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) stan-dards in the United States mandate substantial improvement in automo-bile fuel economy over the next fifteen years. One of the ways that man-ufacturers improve fuel economy is to lower vehicle weights, which hasimpacts on safety. The innovation of this project is a novel maximumlikelihood model that avoids issues of driver selection to separately iden-tify the impact of vehicle weight on accident mortality. The key findingsof the paper are: (1) A modest 5% average reduction in vehicle weightcould increase annual accident fatalities by 4.9% or decrease them by 3.4%depending upon whether the reductions are concentrated at the lighter orheavier end of the current weight distribution; (2) Safety externalities at-tributiable to vehicle weight substantially exceed environmental ones; and(3) The relationship between vehicle weight and external safety e↵ects issuch that a simple Pigovian excise tax on gasoline is unlikely to muchimprove e�ciency.

1 Introduction

Recent dramatic increases in Corporate Average Fuel Economy (CAFE) stan-dards (Environmental Protection Agency and Department of Transportation,2012) will likely lead to substantial changes in the composition of the UnitedStates passenger vehicle fleet. While most of the improvement in fuel economywill necessarily come from technological improvements, an inexpensive way toimprove fuel economy is simply to lower vehicle weights. Indeed, the text of thenew regulations states that “we expect manufacturers to reduce vehicle mass” asa compliance strategy (p. 62741). The reduction in vehicle weight that occurredin response to the oil price shocks of the 1970s and the initial CAFE standards

⇤Department of Economics, Wesleyan University, Middletown, CT 06459; dsheehan-conn@wesleyan.edu

1

was predicted by Crandall and Graham (1989) to substantially increase auto-mobile accident fatalities. The passenger vehicle fleet has changed greatly since1989, with one of the most notable features being the increase in the prevalenceof light trucks, a category that includes minivans, pickup trucks, and sport util-ity vehicles (SUVs). Several authors have suggested that the external impactson the safety of occupants of other vehicles may exceed the protective benefita↵orded to light truck owners so that the now heavier vehicle fleet might actu-ally be detrimental to overall safety (see especially Gayer (2004), White (2004),and Anderson (2008)).

An important problem that must be addressed in interpreting automobile ac-cident data is to disentangle vehicle fatality rates into a vehicle safety component(treatment e↵ect) and a driver safety component (selection e↵ect). This paperpresents a novel model that allows simultaneous estimation of the relationship ofvehicle weight with the safety of the “own” vehicle occupants (internal impacts)and that of “other” vehicles occupants (external impacts) conditional upon anaccident occurring. The model is estimated using maximum likelihood tech-niques and data from the Fatality Analysis Reporting System (FARS), whichincludes data on every fatal accident that occurs in the United States, but ex-cludes all non-fatal accidents. The nature of the model lends itself to simulatingthe potential impact of relatively arbitrary changes to vehicle fleet composition(within the support of the data used to estimate the model). These simulationsdo not assume that drivers of di↵erent vehicle types will have similar accidentrates, but rather estimates the accident propensities directly from the data.

The main empirical finding of the paper is that the protective e↵ects ofweight on own occupants are diminishing while the destructive external e↵ectson other vehicle occupants are increasing. For marginal vehicle weight changesabove approximately 3,800 lbs., the external costs outweigh the internal benefitsin two-vehicle crashes. While the protective e↵ect of vehicle weight in single-vehicle crashes partly compensates for this, a substantial fraction of the vehiclefleet is above the weight where net safety costs exceed benefits. As a result,simulations show that reducing the weight of vehicles above the current meanweight would substantially reduce accident mortality while reduction below themean weight would substantially increase it. Thus, exactly how the CAFEstandards are achieved will have significant impacts on motor vehicle accidentfatalities.

There are several important implications of the main findings. First, datais presented suggesting that recent changes to the vehicle weight distributionhave been concentrated in the lighter portion of the current distribution. Theresults of this paper thus suggest that increases in accident mortality are likely,a prediction consistent with a recently observed increase in mortality rates re-ported by the National Highway Tra�c Safety Administration (2012). Second,safety externalities attributable to vehicle weight are of greater magnitude thanenvironmental ones. This result is consistent with recent work by Anderson andAu↵hammer (2011) and suggests that changes in the CAFE standards couldhave safety costs that exceed their environmental benefits. Lastly, a simplegasoline excise tax is not likely to be an e↵ective way to internalize the safety ex-

2

ternalities since these externalities increase in vehicle weight significantly fasterthan fuel e�ciency decreases.

2 Background

In response to the high gasoline prices of the early 1970s, Congress passed theEnergy Policy and Conservation Act of 1975 (Portney et al., 2003), which estab-lished the CAFE standards. The evolution of corporate average fuel economystandards and actual fuel economy in the US vehicle fleet since 1975 is shownin the upper panel of Figure 1. Realized fuel economy has equaled or exceededthat mandated by the standards in most years, generally by a small amount sug-gesting that the standards are typically binding on automobile manufacturers.The standards increased steadily from 1978 to the mid-1980s before remain-ing flat for the next two decades. A series of recent changes to the standardshave culminated in new rules that will require approximately a doubling of fuele�ciency by 2025.1

The second panel of Figure 1 shows the evolution of average vehicle weightduring the same time period. In 1975, the average car weighed approximatelythe same as the average light truck. This changed dramatically in the late 1970swith the mean weight of cars falling by 25% while light trucks’ weight droppedby only about 5%. Starting in 1980, average vehicle weight began to increaseagain. Initially this weight increase was due mainly to an increasing proportionof 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 lighttrucks begain to increase. In 2004, the fraction of new vehicles that were lighttrucks stopped increasing and average vehicle weight stabilized at about 4,000pounds, thus returning to approximately the same level as 1975 though witha greater variance between the average weights of cars and light trucks. Thebottom panel of the figure also shows how motor vehicle occupant death ratesevolved over this period. There has generally been a steady decline, though thedecline was more rapid from 1975 to 1990 than afterward and the most recentthree 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 recentdata from the National Highway Tra�c Safety Administration (2012) shows asubstantial 8% increase for the first six months of 2012.

The trends shown in Figure 1 are important to keep in mind, but are in-su�cient to infer relationships between CAFE standards, vehicle weight, andaccident death rates. Many other things were changing over this time, such asthe mix of vehicle miles traveled on di↵erent types of highways, average vehiclespeeds, seatbelt usage, and safety technology used in motor vehicles.

The seminal paper investigating the relationship between CAFE standardsand motor vehicle accident death rates is Crandall and Graham (1989). Theauthors primary empirical contribution is a policy evaluation of the impact of

1Because the standards for a given year depend upon the size of the vehicles actually soldduring that year, the precise average level of the standards is uncertain in advance.

3

Figure 1: Fuel E�ciency, Vehicle Weight, and Motor Vehicle AccidentMortality Rates Over Time

1525

35M

iles

per G

allo

n

1525

35M

iles

per G

allo

n

1975 1980 1985 1990 1995 2000 2005 2010year

CAFE Std- Car CAFE Std- Lt TruckActual CAFE- Car Actual CAFE- Lt Truck

3000

4000

5000

Wei

ght i

n Po

unds

3000

4000

5000

Wei

ght i

n Po

unds

1975 1980 1985 1990 1995 2000 2005 2010year

Mean Weight Weight- CarsWeight- Lt Truck

.51

1.5

22.

5D

eath

s pe

r 100

m M

iles

.1.2

.3.4

.5Fr

actio

n Lt

Tru

cks

1975 1980 1985 1990 1995 2000 2005 2010year

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

the fuel economy standards on the distribution of weight in the US vehiclefleet. They combined these estimates with existing estimates of the relationshipbetween vehicle weight and fatality risk to calculate that the lower weight ofvehicles sold in 1989 attributable to CAFE standards would result in 2,200 to3,900 additional fatalities over the course of a decade.

While this may have been true in the 1980s, it is possible that things havechanged because the vehicle fleet has continued to evolve substantially sincethen. As shown in Figure 1, vehicles have again become heavier, there has beena big shift away from cars and toward light trucks, and safety standards andequipment have continuously evolved. Numerous authors (e.g. Gayer (2004),White (2004), Anderson (2008), and Anderson and Au↵hammer (2011)) havesince suggested that the external impacts of weight that increase fatalities ofother vehicles drivers now exceed the internal benefits. One di�culty in manyof these papers has been accounting for selection e↵ects that could result indi↵erential driver quality (i.e. likelihood of accident) across vehicle types ofdi↵erent weights.

Anderson (2008) took an important step in addressing potentially di↵erentcrash rates among cars versus light trucks. His analysis combines a state-levelpanel estimation of the impact of weight on fatality rates with a random sampleof accidents to separate external from internal impacts. His results suggest anelasticity 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 lighttrucks.

A methodological limitation of Anderson (2008) was its reliance on aggregatestate level data for estimation of the key variables of interest. His paper withAu↵hammer (Anderson and Au↵hammer, 2011) addresses this by looking atmicro-level data. To address concerns about selection, the entire population ofaccidents from multiple states over several years is analyzed. A principal findingis 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 similarto that obtained here.

Jacobsen (2011) investigates di↵erential driver selection by vehicle type usingFARS data. His main identifying assumption is that the results of crash testscan be used to infer accident fatality risk. He then uses this inferred fatality riskcombined with data about single vehicle fatality rates to calculate the riskinessof drivers of di↵erent vehicle types. These estimates of driver riskiness are thenused, along with the estimates of vehicle riskiness inferred from crash tests, tocalculate the results of changing the weight distribution of vehicles in responseto CAFE standards. He finds that models that fail to account for the higherriskiness he finds for drivers of larger vehicles predict a decline in deaths of135 for each 0.1 miles per gallon increase in fuel economy that results froma reduction in vehicle weight. Accounting for his estimates of driver riskinesssuggests that fatalities will instead increase by 150. He also finds that unifyingthe fuel economy standards applied to cars and light trucks could mitigate muchof this increase in fatalities. The main di↵erence between Jacobsen’s approachand that taken here is that the current paper does not assume that vehicle

5

fatality risk is perfectly correlated with crash test results or even that this riskis the same in one and two vehicle accidents. Rather, the model developed hereallows direct estimation of vehicle riskiness from real world crash data. Theresults thus complement Jacobsen’s by providing estimates of similar importantpolicy 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 wouldenable one to measure the relationship of interest. To evaluate the impact ofown and other car characteristics on occupant death, one could imagine usingan (obviously highly unethical) experimental framework in which occupied carswere crashed into one another under controlled conditions. The experimentcould be repeated many times, varying any car characteristics of interest, andthe survival or death of the occupants recorded after each collision.

The model developed below is an attempt to approximate this idealizedexperimental design using available data. In particular, the model is based onthe notion that there are many “potentially fatal” accidents that occur betweentwo di↵erent “types” of vehicles. “Potentially fatal” or “severe” accidents arethose in which there is a non-negligible probability of driver death. The modelis based on the assumption that potentially fatal accidents are all of equivalentseverity. While this is clearly not literally true, there will be substantiallyless heterogeneity in accident severity when only potentially fatal collisions areconsidered than when all collisions are considered. But an important identifyingassumption of the model is that the explanatory variables of interest (e.g. ownor other car weight) are orthogonal to any residual variation in accident severityafter controlling for observed characteristics. “Types” of vehicles are identifiedas cars of the same make, model, and generation. While there may still bevariation 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 ofinformation:

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 conditionalon being in a severe accident is given by the constant p

i

. For severe accidents

6

involving each pair of car types (i, j), there are four possible outcomes. Theseoutcomes, along with the probability that each one of them will be observed ina 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

pi

(1� pj

)

2. The type i car driver does not die and the type j car driver dies

(1� pi

)pj

3. Both the type i car and the type j car drivers die

pi

pj

4. Neither the type i car nor the type j car drivers die

(1� pi

)(1� pj

)

If data were available that contained the types of cars involved in, and driveroutcomes for, a random sample of severe two-car crashes, the parameter vectorp could easily be estimated using maximum likelihood techniques. For n obser-vations, the likelihood function would simply be a product of n terms equal toone of the four probabilities given above. In practice, one is not likely to finda dataset that contains observations of a random sample of “potentially fatal”accidents. Most accident datasets include accidents that are highly unlikely tohave been fatal so that the assumption of a constant fatality probability acrossaccidents is untenable. On the other hand, the FARS dataset includes only“potentially fatal” accidents, but not a random sample of them. All accidentsof types 1 through 3 in the above list are included in FARS, but accidents oftype 4, which were potentially fatal but in which neither driver actually died,are excluded. This exclusion is obviously non-random as accidents involving cartypes with low probabilities of driver death are more likely to be excluded.

To apply this model using the FARS dataset, the probabilities of events oftypes 1 through 3 must be modified to be conditional upon the accident beingpresent in FARS. For compatibility with the above model, the FARS datasetis restricted to include only accidents in which one of the drivers died. Theprobability of a particular severe accident between cars of type i and j beingobserved in the restricted FARS data is equal to the probability that at leastone of the drivers died, p

i

+ pj

� pi

pj

. If a particular accident in the restrictedFARS dataset involves cars of types i and j, the probabilities of observing thethree patterns of drivers death are:

1. The type i car driver dies and the type j car driver does not die

pi

(1� pj

)

pi

+ pj

� pi

pj

7

2. The type i car driver does not die and the type j car driver dies

(1� pi

)pj

pi

+ pj

� pi

pj

3. Both the type i car and the type j car drivers die

pi

pj

pi

+ pj

� pi

pj

The likelihood of observing the entire restricted FARS dataset is simply a prod-uct 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 likeli-hood function. The logarithm of the likelihood function was maximized and thevariance-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 severeaccidents for each make, model, and generation of car in the FARS data using thesingle parameter p

i

to capture this probability for each car type. A refinementthat models the probability p

i

as a function of other variables is desirable forseveral reasons. First, it allows direct exploration of the impact of particularvehicle characteristics, such as own car weight, on the probability of driver death.Second, it allows the introduction of some heterogeneity in accident severity byallowing the inclusion of characteristics of the other car in the collision, such asweight or class, as potential determinants of p

i

. Finally, it makes the model morenumerically tractable by reducing the number of parameters to be estimated.

The probability of driver death is modeled as a function of own and othercar characteristics:

pi

= g(Zi

, Zj

) (1)

where Zi

is a vector of own car characteristics and Zj

is a vector of other carcharacteristics. Because the logarithms in the likelihood function require posi-tive arguments, a simple linear functional form is problematic here as predictedprobabilities could be less than zero (as with a linear probability model). Toavoid this problem, the probabilities are modeled as the normal cumulativedistribution function of a linear combination of the explanatory variables:

pi

= �(Zi

↵i

+ Zj

↵j

) (2)

With these modifications, the same maximum likelihood technique previouslydescribed can be used to estimate the ↵

i

and ↵j

parameter vectors and thus theimpact of the explanatory variables upon the probability of death.

8

3.3 Adding Risk of Accident to the Model

The above model does not depend upon whether some vehicle types are morelikely to be involved in severe accidents than others. Rather, it simply infersthe impact of vehicle weight (and other characteristics) on mortality conditionalon the types of vehicles involved in a given accident. But there are two reasonsit is useful to determine which car types are more or less likely to be in severeaccidents. First, estimates of the relative risk of severe accidents for each typeof car can be correlated with type characteristics, such as vehicle weight. Thiswould yield insight into whether these car characteristics are associated withriskiness, though causality would not be clear. Second, the rate of severe acci-dents for each type can be combined with data on single-car accident fatalityrates to calculate the relative risk of driver death for each car type in severesingle car accidents, as described below in Section 3.4.

Using the FARS dataset, we can directly calculate the quantity ffat

i

, thefraction of all vehicles in fatal accidents that are of type i. From this, we wouldlike to calculate the quantity f

i

, the fraction of all vehicles in severe accidentsthat are of type i. The two quantities di↵er because the probability that a severeaccident involving a type i car will be fatal depends upon the probability thatdrivers of type i cars die in a severe accident and the probability that drivers ofother cars die when in an accident with a type i car. We have already estimatedthe probabilities of driver death and write the probability that the driver of ani-type car dies in an accident with a j-type car as p

i|j . We start with:

ffat

i

= fi

Rf

i

(3)

where Rf

i

is the relative risk of a fatality occuring in a severe accident involvinga type i car compared with the average severe accident. To derive an expressionfor this relative risk, we assume that the types of the two cars involved in asevere accident are independent so that the fraction of severe accidents thatinvolve cars of type i and j is equal to f

i

fj

. Then:

Rf

i

=

Pj

fj

(pi|j + p

j|i � pi|jpj|i)P

j

Pk

fj

fk

(pj|k + p

k|j � pj|kpk|j)

. (4)

Together, equations 3 and 4 provide a system of implicit equations that can besolved for the vector f . The solution was calculated using the “fsolve” commandin Matlab’s optimization toolbox (MathWorks, 2012).

The variable fi

is not of much interest by itself– a high value could simplymean that type i cars are very common rather than that they are more likelythan average to be in severe accidents. The variable, v

i

, the total fraction ofvehicle miles traveled accounted for by type i cars, was calculated using datafrom the 2009 National Household Travel Survey. The relative risk of type i

9

cars being involved in severe accidents is simply:2

ri

=fi

vi

. (5)

This relative risk was regressed on various vehicle characteristics, in particularvehicle weight, to determine what factors are correlated with higher risk ofsevere accident.

3.4 Single Vehicle Accidents

The model described so far has allowed estimation of the impact of vehiclecharacteristics on the risk of being involved in a severe two car accident andthe probability of driver death in such accidents. But nearly half of automobileaccident fatalities occur in single vehicle accidents. Thus, any investigation ofthe impact of vehicle characteristics on accident fatalities requires considerationof how those characteristics a↵ect safety in single car accidents.

One possible approach would be to assume that impacts on safety are thesame in single and multi-vehicle accidents. There are reasons to doubt thisassumption. Consider the case of vehicle weight. Increasing vehicle weight in-creases the kinetic energy that must be dissipated in a crash, but may alsobe protective by dissipating more of the energy outside of the passenger com-partment. When much of the energy is brought by another vehicle (and thusindependent of own car weight), the protective e↵ect may dominate. But in asingle car crash, perhaps the increased energy e↵ect dominates. In fact, crashtest authorities recommend that one not compare the results of frontal crashtests (where all of the energy in the crash is imparted by the tested car) acrossvehicles of di↵erent weights for just this reason.3

An alternative approach, taken here, is to assume that vehicles that areinvolved 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 areof type i, will be the same in both one and two car crashes. An estimate offi

was obtained in section 3.3 using the basic model described above and datafrom two car crashes. Define f1

i

as the fraction of cars observed in one-car fatalaccidents that are of type i. The relative risk of dying (that is the risk of thedriver dying in a type i car relative to being in a car of average risk) in a severeone-car accident is given by:

r1i

=f1i

fi

(6)

The relative risk thus calculated for each of the n car types can be regressed oncharacteristics of the types to investigate whether weight or other characteristicsare correlated with risk of death in single car accidents.

2Note that for this analysis, fi was calculated using values of ffati from 2009 only to match

the vehicle miles traveled data.3According 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 becausethe kinetic energy involved in the moderate overlap and small overlap frontal tests depends onthe speed and weight of the test vehicle. Thus, the crash is more severe for heavier vehicles.”

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3.5 Simulating Changes in the Weight Distribution

The results from the previous three sections can be used to simulate the impactof changes in the distribution of vehicle weights. Simulations for the number ofdeaths in two-car accidents proceed as follows:

1. Calculate a matrix, P, where the (i, j) entry contains the probability ofdriver death for drivers of each car type i conditional on being in a severetwo-car collision with each other car type j.

2. Multiply each each probability of driver death in P by the average num-ber 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 carconditional on collison with a type j car.

• Assumption: The probability of death for non-driver occupants is thesame as the probability of driver death.

3. Calculate a matrix, F, whose (i, j) entry is equal to the proportion of allsevere two car accidents that are between cars of types i and j. Thismatrix is equal to f

i

f 0i

, where fi

is the fraction of cars in severe accidentsthat are of type i.

• Assumption: The types of cars involved in two-car accidents are in-dependent.

4. Multiply each element of F by a calibration parameter, N2, which is equalto 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 typei cars involved in accidents with type j cars each year.

5. Perform element-by-element multiplication of the matrices D and N toobtain a matrix T whose (i, j) entry is the expected number of deaths ofoccupants 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 ofdeaths in two-car crashes per year.

7. Choose a value for the calibration parameter, N2, such that the predictednumber of deaths in two-car crashes is equal to the actual number ofdeaths in multiple car crashes for 2009.

• Assumption: The results for two car crashes are a valid proxy forwhat 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 N2 to obtain thepredicted number of deaths in two-car crashes for the modified vehicleweight distribution.

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The procedure for simulating the impact on deaths in one-vehicle crashes isanalogous except that the matrices are replaced with vectors. The calibrationparameter N1 is chosen such that the predicted number of deaths in one-caraccidents equals the actual number observed in 2009.

3.6 Data

Automobile accident data was obtained from the FARS dataset for the years2000-2010. For the two-car accident model, the FARS data was restricted toaccidents involving two cars in which one of the drivers died. The data fields ofinterest contained the make, model, and model year of the involved cars as wellas whether the driver of each car died. The dataset was further restricted toaccidents in which both of the cars were of model year 2000 or later and had dataavailable in the automobile characteristics dataset, described below. Analysesthat focused on determinants of the relative risk of being in an accident werefurther restricted to accidents that occurred in 2009 to match the automobileusage data available. The FARS data was also used to calculate the total numberof deaths that occurred in one- and multiple-car accidents in 2009.

The 2009 National Household Travel Survey (NHTS) was used to obtaininformation on automobile usage by make, model, and generation (or “type”)of vehicle. Total vehicle miles travelled and person miles travelled (to computemean occupancy) by vehicle type were calculated using this data.

Data on vehicle characteristics by type was obtained from the ConsumerReports web site (Consumer Reports, 2011). This data included weight, class,fuel e�ciency, cost of operation, and other characteristics. Only vehicle types forwhich data was available from Consumer Reports were included in the restrictedFARS dataset described above.

4 Results

4.1 Two-Car Crashes

The impact on driver survival probability of own and other vehicle character-istics was evaluating using the basic model with vehicle characteristics and theFARS data for the years 2000 to 2010. The results of several specifications arepresented in Table 1. The specification in column 1 suggests that the class ofthe own and other vehicles are not important determinants of driver mortality–these variables are omitted in the remainder of the specifications. The impactof own vehicle weight shows some evidence of non-linearity, while other vehi-cle weight is not well described by the quadratic specification. The results incolumn 2 suggest that increasing own vehicle weight lowers driver mortality,but that this e↵ect is diminishing in additional weight. Other vehicle weightincreases driver mortality with a 1,000 pound increase in weight increasing theprobability of death by approximately 8 percentage points, or 43%. This resultvery closely matches the results of Anderson and Au↵hammer (2011) who find

12

a 47% increase per 1,000 pounds. Examination of columns 3 through 5 revealsthat the impacts of own and other weight are robust to inclusion or exclusionof vehicle make fixed e↵ects,4 time controls, and geographic controls. The spec-ification in column 2 is used as the preferred specification in subsequent graphsand analyses.

Figure 2 shows the probability of driver death as a function of own and othercar weight. Note that the impact of other car weight is not precisely linear- thisis 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 anaverage car is nearly 35% but drops to less than 10% for the driver of a 6,000pound vehicle. When colliding with a 2,000 pound car, the driver of an averagecar has less than a 5% chance of death, but the probability increases to morethan 30% when colliding with a 6,000 pound car. Figure 3 shows the slope ofthe curves in Figure 2. For two car collisions, the marginal benefit to a driverfrom increasing the weight of her car exceeds the marginal cost imposed upondrivers of other cars until the weight of her car reaches approximately 3,800pounds. At higher weights, the marginal private safety benefit of additionalweight 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 ofsevere accident for each vehicle type in the data. Specification 2 from table 1was used to create the probabilities required for the calculation of the fractionof vehicles in severe accidents that are of a given type. The relative risks wereregressed on vehicle weight, class, and indicators for vehicle make. The results ofthese regressions, presented in Table 2, show no evidence of a correlation betweenvehicle weight and the relative risk of severe accident. This is consistent withthe observation in the final CAFE rule (Environmental Protection Agency andDepartment of Transportation, 2012) that a conference of experts failed to reach“consensus on whether smaller, lighter vehicles maneuver better, and thus avoidmore crashes, than larger, heavier vehicles” (p. 62744). The results do showevidence that the relative risk of accident is lower for minivans and sport utilityvehicles than for cars and pickup trucks, but there is no reason to suppose thisrelationship is causal. Minivans and SUVs are typically “family cars” and so thedrivers of such vehicles may simply be more cautious than average. Because thisanalysis 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.

4Note that the controls for vehicle make are not strict fixed e↵ects. All larger makes havean indicator included, but smaller makes are grouped together into three groups: 1. Asianluxury 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

Table 1: Impact of Vehicle Weight on Probability of Driver Death inTwo Car Accidents

VARIABLES (1) (2) (3) (4) (5)

wt1 -0.141** -0.134*** -0.118*** -0.132*** -0.131***(0.0679) (0.0416) (0.0384) (0.0416) (0.0407)

wtsq1 0.0104 0.00959** 0.00801* 0.00934** 0.00865*(0.00764) (0.00464) (0.00425) (0.00464) (0.00456)

wt2 0.0495 0.0803*** 0.0806*** 0.0810*** 0.0738***(0.0598) (0.00700) (0.00699) (0.00698) (0.00704)

wtsq2 0.00307(0.00713)

suv1 0.00418(0.0248)

minivan1 0.00583(0.0303)

pickup1 -0.00148(0.0263)

suv2 0.0159(0.0221)

minivan2 0.0297(0.0288)

pickup2 0.0108(0.0248)

age1 -0.00347*** -0.00347*** -0.00375*** -0.00346*** -0.00325***(0.00106) (0.00106) (0.00105) (0.00106) (0.00105)

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 yr1 -0.00570*** -0.00553*** -0.00472*** -0.00575*** -0.00571***(0.00130) (0.00124) (0.00117) (0.00125) (0.00124)

year 0.00506 0.00478(0.00380) (0.00374)

rural 0.0189(0.0277)

Make FE yes yes no yes yesRegion FE no no no no yesMean of p

i

0.186 0.186 0.184 0.186 0.184Observations 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 pi” refers to the mean predicted probability of

driver death observed in the sample.

14

Figure 2: Probability of Driver Death by Own and Other Car Weight

0.1

.2.3

.4Pr

obab

ility

of D

river

Dea

th

2 3 4 5 6Weight (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

a vehicle of the indicated weight with otherwise average characteristics in a collision with a

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

Figure 3: Change in Probability of Driver Death by Own andOther Car Weight

0.0

5.1

.15

Cha

nge

in P

rob

of D

eath

for 1

,000

lb C

hang

e

2 3 4 5 6Weight (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 prob-

ability 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

2 of Table 1.

16

Table 2: Impact of Weight on Relative Risk of Accident

VARIABLES (1) (2) (3) (4)

wt 0.0477 0.258 0.204 0.129(0.162) (0.181) (0.168) (0.213)

suv -0.816*** -0.801*** -0.858***(0.278) (0.276) (0.259)

minivan -1.138*** -0.925*** -1.091***(0.314) (0.281) (0.374)

pickup 0.169 0.342 0.0373(0.660) (0.686) (0.604)

redesign yr 0.119** 0.131***(0.0485) (0.0500)

Make FE no no no yes

Observations 239 239 239 239R-squared 0.001 0.054 0.101 0.241

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

4.3 One-Car Crashes

The procedure described in section 3.4 was used to calculate ri

, the relative riskof death in a severe one car accident for each vehicle type. The interpretationof r

i

is that if the probability of death in a one car accident averaged across allcars is equal to p1, then the probability of death for a driver of a type i car ispi

= ri

p1. It is not possible to estimate p1 with the available data, but choosingan arbitrary value serves simply as a normalization. To see this, recall that theanalysis will proceed by regressing p

i

on vehicle type characteristics. Supposethat the value chosen for p1 is twice the “true” value. The estimated coe�cientsin the above regression would then also be twice the “true” values, but thevalues relative to the chosen p1 would be correct. Also, when the simulationsare carried out, they are calibrated by choosing the number of one-car accidentsthat generates a predicted number of fatalities equal to the observed number. Ifthe value chosen for p1 were twice the “true” value, then the calibration numberof accidents would simply be half as large. Changes in vehicle characteristicswould change the predicted number of fatalities by the same number whatevervalue is chosen for p1.

Because it is simply a normalization, the value chosen for p1 is equal to themean predicted probability of death in the preferred two-car specification, or0.186. The calculated and normalized value for p

i

was then used as the de-pendent variable in the regressions presented in Table 3. The estimates of theimpact of weight on the probability of driver death in one car accidents are notstrongly statistically significant, but are relatively robust across specifications 2through 5, which use multiple control variables. Specifications 2 and 3 includeindicators for vehicle class: suv, minivan, and pickup with car being the omittedcategory. 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 propen-sity to rollover in accidents (Insurance Institute for Highway Safety, 2012c), ordue 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 indi-cators since they were found to be insignificant, but are highly correlated withvehicle weight and so could obscure the statistical significance of weight in theregressions. In these specifications, weight is significantly protective of driverdeath with an e↵ect that diminishes with increasing weight.

Figure 4 shows the predicted value of the probability of driver death forthe specification in column 4. Note that while the estimated probability beginsincreasing at approximately 4,700 pounds, the 95% confidence interval includesthe possibility that the probability is always decreasing. It is plausible thatadditional weight could reduce safety at higher weights, but the estimates hereare far from definitive. In fact, for a wide range of weights, from about 3,500to 6,000 pounds, the predicted probability of death varies only between about17 and 20 percent. For these reasons, in the simulations it is assumed thatthe probability of driver death decreases to the estimated minimum and thenremains flat as weight is increased further. Also note that the fact that thereis little additional protective benefit from weight above 3,800 pounds suggests

18

Table 3: Impact of Vehicle Weight on Relative Risk of Driver Deathin One-Car Accidents

VARIABLES (1) (2) (3) (4) (5)

wt -0.0541 -0.198* -0.0231 -0.203** -0.0230*(0.102) (0.101) (0.0156) (0.0982) (0.0126)

wtsq 0.00519 0.0207* 0.0218*(0.0122) (0.0119) (0.0117)

suv 0.0174 0.00949(0.0301) (0.0305)

minivan -0.0232 -0.0437(0.0425) (0.0420)

pickup 0.103** 0.0969** 0.0948*** 0.0984***(0.0432) (0.0431) (0.0340) (0.0356)

redesign yr -0.0192*** -0.0184*** -0.0189*** -0.0178***(0.00348) (0.00329) (0.00346) (0.00324)

Make FE no yes yes yes yes

Observations 239 239 239 239 239R-squared 0.004 0.312 0.303 0.309 0.298

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. The mean probability of death was

normalized to 0.186 as described in section 4.3. Vehicle weight is measured in 1,000s of

pounds.

that marginal private benefits from additional weight in one car crashes will dolittle to o↵set the fact that marginal social cost exceeds marginal private benefitin two car crashes in this weight range.

4.4 Simulation Results

The procedure described in Section 3.5 was used to simulate the impact ofchanging the distibution of vehicle weights. Probabilities of death in one- andtwo-car accidents were calculated using the specifications in column 4 of Table 3and column 2 of Table 1, respectively. Values for the simulation parameters N1

and N2 were chosen so that the predicted number of deaths in one- and two-caraccidents using the original weight distribution matched the observed number ofdeaths in 2009, 14,842 deaths in one-car accidents and 13,073 deaths in multi-caraccidents.5

5Note that these figures sum to less than the total number of deaths reported in 2009because they omit deaths of pedestrians and motorcyclists.

19

Figure 4: Probability of Driver Death in Severe One Car Accident

.1.2

.3.4

.5Pr

obab

ility

of D

river

Dea

th

2 3 4 5 6Weight (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

Table 4: Simulation Results for a 5 Percent Reduction inMean Vehicle Weight

Baseline Sim 1 Sim 2 Sim 3

Weight change below mean 0 -5% -11.40% 0Weight change above mean 0 -5% 0 -8.90%

Change for overall fleet 0 -5% -5% -5%

Deaths in 1 Car Accidents 14,842 15,277 15,759 14,980Change vs. baseline - +435 +917 +138

Deaths in 2+ Car Accidents 13,073 12,559 13,514 11,994Change vs. baseline - -514 +441 -1,079

Total Deaths 27,915 27,836 29,273 26,974Change vs. baseline - -79 +1,358 -941

The results of three simulations are presented in Table 4. For each simu-lation, the vehicle miles traveled-weighted average weight of the vehicle fleet isdecreased by 5 percent relative to the base year of 2009. This is a relativelymodest overall weight reduction– many new models being released are lighterthan the preceding generation by this amount already. The first simulation as-sumes a uniform 5 percent reduction in the weight of all vehicle types. Thisresults in an increase in deaths in one-car accidents that is slightly more thano↵set by a reduction in deaths in two-car accidents, but the overall change inthe number of deaths is small. The second simulation assumes that all weightreduction occurs in vehicles below the mean weight and that the reduction issu�cient to reduce the mean of the whole fleet by 5 percent. In this case, thesimulation suggests that there will be increased deaths in both one- and two- caraccidents with a total of 1,358 more deaths, which is 4.9 percent more than thebaseline number. The third simulation assumes that all weight reduction occursin vehicles above the mean weight. The small increase in one-car fatalities ismuch more than o↵set by the resulting decrease in two-car fatalities so that atotal 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 Dis-tribution

The results of the simulations presented in Section 4.4 suggest that reductionsin vehicle weight can result in net improvements or reductions in motor vehicleaccident deaths, depending on where in the current weight distribution thereductions are concentrated. There are several reasons why the safety-reducing

21

path of weight decreases concentrated among currently lighter vehicles mightoccur. First, the new standards require a greater percentage improvement infuel economy for passenger cars than for light trucks, which include SUVs andpickup trucks. Second, the optimal compliance strategy for a given vehiclewill depend upon the “elasticity of demand for weight” among likely buyersof that vehicle. Buyers of heavier vehicles sometimes need a larger vehicle forcommercial reasons or to transport large numbers of people. Heavier vehiclesare also more expensive and so buyers of these vehicles are less likely to beprice-sensitive. This would enable automakers to use costly technologies, such asturbochargers and hybrid systems, to achieve fuel e�ciency gains in heavier carsmore easily than they could in lighter ones. Third, recent work by Whitefoot andSkerlos (2012) suggests that automakers may find it advantageous to increasethe size of vehicles in response to the new standards. This is because vehicleswith 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. 62740-62741), but theincentives at work are complicated, particularly when one considers consumerdemand as Whitefoot and Skerlos do in their work.

There are also empirical reasons to be concerned that vehicle weight re-ductions might be concentrated among lower weight vehicles. Figure 5 showsthe cumulative distribution function for vehicle weight for vehicles sampled inthe 2009 National Household Travel Survey and separately for vehicles sold in2011.6 It is clear that at low weights, the cdf for cars sold in 2011 lies abovethat for the vehicle fleet estimated for 2009. At higher weights, the two cdf’smove closer together, eventually crossing, implying that the weight distributionfor vehicles sold in 2011 was more uneven than was the case for vehicles on theroad in 2009. This fact is confirmed by the summary data in Table 5. Whilethe mean vehicle weight of vehicles sold in 2011 was 3.2% lower than the meanweight of the vehicle fleet in the 2009 NHTS, the standard deviation of weightswas 3.7% higher. Conditional upon being above the average weight of eithersample, vehicles sold in 2011 are actually heavier than those in the 2009 vehiclefleet. Conversely, conditional upon being below average weight, the vehicles soldin 2011 were lighter than those on the road in 2009. All of this suggests that thevariance in weights has been increasing even as the mean weight has been de-creasing. To get an idea of which of these impacts is likely to be more importantin 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 4947pounds. For cars sold in 2011, the mean weight of an above average weightvehicle is 4892 pounds, a reduction of 1.1%. The comparable comparison forbelow average weight cars shows a reduction of 4.3%. Thus, while the averageweight of vehicles sold in 2011 is lower than the average for the 2009 vehiclefleet, the weight reductions have been disproportionately concentrated amonglower weight vehicles.

6The data for vehicle sales in 2011 was obtained from Cain (2012).

22

Figure 5: Cumulative Distribution Function for Vehicle Weight, 2011 Salesand 2009 Fleet

0.2

.4.6

.81

Cum

ulat

ive

Dis

tribu

tion

2000 3000 4000 5000 6000Vehicle 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 Fleetand 2011 Vehicle Sales

2009 Fleet 2011 Sales % Di↵erence

Mean wt 4112 3980 -3.2%Std. Dev. wt 902 935 3.7%

wt|wt > 4112 4947 4951 0.1%wt|wt < 4112 3434 3325 -3.2%

wt|wt > 3980 4801 4892 1.9%wt|wt < 3980 3323 3291 -1.0%

23

5.2 Comparison of Potential Safety Costs to Environmen-tal Benefits

The motivation behind CAFE standards is to reduce carbon dioxide (CO2)emissions, thus mitigating the costs of global climate change. The results ofthe simulations presented in Section 4.4 suggest that this goal need not be intension with enhancing motor vehicle safety, but that a tradeo↵ may occur if thereactions of automakers and consumers to the standards result in vehicle weightreduction occuring disproportionately among lower weight vehicles. Further-more, the observations made in Section 5.1 suggest that such a tradeo↵ maybe beginning to occur. Even so, the current approach might be justifiable ifthe environmental benefits far outweight any potential safety costs, because theflexibility allowed by the current policy might allow the standards to be met atlower social cost. It is reasonable, then, to compare the potential safety coststo the anticipated environmental benefits.

According to data from the Federal Highway Administration (2012), lightduty vehicles travelled a total of 2.65 ⇥ 1012 miles in 2010. The harmonicmean fuel e�ciency of vehicles used in this analysis is 18.1 miles per gallon7

for a total gasonline usage of 1.46 ⇥ 1011 gallons of gas used annually. Toevaluate the impact of weight reduction on fuel e�ciency, the logarithm of fuele�ciency was regressed on the logarithm of weight. The coe�cient estimate of-0.999 (and standard error of 0.028) suggests that the elasticity of fuel e�ciencywith respect to weight is almost exactly -1. Thus, the 5% reduction in weightassumed for the simulations would reduce gasoline usage by approximately 5%,or 7.32⇥ 109 gallons. According to the U.S. Environmental Protection Agency(2012), burning one gallon of gas results in 8.92⇥10�3 tons of CO2 emissions sothat a 5% average vehicle weight reduction would reduce emissions of CO2 by6.53⇥ 107 metric tons per year. An authoritative estimate of the social cost ofcarbon (SCC) for use in US government regulatory analysis has been provided bythe Interagency Working Group on Social Cost of Carbon (2010). The workinggroup provides a mean estimate of (2007$)21.4 per metric ton of CO2 with the95th percentile of estimate of (2007$)64.9.8 The expected social benefit of CO2

reduction resulting from a 5% average vehicle weight reduction would thus be onthe order of $1.4 billion annually with a 95th percentile estimate of $4.2 billion.

The safety cost of vehicle weight reduction occurs because of small changesin survival probability for many individuals. In such cases, the value of statis-tical life (VSL) approach is useful for quantifying the safety impact of a policy(Mishan, 1971; Bergstrom, 1982; Dreze and Dehez, 1982). Viscusi and Aldy(2003) provide a thorough survey of the literature estimating the appropriateVSL to use and note that most estimates cluster in the $4 million to $9 million

7The value for vehicle mileage was obtained from Consumer Reports (Consumer Reports,2011) and reflects a mix of highway and city driving. The harmonic mean was weighted byvehicle miles travelled in the NHTS.

8Both of these figures are based on a 3% discount rate. The working group also considersboth higher and lower discount rates, but using the 95th percentile estimate allows a widerrange of uncertainty than using a lower discount rate.

24

range. The second simulation presented in Table 4 predicts 1,358 additionalfatalities per year if a 5% mean vehicle weight reduction is attained purely byreducing the weight of already lower weight vehicles. The expected social costof such an outcome would thus be on the order of $5.4 to $12.2 billion annually.This implies that expected costs would exceed expected benefits by almost afactor of four. Even at the low end of estimates for the value of statistical lifeand the 95th percentile for the social cost of carbon, safety costs would exceedenvironmental benefits.

5.3 Safety and Environmental Externalities

A policy alternative to the CAFE standards is to impose a Pigovian tax ongasoline or on the operation of vehicles. An important parameter in evaluatingthe optimal tax is the total external cost imposed by the taxed activity. Thissection separately calculates the external cost assoicated with the safety andenvironmental impacts of operating a motor vehicle.9

The total external safety cost of driving a vehicle of weight w for one mile canbe calculated as follows.10 Define p(w) to be the probability of driver death in avehicle of average characteristics involved in a severe accident with a vehicle ofweight w. Define l(w) as the expected number of lives lost in a vehicle involvedin a collision with a vehicle of weight w. Assuming that non-driver occupantsare impacted similarly to drivers,

l(w) = nocc

p(w)

where nocc

is the expected number of occupants in the other vehicle. Next, defineL(w) as the expected number of lives lost in other vehicles per mile driven by avehicle of weight w. L(w) will simply be equal to l(w) times the probability ofbeing in a severe accident when traveling one mile, p

acc

:

L(w) = pacc

l(w)

A measure of the expected external safety cost of driving a vehicle of weight w

9 The optimal gasoline tax in a general equilibrium setting depends upon how consumerswill respond to the tax. For example, a calculation by Parry and Small (2005) considerssubstitution toward vehicles of lower weights and West and Williams (2007) emphasize theimportance of the cross-price elasticity of demand for leisure. I do not attempt to account forsuch general equilibrium e↵ects here because the main purpose of this article is to quantifythe safety externalities associated with vehicle weight and to compare their magnitude to theenvironmental ones.

10The counterfactual to driving a vehicle mile considered here is not to drive at all. Thisdi↵ers from the approach of Anderson and Au↵hammer (2011) who use the counterfactual ofdriving an alternative lighter vehicle. The reason for calcuating a safety cost even for lightvehicles is that I wish to compare safety externalities with environmental ones, and the socialcost of carbon that results from driving a minimal weight vehicle is not generally assumed tobe zero. Because the external safety cost of a 2,000 pound vehicle is quite low relative to thatfor heavier vehicles, the main results are not materially a↵ected by taking this approach.

25

for one mile, c(w), is obtained by multiplying by the value of statistical life, v:

c(w) = vL(w)

c(w) = vpacc

nocc

p(w)

This equation is parameterized as follows:

• The value of statistical life, v, used is $6.5 million, the midpoint of therange discussed in Section 5.2.

• The probability of a severe accident in one mile of driving is estimated bydividing the calibration number of vehicles involved in severe two car ac-cidents by the total number of vehicle miles traveled by light duty vehiclesin 2010 according to Federal Highway Administration (2012). The valueobtained is p

acc

= 2.68⇥ 10�8.11

• The expected number of vehicle occupants was taken as the mean numberof occupants across all vehicle types, as estimated using the 2009 NHTS,weighted by vehicle miles traveled. The result is n

occ

= 1.43

• p(w) was estimated in Section 4.1 and is shown in Figure 2.

The resulting estimate of external costs as a function of weight is shown inFigure 6.

The environmental costs attributable to vehicles of di↵erent weights are cal-culated in a straightforward manner. Using the vehicle type data, the logarithmof fuel e�ciency was regressed on the logarithm of vehicle weight. This univari-ate regression has an R2 value of 0.79. The regression results were used topredict fuel e�ciency for vehicle weights between 2,000 and 6,000 pounds. Theinverse of fuel e�ciency gives the number of gallons of gas used per mile. Mul-tiplying by the figures for the tons of carbon dioxide emissions per gallon of gasand the social cost of carbon values discussed in Section 5.2 yields an estimateof the environmental costs of driving a vehicle one mile as a function of vehicleweight. The results of this calculation are presented with the results for externalsafety costs in Figure 6.

An examination of Figure 6 reveals that the external safety costs of vehicleweight exceed the environmental costs. The two costs can be summed to obtaina measure of the total externality imposed by driving a vehicle of given weightone mile. The resulting total external costs are presented in the third columnof Table 6. The second column of the table shows an estimate of the average

11As a check of internal consistency, consider that the National Highway Tra�c Safety Ad-ministration (2012) reported a mortality rate of 1.04⇥ 10�8 deaths per mile for the first halfof 2011. According to the Insurance Institute for Highway Safety (2012a) approximately 68%of these deaths are for passengers of motor vehicles (as opposed to pedestrians or motorcy-clists), so that the vehicle passenger death rate is approximately 7.0 ⇥ 10�9. Dividing thisrate by the estimated accident rate and dividing again by mean vehicle occupancy of 1.43 (seenext bullet point) yields an estimated probability of occupant death conditional on being in asevere accident of 18.3%, which almost exactly matches the mean predicted probabilities fromthe regressions reported in Table 1.

26

Figure 6: External Safety and Environmental Costs Per Mile Driven

0.0

2.0

4.0

6.0

8Sa

fety

or E

nviro

nmen

tal C

ost (

$ pe

r Mile

)

2 3 4 5 6Vehicle Weight (1,000s of pounds)

External Safety Cost External Environmental Cost

Notes: One plot shows the calculated total external safety cost due to mortality in motor

vehicle accidents attributable to vehicles of di↵erent weights. The other plot shows total

environmental costs due to carbon emissions as a function of vehicle weight. The calculations

are described in the text.

27

internal cost per mile incurred by drivers of vehicles of di↵erent weights.12 Thepercentage increase in average cost that drivers would face if taxed at a levelequal to external costs is presented in Column 4. While the external cost permile on 6,000 pound vehicles is about nine times that of 2,000 pound vehicles,the implied tax rate is only about two-and-a-half times higher for the largervehicles because of their higher average costs.

Table 6: External Costs by Vehicle Weight

Tax Rate

Naive Implied by

Internal External Pigovian External $0.78/gal

Cost Cost Tax Rate Cost Gas Tax

Weight per Mile per Mile (% of per Gallon (% of

(pounds) (dollars) (dollars) Int. Cost) (dollars) Int Cost)

2,000 0.31 0.01 4.4% 0.51 6.8%3,000 0.44 0.02 5.6% 0.62 7.0%4,000 0.58 0.04 7.2% 0.78 7.2%5,000 0.71 0.06 9.1% 0.97 7.3%6,000 0.85 0.09 11.2% 1.18 7.4%

Notes: “Internal cost” refers to the total average cost per mile when driving a vehicle of the

given weight 96,000 miles over eight years. “External Cost” refers to the sum of the external

costs due to safety and environmental externalities. The “Naive” Pigovian tax rate is simply

external costs as a percent of internal costs and does not account for general equilibrium

e↵ects.

If it were possible to impose “naive”13 Pigovian tax rates equal to externalcosts, it seems likely that there would be a shift away from heavier vehicles.With a tax rate 2.5 times as high for the heaviest vehicles compared with thelightest, purchases of heavier vehicles would fall by more than those of lightervehicles as long as the price elasticity of demand for heavy vehicles was not lessthan 40% that for lighter vehicles. Along with this shift, the simulation resultsin Section 4.4 suggest that motor vehicle accident deaths would decline.

As a practical matter, it is not likely to be convenient to impose a tax

12The emphasis on average, as opposed to marginal, cost is because I am more interestedin likely long run responses to Pigovian taxation in which consumers can change what vehiclethey purchase as opposed to simply reducing use of existing vehicles. The estimate of averagecost per mile was obtained from data available on the web site of Consumer Reports (ConsumerReports, 2011). The data consists of estimates of the total cost of driving a vehicle 12,000miles per year for eight years. The cost estimate includes vehicle depreciation, maintenance,financing (opportunity) cost, insurance, fuel, and taxes. Total cost per mile for each vehicletype is simply the total cost divided by 96,000 miles. The resulting cost per mile estimateswere regressed on vehicle weight and indicator variables for luxury car and European model.The R2 for the regression was 0.73 and the t-statistic for the weight variable was 20.58.The values for cost per mile reported in column 1 of Table 6 are predicted values from thisregression for non-luxury, non-European vehicles.

13I refer to tax rates that take into account external costs, but not the general equilibriume↵ects discussed in footnote 9, as “naive” rates.

28

per mile driven with rates that vary by vehicle weight. Policy emphasis hasthus centered on whether a gasoline tax could accomplish much the same endsince heavier vehicles use more gasoline per mile traveled and would thus pay ahigher per mile tax rate (Anderson and Au↵hammer, 2011). The fifth columnof Table 6 contains the external costs per gallon of gas, which is obtained simplyby multiplying the external cost per mile by fuel e�ciency. Comparing columns3 and 5 we see that the lower fuel e�ciency of heavier vehicles does reduce thediscrepancy in naive tax levels when gasoline is taxed instead of mileage. Thenaive tax per gallon for a 6,000 pound vehicle is less than a factor of three largerthan that for a 2,000 pound vehicle compared with the factor of nine di↵erencealready noted in the optimal per mile taxes. A simple gasoline tax per gallonwould not vary by vehicle weight, so we consider the impact of a gasoline taxin the middle of the range of optimal taxes: $0.78 per gallon, corresponding tothe optimal rate for a 4,000 pound vehicle. The percentage increase in averagecosts per mile implied by such a tax is presented in the final column of the table.While the naive Pigovian tax rate would by approximately 2.5 times higher forthe heaviest vehicles than the lightest, the result of simple gasoline tax is a taxrate that is nearly constant across vehicle weights. The reason is that although a6,000 pound vehicle uses about three times more gasoline per mile than a 2,000pound vehicle, its baseline average costs are also about three times as high.

These results suggest that simple per gallon gasoline taxes are not likely tobe an e↵ective means of pricing safety and environmental externalities into thecost of vehicle operation. They are also unlikely to cause substantial shifts fromheavier to lighter vehicles due to substitution e↵ects. Because the impact ofsuch taxes is roughly proportional to initial costs, the e↵ective price of heavierand lighter vehicles will increase by a similar percentage. There could be shiftsin the vehicle fleet due to income e↵ects, however, as the calculated tax ratesare high and typical household spending on gasoline is substantial. If wealthierhouseholds buy heavier vehicles and also have a lower income elasticity of de-mand for those vehicles, there could be a greater shift toward lighter vehiclesat the low end of the weight distribution than at the high end. The simula-tion results in Section 4.4 suggest that deaths in motor vehicle accidents couldincrease in this case, unless total vehicle miles traveled declined by enough too↵set the predicted increase in accident deaths per mile traveled.

6 Conclusion

The estimates and simulations described in this paper suggest that changes inthe distribution of weights in the vehicle fleet can have substantial impacts onmotor vehicle accident fatalities. While it does not appear that a small reduc-tion in vehicle weights across the whole fleet would have substantial mortalityimpacts, asymmetric changes in the weight distribution may have big e↵ects.The di↵erence in the number of deaths predicted when a 5 percent weight re-duction is concentrated among the now heavier or now lighter vehicles is morethan 8 percent of the current number of fatalities. It is therefore important to

29

consider how automobile manufacturers and consumers are likely to respond tothe incentives included in the new CAFE standards.

The writers of the standards are aware that weight reductions among lightercars could lead to increases in accident fatalities. The final rule (EnvironmentalProtection Agency and Department of Transportation, 2012) states that “weexpect manufacturers to reduce vehicle mass in response to the final rule” (p.62741), but assume that the weight reductions will occur in such a way thatis “technologically feasible without compromising safety.” (p. 62763). Theydo this by finding a “safety neutral compliance path” (p. 62764) that predictsweight reductions among heavier, but not lighter, vehicles (Table II-31 and II-32). While the simulations here support the existence of safety-neutral, or evensafety-improving, ways in which average vehicle weight could be reduced, it isnot clear that the technological, regulatory, and consumer demand constraintsfacing automakers favor such paths. The simulation results and the observationthat recent weight reductions have been concentrated among already below av-erage weight vehicles provide reason for concern that the more stringent fueleconomy standards recently enacted could have substantial negative impacts onpublic health by increasing deaths in motor vehicle accidents. Whether this fac-tor can account for some of the 8% increase in the tra�c fatality rates reportedby the NHTSA for the first half of 2012 remains to be seen.

In additon to considering the safety impact of changes to the CAFE stan-dards, it is worth questioning the relative emphasis on the environmental exter-nalities imposed by motor vehicles. An important finding of this paper, consis-tent with the recent findings of Anderson and Au↵hammer (2011), is that thesafety externalities attributable to vehicle weight are substantially larger thanthe environmental ones, particularly among heavier vehicles. By concentratingon environmental costs and the improvement of fuel e�ciency in a “safety neu-tral” manner, an opportunity may be missed to simultaneously improve motorvehicle safety.

The question of how best to attain an e�cient distribution of vehicle weightsthat accounts for both environmental and safety costs does not appear to havea simple answer. Instituting a per mile tax that varies by vehicle weights is cer-tainly feasible. The tax could be imposed continuously by using technologicalvehicle monitoring or periodically by requiring odometer checks. The techno-logical approach would likely raise privacy concerns; both approaches are likelyto be costly; and the variation in the optimal tax rates– more than a factor ofeight– is likely to be unpopular. An alternative approach would be to impose aper gallon gasoline excise tax equal to the marginal damage caused by a vehiclein using a gallon of gas. The problem is that the optimal tax rate would stillvary substantially with vehicle weight and attempts to apply di↵erent tax ratesto di↵erent vehicles would also be likely to be costly and unpopular. Settinga simple excise tax at the optimal level for an average weight vehicle wouldsubstantially overtax lighter vehicles and undertax heavier ones. The ine�-ciency resulting from this suboptimal approach would likely manifest in a largernumber of motor vehicle accident deaths.

The reason that fuel e�ciency is currently subject to complicated regula-

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tion, the CAFE standards, seems to be due to political economy– regulation isunpopular, but taxation far more so. While more e�cient, it seems quite likelythat the weight-varying Pigovian taxation that would be required to price ex-ternalities into vehicle usage would prove even more unpopular than simple gastaxes. It may thus be best to attempt to improve current policy on the marginby modifying the CAFE standards so that they account for safety, as well as en-vironmental, externalities. While the details will inevitably be complicated, thebasic approach is simple: move away from a “safety neutral” compliance pathand towards a “safety improving” one. This could be accomplished by makingstandards more stringent for heavier vehicles and by rewarding fuel e�ciencygains in larger vehicles more when the gains are due to weight reduction thanwhen they are accomplished using technology that is not safety enhancing. Thecosts of such a policy will be felt by those who sacrifice the benefits of heaviervehicles or pay a higher price for them. But given the current vehicle fleet,there does not need to be a safety cost to attaining an environemental benefit.By reducing the weights of heavier vehicles on the road, it is possible to reduceboth carbon emissions and motor vehicle accident deaths.

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