Observed Patterns of Free-Floating Car-Sharing Use

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Worldwide, a breadth of policies are being implemented to mitigate these externalities, including congestion pricing (Anas and Lindsey, 2011;Börjesson et al., 2012), subsidies for electric vehicle purchases (Rapson and Muehlegger, 2021), or low-emission zones in cities (Galdon-Sanchez et al., 2022;Börjesson et al., 2021), among others.Reliance on these policies is expected to grow as countries seek to comply with their commitments to achieve net-zero emissions by 2050 (European Comission, 2020; U.S. DoS and EOP, 2021).To improve their effectiveness, we still need a deeper understanding of the benefits and costs of the various policy options.For equity purposes, we must also understand who benefits and who is harmed by those policies.Significant headway has been made in some fronts (Parry, 2002), yet little is known about the potential impacts of some rapidly proliferating technologies.This study contributes in this direction by analyzing the characteristics of users and usage patterns of one such technology, free-floating carsharing (FFCS).
In part thanks to advances in communications and tracking technologies, as well as the widespread adoption of smartphones, companies are now able to rent cars by the minute, at rates ranging from approximately 0.19 e/min to 0.31 e/min. 1 In earlier stages of the deployment of these services, users were required to drop off the vehicles at specific locations, or at charging stations.However, in recent years, there has been a rapid growth of demand for FFCS services allowing users to pick up the vehicle and drop it off at any place within the service area of the rental company (Ampudia-Renuncio et al., 2020a).
Importantly, the companies providing these services often do so with electric vehicles.Therefore, FFCS can potentially affect congestion and environmental externalities in opposing directions, depending on which mode of transport it is substituting.On the one hand, FFCS may alleviate urban congestion and pollution through the extensive and intensive margins, i.e., if they reduce car ownership (car shedding) or the number of trips with private polluting cars (Bucsky and Juhász, 2022).This possibility is supported by the fact that shared vehicles are mostly electric and have much higher utilization rates than private vehicles (Habibi et al., 2017).On the other hand, car-sharing may increase congestion if used as a substitute for public transport, walking, or cycling (Machado et al., 2018).Whether one effect or the other dominates is an empirical question related to the usage patterns of FFCS.
As a starting point for shedding light on the welfare effects of FFCS, this study provides a comprehensive description of car-sharing usage patterns, seasonality of use, users' incomes, and primary usage purposes.In particular, we investigate the correlations between the variables of interest without claiming causation.While most of the early literature on car-sharing has focused on German cities,2 , or relied mostly on survey data (Amirnazmiafshar and Diana, 2022;Müller et al., 2017;Schmöller et al., 2015;Kopp et al., 2015), in this paper, we provide new evidence based on thousands of observed trips in the city of Madrid.According to surveys across several European and North-American cities (Sprei et al., 2019;Habibi et al., 2017), Madrid had the highest FFCS utilization rate (between 17% and 21.6% of the time when cars can be potentially driven per day).
Additionally, together with Amsterdam, Madrid is one of the only cities in Europe where the FFCS fleet is fully electric (Ampudia-Renuncio et al., 2020a).
One of the strengths of this study is that it combines a rich set of data sources.
Importantly, we have access to a unique proprietary database of the universe of carsharing trips (more than 1,500,000) carried out in 2019 by one of the leading FFCS companies operating in Madrid. 3To correlate car-sharing usage patterns with socio-demographic characteristics, we use neighborhood-level data on population, income, car ownership, public transport network, and parking availability data.We also analyze daily road traffic data, comparing it against the seasonality of car-sharing trips.
Our main data set contains precise geo-referenced data on the car-sharing trip timing, origin, and destination but lacks information on the customers' demographics.In particular, while we can track users through unique identifiers, we do not observe where they live.
Hence, we have developed a strategy to impute users' neighborhood of residence based on repeated trips from and to the same destination during commuting times.Our approach constitutes an improvement relative to the previous literature, which was restricted to analyzing the characteristics of the place of origin/destination of trips (Schmöller et al., 2015;Ampudia-Renuncio et al., 2020a) and therefore abstracted away from users' place of residence.Besides imputing members' residences, we also exploit the hourly frequency of repeated origins and destinations to infer the trips' purposes, as either commute or leisure.These strategies allow us to match the trip data and the socio-demographics to study the determinants of car-sharing usage and the differences across income groups.
We obtain meaningful insights into the usage patterns and characteristics of the FFCS users.First, we find that car-sharing users mostly live in middle-and high-income neighborhoods.This finding is partly driven by the characteristics of the service area chosen by the FFCS company (Figure 1), revealing that FFCS companies expect to have greater demand in higher-income areas.Hence, lower-income neighborhoods do not have access to FFCS, which is a strong force toward a positive correlation between neighborhood income and car-sharing use.Usage intensity in the covered neighborhoods provides a different picture, as the most loyal users tend to live in middle-income neighborhoods, i.e., conditionally on having access to FFCS, there is a negative correlation between neighborhood income and the frequency of car-sharing use.
Based on the timing of use, we also provide evidence on the purposes of car-sharing trips.We are able to classify almost 536 thousand commuting trips, and 386 thousand leisure trips, allowing us to explore heterogeneity along these dimensions.For example, we find that income is positively correlated with commuting trips but negatively correlated with leisure trips.
Since most loyal customers live in neighborhoods with higher car ownership rates and costs depended exclusively on the trip duration.There was no price discrimination across users and no rebates for frequent users.Notes: The figure presents the study area of this paper and the coverage area of the car-sharing service, i.e., the area in which customers can start or end a trip.Users are allowed to drive outside the coverage area and leave the car in standby mode if they need to make a stop outside the coverage area.All territorial units represented are neighborhoods inside Madrid Municipality, except for the darker shaded units: Alcobendas, Coslada, Pozuelo de Alarcón, and San Sebastian de los Reyes municipalities.
fewer public transport options, our analysis suggests that these customers use the service to complement public transport.If car-sharing members are car owners who prefer to leave their car at home, or even eventually sell it, FFCS would imply an overall reduction of vehicles in the city and, consequently, reduced use of parking space, decreased road traffic, and improved air quality.
Additionally, we find that the seasonality of car-sharing trips closely matches the trends of other motorized vehicles, although car-sharing usage peaks slightly earlier.
Moreover, while road traffic decreases during the summer months, the number of carsharing trips increases in the months of July and September.These patterns suggest that FFCS contributes to smoothing overall traffic and, thus, reducing congestion in the city.Importantly, during summer months, usage by the highest-income customers decreases substantially.Car-sharing service is mostly used during workdays, particularly on Fridays.During weekends, trips are less frequent but longer.Overall, car-sharing trips are generally short, both regarding duration and distance.
Finally, we implement gravity-type regression specifications to uncover potential frictions or facilitators for adopting car-sharing across the city.This analysis is performed at the level of "commuting zones" in Madrid.We observe nearly 500 commuting zones within the car-sharing company's area, corresponding to about 250 thousand origin/destination pairs (or dyads).Our results suggest that the likelihood of taking a car-sharing trip decreases with the distance between origin and destination, possibly due to the high costs associated with long car-sharing trips.Conversely, the likelihood of car-sharing is higher for origin/destination dyads poorly connected by public transit (i.e., dyads with long expected travel times by public transit).This finding again points to the complementarity between FFCS car-sharing and public transport.

Data Sources
Table 1 provides a summary of the main variables used in this study, including sample sizes, and data sources.We describe each data source in detail below.

Free-floating car-sharing trips
We use the universe of car-sharing trips made through one of the leading companies operating in Madrid during 2019.This database, which the company provided directly to the authors, contains unique vehicle and customer IDs, the starting and ending time and location of each trip, and the duration and distance traveled.During the analyzed sample period, the company had a fleet of 656 operating electric vehicles, which virtually remained constant throughout the year 2019 (Figure A1).We excluded trips by company employees and focused only on trips made by customers.We exclude trips that last less than 2 minutes or more than 180 minutes.We further excluded observations for which the same member used the service more than 6 times on the same day. 44 These are outlier cases that may represent bugs in the recording of trip durations.

Demographics
In terms of demographics, we primarily use data on population and income, obtained from the Madrid City Council (AM, 2018c) and the National Statistics Institute (INE, 2018a,b).This entails combining data at different spatial aggregation levels.For the city of Madrid, we obtain neighborhood-level demographics for its 131 neighborhoods.
We also collect municipality-level data for the other municipalities that are part of the Community of Madrid (metropolitan area).We also collect data on other demographic variables, such as gender and age.However, we find no significant heterogeneity along those dimensions, such that they are omitted from the remainder of this paper.Note that we do not directly observe demographics of the car-sharing users, which limits the scope of our heterogeneity analysis.Regardless, in Section 3 we present a proposal for imputing demographics. 5

Mobility-related data
Another key data source is Madrid's Mobility Survey (Encuesta Domiciliaria de Movilidad, CRTM, 2018b).This is a recall survey of over 58 thousand households, aiming to assess mobility patterns in the Community of Madrid during working days. 6The mobility survey includes information on the number of cars per household, which we use to proxy car ownership in each neighborhood.Moreover, using trip data from the mobility survey, we build a measure of the adequacy of the public transport network to assess the degree of complementary and substitutability between the car-sharing service and public transport (see Section 3 for further details).
We also downloaded data from Madrid's Regional Transport Consortium (Consorcio Regional de Transportes de Madrid, CRTM, 2018a) containing the geographical coordinate of each metro, train, and bus station in the Madrid Autonomous Community, to measure neighborhood-level density of public transport stations in Madrid and neighboring municipalities.The Consortium also provides detailed georeferenced information about all public transit stops and schedules in GTFS format (General Transit Feed Spec-5 Previous studies, mostly relying on survey data, found that car-sharing users are predominately male, high-income, and young (Amirnazmiafshar and Diana, 2022;Vine and Polak, 2020).Similarly, Schmöller et al. (2015) argue that car-sharing services can be especially appealing to young adults, since owning a private car is becoming less valuable now, compared to the past. 6Respondents were asked to describe all of their trips from the day prior to the interview.Data are representative for trips taken from Monday to Thursday.ification). 7We use these to estimate public transit travel times, which are later used in our gravity-type specifications (Section 3.5).
To study the influence of parking availability, we use data from the regulated parking service, obtained in Madrid City Council's open data portal (AM, 2018b).In Madrid, the parking policy was designed to contribute to the air quality improvement objectives.
The Regulated Parking Service (Servicio de Estacionamiento Regulado, SER) covers the more congested areas of the city and differentiates parking fares according to vehicle technology and the daily pollution levels.The City Council establishes base prices for parking in each location of the city and provides discounts for low-emission vehicles.
In high pollution periods, the base price increases, as an incentive to opt for public transport or low-emission travel modes.Importantly, electric vehicles receive a 100% discount, being exempted from parking fares.This exemption applies to car-sharing services, thus, car-sharing members are allowed to park for free and without restrictions in Madrid Municipality.The current SER coverage area was established in 2021 and extends through the so-called Central Almond.However, during our year of analysis, the coverage area was considerably narrower.In 2018, SER comprised 47 neighborhoods in Madrid Municipality, with a total of 153,082 parking slots.We collected data on the number of SER parking slots in each neighborhood, in 2018.To normalize the number of parking slots, we further downloaded data on the number of cars registered in each neighborhood.Figure A2 portrays the spatial distribution of SER parking slots, normalized by the number of cars.
Finally, we rely on daily road traffic data in Madrid (AM, 2018a) and compare it against the seasonality of car-sharing trips.

Imputing users' residences
In the absence of demographic information on each car-sharing member, we established a strategy to impute users' potential neighborhood of residence.Using this methodology, we are able to study socioeconomic determinants of car-sharing usage.We can do this thanks to access to precise geo-referenced data on the trip timing, origin, and desti-nation, as well as unique user identifiers.
Our strategy exploits the frequency with which the same member starts and ends a trip in the same location.To achieve our preferred specification, we explored distinct frequencies, starting times, and days of the week.Notably, we explored trips for which the morning origin (with time intervals ranging from 6 am to 12 pm) and evening (from 1 pm to 8 pm) or night destination (from 9 pm to 5 am) coincide for at least 5 and 10 times. 8The criteria used are presented in Table 2. Using a frequency of 5,9 we were able to identify the residence of 12,143 members (8.5% of the total number of users), which sum 511,070 trips (34.7% of the total number of trips).This sub-sample was used to infer socio-demographic determinants of car-sharing members.For this purpose, we used data on population and net annual income for all neighborhoods and municipalities of analysis, as explained in Section 2.2.In all regressions incorporating demographics, we restrict our analyses to this sub-sample of users with identified residence, always excluding the neighborhoods where the main train stations and the airport are located (Atocha, Castilla, and Aeropuerto), which also have the smallest population size in our study area (1100-1800 inhabitants).The trips in these neighborhoods are most likely for multi-modal purposes, not necessarily conducted by residents.
Our approach constitutes an improvement relative to the previous literature, which was restricted to analyzing the characteristics of the place of origin/destination of trips (Schmöller et al., 2015;Ampudia-Renuncio et al., 2020a) and therefore abstracted away from users' place of residence.

Measure of customer loyalty
We construct a measure of customer loyalty that is intended to capture the number of days that a given customer uses the FFCS service within a full year.We use the following formula:  6:00am -9:59am  1:00pm -8:59pm  Any day  5,964  1,918  6:00am -9:59am  9:00pm -5:59am Work days  734  178  6:00am -9:59am  9:00pm -5:59am  Any day  1,336  198  10:00am -12:59pm 1:00pm -8:59pm Work days  1,090  580  6:00am -9:59am  5:00pm -5:59am  Weekend  76  10  10:00am -12:59pm 5:00pm -5 where L i is the measure of loyalty for customer i.The count N used i is the number of days that customer i used the service during the whole year of 2019.The count N samp i is the total number of days elapsed between the first date when customer i used the service in 2019 and the last day of the year.The fraction on the right-hand side thus serves as a normalization that takes into account that some customers became aware and started using the FFCS service at different points within the year.

Inferring the purpose of trips
We exploit the frequency of repeated origins and destinations to categorize trips into two purposes: commuting and leisure.Firstly, we considered all trips occurring during the week, where the member leaves their residence in the morning (from 6:00 am to 9:59 am), or returns to their residence at lunchtime (2:00 pm to 3:59 pm) or afternoon (6:00 pm to 8:59 pm, excluding Fridays) as commuting trips.We exclude trips happening between 6 pm and 9 pm on Fridays because many Spaniards do not work on Friday afternoons.With regards to leisure, we considered all trips where members leave/return to their residences during the weekend.
To cross this information with demographic characteristics (in particular, income), we need to restrict the analysis to our sub-sample of members with imputed residence.
Nevertheless, we are aware that the criteria that we established to impute members' residence strongly influences the determined trip purpose.Hence, in Table 3, we include descriptive statistics for both the full sample and the sub-sample, to compare the per-centage of trips classified as commuting and leisure.For the full sample, we considered any trip happening in the aforementioned time intervals, regardless of the trip's origin and destination.In Table 3, we show the fraction of trips according to their purpose, comparing the sample of all customers versus the sub-sample of customers with identified residence.We find that the sub-sample with identified residence is relatively more likely to represent commuting trips.This is expected given that both our strategies for imputing residence and classifying commuting trips partially rely on observing customers who take a trip in the morning and return to the same location in the evening, for example.

Measuring the availability of public transport
We measure the density of public transport stations in each neighborhood and municipality using the geographical data from Madrid Regional Transport Consortium.However, since the number of stations is not informative of the degree of connection between different destinations, we created a measure of the adequacy of the public transport network.For this purpose, we use the Mobility Survey of 2018 (Encuesta Domiciliaria de Movilidad, EDM ), the most recent mobility survey available for Madrid, which comprises a questionnaire that aims to assess mobility patterns during weekdays.To build our measure of the adequacy of the public transport network, we make use of a question in the EDM 2018 that asks respondents which travel mode they choose for a particular trip.If the chosen travel mode was not public transport, EDM proceeds to ask the reason for not picking a public transport alternative.Among the possible answers, we are interested in two: (i) improper connection and (ii) nonexistence of a public transport option.Ex-ploiting this question from the mobility survey, we create an index for inadequate public transport network, which measures the percentage of trips for which the respondents declare to use a car because there is no public transport alternative (improper connection or nonexistence), out of the total number of trips made by car, to or from their neighborhood of residence.Finally, we aggregate the microdata from EDM 2018 to obtain an average measure for each of the 95 geographical units where we identified car-sharing members.

Gravity model
We estimate gravity-type specifications to provide insight into potential frictions or facilitators of car-sharing trips across the city.Note that gravity specifications are typically based on linked origin/destination pairs or "dyads."In our case, working with specific origin/destination points is computationally intractable as it results in too many unique dyads for which a single trip is observed.Rather, we aggregate the car-sharing trip data to the level of Madrid's commuting zones. 10We focus on the commuting zones within the car-sharing company's coverage area for which we have data, corresponding to about 500 commuting zones and 250 thousand origin/destination dyads.
Regarding frictions or facilitators, we consider two factors: (i) geographical distance between origins/destinations and (ii) the travel time between origins/destinations expected under Madrid's current public transit system.For the former, we take the straightline distance between the centroids of the commuting zones.For the latter, we rely on data from Madrid's Regional Transport Consortium (CRTM, 2018a).In particular, we take the georeferenced data (in GTFS format) from all stops and schedules of metro, train, and bus routes across the Community. 11These serve as inputs for the r5r R package, which identifies optimal public transit itineraries and associated travel times between specified origin/destination pairs (Pereira et al., 2021).We focus on the optimal travel times, i.e., we compute how long a trip would take between each of the 250 thousand relevant origin/destination pairs in our sample by public transit.The r5r router incorporates factors such as waiting time required when switching transit lines, for example, 10 These zones were established by Madrid's Regional Transport Consortium (CRTM, 2018a).The zones are at a level of aggregation typically smaller than neighborhoods but larger than census tracts.More details at https://datos.crtm.es/datasets/crtm::zonificacionzt1259/about.
11 The currently available GTFS public transit data for Madrid is representative of the year 2022.We use that as a proxy of public transit availability in 2018.
and accommodates multi-modal trips (details in Pereira et al., 2021).The router requires choosing a "representative" starting date/hour for the trips (as optimal itineraries may change depending on the starting hour).We choose a non-holiday Wednesday at 10 am for our main specification, and we show that our results are not sensitive to this choice. 12he outcome variable for this analysis is the count of car-sharing trips we observed between each dyad in our sample.That implies that we aggregate the trips we observe to the dyad level, considering all of the observations for 2019.Specifically, we implement the following regression: where and β 2 , which capture how the frequency of car-sharing trips is affected by dyad distances and optimal public transit travel times, respectively.
Note that our outcome of interest is a count variable, which may also include some zeroes.For this reason, following recommendations from the trade literature (e.g., Silva and Tenreyro, 2006;Buggle et al., 2023), we estimate the specification (1) through poisson pseudo-maximum-likelihood (PPML).Specifically, we use the ppmlhdfe package by Correia et al. (2020).We cluster standard errors at the dyad level.We also implement variants of specification (1), restricting the sample to either commuting or leisure trips or for observations at different time windows throughout the day.

Geographical distribution of car-sharing members
Based on our approach to infer the neighborhood of residence of each user in our sample, we explore the socio-demographic determinants of car-sharing.
In Figure 2  Second, there is a high concentration of users in the northern peripheral neighborhoods of Madrid.Conversely, the Central District exhibits the lowest car-sharing member density.
According to our methodology, the neighborhood with the highest member density is Atocha (3.65%).However, this density might be overestimated since that neighborhood houses Madrid's central train station.It is thus plausible that many trips that start or end in Atocha are multi-modal.For example, users might take a train to Atocha and, from there, take the car-sharing service to their final destination.Thus, as explained in Section 3, we exclude Atocha from our analyses.Likewise, we exclude the Castilla and Aeropuerto neighborhoods, which are almost entirely occupied by the Chamartín train station and Madrid-Barajas Airport.According to our methodology, the Castilla and Aeropuerto neighborhoods would be the 5 th and 7 th areas with the highest member density (1.66% and 1.52%, respectively).

Income distribution
Prior literature suggests that FFCS in Madrid is about three times more expensive than public transport when considering single-trip fares (Ampudia-Renuncio et al.,  2020b).The availability of monthly passes for public transportation increases the cost difference.However, car-sharing is cheaper than ride-hailing and, depending on the usage intensity, car-sharing can be a more affordable option than owning a car.The implication of these cost differences is that car-sharing might not be accessible or attractive to some income groups while appealing to others.
In this section, we provide insights into how income relates to car-sharing usage in the city of Madrid.Having identified the users' residence location through the car-sharing usage patterns, we then impute their income based on neighborhood-level data (see Table 1).This shows that the average annual net income of car-sharing users in our sample is close to e20 thousand, which is substantially higher than the average income per capita for the entire municipality of Madrid (e16,700) (INE, 2018b).13This is in line with the fact that the car-sharing service area (Figure 1) excludes some of the lowest-income neighborhoods in the city.Our findings are consistent with prior literature showing that car-sharing users tend to have an above-average income (Amirnazmiafshar and Diana, 2022;Caulfield and Kehoe, 2021).
Although our data suggests a positive correlation between car-sharing member density and income, we would expect to find a negative correlation between member loyalty and income, given that, as discussed in Section 4.1, neighborhoods with a higher percentage of car-sharing customers seem to have a lower loyalty to the service.We formally test these relationships with regressions as follows: where Y i is the outcome of interest (customer density or loyalty) for the unit of analysis i; the unit of analysis is the neighborhood for the density variable, and the customer for the loyalty variable; α is a regression constant; the indicators ✶[i ∈ income quartile g] are equal to one when i belongs to a given income quartile, zero otherwise; note that the 1st quartile (income from e8,000 -e14,500) is the omitted comparison group; and ε i is an idiosyncratic error term.The coefficients β g thus capture how density or loyalty changes depending on the income quantile of neighborhoods or customers.
Table 4 shows the regression estimates of equation ( 2).Column (1) shows that member density in the highest-income neighborhoods is about 0.72% higher than in the lowestincome neighborhoods.Conversely, column (2) suggests that higher-income customers are less loyal, i.e., they use the service almost 6.6 days less than lower-income customers.This is in line with the correlations reported in Figures 3 and 4, panel (a).While higherincome neighborhoods tend to have a higher proportion of car-sharing users, the most loyal members are located in the lowest-income neighborhoods in our study area (which as already discussed, are middle-income neighborhoods when considering the city as a whole).Accordingly, results presented in the appendix (see Table A1) show that, for our sample, income is negatively correlated with the probability of a car-sharing trip.The above linear regressions are restricted to the sub-sample of car-sharing users with identified residence, excluding those living in Atocha, Aeropuerto and Castilla neighborhoods.The regressions provide correlations between car sharing member density and loyalty with the neighborhood income quartiles, using as base category the lowest quartile: e8,000 -e14,500.Column (1) uses neighborhood observations, while in columns ( 2) -( 4) each observation represents a customer.The outcome variable in column (1) measures the percentage of car-sharing users in a neighborhood, i.e. total number of users divided by total resident population.Columns (2) to (4) provide different measures of member loyalty.The dependent variable in column (2) measures the total number of days a customer used the car-sharing service in 2019, while column (3) measures the number of times she/he used the service.In column (4), the outcome variable measures the weighted number of days used, given by the number of days the customer used the car-sharing service, weighted by the total number of days left in 2019 since the first day they used the service, multiplied by total number of days in a year.Notes: The scatter plots correlate car-sharing member loyalty with two neighborhood attributes.Member loyalty is measured as the weighted average number of days the members living in the neighborhood used the service in 2019.This loyalty measure is computed by taking the total number of days each customer used the service, weighted by the total number of days left in 2019 since they first used the service, and multiplied by the total number of days in a year.Panel (a) correlates member loyalty with the average annual net income per capita (INE, 2018b; AM, 2018c), while panel (b) provides the correlation with the average number of cars per household (CRTM, 2018b) in each neighborhood of the study area.We exclude the neighborhoods of Atocha and Castilla (where the main train stations are), and Aeropuerto.We also exclude the Pavones neighborhood, which exhibits outlier loyalty above 100.

Effect on mobility patterns
One crucial factor to consider when assessing the implications of FFCS in cities is the impact of the car-sharing service on mobility patterns.For example, fully electric FFCS cars could accelerate the decarbonization of cities through car shedding.In this scenario, the majority of car-sharing members would be car owners considering the possibility of selling their vehicle and using the car-sharing service as an alternative (Jochem et al., 2020;Becker et al., 2018). 14This may be particularly likely for households owning more than one car.Another potential mechanism is that drivers may switch their polluting vehicle for an electric one following a positive car-sharing experience.In that case, even when shedding is limited, car-sharing may contribute to reducing pollution by accelerating the electrification of the fleet.Moreover, FFCS might prevent future vehicle purchases if drivers consider that the FFCS service already fulfills their needs.
Besides the effect on car ownership, however, it is essential to analyze the relationship between the use of car-sharing services and public transport.On the one hand, if users consider them to be substitutes, FFCS could reduce the use of collective public transport, 14 According to a survey conducted among car-sharing users in 11 European cities (Jochem et al., 2020), the share of survey participants selling a car after trying the service ranged from 3.6% to 16.0%, with the lowest value being found in Madrid.However, compared to station-based car-sharing, FFCS members are less likely to decrease vehicle ownership, as these users see the FFCS service as a complement rather than a replacement for their private car (Amirnazmiafshar and Diana, 2022).
leading to an overall increase in the number of cars in the city.For instance, users may see FFCS and public transportation as substitutes for short trips between nearby areas, for which the travel time by public transport is generally higher than by car (Ampudia-Renuncio et al., 2020b).However, when considering the time required to reach the vehicle and to find a parking slot, the travel time difference between FFCS and public transport may not be significant (Sprei et al., 2019).Indeed, this outcome is unlikely, according to prior literature (Habibi et al., 2017;Becker et al., 2018;Tyndall, 2019).
On the other hand, FFCS could be a complement to public transport, particularly in areas where the public transport network is scarce (Vine and Polak, 2020).In this case, FFCS would prevent the use of private vehicles, contributing to reduced land occupancy and lowering emissions.However, even where car-sharing complements incomplete public transport networks, FFCS services must be implemented where alternative transport modes exist, given the uncertainty regarding the availability of cars for the return trip (Ampudia-Renuncio et al., 2020a).This is another important source of complementarity.
Building on data from several sources, we provide insights into which of the above mechanisms is more likely to dominate in Madrid.We relate FFCS usage with car ownership and the public transport network in the city.To measure the availability of public transport services, we first focus on the density of metro, train, and bus stations/stops, i.e., the number of stations/stops per Km 2 in each neighborhood.Since more stations might not imply a proper connection between different destinations, we further created a measure of public transport adequacy based on Madrid's Mobility Survey (see Section 3).
We assess the correlation between car-sharing usage and mobility patterns through the following regression: where Y i is the outcome of interest (customer density) for neighborhood i; γ is a regression constant; X is a vector of explanatory variables; and ε i is an idiosyncratic error term.
The coefficients θ i capture how car-sharing member density changes according to neighborhood characteristics and amenities, notably, annual income per capita, car ownership rate, and adequacy of the public transport network.
Table 5 provides the results of estimating the above regression.Firstly, neighborhoods with higher car ownership rates tend to have a higher percentage of car-sharing members (see also panel (b) of Figure 3).In particular, columns (1) and ( 5) suggest that an additional car per household is associated with a 0.56% increase in member density.
Since these regressions already control for neighborhood income, these results suggest that car-sharing users are car owners who substitute their private vehicle for a shared one.In column (2), we test for the influence of the public transport network on carsharing usage.The estimates indicate that neighborhoods with fewer metro and bus stops per Km 2 have a higher density of car-sharing members.Notes: The linear regressions use neighborhood observations.Columns (1) to ( 5) are restricted to the sub-sample of car-sharing users with identified residence, excluding those living in Atocha, Aeropuerto and Castilla neighborhoods.The outcome variable in columns (1) to ( 5) measures the neighborhood member density, i.e., the percentage of car-sharing users in each neighborhood, out of the total resident population.These regressions provide correlations between car-sharing membership and the characteristics and amenities of the neighborhood.The dependent variable in column (6) measures the total number of trips ending in each neighborhood, weighted by the resident population, while the independent variable is given by the number of parking slots per car.These parking slots are integrated within the Regulated Parking Service (SER), which, in 2018, only covered 48 neighborhoods in the Municipality of Madrid.Regression (6) provides the correlation between the number of trips and parking availability at the destination.and more complaints of inadequate public transport network have the most loyal customers.However, these effects are muted once we control for car ownership, which is negatively correlated with public transport availability.Overall, these results suggest that car-sharing might be used in Madrid as a substitute for private vehicles and a com-plement to public transport.In fact, the negative correlation between car ownership and the availability of public transport could indicate that residents in areas with poorer public transport networks own a car to counter insufficient public transport options.
Our findings could imply that FFCS services decrease commuting/travel times, improve connections, and promote car shedding.
Table A3 in the appendix shows the results of estimating the original equation ( 3) for all neighborhoods in Madrid municipality.In neighborhoods where we did not identify car-sharing members, we impute a member density of zero.Our results are robust to this sample modification.
For the complete decarbonization of the city, preference should be given to more sustainable travel modes, such as walking, cycling, and public transport.The first two modes are not feasible for long distances, and expanding the public transport network is generally costly and requires a long implementation period.In this sense, electric freefloating car-sharing services might be an optimal solution to complement the existing public transport network.It is important to stress that these shared vehicles are considerably more efficient than private cars.Firstly, the FFCS fleet in Madrid is fully electric.
Secondly, FFCS provides more efficient use of the scarce space in cities, particularly parking.On average, a private car is parked 23 hours a day, translating into a usage rate of 4% (Nagler, 2021).By being shared among several individuals, FFCS vehicles have a higher utilization rate.In our data, vehicles' average usage rate was 23%, measured by the total number of hours each car was used, divided by the maximum number of hours it could have been used.Habibi et al. (2017), andSprei et al. (2019), which studied FFCS in several European and North-American cities, concluded that Madrid had the highest usage rate of all cities analyzed.

Seasonality and purpose of car-sharing usage
Figure 5 shows the temporal distribution of car-sharing trips.For graphs on the lefthand side, we use the full sample of car-sharing trips in 2019.Right-hand side graphs are for a restricted sample of trips for which we identified users' residences, such that we can correlate seasonality patterns with demographic characteristics (income).
For graphs on the left, we contrast the car-sharing trip seasonality with road traffic on the main highway (M-30) and in urban areas inside the municipality.We observe that the seasonality of car-sharing trips closely follows the pattern of other motorized vehicles in Madrid.We see a higher usage during peak hours (morning and afternoon) on weekdays (panel a).In Madrid, there is a third peak hour at lunchtime, between 2 pm and 5 pm, when many stores close (Ampudia-Renuncio et al., 2020b;Habibi et al., 2017).Nonetheless, we notice that the morning peak for car-sharing users happens earlier, between 6 am and 7 am, with the number of car-sharing trips dropping significantly during the usual morning peak, between 8 am and 9 am.This might suggest that car-sharing users avoid high congestion hours to avoid paying higher bills, since the car-sharing service is charged by the minute.Additionally, car-sharing trips exhibit a higher peak at lunchtime than road traffic.According to the graphs on the right, during both these peaks, most car-sharing members are above the medium income of all car-sharing users.
There are only two peaks at lunchtime and in the afternoon on weekends (panel b).
Similarly, the peaks for car-sharing users happen slightly earlier than usual road traffic.
Looking at the patterns by day of the week (panel c), we see higher usage of the car-sharing service on weekdays, particularly on Fridays.We also note that trips during the weekend are dominated by below-average income customers, while during weekdays, especially at peak hours, higher-income users are more prevalent.These figures suggest that higher-income customers use the service for commuting rather than leisure.This is in line with findings for Germany, where most free-floating car-sharing trips happen on Saturday, and the peak usage hours happen considerably later than those of private cars, particularly during the afternoon (Schmöller et al., 2015).The seasonality of car-sharing trips seems to be city-specific, especially when comparing workdays versus weekends (Sprei et al., 2019).
Regarding the distribution of trips throughout the year (panel d), July and September show more car-sharing usage.However, road traffic, which is relatively consistent throughout the year, sees a drop in these months, intensifying in August.Although we see the same drop in August for car-sharing trips, the reduction is much less pronounced, suggesting that tourists also use this service.A study in Berlin and Munich found a drop in car-sharing utilization between June and September, arguing that during these months, users opt for other travel modes, such as walking and cycling (Schmöller et al., 2015).The right-hand side graph of panel (d) is consistent with higher-income customers leaving the city during the summer for holidays.
To test the hypothesis that higher-income customers predominantly use the service to commute, we categorized trips according to their purpose, based on the frequency of usage at different times of the day and the week (see Section 3).With this specification, we could categorize 56% of the trips from members with an identified residence.Of those, 68.8% were commuting trips, while 31.2% had a leisure purpose.The regression estimates from Table 6 suggest that higher-income customers are more likely to take car-sharing trips to commute and less likely to use this service for leisure purposes.Notes: This table provides regressions results using linear probability models.For columns (1) to (3), the dependent variable is an indicator equal to 1 when a customer takes a car-sharing trip for commuting, and 0 otherwise.For columns (4) to ( 6) the dependent variable is equal to 1 for leisure trips, and 0 otherwise.The dependent variables are set to missing for all dates prior to the first usage date of a given customer.These variables therefore measures the probability of taking a car-sharing trip after trying the service for the first time in 2019.The sample is restricted to car-sharing users with identified residence, excluding those living in Atocha, Aeropuerto and Castilla neighborhoods.
1 Weighted number of days a customer used the car-sharing service in 2019.
According to Becker et al. (2017), who focus on the case of Switzerland, "free-floating car-sharing is mainly used for discretionary trips, for which only substantially inferior public transportation alternatives are available."Schmöller et al. (2015) find that carsharing services in Berlin and Munich are used predominately for shopping and socialrecreational activities.In Vine and Polak (2020), the authors argue that the purpose of car-sharing usage differs according to car ownership status.Car owners are more likely to use the service for business purposes (for instance, meetings), while non-car owners use the service for shopping purposes.
Finally, Figure 6 represents the seasonality of trips according to their distance and duration.Car-sharing trips were generally short as a function of distance and travel time.The average figures were 23 minutes and 7 Km per trip (in line with previous studies, e.g., Ampudia-Renuncio et al., 2020b;Sprei et al., 2019).As expected, trips take longer during peak hours due to heavier road traffic.On weekends and Fridays, trips       are relatively longer in distance and time traveled.Additionally, over time, customers started to take longer trips (in terms of distance).

Gravity specifications
Tables 7 and 8 present results from the estimation of gravity-type models such as the one in equation ( 1).Table 7 is for baseline specifications.In the first column, we show results when only log distance is included as a friction variable, ignoring the availability of public transit.We find that car-sharing trips become less likely with increased distance between origin/destination pairs.The point estimate in our preferred specification, column (3), is −0.47.Given our Poisson specification, this coefficient needs to be transformed for ease of interpretation.For example, if the distance between origins/destinations were to double, then the number of car-sharing trips would drop by almost 28% [= exp(−0.47× log2) − 1].This result may be partly explained by the fact that the costs of car-sharing trips can also increase significantly with distance (as rentals are paid by the minute).Regarding the impact of public transit travel times, column (2) of Table 7 suggests a negative elasticity.However, this finding may be confounded by the effect of distances.
Column (3) is the preferred specification in that it estimates the elasticity of car-sharing with respect to public transit travel times while simultaneously controlling for the trip distance.In that case, the elasticity becomes positive, indicating that car-sharing is more likely between origins and destinations not well-connected through public transit.suggesting that car-sharing is relatively more likely in neighborhoods not well-connected through public transit options.
Columns (4) and ( 5) of Table 7 present the elasticities associated with commuting and leisure trips, respectively.Results are similar to those using the full sample, with only a slight decrease in the elasticities for the commuting trips.Finally, Table 8 shows the elasticities for different hours of the day.Point estimates are generally similar to those from the baseline specifications.The elasticities are only slightly lower for trips from 7 am to 9 am, which may be primarily considered commuting trips.This finding suggests that when there is an urgency to arrive at work on time during the early hours of the day, car-sharing customers are less sensitive to distance and public transit availability.

Conclusions
Free-Floating Car-Sharing (FFCS) services allow users to rent electric vehicles by the minute without restrictions on where to pick them up or drop them off within the company's service area.Beyond enlarging the choice set of mobility options, FFCS can reduce congestion and emissions in cities as they promote higher utilization rates of green vehicles.However, whether this potential is fully realized depends on the service's usage and substitution patterns.In this paper, we analyze these patterns through the lens of a unique dataset comprising the universe of FFCS rentals from a leading company in Madrid during 2019.
We contribute to answering the critical question of whether users view FFCS as a complement or substitute for public transport, cycling, or walking.If viewed as a complement, the increased demand for FFCS will promote public transport, cycling, or walking, reducing the use and sales of private vehicles and thus lowering congestion and local pollution.
On the contrary, if viewed as a substitute, FFCS will lower public transport use, and increase private vehicle use, thus increasing urban congestion.
Our analyses suggest that the most loyal customers, i.e., those who use the service more often, live in middle-income neighborhoods with relatively limited public transport options, making FFCS more appealing.These customers also typically live in areas with high pre-existing car ownership rates.Furthermore, with a gravity model, we find that an increase in public transit travel times leads to an increased likelihood of car-sharing trips.Conversely, car-sharing is less likely for longer trips, possibly due to the substantial associated costs (as rentals are paid by the minute).
Taken together, our results are better aligned with a hypothesis that FFCS is a substitute for private vehicles and a complement to public transport, especially in areas with limited public transport options.We also find that many customers take FFCS for leisure purposes.Therefore, even if these users are unable or unwilling to pay for car-sharing for their regular commutes, the service is still a valuable option for them for leisure trips when good public transport alternatives are scarce.
We also analyze how FFCS usage patterns compare with those of privately owned vehicles.We note that FFCS can contribute to reducing congestion even when used as substitutes for private vehicles, through a process of smoothing out the time at which drivers choose to start their trips.We find that the use of FFCS peaks earlier than overall traffic and is more broadly used during the summer months.This may be partly explained by the fact that FFCS users wish to avoid peak hours and congestion to reduce the trip cost.
Last but not least, FFCS can have distributional implications depending on who uses the service most frequently.We find that FFCS companies tend to cover mostly high-and middle-income neighborhoods, thus reducing the possibility for lower-income individuals to use the service.Indeed, the average annual net income of car-sharing users in our sample is close to e20,000, thus substantially higher than the average net income for the entire municipality of Madrid (e16,700).The expansion of FFCS on the intensive margin (within currently covered neighborhoods) may therefore exacerbate inequality in mobility options.
We conclude by acknowledging some limitations of this study.For example, the methodology used to impute users' neighborhoods of residence allows for insights not previously explored but might suffer from classification errors.In particular, there is classification uncertainty for FFCS users who live close to the borders of neighborhoods, as they may choose to park on either side of the border.Also, our methodology only allows classifying a fraction of all trips.This may limit the applicability of our findings to a broader population.We have shown that results depend on several variables that might be time and location-specific.For instance, usage depends on the availability of other modes of transport, and their monetary and time costs, which in turn depend on traffic conditions and the availability of parking.Therefore, some of our findings do not necessarily extend to other municipalities or other moments in time.Nevertheless, our framework can well be implemented within other contexts, to strengthen the body of evidence regarding the benefits and costs of FFCS.The loyalty measure, used as outcome variable, measures the weighted number of days a customer used the car-sharing service, given by the total number of days used, weighted by the total number of days left in 2019 since the first day they used the service, multiplied by the total number of days in a year.The regressions provide correlations between the characteristics and amenities of the neighborhood and the loyalty/intensity of usage of the resident customers.Note: The figure shows the frequency distribution of the weighted member loyalty measure, which is given by the number of days a customer used the car-sharing service, weighted by the total number of days left in 2019 since the first day he/she used the service, multiplied by the number of days in a year.The vertical lines give the average loyalty of the full sample of customers (14.7 days).The median loyalty is 6.8 days.Note: The figures show the geographical location of each metro, train, and bus station /stop in the municipalities of our study area (CRTM, 2018a).All territorial units correspond to neighborhoods inside Madrid Municipality, except for the dashed units: Alcobendas, Coslada, Pozuelo de Alarcón, and San Sebastian de los Reyes municipalities.

Figure 1 :
Figure 1: Coverage area of the car-sharing service, in 2019.
panel (a), we present car-sharing members' geographical distribution, normalized by the number of inhabitants living in the respective neighborhood.Figure2panel (b) portrays the average member loyalty per neighborhood.Panel (a) shows that car-sharing members are concentrated in two axes.First, we note a high concentration of users along the main road connecting the city from south to north (Paseo de la Castellana), around which significant businesses and tourist attractions are located.

Figure 2
Figure 2 panel (b) shows that more loyal car-sharing members live in the periphery of our study area, particularly in the four municipalities outside Madrid and the southeastern neighborhoods.A comparison of panels (a) and (b) reveals that neighborhoods with a higher percentage of car-sharing customers have a lower loyalty to the service, which might suggest that those customers use the service for distinct purposes.The sections below explore this further.

Figure 2 :
Figure 2: Geographical distribution of car-sharing members

Figure 3 :
Figure 3: Correlation plots between member density and neighborhood level attributes

Figure 4 :
Figure 4: Correlation plots between member loyalty and neighborhood level attributes

Figure 6 :
Figure 6: Seasonality of car-sharing trips, according to trip distance and duration

Figure A3 :
Figure A3: Number of car-sharing customers per month, in 2019.

Figure A4 :
Figure A4: Frequency distribution of member loyalty.

Table 2 :
Methodology to impute users' residence location Notes: The table summarizes the criteria used to identify FFCS users' residence location.The neighborhood/municipality of residence is identified if a user starts and/or ends their trips at least 5 times according to the criteria presented in the table.

Table 3 :
Identifying trip purpose -commuting or leisure

Table 5 :
Regression results for mobility patterns: neighborhood level (sub-sample with identified residence) * p < 0.1, * * p < 0.05, * * * p < 0.01 TableA2in the appendix shows the results of estimating equation (3) for a different outcome variable: member loyalty.In this specification, θ i captures changes in customer loyalty, controlling for neighborhood characteristics and amenities.The results support the conclusion that neighborhoods with fewer public transport stations/stops per Km 2

Table 6 :
Regression results for purpose of trip: trip level (sub-sample with identified residence) * p < 0.1, * * p < 0.05, * * * p < 0.01 ).The red lines in the righthand side figures represent the imputed average annual net income of the car-sharing members with identified residence, excluding those living in Atocha, Aeropuerto and Castilla neighborhoods (20,435e)(INE, 2018b; AM, 2018c).

Table 7 :
Results from baseline gravity-type specifications * p < 0.1, * * p < 0.05, * * * p < 0.01 Notes: Results from pseudo-maximum-likelihood specification relating the count of car-sharing trips with covariates of interest (equation (1)).All specifications control for origin and destination fixed effects.Standard errors are clustered at the dyad level.

Table 8 :
Results from gravity-type specifications for differnt hours of the day p < 0.1, * * p < 0.05, * * * p < 0.01 Notes: Results from pseudo-maximum-likelihood specification relating the count of car-sharing trips with covariates of interest.Specifications are variants of equation (1), restricting the sample to car-sharing trips at different hours of the day.All specifications control for origin and destination fixed effects.Standard errors are clustered at the dyad level.
The point estimate (0.0037) can be interpreted as follows: if travel time by public transit increases by 10 minutes, the likelihood of car-sharing trips increases by approximately 3.7% [= (exp(0.0037× 10) − 1].Overall, these results are consistent with prior sections, *

Table A2 :
Regression results for mobility patterns: customer level (sub-sample with identified residence) p < 0.1, * * p < 0.05, * * * p < 0.01 Note: The linear regressions use customer observations and are restricted to the sub-sample of car-sharing users with identified residence, excluding those living in Atocha, Aeropuerto and Castilla neighborhoods. *