Recent Decline in Public Transportation Ridership: Hypotheses, Methodologies, and Detailed City-by-City Results (2022)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

F-1 Appendix F: Modeling Framework for Temporal Dynamics The demand for transportation is derived from the utility of accessing destinations. This utility, which cannot be measured with the data available, creates unobserved heterogeneity in cross- sectional models of ridership (Berrebi et al., 2020). In other words, at one point in time, locations and times are different from each other in ways that cannot be explained without knowing why passengers are traveling. These differences are referred to as “fixed effects” and denoted αip where i represents a combination of route-segment and season, and p represents a time-period. In a model of ridership change over time these fixed effects can be controlled for. In this section, we develop the fixed effects model to evaluate the impact of service frequency on bus ridership over the years by time-period. All terms are defined in Table F-1 Table F-1: Summary of Variable Definitions Variable Definition Rid Total ridership in passenger boarding and alightings Freq Total frequency in vehicle-trips Pop+Job Total population and jobs within ¼ mi of segment t Year ∈ (0, ..., T ) i Combination of route-segment and season ∈ (0,…,n) p Time-period ∈ {WE, WD} WD Set of weekday time-periods {AM Peak, Midday, PM Peak, Night WD} WE Set of weekend time-periods {Day WE, Night WE} Equation F-1 shows the structure of the fixed effects model. The ridership for the combination of route-segment and season i, and time-period p in year t is assumed to follow a Poisson distribution whose mean is determined by the explanatory variables xitp. The terms βp represent the elasticity of ridership to frequency specific to each time-period p ∈ {WE, WD}. These coefficients allow to compare the relative change in ridership resulting from a 1% increase in service during each time- period. The impact of changing population and jobs are assumed to be uniform across time-periods. Likewise, the term eµp t accounts for a linear time-trend specifically for time-period p.

F-2 Equation F-1 𝐸𝐸�𝑅𝑅𝑅𝑅𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖�𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖� = 𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 𝛽𝛽𝑝𝑝 ∗ (𝑃𝑃𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖 + 𝐽𝐽𝑜𝑜𝐽𝐽𝑖𝑖𝑖𝑖)𝛽𝛽1 ∗ 𝑒𝑒𝛼𝛼𝑙𝑙𝑝𝑝 ∗ 𝑒𝑒𝜇𝜇𝑝𝑝𝑙𝑙 Unlike transit agencies, for whom operating costs grow proportionally to frequency, passengers perceive the inverse of frequency, i.e., the headway, as a cost. When a passenger decides to make a trip, the service frequency determines how long they have to wait for the next available bus and the penalty in case they miss that bus. But the reliability linked to service frequency goes beyond the specific time-period when a trip is made. If the frequency in other time-periods is too low, the passenger may have to wait for a long time on the way back, making the trip unfeasible altogether. Therefore, it is important to evaluate the cross elasticity of ridership to frequency in other time-periods. In order to differentiate how ridership is affected by the frequency in that same time-period versus all-day frequency, Equation F-2 combines period-specific and all-day frequency. Equation F-2 𝐸𝐸�𝑅𝑅𝑅𝑅𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖�𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖� = 𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 𝛽𝛽𝑝𝑝 ∗ � � 𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑖𝑖𝑖𝑖𝑘𝑘 𝑘𝑘 ∈ Weekday � �𝛽𝛽𝑊𝑊𝑊𝑊 𝑓𝑓𝑓𝑓𝑓𝑓 𝑖𝑖 ∈ Weekday0 𝑓𝑓𝑓𝑓𝑓𝑓 𝑖𝑖 ∈ Weekend ∗ � � 𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑖𝑖𝑖𝑖𝑘𝑘 𝑘𝑘 ∈ Weekend � �0 𝑓𝑓𝑓𝑓𝑓𝑓 𝑖𝑖 ∈ Weekday𝛽𝛽𝑊𝑊𝑊𝑊 𝑓𝑓𝑓𝑓𝑓𝑓 𝑖𝑖 ∈ Weekend ∗ (𝑃𝑃𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖 + 𝐽𝐽𝑜𝑜𝐽𝐽𝑖𝑖𝑖𝑖)𝛽𝛽1 ∗ 𝑒𝑒𝛼𝛼𝑙𝑙𝑝𝑝 ∗ 𝑒𝑒𝜇𝜇𝑝𝑝𝑙𝑙 The model in Equation F-2 considers the ridership elasticity to frequency in two different ways. As in Equation F-1, the terms βp capture the time-period-specific elasticity. In addition, the terms βWD and βWE capture the impact of all-day frequency on each specific time-period’s ridership. The terms βWD and βWE differentiate between weekdays and weekends because trip-chaining typically happens over the course of a single day. While weekend service frequency may affect weekday ridership (and vice versa), this effect does not intervene in immediate travel decisions. Instead, weekday-weekend cross elasticity of ridership to frequency has long-term implications for vehicle ownership, home location, etc. To make the model as sensitive as possible to fluctuations in ridership directly resulting from changes in service frequency, weekdays and weekends have their own specific terms.