ridership by improving acce ssibility to those households located farther than the one-mile threshold. Furthermore, as high lighted by TCRP Report 95 (2007), the presence of park-and-ride lots pr ovides increases oppor tunities to trip chain from the residence to the transit station on the way to work The relevance of park-and-ride lots is measured by a dichotomous variable indicating the presence of a park-and-ride lot within a half-mile of a transit stop. To produce thes e transit-supply explan atory variables, the same GIS maps created by MTC as part of th eir transit station proximity study were used (MTC 2008) (a detailed discussion of the GIS methodology is provide d in Appendix G of the MTC study). Finally, to test the relevance of urban design policies on transit patronage, we introduce in the model a dichotomous variable qualifying a transit stop as having the characteristics of a TOD station. TOD stops are characterized by la nd development policies geared at facilitating transit use by improvi ng transit station accessibility (by reducing physical barriers), and by promoting mixe d land-use development (residential and commercial) in their immediate surroundings. For example Cervero (2007) used BATS2000 and census land-use data to evaluate transi t-oriented development (TOD) impacts on ridership and self-selection. In his analysis, he notes that between 1998 and 2002 about

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76 13,500 apartment and condominium units were bu ilt within a half-mile of urban stations of southern California and the San Francisco Bay Area, often using la nd previously occupied by park-and-ride lots; this makes the data set suitable to also test the impact of TOD on ridership. We relied on the California Depa rtment of Transporta tion Transit-Oriented Database to identify these stations (CALTRANS 2008). Table 4.9 summarizes the full set of e ndogenous and exogenous explanatory variables.

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77 TABLE 4.9 List of Variables for Model Estimation Variable Definition Use inc Household income Socio-demographic sch Number of children of school age (pre-k to middle) Socio-demographic veh Number of vehicles Socio-demographic own Tenure (1 = owner; 0= renter) Socio-demographic licensed Number of persons with driving license Socio-demographic tswork Presence of a transit stop within 0.5 mile of workplace (1=yes, 0=otherwise) Transit supply prkride Presence of a park-and-ride within 0.5 mile of a transit stop (1=yes, 0=otherwise) Transit supply ts_tod Transit stop characterized as transit-oriented development stop (1=yes, 0=otherwise) Transit supply cbd_dist Residential unit distance from CBD Urban form/land use subc_dist Residential unit distance from nearest subcenter (cities and designated places) Urban form/land use r_est Number of retail establishments, zip code level Urban form/land use mix w_est Number of wholesale establishments, zip code level Urban form/land use mix hprice Median house price, block group level Residential/neighborhood characteristics hage Median house age, block group level Residential/neighborhood characteristics room Median number of rooms owner occupied unit, block group level Residential/neighborhood characteristics inc_blkgrp Median household income, block group level Residential/neighborhood characteristics pov Proportion of households living below poverty line, block group level Residential/neighborhood characteristics div Diversity index (ranges from 0 if block group level is ethnically homogenous to 1 if heterogeneous) Residential/neighborhood characteristics act_dur Mean non-work activity duration Travel behavior act_tt Mean travel time to non-work activities Travel behavior TC Trip chain; number of non-work trip stops on the jobresidence commute Trip chaining behavior AS Household activity space; standard distance ellipse area (mile2) Spatial extent of nonwork activities RL Residential location (home-work distance) Household residential location WD Walking distance from the residential unit to the nearest transit station Transit station proximity D Gross population density (persons/mile2) Urban Form

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78 Method of Analysis Given the structural framework of Chapte r 3, the empirical test of the proposed hypotheses requires the use of st ructural equation modeling (SEM ). SEM is used to capture the causal influences of the exogenous variables on the endogenous variables and the causal influences of the e ndogenous variables upon one another. The use of SEM in transportation research is linked to the development of activity-based modeling in travel behavior research, which explicitly points out the causal mechanisms underlying individuals’ location and travel decisions. Furthermor e, more recent developments in the literature studying the efficacy of urban design polic ies dealing with reside ntial sorting effects try to sort out causality links between urba n form and travel behavior. To uncover causality when travel behavior and urban form simultaneously affect each other, requires suitable econometric techniques. As the litera ture review of Chapte r 2 highlighted, it is only recently that transporta tion researchers have recognized that causal relationships among travel behavior and urban form can be ef fectively represented in a structural equation framework (Cao, Mokhtarian, and Handy 2006, 2007; Guevara and Moshe 2006; Mokhtarian and Cao 2008; Peng et al. 1997). Available methods include maximum likelihood estimation (ML), generalized least square s (GLS), two-stage least squares (2SLS), three-stage least squares (3SLS), and asympt otically distributionfree estimation (ADF). Before proceeding with the estimation, it is necessary to ensure that the model is identified. We subject each of the three mode ls presented in Chapter 3 to the rank condition for identification prior to estimation. Detailed rank c onditions are reported in Appendix B. We also discuss the inclusion and exclusion of relevant explanatory variables for each equation.

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79 Model I Results Using the set of variables summarized in Table 4.7, we specify the first model of Chapter 3 with exogenous residential location, RL and density, D as (4.4) (4.5) (4.6) Equation (4.4) describes trip -chaining behavior occurri ng on the commute trip to and from the work location. Trip chaining, jo intly determined with the activity space, AS is affected by vehicle availability ( veh ) and transit-station proximity, activity travel time and duration ( act_tt and act_dur ), and household structure ( sch ). Vehicle ownership and transit proximity, together with household char acteristics (income and children), affect the capability of engaging in complex tours. Equation (4.5) describes how the spatial ex tent of non-work ac tivities responds to changes in urban form, being affected directly by density levels and retail establishment concentrations ( r_estd ). Drawing from the work of Anas (2007) on trip-chaining behavior and non-work travel, we assume that ac tivity space is a result of utility maximizing behavior determining goods consumption and no n-work travel. As income levels increase, so does the demand for (normal) goods and travel. We assu me that individuals have preferences for heterogeneity in consum ption (convexity of indifference curves indicates preference for balanced consumpti on bundles). As assume d by Anas (2007), in-

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80 dividuals prefer to visit different locations, a behavior that positively affects the size of the activity space. Equation (4.6) describes the demand for tr ansit trips as brought about by the necessity to engage in non-work travel (directly affected by AS and TC ) and by the relative distance of the residential unit to the work location, RL We expect that transit supply directly affects transit ridership in terms of tr ansit station accessibility both at origin and destination. We also wish to test the rele vance of TOD policies in affecting ridership by including the dichotomous variable ts_tod which measures the imp act of a TOD station. All three equations pass the rank condition for identification. Equation (4.4) is overidentified, and equation (4.5) and (4.6) are classified as ju st identified. The results of a three-stage least square regression (3SLS) are displayed in Table 4.10. The results show that the joint determinat ion of trip chaining and the spatial extent of non-work activities relate to transi t patronage as hypothesized in Chapter 3. The presence of a transit stop at workplace ( tswork ) positively affects transit demand, as well as the presence of a TOD transit stop in proximity of the residence unit ( ts_tod ). The size of the activity space reduces as density incr eases, which, in turn, positively affects the demand for transit. This assumption, as stat ed in Chapter 3, relates more compact urban environments to increased transit patronage. As locations where non-work activities are more clustered, the need to engage in long and complex journeys requiring modes other than transit decreases, resulting in increased transit usage. The converse is also true, suggesting that policy interventions related to di rectly affect the clustering of non-work activity locations, such as mixed-land use policies, are likely to signifi cantly affect ridership

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81 levels. However, the relevance of this re lationship is better appr eciated in a context where residential location is also treated as a choice va riable (i.e., endogenous). To better appreciate the magn itude of these effects, Table 4.11 reports point elasticities of transit demand with respect to select ed explanatory variables. For example, to obtain the elasticity of trav el demand with respect to changes in density, we use (4.8) where is from equation (3.4) of Model I. Table 4.11 shows that, for example, a 20percent increase in gross population density, D which is equal to about 1,830 persons per square mile, produces an approximate nine-percent increase in transit demand (linked trips at household level). Transit station proximity also plays a relevant role A doubling of the average walking distance, WD to the nearest transit station, or an in crease from 0.3 miles to 0.6 miles, decreases transit demand by 14 percent; at about one mile, transit demand declines by 28 percent. The presence of a transit station ( tswork ) within a half-mile of the workplace increases transit demand by 69 percent. Living in proximity to a TOD transit station ( tstod ) increases transit de mand by about 28 percent. There seems to be a ridership bonus associated with proximity to a station char acterized by accessibility features intended to promote transit use.

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82 TABLE 4.10 3SLS Regr ession Results—Model I Equation Coefficient Std. Error P Trip chaining, TC RL 0.00960.00400.0160 AS 0.06480.16580.6960 WD -0.05700.01370.0000 veh -0.07930.03080.0100 act_tt 0.00140.00040.0010 act_dur -0.00220.00030.0000 subc_dist 0.04390.00680.0000 sch 0.07780.01440.0000 constant 1.27710.26110.0000 Activity space, AS TC 0.58630.05920.0000 D -0.09740.01210.0000 act_dur 0.00010.00020.6880 inc 0.02990.00500.0000 r_estd -0.00220.00030.0000 constant 1.72260.13510.0000 Transit demand, TD TC 0.65480.07320.0000 AS -0.30020.09200.0010 WD -0.08000.01240.0000 RL 0.00570.00210.0070 tswork 0.38480.04220.0000 prkride -0.07370.05140.1510 ts_tod 0.20630.10970.0600 veh -0.04560.02210.0390 constant -0.1256 0.1014 0.2150 Note: N= 8,229; FT C =49.3; F AS =73.6; FTD=122.1

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83 TABLE 4.11 Elasticity Estimates—Model I Elasticity RL WD D subc_dist r_estd tswork* ts_tod* TC 0.087 -0.007 -0.044 0.109 0.000 AS 0.100 -0.008 -0.066 0.125 0.000 TD -0.157 -0.137 0.475 -0.388 0.001 0.687 0.279 Indicates a proportional change The model reports a negative elastici ty between reside ntial location, ( RL ) and transit use. This is consis tent with the assumption that households characterized by longer commutes engage in more complex trip chains, which positively affect the spatial extent of non-work activities. With exogenously fixed transit supply, as the activity space expands, transit demand declines. The results also show that transit demand is sensitive to the presence of nearby subcenters ( subc_dist ), or, in general, to decentralization. The negative sign associated with the elasticities shows that increased pol ycentricity significantly affects transit demand adversely. The farther a household lives fro m a subcenter, the less it uses transit. A 50-percent increase in distance to a subcente r (from 2.9 to 4.3 mile s) decreases transit demand by about 19.4 percent. This is so b ecause households tend to rely more on other transport modes to carry out more complex trip chains. This result is consistent with the current literature on transit competitiveness and polycentric metropolitan regions. For example, in a study of transit services and d ecentralized centers, Casello (2007) finds that transit improvements between and within activit y centers (i.e., subcenters) are necessary to realize the greatest improvements in transit performance.

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84 Next, we extend Model I to ascertain the extent to which the above relationships are affected by treating residentia l location as a choice variable. Model II Results As discussed in Chapter 3, residential se lf-selection refers to individuals or households preferring certain re sidential locations due to id iosyncratic preferences for travel. In applied work, if re sidential self-selectio n is not accounted for, findings tend to overstate the importance of policies to increase transit use by mixed-used development. To deal with this issue, Model II trea ts residential location as endogenous while retaining density as exogenous. Theoretical co nsiderations inferred in Chapter 3 lead us to specify a model where individuals can loca te anywhere within an urban area, choosing a utility-maximizing job-residence pair. This process is carried out in conjunction with the optimal choice of both consumption and non-work travel. A household optimally located at a distance to work engages in trip-c haining to benefit from time-savings gained by combining errands to and from work. Time savings can either be allocated to a move farther out or to engage in additional non-work travel. We specify Model II as (4.9) (4.10) (4.11) (4.12)

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85 We consider housing characteristics (pricing, age, size) as releva nt factors affecting residential location, as well as neighborhood characteristics (ethnicity, crime). In terms of exclusion restrictions, Equation (4.12 ) assumes that while re sidential location is affected by travel decisions (trip chaini ng and transit use), housing and neighborhood characteristics do not directly affect travel behavior at th e disaggregate level. Other housing-characteristics variables, such as the stock of housing built before 1945, are not included in Equation (4.12) as they serve the same role of those just discussed (beside being highly correlated with pricing and size, thus potentially causing multicollinearity). Equation (4.10) passes the rank condition fo r identification and is classified as just identified. Table 4.12 displays the results of the 3SLS regression.

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86 TABLE 4.12 3SLS Regre ssion Results—Model II Equation Coefficient Std. Err. P Trip chaining, TC RL 0.00960.0118 0.4130 AS 0.07250.1980 0.7140 WD -0.05730.0142 0.0000 veh -0.07860.0316 0.0130 act_tt 0.00140.0005 0.0020 act_m -0.00220.0003 0.0000 subc_dist 0.04350.0070 0.0000 sch 0.07780.0144 0.0000 constant 1.26040.2673 0.0000 Activity space, AS TC 0.23570.0538 0.0000 D -0.08580.0107 0.0000 act_m -0.00070.0002 0.0000 hhinc 0.04120.0045 0.0000 r_estd -0.00140.0003 0.0000 constant 2.09430.1202 0.0000 Transit demand, TD TC 0.69640.0753 0.0000 AS -0.25980.1157 0.0250 WD -0.06690.0127 0.0000 RL -0.00900.0088 0.3110 tswork 0.37160.0446 0.0000 prkride -0.06690.0524 0.2020 ts_tod 0.13040.1147 0.2560 veh -0.03650.0221 0.0990 constant -0.11190.1020 0.2720 Residential location, RL TC 3.73240.5009 0.0000 TD -1.24080.4660 0.0080 hprice -2.81170.2722 0.0000 hage -0.08490.0094 0.0000 rooms 1.12790.1468 0.0000 div -2.63120.7238 0.0000 pov -5.96292.4133 0.0130 own 0.49660.2658 0.0620 constant 39.1808 3.3743 0.0000 Note: N= 8,212; FT C =42.7; F AS =72.5; FTD=118.5;FRL=57.2

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87 The relevant signs and coefficient magnit udes of the first three equations are consistent with those of Model I. Table 4.12 reports a negative sign but statistically insignificant sign of the effect of resi dential location on transit demand This might be due to the transit supply char acteristics where the travel survey was conducted (e.g., fairly well-served commute routes). The parameter does not have a ceteris paribus interpretation as it changes concurrently with th e other endogenous variables. Compared to Model I, changes in activity sp ace negatively affect transit us e. More dispersed activitytravel locations result in reduced transit pa tronage, although this effect is now less important. As with Model I, we produce the releva nt point elasticities, summarized by Table 4.13 (only reporting statistically significant estimates). TABLE 4.13 Elasticity Estimates—Model II Elasticity WD D subc_dist r_estd tswork* TC -0.009-0.0360.108-0.014 AS -0.003-0.0690.041-0.232 TD -0.0280.2690.0650.170 0.766 RL 0.002-0.0270.052-0.017 Indicates a proportional change Compared to Model I, the endogenous tr eatment of residential location reduces the magnitude of the elasticity of travel dema nd with respect to density elasticity by 56 percent. When households can locate anywhere in an urban area and they adjust trip chaining and commuting costs, an exogenous 20-percent increase in density produces a 5.4-percent increase in the dema nd for transit (household linked trips). Transit station

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88 proximity to the workplace, however, increase s in importance. The presence of a transit stop within a half-mile of the workplace incr eases transit demand by about 76 percent. Accounting for self-selection reduces the relevance of trans it-station proximity indicated by an 80-percent decrease in magnitude in its point elasticity estimate with respect to Model I. An increas e from 0.3 to 0.6 miles to the ne arest transit station reduces transit demand by only 2.8 percent as opposed to the 14 percent reduction of Model I. This result shows that self-selection is more relevant than what noted by Cervero (2007), who found that self-selection a ccounts for about 40 percent of transit ridership for individuals residing near a transit station. To understand the reasons for these changes, it is sufficient to look at the specification of Model II. Equation (4.12) assumes households optimally choose residential location and non-work activities, which also opt imally define the sp atial extent of nonwork activities. Households locate their re sidences farther from the job locations, trading lower housing costs against increased commute distance. Trip chaining optimization is part of this trade-off process, which leads to an expansion of the activity space. This in turn reduces the opportun ities to use transit to engage in non-work travel. This behavior is empirically validated by the statistical significance of all housing and neighborhood controls in equation (4.12). Model III Results Up to this point, we have treated urba n form as exogenous. What happens if urban form, as measured by gross population dens ity, is affected by travel decisions? To what extent is the relationship between dens ity and transit in Model I and Model II affected by treating density as endogenous? The following model endogenizes density

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89 (4.13) (4.14) (4.15) (4.16) (4.17) Equation (4.17) treats as endogenous population density at the residential unit location. This model introduces e xogenous variables serving as a proxies for centrality dependence ( cbd_dist ) and for polycentricity ( subc_dist ). Compared to Model I and Model II, the joint endogenous treatmen t of residential location a nd density produces a model whose relevant hypotheses are confirmed. Regarding Equation (4.17) both CBD and s ubcenter distance are statistically significant. The sign of the CBD measure of centrality ( cbd_dist ) is negative as expected. As distance to the CBD or the nearest subcente r increases, density decreases. This finding indicates the spatial attraction of the CBD relative to subcenters even within a polycentric urban area, such as the San Francisco Bay area. The relevance of these two variables is better highlighted by the elasticities presented in Table 4.15. The elasticity of travel dema nd with respect to walking distance is less than that of Model I, but greater (in absolu te terms) than that of Model II. An increase from 0.3 to

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90 0.6 miles to the nearest transi t station reduces transit dema nd by 9 percent, compared to the 14-percent reduction of Mode l I and 2.4-percent reduction of Model II. The presence of a transit stop at the workplace almost doubl es the demand for transit, substantially increasing the importance of that variable in this model as compared to the others. The sign and statistical significance asso ciated with the centrality measure ( cbd_dist ) confirms the relevance of the CBD as a generator of transit ridership. Treating density endogenously results in a more elastic travel demand with respect to distance to the nearest transit center. It is relevant to note that both cbd_dist and subc_dist appear as explanatory variables but are tr eated as endogenous in the mode l. An initial specification treated these two variables as exogenous, but overidentificat ion tests (discussed in the next chapter) revealed that this treatment le d to weak instruments (a problem leading to inconsistent estimates). The exogenous treatment of subcenters assu mes that they directly affect density, D without being affected by its changes. Th e literature on the formation of subcenters demonstrates that the exogenous treatment of subcenters presents problems related to their identification and to the role they play in aff ecting both employment and population density. Recent studies show that the form ation of subcenters is endogenous to the process leading to urban development (i.e., s ubcenters are endogenous to changes in density) (McMillen 2001). Thus this study treats them as endogenous.

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91 TABLE 4.14 3SLS Regre ssion Results—Model III Equation Coefficient Std.Error P Trip chaining, TC RL 0.07770.0158 0.0000 AS 1.00870.2241 0.0000 WD -0.66260.0554 0.0000 veh -0.02920.0316 0.3570 act_tt -0.00090.0005 0.0560 act_m -0.00040.0003 0.2650 subc_dist 0.18750.0317 0.0000 sch 0.05700.0132 0.0000 constant -2.93690.3204 0.0000 Activity space, AS TC 0.53890.0654 0.0000 D -0.28170.0002 0.0000 act_m 0.00000.0050 0.8390 hhinc 0.01820.0316 0.0000 r_estd -0.00180.0010 0.0000 constant 3.51090.2583 0.0790 Transit demand, TD TC 0.23100.0782 0.0030 AS 0.21300.1103 0.0540 WD -0.47400.0405 0.0000 RL 0.01620.0089 0.0700 tswork 0.44630.0414 0.0000 prkride -0.07880.0457 0.0840 ts_tod 0.12800.0995 0.1980 veh -0.06410.0204 0.0020 constant -1.31140.1379 0.0000 Residential location, RL TC 2.46950.4889 0.0000 TD 1.16770.4700 0.0130 hprice -2.79300.2491 0.0000 hage -0.09610.0080 0.0000 rooms 1.34320.1071 0.0000 div -6.19040.5571 0.0000 pov -4.50751.6515 0.0060 own 1.37800.1901 0.0000 constant 40.31053.0969 0.0000 Density, D RL -0.00910.0108 0.4000 AS -0.53330.0710 0.0000 cbd_dist -0.04010.0016 0.0000 subc_dist -0.07070.0301 0.0190 constant 11.7688 0.1800 0.0000 Note: N= 8,212; T C 2=2,512.8; AS 2=611.2; 2 TD=1,712.7; 2 R L=646.3; 2 D =1,448.6

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92 TABLE 4.15 Elasticity Estimates—Model III Elasticity WD subc_dist cbd_dist r_estd tswork* TC -0.067 -0.195 -1.066 0.014 -AS -0.060 -0.088 -0.102 -0.009 -TD -0.093 -0.522 -1.177 -0.366 0.961 RL -0.023 -0.076 -0.301 0.011 -D -0.012 -0.153 -2.972 -0.002 -* Indicates a proportional change The elasticity of transit demand with resp ect to distance to the CBD (– 1.17) is greater in absolute value than the elasticity with respect to distance to the nearest subcenter (– 0.52). In other words tr ansit patronage is more respon sive to a residential location near the CBD than near subcenters. This is probably due to differences in existing transit station locations near the CBD compared to suburban areas. This result is inconsistent with recent findings that found increased tran sit use in better served decentralized urban areas (Brown and Thompson 2008; Thompson and Brown 2006) and empirical findings showing that transit ridership is not a ffected by the CBD (Brown and Nego 2007). Next, we subject the models to post-estimation testing to confirm their statistical validity. We also discuss addi tional factors that could potenti ally affect the validity of results. Post Estimation Analysis The validity of the empirical results hinge s on factors associated with the quality of the data used and the stat istical techniques employed. This section discusses some of the key factors that might affect the result s of the empirical investigation, namely:

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93 Dataset issues o Measurement problems o Scaling Modeling issues o Use of cross-sectional data o Misspecification o Endogeneity not accounted for o Nonlinearities Dataset Issues The travel-behavior dataset relies on the travel-diary information from BATS2000. The geographic coordinates of house holds’ residences and their travel destinations allow the calculations of residential location, RL activity space, AS and other measures, such distance from the household re sidential location to the CBD and the nearest subcenter. Land-use data from the Cens us 2000 Summary File 3 are measured at the block-group level, while data from the Cens us county business patterns survey (CBP) are measured at the zip-code level. The differe nt geographical units can lead to scale measurement issues. Measurement Problems While we measure residential location as home-work distance, we could have considered other measures as well. For exam ple, an alternative is represented by the average commute time between work and home. This measure has the advantage of accounting for spatial characteristics as well as network characteristics (such as street net-

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94 work design and level of servic e). It also represents a meas ure of the opportunity cost of residing at a certain distan ce from work. This measur e can be expressed as (5.1) where is commute length (measured in minutes of travel) to the residential unit located at j from a household member work location m and k is the total number of employed household members. In the models of Chapter 4, residential lo cation is measured by linear distance between work and home using geographical coordi nates of the residen ce and the work location, thus providing a relatively accurate measure. In contrast, measuring residential location by travel time entails using the survey reported travel time, which is subject to measurement error (under or overstatement of actual travel time by the respondents) and unobserved factors related to the time the survey was conducted (unobserved, nonrandom, factors affecting traffic levels dur ing the two-day data collection period). Chapter 3 and Chapter 4 discussed the definition and measurement of activity space, AS and the adoption of the standard dist ance ellipse (SDE) to measure the household spatial dispersion of non-wo rk activities. In choosing SDE, we compared it to the second-best alternative, the st andard distance circle (SDC). As discussed, the advantage of SDE over SDC is the diminished relevance of outliers. Indeed, sample descriptive statistics showed outlier influen ce that could not be eliminated without relevant loss of information. In addition, we normalized SDE using a log transformation. The literature provides additional activity-space measures. For example, while Buliung and Kanaroglou (2006) use SDE, th ey also introduce the household activity space (HAS). HAS is an area-based geom etry that defines a minimum convex polygon

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95 containing activity locations visited by a household during a reference period (i.e., the travel-survey period). The advantage of HAS is that it weights the activity space by the relevance of activities, such as their type (r ecreational, maintenance, etc.) and their relative frequencies. Although HAS reports an accurate geographical measurement of the activity space, Buliung and Re mmel (2008) show that the use of the minimum convex polygon algorithm provides similar results to SDE in terms of behavior al interpretation. Other research shows that the c hoice of an appropriate shape representing an individual’s activity space is highly depende nt on the spatial dist ributions and frequencies of the locations visited by the person in the gi ven time period (Rai et al. 2007). Scaling Issues As described in detail in Chapter 4, land use and urban form are measured at two geographic levels. Gross population density is measured at the Census block-group level. This scale of measurement, besides being th e level that corresponds closely to the neighborhood, is also consistent with the literature and allows co mparison of findings. Retail establishment density, a proxy for land-use mi x (commercial land uses) is measured at the zip-code level, which is a wider geogra phical area. As argued by Boarnet and Crane (2001), this scale is appropriate when investigating the role of non-work travel, as nonwork trips usually involve distances more than a block from the residential unit. Also, in the sample dataset, geocodes coincide with traffic analysis zones (TAZ)5. In this study, retail establishment density dire ctly affects the activity space. As summarized in Table 4.16, the average size of the activity space is mu ch larger than the average size of a cen5 According to the U.S. Census Bureau, a TAZ is a special area delineated by state and/or local transportation officials for tabulating traffic-relate d data, especially journe y-to-work and place-of-work statistics (2008).

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96 sus block group level, while the average size of a zip code is more is approximately the size of the activity space, at least for the household using transit. TABLE 4.16 Land-Area Geographic Measures Transit Household Household Activity Space (mile2) Block Group Area (mile2) Zip Code Area (mile2) No Mean 17.16 2.30 42.88 SD 38.40 10.92 88.66 N 10,548 12,260 12,260 Yes Mean 19.14 0.87 18.37 SD 37.84 4.18 51.33 N 2,176 2,503 2,503 Overall Sample Mean 17.50 2.06 38.72 SD 38.31 10.11 84.02 N 12,724 14,763 14,763 Modeling Issues Post Estimation Tests The models presented above explicitly d eal with endogeneity of urban form and travel by applying simultaneous equation modeli ng. As seen, the first step requires correctly identifying a model. This step generate s models that are either just identified or overidentified, based on the number of exclusi on restrictions applied to each equation (See Appendix B for more details).

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97 Tests of Endogeneity and Overidentification A property of the 3SLS regression is its loss of efficiency if the explanatory variables treated as endogenous are, in fact exogenous, making its use unnecessary when compared to OLS. It is thus useful to test the explanatory variable s suspected to be endogenous to the model. The null hypothesis of the endogeneity test is that an OLS estimator of the same equation would yield consistent estimates; th at is, any endogeneity among the regressors would not have deleterious effects on the OL S estimates. A rejection of the null hypothesis indicates that endogenous regressors' eff ects on the estimates are meaningful, and instrumental variables are required. The test was first proposed by Durbin (1954) and later by Wu (1974) and Hausman (1978). The proced ure to test endogeneity of multiple explanatory variables requires (i ) estimating in reduced form each endogenous variable on all exogenous variables (includi ng those in the structural eq uation and those used as instruments; i.e., the explanatory variable incl uded in the other equatio ns); (ii) adding the estimated error terms back into the structural equation; and, (iii) te sting for the joint significance of these residuals in the structural equation. Joint significance indicates that at least one variable is endogenous to the model. Under the null hypothesis, the test statistic is distributed q 2 (Chi-squared) with q degrees of freedom, where q is the number of regressors specified as endogenous in the orig inal instrumental vari ables regression. The procedures to conduct this test are available in Stata (the statistical package used in this study) using the ivreg2 routine (specifically, by using the command ivendog ) developed by Baum et al. (2007).

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98 Furthermore, after verifying the pres ence of endogeneity, additional tests are needed to confirm the correct choice of the exclusion restrictions characterizing the system of equation. These tests are needed to confirm the proper choice of instruments and to eliminate doubts of a poor model performan ce (bias and inconsistency). The overidentification tests used here ar e conducted by regressing the resi duals from a 3SLS regression on all exogenous variables (both include d exogenous regressors and excluded instruments). Under the null hypothesis that all instruments are uncorrelated with the residuals, a Lagrangean multiplier (LM) statistic of the form NxR2 ( N = number of regressors, while R2 is calculated from the re siduals’ regression), has a la rge sample Chi-squared distribution, r 2, where r is the number of overidentifying restrictions (i.e ., the number of excess instruments). If the hypot hesis is rejected, there is do ubt about the validity of the instrument set; one or more of the instruments do not appear to be correlated with the disturbance process. The Stata procedure reports the Sargan (1958) overidentification test (using the overid command). Finally, when dealing with a relatively large number of exclusion restrictions, a situation encountered in Model III, it has been shown that the power of the overidentification tests is reduced (Baum, Schaffer, and Stillman 2007). Furthermore, there is a need to be able to test subsets of instruments to identify weak ones, which would adversely affect validity of results. In this context, anot her test statistic can be used to test a subset of instruments; the difference-in-Sargan test, or C test. The statistic is computed as the difference between two statistics; one obtained by regression using th e entire set of instruments and a second one obtained with the smaller set of restri ctions (excluding the suspected variables). Under th e null hypothesis that the variab les are proper instruments,

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99 the C -test statistics is distributed k 2with k degrees of freedom equal to the number of suspect instruments being tested. Table 4.17 reports the results of the endoge neity and overidentification tests for the travel demand equation, TD (the same tests and same re sults were obtained for the other equations but are not reported here). The Durbin-Wu-Hausman (DWH) test is numerically equivalent to the standard Hausma n endogeneity test. Re sults across the three models indicate the presence of endogeneit y, confirming the appropriateness of 3SLS versus OLS regression. Model III fails the overidentification test in its initial specification that treated the land-use measures ( cbd_dist subc_dist r_estd ) as exogenous to the system (Sargan test = 24.951; p-value = 0.0030). After their e ndogenous treatment, M odel III passes the overidentification test, as signaled both by the Sargan (7.1540 with p-value of 0.3068) and C tests. Overall, the tests indicate that SEM is an appropriate technique and that the equation specifications of Chapter 4 produce models that also pass the overi dentification tests. The validity of the models allows making conc lusions regarding the parameters of interest. Other Issues The use of SEM is best exploited in the c ontext of panel datasets, which are better suited to uncover underlying causali ty among the relationships of interest. In the transportation literature there exist several appli cations of SEM using cross-sectional data. For example, Pendyala (1998) uses SEM to inve stigate the homogeneity of causal travel behavior across a population of interest; Fuji and Kitamura (2000) and Golob (2000) de-

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100 velop models of trip generation developing m odels of activity durat ion and trip generation. Additional examples of applications of SEM using cross-secti onal datasets are discussed by Golob (2003). TABLE 4.17 Endogeneity and Overidentification Tests Test Model I Model II Model III Wu-Hausman F test 78.07383.369 13.000 p-value 0.0000.000 0.000 Durbin-Wu-Hausman 2 test 153.423243.059 90.217 2 p-value 0.0000.000 0.000 Anderson canon. corr. LR statistic (identification/IV relevance test): 42.13727.137 33.524 2 p-value 0.0000.003 0.000 Sargan statistic (overide ntification test of all instruments): 9.63811.365 24.951 2 p-value 0.0570.252 0.003 Sargan statistic without suspect instruments* 7.154 2 p-value 0.307 C statistic (exogeneity /orthogonality of suspect instruments)** 17.798 2 p-value 0.001 Test conducted after endogenous trea tment of: cbd_dist, subc_dist, r_estd ** Test conducted on exclus ion of instruments: cb d_dist, subc_dist, r_estd The models of this study require a subs tantial amount of information, not only in terms of travel behavior data from travel di aries, but also on the sp atial location of residences, work, and non-work activities. The increased sophistication of communicat ion systems that can easily track individuals’ travel patterns in space and time ma kes the data-collection effort less daunting than otherwise, allowing increased used of sophisticated models, such as the ones developed in this study. For example, the recent uses of GPS tracking devices reveals that

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101 human behavior results in optimized patterns of travel based on socio-demographic characteristics. These methods not only allow tracking travel and nonwork activity locations, they also provide more accurate measures of travel itself, such as actual travel-time speed based on network characteristics. Transit-Station Proximity Notwithstanding the validity of the above post-estimation tests, there still exists the possibility of endogeneity of some of the exogenous variables. This endogeneity, although confuted by statistical tests, is not ru led out by theoretical assumptions. For example, while this study treats vehicle ownershi p as exogenous and not directly influenced by the location decision, the litera ture contains studies that co nsider vehicle ownership as a discrete-choice variable endogenous to the residential location process and to density levels. One extension of this dissertation might include an endogenous treatment of this variable, while overcoming the limitations im posed by ad-hoc choice -set specifications. Endogeneity also extends to transit supply measures. For example, measures of supply, such as the number of tr ansit stations and frequency of service are treated as exogenous to the model. As discussed in se veral places throughout this dissertation, the implications of treating a va riable as exogenous, while bei ng endogenous to the process, are not trivial. An additional consideration must be made regarding the use of walking distance as a measure of transit-station proximity that cannot be made when using the more traditional half-mile buffer. As density increases, the number of transit stops at the geographical unit (i.e., block group) increases. This reduces the average distance from any given household to its nearest trans it station independently of lo cation preferences. Further-

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102 more, as shown in Figure 4.2, in densely populat ed areas, stations are located in neighborhoods characterized by higher than average poverty levels and that are increasingly diverse (i.e., characterized by ethnic minorities). In other words, in higher urban density settings, a supply-side spatial bias is presen t and correlated with relevant instrumental variables that control for nei ghborhood characteristics. For this reason, Model III, which endogenously treats residential location and de nsity, considers walking distance as endogenous. FIGURE 4.2 Poverty and Tr ansit-Station Proximity 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 to 499500 to 5,9996,000 to 9,999>=10,000Poverty (% households in poverty) Transit Station Proximity (miles)Density (persons/mile2) Transit Station Proximity (miles) Poverty (% households in poverty)

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103 Implications The models of Chapter 3 are innovative in many aspects, above all for its explicit incorporation of the links between consump tion, travel, the spatial location of non-work activities, and the en suing interrelationship with the surrounding built environment. The empirical application of the behavior al model requires the use of simultaneous equation modeling. The biggest challenge when empl oying structural equation modeling lies in defining properly specified models. The nece ssary identification steps outlined in Chapter 4 and summarized in Appendi x B are paramount to reliable estimates. The literature reviewed in this study revealed that none of the papers and studies formally follows this process. The result is the esti mation and presentation of sets of parameters that are not unique, which make statistical inference unreliable. The validity of the empirical models of Chapter 4 is confirmed by the relevant endogene ity and overidentification tests presented in this chapter.

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104 Chapter 5: Conclusions Summary of Findings This dissertation research sought to overc ome shortcomings of the empirical literature modeling of the relationship between tr ansit travel behavior and urban form. A review of the current state of empirical res earch on the subject uncovered the main weaknesses of findings relating the built environment to travel behavior as well as noting the paradigm shift epitomized by the activity-based literature. The findings of this review show that there has been a shif t from the study of density thre shold levels that make transit cost-feasible to an analysis of the eff ect of urban design and land-use mix on travel behavior, after controlling for density levels. The issue is no longer at what density thresholds it makes sense to implement transit, but what is the best set of policies affecting urban design and land-use mix that most infl uences the spatial arra ngements of activity locations, so that individuals are more likely to utilize transit. This shift is reflected by an increasing number of studies that assess the relevance of transit-oriented development (TOD) to transit use when households or indi viduals prefer certain urban setting to others. While early work sought to provide a fram ework that made use of aggregate data, the more recent literature models the simu ltaneous decision of location and travel when individuals choose locations based on idiosyncratic travel preferences.

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105 Finally, there is a lack of empirical work that examines the relationship between urban form and travel behavior within an anal ytical framework that takes into account the complexity of travel by considering trip ch aining among other travel complexities. To avoid these shortcomings and to incorporat e the activity-based a pproach, we developed and estimated a simultaneous equation m odel of transit usage and urban form. Empirically Estimable Model of Transit and Urban Form The models of Chapter 3 allow household travel to respond to changes in urban form, by considering trip-chaining for non-work travel. In the model, trip-chaining results from households’ reduc tions in non-work travel time while accounting for constraints that the built environment imposes. Any travel-time saving is spent on additional non-work travel or provides inducement to r eassess residential loca tion decisions. These changes in travel behavior and residential lo cation then affect the demand for travel. The constraints imposed by the built envi ronment are captured by the activity space. Empirical evidence in Chapter 4 shows th at lower densities define a larger activity space, which, in turn, decreases transit use. Conversely, as density increases, the activity space contracts, as does the need to engage in complex trip chains. Idiosyncratic preferences for transit also affect transit demand. For example, in the absence of adequate transit, households that need to engage in complex trip-cha in patterns, independent of changes in the surrounding built -environment, may use the auto mobile. In contrast, if adequate transit services ar e available to accommodate thei r travel patterns, households would choose transit, other things equal.

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106 To facilitate a summary of Chapter 4’s findings and for ease of comparison, Table 5.1 presents elasticities from th e three estimated models (onl y statistically significant results are shown). Exogenous density change does not have a large effect on transit demand, and the magnitude of the effect decreases when re sidential location becomes endogenous. A 20percent increase in gross population density (1,830 persons per square mile) increases transit demand from a minimum of 5.4 pe rcent to a maximum of 9.5 percent. TABLE 5.1 Relevant Land-Use and Transi t-Supply Elasticities of Transit Demand Elasticity Model Ia Model IIb Model IIIc Density 0.475 0.269 n/a Walking distance -0.137 -0.028 -0.093 Transit station at workplace* 0.687 0.766 0.961 TOD station* 0.279 n/a n/a Distance to CBD n/a n/a -1.177 Distance to nearest subcenter -0.388 -0.065 -0.522 Retail establishments density 0.001 0.170 n/a Residential location -0.157 n/a n/a a residential location exogenous; density exogenous b residential location e ndogenous; density exogenousc residential location and density endogenousn/a = not available Indicates a proportional change The importance to transit demand of stat ion proximity, as measured by walking distance, decreases after account ing for idiosyncratic preferen ces for location. In Model III, the elasticity of transit demand with resp ect to walking distance is about one-third

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107 smaller than in Model I, in which resident ial location and density are exogenous. This decline in magnitude is due to allowing hous eholds to choose thei r residential location and by accounting for omitted-variable bias error. This contrasts with what found by Cervero (2007), who shows that self-selecti on accounts for about 40 percent of transit ridership for individu als residing near a transit station. The presence of a transit station in proximity to a workplace also has a significant positive impact on ridership, as indicated by the magnitude of the proportional changes across all three models. In Model I, transit-oriented development n ear transit stations has a positive impact on transit use; a TOD stop increases transit de mand by about 28 percent. In conformity to the literature, a trans it station near a workplace exerts a positive impact on ridership, as indicated by the magnitude of the propor tional changes across all three models. An established central business district (CBD ) is still a relevant driver of transit use, as highlighted by an elas ticity of transit demand with respect to distance to the CBD of –1.17. Although subcenters play a less importa nt role, our findings support a policy of providing transit services in decentralized employment and residential areas to increase ridership. The importance of mixed-us e development to increase transit patronage is highlighted by the elasticity of tr avel demand with respect to retail establishment density. Model II shows that a 20-percent increase in retail establishment density (or about 28 establishments per square mile) increa ses transit demand by 3.4 percent. Households living farther from work, as measured by residen tial location use less transit, which is due to trip -chaining behavior. Such househ olds engage in complex trip

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108 chains and have, on average, a more disperse d activity space, which requires reliance on more flexible modes of transportation. Th e results support policies that would reduce the spatial allocation of activities and improve tr ansit accessibility at and around subcenters. Similar results can be obtained by policies that increase the presence of retail locations in proximity to transit-oriented households. Research Contributions The major contribution of this research e ffort is the development of a simultaneous equation model of transit patronage and landuse that acknowledges th e interrelationship between travel behavior and urban form. In particular, the framework embraces the paradigm shift from trip generation to activ ity-based modeling by considering travel demand as a derived demand brought about by the necessity to engage in out-of-home activities. In addition, this fr amework presented in Chapter 3 departs from the monocentric models of residential location, which do not account for decentralized work places, by explicitly acknowledging both the presence and the relevance of subcenters. The models take into account for the trade-off between consumption and travel brought about by the finite nature of time and its al location among household members. Another contribution of this dissertation is the empirical treatmen t of density as an explanatory variable for trip-m aking behavior. As opposed to the current practice of regressing trip making behavior ag ainst density measures, we assume that density does not directly to affect the demand for travel. In our models, density first directly affects the spatial dispersion of goods and services, as m easured by the activity sp ace. It is only by affecting the size of the activity space that density affects both trip chaining and the de-

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109 mand for transit services. Th e consequences introduced by th is structure are not trivial and as demonstrated by the empirical results. In addition, the empirical analysis shifts the analysis from individual travel behavior to household travel beha vior, recognizing that travel decisions are taken jointly among individuals. The models Finally, the empirical work takes advantag e of the advances in geographic information systems (GIS) tools and geographic scien ce contributions to the spatial analysis of the interactions of travel behavior and urban form. Directions for Further Research Notwithstanding the validity of the post-estimation tests performed in Chapter 5, there still exists the possibili ty that some of the variable s treated as exogenous are, in fact, endogenous. For example, this study tr eats vehicle ownership as exogenous. The literature review, however, rev ealed studies that consider vehicle ownership endogenous to residential location and densit y. One extension to this research, therefore, would be to include an endogenous treatment of this and other mode-choice variables. Another extension would be to include le isure time available to households. Indeed, the behavioral model of Chapter 3 a ssumes that households can save time by engaging in trip chaining. Time savings are then reallocated to either more non-work travel or to an extended commute. The model does not explicitly explain what happens to leisure time. The inclusion of total time constr aints that includes all re levant time uses (inhome and out-of-home) would provide insight on time use and its effect on trip chaining. Finally, in contrast to multiple linear regression analysis, nonparametric estimation methods would permit less restrictive assumpti ons. These methods can uncover the pres-

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110 ence of nonlinearities among dependent and inde pendent variables whic h could lead to a better parameterization of equations of inte rest. Although nonlineari ty in trip-chaining formation and density levels is better captu red by these methods than by more commonly used techniques, being computationally challeng ing, they are rarely used in applied work, especially in the field of tr avel behavior research and si multaneous equation modeling. Further research that makes use of these methods is warranted.

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111 References Adler, Thomas and Moshe Ben-Akiva. 1979. "A Theoretical and Empirical Model of Trip Chaining Behavior." Transportation Research Pa rt B: Methodological 13B, 243–257. Alonso, William. 1964. Location and Land Use Cambridge, Mass.: Harvard University Press. Anas, Alex. 2007. "A Unified Theory of C onsumption, Travel and Trip Chaining." Journal of Urban Economics 62, 162–186. Anas, Alex, Richard Arnott and Kenneth A. Small. 1998. "Urban Spatial Structure." Journal of Economic Literature 36, 1426--1464. Anas, Alex and Ikki Kim. 1996. "General Equi librium Models of Polycentric Urban Land Use with Endogenous Congestion and Job Agglomeration." Journal of Urban Economics 40, 232–256. Anas, Alex and Rong Xu. 1999. "Congestion, La nd Use and Job Dispersion: A General Equilibrium Analysis." Journal of Urban Economics 45, 451–473. Arnott, Richard. 1998. "Economic Theory a nd the Spatial Mismatch Hypothesis." Urban Studies 35, 1171--1185. Badoe, Daniel A. and Eric J. Miller. 2 000. "Transportation--Land-Use Interaction: Empirical Findings in North America, and Their Implications for Modeling." Transportation Research Part D 5, 235–263. Bagley, Michael N. and Patr icia L. Mokhtarian. 2002. "The Impact of Residential Neighborhood Type on Travel Behavior : A Structural Equations Modeling Approach." The Annals of Regional Science 36, 279–297.

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112 Baum-Snow, Nathaniel and Matthew E. Kahn. 2000. "The Effects of New Public Projects to Expand Urban Rail Transit." Journal of Public Economics 77, 241–263. Baum, Christopher F., Mark E. Schaffer and Steven Stillman. 2007. "Enhanced Routines for Instrumental Variables/Generali zed Method of Moments Estimation and Testing." Stata Journal 7, 465–506. Begon, M. J. and C.R. Towsend. 1996. Ecology: Individuals, Populations, and Communities Cambridge, MA: Blackwell Science Ltd. Ben-Akiva, Moshe and John L. Bowman. 1998. "Integration of an Activity-Based Modeling System and a Residential Location Model." Urban Studies 35, 1131– 1153. Bento, Antonio M., Maureen L. Cropper, Ahmed Mushfiq Mobarak and Katja Vinha. 2005. "The Effects of Urban Spatial Stru cture on Travel Demand in the United States." The Review of Econom ics and Statistics 87, 466–478. Bertaud, Alain. 2003. "Clearing the Air in At lanta: Transit and Smart Growth or Conventional Economics?" Journal of Urban Economics 54, 379–400. Bhat, Chandra. 1997. "An Econometric Framework for Modeling the Daily ActivityTravel Pattern of Individuals," pape r presented at Activity-Based Workshop National Institute of Statistical Sciences, North Carolina ———. 1999. "An Analysis of Evening Co mmute Stop-Making Behavior Using Repeated Choice Observations from a Multi-Day Survey." Transportation Research Part B: Methodological 33, 495–510. ———. 2001. "Modeling the Commute Activity-Trave l Pattern of Work ers: Formulation and Empirical Analysis." Transportation Science 35, 61–79. Bhat, Chandra and Jessica Guo. 2004. "A Mi xed Spatially Corre lated Logit Model: Formulation and Application to Residential Choice Modeling." Transportation Research Part B: Methodological 38, 147-168. ———. 2004. "A Mixed Spatially Correlated Log it Model: Formulation and Application to Residential Choice Modeling." Transportation Research Part B: Methodological 38, 147–168.

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123 Appendices

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124 Appendix A: Comparat ive Static Analysis In this appendix, we derive the most releva nt comparative static results of Model I through Model III. In Model I, we consider the impact of changes in exogenous density, D and exogenous residential location, RL on trip chaining, TC activity space, AS and travel demand, TD Starting from an equilibrium state, we consider the impact of an increase in density and resident ial location. To conduct comp arative static analysis, we first introduce a set of basic as sumptions related to resident ial location, trip chaining behavior, activity space, and urban form. Als o, although trips are inte gers in reality, we treat them as a continuous non-negativ e variable for analytical purposes. We begin with some definitions and a ssumptions followed by a detailed discussion of the behavioral equations of the model. We first s how how we derive the residential location, RL trip chaining, TC transit demand, TD and activity space, AS equations by relaying on a generalized form of a model of consumption, travel and trip chaining first exposited by Anas (2007). Definitions and Assumptions We assume the urban area is divided into zones, which are li nked via a transport network. To focus on consumer decisions, we consider a partial equilibrium model in which urban density and firm location are predet ermined. In this context, we derive the demands for goods consumption and non-work trav el. Consumers are price takers in all

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Appendix A (Continued) 125 markets and take as given all transport cost s and travel times. They supply labor hours after allocating time to work and non-work travel, and leisure. The following notation is used: the number of stores a consumer visits of a period of time goods consumption, with being housing goods prices, with being housing price individual round trip costs individual round tr ip times, with being commuting time n number of chained trips c chained-trip costs t chained-trip times W work time T travel time L leisure time M total time Assumptions i.e., housing price is a function of time distance between home and work. We also assume that housing pri ce falls with distance from the CBD and that residential locations are more d ecentralized than job locations. Hence

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Appendix A (Continued) 126 i.e., total travel time incl udes commuting, individual shopping trips, and trip chains. represents (time) distance between ho me and work, not necessarily the CBD. Note that the choice of will determine so and Also while , and for Furthermore Following Anas (2007), we assume that ch ained trips involve trips to all places selling and that individual trips are in addition to trip ch ains. This could be restrictive, but Anas argues that not all trips ma y involve a chained tri p, i.e., that there are corner solutions. In our empirical model we assume that chained trips occur as part of the commute. This is consistent with empiri cal findings (see refere nce) on trip-chaining formation. Consider a consumer who visits each of i = 1,..., I stores over a period of time. Although the number of trips may be an integer, we treat it as continuous, for over a period of time involving many trips, the per-unit-tim e number of trips can be continuous, e.g., five trips per week is 0.71 trips pe r day. The consumer buys a quantity i z ( i = 1,..., I ) from each store per trip. The utility function is The budget constraint is (1) Considering the identity (2)

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Appendix A (Continued) 127 where (3) with (4) The Lagrangean objective function is then given by (5) from which we obtain the follo wing first-order conditions (housing consumption) (6) (consumption of non-housing goods) (7) (number of commuting trips) (8) (number of non-commuting individual trips) (9) (number of non-commuting chained trips) (10) (commuting time) (11) (non-commuting individual travel time) (12) (non-commuting chained trip travel time) (13) (leisure choice) (14)

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Appendix A (Continued) 128 (budget constraint) (15) From the first-order conditions, we derive so lutions for the equations of interest. The demand for commuting trip s plus non-commuting trips is (16) The demand for non-commuting chained trips (17) The optimal work-reside nce travel time is (18) From this, we obtain the demand for chained trips, the demand for individual trips and the optimal commuting time, which are related to the demand equations of Chapter 3 as (trip chaining equation) (19) (transit demand equation) (20) (residential location equation) (21) Next, we introduce some additional assumptions to carry out the comparative static analysis. Assumption A.1. We assume that as the distance defining the job-residence pair increases, then the need to ch ain non-work trips increases (22) The partial equilibrium model of trip chaining and consumption, Anas (2007), shows that trip chaining saves time, which, in turn can be allocated to more consumption

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Appendix A (Continued) 129 and discretionary travel. In this study, we a ssume that individuals can allocate the travel time savings of trip chaining to either more commute time, a move farther from work (more commute time), or more non-work trav el time. Empirical evidence linking complex trip chaining to the work commute is found in Oster (1978) Kondo, and Kitamura (Kondo and Kitamura 1987), Nishii et al. (1988), and Strathman et al. (1994). These studies find that the propensity to link non-work travel to the work commute increases with distance from work. Oster (1978) shows that the probability of adding non-work trips to the commute increases with the distance to household members’ employment destinations. Adopting Hgerstrand ‘s (1970) con cept of space-time prisms, Kondo and Kitamura (1987) model the formation of trip chains and empirically show that under diminishing marginal benefits households living farther from work tend to chain non-work trips to the work commute. Assumption A.2. If density, increases, then non-work activity locations, such as shopping or recreational locations tend to be more clustered together, thus reducing the activity space (23) Although this assumption seems intuitively ac ceptable, it is obtained theoretically from the generalization of the partial equi librium model of trip chaining developed by Anas (2007) and reported in Appendix A. Em pirical evidence on this assumptions is found in Noland and Thomas (2007) who, in a mu ltivariate analysis of trip chaining behavior, show a positive relationship between lo wer densities and the complexity of trip

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Appendix A (Continued) 130 chaining behavior. Noland and Thomas (2007) find that low density leads to both a greater reliance upon trip chaining and tours that involve more stops, thereby expanding the activity space.. Assumption A.3. As the activity space gets more di spersed (increases) then trip chaining increases (24) As with assumption (a.2), this assu mption seems intuitively acceptable, but it is justified from generalizing the part ial equilibrium model of trip chaining developed by Anas (2007) and reported in Appendix A. Also, empirical work supports this assumption (Noland and Thomas 2007). Assumption A.4 As trip chaining increases, the household activity space decreases (25) The optimization of a trip chaining sequen ce results in a reduction of the activity space. The rate of reduction decreases as trip chaining increases. This is so because the activity space contracts up to a point where the location of activities is close enough to make the individual indifferent between chai ning the additional trip and making a separate trip to a given store

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Appendix A (Continued) 131 Model I Comparative Static Results Now, consider Model I. Equations (3.1), (3.2), and (3.3) can be written as implicit functions in the form where With continuous partial deriva tives and with the relevant assumptions (A.3) and (A.4), the Jacobian determinant is (26) Therefore, TC AS and TD [no comma] can be consid ered implicit functions of at and around any point that sa tisfies Equations (3.1), (3.2), and (3.3). Hence the implicit f unction theorem ju stifies writing (27) (28) (29) indicating that the equilibrium values of the endogenous vari ables are implicit functions of the exogenous vari ables and parameters. The pa rtial derivatives of the implicit functions provide the comparative-static results. Next, we obtain the comparative static re sults of changes in density, residential location and transit station proximity. Effects of an Increase in Density, The general form for the comparative stat ic analysis of Model I for changes in D is given by

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Appendix A (Continued) 132 (30) Density Effect on Trip Chaining, TC The effect of density on trip chaining is (31) An increase in density causes a clustering of activities which contracts the activity space, which, in turn, reduces the need to enga ge in trip chaining. This outcome has been confirmed in the literature on trip chaining behavior, which shows that lower density environments increase the need to engage in tr ip chaining (Wallace, Barnes, and Rutherford 2000; Noland and Thomas 2007). Density Effect on Activity Space, AS The effect of an increase in density on the activity space is (32)

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Appendix A (Continued) 133 Note, by assumption (A.2), we have An increase in density contracts the activity space both directly and indirectly through feedback effect coming by way of ( ) in the denominator of (32). Density Effect on Transit Demand, TD The effect of an increase in density on transit demand is (33) where the product give the increase in tran sit demand caused by a contraction in the activity space as a result of increased density, and gives the increase in transit demand caused by decrea sing trip chaining as a result of increased density. First, increased density reduces the extent of the activity space, which increases the demand for transit trips. Second, highe r densities reduce the activity space, which reduces the need to chain tr ips (as time savings opportunitie s decrease) and increases the demand for transit trips. Thus transit demand increases since it is sensitive to changes affecting the spatial allocation of non-work act ivities and to changes affecting trip chaining behavior. This result relies on the assumption that demand for transit trips decreases as trip chaining increases (34)

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Appendix A (Continued) 134 An increase in the number of chained trip s decreases the demand for transit as the need to rely on more flexible modes of trans port increases. This is also reflected by the following assumption on the relationship betw een transit demand and the size of the activity space (35) That is, the increased spatial dispersi on of non-work activities cannot be accommodated by additional transit trip s. Given the characteristic s of transit service supply (being fixed at least in the short to medium run), increased spatial dispersion is accommodated by substituting transit tr avel with other, more flexib le, modes, such as auto travel. Auto is a more flexible mode in term s of allowing serving a more dispersed activity space. Effect of a Change in Residential Location, RL Next, we look at the effect of a chan ge in exogenous residential location, RL Applying Cramer’s rule to Model I, we have (36) Residential Location Effect on Trip Chaining, TC From assumption (A.1), as distance between home and work increases, trip chaining increases. The new equilibrium result s in a higher number of trips per chain

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Appendix A (Continued) 135 (37) When testing this hypothesis with using cross-sectional data, individuals with a more living farther from work are expected to engage in a higher number of trips per chain (or in more complex tours characterized by more stops). In a longitudinal context, a move farther out entails more time spent commuting, which increase s the propensity to engage in trip chaining to save overall time. Residential Location Effect on Activity Space, AS The effect of an increase in RL on the activity space is given by (38) A move farther away from work increases trip chaining, which in turn decreases the activity space. Residential Location Effect on Transit Demand, TD The change in transit demand caused by a ch ange in residential location is given by: (39) The sign is ambiguous as the overall eff ect on transit demand hinges on the sign of We posit that to the extent that an urban area is well served by transit, then the

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Appendix A (Continued) 136 relationship between transit demand and reside ntial location is posit ive. A positive relationship is observed in older, more monocentr ic-type cities, with existing transit services supporting major work commute travel routes. On the other hand, if supply constraints exist, transit demand declines as the job-re sidence distance increases. Therefore, the overall effect on transit demand due to a cha nge in location depends on both the sign and magnitude of Effect of a Change in Walking Distance, WD Effect of Walking Distance on Transit Demand We now look at the effect on transit demand from an increase in distance fr om the nearest transit station. The empirical literature provides unequi vocal evidence of a negative relationship between distance to transit stops and the demand for trans it services (Cervero 2007; Cervero and Kockelman 1997). The debate is mostly cent ered on the magnitude of this relationship, as high-lighted by the growing body of literature on residential self-selection. All else equal, being located farther away from a transi t station results in a change in transit demand as (40) The overall effect of an increase in wa lking distance is ambiguous. An increase in distance to the nearest stati on directly reduces transit demand ). At the same time, reduced accessibility impacts and th e ability to engage in trip chaining using transit, producing an ambiguous effect on tr ansit demand. The sign hinges on the rela-

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Appendix A (Continued) 137 tionship between trip chaining and dist ance to the nearest transit station, which is undetermined.

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138 Appendix B: Equation Identification Identification In the context of simultaneous equation modeling, the validity of results hinges on the determination of the exclusi on restrictions. That is, the researcher must a priori determine what explanatory variables are to be included and excluded from each equation. The determination of the exclus ion restrictions defines a mode l that is correctly specified in the sense that the matrix of the reduced form parameters to be estimated is unique in its representation of the more primitive structural matrix. Exclusion restrictions need to be drawn outside of the variables a researcher ha s available from a given dataset (i.e, they should be based on sound behavioral theory). A necessary and sufficient condition for iden tification of a stru ctural equation is provided by the rank condition. The rank condition assures that the exclusion restrictions are sufficient and are unique. The following steps are required to obtain the rank condition for a given structural equation: 1) Let be a matrix of all the structural parameters (1) and let Ri be the matrix of exclusion restri ctions defining stru ctural equation i

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Appendix B (Continued) 139 (2) 2) Premultiply (c.1) by (c.2) to obtain the list of variables excluded from equation i (3) 3) Compute the rank of 4) Equation ( i ) is identified (overidentified) if the rank is equal (greater) to G-1; where G is equal to the nu mber of endogenous variables Next, each of the four models presented next is subject to the rank condition for identification prior to estimation and results are reported below. Note that the size of depends on the number of exogenous and endoge nous structural parameters excluded by each equation. The following notation is used to denote exogenous and endogenous appearing or being excluded by each equation G = total number of endogenous variables K = total number of exogenous variables = number of endogenous variab les included in equation i = number of endogenous variables excluded from equation i = number of exogenous variables included in equation i = number of exogenous variables excluded from equation i

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Appendix B (Continued) 140 Model I Following the equation specifications of Chapter 3, the following rank conditions for identification are obtained. Given the dime nsions of the matrices involved, we used the mathematica software package to compute the rank conditions. Trip Chaining Equation, TC Inclusions/ExclusionsNumber G 3 K 13 1 1 7 6 The rank condition is (just identified) (4) Activity Space Equation, AS Inclusions/ExclusionsNumber G 3 K 13 1 1 4 9 The rank condition is (overidentified) (5)

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Appendix B (Continued) 141 Transit Demand Equation, TD Inclusions/ExclusionsNumber G 3 K 13 2 0 4 7 The rank condition is (just identified) (6) Model II Following the specification of Chapter 4, the following rank conditions for identification are obtained. Trip Chaining Equation, TC Inclusions/ExclusionsNumber G 4 K 18 2 1 6 12 The rank condition is given by (just identified) (7)

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Appendix B (Continued) 142 Activity Space Equation, AS Inclusions/ExclusionsNumber G 4 K 18 1 2 4 14 The rank condition is given by ( just identified) (8) Transit Demand Equation, TD Inclusions/ExclusionsNumber G 4 K 18 3 0 5 13 The rank condition is given by ( just identified) (9)

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Appendix B (Continued) 143 Residential Location Equation, RL Inclusions/ExclusionsNumber G 4 K 18 2 1 6 12 The rank condition is given by (just identified) (10) Model III Following the specification of Chapter 4, the following rank conditions for identification are obtained. Trip Chaining Equation, TC Inclusions/ExclusionsNumber G 5 K 18 2 2 6 12 The rank condition is given by (just identified) (11)

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Appendix B (Continued) 144 Activity Space Equation, AS Inclusions/ExclusionsNumber G 5 K 18 2 2 3 15 The rank condition is given by ( just identified) (12) Transit Demand Equation, TD Inclusions/ExclusionsNumber G 5 K 18 3 1 5 13 The rank condition is given by (just identified) (13)

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Appendix B (Continued) 145 Residential Location Equation, RL Inclusions/ExclusionsNumber G 5 K 18 2 2 6 12 The rank condition is given by (just identified) (14) Density Equation, D Inclusions/ExclusionsNumber G 5 K 18 2 2 2 16 The rank condition is given by ( just identified) (15)

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About the Author Sisinnio Concas is a transportation econom ist with broad experience in urban and regional economic impact analysis He currently serves as se nior research associate for the Center for Urban Transporta tion Research (CUTR) at the Un iversity of South Florida, Tampa, USA. He has extensive expertise in evaluating transportati on infrastructure investments for state and local transportation ag encies. His research interests include the study of the linkages between transportation infrastructure investment and economic development, the application of nonparametric estimation and inference techniques to transportation research, and th e theoretical underpinnings of the linkages between household activity-travel patterns and land-use in urban areas. A native of Sardinia, Italy, he holds a Doctoral degree in Political Sciences with a field specialization in Political Economy from the University of Sassari, Ital y, and a Master of Arts in Economics from the University of South Florida.


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The interaction between urban form and transit travel
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ABSTRACT: This study presents an analytical model of the interaction between urban form and the demand for transit travel, in which residential location, transit demand, and the spatial dispersion of non-work activities are endogenously determined. In this model, travel demand is considered a derived demand brought about by the necessity to engage in out-of-home activities whose geographical extent is affected by urban form. In a departure from the urban monocentric model, residential location is defined as a job-residence pair in an urban area in which jobs, residences, and non-work activities are dispersed. Transit demand is then determined by residential location, work trips, non-work trip chains, and goods consumption. Theoretically derived hypotheses are empirically tested using a dataset that integrates travel and land-use data. There is evidence of a significant influence of land-use patterns on transit patronage. In turn, transit demand affects consumption and non-work travel. Although much reliance has been placed on population density as a determinant of transit demand, it is found here that population density does not have a large impact on transit demand and, moreover, that the effect decreases when residential location is endogenous. To increase transit use, urban planners have advocated a mix of residential and commercial uses in proximity to transit stations. In this study, it is found that the importance of transit-station proximity is weakened by idiosyncratic preferences for residential location. In addition, when population density and residential location are jointly endogenous, the elasticity of transit demand with respect to walking distance to a transit station decreases by about 33 percent over the case in which these variables are treated an exogenous. The research reported here is the first empirical work that explicitly relates residential location to trip chaining in a context in which individuals jointly decide residential location and the trip chain. If is found that households living farther from work use less transit and that trip-chaining behavior explains this finding. Households living far from work engage in complex trip chains and have, on average, a more dispersed activity space, which requires reliance on more flexible modes of transportation. Therefore, reducing the spatial allocation of non-work activities and improving transit accessibility at and around subcenters would increase transit demand. Similar effects can be obtained by increasing the presence of retail locations in proximity to transit-oriented households. Although focused on transit demand, the framework can be easily generalized to study other forms of travel.
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