Fueling Alternatives: Evidence from Naturalistic Driving Data

Transcription

1 Fueling Alternatives: Evidence from Naturalistic Driving Data Ashley Langer and Shaun McRae July 4, 2013 PRELIMINARY AND INCOMPLETE Abstract We use naturalistic driving data to analyze the refueling behavior of drivers. The data come from a year-long study in which drivers were provided with experimental vehicles to use for seven weeks. We use data logged during the experiment to identify the time and location of refueling stops. With this dataset, we estimate a discrete choice model for the driver s choice of refueling location. We show that drivers make a trade-off between the price of fuel and the time taken to deviate from their route to arrive at the chosen gas station. People differ in their willingness to travel out of their way to pay less for gasoline. Based on the estimated model of refueling demand, we simulate the willingness of drivers to adopt alternative fuel vehicles under different assumptions about the density of the alternative fueling network, and we use these results to understand the role of subsidies in encouraging alternative fuel vehicle adoption. We show that driver heterogeneity has important implications for the design of policies to promote alternatives to gasoline. Department of Economics, University of Arizona. alanger@ .arizona.edu Department of Economics, University of Michigan. sdmcrae@umich.edu. 1

2 1 Introduction Gasoline is the largest non-durable expenditure item for most households, comprising one sixth of consumer non-durable purchases. 1 It occupies a singular position in the public consciousness. When gasoline prices were high in 2008, 25 percent of households reported that these prices were the single most important problem facing the country. 2 As Yergin (1991) observed for the first oil crisis, No other price change had such visible, immediate, and visceral effects as that of gasoline. Consumer demand for gasoline also plays a major role in many academic and policy debates. The sensitivity of gasoline purchases to changes in price is a key parameter for much work in industrial organization, public finance, and environmental economics. Given the amount of attention paid to gasoline prices, there is remarkably little empirical research on how consumers shop for gasoline. Studies of gasoline demand use aggregate data, household survey data (which aggregates purchases over time), or station-level volumes. To our knowledge, no existing research uses repeated transaction-level information for individual drivers. Without this data it is difficult to analyze patterns in gasoline shopping behavior such as repeat purchases at a single station or willingness to go out of the way for a lower price. Given the high level of price salience in this market, it represents an ideal environment to test models of consumer behavior. This paper is the first to use naturalistic driving data to analyze the refueling behavior of drivers. The data come from a year-long study in which drivers were provided with experimental vehicles to use for about seven weeks. We use data logged during the experiment to identify the time and location of refueling stops. With this dataset, we estimate a discrete choice model for the driver s choice of refueling location. We show that drivers make a trade-off between the price of fuel and the distance of the deviation from their route to arrive at the chosen gas station. There is heterogeneity across drivers in their willingness to go out of their way to pay less for gasoline. Understanding how drivers make their refueling decisions is of great importance for explaining market structure in gasoline. Market power in retail gasoline markets is a major preoccupation for antitrust authorities. 3 Many models of firm behavior have been pro- 1 Bureau of Economic Analysis, Personal Consumption Expenditures by Type of Product (Table 2.4.5) for Gallup poll on June 9 12, Divestiture of retail gasoline stations was a requirement for the approval of mergers between major oil firms, including BP and Amoco ( and Exxon and 2

3 posed to explain observed patterns in gasoline prices such as asymmetric price responses or rockets-and-feathers (Borenstein et al., 1997), periodic cycling (Lewis, 2012), and spatial price dispersion. However, a severe limitation for testing these models is the absence of quantity data. A few authors use monthly station volumes combined with census-tract demographic data to estimate gasoline demand and analyze mergers between gasoline station owners (Manuszak, 2010; Houde, 2012). This level of temporal aggregation is less-thanperfect for studying a market in which many firms change their prices daily. Little is known about how drivers respond to these small frequent price changes. Heterogeneity across drivers in their willingness to go out of their way to save a few cents per gallon could explain much of the observed spatial price dispersion. A second reason for understanding fuel purchasing behavior is to model the willingness of consumers to drive vehicles that use alternatives to gasoline. Several different transportation fuels have been developed as alternatives, including ethanol, hydrogen, electricity, propane, and natural gas. However, all of these fuels suffer from two problems. The range of the vehicles (the maximum distance that can be travelled between fueling stops) is lower than the range of gasoline vehicles. 4 This problem is compounded by the limited availability of refueling locations. Using data on gasoline refueling, we can understand how drivers make the trade-off between lower fuel prices and greater distance, and how this trade-off might vary based on the amount of fuel remaining in their tank. The data used in this paper come from a year-long study conducted by the University of Michigan Transportation Research Institute (UMTRI) in which 117 randomly-selected drivers were provided experimental vehicles that included advanced crash-warning technology as well as monitoring equipment. During the experiment, detailed data from more than 210,000 miles of real-world driving were recorded. Drivers in the experiment were responsible for paying for their own gasoline during the 40 days that they drove the vehicle. By matching vehicle data to gas station locations, we identify over 700 refueling stops. Using daily stationlevel price data, we identify the price of gasoline at the station where the driver stopped as well as the price at nearby stations where the driver could have chosen to stop. With this dataset we estimate a discrete choice model for the driver s choice of refueling Mobil ( Since 2002 the Federal Trade Commission has tracked retail gasoline prices in 360 cities in order to identify possible anticompetitive activity (http: //ftc.gov/ftc/oilgas/gas_price.htm). 4 No alternative fuel has greater energy content per unit volume than gasoline and diesel. Therefore, the only way for the range of an alternative fuel vehicle to equal that of a gasoline vehicle is devote greater space to fuel storage. Although natural gas and hydrogen have greater energy content per unit weight than gasoline, they require more storage space ( 3

4 location. We show that drivers make a trade-off between the price of fuel and the distance (or time) of the deviation from their route to arrive at the chosen gas station. People are willing to go further out of their way in order to pay less for gasoline. As in Houde (2012), these results give an estimated value of driver s time. However, unlike that paper, we have data on trips by individual drivers and so are able to demonstrate the heterogeneity in the estimated value of time across groups. We show that older drivers have a low implied value of time while drivers from high-income neighborhoods have the highest implied value of time. This heterogeneity has important implications for the design of alternative fuel policies. Drivers with characteristics that suggest a greater propensity to purchase an alternative fuel vehicle are also the drivers that have a high value of time. This implies that they would be unwilling to deviate from their normal route in order to refuel their vehicle, even if the alternative fuel is significantly cheaper than gasoline. We illustrate this using the estimates from the discrete choice model to simulate demand for a hypothetical alternative to gasoline, under policies that target different combinations of fuel price and fuel availability. Our paper contributes to three distinct literatures. The first of these is the marketing and industrial organization literature on dynamic demand and stockpiling behavior for nondurable goods. Hendel and Nevo (2006) estimate a dynamic model of demand for laundry detergent in which households not only choose which brand to buy, but also choose the quantity to buy based on the tradeoff between lower prices and higher inventory costs. Erdem et al. (2003) estimate a similar dynamic model of demand for ketchup. Like ketchup and laundry detergent, purchasers of gasoline do not immediately consume what they buy. Instead, they store it (in this case, in the fuel tank of their car) for future consumption. An advantage of our setting compared to the previous papers is that we not only observe purchases, but also consumption and inventory of the product. Our static model of brand choice is considerably simpler because gasoline is essentially a homogeneous product: the only choice for the driver is which store to go to, not the brand or size to buy within a store. Second, this paper contributes to the large literature on gasoline demand. Many papers in this literature use aggregate data at a national or state level. 5 Apart from papers using aggregate data, other research estimates household-level demand for gasoline using data from household surveys. 6 All of these papers necessarily involve a high level of aggregation, either 5 For example, Hughes et al. (2006) use a monthly time-series of national gasoline shipments to estimate the price elasticity of gasoline demand for two periods, and They show that demand is significantly more inelastic in the more recent period. 6 Wadud et al. (2010) use household data from the Consumer Expenditure Survey to estimate price elasticities for groups with different characteristics. Urban households with multiple vehicles are the most price-elastic, whereas rural households with a single vehicle are the least price-elastic. Puller and Greening 4

5 across consumers or, in the case of survey data, over time within a single household. This aggregation obscures the short-term dynamics in gasoline purchasing. 7 These short-term dynamics where, when, and how much gasoline drivers buy are of great theoretical and policy importance. To our knowledge, no other paper uses transaction-level data on gasoline purchases to understand these dynamics. Finally, the policy application in this paper contributes to the literature on the adoption of alternative fuel vehicles. Empirical studies on the demand for ethanol include Anderson (2012) in a U.S. state and Salvo and Huse (2013) in Brazil. Corts (2010) shows how a government policy to increase the number of alternative fuel vehicles led to an increase in investment in alternative fuel infrastructure. Our analysis is more closely related to simulations that jointly model alternative fuel consumption, vehicle purchase, and infrastructure investment (Greaker and Heggedal, 2010; Chen, 2012). Other papers in this literature model the optimal placement of alternative fuel infrastructure. The remainder of the paper is organized as follows. The next section describes the driving and refueling data and provides a descriptive analysis of refueling behavior. Section 3 describes the empirical model for the driver s choice of gas station. Section 4 provides the results for this model. Section 5 then uses the results to simulate adoption of alternative fuel vehicles under different assumptions about the price and availability of the alternative fuel. Section 6 concludes. 2 Data 2.1 IVBSS experimental data The driving data used in the paper are from the Integrated Vehicle-Based Safety Systems (IVBSS) study conducted by UMTRI from April 2009 to May During this study, identical vehicles were provided to 117 drivers in southeast Michigan for about seven weeks each. The objective of the study was to observe driver responses to modern safety equipment including lane-departure and collision warning systems. The drivers used the vehicles as if they were their own (including purchasing their own gasoline) and UMTRI collected a detailed dataset that included driving data such as location, speed, acceleration, heading, (1999), also using Consumer Expenditure Survey data, decompose gasoline demand into demand for vehicle miles traveled and demand for fuel efficiency. More recently, Bento et al. (2009) use the National Household Travel Survey to jointly estimate demand for vehicle miles traveled and the discrete demand for vehicles, in a utility-theoretic framework. 7 Levin et al. (2012) use daily city-level gasoline expenditure data to show that estimated elasticities are much higher with the daily data than using the same data aggregated to a monthly level. 5

6 weather, and instantaneous fuel use, at a frequency of ten observations per second. Cameras in the vehicles captured video of the driver and the surrounding roadway, while radar identified nearby vehicles. Table 1 provides characteristics of drivers in the sample. 8 Potential participants were selected at random from all Michigan license holders living within a radius of approximately one hour s driving time from Ann Arbor. The sample was stratified to give equal numbers of males and females in three age categories: 20 30, 40 50, and In order to be included in the experiment, participants were required to drive a minimum number of miles per day on average. As shown in the table, the mean distance for the experimental participants was 48.7 miles per day, equivalent to about 17,800 miles per year. In total, data from 6,750 hours (231,000 miles) of driving were observed and recorded. Variables recorded by the monitoring equipment provide comprehensive, high-frequency information on vehicle operation and driver behavior. They include vehicle location, speed, heading, fuel consumption, and the distance to surrounding vehicles. One variable not recorded by the monitoring equipment was the fuel tank level. The amount of fuel remaining in the tank is the major factor that determines whether a driver stops for gasoline. recovered an estimate of the fuel tank level using images from an in-car over-the-shoulder camera directed at the steering wheel and dashboard, combined with second-by-second fuel consumption data. The details of this procedure are described in the data appendix. 2.2 Gas station stops and prices We matched the vehicle locations from the driving data to a database of gasoline stations in order to identify potential refueling stops. The gas station data are from OPIS (Oil Price Information Service) and contain the name, brand, address, and approximate geographic coordinates for every gas station in Michigan and Ohio. For gas stations in southeast Michigan, we supplemented this information using aerial photography from Google Earth to add the exact latitude and longitude of the gas pumps and each of the station entrances. As shown in Figure 1, we identified every vehicle stop within a radius of 100 meters of a gas pump. We reviewed the left-side camera images for all of these potential stops. If the camera showed that the vehicle was stopped beside a gas pump (as in the figure), the stop was coded as a gasoline refueling stop. 8 The final sample for the analysis comprises 108 drivers. There were 117 drivers who were provided a vehicle. However, nine people were subsequently excluded from the sample due to non-compliance (such as insufficient use of the vehicle or sharing the vehicle with another driver). We 6

7 Daily station-level prices for the entire sample period are from OPIS. 9 These provide the gas price paid by the driver in each of the stops. 10 The data also provide the gas price at every alternative station where the driver could have chosen to stop instead. Table 2 provides descriptive information for the 760 gas stops in Michigan and Ohio identified in the driving data. 11 The mean quantity of gasoline purchased at each stop is 8.1 gallons. The mean gas price paid by drivers in the sample is $2.61 per gallon, with a range from $1.97 to $2.96. Figure 2 shows the date and price of the gas stops, as well as the average daily gas price in southeast Michigan. Figure 3 shows the observed probability of stopping for gasoline at the end of a trip, as a function of the fuel tank level at the end of the trip. Very few drivers stop for gasoline when the fuel tank is half-full or more. The probability of stopping for gasoline rises steeply below one quarter of a tank. Drivers will stop to buy gas on nearly 30 percent of trips in which the gauge shows an empty tank. For each gas stop we calculated a measure of the excess time for the driver to arrive at the gas station. The calculation method for excess time is similar to that used by Houde (2012). Suppose the driver starts at location A, drives to the gas station at B, then continues on to location C. The excess time for the gas station stop is the fastest time for the route A to B to C, less the fastest time for the direct route from A to C. Travel times between points were calculated using Dijkstra s algorithm applied to street network data for Michigan and Ohio. Further details of the travel time calculation are described in the data appendix. Figure 4 shows the distribution of excess times to the gas stations that drivers stop at. Slightly more than half of gas stops have an excess time of 30 seconds or less. In most cases, these represent stops at gas stations along the route that the driver was on, with no deviation from the optimal route. As shown in Table 2, the median excess time for the chosen gas stations is 0.3 minutes The OPIS data only report the price for regular gasoline. The Honda Accords used for the experiment run on regular gasoline and we consider it unlikely that drivers used a different (and more expensive) gasoline grade. 10 There are two potential issues with the OPIS price data. First, the data only report one price for each station and day. If the price changes during the day, then the reported price may not be the same as the price paid by the driver. Second, the data contain many missing daily price observations, particularly for gas stations in remote areas. We used several different interpolation mechanisms for the missing data. Final results are not sensitive to the interpolation method. 11 A small number of gas stops were identified in states other than Michigan and Ohio. These stops are excluded from our analysis due to the lack of price data. 12 Table 2 also shows summary statistics for the excess distances for the observed gasoline stops. Some of these excess distances are negative: the optimal distance from origin A to gas station B then to destination C is less than the optimal distance directly from A to C. This is a result of the optimal routes minimizing travel times, not travel distances. Traveling directly from A to C may be fastest on a highway but have a 7

8 Finally, Figure 5 shows the distribution of the value of gasoline purchases for the stops in the data. Peaks in the distribution near $10 and $20 (possibly $30) suggest that some drivers choose the amount of gasoline to purchase based on these round dollar amounts. 3 Empirical Approach To understand how drivers would react to a limited choice of alternative fueling locations, we first investigate how drivers choose between gasoline fueling stations with different characteristics. In particular, we analyze how drivers make decisions about when and where to stop for gasoline based on the location of the station relative to the driver s route and the price of gasoline at different stations. Through this model we can better understand whether drivers are willing to drive out of their way to purchase less expensive gasoline and when drivers are most likely to consider stopping for gasoline. This then allows us to simulate how drivers would respond to having an alternative fuel available at a sub-set of stations, and what that behavior would imply for drivers willingness-to-pay for alternative fuel vehicles relative to conventional gasoline vehicles. We empirically model drivers decisions over when and where to stop for gasoline as a full-information discrete choice model. On a given trip t = 1,..., T each driver i = 1,...N has a choice of whether to stop at each of j = 0,..., J stations, with station j = 0 representing the choice not to stop. The utility that each driver receives for each choice is given by: U ijt = C + αp jt + X ijt β + ξ i0t + ɛ ijt (1) where P jt is the price at station j on the date of trip t, X ijt is a vector of characteristics of the station including the time out of the way the driver would have to go to get to the stations, and ɛ ijt is an extreme-value type 1 error. ξ 0t is the value of not stopping on this trip, which we model as: ξ i0t = γw i0t (2) where W 0t is a vector of characteristics of the trip such as whether the trip is on a weekend and the amount of gasoline remaining in the fuel tank at the start of the trip. Not stopping is assumed to have a price of zero and a time driven out of the way of zero. Therefore, in this model, the driver simultaneously makes the choice of whether to stop on each trip and, if she stops, where to stop. longer distance. 8

9 We also present results for a model of the driver s choice of gas station conditional on stopping on a particular trip. For this model there is no outside option of not stopping. For the refueling trips only, each driver i = 1,...N has the choice of j = 1,..., J stations, and from each choice receives utility given by: U ijt = C + αp jt + X ijt β + ɛ ijt (3) Finally, we present results for a model in which the quantity of gasoline to be purchased on a trip is known before the driver chooses the gas station to stop at. The choice of gas station depends, not on the unit price of gasoline, but on the total cost of purchasing the given quantity of gasoline at each gas station. Unlike the previous models, this model would enable drivers to choose a more expensive gas station along their route for buying a small quantity of gasoline, while taking a longer detour to a cheaper gas station in order to buy a full tank of gasoline. Utility is given by equation (4), where Q it is the quantity of gasoline purchased by driver i on trip t. U ijt = C + αp jt Q it + X ijt β + ɛ ijt (4) As in model (3), only trips in which the driver stops for gasoline are included in this model. 13 This model is equivalent to the static first step of the dynamic demand model of Hendel and Nevo (2006). They show that, provided the consumption quantity does not depend on the brand choice, the parameters of this model can be estimated without solving the dynamic programming problem. These models provide information on the trade-offs that drivers make when choosing between stations. Apart from the price of gasoline at each station, the most important characteristic for the driver is the location of the station relative to the driver s route. All else being equal, we would expect that stations located further from the driver s planned route are less likely to be chosen. For every trip and every potential gas station choice, the additional trip time in minutes that the driver would require to visit that gas station is calculated. Further details of this travel time calculation are described in the data appendix. The trade-off between more expensive gasoline along the route or driving out of the way for cheaper gasoline provides an estimate of drivers average value of time. Another important geographical variable is the ease of access by drivers to the gas station. 13 It is difficult to define the counterfactual quantity of gasoline that would be purchased on trips in which the driver does not currently stop for gasoline. In particular, this will depend on the available capacity in the driver s fuel tank. However, the available capacity is correlated with the value of not stopping. 9

10 We expect that gas stations that require a driver to make a left-hand turn across oncoming traffic are less likely to be chosen than gas stations that the driver can enter by making a right-hand turn. The side of the road that the gas station is located on depends on the direction from which the driver approaches, and so will differ by trip. It is determined as part of the calculation of the excess time for the driver to arrive at the station. Other characteristics of gas stations in the analysis include the gasoline brand and whether the station is located near a highway exit. In all three models, drivers choose between a set of stations on each trip. The set of possible gas stations includes all gas stations within the same Core Based Statistical Area (CBSA) as the trip. Trips that cross several CBSAs are split into multiple trips, each within one CBSA. Most of the trips in the data take place in the Detroit-Warren-Dearborn CBSA. There are nearly 2,000 gas stations in this metropolitan area. For tractability, the choice set is defined based on a cutoff value for the excess time to the gas station on a given trip. In the main specification this cutoff is 10 minutes. As a robustness check the results for cutoffs of 5 minutes and 15 minutes are also presented. We make several other important assumptions in estimating the model. First, we assume that if the driver had made a different choice about where to stop for gasoline, she would still have traveled to that station from the same starting location and would travel to the same destination after leaving the station. This assumption is required to calculate the excess time traveled to each station, including those the driver does not stop at. However, it rules out a scenario, for example, where a driver chooses to pick up coffee at a different coffee shop depending on which gas station she stops at. In addition, we assume that the driver knows the location of all gasoline stations near her route, and, perhaps less plausibly, that she knows the current price at each of those stations when she starts her trip. In other work, we are further investigating the extent to which drivers may not be aware of lower prices away from their normal routes and the value of this information. Finally, in this formulation consumers are unable to make dynamic decisions about where to stop for gas. The consumer makes a choice about whether and where to stop without any information about the characteristics of stations near the next trip. We plan to relax this assumption in future work, based on a similar setup to Hendel and Nevo (2006). The third model above, with the static choice of gas station conditional on purchase quantity, would be the first step in this dynamic demand estimation. 10

11 4 Results Table 4 shows the results for the basic version of the first two models described above, in the absence of any heterogeneity across drivers. Columns 1 and 2 show the results for the model conditional on stopping, without an option not to stop. Columns 3 and 4 show the results for the model that includes all trips and the option of not stopping on any trip. Columns 2 and 4 include brand dummy variables for the 12 largest gas brands. For all specifications, both the price and the excess time coefficients have the expected sign and are statistically significant. That is, more expensive stations and stations further from the driver s route are less likely to be chosen. Scaling the estimates by the price coefficient allows the magnitude of the effects to be more easily interpreted. From the results in Column 2, each additional minute that the driver must deviate from their route to reach the chosen gas station is equivalent to 11.6 cents per gallon of gasoline (-.854/7.509). The average amount of gasoline purchased is 8 gallons, so the value of the time spent deviating from the route is 92 cents, or $55 per hour. This value is high relative to wages. However, it is remarkably close to the value of time estimate of Houde (2012), who finds a value of time of $54 per hour using aggregate data on gasoline purchasing. In Columns 3 and 4, the value of not stopping depends on the amount of fuel remaining in the tank in the expected way (results not reported). Not stopping is highly preferred when the gas tank is nearly full. However, the price and excess travel time coefficients in this model are more difficult to interpret. The implied value of time estimates using the same calculation as before are unreasonably high (nearly $400 per hour). This may reflect the difficult of defining an outside good for a nondurable such as gasoline. Even if the driver decides not to stop for gas on a particular trip today, she will certainly have to stop on some future trip. Therefore, the relevant price for today s decision may not be the zero price of buying nothing today, but instead the expected future price of delaying purchase until tomorrow. The other estimated coefficients are interesting. Gas stations with entrances that require only a right turn to enter are more likely to be chosen. The results in Column 2 suggest that a driver would pay an additional 3 cents/gallon to avoid crossing the road to a gas station directly opposite. Stations that are located close to a highway exit are less likely to be chosen. 14 The gas brand coefficients (not reported) show that Costco, Speedway, Kroger, 14 The current specification does not distinguish between trips that are on-highway and off-highway. It is possible that highway drivers are more likely to choose stations near the exit while city drivers choose to 11

12 and Meijer are the brands most likely to be chosen after controlling for price and location. 15 Sunoco, Citgo, Valero, and 7-Eleven are the brands least likely to be chosen. The disaggregate nature of our data allows us to further explore the heterogeneity in preferences for fueling stations across different types of drivers in our sample. Table 5 shows the results by gender. Women appear to be more price sensitive than men, and more willing to cross to the other side of the road, although these differences are not statistically significant. The breakdown by age group in Table 6 shows greater differences across demographic groups. Sensitivity to price is larger for both year-olds and year-olds, and this difference is statistically significant. However, there is no difference between age groups in the excess time coefficient. The implied value of time is different but only as a result of the differences in the price coefficient: $95/hour for the youngest group, $55/hour for the middle group, and $30/hour for the oldest group. A particularly striking result is that the rightturn bias of drivers disappears for drivers in the youngest age group. For both other groups the value of making a right-turn to enter a gas station is equivalent to about 4 cents/gallon. The choice set for all of the results presented so far includes all gas stations within the same CBSA as the trip that are no more than a 10-minute deviation from the driver s optimal route. Table 7 shows the results for two alternative choice sets: all stations within a 5-minute deviation from the driver s route (Columns 1 and 3) and all stations within a 15-minute deviation (Columns 2 and 4). The results in this table indicate that changing the cutoff value for excess time has no qualitative effect on the results. Finally, Table 8 shows the results for the model with the purchase value of gasoline in dollars instead of the price of gasoline in cents per gallon. The results from this table are similar to Table 4. The ratio of the excess time coefficient to the purchase value coefficient can be interpreted directly as the value of time. This gives a slightly higher estimate than before: about $59/hour. As mentioned in the previous section, future work will use these results as the first stage in a dynamic demand model. 5 Alternative Fuel Vehicle Adoption [to update] While understanding how and why drivers choose stations that are not on their shortest route aids our understanding of how current gasoline markets work, we can also use our avoid them. 15 These brands offer discount cards or promotions bundled with supermarket purchases. As a result, the price paid by some drivers may be less than the list price in our OPIS data. This may explain why these brands are preferred after controlling for (list) price and location. 12

13 results to examine the difficulties faced by any alternative to gasoline that might hope to capture a substantial share of new vehicle purchases. Producers of alternative fuel vehicles face a quintessential chicken and the egg problem: no one wants to purchase an alternative fuel vehicle if they will not have anywhere to fill it and no one wants to convert part of their gas station to an alternative fuel if no consumers own alternative fuel vehicles. This has generally led analysts to believe that government intervention to subsidize alternative fuel vehicles would be necessary. Our model of gasoline station choice allows us to take a unique perspective on the question of how drivers might value a dense network of alternative fueling stations relative to a subsidy of the alternative fuel vehicle or the availability of an alternative fuel that is cheaper than gasoline per mile. 16 Our model allows drivers to travel out of the way for cheaper gasoline, which would be the exact scenario if the alternative fuel is relatively cheap but the fueling infrastructure is not very well developed. For the time being, we will consider the trade off between the relative alternative fuel price and the density of alternative fuel stations, and construct willingness-to-pay differentials that allow us to quantify the cost to drivers of the limited availability of the alternative fuel. This cost can then be paired with any assumption about the cost to drivers of different alternative fuel vehicle characteristics to understand the fraction of drivers who would prefer to purchase an alternative fuel vehicle to a gasoline vehicle at any given subsidy level. 5.1 Simulation Once we have estimated the discrete choice model above, we use these estimates to simulate the effect of different levels of alternative fueling station penetration. In particular, we want to understand how consumers value alternative fuel vehicles relative to gasoline vehicles if the alternative fuel is cheaper than gasoline but only available at a subset of gas stations. Since the supply of and access to the alternative fuel will largely determine the relative cost of the alternative fuel per gallon of gasoline equivalent, we focus on the differential value to drivers of gasoline vehicles over alternative fuel vehicles. By looking at the distribution of this value over the drivers in our sample, we are able to calculate the effect on vehicle purchasing of either subsidizing alternative fuel vehicle purchase or improving the performance or design of alternative fuel vehicles. To understand how drivers value gasoline vehicles relative to alternative fuel vehicles, 16 Note that this could either mean that the alternative fuel itself is cheap or that the alternative fuel vehicle technology is sufficiently efficient to make the per-mile cost of driving lower than gasoline. 13

14 we begin by calculating each driver s expected consumer surplus from having the option of stopping at the set of gasoline stations on each trip over the entire period the driver has the vehicle. This consumer surplus is given by: where E[CS(gas) i ] = 1 α T ln t=1 J V ijt (5) j=0 V ijt = αp jt + X ijt β + ξ i0t We can then compare this consumer surplus to the consumer surplus the driver would get from driving an alternative fuel vehicle that can only stop for fuel at a subset of stations that have both gasoline and the alternative fuel. We label these stations a = 1,..., A and assume that the station has the same characteristics as it does in the real world where it only offers gasoline, with the exception that that alternative fuel may be offered at a different price than the gasoline. Using this notation, the consumer surplus a driver gets from purchasing alternative fuel over the period of study is given by: where E[CS(alt) i ] = 1 α T ln t=1 A V iat (6) a=0 V iat = αp at + X iat β + ξ i0t Combining these two values gives us the driver s willingness-to-pay for a gasoline vehicle relative to an alternative fuel vehicle, given a set of stations which offer the alternative fuel: E[W T P (alt) i ] = E[CS(gas) i ] E[CS(alt) i ] (7) This approach clearly requires a few substantial assumptions. First, we must assume that the trips a driver would take in an alternative fuel vehicle would be identical to the trips she would take in a gasoline vehicle, so that the distance traveled out of the way to each station is identical in both cases. 17 Second, we are assuming that the experience of filling an alternative fuel vehicle is identical to the experience of filling a gasoline vehicle. For instance, this formulation rules out a situation where the driver must wait for an extended period of time for the vehicle to finish fueling. If that were the case, presumably the driver would make different decisions about when to refuel based on her ability to do other things like work, shop, or eat while the car is fueling. Third, in using the expectations operator, we are assuming that the driver is not aware of her iid random error draws ɛ ijt when she makes her 17 We are currently working to expand the model to account for the fact that drivers are likely to drive farther if the alternative fuel is less expensive per mile. 14

15 vehicle purchase decision. In order to implement this simulation, we will assume that the market for the alternative fuel sets prices very similarly to the market for gasoline. Therefore, we will assume that the spread between the gasoline price and the alternative fuel price (per gallon of gasoline equivalent) is constant across stations. For instance, if the alternative fuel is 10 cents per gallon cheaper than gasoline, that means that every station that offers the alternative fuel prices it 10 cents cheaper than it prices gasoline. This creates a distribution of prices of the alternative fuel that mimics the distribution of prices of gasoline in the market, but at a lower mean price. Additionally, in initial simulations we will assume that stations offering the alternative fuel are randomly allocated across all existing gasoline stations, although in continuing work we plan to explore the consumer surplus implications of allocating alternative fueling infrastructure non-randomly. Finally, because drivers in our sample only drove the vehicles for 40 days, we need to scale the willingness-to-pay up to the value consumers would have for a new vehicle purchase. We assume that the 40-day distribution of driving is representative of the driver s annual driving and multiply the willingness-to-pay from equation 7 by 365/40 = to get the annual willingness-to-pay. We then assume that both alternative fuel and gasoline vehicles survive for 14 years and that consumers have a discount rate of 7%. Both of these assumptions are in keeping with the literature on new vehicle purchasing. With this approach to estimating willingness-to-pay in hand, we can simulate the value the drivers place on a gasoline vehicle relative to an alternative fuel vehicle given different fuel prices and alternative fuel availability levels. 5.2 Simulation Results Using the simulation described above and the discrete choice results that incorporate gender differences in preferences, we are able to compute the distribution of the excess value drivers place on gasoline vehicles over alternative fuel vehicles at different fuel price differentials and alternative fuel station penetration rates. Figure 6 shows the kernel estimate of the distribution of willingnesses-to-pay for gasoline vehicles over alternative fuel vehicles for 1, 10, 25, and 50 cent per gallon of gasoline equivalent alternative fuel price advantages and for 10, 50, and 90 percent of stations offering the alternative fuel. These distributions may be thought of as probability distribution functions of the incentive needed for consumers to be indifferent between a gas vehicle and an alternative fuel vehicle if the only difference between the two vehicles is the fuel used and the stations at which that fuel may be purchased. A 15

16 negative value means that a driver would prefer to purchase the alternative fuel vehicle even without a subsidy. Of course, if the alternative fuel vehicle has characteristics such as reduced performance or cargo space that make it less desirable than a gasoline vehicle, then this value must be added to any necessary subsidy. From a policy perspective, we would like to know how large a subsidy would have to be to convince different percentages of drivers to adopt alternative fuel vehicles. Our results speak to the value that drivers place on the availability and relative price of the alternative fuel, but we cannot speak to the value drivers place on any non-fuel differences in vehicle characteristics such as driving performance, vehicle design, or trunk space. 18 However, as shown in figure 6, we can say that with similar prices (1 cent per gallon of gasoline equivalent price advantage for the alternative fuel) and a low alternative fuel station penetration rate of 10%, subsidies of less than $500 would make up for the limited availability of the alternative fuel for most drivers. As the percent of stations offering the alternative fuel increases, the required subsidy drops substantially so that with a 1 cent per gallon price difference and 90% of stations offering the alternative fuel, a $100 subsidy would be enough to compensate every driver for the limited availability of the alternative fuel. Similarly, with larger price differences (say a 25 cent per gallon price advantage for the alternative fuel), while a subsidy of $200 is required to compensate the median driver for the limited availability of the alternative fuel, once 90% of stations offer the alternative fuel every driver prefers purchasing the alternative fuel to spending more on more widely available gasoline. In fact, with the 25 cent price difference and 90% of stations offering the alternative fuel, the median driver would pay an additional $145 to purchase the alternative fuel instead of gasoline. These results show that there are multiple ways to encourage the adoption of alternative fuel vehicles. If alternative fuel vehicles have less attractive characteristics to drivers, then either subsidies or increased alternative fuel availability will be required to encourage adoption even if the alternative fuel is cheaper than gasoline per mile driven. One additional interesting result from these simulations is the effect that the availability of the alternative fuel has on the distribution of relative willingness-to-pay for alternative fuel vehicles. When a low percentage of stations offer the alternative fuel, the distribution of willingness-to-pay is relatively flat. While some drivers pass many stations daily and therefore would have relatively easy access to alternative fuel, there are some drivers who 18 Trunk space is of particular interest for alternative fuel vehicles because most alternative fuels are less energy-dense than gasoline, so they require larger tanks in order to travel the same distance per fuel stop as conventional gasoline vehicles. Generally this means that their trunk must be smaller to accommodate the larger tank. 16

17 would need subsidies of over $1500 to consider an alternative fuel vehicle since they pass relatively few stations and would be severely constrained in their driving if they could only use the alternative fuel. However, as the availability of the alternative fuel increases, the variance of the distribution decreases. It makes sense that as the alternative fuel is more available, but not available everywhere, drivers who pass many stations are relatively unaffected while drivers who pass only a few stations are more likely to have the choice to purchase the alternative fuel on any given trip. However, because the alternative fuel is still not widely available, for small price differences between gasoline and the alternative fuel, it is still unlikely that the alternative fuel will be the best choice for either driver, so the distribution is compressed close to zero. At some level of alternative fuel station penetration, however, the combination of wide availability and a price savings at any given station combine to make the alternative fuel vehicle more attractive a gasoline vehicle for drivers. Again, this happens more quickly for drivers who drive in station-rich areas than drivers who have relatively few nearby stations, which eventually results in the distribution flattening again with the mass of drivers favoring alternative fuel vehicles to gasoline vehicles. As far as we are aware, this is the first paper to look at the heterogeneity across drivers in their willingness to trade-off driving further for cheaper gasoline. This allows us to better understand which groups might be more willing to adopt alternative fuel vehicles first, even with relatively low alternative fueling station density. The results we present here speak to the variation in willingness-to-pay across drivers who drive different amounts or on different routes, but in continuing work we plan to be more explicit about this variation in willingnessto-pay by adding greater heterogeneity to the discrete choice model and breaking down our simulation results by gender, age, daily mileage driven, and the type of driving (commuting vs shopping or freeway vs arterial). We expect that these results may also allow us to say something about where alternative fuel stations may have the largest impact based on the type of drivers who regularly pass by. 6 Conclusion Using a unusual dataset of drivers actual driving behavior, we have begun to investigate the trade-offs that consumers make when deciding when and where to stop for gasoline. We find that consumers do trade-off the distance traveled out of the way for gasoline with the price, and that this relationship varies across drivers with different demographic characteristics. In continuing work, we intend to make this currently static model dynamic in order to more 17

18 fully understand drivers willingness to delay stopping for gas if they know that they are passing close to an inexpensive station on a trip in the near future. We then use this model to better understand how consumers evaluate the choice of whether to purchase an alternative fuel vehicle given a limited number of stations selling the alternative fuel. We find that a substantial price advantage would have to exist in order for drivers to choose to purchase alternative fuel vehicles without a price subsidy. In continuing work, we are further analyzing what heterogeneity across groups in their willingness to travel out of the way for inexpensive gas implies for their potential willingness to drive out of the way for an alternative fuel if either the alternative fuel is less expensive per mile or the vehicle purchase price is subsidized. Additionally, in separate work, we are further investigating the role of information in the gasoline purchase decision. In this paper we have assumed that drivers have perfect information about the price of gasoline at all stations, and in that work we relax that assumption and attempt to understand the value to consumers of having better price information. 18

19 References Anderson, Soren T., The demand for ethanol as a gasoline substitute, Journal of Environmental Economics and Management, March 2012, 63 (2), Bento, Antonio M, Lawrence H Goulder, Mark R Jacobsen, and Roger H von Haefen, Distributional and Efficiency Impacts of Increased US Gasoline Taxes, American Economic Review, May 2009, 99 (3), Borenstein, Severin, A. Colin Cameron, and Richard Gilbert, Do gasoline prices respond asymmetrically to crude oil price changes?, The Quarterly Journal of..., 1997, 112 (February), Chen, Cuicui, Working Towards a Future on Alternative Fuels : The Role of the Automotive Industry. PhD dissertation, Massachusetts Institute of Technology Corts, Kenneth S., Building out alternative fuel retail infrastructure: Government fleet spillovers in E85, Journal of Environmental Economics and Management, May 2010, 59 (3), Erdem, Tulin, Susumu Imai, and Michael P. Keane, Brand and quantity choice dynamics under price uncertainty, Quantitative Marketing and Economics, 2003, 1, Greaker, Mads and Tom-Reiel Heggedal, Lock-In and the Transition to Hydrogen Cars: Should Governments Intervene?, The B.E. Journal of Economic Analysis & Policy, 2010, 10 (1). Hendel, Igal and Aviv Nevo, Measuring the implications of sales and consumer inventory behavior, Econometrica, 2006, 74 (6), Houde, Jean-François, Spatial Differentiation and Vertical Mergers in Retail Markets for Gasoline, American Economic Review, August 2012, 102 (5), Hughes, Jonathan E., Christopher R. Knittel, and Daniel Sperling, Evidence of a Shift in the Short-Run Price Elasticity of Gasoline Demand, The Energy Journal, 2006, 29 (1), Levin, Laurence, Matthew S. Lewis, and Frank A. Wolak, High Frequency Evidence on the Demand for Gasoline,

20 Lewis, Matthew S., Price leadership and coordination in retail gasoline markets with price cycles, International Journal of Industrial Organization, July 2012, 30 (4), Manuszak, Mark D., Predicting the impact of upstream mergers on downstream markets with an application to the retail gasoline industry, International Journal of Industrial Organization, January 2010, 28 (1), Puller, Steven L and Lorna a Greening, Household adjustment to gasoline price change: an analysis using 9 years of US survey data, Energy Economics, February 1999, 21 (1), Salvo, Alberto and Cristian Huse, Build it, but will they come? Evidence from consumer choice between gasoline and sugarcane ethanol, Wadud, Zia, Daniel J. Graham, and Robert B. Noland, Gasoline Demand with Heterogeneity in Household Responses, The Energy Journal, January 2010, 31 (1). Yergin, Daniel, The Prize: The Epic Quest for Oil, Money & Power, Simon & Schuster,

21 Table 1: Descriptive statistics for drivers in IVBSS experiment N a Mean Min Median Max Number of trips Days with vehicle Total miles driven 117 1, , ,542.4 Total hours of driving Total gasoline used (gallons) Miles per trip Miles per day with vehicle Miles per hour of driving Miles per gallon Number of gas stops Gas used per stop (gallons) Household income (US$) b ,501 24,188 74, ,285 Demographic characteristics Number Proportion Male Female Age Age Age a There were 117 drivers who started the experiment, with nine drivers either dropping out or being excluded from the final sample. Descriptive statistics (except demographic characteristics) are for all 117 drivers. b Mean household income for the census block of the driver s primary residence. 21

22 Table 2: Descriptive statistics for gasoline stops N Mean Min Median Max Gas price ($/gallon) Excess time from route (minutes) Excess distance from route (miles) Amount purchased (gallons) Purchase value ($) Day and time of gas stop Number Proportion Day of stop = weekend :00AM 6:00AM :00AM 10:00AM :00AM 2:00PM :00PM 6:00PM :00PM 12:00AM Gas station brand Number Proportion BP Speedway Marathon Mobil Sunoco Shell Meijer Other Gas station characteristics Number Proportion Right-turn entrance Right-turn exit Near highway exit a Excess distance is calculated as the additional distance for the driver stopping at the chosen gas station, compared to an optimal direct route between the stop before and the stop after the gas station. 22

23 Table 3: Descriptive statistics for trips N Mean Min Median Max All trips Distance (miles) 26, Duration (minutes) 26, Gasoline used (gallons) 26, Miles per hour 26, Miles per gallon 25, Time between trips (minutes) 26, Trips longer than 1 mile Distance (miles) 20, Duration (minutes) 20, Gasoline used (gallons) 20, Miles per hour 20, Miles per gallon 20, Time between trips (minutes) 19,

24 Table 4: Gas Station Choice Results Conditional on stopping All trips (1) (2) (3) (4) Price ($/gallon) (0.637) (0.677) (0.272) (0.266) Excess time (min) (0.042) (0.042) (0.035) (0.035) Right-turn entrance (0/1) (0.079) (0.08) (0.073) (0.074) Right-turn exit (0/1) (0.078) (0.079) (0.073) (0.073) Highway exit (0/1) (0.104) (0.107) (0.066) (0.066) No stop weekend (0.103) (0.104) Gas brand dummies. Y. Y No stop tank levels.. Y Y Obs Choice situations Notes: Each column shows the estimates from a conditional logit model. Each observation is a possible gas station that a driver could have chosen to stop at on a particular trip. Possible gas stations are within the same CBSA as the trip and no more than a 10-minute deviation from the driver s optimal route. For Columns 1 and 2, only trips for which the driver did stop at a gas station are included. Columns 3 and 4 include all trips and an outside good: the option for the driver not to stop at any station on a particular trip. Not stopping is interacted with a weekend dummy and dummies for eighth of a tank increments of the fuel tank level at the start of the trip. Gas brand dummies include the twelve largest brands and an other category for all other brands. 24

25 Table 5: Gas Station Choice Results: Heterogeneity by Gender Conditional on stopping All trips (1) (2) (3) (4) Price ($/gallon) (0.804) (0.837) (0.32) (0.311) female (1.311) (1.325) (0.588) (0.577) Excess time (min) (0.055) (0.056) (0.048) (0.048) female (0.083) (0.083) (0.071) (0.07) Right-turn entrance (0/1) (0.102) (0.103) (0.095) (0.096) female (0.156) (0.157) (0.148) (0.148) Right-turn exit (0/1) (0.078) (0.079) (0.073) (0.073) Highway exit (0/1) (0.104) (0.107) (0.067) (0.066) No stop weekend (0.133) (0.133) female (0.211) (0.21) Gas brand dummies. Y. Y No stop tank levels.. Y Y Obs Choice situations See the notes to Table 4 for further information. 25

26 Table 6: Gas Station Choice Results: Heterogeneity by Age Group Conditional on stopping All trips (1) (2) (3) (4) Price ($/gallon) (0.878) (0.945) (0.447) (0.445) Age (1.410) (1.449) (0.643) (0.636) Age (1.722) (1.743) (0.646) (0.622) Excess time (min) (0.062) (0.061) (0.05) (0.05) Age (0.1) (0.099) (0.084) (0.084) Age (0.099) (0.101) (0.088) (0.087) Right-turn entrance (0/1) (0.119) (0.119) (0.11) (0.11) Age (0.178) (0.181) (0.169) (0.168) Age (0.199) (0.2) (0.185) (0.186) Right-turn exit (0/1) (0.079) (0.079) (0.073) (0.073) Highway exit (0/1) (0.105) (0.107) (0.067) (0.067) No stop weekend (0.158) (0.158) Age (0.248) (0.247) Age (0.249) (0.247) Gas brand dummies. Y. Y No stop tank levels.. Y Y Obs Choice situations See the notes to Table 4 for further information. 26

27 Table 7: Gas Station Choice Results: Robustness to Alternative Choice Sets Conditional on stopping All trips (1) (2) (3) (4) Price ($/gallon) (0.712) (0.677) (0.266) (0.26) Excess time (min) (0.044) (0.027) (0.038) (0.023) Right-turn entrance (0/1) (0.08) (0.077) (0.075) (0.073) Right-turn exit (0/1) (0.08) (0.077) (0.074) (0.072) Highway exit (0/1) (0.105) (0.097) (0.064) (0.062) No stop weekend (0.1) (0.097) Gas brand dummies. Y. Y No stop tank levels.. Y Y Obs Choice situations Notes: Each column shows the estimates from a conditional logit model. Each observation is a possible gas station that a driver could have chosen to stop at on a particular trip. Possible gas stations are within the same CBSA as the trip. For Columns 1 and 3, the stations in the choice set have a maximum 5-minute deviation from the driver s optimal route. For Columns 2 and 4, the stations have a maximum 15-minute deviation from the optimal route. Gas brand dummies are included in all columns. See the notes to Table 4 for additional details. 27

28 Table 8: Gas Station Choice Results: Purchase Amount instead of Gas Price Conditional on stopping (1) (2) Purchase value ($) (0.077) (0.082) Excess time (min) (0.042) (0.043) Right-turn entrance (0/1) (0.081) (0.082) Right-turn exit (0/1) (0.08) (0.08) Highway exit (0/1) (0.106) (0.109) Gas brand dummies. Y Obs Choice situations Notes: Both columns show the estimates from a conditional logit model. For both columns, only trips for which the driver did stop at a gas station are included. Each observation is a possible gas station that a driver could have chosen to stop at on a particular trip. Possible gas stations are within the same CBSA as the trip and no more than a 10-minute deviation from the driver s optimal route. Gas brand dummies are included in Column 2 only. 28

29 Figure 1: Procedure for identifying gas station stops All vehicle stops within a 100-meter radius of gasoline station pumps were considered as possible refueling stops (left image). Images from the driver s side camera were used to confirm that the car was stopped at a gas pump (right image). Figure 2: Average gasoline price and observed purchase price through sample period 3.00 Gas price ($/gallon) apr jul oct jan apr jul2010 Date The thick black line shows the daily average gasoline price for the eight counties in southeast Michigan from the OPIS data. Each small dot represents the date and price of one of the gas station stops that we identify. 29

30 Figure 3: Probability of stopping for gas based on fuel tank level at end of trip.3 Empirical Probability of Stopping E 1/4 1/2 3/4 F Tank Level at End of Trip The graph shows a local polynomial regression of an indicator for stopping for gasoline at the end of a trip on the fuel tank level at the end of the trip. The fuel tank quantities range from 15 to 65 liters. These are marked on the graph as E and F respectively. Figure 4: Distribution of excess time travelled to chosen gas station.6 Fraction of gas stops Excess time to selected gas station (minutes) The map shows the distribution of excess times that drivers travelled away from their route in order to arrive at their chosen gas station. The calculation method for the excess times is described in the data appendix. Times greater than 10 minutes are combined in the final right-side bar. 30

31 Figure 5: Distribution of gasoline purchase quantities Density Gas purchase value ($) The histogram shows the distribution of the value of gasoline purchases for the stops in the data. 31

32 Figure 6: Willingness-to-pay for gas vehicles over alternative fuel vehicles cent alt. fuel price advantage cent alt. fuel price advantage Density Density Value of gas over alt. fuel vehicle cent alt. fuel price advantage 90% of stations 50% of stations 10% of stations Value of gas over alt. fuel vehicle cent alt. fuel price advantage Density Density Value of gas over alt. fuel vehicle Value of gas over alt. fuel vehicle 32

33 A Data appendix A.1 Fuel tank levels The data recorder in the experimental vehicles did not record the fuel tank level. For the current analysis, the fuel tank level is an important determinant of the driver s refueling decision. This section describes the procedure used to recover information on the fuel tank level using images of the fuel tank gauge extracted from an in-cabin video camera. The experimental vehicles have five video cameras, including two in-cabin cameras. One of these cameras records the driver s face. The other camera records the driver s hands and steering wheel. The instrument panel, including the fuel gauge, is visible on the images from this second camera. As shown in Figure 7, visibility of the fuel gauge varies depending on lighting conditions. In bright sunlight, the instrument panel is underexposed on the camera image and the fuel gauge is not visible. At night, the instrument panel is lit up and the camera image is overexposed. The optimal visibility of the fuel gauge in the camera images is in low light (such as dawn or dusk) or cloudy conditions. Images from the cabin camera were extracted from the video at five minute intervals using a custom software program developed by UMTRI. This interval was chosen to increase the probability of observing the fuel gauge during optimal lighting conditions, while still giving a manageable number of images. A total of 92,577 images were extracted from the video. Each image is a grayscale bitmap with a resolution of pixels. Slight variation across vehicles in the placement of the camera means that the location of the fuel gauge within the extracted video images varies between vehicles. 19 For each vehicle and driver, a selected image was opened in Adobe Photoshop and a pixel cropping rectangle was defined, centered on the fuel gauge. Coordinates of the cropping rectangle for vehicle and driver were recorded. A batch image processing program called ImageMagick was used to process the images. Each image was cropped to the predefined pixel rectangle. Images were then enlarged by a factor of seven, to pixels. The enlarged images were sharpened and normalized. Normalization expands the dynamic range of the grayscale image so that small variations in gray intensity are more easily visible. The processed images were converted to JPEG format. Figure 8 shows three examples of the converted images. As part of the image batch analysis, pixel-level summary statistics on each unprocessed 19 For the same vehicle, there is sometimes even variation across drivers in the camera placement, caused by maintenance and cleaning that undertaken between each driver. 33

34 image were extracted using ImageMagick. These included the minimum, maximum, and mean brightness of the pixels in the cropped fuel gauge image. Based on these statistics, images were sorted into three categories: underexposed (low mean pixel brightness), overexposed (high mean pixel brightness), and low contrast (small difference between maximum and minimum brightness). 28,205 images did not belong to any of these categories and were used for additional analysis. The quality of the fuel gauge images was too low for machine-based measurement of the fuel gauge angle to be feasible. Instead, human analysis of the images was implemented using the Amazon Mechanical Turk service. This is an online crowdsourcing marketplace in which workers complete small tasks for monetary payment. For the fuel gauge task, workers were shown three of the processed images and asked to answer two questions for each image: an assessment of the image quality and legibility on a five-point scale, as well as an estimate of the amount of fuel in the tank. There were nine possible values for the tank level, from empty to full in one eighth of a tank increments. An additional option could be selected if the gauge was illegible. Workers were shown an example image (including superimposed Empty and Full indicators) and the appropriate corresponding answer. Each image was assessed by three independent workers. The three assessments of the fuel tank level were averaged to give a single estimate. If the three estimates differed by at most one quarter of a tank, all three estimates were included in the calculation. If two estimates differed by at most one eighth of a tank, and the third estimate differed by a quarter of a tank or more, then the outlier was dropped from the calculation and only the two closest estimates were used. If all estimates differed from one another by one quarter or more, then no value was recorded for the tank level of that image. The above procedure produced tank level estimates at discrete time intervals for each driver. These were combined with second-by-second fuel consumption data from the vehicle to estimate the fuel tank level at each second. Let h it be the fuel tank level, in liters, for driver i at time t. Driver i refuels the vehicle J i times during the experiment, at times τ ij for j from 0 to J i. For all drivers, τ i0 = 0 and so h τi0 is the initial fuel tank level when the driver receives the car. 20 Let c it be the second-by-second consumption of gasoline for driver i at time t. 20 In theory the participants in the experiment received the vehicle with a full tank of gasoline. In practice there appears to be some small variation in the initial tank levels, possibily reflecting uncertainty in the refueling procedure. 34

35 Equation (8) is the physical relationship between fuel tank level and fuel consumption: Both h it and h iτij h it = h iτij are unobserved. t s=τ ij c is for τ ij < t < τ i,j+1 (8) Let x it be the estimated tank level for driver i at time t from the Mechanical Turk analysis of the fuel gauge images. Equation (9) is a polynomial that maps the tank level in the fuel gauge (in one eighth increments) to the physical fuel tank level (in liters). Combining equations (8) and (9) gives: h iτij h it = α + βx it + γx 2 it + ε it (9) t s=τ ij c is = α + βx it + γx 2 it + ε it t Rewrite expression (10) using the following definition: s=τ ij c is = h iτij α βx it γx 2 it + ε it (10) y it = t s=τ ij c is and dummy variables for the fuel tank level after each refueling: Θ it = N J i i =1 j =0 θ i j I(i = i and τ i j < t < τ i,j +1) This gives equation (11), which is estimated using ordinary least squares to give both the fuel tank levels after each refueling and the parameters that map gauge readings into tank levels: y it = Θ it α βx it γx 2 it + ε it (11) There is one free parameter, which is chosen so that the maximum fuel tank level after refueling is equal to the fuel tank capacity of the experimental vehicle. Given the estimated levels of the fuel tank after each refueling, the entire history of 35

36 fuel tank levels for each driver can be constructed using equation (8). Figure 9 shows two examples of the constructed fuel tank history. The horizontal axis in each figure represents the time since the driver received the vehicle. The vertical axis shows the fuel tank level. In each figure, the red line represents the predicted fuel tank levels from the estimated purchase quantities and equation (8). Each blue cross represents an observation of the fuel tank gauge image, mapped to liters using equation (9). The two images illustrate the variation across drivers in refueling behavior. In the top image, the driver waits until the gauge is showing empty and then refills the fuel tank completely. In the second image, the driver refuels more frequently and never completely fills the tank. Using such figures for each driver, the above data analysis and estimation procedures were iterated to improve the data quality. A small number of additional gasoline stops were identified from the pattern of residuals. These include, for example, additional out-of-state stops for which we do not have gas station location data. Gasoline stops were eliminated for several drivers where the estimated refueling quantity was close to zero or even negative. Finally, outliers from the Mechanical Turk image analysis were corrected or eliminated. A.2 Calculation of excess distance to gas stations For a driver choosing between alternative gas stations, a major factor in the decision is the additional time required to deviate from the driver s original route to arrive at the chosen gas station. This section summarizes the procedure used to compute the excess distance for each trip and each possible gas station choice. The analysis uses the ArcGIS Network Analyst module for Python and is based on the ESRI North America Streetmap dataset. Figure 10 provides a summary of the calculation. Consider a trip from start location A to end location C for which the driver does not stop at a gas station. The network analysis software is used to compute the fastest time from A to C, accounting for differences in speed limits along the route but not actual traffic conditions. This time may be faster or slower than the actual route and time chosen by the driver from A to C. All analysis is based on the optimal calculated duration of the trip, not the observed duration. Suppose the driver chooses to stop at the gas station B before continuing to his original planned destination C. We can calculate the optimal time to travel from A to B. Most gas stations have multiple entrances and, depending on the location A, one or another entrance may provide the quickest route. We have coded every entrance for every gas station in 36

37 southeast Michigan. Using this data, we solve the optimal travel time problem from A to each of the entrances of B. This calculation is solved twice for each entrance: once with a restriction that the driver arrives with the entrance on the left-side of the road, and again with a restriction that the driver arrives with the entrance on the right-side of the road. The difference in time between the cases may be a few seconds to several minutes, depending on the structure of the street network near the gas station. The minimum time out of all possible routes is used as the time from A to B. For the calculation shown in the figure, the fastest route from A to B would be the one that arrives with entrance 2 on the left-side of the car. Gas station B is then coded as having a left-side entrance for the driver starting from A. The same procedure is repeated for cars travelling from B to C. This gives the quickest travel time from B to C as well as whether the car exits the gas station to the left or to the right. Finally, the excess time to gas station B on the trip AC is the time from A to B, plus the time from B to C, less the direct time from A to C. 37

38 Figure 7: Example raw images from the cabin camera (i) Underexposed (ii) Overexposed (iii) Visible gauge image The visibility of the fuel gauge in the cabin video images depends on the lighting conditions. With too much light (i) or too little light (ii) the fuel gauge will be under or over-exposed respectively. Visibility is greatest in cloudy weather or at dawn or dusk (iii). Figure 8: Enlarged and enhanced fuel gauge images (i) Empty (ii) Full (iii) 3/4 full The three images show examples of the cropped and processed fuel gauge images that were analyzed by Mechanical Turk workers. 38