My objective in this research is to estimate if travelers at different times and in different locations pay a different share of their travel costs through fares in any statistically significant way such that transit operations are not only allocative inefficient, but inequitably so on spatial and temporal dimensions. “Times” include the various time periods that a transit operator scales its output to, while “locations” are links and stations of the railroad. In addition, I test whether OD trip subsidies are more explained by trips’ lengths or orientation around the transit system’s urban core, and whether the subsidy patterns correlate with the socioeconomic makeup of riders. Finally, I infer fare structure implication by contrasting the difference in findings between BART and MARTA, two transit systems with similar operating environments but different fare structures.
To do this, I use FY19 OD fare data provided by BART and MARTA, as well as findings from the cost allocation study (Mallett, 2022), which used FY19 budgetary, operating, and OD ridership data and semi-fixed asset costs provided by BART and MARTA. To analyze socioeconomic impacts, I use rider survey data from BART’s 2015 Station Profile Study and the Atlanta Regional Commission’s (ARC) 2019 Transit On-Board Survey. While the survey data provided by BART are already weighted to trip count, I manually weighted the survey data provided by ARC.
I do not control for directionality in my analysis; a trip from one station to another is analyzed in tandem with a trip in the reverse direction. Again, for consistency in analysis, I include only mainline tracks of the BART network (i.e., where traditional BART trains/technology operate), so exclude any trips that solely use non-mainline portions of track. This results in 1,124 two-way 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, destination station, and each mainline link used to fulfill the trip.
Measuring cost recovery variability amounts to analyzing how costs and fare receipts covary across time and space. I document cost and cost per rider variability in the cost allocation study (Mallett, 2022). In brief, I found that costs decrease but costs per rider increase with distance from the core of the BART system, that there is no clear spatial pattern in the MARTA system, and that the weekday peak period — out of eight operating time periods for BART and five for MARTA — has the lowest cost per rider in both networks but the highest cost for BART and barely lower costs than the weekday base period for MARTA. For details on the costs I allocated, how I allocated them, and the results, see Mallett (2022).
To analyze temporal cost recovery variability, I calculate the ratio between total fare revenues and total costs by time period (Eq. 1). I also run pairwise correlations to assess how costs, fare revenues, cost recoveries, passenger-miles, trip counts, and the spatial variables explained below interact across time periods. Because ARC and BART did not survey weekend riders, socioeconomic data are insufficient to investigate how temporal subsidies interact with the makeup of riders of different time periods.
$$percentpai{d}_{t}=\frac{fare{s}_{t}}{cos{t}_{t}}$$
1
where
percentpaid t is the cost recovery during time period, t
fares t is the amount of fare revenue generated in time period, t, and
cost t is the share of total costs allocated to serving time period t (see Mallett, 2022)
Analyzing spatial cost recovery variability is more complex, as there are both OD and location (i.e., stations and links) considerations. Furthermore, unlike with time periods, which are one-dimensional, there is no practical way to divvy up fares into link and station parts. Thus, links and stations do not have their own cost recovery per se. Instead, I calculate OD cost recoveries, then scale to stations and links using averages to understand the spatial incidence of subsidies.
I first assign every OD pair a cost equal to the sum of the costs per rider of the entry station, exit station, and each link used to complete the trip (Eq. 2). I then calculate the OD cost recovery rate, which is the ratio of the average fare paid for an OD trip to the OD trip cost (Eq. 3).
\(cos{t}_{od}=costpp{x}_{o}+costpp{x}_{d}+\sum _{l=1}^{n}costpp{x}_{l}\) | (2) |
\(percentpai{d}_{od}=\frac{far{e}_{od}}{cos{t}_{od}}\) | (3) |
where
cost od is the cost of serving a particular OD trip, od,
costppx o is the cost per passenger of origin station, o (see Mallett, 2022),
costppx d is the cost per passenger of destination station, d (see Mallett, 2022),
costppx l is the cost per passenger of link, l (see Mallett, 2022),
percentpaid od is the cost recovery of a particular OD trip, od, and
fare od is the average fare paid for consuming a particular OD trip, od
To test how much trip subsidies are explained by trip length relative to their orientation around the urban core, I run ordinary least squares regressions. I regress the log of OD cost recovery onto the log of both trip length and the average straight-line distance that the origin and destination stations are from a defined core station of the network — West Oakland for BART and Five Points for MARTA. This is defined in Eq. 4.
$$\text{l}\text{n}\left(percentpai{d}_{od}\right)={\beta }_{0}+{\beta }_{1}\text{l}\text{n}\left(triplength\right)+{\beta }_{2}\text{l}\text{n}\left(distancecor{e}_{average}\right)$$
4
where
percentpaid od is the cost recovery of a particular OD trip, od (see Eq. 3),
triplength is the trip length, in track-miles, of a particular OD trip, and
distancecore average is the average straight-line distance, for a particular OD trip, that the origin and destination station are from a defined core station.
In essence, distancecoreaverage proxies for an OD pair’s monocentricity. An OD pair whose origin and destination are distant from the core will have a large value for this term; one whose origin and destination are both near the core, a small value; and one with a distant origin or destination and the other near the core, a moderate value. Notably, this term is not inherently collinear with trip length, as OD pairs can have origins and destinations distant from the core and be either short or long in length.
To understand the geographic incidence of subsidies, I devise cost recovery profiles of stations and links equal to the weighted average of what users of each station and link pay as a share of their trip costs. Hence, subject to an OD trip being associated with a station or link, the average cost recovery of all OD trips consumed defines the station or link cost recovery profile. I define these calculations in Equations 5 and 6, respectively. Referring to Fig. 1(a), a trip from MacArthur to Fruitvale and a trip from Dublin/Pleasanton to Montgomery Street will both be included in the weighted average cost recovery of the Lake Merritt–Fruitvale link, but only the former trip will be included in the weighted average cost recovery of Fruitvale Station.
\(percentpai{d}_{s}=\frac{\sum _{s=o,d}\left(trip{s}_{od}*percentpai{d}_{od}\right)}{trip{s}_{s}}\) | (5) |
\(percentpai{d}_{l}=\frac{\sum \left(trip{s}_{od}*percentpai{d}_{od}\right)\in l}{trip{s}_{l}}\) | (6) |
where
percentpaid s is the cost recovery profile of a particular station, s,
trips od is the total number of times that a particular OD trip, od, was consumed,
percentpaid od is the cost recovery of a particular OD trip, od (see Eq. 3)
trips s is the total number of trips to and from a particular station, s,
percentpaid l is the cost recovery profile of a particular link, l,
trips l is the total number of trips that traverse a particular link, l,
Finally, as with the temporal analysis, I evaluate the covariance of costs, fares, cost recovery, average trip lengths, and more across stations and links of the railroads. For the station-level analysis, I include socioeconomic variables of race and income, as the data provided by ARC and BART are scaled for station profile purposes. Admittedly, both regression analysis and use of OD data would be preferred. However, they are infeasible because there are insufficient sample sizes of the socioeconomic data at the OD level, and with 38 and 48 stations for MARTA and BART, respectively, there are too few observations for multivariate regression across stations.