Measuring Toll Burdens Applying Lorenz Curves to a Detailed Data Set of Users of Metropolitan Transportation Administration Bridges in New York City Cameron Gordon and Jonathan R. Peters T h i s p ap e r u s e s a u n i q u e s u r v e y d at a s e t o f t o l l r e v e n u e co l l e ct i o n o n sion in some of his earliest writings on marginal cost pricing for N e w Y o r k C i t y br i d g e s ad m i n i s t e r e d by t h e M e t r o p o l i t an T r an s p o r t a- public utilities (3). Distributional issues are even more important for t i o n A u t h o r i t y ’ s B r i d g e s an d T u n n e l s (M T A B r i d g e s an d T u n n e l s ). T h i s some older toll facilities that are now producing net revenues and d at a s e t , w h i ch co n t ai n s d e t ai l e d i n f o r m at i o n o n r o ad u s e r i n co m e an d where toll rate setting is not just an issue of covering project costs. l o cat i o n , i s an al y z e d t o as s e s s d i s t r i bu t i o n al e q u i t y o f bu r d e n acr o s s Economists and other theorists have not neglected the general issue r o ad u s e r s o f v ar i o u s t o l l f aci l i t i e s (bo t h v al u e - p r i ce d an d fi x e d - r at e of distributional fairness. But in the case of road pricing, equity analy- t o l l s ) i n t h e N e w Y o r k – N e w J e r s e y r e g i o n . T h e d i s t r i bu t i o n al i m p act i s sis is still in its relative infancy (4, 5). There is no a priori reason for s u m m ar i z e d w i t h t h e u s e o f L o r e n z cu r v e s an d G i n i co e f f i ci e n t s , a s t an - this omission since tolls and prices, like taxes and income, are very d ar d e co n o m i c m e as u r e w i t h t h e s e an d o t h e r m e as u r e s , t h e au t h o r s amenable to burden and proportionality measurement and analysis. d e v e l o p e m p i r i cal e s t i m at e s o f t h e s o ci al e q u i t y co n d i t i o n s o n t h e e x i s t - However, detailed toll and charge collection data are surprisingly i n g p r i ce d f aci l i t i e s . T h e au t h o r s fi n d t h at bu r d e n s ar e l e as t e q u i t abl e o n scarce in many instances, which may be part of the reason. f aci l i t i e s w h e r e t h e r e ar e f e w al t e r n at i v e r o u t e s an d m o r e e q u i t abl e o n This paper utilizes a unique survey data set of toll revenue collec- t h o s e w i t h m o r e al t e r n at i v e s bu t t h at , i n g e n e r al , u s e r s o f M T A B r i d g e s tion on New York City bridges administered by the Metropolitan an d T u n n e l s f aci l i t i e s h av e h i g h e r i n co m e t h an t h e g e n e r al p o p u l at i o n Transportation Authority’s Bridges and Tunnels (MTA Bridges s u r r o u n d i n g t h o s e f aci l i t i e s . and Tunnels). This data set, which contains detailed information on road user income and location, is analyzed by use of Lorenz curves and Gini coefficients (described in more detail below) of burden on In , the economist William Vickrey wrote a seminal paper that users of various toll facilities (both value-priced and fixed-rate tolls) argued a simple point: roads should carry tolls that effectively inter- in the New York–New Jersey region. The authors develop empiri- nalize, for each user, the costs of congestion that would result when cal estimates of the social equity conditions on the existing priced the road was unpriced and hence overused. Such tolls would result facilities. The paper concludes with a discussion of policy solutions in the efficient use of the road. This point is widely accepted today to address equity concerns and market power conditions. and congestion prices have been put in place for many roads and other transport facilities worldwide (including transit, an area that Vickrey addressed before roads) (1). MEASURING DISTRIBUTIONS: GENERAL However, efficiency in resource allocation by no means guaran- TECHNIQUE OF LORENZ CURVES tees fairness in that allocation. The issue of distribution of resources, AND GINI COEFFICIENTS colloquially referred to as “who pays for what,” has been a long- standing discussion among theorists and analysts. Economists, who “Equitable” is a value-based term that implies some favored pattern of have been particularly influential in this discussion and have grap- resource allocation as socially preferred to others. What this favored pled with both practical and definitional aspects of distribution since allocation might be is controversial but any measure of equity requires the field of economics was invented, have summed up the basic ques- some sort of benchmark against which to compare actual resource tion as, “How equitably does the economic system allocate levels of patterns in any given time or place (6). living among its economic citizens?” (2, p. 7). This may seem conceptually straightforward, but choosing a bench- Distribution of a road’s benefits and the direct costs of the toll mark, even for comparison’s sake, is not easy. Actually measuring (and other relevant indirect costs) should be analyzed along with both the benchmark and the allocation without succumbing to various efficiency concerns. Vickrey recognized the importance of this dimen- biases, such as distortions caused by choice of units of measurement, is fraught with difficulty. It took quite a few decades to arrive at a technique that is now the C. Gordon, University of Canberra, Bruce, ACT , Australia. J. R. Peters, City University of New York–College of Staten Island, Victory Boulevard, standard and was perfected simultaneously by both Lorenz and Gini Staten Island, NY Corresponding author: C. Gordon, [email protected] (6). The basic idea is to choose proportionality in distribution as a mynewextsetup.us unit of measurement. Proportionate shares are invariant to shift in units of measurement (e.g., monetary versus nonmonetary) and can Transportation Research Record: Journal of the Transportation Research Board, No. , Transportation Research Board of the National Academies, Washington, be applied to various concepts (e.g., income or wealth). A benchmark D.C., , pp. 96– of exact proportionate cumulative equality across a population is cho- DOI: / sen as a reference standard. One then measures actual proportionality 96 Gordon and Peters 97 The basic benchmark of notional equal distribution of toll burden (the 45° line) remains the starting point. But comparing a distribu- tion of tolls across the user population would be misleading if the Cumulative Percent Income 75 socioeconomic and demographic characteristics of the users dif- Equal fered significantly from the general population that lives around the Distribution toll road. This will often be the case, because tolls are borne only by people who choose the road and that choice will be affected and con- 50 strained by various factors, such as ownership of a vehicle and the amount of the toll. Thus, some people are less likely than others in A B a given population to be driving on the tolled facility. 25 To account for this divergence, there must be two comparisons Less than Equal to the equality line. The distribution of tolls across road users Distribution must be calculated, followed by the characteristics of the popula- tion from which those users are drawn. Comparing these three 0 metrics—user burden distribution, general distribution burden, and 25 50 75 line of equality—provides a more complete idea of the incremental Cumulative Percent Households inequality of tolls. The obvious question remains: what is the relevant population of FIGURE 1 Lorenz curve. potential users for a given road? In theory, the answer is the spatial area around the facility in which usage makes economic sense for the of distribution of a resource (typically income) across the reference user. The viability of using a toll road decays with distance and price, population and compares the divergences between the two to see the depending on various factors such as available alternatives. This spa- extent of inequality. tial relationship could be termed as a “market area” outside of which This process, operationalized through the Lorenz curve, is fairly the facility is no longer relevant in terms of travel decisions. Concep- simple. The typical curve (shown in Figure 1) plots the relationship tually, this area would likely follow no regular contour and would for a given population of the cumulative distribution of the resource vary with time of day, toll level, season, and so on. The definition of in question (income, in this case) and compares that to the reference the market area is a critical part of doing a distributional analysis, standard of exact proportionality in distribution. Plotting of the data since it delineates the potential user population from which actual shows the level of inequity as a convex curve, with a more pro- users are drawn. nounced convexity indicating greater levels of inequity. Gini coeffi- cients express the Lorenz curve relationship as a metric of distortion, with a Gini coefficient of 0 indicating no inequality (all members DATA AND ANALYSIS FRAMEWORK have the same share of income) and a Gini coefficient of 1 indicating complete inequity (one member has all income), [Gini coefficient = Construction of a Lorenz curve requires relatively detailed data. (Area A)/(Areas A + B)]. These data are often unavailable for road and other transport facil- There are various issues with Lorenz curves and Gini coefficients. ity pricing. Toll collection data should be easily obtainable but In particular, comparing different unequal distributions with each many, if not most, road authorities do not release it. Even with such other (as opposed to the equality benchmark) must be done with care data, user characteristics need to be collected or at least imputed, and (7 ). Moreover, many alternative measures have been proposed to here such information may not be collected at all. analyze equity issues that offer different perspectives as well as dif- The Triborough Bridge and Tunnel Authority (TBTA), known as ferent strengths and weaknesses. In addition the causal factors behind MTA Bridges and Tunnels, conducted an origin–destination survey unequal distributions and judgments about “fairness” cannot be settled in October The authors, through a Freedom of Information by plotting of a Lorenz curve alone (2). Act request, obtained the raw survey data from the TBTA. The sur- Nonetheless, Lorenz curves remain the accepted standard for a vey contained 61, observations of passenger car usage on the foundational measure of distributions of resources across a popula- nine TBTA facilities in New York City. The survey asked respon- tion. Their application to transport, as noted previously, has been rel- dents for various user characteristics information, most notably res- atively limited but has much to contribute in that area. The following idence, income class, and trip purpose. These data on users provided section addresses this application. the basic information needed to conduct an equity analysis. At this point the basic task was to assess how the toll burden was distributed across the facility users. This involved a number of con- ISSUES IN ASSESSING DISTRIBUTION ceptual steps. User locations had to be matched with individual facil- OF ROAD TOLLS ities and those users had to be placed within the spatial area around those facilities. This amounted to a rough definition of market areas The distribution of income is spread across a given population. But for each tolled facility as described in the previous section. For the the distribution of toll payments is distributed only across a subset of purposes of this paper, market areas were loosely estimated by draw- a given population, namely that of facility users. Moreover, this sub- ing radii of increasing diameter around the facility to see how many set is going to be directly affected by the spatial distribution of tolls of the total users fell within a given radius. Since survey respondents and toll facilities. Thus, while Lorenz curves are applicable to an gave their home zip code, there was sufficient information to create analysis of toll burden distribution, some adaptations have to be detailed approximate market area profiles within these radii. made conceptually which, in turn, have practical implications for any Survey respondents also provided information about their income distribution estimation. class. This allowed for the next two steps: (a) to sort users within the 98 Transportation Research Record market area by income class and (b) to use U.S. Census data to from the U.S. Census Bureau. Zip codes were selected for the geo- describe the basic socioeconomic profile of the total population of graphic areas surrounding a given facility that corresponded to the high that same market area. This allowed for a comparison of the socio- user areas as identified by the toll collection survey data. Data were economic profile of the actual user population with the total potential obtained at the 5-, , and mi radius from each facility and then user population to see if there was a significant divergence between those data were compared to the self-reported demographic profile of the two. toll facility users. This process is illustrated in the maps presented in The average income class of the various users could be compared Figure 3. with the average socioeconomic status within the market area by As an example of this analysis, Table 2 provides an overview of calculating the estimated toll revenue collected within a U.S. zip the households and income (for the total population in the area, both code (i.e., post code), summarizing the data by zip code tabulation users and nonusers) by distance from the Queens Midtown Tunnel area (an area developed by the U.S. Census to track with U.S. zip (QMT). This detailed example is representative of the overall find- codes), and then combining the information with data from the U.S. ings across all facilities; that is, there is little difference in income Census Bureau on income, race, household size, and geography. between distance measures (and by facility) for the general popula- Since the TBTA facilities serve a diverse set of users in the five tion around each of the toll crossings. The Gini coefficients thus boroughs of New York City and the surrounding states, the authors examined were all in the range of to for the communities allocated the full automobile usage data from the TBTA financial around each of the facilities listed in Table 1 (with the QMT data in reports to each zip code based on the survey weight. Survey weights Table 2 having a slightly more narrow range between and were adjusted to reflect the true balance of cash and electronic toll ). Therefore, the income profile of residents surrounding these customers. facilities is remarkably similar in terms of income distribution to each This process was carried out in steps, moving from general rev- other as well as to New York State and the United States in general. enue collection spatially and moving down to estimations of average In sharp contrast, actual users of the QMT reported higher income toll burden by user. Table 1 shows a first-order toll burden analysis than the general population, with a reported mean income of $, by spatial area. The analysis is first order because what is actually and a median income of $, (The average across all TBTA shown is the proportion of revenue collected within a given market facilities was a mean income of $99, and a median income of area rather than burden to the average user, a topic to be addressed in $87,). For the QMT, the Gini coefficient was , indicat- more detail below. What this analysis shows is that a vast bulk (60%+) ing an inequality far higher than the community average around the of the tolls on these facilities are collected within a mi radius of a facility. Figure 4 provides the Lorenz curves for QMT users and given facility on average. Therefore, there is good evidence that mem- community income distributions at the 5- and mi radii. bers of the community that surrounds a given facility are the prime users of these transportation facilities, as would be expected. Figure 2 provides a display of the density of toll use for New York, New Jersey, MARKET POWER, MARKET AREA, and Connecticut. AND BURDEN DISTRIBUTION As mentioned above, user characteristics are quite likely to be dif- ferent from the characteristics of the overall community from which A critical determinant of market area for a given toll road is the they are drawn because the significant price (toll) of using these availability of an untolled road and other modal alternatives. This facilities as well as the automobile-only nature (no rail or walkways is also a determinant of the “market power” of the facility. A toll in many cases) of their design serve as effective barriers to use for road with few alternative routes or modes nearby will have more many low-income residents. The survey data are therefore truncated, ability to charge higher tolls and have users bear those burdens and, with many residents excluded from the analysis. simultaneously, will have larger market areas as well. Conversely, To get some idea of the population characteristics within the market roads with many alternatives will have smaller market areas and less areas, the authors utilized detailed demographic data by zip code market power. TABLE 1 TBTA Toll Burden Within 5, 10, and 15 mi of Facilities 5-mi mi mi Total Tolls per Location 5-mi Tolls Tolls (%) mi Tolls Tolls (%) mi Tolls Tolls (%) Facility Verrazano–Narrows Bridge 75,, ,, ,, ,, Throgs Neck Bridge 18,, 53,, 75,, ,, Triborough Manhattan Bridge 37,, 60,, 76,, ,, Triborough Bronx Bridge 26,, 60,, 77,, ,, Queens Midtown Tunnel 22,, 40,, 53,, 98,, Marine Parkway Bridge 6,, 9,, 10,, 10,, Henry Hudson Bridge 7,, 18,, 25,, 37,, Cross Bay Bridge , 2,, 2,, 3,, Brooklyn Battery Tunnel 13,, 44,, 54,, 62,, Bronx Whitestone Bridge 29,, 70,, 95,, ,, Total ,, ,, ,, ,, SOURCE: TBTA Survey, January 2, Gordon and Peters 99 FIGURE 2 Dispersion of TBTA tolls: citywide and regionwide. This can have significant implications for toll burden distri- With these criteria, MTA facilities can be characterized as follows butions. To assess these impacts, the authors examined both the (and are mapped in Figure 5): TBTA reported price elasticity for each facility and the location and quality of other bridge facilities in the region to establish • Monopoly: Verrazano–Narrows Bridges (VNB); the relative level of competition in a particular corridor. Bridges • Low competition: Bronx Whitestone, Throgs Neck, Cross Bay, without free alternative routes are considered monopoly corri- and Marine Parkway; and dors, while bridges with free but poor-quality alternatives (distant • Competitive: Brooklyn Battery Tunnel, Henry Hudson Bridge, from the facility or poor level of service) are considered low com- QMT, and Triborough Bridge. petition corridors, and bridges with good free alternatives are con- sidered competitive facilities. It is expected that corridors with Competition from free alternative facilities alters the demographic less competition will exhibit less income sensitivity in terms of profile of toll facility users in New York City. The toll burdens of facility use. two of these facilities—the VNB and the QMT—are illustrated in Corridor competition varied considerably, with some facilities Figure 6. having free alternative bridges less than 1 mi from the toll facility. First, it is clearly observable that there are significant differences In other cases, no free alternative existed and the toll alternative was in usage patterns by zip code depending on the location of the facil- mi away. High levels of competition are expected to affect the ity. Second, the two facilities have highly different levels of market demographics of toll facilities, because good alternative free routes power, with the QMT having free alternative routes to the north and will allow low-income users to avoid the toll, trading costs for time. south of the facility, one of which is within mi of the facility. Monopoly corridors are expected to have both low- and high-income The VNB has no good free alternative and the only nearest toll alter- users on the facility, with fewer low-income users because of their native is mi to the north. Third, the Gini coefficients indicate that lack of income to pay the toll and also less ability to pay the fixed and there are significant differences in the income profile of toll facility variable costs of operating a vehicle. users, in spite of very similar community demographics. Transportation Research Record (a) (b) (c) FIGURE 3 Example of geographic selections of census demographic data by distance: QMT at (a) 5-, (b) , and (c) mi radius. The authors found little variation in the background income pro- QMT Gini coefficient was compared with a community Gini files caused by the location of the facility. Population demographics coefficient of (The curves are shown in Figure 6.) are reasonably consistent at the macroeconomic level across the What this indicates is that both facilities had similar community region. However, the authors found wide variation in the Lorenz characteristics and distributions, but the monopoly facility (VNB) curves and Gini coefficients for individual toll facilities. user characteristics were more downscale than the users of the com- The implied facility Gini coefficient for the VNB was , petitive QMT. This was the case even though the toll on the VNB was which compared with a community Gini coefficient of The the same as on the QMT. This indicates that use of the VNB was less TABLE 2 Impact of Distance from QMT on Background Demographics 5-mi mi mi QMT User NYS HH U.S. HH Households 1,, 2,, 3,, — 7,, ,, Mean HH income ($) 68, 55, 57, , 72, 67, Median HH income ($) 42, 37, 37, , 67, 66, Gini coefficient NOTE: HH = household; NYS = New York State. Gordon and Peters FIGURE 4 QMT equity comparisons of alternative distances. FIGURE 5 MTA bridges and tunnels. Transportation Research Record This impression is reinforced by looking at the frequency distri- butions of income for both the facilities in question. The QMT has an extremely high average income, as well as an elevated rate of users in the $,+ cohort (% of users). In comparison, the VNB has a much greater level of low- and moderate-income users (28% of users with less than $50, household income per year), with a pro- nounced middle-income cohort. More than half of the VNB user households earn less than $75, per year. At the QMT, 54% of users earn more than $, in household income per year. These patterns of income are considerably different than the average house- hold in this region, with % of households in this region reporting income of less than $35, per year (Figures 7 and 8). FIGURE 6 Income equity in TBTA bridge use: comparison of VNB CONCLUSIONS and QMT. Lorenz curves and Gini coefficients are useful and sensitive perfor- mance measures for transportation professionals and agencies to use of a choice for users than in the case of the QMT and more people in evaluating the social equity conditions at priced transportation of lower incomes had to use the facility (though as the bridge user facilities. Using these tools, the authors are able to observe that when demographics show, users were still relatively well-off as com- alternatives are poor or nonxistent (as is the case with the VNB), the pared with the income of surrounding communities). The bene- proximity of the users to the toll collection point is a more impor- fit of the facility was less unequally distributed (the average tant determinant of toll burden, whereas income takes on added income of users on the VNB was lower than on the QMT) but at importance when competition exists (as is the case with the QMT). the same time these lower average income users had to bear more These results indicate that the opportunity exists to price segments of the cost. of the road network to reflect the relative income of the average user FIGURE 7 Community area selections: QMT. Gordon and Peters FIGURE 8 Community area selections: VNB. of the facility. This would allow more vertical equity in the tolling sys- REFERENCES tem, where higher-income users would be charged higher amounts for transportation services. 1. Vickrey, W. Pricing in Urban and Suburban Transport. American Eco- The measures used here could be used to help design and set toll nomic Review, Vol. 53, No. 2, , pp. – 2. Bronfenbrenner, M. Income Distribution Theory. Altsom-Atherton, rates that have equitable distribution of burdens. For example, recently Chicago, Ill., and New York, announced hikes in tolls on the MTA facilities, which took effect 3. Vickrey, W. Some Implications of Marginal Cost Pricing for Public Util- on December 30, , could have been more equitable if tolls had ities. American Economic Review, Vol. 45, No. 2, , pp. – been increased more on high-median-income facilities that have 4. Cain, A., and P. M. Jones. Does Urban Road Pricing Cause Hardship to Low-Income Car Drivers? An Affordability Approach. In Transportation numerous transit alternatives, such as the Henry Hudson Bridge, and Research Record: Journal of the Transportation Research Board, No. , increased less on low-median-income facilities with few transit Transportation Research Board of the National Academies, Washington, alternatives such as the VNB (8). This could have been done while D.C., , pp. 47– maintaining overall toll revenue neutrality. 5. Ramjerdi, F. Equity Measures and Their Performance in Transportation. In Transportation Research Record: Journal of the Transportation Research Board, No. , Transportation Research Board of the National Academies, Washington, D.C., , pp. 67– ACKNOWLEDGMENTS 6. Lorenz, M. O. Methods of Measuring the Concentration of Wealth. Pub- lications of the American Statistical Association, Vol. 9, No. 70, , This research was supported in part by grants from the National pp. – Science Foundation and the City University of New York, High 7. Atkinson, A. B. On Economic Inequality. Oxford University Press, Oxford, United Kingdom, Performance Computing Center. The authors thank Nora Santiago 8. NY1 Network. MTA Board Approves Toll Increases. mynewextsetup.us1. of the College of Staten Island–Geographic Information Systems com/content/news_beats/transit//mta-board-approves-toll-increases. Group and Bukurije Begai of the City University of New York, High Performance Computing Facility, for their technical support of this project. The Transportation Economics Committee peer-reviewed this paper.