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Spatial and temporal expenditure-pricing equity of rail transit fare policies

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Spatial and temporal expenditure-pricing equity of rail transit fare policies

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Content Copyright 2022 Zakhary Mallett Spatial and Temporal Expenditure-Pricing Equity of Rail Transit Fare Policies by Zakhary Mallett A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (URBAN PLANNING AND DEVELOPMENT) December 2022 ii Acknowledgements This research and the education that supported it were generously funded through merit- based awards provided by the American Public Transportation Foundation, California Transportation Foundation, Railway Association of Southern California, United States Department of Transportation Dwight David Eisenhower Transportation Fellowship Program, and the University of Southern California. I extend sincerest appreciation to these organizations and their members, donors, and funding sponsors. I also want to personally thank the many staff of BART and MARTA who provided time and resources in collecting and sharing data for this research; the many esteemed scholars who provided input throughout my development of this dissertation, including Drs. Marlon G. Boarnet, Genevieve Giuliano, Lisa Schweitzer, and Brian D. Taylor; Dr. Victoria Deguzman who provided editorial feedback; and a colleague, Clemens A. Pilgram, who built the R code template that was used for key parts of the analysis. iii Table of Contents Acknowledgements ............................................................................................................................................ ii List of Tables ...................................................................................................................................................... v List of Figures .................................................................................................................................................... vi Abstract ............................................................................................................................................................. vii Introduction ........................................................................................................................................................ 1 Paper 1: Transit Costs and Fare Equity: An Intrinsic Relationship Untold .............................................. 7 Abstract ........................................................................................................................................................... 7 Introduction .................................................................................................................................................... 8 Variations in Transit Cost Modeling ......................................................................................................... 11 Economic Cost Models .......................................................................................................................... 11 Accounting Cost Models ........................................................................................................................ 14 A Synthesis ............................................................................................................................................... 19 Scale Economies of Transit ........................................................................................................................ 20 Economic Bases for Transit Subsidies ................................................................................................. 24 Transit Expenditure and Pricing Equity Literature ................................................................................ 33 Measurements of Equity in Transportation ......................................................................................... 33 Empirical Findings .................................................................................................................................. 38 Conclusions and Recommendations ......................................................................................................... 44 Paper 2: Spatial and Temporal Variability of Rail Transit Costs and Cost Effectiveness ..................... 47 Abstract ......................................................................................................................................................... 47 Introduction .................................................................................................................................................. 47 Accounting Cost Models in Transit .......................................................................................................... 49 Accounting for Capital Costs ..................................................................................................................... 51 Literature Review ......................................................................................................................................... 53 Data and Methods ....................................................................................................................................... 58 Case Selection ........................................................................................................................................... 59 Data ........................................................................................................................................................... 63 Model — Temporal ................................................................................................................................. 66 Model — Spatial ...................................................................................................................................... 70 iv Findings — Temporal Allocations ............................................................................................................ 71 Findings — Spatial Allocations ................................................................................................................. 75 Discussion and Conclusion ........................................................................................................................ 78 Paper 3: Inequitable Inefficiency: A Case Study of Rail Transit Fare Policies ....................................... 81 Abstract ......................................................................................................................................................... 81 Introduction .................................................................................................................................................. 81 Literature Review ......................................................................................................................................... 84 Data and Methods ....................................................................................................................................... 89 Descriptive Statistics ................................................................................................................................... 92 Spatial Analysis ......................................................................................................................................... 94 Temporal Analysis ................................................................................................................................ 104 Results — Spatial Analysis ...................................................................................................................... 107 Results — Temporal Analysis ................................................................................................................. 113 A Synthesis of Cost Recovery Measurements ...................................................................................... 116 Discussion and Conclusion ..................................................................................................................... 118 Conclusion ..................................................................................................................................................... 124 Bibliography ................................................................................................................................................... 128 APPENDIX: Table of Included and Excluded Costs ............................................................................ 137 v List of Tables Table 1-1: Methods of temporal allocation of capital costs....................................................................... 16 Table 1-2: Results of Different Allocation Models from Cherwony and Mundle (1980) ..................... 17 Table 1-3: Economies of scale literature findings ....................................................................................... 22 Table 1-4: Travel mode indices for Glaister and Lewis (1978) model ..................................................... 31 Table 1-5: Theories of Justice and Types of Equity in Transportation Equity Research (adapted from Taylor and Norton, 2009) ..................................................................................................................... 35 Table 1-6: Select literatures on transit expenditure and pricing equity .................................................... 38 Table 2-1: BART and MARTA Reported Operating Data ....................................................................... 60 Table 2-2: Costs, Classifications, and Cost Input Metrics ......................................................................... 64 Table 2-3: Cost and Cost effectiveness Relative to Distance from Core ................................................ 78 Table 3-1: Table of Variables ......................................................................................................................... 90 Table 3-2: Agency Profiles .............................................................................................................................. 92 Table 3-3: Descriptive Statistics of OD Pairs — BART ............................................................................ 95 Table 3-4: Descriptive Statistics of OD Pairs — MARTA ....................................................................... 95 Table 3-5: Descriptive Statistics of Station Profiles — BART .............................................................. 101 Table 3-6: Descriptive Statistics of Station Profiles — MARTA .......................................................... 101 Table 3-7: Descriptive Statistics of Link Profiles — BART ................................................................... 101 Table 3-8: Descriptive Statistics of Link Profiles — MARTA ............................................................... 101 Table 3-9: Temporal Descriptive Statistics — BART ............................................................................. 106 Table 3-10: Temporal Descriptive Statistics — MARTA ....................................................................... 106 Table 3-11: Origin-Destination Cost Recovery Model Results — BART ........................................... 108 Table 3-12: Origin-Destination Cost Recovery Model Results — MARTA ....................................... 108 Table 3-13: Cost Recovery Measurements ................................................................................................ 116 vi List of Figures Figure 1-1: Matrix of economies of scale, scope, and density ................................................................... 14 Figure 1-3: Marginal cost approach to capital resource allocations .......................................................... 18 Figure 2-2: BART System Map effective July 1, 2018 to February 10, 2019 .......................................... 61 Figure 2-3: BART Weekday/Saturday System Map effective February 11, 2019 to June 30, 2019 .... 61 Figure 2-4: BART Sunday System Map effective February 11, 2019 to June 30, 2019 ......................... 62 Figure 2-5: MARTA System Map effective in Fiscal Year 2019 ............................................................... 63 Figure 2-6: BART Distribution of Cars and Trains In-Service — Weekdays ........................................ 67 Figure 2-7: BART Distribution of Cars and Trains In-Service — Saturdays ......................................... 67 Figure 2-8: BART Distribution of Cars and Trains In-Service — Sundays/Holidays .......................... 67 Figure 2-9: MARTA Distribution of Cars and Trains In-Service — Weekdays .................................... 68 Figure 2-10: MARTA Distribution of Cars and Trains In-Service — Weekends/Holidays ................ 68 Figure 2-11: BART Share of Cost Inputs by Time Period ........................................................................ 72 Figure 2-12: MARTA Share of Cost Inputs by Time Period .................................................................... 73 Figure 2-13: BART Cost v. Cost per rider by Time Period ....................................................................... 74 Figure 2-14: MARTA Cost v. Cost per rider by Time Period ................................................................... 74 Figure 2-15: BART Station and Link Costs ................................................................................................. 76 Figure 2-16: BART Station Costs per rider and Link Costs-Per-Passenger-Mile .................................. 76 Figure 2-17: MARTA Station and Link Costs ............................................................................................. 76 Figure 2-18: MARTA Station Costs per rider and Link Costs-Per-Passenger-Mile .............................. 76 Figure 3-1: BART System Map effective July 1, 2018 to February 10, 2019 .......................................... 83 Figure 3-2: MARTA System Map effective in Fiscal Year 2019 ............................................................... 83 Figure 3-3: Ridership Patronage by Station — BART ............................................................................... 97 Figure 3-4: Ridership Patronage by Station — MARTA ........................................................................... 97 Figure 3-5: Spatial Pattern of Station Patronage and Link Usage — BART .......................................... 99 Figure 3-6: Spatial Pattern of Station Patronage and Link Usage — MARTA .................................... 100 Figure 3-7: Average Percent Paid Across Links and Stations — BART ............................................... 102 Figure 3-8: Average Percent Paid Across Links and Stations — MARTA ........................................... 103 Figure 3-9: Cost v. Cost Per Rider by Time Period — BART ................................................................ 105 Figure 3-10: Cost v. Cost Per Rider by Time Period — MARTA ......................................................... 105 Figure 3-11: Station Cost Recovery Profile Relationship with Average Trip Lengths and Station Distance from Core of Network — BART ............................................................................................... 110 Figure 3-12: Link Cost Recovery Profile Relationship with Average Trip Lengths and Link Distance from Core of Network — BART ............................................................................................... 110 Figure 3-13: Station Cost Recovery Profile Relationship with Average Trip Lengths and Station Distance from Core of Network — MARTA ........................................................................................... 111 Figure 3-14: Link Cost Recovery Profile Relationship with Average Trip Lengths and Link Distance from Core of Network — MARTA ........................................................................................... 111 Figure 3-15: BART Time Period Costs, Subsidies, and Cost Recoveries .............................................. 113 Figure 3-16: MARTA Time Period Costs, Subsidies, and Cost Recoveries .......................................... 114 Figure 3-17: Correlation Matrix of Temporal Variables .......................................................................... 115 vii Abstract In this dissertation, I evaluate the equity of rail transit fare policies using highly disaggregate cost, ridership, and fare data to compare how spatial and temporal variance of costs compare to spatial and temporal variance of fare collection. I measure “equity” by how evenly costs are recovered through the fares paid by transit users across space and time. I innovate by controlling for the cost sharing nature of a transport network — that is, accounting for how traveler density across space and time affects average costs per rider and resulting cost recovery across space and time. I use two transit providers, the San Francisco Bay Area Rapid Transit District (BART) and the Metropolitan Atlanta Rapid Transit Authority (MARTA), as parallel case studies. Furthermore, since both agencies have different fare structures, I offer insights on how different fare structures affect outcomes. The dissertation follows a three-paper format, starting with a critical literature review that interrogates literature on transit cost modeling and transit pricing equity. I follow this up with a two-part (two paper) case study wherein I first evaluate how costs and costs per rider vary across space and time in the two rail networks, then test for spatial and temporal disparities in cost recovery patterns in the two rail networks to determine if transit subsidies are unevenly distributed geographically or temporally. I find that outlying areas and off-peak travel times in the BART network cost less to serve in gross terms but are more costly on a per-rider basis and recover less of their costs through fares. In the MARTA network, I find no clear spatial patterns of cost and costs per rider, though cost recovery patterns indicate that outlying areas are also subsidized more than inner areas of the network, while temporal cost and cost-recovery patterns are similar to the findings for BART. 1 Introduction Transportation in the United States is heavily subsidized. Public transit is especially subsidized due to it serving two principal policy objectives: providing a transportation lifeline to those who cannot or choose not to drive, and combating negative externalities produced by automobile travel. Meeting these objectives require immense subsidies. Without them, transit- dependent populations may not be able to afford travel at all. And attracting those who would otherwise drive requires compensation (i.e., subsidy) equal to the opportunity cost of using transit instead of driving. These objectives of public transit pose many policy-relevant questions regarding efficiency and equity in how transit is operated and priced. However, as I describe in the following paragraphs, research on transit investment and pricing equity and efficiency is piecemealed, leaving an incomplete understanding about the conflicts or parallels between these. In this dissertation, I seek to integrate these concepts while also focusing on rail, a mode of transit underrepresented in cost modeling and pricing equity literature. As a publicly financed service, minimizing the cost of transit service production and maximizing public benefits are a public interest. For example, understanding the economic structure of transit service production can inform how to size transit operators, as well as how to allocate and conditionalize subsidies from higher levels of government to the operator. Much research — again, disproportionately focused on bus transit — has shown that the industry is characterized by economies of scale for small operators, constant economies for medium-sized operators, and diseconomies of scale for larger operators (e.g., Berechman, 1993, Karlaftis et al., 1999). This suggests that there is some optimal size of a transit operator that can minimize per unit costs of output. Other research has shown that the incidence of state and federal transit subsidies have gone towards increasing unionized labor salaries in excess of their market rate without generating the 2 intended increase in transit service levels (e.g., Wachs, 1989; Winston and Shirley, 1998, as referenced by Parry and Small, 2009), disincentivized labor innovation to reduce these costs (Jones, 1985; Morales Sarriera and Salvucci, 2016), and incentivized agencies to over-invest in vehicle capacity (e.g., Viton, 1981; Obeng, 1984; as cited in Berechman, 1993). These exemplify the importance of regulating how subsidies are expended. One final example is that knowing the economic structure of transit production can help identify what an economically optimal fare is — which can help inform user subsidy policies, if the economically optimal fare is not equal to a fare calculus consistent with public policy objectives. Apart from economic optimization considerations, transit being priced and invested in fairly — however it is measured — is also a public interest. Equity can be measured as the amount travelers pay per unit of benefit they receive (e.g., miles of travel), amount of subsidy different travelers receive regardless of what they pay, among other examples. Unlike the complex cost models used to measure the economic structure and efficiency of transit service production, inquiries about investment and pricing equity use accounting cost models that distribute (i.e., allocate) costs to parts of a transit system in order to see how investments and revenues correlate with different parts of the network (e.g., locales served) and groups of travelers. Conducting this analysis can help identify whether there are disparities in who benefits from transit capital investments or operating subsides, or who receives those same benefits relative to what they pay for it. Also, while not highlighted in pricing equity research, to the extent that there is a spatial dimension in investment or fare equity disparities, this may have relevance to urban economics inquiries about the relationship between transport costs and urban form. That is, if select areas are especially subsidized, their growth may be a byproduct of, or enabled through, transport subsidies. Yet, as may be inferred from the preceding paragraphs, literature on these topics is fragmented; different paradigms of scholarship evaluate only select topics amongst these, resulting in 3 limited comprehensive understanding of how efficiency and equity interact in the production and delivery of public transit. Among other examples, transport economists who study the economic structure of transit and how efficient it is at an aggregate level use complex cost models to conduct their research. By focusing on systemwide considerations, these studies inherently ignore important analyses that rely on assessing variation across parts of the system, including distributional impacts of how a system is priced and operated and whether inefficiencies are concentrated in select segments of the system being studied. Some suggest this is due to models for economically evaluating objectives other than the economic structure and productivity of the industry are underdeveloped (e.g., De Borger et al., 2002). On the flip side, while planning scholars who focus on the distributional impacts of how transit is priced and operated may deduce that inequities in investments and fare policies exist and warrant change, such findings are often ignorant of any macro-level impacts that could result from the proposed change. A possible result of a fare adjustment, for example, is a change in demand or usage patterns that may simply revise the distributional disparity results rather than solve them. In addition to literature on the equity and efficiency of transit being fragmented, within these domains of the literature, there are many limitations. For one, bus transit is overwhelmingly represented in the literature; other modes of transit — rail, ferries, taxis, and more — are not well- covered in literature on the economic structure, investment equity, or pricing equity of transit. To be sure, this does not mean that no such research exists — for instance, Parody et al. (1990) and Taylor et al. (2000) have evaluated temporal dimensions of heavy rail transit and light rail transit, respectively, and Savage (1997) has looked at the economic structure of rail transit. But other modes of transit are understudied relative to bus transit. In addition, spatial variability of transit costs is both methodologically underdeveloped and underrepresented in the research. For the most part, these studies only look at route-by-route 4 variability of costs by either allocating costs and revenues to routes (e.g., Cherwony and Mundle, 1980), or classifying routes (Cervero, 1981) or parts thereof (Hodge, 1988; Iseki, 2016) as urban or suburban based on the bus yard they are associated with (Cervero, 1981) or city limits the portion of the route operates in (Hodge, 1988; Iseki, 2016) to draw generalized conclusions about urban- suburban disparities in transit investments and pricing. Such analyses, while more spatially disaggregated than a systemwide analysis, lacks granularity. As one example, many bus routes converge along a particular corridor to provide a combined frequency there while providing lower frequency along their diverged areas of service. Looking route-by-route ignores the impacts of the routes’ combined frequency along such shared corridors of service. Finally, in my review of literature on spatial variability of costs, transit modes other than bus transit are not whatsoever represented in this sub-domain of the literature. My objective in this dissertation is to contribute to transit efficiency and equity literature by evaluating the spatial and temporal variability of costs and cost recovery of rail transit. The dissertation is organized in three chapters, starting with a critical literature review that elaborates on the literature summary provided above. In the critical literature review, I focus especially on transit subsidy patterns, the equity impacts this creates, and whether there is a conflict between equity and efficiency. Thus, my review of economic literature mainly concerns justifications for subsidizing transit and how optimally this is being done from an economic perspective. Similarly, my review of accounting cost model literature focuses on methods used to allocate costs in a way that can inform disparity patterns. I close with suggestions on areas for further research that can better integrate economic and equity research that heretofore tends to talk past one another. In the second and third chapters, I conduct a two-part case study of the spatial and temporal cost variability and cost recovery of rail transit. I use the San Francisco Bay Area Rapid Transit District (BART) and Metropolitan Atlanta Rapid Transit Authority (MARTA) as the case studies. In 5 the cost variability chapter, I develop an accounting cost model that allocates costs spatially and temporally (two separate exercises) and devises average costs per rider across the spatial and temporal dimensions of the networks. I do this by using a partially allocated cost model (Taylor et al., 2000) that only includes input factors that reasonably vary across space and time. Both allocation exercises use much more granular dimensions of space and time than past studies. Instead of allocating temporal costs to peak and base time periods, I identify multiple different time periods by evaluating the number of transit revenue vehicles in use throughout the day. For the spatial cost allocation, I allocate costs not to routes or rail yards, but to links and stations of the networks. In the third chapter, I use the average cost per rider findings from the second chapter to define origin-destination (OD) trip costs — which are equal to the sum of the cost per rider of the origin station, destination station, and every link used to complete the trip. I then measure the cost recovery of every OD trip taken in the two systems by dividing the average fare paid for each OD trip by the cost of the OD trip. Finally, I estimate the average OD trip cost recovery for all users of every station, link, and time period and, using ordinary least squares regressions, test whether there are spatial dimensions to the resulting variability of cost recovery. To evaluate temporal variability of cost recovery, I divide the fare revenue generated during each time period by the cost of serving the time period. Together, these essays show the extent to which different times and locations of travel on the BART and MARTA systems receive different levels of transit subsidies. Furthermore, since the two systems have different fare structures (i.e., BART uses a stepwise distance-based fare structure; MARTA, a flat rate fare structure), the findings contribute to discourse about the equity or inequity of different fare policies. While rail transit is a focal point of this dissertation, I ultimately seek for this research to motivate further research on spatial and temporal disparities in transport subsidies 6 more broadly. Are select areas and times of travel especially subsidized? If so, who are we subsidizing from a socioeconomic standpoint? 7 Paper 1: Transit Costs and Fare Equity: An Intrinsic Relationship Untold Abstract Research on transit costs and transit pricing equity are both topically and methodologically isolated in literature. This leaves an incomplete picture about how equity and efficiency relate or conflict with each other in the provision of transit services. On the one hand, transport economic literature uses economic cost models to evaluate the economic structure of the industry and test whether it is being produced efficiently. These analyses are done at a systemwide level, so inherently ignore variability in efficiency throughout parts of a network. And while the economic structure and efficiency of transit service production can be analyzed under different economic objectives, such as profit-maximization or welfare-maximization, limited research under a welfare maximizing case empirically evaluates the optimal subsidy to give to transit. Finally, transport economic literature, by being systemwide-centric, tends to ignore equity implications that are variable across the network, such as different locations of the network receiving more service relative to what they pay in comparison to other locations of the network. In stark contrast, equity research relies on accounting cost models that use input-output relationships to allocate costs to parts of the network so that variability of resource allocations and fare receipts can be evaluated and used to test for disparities in service delivery and pricing. These analyses have the shortcoming of ignoring the systemwide implications of correcting inequities found. In both bodies of literature, bus transit is disproportionately represented, temporal variability is far more represented than spatial variability, and the units of spatial and temporal analysis are quite aggregate by today’s data standards. The literature can benefit from better representation of transit modes other than bus transit, the use of disaggregate operating and ridership data to evaluate spatial and temporal variation of transit service 8 production costs at a more granular level and in unison with fare equity, and the relationship this has with systemwide efficiency. Introduction Transportation in the United States is heavily subsidized; travelers generally do not pay the full costs of the travel that they consume. This is particularly true for transit. In 2017, just 20% of expenditures on transit were financed through fares in the United States (United States Census Bureau, 2017). This is largely a derivative of public policy objectives for transit in the United States. On the one hand, transit is provided as a transportation lifeline for those who cannot or choose not to drive; on the other, transit is an intervention instrument for combatting negative externalities of automobile travel, such as pollution and congestion (e.g., Meyer and Gomez-Ibanez, 1981, as cited by Giuliano, 2005; Fielding, 1995, as cited by Giuliano, 2005). In both instances, heavy subsidization is required; without it, the captive audience would not be able to afford much travel at all, and so-called “choice riders” may not be lured to use transit due to other generalizable high costs of it relative to the automobile such as travel time. This web of subsidies begs a question: who reaps the greatest benefit from transit subsidies? This question can be answered on several dimensions — time of travel, geography of travel, socioeconomic makeup of travelers, and more. That is, do people who — among other examples — travel during certain times of the day or seasons of the year, to or from certain communities, or are of a certain socioeconomic class, receive greater transit subsidies than others? Answering this question is necessary to evaluate how well transit subsides achieve their policy objective(s). But answering it well requires an understanding of how the costs of transit service provision, incidence of transit resource allocations, and fare receipts vary across these dimensions of a network. How much does it cost to provide transit? When, where, and to whom are we investing the most in providing transit? Who is paying the most for transit either in total or relative to what they receive? 9 Research on these questions to-date is disjointed, both topically and methodologically, leaving our understanding of the union between transit costs and pricing equity fragmented. On the one hand, transport economics literature relies on economic cost models to evaluate the economic structure of transit service provision. Among other uses, studies of this sort estimate the scale economies of transit service and whether transit service is being operated efficiently given its economic structure. Such analyses inherently treat a transport network as fixed when measuring scale economies and efficiency, so cannot estimate how findings vary across different dimensions of a network; the network as built and operated has a particular economic structure and either operates efficiently or inefficiently. Thus, studies in this realm do not measure how service provision, pricing, and the union of these varies across time, location, or other dimensions of a network. By extension, they generally do not investigate equity implications of a network as built and operated. But they are imperative for evaluating whether a system as a whole operates efficiently. On the flip side is research on — what I define as — “expenditure equity,” “pricing equity,” and “expenditure-pricing equity” in transit. I distinguish these as measuring disparities in the gross amount expended delivering transit to different populations, measuring disparities in how much different populations pay for transit, and measuring disparities in how much different populations pay for transit relative to what they receive, respectively. I elaborate on these measurements of equity in the following sections. Particularly in the foremost and latter instances, these studies rely on estimating the amount of expenditure being spent on different populations. For transit capital expenditures, correlation between the cost of the investments and the makeup of the communities it serves or riders it serves are evaluated (e.g., Garrett and Taylor, 1999). When the focus is on transit operations, accounting cost models (e.g., Pels and Rietveld, 2007) — also called cost allocation models (e.g., Berechman, 1993) or “activity-based” cost models (e.g., Basso et al., 2011) — are typically used to allocate costs to different parts of a network, then evaluate whether there is parity 10 in the amount of service being provided or expenditures made across the network either in gross terms (e.g., Taylor et al., 2000) or relative to what benefitting riders pay (e.g., Parody et al., 1990). As can be inferred, these equity studies focus on micro-level variations, so have the counter limitation of transport economics literature: they do not evaluate the macrolevel impacts that correcting equity findings may have on a network. It is conceivable that adjusting fares, changing service levels, or changing capital expenditure patterns across parts of a network in an attempt to achieve parity would merely redistribute disparities rather than correct them or not be viable for operational efficiency. Thus, transport economic literature and literature on transit expenditure and pricing equity functionally operate in silos. They rely on different scales of analyses (macro v. micro), use distinct methodologies to allocate or assess costs, and ignore the implications their findings may have on the other considerations; the literatures talk past one-another. This leaves an incomplete understanding about how equity and efficiency of transit service provision may be in tension with one-another, and whether and how they can be jointly optimized. In addition, both bodies of literature have methodological or transit mode focus limitations. While some expenditure equity literature, particularly with respect to capital investment equity, looks at many modes of transit; bus transit is disproportionately represented in transport economic and pricing equity literatures. That is, rail and ferry transit modes are not well represented in either cost structure or pricing equity literature. In addition, equity literatures tend to use data that is highly aggregate by today’s standards, and pricing equity research disproportionately focuses on temporal dimensions of equity. Among other examples, Hodge (1988) and Iseki (2016) use geopolitical boundaries, while Cervero (1981) uses bus yards (cost centers) that he labels “urban” or “suburban,” to evaluate spatial variability in cost and cost recovery patterns; and Parody et al. (1990) use aggregate nationwide data and a then-industry accepted peak-to-base ratio of costs to evaluate 11 temporal variability in net costs. Today, much more granular spatial and temporal units of analyses are available, but quite little research has been done that employs them. In the following sections, I interrogate transit cost and transit expenditure and pricing equity research, then surmise what they jointly suggest about the relationship between efficiency and equity of transit service provision and pricing. In the immediate succeeding section, I define economic cost models and accounting cost models, their evolutionary development, and their applications to transit cost and equity research. I then review literature on scale economies of transit and economic bases for transit, followed by a review of transit expenditure and pricing equity research. I close with ideas for future transit cost and pricing equity research that can meaningfully expand on the knowledge produced by past research. Variations in Transit Cost Modeling Transit cost modeling is generally approached in one of two ways, economic cost modeling or accounting cost modeling. Economic cost models are used to evaluate the economic structure of transit. They estimate total and marginal output costs for a transit operator whilst controlling for the inherent relationship across various factors of production and, in some instances, the interaction between production output and demand. By comparison, accounting cost models decompose total costs of an operator by allocating different cost items, such as fuel, to service outputs, such as vehicle-miles. Accounting cost models are not so focused on the structure of transit production as they are the occasions of transit service costs. I elaborate on these functional roles of each in the following subsections. Economic Cost Models Economic cost models evaluate the economic structure of an industry, as well as how efficiently it is operating given its structure. In transit cost literature, they are overwhelmingly used to evaluate the scale economies of the industry — namely, whether the industry is characterized by 12 economies of scale, constant economies, or diseconomies of scale. A production environment with economies of scale experiences costs of production that decrease with output. That is, the cost of each additional unit (i.e., marginal cost) is less than the last produced unit. In contrast, production environments characterized by constant economies and diseconomies experience constant marginal costs and increasing marginal costs, respectively. Economic cost models include linear, Cobb-Douglas, and transcendental logarithmic (translog) variations, each of which measure the cost of output as a function of the per-unit cost of input factors of production. Of these, the translog form has evolved to be preferred for evaluating the economic structure of transit service provision because linear and Cobb-Douglas cost functions impose restrictions that are not characteristic of transit service production (Karlafitis et al., 1999) — constant returns to scale and one-to-one substitutability amongst production inputs. The translog function removes these restrictions when evaluating the cost structure of an industry. Equation 1-1, taken from Karlafitis et al. (1999), represents a generalized translog cost function. ln𝐶 =𝛼 0 +𝑎 𝑦 ln𝑦 +∑𝛼 𝑖 ln𝑝 𝑖 +𝛼 𝑡 𝑡 𝐽 𝑖 =1 +∑𝛾 𝑖𝑦 ln𝑝 𝑖 ln𝑦 𝐽 𝑖 =1 +∑𝛾 𝑖𝑡 ln𝑝 𝑖 ∗𝑡 𝐽 𝑖 =1 +𝛾 𝑦𝑡 ln𝑦 ∗𝑡 + 1 2 ∑∑𝛾 𝑖𝑗 ln𝑝 𝑖 ln 𝑝𝑗 𝐽 𝑗 =1 + 1 2 𝛾 𝑦𝑦 (ln𝑦 ) 2 𝐽 𝑖 =1 + 1 2 𝛾 𝑡𝑡 𝑡 2 +𝘀 (1-1) where C is a total cost y is a measurement of output p i is a price per unit of input factor, i t is a time trend, and ε is a disturbance 13 Understanding the economic structure of the transit industry can help determine, among other things, how to size agencies to minimize aggregate costs, including whether provision of transit is best done through a monopoly. If there are economies of scale, then very large operators are ideal, as scale minimizes per-unit costs of production. In this case, perhaps a single transit operator would be best to operate public transit throughout the entire United States. On the other hand, if there are diseconomies of scale or a point at which economies of scale become diseconomies of scale, then there is an optimal size of transit operators that can minimize marginal costs of production. In addition, by accounting for the substitutability and interrelationship amongst input factors, economic cost models can ascertain whether there is over- or under-usage of different input factors that affect total or marginal costs. With respect to input substitutability, among other examples, for similar levels of net capacity, there is substitutability between smaller vehicles with frequent service (labor intensive) and larger vehicles with less frequent service (capital intensive). An economic cost model can measure this substitutability to identify the balance of vehicle size and service frequency that minimizes costs. An example of the interrelationship amongst input factors is the relationship between vehicle operators and fleet size. That is, only so many vehicles can be operated given the size of a labor force. If there is a larger fleet size than there are operator-hours available for use or vice-versa, this infers that there is over- or under-investment in capital or labor. Many (e.g., Vickrey, 1980) argue that the structure of the industry can help determine what, if any, subsidy ought to be given to transit service production. If transit production is characterized by economies of scale, then marginal costs will always be less than average costs, which will lead to an inefficient level of output. This is so because an operator would need to charge at the average cost rate to breakeven, which will lead to demand levels that are less than if the operator charged at the marginal cost rate in an economies of scale environment. As the argument goes, if transit 14 production is characterized by economies of scale, this is a basis for subsidizing transit equal to the difference between marginal cost and average cost so that an efficient output level is produced. However, this rationale rests on an enthymeme that the role of transit would be compromised without efficient levels of output. I deduce this line of thought further in the below review. Finally, to a much lesser extent, some transport economic literature evaluates the spatial economies of scale, scope, and density of the industry. Whereas non-spatial economies of scale measure whether costs decrease, increase, or stay constant with more production; spatial economies of scale, scope, and density, respectively, evaluate if measure whether costs decrease by expanding a route structure whilst keeping the locations served (e.g., unique stations or airports) fixed, by expanding the network by serving new locations, or by increasing the frequency of service whilst leaving the route structure and network size fixed. Figure 1-1, adapted from Basso and Jara-Díaz (2006), offers a visual schematic of these different measurements of transport spatial economies. Route Structure Fixed Variable Network Size Fixed Economies of Density Economies of Scale Variable Economies of Scope Figure 1-1: Matrix of economies of scale, scope, and density Accounting Cost Models In stark contrast to economic cost models that seek to explain the economic structure of a business or industry, accounting cost models merely allocate different cost inputs to different service outputs — often with the purpose of understanding dimensional variation of production. Cost inputs are foundational elements of production, whereas service outputs are occasions of expenditure. Among other examples, fuel and hourly wages are common cost inputs, while vehicle- miles and vehicle-hours are commonly used service outputs. Accounting cost models allocate cost inputs to service outputs to understand how much is being spent per unit of service output, on 15 average. Equation 1-2 offers a simple example of an accounting cost model where the variables are cost inputs, their coefficients are per-unit costs, and the subscripts correspond to unique service outputs that the cost inputs are allocated to. The summation of costs across all service outputs will equal the total cost of the operator. 𝐶 =𝛽 0 +∑𝛽 1 𝑎 𝑖 +𝛽 2 𝑏 𝑖 +⋯+𝛽 𝑛 𝑛 𝑖 𝑁 𝑖 =1 (1-2) where C is total cost Β 0 is a fixed cost i is a unique service output β 1, β 2, β 3, …, β n are per unit costs of cost inputs a i, b i, c i, …, n i are unique cost inputs allocated to service output i To understand dimensional variability, such as how much it costs to serve different times of the day, locations of a network, or routes in a network, the amount of different service outputs generated in each dimension is calculated and costs are proportionally assigned. Equation 1-3 illustrates this. The sum of all dimensions’ costs will represent the total cost of the network. 𝐶 𝑖 = 𝛿 𝑖 ∑ 𝛿 𝑖 𝑁 𝑖 =1 ∗∑𝛾 𝑗 𝑁 𝑗 =1 (1-3) where C i is the cost of serving dimension, i δ i is a service output, δ, in dimension i γ j is the cost, γ, of cost input, j, allocated to service output, δ Early accounting cost models used vehicle-miles and vehicle-hours as the only outputs to allocate costs to (in some cases, only vehicle-miles were used) (Cherwony and Mundle, 1978). However, several costs do not realistically correlate with vehicle-miles and vehicle-hours, such as administrative costs, infrastructure and maintenance of storage facilities, vehicle capital costs, etc. This is particularly true when evaluating dimensional variation of a network. For example, some 16 costs, such as the capital costs of transit vehicles and the facilities used to store them, are reasonably more intensively used in serving peak period travel — which means that allocating all costs based just on vehicle-hours and vehicle-miles can deflate peak period costs and inflate off-peak costs. This created an impetus for dialogue about how to allocate capital costs. Table 1-1 summarizes early arguments in the literature. Some (e.g., Meyer et al., 1965) argued that all capital costs should be charged to the peak period since, but for the peak period, investments would likely not occur. Similar to how freeway width is often criticized as being built to serve peak travel and is underutilized at other times, so too is transit capacity. However, this perspective overlooks that capacity and infrastructure are common or joint costs; despite the peak period perhaps being a trigger for the investment, it is an investment whose benefits is shared by all (e.g., Coase, 1970; McGillivray et al., 1980; as cited by Parody et al., 1990). Capital allocation method Summary of rationale Applied and theoretical studies 100% to peak period But for peak demand, there would be no capital investment to begin with, such as construction of a rail system. Therefore, 100% of the capital costs ought to be allocated to the peak period. Meyer et al. (1965) 85-15 peak-to-base rule In the absence of a clearer definition of how asset costs shall be divided between time periods, allocating 85% of the cost to the peak period and 15% to the base is accepted as a reasonable split. Boyd et al., (1973), Cervero (1981), Charles Rivers Associates (1989), Parody et al. (1990) Marginal cost approach Capital costs are a common cost that is shared by all who use it. Every time period should pay for each capital asset proportional to its use of the asset. In some cases, the peak period will be charged 100% for an asset only used by it, but will not be wholly responsible for all assets. Savage (1989), Taylor et al. (2000) Table 1-1: Methods of temporal allocation of capital costs One solution to proportionally allocating these costs was advanced by Cherwony and Mundle who tested applying peak vehicles as an allocation factor for peak-to-base temporal analysis (1978) and route-by-route analysis (1980). In their temporal analysis, they evaluate peak-to-base 17 costs of express bus service in the Minneapolis-Saint Paul region by proportioning vehicle costs by labor productivity — the ratio of pay-hours to vehicle-hours — during peak and base periods, so account for the greater volume of vehicles used during the peak period. They find that the peak period costs 56% more than the base period. In their route analysis, they use the Birmingham- Jefferson County Transit Authority as a case study and tested how expanding the number of output variables from one to three — vehicle-miles, vehicle-hours, and peak vehicles, in incremental order — affected findings in route-by-route cost variability. Table 1-2 shows their resulting calibrations of cost per unit of service output with each model. When used to evaluate route cost variability, they found much variability in how the cost of the 21 routes were estimated across each model. The variation depended on the length of the route (vehicle-miles), average speed of the route (vehicle- hours), and, related to both of these, number of vehicles required for the route (peak vehicles). These variables are among the most common used in the industry today. Model Variable Share of Costs Per Unit Costs Single Variable Vehicle-Miles 100% $1.13 Two Variables Vehicle-Miles 37.2% $0.42 Vehicle-Hours 62.8% $9.34 Three Variables Vehicle-Miles 27.9% $0.32 Vehicle-Hours 62.8% $9.34 Peak Vehicles 9.3% $3,459.17 Table 1-2: Results of Different Allocation Models from Cherwony and Mundle (1980) Another study, the Bradford Bus Study (Savage, 1989), introduced allocating capital resources using a marginal cost approach. Specifically, base level capital resources are shared amongst all time periods. Then, the marginal additional capital resources employed to serve each further resource-intensive time period are shared between that time period and further resource- intensive time periods, if any. Figure 1-2 represents this approach. If the resources in this figure are buses, the graveyard shift is responsible for 25% of the costs of the first 10 buses, while the peak period is responsible for 33% of the costs of the next 20 buses and solely responsible for the costs of the last 40 buses. 18 Figure 1-2: Marginal cost approach to capital resource allocations Throughout this debate, and in various applied studies to this day, scholars and practitioners have evaluated temporal variability of capital costs using an approximate representation of the peak- to-base share rather than embedding a calculation in their analysis. The common ratio used is 85 peak/15 base (e.g., Boyd et al., 1973; Cervero, 1981; Charles Rivers Associates, 1989; Parody et al., 1990). Finally, there are both partially allocated cost models and fully allocated cost models (Cherwony et al., 1981; Taylor et al., 2000), which serve different types of analyses. Partially allocated cost models are used to evaluate how costs vary across some dimension within an entity or to compare a particular subset of expenditure patterns between or amongst multiple entities. Thus, they are “partial” because only costs that vary by the dimension being analyzed need to be allocated to understand this variability. For example, if a researcher or analyst wishes to understand how costs vary by time of service, they would only include temporally variant costs in their assessment. By comparison, if a researcher wishes to compare two or more systems to make a comprehensive cost-benefit or efficiency analysis, such as when doing an alternatives analysis between multiple transit investment options to make an investment choice, a fully allocated cost model would be used. 19 Because accounting cost models allow costs to be dimensionally allocated, they are a primary type of cost model used in expenditure and pricing equity research. If, for example, we wish to understand how much more money is expended serving different populations of travelers, we may first evaluate how costs vary by time of service, then associate these findings with the makeup of travelers during those different times to estimate if there is disparity in service delivery by class of rider. A Synthesis To summarize, accounting cost models’ lack of simultaneous equating of inputs and outputs — that is, their lack of interaction across cost inputs and service outputs — make them inferior to economic cost models for prospective or predictive analyses. In other words, accounting cost models cannot be used test, among other things, how a change in service plan would affect total costs because they impose a linearity restriction that is not reflective of the costs of transit service provision (Cherwony et al., 1981). By comparison, economic cost models inherently account for these interrelationships, making them ideal for prospective research or inquiries about economic structure. Furthermore, economic cost models are founded in theory that there is a relationship between various inputs of production, whereas accounting cost models are subjectively-derived algebraic relationships. On the other hand, accounting cost models are superior to economic cost models for retrospective and descriptive analyses of a system as it is built and operated. This is because, whereas economic cost models are fundamentally macro-focused, accounting cost models allow a researcher to decompose a network into parts to measure cost variability. Thus, both approaches to transport cost modeling have legitimate uses and limitations. However, little research comprehensively applies both methods to evaluate the interaction between microlevel impacts and network impacts. Instead, cost literature focused on economic efficiency or economic structure that employ economic cost models tend to ignore or discount distributional inequities that 20 may result, while literature that uses accounting cost models to evaluate distributional disparities tend to ignore or discount the network impacts of any changes suggested therefrom. Scale Economies of Transit Literature on scale economies of transit evolved greatly in the 1980s and 1990s. Most notably, the equations used have converged around translog functions. The production of transit service is much different than most other production environments due to the spatial and temporal dimensions of production making it non-linear. This has been demonstrated through multiple studies of both the short-term scale economies of transit production (Viton, 1981; De Borger, 1984; Obeng, 1984; as cited in Berechman, 1993) and long-term scale economies of transit production (Williams and Dalal, 1981; Williams and Hall, 1981; Berechman and Giuliano, 1984; as cited in Berechman, 1993). Some point out that translog functions embed an assumption that a firm has cost-minimizing interests and that there are identical outputs of production across the firms analyzed in a study (e.g., Iseki, 2008). However, the fact that a transit agency may not have cost- minimizing motivations due to subsidies it receives, as Iseki (2008) suggests, does not void the importance of studying the cost efficiency of the agency. Given model development to-date, translog functions are the predominantly accepted form used in contemporary transit cost structure research. Since this general coalescence around the translog function, findings on the economic structure of transit at a foundational level has not made much headway. Consistently, findings vary by the size (and mix of sizes) of operators analyzed, whether supply-side outputs like vehicle-miles or demand-side outputs like passenger count are used, the type of data used in the analysis (cross- sectional, panel, or time series) (Berechman and Giuliano, 1985; Berechman, 1993; Gwilliam, 2008). For example, the use of a sample that includes heterogeneous sizes of operators will typically lead to the most influential operator(s) in the sample skewing the results (Berechman, 1993). For cross- 21 sectional studies, this is especially true because such studies inherently assume that all observations in the sample — unique transit agencies, in this case — are comparable (Berechman and Giuliano, 1985). Due to these implications, time-series studies that have multiple time observations of the same operator or panel studies that of multiple operators at multiple times are preferred. Furthermore, panel studies allow types of operations to be pooled in the analysis to test for whether cost structure varies by some characteristic of firms. Finally, the use of demand-side outputs tend to bias lead to economies of scale because they are not a measurement of the relationship between supplier costs and supplier outputs, but a measurement between supplier costs and travel density (Berechman, 1993). Table 1-3 shows various studies, their characteristics, and their scale economy findings. Several observations can be made from Table 1-3, not the least of which is that findings vary. However, another takeaway is that panel studies have allowed an analysis in how economies of scale vary by transit agency size. Among studies that use translog functions and vehicle-distance (i.e., vehicle-miles or vehicle-kilometers) as the output metric, the prevailing finding is that there are decreasing returns to scale in transit service production, particularly for large agencies. To directly illustrate the differing results by using supply-side versus demand-side outputs, Berechman and Giuliano (1984) conducted parallel time series analyses of the same United States bus operator using passenger count and vehicle-miles as output measurements. They found opposing conclusions on scale economies: using passenger count as the output measurement leads to economies of scale, whereas using vehicle-miles as the output measurement leads to there being diseconomies of scale. However, Berechman (1987) did a similar parallel study in Israel and found 22 Study Sample size Model fo/rm Data organization Output measurement Scale economies findings Koshal (1972) 1 10 Linear Cross-sectional Vehicle-miles Constant Veatch (1973) 1 29 Linear Cross-sectional Vehicle-miles Constant Veatch (1973) 1 37 Linear Cross-sectional Vehicle-miles Constant Wabe and Coles (1975) 1 61 and 76 Linear Cross-sectional Vehicle-miles Decreasing Nelson (1972) 1 40 and 45 Log-linear Cross-sectional Vehicle-miles Constant Williams and Dalal (1981) 1/2 22 Translog Cross-sectional Vehicle-miles Decreasing (small), Increasing (large) Viton (1981) 1/2 54 Translog Cross-sectional Vehicle-miles Decreasing Obeng (1984) 2 62 Translog Cross-sectional Passenger-miles Decreasing Button and O’Donnell (1986) 2 Cross-sectional Passenger-miles Decreasing Obeng (1985) 2 62 Translog Cross-sectional Passenger-miles Decreasing Williams and Hall (1981) 1/2 50 Translog Cross-sectional Passenger-miles Increasing Caves and Christensen (1988) 2 Linear Cross-sectional Multi-output Constant Berechman and Giuliano (1984) 1/2 28 Translog Time-series Vehicle-miles Decreasing Passenger trips Increasing Berechman (1987) 10 Translog Time-series Vehicle-kilometers Increasing Passenger trips Berechman (1983) 1 28 Translog Time-series Fare revenue Increasing Applebaum and Berechman (1991) 2 38 Translog Time-series Multi-output Increasing Colburn and Talley (1992) 2 36 Translog Time-series Multi-output Increasing de Rus (1990) 2 861 Log-log Panel Vehicle-kilometers Decreasing/constant Karlaftis et al. (1999) 2 216 Translog Panel Vehicle-miles Increasing (small, medium), Decreasing (large) Karlaftis (2004) 1,295 Translog Panel Vehicle-miles Increasing (small, medium), Decreasing (large) Passenger trips Multi-output Farsi et al. (2007) 300 Translog Panel Seat-kilometers Increasing Iseki (2008) 3,329 Linear, Log, Quadratic Panel Maximum vehicle use Decreasing Karlaftis and McCarthy (2002) 2,304 Translog Panel Multi-output Increasing/constant Batarce and Galilea (2018) 105 Log-log Panel Multi-output Increasing Table 1-3: Economies of scale literature findings 1 As reported by Berechman and Giuliano (1985) 2 As reported by Karlaftis and McCarthy (2002) 23 that both output measurements lead to economies of scale. This perhaps implies that there are distinctions between the two agencies not fully captures in the cost model. Some things not conveyed in Table 1-3 is how panel studies group the data and what cost inputs are used. Most panel studies group transit operators by their size (e.g., volume of vehicle- miles) to test if economies of scale vary by production level, though the number of groups and their boundaries vary. Exceptions to this are Iseki (2008) and Farsi et al. (2007) who grouped agencies by their level of outsourcing and transit mode, respectively. In both studies, the ultimate findings did not vary across the groupings. As for cost inputs, most models use common cost inputs, such as capital, labor, fuel, and maintenance. However, Batarce and Galilea (2018) also use demand-side costs — a practice made popular by Mohring (1972) that will tend to lead to economies of scale results, but that goes beyond measuring production cost structure (Berechman, 1993). Except for Farsi et al. (2007), all the studies reviewed in Table 1-3 focus on bus transit. This is a limitation in existing transit scale economies literature; other modes of transit are not well- evaluated. Besides Farsi et al. (2007) who found economies of scale when using seat-miles as an output, Savage (1997) reviewed the scale economies of rail using panel data for 22 systems across six years. He grouped agencies by the type of rail — light rail and heavy rail — and found relatively constant returns to system size. Berechman and Giuliano (1985), Berechman (1993), and Gwilliam (2008) offer a more comprehensive review of economies of scale literature. In what I have reviewed, when only supply- side factors are considered and a flexible form cost model is used, the plurality consensus in the literature is that smaller bus agencies experience economies of scale, moderate-sized agencies experience constant scale economies, and larger operators experience diseconomies of scale. While different studies have tested whether one factor or another is important to include in a cost function as an input or output — for example, testing if economies of scale are explained by the level of 24 contracting (Iseki, 2008) — these basic findings about the economic structure of the industry have remained steady over the past several decades. Most important for this review is the implication that the economies of scale argument for transit subsidies — which I evaluate further in the following section — likely only applies to small transit systems. Economic Bases for Transit Subsidies More central to this paper is what transit economic literature has to say about transit subsidies, fare setting, and the equity thereof. That is, given the cost structure of transit, what, if any, economic bases exist to provide transit subsidies? While there are many arguments for subsidizing transit, there are few notable economic arguments for doing so. Yet, little research evaluates what the “right” subsidy amount ought to be based on these arguments. An economic basis for transit subsidization is one that is justified as a means of correcting a market failure that is otherwise present. A market failure occurs when the level of production is inefficient for what the market demands. Four common categories of market failures include if the good is a public good, if there are negative or positive externalities of production that are not internalized to the producer, if the costs of production can be minimized under a monopoly, and if consumers have incomplete information to make rational decisions. In transit, the often-referenced bases for subsides are that it produces positive externalities, that it is a natural monopoly (i.e., has economies of scale), or as a second-best solution (Elgar and Kennedy, 2005). A second-best solution effectively means that, in the absence of correcting policies or other interferences that create a market failure, an offsetting intervention is necessary. As explained in the succeeding paragraphs, the former two economic bases for transit subsidies are arguably applied examples of the second-best argument. The second-best pricing argument for transit subsidies rests on the notion that the automobile is heavily subsidized, making it necessary for transit to receive proportionally similar 25 subsidies to be on an “equal footing” in its attractiveness as a travel mode. In an economically efficient environment, consumer prices are set to the marginal costs of production. This does not occur for any mode of transportation in the United States, especially when externalities are considered. In 2017, just over half of nationwide expenditures on roadways was financed through user fees (United States Census Bureau, 2017). Apart from direct expenditures not being fully financed by users, marginal externalities of auto travel — including, among other examples, the delay time that each individual motorist imposes on other motorists by using a roadway and pollution from emissions — are also not paid by drivers. By failing to institute so-called “first best” strategies by internalizing these costs onto motorists, the mode share of driving relative to transit is greater than it otherwise would be. That is, motorists effectively receive a discount, so will consume more car-oriented travel. In the absence of instituting first best pricing, a proportionally equivalent subsidy for transit use is a second-best solution. With the right level of transit subsidy, the private cost of using transit relative to the automobile can theoretically lead to travel consumption patterns that mimic what a fully unsubsidized (i.e., first best pricing) transportation system would experience. The notion that transit service production and consumption generates positive externalities that warrant subsidizing is often subject to a “relative to driving” caveat. Compared to driving, more people taking transit generates less pollution (assuming enough people take it), so its provision and consumption is a positive externality relative to driving. For the same reason, more people taking transit and it leading to less vehicle congestion is a positive externality relative to driving. In these examples and more, the positive externality argument is premised on correcting subsidies given to auto travel, making it a second-best argument. Some also argue that there are positive externalities from transit generating economic development. However, much literature has all but disproven this by demonstrating that development patterns and rent premiums being induced through transit is weak, at-best, in the decades following system opening (e.g., Cervero and Landis, 1993; Cervero and 26 Landis, 1997; Bollinger and Ihlanfeldt, 1997). Finally, many argue that transit provides accessibility for those who do not have access to a car. Yet, transit providing accessibility to those without a car is, by definition, a derivative of circumstances induced by car-oriented spatial structures. Hence, positive externality arguments for transit subsidies are often indirect second-best arguments for them. Similarly, the argument that transit production is characterized by economies of scale, and that this is a basis for subsidizing transit, is really a second-best argument. As the argument goes, if transit operates under economies of scale, an operator must charge at the average cost rate, which will always be greater than the marginal cost rate. This will lead to an inefficiently low level of transit service provision. To achieve an efficient level of service provision, a supplier subsidy equal to the difference between the average cost and marginal cost at the efficient output level is warranted. However, many natural monopolies, such as utility companies, charge at an average cost rate without subsidy. Thus, this by itself does not justify subsidizing transit. Rather, as Vickrey (1980) argues, “the existence of sharp economies of scale is not unique to the transit industry … [But,] while … other utilities can manage, albeit inefficiently, without a subsidy, transit in many cases can no longer do so.” He goes on to infer that this is because of the role of transit relative to other utilities: to provide a transportation lifeline to those who cannot or do not drive, and to correct for subsidies given to auto travel. Accordingly, apart from the preponderance of evidence showing that the transit industry — particularly larger operators — does not operate under economies of scale, even if it did, this argument is really a second-best argument for transit subsidies. The “Mohring Effect” The economies of scale argument gained popularity following the seminal work of Mohring (1972). He showed that if the traveler costs of travel time, including wait time, are accounted for in a transit operator’s costs, there are economies of scale in the production of transit. That is, to 27 provide a sufficient level of frequency to minimize traveler wait time to a social welfare-optimizing level, a subsidy is needed to achieve this level of scale. Turvey and Mohring (1975) adapted the concept to explain a model for optimal bus fares, exclusive of relative externalities to the car, but inclusive of time externalities of transit users. Hence, they control for the temporal “joint cost” (i.e., a dimensional cost) of transit use. They suggest that the fare should not only account for the producer’s costs, but also the cost of total travel time of consumers. This includes time waiting at a bus stop, which can be compounded if a bus is full and must pass the stop, which can be further compounded by the direction and time of travel (e.g., inbound in the morning commute and outbound in the evening commute) and location of travel (e.g., distance from city center relative to travel time and direction). Further, the costs of a rider seeking to travel are partly derived from other riders consuming travel — meaning the congestion costs should also be accounted for. Since Mohring (1972) and Turvey and Mohring (1975) explained this concept, it has been theoretically modeled by various scholars (e.g., Jansson, 1979; Larsen, 1983; Else, 1985; Jansson, 1993; Pederson, 2003), though empirical testing is near-null. However, some recent literature has challenged the significance of travelers’ time in justifying transit subsidies in both direct and indirect ways. Van Reevan (2008) argues that Mohring improperly equivocates users of infrequent services, who will plan their travel around the transit service timetable, with users of frequent service, who will “show and go.” Indeed, an embedded assumption in the Mohring theory is that consumers access transit with a random distribution, making all costs of wait time proportional to 50% of the frequency. Van Reevan shows that, if these different “types” of users are controlled for and their wait time costs incorporated into an operators pricing, the profit-maximizing fare is at least equal to the welfare-maximizing fare, making it such that there is no basis to publicly subsidize the scaling of transit service on the grounds of minimizing user costs. However, van Reevan misses a point in the Mohring theory, which is that demand is a 28 function of frequency. Relative to a car that one can access anytime they want, a low-frequency transit service forces travelers to revolve their personal schedules around trip-making opportunities rather than those opportunities being open ended so that they revolve around their schedules. Basso and Jara-Diaz (2010) make this point by exposing that van Reevan’s model assumes a uniform reservation price for transit and, if that reservation price were allowed to vary across travelers, there in fact is a difference between the profit-maximizing and welfare-maximizing fare, with the latter being less than the former and requiring subsidy under the Mohring theory. On the other hand, recent empirical research suggests that, while frequency is an important consideration in travelers’ decision to use transit for their travel, its importance may be inflated. Some research shows that travelers weight their time waiting at least 1.3 times greater than actual, but that this impact can be offset with improved amenities at the station (Fan et al., 2016). Fan et al.’s research involved a combination of transit rider surveys and observations of traveler behaviors at different types of transit stops. Other scholars, using stated preference surveys, emphasize that travelers would prefer more frequent service over stop amenities, but that certain foundational characteristics of transit such as safety are of foremost importance (e.g., Iseki and Taylor, 2010; Yoh et al., 2011). In addition, Berrebi et al. (2021), studying Atlanta, Georgia, Miami, Florida, Minneapolis/Saint Paul, Minnesota, and Portland, Oregon, show that there are diminishing returns on frequency for users; as frequency increases, the value of each incremental increase means less and less to a user. Thus, while service frequency is a relevant factor for traveler’s option of transit as a mode of travel, it mainly is with respect to low frequency service and can be countered with station amenities. In any event, the “Mohring effect” is not a supply-side factor in transit service production, so is not cornerstone to understanding the cost structure of transit. Instead, it is important for estimating transit subsidies, if transit is assumed to be provided on a social welfare basis, or if 29 second-best intervention strategies to auto subsidies and their impact on transit patronage are assumed preferred to first-best strategies. Optimal Subsidization and Fare Setting Despite these economic bases for transit subsidization, defining an optimal subsidy level or fare based on these objectives is not well-represented in transport economic literature. Also not represented in the literature are analyses of the equity implications of subsidies — or, inversely, ways to “optimize” equity through transit pricing. De Borger et al. (2002) suggest this is due to models for measuring objectives other than efficiency not being well-developed and, referencing Merchand et al. (1984) and Pestieau and Tulkens (1993), that efficiency is the foremost important measurement of transit performance even if there are other objectives. To the extent that models of these sorts have been generated, they are almost exclusively theoretical; very little applied or empirical research has occurred. Elgar and Kennedy (2005) review three models — Glaister and Lewis (1978), Henderson (1977), and Viton (1983) — that have been developed to estimate optimal transit subsidies. Each model has great limitations but are among few generalized models that have been developed to estimate the “right” amount of subsidies to give to transit. Viton (1983) developed a Pareto-optimal model that internalizes all travel costs across all modes, using San Francisco, California and Pittsburgh, Pennsylvania as his test cases. The model assumes, among other things, only two modes of travel, bus transit and automobile; a monocentric travel pattern; uniform travel volumes from all residential nodes of equal distance from the central business district; a single bus terminus at the central business district; fixed shares of trips between peak and other times of travel; and that the city street and highway networks are fixed with only the highway capacity able to vary with demand and pricing. With those limitations considered, he found that under Pareto optimal pricing that internalizes direct and externality costs, transit mode share in San Francisco ranged between 73% 30 and 83%, depending on the net travel volume with this share diminishing as net travel volume increases. In Pittsburgh, effectively all travel mode under all travel volume scenarios opted for transit. Viton further found that there are economies of scale in transit under this model, thereby implying a need for subsidies if an efficient level of service is to be provided, even under a systemwide Pareto-optimal pricing framework. Henderson’s (1977) model more simplistically identifies the optimal amount of expenditure on highways to be economically based — that is, construction and maintenance costs should be increased until marginal costs equal marginal willingness to pay by travelers. He then defines the subsidy for transit to be equal to the marginal rate of substitution between the private cost of road use and the cost of road provision, factored by a ratio of the cross-elasticity of road-use to transit use and the price elasticity of transit use. I define this in Equation 1-4, which is derived from Henderson (1977), as cited by Elgar and Kennedy (2005). In effect, this subsidizes transit use approximately equal to the share of roadway costs that a consumer would pay if they drove scaled to the generalizable costs they suffer by using transit instead of driving. 𝑆 = 𝑋 ( 𝜕𝐶 𝜕𝑋 ⁄ )𝑋𝛼 𝑋 ( 𝜕𝐶 𝜕𝐾 ⁄ )𝑍𝛾 (1-4) where S is a transit use subsidy C is cost, X is the number of road trips, K is capital expenditure on road capacity, Z is number of transit trips, α is the cross-elasticity between road and transit use, and γ is the price elasticity of transit Unlike the Viton (1983) and Henderson (1977) models, the Glaister and Lewis (1978) model allows for multiple forms of transit and times of travel. They account for six modes — all combinations of car, bus, and rail modes across peak and off-peak times — and treat the cost of peak and off-peak road provision as constant, assume negligible externalities of off-peak travel, focus only on internalizing externality costs of congestion, and assume there are no congestion costs 31 of rail transit use. They use London as their case study and have as their objective to set the subsidy level to be the difference between base per-rider costs of transit and aggregate utility loss of using transit instead of driving. This is reflected in Equation 1-5, while Table 1-4 defines indices used — both taken from Glaister and Lewis (1978). Index Transport Mode 1 Automobile, peak 2 Automobile, off-peak 3 Bus transit, peak 4 Bus transit, off-peak 5 Rail transit, peak 6 Rail transit, off-peak Table 1-4: Travel mode indices for Glaister and Lewis (1978) model max 𝑝 3 ,𝑝 4 ,𝑝 5 ,𝑝 6 { 𝐺 (𝛼 3 ,𝛼 4 ,𝛼 5 ,𝛼 6 ,𝑋 1 (𝛼 3 ,𝛼 4 ,𝛼 5 ,𝛼 6 ),𝑋 3 (𝛼 3 ,𝛼 4 ,𝛼 5 ,𝛼 6 ),𝑝 ̂,𝑢 ) −𝐺 (𝑝 3 ,𝑝 4 ,𝑝 5 ,𝑝 6 ,𝑋 1 (𝛼 3 ,𝛼 4 ,𝛼 5 ,𝛼 6 ),𝑋 3 (𝛼 3 ,𝛼 4 ,𝛼 5 ,𝛼 6 ),𝑝 ̂,𝑢 ) −[𝐶 3 (𝑋 1 ,𝑋 3 )−𝑝 3 𝑋 3 ] −[𝐶 4 (𝑋 4 )−𝑝 4 𝑋 4 ] −[𝐶 5 (𝑋 5 )−𝑝 5 𝑋 5 ] −[𝐶 6 (𝑋 6 )−𝑝 6 𝑋 6 ] } (1-5) where G(α, X 1 , X 3 , 𝑝 ̂, u) is the base price function aggregated across individuals G(p, X 1 , X 3 , 𝑝 ̂, u) is the expenditure (willingness to pay) function aggregated across individuals X i is the demand per hour of travel mode, i α i is the “base price” of travel mode, i p i is the “variable price” of travel mode, i 𝑝 ̂ is a vector of all other fixed prices, including p 1 and p 2 C i is a per person cost of serving travel mode, i G(α, X 1 , X 3 , 𝑝 ̂, u) defines the base fares for transit service provision, which are considerably higher than G(p, X 1 , X 3 , 𝑝 ̂, u), the willingness to pay levels of travelers. The remaining terms are operating cost subsidies. Hence, a price change from willingness to pay levels to base levels is a compensating variation that must be offset with subsidies. After aggregating this to all travelers, they find that the aggregate transit subsidies made in London at the time were within the statistical range of their study. However, when applied to a study in Canada, it was found that Canada underinvests in transit by a factor of 2.7 (HLB Decision Economics, 2001; as cited by Elgar and Kennedy, 2005). 32 Parry and Small (2009) are among few who have conducted more recent empirical research on the second-best argument for transit subsides. They applied their research to Washington, Los Angeles, and London and evaluated the welfare value of transit subsidies, inclusive of both user-side costs (i.e., the “Mohring effect”) and externality costs of different travel modes. They found that transit subsidies are welfare improving from a second-best standpoint, particularly if an operator is incentivized to minimize costs and efficiency losses. More generally, they determine that a subsidy level equal or greater than 50% of operating costs is generally justified from a second-best standpoint. As well, Mattson and Ripplinger (2012) use panel data of small transit operators in the United States to measure economies of scale and estimate subsidy levels that will account for the difference between average costs and marginal costs at efficient output levels. They include environmental and demand-side social costs in their model, find that economies of scale exist for small operators and dimmish with operator size, and estimate that the optimal operating subsidy level averages $0.665 per vehicle-mile for medium-sized agencies in the sample and as high as $1.80 per vehicle-miles for the smallest of agencies. Finally, Basso and Silva (2014) evaluated the substitutability between car congestion pricing, dedicated bus lane installation, and transit subsidies in achieving welfare maximum outcomes. In accounting for the traveler cost of transit use, they found that transit subsidies have a diminishing value when the other congestion management strategies are implemented; that is, with internalized costs of vehicle congestion and the provision of dedicated transit rights of way, there is a diminishing basis for transit subsidies. As suggested by Elgar and Kennedy (2005) and affirmed in this review, there is much to be desired in empirical economic cost research when it comes to estimating the “right subsidy” level for transit. Furthermore, the models that have been developed and applied are done at an aggregate level. If, for example, Canada expended the additional CA$3.6 billion on transit mega projects suggested by HLB Decision Economics (2001) in the Northwest Territories, that would have 33 satisfied the test for efficient investment in transit using the Glaister and Lewis (1978) model. Yet, it is prima facie obvious that this would be a wasteful application of the $3.6 billion; there is obviously a spatial dimension to production efficiency. However, this spatial dimension in efficient production and pricing has not been evaluated much at all in transit economic literature, theoretical or applied. Finally, a common theme across these studies — theoretical and applied — is that their authors acknowledge that they do not account for distributional (equity) impacts or efficiency loss from reliance on a tax base that could potentially disincentivize tax-generating income. A few scholars have acknowledged this hole in the research (e.g., Dodgson and Topham, 1987), but filling it seems yet to have occurred. Transit Expenditure and Pricing Equity Literature Equity is the quality of something being fair and impartial. However, how it is measured varies greatly, including in transportation literature. Among other considerations is the unit of measurement (e.g., geographic areas, individuals, socioeconomic groups, etc.) and the subject of measurement (e.g., accessibility, transport investment, decision-making process, pricing, etc.). In the following subsection, I summarize measurements of equity in transportation. Thereafter, I review research on transit expenditure and pricing equity with a focus on research that uses accounting cost models to inform its conclusions. Measurements of Equity in Transportation Past literature reviews show that most transportation equity research is concerned with access equity — that is, how many places different people can get to within a particular amount of time and on a particular monetary budget (Pereira et al., 2017; van Wee and Mouter, 2021). As travel in the United States has become increasingly spread out, disparity in how many places different members of society can reach has become distributionally inequitable: those with great means can access many more places than those with less means, creating so-called “psychic costs” of 34 “environmental deprivation” from the outdoors and “access deprivation” from locations more generally (Ewing, 2008; Popenoe, 1979). Access equity literature focuses on these sorts of issues. There is also transportation (or mobility) justice that focuses less on how fair a transportation system is as built, operated, and priced; and more on how inclusive the planning and decision-making process of transportation is (Karner et al., 2020; Sheller, 2018). Dating back to the urban renewal era of the 1950s that defined clearing slums with megaprojects as a mechanism to combat the “eyesore” of poverty, disadvantaged communities have historically been excluded from participating in the decision-making process of transportation investments while at the same time being disproportionately burdened with the negative impacts of these decisions (e.g., Altshuler and Luberoff, 2004; Carmon, 1999; Couch, 1990). Transportation justice is concerned with making the planning process equitable by correcting systemic power structures that facilitate marginalized communities being discounted in decision-making and bearing the blunt of negative impacts of transportation. However, of interest in this literature review is transit expenditure and pricing equity. What is a fair price for transit users to pay, what is a fair way for transit expenditure to be distributed, and how ought these be measured? Taylor and Norton (2009) synthesize various theories of justice, types of equity, and units of equity analysis commonly applied to transportation equity research and policymaking. Table 1-5, adapted from Taylor and Norton (2009), define the relationship between the many theories of justice — strict egalitarianism, difference principles, resource-based principles, desert-based theories, and libertarianism — and types of equity — market equity, opportunity equity, and outcome equity — they evaluate. Theory of Justice Type of Equity Strict egalitarianism: All members of society receive the same magnitude of goods, regardless of their contribution to costs. Outcome equity: Spending or investment achieves parity in outcome across people, groups, or geographies. In transportation, accessibility is a typical measurement of outcome. 35 Difference principles: All members of society have equal rights and liberties, but differences in outcomes that reward individual achievements are warranted. Opportunity equity: Spending per person — or proportional to group/geography size — is equal. Resource-based principles: All members of society receive a baseline level of goods, anything beyond which is not of societal concern. Desert-based theories: Members of society shall receive social benefits proportional to what they contribute to society. Market equity: Spending or investment is proportional to what individuals, groups, or geographic areas pay (or contribute). Libertarianism: Members of society shall receive benefits proportional to what they pay; benefits should be fully market driven. Table 1-5: Theories of Justice and Types of Equity in Transportation Equity Research (adapted from Taylor and Norton, 2009) As implied in Table 1-5, common units of equity analysis in transportation include individual equity, group equity, and geographic equity. Respectively, that is whether individuals pay for and receive transportation in a way that is equitable, whether there is parity across groups (typically, socioeconomic groups) in terms of the incidence of investments they receive or fees they pay into transportation relative to the investments they receive, and whether there is parity with respect to these same considerations across different geographic areas. Taylor and Norton (2009) surmise that transportation finance and investment decisions in the United States are overwhelmingly based on geographic — more specifically, geopolitical — units of analysis with a focus on opportunity and outcome equity, and that this ethos in policymaking conflicts with individual and group equity because it depends on financing structures that manifest inequities across individuals and groups. Among other examples, because investments are geopolitically determined rather than based on facility or service usage (e.g., efficiency), market pricing simultaneously does not and cannot cover the ongoing costs of transportation services or facilities, leading to a reliance on such revenue streams as local option sales taxes for financing, which have been shown to be socioeconomically regressive with respect to both income and usage. That is, marginalized communities pay more relative to their income levels and relative to their consumption of transportation (e.g., Davis et al., 2015; Dill et al., 1999; Lederman et al., 2020; Schweitzer and Taylor, 2008; West, 2009). 36 While geopolitical outcome and opportunity equity dominate policymaking, equity across individuals and socioeconomic groups is prevalent in transit expenditure and pricing equity research. I distinguish between “expenditure equity,” “pricing equity,” and “expenditure-pricing equity” in that the former focuses merely on disparity in gross expenditures made; the second, disparity in the amount paid for services rendered regardless of the amount of service received or cost thereof; and the latter, a combination of these that measures disparity in the amount individuals and groups receive relative to what they pay. For example, if more money is spent operating two-minute frequency transit service in an urban corridor compared to 30-minute frequency in an outlying area, we would conclude that the urban corridor receives inequitably high levels of service from an expenditure equity perspective. Similarly, if more capital investment money is spent building a heavy rail system used by affluent people compared to bus capital investments for services used principally by low-income persons, we would conclude that capital investment patterns are expenditure inequitable and regressively so. However, if travelers of the 30-minute frequency service pay a higher fare than those who use the two-minute frequency service, then users of the 30-minute frequency service pay an inequitably high fare from a pricing equity standpoint. Finally, if more costs are recovered through fare revenue along the high-frequency route than the low-frequency route, we would conclude that the latter route receives inequitably high levels of net subsidy from an expenditure-pricing equity standpoint. In Table 1-6, I outline various studies — some of which do not explicitly venture to evaluate equity but have equity implications — that fall under either of these measurements. I also label each study with either a focus on capital expenditures, operating expenditures or pricing with a spatial focus, or operating expenditures or pricing with a temporal focus. In the following subsections, I evaluate the findings of select literature further. 37 Study Essence of Relevant Findings Capital or Operational, Spatial or Temporal Type of Equity Cherwony and Mundle (1978) There is disparity in gross costs between peak and off-peak operating costs. Operational, temporal Expenditure Equity Cherwony and Mundle (1980) There is disparity in gross costs across different routes of a network. Operational, spatial Pucher (1982), Garrett and Taylor (1999) There is disparity in gross levels of capital investments made to different socioeconomic groups of riders. The pattern is regressive; more expenditure is spent on transit capital projects used by non-minority, higher-income persons. Capital Taylor et al. (2000) There is disparity in gross levels of operating costs expended across different times of the day and modes of transit. The pattern is regressive; more costly service tends to be consumed by non-minority, higher-income persons. Operational, temporal and spatial Zhao and Zhang (2019) Compared to flat rate fares, distance- based fares impose a greater cost on marginalized communities relative to non-marginalized communities in Beijing because marginalized persons live further from the central business district. Operational, spatial Pricing Equity Rubensson et al. (2020) Compared to flat rate fares, distance- based fares impose a greater cost on marginalized communities relative to non-marginalized communities in Stockholm because marginalized persons live further from the central business district. Operational, spatial Farber et al. (2014) The impact on different socioeconomic groups of a distance-based fare structure will vary across spatial areas, as the distance different socioeconomic communities travel is not spatially constant. Operational, spatial Nuworsoo et al. (2009) In evaluation of potential fare structure changes, flat rate fares that charge per trip segment were found to affect marginalized communities most adversely, while structures that allow free or low-cost transfers have the least adverse impact on marginalized communities. Operational, spatial Zhou et al. (2019) There is spatial disparity in the fare per kilometer paid for transit in zonal fare structures. Operational, spatial Bandegani and Akbarzadeh (2016) Converting from a flat rate fare structure to a distance-based fare structure improves equity in the cost per mile paid by travelers. Operational, spatial Wang et al. (2021) A change from a 23-zone fare structure to an 8-zone fare structure decreased cost per zone disparities overall and across passenger types, but increased Operational, spatial 38 cost per zone disparities across zonal origins of travel. Reilly (1977), Parody et al. (1990) There is disparity in net levels of transit service provision across time periods. Operations, temporal Expenditure- Pricing Equity Cervero (1981), Cervero and Wachs (1982) There is disparity in net levels of transit service provision across time periods and bus routes aggregated to their bus yards (cost centers). The patterns are regressive; lower-income, minority persons pay a higher share of costs through fares. Operational, spatial and temporal Hodge (1988), Iseki (2016) There is spatial disparity in the cost recovery through fares and tax base. Urban areas pay a higher share of costs through fares, but suburban areas pay an even higher share of costs through taxes. Operational, spatial Brown (2018) In evaluation of current fare structure and potential fare structure changes, flat rate structures are inequitable in net terms and disproportionately burden marginalized communities. Time- and distance-based fare structures would achieve greater equity in both frameworks. Operational, spatial and temporal Pricing Equity (spatial) Expenditure- Pricing Equity (temporal) Table 1-6: Select literatures on transit expenditure and pricing equity Empirical Findings As can be deduced from Table 1-6, much transit expenditure and pricing equity research does not unite the two, meaning expenditure equity and pricing equity are better represented in the literature than expenditure-pricing equity is. Furthermore, of the research that does evaluate expenditure-pricing equity, much of it is decades’ old or uses highly aggregate dimensional units of analysis, such as geopolitical boundaries (e.g., Hodge, 1988; Iseki, 2016) or “urban”- and “suburban”-labeled bus yards (Cervero, 1981) for spatial variability, or peak and base time periods for temporal variability (e.g., Cervero, 1981; Parody et al., 1990; Brown, 2018), making the findings less informative than they could be with the granular data available today. Specifically, municipal boundaries and cost centers, while more disaggregate than a systemwide analysis, are still highly aggregate units of analysis; and transit operators have many more time periods they scale to than peak and base. Finally, while expenditure equity research that focuses on capital expenditure patterns evaluates many modes of transit, bus transit is disproportionately represented in operational 39 expenditure and pricing equity literature, and the temporal dimension of operational expenditure and pricing equity is much more represented than the spatial dimension. Temporal Equity Research on how transit costs and pricing vary by time is by far the most represented in transit equity research that uses accounting cost models. The overwhelming consensus in the literature is that the peak period is the costliest to operate in both gross and net terms — that is, there is both expenditure inequity and expenditure-pricing inequity that favors peak period service/travelers. A deciding factor in the findings is if and how fixed or semi-fixed asset costs are allocated. Among the few studies that suggest the peak period is the least costly is Reilly (1977). He studied the Capital District Transportation Authority bus system in Albany, New York and found that the off-peak costs 55% more per rider than the peak period in net terms (i.e., after accounting for fare revenue). However, Reilly did not include any capital asset costs in his cost allocations. Cherwony and Mundle (1978), as previously discussed, used peak vehicles as a service output to evaluate temporal variability in the operations of express bus service in the twin cities region of Minnesota and found that the peak period costs 56% more in gross terms (i.e., before accounting for fare revenue). Cervero (1981) included annual depreciation costs of capital using the 85/15 rule for three California bus transit operators and found that the peak period costs between 16% and 43% more to operate than the base period in net terms. Finally, Parody et al. (1990), often credited as the first to evaluate temporal cost variability of rail, used 1983 national aggregate data of all transit modes, applied the 85/15 peak-to-base rule for capital depreciation, and found that the peak period costs 45% more per rider in net terms — again, at a nationwide aggregate level. Of these studies, only Cervero (1981) looks at the socioeconomic makeup of riders across different time periods to determine if there are disparate impacts. Using on-board surveys of riders, 40 he found that lower-income, minority persons consume more off-peak trips while their white, higher-income counterparts consume more travel during the peak period. Thus, not only is there temporal inequity in cost and cost recovery, but it has socioeconomic regressive implications. Somewhat more recently, Taylor et al. (2000) measured peak-to-base cost variability of bus transit of the Los Angeles Metropolitan Transportation Authority (LA Metro) and contrasted it to what the peak-to-base cost variability of LA Metro’s model would suggest. They used the marginal cost method (Savage, 1989) to allocate vehicle costs to different time periods and the peak vehicle method (Cherwony and Mundle, 1978) to allocate other capital and administrative costs. They found that, by excluding the costs of capital, LA Metro overestimates the cost of base bus service by 17%, underestimates the cost of peak bus service by 36%, and, by aggregating costs across modes, fail to account for the 266% additional cost per unit of light-rail service relative to bus service. Since these studies, most others simply apply past studies’ statistics to estimate the equity impacts of current fare policies or test alternative fare policies. Likely the most contributing is Brown (2018), who tested the socioeconomic impacts of LA Metro’s current fare policies and contrasted it to various other fare structure possibilities, including distance- and time-based fare policies. She relied on the findings of Parody et al. (1990) that the peak period costs 45% more per rider in net terms than the base time period, and 2012 California Household Travel Survey data to estimate time of travel and length of travel of different socioeconomic groups of LA Metro riders. Based on these sources, she estimates that LA Metro’s flat rate fare structure is expenditure-pricing inequitable because it charges off-peak riders more for the cost of services rendered to them, relative to peak period riders. She suggests that a time-based fare structure would be more equitable. However, by assuming that temporal cost per rider variability findings from 1983 nationwide data are representative of LA Metro in 2018, these findings are not without doubts. Specifically, it is 41 doubtful that 1983 and 2018 travel patterns are similar, and that Los Angeles transit use and operating patterns are representative of a national “average” case. Spatial Equity Research that evaluates the spatial variability of transit expenditure and pricing equity is quite limited in mode representation and the geographic units of analysis. For example, while in Table 1-6 I classify research on fare per mile equity and route-by-route equity as spatially-focused, many such studies do not measure geographic incidence of expenditure and pricing. For example, while Cherwony and Mundle (1980) and Taylor et al. (2000) show that there is variation in expenditure across routes of service, they do not measure what this means about the spatial incidence (i.e., at some geographic unit) of costs or subsidies. The same is true in Garrett and Taylor’s (1999), Pucher’s (1982), and others’ review of the incidence of capital investment patterns. They show that much more capital investment is spent on expensive transit infrastructure projects, like suburban- focused commuter rail that is disproportionately used by socioeconomically privileged persons relative to less capital-intensive bus services used more by inner-city and marginalized communities, but do not measure the geographic incidence of these investments nor how it compares to what the different groups pay either in terms of fares or taxes. In terms of pricing equity, most studies merely measure the fare paid relative to the distance travelled, so do not directly evaluate the spatial incidence of impacts. Brown (2018), in the same study reviewed in the preceding subsection, tested the socioeconomic impacts of LA Metro changing to a distance-based fare structure and found that it is more pricing-equitable because marginalized communities travel less, so pay more per mile with a flat rate fare structure than a distance-based fare structure when compared to non-marginalized travelers who tend to travel longer distances. Some scholars find that this pattern is reverse in other parts of the globe, including Stockholm, Sweden (Rubensson et al., 2020) and Beijing, China (Zhao and Zhang, 2019), because 42 marginalized populations in these regions travel longer distances than their non-marginalized counterparts. Nuwosoo et al. (2009) evaluate different fare structure changes for the Alameda- Contra Costa Transit District in Oakland, California, and find that a fare structure that charges little or no fee for transfers and retains multi- and unlimited-ride discount options, are the most equitable because they limit the incidence of costs on low-income riders. Finally, Bandegani and Akbarzadeh (2016) evaluate how converting from a flat rate fare to a distance-based fare would affect the equity in the fare per mile paid by travelers. Unsurprisingly, it is more equitable in this sense. Likely their strongest contribution is that they controlled for price elasticity in measuring consumption response patterns unlike most other equity research. However, none of these studies — Brown (2018), Rubensson et al. (2020), Zhao and Zhang (2019), Nuwosoo et al. (2009), or Bandegani and Akbarzadeh (2016) — include the cost of service in their measurements of per-mile equity, so do not account for the fact that the cost per rider of different miles of service will vary by both ridership and input costs. Zhou et al. (2019) and Wang et al. (2021) do evaluate the spatial incidence of pricing equity impacts in their reviews of as fare structure change in Brisbane, Australia, where the local transit provider changes from a 23-zone fare structure to an 8-zone fare structure. Zhou et al. find that the fare per kilometer paid in a zonal fare structure has spatial variation with persons from select zones paying more per kilometer travelled, on average. Wang et al. (2021) evaluated how the agency’s zonal structure change affected the fare per zone paid by traveler types — including adult, child, concession, and senior — and the zonal origins of travel, and found that the change improved cost per zone equity overall and for most of the traveler types studied but worsened cost per zone equity across zonal origins of travel with travelers in select zones paying disproportionately more per zone traveled. While Wang et al. (2021) and Zhou et al. (2019) contribute by illustrating the granularity of analysis now available and looking at spatial variability, neither account for expenditure variability in 43 their equity calculi. It is possible that while different riders pay more per kilometer or per zone, it costs more per passenger-kilometer or “passenger-zone” to serve them. Finally, Farber et al. (2014) measure how implementing a distance-based fare structure would affect different socioeconomic populations who use Utah Transit Authority services. They find that the costs different socioeconomic populations would pay under a distance-based fare structure varies across locations of the network because trip lengths are not uniform across the region, even within a given socioeconomic group. However, they do not weight these findings to consumed trips to evaluate the net socioeconomic incidence that could result. Like Wang et al. (2021) and Zhou et al. (2019), they contribute most by illustrating how now-available highly disaggregate data can be used in fare equity analyses. Among the few studies that evaluate expenditure-pricing equity and focus on the spatial incidence of costs and subsidies is Cervero (1981) — also reported in Cervero and Wachs (1982). He evaluated costs at a “cost center” (i.e., bus yard) level for the three California bus agencies he studied and labeled each cost center as urban or suburban. For context, most transit operators assign the operations of different routes to a select yard such that all a particular route’s vehicles and operating history is managed at that yard. To measure how cost recovery (i.e., expenditure-price equity) spatially varies, Cervero calculated the ratio between the revenue (i.e., fare) per-mile and the cost per-mile of all revenue-miles produced through different cost centers. He found that suburban cost centers have a lower per-mile cost recovery than urban cost centers. Hence, suburban routes of the networks studied cost more per mile in net terms; there is expenditure-pricing disparity that disproportionately benefits suburban locations. Cervero also evaluated the socioeconomic impacts of this result by using on-board surveys to measure the socioeconomic makeup of riders. He found that the inequity is socioeconomically regressive, as those who use suburban routes of the networks and receive more service output relative to what they pay are white and higher income, on average. 44 Finally, Hodge (1988) and Iseki (2016) also measure cost recovery variability, but include the tax base in their assessment. Hodge focused on the Seattle, Washington region, only used vehicle- miles and vehicle-hours as service outputs, and classified different route-miles as either “central city” or “suburban” using geopolitical boundaries. He measured how much central city versus suburban route-miles are paid for by fares and how much are paid for by tax revenues. He found that, when just fares are accounted for, urban riders pay a higher share of costs than suburban riders do, but that when the tax base is accounted for the net flow of subsidies go from suburban segments of the network to urban segments. Iseki used a more robust cost allocation model that accounted for capital, but came to similar conclusions for the Toledo, Ohio region. As is clear from the above, very little literature explicitly measures the spatial variability of transit expenditure-pricing equity. Of the literature that does, the spatial units of analysis — cost centers and municipal boundaries — are quite aggregated, even if not as aggregated as a systemwide analysis. In addition, non-bus modes of transit are sorely missing from spatial equity analysis in the literature. Most especially, none of the above expenditure-pricing equity studies look at rail or ferry service. Conclusions and Recommendations The above review shows that efficiency of transit costs and fare equity are distinct topics that are approached through different lenses, and that the combinations of topics and paradigms through which they are studied lacks integration. Yet they all have relevancy to one-another and the global topic they contribute, transit efficiency and equity. While economic cost models can be used to measure whether a system is operating efficiently, the analysis is done at an aggregate level, so inherently relies on a system being fixed. This can blind an analyst from being able to identify wasteful areas or times of operation and distributional impacts of fares, among other things. At the same time, equity research overlooks the systemwide impacts of addressing distributional disparities. 45 Economies of scale literature on transit suggests that, when looking solely at supply-side factors, smaller agencies have economies of scale while larger agencies have diseconomies of scale. In large part for this reason, the strongest economic argument for transit subsidies is the second-best argument. Yet, literature that measures an optimal “second-best” price for transit is very limited, overwhelmingly theoretical, and outdated. Parry and Small (2009) offer an applied assessment and show that transit subsidies are welfare improving as a second-best option but acknowledge that they do not account for various considerations, including distributional impacts. On the other hand, although extensive research that employs accounting cost models suggests that fare policies are inequitable, the authors of these studies do not go the next step in evaluating whether their proposals for more equitable fares is viable. If, for example, peak period travelers paid a rate so that they cover an equal share of their costs as off-peak travelers, how would this affect demand? How would that then affect cost and cost recovery variability? Is there an equilibrium price that achieves the desired equity whilst being operationally viable? Answering this may require a multi-stage model that includes a statistical cost model with demand-side cost and output variables to account for user elasticity, as well as a cost allocation model than can calibrate how costs and cost recoveries are distributed. Additionally, the granularity of spatiality in spatial equity analysis leaves much to be desired. While innovative at its time, Cervero’s (1981) use of cost centers to generalize all miles of service provided through that cost center overlooks the variability across miles of service. It is conceivable that different routes or segments of routes associated with the different cost centers have different cost recovery outcomes. So, while using a handful of cost centers is more disaggregate than using systemwide numbers, it is still quite aggregated by today’s standards. A similar story holds for Hodge’s (1988) and Iseki’s (2016) use of geopolitical boundaries of routes. There is likely variation in cost recovery patterns across different routes and route segments in urban and suburban areas of 46 the regions they study that can be evaluated with the granularity of data available today. Other spatial research does not account for cost variability whatsoever; they embed an assumption that every mile or zone of service has similar costs or merely do not consider cost relevant in their measurement of fare equity (e.g., Brown, 2018; Zhou et al., 2019; Wang et al., 2021). New research should look more granularly at the spatial variability of cost recovery (i.e., expenditure-pricing) equity patterns. Similarly, all temporal expenditure and equity studies surveyed look solely at peak-to-base variability. In practice, transit operators tend to have multiple time periods of operation, such as graveyard, base, peak, weekend morning, and weekend evening. Future research should account for this variability. Finally, rail and ferry transit modes are underrepresented in all aspects of the research evaluated. Bus transit is overrepresented in economies of scale literature and all variations of expenditure and pricing equity literature. This is important because rail transit functions much differently than bus transit from a cost standpoint, as a rail operator must maintain not only its rolling stock, but the infrastructure it operates on. Furthermore, the capital cost is much more expensive than in the case of bus transit. Rail is also a much different operating environment, as construction of a rail line creates more finality in routes, leading to a “commitment trap” to operate it once it is built (Schweitzer, 2017). Building rail — in part because of its finality after construction and grade-separated design — is also politically popular to invest in. For these reasons and more, much more attention should be given to rail transit in future transport economic, cost, and pricing equity research. 47 Paper 2: Spatial and Temporal Variability of Rail Transit Costs and Cost Effectiveness Abstract Previous research has evaluated the temporal variability of transit costs and shown that peak period service costs more to operate in both gross and net terms. However, research on spatial variability of transit costs, particularly for modes other than bus transit, is quite limited and methodologically underdeveloped. Using transit agency data on labor and train allocations, I develop an accounting cost model that allocates variable and semi-fixed capital costs to times of day and each link and station of two regional rapid rail transit networks, BART and MARTA, in order to evaluate temporal and spatial variability of costs and average costs per rider. I find that costs per hour are highest but average costs per rider are lowest during weekday peak periods in both systems, and that costs are highest and costs per rider are lowest in the urban core area of the BART system while there is no clear spatial pattern in the MARTA system. Introduction Public transit agencies in the United States regularly monitor operating costs, cost recoveries through fares (farebox recovery ratio), and various factors of production. These data are internally used for such things as operating and capital planning, as well as externally reported to local, state, and federal agencies for such things as determining funding allocations. Although transit operators use these data to account for spatial and temporal variations in costs and performance for service and capital planning purposes, the cost models used tend to be underspecified and exclude both fixed and semi-fixed asset costs, leading to their estimations of spatial and temporal variations being incomplete (e.g., Taylor et al., 2000). Among other examples, the cost of providing peak service is often underestimated, the cost of providing off-peak service is often overestimated, and the cost of providing more capital-intensive modes of transit is often underestimated (e.g., Taylor et al., 2000). 48 So, while better than the aggregate data reported to higher levels of government, transit operators’ monitoring of the occasions of costs still limit how informed their operating, fare policy, or capital investment decisions that account for location or temporal variabilities can be. Similarly, while state and federal governments’ ratings of transit capital projects have increasingly incorporated an applicant’s ability to finance operations of the project once it is built, this assessment is based on the resulting systemwide operating costs; spatial and temporal variabilities in operating costs are not evaluated. Thus, even though the construction of a new rail line may lead to cost-effective operations (i.e., a low average cost per trip) in one area and cost- ineffective operations (i.e., a high average cost per trip) in another, the entire project may be eligible for funding based on an aggregate assessment. While much research has evaluated the temporal variability of transit service costs, it has focused principally on bus transit, has relied on far less granular data than is available today, and typically only compares peak service to off-peak service despite transit operators having more than just two service levels. Surprisingly, almost no research has been done on the spatial variability of transit costs. Of what has been done, only bus transit has been studied, and the analyses highlight route-by-route variability (e.g., Cherwony and Mundle, 1980) or urban-suburban variability by either aggregating to bus yards (e.g., Cervero, 1981) or city boundaries (e.g., Hodge, 1988; Iseki, 2016) and labeling all route-miles associated therewith as urban or suburban. In addition, the time and location variability of outcomes, or cost effectiveness, is not considered in much prior research. While providing service at a particular time or in a particular location may cost more, it may deliver more in the form of ridership, so be more cost effective. In this research, I develop an accounting cost model to evaluate the spatial and temporal variability of rail transit costs and cost effectiveness measured using average cost per rider. My objective is to evaluate whether there is a temporal or spatial pattern of the incidence of transport 49 costs in both total and per-rider terms. Based on past research findings, I hypothesize that there is, and that both the total and per-rider costs are highest during the peak period and in outlying areas of the networks. Two rail transit operators with similar operating characteristics, the San Francisco Bay Area Rapid Transit District (BART) and the Metropolitan Atlanta Rapid Transit Authority (MARTA), are used as case studies. Fiscal Year 2019 (FY19) — July 1, 2018 to June 30, 2019 — is used as the study period to mitigate the impacts of the COVID-19 pandemic in the analysis. I intend to use findings from this research in subsequent research to evaluate whether farebox recovery is temporally and spatially variable such that different times and locations of service receive more subsidies than others, and whether there is an optimal pricing structure that equalizes cost recovery across the network. Accounting Cost Models in Transit Cost models relate an entity’s total costs to a set of cost inputs. Equation 2-1 offers a simplified cost function, derived from Pels and Rietveld (2007), wherein the cost of the entity is the sum of a fixed cost and the product of a variable cost and the number of variable inputs. 𝐶 =𝑎 +𝑏𝑦 (2-1) where C is the total or per-output cost a is a fixed cost b is a variable cost y is the number of units produced subject to b costs To measure service output costs (i.e., elements of expenditure) for an entity, accounting cost models (Pels and Rietveld, 2007) — sometimes called cost allocation models (e.g., Berechman, 1993) or “activity-based” cost models (e.g., Basso et al., 2011) — are used to relate service outputs to a series of input costs, as reflected in Equation 2-2. That is, they measure the occasions of outputs for an entity by associating them with the costs of inputs (i.e., base level costs incurred in 50 production). Some common input-output relationships in transit industry accounting cost models include the relationship between the output of vehicle-miles and the inputs of fuel and vehicle maintenance, and between the output of vehicle-hours and the input of vehicle operators (labor). As is evident, Equation 2-2 effectively subdivides Equation 2-1; the summation of all output costs will equal total costs. 𝐶 𝑖 =𝑎 𝑖 +∑𝑏 𝑗 𝑦 𝑁 𝑗 =1 (2-2) where C i is a cost of output, i a i is a fixed cost allocated to output, i b j are per-unit costs of cost input, j, allocated to output, i y are the number of cost input units used. To measure variability across some dimension, such as time or space, an accounting cost model can be further subdivided by adding dimensional subscripts to Equation 2-2. This would be done if, for example, a transit operator wants to understand how its total costs or specific output costs (e.g., vehicle-miles) vary by different production activities across times of the day (e.g., morning commute, midday, late evening, etc.). In this example, the cost of vehicle-miles during a particular time period would equal a fixed cost assigned thereto plus the sum-product of the volume of each allocated cost input and their per-unit cost. Adding dimensions to the model can support a transit operator’s evaluation of where different investments can reduce costs, such as substituting between the size of buses and the frequency of buses in serving peak period travel, and whether there are disproportionate allocations of resources to a particular time period or location relative to fare revenue or demand (i.e., ridership). Each of the above equations are generalized examples. Among variations, some analytical inquiries may not include a fixed cost, such as if the analysis employs a long-run cost model and sunk costs are the predominate fixed cost in the case being studied — which, by definition, are not included in long-run cost models (Wang and Yang, 2001). 51 In research, accounting cost models are useful for descriptive or case studies, as done here, because they can allow an evaluation of when, where, or how costs are occasioned. They are useful in practice for similar reasons and are the overwhelmingly preferred cost model used in practice. On the other hand, this approach is substandard from an econometric perspective because, by merely using judgment to associate input costs with different outputs, it lacks theoretical foundation and does not account for the interrelationships among cost inputs and outputs (Basso et al., 2011). As one example, the number of operator-hours generated is clearly conditional on the number of railcars or buses in inventory for operation, but such constraints are ignored in accounting cost models. To account for the interrelationship of costs, statistical cost models that relate production output costs to various inputs and the interrelationship among them are more appropriate. In addition, as alluded to in the introduction, many — but not all — transit agencies’ accounting cost models are aggregate in nature; they lack dimensional variability. In these instances, temporal, spatial, and other cost variability is not monitored or used in making resource allocation decisions. Instead, many transit operators, through either administrative choice or policy direction, supply transit service either in a coverage-based format that emphasizes equal or minimal levels of service across the network, or a performance-based format that is more demand-focused but not necessarily considerate of cost or cost recovery patterns (Mallett and Boarnet, 2021). As well, transit operators generally do not account for capital assets in their accounting cost models, leading to service times or locations that are capital-intensive but not labor-intensive having deflated cost estimates, or vice-versa for services that are labor-intensive but not capital-intensive (e.g., Taylor et al., 2000). Accounting for Capital Costs Capital assets are assets that have a life greater than the timeframe covered by the cost allocation model — typically one year (Walker and Kumaranayake, 2002, referencing Creese and 52 Parker, 1994). In transportation, many fixed capital assets, such as physical infrastructure, are arguably sunk costs because they are “irrevocably committed and cannot be recovered” (Wang and Yang, 2001). Once land is bought and tunnels, bridges, and tracks constructed, these investments are a sunk cost of doing business; they cannot be recovered if operation of them is to continue. So, while these assets may require continued maintenance or rehabilitation, I contend that the original capital, by definition, are not a long-run cost because, ex-post construction, it is an investment that cannot be recovered. By comparison, semifixed capital assets last longer than one year, so are a “capital asset” based on the Walker and Kumaranayake (2002) definition. However, unlike fixed capital assets, there are variable components to the use of semifixed assets. Vehicles, computers, and heavy maintenance equipment — all whose use and scale vary by service output patterns — are examples of semifixed assets in the transit industry. How capital assets are accounted for in an accounting cost model depends on the objective of the model. Because capital assets last longer than the study period, a researcher or analyst must determine how to charge capital assets to the study year even if they were purchased in a different year or last into later years. Walker and Kumaranayake (2002) survey five common reasons for measuring annual capital asset costs, including for budgeting, project efficiency and sustainability review, project expansion, project replication, and economic evaluation. If the objective is to conduct a benefit-cost analysis, it is important to account for the opportunity cost of the investment. In this case, estimating the cost of the asset in study-year dollars and dividing by its life expectancy is appropriate, as this allows for a side-by-side comparison of options. Furthermore, to account for the lost opportunity to earn interest on the money and use it for a future investment (i.e., the time value of money), applying a discount rate is appropriate in this type of model. Conversely, if the goal is merely to account for realized expenditure (i.e., for budgetary purposes) and charge it to the study period, a straight-line depreciation based on the original purchase price and life expectancy of 53 the asset is appropriate for annualizing assets’ costs and charging them to the respective year(s) of the study. Finally, not all capital assets are necessarily relevant for a model. If the goal is to internally compare total or marginal costs across some dimensional variation, such as time periods of service, only assets whose use or allocations vary across that dimension are particularly relevant. These are partially-allocated cost models (Cherwony et al., 1981; Taylor et al, 2000). By comparison, fully-allocated cost models allocate all capital assets and are useful for comparing the costs of two or more systems or options, such as when conducting an alternatives analysis before making a major investment (Cherwony et al., 1981; Taylor et al., 2000). In this research, I develop a partially-allocated cost model that accounts for assets whose scale varies by time and location of service, and apply the budgetary approach for annualizing asset costs. This supports my objective of analyzing the spatial and temporal incidence of long-run rail transit operating costs — that is, the ex-post construction costs of operating the rail network — in both gross and per-rider terms. Literature Review Transit cost model research includes both social science research and transport economics research. The former aims to estimate the efficiency or equity implications of transit services as they are operated. These types of studies tend to rely on activity-based cost models that allow costs to be assigned to different times or locations of service so that the incidence of costs or subsidies of the system as built and operated can be evaluated. By comparison, transport economic cost model research aims to identify optimal operating supply that achieves some economic objective, such as welfare or profit maximization. For these types of analyses, statistical models are ideal. Research on the efficiency and equity incidence of transportation operations was popular in the late-1970s and 1980s, but has had limited empirical contribution since. Apart from being 54 outdated, the research has almost exclusively focused on bus transit and temporal variability. Rail transit and spatial variability are not well-represented in social science-focused transit cost allocation research to-date, largely due to historically insufficient data granularity. Furthermore, much of the research evaluates cost (i.e., the amount spent) variability, despite cost effectiveness (i.e., the amount spent per unit of benefit) being more important for program evaluation. Early research involved methodology development. Cherwony et al. (1981) provide a comprehensive overview of various transit costing procedures, including various “methods” and associated “approaches.” They suggest that accounting cost models that use one variable (what they call “average cost models”) are inviable because they are too insensitive to marginal costs and dimensional cost variability to reasonably evaluate the costs of service changes or occasions of costs, respectively. Among more ideal models are multi-variant accounting cost models (what they call “fixed/variable cost allocation models”) because they are simple to implement and more accurately measure occasions of costs than their single-variable counterpart. However, these models still inherently rely on average costs, so are not ideal for measuring marginal costs or the costs of service changes. Finally, statistical approach (cost) models have the opposite pros and cons; they are ideal for measuring marginal costs and the costs of service changes but are not as simple to set up nor ideal for estimating the occasions of costs. How capital assets are to be allocated to different time periods was subject to much debate as well. Some argue that, since services would likely not be built and operated but for peak demand, the peak period should be charged fully for capital costs (e.g., Meyer et al., 1965; Keeler and Small, 1975). Others suggest this arbitrarily charges common or “lumpy” costs to a single group of users, thereby overlooking the common cost nature of these investments and the variability to which the resources are used by different time periods of travelers (e.g., Boyd et al., 1973; McGillivray et al., 55 1980; Merewitz, 1975). Parody et al. (1990) reference various studies in utility pricing (e.g., Coase, 1970) in furtherance of this. The answer to this debate for some empirical studies was to take a “middle ground” by allocating an 85% share of capital costs to the peak and 15% to the base (Cervero, 1981; Charles River Association, Inc., 1989; Parody et al., 1990). A more robust approach was developed for the Bradford Bus Study (Savage, 1989) and applied by Cervero (1981) for labor costs and Taylor et al. (2000) for transit vehicle costs. The method identifies marginal costs based on the share of units used during a particular time period. To be sure, this is not the traditional economic marginal cost of producing one more trip or one more seat-mile, but the lumpy marginal investment cost of serving a particular time period. Thus, assets used solely during the peak period are fully charged to the peak period, while those used across multiple time periods will have their costs shared amongst those time periods. This method is illustrated in Figure 1-2 of the preceding chapter. Although allocating transit vehicle costs based on some variant of vehicle-hours or capacity allocations is the going standard, Kerin (1989) theoretically showed that if vehicle-miles were used for allocating transit vehicle costs, the off-peak can be more costly to serve than the peak. Specifically, if a longer time period demands fewer vehicles but generates far more vehicle-miles during the length of the time period compared to the peak period, then the wear-and-tear costs of this time period’s mileage-intensity can outpace the costs of the peak period’s capital-intensity. Again, industry practice today, including the federally defined life of transit vehicles, is to base vehicle costs on units of time. Even so, as is evident by the average retirement age of buses being three years later than their standardized life expectancy (Laver et al., 2007), and many vehicle warranties having both a time-life and a mileage-life element to them, there is a basis for evaluating life and allocating costs of vehicles by their miles of use. 56 The research broadly shows that there are high marginal costs for providing peak period service (Charles River Associates, Inc., 1989; Cherwony and Mundle, 1978; Parody et al., 1990; Oram, 1979). Although Vickrey (1955) theoretically showed that congestion pricing was warranted for the New York City Subway system due to peak-to-base cost and externality differences, Parody et al. (1990) are credited for being the first to empirically estimate the time-variant cost recovery for rail transit. They used 1983 cost and ridership data submitted to the Urban Mass Transportation Administration by all transit operators, allocated operating costs based on revenue-miles, and allocated capital costs based on the aforementioned 85/15 peak-to-base share. They found that it costs 45% more (net) per trip to serve peak period travel overall; for bus, subway, and commuter rail, independently, these numbers are 27%, 27%, and 41%, respectively. This research is also among few that measures cost effectiveness (i.e., the average cost per rider). Cervero (1981) evaluated the equity of fares using a revenue-to-cost ratio factored by miles and found that the peak period has a lower cost recovery per mile amongst its users. But, like Parody et al. (1990), he focused only on base v. peak service and allocated capital costs using an arbitrary 85/15 peak-to- base ratio. His allocation of labor, however, followed Cherwony and Mundle (1978) by factoring peak costs using a relative productivity ratio. Some studies from this era suggest that peak service subsidizes off-peak service because the revenue generated by peak travel offsets the additional costs of serving it (Reilly, 1977). However, studies in this latter group generally ignore the capital costs of serving peak travel. Among more recent studies are Taylor et al. (2000) and Ripplinger and Bitzman (2018). Taylor et al. (2000) run parallel partially-allocated and fully-allocated cost models for the Los Angeles Metropolitan Transportation Authority’s transit system and contrast it against the agency’s cost model. They find that peak period service costs much more than base service on both a marginal and total basis; and that the agency’s model, which does not include any asset costs, underestimates 57 peak bus service costs by 36%, overestimates base bus service by 17%, and underestimates the cost of light rail service relative to bus service by 266% because of not distinguishing between them. However, Taylor et al. do not evaluate cost effectiveness (i.e., cost per rider) or spatial variability. Ripplinger and Bitzman (2018) devise a transcendental-log cost function to evaluate the economies of scale and monopolistic opportunities of small transit operators. While their research does not contribute to the questions of spatial or temporal cost variability, they find that the provision of service by multiple providers in a single area creates a Hotelling effect and is basis for natural monopoly — implying there is such a thing as too much service relative to demand in an area. Finally, transport economics literature broadly shows that some areas of a transport network may inevitably be more subsidized than others, depending on the objective of the operator — for example, cost minimization, profit maximization, or welfare maximization (e.g., Chang and Schonfeld, 1991; Hörcher and Graham, 2018). As multioutput firms, transit agencies serve multiple different origin-destination pairs of trips, each a unique output, and all consumers depend collectively on each other to share in the costs of travel. However, these studies assume that a network is fixed and evaluate optimal operations based thereupon, so do not foster an assessment of whether particular segments of a network are wasteful or particularly high-performing. It is possible that a poor performing segment of a network makes it not viable for further operation (or construction to begin with), and this cannot be assessed if we assume a network is fixed. Other transport economics literature explores the economies of scale, economies of scope, or economies of density of transport networks (e.g., Basso and Jara-Díaz, 2006). These studies also focus on fixed networks and are more theoretical than applied. Missing from the above review is spatial variability in costs. At best, Cervero (1981) indirectly evaluates this using “cost centers” or yard facilities to evaluate how cost patterns vary by the areas serviced by each yard. He finds that yards with routes that cater to peak travelers and 58 longer distance travelers — both of whom are more concentrated in suburban areas — cost more and recover less. Otherwise, the literature on spatial cost variability emphasizes variation in tax-base recovery. Hodge (1988) allocated operating costs to urban and suburban Seattle, Washington using vehicle-miles and vehicle-hours as cost outputs, and evaluated the extent to which these costs are recovered through fares and the tax base in urban and suburban areas. Iseki (2016) used a more robust cost allocation model to conduct similar analysis in Toledo, Ohio. They both find that the urban area has higher transit patronage and farebox recovery, but that net subsidies when the tax base is accounted for go from suburban areas to urban areas. Still, these studies rely on highly aggregate geographic units, focus on bus transit, and emphasize tax reliance variation as opposed to spatial and temporal cost effectiveness variation. Fully missing from the aforementioned analysis is anything that looks specifically at rail cost effectiveness. Parody et al. (1990) evaluate rail cost recovery, but do so at a national level and focus only on peak-to-base variability using allocation methods that today are primitive. And while Taylor et al. (2000) built a more robust model to assess the time-variant costs of light rail in Los Angeles, California, they conduct no cost effectiveness evaluation of the service. Data and Methods My objective in this research is to evaluate the long-run spatial and temporal variability of rail transit service costs and cost effectiveness (measured by average cost per rider). To do this, I devise a partially-allocated accounting cost model for rail transit that excludes fixed capital assets, but includes variable costs and high-cost semi-fixed assets whose use or inventory vary by time and location. Several other costs — pollution externalities, congestion (crowding) externalities, value of land, and parking facilities, to name a few — are also excluded due to these being independent of railroad operating costs. I provide an outline of various types of costs and why they are or are not included in the analysis in the attached appendix. By using an accounting-based model and only 59 including long-run costs (i.e., exclusive of the sunk costs of construction, etc.) that are spatially and temporally variable, I can better analyze when and where ongoing costs are occasioned relative to demand in ways that cannot be done with a statistical cost model. To be sure, this does not measure the total cost of rail investments and cumulative spatial and temporal incidence of costs; that would require a fully allocated cost model, inclusive of fixed costs. Rather, by limiting what I include in the following model, I measure the location- and time-variability of operating costs of the rail networks, as built and operated. This is useful for understanding the long-run, recurring cost impacts of the investment. Case Selection To generalize the findings and support subsequent research on how efficiency and fare equity varies by fare structure, I use two regional rapid rail transit operators with different fare structures, BART and MARTA, as case studies. Both agencies’ mainline rail systems functionally link sparsely spaced suburban stations to an urban core set of stations and operate using rapid rail technology and relatively fixed headway schedules, and provide few, if any, skip-stop services. This is functionally distinct from commuter rail systems that generally terminate at a single “union station” in the urban core, have variable schedules, and offer skip-stop runs; as well as traditional rapid rail transit systems that are urban-focused with frequent stops and no-to-little emphasis on linking suburban areas to an urban core. In addition, regional rapid rail transit operators are the only rail operators with highly granular ridership data due to riders having to tap on and off the systems, making them ideal for this analysis. 60 BART and MARTA System Information Table 2-1 shows summary operating information of the BART and MARTA mainline rail systems for FY19, based principally on the agencies report in their National Transit Database (NTD) 2019 agency profile. BART MARTA Miles (mainline) 109.4 miles 48 miles Stations 48 stations 38 stations Schedule Structure Fixed headway Fixed headway Fare Structure Distance-based Flat-rate Farebox Recovery Ratio (reported) 72.2% 37.4% Vehicle Revenue-Miles 77,986,155 miles 22,511,413 miles Annual Trips 125,105,460 trips 65,217,325 trips Annual Passenger-Miles 1,756,364,558 passenger-miles 450,023,139 passenger-miles Table 2-1: BART and MARTA Reported Operating Data Figure 2-2 shows BART’s system map effective July 1, 2018 through February 10, 2019; Figures 2-3 and 2-4, the Weekday/Saturday and Sunday/Holiday system maps, respectively, effective February 11, 2019 through June 30, 2019. During FY19, BART’s mainline rail system consisted of 109.4 miles of track and 45 stations. The agency has three “full-time” routes that operate fixed headways on weekdays, Saturdays, and Sundays from opening to closing. One of these routes, the Pittsburg/Bay Point to San Francisco Airport line, has increased peak period headway that is provided with part-time labor. Two “part-time” routes operate from opening through the late shoulder of the evening commute on weekdays and during the midday on Saturdays. With the exception of the aforementioned supplemental service, the agency scales capacity by resizing its trains rather than changing frequency. During the latter half of the fiscal year, BART adjusted some operating patterns. Most notably, the Dublin/Pleasanton to Daly City line was diverted to terminate at MacArthur instead of Daly City on Sundays, and weekday operations began at 5AM instead of 4AM. The agency also operates a cable-drawn automated guideway and diesel multiple unit (DMU) spur line – the costs of which I exclude to ensure a consistent analysis. 61 Figure 2-1: BART System Map effective July 1, 2018 to February 10, 2019 Figure 2-2: BART Weekday/Saturday System Map effective February 11, 2019 to June 30, 2019 62 Figure 2-3: BART Sunday System Map effective February 11, 2019 to June 30, 2019 Figure 2-5 shows MARTA’s rail system map. The system consists of four routes – two along a north-south corridor and two along an east-west corridor. The Blue and Gold Lines operate their full length from opening to closing, while the Green and Red Lines are reduced during evening hours to only operating shuttle service between their spur termini and the first station on their mainline. Service capacity is scaled by increasing or reducing the number of trains in-service; MARTA does not resize its trains to serve different levels of demand. In addition, whereas BART has both lead railcars with an operator cab and middle railcars without an operator cab, leading to variation in railcar capital costs across time periods, all MARTA railcars have an operator cab. MARTA also operates bus and streetcar services, both of which I exclude to ensure consistency in analysis. 63 Figure 2-4: MARTA System Map effective in Fiscal Year 2019 Data To spatially allocate costs, I classify asset, labor, and certain variable costs as either a railroad or station cost. Table 2-2 defines the costs included and how they are labeled. For administrative costs, such as expenditures made within the Office of the General Manager, I first split these between transit modes (excluding demand-response transit) based on each mode’s share of revenue- miles reported in the NTD annual profile. So, if an agency operates bus and rail, and 70% of the reported revenue-miles are associated with rail, I allocate 70% of administrative costs to rail. I then classify these costs as station or railroad costs and allocate them to time periods and links or stations, in proportion with other costs assigned to each; they are a “commissioned” expense. This is 64 different from some others (e.g., Taylor et al., 2000) who treat administrative costs as a fixed cost on the premise that some “fixed” amount of management is required to run a system. However, I treat this as a variable cost on the basis that administrative size scales with the size of operations. Finally, BART’s San Francisco International Airport Station has a unique annual cost of $2 million in lease payments and $800,000 in janitorial service paid to the airport. I allocate these costs solely to the San Francisco International Airport Station. Cost Classification Cost-Input Metric Temporal Spatial Station Agents Station Worker- Hours Station Cleaners Station AFC Assets Station Railcar- Miles AFC Assets Per Station AFC Technicians Station VT Assets Station Vertical Transportation Assets Per Station Elevator/Escalator Workers Station Station-Classified Department Station Assets Per Station Train Operators Railroad Train-Minutes Railcars Railroad Marginal Allocations Link Runs Railcar Maintenance Assets Railroad Railcar- Miles Trackway Maintenance Assets Railroad Traction Power Railroad Railroad-Classified Department Railroad Administrative Personnel Proportional to Other Costs Table 2-2: Costs, Classifications, and Cost Input Metrics Most data came from the transit agencies. Each agency provided asset inventory data and, for station assets, the allocation of them by station. The agencies also provided purchase or replacement price and life expectancy of the assets. And, where available, they provided rehab costs and extended life expectancies from rehab of the included assets. Equation 2-3 defines how annual costs of assets are derived. 𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑖 = ∑ (𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙𝐶𝑜𝑠𝑡 𝑠 𝑖 +𝑅𝑒 ℎ𝑎𝑏𝐶𝑜𝑠𝑡𝑠 𝑖 ) 𝑛 𝑖 =1 ∑ (𝑂𝑟𝑖𝑔𝑖 𝑛 𝑎𝑙𝐿𝑖𝑓𝑒𝐸𝑥𝑝𝑒𝑐𝑡𝑎𝑛𝑐 𝑦 𝑖 +𝑅𝑒 ℎ𝑎𝑏𝐿𝑖𝑓𝑒𝐸𝑥𝑝𝑒𝑐𝑡𝑎𝑛𝑐 𝑦 𝑖 ) 𝑛 𝑖 =1 (2-2) where AnnualCost i is the annualized cost of asset, i OriginalCosts i is the purchase price of asset, i RehabCosts i is the rehab costs expended on asset, i OriginalLifeExpectancy i is the original expected life (in years) of asset, i RehabLifeExpectancy i is the expected life extension from rehabilitation of asset, i i is a unique asset within an asset group 65 Track rail costs are not reflected in any cost data, so are not allocated in this way. Instead, I charge the cost-per-mile of track rail — $199,267.20, according to Compass International, Inc.’s 2017 Railroad Engineering & Construction Costs Benchmark, inflated to 2019 —to each link and each time period based on the number of railcar-weight-miles and passenger-weight-miles generated along the link or during the time period relative to the weight-life of rail (Equation 2-4). The weight used for a BART railcar is 63,000 pounds (Holland and Shivy, 2016); MARTA railcar, 81,000 pounds (MARTA, 2016); passengers, 181 pounds (Saad, 2021). A BART engineer indicated that the agency relies on the American Railway Engineering and Maintenance-of-Way Association’s (AREMA) standards to make track rail replacement decisions, and that AREMA’s documented life expectancy of straight track rail for BART is 360 million gross tons (MGT). This number was not found in a review of the AREMA manual, but is not far astray from some research, including Zhao et al. (2006) finding that life cycle costs of rail are minimized at a life of around 308 MGT. 𝐶𝑜𝑠 𝑡 𝑖 = $199,267.20∗{(𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑊𝑒𝑖𝑔 ℎ𝑡 ∗𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑖 )+(181∗𝑃𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟𝑀𝑖𝑙𝑒 𝑠 𝑖 )} 360 𝑀𝐺𝑇 (2-3 ) where Cost i is the annualized cost of link, i, or time period, i RailcarWeight is the weight of a railcar RailcarMiles i is the number of railcar-miles generated along link, i, or during time period, i PassengerMiles i is the number of passenger-miles generated along link, i, or during time period, i In addition, the agencies provided end-of-year financial reports of each department’s expenditure on human capital and ancillary expenses; bid schedules of train operators, station agents, and station cleaners; wages and fringe rates of select positions; train run schedules, including the train length of each train run; track distance and runtime matrices; and collective bargaining agreements. They also provided the count of riders for all origin-destination trips organized by the time periods I derived (BART) or at 15-minute intervals for the entire study period (MARTA). 66 Much literature has shown that the peak period is markedly more expensive to operate due to union work rules that require premium payments for split shifts or other inefficiencies (Chomitz and Lave, 1984; Pickrell, 1985; Wachs, 1989; Winston and Shirley, 2010). However, while MARTA has split shift workers, no premium is paid for this. And while BART pays shift differentials, they do not have split shifts to serve the peak period and the shift differentials do not align with the operating time periods identified in this study. BART also has other workforce inefficiencies, including a low pay-to-platform ratio for their train operators by industry standards, according to agency staff I consulted. As with the shift differentials, these are broadly inefficient work rules that are not unique to spatial and temporal operating patterns. Lastly, I collected each agency’s 2019 NTD annual profile. Model — Temporal To temporally allocate costs, I devise time periods using the marginal allocation method for railcars. Figures 2-6 through 2-10 shows the count of trains and railcars in-service for every minute of the day in each system, derived from run schedules. For BART, the period from July 1, 2018 through February 10, 2019 is shown and not dissimilar to the distribution for the period from February 11, 2019 onward. 67 Figure 2-5: BART Distribution of Cars and Trains In-Service — Weekdays Figure 2-6: BART Distribution of Cars and Trains In-Service — Saturdays Figure 2-7: BART Distribution of Cars and Trains In-Service — Sundays/Holidays 68 Figure 2-8: MARTA Distribution of Cars and Trains In-Service — Weekdays Figure 2-9: MARTA Distribution of Cars and Trains In-Service — Weekends/Holidays I assign a train and its railcars to a time period based on the departure time of the train. So, if 10:00AM is a time period cutoff and a train departs at 9:59AM, I assign it to the time period ending at 10:00AM, even as it may spend most of its time in the adjacent time period. In addition, I assume any resizing of trains occurs upon arrival to a terminus. I then use the cost allocation metrics defined in Table 2 to allocate costs to time periods using Equation 2-5 — the summation across which equals total FY19 costs (Equation 2-6). Time period costs are proportioned to the number of days operated as a weekday, Saturday, or Sunday/Holiday during FY19 and the corresponding total number of annual-hours associated with 69 each time period. To account for BART’s change in operating schedule mid-year, I use the weighted average of cost inputs during the two schedule periods to allocate costs. 𝐶𝑜𝑠 𝑡 𝑡 =(∑ 𝑊𝑜𝑟𝑘𝑒𝑟𝐻𝑜𝑢𝑟 𝑠 𝑎 𝑡 𝑊𝑜𝑟𝑘𝑒𝑟𝐻𝑜𝑢𝑟 𝑠 𝑎 𝑇𝑜𝑡 𝑁 𝑎 =1 ∗𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑎 ) +( 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑡 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑇𝑜𝑡 ∗∑𝐴𝑛𝑛𝑢𝑎 𝑙𝐶𝑜𝑠 𝑡 𝑏 𝑁 𝑏 =1 )+( 𝑇𝑟𝑎𝑖𝑛𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑡 𝑇𝑟𝑎𝑖𝑛𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑇𝑜𝑡 ∗𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑐 ) +(∑ 𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑡 𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑑 𝑁 𝑑 =1 ∗𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑑 ) + $199,267.20∗{(𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑊𝑒𝑖𝑔 ℎ𝑡 ∗𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑡 )+(181∗𝑃𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟𝑀𝑖𝑙𝑒 𝑠 𝑡 )} 360 𝑀𝐺𝑇 +𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑓 𝑡 (2-4 ) 𝐶𝑜𝑠 𝑡 𝑇𝑜𝑡𝑎𝑙 =∑𝐶𝑜𝑠 𝑡 𝑡 𝑁 𝑡 =1 (2-5) where Cost t is the cost of time period, t WorkerHours at is the number of worker-hours of temporally-allocated classification, a, generated during time period, t WorkerHours aTot is the total number of annual worker-hours generated in temporally-allocated classification, a AnnualCost a is the total annualized costs expended on worker classification, a RailcarMiles t is the number of annual railcar-miles generated during time period, t RailcarMiles Tot is the total number of annual railcar-miles generated AnnualCost b is the total annualized costs expended on asset, b, department, b, worker classification, b, or traction power that is temporally allocated by railcar-miles TrainMinutes t is the number of train-minutes generated during time period, t TrainMInutes Tot is the total number of annual train-minutes generated AnnualCost c is the total annualized costs expended on the train operator worker classification Minutes t is the number of annual-minutes associated with time period, t Minutes d is the number of annual-minutes asset, d, is utilized AnnualCost d is the annualized cost of railcar, d RailcarWeight is the weight of a railcar PassengerMiles i is the number of passenger-miles generated during time period, t AnnualCost ft is a commission-based administrative cost allocated to time period, t Cost Total is the total annual costs accounted and expended by the agency t is a time period a is a worker classification temporally allocated by worker-hours (see Table 2) b is an asset, department, worker classification, or traction power temporally allocated by railcar-miles (see Table 2) d is a railcar or station asset 70 Model — Spatial To spatially allocate costs, I allocate costs to links (Equation 2-7) or stations (Equation 2- 8) based on how they are classified in Table 2-2. Hence, two cost allocations models are used, the sum across which will equal the total in expenditures for the year (Equation 2-9). 𝐶𝑜𝑠 𝑡 𝑙 =( 𝑇𝑟𝑎𝑖𝑛𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑙 𝑇𝑟𝑎𝑖𝑛𝑀𝑖𝑛𝑢𝑡𝑒 𝑠 𝑇𝑜𝑡 ∗𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑎 )+( 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑅𝑢𝑛 𝑠 𝑙 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑅𝑢𝑛 𝑠 𝑇𝑜𝑡 ∗∑𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑏 𝑁 𝑏 =1 ) +( 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑙 𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑇𝑜𝑡 ∗∑𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑐 𝑁 𝑐 =1 ) + $199,267.20∗{(𝑅𝑎𝑖𝑙𝑐𝑎𝑟 𝑊𝑒𝑖𝑔 ℎ𝑡 ∗𝑅𝑎𝑖𝑙𝑐𝑎𝑟𝑀𝑖𝑙𝑒 𝑠 𝑙 )+(181∗𝑃𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟𝑀𝑖𝑙𝑒 𝑠 𝑙 )} 360 𝑀𝐺𝑇 +𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑑 𝑙 (2-6 ) where Cost l is the cost of a link of the railroad TrainMinutes l is the number of annual train-minutes generated on link, l TrainMinutes Tot is the total number of annual train-minutes generated AnnualCost a is the total annualized costs expended on the train operator worker classification RailcarRuns l is the number of annual railcar runs across link, l RailcarRuns Tot is the total number of annual railcar runs across all links of the network AnnualCost b is the annualized cost of a railcar, b RailcarMiles l is the number of annual railcar-miles generated across link, l RailcarMiles Tot is the total number of annual railcar-miles generated AnnualCost c is the annualized cost of asset, c, department, c, wrker classification, c, or traction power that is spatially allocated by railcar-miles RailcarWeight is the weight of a railcar PassengerMiles l is the number of passenger-miles generated along link, l AnnualCost dl is a commission-based administrative cost spatially allocated to link, l b is a railcar c is a railroad-classified asset, department, worker classification, or traction power spatially allocated by railcar-miles (see Table 2) 𝐶𝑜𝑠 𝑡 𝑠 =(∑ 𝑊𝑜𝑟𝑘𝑒𝑟𝐻𝑜𝑢𝑟 𝑠 𝑎 𝑠 𝑊𝑜𝑟𝑘𝑒𝑟𝐻𝑜𝑢𝑟 𝑠 𝑎 𝑇𝑜𝑡 𝑁 𝑎 =1 ∗𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑎 ) +{ 𝐶𝑜𝑢𝑛 𝑡 𝑏 𝑠 𝐶𝑜𝑢𝑛 𝑡 𝑏 𝑇𝑜𝑡 ∗(∑𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑏 +∑𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑐 𝑁 𝑐 =1 𝑁 𝑏 =1 )} +𝐴𝑛𝑛𝑢𝑎𝑙𝐶𝑜𝑠 𝑡 𝑑 𝑠 (2-7) where Cost s is the cost of a station WorkerHours as is the number of worker-hours of classification, a, that is spatially allocated to station, s. WorkerHours aTot is the total number of annual worker-hours of classification, a AnnualCost a is the total annualized costs expended on worker classification, a Count bs is the number of station-based asset, b, located at station, s 71 Count bTot is the total number of station-based asset, b, allocated to stations AnnualCost b is the annualized cost of station-based asset, b AnnualCost c is the total annualized costs expended on department, c, or worker classification, c, that is spatially allocated by station asset count a is a worker classification spatially allocated by worker-hours b is a station-classified asset c is a station-classified department or worker classification allocated by asset count 𝐶𝑜𝑠 𝑡 𝑇𝑜𝑡𝑎𝑙 =∑𝐶𝑜𝑠 𝑡 𝑙 𝑁 𝑙 =1 +∑𝐶𝑜𝑠 𝑡 𝑠 𝑁 𝑠 =1 (2-8) where Cost Total is the total annual costs accounted and expended by the agency Cost l is a cost spatially allocated to links of the railroad Cost s is a cost spatially allocated to stations of the railroad l is a link of the railroad s is a station Findings — Temporal Allocations Figures 2-11 and 2-12 show the cost input shares of the different time periods for BART and MARTA, respectively. Unsurprisingly, the peak period generates the highest share of many cost inputs for both agencies, and many of the peak period’s shares of cost inputs are high relative to its share of operating hours. Whereas the peak period accounted for just 25% of BART’s and 23% of MARTA’s FY19 operating hours, its share of railcar allocations was 57% and 40%, respectively. In contrast, the weekday evening hours for both agencies are marked by cost input shares that are low relative to the time periods’ share of operating hours. This is partly explained by the agencies not providing 24-hour service, leading to these time periods including when the last trains of the day are incrementally going out of service (see Figures 2-6 to 2-10). 72 Figure 2-10: BART Share of Cost Inputs by Time Period 73 Figure 2-11: MARTA Share of Cost Inputs by Time Period As a result and reflected in Figure 2-13, BART’s weekday peak service cost $316M to operate in FY19 — about 1.25 times more than the next most expensive time period, weekday base service. For MARTA, although the peak period generates more cost inputs relative to its share of operating hours, the total amount of cost inputs generated is about equal to weekday base service. Consequently, MARTA’s weekday base and peak period service each cost around $87M (Figure 2- 14), with weekday base period costing nominally more. 74 Figure 2-12: BART Cost v. Cost per rider by Time Period Figure 2-13: MARTA Cost v. Cost per rider by Time Period However, when the volume of passengers served during different time periods is considered, the peak period is the most cost-effective operating time period for both agencies. That is, the average cost per unit of benefit, measured as a trip, is lowest during the peak period. Whereas BART’s base service cost $10.67 per rider, on average, in FY19, its peak service cost $5.14 per rider, on average. For MARTA, these values are $9.17 and $5.31, respectively. So, while the peak period 75 costs more to operate, it serves so many more trips, thereby reducing the average per-unit cost of a trip. Findings — Spatial Allocations As with temporal findings, when costs are allocated spatially, more expensive links and stations of the BART system tend to also be more cost effective, and vice-versa. Furthermore, there appears to be a monocentric spatial pattern for both costs and cost effectiveness in the BART system. That is, high cost, low average cost per rider stations, and high cost, low average cost per passenger-mile links, tend to be concentrated in the core of the system. This is reflected in Figures 2-15 and 2-16. At $58M in FY19, BART’s most costly link to operate is its transbay tube. This is 2.6 times more costly than the next most expensive link of the system. Yet, it is also the most cost- effective link of the system, costing only $0.15 per passenger-mile, on average. By comparison, the link between Pittsburg/Bay Point Station and the Pittsburg/Bay Point transfer platform had the lowest FY19 annualized cost of $2.5M but the highest average cost per passenger-mile at $2.34. For stations, BART’s two highest cost stations, Montgomery Street and Embarcadero Stations, are also the lowest average cost per rider stations. However, this spatial pattern does not appear to hold for the MARTA system, as reflected in Figures 2-17 and 2-18. 76 Figure 2-14: BART Station and Link Costs Figure 2-15: BART Station Costs per rider and Link Costs-Per-Passenger-Mile Figure 2-16: MARTA Station and Link Costs Figure 2-17: MARTA Station Costs per rider and Link Costs-Per-Passenger-Mile To quantify this monocentric variation, I run ordinary least squares (OLS) regressions for both cost and cost effectiveness, regressing either of these onto track-mile distance from a defined 77 core station — West Oakland Station for BART and Five Points Station for MARTA. I run this for both links and stations, and define a link’s mileage from the core based on the distance of the station furthest from the core station. Table 2-3 shows these results. For BART, station costs decrease with distance from the core in a statistically significant way, while both link costs per passenger-mile and station costs per rider increase with distance from the core in a statistically significant way. The model for MARTA’s station cost effectiveness suggests that station costs per rider decrease with distance from the core in a statistically significant way. 78 Cost Cost effectiveness Agency BART MARTA BART MARTA Links / Stations → Variables ↓ Links Stations Links Stations Links Stations Links Stations distance_core -72,213.07 -110,635.3* 118,942.3 -77,139.9 0.0314** * 0.0287* -0.0005 -0.0508** constant 13,600,000*** 6,781,186*** 3,589,899*** 2,530,831*** 0.1141 1.0693** * 0.5943** * 1.48*** N 47 49 37 38 47 49 37 38 Adjusted R- squared -0.0712 0.0975 0.0344 0.044 0.3486 0.0851 -0.0285 0.1676 Statistical Significance: *** p ≤ 0.001, ** p ≤ 0.01, * p ≤ 0.1 Table 2-3: Cost and Cost effectiveness Relative to Distance from Core Discussion and Conclusion In the preceding analysis, I employed a partially-allocated long-run cost model and have shown that, when variable and semi-fixed capital costs are allocated to times and locations of a rail transit system, a great amount of variability exists. My analysis also underscores that cost and cost effectiveness are distinct evaluation measurements and can lead to opposing conclusions. While core stations and links and peak period service are the most input-intensive and often costliest to operate, they tend to be the most cost effective to operate due to the high density of riders served. When making an investment decision, both short-run and long-run costs are important to consider. Short-run costs include upfront sunk costs of investment, whereas long-run costs only account for the variable and recurring fixed costs that continue to be incurred into the future (Wang and Yang, 2001). Once a transit capital project is constructed, the operator will incur a “commitment trap” of having to operate the service (Schweitzer, 2017). This research underscores the importance of considering these long-run, commitment trap costs and the long-run cost effectiveness of major transit investment projects. Several portions of the BART and MARTA networks have high average per rider annual costs, even when the total annual costs I allocate are low. This suggests that some stations or extensions of these networks may have been a poor capital investment choice from a strictly financial, long-run operations standpoint; they bear a high long-run average cost per unit of benefit. 79 BART’s and MARTA’s spatial cost and cost effectiveness outcomes differ. Whereas BART has a monocentric pattern of costs and cost effectiveness, MARTA’s spatial cost and cost effectiveness pattern is scattered. One possible explanation of this is that, whereas BART has at least one station agent allocated to every station during all operating hours, MARTA spaces station agent assignments out and their allocations do not necessarily follow ridership patterns. In addition, travel patterns on the BART system are much more monocentric compared to on the MARTA system; whereas two-thirds of all BART trips begin or end at its four Downtown San Francisco Stations (8% of stations) that are also the highest ridership stations in the system, the five highest ridership MARTA stations (13% of stations) that account for two-thirds of all trips are not spatially concentrated. Finally, with regards to links, four of BART’s five routes converge through San Francisco, resulting in 2.5-minute frequency along this portion of the network during commute hours; whereas MARTA’s highest combined frequency is one train every five minutes. BART also operates longer trains and carries more passengers, particularly through the core of the system, leading to both greater weight-miles and passenger-miles. The difference between peak and base cost effectiveness patterns is counter-intuitive to past research findings, but not necessarily inconsistent. Past research suggests that peak period and suburban services are more costly to operate, rely on higher levels of subsides, and are regressively financed (Cervero, 1981; Garrett and Taylor, 1999; Parody et al., 1990; Pucher, 1982; Taylor et al., 2000). Yet, this research shows that weekday base and weekend periods are the costliest to operate on a per-rider basis. On the one hand, this seeming variance from past findings may be attributable to my not including amortized fixed capital costs — most notably, construction costs — since my analysis is focused on long-term costs. I posit that a greater influence is the fact that BART and MARTA maintain a relatively fixed level of service throughout the day, leading to their peak costs — particularly labor — being less “peaked” than is typical. Increasing midday transit service levels 80 has been a growing point of advocacy, is often promoted as a transport and access equity strategy, and is financially justified based on there being no marginal cost since a train that would otherwise be in storage is put to use. But there is in fact a marginal cost by way of this reducing the peak period’s marginal cost of a railcar — never mind the other cost inputs generated. BART’s and MARTA’s operating patterns show that providing off-peak service levels similar to peak service leads to off-peak periods costing more per-rider. However, peak period and core areas of these systems having a lower cost per rider does not answer whether certain times or locations of service are more heavily subsidized. Even the most cost ineffective times, links, and stations can be the most efficient (i.e., cost recovery) if fare payments cover more of these costs than other times or locations. To evaluate the time and location variability of efficiency and equity (i.e., parity in cost recovery), findings from this research need to be compared to the time- and location-variant fare revenues generated. Future research ought to evaluate this. This research is not without some limitations. For one, every mile of track is treated the same even though grade, curvature, tangent, and the number of tracks per link will influence wear, maintenance, and rehab costs. Among other examples, the use of a tamper machine is assigned to every grade and mile of track even though this machinery is only used on at-grade track. However, in the absence of structure rehab costs and intervals, which are highest for tunnel and aerial grades of the networks, I generalized the annualized cost of tamper machines. Finally, location and time are not interacted; it is possible that select areas of service are especially costly or cost ineffective during select times and not so during other time. Future research might expand this analysis to interact time and location, as well as incorporate construction and land costs to evaluate their impacts on cost and cost effectiveness patterns. 81 Paper 3: Inequitable Inefficiency: A Case Study of Rail Transit Fare Policies Abstract Research on transit fare equity often includes a calculation of disparity in the fare per mile paid by different groups of riders. This cost-benefit measurement overlooks the cost sharing nature of transit; as more riders consume a service, the average cost per rider declines. Using an average cost per rider metric to assign trip costs, and origin-destination fare data to estimate cost recovery through fares, I estimate the spatial and temporal variability of cost recovery across two rail systems, BART and MARTA. I find that cost recovery patterns are spatially monocentric and that the weekday peak period recovers more of its costs through fares than other time periods. I offer ideas on why these findings appear divergent to past research. Introduction Transportation finance policy in the United States tends to treat travel as largely exogenous and assumes that the purpose of transportation finance is to fund facilities and services to accommodate this travel. Hence, travelers generally do not directly pay for the full costs of their travel and, to the extent that they do, what they pay is not proportional to the marginal costs of their travel. While this is broadly documented in research, surprisingly little research has evaluated how transport subsidies — the difference between the cost of providing transport and what travelers pay for the transport they consume — are distributed across space and time. Are travelers in different locations or at different times subsidized more than others? If so, this suggests that certain travel and development patterns may be encouraged or discouraged through largely opaque and poorly documented transport subsidies. Research on the incidence of transport subsidies is especially limited when it comes to public transit. This may be due to transit in the United States functioning as a transportation lifeline for those who cannot or choose not to drive, as well as an alternative to driving that can reduce the 82 negative externalities of driving. Hence, rather than upend transportation finance policy to internalize travel costs, policy interventions overwhelmingly prioritize marginally reducing the negative externalities of automobile travel — dispersed travel patterns (i.e., sprawl), congestion, and pollution, to name a few — with incentives for travelers to change their behavior, such as by luring them from driving to using transit, whilst not taking away or taxing behaviors they have become accustomed to — the so-called “Do No Harm” ethos in transportation policy (Altshuler and Luberoff, 2004; Altshuler, 2010). Because of this role of transit, it is an especially subsidized travel mode in the United States. In 2017, nationwide highway costs were financed 53% by users (through tolls, fuel taxes, and license fees); transit, 21% (through fares) (United States Census Bureau, 2017). On face value, it would seem that those who travel more receive more transport subsidy. However, this overlooks the distributional spread of costs, user payments, and, by extension, efficiency and user subsidies, across a transport network. If there is any variability in these — for example, two bus routes with equal costs having different farebox recovery ratios — this implies that there is inequitable inefficiency in the network. As I showed in the previous chapter, total and average per trip annualized operating costs of rail transit, inclusive of semi-fixed assets, is spatially and temporally variable. I used the San Francisco Bay Area Rapid Transit District (BART) and Metropolitan Atlanta Rapid Transit Authority (MARTA) as case studies due to their heavy rail technology and service patterns being similar, which allows for a consistent and comparative analysis. In addition, their collection of highly disaggregate trip data (the origin, destination, and fare of every trip in the systems are recorded) and different fare structures allows for an assessment of trip-level subsidies, including whether this varies by fare structure. Figures 3-1 and 3-2 show the BART and MARTA system maps, respectively, in operation during most of fiscal year 2019 (FY19) — July 1, 2018 to June 30, 2019 — which is the time period for both the cost allocation research and research of this paper. In 83 this cost allocation research, I found that BART’s total annual costs are highest, and average per-trip costs lowest, in the urban core of the system and during weekday peak periods; whereas MARTA’s cost variability has no clear spatial pattern but similar temporal variability as BART. Figure 3-1: BART System Map effective July 1, 2018 to February 10, 2019 Figure 3-2: MARTA System Map effective in Fiscal Year 2019 In this paper, I combine findings from my cost allocation research with data on ridership and fare revenues to evaluate whether subsidies have a spatial or temporal pattern in the BART and 84 MARTA networks. I hypothesize that travelers in outlying areas, who travel longer distances, and who travel outside of the weekday peak period each pay a lower share of their costs; but that the middle hypothesis is attenuated with fare policies that are distance-based. In other words, I hypothesize that non-peak period travel, long-distance travel, and travel to/from suburban and exurban areas are disproportionately subsidized relative to their counters, but that distance-based fare policies can reduce this effect for long-distance travel. My hypothesis that peak period travelers are less subsidized than others is contrary to what past research suggests (e.g., Cervero, 1981; Parody et al., 1990), but aligns with my cost allocation findings that the peak period has the lowest average per trip cost of any operating time period in the two systems. Finally, unlike past research that measures the spatial equity of transit pricing based on whether there is parity in the fare paid per mile of travel consumed by different riders, I innovate by controlling for the cost sharing nature of transit, which allows me to account for the variability of costs across unique miles and stops of the network and measure equity based on how equally different riders cover the cost of their trip through the fare that they pay. Literature Review Transit subsidies are generally categorized as either a supply-side subsidy or demand-side subsidy. Supply-side subsidies are intended to cover the costs of service provision that exceed income generated from fares, while demand-side subsidies are offered to riders to reduce the fares they pay. As reasoned, the incidence of both subsidies “trickle down” to riders; by partially covering operating costs, subsidies have the potential to reduce the fares needed to cover costs, while fare subsidies directly reduce fares paid by riders. However, supply-side subsidies have been shown to disproportionately benefit unionized transit workers and enable the industry to suffer from workforce inefficiencies and Baumol’s Cost Disease (Jones, 1985; Wachs, 1989; Pickrell, 1985; Morales Sarriera and Salvucci, 2016). At various times, as transit subsidies have increased with the 85 goal of increasing service levels, service levels were either maintained or reduced while unionized worker salaries were increased (Wachs, 1989). Morales Sarriera and Salvucci (2016) suggest this is partly driven by the industry being stagnant in technological and efficiency advancements relative to other industries; according to Jones (1985), because there are few promotional opportunities for operators and mechanics, across-the-board salary increases are the primary way frontline workers can increase their incomes. As for whether and how subsidies trickle down to users, Serebrisky et al. (2009) conduct a critical literature review and surmise that most supply-side subsidy programs are socioeconomically neutral or regressive, while few demand-side subsidies are effective. More recently, federal transit subsidies have focused on capital projects rather than operations, often motivated by the short-term expenditure effects they generate rather than their long-term transportation effects (Taylor and Samples, 2002; Taylor, 2017). Respectively, these refer to the economic activity generated during the construction of a project (i.e., jobs, local spending from workers, etc.) and the project’s effectiveness in addressing whatever transportation challenge it is justified under. In the long-run, major transit investments can create an operating “commitment trap” wherein an operator is de facto committed to providing the service even if usage does not warrant it (Schweitzer, 2017). The spatial and temporal variability of these long-term operating costs are what I seek to evaluate in this research. Apart from these top-level considerations, user equity of different transit fare structures has also been studied. This was a popular research topic in the 1980s as transit agencies migrated from using time- and distance-variant fare structures to using flat-rate fare structures. Researchers and policymakers sought to understand the equity and efficiency implications of the transition. However, much of the methodologies and empirical findings to-date rely, at best, on weakly disaggregate agency data — for example, allocating costs and fare revenues to just two time periods to evaluate temporal variability of costs and subsidies (e.g., Reilly, 1977; Parody et al., 1990) or to 86 bus yards (“cost centers”) to evaluate spatial variability of costs and subsidies (e.g., Cervero, 1981). In addition, the literature overwhelmingly focuses on bus transit and temporal variability. The research broadly finds that it is more costly to serve peak period travel than off-peak period in both gross and net terms (Cervero, 1981; Parody et al., 1990; Taylor, 2000); and that flat rate fare policies relative to time- and distance-variant policies are less effective in recovering total costs, lead to peak period and suburban riders being more subsidized than off-peak and urban riders, and that this pattern is socioeconomically regressive since a higher share of peak period and suburban travel is consumed by higher-income, non-minority persons relative to off-peak and urban travel (Cervero, 1981; Meyer and Gomez-Ibanez, 1981). A small number of studies show that, because the fare revenue generated during the peak period well exceeds the additional costs of serving it, the peak period is less costly on a per rider basis (i.e., it is more cost effective) than the off-peak (Reilly, 1977). A deciding difference in these findings is whether and how fixed and semi-fixed asset costs are included in the cost allocation step of the research. Cervero (1981) and Parody et al. (1990) allocate asset costs 85% to the peak period and 15% to the off-peak period in evaluating cost recovery variability; Taylor et al. (2000) use a marginal allocation method, derived from the Bradford Bus Study (Savage, 1989), based on the share of transit vehicles in-use during different time periods; and Reilly (1977) does not allocate asset costs. In these studies, only Cervero (1981), Parody et al. (1990), and Reilly (1977) made any measurement of the temporal variability of subsidy patterns; other studies focused on cost variability only. Of these, Cervero (1981) and Parody et al. (1990) clearly use the most thorough cost allocation method in that they included capital costs. Even so, the peak-to-base “rule-of-thumb” ratio they used for allocating asset costs is primitive and discounts the many other time periods to which transit operators scale their resources. For example, in my cost allocation research from the previous chapter, I showed that BART and MARTA have eight and five unique operating time periods they scale to, respectively; not two! And while Taylor et al. 87 (2000) used a more robust temporal cost allocation method that includes all capital and operating costs and accounts for there being more than two time periods, they do not evaluate temporal cost recovery (i.e., subsidy) patterns. Similar findings have been shown with respect to capital transit investments; they tend to benefit higher income, non-minority persons more than lower-income, minority persons who are more transit dependent and use less capital-intensive transit services (Pucher, 1982; Garrett and Taylor, 1999; Taylor and Morris, 2015). However, the extent to which these costs are paid by the beneficiaries, such as through fares, is not considered in these analyses. So while these studies demonstrate that certain areas and populations receive more investment in gross terms, if those same areas and populations contribute more through what they pay into the system, the equity implications in terms of net costs may be different. Since the aforementioned studies, data granularity has greatly improved, which can allow for much more informative findings about how cost recovery and fare equity varies by time and location of travel. Yet, instead of using this newly-available, highly disaggregate data, recent research has relied on past studies’ findings to inform their analyses about the equity of current fare policies. For example, Brown (2018) uses the 45% peak-to-base net cost ratio from Parody et al. (1990) based on 1983 national aggregate data and 2012 California Household Travel Survey data to conclude that the current Los Angeles Metropolitan Transportation Agency’s transit fare structure is regressive and would be more equitable if it adopted time- and distance-variant fares. Other recent studies are international and suggest that, contrary to findings in the United States, flat rate fares benefit lower income persons in Stockholm (Rubensson, 2020) and China (Zhou, 2019) — likely due to lower income persons settling further from the urban core, unlike in the United States. Finally, research on the spatial equity of transit fare policies is practically non-existent. Geopolitical considerations inform transport investments, as politicians and voters typically desire a 88 visible return on their tax investments (Taylor, 2017; Taylor and Norton, 2009). However, the extent to which different geopolitical areas are subsidized at the user level is not a focus of much transit fare policy research. Among few exceptions are Hodge (1988), Iseki (2016), and the previously- referenced study of Cervero (1981). Cervero (1981) used bus facilitates as “cost centers” and labeled them as suburban or urban to draw his conclusion that suburban riders pay less per mile of travel consumed, on average. In this way, he used highly aggregate geographies, vehicle-miles, and passenger-miles for his spatial analysis. Hodge studied the Seattle, Washington transit network, labeled every mile of service as urban or suburban using geopolitical boundaries, and found that when only fares are considered, core (urban) riders subsidize suburban riders; but that the net flow of subsidies goes from suburban areas to urban areas when the tax base is included in the analysis. However, Hodge’s method of asset and operating cost allocations used only vehicle-miles and vehicle-hours as inputs, so was not robust. Iseki used a more robust cost allocation method and had similar findings in the Toledo, Ohio region; the urban area of Toledo is dependent on tax revenue from suburban areas, despite urban Toledo generating the highest ridership and fare revenue. In sum, past literature suggests that, when asset costs are accounted for, the peak period is subsidized more than the off-peak period, but that the pattern is reversed when these costs are not accounted for; flat rate fare structures are socioeconomically regressive because they allow persons who consume longer and more suburban-based trips — whom tend to be higher income and wealthy — to pay less per mile; and urban areas pay a higher share of travel costs through fares than suburban areas, but a lower share on net when tax source revenues are accounted. Among missing elements in the literature are more thorough analyses of transit modes other than bus transit, as well as the use of available granular data to evaluate temporal and spatial variability of cost recovery patterns more precisely. For example, transit operators’ time periods often are more nuanced than merely peak and base, and spatial variability is more varied than geopolitical boundaries. Most 89 significantly, past research on spatial fare equity (e.g., Cervero, 1981) does not account for the cost sharing nature of transit — that is, how much the cost of each unique mile of travel is shared amongst the consumers of that unique mile of travel. Some game theory literature on how transit riders may change travel patterns in a cost sharing scheme (Rosenthal, 2017), as well as research on private sector “collaborative transportation” concepts (e.g., Frisk et al., 2010; Guajardo and Ronnqvist, 2016), exist; but no research on transit cost recovery and fare equity accounts for this. Data and Methods The objective of this work is to evaluate the temporal and spatial variability of farebox recovery of rail transit networks. Do travelers of different times and locations pay a different share of their travel costs through fares in any statistically significant way such that transit operations are not only inefficient (i.e., costs are not fully recovered through user payments), but inequitably so on spatial and temporal dimensions? To answer this, I rely on findings from the cost allocation research in the previous chapter and trip-level ridership and fare data to estimate the costs and cost recoveries of unique origin-destination (OD) trips and time periods. I then weight trip-level findings to travel consumption patterns to evaluate what average riders of different links and stations of the network pay as a share of the cost of their trip. All original data came from the transit agencies, BART and MARTA. Table 3-1 defines variables that are used in my analysis. Variable Description cost od The cost of serving a particular OD trip, od. cost t The total cost expended on serving a particular time period, t. cost tot The total cost expended during the study period. costppm The cost per passenger-mile of a particular link; that is, the total annualized cost of a particular link divided by the sum-product of the length (in track-miles) and number of annual trips that traverse the particular link. costppx costppx l costppx o costppx d The cost per passenger of a particular station or link; that is, the total annualized cost of a particular station or link divided by the number of trips into or out of the particular station or that traverse the particular link. Subscripts “l,” “o,” and “d” correspond to a unique link, origin station, and destination station, respectively. fare od The average fare paid for consuming a particular OD trip, od. fares t The total fare revenue generated during a particular time period, t. fares tot The total fare revenue generated during the study period. 90 percentpaid effective The average fare paid for a particular OD trip divided by the cost of serving the OD trip. percentpaid l percentpaid s The average cost recovery (percentpaid effective) for all OD trips associated with a particular link, l, or station, s. percentpaid t The total costs recovered through fares generated in a particular time period, t. pxmiles The total passenger-miles generated — that is, the sum-product of the count of trips associated with each OD trip and the trip length of each OD trip. subsidy effective The cost of a particular OD trip not paid by the average fare of the OD trip; 100% minus the effective percent paid. triplength The length of a particular OD trip, in track-miles. Limited to mainline track only. triplength average The average length, in track-miles, of all annual OD trips made that used a particular station or link of the network. Limited to mainline track only. distancecore distancecore l distancecore s distancecore o distancecore d The distance, in track-miles, that a particular station or link associated with an OD trip is from a defined core station of the network — West Oakland Station for BART, Five Points Station for MARTA. Subscripts “l,” “s,”, “o,” and “d” correspond to a unique link, station, origin station, or destination station, respectively. For links, the distance that the station farthest from the core station is defines this value. Limited to mainline track only. trips od trips l trips s trips t trips tot The number of trips generated across the study period. Subscripts “od,” “l,” “s,” “t,” and “tot” correspond to unique ODs, links, stations, time periods, and the total for the entire study period, respectively. Table 3-1: Table of Variables The cost of serving a particular OD trip is equal to the sum of the average cost per rider of the origin station, destination station, and each link used to complete the trip, as derived from the cost allocation study in the preceding chapter. This is modeled in Equation 3-1. Equation 3-2 defines the effective percent paid for a particular OD trip, which is equal to the weighted average of what every rider who consumed a particular OD trip paid divided by the cost of serving the trip. This accounts for the different fares that different riders paid based on the discount programs, etc. that applied to their fare payment. One minus the effective percent paid is the effective subsidy given to consuming a particular OD trip. 𝑐𝑜𝑠 𝑡 𝑜𝑑 =𝑐𝑜𝑠𝑡𝑝𝑝 𝑥 𝑜 +𝑐𝑜𝑠𝑡𝑝𝑝 𝑥 𝑑 +∑𝑐𝑜𝑠𝑡𝑝𝑝 𝑥 𝑙 𝑛 𝑙 =1 (3-1) 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 𝑓𝑎𝑟 𝑒 𝑜𝑑 𝑐𝑜𝑠 𝑡 𝑜𝑑 (3-2) To test how much trip subsidies are explained by trip length and distance from the urban core of the network, I run ordinary least squares regressions. I regress the effective percent paid of 91 an OD trip onto trip length, the distance the origin station is from the defined core station of the network, and the distance that the destination station is from the defined core station of the network. This is defined in Equation 3-3. 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 =𝛽 0 +𝛽 1 𝑡𝑟𝑖𝑝𝑙𝑒𝑛𝑔𝑡 ℎ+𝛽 2 𝑑𝑖𝑠𝑡 𝑎𝑛𝑐𝑒𝑐𝑜𝑟 𝑒 𝑜 +𝛽 3 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑐𝑜𝑟 𝑒 𝑑 (3-3) While Equation 3-3 will estimate how an average consumer of a particular OD trip pays relative to the cost of serving them, it does not explain the geographic incidence of subsidies — that is, whether subsidies flow to particular geographic areas of the network more than others, given weighted consumption and distribution of OD trips throughout the network. To evaluate the geographic concentration of transit subsidies, I calculate the average cost recovery of all trips associated with every station and link of the network, as shown in Equation 3-4 and 3-5, respectively. A trip is associated with a station if the station is the origin or destination of the trip; with a link, if it traverses the link. To be clear, fare revenues are not allocated to links or stations, as there is no practical way to divvy up a fare into time, mileage, and station components for link and station fare revenue allocations. So, these are not link and station cost recoveries, per se; they are the weighted average cost recovery of all OD trips that used the link or station during the study period (i.e., FY19). Because there are just 38 stations and 37 links in the MARTA network, and 48 stations and 47 links (studied) in the BART network, there is an insufficient sample size to use multivariable regression analysis in this portion of the study. As an alternative, I provide descriptive findings and offer interpretation. 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑠 = ∑ (𝑡𝑟𝑖𝑝 𝑠 𝑜𝑑 ∗𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ) 𝑠 =𝑜 ,𝑑 𝑡𝑟𝑖𝑝 𝑠 𝑠 (3-4) 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑙 = ∑ (𝑡𝑟𝑖𝑝 𝑠 𝑜𝑑 ∗𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 )∈𝑙 𝑡𝑟𝑖𝑝 𝑠 𝑙 (3-5) 92 Finally, to estimate the incidence of temporal subsides, I divide the total fare revenue generated during a particular time period by the cost of serving that time period — the latter derived from the cost allocation study in the previous chapter. This is modeled in Equation 3-6. 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑝𝑎𝑖 𝑑 𝑡 = 𝑓𝑎𝑟𝑒 𝑠 𝑡 𝑐𝑜𝑠 𝑡 𝑡 (3-6) As with the link- and station-level spatial analysis, there is an insufficient number of time periods — just five and eight for MARTA and BART, respectively — for any multivariant regression analysis. In lieu of this, I calculate the correlations between cost recovery and travel pattern variables — including the count of trips, total passenger-miles generated, average trip length, and average distance of origin and destination stations from the defined core station — for trips taken during each respective time period. This will not show the variation of net travel patterns, but the variation of travel patterns across time periods. Descriptive Statistics Table 3-2 provides agency profile information of the BART and MARTA rail networks, effective during FY19. Noteworthy is that, although BART has a network about 2.3 times the size of MARTA’s, it generated 3.5 times as many vehicle revenue-miles and 3.9 times as many trip-miles, but only 1.9 times as many trips. BART MARTA Miles (mainline) 109.4 miles 48 miles Stations 48 stations 38 stations Fare Structure Distance-based Flat rate Net Fare Revenue $448,688,735 $58,576,496 Gross Costs $847,799,127 $237,992,718 Farebox Recovery Ratio 52.9% 24.6% Vehicle Revenue-Miles* 78M vehicle-miles 23M vehicle-miles Annual Trips* 125M trips 65M trips Annual Passenger-Miles* 1.756B passenger-miles 450M passenger-miles *As reported in 2019 Agency Profiles of National Transit Database Table 3-2: Agency Profiles 93 During FY19, the MARTA system had a total of 38 stations, resulting in 1,406 OD pairs. By comparison, BART had a total of 48 stations, resulting in 2,256 OD pairs. However, BART’s network includes three rail service types — standard BART trackage (mainline), a diesel multiple unit segment of service (eBART), and the Oakland Airport Connector (OAC) that operates as a cable-powered people mover. As in the cost allocation research, while I include all stations, I only include mainline portions of the BART track network to ensure consistency in analysis. By extension, any trips that solely use non-mainline portions of track are excluded from my analysis in this paper. This results in a total of 2,248 OD pairs. Finally, for any trips that partially used a non- mainline portion of track, I assign trip costs using only the mainline links of the networks — that is, a trip’s cost is equal to the summation of the costs per rider of the origin station of the trip, destination station of the trip, and each mainline link used to fulfill the trip. As an example, a trip from Oakland International Airport Station to Antioch Station will exclude the Oakland Airport Connector and eBART segments of trackway, so will be charged as a trip that utilizes links from Coliseum Station to Pittsburg/Bay Point Station, plus the cost per rider of Oakland International Airport Station and Antioch Station. The two agencies’ fare structures are also different. MARTA’s fare structure is flat rate at $2.50 per trip, regardless of trip length, origin, or destination. However, there are various discounts, including through transfer agreements with other transit operators, cooperative arrangements with area employers, multi-day passes, and more. At BART, base fares are distance-based, but follow a stepwise function. Riders pay a minimum fare for the first six miles of travel. Beyond six miles, riders pay for the first six miles plus a rate per mile up to 14 miles; beyond 14 miles, riders pay for the first 14 miles plus a lower cost per mile greater than 14 miles. Accordingly, although riders pay more for every additional mile they travel beyond six, longer distance travel is discounted on a per mile basis. There are also various fees, including a fee for use of the transbay tube, for travel to or 94 from San Mateo County (a county that does not pay into the BART District through taxes), and for travel to or from San Francisco or Oakland International Airports; as well as various discount programs, including for senior and disabled riders, youth, and high-value discount (HVD) tickets. The effective percent paid calculations of every OD trip are reflective of the weighted average of these many discounts used by riders of the OD pairs. Spatial Analysis Tables 3-3 and 3-4 show descriptive statistics of key variables in the OD cost recovery analysis, including the count of trips associated with every OD pair, the effective percent paid of every OD pair, the trip length of every OD pair, the distance the origin station is from the defined core station of the network, and the distance that the destination station is from the defined core station of the network — for BART and MARTA, respectively. In these tables, I show both the unweighted distribution, which weights all OD trips equally so is irrespective of cumulative trip consumption patterns; as well as the distribution weighted to trip count, which reflects cumulative trip patterns rather than station-to-station pairs. So, while a particular OD trip may have a cost recovery higher than another, if the former has more consumption (i.e., trip counts) than the latter, the mean weighted to trip count will be higher than the unweighted mean. Similarly, the average, median, and standard deviation of trip length for all actualized trips will be different than the same statistics for the set of OD pairs without weighting. I use unweighted values to calculate how OD trip cost recoveries are associated with trip length and station distances from the core, but show both unweighted and weighted statistics here to demonstrate how OD pair patterns differ from aggregate trip consumption patterns — which is pertinent for the station and link analysis that evaluates the incidence of subsidies. 95 Minimu m Mean Median Standard Deviation Maximu m Unweighte d Weighte d Unweighte d Weighte d Unweighte d Weighte d percentpaid effectiv e 10.10% 44.24% 63.31% 39.34% 57.21% 19.24% 25.59% 158.29% distancecore o 0 13.53 10.16 11.98 7.18 8.33 7.09 29.61 distancecore d 10.04 6.68 7.04 triplength 0.35 21.82 14.98 20.97 12.63 12.5 10.05 56.44 trips 176 52,257 — 15,874 — 92,539 — 751,744 N (OD pairs) = 2,248 Table 3-3: Descriptive Statistics of OD Pairs — BART Minimu m Mean Median Standard Deviation Maximu m Unweighte d Weighte d Unweighte d Weighte d Unweighte d Weighte d percentpaid effectiv e 10.2% 30.10% 36.05% 27% 31.44% 13.38% 17.50% 105.25% distancecore o 0 5.66 5.75 4.73 5 4.61 4.72 15.95 distancecore d 5.69 5 4.71 triplength 0.38 9.62 9.13 9.05 8.45 5.95 6.05 26.39 trips 355 29,341 — 14,854 — 38,910 — 404,000 N (OD pairs) = 1,406 Table 3-4: Descriptive Statistics of OD Pairs — MARTA One thing that stands out in these tables is the difference between the two networks in terms of how the unweighted (i.e., OD pairs, irrespective of trip count) and weighted (i.e., total OD trips) statistics vary. BART’s weighted data are notably different than the unweighted data — implying that trip consumption patterns vary significantly across the network; trip consumption is not normally distributed. Specifically, the average cost recovery of trips consumed (weighted) is 1.4 times more, average trip length 32% less, and the distance from the core of the system that trips begin or end about 26% less, than if trips were equally spread across all OD pairs (unweighted). By comparison, MARTA’s trip consumption patterns are similar to the network’s unweighted spread of OD pairs. As I show later, this variance between the two networks reflects the difference in spatial concentration of travel across stations and links of the networks. Focusing on cumulative trip patterns (weighted data), the mean OD trip cost recovery for BART and MARTA is 63% and 36%, respectively — higher than the systemwide cost recovery of 53% and 25%, respectively, as reported in Table 3-2. The unweighted mean is also different from the systemwide total. One might think that the mean trip-level cost recovery should be equal the 96 systemwide cost recovery; that is, the mean of all trips’ fares divided by their costs should equal the sum of fares divided by the sum of costs (Equation 3-8). ∑ 𝑓𝑎𝑟𝑒 𝑂𝐷 ∑ 𝑐𝑜𝑠𝑡 𝑂𝐷 = ? 𝑓𝑎𝑟𝑒𝑠 𝑡𝑜𝑡 𝑐𝑜𝑠𝑡𝑠 𝑡𝑜𝑡 (3-7) However, the sum of OD trip costs is not equal to aggregate systemwide costs because OD trip costs are derived from a subset of costs after costs have been allocated to stations and links and divided by ridership (see Equation 3-1). Hence, OD trip costs move across different subsets of costs (i.e., parts of the network). Furthermore, OD trips that utilize low cost per rider/high ridership stations and links will skew the OD trip cost recovery pattern higher than the aggregate systemwide cost recovery. That is, while more cost-effective trips may be consumed, cost- ineffective trips and segments of a network are still served. As a result, the average cost recovery of consumed trips will tend to be greater than the systemwide cost recovery. This is consistent with an objective of this research: the aggregate pattern of a network does not necessarily reflect patterns across its parts. Apart from cost recovery, trips taken on BART, on average, begin or end just over ten miles, or 34% of the maximum possible distance, from the defined core station of the network. For MARTA, the average trip begins or ends about 5.7 miles from the defined core station, or about 36% of the distance the furthest away station is from the defined core station. Similarly, the average length of consumed trips taken on BART is about 15 miles or 39% of the maximum possible trip length; on MARTA, 9.1 miles or 35% of the longest possible trip. Thus, as a percentage of the maximum possible, trips are about as “suburban” and long in both networks. On the other hand, the spatial pattern of how trips are concentrated in the two systems is distinct. Figures 3-3 and 3-4 show the distribution of ridership patronage of stations — that is, out of all trips taken, the share that begin or end (inclusive) at each station — in the BART and MARTA 97 network, respectively. We can see from this that about two-thirds of all trips taken in the BART system begin or end at BART’s four busiest stations, which account for 8% of the system’s stations, and that there is a notable drop off after these stations. By comparison, 53% of all trips taken on MARTA begin or end at its four busiest stations, which represent 11% of its stations, and the drop off is less abrupt. In both systems, these four stations are the only stations with a double-digit share of passenger patronage. Figure 3-3: Ridership Patronage by Station — BART Figure 3-4: Ridership Patronage by Station — MARTA BART’s four busiest stations — Embarcadero, Montgomery Street, Powell Street, and Civic Center/UN Plaza Stations — are adjacent to one-another in Downtown San Francisco. By contrast, 0% 5% 10% 15% 20% 25% Station Patronage Stations 0% 5% 10% 15% 20% 25% Station Patronage Stations 98 the four busiest MARTA stations — Five Points, Airport, Peachtree Center, and College Park Stations — are associated with two different epicenters of ridership, Downtown Atlanta and the airport. The ridership at the eight adjacent Downtown Atlanta stations (21% of stations) — North Avenue, Civic Center, Peachtree Center, Five Points, Garnett, Georgia State, Dome/CNN Center, and Vine City — individually ranged from first (or upper third percentile) to 35 th (or lower 11 th percentile) in passenger patronage; collectively, 51% of trips begin or end in Downtown Atlanta. Further, exclusive of the four busiest stations, every BART station’s ridership has its highest destination relationship with one of the four busiest stations, ranging from 10% to 30%, with an average of 19%, of trips destined to a Downtown San Francisco station. When the busiest stations are analyzed as a group, every other BART station has between 29% and 73% (with a 50% average) of its trips destined to Downtown San Francisco. At MARTA, just 27, or 79%, of stations exclusive of the busiest four, have their strongest destination relationship with one of the four busiest stations. When the four busiest stations are grouped, their destination market-share of trips originating at other stations ranges from 15% to 42% with an average of 28%. Focusing on the eight Downtown Atlanta stations, 22, or 73%, of other stations have one of the Downtown Atlanta stations as their highest market-share destination station. As a group, Downtown Atlanta accounts for between 18% and 47% of the destination market-share of other stations with an average of 31%. It is clear from this that BART’s OD ridership patterns revolve around a monocentric center, Downtown San Francisco, whereas MARTA’s OD ridership patterns are polycentric, if not broadly dispersed. This can influence how origin and destination station distance from the urban core of each network, as well as trip length, influences spatial cost recovery patterns It is important to note that, while the level of monocentricty in origin-destination travel patterns is markedly different between BART and MARTA, this does not necessarily extend to the links used to complete various trips. Figures 3-5 and 3-6 geographically show how travel patterns 99 on BART and MARTA affect station patronage and link usage (note that the link usage scales vary significantly). These figures suggest that, while station patronage is relatively monocentric for BART and dispersed for MARTA, the bi-directional flow of ridership along links is centrally concentrated in both networks. This makes sense, as even in a polycentric or dispersed travel environment, trip paths can be centrally concentrated along links of a network even if origins and destination are not. This is especially subject to occur if the network has a defined central node that many origin- destination trips must pass through, as is the case for MARTA. I investigate these observations more thoroughly in the Results section. Figure 3-5: Spatial Pattern of Station Patronage and Link Usage — BART 100 Figure 3-6: Spatial Pattern of Station Patronage and Link Usage — MARTA Tables 3-5 and 3-6 show the resulting descriptive statistics for the station-level analysis — that is, each station’s distance from the defined core station of the network, the weighted average percent paid for all trips that began or ended at the station, the weighted average trip length for all trips that began or ended at the station, and the number of trips that began or ended at the station — for BART and MARTA, respectively. These data are generated from the above-summarized OD data, conditional on a station being an origin or destination station. Tables 3-7 and 3-8 show the same descriptive statistics for the link-level analysis — in this case, corresponding to all trips that traversed a particular link, which is easily derived through trip path assignment. The objective of this part of the analysis is to evaluate whether user subsidies have a spatial pattern. Since fares are not allocated to links and stations, the percentpaid variable in these tables does not (and cannot) reflect station and link cost recoveries; they are a cost recovery “profile” of the average rider of each unique 101 station and link. Therefore, these numbers will not necessarily align with OD trip or systemwide aggregate cost recovery statistics. Variable Minimum Mean Median Standard Deviation Maximum percentpaid s 24.86% 54.47% 54.57% 14.36% 99.79% distancecore s 0 13.56 12.07 8.44 29.61 triplength average 7.67 17.36 15.25 7.8 42.25 trips s 617,004 4,897,543 3,473,553 5,053,904 24,571,444 N (stations) = 48 Table 3-5: Descriptive Statistics of Station Profiles — BART Variable Minimum Mean Median Standard Deviation Maximum percentpaid s 13.38% 29.37% 29.93% 6.27% 40.71% distancecore s 0 5.66 4.73 4.67 15.95 triplength average 5.02 8.81 7.47 3.21 16.36 trips s 430,987 2,171,240 1,728,397 1,529,423 7,356,599 N (stations) = 38 Table 3-6: Descriptive Statistics of Station Profiles — MARTA Variable Minimum Mean Median Standard Deviation Maximum percentpaid l 24.86% 47.61% 48% 9.29% 64.58% distancecore l 1.59 13.61 12.16 8.21 30.02 triplength average 1.82 22.14 19.88 7.36 39.78 trips l 154,130 18,199,306 13,028,305 15,014,428 64,656,418 N (links) = 47 Table 3-7: Descriptive Statistics of Link Profiles — BART Variable Minimum Mean Median Standard Deviation Maximum percentpaid l 13.38% 23.61% 23.83% 2.85% 27.35% distancecore l 0.38 5.82 4.8 4.64 15.95 triplength average 6.37 12.28 12.42 2.45 16.57 trips l 430,987 8,194,683 6,654,606 4,931,187 17,505,807 N (links) = 37 Table 3-8: Descriptive Statistics of Link Profiles — MARTA Comparing these statistics with the weighted OD trip statistics in Tables 3-3 and 3-4, station and link mean cost recovery profiles are clearly less than the mean weighted OD trip cost recovery. With smaller standard deviations, the spread is also much less than in the case of weighted OD trip cost recoveries. This is principally explained by these being different measurements: the latter is a measurement of trip cost recoveries, while the former are measurements of trip cost recovery averages for trips that are associated with the link or station. As a result, although high cost recovery 102 OD trips “crowd out” low cost recovery OD trips in the OD trip cost recovery statistics, those same OD trips share links and stations with low cost recovery OD trips. Hence, even the links or stations with the highest cost recovery profile will inherently have a value less than the highest cost recovery OD trip. Furthermore, there are far fewer links and stations than there are OD pairs, and high cost recovery trips may be concentrated across few links and stations, leaving the remainder of links and stations to be associated with lower cost recovery OD trips. This last concept is evaluated in the Results section. Figures 3-7 and 3-8 geographically show the distribution of the percentpaid variable across stations and links in the BART and MARTA network, respectively. Figure 3-7: Average Percent Paid Across Links and Stations — BART 103 Figure 3-8: Average Percent Paid Across Links and Stations — MARTA To illustrate interpretation of these maps, the “average rider” who travels to or from MARTA’s Five Points Station pays 34.1% of the costs of their trip, while the “average rider” who traverses BART’s link between West Oakland and Embarcadero Stations (the transbay tube) pays 63.9% of their total trip cost. With few exceptions, these figures surmise that the average cost recovery of riders of different links and stations generally declines with distance from each system’s core — though, as suggested by the different scale on the maps, the magnitude of variance is significantly less for MARTA relative to BART. Also notable and consistent with my cost v. cost per rider analysis in the preceding chapter, BART’s most expensive stations and links to operate — and likely to build due to their being tunneled — also have the highest level of ridership. 104 Temporal Analysis For temporal analysis, Figures 3-9 and 3-10 show the total annualized allocated costs (left axis) and average cost per rider (right axis) of the different time periods for BART and MARTA, respectively. These data are derived from the cost allocation study in the preceding chapter. Tables 3-9 and 3-10 show full descriptive statistics for trips consumed during different time periods for each agency. Five of the variables — cost, fare revenue, cost recovery, trip count, and passenger- miles — are aggregated to the time period; they reflect the total costs, fare revenue, etc. for the time period. The other three variables — origin station distance form the core station, destination station distance from the core station, and trip length — are disaggregated to trips consumed during reach time period. Accordingly, the variation in these values reflects how trip consumption patterns vary across time periods. 105 Figure 3-9: Cost v. Cost Per Rider by Time Period — BART Figure 3-10: Cost v. Cost Per Rider by Time Period — MARTA $- $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 $14.00 $16.00 $18.00 $- $50 $100 $150 $200 $250 $300 $350 Weekday - Base Weekday - Peak Weekday - Evening Weekday - Late Evening Saturday - Base Saturday - Midday Sunday - Base Sunday - Evening Cost Per Rider Cost (millions) Cost Cost Per Rider $- $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 $- $10 $20 $30 $40 $50 $60 $70 $80 $90 $100 Weekday - Base Weekday - Peak Weekday - Evening Weekend - Base Weekend - Evening Cost Per Rider Cost (millions) Cost Cost Per Rider 106 Time Period Weekday Saturday Sunday/Holiday Total Base Peak Evening Late Evening Base Midday Base Evening costt $258,037,518 $325,430,391 $67,444,710 $37,682,645 $32,792,752 $53,279,185 $51,104,798 $22,027,128 $847,799,127 farest $89,697,710 $243,146,564 $35,114,074 $23,259,610 $9,622,910 $22,504,842 $19,464,467 $5,878,558 $448,688,735 percentpaidt 34.76% 74.72% 52.06% 61.72% 29.34% 42.24% 38.09% 26.69% 52.92% tripst 24,177,808 63,242,768 8,732,436 6,017,829 2,514,618 6,141,670 5,208,938 1,438,202 117,474,269 pxmiles 343,857,182 970,670,140 138,290,468 89,440,215 36,825,580 84,332,354 72,345,257 22,255,671 1,758,016,867 triplength Minimum 0.35 0.35 0.35 0.35 Mean 14.22 15.35 15.84 14.86 14.64 13.73 13.89 15.47 14.97 Standard Deviation 10.16 9.96 10.45 10.15 10.01 9.84 9.86 10.6 10.07 Maximum 56.92 56.92 56.92 56.92 distancecoreo Minimum 0 0 0 0 Mean 11.04 10.27 8.14 8.4 9.4 10.34 10.44 9.82 10.16 Standard Deviation 7.59 7.18 5.38 5.54 6.4 7.03 7.12 6.8 7.09 Maximum 29.61 29.61 29.61 29.61 distancecored Minimum 0 0 0 0 Mean 8.89 9.99 12.41 11.79 10.89 9.54 9.8 11.46 10.04 Standard Deviation 6.09 7.06 8.13 7.89 7.47 6.46 6.71 7.69 7.04 Maximum 29.61 29.61 29.61 29.61 Table 3-9: Temporal Descriptive Statistics — BART Time Period Weekday Weekend/Holiday Total Base Peak Evening Base Evening costt $86,991,391 $86,950,887 $14,582,218 $43,032,908.02 $6,435,315 $237,992,718 farest $15,839,966 $29,559,350 $2,626,714 $9,450,864 $1,099,602 $58,576,496 percentpaidt 18.21% 34% 18.01% 21.96% 17.09% 24.61% tripst 12,391,117 19,898,647 2,057,750 6,985,699 841,506 42,174,719 pxmiles 109,206,799 188,547,757 17,270,565 61,508,060 6,977,054 383,510,235 triplength Minimum 0.38 0.38 0.38 Mean 8.81 9.48 8.39 8.8 8.29 9.09 Standard Deviation 6.22 5.94 5.86 6.04 5.79 6.04 Maximum 26.39 26.39 26.39 distancecoreo Minimum 0 0 0 Mean 5.56 5.96 5.17 5.69 4.81 5.74 Standard Deviation 4.57 4.9 4.31 5.54 4.27 4.71 Maximum 15.95 15.95 15.95 distancecored Minimum 0 0 0 Mean 5.57 5.77 8.39 8.8 8.29 5.68 Standard Deviation 4.61 4.87 5.86 6.04 5.79 4.7 Maximum 15.95 15.95 15.95 Table 3-10: Temporal Descriptive Statistics — MARTA 107 As evident from these data, the peak period is the most expensive to operate by far for BART and almost as expensive to operate as the weekday base period for MARTA. But in both cases, the weekday peak period serves so many more riders and passenger-miles that the cost per rider and per passenger-mile is lowest during the weekday peak period. Similarly, by serving so many more riders and passenger-miles, much more fare revenue is generated during the weekday peak period — so much that it offsets any additional costs of serving the weekday peak period, even when semi-fixed costs are accounted for. As a result, the weekday peak period recovers the greatest share of costs of any time period. In the following section, I show correlates between the descriptive statistics and offer interpretation. Results — Spatial Analysis Tables 3-11 and 3-12 show the results of the OD cost recovery model defined in Equation 3-3 for BART and MARTA, respectively. In both systems, for a given OD trip, its trip length is negatively associated with cost recovery, though the magnitude is markedly greater for MARTA. Whereas every mile longer that a trip is, is associated with a 0.07 percentage point decrease in cost recovery for BART; it is associated with a 2.1 percentage point decrease in cost recovery for MARTA. On the other hand, the distance that origin and destination stations are from the core of the networks has an opposing effect. For BART, every additional mile an origin or destination station is from the core station is associated with a 0.9 percentage point reduction in farebox recovery for the trip. Furthermore, this has a greater statistical significance on cost recovery than trip length for BART. In stark contrast, for MARTA, every additional mile further that an origin or destination station is from the core is associated with a 0.7 percentage point increase in cost recovery and has the same degree of statistical significance as trip length. This implies that travelers who use outlying stations of the MARTA network pay a greater share of their trip costs, on average, after controlling for other factors. 108 Variable Coefficient Standard Error 95% Confidence Interval triplength -0.067* 0.04 (-0.14, 0.01) distancecore o -0.94*** 0.05 (-1.04, -0.85) distancecore d -0.94*** 0.05 (-1.04, -0.84) constant 71.15*** 0.83 (69.53, 72.77) N 2,248 Adjusted R-squared 0.3577 Statistical Significance: *** p ≤ 0.001, ** p ≤ 0.01, * p ≤ 0.1 Table 3-11: Origin-Destination Cost Recovery Model Results — BART Variable Coefficient Standard Error 95% Confidence Interval triplength -2.12*** 0.07 (-2.25, -1.99) distancecore o 0.73*** 0.07 (0.59, 0.87) distancecore d 0.73*** 0.07 (0.59, 0.87) constant 42.27*** 0.52 (41.25, 43.28) N 1,406 Adjusted R-squared 0.5073 Statistical Significance: *** p ≤ 0.001, ** p ≤ 0.01, * p ≤ 0.1 Table 3-12: Origin-Destination Cost Recovery Model Results — MARTA However, what more reasonably explains this counterintuitive result for MARTA is a combination of the collinearity of the independent variables, travel patterns in the network, and MARTA’s flat rate fare structure. In both networks, the one-to-one relationship that OD trip cost recovery has with each independent variable is negative and statistically significant. For MARTA, the one-to-one correlation between cost recovery and trip length and between cost recovery and station distance from the core, is -0.68 and -0.26, respectively. For BART, these numbers are -0.45 and -0.42, respectively. At the same time, the station distance variables have a statistically significant positive relationship with the trip length variable — 0.53 for MARTA and 0.5 for BART. This makes intuitive sense, as suburban travel is associated with longer trips, in general (e.g., Sultana and Weber, 2007). Thus, despite both independent terms having a negative influence of cost recovery, there is a cancelling out effect between them in the regression, and trip length has a greater level of influence for MARTA partly due to its stronger one-to-one influence to begin with. In addition, spatial patterns of travel in the MARTA network are markedly more dispersed than in the BART network. The more evenly dispersed travel in a network is, the less influence a node’s distance from the core of the network will have on the cost recovery, all else being equal. 109 Finally, in a flat rate fare structure environment, like MARTA, all else being equal, every additional mile traveled on a network will be associated with a lower cost recovery. That is, the consumer is consuming more wear, labor-hours, etc. and not paying anything more for it, unlike in the BART network. Taken together, trip length will reasonably have a greater influence on cost recovery outcomes in the MARTA network than in the BART network. My analysis heretofore has measured how the cost recovery of single OD trips are explained by their lengths and the distance that their origin and destination stations are from the core of the network. This does not explain the geographic incidence of rail transit subsidies. If, for example, a station or link has a disproportionate share of riders who consume low cost recovery OD trips compared to other stations and links in the network, consumers of the subject station or link, on average, are disproportionately subsidized relative to consumers of other stations or links. Evaluating this requires weighting OD trip findings to net travel patterns (i.e., Equation 3-9), then estimating how cost recoveries (and subsidies) flow to different geographic areas of the network. To evaluate this, I calculate the average cost recovery of every trip that begins or ends at a station, which defines the cost recovery profile of the station (i.e., Equation 3-4). Similarly, I define the cost recovery profile of a link as the average cost recovery of every trip that traverses the link (i.e., Equation 3-5). Figures 3-11 to 3-14 show the relationship that station and link cost recovery profiles have with the distance they are from the core station of the network (right axis) and the average trip length of all trips associated with them (left axis). 110 Figure 3-11: Station Cost Recovery Profile Relationship with Average Trip Lengths and Station Distance from Core of Network — BART Figure 3-12: Link Cost Recovery Profile Relationship with Average Trip Lengths and Link Distance from Core of Network — BART y = 36.558 - 35.255x R² = 0.4215 y = 37.847 - 44.587x R² = 0.5756 -10 -5 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 40 45 0 20 40 60 80 100 120 Station Distance from Core Station (distance_core) Average Trip Lengths (triplength_average) Cost Recovery (percentpaid_effective) triplength_average distance_core Linear (triplength_average) Linear (distance_core) y = 39.549 - 0.3656x R² = 0.213 y = 41.755 - 0.5911x R² = 0.4473 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 40 45 20 25 30 35 40 45 50 55 60 65 70 Link Distance from Core Station (distance_core) Average Trip Lengths (triplength_average) Cost Recovery (percentpaid_effective) triplength_average distance_core Linear (triplength_average) Linear (distance_core) 111 Figure 3-13: Station Cost Recovery Profile Relationship with Average Trip Lengths and Station Distance from Core of Network — MARTA Figure 3-14: Link Cost Recovery Profile Relationship with Average Trip Lengths and Link Distance from Core of Network — MARTA y = 15.403 - 0.2243x R² = 0.1919 y = 16.414 - 0.3661x R² = 0.2417 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 10 15 20 25 30 35 40 45 Station Distance from Core Station (distance_core) Average Trip Lengths (triplength_average) Cost Recovery (percentpaid_effective) triplength_average distance_core Linear (triplength_average) Linear (distance_core) y = 3.603 + 0.3676x R² = 0.183 y = 12.858 - 0.2983x R² = 0.0337 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 10 12 14 16 18 20 22 24 26 28 30 Link Distance from Core Station (distance_core) Average Trip Lengths (triplength_average) Cost Recovery (percentpaid_effective) triplength_average distance_core Linear (triplength_average) Linear (distance_core) 112 These plot charts show that, in almost all instances, station and link distances from the core of the network, and the average trip length for trips associated with them, have negative relationships with the cost recovery profile. That is, the further away links and stations are from the core station, and the longer the average trip associated with the link or station, the lower the cost recovery profile. The one exception is the positive influence average trip length has on link cost recovery profiles in the MARTA system. You will note that MARTA has one station and link outlier, which is Bankhead Station and the spur link that serves it. Removing this observation does not greatly change the resulting relationship. On the other hand, the strength of the relationships is notably different between the two systems. In the BART system, both correlations have high R 2 values, especially for stations. The R 2 is consistently greater than 0.4, except for trip length’s relationship with link cost recovery profiles, which is around 0.2. In stark contrast, the R 2 of the relationships for MARTA never reach 0.25 and is particularly low for the link cost recovery profile relationships. The dispersion of independent variable values across a narrow range of cost recovery profile scores explains this result for MARTA links. Thus, with high confidence, station cost recovery profiles appear to decrease the further the stations are from the core of each system. In fact, the distance the station is from the core of the network has both stronger magnitude and statistical significance of influence on cost recovery profile than average trip length does. The same story general holds for links in the BART network. However, the relationship that distance from the system core and average trip length has on links for the MARTA system is probably too statistically insignificant to draw meaningful conclusions from. 113 Results — Temporal Analysis Figures 3-11 and 3-12 show the total costs that are allocated (left axis), cost recovery (right axis), and resulting monetary subsidy (left axis) of different time periods in the BART and MARTA systems, respectively. While one time period’s ridership may pay more of their costs on a percentage basis (cost recovery), an agency may still expend more money subsidizing travel during that time period (monetary subsidy). Figure 3-15: BART Time Period Costs, Subsidies, and Cost Recoveries 0% 10% 20% 30% 40% 50% 60% 70% 80% $- $50 $100 $150 $200 $250 $300 $350 Weekday - Base Weekday - Peak Weekday - Evening Weekday - Late Evening Saturday - Base Saturday - Midday Sunday - Base Sunday - Evening Cost Recovery Rate Total Cost or Subsidy (millions) Time Periods Total Cost Total Subsidy Cost Recovery 114 Figure 3-16: MARTA Time Period Costs, Subsidies, and Cost Recoveries These findings show that, although the weekday peak period is the most expensive to serve for BART and about equally as costly as the weekday base period for MARTA, it recovers the highest amount of its costs through fare payment in both systems — 75% at BART and 34% at MARTA. In fact, the weekday peak period recovers twice as much of its costs compared to the weekday base period in both systems — so much that even the monetary subsidy expended on weekday peak service is less than weekday base service. Other time periods’ total and marginal costs — that is, the additional costs of serving a time period relative to the next highest cost time period — are much smaller compared to weekday base and peak periods. Even so, it is noteworthy that the weekend base period at MARTA and Sunday base period at BART also have higher cost recoveries than the weekday base period. Figure 3-13 shows the correlations between the cost recovery of different time periods (percentpaid t) and time-variant travel patterns. In this figure, BART is represented in blue; MARTA, in red. 0% 5% 10% 15% 20% 25% 30% 35% 40% $- $10 $20 $30 $40 $50 $60 $70 $80 $90 $100 Weekday - Base Weekday - Peak Weekday - Evening Weekend - Base Weekend - Evening Cost Recovery Rate Total Cost or Subsidy (millions) Time Periods Total Cost Total Subsidy Cost Recovery 115 Figure 3-17: Correlation Matrix of Temporal Variables This matrix shows the relationship between variables across time periods. Looking at the bottom-right, at BART, time periods in which the origin or destination station of an average trip is further from the core of the network will have the other station in the OD pair closer to the core of the network and in a statistically significant way. By contrast, this OD relationship across time periods has no statistical significance for MARTA. The only variables that relate with cost recovery of time periods in any statistically significant way for BART is the number of trips and passenger-miles generated during a time period. Specifically, time periods with more trips and passenger-miles generate higher cost recoveries, on percentpaid_t 0.6893* trips_t pxmiles 0.6893* trips_t 0.8367* 0.6998* 0.9995*** triplength pxmiles 0.8576* 0.999*** 0.3321 0.2238 0.2449 0.6998* 0.9995*** distancecore_o triplength 0.924* 0.9704** 0.9751** -0.2828 0.3403 0.3192 -0.6138 0.3321 0.2238 0.2449 distancecore_d 0.1423 -0.3625 -0.3386 0.7554* -0.9407*** distancecore_o 0.7772 0.8831* 0.8763* 0.9273* -0.2828 0.3403 0.3192 -0.6138 distancecore_d -0.3275 -0.5693 -0.5436 -0.5436 -0.7978 0.1423 -0.3625 -0.3386 0.7554* -0.9407*** 116 average. For MARTA, in addition to these two influencing factors, time periods having longer trip lengths is positively associated with cost recovery. However, with both networks, the travel pattern variables that correlate with cost recovery in a statistically significant way also correlate with each other in a statistically significant way, suggesting potential interaction between or across these terms. Importantly, the distance that origin or destination stations of average trips are from the core does not correlate with temporal variability of cost recovery in any statistically significant way. This suggests that, to the extent cost recovery is influenced by how “suburban” a trip is, the influence does not vary across time. A Synthesis of Cost Recovery Measurements In the preceding sections, I introduced multiple ways of measuring cost recovery, each with a different purpose and finding. I then used a select subset of these in my analyses. The measurements of cost recovery included an aggregate or systemwide measurement, a measurement for each OD trip (unweighted and weighted to trip count), a measurement based on station cost recovery profiles, a measurement based on link cost recovery profiles, and a measurement across time periods. Table 3-13 offers a brief breakdown of definitions each of these. Cost Recovery Measurement Description Systemwide cost recovery The share of total expended costs covered through fares OD trip cost recovery The cost of a unique OD trip that is paid for through the fare charged for consuming it. Station cost recovery profile The weighted average OD trip cost recovery of all trips consumed that began or ended at a particular station. Link cost recovery profile The weighted average OD trip cost recovery of all trips consumed that traversed a particular link. Time period cost recovery The share of total expended costs in a particular time period that were covered through fares generated during that particular time period. Table 3-13: Cost Recovery Measurements Systemwide cost recovery measures how much of an agency’s total costs are covered by its total fare revenue. Based on the costs I included in the preceding chapter on cost allocations, I find that BART and MARTA recover 52.6% and 24.6% of their costs through fares, respectively. However, as is a motivation of this research, systemwide cost recovery overlooks dimensional 117 variability, such as spatial and temporal variability. It is possible that certain times of travel or locations of travel recover more of their costs such that these riders subsidize others. Systemwide cost recoveries combine all fare revenues and costs together, so obscure such variability. The unweighted OD trip cost recovery measures how much of the cost of serving a particular OD trip is recovered through the fare paid for that trip. The calculation depends on dividing a system into its parts to estimate costs of each “part” (i.e., stations and links), then estimating the cost per rider of each station and link as the ratio of its cost to the number of trips that used it. I calculate a cost for every possible OD trip as the sum of the cost per rider of every link and station used to complete the trip (i.e., Equation 3-1). Importantly, even if no real traveler ever consumes a particular OD trip, the trip still has a cost, fare, and associated cost recovery. The unweighted OD trip cost recovery represents the cost recovery of a one-off OD trip taken in a system as it is built and priced, treating station and link usage as fixed. When weighted to actual consumption patterns, the resulting statistics will reflect net consumption patterns rather than a baseline distribution. This is reflected in Tables 3-3 and 3-4, where, for example, the unweighted mean OD trip cost recovery for MARTA is 30.1%, while the weighted mean OD trip cost recovery is 36.1%. Both unweighted and weighted OD trip cost recovery statistics will deviate from the systemwide cost recovery principally because the source of costs is different. The systemwide cost recovery bundles all parts and their costs together, whereas OD trip cost recoveries only account for costs of the parts of the system that the OD trip utilizes. Furthermore, by using a cost per rider metric, OF trip costs account for how all OD trips share in the costs of parts of the system. When weighted to actual ridership, OD trips along high usage/low cost per rider parts of the network will influence the OD trip cost recovery statistics. In most instances, this will lead to a mean cost recovery greater than the systemwide cost recovery because higher rates of trip consumption will 118 typically occur along low cost per rider parts of the network, whereas the systemwide cost recovery must also account for low ridership/high cost per rider segments of the network. Station and link cost recovery profiles are the average cost recovery of all trips taken that are associated with the station or link. The purpose of this measurement is to evaluate the spatial incidence of subsidies. In the absence of being able to allocate fare revenues to links and stations like costs are so that a formal cost recovery can be calculated, taking the average cost recovery of all users of a link or station is an alternative. Users of stations and links with higher cost recovery profile scores are less subsidized, on average, because they pay a higher percentage of the cost of their trip through their fare, on average. Similarly, users of stations and links with lower cost recovery profiles are more subsidized, on average, because they pay a lower share of the cost of their trip through their fare, on average. My findings show that station distance from the core of both networks has the strongest influence on the spatial incidence of subsidies. In particular, the further away that an origin or destination station is from the core of the network, the more subsidized that station’s riders are, on average. Finally, time period cost recoveries focus on a different dimension of the network — time periods. Unlike with the spatial cost recovery metrics, there are not multiple combinations of time “parts” to define time period cost recoveries. Instead, it is merely the sum of fares collected during a time period divided by the costs allocated to that time period. My findings show that the weekday peak period has the highest cost recovery of any time period in both networks. Discussion and Conclusion Using a long-run partially allocated cost model, I have shown that cost recovery patterns on BART and MARTA have spatial and temporal dimensions. My research is cross-sectional and OD trip costs are defined by how travelers use the system. Thus, findings are inherently based on — and likely sensitive to — travel patterns in the networks being fixed. And by not allocating fares to 119 links and stations, I do not estimate the cost recovery of links and stations, so focus on travelers that use each link and station instead. Nevertheless, during the study period, travelers with trips to or from outlying areas of the networks and who travel during off-peak travel periods pay a lower share of their costs relative to travelers in core areas and during peak travel periods — meaning the former are subsidized more. In the case of MARTA, although station distance from the core has a positive relationship with cost recovery at the OD level, this appears to be driven by the positive correlation between trip length and the distance that origin and destination stations of a trip are from the core station. Given that trip length has such a large and negative influence on OD trip cost recovery, the smaller magnitude positive influence that origin and destination station distance from the core have on cost recovery effectively offsets this whilst leaving their shared effect negative. The same story holds in the analysis of cost recovery profiles of stations and links, though in these instances trip length carries the positive coefficient, while distance from the core has the negative coefficient. Given this, when the distribution of consumed trips are accounted for at the link and station level, the monocentric spatial pattern of cost recovery is evident; although origins and destinations are “scattered” in the MARTA network, a sufficient number of trips converge on the core links and stations of the network for some degree of central concentration in average cost recovery to exist. However, given the dispersion in MARTA travel patterns, the centralized pattern of cost recovery is significantly less for MARTA relative to BART, as evident by the small range in link and station cost recovery profiles. Apart from the spatial finding that travelers who go to or from outlying stations pay a lesser share of costs, the influence that trip length has on OD cost recovery is negative in both networks; those who travel further on the systems pay less of a share of their costs, on average. But the influence trip length has on OD cost recovery on the MARTA system is about 32 times the 120 magnitude relative to the BART system (Tables 3-11 and 3-12) — though, as explained above, this magnitude of difference is partly explained by the interaction between trip length and station distance from the core station at MARTA. Regardless of this caveat, this general finding suggests both that flat rate fares greatly increase trip subsidies on a per-mile basis, and this effect is greatly reduced, though not eliminated, with distance-based fares. This second implication is partly explained by the fact that those who travel longer distances tend to begin or end their trips in outlying areas of both networks, where there tend to be fewer total riders, making them more expensive to operate on a per-rider basis, as reported in the preceding chapter. A distance-based fare structure does not account for this variability in per-mile and per-rider costs throughout the network, so does not correct for the spatial variability in cost recovery patterns. BART’s distance- based fare structure rewarding distance through its stepwise formula amplifies this. The net result in both systems is that the spatial cost recovery pattern leads to the incidence of transport subsidies being geographically concentrated in suburban and exurban areas of the respective region; persons who begin or end their trips in outlying areas of the networks are disproportionately subsidized. The finding that off-peak travel is more subsidized than weekday peak period travel runs counter to findings from past research. Cervero (1981), Parody et al. (1990), and others show that the peak period is the costliest to serve in net terms — meaning, even after cost recovery is considered. This is partly because these other studies include fixed asset costs in their cost allocations, whereas I do not. However, as shown in the cost allocation research I performed in the previous chapter, this divergence in findings is also explained by the fixed headway schedule that BART and MARTA operate throughout the day. Because of this practice, the weekday peak period has a low marginal cost of operating compared to what is typical of traditional commuter rail systems and bus networks. At BART, the additional cost of serving the weekday peak period is almost exclusively driven by capital because the agency resizes the length of its trains without 121 compromising frequency of service. By comparison, MARTA has a nominal number of additional trains in service during weekday peak period relative to weekday base period and does not resize its trains, leading to an even smaller marginal gross cost difference — so small that the additional operating hours associated with base service makes it slightly more expensive than the weekday peak period. The correlations between time period cost recoveries and travel pattern variables associated with different time periods indicates that the number of trips and passenger-miles generated across time periods explains much of the difference in time period cost recoveries. Given the relatively fixed headway schedules of both agencies, this makes sense; holding all else equal, more trips and trip-miles will result in more revenues, which will increase cost recovery. This is especially true for BART, given its fare structure being distance-based. On the other hand, the distance that origin and destination stations are from the core of the respective system does not have any statistically significant influence on temporal cost recovery variation. Indeed, there is little variability in these terms across time periods. Considering that spatial patterns of cost recovery are negatively associated with the distance origin and destination stations are from the core in both networks, this suggests that outlying areas are subsidized regardless of the time of travel. Thus, while there is geographic incidence of subsidies, it is not temporally variable. Even so, research that explicitly interacts space and time could more decisively test this. While this research shows that core stations and links and the weekday peak period are less subsidized than suburban stations and links and other time periods, there may be bases for charging premiums for travel in these areas and during these times. My cost allocation study does not account for externalities, including the costs of congestion beyond expenditure costs of serving it. Core areas of these networks and peak times of travel may generate so much crowding and inconvenience costs for passengers — for example, BART passengers departing Downtown San 122 Francisco during the evening commute often backtrack to secure a seat — that a premium for use in these areas or during these times to internalize delay time costs and manage demand is warranted. In addition, minimum fares or trip length restrictions are often used to manage capacity or product- differentiate one service from others — for example, a regional service relative to a local service. Among other examples, BART’s minimum fare assumes a trip of at least six miles to distinguish its regional focus from peer agencies’ local focus, and New York City’s Metro-North Railroad does not sell fares for travel between Harlem/125 th Street and Grand Central Terminal Stations to distinguish its commuter rail-orientation from New York City Transit’s local travel focus. In this analysis, I do not control for these policies or objectives, which can inflate the cost recovery level found for peak period travel and travel in core areas of each network. Future research can also benefit by interacting these findings with the socioeconomic makeup of riders to evaluate whether cost recovery equity patterns in these networks has a disparate impact. Do different socioeconomic groups of riders consume more subsidized OD pairs than others, such that they are more subsidized, on average? While both BART and MARTA survey riders to create socioeconomic profiles of stations, different socioeconomic groups consume different OD pairs from each station. So, although there is a sufficient sample size of riders at each station to devise station profiles, there is not a sufficient sample of riders of different OD pairs to evaluate the incidence of trip subsidies. Finally, this analysis uses rail transit as a case study of how transport subsidies more broadly have a spatial and temporal dimension. It is conceivable that the findings from this research similarly apply to other modes of travel, such as highways. Future research should explore if other modes of transport have spatial and temporal dimensions of subsidies. In addition, these findings and findings of research on other modes can be used to evaluate a bigger question this research 123 contributes: To what extent are suburban and exurban location choices enabled through transport subsidies? 124 Conclusion In this dissertation, I contributed to bridging a topical and scholastic divide in research on transit costs, pricing (fare) equity, investment equity, economic structure, and production efficiency. Past research on each of these topics has often been done without account of one or more of the others despite their inherent interrelationship, and the paradigms through which these are investigated have tended to only focus on a subset of them. For example, some transport economic research argues that, if demand-side costs of using transit are accounted for, there are economies of scale in transit production that form a basis for subsidizing transit (e.g., Mohring, 1972; Turvey and Mohring, 1975; Vickrey, 1980; Basso and Jara-Diaz, 2010). Such arguments rely on there being objectives of transit service provision — for example, to provide access to dependent persons or attract auto travelers to use transit — that require an efficient level of service, which is not achievable with average cost pricing. But little applied research exists to ascertain what this subsidy level ought to be and effectively no transport economic research evaluates if an optimal subsidy can also be distributionally equitable. In addition, some research shows that transit capital investment and operating cost patterns are socioeconomically regressive because more money is spent catering to higher-income and non-minority persons (e.g., Pucher, 1982; Garrett and Taylor, 1999; Taylor et al., 2000). But the same research fails to account for the revenue generated from different users to understand net investment and operating cost (i.e., subsidy) patterns as opposed to gross investment and operating cost patterns. Finally, the limited research on temporal and spatial variability of net costs that does exist (e.g., Cervero, 1981; Hodge, 1988; Parody et al., 1990; Iseki, 2016) only weakly disaggregates spatial and temporal dimensions in the analysis, leaving much to be desired in terms of its dimensional granularity. In the foregoing research, I contributed by both investigating a transit mode other than bus transit — namely, rail transit — and developing a highly disaggregate cost model to allocate costs 125 across space and time, generate origin-destination trip costs using these allocations and ridership data, and correlate these with fare data to ascertain if there are transit subsidy disparities across highly granular dimensions of space and time. Unlike past studies that evaluate spatial cost and cost recovery variability by route (Cherwony and Mundle, 1980), bus yard (Cervero, 1981), or municipal geography (Hodge, 1988; Iseki, 2016); I spatially allocate costs to every link and station of the rail networks. In addition, rather than assuming that there are just two time periods of operation — peak and everything else — I identified five and eight unique operating time periods in the two rail networks studied, the San Francisco Bay Area Rapid Transit District (BART) and the Metropolitan Atlanta Rapid Transit Authority (MARTA). My temporal findings show that the peak period is the costliest to serve in gross terms, but the least costly to serve in both net terms and on an average per rider basis (i.e., after fare revenue is accounted for). This is contrary to most past research that finds that the peak period is the costliest in both gross and net terms, and on a per rider basis (Cervero, 1980; Parody et al., 1990; Taylor et al., 2000). I posit that this result stems from the agencies studied maintaining relatively fixed service headways on weekdays such that there is limited temporal variability in weekday peak and base costs; my identifying and allocating costs across multiple time periods, thereby accounting for weekday base resource demands being greater than the lowest operating time period; and my focusing on long-run costs of operating, which incorporates costs of semi-fixed assets that require replacement but not fixed assets. By contrast, past studies include fixed asset costs in their allocations, label all operating house as “peak” or “off-peak,” and study networks with markedly different headways between peak and other operating hours such that there are much higher resource demands to serve the peak period relative to other times. My spatial analysis of costs found that the BART network is most costly to operate through its core service area and least costly along the outer parts of its network, but that the cost per rider 126 pattern is reversed due to the agency’s monocentric travel pattern. In the MARTA network, I found no clear spatial pattern of costs and costs per rider. However, in both networks, the average cost recovery of unique links and stations decreases with distance from the core of the network and with increases in the average trip length for trips that use the link or station. For MARTA, there is strong correlation between the average trip length of trips associated with each link and station, and the distance that the link or station is from the core of the network. This leads to these variables having a canceling effect in the regression analysis, even though both variables independently have the aforementioned influence on cost recovery. The general takeaway from the spatial analysis is that both transit agencies’ fare structures lead to transit subsidies being disproportionately distributed to travelers in outer portions of the network and who travel longer distances, but that the latter effect can be lessened with a distance-based fare structure. While various key temporal and spatial findings are consistent between the two networks, there is also variation that I do not evaluate, which limits the generalizability of the findings. For example, station and link cost recovery profiles’ relationship with distance from the core station and trip length is much more efficient in the BART system than the MARTA system. There is also more spread in all measurements of cost recovery in the BART system than in the MARTA system. Among other considerations, these variations are likely explained by differences in travel patterns, urban form patterns, and transportation pricing patterns between the two regions. Such considerations would need to be incorporated into the analysis for the research to be generalizable. As described in the critical literature review chapter, past research on fare equity — a measurement of disparity in fares paid by different groups of riders relative to the miles of travel they consume, or the cost of services rendered to them — does not evaluate how demand and network performance would be affected by a more equitable fare structure implied by the findings. For example, while Cervero (1981) found that bus riders who travel less than six miles pay as much 127 as 5.2 times more per mile than those who travel more than six miles, and that this is socioeconomically regressive because it leads to low-income and minority riders paying more per mile than their high-income and white counterparts; he does not test what the demand and equity implications would be under a distance-based fare structure as he proposes. While I, too, do not test for demand and equity impacts of fare structures that may be more equitable as I suggest in this research (i.e., more even cost recovery patterns), I intend for this dissertation to seed future research that will answer this question. Finally, while I focused on the spatial and temporal variability of subsidies given to transit use in this dissertation, the analysis can and does apply to other modes. 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Transportation Research Part A: Policy and Practice 121 (2019): 309-324. 137 APPENDIX: Table of Included and Excluded Costs Type of Cost Included/Excluded Rationale and methodology Select frontline worker costs Included The volume of select frontline workers — train operators, station agents, station janitors — varies by time and location. A large station or busy station will have more station agents and janitors, and a high-frequency or high travel time segment of the network will generate more train- hours, so generate more train operator-hours. The costs for these workers are proportioned based on their actual work schedules. That is, the total costs paid to a classification are assigned to a particular location or time period proportional to the share of the number of worker-hours generated at the particular location or during the particular time. For track and railcar maintenance personnel, railcar-miles are used to allocate costs. For AFC technicians and elevator/escalator workers, these workers’ costs would ideally be allocated to stations and time periods based on a measurement of asset wear patterns, such as each stations share of passengers per asset. However, the use of passenger counts creates endogeneity due to passenger counts being an input in the cost effectiveness evaluation. As a proxy, the share of AFC assets and elevators/escalators by station is used, respectively. Administrative and other frontline personnel costs Included An agency’s administration is proportional to its scale of operations. Smaller transit operators are top-light, whereas larger transit operators are top-heavy. In this way, these costs are location- and time- variable since the demand and levels-of-service at different times and locations inform the net scale of an agency’s administration. These costs are allocated as a commission; the share of other costs allocated to a time period, station, or link is used to define that unit’s share of administrative costs. The same approach is used for other frontline personnel not described above, such as police officers and fare inspectors. Transit vehicle assets Included Transit vehicle inventory is scaled with travel demand and service supply. As with highways being built with a width to accommodate peak travel demand and going underutilized at most other times, transit agencies scale their fleet size to accommodate peak travel and do not use them at most other times. Similarly, scale will vary by location based on demand patterns. For spatial allocations, each link is charged the annual cost of all railcars in inventory proportional to its share of railcar pass-throughs. For temporal allocations, each time period is charged for its share of base level railcars plus the marginal cost of additional railcars used during that time period (e.g., Savage, 1989; Taylor et al., 2000). Heavy maintenance assets Included Select heavy maintenance assets — cranes, lifts, wheel truing machines, rail grinders, tampers, rail carriers, and tie loaders — are included on the basis that their use and quantity is driven by railcar usage. Times and locations that generate more railcar wear and more track wear will make a greater use of these assets and proportionately drive the inventory of them. Accordingly, the annualized cost of these assets is allocated based on the share of railcar-miles generated during each time period or along each link of the railroad. 138 Type of Cost Included/Excluded Rationale and methodology Vertical transportation assets Included Vertical transportation assets include elevators and escalators. The count of these are location-variant and driven by a combination of station design and ridership demand patterns. For temporal analysis, each time period’s share of total annual operating hours is used to allocate these costs, while each station’s share of total elevator/escalators in inventory is used for spatial cost allocations. Automatic fare collection (AFC) assets Included As with vertical transportation assets, the count of AFC assets varies by station based on both the station’s design and trip generation. For spatial analysis, these asset’s annualized costs are allocated to stations based on each station’s share of the AFC asset inventory, while each time period’s share of annual operating hours is used for temporal cost allocations. Other equipment assets Excluded A transit agency has many equipment assets besides those previously listed, ranging from computers and telephones to non-revenue vehicles. The enormity of these assets makes allocating their costs challenging, and the inventory of much of these do not clearly vary with time or location of service. Thus, including these assets would exceed of the objective of this research, which is to evaluate the time and location variability in cost and cost effectiveness. Parking lot operations and maintenance Excluded Parking lot construction, operations, and maintenance serve a subset of ridership — park and ride customers — and are distinct from the operations and maintenance of the railroad. On the premise that the cost and cost effectiveness of these facilities are most efficiently evaluated in terms of this subset of ridership, they are not included in this analysis of railroad operation costs and cost effectiveness. That is, while use of the railroad is a cost that all riders share in, the cost of parking facilities is unique to park and ride customers. Land value Excluded The value of land owned by a railway network represents opportunity costs of keeping a station or link open in lieu of selling it. Including this variable goes beyond the scope of this research, which seeks to answer the extent to which operating expenditure varies by time and location. Furthermore, to the extent this analysis finds that a station or link is highly costly relative to other segments of the network from an expenditure standpoint, inclusion of land value would only serve to inflate this finding; not substantively change it. In addition, a benefit-cost analysis of alternatives is necessary to evaluate a best-use of the land, which clearly exceeds the objective of this research. Original construction costs Excluded For the systems analyzed in this research, original construction costs of unique stations and links of the railroad are not known. Furthermore, the life expectancy of original construction is very long, conditional on the infrastructure being maintained. Even if this cost is annualized, the per year cost of an asset with a very long life converges towards $0. In this way, original construction costs can be viewed as a sunk cost or a short-term investment expense with no long-term effect. It is, therefore, not included in this analysis on annual expenditures. 139 Type of Cost Included/Excluded Rationale and methodology Rehab and reconstruction costs Excluded While original construction costs may be sunk, the costs of maintaining the infrastructure can include retrofitting, rehab, or reconstruction. Aerial structures, tunnels, and at-grade segments of rail may need rehab or reconstruction at different iterations and at different costs. Ideally, these time-frames and costs are known and included in this analysis. However, the agencies do not have a rehab or reconstruction schedule for their fixed infrastructure, and much of their fixed infrastructure is original. Accordingly, infrastructure-related costs are almost exclusively accounted through maintenance of the infrastructure; not rehab or reconstruction of it.

Abstract (if available)

Abstract In this dissertation, I evaluate the equity of rail transit fare policies using highly disaggregate cost, ridership, and fare data to compare how spatial and temporal variance of costs compare to spatial and temporal variance of fare collection. I measure “equity” by how evenly costs are recovered through the fares paid by transit users across space and time. I innovate by controlling for the cost sharing nature of a transport network — that is, accounting for how traveler density across space and time affects average costs per rider and resulting cost recovery across space and time. I use two transit providers, the San Francisco Bay Area Rapid Transit District (BART) and the Metropolitan Atlanta Rapid Transit Authority (MARTA), as parallel case studies. Furthermore, since both agencies have different fare structures, I offer insights on how different fare structures affect outcomes.
The dissertation follows a three-paper format, starting with a critical literature review that interrogates literature on transit cost modeling and transit pricing equity. I follow this up with a two-part (two paper) case study wherein I first evaluate how costs and costs per rider vary across space and time in the two rail networks, then test for spatial and temporal disparities in cost recovery patterns in the two rail networks to determine if transit subsidies are unevenly distributed geographically or temporally. I find that outlying areas and off-peak travel times in the BART network cost less to serve in gross terms but are more costly on a per-rider basis and recover less of their costs through fares. In the MARTA network, I find no clear spatial patterns of cost and costs per rider, though cost recovery patterns indicate that outlying areas are also subsidized more than inner areas of the network, while temporal cost and cost-recovery patterns are similar to the findings for BART.

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Asset Metadata

Creator Mallett, Zakhary (author)

Core Title Spatial and temporal expenditure-pricing equity of rail transit fare policies

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Urban Planning and Development

Degree Conferral Date 2022-12

Publication Date 08/22/2022

Defense Date 06/21/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag cost models,equity,fare policy,OAI-PMH Harvest,passenger rail,Public transportation,spatial economics,transit,transit economies,transport economics,transportation equity

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Giuliano, Genevieve (committee chair), Boarnet, Marlon G. (committee member), Taylor, Brian D. (committee member)

Creator Email mallettzg@gmail.com,zmallett@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111379832

Unique identifier UC111379832

Legacy Identifier etd-MallettZak-11149

Document Type Dissertation

Format application/pdf (imt)

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Type texts

Source 20220825-usctheses-batch-975 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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