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, [email protected]. 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

1 2 3 4 5 6 7 8

R045 R045 R061 R061 R014 R014 R055 R055

Woodland Woodland Eltopia Eltopia Tyler Tyler Moses Lake Moses Lake

I-5 MP 20.14 I-5 MP 20.14 SR 395 SR 395 I-90 I-90 I-90 I-90

Northbound Southbound Northbound Southbound Westbound Eastbound Westbound Eastbound

NOAA Weather Site Kelso Kelso Tri-cities Tri-cities Spokane Spokane Ephrata 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

Nov‐08

Sep‐08

Jul‐08

May‐08

Mar‐08

Jan‐08

Nov‐07

Sep‐07

Jul‐07

May‐07

Mar‐07

Jan‐07

Nov‐06

Sep‐06

Jul‐06

May‐06

Mar‐06

Jan‐06

Nov‐05

Sep‐05

Jul‐05

May‐05

Mar‐05

Jan‐05

$1.50

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 6

Available at http://data.bls.gov/cgi-bin/surveymost?la+53. Available at http://www.bea.gov/regional/reis/drill.cfm.

9   

Table 2: Descriptive Statistics of Washington speed data of eight highway sites Variable Average speed Gasprice Volume Error Precipitation Temperature Income Unemployment

Unit mph U.S. dollar vehicles per hour vehicles per hour inches per hour Fahrenheit U.S. $ %

Observations 228164 280128 228164 228164 280512 270802 280512 280512

Mean 69.20 2.91 538.91 6.13 .002 51.12 29955.3 6.12

Std. Dev. 2.71 .59 645.11 39.36 .022 17.60 2304.1 1.29

Min 32.5 1.831 5 0 0 -14 25963 4

Max 76.88 4.412 4000 979 6.6 111 34011 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

68

2

3 4 Gas Price ($)

Average Speed (mph) 70

5

72

Site 1

2005

2006

2007 date

2008

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 VARIABLES

gasprice

(1) 2 am to 4 am basic

(2) 2 am to 4 am basic with Month FE

(3) 2 am to 4 am site interacted with Month FE

(4) PM basic

(5) PM basic with Month FE

(6) PM site interacted with Month

0.4679*** (0.131)

0.2073 (0.155)

-0.4582*** (0.156) -0.0314 (0.172) 0.5313*** (0.203) 0.3610** (0.152) 1.0289*** (0.224) 1.2176*** (0.258) 0.8790*** (0.188) 1.1501*** (0.177) 1.3007*** (0.210) 1.4485*** (0.227) 1.6486*** (0.258) 1.5032*** (0.300) 1.8621*** (0.298) 2.1029*** (0.310) 2.0166***

0.4696*** (0.149)

0.1827 (0.168)

-0.6488*** (0.155) 0.0456 (0.147) 0.4758*** (0.182) 0.7060*** (0.131) 1.4334*** (0.245) 1.3603*** (0.235) 1.0636*** (0.159) 1.1742*** (0.135) 1.3403*** (0.153) 1.5412*** (0.177) 1.5970*** (0.218) 1.3565*** (0.270) 1.5621*** (0.257) 1.7941*** (0.269) 1.8768***

_IsitXgaspr_2 _IsitXgaspr_3 _IsitXgaspr_4 _IsitXgaspr_5 _IsitXgaspr_6 _IsitXgaspr_7 _IsitXgaspr_8 _Imonth_2 _Imonth_3 _Imonth_4 _Imonth_5 _Imonth_6 _Imonth_7 _Imonth_8

1.2738*** (0.212) 1.3954*** (0.225) 1.5332*** (0.256) 1.3759*** (0.304) 1.7084*** (0.299) 1.9709*** (0.312) 1.8821***

1.3156*** (0.156) 1.4844*** (0.176) 1.4661*** (0.213) 1.2188*** (0.273) 1.3954*** (0.257) 1.6339*** (0.270) 1.7218***

13   

_Imonth_9 _Imonth_10 _Imonth_11 _Imonth_12 hourlyrain summer Xmas unemploy income Constant

-1.6060*** (0.567) 0.6361*** (0.073) -1.3232*** (0.446) -0.3650*** (0.038) -0.0004*** (0.000) 78.3192*** (2.898)

(0.292) 1.6039*** (0.308) 1.5546*** (0.297) 1.3283*** (0.251) -0.4046 (0.401) -0.7355 (0.544) 0.2556*** (0.099) -0.1325 (0.563) -0.1435** (0.063) -0.0002* (0.000) 71.2820*** (2.981)

(0.291) 1.7603*** (0.313) 1.6949*** (0.305) 1.4033*** (0.252) -0.3359 (0.401) -0.8236 (0.530) 0.2338** (0.096) -0.1241 (0.554) -0.0921 (0.067) -0.0006*** (0.000) 84.6710*** (3.676)

-3.2910*** (0.496) 0.4030*** (0.070) -1.2489*** (0.399) -0.3166*** (0.036) -0.0001 (0.000) 74.9491*** (2.840)

(0.249) 1.3886*** (0.268) 1.3907*** (0.249) 0.4688** (0.208) -1.1133*** (0.355) -2.1376*** (0.452) 0.0469 (0.087) 0.3707 (0.475) -0.1451*** (0.055) 0.0000 (0.000) 69.9927*** (2.795)

(0.251) 1.5692*** (0.276) 1.5506*** (0.261) 0.5636*** (0.210) -1.0293*** (0.350) -2.3832*** (0.433) 0.0200 (0.086) 0.3779 (0.457) -0.0889 (0.060) -0.0005*** (0.000) 85.0389*** (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