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Speeding Behavior, Gasoline Prices and Value of Time Hendrik Wolff University of Washington Kari Edison Watkins University of Washington June 9th, 2011 Very Preliminary! & Comments very welcome! Abstract Do drivers seek to conserve gasoline by reducing speeds when gasoline prices are high? While economic theory predicts that a rational driver adjusts driving speeds, previous empirical studies produced mixed results. Here we take a fresh look at the data and estimate a statistical significant and robust negative relationship between speeding and gasoline prices. From this result, we infer a number of findings: (i) By providing a new methodology of deriving the ‘value of time’ (VOT) based on comparisons on the intensive margin (previous VOT studies instead compare across the extensive margin) we find this coefficient to be 54% of the average wage rate. The VOT method of this paper has several important advantages to circumvent omitted variable bias which has plagued the prior VOT literature. (ii) In terms of heterogeneity, we find that the fastest drivers reduce speeds under-proportionately, potentially undermining the safety objective of a gasoline tax. (iii) As a dynamic aspect of habit formation, we find that once drivers experience the benefits of gasoline conservation with prices above $4 per gallon, the speed-price elasticity reduces to about half, implying that reduced speeds are continued even in periods of low gasoline prices. (iv) Finally, we show that the changes are mainly caused by the gas price that drivers pay at the pump. The high public media attention given to gasoline prices had relatively little effect on changing drivers speeding behavior. For correspondence contact Hendrik Wolff, Department of Economics, University of Washington, 349 Savery Hall, Box 353330, Seattle, WA 98195-3330. phone: (510) 220-7961, hgwolff@u.washington.edu. Thanks are due to Jim Hawkins of the Washington Department of Transportation for providing the speed data. Jim was himself quite speedy with providing the data and answers to questions. 1 1. Introduction 1.1. Gasoline Prices and Speeding This paper studies the relationship between gasoline prices and drivers’ speeding behavior. As the debate on gasoline taxes continues to unfold, economists are increasingly interested in the mechanisms by which gasoline prices affect gasoline demand. It has been repeatedly hypothesized (Peltzman 1975, Dahl 1979, Blomquist 1984, Goodwin et al. 2004) that vehicle speeds decrease with higher gas prices. But, recently Burger and Kaffine (2009) measured this relationship and find the opposite: with rising gas prices, speeds increase. This—at first counterintuitive—result stems from the fact that higher gas prices decrease congestion. Burger and Kaffine (2009) then investigate the price-speed relationship during strictly uncongested periods only (i.e. in the middle of the night) and they reject the hypothesis that drivers reduce speeds when gas prices are high. In this paper, we take a fresh look at the data and estimate a statistical significant and robust negative relationship between drivers’ speeding behavior and gasoline prices. We make a number of methodological contributions. First—instead of using average annual data of vehicle speeds (as in Peltzman 1975, Dahl 1979, Blomquist 1984) or average weekly speed data (Burger and Kaffine 2009)—we collected the most disaggregated available hourly dataset of speeds for the highway system within the State of Washington. Second, because gasoline prices are highly cyclical over the calendar year (with increased prices during the summer and lower prices during darker winter months), we find that not cautiously controlling for external driving conditions will produce an erroneous rejection of the gasoline conservation hypothesis. To this end, we construct a dataset of speeds with the most homogenous exterior environment as possible and control for hourly weather and traffic related congestion effects. In sum, these changes to the estimation 2 method turn out crucially important to obtain, what we believe to be a much cleaner and more precise coefficient estimate of the causal effect of gasoline prices on drivers’ speeding behavior. Using this new dataset, we estimate that for a one dollar price increase per gallon of gasoline, speeds reduce by 0.4 miles per hour, lowering the average speed from 70.5 to 70.1 miles per hour. Although this change may be considered low in magnitude, we argue this will have important advantages in developing an estimate of Value of Time (VOT). 1.2. Value of Time Methodology VOT is a key economic parameter used in many different settings in academia and policy. Ashenfelter and Greenstone (2004) use VOT to calculate the Value of Statistical Life. VOT estimates have been applied repeatedly to evaluate environmental projects that use hedonic travel cost methods (Brown and Mendelsohn 1984), and in policy, transportation departments actively work with VOT coefficients to produce cost-benefits analysis for large public transportation projects such as to decide whether to build a subway or an additional highway lane. 1 So far, broadly speaking, VOT has been measured by the three following methods which are all based on agents choosing options across the extensive margin: Estimates are derived by comparing different modes of travel (car, plane, train) with each other relative to the travel cost and time requirements (Beesley, 1965, Gunn 2000). These results are likely however confounded due to different preferences towards and different attributes of the travel mode itself (i.e. while it is convenient to read a book on a train, one cannot read while driving). 1 In the U.S. there exist ‘low’, ‘middle’, and ‘high’ VOT estimates for travel time which range from 6.19 to 18.57, depending on specific circumstances (DOT 1997, Table III-11). For VOT coeficients used in public infrastructure projects in Great Britain Britain see Mackie et al. (2003). 3 Studies that use datasets on the same mode of travel aim to overcome this first problem, for example by comparing the choice of paying for a toll lane to circumvent congestion (i.e. Small et al. 2005) or to circumvent waiting in front of differentially priced neighboring gasoline stations (Deacon and Sonstelie 1985). However, this set of studies also faces the problem that the VOT estimate may be confounded. Drivers may have a distaste of being in a congested lane due to psychological costs. Also fuel consumption is higher in a stop and go setting. Further, if drivers are risk averse, predictability (at what time to arrive) has its own value, a feature that generated the literature on estimating the coefficient of “Value of Reliability” (i.e. see Small et al. 2005, Carrion-Madera and Levinson 2011). Lastly, stated preference methods (i.e. Calfe, Winston Stempski 2001, Small et al. 2005) use survey designs to orthoganalize the confounding variables. This method has been criticized however, that the hypothetical results are not generalizable to real world settings. This paper substantially adds to the literature2 on the value of time (VOT) providing a new methodology to estimate VOT which is based on the intensive margin of behavioral adjustments. This, we argue, has many important advantages compared to the previous VOT methods that are based on choices across the extensive margin. We find that the average driver values time according to 54% of the average wage rate. In our setting, the price affects a driver in the same vehicle making freely the choice on the intensive margin of how fast to drive on an uncongested highway. (The driver is not required to make a discrete choice on the extensive margin between a congested lane or a faster 2 See Wardman (2004) for a comprehensive review of the literature on the value of time. 4 HOV/priced lane, that come with different attributes with respect to safety, psychological cost of driving in stop and go, predictability of arriving in time and other factors). While our estimate of minus 0.4 mph for a one dollar increase in the price of gasoline may seem to be low in magnitude, we actually see this as an advantage because this small change of speed is arguably much less confounded with any of the variables potentially biasing previous results (such as the risk of getting involved in an accident as a function of speed). To put our VOT estimate into context, our result is in the middle between stated preference derived estimates and revealed preference methods. The two most prominent studies in economics using revealed preference methods are Small et al. (2005) and Deacon and Sonstelie (1985) estimating VOT being 93% of the hourly wage and “quite similar to individuals' after-tax wages”, respectively. Our estimate of 54% of the wage is lower, indicating that prior studies may have capitalized into the VOT the omitted disamenities of the outside option (i.e. being nerved when waiting in line or in traffic jam). On the other hand, at 54%, our estimate of the VOT is higher than when estimated by most stated preference methods. Calfe et al. (2001) estimate stated preference VOTs in the range of 14% to 27% of the average hourly gross wage (based on rank ordered logit and rank ordered probit models). Furthermore, we are interested if the incentive mechanism is heterogeneous across different types of drivers. Because our dataset contains the whole distribution of speeds within each hour, we are able to estimate the gasoline-price speed relationship at various percentiles of the distribution. We find that speeds are reduced most by vehicles in the range 75 mph to 85 mph. Fast drivers (above 95 mph) reduce speeds under-proportionately. In the extreme tail of the distribution, we find that the number of drivers speeding above 100 mph even increases with rising gas prices. We explain this effect indirectly: Higher gasoline prices reduce traffic volumes 5 and the additional space between vehicles provides opportunities to test maximum vehicle speeds on empty highways. Hence, if one is concerned about traffic safety, as speed reductions are less observed for the fastest drivers, the gasoline tax targeting safety has limited effects3. Finally, in order to investigate the information mechanism by which drivers are affected, one may ask whether the changes in speeding are affected by the price signal at the gasoline station, or whether the public media attention affected the changes in driving behavior. To this end, we construct from the New York Times and the Seattle Times a weekly dataset on the number of articles that referred to gas prices.4 We find that the time series of gas prices and media coverage are highly correlated. However, statistically, it is the price at the pump which dominates the observed changes to speeding behavior. These findings clearly have broader policy implications to both fuel conservation, safety on freeways and public infrastructure projects. This paper proceeds as follows: The next section describes our data, section 3 outlines the estimation methods and provides results, section 4 discusses our VOT approach, and section 5 concludes. 3 Recently Chi et al. (2010) empirically investigate the relationship between gasoline prices and traffic safety (i.e. accidents per vehicle mile traveled). For complimentary research see Leigh and Geraghty (2008) and Wilson, Stimpson and Hilsenrath (2009) and for estimates with respect to the value of safety, see Steimetz 2008, estimating the coefficient of “Value of Density”. 4 Repeatedly, news media covered tips on how to save on gas expenditures. One of the recommendation include to reduce speeds as gas mileage decreases at speeds above 60 miles per hour: “You can assume that each 5 m.p.h. you drive over 60 m.p.h. is like paying an additional $0.24 per gallon for gas” (New York Times, 2011). 6 2. Data The ideal situation to observe the effect of gas price on vehicle speeds would be a freeway with no speed limit in a location with no congestion or weather factors present. Drivers would only be constrained by their value of time compared to gas prices and the perceived safety impacts of speed. We have therefore limited our study to locations with a speed limit of 70 mph, the highest speed limit in Washington State. For this study, we merge hourly data from the following five datasets from January 2005 to December 2008. First, we are using hourly speed data collected by the Transportation Data Office of the Washington State Department of Transportation (WSDOT) at four locations in Washington with speed limits of 70 mph in both directions. The site locations are shown in Figure 1 and detailed in Table 1. WSDOT records all vehicles passing over the loop detectors and quantifies speeds in five mile per hour (mph) increments per hour from above 35 mph to above 100 mph. The WSDOT dataset also contains information about the number of error vehicles in the data per hour. Error vehicles are vehicles that got counted in the variable of the total sum of vehicles per hour, but that did not get counted in any speed category. We drop all observations if the error variable is greater than 30 vehicles per hour. Table 1: Speed Data Site Locations Site WSDOT Site Jurisdiction Freeway Direction NOAA Weather Site 1 R045 Woodland I-5 MP 20.14 Northbound Kelso 2 R045 Woodland I-5 MP 20.14 Southbound Kelso 3 R061 Eltopia SR 395 Northbound Tri-cities 4 R061 Eltopia SR 395 Southbound Tri-cities 5 R014 Tyler I-90 Westbound Spokane 6 R014 Tyler I-90 Eastbound Spokane 7 R055 Moses Lake I-90 Westbound Ephrata 8 R055 Moses Lake I-90 Eastbound Ephrata 7 Figure 1: Speed Data Sites Map Because weather conditions can severely impact driving conditions, we collected hourly temperature and precipitation information from the weather stations closest to our speed measurement sites, as indicated in Table 1. Hourly weather data are downloadable from the NOAA Local Climatological Data database from January 2005 to December 20008. We collected gasoline prices from the Department of Energy’s Energy Information Administration. Prices are given as an average of retail prices across the state of Washington using sales of all grades. The gas prices for January 3, 2005 to December 31, 2008 are shown in Figure 2. As is clearly visible, gas prices have been generally increasing with a definite spike in mid-2008. Also Figure 2 shows that gas prices are cyclical in nature with higher prices in the summer and lower prices in the winter months. 8 Figure 2: Average Retail Gas Prices for State of Washington by week $4.50 $4.00 $3.50 $3.00 $2.50 $2.00 $1.50 Mar‐05 May‐05 Sep‐05 Mar‐06 May‐06 Sep‐06 Mar‐07 May‐07 Sep‐07 Mar‐08 May‐08 Sep‐08 Jan‐05 Jul‐05 Nov‐05 Jan‐06 Jul‐06 Nov‐06 Jan‐07 Jul‐07 Nov‐07 Jan‐08 Jul‐08 Nov‐08 Finally, we collected site specific monthly local unemployment rate statistics and per capita personal income of the respective nearest metropolitan statistical areas to the highway location. Unemployment data are drawn from Local Area Unemployment Statistics of the Bureau of Labor Statistics5 and income from the CA1-3 series of the Regional Economic Accounts at the Bureau of Economic Analysis6. Table 2 summarizes the descriptive statistics of our data collection. 5 Available at http://data.bls.gov/cgi-bin/surveymost?la+53. 6 Available at http://www.bea.gov/regional/reis/drill.cfm. 9 Table 2: Descriptive Statistics of Washington speed data of eight highway sites Variable Unit Observations Mean Std. Dev. Min Max Average speed mph 228164 69.20 2.71 32.5 76.88 Gasprice U.S. dollar 280128 2.91 .59 1.831 4.412 Volume vehicles per hour 228164 538.91 645.11 5 4000 Error vehicles per hour 228164 6.13 39.36 0 979 Precipitation inches per hour 280512 .002 .022 0 6.6 Temperature Fahrenheit 270802 51.12 17.60 -14 111 Income U.S. $ 280512 29955.3 2304.1 25963 34011 Unemployment % 280512 6.12 1.29 4 10.5 Note: unit of observation is per site and hour. The relationship between the gasoline prices and weekly averaged vehicle speeds is displayed in Figure 3, here using the data of the Woodland Northbound speed measuring site. As can be visually seen, often observations are missing in large portions of the dataset, which is typical for speed measures. Rather than interpolating the missing hourly speed data, all observations are dropped from the dataset with missing speed information, which reduced the original dataset by 19%. 10 Figure 3: Average Speed per week and gas prices from January 1, 2005 to December 31, 2008 on I5 Northbound at Woodland Site 1 72 5 Average Speed (mph) 4 Gas Price ($) 70 23 68 2005 2006 2007 2008 date Average Speed (mph) Gas Price ($) 3. Method and Results In order to test whether drivers seek to conserve energy by reducing speeds, our main task is to estimate the direct causal effect of the price of gasoline on speeding behavior. Burger and Kaffine (2009) showed that this direct effect has to be estimated in the absence of congestion because otherwise observed speeds are merely a reaction of changed congestion and not because of the direct behavioral response that drivers seek to conserve gasoline by reducing speeds. As a reference, here we first start by estimating the relationship between speed and gasoline using the same method as in Burger and Kaffine (2009). Using the night hours of 2am to 4am as the time of the uncongested condition, the average speed in week t and highway i is estimated by 11 Speedit = α + β1 *pricet + Xit + Fi + Yt + εt (1) where Fi are freeway site fixed effects, Yt are year fixed effects and Xit are precipitation, holiday and summer dummies as well as income and unemployment. The results in Table 3 column (1) show that across all sites, speeds significantly increase by 0.47 miles per hour for a one U.S. dollar increase in gasoline prices. Hence, similar to the results of Los Angeles by Burger and Kaffine (2009), according to this methodology, also our dataset would suggest that the energy conservation hypothesis had to be rejected.7 To explore the causes that drive this result, we analyze the potential effect of road conditions that could confound this estimate. The seasonality of road conditions turn out to be important because these are correlated with the cyclicality of gas prices (see Figure 2). In the summer, speeds may be higher because of better visibility—extended daylight and less rain— and no freezing temperatures. In column (2), we control for seasonality by introducing month dummies Mt. The estimates of column (2) confirm this hypothesis: speeds are 2.4 mph lower in December compared to the fastest month of the year, July, and the gasprice coefficient renders insignificant. Because gas prices exhibit cyclicality, in this paper we will control for seasonality in all further regressions. To investigate into the robustness of these results further, in column (3) we unpool the price effect by traffic site and find that for the majority of the sites the price effect is insignificant. 7 Burger and Kaffine (2009) obtained an insignificant yet negative point estimate during uncongested times and note that speed limits in L.A. are 65 mph (instead of 70 mph as at the WA sites) and average income is higher, which may make drivers less reactive to gas price changes. These causes, together with the less precise weekly dataset likely contributed to the insignificant point estimate. 12 Finally, column (4) to (6) repeat the estimation for the evening hours from 4pm to 6pm, which we define as the PM time period. Here, again, we find that the within year speed difference of 2.9 miles per hour shows the importance of controlling for seasonality and we show that unpooling the coefficient on price across sites leads to non-robust results. Overall, these first estimation results of the effect of gasoline prices on speeds are inconsistent with the finer conditioning method that we will apply in the following. Table 3: Regression Results for Freeway Speeds in Washington State, unit of observation by site and week (1) (2) (3) (4) (5) (6) VARIABLES 2 am to 4 am 2 am to 4 am 2 am to 4 am PM basic PM basic PM site basic basic with site interacted with Month interacted Month FE with Month FE with Month FE gasprice 0.4679*** 0.2073 -0.4582*** 0.4696*** 0.1827 -0.6488*** (0.131) (0.155) (0.156) (0.149) (0.168) (0.155) _IsitXgaspr_2 -0.0314 0.0456 (0.172) (0.147) _IsitXgaspr_3 0.5313*** 0.4758*** (0.203) (0.182) _IsitXgaspr_4 0.3610** 0.7060*** (0.152) (0.131) _IsitXgaspr_5 1.0289*** 1.4334*** (0.224) (0.245) _IsitXgaspr_6 1.2176*** 1.3603*** (0.258) (0.235) _IsitXgaspr_7 0.8790*** 1.0636*** (0.188) (0.159) _IsitXgaspr_8 1.1501*** 1.1742*** (0.177) (0.135) _Imonth_2 1.2738*** 1.3007*** 1.3156*** 1.3403*** (0.212) (0.210) (0.156) (0.153) _Imonth_3 1.3954*** 1.4485*** 1.4844*** 1.5412*** (0.225) (0.227) (0.176) (0.177) _Imonth_4 1.5332*** 1.6486*** 1.4661*** 1.5970*** (0.256) (0.258) (0.213) (0.218) _Imonth_5 1.3759*** 1.5032*** 1.2188*** 1.3565*** (0.304) (0.300) (0.273) (0.270) _Imonth_6 1.7084*** 1.8621*** 1.3954*** 1.5621*** (0.299) (0.298) (0.257) (0.257) _Imonth_7 1.9709*** 2.1029*** 1.6339*** 1.7941*** (0.312) (0.310) (0.270) (0.269) _Imonth_8 1.8821*** 2.0166*** 1.7218*** 1.8768*** 13 (0.292) (0.291) (0.249) (0.251) _Imonth_9 1.6039*** 1.7603*** 1.3886*** 1.5692*** (0.308) (0.313) (0.268) (0.276) _Imonth_10 1.5546*** 1.6949*** 1.3907*** 1.5506*** (0.297) (0.305) (0.249) (0.261) _Imonth_11 1.3283*** 1.4033*** 0.4688** 0.5636*** (0.251) (0.252) (0.208) (0.210) _Imonth_12 -0.4046 -0.3359 -1.1133*** -1.0293*** (0.401) (0.401) (0.355) (0.350) hourlyrain -1.6060*** -0.7355 -0.8236 -3.2910*** -2.1376*** -2.3832*** (0.567) (0.544) (0.530) (0.496) (0.452) (0.433) summer 0.6361*** 0.2556*** 0.2338** 0.4030*** 0.0469 0.0200 (0.073) (0.099) (0.096) (0.070) (0.087) (0.086) Xmas -1.3232*** -0.1325 -0.1241 -1.2489*** 0.3707 0.3779 (0.446) (0.563) (0.554) (0.399) (0.475) (0.457) unemploy -0.3650*** -0.1435** -0.0921 -0.3166*** -0.1451*** -0.0889 (0.038) (0.063) (0.067) (0.036) (0.055) (0.060) income -0.0004*** -0.0002* -0.0006*** -0.0001 0.0000 -0.0005*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Constant 78.3192*** 71.2820*** 84.6710*** 74.9491*** 69.9927*** 85.0389*** (2.898) (2.981) (3.676) (2.840) (2.795) (3.315) Observations 1,429 1,429 1,429 1,416 1,416 1,416 R-squared 0.354 0.425 0.448 0.332 0.459 0.492 Regresssion includeds Site and Year fixed effects. Robust standard errors in parentheses clustered by site and week *** p<0.01, ** p<0.05, * p<0.1 14 Dataset Refinement Compared to the above estimation method, in the following, we make two major changes. First, instead of using weekly speed averages, we will work with hourly speed data. Secondly, we rely on constructing a dataset of speeds with the most homogenous exterior conditions as possible. Our first step is the filtering (dropping) of data for any hour in which the following conditions are not met: A. All observations are dropped if the average speed is less than 67 mph. By filtering for time periods with unusually low speeds, any congested or unusually slow time periods (due to accidents, temporal construction activities, and other factors) are removed from these typically uncongested segments of roadway. B. Precipitation can substantially alter traffic behavior due to changes in visibility. To account for this, all hours are dropped from the data set when precipitation was present during the hour. We also delete the observations two hours after the rain occurred because the spray from wet roads may still alter traffic flows. C. All hours are dropped with outside temperatures less than 32 degrees Fahrenheit. In addition all hours are dropped if temperature is missing in a ‘winter’ month, whereby ‘winter’ is defined site-specific to be the set of months with historic minimum temperatures below 32 Fahrenheit. D. Finally, we filtered out hours in which the total number of vehicles is less than 50. Note that none of the conditions A. to D. should be correlated with the direct behavioral response of speeds due to a change in gas price. To obtain this dataset, the total number of observations was reduced by 37%. The percentage reductions by each variable are displayed in Table 4 for the 24hour period in columns (1) and (2) and the PM period in column (3) and (4). As will be 15 explained below, the PM period is our major time period we will focus on in the analysis. Overall Table 4 shows that the weather variables have the largest influence on the reduction of the number of observations. Condition A—that the average speed is below 67 mph—reduced the dataset by 15% in the 24 hour period. However, in the more important afternoon PM period, only 2% of the data are dropped because of this condition. Table 4: Data Removed for regressions All Day PM period (1) (2) (3) (4) Data Obs % Obs % Rain 30759 13.5% 1774 13.7% Temp<32 30023 13.2% 899 6.9% Error>30 3301 1.4% 275 2.1% Volume<50 20742 9.1% 0 0% Avg Speed<67 33337 14.6% 294 2.3% Total observations 83765 36.7% 2843 21.9% Removed Total observations 144399 63.3% 10133 78.1% remaining By conditioning on the set A. to D. to obtain the dataset of speeds with the most homogenous exterior conditions as possible, we are now in the position to estimate the direct impact of the price of gasoline on drivers speeding behavior by Speedit = α + β1 *pricet + Mt + εt (2) where Speed is the hourly average speed, price is the weekly average gas price, and Mt are the monthly fixed effects. The resulting estimates of coefficients together with their robust standard errors which are clustered by week and site are shown in Table 5, along with the R-squared statistic measuring the fit for each equation. 16 Table 5: Vehicle speed regressions, conditioned on set A. to D. (1) (2) (3) COEFFICIENT Basic Model Hour Fixed Effects Hour and Site Fixed Effects gasprice -0.3248*** -0.3595*** -0.4206*** (0.0253) (0.0234) (0.0184) monthd1 -0.5270*** -0.7049*** -0.6948*** (0.0626) (0.0658) (0.0665) monthd2 -0.1892*** -0.4078*** -0.4355*** (0.0618) (0.0603) (0.0555) monthd3 -0.1001* -0.1574*** -0.1783*** (0.0582) (0.0579) (0.0501) monthd5 0.1745*** 0.2210*** 0.2400*** (0.0588) (0.0584) (0.0499) monthd6 0.1429** 0.2628*** 0.3040*** (0.0658) (0.0649) (0.0531) monthd7 0.3788*** 0.5351*** 0.5760*** (0.0623) (0.0616) (0.0495) monthd8 0.3313*** 0.4853*** 0.5020*** (0.0632) (0.0630) (0.0496) monthd9 0.0775 0.1720*** 0.1923*** (0.0641) (0.0640) (0.0535) monthd10 -0.0372 -0.0127 -0.0274 (0.0625) (0.0607) (0.0495) monthd11 -0.1395** -0.1963*** -0.1711*** (0.0681) (0.0660) (0.0602) monthd12 -0.3300*** -0.4748*** -0.4333*** (0.0889) (0.0943) (0.1054) timed1 -0.3577*** -0.3411*** (0.0239) (0.0236) timed2 -0.6540*** -0.5947*** (0.0323) (0.0319) timed3 -0.8410*** -0.7549*** (0.0319) (0.0315) timed4 -0.5816*** -0.5051*** (0.0293) (0.0282) timed5 0.2029*** 0.2536*** (0.0328) (0.0321) timed6 0.7369*** 0.7547*** (0.0359) (0.0353) timed7 1.1611*** 1.1670*** (0.0290) (0.0284) timed8 1.2134*** 1.2157*** (0.0242) (0.0237) timed9 1.2666*** 1.2656*** (0.0229) (0.0227) timed10 1.3397*** 1.3372*** (0.0235) (0.0235) timed11 1.4502*** 1.4447*** (0.0245) (0.0245) timed12 1.5571*** 1.5504*** (0.0249) (0.0251) 17 timed13 1.6772*** 1.6696*** (0.0249) (0.0251) timed14 1.8685*** 1.8609*** (0.0248) (0.0249) timed15 2.1039*** 2.0969*** (0.0234) (0.0236) timed16 2.2457*** 2.2389*** (0.0228) (0.0231) timed17 2.2181*** 2.2126*** (0.0238) (0.0240) timed18 2.0398*** 2.0368*** (0.0239) (0.0240) timed19 1.6898*** 1.6888*** (0.0236) (0.0236) timed20 1.2688*** 1.2683*** (0.0219) (0.0221) timed21 0.8569*** 0.8595*** (0.0204) (0.0206) timed22 0.5939*** 0.5983*** (0.0190) (0.0190) timed23 0.2750*** 0.2883*** (0.0178) (0.0177) sited2 -0.1424*** (0.0488) sited3 -0.2934*** (0.0441) sited4 0.3707*** (0.0478) sited5 0.2086*** (0.0439) sited6 0.4435*** (0.0430) sited7 0.4635*** (0.0448) sited8 0.1641*** (0.0429) Constant 71.0888*** 69.9232*** 69.9414*** (0.0884) (0.0871) (0.0725) Observations 142259 142259 142259 R-squared 0.024 0.309 0.341 Robust standard errors in parentheses clustered by site and week *** p<0.01, ** p<0.05, * p<0.1 Table 5 show that speeds significantly decrease by 0.32 to 0.42 miles per hour (mph). Column (1) confirms the significance of the month dummies. Note however that the inter-year speed range is equal to 0.7 miles per hour from January to July and hence the cyclicality is much less pronounced compared to the cyclicality in the weekly regression of Table 3. Column (2) and 18 (3) of Table 5 display the hourly fixed effects and show that speeds are generally highest in the afternoon/after-work time period of 4pm to 6pm. With our objective to work with a sample of drivers as homogenous as possible, we will continue to analyze the PM time period in more detail. This PM vehicle fleet is likely more representative with respect to the behavior of private vehicle owners. Instead, in other time periods of the day, the share of private vehicles to trucks and commercial vehicles is lower. Speed reactions by trucks and commercial vehicles are arguably more heterogeneous because their speeds are constrained by vehicle type and weight. Also, the incentive to conserve gasoline by commercial drivers is different if gasoline expenses get reimbursed. Table 6 displays the results of the PM models. Gas prices on average over all sites reduce by 0.38 or 0.44 mph for a $1 increase in the price of gasoline per gallon (column 1 and 2 without and with site fixed effects respectively). In column (3), we unpool the gas price coefficient over sites, and again find that at site 1, the effect is largest with a decrease of 0.97 mph and the smallest decrease of 0.13 mph at site 8. Table 6: Gas price speed relationship, conditioned on set A. to D., PM time period (1) (2) (3) (4) (5) (6) COEFFICIENT Basic Model Basic Model Basic Model Basic Model Basic Model Basic Model Sites Unpooled Year Year Sites Year Unpooled Gasprice -0.3752*** -0.4423*** -0.9692*** -0.2082*** -0.2826*** -0.8041*** (0.0303) (0.0258) (0.0598) (0.0546) (0.0451) (0.0725) _IsitXgaspr_2 0.2507*** 0.2383*** (0.0768) (0.0744) _IsitXgaspr_3 0.4601*** 0.4280*** (0.0854) (0.0865) _IsitXgaspr_4 0.5503*** 0.5375*** (0.0776) (0.0770) _IsitXgaspr_5 0.5960*** 0.5877*** (0.0759) (0.0755) _IsitXgaspr_6 0.7001*** 0.6865*** (0.0800) (0.0796) _IsitXgaspr_7 0.6754*** 0.6610*** 19 (0.0735) (0.0732) _IsitXgaspr_8 0.8424*** 0.8392*** (0.0754) (0.0748) _Isite_2 -0.4051*** -1.1023*** -0.3946*** -1.0565*** (0.0674) (0.2371) (0.0662) (0.2287) _Isite_3 -0.3525*** -1.6842*** -0.3579*** -1.6014*** (0.0578) (0.2449) (0.0575) (0.2471) _Isite_4 0.3170*** -1.2637*** 0.3191*** -1.2249*** (0.0605) (0.2408) (0.0597) (0.2389) _Isite_5 0.1720*** -1.5475*** 0.1698*** -1.5262*** (0.0622) (0.2457) (0.0614) (0.2436) _Isite_6 0.4100*** -1.6089*** 0.4084*** -1.5715*** (0.0606) (0.2415) (0.0598) (0.2394) _Isite_7 0.2439*** -1.7150*** 0.2514*** -1.6659*** (0.0627) (0.2282) (0.0624) (0.2264) _Isite_8 -0.0954 -2.5403*** -0.0999 -2.5364*** (0.0621) (0.2334) (0.0615) (0.2309) monthd1 -1.1709*** -1.1907*** -1.2117*** -1.0967*** -1.1209*** -1.1445*** (0.0787) (0.0760) (0.0718) (0.0819) (0.0785) (0.0748) monthd2 -0.5376*** -0.5921*** -0.5811*** -0.4625*** -0.5209*** -0.5130*** (0.0751) (0.0673) (0.0636) (0.0787) (0.0706) (0.0669) monthd3 -0.1125 -0.1371** -0.1411** -0.0714 -0.0988 -0.1046 (0.0737) (0.0648) (0.0619) (0.0753) (0.0666) (0.0638) monthd5 0.0155 0.0554 0.0687 -0.0310 0.0098 0.0241 (0.0788) (0.0687) (0.0690) (0.0805) (0.0702) (0.0702) monthd6 0.0389 0.1096 0.1130 -0.0185 0.0535 0.0584 (0.0870) (0.0729) (0.0722) (0.0881) (0.0740) (0.0737) monthd7 0.3446*** 0.4264*** 0.4129*** 0.2760*** 0.3602*** 0.3505*** (0.0814) (0.0636) (0.0632) (0.0840) (0.0658) (0.0655) monthd8 0.4134*** 0.4696*** 0.4618*** 0.3542*** 0.4119*** 0.4060*** (0.0820) (0.0658) (0.0645) (0.0843) (0.0679) (0.0661) monthd9 0.0488 0.0943 0.0961 -0.0025 0.0441 0.0476 (0.0793) (0.0673) (0.0661) (0.0809) (0.0686) (0.0669) monthd10 -0.0542 -0.0646 -0.0671 -0.0573 -0.0688 -0.0712 (0.0775) (0.0632) (0.0626) (0.0778) (0.0631) (0.0623) monthd11 -1.0119*** -1.0083*** -1.0068*** -0.9517*** -0.9521*** -0.9530*** (0.0823) (0.0717) (0.0735) (0.0824) (0.0720) (0.0727) monthd12 -1.1866*** -1.1654*** -1.2182*** -1.1146*** -1.0982*** -1.1540*** (0.0860) (0.0934) (0.0941) (0.0864) (0.0913) (0.0949) Yearline -0.0900*** -0.0864*** -0.0837*** (0.0243) (0.0206) (0.0206) Constant 71.9638*** 72.1126*** 73.6268*** 71.6920*** 71.8541*** 73.3467*** (0.1075) (0.0993) (0.1896) (0.1310) (0.1172) (0.2032) Observations 8596 8596 8596 8596 8596 8596 R-squared 0.171 0.247 0.271 0.174 0.250 0.274 Robust standard errors in parentheses clustered by site and week *** p<0.01, ** p<0.05, * p<0.1 One may be concerned that over the four years from 2005 to 2008, the vehicle fleet changed, which could affect speeds. Introducing a linear trend variable to equation (2) produces the results displayed in column (4) to (6) in Table 6. At all sites, on average, speeds significantly 20 reduce by 0.21 mph (column 4) and 0.28 mph (column 5) without and with site fixed effects respectively. In column (6), we unpool the gas price coefficient over sites, and again find that at site 1 the effect is largest with a decrease of 0.8 mph. All other sites also show a significant reduction of speeds, except for site 8, where the gasoline price is statistically insignificantly different from zero (p = 0.58 based on F-test). The yearline variable itself is stable across the different specifications indicating that per year speeds decrease on average by 0.08 to 0.09 mph. Alternative regressions using year dummies and other time polynomials lead to qualitatively similar results. In Table 7, we aim to investigate whether the changes in gasoline prices signal the drivers to slow down or whether the public media news has a similar effect. To this end, we collected all articles from the New York Times from 2005 to 2008 and counted the number of times the term “gas price” occurred by week. By comparing column (1) with column (3) we see that both the gasoline price and the news report reduce traffic speeds. When we include both variables simultaneously in the regression, displayed in column (2), the news variable becomes less significant and about one third in magnitude, while the price coefficient is qualitatively the same as in the basic model. From these regressions, we conclude that drivers react primarily to the price signal and that the news reports merely are correlated with gas prices but do seem to substantially effect driving behavior. Columns (4) and (5) repeat the regressions for the Seattle Times which leads to qualitatively the same results. 21 Table 7: Prices versus Information Effects, conditioned on set A. to D., PM time period (1) (2) (3) (4) (5) VARIABLES Basic Model NYT News NYT News SEA News SEA News Model Model 2 Model Model 2 gasprice -0.4423*** -0.4186*** -0.4371*** (0.026) (0.027) (0.027) NY Times -0.0055** -0.0174*** (0.002) (0.002) Seattle Times -0.0007 -0.0063*** (0.001) (0.001) Constant 72.1126*** 72.1000*** 70.9862*** 72.1083*** 70.9085*** (0.099) (0.099) (0.078) (0.099) (0.078) Observations 8,596 8,596 8,596 8,596 8,596 R-squared 0.247 0.248 0.208 0.247 0.202 Note: All regression includes month and site fixed effects. Robust standard errors in parentheses clustered by site and week *** p<0.01, ** p<0.05, * p<0.1 Habit Formation While the time period before July 2008 saw an unprecedented increase in retail gas prices to over $4.40 per gallon, by the end of 2008, gas prices had returned to less than $2.00, which represents the fastest ever decline in retail prices. We next investigate whether the speed adjustments are symmetric around the July 2008 spike, hence whether the change in behavior is temporary or permanent. Starting from our basic regression of Table 6, column (2), we include a post-June 2008 dummy, which is one for all days in 2008 after the gas spike occurred and we interact this dummy further with the gasprice variable itself. Results are shown in Table 8, column (1). We find that prior to the spike of July 2008, the marginal effect on speeds is 0.42 mph per dollar gallon price increase which is consistent with our prior results of Table 6. The coefficient of the Post-June variable indicates that after the 2008 spike, drivers maintained a 0.83 mph lower level of speed, hence adapting their behavior to a more fuel efficient driving. Furthermore, since gas prices drastically decreased for the remainder of the year, one may expect that drivers increase speeds again. We find that the marginal speed increase is about a half per 22 dollar price increase per gallon—the marginal effect decreases by 0.18 mph from 0.42 to 0.24 (according to the interaction term of the Post-June dummy with the gasprice variable). In summary, with rising gas prices, drivers reduce speeds by 0.42 mph per one dollar per gallon price increase, while with falling gas prices, the speed increases back by 0.24 mph per dollar price increase only, and drivers permanently reduce speeds for the rest of the year, conditional on gas price, by 0.83 mph. This relationship is displayed in Figure 4, which also includes the results of columns (2) to (3) of Table 8, showing that the overall finding is generally consistent for different specifications from which date on in 2008 the behavioral adjustments occur. Figure 4: Habit formation mph $/gallon 23 Table 8: Habit Formation (1) (2) (3) COEFFICIENT July Model Aug Model Sept Model gasprice -0.4245*** -0.4393*** -0.4399*** (0.0338) (0.0283) (0.0272) postJun08 -0.8288*** (0.1983) postJunXgas 0.1794*** (0.0584) postJul08 -0.9484*** (0.2153) postJulXgas 0.2220*** (0.0655) postAug08 -0.8931*** (0.2325) postAugXgas 0.2000*** (0.0735) postSept08 postSeptXgas Constant 72.0475*** 72.0922*** 72.0939*** (0.1219) (0.1070) (0.1034) Observations 8596 8596 8596 R-squared 0.252 0.252 0.252 Note: All regression includes month and site fixed effects. Robust standard errors in parentheses clustered by site and week *** p<0.01, ** p<0.05, * p<0.1 The price of gas and its impact on the distribution of speeds The drivers speeding the most are the least efficient from a consumption perspective.8 Do high gasoline prices effect these fast drivers overproportionally? Or do these drivers enjoy speeding on its own, irrespective of the price of gas? To test this, we take advantage of the information on the hourly speed distributions and run percentile regressions of the proportion of vehicles in each hour above the speed thresholds from 70 mph to 100 mph. The resulting estimates of elasticity coefficients are shown in Figure 4. This sequence of estimated elasticities is approximately U 8 New data by Davis et al. (2010) show that vehicles traveling 75 mpg consume on average between 24% (midsize car) to 34% (large SUV) more gasoline compared to a speed of 55 mph. While similar detailed information on the gasoline consumption speed relationship in the U.S. is sparse for vehicles traveling above 75 mph, data from Germany suggest that the average fuel consumption of an average vehicle is 40% higher if traveling above 100 mph and this percentage further increases with the weight of the vehicle. For details see Table 4.26 in Davis et al. (2010). 24 shaped with a minimum at the 80 mph percentage regression. All estimated elasticities are negative but for the very fastest drivers with speeds above 100 mph. We interpret this positive elasticity for the fasted vehicles as evidence that these drivers enjoy speeding by itself, irrespective of the gas price. Further, because with higher gas prices traffic volumes decrease, more space between vehicles on the highway may provide an additional incentive to ‘test’ the vehicles speeding ability. The standard errors are clustered by week and site and the resulting 95% confidence intervals displayed as upper and lower elasticity bounds in Figure 5. It shows that all estimates are significantly different from zero, with the exception of the 95 mph percentile elasticity. 25 Figure 5: Percentage speed elasticities with respect to the price of gasoline, conditional on A to D. and PM period Elasticity 0.6 0.4 0.2 0 mph 70 75 80 85 90 95 100 ‐0.2 ‐0.4 ‐0.6 ‐0.8 Note: Figure 4 displays seven elasticities, indicating the percentage change in vehicles driving above 70 mph (the most left elasticity point estimate) to 100 mph (the most right estimate) caused by a percent change in the price of gasoline. The seven displayed elasticities are derived by respective seven separate regressions with the dependent variable being the natural logarithm of the proportion of vehicles driving above the indicated speed and the independent variable defined as the logarithm of the gas price. Also all regressions include month and site fixed effects. The confidence intervals are computed via robust standard errors clustered by site and week. To investigate whether more empty highways provide an incentive for speeding, we next present our speeding-gas price elasticities conditional on traffic volumes. The resulting elasticities are displayed in Figure 6, represented by the red line and the intercepted blue graph for the linear and quadratic control of traffic volumes respectively. For comparison, also the base case elasticities unconditional on traffic volumes (the same point elasticities as in Figure 4) are displayed, here represented by the green dotted line. As expected, the results show that 26 controlling for traffic volumes decreases the speeding gas price elasticity for the fastest drivers from 0.31 (base case) to 0.22 (linear control of traffic volumes) and 0.20 (quadratic control function of traffic volumes). This suggests that because higher gas prices produce more space between vehicles, the fastest drivers were able to speed above 100 mph more often in times of high gas prices. Overall the U-shaped functions, however remains in all three specifications. Hence, if one is concerned about traffic safety, as speed reductions are less observed for the fastest drivers, the gasoline tax targeting safety has limited effects. Figure 6: Speed Elasticities with respect to the Price of Gasoline conditional on a linear and a quadratic Specification of Traffic Volumes. 0.4 0.3 0.2 0.1 0 quadratic 70 75 80 85 90 95 100 ‐0.1 linear from Figure 4 ‐0.2 ‐0.3 ‐0.4 ‐0.5 ‐0.6 Note: Figure 5 displays elasticities, indicating the percentage change in vehicles driving above 70 mph (the most left elasticity point estimate) to 100 mph (the most right estimate) caused by a percent change in the price of gasoline. The elasticities are derived by respective separate regressions with the dependent variable being the natural logarithm of the proportion of vehicles driving above the indicated speed and the independent variable defined as the logarithm of the gas price. Also all regressions include month and site fixed effects. In addition the linear specification also controls for traffic volume. The quadratic specification controls for the linear and a quadratic term of the traffic volume. The confidence intervals are computed via robust standard errors clustered by site and week (not displayed here): except for the elasticity at the 95 mph elasticity, all coefficient estimates are significantly different from zero for all three specifications. 27 4. Value of Time The literature on estimating the Value of Time (VOT) started with the seminal work by Beesley (1965) and today can be categorized into the following three approaches. Estimates derived by comparing different modes of travel (car, plane, train) with each other relative to the travel cost and time requirements (Beesley, 1965, Gunn 2000). Pricing studies and others that use datasets on the same mode of travel (e.g. Deacon and Sonstelie 1985, Small et al. 2005) but with drivers making discrete choices of either paying to avoid congestions, or waiting often for a prior unknown amount of time. Stated preference methods (i.e. Calfe, Winston Stempski 2001, Small et al. 2005) In this paper we provide a new method to estimate VOT which permits us to address some of the conceptual problems that have plagued the VOT literature. Our method does not depend on either different travel modes, or substantially different travel characteristics, such as choosing an HOV lane or paying to drive on an uncongested lane on a highway. As such, our empirical estimate promises to be less confounded. We find that a one dollar increase in gasoline/gallon reduces speeds by 0.44 mph. This suggests that concerns of other confounding factors can likely be omitted in the interpretation of our resulting VOT estimate (i.e. changes to the probability of obtaining a traffic ticket or the risk of getting involved in an accident are likely small given the change of speeds of 0.44 mph). More generally, the advantages of our study are that the VOT is derived by basing the estimate on the intensive margin and not (as in previous studies) on the extensive margin of making different choices among different bundles of attributes. 28 From the theory point of view, the approach is simple. Increasing the speed S (above 60 miles per hour) increases gasoline consumption g(S). Given the price of gasoline P, drivers cost minimize total costs C(S|P) = Pg(S|P) + VOTt(S|P) + R(S|P). Hence drivers equalize the marginal cost of gasoline expenditures Pδg/δS with the marginal time saving δt /δS with respect to speed, times the drivers subjectively perceived value of time (VOT), minus the marginal risk of driving at a higher speed. Here, R(S) can represent the dollar value of any disamenity of fast driving such as obtaining a speeding ticket, the cost of stress related to a higher concentration levels or the risk of getting involved in a traffic accident, with R(S) monotonic increasing and convex in S. So far in this paper, we empirically estimated S(P) and find that dS/dP = -0.44. (In fact, totally differentiating VOT = -[Pδg/δS+R(S)]/δt/δS it is easy to show that dS/dP < 0). In order to calculate VOT, we need to derive a number of additional parameters that we re-estimate from prior results in the engineering literature. First, t(S) = 1/S is simply a physical relationship. Second, we assume that R(S [70.1,70.5]) = constant. Hence for a small enough change of S, the change in perceived risk can be neglected. For any price change P2 > P1, VOT can hence be calculated by VOT = [(P2)g(S|P2)- P2g(S|P1)]/ [t(S|P2)- t(S|P1)], which is the amount of gasoline expenditure savings per mile by reducing the speeds from S|P2 to S|P1 relative to the additional time needed to travel that mile at the reduced speed S|P1. Finally, we derive g(S) by using the data of West et al. (1999) as summarized by Davis (2001). Based on nine vehicles sampled from a mix of automobiles and light trucks of model years 1988–1997, we estimate that the derivative δg/δS = 0.06018 in the relevant interval of S [70,75]. For a price increase from three to four dollar per gallon, we estimate that speeds reduce by 0.44 from 70.79 mph to 70.34 mph. To exemplify, consider a driver traveling exactly 70.79 miles. Hence his travel time increases from one hour to one hour and 23 seconds. This increase in travel times comes at savings in gasoline consumption of 29 g(70.79)=2.67 to g(70.34)=2.65 gallons, equivalent to expenditure savings of 75 cents. These saved 75 cents over the additional 23 seconds results in a VOT of $11.99 per hour. According to the Bureau of Labor Statistics, the average hourly wage in 2008 in the State of Washington was $22.32 (BLS, 2008) and after taxes the average hourly wage is roughly $17.44. Hence, $11.99 VOT accounts for 54% of the average hourly wage. 54% is considerably lower than the 93% estimate by Small et al. (2005) and also lower than the previous estimate by Deacon and Sonstelie (1985) referring to VOT as approximately being the after tax wage rate. We interpret our lower VOT estimate as evidence that these prior studies may be confounded by other psychological costs of waiting in a queue at a gasoline station, as in the study by Deacon and Sonstelie 1985. In the case of the study by Small et al. (2005), our results suggest that further subjective costs of being in a potential traffic jam have been capitalized into the 93% estimate. At the same time our VOT is larger than in prior stated preference studies. To investigate the divergence between revealed and stated preference studies continues to be an active research area by John List et al. and is beyond the scope of this paper here. 30 5. Conclusion Do drivers seek to conserve gasoline by reducing speeds in times of high gasoline prices? The time period from July 2004 to July 2008 saw an unprecedented increase in retail gas prices from $2.05 to over $4.40 per gallon of gasoline. By the end of 2008, retail gas prices were down to less than $2.00. The headlines from the summer 2008 tell the story best: “Record gas prices may curb summer demand.” (USA TODAY, 4/7/08); or “Outraged consumers look to sustainable fuel solutions for gas price pain relief” (FOX Business, 6/16/08). As the debate on gasoline taxes continues to unfold (Parry & Small 2005, Bento et al. 2009), economists are increasingly interested in the mechanisms by which gasoline prices affect gasoline demand. Vehicle mile traveled’ (VMT), as well as scrappage and adoption rates of vehicles are important determinants of the gasoline elasticity of demand (Hughes et al. 2010, Klier and Linn 2010). Here, we add to this literature by providing the first empirical estimate using disaggregated hourly speeding data, and find that a one dollar increase in gas prices modestly reduced the average speed by 0.4 mph. While this change is small it and enables us to calculate the VOT. In fact, for any much larger change of speeds, instead, the method of estimating VOT would be clearly worrisome due to changes in the value of safety among other confounders. Most importantly our studies contributes in providing a new methodology of deriving the VOT that relies on the first order condition of the price change directly, holding everything else constant. This ceteris paribus feature is important. Note that instead all prior research on travel time has been plagued with the “congestion effect”, but that congestion itself is “devalued”, so obtaining relatively high VOTs (Small et al. 2005 VOT = 93% of wage rate). Our estimate of VOT is 54% of the wage rate, hence substantially lower, as we condition the effect on 31 uncongested conditions directly. This suggests that disamenities of the outside option may have been capitalized in prior VOT studies. At the same time our VOT estimate is larger than in prior stated preference studies. To investigate the divergence between revealed and stated preference studies continues to be an active research area by John List et al. and is beyond the scope of this paper here. 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