Docked Bikeshare Equity and Goal Conflict: An Evaluation Using Gini Coefficients and Lorenz Curves

Abstract

The equitable distribution of docked bikeshare is an important issue for transportation decision-makers. Gini coefficients and Lorenz curves can be used to study transportation inequality. This study used these methods to achieve three outcomes. First, this study identified a gap in bikeshare equity literature and provided a more nuanced measure of bikeshare supply to better evaluate how well bikeshare meets demand. Second, the updated measure of distributional equity was used to evaluate bikeshare equity in Washington, DC. Third, using historical trip data, the Gini coefficient calculations indicated which trip types are better served. Comparison of the results highlighted a potential conflict in program goals: equity versus supporting existing bikeshare members. Policy feedback may bias this trade-off in favor of members, reinforcing spatial inequalities. Overall, this paper further demonstrated how Gini coefficients and Lorenz curves can be useful tools for evaluating inequality in transportation systems.

Keywords

bikeshare gini lorenz equity Washington DC

Introduction

The equitable distribution of transportation is an issue with which many in transportation are concerned. Given that resources are finite, transportation decision-makers must decide who benefits and who does not, a challenge for transportation researchers and practitioners alike. Bikeshare is a particularly important mode for which to consider equity as it provides the environmental, health, and spatial efficiency benefits of cycling without the need of accessing a personal bicycle (Fishman & Allan, 2019). Docked bikeshare is worth special consideration because, unlike its dockless cousin, the supply of docked bikeshare is relatively fixed, meaning the placement of stations are the result of conscious longer-term decisions around who should get access to the system. While bikes can move between stations, the fixing of stations concentrates the location of bikes. The placement of bikeshare stations is important as previous research has suggested the location of docked bikeshare has a direct impact on who can and who does use the system (Fishman et al., 2013; Fishman et al., 2014; Ogilvie & Goodman, 2012; Willberg et al., 2021). Consequently, the placement of docked bikeshare stations generate a real equity concern, a concern that, although shared by dockless bikes, is not as significant when operational locations are not fixed (Mooney et al., 2019; Qian et al., 2020). This equity concern is known to bikeshare operators who have identified station siting as a common way to address equity (Howland et al., 2017). Gini coefficients and Lorenz curves are a method adapted from economics to study transportation inequality. Traditionally used to measure income inequality between or within countries, Gini coefficients are a useful tool for comparisons between and within groups (Wang & Lindsey, 2017). Over the last decade, researchers have demonstrated these tools are effective at diagnosing both horizontal and vertical inequality in transportation. Horizontal equity is the distribution of impacts between groups that are equal in ability and need while vertical equity is the distribution of impacts between groups with differing abilities or needs (Litman, 2016). This paper adapts this evaluation method to evaluate docked bikeshare equity in Washington, DC. There are three goals for this paper:

1. Adapt Gini coefficients and Lorenz curves to the evaluation of docked bikeshare systems.

2. Use census data to evaluate horizontal and vertical equity for the Washington, DC Capital Bikeshare system.

3. Evaluate whether Gini coefficients and Lorenz curves can be used for better understanding bikeshare trip segmentation.

Through evaluation of two forms of bikeshare demand, census population¹ and historical trips, this paper establishes both whether inequalities exist as well as if and how program goals potentially conflict. While this paper is not the first attempt at developing Gini coefficients and Lorenz curves for docked bikeshare (see (Wang & Lindsey, 2018)), this paper evaluates bikeshare in a different geography, performs more extensive evaluation of bikeshare supply, and, using both trip history data and census data, provides a more nuanced evaluation of bikeshare demand that allows for a comparison of program goals. Through this evaluation transportation practitioners and researchers can obtain a better understanding of who bikeshare serves well and who is underserved. After providing a brief background on the bikeshare system in Washington, DC, Capital Bikeshare (CaBi), this paper provides a review of the literature, describes the methodology and data, and explains the results with some discussion before concluding.

Docked Bikeshare in Washington, DC

Beginning operation in 2010, Washington, DC’s CaBi was one of the first publicly owned docked bikeshare systems in the United States (US). Initially available in Arlington, VA and Washington, DC, the system has since expanded into Alexandria, Falls Church and Fairfax in Virginia as well as Montgomery County in Maryland with over 4500 bikes and almost 700 stations (Lyft, 2021a). Figure 1 shows how the CaBi stations are dispersed through Washington, DC (as this paper focuses on Washington, DC, stations outside of the district are not shown). Stations within Washington, DC are owned by the District Department of Transportation (DDOT) with system operations, including maintenance and rebalancing, managed by Motivate LLC (Lyft, 2021a). Expansion and siting decisions are also under DDOT’s purview (Kittelson & Associates, 2020).

Figure 1.

Capital Bikeshare locations in Washington, DC (made by author using Government of the District of Columbia, 2022).

Equity is an important goal for the system, as outlined in DDOT’s draft bikeshare development plan (Kittelson & Associates, 2020). However, the inequity of the system has been the subject of past analysis and criticism. In 2019 the Urban Institute (Su & Wang, 2019) performed a spatial analysis of CaBi where researchers evaluated how bikeshare varied across the city. The study showed census tracts with higher white populations and higher incomes had higher average station counts and recorded higher bikeshare use. A survey of CaBi members also found users were more likely to be white, male, younger, and without access to a personal vehicle (LDA Consulting, 2017). Finally, a study by Virginia Tech (2012) also found CaBi users were more likely to be white and more likely to be better educated compared to Washington, DC census data. These results provide some indication as to how the current system may be inequitable.

Literature Review

As docked bikeshare has existed for over a decade, there is much research evaluating bikeshare equity. Table 1 summarizes a dozen papers and studies that explicitly evaluate equity in docked bikeshare programs. As the table shows, the research has focused on three primary evaluation strategies: comparing geographies with and without bikeshare (Duran et al., 2018; Hosford & Winters, 2018; Ogilvie & Goodman, 2012; Ursaki & Aultman-Hall, 2015; Wang & Lindsey, 2018), estimating bikeshare trips or supply using regression methods (Cohen, 2016; Couch & Smalley, 2019; Qian & Jaller, 2020; Wang & Lindsey, 2018), and evaluating bikeshare programs (Babagoli et al., 2019; Lovelace et al., 2020; Qian et al., 2020), whether against themselves over time or against competing programs. While some of the research had mixed findings, in general it appears that geographies that are whiter and wealthier tended to have better bikeshare access. Areas with a higher proportion of zero car households also generally had more bikeshare access but this is likely, at least partially, because these areas also tended to be some of the highest concentrations of population. Defining bikeshare supply is one of the primary limitations of existing equity research. As Table 1 shows, most research evaluated docked bikeshare at the station level, even when information about station dock or bicycle capacity is available. Research at the more granular bike dock level either did not account for bike accessibility by excluding walk buffers (Couch & Smalley, 2019) or focused more on comparing programs (Qian et al., 2020) rather than evaluating geographic access, the focus of this research.

Table 1.

Summary of Bikeshare Equity Literature.

Source	Bikeshare supply definition		U.S. Geographic unit	CaBi included in study?	Methods	Relevant key findings
Source	Bike supply data	Buffer	U.S. Geographic unit	CaBi included in study?	Methods	Relevant key findings
(Ogilvie & Goodman, 2012)	# Of stations	500 m (.31 miles)	Not applicable	No	Linear and logistic regression to compare trips in areas with and without bikeshare	• Registered users were more likely to be male and live in economically advantaged areas
						• Deprived areas were less likely to be close to docking stations
						• Accounting for proximity, users in deprived areas made more trips per month than those in least deprived areas
(Ursaki & Aultman-Hall, 2015)	# Of stations, # of docks^a	500 m (.31 miles)	Census block groups	Yes	Student t-test to compare sociodemographic differences between areas with and without bikeshare	• Statistically significant findings include white people, more educated people, and younger people are more likely to have access to bikeshare
(Ursaki & Aultman-Hall, 2015)	# Of stations, # of docks^a	500 m (.31 miles)	Census block groups	Yes		• CaBi system was the most equitable among the cities studied but still showed differences by income
(Cohen, 2016)	# Of stations	400 m (.25 miles)	Census block groups	Yes	Regression to estimate trips in different areas	• Low-income residential areas were negatively correlated with bikeshare trips
(Cohen, 2016)	# Of stations	400 m (.25 miles)	Census block groups	Yes	Regression to estimate trips in different areas	• Medium wage jobs were positively correlated with trips
(Duran et al., 2018)	# Of stations, # of docks^a	500 m (.31 miles), 1000 m (.62 miles)	Not applicable	No	Statistical sociodemographic comparisons of areas with and without bikeshare	• Authors identified both spatial and social inequalities with bikeshare concentrated in wealthier and whiter neighborhoods
(Hosford & Winters, 2018)	# Of stations	500 m (.31 miles)	Not applicable	No	Descriptive sociodemographic comparisons of areas with and without bikeshare	• “More advantaged” areas, represented by lower pampalon deprivation index score, had more bikeshare access
(Wang & Lindsey, 2018)	# Of stations	400 m (.25 miles)	Census blocks	No	Gini coefficients and Lorenz curves; spatial random effect model to predict trips per station	• Populations that are whiter, more female, and less educated have greater equity
						• Households without vehicles have greater equity
						• Populations with low monthly earnings or under poverty have greater equity
						• High-paid jobs and jobs for non-white workers have greater equity
(Babagoli et al., 2019)	# Of stations	—	Census tract	No	Descriptive summary of areas with bikeshare over time	• Bikeshare is mostly located in wealthier census tracts
(Babagoli et al., 2019)	# Of stations	—	Census tract	No	Descriptive summary of areas with bikeshare over time	• System expansion did not significantly change where bikeshare was located
(Bhuyan et al., 2019)	# Of stations	400 m (.25 miles)	Census block groups	No	Geographic and descriptive comparisons of over and under supply of bikeshare coverage	• A larger proportion of Baltimore’s population is underserved than overserved or adequately served by bikeshare
(Bhuyan et al., 2019)	# Of stations	400 m (.25 miles)	Census block groups	No		• Many of the outlying areas of Baltimore without bikeshare were deemed to not need bikeshare
(Couch & Smalley, 2019)	# Of bikes	—	Census tract	Yes	Poisson regression model to predict bike count per census tract	• No CaBi specific findings
						• Dockless more spatially equitable along educational lines (statistically significant)
						• Docked more spatially equitable along racial lines (not statistically significant)
(Lovelace et al., 2020)	# Of stations	150, 200, and 300 m (.09, .12, .19 miles)	Not applicable	No	Descriptive comparisons of bikeshare use over time	• Bikeshare has become more geographically distributed over time
(Lovelace et al., 2020)	# Of stations	150, 200, and 300 m (.09, .12, .19 miles)	Not applicable	No	Descriptive comparisons of bikeshare use over time	• Bikeshare accessibility has particularly increased in low-income areas
(Qian & Jaller, 2020)	# Of stations	400 m (.25 miles)	Census block groups	No	Poisson and binomial regression to estimate trips in different areas	• Bikeshare stations in disadvantaged communities generate fewer trips than average
(Qian & Jaller, 2020)	# Of stations	400 m (.25 miles)	Census block groups	No		• Annual members who are residents in disadvantaged communities tend to make longer trips
(Qian et al., 2020)	# Of bikes	400 m (.25 miles)	Census tract	No	Descriptive and statistical comparisons between docked and dockless bikeshare trips and bike availability	• Dockless bikeshare provide more bikes to disadvantaged communities than docked bikeshare
(Qian et al., 2020)	# Of bikes	400 m (.25 miles)	Census tract	No		• Dockless bikeshare attracts more potential bikeshare trip demand in disadvantaged communities because of larger service area and more frequent rebalancing

^aData was identified and available but not used in the evaluation of docked bikeshare.

This gap is an important limitation as it somewhat masks how supply varies with demand. Previous work generally focused on whether bikeshare supply existed, not how much supply existed or if it was adequate for the adjacent population. As a basic example, a bikeshare station with capacity for 10 bikes might be insufficient for a population of 30 people but it might be adequate if it were replaced with a bikeshare station with capacity for 40 bikes. The number of stations does not change but the bikeshare supply does. Much of the previous work does not capture these differences. Understanding how bikeshare supply varies with population can be key for understanding differences in usage, as discovered with research on London’s bikeshare system that found a connection between bikeshare supply in low-income areas and bikeshare use (Goodman & Cheshire, 2014; Ogilvie & Goodman, 2012). Overlooking bikeshare station capacity may consequently underestimate equity concerns.

Gini coefficients, a statistical measure of distribution that represents the degree of inequality in a resource distributed among a population, can highlight these equity limitations. The measure of supply can be designed to account for both bikeshare station accessibility as well as station capacity. Previous transportation research has used Gini coefficients and Lorenz curves to measure inequality in transit (Bertolaccini & Lownes, 2013; Delbosc & Currie, 2011; Hörcher & Graham, 2020; Lope & Dolgun, 2020) and bicycling (Wang & Lindsey, 2018; Wang & Lindsey, 2017). Wang and Lindsey have particularly focused on using these tools in bicycling. The authors have used Gini coefficients to evaluate access to bicycling facilities (Wang & Lindsey, 2017) as well as access to bikeshare stations (Wang & Lindsey, 2018) (see Table 1). Although their bikeshare research was subject to some of the same limitations around supply described earlier, their work is an important contribution to the use of Gini coefficients in transportation on which this paper builds.

Overall, while bikeshare equity literature is well-established, there are some limitations to existing methods that encourage additional research. By leveraging related research in transit, Gini coefficients and Lorenz curves can overcome these limitations to provide insight into both vertical and horizontal equity. This paper adds to bikeshare literature by filling a gap in bikeshare equity research and expanding on previous work on the use of Gini coefficients in bikeshare equity evaluation by using a more robust calculation of bikeshare supply. The paper also evaluates new data for understanding equity in bikeshare trip types as well as a more in-depth analysis of the CaBi system. Finally, comparing the two analyses might provide more insight into why some bikeshare inequalities exist.

Methodology and Data

Lorenz curves and Gini coefficients describe how a resource is distributed among a population using cumulative measures of supply and demand. Although these methods are primarily used for evaluating horizontal equity, previous transportation research has demonstrated that these methods could be used for vertical equity. As Wang and Lindsey (2017) put it, “for vertical equity, potentially disadvantaged or vulnerable groups should be provided with a higher quality or quantity of services than other advantaged groups.” These authors compared Gini coefficients among historically disadvantaged groups including zero car households, percentage of African Americans, percentage below the poverty level, and percentage of people younger than 18 or older than 65 years of age. Other transportation research has also used Gini coefficients to evaluate vertical equity. Lope and Dolgun (2020), for example, compared Gini coefficients to describe differences in tram accessibility for people with disabilities compared to the general population. Gini coefficients have also been used to show relative differences in income distribution between different country populations (see (OECD, 2011) e.g.). This paper uses Gini coefficients in a similar way, comparing coefficients to show relative differences between different populations.

For this paper, both supply and demand are estimated at the census block group level within Washington, DC’s borders. Gini coefficients are influenced by data granularity, the paper uses the smallest available geographic scale for the demand data. As Table 1 showed, some previous bikeshare research has also been performed at this scale. The following sections describe what data were used and how the results were calculated. To support the Lorenz curve and Gini coefficient results, multiple linear regression was used to show how bikeshare varies based on different attributes, with particular attention paid to historically disadvantaged populations.

Supply Data

Capital Bikeshare station data was obtained from Washington, DC’s open data portal (Government of the District of Columbia, 2022). These data are a snapshot of CaBi supply, including the location of a bikeshare station as well as its capacity (number of docks). The dataset includes 679 bikeshare stations with 344 accessible to Washington, DC residents. Bikeshare stations are assumed to be accessible within a quarter mile of the station, consistent with previous work (Bhuyan et al., 2019; Cohen, 2016; Qian & Jaller, 2020; Qian et al., 2020; Wang & Lindsey, 2018) as well as assumptions used by CaBi (Lyft, 2021b). These data were used to calculate a bikeshare supply index (BSI), a spatial measure of bikeshare supply. Equation (1) shows how BSI was calculated. Figure 2 provides an example of how BSI was calculated.

{B S I}_{G U} = \sum_{N} (\frac{{C o v e r a g e A r e a}_{N, G U}}{{T o t a l A r e a}_{G U}} * B_{N, G U})

(1)

Where

B_{N, G U}

is the bike capacity for a bikeshare station, N is the number of walk access buffers to each bikeshare station, and GU is the geographic unit, census block groups in this case.

Figure 2.

Example supply score calculation with three bikeshare stations.

Coverage is calculated using .25 mile buffers around a bikeshare station. Importantly, a bikeshare station does not have to be within a GU for its coverage area to extend into that GU, as Station 2 in Figure 2 demonstrates. As previously mentioned, Wang and Lindsey (2018) have also calculated Gini coefficients and Lorenz curves for docked bikeshare. While this previous work used the same walk buffer, the authors used bike share stations as their measure of supply without accounting for the number of docks per station (effectively meaning all $B_{N, G U}$ = 1). As more docks means more potential supply, this paper instead used based on the transit supply index (TSI) used in transit literature (Bertolaccini & Lownes, 2013; Delbosc & Currie, 2011). Where TSI used vehicle frequency, the BSI calculation uses bikeshare station capacity. One key difference between BSI and the TSI is the definition of coverage. For TSI, if bus stops for a route were close enough to overlap, the coverage areas were spatially joined to prevent double counting as the same bus would serve both stops. Conversely, for BSI the full area was counted as each bikeshare station provides its own supply (equivalent to each bikeshare station being served by a different route in TSI calculations); having access to two bikeshare stations at the same point in space does not result in double counting.

The lack of bikeshare installation date is a limitation with this dataset. However, bikeshare trip data (explained in more detail in Section 3.2) can overcome this limitation. As trip data are linked to station stops, trip data can be tracked over time to see when bikeshare stations come into service. For example, if in April 2019 bikeshare trips can be connected to 300 bikeshare stations, and in June 2019 trips can be connected to 305 bikeshare stations, it can inferred that 5 stations were installed over that time period. This information is used to ensure changes in bikeshare supply over time are captured in time dependent analyses, like those described in the next section and Table 2.

Table 2.

Capital Bikeshare Trip Data Summary.

Variable	Attribute	Count	Percent of trips, %	Average trip length (Mins)	Standard deviation (Mins)
All	—	1,525,165	100.00	13.6	28.3
Month of data	April, 2019	307,849	20.18	20.6	41.0
	June, 2019	304,002	19.93	19.2	39.0
	August, 2019	314,534	20.62	18.2	33.4
	October, 2019	295,951	19.40	16.4	30.9
	December, 2019	144,348	9.46	13.8	28.6
	February, 2020	158,481	10.39	13.6	28.3
Trip length	Short (<25th percentile trip length, <5.8 minutes)	379,743	24.90	4.6	1.4
Trip length	Long (>75th percentile trip length, >15.7 minutes)	381,827	25.04	42.1	63.5
Day/Night	Day (after sunrise, before sunset)	1,209,694	79.32	18.0	33.4
Day/Night	Night	315,471	20.68	16.3	40.7
User type	Member	1,331,598	87.31	14.3	27.2
User type	Casual	193,567	12.69	40.8	62.8
Trip type	Peak travel period (weekday trips occurring 6am to 9am or 4pm to 7pm)	548,094	35.94	14.0	23.7
Trip type	Off peak travel period (trips not occurring in peak weekday periods)	977,071	64.06	19.7	39.8
Day	Weekday	1,100,108	72.13	15.7	31.2
Day	Weekend	425,057	27.87	22.6	43.0

Demand Data

Two types of demand data were used for this evaluation. 2019 American Community Survey (ACS) 5-year Estimates were obtained at the census block group level, its most granular level, to ascertain which populations have more or less access to docked bikeshare. Specifically, in addition to total population, data were gathered for race, poverty level, and cars per household. These data allow us to see how bikeshare is distributed across historically marginalized populations including Black or African American populations, low-income residents, and zero car households. For the purposes of this study, low-income is defined as below 150% of the US poverty level. This threshold was used to reflect the fact Washington, DC’s median income is almost 70% higher than the national median income and is consistent with how low-income populations are defined by the Metropolitan Washington Council of Governments (MWCOG) Transportation Planning Board (TPB), the metropolitan planning organization (MPO) in which Washington, DC is located.

The second form of demand data is trip history data available from the CaBi data webpage (Lyft, 2021b). Trip history provides a form of revealed preference demand, allowing us to see how supplied bikeshare can serve different types of trips. There are three purposes to evaluating the distribution of bikeshare trips against the supply of bikeshare. First, a horizontal equity evaluation of trips against bikeshare supply can give a high-level understanding of the inefficiency of station siting. A higher Gini coefficient might indicate some bikeshare stations have more capacity than is needed while other bikeshare stations are underserved, suggesting changes to existing bikeshare infrastructure, or the siting decision process, might be required. Second, the comparison of Gini coefficients can provide a relatively quick and simple assessment of how well a program is meeting its goals. For example, if a program goal includes designing a system around shorter trips, then comparing Gini coefficients for different trip lengths can help us understand how well station siting is helping to meet that goal. Third, the evaluation of trip data against bikeshare supply can help us better understand user behavior. For example, a significantly different Gini coefficient for trips made during peak travel periods compared to off peak travel periods can help program administrators understand how and, to an extent, why their system is being used. This can inform both operational decisions, like rebalancing strategies, as well as future siting decisions. Understanding these differences could also help with program goals while helping program administrators understand why some horizontal inequities might exist. Finally, by repeating these evaluations over time, Gini coefficients provide a succinct indication of whether the efficiency of station siting and the achievement of program goals is improving.

The trip dataset includes trip start time, end time, duration, starting station, ending station, and member type. This research uses every second month from April 2019 to February 2020, giving six months of pre-pandemic data, accounting for possible seasonal variations. The six months of data provided 1,734,029 trip records. As the study’s focus is Washington, DC, trip records were removed if they could not be matched to a bikeshare station or if the trip did not begin in the District, leaving 1,526,165 records. Because of the large number of records, the data was able to be split into five different trip characteristics. These trip characteristics are summarized in Table 2. Finally, after disaggregating data by trip characteristic, data were spatially joined to census block groups based on the location of the trip’s starting station to show where the bikeshare demand was concentrated. A limitation of these data is that they do not show unmet demand. However, the complementary analysis using census data fills this gap.

Lorenz Curve and Gini Coefficient Calculation

Once the BSI and demand data has been estimated for each block group, Lorenz curves can be generated. The supply and demand values are first sorted from smallest to largest. Next, each row of BSI data, which represents the supply data for a specific block group, is divided by the sum of BSI for all block groups. This gives the proportion of BSI for a specific block group. This is repeated for the demand data. Following this, cumulative supply data is calculated by creating a new column with each row summing the proportion of BSI for a specific block group with all of the block groups with smaller proportions of BSI. This process is repeated for the demand data to get cumulative demand. Finally, a Lorenz curve is created by plotting the cumulative proportion of bikeshare demand against the cumulative proportion of supply. These curves are interpreted by identifying a point on the line and reading it as X% of demand receives Y% of supply. Looking at the example in Figure 3, 60% of demand receives 25% of supply. Lorenz curves plotted against a line of equality, where cumulative demand matches cumulative supply, provides us with the information needed to calculate Gini coefficients. Equation (2) shows how Gini coefficients are calculated.

G i n i = \frac{A_{e q u a l} - A_{L o r e n z}}{A_{e q u a l}}

(2)

Where A_Lorenz is the area under the Lorenz curve and A_equal Is the area under the line of equality. As the maximum cumulative demand and supply is 1.0 for both, A_equal will always be .5. Given this, a Gini coefficient of 0 represents perfect distribution while a value of 1 means distribution is perfectly inequal.

Figure 3.

Example Lorenz curve.

Multiple Linear Regression

To support the Lorenz curve and Gini coefficient evaluation, regression was used to determine whether variation in bikeshare distribution (BSI) could be explained by the presence of historically marginalized populations, while controlling for average job density, population density, and the existence of transit service. The latter was included because trip patterns observed in CaBi member surveys (LDA Consulting, 2017) indicate many members use bikeshare to access transit. Washington Metropolitan Area Transit Authority (WMATA) general transit feed specification (GTFS) data was used to determine how many Metrorail stations are located within a census block group as siting near rail stations has been noted as a CaBi strength (Kittelson & Associates, 2020). The generalized equation for the regression is given in equation (3):

Log (1 + Y) = a_{0} + b_{1} X_{1} + \dots + b_{i} X_{i} + e

(3)

Where Y is the BSI calculated for a census block group,²

a_{0}

is the average value of Y when each independent variable is equal to zero, X represents the explanatory variables, and b represents the average change to BSI associated with a change in X. Table 3 lists all variables included in the regression.

Table 3.

Regression Variables.

Variable	Source	Definition
PctBlack (EXPLANATORY)	2015–2019 ACS 5-yr estimates	Number of black residents/All residents; percentage of census block residents who are black or African American
ZeroCarTotal (EXPLANATORY)	2015-2019 ACS 5-yr estimates	Households with zero cars/All households; percentage of zero car households (HH) in a census block group
LogJobDensity (EXPLANATORY)	MWCOG Cooperative Forecast 9.2 draft 2020 employment	(Jobs/Area)/1000; log transformed average job density in census block group
LogPopDensity (EXPLANATORY)	2015–2019 ACS 5-yr estimates	(Population/Area)/1000; log transformed average population density in census block group
Under150PctPoverty (EXPLANATORY)	2015–2019 ACS 5-yr estimates	Number of residents below 150% of national poverty level/All residents; percentage of census block Residents who are low-income
WMATA_count (EXPLANATORY)	WMATA 2021 GTFS	Number of WMATA train stations per census block group
BSI (DEPENDENT)	Washington, DC’s open data portal and census boundary data	Estimate of the quantity of bikeshare supply in a given census block group

Results and Discussion

The bikeshare supply index (BSI) was calculated for every census block group in Washington, DC and plotted in Figure 4. The graphic shows the highest scores appear around central Washington, DC, near the central business district and many of the major tourist attractions. The lowest BSI scores are observed on the periphery of the city. Medium-low scores were also observable to the north as well as the east and south where there are higher Black or African American populations. While there are small differences for BSI per capita, the general trends described do not change. These visual results support some of the previous empirical work evaluating bikeshare equity in Washington, DC.

Figure 4.

BSI by census block group for Washington, DC.

Lorenz curves were graphed for four population measures: total population, Black or African American population, low-income population, and zero car households, as shown in Figure 5. The difference between supply (BSI) and demand (population) indicates where there are bikeshare supply distributional inequalities. Table 4 shows the Gini coefficients for these curves, which indicate the degree of distributive inequality. To demonstrate the limitations with previous equity calculations highlighted in the literature review, Gini coefficients were calculated based on both station capacity (“Using Docks”) and just stations (“Using Stations; ” $B_{N, G U}$ = 1).

Figure 5.

Lorenz curves for census populations.

Table 4.

Gini Coefficients for Census Data.

Variable	Gini coefficient
Variable	Using docks	Using stations
Total population	.584	.558
Black or African American population	.740	.720
Low-income population	.732	.711
Zero car households	.525	.513

As Table 4 shows, using bikeshare stations rather than using station docks results in lower Gini coefficients (meaning more equitable bikeshare distribution). This indicates that focusing on stations rather than a more granular measure, like docks, might underestimate distributional inequity. In this case, using just stations underestimates Gini coefficients by about 2–5%, depending on the specific population. This is a useful finding because, in addition to showing limitations with how equity is measured, these results indicate distribution equity might be improved by increasing docks per station or strategic rebalancing policies, rather than the more time and resource intensive decisions around where a docking station should be placed.

Focusing on just the more nuanced measure of station capacity, Table 4 shows that the general population had a Gini coefficient of .584. Looking at the Lorenz curve in Figure 5, 60% of the total population had access to just 16% of bikeshare supply. As a majority of the population only has access to a small portion of bikeshare supply, these results indicate low horizontal equity.

As described earlier, vertical equity requires some groups have different quality of bikeshare supply due to differences in ability or need. For example, this may mean groups that are vulnerable or historically marginalized should be provided with more bikeshare supply than other groups (Delbosc & Currie, 2011). The Lorenz curves and Gini coefficients indicate how bikeshare is distributed among different vulnerable or historically marginalized groups in Washington, DC. As Table 4 and Figure 5 show, docked bikeshare in Washington, DC distributed differently across different populations. Although bikeshare supply is distributed better among zero car households than the general population, low-income populations and Black or African American populations have relatively less equitable distributions. While 60% of the general population has access to about 17% of bikeshare supply, 60% of low-income households have access to 8% of supply while 60% of the Black or African American population only has access to 9% of supply. The results for low income and Black or African American populations are consistent with the previous work (Su & Wang, 2019; Ursaki & Aultman-Hall, 2015). Conversely, 60% of zero car households have access to 22% of supply. The comparatively better result for zero car households is consistent with previous research (Wang & Lindsey, 2018). Overall, in addition to low horizontal equity, these results indicate low vertical equity for bikeshare in Washington, DC.

To further assess the distribution of docked bikeshare in Washington, DC BSI was evaluated for census block groups where one of the historically marginalized populations is a majority (more than 50% of the block group population), and then again for when they were not a majority. The results are shown in Table 5. While the results are similar to the distribution trends shown in Table 4 and Figure 5, the magnitude of the differences is particularly salient in Table 5. After controlling for population, majority Black or African American census block groups received about 2.5 times lower BSI per capita while majority low-income census block groups receive about 1.7 times lower BSI per capita. Conversely, majority zero car households had almost twice the BSI per capita.

Table 5.

Comparison of BSI per Capita.

Variable		Census block group count	Average BSI per BG	BSI per capita (x10^-5)	Average population density (population/square mile)
Census Block Group >50% Black or African American	Yes	204	.85	57.1	9966.7
	No	246	2.23	140.8	10,293.8
	Difference		163.1%	146.8%	3.3%
Census Block Group >50% Low-Income (<= 150% of the federal poverty level)	Yes	41	1.15	63.9	9387.8
	No	409	1.65	109.0	10,247.0
	Difference		43.4%	70.6%	9.2%
Census Block Group >50% Zero Car Households	Yes	84	2.68	165.1	14,194.9
	No	366	1.36	89.3	9485.6
	Difference		−49.3%	−45.9%	−33.2%

It is reasonable to think docked bikeshare might be sited in places with higher population density, meaning some of these differences might be explained by density. For example, zero car households might be benefitting from bikeshare supply because they tend to be in the densest residential areas of Washington, DC, areas that are well served by public transportation where a car is less needed. Population and employment density is also the principal component of high ridership estimates in the draft CaBi development plan (Kittelson & Associates, 2020). Consequently, calculations for average block group population density were also included in Table 5. As the results show, the magnitude of the differences is much smaller than for bikeshare per capita for census BG with majority Black or African American populations or majority low-income populations. This suggests that, while population density might play some role, it cannot explain the large differences in inequitable BSI distributions.

Some of these findings might also be due to docked bikeshare’s role as a first/last mile connection. For example, siting bikeshare stations near rail transit provides an opportunity for people using bikeshare to access train stations or complete their trips from a train to their final destination. These types of trip patterns are observed in CaBi member surveys with over 70% of respondents stating they use bikeshare to access transit (LDA Consulting, 2017). The colocation of bikeshare stations and WMATA Metrorail stations has been cited as a strength of the current system (Kittelson & Associates, 2020). However, while siting bikeshare near transit facilitates first/last mile connections, and may therefore be useful for generating trips, it may not be as conducive to achieving equity goals considering transit-accessible neighborhoods tend to be whiter and wealthier, especially neighborhoods near rail (Mckenzie, 2015). Thus, these results may be reflecting trade-off decisions between bikeshare productivity and equity.

These relationships were further evaluated in a regression to determine if different census block group characteristics were correlated with calculated bikeshare supply. Table 6 summarizes the results of the regression.

Table 6.

Regression for Census Block Group Bikeshare Supply Index.

	Dependent variable:
	Log(1 + BSI)
PctBlack	−.005** (.002)
Under150PctPoverty	−.004 (.04)
ZeroCarTotal	.012*** (.003)
LogJobDensity	.313*** (.044)
LogPopDensity	.517*** (.059)
WMATA_count	.522*** (.155)
Constant	−4.874*** (.633)
Observations	450
R²	.500
Adjusted R²	.493
Residual Std. Error	.954 (df = 443)
F statistic	73.911*** (df = 6; 443)

Note: *p < .1; **p < .05; ***p < .01.

As Table 6 shows, all variables except the poverty measure are statistically significant to the 5% level or better. As expected, the model shows changes in zero car households, job density, population density, and WMATA Metrorail stations are all positively correlated with changes in the BSI. The presence of WMATA Metrorail stations has the largest coefficient and is thus potentially the most useful for understanding changes to BSI. Changes in the proportion of Black or African American residents are correlated with a decrease in the change in BSI, aligning with the Lorenz curves and Gini coefficient results. Although the poverty variable coefficient was in the expected direction, it was not statistically significant, indicating it might be less useful for explaining differences in BSI. Poverty might have a lower correlation with BSI in the regression because of the inclusion of Black or African American populations who tend to have some of the lowest incomes in Washington, DC (DC Health Matters, 2021). Thus, some of the observed trends in the poverty Lorenz curves might be partially reflecting racial trends. The closeness of the poverty and Black or African American Lorenz curves in Figure 5 supports this explanation. Overall, the model explains about 50% of BSI variance while generally supporting the trends identified using Lorenz curves and Gini coefficients.

Gini coefficients were also calculated for the different groupings of historical trip data. The results are shown in Table 7. As different types of demand data are used for these calculations, the Gini coefficients cannot be directly compared to the earlier calculations for census data.

Table 7.

Gini Coefficients for Bikeshare Trip-Generated Demand.

Variable	Attribute	Gini coefficient
All trips	—	.500
Month	April, 2019	.530
	June, 2019	.510
	August, 2019	.502
	October, 2019	.486
	December, 2019	.466
	February, 2020	.462
Trip length	Short (<25th percentile trip length, <5.8 minutes)	.454
Trip length	Long (>75th percentile trip length, >15.7 minutes)	.630
Day/Night	Day (after sunrise, before sunset)	.505
Day/Night	Night	.492
User type	Member	.472
User type	Casual	.722
Trip type	Peak travel period (weekday trips occurring 6am to 9am or 4pm to 7pm)	.498
Trip type	Off peak travel period (trips not occurring in peak weekday periods)	.515
Day/Night	Weekday	.492
Day/Night	Weekend	.532

Overall, like with census data, there appears to be some horizontal inequality concerns with the trip data. However, as the months of data in Table 7 demonstrate, the distribution of BSI across trips is becoming more equitable over time, relatively speaking. An inspection of the data indicates this is possibly because more bikeshare stations were being installed over time. While April 2019 trip data connected to 291 unique bikeshare stations, February 2020 data included 305 unique bikeshare stations, although not all April 2019 bikeshare stations are reflected in the February 2020 dataset. As previously mentioned, the bikeshare location dataset did not include installation data so it was not possible to tell when bikeshare stations become available for use or stopped being used. While this data gap somewhat limits what can be learned from the results over time, the results do indicate that the changes in station siting are correlated with a better distribution of trips across bikeshare stations.

Looking at different trip characteristics, the results in Table 7 suggest CaBi supply is better distributed for people making shorter trips relative to longer trips. As the bikeshare program incentivizes shorter trips with its pricing strategy (LDA Consulting, 2017), these results indicate the siting of physical infrastructure support program goals around trip length. The average trip lengths in Table 2 reinforce this postulation. As Table 2 shows, average trip length decreases over the different months of data indicating the change to station siting appears to be making it easier for people to make shorter trips.

In addition to trip length, Table 7 shows CaBi provides a more equitable distribution of bikeshare supply for trips started during the night relative to day. This is somewhat unexpected as Table 2 showed almost 80% of trips occur during the day. However, the difference is small, suggesting there might not be much difference between trips at night and trips during the day. Trips taken during weekdays do have a more equitable distribution of bikeshare supply relative to trips on weekends, as expected. However, like with day and night, the difference is small. Finally, bikeshare supply is more equitably distributed for trips made during peak periods relative to trips made outside of peak commuting periods. As rebalancing information was not available, this analysis just used bikeshare station capacity without accounting for rebalancing differences. This could impact how many bikes are available, especially during peak travel periods. Overall, these three sets of results appear to indicate when bikeshare trips begin is not a significant factor in the equitable distribution of bikeshare supply.

As expected, Table 7 indicates trips made by CaBi members receive a better distribution of bikeshare supply relative to trips taken by casual CaBi users. As shown in Table 2, 87% of trips were made by members. This result also aligns with public statements from CaBi officials who have stated the program’s emphasis was on members, not casual users like tourists (Chester, 2013). As Table 2 also indicates, CaBi members have a significantly shorter average trip length than casual users. Thus, overall, these results suggest that CaBi bikeshare supply has been better designed to support trips made by members than casual users.

Although the two types of Gini coefficients cannot be directly compared, the summary results of the two types of demand data analyzed demonstrate that the distribution of CaBi bikeshare supply produces both horizontal and vertical equity concerns in Washington, DC, yet does not disproportionately impact system members. Rather, the results suggest that, over time, the system is being better designed for members who tend to make shorter trips. Thus, there appears to be a program conflict between achieving equity goals and serving the program’s members. This contrast is hinted at in CaBi member surveys which indicates members are “much more likely to be Caucasian” (LDA Consulting, 2017), even though this research has demonstrated areas with higher Black or African American populations receive a disproportionately low share of bikeshare supply. The propensity maps in the CaBi draft development plan (Kittelson & Associates, 2020) support the fact that goals focusing on ridership and revenue result in a different geographic emphasis than a focus on “public need,” where historically marginalized groups are counted. Thus, the persistence of bikeshare inequities in Washington, DC, even after over a decade of operation, may be partially explained by program goal conflict. One potential cause of goal conflict is the relationship between DDOT, who owns the bikeshare stations, and Motivate, who is in charge of system operations. Contracting out costs to a private organization might provide an incentive to focus on improving cost efficiency rather than social equity. Alternatively, goal conflict may be reinforced by policy feedback where people benefiting from the program might provide feedback to program administrators, either through their activities or through involvement in participatory processes, to shape a program in a way that further benefits them (Campbell, 2012). For example, program administrators may aim to support existing members with good bikeshare supply by upgrading bike capacity at stations with higher member use, which might in turn be good for member satisfaction and encouraging membership renewal. However, such a decision may draw limited resources away from areas with higher concentrations of historically marginalized groups, reinforcing spatial inequalities. In terms of Gini coefficients, it might mean that decreasing Gini coefficients for member trips might mean increasing Gini coefficients for Black or African American populations.

While past membership surveys and the results described from this research have indicated a clash between serving marginalized groups and serving program members, this does not necessarily need to be the case. As mentioned in the introduction, the placement of bikeshare stations has a direct impact on who can and who does use the system (Fishman et al., 2013, 2014; Ogilvie & Goodman, 2012; Willberg et al., 2021). Increasing BSI in Washington, DC, especially in census block groups with higher concentrations of historically marginalized groups, can expand accessibility, likely use, and potentially diversify what a CaBi member looks like. As a result, focusing on members after expanding coverage in areas with higher marginalized populations might not negatively impact equity goals as significantly.

Conclusion

The equitable distribution of docked bikeshare is an important issue for transportation decision-makers to consider. Unlike dockless bikeshare, the placement of docked bikeshare can have longer term community and user equity impacts. This study began with three goals to try and better diagnose and evaluate equity in docked bikeshare systems. First, while some work had been done using Gini coefficients in docked bikeshare, this study adapted the transit supply index from transit literature to provide a better measure of bikeshare supply (BSI). This more nuanced measure of bikeshare supply revealed previous evaluations of bikeshare using just bikeshare stations may have understated the severity of equity concerns. Second, this updated measure of BSI was used in the calculation of Lorenz curves and Gini coefficients to demonstrate bikeshare horizontal and vertical equity in Washington, DC. While horizontal equity concerns were demonstrated across the city, the lack of comparative access for low-income and Black or African American populations showed there are vertical equity concerns too. The supporting regression analysis particularly emphasized that increases in Black or African American populations are associated with a statistically significant decrease in bikeshare supply. Finally, Gini coefficients were calculated using trip data to better understand how the system is used. Over time, it appears horizontal inequity for bikeshare trips has been decreasing. With trips segmented into five different trip characteristics, this paper also demonstrated bikeshare in Washington, DC better serves short trips and trips made by members. No significant difference was found for trips made during peak travel periods, during night or day, or during weekdays or weekends.

Comparing the results for the two types of study populations suggests there may be conflicts between designing a system for members and designing a more equitable bikeshare system, especially for Black or African American residents living in Washington, DC. Policy feedback driven by current members could potentially reinforce spatial inequalities, making change more difficult. However, increasing bikeshare supply in neighborhoods with higher concentrations of historically marginalized populations can help to address this difference by helping to change what a CaBi member looks like. Overall, this paper further demonstrated how Gini coefficients and Lorenz curves can be useful tools for evaluating inequality in transportation systems.

Although this paper offers a more robust evaluation of bikeshare supply, it has limitations. First, in the study, bikeshare station capacity was assumed to be an adequate measure of bikeshare station supply. While this gives a more accurate sense of bikeshare supply than just the existence of a bikeshare station, as this paper has demonstrated, it does not reflect bicycle rebalancing efforts. Because of travel patterns, bikes can end up concentrated in some areas (Fishman et al., 2013), furthering inequality concerns, meaning rebalancing is a key equity activity. Consequently, a more accurate but more complicated evaluation would incorporate rebalancing throughout the day into the supply calculations. Second, the demographics of census block groups do not necessarily translate to the demographics of bikeshare users, especially as users many times do not look like the typical resident. This might indicate that the presence of bikeshare might sometimes not be enough, that there may be more than just physical barriers to access. Consequently, this work could be complemented by research that focuses more on demand equity (e.g., (Grasso et al., 2020)).

In addition to addressing these limitations, there are several avenues for future work. First, as electric bikes are becoming more ubiquitous, this type of evaluation could incorporate multiple types of bike power in the analysis. Second, while this paper focused on geographic equity, the literature review demonstrated there is also a need to look at bikeshare equity across programs. Third, this analysis could be repeated to see how equity varies over time with the potential to evaluate the effects of the COVID-19 pandemic on bikeshare. Fourth, while this paper has provided some evidence of a tradeoff between economic feasibility and equity in docked bikeshare programs, more research needs to be done in this area. Finally, due to the relative simplicity and accessibility of these methods, there is an opportunity to incorporate these methods into bikeshare siting decisions made by municipalities.

Footnotes

Acknowledgements

The author would like to thank Ralph Buehler and three anonymous reviewers for their insightful feedback.

Author Contributions

The author confirms sole responsibility for the following: study conception and design, data collection, analysis and interpretation of results, and manuscript preparation.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, or publication of this article.

ORCID iD

Xavier Harmony

Notes

Author Biography

Xavier Harmony is currently a PhD candidate at Virginia Tech where his research focuses on transportation policy and politics. Xavier’s expertise and research interests include urban policy and politics, transportation equity, transit planning, and transportation funding and governance.

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