Life and Death at the CAFE: Predicting the Impact of Fuel Economy Standards on Vehicle Safety

Transcription

1 Life and Death at the CAFE: Predicting the Impact of Fuel Economy Standards on Vehicle Safety Damien Sheehan-Connor October 26, 2012 Abstract Recent changes to the Corporate Average Fuel Economy (CAFE) standards in the United States mandate substantial improvement in automobile fuel economy over the next fifteen years. One of the ways that manufacturers improve fuel economy is to lower vehicle weights, which has impacts on safety. The innovation of this project is a novel maximum likelihood model that avoids issues of driver selection to separately identify the impact of vehicle weight on accident mortality. The key findings of the paper are: (1) A modest 5% average reduction in vehicle weight could increase annual accident fatalities by 4.9% or decrease them by 3.4% depending upon whether the reductions are concentrated at the lighter or heavier end of the current weight distribution; (2) Safety externalities attributiable to vehicle weight substantially exceed environmental ones; and (3) The relationship between vehicle weight and external safety e ects is such that a simple Pigovian excise tax on gasoline is unlikely to much improve e ciency. 1 Introduction Recent dramatic increases in Corporate Average Fuel Economy (CAFE) standards (Environmental Protection Agency and Department of Transportation, 2012) will likely lead to substantial changes in the composition of the United States passenger vehicle fleet. While most of the improvement in fuel economy will necessarily come from technological improvements, an inexpensive way to improve fuel economy is simply to lower vehicle weights. Indeed, the text of the new regulations states that we expect manufacturers to reduce vehicle mass as a compliance strategy (p ). The reduction in vehicle weight that occurred in response to the oil price shocks of the 1970s and the initial CAFE standards Department of Economics, Wesleyan University, Middletown, CT 06459; dsheehanconn@wesleyan.edu 1

2 was predicted by Crandall and Graham (1989) to substantially increase automobile accident fatalities. The passenger vehicle fleet has changed greatly since 1989, with one of the most notable features being the increase in the prevalence of light trucks, a category that includes minivans, pickup trucks, and sport utility vehicles (SUVs). Several authors have suggested that the external impacts on the safety of occupants of other vehicles may exceed the protective benefit a orded to light truck owners so that the now heavier vehicle fleet might actually be detrimental to overall safety (see especially Gayer (2004), White (2004), and Anderson (2008)). An important problem that must be addressed in interpreting automobile accident data is to disentangle vehicle fatality rates into a vehicle safety component (treatment e ect) and a driver safety component (selection e ect). This paper presents a novel model that allows simultaneous estimation of the relationship of vehicle weight with the safety of the own vehicle occupants (internal impacts) and that of other vehicles occupants (external impacts) conditional upon an accident occurring. The model is estimated using maximum likelihood techniques and data from the Fatality Analysis Reporting System (FARS), which includes data on every fatal accident that occurs in the United States, but excludes all non-fatal accidents. The nature of the model lends itself to simulating the potential impact of relatively arbitrary changes to vehicle fleet composition (within the support of the data used to estimate the model). These simulations do not assume that drivers of di erent vehicle types will have similar accident rates, but rather estimates the accident propensities directly from the data. The main empirical finding of the paper is that the protective e ects of weight on own occupants are diminishing while the destructive external e ects on other vehicle occupants are increasing. For marginal vehicle weight changes above approximately 3,800 lbs., the external costs outweigh the internal benefits in two-vehicle crashes. While the protective e ect of vehicle weight in singlevehicle crashes partly compensates for this, a substantial fraction of the vehicle fleet is above the weight where net safety costs exceed benefits. As a result, simulations show that reducing the weight of vehicles above the current mean weight would substantially reduce accident mortality while reduction below the mean weight would substantially increase it. Thus, exactly how the CAFE standards are achieved will have significant impacts on motor vehicle accident fatalities. There are several important implications of the main findings. First, data is presented suggesting that recent changes to the vehicle weight distribution have been concentrated in the lighter portion of the current distribution. The results of this paper thus suggest that increases in accident mortality are likely, a prediction consistent with a recently observed increase in mortality rates reported by the National Highway Tra c Safety Administration (2012). Second, safety externalities attributable to vehicle weight are of greater magnitude than environmental ones. This result is consistent with recent work by Anderson and Au hammer (2011) and suggests that changes in the CAFE standards could have safety costs that exceed their environmental benefits. Lastly, a simple gasoline excise tax is not likely to be an e ective way to internalize the safety ex- 2

3 ternalities since these externalities increase in vehicle weight significantly faster than fuel e ciency decreases. 2 Background In response to the high gasoline prices of the early 1970s, Congress passed the Energy Policy and Conservation Act of 1975 (Portney et al., 2003), which established the CAFE standards. The evolution of corporate average fuel economy standards and actual fuel economy in the US vehicle fleet since 1975 is shown in the upper panel of Figure 1. Realized fuel economy has equaled or exceeded that mandated by the standards in most years, generally by a small amount suggesting that the standards are typically binding on automobile manufacturers. The standards increased steadily from 1978 to the mid-1980s before remaining flat for the next two decades. A series of recent changes to the standards have culminated in new rules that will require approximately a doubling of fuel e ciency by The second panel of Figure 1 shows the evolution of average vehicle weight during the same time period. In 1975, the average car weighed approximately the same as the average light truck. This changed dramatically in the late 1970s with the mean weight of cars falling by 25% while light trucks weight dropped by only about 5%. Starting in 1980, average vehicle weight began to increase again. Initially this weight increase was due mainly to an increasing proportion of light trucks in the new vehicle fleet as shown in the bottom panel of the figure. Starting in the late 1980s, however, the average weights of both cars and light trucks begain to increase. In 2004, the fraction of new vehicles that were light trucks stopped increasing and average vehicle weight stabilized at about 4,000 pounds, thus returning to approximately the same level as 1975 though with a greater variance between the average weights of cars and light trucks. The bottom panel of the figure also shows how motor vehicle occupant death rates evolved over this period. There has generally been a steady decline, though the decline was more rapid from 1975 to 1990 than afterward and the most recent three years of data show some evidence of the decline becoming faster again. While the death rate did not increase in any year since 1986, the most recent data from the National Highway Tra c Safety Administration (2012) shows a substantial 8% increase for the first six months of The trends shown in Figure 1 are important to keep in mind, but are insu cient to infer relationships between CAFE standards, vehicle weight, and accident death rates. Many other things were changing over this time, such as the mix of vehicle miles traveled on di erent types of highways, average vehicle speeds, seatbelt usage, and safety technology used in motor vehicles. The seminal paper investigating the relationship between CAFE standards and motor vehicle accident death rates is Crandall and Graham (1989). The authors primary empirical contribution is a policy evaluation of the impact of 1 Because the standards for a given year depend upon the size of the vehicles actually sold during that year, the precise average level of the standards is uncertain in advance. 3

4 Figure 1: Fuel E ciency, Vehicle Weight, and Motor Vehicle Accident Mortality Rates Over Time Miles per Gallon Miles per Gallon year CAFE Std- Car Actual CAFE- Car CAFE Std- Lt Truck Actual CAFE- Lt Truck Weight in Pounds year Weight in Pounds Mean Weight Weight- Lt Truck Weight- Cars Fraction Lt Trucks Deaths per 100m Miles year Fraction Lt Trucks Deaths per 100m Miles Data Sources: CAFE Standards from United States Department of Transportation (2011); Actual fleet CAFE, average vehicle weight, and proportion light trucks from United States Environmental Protection Agency (2012); and motor vehicle accident deaths in passenger vehicles and vehicle miles traveled from Insurance Institute for Highway Safety (2012a). 4

5 the fuel economy standards on the distribution of weight in the US vehicle fleet. They combined these estimates with existing estimates of the relationship between vehicle weight and fatality risk to calculate that the lower weight of vehicles sold in 1989 attributable to CAFE standards would result in 2,200 to 3,900 additional fatalities over the course of a decade. While this may have been true in the 1980s, it is possible that things have changed because the vehicle fleet has continued to evolve substantially since then. As shown in Figure 1, vehicles have again become heavier, there has been a big shift away from cars and toward light trucks, and safety standards and equipment have continuously evolved. Numerous authors (e.g. Gayer (2004), White (2004), Anderson (2008), and Anderson and Au hammer (2011)) have since suggested that the external impacts of weight that increase fatalities of other vehicles drivers now exceed the internal benefits. One di culty in many of these papers has been accounting for selection e ects that could result in di erential driver quality (i.e. likelihood of accident) across vehicle types of di erent weights. Anderson (2008) took an important step in addressing potentially di erent crash rates among cars versus light trucks. His analysis combines a state-level panel estimation of the impact of weight on fatality rates with a random sample of accidents to separate external from internal impacts. His results suggest an elasticity of tra c fatalities with respect to light truck share of 0.34, with 80% of the additional fatalities accruing to those who were not occupants of the light trucks. A methodological limitation of Anderson (2008) was its reliance on aggregate state level data for estimation of the key variables of interest. His paper with Au hammer (Anderson and Au hammer, 2011) addresses this by looking at micro-level data. To address concerns about selection, the entire population of accidents from multiple states over several years is analyzed. A principal finding is that the external e ect of increasing vehicle weight by 1,000 lbs. is a 47% increase in the fatality risk of occupants of other vehicles, a result that is similar to that obtained here. Jacobsen (2011) investigates di erential driver selection by vehicle type using FARS data. His main identifying assumption is that the results of crash tests can be used to infer accident fatality risk. He then uses this inferred fatality risk combined with data about single vehicle fatality rates to calculate the riskiness of drivers of di erent vehicle types. These estimates of driver riskiness are then used, along with the estimates of vehicle riskiness inferred from crash tests, to calculate the results of changing the weight distribution of vehicles in response to CAFE standards. He finds that models that fail to account for the higher riskiness he finds for drivers of larger vehicles predict a decline in deaths of 135 for each 0.1 miles per gallon increase in fuel economy that results from a reduction in vehicle weight. Accounting for his estimates of driver riskiness suggests that fatalities will instead increase by 150. He also finds that unifying the fuel economy standards applied to cars and light trucks could mitigate much of this increase in fatalities. The main di erence between Jacobsen s approach and that taken here is that the current paper does not assume that vehicle 5

6 fatality risk is perfectly correlated with crash test results or even that this risk is the same in one and two vehicle accidents. Rather, the model developed here allows direct estimation of vehicle riskiness from real world crash data. The results thus complement Jacobsen s by providing estimates of similar important policy outcomes using a di erent set of identifying assumptions. 3 Methods 3.1 The Basic Model In their book Mostly Harmless Econometrics, Angrist and Pischke (2008) suggest envisioning an experiment, generally infeasible in practice, which would enable one to measure the relationship of interest. To evaluate the impact of own and other car characteristics on occupant death, one could imagine using an (obviously highly unethical) experimental framework in which occupied cars were crashed into one another under controlled conditions. The experiment could be repeated many times, varying any car characteristics of interest, and the survival or death of the occupants recorded after each collision. The model developed below is an attempt to approximate this idealized experimental design using available data. In particular, the model is based on the notion that there are many potentially fatal accidents that occur between two di erent types of vehicles. Potentially fatal or severe accidents are those in which there is a non-negligible probability of driver death. The model is based on the assumption that potentially fatal accidents are all of equivalent severity. While this is clearly not literally true, there will be substantially less heterogeneity in accident severity when only potentially fatal collisions are considered than when all collisions are considered. But an important identifying assumption of the model is that the explanatory variables of interest (e.g. own or other car weight) are orthogonal to any residual variation in accident severity after controlling for observed characteristics. Types of vehicles are identified as cars of the same make, model, and generation. While there may still be variation in car characteristics within types thus defined (e.g. di erent engines, optional features), this variation is small relative to that across types. A severe accident in this framework can be characterized by four pieces of information: 1. The type of the first car (first vs. second is an arbitrary designation) 2. The type of the second car 3. Whether the driver of the first car died 4. Whether the driver of the second car died Denote the k types of cars using the integers K =1, 2...k. As a starting point, assume that the probability that the driver of a car of type i 2 K dies conditional on being in a severe accident is given by the constant p i. For severe accidents 6

7 involving each pair of car types (i, j), there are four possible outcomes. These outcomes, along with the probability that each one of them will be observed in a randomly selected severe accident between i and j car types, are as follows: 1. The type i car driver dies and the type j car driver does not die p i (1 p j ) 2. The type i car driver does not die and the type j car driver dies (1 p i )p j 3. Both the type i car and the type j car drivers die p i p j 4. Neither the type i car nor the type j car drivers die (1 p i )(1 p j ) If data were available that contained the types of cars involved in, and driver outcomes for, a random sample of severe two-car crashes, the parameter vector p could easily be estimated using maximum likelihood techniques. For n observations, the likelihood function would simply be a product of n terms equal to one of the four probabilities given above. In practice, one is not likely to find a dataset that contains observations of a random sample of potentially fatal accidents. Most accident datasets include accidents that are highly unlikely to have been fatal so that the assumption of a constant fatality probability across accidents is untenable. On the other hand, the FARS dataset includes only potentially fatal accidents, but not a random sample of them. All accidents of types 1 through 3 in the above list are included in FARS, but accidents of type 4, which were potentially fatal but in which neither driver actually died, are excluded. This exclusion is obviously non-random as accidents involving car types with low probabilities of driver death are more likely to be excluded. To apply this model using the FARS dataset, the probabilities of events of types 1 through 3 must be modified to be conditional upon the accident being present in FARS. For compatibility with the above model, the FARS dataset is restricted to include only accidents in which one of the drivers died. The probability of a particular severe accident between cars of type i and j being observed in the restricted FARS data is equal to the probability that at least one of the drivers died, p i + p j p i p j. If a particular accident in the restricted FARS dataset involves cars of types i and j, the probabilities of observing the three patterns of drivers death are: 1. The type i car driver dies and the type j car driver does not die p i (1 p j ) p i + p j p i p j 7

8 2. The type i car driver does not die and the type j car driver dies (1 p i )p j p i + p j p i p j 3. Both the type i car and the type j car drivers die p i p j p i + p j p i p j The likelihood of observing the entire restricted FARS dataset is simply a product of terms of these three types with one term for each observation. In principle, the p vector can be estimated by finding the values that maximize the likelihood function. The logarithm of the likelihood function was maximized and the variance-covariance matrix of the estimates was obtained using Stata s ml commands (Gould et al., 2010). 3.2 Adding Vehicle Characteristics to the Basic Model The basic model allows estimation of the probability of driver death in severe accidents for each make, model, and generation of car in the FARS data using the single parameter p i to capture this probability for each car type. A refinement that models the probability p i as a function of other variables is desirable for several reasons. First, it allows direct exploration of the impact of particular vehicle characteristics, such as own car weight, on the probability of driver death. Second, it allows the introduction of some heterogeneity in accident severity by allowing the inclusion of characteristics of the other car in the collision, such as weight or class, as potential determinants of p i. Finally, it makes the model more numerically tractable by reducing the number of parameters to be estimated. The probability of driver death is modeled as a function of own and other car characteristics: p i = g(z i,z j ) (1) where Z i is a vector of own car characteristics and Z j is a vector of other car characteristics. Because the logarithms in the likelihood function require positive arguments, a simple linear functional form is problematic here as predicted probabilities could be less than zero (as with a linear probability model). To avoid this problem, the probabilities are modeled as the normal cumulative distribution function of a linear combination of the explanatory variables: p i = (Z i i + Z j j ) (2) With these modifications, the same maximum likelihood technique previously described can be used to estimate the i and j parameter vectors and thus the impact of the explanatory variables upon the probability of death. 8

9 3.3 Adding Risk of Accident to the Model The above model does not depend upon whether some vehicle types are more likely to be involved in severe accidents than others. Rather, it simply infers the impact of vehicle weight (and other characteristics) on mortality conditional on the types of vehicles involved in a given accident. But there are two reasons it is useful to determine which car types are more or less likely to be in severe accidents. First, estimates of the relative risk of severe accidents for each type of car can be correlated with type characteristics, such as vehicle weight. This would yield insight into whether these car characteristics are associated with riskiness, though causality would not be clear. Second, the rate of severe accidents for each type can be combined with data on single-car accident fatality rates to calculate the relative risk of driver death for each car type in severe single car accidents, as described below in Section 3.4. Using the FARS dataset, we can directly calculate the quantity f fat i,the fraction of all vehicles in fatal accidents that are of type i. From this, we would like to calculate the quantity f i, the fraction of all vehicles in severe accidents that are of type i. The two quantities di er because the probability that a severe accident involving a type i car will be fatal depends upon the probability that drivers of type i cars die in a severe accident and the probability that drivers of other cars die when in an accident with a type i car. We have already estimated the probabilities of driver death and write the probability that the driver of an i-type car dies in an accident with a j-type car as p i j. We start with: f fat i = f i R f i (3) where R f i is the relative risk of a fatality occuring in a severe accident involving atypei car compared with the average severe accident. To derive an expression for this relative risk, we assume that the types of the two cars involved in a severe accident are independent so that the fraction of severe accidents that involve cars of type i and j is equal to f i f j.then: P R f i = P j j f j(p i j + p j i p i j p j i ) Pk f jf k (p j k + p k j p j k p k j ). (4) Together, equations 3 and 4 provide a system of implicit equations that can be solved for the vector f. The solution was calculated using the fsolve command in Matlab s optimization toolbox (MathWorks, 2012). The variable f i is not of much interest by itself a high value could simply mean that type i cars are very common rather than that they are more likely than average to be in severe accidents. The variable, v i, the total fraction of vehicle miles traveled accounted for by type i cars, was calculated using data from the 2009 National Household Travel Survey. The relative risk of type i 9

10 cars being involved in severe accidents is simply: 2 r i = f i v i. (5) This relative risk was regressed on various vehicle characteristics, in particular vehicle weight, to determine what factors are correlated with higher risk of severe accident. 3.4 Single Vehicle Accidents The model described so far has allowed estimation of the impact of vehicle characteristics on the risk of being involved in a severe two car accident and the probability of driver death in such accidents. But nearly half of automobile accident fatalities occur in single vehicle accidents. Thus, any investigation of the impact of vehicle characteristics on accident fatalities requires consideration of how those characteristics a ect safety in single car accidents. One possible approach would be to assume that impacts on safety are the same in single and multi-vehicle accidents. There are reasons to doubt this assumption. Consider the case of vehicle weight. Increasing vehicle weight increases the kinetic energy that must be dissipated in a crash, but may also be protective by dissipating more of the energy outside of the passenger compartment. When much of the energy is brought by another vehicle (and thus independent of own car weight), the protective e ect may dominate. But in a single car crash, perhaps the increased energy e ect dominates. In fact, crash test authorities recommend that one not compare the results of frontal crash tests (where all of the energy in the crash is imparted by the tested car) across vehicles of di erent weights for just this reason. 3 An alternative approach, taken here, is to assume that vehicles that are involved in more two-car crashes will also be involved in more one-car crashes. That is, it is assumed that f i, the fraction of cars in a severe crash that are of type i, will be the same in both one and two car crashes. An estimate of f i was obtained in section 3.3 using the basic model described above and data from two car crashes. Define fi 1 as the fraction of cars observed in one-car fatal accidents that are of type i. The relative risk of dying (that is the risk of the driver dying in a type i car relative to being in a car of average risk) in a severe one-car accident is given by: r 1 i = f 1 i f i (6) The relative risk thus calculated for each of the n car types can be regressed on characteristics of the types to investigate whether weight or other characteristics are correlated with risk of death in single car accidents. 2 Note that for this analysis, f i was calculated using values of f fat i from 2009 only to match the vehicle miles traveled data. 3 According to the Insurance Institute for Highway Safety (2012b), Frontal crash test results can t be used to compare vehicle performance across weight classes. That s because the kinetic energy involved in the moderate overlap and small overlap frontal tests depends on the speed and weight of the test vehicle. Thus, the crash is more severe for heavier vehicles. 10

11 3.5 Simulating Changes in the Weight Distribution The results from the previous three sections can be used to simulate the impact of changes in the distribution of vehicle weights. Simulations for the number of deaths in two-car accidents proceed as follows: 1. Calculate a matrix, P, where the(i, j) entry contains the probability of driver death for drivers of each car type i conditional on being in a severe two-car collision with each other car type j. 2. Multiply each each probability of driver death in P by the average number of occupants of type i cars. The (i, j) entry of the resulting matrix, D, gives the expected number of deaths that will occur in a type i car conditional on collison with a type j car. Assumption: The probability of death for non-driver occupants is the same as the probability of driver death. 3. Calculate a matrix, F, whose (i, j) entry is equal to the proportion of all severe two car accidents that are between cars of types i and j. This matrix is equal to f i fi 0,wheref i is the fraction of cars in severe accidents that are of type i. Assumption: The types of cars involved in two-car accidents are independent. 4. Multiply each element of F by a calibration parameter, N 2, which is equal to the number of cars involved in severe two car accidents in a year. The (i, j) entry of the resulting matrix, N, gives the expected number of type i cars involved in accidents with type j cars each year. 5. Perform element-by-element multiplication of the matrices D and N to obtain a matrix T whose (i, j) entry is the expected number of deaths of occupants of type i cars involved in accidents with type j cars in a year. 6. Sum all of the elements of T to obtain the total predicted number of deaths in two-car crashes per year. 7. Choose a value for the calibration parameter, N 2, such that the predicted number of deaths in two-car crashes is equal to the actual number of deaths in multiple car crashes for Assumption: The results for two car crashes are a valid proxy for what happens in (the much smaller number of) multiple car crashes. 8. Modify the vehicle weights used in calculating the P matrix in step 1. Repeat steps 2 through 6 using the calibrated value for N 2 to obtain the predicted number of deaths in two-car crashes for the modified vehicle weight distribution. 11

12 The procedure for simulating the impact on deaths in one-vehicle crashes is analogous except that the matrices are replaced with vectors. The calibration parameter N 1 is chosen such that the predicted number of deaths in one-car accidents equals the actual number observed in Data Automobile accident data was obtained from the FARS dataset for the years For the two-car accident model, the FARS data was restricted to accidents involving two cars in which one of the drivers died. The data fields of interest contained the make, model, and model year of the involved cars as well as whether the driver of each car died. The dataset was further restricted to accidents in which both of the cars were of model year 2000 or later and had data available in the automobile characteristics dataset, described below. Analyses that focused on determinants of the relative risk of being in an accident were further restricted to accidents that occurred in 2009 to match the automobile usage data available. The FARS data was also used to calculate the total number of deaths that occurred in one- and multiple-car accidents in The 2009 National Household Travel Survey (NHTS) was used to obtain information on automobile usage by make, model, and generation (or type ) of vehicle. Total vehicle miles travelled and person miles travelled (to compute mean occupancy) by vehicle type were calculated using this data. Data on vehicle characteristics by type was obtained from the Consumer Reports web site (Consumer Reports, 2011). This data included weight, class, fuel e ciency, cost of operation, and other characteristics. Only vehicle types for which data was available from Consumer Reports were included in the restricted FARS dataset described above. 4 Results 4.1 Two-Car Crashes The impact on driver survival probability of own and other vehicle characteristics was evaluating using the basic model with vehicle characteristics and the FARS data for the years 2000 to The results of several specifications are presented in Table 1. The specification in column 1 suggests that the class of the own and other vehicles are not important determinants of driver mortality these variables are omitted in the remainder of the specifications. The impact of own vehicle weight shows some evidence of non-linearity, while other vehicle weight is not well described by the quadratic specification. The results in column 2 suggest that increasing own vehicle weight lowers driver mortality, but that this e ect is diminishing in additional weight. Other vehicle weight increases driver mortality with a 1,000 pound increase in weight increasing the probability of death by approximately 8 percentage points, or 43%. This result very closely matches the results of Anderson and Au hammer (2011) who find 12

13 a 47% increase per 1,000 pounds. Examination of columns 3 through 5 reveals that the impacts of own and other weight are robust to inclusion or exclusion of vehicle make fixed e ects, 4 time controls, and geographic controls. The specification in column 2 is used as the preferred specification in subsequent graphs and analyses. Figure 2 shows the probability of driver death as a function of own and other car weight. Note that the impact of other car weight is not precisely linear- this is due to the fact that the linear specification is embedded in the normal cdf, which displays significant curvature through the range of predicted probabilities. The probability of death for a driver of a 2,000 pound car in a collision with an average car is nearly 35% but drops to less than 10% for the driver of a 6,000 pound vehicle. When colliding with a 2,000 pound car, the driver of an average car has less than a 5% chance of death, but the probability increases to more than 30% when colliding with a 6,000 pound car. Figure 3 shows the slope of the curves in Figure 2. For two car collisions, the marginal benefit to a driver from increasing the weight of her car exceeds the marginal cost imposed upon drivers of other cars until the weight of her car reaches approximately 3,800 pounds. At higher weights, the marginal private safety benefit of additional weight is lower than the marginal social cost in terms of safety. 4.2 Risk of Accident The procedure described in section 3.3 was used to calculate the relative risk of severe accident for each vehicle type in the data. Specification 2 from table 1 was used to create the probabilities required for the calculation of the fraction of vehicles in severe accidents that are of a given type. The relative risks were regressed on vehicle weight, class, and indicators for vehicle make. The results of these regressions, presented in Table 2, show no evidence of a correlation between vehicle weight and the relative risk of severe accident. This is consistent with the observation in the final CAFE rule (Environmental Protection Agency and Department of Transportation, 2012) that a conference of experts failed to reach consensus on whether smaller, lighter vehicles maneuver better, and thus avoid more crashes, than larger, heavier vehicles (p ). The results do show evidence that the relative risk of accident is lower for minivans and sport utility vehicles than for cars and pickup trucks, but there is no reason to suppose this relationship is causal. Minivans and SUVs are typically family cars and so the drivers of such vehicles may simply be more cautious than average. Because this analysis found no evidence of an impact of vehicle weight on risk of accident, no such relationship is assumed in the analyses and simulations that follow. 4 Note that the controls for vehicle make are not strict fixed e ects. All larger makes have an indicator included, but smaller makes are grouped together into three groups: 1. Asian luxury cars (Lexus, Infiniti, Acura); 2. European other than Volkswagen (Mercedes, BMW, Audi, Volvo, Saab, Land Rover, Jaguar, Mini, Smart); 3. Other Asian (Mitsubishi, Suzuki). 13

14 Table 1: Impact of Vehicle Weight on Probability of Driver Death in Two Car Accidents VARIABLES (1) (2) (3) (4) (5) wt ** *** *** *** *** (0.0679) (0.0416) (0.0384) (0.0416) (0.0407) wtsq ** * ** * ( ) ( ) ( ) ( ) ( ) wt *** *** *** *** (0.0598) ( ) ( ) ( ) ( ) wtsq ( ) suv (0.0248) minivan (0.0303) pickup (0.0263) suv (0.0221) minivan (0.0288) pickup (0.0248) age *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) agesq1 8.10e-05*** 8.10e-05*** 8.41e-05*** 8.08e-05*** 7.82e-05*** (1.15e-05) (1.14e-05) (1.13e-05) (1.14e-05) (1.13e-05) redesign yr *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) year ( ) ( ) rural (0.0277) Make FE yes yes no yes yes Region FE no no no no yes Mean of p i Observations 4,238 4,238 4,238 4,238 4,238 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Entries are marginal e ects on probability of driver death. Variables ending in 1 refer to own-car characteristics while 2 refers to other-car characteristics. Weight is measured in 1,000s of pounds. Mean of p i refers to the mean predicted probability of driver death observed in the sample. 14

15 Figure 2: Probability of Driver Death by Own and Other Car Weight Probability of Driver Death Weight (1,000s of pounds) Own car weight Other car weight Notes: The line labeled Own car weight shows the probability of death for the driver of avehicleoftheindicatedweightwithotherwiseaveragecharacteristicsinacollisionwitha vehicle of average characteristics. The line labeled Other car weight shows the probability of death for the driver of a car of average characteristics in a collision with a car that is of the indicated weight but has otherwise average characteristics. These probabilities were calculated using the specification in column 2 of Table 1. 15

16 Figure 3: Change in Probability of Driver Death by Own and Other Car Weight Change in Prob of Death for 1,000 lb Change Weight (1,000s of pounds) Decrease in own driver prob Increase in other driver prob Notes: The line labeled Decrease in own driver prob shows the marginal decrease in probability of death from increasing vehicle weight by 1,000 pounds for the driver of a vehicle of the indicated weight with otherwise average characteristics in a collision with a vehicle of average characteristics. The line labeled Increase in other driver prob shows the marginal increase in probability of death for the driver of a car of average characteristics in a collision with a car that is of the indicated weight increased by 1,000 lbs, but which has otherwise average characteristics. These probabilities were calculated using the specification in column 2ofTable1. 16

17 Table 2: Impact of Weight on Relative Risk of Accident VARIABLES (1) (2) (3) (4) wt (0.162) (0.181) (0.168) (0.213) suv *** *** *** (0.278) (0.276) (0.259) minivan *** *** *** (0.314) (0.281) (0.374) pickup (0.660) (0.686) (0.604) redesign yr 0.119** 0.131*** (0.0485) (0.0500) Make FE no no no yes Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The relative risk of accident for each vehicle type was calculated as described in section 3.3 using the specification in column 2 of table 1. Relative risk was regressed on vehicle type characteristics, including vehicle weight. 17

18 4.3 One-Car Crashes The procedure described in section 3.4 was used to calculate r i, the relative risk of death in a severe one car accident for each vehicle type. The interpretation of r i is that if the probability of death in a one car accident averaged across all cars is equal to p 1, then the probability of death for a driver of a type i car is p i = r i p 1. It is not possible to estimate p 1 with the available data, but choosing an arbitrary value serves simply as a normalization. To see this, recall that the analysis will proceed by regressing p i on vehicle type characteristics. Suppose that the value chosen for p 1 is twice the true value. The estimated coe cients in the above regression would then also be twice the true values, but the values relative to the chosen p 1 would be correct. Also, when the simulations are carried out, they are calibrated by choosing the number of one-car accidents that generates a predicted number of fatalities equal to the observed number. If the value chosen for p 1 were twice the true value, then the calibration number of accidents would simply be half as large. Changes in vehicle characteristics would change the predicted number of fatalities by the same number whatever value is chosen for p 1. Because it is simply a normalization, the value chosen for p 1 is equal to the mean predicted probability of death in the preferred two-car specification, or The calculated and normalized value for p i was then used as the dependent variable in the regressions presented in Table 3. The estimates of the impact of weight on the probability of driver death in one car accidents are not strongly statistically significant, but are relatively robust across specifications 2 through 5, which use multiple control variables. Specifications 2 and 3 include indicators for vehicle class: suv, minivan, and pickup with car being the omitted category. Of these, only pickup trucks show a significant di erence in safety. This could be due to a feature inherent to pickups, such as their greater propensity to rollover in accidents (Insurance Institute for Highway Safety, 2012c), or due to selection e ects (e.g. pickup drivers are less likely to wear seat belts (Pickrell and Ye, 2011)). Specifications 4 and 5 omit the suv and minivan indicators since they were found to be insignificant, but are highly correlated with vehicle weight and so could obscure the statistical significance of weight in the regressions. In these specifications, weight is significantly protective of driver death with an e ect that diminishes with increasing weight. Figure 4 shows the predicted value of the probability of driver death for the specification in column 4. Note that while the estimated probability begins increasing at approximately 4,700 pounds, the 95% confidence interval includes the possibility that the probability is always decreasing. It is plausible that additional weight could reduce safety at higher weights, but the estimates here are far from definitive. In fact, for a wide range of weights, from about 3,500 to 6,000 pounds, the predicted probability of death varies only between about 17 and 20 percent. For these reasons, in the simulations it is assumed that the probability of driver death decreases to the estimated minimum and then remains flat as weight is increased further. Also note that the fact that there is little additional protective benefit from weight above 3,800 pounds suggests 18

19 Table 3: Impact of Vehicle Weight on Relative Risk of Driver Death in One-Car Accidents VARIABLES (1) (2) (3) (4) (5) wt * ** * (0.102) (0.101) (0.0156) (0.0982) (0.0126) wtsq * * (0.0122) (0.0119) (0.0117) suv (0.0301) (0.0305) minivan (0.0425) (0.0420) pickup 0.103** ** *** *** (0.0432) (0.0431) (0.0340) (0.0356) redesign yr *** *** *** *** ( ) ( ) ( ) ( ) Make FE no yes yes yes yes Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Entries are coe cients from regressions with a dependent variable equal to the probability of driver death in one car accidents. normalized to as described in section 4.3. pounds. The mean probability of death was Vehicle weight is measured in 1,000s of that marginal private benefits from additional weight in one car crashes will do little to o set the fact that marginal social cost exceeds marginal private benefit in two car crashes in this weight range. 4.4 Simulation Results The procedure described in Section 3.5 was used to simulate the impact of changing the distibution of vehicle weights. Probabilities of death in one- and two-car accidents were calculated using the specifications in column 4 of Table 3 and column 2 of Table 1, respectively. Values for the simulation parameters N 1 and N 2 were chosen so that the predicted number of deaths in one- and two-car accidents using the original weight distribution matched the observed number of deaths in 2009, 14,842 deaths in one-car accidents and 13,073 deaths in multi-car accidents. 5 5 Note that these figures sum to less than the total number of deaths reported in 2009 because they omit deaths of pedestrians and motorcyclists. 19

20 Figure 4: Probability of Driver Death in Severe One Car Accident Probability of Driver Death Weight (1,000s of pounds) Predicted P(driver death) 95% CI of Prediction Notes: The figure shows the predicted probability of driver death in a severe one car accident using the specification in column 4 of Table 3. 20

21 Table 4: Simulation Results for a 5 Percent Reduction in Mean Vehicle Weight Baseline Sim 1 Sim 2 Sim 3 Weight change below mean 0-5% % 0 Weight change above mean 0-5% % Change for overall fleet 0-5% -5% -5% Deaths in 1 Car Accidents 14,842 15,277 15,759 14,980 Change vs. baseline Deaths in 2+ Car Accidents 13,073 12,559 13,514 11,994 Change vs. baseline ,079 Total Deaths 27,915 27,836 29,273 26,974 Change vs. baseline , The results of three simulations are presented in Table 4. For each simulation, the vehicle miles traveled-weighted average weight of the vehicle fleet is decreased by 5 percent relative to the base year of This is a relatively modest overall weight reduction many new models being released are lighter than the preceding generation by this amount already. The first simulation assumes a uniform 5 percent reduction in the weight of all vehicle types. This results in an increase in deaths in one-car accidents that is slightly more than o set by a reduction in deaths in two-car accidents, but the overall change in the number of deaths is small. The second simulation assumes that all weight reduction occurs in vehicles below the mean weight and that the reduction is su cient to reduce the mean of the whole fleet by 5 percent. In this case, the simulation suggests that there will be increased deaths in both one- and two- car accidents with a total of 1,358 more deaths, which is 4.9 percent more than the baseline number. The third simulation assumes that all weight reduction occurs in vehicles above the mean weight. The small increase in one-car fatalities is much more than o set by the resulting decrease in two-car fatalities so that a total reduction in deaths of 941, or 3.4 percent of baseline, is predicted. 5 Discussion 5.1 Early Evidence on Changes in the Vehicle Weight Distribution The results of the simulations presented in Section 4.4 suggest that reductions in vehicle weight can result in net improvements or reductions in motor vehicle accident deaths, depending on where in the current weight distribution the reductions are concentrated. There are several reasons why the safety-reducing 21

22 path of weight decreases concentrated among currently lighter vehicles might occur. First, the new standards require a greater percentage improvement in fuel economy for passenger cars than for light trucks, which include SUVs and pickup trucks. Second, the optimal compliance strategy for a given vehicle will depend upon the elasticity of demand for weight among likely buyers of that vehicle. Buyers of heavier vehicles sometimes need a larger vehicle for commercial reasons or to transport large numbers of people. Heavier vehicles are also more expensive and so buyers of these vehicles are less likely to be price-sensitive. This would enable automakers to use costly technologies, such as turbochargers and hybrid systems, to achieve fuel e ciency gains in heavier cars more easily than they could in lighter ones. Third, recent work by Whitefoot and Skerlos (2012) suggests that automakers may find it advantageous to increase the size of vehicles in response to the new standards. This is because vehicles with a larger footprint must meet a lesser standard. The CAFE final rule (Environmental Protection Agency and Department of Transportation, 2012) argues that the standards are footprint-neutral (pp ), but the incentives at work are complicated, particularly when one considers consumer demand as Whitefoot and Skerlos do in their work. There are also empirical reasons to be concerned that vehicle weight reductions might be concentrated among lower weight vehicles. Figure 5 shows the cumulative distribution function for vehicle weight for vehicles sampled in the 2009 National Household Travel Survey and separately for vehicles sold in It is clear that at low weights, the cdf for cars sold in 2011 lies above that for the vehicle fleet estimated for At higher weights, the two cdf s move closer together, eventually crossing, implying that the weight distribution for vehicles sold in 2011 was more uneven than was the case for vehicles on the road in This fact is confirmed by the summary data in Table 5. While the mean vehicle weight of vehicles sold in 2011 was 3.2% lower than the mean weight of the vehicle fleet in the 2009 NHTS, the standard deviation of weights was 3.7% higher. Conditional upon being above the average weight of either sample, vehicles sold in 2011 are actually heavier than those in the 2009 vehicle fleet. Conversely, conditional upon being below average weight, the vehicles sold in 2011 were lighter than those on the road in All of this suggests that the variance in weights has been increasing even as the mean weight has been decreasing. To get an idea of which of these impacts is likely to be more important in determining changes in vehicle fatalities, it is useful to do a final comparison. In the 2009 fleet, the mean weight of an above average weight vehicle is 4947 pounds. For cars sold in 2011, the mean weight of an above average weight vehicle is 4892 pounds, a reduction of 1.1%. The comparable comparison for below average weight cars shows a reduction of 4.3%. Thus, while the average weight of vehicles sold in 2011 is lower than the average for the 2009 vehicle fleet, the weight reductions have been disproportionately concentrated among lower weight vehicles. 6 The data for vehicle sales in 2011 was obtained from Cain (2012). 22

23 Figure 5: Cumulative Distribution Function for Vehicle Weight, 2011 Sales and 2009 Fleet Cumulative Distribution Vehicle Weight (pounds) Vehicle Sales, 2011 Vehicle Fleet, 2009 NHTS Notes: The figure shows the cumulative distribution for vehicle weight for two populations: (1) new vehicles sold in 2011; and (2) the existing vehicle fleet as estimated using the 2009 NHTS. Note that the large vertical jump in the 2009 vehicle fleet data is due to the fact that three popular models of pickup truck had very similar weights. Table 5: Comparison of Vehicle Weights between 2009 Vehicle Fleet and 2011 Vehicle Sales 2009 Fleet 2011 Sales % Di erence Mean wt % Std. Dev. wt % wt wt > % wt wt < % wt wt > % wt wt < % 23