LBNLAn Analysis of the Relationship between Casualty Risk Per Crash and 

Vehicle Mass and Footprint for Model Year 2000-2007 Light-Duty 

Vehicles

Final report prepared for the Office of Energy Efficiency and Renewable Energy,

US Department of Energy

Prepared by

Tom Wenzel

Building Technology and Urban Systems Department

Environmental Energy Technologies Division

Lawrence Berkeley National Laboratory

Berkeley, CA 94720

August 2012

This work was supported by the Vehicle Technologies Program, 

Office of Energy Efficiency and Renewable Energy of the U.S. Department of Energy 

under Contract No. DE-AC02-05CH11231.
DISCLAIMER

This document was prepared as an account of work sponsored by the United States Government. While this

document is believed to contain correct information, neither the United States Government nor any agency thereof, 

nor The Regents of the University of California, nor any of their employees, makes any warranty, express or 

implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, 

apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. 

Reference herein to any specific commercial product, process, or service by its trade name, trademark, 

manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring 

by the United States Government or any agency thereof, or The Regents of the University of California. The views 

and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or 

any agency thereof, or The Regents of the University of California. 

Ernest Orlando Lawrence Berkeley National Laboratory is an equal opportunity employer.
i

Acknowledgements

We would like to thank those who reviewed earlier drafts of this report, and provided helpful 

comments and insights: Tom White and Peter Whitman, Office of Policy, U.S. Department of 

Energy; Chi Li, Office of Transportation and Air Quality, U.S. Environmental Protection 

Agency; Chuck Kahane, National Highway Transportation Safety Administration, U.S. 

Department of Transportation; and Phil Price, Lawrence Berkeley National Laboratory. We also 

would like to thank the formal peer reviewers of the Final Draft: Charles Farmer, Insurance 

Institute for Highway Safety; David Greene, Oak Ridge National Laboratory; Kara Kockelman

and Donna Chen, University of Texas; and Michael Van Auken, Dynamic Research, Inc.

The report was funded by Carol Schutte of the Vehicle Technologies Program in the Office of 

Energy Efficiency and Renewable Energy of the U.S. Department of Energy. We are grateful for 

her support of this research.

This work was supported by the Assistant Secretary for Energy Efficiency and Renewable 

Energy, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
ii
iii

Executive Summary

NHTSA recently completed a logistic regression analysis (Kahane 2012) updating its 2003 and 

2010 studies of the relationship between vehicle mass and US fatality risk per vehicle mile 

traveled (VMT). The new study updates the previous analyses in several ways: updated FARS 

data for 2002 to 2008 involving MY00 to MY07 vehicles are used; induced exposure data from 

police reported crashes in several additional states are added; a new vehicle category for carbased crossover utility vehicles (CUVs) and minivans is created; crashes with other light-duty 

vehicles are divided into two groups based on the crash partner vehicle’s weight, and a category 

for all other fatal crashes is added; and new control variables for new safety technologies and 

designs, such as electronic stability controls (ESC), side airbags, and methods to meet voluntary 

agreement to improve light truck compatibility with cars, are included.

In a companion report (Wenzel 2012b), we use the updated databases NHTSA has created to 

replicate their findings on the relationship between vehicle weight, size (actually footprint, or 

vehicle wheelbase times track width), and US fatality risk per vehicle miles traveled (VMT), for 

model year 2000 to 2007 light-duty vehicles involved in fatal crashes between 2002 and 2008. 

The data are examined in slightly different ways, to get a deeper understanding of the 

relationship between reductions in vehicle mass and footprint, and overall safety. 

This report compares the logistic regression results of the NHTSA analysis of US fatality risk per 

VMT with an analysis of 13-state fatality risk and casualty risk per crash. This final report 

incorporates revisions from the preliminary report released in November 2011, including revised 

estimates of national weights for vehicle miles traveled, inclusion of 2008 police-reported crash 

data from eight additional states, and responses to reviewers’ comments. 

Our analysis differs from the NHTSA analysis in two respects: first, it analyzes risk per crash, 

using data on all police-reported crashes from thirteen states, rather than risk per estimated 

VMT; and second, it analyzes casualty (fatality plus serious injury) risk, as opposed to just 

fatality risk. There are several good reasons to investigate the effect of mass and footprint 

reduction on casualty risk per crash. First, risk per VMT, includes two effects that influence 

whether a person is killed or seriously injured in a crash: how well a vehicle can be, or actually 

is, driven (based on its handling, acceleration, and braking capabilities) to avoid being involved 

in a serious crash (crash avoidance), and, once a serious crash has occurred, how well a vehicle 

protects its occupants from fatality or serious injury (crashworthiness) as well as the occupants of 

any crash partner (compatibility). By encompassing both of these aspects of vehicle design, risk 

per VMT gives a complete picture of how vehicle design can promote, or reduce, road user 

safety. On the other hand, risk per crash isolates the second of these two safety effects, 

crashworthiness/compatibility, by examining the effect of mass and footprint reduction on how 

well a vehicle protects its occupants once a crash occurs. 

Second, estimating risk on a per crash basis only requires using data on police-reported crashes 

from states, and does not require combining them with data from other sources, such as vehicle 

registration data and VMT information, as in NHTSA 2011. Because only sixteen states 

currently record the vehicle identification number of vehicles involved in police-reported 

crashes, which is necessary to determine vehicle characteristics, and only thirteen states also 
iv

report the posted speed limit of the roadway on which the crash occurred, extending the analysis 

to casualties (fatalities plus serious/incapacitating injuries; i.e. level “K” and “A” injuries in 

police reports) reduces the statistical uncertainty of analyzing just fatalities per crash. Finally, a 

serious incapacitating injury can be just as traumatic to the victim and her family, and costly 

from an economic perspective, as a fatality. Limiting the analysis to the risk of fatality, which is 

an extremely rare event, ignores the effect vehicle design may have on reducing the large number 

of incapacitating injuries that occur each year on the nation’s roadways. All risks in this report 

are societal risk, including fatalities and serious injuries in the case vehicle and any crash 

partners, and include not only driver casualties but passenger and non-occupant casualties as 

well.

However, the frequency of police-reported crashes per VMT and of casualties per policereported crash can both be influenced, in opposite directions, by the probability that a collision 

event becomes a police-reported crash. If collisions of certain vehicles are slightly less likely to 

be reported, because these vehicles are either somewhat less damage-prone or are uninsured, this 

would tend to increase the observed detrimental effect of mass reduction on reported crashes per 

VMT and conversely decrease its detrimental effect on casualties per reported crash. By 

contrast, fatalities or casualties per VMT would be not be affected by crash-reporting rates, 

because the crash-reporting rate is not part of the formula for calculating risk. The extent to 

which any reporting bias of non-injury crashes exists, the observed effects for police-reported 

crashes per VMT might not correspond exactly to the “effect of mass reduction on crash 

avoidance” and the observed effects for casualties per police-reported crash might not 

correspond exactly to the “effect of mass reduction on crashworthiness/compatibility.” We 

suspect that large pickups are less likely to suffer damage in non-injury crashes than other 

vehicle types; and that older, less expensive, or uninsured vehicles are less likely to report crash 

damage to police. In addition, one vehicle crashes are more likely to suffer from this reporting 

bias, as there is no crash partner who may file an insurance claim. 

Table ES.1 summarizes the results of our analysis of the effect of vehicle mass or footprint 

reduction on the two components of risk per VMT, crash frequency (number of crashes per 

VMT) and crashworthiness/compatibility (risk per crash), for both fatality and casualty risk, 

using data from 13 states. We convert the percent change in the log-odds of casualty or fatality

per crash output from the SAS LOGIST procedure to the percent change in the probability of 

casualty or fatality per crash. This conversion has no effect on the output regression coefficients 

when the change in the log-odds of casualty is small, but substantially increases the percent 

change for explanatory variables that have a large effect on the log-odds of casualty. Effects that 

are statistically significant are shown in red in the table; significance is based on the 95% 

confidence interval derived from the standard error of the output of the SAS LOGIST procedure, 

converted to a percent probability interval.

Table ES.1 indicates that for cars and light trucks, the effects from the two components, crash 

frequency and crashworthiness/compatibility, roughly add together to result in the overall effect 

on fatality risk per VMT. For example, the models estimate that 100-lb lower mass in lighterthan-average cars is associated with a 2.00% increase in crash frequency (column B), while 

lower mass is associated with a 0.54% decrease in the number of fatalities per crash (column C); 

the net effect is only a 1.42% increase in the risk of fatality per VMT (column D), which is 
v

roughly the sum of the crash frequency and crashworthiness/compatibility effects (2.00% -

0.54% = 1.45%). For CUVs/minivans, the relationship is different; lower mass is associated 

with a 0.95% increase in crash frequency, as well as a 0.98% increase in the number of fatalities 

per crash; however, the net result, an estimated 1.60% increase in the number of fatalities per 

VMT, is less than the sum of the two components (0.95% + 0.98% = 1.92%). Solving the three 

equations (crashes per VMT, risk per crash, and risk per VMT) simultaneously, as DRI has done, 

forces the estimates for the first two-stages of the regression (crashes per VMT and risk per 

crash) to equal that of the third state of the regression (risk per VMT).

The regression results in Table ES.1 estimate that mass reduction increases crash frequency 

(columns B and E) in all five vehicle types, with larger estimated increases in lighter-thanaverage cars and light-duty trucks. As a result, mass reduction is estimated to have a more 

beneficial effect on crashworthiness/compatibility, or casualty risk per crash (column F), than on 

casualty risk per VMT (column G), and on fatality risk per crash (column C) than on fatality risk 

per VMT (column D). Mass reduction is associated with decreases in casualty risk per crash 

(column F) in all vehicles except lighter cars; in two of the four cases these estimated reductions 

are statistically significant, albeit small. Footprint reduction is associated with increases in crash 

frequency (columns B and E) in cars and light trucks, but with a small decrease in crash 

frequency in CUVs/minivans; footprint reduction does not have a statistically-significant effect 

on fatality risk per crash (column C), and only for casualty risk per crash (column F) for light 

trucks. For cars and light trucks, lower mass is associated with a more beneficial effect on 

fatality risk per crash (column C) than on casualty risk per crash (column F), while lower 

footprint is associated with slightly more detrimental effects. For CUVs/minivans Table ES.1 

shows the opposite: lower mass is associated with a more beneficial effect, while lower footprint 

is associated with a more detrimental effect, on casualty than fatality risk per crash.

It is unclear why lower vehicle mass is associated with higher crash frequency, but lower risk per 

crash, in the regression models. It is possible that including variables that more accurately 

account for important differences among vehicles and driver behavior would reverse this 

relationship. For example, adding vehicle purchase price substantially reduces the estimated 

increase in crash frequency as vehicle mass decreases, for all vehicle types; in the case of 

heavier-than-average cars, mass reduction is estimated to slightly decrease crash frequency. On 

the other hand, it is also possible that over thirty years of improvements in vehicle design to 

achieve high crash test ratings have enabled manufacturers to use clever vehicle design to 

mitigate the hypothetical safety penalty of low mass vehicles.

The association of mass reduction with 13-state casualty risk per VMT (column G) is quite

consistent with that NHTSA estimated for US fatality risk per VMT (column A), although we 

estimate the effects on casualty risk to be more detrimental than the effects on fatality risk, for all 

vehicle types. The association of footprint reduction also is similar, with 13-state casualty risk 

per VMT slightly more beneficial than US fatality risk per VMT for cars and CUVs/minivans, 

while 13-state casualty risk is substantially more detrimental than US casualty risk for light-duty 

trucks.
vi

Table ES.1. Estimated effect of mass or footprint reduction on two components of 13- state 

fatality and casualty risk per VMT: crash frequency (crashes per VMT) and 

crashworthiness/compatibility (risk per crash)

Variable

Case vehicle 

type

A. NHTSA US fatalities per VMT

B. 13-state crashesper VMT

C. 13-state fatalitiesper crashD. 13-state fatalities per VMTE. 13-state crashes 

per VMT

F. 13-state casualties per crashG. 13-state casualties per VMT

Mass

reduction

Cars < 3106 lbs 1.55%* 2.00% -0.54% 1.42% 2.00% 0.09% 1.86%

Cars > 3106 lbs 0.51% 1.50% -2.39% -1.07% 1.50% -0.77% 0.73%

LTs < 4594 lbs 0.52% 1.44% -1.61% -0.13% 1.44% -0.11% 1.55%

LTs > 4594 lbs -0.34% 0.94% -1.25% -0.34% 0.94% -0.62% -0.04%

CUV/ minivan -0.38% 0.95% 0.98% 1.60% 0.95% -0.16% 0.10%

Footprint

reduction

Cars 1.87% 0.64% 0.92% 2.11% 0.64% 0.23% 1.54%

LTs -0.07% 1.04% 0.48% 1.64% 1.04% -0.25% 0.94%

CUV/ minivan 1.72% -0.55% -1.67% -1.24% -0.55% 0.56% 1.54%

* Based on NHTSA’s estimation of uncertainty using a jack-knife method, only mass reduction in cars less than 

3,106 lbs has a statistically significant effect on US fatality risk.

Estimates that are statistically significant at the 95% level are shown in red.

In contrast with NHTSA’s estimates on US fatality risk per VMT (column A), mass reduction is 

estimated to reduce casualty risk per crash (column F) for four of the five vehicle types, with two 

of these four reductions estimated to be statistically significant. Mass reduction is associated 

with a small but insignificant increase in casualty risk per crash for lighter cars. And footprint 

reduction is associated with much smaller, and not statistically significant, estimated increases in 

casualty risk per crash (column F) than in US fatality risk per VMT (column A).

Many of the control variables included in the logistic regressions are statistically significant, and 

have a large effect on fatality or casualty risk per crash, in some cases one to two orders of 

magnitude larger. However, the estimated association of these variables with risks per crash are 

not as large as their estimated association with fatality risk per VMT. While the estimated effect 

of mass reduction may result in a statistically-significant increase in risk in certain cases, the 

increase is small and is overwhelmed by other known vehicle, driver, and crash factors.

ABS and ESC in cars are estimated to reduce crash frequency more than risk per crash, as 

expected, while AWD in light trucks and CUVs/minivans is estimated to increase crash 

frequency more than risk per crash. Two-door cars and the side airbag variables in cars have a 

larger effect on risk given a crash than on crash frequency; two-door cars increase risks per 

crash, while side airbags decrease risks per crash. The driver age variables estimate that crash 

frequency consistently increases for the youngest and oldest drivers, and that risk per crash

consistently increases for the two oldest groups of drivers (over 50 years old). All of these 

results are expected. 

On the other hand, there are several unexpected results: side airbags in light trucks and 

CUVs/minivans are estimated to reduce crash frequency; ESC and ABS are estimated to reduce 

risk once a crash has occurred; and AWD and brand new vehicles are estimated to increase risk 
vii

once a crash has occurred. In addition, male drivers are estimated to have essentially no effect on 

crash frequency, but are associated with a statistically significant increase in fatality risk once a 

crash occurs. And driving at night, on high-speed or rural roads, are associated with higher 

increases in risk per crash than on crash frequency. These unexpected results suggest that 

important control variables are not being included in the regression models. For example,

crashes involving male drivers, in vehicles equipped with AWD, or that occur at night on rural or 

high-speed roads, may not be more frequent but rather more severe than other crashes, and thus 

lead to greater fatality or casualty risk. And drivers who select vehicles with certain safety 

features may tend to drive more carefully, resulting in vehicle safety features designed to 

improve crashworthiness or compatibility, such as side airbags, being also associated with lower 

crash frequency.

In contrast with NHTSA’s results for US fatalities per VMT, allowing footprint to vary along 

with weight results in little change in the estimated effect of mass reduction on casualty risk per 

crash than when footprint is held constant; however, the estimated detrimental effect of mass 

reduction on casualty risk per crash in lighter cars is increased just enough to make it statistically 

significant. When mass is allowed to vary along with footprint, footprint reduction is estimated 

to be slightly more beneficial for cars and light trucks (Alternative 3 in Table ES.2; further 

addressed in Section 3 of this report). As with NHTSA’s analysis of fatality risk per VMT, 

lower mass is not consistently associated with increased casualty risk per crash across all 

footprint deciles for any combination of vehicle type and crash type. Lower mass is associated 

with increased casualty risk per crash in a majority of footprint deciles for 9 of the 27 crash and 

vehicle combinations, but few of these increases are statistically significant. On the other hand, 

lower mass is associated with decreased risk in a majority of footprint deciles for 12 of the 27 

crash and vehicle combinations. 

Similar to our findings on US fatality risk per VMT, after accounting for all of the control 

variables in the logistic regression model, except for vehicle mass and footprint, we find that the 

correlation between mass and the casualty risk per crash by vehicle model is very low. There 

also is no significant correlation between the residual, unexplained risk and vehicle weight. 

These results corroborate our earlier finding that, even after accounting for many vehicle, driver, 

and crash factors, the variation in risk by vehicle model is quite large and unrelated to vehicle 

weight (addressed in more detail in Section 4). The large remaining unexplained variation in risk 

by vehicle model could be attributable to other differences in vehicle design, or how drivers who 

select certain vehicles drive them. It is possible that including variables that account for these 

factors in the regression models would change the estimated relationship between mass or 

footprint and risk.

Other changes in the data and variables used in the regression models result in changes in the 

estimated effect of mass or footprint reductions on casualty risk per crash, as summarized in 

Tables ES.2 and ES.3. For example:

• Regression analyses using police-reported crash data from states must use control variables 

to account for differences in definitions of “serious” or “incapacitating” injuries, and 

reporting requirements, across states. Removing the 12 state control variables results in a 

large reduction in estimated casualty risk per crash from mass reduction in all five vehicle 
viii

types, a large increase in estimated risk from footprint reduction in cars and 

CUVs/minivans, and a small reduction in estimated risk from footprint reduction in light 

trucks (Alternative 4 in Table ES.2). Including only two variables to control for states with 

high and low casualty risk per crash substantially reduces the estimated effect of mass and 

footprint reduction on casualty risk (Alternative 5 in Table ES.2), while including the 12 

control variables for individual states reduces the estimated effect a little bit more. These 

results indicate that excluding control variables for the state in which a crash occurred from 

a regression model using state police-reported crash data can give inaccurate estimates of 

the effect of mass or footprint reduction on casualty risk per crash (addressed in Section 

5.1).

• Calculating risk as casualty crashes, rather than total casualties, per crash results in little 

change in the association between mass or footprint and risk, but does increase the small 

estimated detrimental effect of footprint reduction in cars on risk, and makes it statistically 

significant (Alternative 6 in Table ES.2; addressed in Section 5.2). 

• Adding control variables for vehicle manufacturer estimates that lower mass is associated 

with higher casualty risk per crash for cars, with little effect on the estimates for light 

trucks and CUVs/minivans. Accounting for vehicle manufacturer turns the small estimated 

increase in casualty risk per crash from footprint reduction in cars to a small decrease in 

risk, and slightly increases the estimated casualty risk per crash in light trucks and 

CUVs/minivans (Alternative 7 in Table ES.3). Also including control variables for five 

luxury vehicle makes has little effect on the estimated relationships between mass or 

footprint and casualty risk per crash (Alternative 8 in Table ES.3; addressed in Section 5.3).

Table ES.2. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, under alternative regression model specifications

Variable

Case vehicle 

type

LBNL 13-state casualties per policereported crash

1. Single regression model for all crash types

2. Weighted by current distribution of fatalities3. Excluding footprint

or weight

4. Excluding state control variables5. Including only two state control variables6. Casualty crashes per crash

Mass

reduction

Cars < 3106 lbs 0.09% 0.07% 0.08% 0.25% -0.64% -0.13% 0.30%

Cars > 3106 lbs -0.77% -0.87% -0.86% -0.61% -1.68% -1.19% -0.63%

LTs < 4594 lbs -0.11% -0.11% -0.09% -0.38% -0.21% -0.15% -0.04%

LTs > 4594 lbs -0.62% -0.74% -0.67% -0.78% -1.84% -0.75% -0.61%

CUV/ minivan -0.16% -0.31% -0.26% 0.13% -2.09% -0.47% -0.21%

Footprint

reduction

Cars 0.23% 0.50% 0.41% -0.10% 1.52% 0.45% 0.34%

LTs -0.25% 0.05% -0.13% -0.49% -1.05% -0.30% -0.05%

CUV/ minivan 0.56% 0.68% 0.75% 0.56% 3.79% 0.69% 0.80%

Estimates that are statistically significant at the 95% level are shown in red.

• An alternative to control variables for vehicle manufacturers is a single continuous variable 

for the vehicle’s initial purchase price; purchase price may better account for other 

differences in vehicle design that may influence traffic safety. Adding this single variable 

turns the estimated small increase in casualty risk per crash from mass reduction into an 
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estimated small decrease in risk for lighter-than-average cars, and increases the estimated 

beneficial effect from mass reduction for other vehicles, particularly heavier-than-average 

cars and CUVs/minivans; the price variable makes the estimated effect of footprint 

reduction slightly more detrimental in cars, more beneficial in light-duty trucks, and less 

detrimental in CUVs/minivans (Alternative 9 in Table ES.3; also addressed in Section 5.3).

• As we found in our assessment of NHTSA’s analysis of US fatality risk per VMT, 

including calendar year variables in the regression models appears to weaken the benefit of 

side air bags in cars and CUVs/minivans, and compatibility measures and ESC in light 

trucks. These variables also appear to minimize the increased risk of SUVs and heavy-duty 

pickup trucks. Excluding the calendar year variables from the regression models slightly 

reduces the beneficial effect of mass reduction on casualty risk per crash in light trucks and 

CUVs/minivans, and slightly increases the detrimental effect of footprint reduction on 

casualty risk per crash in cars (Alternative 10 in Table ES.3; addressed in Section 5.4).

• Because details on the driver’s condition or behavior are not consistently reported in the 

state crash data, we cannot account for the behavior of individual drivers in our estimates. 

One possible surrogate for the behavior of drivers who tend to select certain vehicle models 

is driver household income. Including a measure of household income by vehicle model 

makes the estimated effect of mass reduction on casualty risk per crash more beneficial, 

and the estimated effect of footprint reduction more detrimental, for cars and 

CUVs/minivans, but has little effect on the estimates for light trucks (Alternative 11 in 

Table ES.3). 

• Including all-wheel-drive, sports, and police cars, and fullsize vans results in virtually no 

change in the estimated effect of mass or footprint reduction on casualty risk per crash for 

cars or light trucks (Alternative 12 in Table ES.3; addressed in Section 5.5). 

Table ES.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, excluding certain data or using different control variables

Variable

Case vehicle 

type

LBNL 13-state casualties per policereported crash7. Accounting for vehicle manufacturer8.Accounting for vehicle manufacturer plus five luxury brands 9. Accounting for initial vehicle purchase price10. Excluding CY variables11. Accounting for median household income12. Including sports, squad, AWD cars and fullsize vans13. Including all additional data

Mass

reduction

Cars < 3106 lbs 0.09% 0.85% 0.96% -0.35% 0.00% -0.04% 0.10% 0.19%

Cars > 3106 lbs -0.77% 0.78% 0.76% -1.72% -0.99% -1.12% -0.76% -0.54%

LTs < 4594 lbs -0.11% -0.24% -0.24% -0.14% 0.43% -0.05% -0.09% -0.02%

LTs > 4594 lbs -0.62% -0.65% -0.60% -0.71% -0.20% -0.68% -0.64% -0.64%

CUV/ minivan -0.16% -0.05% -0.40% -0.64% 0.28% -0.65% -0.16% -0.34%

Footprint

reduction

Cars 0.23% -0.52% -0.60% 0.29% 0.69% 0.69% 0.25% 0.02%

LTs -0.25% -0.09% -0.11% -0.40% -0.49% -0.26% -0.27% -0.30%

CUV/ minivan 0.56% 0.88% 1.16% 0.41% 0.47% 1.01% 0.56% 0.44%

Estimates that are statistically significant at the 95% level are shown in red.
x

• Adding data from three additional states, including vehicles with unreported model year, 

correcting VIN transcription errors, and expanding the analysis to calendar years 2000, 

2001, and 2008, increases the number of state crash records by about 40 percent. Including 

these data in the regression analyses makes the estimated effect of mass reduction in cars 

and lighter light trucks more detrimental, and in CUVs/minivans more beneficial. 

Including these data slightly reduces the estimated detrimental effect of footprint reduction 

on casualty risk per crash in cars and CUVs/minivans. However, increasing the sample 

size included in the regression analysis by 40% does not noticeably reduce the confidence 

intervals around the point estimates (Alternative 13 in Table ES.3; addressed in Section 

5.6).

Table ES.4 shows the results of additional sensitivity tests NHTSA conducted in response to 

comments from peer reviewers of its preliminary 2011 report. Replacing vehicle footprint with 

its two components, track width and wheelbase, increases the estimated beneficial effect of mass 

reduction on casualty risk per crash, making it statistically significant for four of the five vehicle 

types, as shown in Alternative 14. Decreasing track width is associated with a significant

increase in casualty risk per crash, while decreasing wheelbase is associated with a small 

decrease in risk. Weighting the distribution of fatalities in CUVs and minivans by their 

respective shares of sales in 2010 (which reflects more CUVs and fewer minivans) has little 

effect on the estimated effects (Alternative 15). Alternative 16 removes non-significant control 

variables from each of the regression models, which results in only small changes in the 

estimated effects.

Table ES.4. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, alternative regression model specifications suggested by NHTSA peer reviewers

Variable

Case vehicle 

type

LBNL 13-state casualties per police-reported crash

14. Including track width and wheelbase instead of footprint

15. Reweighting CUVs and minivans by 2010 sales16. Excluding nonsignificant control variables

Mass

reduction

Cars < 3106 lbs 0.09% -0.37% 0.09% 0.17%

Cars > 3106 lbs -0.77% -1.05% -0.77% -0.58%

LTs < 4594 lbs -0.11% -0.40% -0.11% -0.24%

LTs > 4594 lbs -0.62% -0.75% -0.62% -0.68%

CUV/ minivan -0.16% -0.34% -0.24% -0.03%

Footprint

reduction

Cars 0.23% — 0.23% 0.11%

LTs -0.25% — -0.25% -0.15%

CUV/ minivan 0.56% — 0.53% 0.64%

Track 

width 

reduction

Cars — 2.58% — —

LTs — 0.40% — —

CUV/ minivan — 2.10% — —

Wheel 

base 

reduction

Cars — -0.59% — —

LTs — -0.15% — —

CUV/ minivan — -0.33% — —

Estimates that are statistically significant at the 95% level are shown in red.
xi

In conclusion, casualty risk per crash is not necessarily a better metric than fatality risk per VMT 

for evaluating the effect of mass or footprint reduction on risk; rather, it provides a different 

perspective in assessing the benefits or drawbacks of mass and footprint reduction on safety in 

vehicles. However, it does allow the risk per VMT to be separated into its two components, 

crash frequency and risk per crash. Our analysis indicates that much of the estimated detrimental 

effect of mass or footprint reduction on risk can be attributed to the tendency for crash 

frequency, rather than crashworthiness/compatibility (risk once a crash has occurred), to increase 

as vehicle mass or footprint decreases.

As with our analysis of US fatalities per VMT, this report concludes that the estimated effect of 

mass reduction on casualty risk per crash is small, and is overwhelmed by other control 

variables, such as vehicle type, specific safety technologies, and crash conditions such as 

whether the crash occurred at night, in a rural county, or on a high-speed road. This report 

indicates that the effects are sensitive to what variables and data are included in the regression 

analysis. Finally, as in our analysis of US fatality risk per VMT, this report shows that after 

accounting for many vehicle, driver, and crash variables there remains a wide variation in 

casualty risk per crash by vehicle make and model, and this variation is unrelated to vehicle 

mass.

Although the purpose of the NHTSA and LBNL reports is to estimate the effect of vehicle mass 

reduction on societal risk, this is not exactly what the regression models are estimating. Rather, 

they are estimating the recent historical relationship between mass and risk, after accounting for 

most measurable differences between vehicles, drivers, and crash times and locations. In essence, 

the regression models are comparing the risk of a 2600-lb Dodge Neon with that of a 2500-lb 

Honda Civic, after attempting to account for all other differences between the two vehicles. The 

models are not estimating the effect of literally removing 100 lbs from the Neon, leaving 

everything else unchanged.

In addition, the analyses are based on the relationship of vehicle mass and footprint on risk for 

recent vehicle designs (model year 2000 to 2007). These relationships may or may not continue 

into the future as manufacturers utilize new vehicle designs and incorporate new technologies, 

such as more extensive use of strong lightweight materials and specific safety technologies. 

Therefore, throughout this report we use the phrase “the estimated effect of mass (or footprint) 

reduction on risk” as shorthand for “the estimated change in risk as a function of its relationship 

to mass (or footprint) for vehicle models of recent design.”
xii
xiii

Table of Contents

Acknowledgements ..........................................................................................................................i

Executive Summary....................................................................................................................... iii

Table of Contents ........................................................................................................................ xiii

List of Tables and Figures........................................................................................................... xiii

1. Introduction .................................................................................................................................1

1.1. Expected relationships between vehicle mass, size and fatality risk....................................3

2. 13-state fatality and casualty risk per crash.................................................................................4

2.1. Data and methods.................................................................................................................5

2.2. Accounting for the state in which the crash occurred ........................................................11

2.3. Effect of mass and footprint reduction on fatality and casualty risk per crash ..................13

3. Multi-collinearity between vehicle mass and footprint.............................................................33

4. Casualty risk by vehicle model..................................................................................................40

5. Sensitivity of 13-state casualty risk per crash results to data used and model specification.....52

5.1. State control variables ........................................................................................................52

5.2. Alternative measure of risk ................................................................................................53

5.3. Vehicle manufacturer .........................................................................................................53

5.4. Calendar year variables ......................................................................................................56

5.5. Effect of household income................................................................................................60

5.6. Effect of including sports, police, and all-wheel drive cars, and fullsize vans ..................61

5.7. Effect of adding additional data .........................................................................................62

5.8. Effect of changes suggested by NHTSA peer reviewers....................................................64

6. Conclusions ...............................................................................................................................66

7. References .................................................................................................................................75

List of Tables and Figures

Table ES.1. Estimated effect of mass or footprint reduction on two components of 13- state 

fatality and casualty risk per VMT: crash frequency (crashes per VMT) and 

crashworthiness/compatibility (risk per crash)...............................................................................vi

Table ES.2. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

under alternative regression model specifications............................................................... viii

Table ES.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

excluding certain data or using different control variables ....................................................ix

Table ES.4. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

alternative regression model specifications suggested by NHTSA peer reviewers ................x

Table 2.1. Control variables used in regression models, by subject vehicle type ...........................7

Table 2.2. Fatal and casualty crash involvements for model year 2000 to 2007 passenger cars in 

2002 to 2008 ............................................................................................................................8

Figure 2.1. Distribution of crash-involved vehicles, by vehicle and crash type..............................9

Figure 2.2. Driver fatality risk per 100,000 crashes in 16 states...................................................12

Figure 2.3. Driver casualty risk per 10,000 crashes in 16 states...................................................12

Figure 2.4. Percent of police-reported crashes that are non-injury crashes, in 16 states...............13
xiv

Figure 2.5. Estimated effect of mass or footprint reduction on three types of risk, by vehicle type

...............................................................................................................................................15

Figure 2.6. Estimated effect of mass or footprint reduction on three types of risk per VMT, by 

vehicle type............................................................................................................................17

Figure 2.7. Estimated effect of mass or footprint reduction on crashes per VMT (vehicle crash 

frequency), fatalities per crash (vehicle crashworthiness/compatibility), and fatalities per 

VMT, by vehicle type............................................................................................................18

Figure 2.8. Estimated effect of mass or footprint reduction on crashes per VMT (vehicle crash 

frequency), casualties per crash (vehicle crashworthiness/compatibility), and casualties per 

VMT, by vehicle type............................................................................................................19

Figure 2.9. One-vehicle, non-injury crashes and all crashes per VMT, by vehicle type...............20

Figure 2.10. Estimated effect of mass or footprint reduction on fatalities per crash and per serious 

crash, by vehicle type ............................................................................................................21

Figure 2.11. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash by 

vehicle type, across all crash types and weighted average effect in each type of crash........22

Figure 2.12. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash in 

cars, by type of crash .............................................................................................................23

Figure 2.13. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash in 

light trucks, by type of crash .................................................................................................24

Figure 2.14. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash in 

CUVs/minivans, by type of crash..........................................................................................25

Table 2.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, by 

type of crash ..........................................................................................................................25

Table 2.4. Estimated effect of variables on US fatality risk, 13-state fatality risk, and 13-state 

casualty risk per VMT...........................................................................................................27

Table 2.5. Estimated effect of variables on US fatality risk per VMT, and 13-state fatality risk 

and 13-state casualty risk per crash .......................................................................................28

Table 2.6. Estimated effect of variables on crashes per VMT, fatalities per crash, and casualties 

per crash, using data from 13 states.......................................................................................31

Figure 3.1. Correlation between vehicle curb weight and footprint, by vehicle model and three 

vehicle types..........................................................................................................................34

Figure 3.2. Correlation between vehicle curb weight and footprint, by vehicle model and seven 

vehicle types..........................................................................................................................34

Table 3.1. Correlation coefficients and variance inflation factors of curb weight with footprint, 

by vehicle type.......................................................................................................................35

Figure 3.3. Estimated effect of reduction in mass or footprint on 13-state casualty risk per crash, 

by vehicle type: holding footprint constant, allowing footprint to vary with mass, and 

allowing mass to vary with footprint.....................................................................................36

Figure 3.4. Range in curb weight for the footprint deciles, by vehicle type .................................37

Table 3.2. Number of footprint deciles in which lower mass is associated with increasing or 

decreasing 13-state casualty risk per crash, by vehicle and crash type .................................38

Figure 3.5. Estimated effect of car mass reduction on 13-state casualty risk per crash, by 

footprint decile and crash type ..............................................................................................39

Figure 3.6. Estimated effect of light truck mass reduction on 13-state casualty risk per crash, by 

footprint decile and crash type ..............................................................................................39
xv

Figure 3.7. Estimated effect of CUV/minivan mass reduction on 13-state casualty risk per crash, 

by footprint decile and crash type .........................................................................................40

Figure 4.1. Relationship between 13-state casualty risk per crash and curb weight, with vehicles 

grouped into 100-lb increments of curb weight, by vehicle type ..........................................41

Figure 4.2. Relationship between 13-state casualty risk per crash and curb weight, with vehicles 

grouped into 100-lb increments of curb weight, passenger cars ...........................................41

Figure 4.3. Relationship between 13-state casualty risk per crash and curb weight, with vehicles 

grouped into 100-lb increments of curb weight, light trucks ................................................42

Figure 4.4. Relationship between 13-state casualty risk per crash and curb weight, with vehicles 

grouped into 100-lb increments of curb weight, CUVs and minivans..................................42

Figure 4.5. Relationship between 13-state casualty risk per crash and curb weight for minivans, 

by average risk for 100-lb increments of curb weight and individual models......................43

Figure 4.6. Relationship between 13-state casualty risk per crash in crashes with stationary 

objects and curb weight, by vehicle type...............................................................................44

Table 4.1. Correlation between risk and a decrease in curb weight, for vehicles grouped in 100-lb 

curb weight bins ....................................................................................................................44

Figure 4.7. 13-state casualty risk per crash and curb weight, by vehicle model ...........................45

Figure 4.8. Predicted 13-state casualty risk per crash after accounting for all driver, crash, and 

vehicle variables except mass and footprint, vs. curb weight ...............................................46

Figure 4.9. Residual 13-state casualty risk per crash after accounting for all driver, crash, and 

vehicle variables except mass and footprint, vs. curb weight ...............................................47

Table 4.2. Relationship between actual, predicted, and residual 13-state casualty risk per crash, 

and vehicle mass reduction, after accounting for all driver, crash, and vehicle variables 

except mass and footprint, by vehicle type and model..........................................................48

Table 4.3. Relationship between actual, predicted, and residual 13-state casualty risk per crash, 

and vehicle footprint reduction, after accounting for all driver, crash, and vehicle variables 

except mass and footprint, by vehicle type and model..........................................................48

Table 4.4. Relationship between frequency of one-vehicle non-rollover crashes and household 

income, vehicle mass, and initial vehicle purchase price, by vehicle type and model..........50

Figure 4.10. Estimated effect of mass or footprint reduction on 13-state crashes per VMT, after 

accounting for vehicle purchase price or median household income, by vehicle type .........51

Figure 5.1. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash by 

vehicle type, under two methods of controlling for the state in which the crash occurred ...52

Figure 5.2. Estimated effect of mass or footprint reduction on 13-state casualties and casualty 

crashes per crash, by vehicle type .........................................................................................53

Figure 5.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash by 

vehicle type, after controlling for vehicle manufacturer .......................................................54

Figure 5.4. Estimated effect of mass or footprint reduction on US fatalities per VMT, after 

controlling for vehicle manufacturer or for initial vehicle purchase price, by vehicle type..55

Figure 5.5. Estimated effect of calendar year variables on 13-state casualty risk per crash, by 

vehicle type............................................................................................................................57

Figure 5.6. Estimated effect of calendar year variables on light truck risk, by crash type............57

Figure 5.7. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash by 

vehicle type, including and excluding calendar year variables.............................................58

Figure 5.8. Estimated effect of selected control variables on car risk, including and excluding 

calendar year variables..........................................................................................................59
xvi

Figure 5.9. Estimated effect of selected control variables on light truck risk, including and 

excluding calendar year variables..........................................................................................59

Figure 5.10. Estimated effect of selected control variables on CUV/minivan risk, including and 

excluding calendar year variables..........................................................................................60

Figure 5.11. Estimated effect of mass or footprint reduction on 13-state casualties per crash, after 

controlling for median household income, by vehicle type ..................................................61

Figure 5.12. Estimated effect of mass and footprint reduction on 13-state casualty risk per crash 

by vehicle type, after including sports, police, and all-wheel drive cars, and fullsize 

passenger and cargo vans ......................................................................................................62

Figure 5.13. Number of vehicles involved in casualty crashes by vehicle type, using additional 

state crash data.......................................................................................................................63

Figure 5.14. Estimated effect of mass or footprint reduction on casualty risk per crash by vehicle 

type, using additional state crash data ...................................................................................64

Figure 5.15. Estimated effect of mass or footprint reduction on casualty risk per crash by vehicle 

type, replacing footprint with track width and wheelbase.....................................................65

Figure 5.16. Estimated effect of mass and footprint reduction on casualty risk per crash, after 

reweighting CUV/minivan fatalities to 2010 sales and excluding non-significant control 

variables, by vehicle type ......................................................................................................65

Table 6.1. Estimated effect of mass or footprint reduction on two components of 13- state 

fatality and casualty risk per VMT: crash frequency (crashes per VMT) and 

crashworthiness/compatibility (risk per crash)......................................................................68

Table 6.2. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

under alternative regression model specifications.................................................................71

Table 6.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

excluding certain data or using different control variables ...................................................72

Table 6.4. Estimated effect of mass or footprint reduction on 13-state casualty risk per crash, 

alternative regression model specifications suggested by NHTSA peer reviewers ..............73
1

1. Introduction

NHTSA recently completed a logistic regression analysis updating its 2003 and 2010 studies of 

the relationship between vehicle mass and US fatality risk per vehicle mile traveled (VMT; 

Kahane, 2012). The new study updates the previous analyses in several ways: updated FARS 

data for 2002 to 2008 involving MY00 to MY07 vehicles are used; induced exposure data from 

police reported crashes in several additional states are added; a new vehicle category for carbased crossover utility vehicles (CUVs) and minivans is created; crashes with other light-duty 

vehicles are divided into two groups based on the crash partner vehicle’s weight, and a category 

for all other fatal crashes is added; and new control variables for new safety technologies and 

designs, such as electronic stability controls (ESC), side airbags, and methods to meet voluntary 

agreement to improve light truck compatibility with cars, are included.

In a companion report (Wenzel, 2012b), we use the updated databases NHTSA has created to 

replicate their findings on the relationship between vehicle weight, size (actually footprint, or 

vehicle wheelbase times track width), and US fatality risk per vehicle miles traveled (VMT), for 

model year 2000 to 2007 light-duty vehicles involved in fatal crashes between 2002 and 2008. 

The data are examined in slightly different ways, to get a deeper understanding of the 

relationship between reductions in vehicle mass and footprint, and overall safety. 

This report compares the logistic regression results of the NHTSA analysis of US fatality risk per 

VMT with an analysis of 13-state casualty risk per crash. This analysis differs from the NHTSA 

analysis in two respects: first, it analyzes risk per crash, using data on all police-reported crashes 

from thirteen states, rather than risk per estimated VMT; and second, it analyzes casualty 

(fatality plus serious injury) risk, as opposed to fatality risk. There are several good reasons to 

investigate the effect of mass and footprint reduction on casualty risk per crash. 

First, risk per VMT, which NHTSA has studied extensively, includes two effects that influence 

whether a person is killed or seriously injured in a crash: how well a vehicle can be driven (based 

on its handling, acceleration, and braking capabilities) to avoid being involved in a serious crash 

(crash avoidance), and, once a serious crash has occurred, how well a vehicle protects its 

occupants from fatality or serious injury (crashworthiness) as well as the occupants of any crash 

partner (compatibility). By encompassing both of these aspects of vehicle design, risk per VMT 

gives a complete picture of how vehicle design can promote, or reduce, road user safety. On the 

other hand, risk per crash isolates the second of these two safety effects, 

crashworthiness/compatibility, by examining the effect of mass and footprint reduction on how 

well a vehicle protects its occupants once a crash occurs. In general, NHTSA safety regulations 

focus on crashworthiness (e.g. crash test requirements and NCAP star ratings, seatbelt and airbag 

requirements, and roof crush standards), although some standards require the installation of 

technologies, such as automated braking systems (ABS) and electronic stability control (ESC), 

that improve a vehicle’s crash avoidance.

Second, estimating risk on a per crash basis requires using data on police-reported crashes from 

states. Although NHTSA generates a national sample of police-reported crashes, the National 

Automotive Sampling System, General Estimates System (NASS GES), that can be used to 

estimate per crash risks on a national basis, the database is relatively small and may be biased 
2

towards crashes that occur in relatively urban areas. Only sixteen states currently record the 

vehicle identification number of all vehicles involved in police-reported crashes, which is 

necessary to determine the model year, make, and model of each vehicle, in order to assign its 

correct curb weight, footprint, type, and installed safety features (such as side airbags, ABS, 

ESC, and all-wheel drive). The sixteen states that report VIN information represent about onethird of the country, so estimating fatality risk per crash from these sixteen states increases the 

statistical uncertainty of the analysis, relative to that from estimating fatality risk per VMT using 

all US fatalities.1 Extending the analysis to casualties (fatalities plus serious/incapacitating 

injuries) reduces the statistical uncertainty of analyzing just fatalities per crash. In addition, a 

serious incapacitating injury can be just as traumatic to the victim and her family, and costly 

from an economic perspective, as a fatality. Limiting the analysis to the risk of fatality, which is 

an extremely rare event, ignores the effect vehicle design may have on reducing the large number 

of incapacitating injuries that occur each year on the nation’s roadways.

In an earlier report LBNL compared fatality risk per vehicle registration-year and casualty risk 

per crash, using the same database of all police-reported crashes in five states (Wenzel, 2012a). 

For the most part, the trend in casualty risk by vehicle type is quite similar to that of fatality risk, 

when vehicle registration-years are used as the measure of exposure, although casualty risks are 

substantially lower than fatality risks for sports cars and for pickups. The trend in casualty risk 

by vehicle type is similar regardless of whether vehicle registration years or police-reported 

crashes are used as the measure of exposure. Casualty risks for subcompact and compact cars 

are relatively lower per crash than per vehicle, while casualty risks for large and import luxury 

cars, minivans, large SUVs, and pickups are relatively higher per crash than per vehicle. We 

accounted for miles driven by vehicle make and model using odometer readings from vehicle 

emission inspection and maintenance programs in four of the five states. For most vehicle types, 

adjusting casualty risk per vehicle registration-year for miles driven has little to no effect 

(although the adjustment does substantially increase casualty risk for sports cars, which are 

driven many fewer miles than other vehicles, by 30%, and slightly reduces casualty risk for 

fullsize vans and 3⁄4-ton pickups, which are driven more miles than the average vehicle).

In summary, casualty risk per crash is not necessarily a better metric than fatality risk per VMT; 

rather, it provides a different perspective in assessing the benefits or drawbacks of mass and 

footprint reduction on safety in vehicles. Unless noted otherwise, all casualty risks in this report 

are societal risk, including fatalities and serious injuries in the case vehicle and any crash 

partners, and include not only driver casualties but passenger casualties as well. 

The section below summarizes the expected relationships between vehicle mass, size and fatality 

risk. In Section 2 we reproduce the logistic regression models NHTSA used in its analysis of US 

fatality risk per VMT, and compare the estimated effect of mass and footprint reduction on US 

fatality risk per VMT, 13-state fatality risk per crash, and 13-state casualty risk per crash. 

Section 3 examines in more detail the multi-collinearity between vehicle mass and footprint, and 

 1

 This report further limits the analysis to the thirteen states that provide the posted speed limit of the roadway on 

which the crash occurred, an important variable NHTSA uses in its regression models that approximates the travel 

speed of the vehicles involved in the crash. In Section 5 we run a sensitivity analysis using data from the three 

additional states that report VIN but not posted speed limit, using a technique developed by NHTSA to impute the 

posted speed limit based on the type of roadway on which the crash occurred (NHTSA, 2003).
3

methods to address that multi-collinearity when assessing their effect on casualty risk per crash. 

In Section 4 we examine the relationship between vehicle mass and casualty risk per crash by 

vehicle model, before and after accounting for the differences in driver characteristics, crash 

locations, and other vehicle attributes included in the NHTSA regression models. In Section 5 

we test alternative specifications of the regression models, in order to examine the sensitivity of 

our results to different model specifications, and using additional data.

1.1. Expected relationships between vehicle mass, size and fatality risk

In Section 1.5 of its 2011 report, NHTSA describes the hypothetical physical factors of vehicle 

design that could explain the historical relationship between vehicle mass and societal fatality 

risk. One would expect lighter vehicles to have higher fatality rates for their own occupants, all 

else being equal, for several reasons: 

• in frontal or rear crashes, light vehicles tend to be smaller than heavy vehicles, and therefore 

do not have the crush space which protects occupants; 

• in two-vehicle crashes, as the mass differential between the two vehicles increases, the delta 

V (change in velocity) for the lighter vehicle, and therefore the risk to its occupants, 

increases relative to that of the heavier vehicle. 

• in crashes with a stationary object additional mass may be sufficient to knock the object, 

such as a tree or pole, down, allowing the vehicle to continue moving and reducing its delta 

V than if it was completely stopped by the object. In a previous study NHTSA estimated 

that the object is knocked down in about 25% of frontal collisions with stationary objects 

(Partyka, 1995). 

• in crashes with a medium- or heavy-duty truck, additional mass in the light-duty vehicle 

would transfer more of its momentum to the truck, reducing the delta V of, and fatality risk 

in, the light vehicle without increasing the risk in the heavier vehicle.

NHTSA notes that accounting for vehicle size in the regression analysis may reduce or eliminate 

the estimated benefit of additional vehicle mass correlated with additional crush space. And that 

accounting for societal risks, that is risk of fatality both to the occupants of the subject vehicle 

and its crash partner, may reduce or eliminate the effect of mass differential in two-vehicle 

crashes, as increased fatalities in the lighter vehicle may be offset by reduced fatalities in the 

heavier vehicle.

On the other hand, there are situations where lower mass is expected to reduce fatality risk:

• in crashes with an immovable stationary object, reducing the mass of a vehicle while 

maintaining its crush space and structural strength would lower the kinetic energy of the 

crash, reducing the amount of energy for the vehicle’s structure to absorb, and likely 

reducing occupant fatality risk;

• in rollovers, reducing mass without changing the vehicle’s roof structure would reduce the 

force applied on the roof once a vehicle turns over.

• lower-mass vehicles should respond more quickly to steering, braking, or acceleration, 

thereby reducing their crash frequency.
4

Changing the size of a vehicle is expected to reduce risk in several ways. Increasing wheelbase 

or track width, or better yet frontal or side overhang, can increase crush space and reduce risk in 

all types of crashes. Adding to a vehicle’s track width also increases a vehicle’s static stability, 

and reduces its propensity to rollover.

Changing other vehicle dimensions also can reduce risk. Lowering bumpers or the “average 

height of force” in larger, heavier vehicles such as pickups and SUVs can make them more 

compatible with cars, and reduce risk to occupants in crash partner vehicles. Similarly, raising 

the door sill of a car provides more structure to engage with a bumper of a taller vehicle, such as 

a pickup or SUV, striking the car in the side. And lowering the center of gravity also is 

important in increasing stability and preventing rollovers. Finally, strengthening a vehicle’s 

frontal or side structure can increase the amount of energy it can absorb in all types of crashes; 

however, increasing frontal stiffness will likely have negative impacts on the occupants of a 

crash partner in a frontal collision.

All of these hypothetical effects of the changes in vehicle mass, footprint, or other dimensions 

assume no other changes to the vehicle. However, this is rarely the case, as often the source of 

the additional mass is the installation of a particular safety feature (such as 4-wheel drive or 

ESC), and manufacturers often make other changes to a vehicle design at the same time they 

change its mass or footprint. In short, it is possible that other changes in vehicle design, as well 

as introduction of safety technologies, can mitigate the hypothetical increase in risk from 

reducing vehicle mass or footprint.

In Section 1.6 NHTSA discusses the issue that, despite their theoretical advantage in terms of 

handling, braking, and accelerating, small and light vehicles historically have had higher crash 

and insurance claim frequency per vehicle mile traveled. This discrepancy suggests that small 

and light vehicles have not been driven as well as larger, heavier ones. NHTSA provides two 

hypotheses for why this would be the case: that less capable drivers tend to chose smaller and 

lighter vehicles; and that drivers of more maneuverable smaller and lighter vehicles tend to drive 

them more recklessly. As an example of the latter, NHTSA cites the high crash rates in vehicles 

with large engines, which in theory should reduce crash frequency because they allow a vehicle 

to accelerate out of dangerous situations.

In summary, the complexity of the factors in vehicle design and operation makes it extremely 

difficult to isolate their effect on occupant and societal risk. As NHTSA concludes, “although 

[the 2010 NHTSA] report and this one both concentrate on the effects of mass and footprint, 

because that is their purpose, these effects are indeed small relative to design and engineering, 

which shape a vehicle’s intrinsic safety and also bear indirectly on its fatality rates by 

influencing what types of drivers choose the vehicle.”

2. 13-state fatality and casualty risk per crash

For its analysis of the effect of changes in vehicle mass on US fatality risk per VMT, NHTSA 

used information on all US traffic fatalities, from the Fatality Analysis Reporting System 

(FARS). For the measure of exposure, NHTSA used a subset of non-culpable vehicles involved 

in two-vehicle crashes from police-reported crash data from thirteen states; NHTSA refers to this 
5

subset of vehicles as “induced exposure” cases. The induced exposure cases provide information 

on driver and crash characteristics for vehicles that are not involved in fatal crashes, as in the 

FARS data. NHTSA developed weighting factors to scale the induced exposure vehicles up to 

national level vehicle registrations. NHTSA then multiplied the vehicle registration-years by 

annual vehicle miles traveled (VMT) factors it developed by vehicle type and age, from 

odometer data provided by RL Polk. For more details on NHTSA’s data and methodology, refer 

to Kahane, 2011.

In this section we use basically the same logistic regression models NHTSA developed for their 

analysis of US fatality risk per VMT to assess the effect of mass and footprint reduction on 13-

state fatality and casualty risk per crash, using data from all police-reported crashes in thirteen 

states. We also examine in detail the effect mass and footprint reduction have on 13-state 

casualty risk per crash in each type of crash, as well as the effects the various other vehicle, 

driver, and crash condition variables have on casualty risk per crash.

2.1. Data and methods

For its analysis NHTSA used FARS data on fatal crashes, and police-reported crash data from 13 

states, for MY00 to MY07 light-duty vehicles between calendar years 2002 and 2008. NHTSA 

used a subset of non-culpable vehicles in two-vehicle crashes as a measure of what it calls

“induced exposure”; these records provide distributions of on-road vehicles by vehicle year, 

make, and model, driver age and gender, and crash time and location (day vs. night, rural vs. 

urban counties, and high-speed roads). Each induced exposure record is then given a registered 

vehicle weighting factor, so that each induced exposure record represents a number of national 

vehicle registrations; the sum of the weighting factors equals the number of vehicles registered in 

the country. Each record is also given a VMT weighting factor, based on vehicle year, 

make/model, and age, using odometer data provided by R.L. Polk. The data can be used to 

estimate US fatality risk per registered vehicle or VMT. Please refer to Sections 2.3 through 2.6 

of NHTSA 2012 for a more thorough discussion of how the vehicle and VMT weighting factors 

were derived.

NHTSA compiled a database of the following vehicle attributes, by model year, make and 

model: curb weight and footprint (wheelbase times track width), as well as the presence of allwheel drive and automated braking systems. NHTSA added several new variables for new 

safety technologies and designs: electronic stability controls (ESC), four types of side airbags, 

and two methods to comply with the voluntary manufacturer agreement to better align light truck 

bumpers to make them more compatible with other types of vehicles.

To reflect changes in the vehicle mix since the 2003 study, NHTSA added a third vehicle 

category, car-based crossover utility vehicles (CUVs) and minivans. It also added two new crash 

types, for a total of nine: crashes with other light-duty vehicles are divided into two groups based 

on the crash partner vehicle’s weight, and all other fatal crashes (involving more than two 

vehicles, etc.). The analysis involves running a logistic regression model with total crash 

fatalities as the dependent variable for each of the nine crash types and the three vehicle types, 

for a total of 27 regressions. Because all fatalities in the crash are used, the risks reflect societal 

risk, rather than just the risk to the occupants of the case vehicle. The induced exposure cases 
6

are weighted by the number of vehicle registrations and the annual mileage, so that the models 

are estimating the effect of changes in the control variables on US fatalities per vehicle mile 

traveled (VMT). 

Table 2.1 shows the control variables NHTSA used in its regression models, for each of the case 

vehicle types. For cars and trucks, NHTSA uses two variables (UNDRWT00, OVERWT00) for 

vehicle weight, allowing the effect of weight on risk to vary for lighter and heavier cars and 

trucks. The determination of the two weight classes is based on the average weight for each 

vehicle type: 3,106 lbs for cars and 4,594 lbs for light-duty trucks. Because there are fewer 

CUVs and minivans in the database, NHTSA uses a single variable, LBS100, for CUV/minivan 

weight. As in the 2003 and 2010 analyses, eight variables for driver age and gender are used. In 

the 2003 analysis, NHTSA excluded the driver airbag control variables in the regressions for 

rollovers and crashes with pedestrians. In the 2011 analysis, NHTSA includes the control 

variable ROLLCURT airbags only in the regression models for rollover crashes involving cars or 

CUVs/minivans; regression models of pedestrian crashes do not include any control variables for 

airbags; and the control variables for CURTAIN, COMBO, and TORSO airbags are included in 

regression models for all other crashes involving cars or CUVs/minivans. No airbag variables

were included in the regression models for light trucks. 

Rather than reporting coefficients for the variables of interest (curb weight and footprint) from a 

single regression model across all crash types, NHTSA reports a weighted average of the 

coefficients from the nine regression models run for each of the nine crash types. NHTSA uses a 

“baseline” distribution of fatalities across the crash types, to represent the expected distribution 

of fatalities in the 2017 to 2025 timeframe of the new CAFE and GHG emission standards. 

Similar to the 2003 study, NHTSA derives the baseline fatalities from MY04-09 vehicles in 

crashes between 2004 and 2008. NHTSA then adjusts this baseline distribution downward to 

account for the assumption that all vehicles in the 2017-2025 timeframe will have ESC installed. 

The assumptions used for this adjustment are taken from a NHTSA analysis that found that ESC 

reduces fatal rollovers by 56% in cars and 74% in light trucks; fixed-object impacts by 47% in 

cars and 45% in light trucks; and other non-pedestrian crashes by 8% in both cars and light 

trucks.2 These assumptions treat crossover SUVs and minivans as light trucks rather than cars. 

This “post-ESC” distribution of fatalities by crash type is then multiplied by the regression 

coefficients for each crash type to create the weighted average effect of each control variable on 

risk. Table 2.2 shows the baseline distribution of fatalities, by case vehicle type and crash type, 

which are used to create the overall coefficient estimates weighted by the results from the 

regressions for each crash type.

For our analysis of fatality and casualty risk per crash, we divided all crashes in the 13-state 

databases into the nine crash categories, and three vehicle types, used by NHTSA in its 2011 

study, for the most part using the same criteria. One important difference is that NHTSA 

considered only “first-events” in classifying one-vehicle crashes as rollovers; vehicles that struck 

an object (or another vehicle) prior to rolling over are not included in NHTSA’s “rollover” 

category. However, since all thirteen states do not consistently code “first” vs. “most harmful” 

 2 Sivinski R. (2011). Update of NHTSA’s 2007 Evaluation of the Effectiveness of Light Vehicle Electronic Stability 

Control (ESC) in Crash Prevention, NHTSA Technical Report No. DOT HS 811 486. Washington, DC: National 

Highway Traffic Safety Administration. http://www-nrd.nhtsa.dot.gov/Pubs/811486.pdf.
7

events in the same manner, as is done in FARS, we included all vehicles involved in singlevehicle rollover crashes in our “rollover” category, regardless of whether they struck an object 

prior to rolling over. 

Table 2.1. Control variables used in regression models, by subject vehicle type

Control variable Cars LTVs CUVs/minivans

UNDRWT00 C C

OVERWT00 C C

LBS100 C

FOOTPRINT C C C

TWODOOR D

SUV D

HD_PKP D

BLOCKER1 D

BLOCKER2 D

MINIVAN D

ROLLCURT * C # C #

CURTAIN * C # C #

COMBO * C # C #

TORSO * C # C #

ABS C # C #

ESC C # C # C #

AWD C # C #

DRVMALE D D D

M14_30 C C C

M30_50 C C C

M50_70 C C C

M70_96 C C C

F14_30 C C C

F30_50 C C C

F50_70 C C C

F70_96 C C C

NITE D D D

RURAL D D D

SPDLIM55 D D D

HIFAT_ST D D D

VEHAGE C C C

BRANDNEW D D D

CY2002 D D D

CY2003 D D D

CY2004 D D D

CY2005 D D D

CY2007 D D D

CY2008 D D D

C: continuous variable

C #: for some models the VIN does not indicate whether a particular vehicle is equipped with that option or not. In 

these cases the fraction of that model that is equipped with the particular feature is used. 

D: dummy variable, coded as either 1 or 0

* The control variable for ROLLCURT airbags is only used in regression models of rollover crashes involving cars 

or CUVs/minivans; regression models of pedestrian crashes do not include any control variables for airbags; the 

control variables for CURTAIN, COMBO, and TORSO airbags are included in regression models for all other 

crashes involving cars or CUVs/minivans.
8

Table 2.2 and Figure 2.1 compare the distribution of light-duty vehicle crashes in the U.S. from 

the NHTSA 2011 report with those from the 13 states. Note that there are higher fractions of 

“other” crashes (that is, crashes involving more than two vehicles, or for which not all 

information was available) in the 13-state data; for example, 22% of U.S. fatal car crash

involvements in FARS are in the “other” category, while 29% of fatality crash involvements, and 

32% of casualty crash involvements, in the thirteen states are in the “other” category. The 

distributions of vehicles involved in crashes in Figure 2.1 exclude the “other” crash category, so 

that the fractions of all other types of crashes equal 100% for each vehicle type. 

Table 2.2. Fatal and casualty crash involvements for model year 2000 to 2007 passenger 

cars in 2002 to 2008

Crash type

Fatal crash involvements 

(FARS)

Fatal crash involvements 

(13 states)

Casualty crash involvements 

(13 states)

Cars LTVs

CUVs/ 

minivans Cars LTVs

CUVs/ 

minivans Cars LTVs

CUVs/ 

minivans

1: Rollovers 2,709 6,269 660 592 1,271 150 4,106 6,813 832

2: w/object 9,373 7,272 1,319 1,862 1,343 248 13,525 9,699 1,934

3: Ped etc. 6,514 6,493 1,904 2,114 1,751 601 11,430 7,501 3,150

4: w/HDT 3,346 2,371 680 1,005 606 235 4,976 2,973 1,106

5: w/lgt car 4,258 5,667 1,245 1,229 1,328 375 17,064 11,906 4,211

6: w/hvy car 4,746 4,928 1,211 1,063 1,041 324 14,159 9,433 3,380

7: w/lgt LT 3,149 2,670 622 1,153 868 267 13,565 8,667 3,095

8: w/hvy LT 3,622 2,196 685 1,047 526 202 9,025 5,221 2,149

9: Other 10,487 9,407 2,810 4,177 3,364 1,068 41,791 28,304 10,568

Total 48,204 47,273 11,136 14,242 12,098 3,470 129,641 90,517 30,425

1: Rollovers 5.6% 13.3% 5.9% 4.2% 10.5% 4.3% 3.2% 7.5% 2.7%

2: w/object 19.4% 15.4% 11.8% 13.1% 11.1% 7.1% 10.4% 10.7% 6.4%

3: Ped etc. 13.5% 13.7% 17.1% 14.8% 14.5% 17.3% 8.8% 8.3% 10.4%

4: w/HDT 6.9% 5.0% 6.1% 7.1% 5.0% 6.8% 3.8% 3.3% 3.6%

5: w/lgt car 8.8% 12.0% 11.2% 8.6% 11.0% 10.8% 13.2% 13.2% 13.8%

6: w/hvy car 9.8% 10.4% 10.9% 7.5% 8.6% 9.3% 10.9% 10.4% 11.1%

7: w/lgt LT 6.5% 5.6% 5.6% 8.1% 7.2% 7.7% 10.5% 9.6% 10.2%

8: w/hvy LT 7.5% 4.6% 6.2% 7.4% 4.3% 5.8% 7.0% 5.8% 7.1%

9: Other 21.8% 19.9% 25.2% 29.3% 27.8% 30.8% 32.2% 31.3% 34.7%

Total 100% 100% 100% 100% 100% 100% 100% 100% 100%

Figure 2.1 indicates that there is a smaller portion of fatal car crashes with stationary objects, 

heavy cars, and rollover crashes in the thirteen states (18.5%, 10.6%, and 5.9%, respectively) 

than in the entire US (24.9%, 12.6%, and 7.2%, respectively). On the other hand, there are more 

fatal car crashes in crashes with pedestrians/pedalcycles, light cars, light and heavy light-duty 

trucks, and heavy-duty trucks in the thirteen states (21.0%, 12.2%, 11.5%, 10.4%, and 10.0%, 

respectively) than in the US (17.3%, 11.3%, 8.3%, 9.6%, and 8.9%, respectively). These trends 

hold for light trucks and CUVs/minivans as well.

In the thirteen states, there are higher fractions of crashes involving rollovers, stationary objects, 

pedestrians/pedalcycles, and heavy trucks, and fewer crashes with other light-duty vehicles, 

when the crashes result in a fatality rather than a casualty. This suggests that rollovers and 

crashes with stationary objects, pedestrians/pedalcycles, and heavy-duty trucks are more likely to 

result in fatalities, as opposed to incapacitating injuries, than crashes with another light-duty 

vehicle. 
9

The distributions of fatal and casualty crashes involving cars in the thirteen states are quite 

similar to those involving CUVs and minivans; however, CUVs and minivans tend to be 

involved in fewer crashes with stationary objects (10.3% of all fatal crashes) than cars (18.5% of 

all fatal crashes). Light trucks tend to have more fatal/casualty crashes in rollovers and crashes 

with lighter cars (14.6% and 15.2% of all fatal crashes, respectively) than cars do (5.9%, and 

12.2% of all fatal crashes, respectively), but relatively fewer crashes with stationary objects 

(15.4%, vs. 18.5% for cars) and heavier light trucks (6.9%, vs. 10.0% for cars).

Figure 2.1. Distribution of crash-involved vehicles, by vehicle and crash type

Note in Table 2.2 that there are many fewer fatal crash involvements in the thirteen states (e.g., 

14,242 cars) than in the US FARS (48,204 cars). Extending the analysis to include 

incapacitating injuries substantially increases the number of casualty crash involvements in the 

thirteen states (to 129,641 cars). The focus of this report is on the estimated effect of mass and 

footprint reduction on casualty risk using data from the thirteen states, although we do compare 

the effect on fatality risk in the next section. And in Section 5 we analyze the effect of extending 

the analysis to sixteen states, and adding other crashes to the analysis. 

To the extent possible, we used the same assumptions as in the NHTSA analysis, in many cases 

using the same SAS programs. For example, we used the VIN decoder programs developed by 

NHTSA to determine model year, make, and model of each vehicle in the state crash data, and 

added detailed vehicle characteristics such as body style, curb weight, footprint, ABS, AWD, 

passive restraint systems, etc. And we used the NHTSA definitions to classify vehicles into five 

types (light cars, heavy cars, light light-duty trucks, heavy light-duty trucks, and 

CUVs/minivans), as well as the nine types of crashes described above. This was done in order to 

7.2% 5.9% 4.7% 

16.6% 14.6% 11.0% 7.9% 6.2% 4.2% 

24.9% 

18.5% 

15.4% 

19.2% 

15.4% 

15.6% 

15.8% 

10.3% 

9.7% 

17.3% 

21.0% 

13.0% 

17.1% 

20.0% 

12.1% 

22.9% 

25.0% 

15.9% 

8.9% 

10.0% 

5.7% 

6.3% 

6.9% 

4.8% 

8.2% 

9.8% 

5.6% 

11.3% 

12.2% 

19.4% 

15.0% 15.2% 

19.1% 

15.0% 

15.6% 

21.2% 

12.6% 

10.6% 

16.1% 

13.0% 

11.9% 

15.2% 

14.5% 

13.5% 

17.0% 

8.3% 

11.5% 15.4% 

7.1% 9.9% 

13.9% 

7.5% 11.1% 

15.6% 

9.6% 10.4% 10.3% 5.8% 6.0% 8.4% 8.2% 8.4% 10.8% 

0% 

10% 

20% 

30% 

40% 

50% 

60% 

70% 

80% 

90% 

100% 

Fatality 

(FARS) 

Fatality 

(13 states) 

Casualty 

(13 states) 

Fatality 

(FARS) 

Fatality 

(13 states) 

Casualty 

(13 states) 

Fatality 

(FARS) 

Fatality 

(13 states) 

Casualty 

(13 states) 

Distribution of crash-involved vehicles 

Distribution of crash-involved vehicles, by crash type 

9: Other 

8: w/hvy LT 

7: w/lgt LT 

6: w/hvy car 

5: w/lgt car 

4: w/HDT 

3: Ped etc. 

2: w/object 

1: Rollovers 

 Cars Light Trucks CUVs/Minivans 
10

allow for a more direct comparison of the results from the two studies, as well as with other 

studies using very similar databases and approaches. 

However, it was necessary to diverge from the NHTSA analysis in several respects. First, as 

discussed above, in analyzing the relationship between vehicle mass and US fatality risk per 

VMT, NHTSA used all US fatalities from FARS, and a subset of non-culpable vehicles in twovehicle crashes from police-reported crash data from the thirteen states to assign driver and 

environment control variables to national vehicle registration years (from Polk). NHTSA 

selected non-culpable vehicles in two-vehicle crashes to determine induced exposure crash 

involvements. Each of these vehicles was assigned a weight representing the national 

registration-years for each particular year, make and model. NHTSA developed other weights 

for total VMT based on a database of vehicle odometer readings by vehicle year, make and 

model, also obtained from Polk. For a more thorough discussion of how NHTSA derived the 

vehicle and VMT weighting factors, refer to Sections 2.3 through 2.6 of NHTSA 2012.

For our analysis of risk per crash, we use all vehicles in the state databases, including those 

involved in one-vehicle crashes and the vehicle NHTSA determined to be responsible for the 

crash in two-vehicle crashes. Therefore both the number of fatalities or casualties, and the 

number of crashes, come from the same datasets. For our analysis of risk per VMT, we again 

use the number of fatalities or crashes from the thirteen state databases, coupled with the VMT 

weights that NHTSA derived from the induced exposure crash involvements, national vehicle 

registrations, and average vehicle odometer readings. Because NHTSA apparently included all 

induced exposure involvements in creating their VMT weights, and did not exclude those that 

resulted in a fatality, we are able to use NHTSA’s VMT weights in our regression models of 13-

state risk per VMT. However, NHTSA used national Polk registration data to scale the induced 

exposure crashes from the thirteen states to the national level. Since we only include casualties 

occurring in the thirteen states, this scaling is not necessary for our analysis. In the future we 

hope to obtain VMT weights adjusted to total registration-years in the thirteen states, rather than 

in the entire US, for our analyses of risk per VMT. 

Second, as noted above, NHTSA included fatal crash involvements from FARS for 2008, even 

though 2008 data were available from only six of the thirteen states NHTSA used to develop the 

induced exposure records. For the remaining seven states, NHTSA assumed the distribution of 

induced exposure crashes in 2008 were identical to those in 2007.4 2008 crash data for 12 of the

13 states have subsequently become available, so NHTSA has revised its vehicle registration 

year and miles traveled weights based on actual induced exposure crashes in 12 of the 13 states; 

however, NHTSA continues to use replicated data for Wyoming crashes in 2008, Pennsylvania 

crashes in 2002, and Michigan crashes in 2002 and 2003. In our analyses we exclude the vehicle 

registration-year and miles traveled for these five years with missing data.

 4 NHTSA made similar assumptions for years of state crash data that were not available, such as 2002 data from 

Pennsylvania and 2002 and 2003 data from Michigan.
11

To make our results most comparable to NHTSA’s results for US fatalities per VMT, we also 

excluded the following records from our initial analysis:

• sports cars, police cars, and all-wheel drive cars; all Ford Crown Victorias5; and 

fullsize passenger and cargo vans;

• vehicles whose reported model year did not match the model year decoded from the 

VIN;

• vehicles whose model year was not reported in the state crash data (with the exception 

of all crash records from Washington, which NHTSA included in their analysis of 

induced exposure crashes); 

• vehicles involved in police-reported crashes in 2008 (in six states);

• vehicles that had apparent VIN transcription errors that we corrected so that the 

reported model year matched the VIN model year.6

Including these records, as well as police-reported crash data from three states that NHTSA did 

not include in its analysis of induced exposure crashes, increases the number of vehicles 

analyzed by about 40%. We test how including all of these records in the regression analyses 

would change the effect of mass and footprint reduction on casualty risk per crash in Section 5. 

2.2. Accounting for the state in which the crash occurred

In its regression models of US fatality risk per VMT, NHTSA included the control variable 

HIFAT_ST, which identifies states with high fatality rates per million vehicle-years. We 

investigated the effect of replacing this single control variable with two variables, for states with 

high and with low fatality risks per crash, as well as with 12 control variables for each state used 

in the analysis except Florida.

Figures 2.2 and 2.3 show the unadjusted fatality and casualty risk per crash in 16 states. Figure 

2.2 indicates that fatality risk per crash is the highest in Florida, Pennsylvania, and Wyoming, 

and the lowest in Michigan, Illinois, and New Jersey. Figure 2.3 suggests that casualty risk per 

crash is the highest in Alabama, Florida, Maryland, and Wyoming, and the lowest in Georgia, 

Michigan, New Jersey, and Washington. Note that driver casualty risks per crash have been 

fairly constant over time in most states, with the exception of Maryland and New Mexico, which 

exhibit fairly large, consistent reductions in casualty risk each year. We have no explanations for 

this trend in these two states.

 5 NHTSA excluded all Crown Victorias, which tend to be high-mileage vehicles, on the basis that the sparse 

odometer data available for this large car model are not representative. 

6 The apparent transcription errors are based on comparing the reported model year with the characters in the 9th and 

10th VIN position. If the reported model year matched a common transcription error (such as a “5” entered as an 

“S”) then we translated the character in the 10th VIN position to match the reported model year. If the reported 

model year matched the character entered in position 9, we shifted the character in position 9, and all subsequent 

characters, to the right one position. These VIN adjustments are described in more detail in Wenzel 2012a.
12

Figure 2.2. Driver fatality risk per 100,000 crashes in 16 states

Figure 2.3. Driver casualty risk per 10,000 crashes in 16 states

0 

100 

200 

300 

400 

500 

600 

1994 1996 1998 2000 2002 2004 2006 2008 

Driver fatality risk per 100,000 crashes 

Year 

Driver fatality risk per 100,000 crashes 

FL 

IL 

MD 

MI 

MO 

NE 

NJ 

NM 

PA 

WA 

WI 

WY 

AL 

GA 

KS 

KY 

0 

100 

200 

300 

400 

500 

600 

700 

1994 1996 1998 2000 2002 2004 2006 2008 

Driver casualty risk per 10,000 crashes 

Year 

Driver casualty risk per 10,000 crashes 

FL 

IL 

MD 

MI 

MO 

NE 

NM 

PA 

WA 

WI 

WY 

NJ 

AL 

GA 

KS 

KY 
13

The relatively high or low risks shown for some states in Figures 2.2 and 2.3 do not necessarily 

reflect more dangerous driving conditions in those states; rather, they reflect either different 

definitions of “incapacitating”, “serious”, or “major” injuries, or different reporting requirements 

or reporting bias in those states. For example, Pennsylvania is unique in that it reports 

“moderate” injuries in addition to “major” and “minor” injury; as a result, there are relatively 

few “major” injuries reported in Pennsylvania, which increases its casualty risk per crash relative 

to other states. In Florida, there is no property damage threshold over which a crash is required 

to be included in the state crash database; in most other states crashes resulting in property 

damage in excess of $500 must be reported. In Figure 2.4, only about 60% of all crashes in the 

Florida database are non-injury crashes, whereas 80% to 90% of the crashes in most other states 

are non-injury crashes. As a result, risks per crash are higher in Florida than in almost any other 

state. 

Figure 2.4. Percent of police-reported crashes that are non-injury crashes, in 16 states

Based on Figures 2.2 through 2.4, we replaced the HIFAT_ST variable NHTSA used for analysis 

of US fatalities per VMT with 12 variables identifying each state except Florida for our analysis 

of fatality and casualty risks per crash. We examine how replacing the 12 state control variables 

with only two variables for high- and low-injury states would change the effect of mass and 

footprint reduction on risk in Section 5.

2.3. Effect of mass and footprint reduction on fatality and casualty risk per crash

All of the regression coefficients presented in the NHTSA 2011 report are the direct output from 

the SAS LOGIST procedure (with the exception of those for the mass and footprint variables 

UNDRWT00, OVERWT00, LBS100, and FOOTPRNT, which NHTSA often multiplies by -1 so 

60% 

65% 

70% 

75% 

80% 

85% 

90% 

1994 1996 1998 2000 2002 2004 2006 2008 

Percent of all police-reported crashes with no injuries 

Year 

Percent of police-reported crashes that are non-injury crashes 

FL 

IL 

MD 

MI 

MO 

NE 

NM 

PA 

WA 

WI 

WY 

NJ 

AL 

GA 

KS 

KY 
14

that they reflect the effect of a reduction in vehicle mass or footprint; we use the same 

convention throughout this report). The output from the SAS LOGIST procedure reflects the 

percent change in the log-odds of casualty (or fatality) per crash for a one-unit increase in the 

explanatory variable. In order to obtain the percent change in the probability of casualty (or 

fatality) per crash, the SAS outputs need to be converted from log-space to linear space, and 

from odds to probabilities. We use the conversion factor e

x – 1, where x is the logistic regression 

coefficient from the SAS output, to make this conversion. This conversion has no effect on the 

output regression coefficients when the change in the log-odds of casualty is small; however it 

substantially increases the percent change for explanatory variables that have a large effect on 

the log-odds of casualty (such as the crash location variables). For example, the casualty risk per 

crash from a lighter-than-average car involved in a rollover crash has a 1.64 times higher logodds of casualty if it occurs in a rural county; after conversion, this crash has a 416 percent 

higher probability of casualty if it occurs in a rural county (EXP(1.64) - 1 = 4.16). Unless noted 

otherwise, the confidence intervals shown in this report are calculated the same way; that is, 

using the standard error of the log-odds output of the SAS LOGIST procedure to derive the 95% 

confidence interval of the log-odds coefficient, and to display it as a percent probability interval.

Figure 2.5 presents the regression coefficients of the effect of reductions in mass and footprint on 

US fatality risk per ten billion VMT, from the NHTSA 2011 analysis (in light blue). The 

coefficients for each of the nine crash types are weighted by the distribution of NHTSA’s 

estimated 2016 baseline fatal crash involvements, after adjustment for full ESC penetration. The 

figure indicates that mass reduction is estimated to increase societal7 fatality risk by about one 

percent for cars and lighter-than-average light trucks, while mass reduction leads to a slight 

reduction in fatality risk for the heavier light trucks and CUV/minivans. The 95% confidence 

intervals in the figure indicate that the changes in risk for lighter cars, and both categories of 

light-duty trucks, are statistically significant. The confidence intervals shown in the figure, and 

all figures in this report, represent the weighted average standard error from the SAS output, 

times 1.96. NHTSA does not report these confidence intervals in its 2011 report; rather it uses a 

jack-knife technique to estimate the range in uncertainty around the point estimates. The 

resulting confidence intervals are larger than those shown in this report. 

Figure 2.5 compares the estimated effect of mass and footprint reduction on US fatalities per 

billion VMT (from NHTSA 2011, in blue) with that on 13-state fatality risk (in red), and 13-state 

casualty risk (in green), per police-reported crash. The effect for each of the nine crash types is 

weighted by the expected distribution of fatal or casualty crashes in 2016, after full adoption of 

ESC, just as in the NHTSA 2011 report. Lower mass in cars and light trucks, while holding 

footprint constant, is associated with a consistent reduction in state fatality risk per crash; the 

estimated reductions are statistically significant for all but the lighter cars. Lower mass in CUVs 

and minivans is associated with a statistically non-significant increase in state fatality risk per

crash. Smaller footprint in cars and light trucks is associated with increases in state fatality risk 

 7

 All of the fatality risks reported in the 2011 NHTSA report are societal risk, that is fatalities to all vehicle 

occupants and non-occupants involved in the crash are included. Unless specified otherwise (i.e. in Section 6, when 

we examine the effect of side impact airbags on risk to car occupants, and steps manufacturers have taken to 

improve light truck compatibility on the risk light trucks impose on other vehicle occupants, in two-vehicle crashes), 

all risks in this report also are societal risk.
15

per crash, while smaller footprint in CUVs and minivans is associated with a decrease in fatality 

risk per crash; however, all three estimated effects are not statistically significant. 

The estimated effects for 13-state fatality risk per crash (shown in red) in Figure 2.5 are quite 

different from the effects NHTSA estimated for US fatality risk per VMT (shown in blue), which 

found that lower mass, while holding footprint constant, is associated with increased risk for cars 

and lighter light trucks, and slightly reduced risks for the heavier light trucks and 

CUVs/minivans. The different results for fatality risk per VMT versus per crash could be 

attributed to at least three factors. 

• First, as discussed above, the estimated effect of mass reduction on fatality risk per VMT 

is the combined effect of a vehicle’s crash avoidance and its 

crashworthiness/compatibility; the ability of a vehicle to avoid a crash altogether, and the 

extent to which a vehicle protects its occupants, as well as the occupants of any crash 

partners, once a serious crash occurs. The net detrimental effect of mass reduction on 

fatality risk per VMT for cars and lighter light-duty trucks may be the result of a large 

detrimental effect of mass reduction on these vehicles’ crash avoidance, combined with a 

smaller, beneficial effect of mass reduction on crashworthiness/compatibility. We address 

this possibility below.

Figure 2.5. Estimated effect of mass or footprint reduction on three types of risk, by vehicle 

type

• Second, the differences between the estimated effect of mass reduction on US fatality risk 

per VMT versus 13-state fatality risk per crash could be the result of differences in the 

mass/footprint relationship with risk in the thirteen states vs. in the country as a whole. 1.55% 0.51% 0.52% -0.34% -0.38% 1.87% -0.07% 1.72% -0.54% -2.39% -1.61% -1.25% 0.98% 0.92% 0.48% -1.67% 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 

-4.0% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (probability) 

Effect of reduction in weight or size on risk, by vehicle type

US fatalities per VMT 

13-state fatalities per crash 

13-state casualties per crash 

 100-lb reduction in weight 1-sq ft reduction in footprint 
16

• Finally, the differences between fatality risk per VMT and casualty risk per crash could 

indicate that casualties are much less sensitive to mass reductions than fatalities, and that 

vehicle mass reduction somehow reduces casualties but not fatalities.

Figure 2.5 indicates that lower vehicle mass is associated with in smaller effects on casualty risk 

per crash than on fatality risk per crash. Lower mass is associated with small statistically 

significant reductions in casualty risk per crash for heavier cars and all light trucks, a small but 

not statistically significant reduction in risk for CUVs/minivans, and a small but not statistically 

significant increase in risk for lighter cars. Lower footprint also is associated with a smaller 

effect on casualty risk per crash than on fatality risk per crash, for all three types of vehicles. 

Figure 2.6 shows the same data as Figure 2.5, but for 13-state fatality and casualty risk per VMT, 

not per crash, using the VMT weights developed by NHTSA using national registration data and 

induced exposure crashes in the thirteen states. Comparing Figure 2.6 with Figure 2.5, one sees 

that the estimated effects of mass and footprint reduction on risk per VMT are quite a bit more 

detrimental than the estimated effects on risk per crash. The difference is so large that a 

reduction in risk per crash becomes an increase in risk per VMT, for mass reduction in lighter 

cars in terms of fatality risk (shown in red, -0.54% in Figure 2.5 to 1.42% in Figure 2.6), and for 

mass reduction in heavier cars and lighter light-duty trucks in terms of casualty risk (shown in 

green, -0.77% in Figure 2.5 to 0.73% in Figure 2.6 for heavier cars, and -0.11% in Figure 25 to 

1.55% in Figure 2.6 for lighter light-duty trucks). 

Figure 2.6 also indicates that the estimated effects of mass reduction on fatality risk per VMT 

from the 13-state data (shown in red) are comparable to NHTSA’s estimated effects on national 

fatality risk per VMT (shown in blue) for only lighter-than-average cars and heavier-thanaverage light-duty trucks. For heavier-than-average cars and lighter-than-average light trucks 

mass reduction is associated with a reduction in fatality risk per VMT using the 13-state data, but 

with an increase in risk using the US data; for CUVs/minivans mass reduction is associated with 

an increase in risk using the 13-state data but a decrease in risk using the US data.

The estimated effects on casualty risk per VMT from the thirteen states (shown in green) are 

comparable to the estimated effects on US fatality risk per VMT (shown in blue) for mass 

reduction in lighter and heavier cars, and heavier light-duty trucks, and for footprint reduction in 

cars and CUVs/minivans. The estimated increase in fatality risk per VMT from mass reduction 

in the lighter light trucks is much larger using the 13-state data (1.55%) than NHTSA’s estimate 

for the US (0.52%). Similarly, the estimated increase in fatality risk from footprint reduction is 

similar for cars and CUVs/minivans using the 13-state or national data, while the estimate for 

light trucks is much higher using the 13-state data (0.94%) than NHTSA’s national estimate (-

0.07%). 

The improved similarity in the US and 13-state risks expressed in terms of VMT exposure in 

Figure 2.6 suggests that the large differences between US fatality risk per VMT and 13-state 

fatality risk per crash in Figure 2.5 are more the result of changing the measure of exposure from 

per VMT to per crash, and less because the relationships between mass and footprint reductions 

and risk in the thirteen states are different from those relationships in the entire US (the second 
17

possible explanation for the differences in fatality risk per VMT vs. per crash, summarized 

above). 

Figure 2.6. Estimated effect of mass or footprint reduction on three types of risk per VMT, 

by vehicle type

Figure 2.7 compares the estimated effect of mass and footprint reduction on the two components 

of risk, the number of crashes per VMT (crash frequency, the inverse of crash avoidance, shown 

in orange) and the fatality risk per crash (crashworthiness/compatibility, shown in light red), with 

the estimated effect on fatality risk per VMT (shown in dark red), from the 13-state crash data. 

The estimates in Figure 2.7 for crash frequency and crashworthiness/compatibility were obtained 

using the same regression models, with the dependent variable changed from fatalities per VMT 

to crashes per VMT (for crash frequency) or fatalities per crash (for 

crashworthiness/compatibility). For cars and light trucks, mass reduction is estimated to increase 

crash frequency, but reduce fatality risk per crash; the effects from the two components roughly 

add together to result in the overall estimated effect on fatality risk per VMT. For example, a 

100-lb reduction in the mass of lighter cars is correlated with a 2.00% increase in crash 

frequency (the number of crashes per VMT), while mass reduction is correlated with a 0.54% 

decrease in the number of fatalities per crash (or a 0.54% increase in 

crashworthiness/compatibility); the net effect is an estimated 1.42% increase in the risk of 

fatality per VMT. For CUVs/minivans, the relationship is different; mass reduction is correlated 

with an increase in both crash frequency (0.95%) and fatality risk per crash (0.98%), and the net 

result, an estimated 1.60% increase in the number of fatalities per VMT, is less than the sum of 

the two components. In its previous studies DRI solved the three equations, crashes per VMT, 

fatalities per crash, and fatalities per VMT, simultaneously, which forces the estimated effects on 

fatalities per VMT to equal the sum of the estimated effects on crashes per VMT and fatalities 

per crash.

1.55% 

0.51% 

0.52% 

-0.34% 

-0.38% 

1.87% 

-0.07% 

1.72% 

1.42% 

-1.07% 

-0.13% 

-0.34% 

1.60% 

2.11% 

1.64% 

-1.24% 

1.86% 

0.73% 

1.55% 

-0.04% 

0.10% 

1.54% 

0.94% 

1.54% 

-4.0% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (probability) 

Effect of reduction in weight or size on risk, by vehicle type

US fatalities per VMT 

13-state fatalities per VMT 

13-state casualties per VMT 

 100-lb reduction in weight 1-sq ft reduction in footprint 
18

Figure 2.7. Estimated effect of mass or footprint reduction on crashes per VMT (vehicle 

crash frequency), fatalities per crash (vehicle crashworthiness/compatibility), and fatalities 

per VMT, by vehicle type

Figure 2.7 indicates that a reduction in car and light truck footprint is estimated to increase both 

the number of crashes per VMT and the number of fatalities per crash, while lower footprint in 

CUVs/minivans is associated with a decrease in both the number of crashes per VMT and the 

number of fatalities per crash. Figure 2.8 shows similar estimates for the two components of 

casualty risk per VMT.

It is unclear why lower vehicle mass is associated with higher crash frequency, but lower risk per 

crash, in the regression models. It is possible that including variables that more accurately 

account for important differences among vehicles and driver behavior would reverse this 

relationship. We examine what effect adding a variable to account for driver behavior, a 

measure of household income, to the regression models has on the estimated relationship 

between increased crash frequency for lighter vehicles, in Section 4. On the other hand, it is also 

possible that over thirty years of improvements in vehicle design to achieve high crash test 

ratings have enabled manufacturers to use clever vehicle design to mitigate the hypothetical 

safety penalty of low mass vehicles. 1.55% 0.51% 0.52% 

-0.34% 

-0.38% 

1.87% 

-0.07% 

1.72% 

2.00% 

1.50% 

1.44% 

0.94% 

0.95% 

0.64% 

1.04% 

-0.54% 

-0.55% 

-2.39% 

-1.61% 

-1.25% 

0.98% 

0.92% 

0.48% 

-1.67% 

1.42% 

-1.07% 

-0.13% 

-0.34% 

1.60% 

2.11% 

1.64% 

-1.24% 

-4.0% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change 

Effect of reduction in weight or size on risk, by vehicle type

US fatalities per VMT 

13-state crashes per VMT 

13-state fatalities per crash 

13-state fatalities per VMT 

 100-lb reduction in weight 1-sq ft reduction in footprint 
19

Figure 2.8. Estimated effect of mass or footprint reduction on crashes per VMT (vehicle 

crash frequency), casualties per crash (vehicle crashworthiness/compatibility), and 

casualties per VMT, by vehicle type

There is a possibility that reporting bias in the state police-reported crash data may influence the 

estimates of crash frequency and casualty risk per crash. Non-injury crashes may be underreported for certain vehicle and crash types, such as large pickups that are less likely to suffer 

damage, and that older, less expensive, uninsured vehicles that are less likely to report crash 

damage to police, or one vehicle crashes in which there is no crash partner that requires a policereport in order to file an insurance claim. If collisions of certain vehicles or crashes are slightly 

less likely to be reported, this would tend to increase the observed detrimental effect of mass 

reduction on reported crashes per VMT and conversely decrease its detrimental effect on 

casualties per reported crash. (By contrast, fatalities or casualties per VMT would be not be 

affected by crash-reporting rates, because the crash-reporting rate is not part of the formula for 

calculating risk.) The extent to which any reporting bias of non-injury crashes exists, the 

observed effects for police-reported crashes per VMT might not correspond exactly to the “effect 

of mass reduction on crash avoidance” and the observed effects for casualties per police-reported 

crash might not correspond exactly to the “effect of mass reduction on 

crashworthiness/compatibility.” 

We suspect that one-vehicle, non-rollover, non-injury crashes by pickup trucks are underreported in the state crash data. Two-vehicle crashes are more likely to be reported, because two 

parties are involved, while rollover and injury crashes are more likely to be reported because 

they tend to be more severe. If pickup truck owners were not reporting one-vehicle non-injury 

crashes, we would expect the crash rate per registered vehicle for pickup trucks in one-vehicle 

non-injury crashes to be lower relative to that of other vehicles than in all crashes. Figure 2.9 1.55% 0.51% 0.52% -0.34% -0.38% 1.87% -0.07% 1.72% 2.00% 1.50% 1.44% 0.94% 0.95% 0.64% 1.04% -0.55% 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 1.86% 0.73% 1.55% -0.04% 0.10% 1.54% 0.94% 1.54% 

-4.0% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change 

Effect of reduction in weight or size on risk, by vehicle type

US fatalities per VMT 

13-state crashes per VMT 

13-state casualties per crash 

13-state casualties per VMT 

 100-lb reduction in weight 1-sq ft reduction in footprint 
20

compares the crash frequency per VMT of all crashes and non-injury crashes, for one-vehicle, 

non-rollover crashes with a stationary object; crash rates for each type of crash are indexed to 

that for heavy four-door cars. For the most part the relative crash frequencies are quite similar for 

all crashes (in blue) and for non-injury crashes (in green), for all types of vehicles. Lighter twodoor cars, and to a lesser extent lighter four-door cars, do have a slightly lower crash frequency 

for non-injury crashes than for all crashes, suggesting that there may be a small reporting bias for 

these vehicles. On the other hand, heavier pickups have slightly higher crash frequency for noninjury crashes than for all crashes. This suggests that pickup truck owners are not underreporting the type of crash least likely to be reported, one-vehicle, non-injury crashes, in the state 

crash databases.

Figure 2.9. One-vehicle, non-injury crashes and all crashes per VMT, by vehicle type

Another type of bias in the state crash data is inaccurate reporting of injury outcomes by police 

officers at the scene of a crash. Using detailed NASS CDS records, in which a crash investigator 

tracks hospital records of victims in a small sample of police-reported crashes, Farmer (2003) 

found that 41% of injuries that police responders coded as “serious” or “incapacitating” received 

Modified Abbreviated Injury Scale (MAIS) ratings of “minor injury” by health care 

professionals. An updated analysis using NASS CDS from 2000 to 2008 finds that 59% of 

injuries police reported as “incapacitating” received eventual MAIS ratings of “minor” or “no 

injury”; 39% of injuries eventually receiving MAIS “serious” rating, and 27% that received a 

MAIS “severe” or “critical” rating, were initially coded as non-incapacitating injuries by the 

initial police responder.8 The possibility that these injury reporting errors are not consistent 

 8 The percentages are calculated using the national weights assigned to each crash in the NASS CDS sample. Using 

unweighted data, 41% of injuries reported as “incapacitating” by initial police responders received an eventual 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

2-dr cars, light 

2-dr cars, heavy 

4-dr cars, light 

4-dr cars, heavy 

Minivans 

Full vans 

SUVs, light 

SUVs, heavy 

CSUVs 

Small PUs, light 

Small PUs, heavy 

Large PUs, heavy 

Crashes per VMT, indexed to heavy 4-door cars 

Crash frequency per vehicle miles traveled, non-injury crashes 

All 1-veh w/obj crashes 

Non-injury 1-veh w/obj crashes 
21

across states is another reason to include a control variable for the state in which the crash 

occurred.

Recall that the risks and crashes per VMT in Figures 2.6 through 2.8 use the VMT weights 

developed by NHTSA using national registration data and induced exposure crashes in the 

thirteen states. To more accurately calculate fatality risk per VMT for the thirteen states, we 

need to obtain vehicle registration data, by calendar year, and vehicle model year and model, for 

the thirteen states, and develop new VMT weights to represent total VMT in the thirteen states, 

as opposed to the national VMT weights NHTSA used in their analysis and here. 

Figure 2.5 shows the estimated effect of mass or footprint reduction on risk per police-reported 

crash; Figure 2.10 shows the estimated effect on fatality risk per serious crash (shown in brown), 

with “serious crashes” defined as any police-reported crash that resulted in a casualty to a vehicle 

occupant or non-occupant. The figure suggests that using serious, or casualty, crashes, rather 

than all police-reported crashes, as the measure of exposure has only a slight change in the 

estimated effect of mass or footprint reduction on risk. 

Figure 2.10. Estimated effect of mass or footprint reduction on fatalities per crash and per 

serious crash, by vehicle type

Figure 2.11 compares the estimated effect of mass or footprint reduction on 13-state casualty risk 

per crash, after accounting for full adoption of ESC by 2017 (in green, from Figure 2.5) with the 

results from the nine regression models by crash type weighted by the current distribution of 

 MAIS rating of “minor” or “no injury”, and 16% of injuries eventually receiving MAIS “serious” rating, and 10% 

receiving a MAIS “severe” or “critical” rating, were initially coded as non-incapacitating by the initial police 

responder. 

1.55% 

0.51% 

0.52% 

-0.34% 

-0.38% 

1.87% 

-0.07% 

1.72% 

-0.54% 

-2.39% 

-1.61% 

-1.25% 

0.98% 

0.92% 

0.48% 

-1.67% 

-1.05% 

-1.74% 

-1.60% 

-0.62% 

1.20% 

0.47% 

0.31% 

-2.92% 

-4.0% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (probability) 

Effect of reduction in weight or size on risk, by vehicle type

US fatalities per VMT 

13-state fatalities per crash 

13-state fatalities per serious crash 

 100-lb reduction in weight 1-sq ft reduction in footprint 
22

crashes (light orange). Full penetration of ESC in the on-road fleet (going from the light orange

to green columns in the figure) results in little change in the estimated effect of mass reduction 

on casualty risk per crash for cars and light trucks, but reduces the estimated detrimental effect of 

mass reduction on risk for CUVs and minivans (from a reduction in risk of 0.26% to a reduction 

of 0.16%). On the other hand, accounting for the change in the distribution of crashes after full 

ESC penetration slightly reduces the estimated penalty from a reduction in footprint for cars

(from an estimated 0.41% increase to an estimated 0.23% increase in risk) and CUVs/minivans

(from an estimated 0.75% increase to an estimated 0.56% increase in risk), and increases the 

estimated benefit from mass reduction in light trucks from 0.13% to a 0.25% decrease in risk.

Estimates from a single regression analysis across all nine crash types are also shown in Figure 

2.11 (in dark orange). The estimated effects of mass or footprint reduction on casualty risk per 

crash using a single regression model are quite similar to those when the estimated effects by 

crash type are weighted by the current distribution of crashes (shown in light orange in the 

figure). 

Figure 2.11. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash by vehicle type, across all crash types and weighted average effect in each type of 

crash

Figures 2.12 through 2.14 and Table 2.3 show the estimated effect of changes in mass or 

footprint on casualty risk per crash, by type of crash. Figure 2.12 indicates that the largest 

estimated effects from mass reduction in cars are in rollovers for lighter-than-average cars (an 

estimated 1.85% increase in risk) and in crashes with objects for heavier-than-average cars (an 

estimated 3.75% reduction in risk). As noted in Section 1.1, all else being equal, lower vehicle 

mass is expected to be associated with higher risk in crashes with small trees or poles that break 

away, but with lower risk in crashes with objects that are immovable. Lower footprint in cars is 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.08% -0.86% -0.09% -0.67% -0.26% 0.41% -0.13% 0.75% 0.07% -0.87% -0.11% -0.74% -0.31% 0.50% 0.05% 0.68% 

-2.0% 

-1.5% 

-1.0% 

-0.5% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (probability) 

Effect of reduction in weight or size on risk, by vehicle type

Wtd by 13-state post-ESC crash distribution 

Wtd by 13-state current crash distribution 

Single regression across all crash types 

 100-lb reduction in weight 1-sq ft reduction in footprint 
23

associated with a large increase in casualty risk in rollovers (4.29%) and crashes with objects 

(3.55%). Because full ESC adoption is expected to substantially reduce the number of rollovers

and crashes with objects, and footprint reduction is estimated to substantially increase casualty 

risk in these types of crashes, removing many of these types of crashes by 2017 will reduce the 

estimated overall detrimental effect of footprint reduction in cars (from 0.41% to 0.23% as 

shown in Figure 2.11).

Figure 2.12 shows the estimated effect of mass and footprint reductions on risk in light trucks, by 

type of crash. In general, although relatively small, more of the estimated effects of mass or 

footprint reduction on risk tend to be statistically significant for light trucks than for cars. Mass 

reduction is associated with a relatively large (2.79%) reduction in casualty risk per crash in 

rollovers for the heavier light-duty trucks. As discussed in Section 1.1, once it has rolled over, a 

lighter vehicle applies less force on its roof than a heavier vehicle. We see the same estimated 

beneficial effect of mass reduction in casualty rollover risk in CUVs/minivans, in Figure 2.13 

(3.91%). As with cars, footprint reduction is associated with increased risk in rollovers and 

crashes with objects (by 2.04% and 0.99%, respectively) in light-duty trucks, and to an even 

greater extent (by 6.23% and 5.56%, respectively) in CUVs/minivans. The large estimated 

detrimental effects of footprint reduction on casualty risk in rollovers and crashes with objects 

account for the decrease in the effect of footprint reduction on risk after removing many of these 

types of crashes in Figure 2.11.

Figure 2.12. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash in cars, by type of crash 1.85% -0.80% 0.32% 1.30% 0.18% -0.89% -0.03% -0.05% 

0.32% 

-0.60% 

-3.75% 

-0.82% 

-1.29% 

-0.62% 

-1.15% 

-0.64% 

0.56% 

-0.57% 

4.29% 

3.55% 

-1.21% 

-0.14% 

0.30% 

0.56% 

0.38% 

0.16% 

-0.27% 

-6% 

-4% 

-2% 

0% 

2% 

4% 

6% 

8% 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

Percent change in risk (casualty probability per crash) 

Effect of reduction in weight or size on risk in cars, by crash type 

100-lb reduction in weight, 100-lb reduction in weight, 1-sq ft reduction in footprint 

 Cars < 3,106 Cars > 3,106 All cars 
24

Lower mass in light trucks is also associated with statistically significant reductions in casualty 

risks in crashes with pedestrians/cyclists, lighter light-duty trucks, and, for the heavier-thanaverage light-duty trucks, in crashes with heavier cars and lighter trucks. For light trucks, as 

well as CUVs/minivans, lower mass is associated with statistically significant increases, while 

lower footprint is associated with decreases, in casualty risk in crashes with heavy-duty trucks.

Lower mass in CUVs/minivans is associated with an increase in casualty risk (1.19%) in crashes 

with lighter light-duty trucks, but a large decrease in risk (2.73%) in crashes with heavier lightduty trucks, as shown in Figure 2.14. Footprint reduction in CUVs/minivans leads to a large 

increase in casualty risk (3.90%) in crashes with heavier light-duty trucks.

Figure 2.13. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash in light trucks, by type of crash 0.65% -0.78% -1.26% 1.86% -0.17% -0.14% -1.17% 0.66% 0.18% 

-2.79% 

0.04% 

-1.16% 

1.16% 

-0.81% 

-1.07% 

-1.32% 

0.77% 

-0.48% 

2.04% 

0.99% 

-0.03% 

-1.33% 

-0.17% 

-0.25% 

0.67% 

-1.00% 

-0.66% 

-6% 

-4% 

-2% 

0% 

2% 

4% 

6% 

8% 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

Percent change in risk (casualty probability per crash) 

Effect of reduction in weight or size on risk in LTs, by crash type 

100-lb reduction in weight, 100-lb reduction in weight, 1-sq ft reduction in footprint 

 LTs < 4,594 LTs > 4,594 All LTs 
25

Figure 2.14. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash in CUVs/minivans, by type of crash

Table 2.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, by type of crash

Type of crash

Mass reduction Footprint reduction

Cars < 

3106 lbs

Cars > 

3106 lbs

LTs < 

4594 lbs

LTs > 

4594 lbs

CUVs/ 

minivans Cars LTs

CUVs/ 

minivans

1: Rollovers 1.85% -0.60% 0.65% -2.79% -3.91% 4.29% 2.04% 6.23%

2: w/object -0.80% -3.75% -0.78% 0.04% -2.60% 3.55% 0.99% 5.56%

3: Ped etc. 0.32% -0.82% -1.26% -1.16% -0.48% -1.21% -0.03% 0.06%

4: w/HDT 1.30% -1.29% 1.86% 1.16% 4.14% -0.14% -1.33% -2.44%

5: w/lgt car 0.18% -0.62% -0.17% -0.81% -0.66% 0.30% -0.17% 0.94%

6: w/hvy car -0.89% -1.15% -0.14% -1.07% -0.06% 0.56% -0.25% 0.11%

7: w/lgt LT -0.03% -0.64% -1.17% -1.32% 1.19% 0.38% 0.67% -0.07%

8: w/hvy LT -0.05% 0.56% 0.66% 0.77% -2.73% 0.16% -1.00% 3.90%

9: Other 0.32% -0.57% 0.18% -0.48% 0.14% -0.27% -0.66% -0.26%

All 1.55% 0.51% 0.52% -0.34% -0.38% 1.87% -0.07% 1.72%

Estimates that are statistically significant at the 95% level are shown in red.

Table 2.4 compares the estimated effect of changes in the other vehicle, driver, and crash control 

variables on US fatality risk, 13-state fatality risk, and 13-state casualty risk, per VMT, by 

vehicle type. In general, the estimates for the control variables on the three types of risk per 

VMT are quite similar. Two-door cars are estimated to have higher risk than four-door sedans 

for each type of risk, while SUVs are estimated to have higher risk per VMT using US fatalities 

and 13-state casualties, but lower risk using 13-state fatalities. Torso side airbags consistently -3.91% -2.60% -0.48% 4.14% -0.66% -0.06% 1.19% -2.73% 0.14% 6.23% 5.56% 0.06% -2.44% 0.94% 0.11% -0.07% 3.90% -0.26% 

-6% 

-4% 

-2% 

0% 

2% 

4% 

6% 

8% 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

1: Rollovers 

2: w/object 

3: Ped etc. 

4: w/HDT 

5: w/lgt car 

6: w/hvy car 

7: w/lgt LT 

8: w/hvy LT 

9: Other 

Percent change in risk (casualty probability per crash) 

Effect of reduction in weight or size on risk in CUVs, by crash type 

 100-lb reduction in weight 1-sq ft reduction in footprint 
26

reduce risk for cars but not always for CUVs/minivans; ABS is estimated to consistently reduce 

risk for cars, and to a greater degree for CUVs/minivans. Similarly, ESC is estimated to

consistently reduce risk in cars, and even more so in light trucks; the models estimated smaller 

and non-significant reductions in risk from ESC in CUVs/minivans. Each additional year of 

vehicle age is estimated to increase risk about 2% to 5%, while a brand new vehicle is estimated 

to increase risk by up to 10%, presumably because the driver is unfamiliar with its controls, 

handling, and/or braking capabilities. The estimated effect of a male driver on risk generally is 

highest for US fatality risk, followed by 13-state fatality risk and 13-state casualty risk, and 

generally is higher in cars and CUVs/minivans than in light trucks. For each type of risk, the 

youngest and oldest drivers have higher risk (around 5% and 8% respectively) than other drivers, 

for all three vehicle types. The estimated effects of driving at night, on high-speed or rural roads 

are higher for US fatality risk, followed by 13-state fatality and 13-state casualty risk for all three 

types of vehicles. In general the calendar year variables are estimated to have a decreasing effect 

on risk over time, and tend to be highest for US fatality risk per VMT in light trucks. 

Note that the four vehicle variables of interest, UNDRWT, OVERWT, LBS100 and 

FOOTPRINT, all have a much lower effect on risk than almost all of the control variables in 

Table 2.4. The estimated effects of vehicle type, other vehicle attributes (such as side airbags, 

ABS, ESC, or AWD), or male drivers on risk per VMT are nearly an order of magnitude larger 

than those estimated for lower mass or footprint, while driving at night, on rural or high-speed 

roads, are estimated to have an effect several hundred times that of vehicle mass or footprint 

reduction. The estimated effects of the crash time and location variables are much higher on US 

or 13-state fatality risk per VMT than on 13-state casualty risk per VMT.

Table 2.5 compares the estimated effect of changes in the other vehicle, driver, and crash control 

variables on 13-state fatality or casualty risk per crash. While 2-door cars continue to have a 

much higher estimated fatality risk per crash than 4-door sedans (11.2%), this effect essentially

disappears in terms of casualty risk per crash (1.14%). Curtain side airbags are associated with a 

larger safety benefit in terms of casualties per crash than in terms of fatalities per crash or US 

fatalities per VMT, while combo side airbags are associated with a larger safety benefit for cars 

but not for CUVs/minivans. The estimated beneficial effects of torso side airbags, ABS, and 

ESC are similar among the three types of risk, with the exception of ABS in fatality risk per 

crash. The estimated effects of vehicle age and brand new vehicles on the risks per crash are 

much smaller than on US fatality risk per VMT. The driver age and gender variables have a 

smaller estimated effect on fatality risk per crash, and a much smaller estimated effect on 

casualty risk per crash, than on US fatality risk per VMT; this suggest that much of the driver 

effect on risk contributes to the occurrence of a serious crash, and not the 

crashworthiness/compatibility of the vehicle once a crash has occurred. Nevertheless, risk 

increases for the oldest drivers, even in terms of casualty risk per crash. Likewise, driving at 

night, on rural or high-speed roads, has a bigger effect on US fatality risk per VMT than on 13-

state fatality or casualty risk per crash. Even so, these three variables do substantially increase 

the likelihood of fatality or casualty once a crash occurs. The estimated effects of the calendar 

year variables also tend to be smaller on risks per crash, and 
27

Table 2.4. Estimated effect of variables on US fatality risk, 13-state fatality risk, and 13-

state casualty risk per VMT

Variable

US fatality risk per VMT 13-state fatality risk per VMT 13-state casualty risk per VMT

Cars LTs CUVs Cars LTs CUVs Cars LTs CUVs

UNDERWT 1.55% 0.52% —— 1.42% -0.13% — 1.86% 1.55% —

OVERWT 0.51% -0.34% -1.07% -0.34% — 0.73% -0.04% —

LBS100 — — -0.38% — — 1.60% — — 0.10%

FOOTPRINT 1.87% -0.07% 1.72% 2.11% 1.64% -1.24% 1.54% — 1.54%

TWODOOR 8.45% — — 19.7% — 8.13% — —

SUV — 8.94% — — -8.50% — — 3.35% —

HD — 1.73% — — 4.73% — — -6.06% —

BLOCKER1 — -1.41% — — -0.35% — — 2.42% —

BLOCKER2 — -2.32% — — -3.70% — — -1.75% —

MINIVAN — — -0.94% — — 12.0% — — 19.2%

ROLLCURT -0.73% — -1.67% -19.3% — -0.61% -2.33% — -0.92%

CURTAIN 1.00% — -2.85% 5.52% — -2.20% -1.37% — -5.69%

COMBO -1.10% — -6.43% -4.21% — 1.36% 1.82% — 1.67%

TORSO -8.77% — 0.86% -16.3% — -2.33% -14.8% — -6.70%

ABS -7.87% — -16.5% -7.18% — -34.8% -12.7% — -26.9%

ESC -11.9% -18.8% -3.89% -19.5% -26.7% -9.51% -14.5% -23.4% -1.32%

AWD — -14.5% -14.0% — 33.9% 9.01% — 25.2% -4.86%

VEHAGE 2.54% 3.57% 5.50% 1.74% 3.39% 2.01% 2.28% 3.44% 3.82%

BRANDNEW 10.2% 3.62% 8.76% 12.4% 5.36% -7.50% 10.4% 2.87% 2.07%

DRVMALE 39.2% 19.3% 37.1% 20.5% 16.0% 46.9% 3.10% -2.97% 9.61%

M14_30 4.63% 3.54% 3.92% 5.22% 3.77% 5.62% 4.67% 4.05% 4.91%

M30_50 1.40% 1.25% 0.84% 1.13% 0.46% -0.66% 0.23% 0.37% -0.01%

M50_70 2.20% 1.24% 1.82% 2.90% 1.42% 2.20% 1.11% 0.99% 1.21%

M70_96 8.08% 7.65% 7.10% 8.74% 8.13% 6.36% 5.87% 5.71% 4.99%

F14_30 2.81% 3.64% 4.77% 3.38% 2.51% 3.23% 3.28% 3.66% 4.04%

F30_50 0.09% 0.22% -0.47% -0.79% -0.55% 0.10% -0.46% -0.06% -0.20%

F50_70 3.21% 3.10% 3.22% 3.14% 2.55% 4.33% 1.42% 1.67% 2.34%

F70_96 8.00% 6.36% 7.69% 8.82% 0.39% 6.61% 5.76% 3.41% 3.99%

NITE 194% 192% 160% 155% 179.8% 126% 45.5% 64.2% 38.3%

RURAL 223% 207% 215% 117% 98.7% 113% 50.4% 50.6% 49.8%

SPDLIM55 414% 409% 405% 387% 379% 381% 158% 164% 152%

CY2002 5.56% 22.4% 7.59% 1.52% 10.4% 11.3% 10.4% 11.7% 15.4%

CY2003 3.60% 18.2% 4.97% 2.80% 10.3% 18.7% 10.7% 9.67% 16.9%

CY2004 1.69% 14.1% -3.28% -6.50% 5.80% -8.19% 7.20% 7.73% 3.16%

CY2005 -0.60% 7.86% 0.02% -1.44% 10.7% 4.05% 5.56% 7.19% 5.45%

CY2007 -1.42% -1.19% -4.99% -4.50% -3.94% -7.58% -5.59% -6.40% -3.73%

CY2008 -13.3% -15.0% -19.7% -8.43% -10.8% -10.8% -10.1% -13.9% -10.8%

HIFAT_ST 29.5% 24.6% 33.8% — — — — — —

AL — — — -6.69% -28.3% -22.0% 158% 97.5% 143%

KS — — — -36.5% -38.1% -27.1% -68.8% -67.4% -65.7%

KY — — — -12.6% -23.8% -19.4% -28.4% -32.7% -17.1%

MD — — — -45.3% -44.5% -61.1% -28.4% -33.3% -29.2%

MI — — — -51.7% -52.8% -47.8% -59.0% -61.1% -60.5%

MO — — — -12.9% -28.5% -16.0% -31.4% -33.3% -27.2%

NE — — — -36.6% -34.5% -44.2% -41.2% -34.6% -40.4%

NJ — — — -44.7% -68.8% -50.7% -84.5% -85.2% -85.0%

PA — — — -36.5% -33.6% -31.8% -82.9% -76.5% -79.5%

WA — — — -50.9% -46.4% -46.7% -77.6% -72.2% -74.3%

WI — — — -35.8% -39.3% -45.4% -54.5% -49.0% -54.1%

WY — — — -1.73% -30.4% -56.1% -23.4% -40.6% -13.2%

* Values in red are statistically significant at the 95% level.
28

Table 2.5. Estimated effect of variables on US fatality risk per VMT, and 13-state fatality

risk and 13-state casualty risk per crash

Variable

US fatality risk per VMT 13-state fatality risk per crash 13-state casualty risk per crash

Cars LTs CUVs Cars LTs CUVs Cars LTs CUVs

UNDERWT 1.55% 0.52% — -0.54% -1.61% — 0.09% -0.11% —

OVERWT 0.51% -0.34% — -2.39% -1.25% — -0.77% -0.62% —

LBS100 — — -0.38% — — 0.98% — — -0.16%

FOOTPRINT 1.87% -0.07% 1.72% 0.92% 0.48% -1.67% 0.23% -0.25% 0.56%

TWODOOR 8.45% — — 11.2% — — 1.14% — —

SUV — 8.94% — — -6.44% — — 2.84% —

HD — 1.73% — — 11.7% — — 0.17% —

BLOCKER1 — -1.41% — — 0.21% — — 1.29% —

BLOCKER2 — -2.32% — — -3.02% — — -3.32% —

MINIVAN — — -0.94% — — 9.06% — — 15.9%

ROLLCURT -0.73% — -1.67% -21.3% — -0.58% -1.98% — -0.91%

CURTAIN 1.00% — -2.85% 4.48% — -1.39% -2.79% — -4.84%

COMBO -1.10% — -6.43% -6.33% — 1.61% -1.79% — 4.97%

TORSO -8.77% — 0.86% -10.2% — 1.52% -9.69% — -3.00%

ABS -7.87% — -16.5% -0.20% — -18.1% -3.26% — -9.16%

ESC -11.9% -18.8% -3.89% -8.75% -12.0% -11.4% -8.78% -13.8% -7.08%

AWD — -14.5% -14.0% — 6.05% 5.63% — 2.56% -3.28%

VEHAGE 2.54% 3.57% 5.50% 0.99% 2.54% -0.68% 1.53% 2.19% 0.64%

BRANDNEW 10.2% 3.62% 8.76% 5.35% 6.42% -5.74% 2.99% 3.20% 1.08%

DRVMALE 39.2% 19.3% 37.1% 14.4% 21.6% 42.5% -2.40% -1.43% 6.96%

M14_30 4.63% 3.54% 3.92% 1.02% 0.20% 0.79% 0.53% 0.45% 0.18%

M30_50 1.40% 1.25% 0.84% 0.50% -0.24% -0.92% -0.22% -0.19% -0.23%

M50_70 2.20% 1.24% 1.82% 3.04% 1.52% 2.04% 1.14% 1.05% 1.06%

M70_96 8.08% 7.65% 7.10% 4.85% 4.28% 3.05% 2.11% 1.62% 1.57%

F14_30 2.81% 3.64% 4.77% 0.16% -0.70% 0.03% 0.17% 0.32% 0.82%

F30_50 0.09% 0.22% -0.47% -0.93% -0.61% -0.04% -0.56% -0.16% -0.30%

F50_70 3.21% 3.10% 3.22% 2.66% 2.27% 3.64% 0.86% 1.13% 1.67%

F70_96 8.00% 6.36% 7.69% 4.49% -3.54% 2.86% 1.57% 0.15% 0.42%

NITE 194% 192% 160% 96.4% 88.7% 70.2% 22.7% 23.6% 15.8%

RURAL 223% 207% 215% 78.7% 59.3% 76.1% 37.3% 34.6% 36.7%

SPDLIM55 414% 409% 405% 214% 216% 235% 79.9% 93.5% 90.7%

CY2002 5.56% 22.4% 7.59% 4.72% 15.5% 17.1% 11.8% 16.7% 19.5%

CY2003 3.60% 18.2% 4.97% 5.88% 9.83% 21.5% 11.5% 9.74% 15.6%

CY2004 1.69% 14.1% -3.28% -5.56% 5.28% -7.72% 6.31% 5.78% 0.36%

CY2005 -0.60% 7.86% 0.02% 0.08% 10.2% 4.54% 3.84% 4.56% 1.67%

CY2007 -1.42% -1.19% -4.99% -6.94% -6.20% -9.23% -8.22% -7.59% -5.29%

CY2008 -13.3% -15.0% -19.7% -10.1% -12.5% -11.4% -10.5% -12.2% -9.88%

HIFAT_ST 29.5% 24.6% 33.8% — — — — — —

AL — — — -69.1% -71.5% -75.3% -11.8% -21.6% -22.1%

KS — — — -76.7% -80.2% -79.2% -87.2% -88.6% -88.8%

KY — — — -74.4% -77.5% -81.6% -79.8% -82.3% -82.4%

MD — — — -60.8% -55.5% -71.8% -47.0% -46.0% -43.6%

MI — — — -86.9% -88.4% -86.7% -87.4% -89.3% -88.6%

MO — — — -67.0% -71.2% -69.9% -74.1% -74.1% -74.6%

NE — — — -76.7% -77.1% -81.6% -76.6% -75.8% -78.1%

NJ — — — -78.6% -88.8% -81.6% -94.0% -94.6% -94.5%

PA — — — -24.1% -36.0% -27.8% -79.7% -78.5% -79.2%

WA — — — -71.5% -73.9% -74.8% -87.1% -86.5% -87.9%

WI — — — -69.9% -75.2% -74.7% -77.2% -78.5% -78.2%

WY — — — -77.2% -78.7% -91.6% -78.6% -80.1% -77.7%

* Values in red are statistically significant at the 95% level.
29

the consistent reduction in risk over time observed in fatality risk per VMT is not as strong in 

terms of fatality risk per crash. The calendar year variables are examined in more detail in 

Section 5.3.

Note that the four vehicle variables of interest, UNDRWT, OVERWT, LBS100, and 

FOOTPRINT, all have a much lower estimated effect on risk than almost all of the control 

variables. For instance, a 100-lb reduction in curb weight for an underweight car is expected to 

increase casualty risk per crash by only 0.09%, while installing ABS would reduce risk by 3.3%. 

Therefore, the regression estimates suggest that, in theory, the mass of a lighter car could be 

reduced by as much as 3,300 lbs while adding ABS, without increasing casualty risk per crash. 

Regarding the estimated effect of the control variables on the three types of risk in crashes 

involving light trucks, SUVs are associated with a much lower, and heavy-duty pickups with a 

much higher, fatality risk per crash than regular pickups, which is opposite of the effects

estimated for fatalities per VMT and casualties per crash. And while AWD is associated with a 

large safety benefit in terms of fatalities per VMT, it is associated with increased risk in terms of 

fatalities or casualties per crash. The other estimates for light trucks in Table 2.5 have similar 

effects for the three types of risk, with the exception of three of the four female driver age 

variables, that show lower fatality risk per crash than for a 50-year old female.

Minivans are associated with a slightly lower fatality risk per VMT, a slightly higher fatality risk 

per crash, and a substantially higher casualty risk per crash, than CUVs. The three side airbag 

variables show inconsistent estimated effects across the three types of risk for CUVs and 

minivans. ABS and ESC tend to provide a higher safety benefit in terms of fatality risk per 

crash, and a lower benefit in terms of casualty risk per crash. AWD provides a large safety 

benefit in terms of fatality risk per VMT, and a smaller benefit in terms of casualty risk per 

crash, but increases fatality risk per crash. As with cars and light trucks, the estimated increased 

risk for elderly drivers in CUVs/minivans is smaller in terms of casualty risk per crash than in 

terms of fatality risk per VMT or per crash, while the estimated effects of vehicle age and brand 

new vehicles on casualty risk per crash are negligible.

As discussed above, the NHTSA regression of US fatality risk per VMT included a variable for 

high-fatality states; our regression models for fatality and casualty risk per crash include twelve 

variables for each state in the database. The bottom of Table 2.5 shows the estimated effect of 

each of the state control variables on casualty risk per crash, relative to the risks in Florida, by 

vehicle type. Note that the model predicts a 12% to 22% lower casualty risk in Alabama than in 

Florida, while Figure 2.3 above indicates that Alabama has a roughly 25% higher actual casualty 

risk per crash than Florida. This discrepancy may be explained by the regression model also 

accounting for where crashes occurred in each state: over half of all police-reported crashes in 

Alabama occurred on roads in rural areas, which tend to have higher risks than crashes in urban 

areas, whereas only 15% of all crashes in Florida were in rural areas. After accounting for the 

greater amount of driving in dangerous rural areas in Alabama, the regression model indicates 

that driving in Alabama is actually 12% to 22% safer in terms of casualties per crash, depending 

on the type of vehicle, than driving in Florida. Similarly, the regression model predicts that a 

vehicle has a nearly 80% lower casualty risk per crash in Wyoming than in Florida, while Figure 
30

2.3 above indicates that the actual casualty risk per crash in Wyoming is only about 40% lower 

than that in Florida. All driving in Wyoming is in rural areas.

Table 2.6 shows the estimated effect of the vehicle, driver, and calendar year control variables on 

the two components of fatality risk per VMT: crashes per VMT (or crash frequency) and fatality 

or casualty risk per crash. ABS and ESC in cars are estimated to reduce crash frequency more 

than risk per crash, as expected, while AWD in light trucks and CUVs/minivans is estimated to 

increase crash frequency more than risk per crash. Two-door cars, SUVs, heavy-duty pickups, 

and the side airbag variables in cars have a smaller effect on crash frequency than risk given a 

crash. Surprisingly, for CUVs/minivans, the side airbag variables are estimated to reduce crash 

frequency but have little effect on fatality risk per crash, ABS has the same benefit in reducing 

crash frequency as fatality risk, and ESC has essentially no effect on crash frequency but a large 

estimated benefit in reducing fatality risk per crash. For light trucks, ESC has about the same 

estimated benefit in reducing crash frequency as in reducing fatality risk given a crash. 

Male drivers are estimated to have essentially no effect on crash frequency, but are associated 

with a statistically significant increase in fatality risk once a crash occurs; a possible explanation 

is that male drivers are not involved in more crashes than female drivers, but the crashes they are 

involved in are more severe. The driver age variables estimate that crash frequency consistently 

increases for the youngest and oldest drivers, and that risk consistently increases for the two 

oldest groups of drivers (over 50 years old). The crash circumstance variables estimate that 

driving on high-speed roads increases crash frequency the most, followed by night driving, 

followed by driving in rural counties. Of the three variables for crash circumstances, driving on 

high-speed roads also has the highest estimated increase in risk per crash. Driving on high-speed 

or rural roads are associated with much higher increases in risk per crash than on crash 

frequency, while driving at night is associated with only a slightly higher increase in risk per 

crash than on crash frequency. Again, the crashes that occur under these conditions may be more 

severe than other crashes, and thus lead to greater fatality or casualty risk. All three crash 

variables are associated with a much higher increase in fatality risk per crash than in casualty risk 

per crash. The control variables for CY2002 and CY2003 show a large reduction in crash 

frequency, but a large increase in risk given a crash, for all three types of vehicles. 

As summarized above, Florida and Pennsylvania substantially under-report non-injury crashes; 

after accounting for other control variables, all of the states have a higher crash frequency than 

Florida, except Pennsylvania (and Maryland, for light trucks and CUVs/minivans). Kentucky 

and Alabama have the highest crash frequencies for all three types of vehicles; Pennsylvania, 

Maryland, Wisconsin, and Washington have the lowest crash frequency. Wyoming has a low 

crash frequency for light trucks, but relatively high crash frequencies for cars and 

CUVs/minivans. All states have a lower fatality or casualty risk per crash than Florida, for each 

type of vehicle. Pennsylvania has a much higher fatality risk relative to its casualty risk per 

crash (the estimate for fatality risk is much higher than the estimate for casualty risk), while 

Alabama has a much lower fatality risk relative to its casualty risk per crash (the fatality risk 

estimate is much lower).
31

Table 2.6. Estimated effect of variables on crashes per VMT, fatalities per crash, and 

casualties per crash, using data from 13 states

Variable

Cars Light trucks CUVs/minivans

Crash/ 

VMT

Fatality/ 

crash

Casualty/ 

crash

Crash/ 

VMT

Fatality/ 

crash

Casualty/ 

crash

Crash/ 

VMT

Fatality/ 

crash

Casualty/ 

crash

UNDERWT 2.00% -0.54% 0.09% 1.44% -1.61% -0.11% — — —

OVERWT 1.50% -2.39% -0.77% 0.94% -1.25% -0.62% — — —

LBS100 — — — — — — 0.95% 0.98% -0.16%

FOOTPRINT 0.64% 0.92% 0.23% 1.04% 0.48% -0.25% -0.55% -1.67% 0.56%

TWODOOR 4.19% 11.2% 1.14% — — —

SUV — — — -0.59% -6.44% 2.84% — — —

HD — — — -3.86% 11.7% 0.17% — — —

BLOCKER1 — — — 0.52% 0.21% 1.29% — — —

BLOCKER2 — — — -0.05% -3.02% -3.32% — — —

MINIVAN — — — 3.81% 9.06% 15.9%

ROLLCURT -0.98% -21.3% -1.98% — — — -0.69% -0.58% -0.91%

CURTAIN -0.05% 4.48% -2.79% — — — -3.51% -1.39% -4.84%

COMBO 2.84% -6.33% -1.79% — — — -0.49% 1.61% 4.97%

TORSO -5.14% -10.2% -9.69% — — — -5.18% 1.52% -3.00%

ABS -7.21% -0.20% -3.26% — — — -20.0% -18.1% -9.16%

ESC -15.1% -8.75% -8.78% -13.8% -12.0% -13.8% 0.15% -11.4% -7.08%

AWD — — — 46.1% 6.05% 2.56% 11.3% 5.63% -3.28%

VEHAGE 0.44% 0.99% 1.53% -0.01% 2.54% 2.19% 1.38% -0.68% 0.64%

BRANDNEW 6.04% 5.35% 2.99% 0.88% 6.42% 3.20% 0.51% -5.74% 1.08%

DRVMALE 6.53% 14.4% -2.40% -0.46% 21.6% -1.43% 2.03% 42.5% 6.96%

M14_30 4.23% 1.02% 0.53% 3.81% 0.20% 0.45% 5.01% 0.79% 0.18%

M30_50 0.31% 0.50% -0.22% 0.36% -0.24% -0.19% 0.18% -0.92% -0.23%

M50_70 0.21% 3.04% 1.14% 0.33% 1.52% 1.05% 0.62% 2.04% 1.06%

M70_96 3.98% 4.85% 2.11% 4.42% 4.28% 1.62% 3.39% 3.05% 1.57%

F14_30 3.35% 0.16% 0.17% 3.53% -0.70% 0.32% 3.58% 0.03% 0.82%

F30_50 -0.03% -0.93% -0.56% 0.02% -0.61% -0.16% 0.00% -0.04% -0.30%

F50_70 0.76% 2.66% 0.86% 0.93% 2.27% 1.13% 1.10% 3.64% 1.67%

F70_96 4.27% 4.49% 1.57% 3.36% -3.54% 0.15% 3.50% 2.86% 0.42%

NITE 22.5% 96.4% 22.7% 32.8% 88.7% 23.6% 17.8% 70.2% 15.8%

RURAL 11.4% 78.7% 37.3% 14.7% 59.3% 34.6% 10.5% 76.1% 36.7%

SPDLIM55 51.1% 214% 79.9% 36.8% 216% 93.5% 29.4% 235% 90.7%

CY2002 -5.40% 4.72% 11.8% -7.63% 15.5% 16.7% -9.09% 17.1% 19.5%

CY2003 -4.05% 5.88% 11.5% -1.43% 9.83% 9.74% -3.48% 21.5% 15.6%

CY2004 -2.39% -5.56% 6.31% -0.72% 5.28% 5.78% -2.05% -7.72% 0.36%

CY2005 -0.26% 0.08% 3.84% 0.90% 10.2% 4.56% 0.83% 4.54% 1.67%

CY2007 3.17% -6.94% -8.22% 2.34% -6.20% -7.59% 3.15% -9.23% -5.29%

CY2008 3.70% -10.1% -10.5% 1.82% -12.5% -12.2% 4.61% -11.4% -9.88%

AL 120% -69.1% -11.8% 79.7% -71.5% -21.6% 123% -75.3% -22.1%

KS 37.0% -76.7% -87.2% 21.4% -80.2% -88.6% 46.6% -79.2% -88.8%

KY 131% -74.4% -79.8% 118% -77.5% -82.3% 187% -81.6% -82.4%

MD 2.32% -60.8% -47.0% -12.9% -55.5% -46.0% -3.90% -71.8% -43.6%

MI 83.8% -86.9% -87.4% 60.3% -88.4% -89.3% 68.4% -86.7% -88.6%

MO 76.3% -67.0% -74.1% 46.8% -71.2% -74.1% 80.9% -69.9% -74.6%

NE 59.3% -76.7% -76.6% 38.7% -77.1% -75.8% 52.6% -81.6% -78.1%

NJ 78.1% -78.6% -94.0% 64.3% -88.8% -94.6% 77.2% -81.6% -94.5%

PA -38.1% -24.1% -79.7% -31.9% -36.0% -78.5% -30.4% -27.8% -79.2%

WA 22.5% -71.5% -87.1% 29.9% -73.9% -86.5% 44.9% -74.8% -87.9%

WI 27.1% -69.9% -77.2% 18.8% -75.2% -78.5% 26.8% -74.7% -78.2%

WY 100% -77.2% -78.6% 15.2% -78.7% -80.1% 79.9% -91.6% -77.7%

* Values in red are statistically significant at the 95% level.
32

In summary, the strong and consistent relationship in Tables 2.4 through 2.6 between the control 

variables for vehicle attributes, driver gender and age, crash circumstances, and crash frequency 

and risk, is encouraging. However, the tables show several unexpected results:

• side airbags are estimated to reduce crash frequency;

• AWD is estimated to increase crash frequency;

• ESC and ABS are estimated to reduce risk once a crash has occurred; and

• AWD, brand new vehicles, and male drivers are estimated to increase risk once a crash has 

occurred.

In some cases these unexpected results apply to all three vehicle types, in other cases only one or 

two of the three vehicle types. These unexpected results suggest that the regression models may

not fully account for all the variables that influence crash frequency or risk per crash. In

particular, they may not account for why risky or unskilled drivers select certain vehicle types, or 

even particular makes and models. Not accounting for these associations may be biasing the 

relationships the models estimate between vehicle mass or footprint and crash frequency and risk 

per crash.
33

3. Multi-collinearity between vehicle mass and footprint

In its 2003 analysis NHTSA resisted including vehicle mass and size (in that case, wheelbase and 

track width) in the same regression model, because the two variables were strongly correlated 

with each other. Including two or more highly-correlated variables in the same regression model 

can lead to biased or incorrect results. DRI showed that regression analyses that included both 

mass and size (i.e. wheelbase and track width) in the same regression model (i.e. that estimated 

the effect of mass while holding size constant, and vice versa) estimated smaller effects for 

changes in mass or size on US fatality risk per VMT (Van Auken and Zellner, 2002, 2003, 2004, 

2005a, 2005b). In its 2010 and 2011 analyses, NHTSA included both mass and size (i.e. 

footprint, or wheelbase times track width) in the same regression model, in part because the 

model year 2012 to 2016 light truck standards adopted in 2010, and the proposed 2017 to 2025 

standards for all light-duty vehicles, assign a target fuel economy/greenhouse gas emission level 

based on a vehicle’s footprint (Kahane 2010 and 2011). 

Using two or more variables that are strongly correlated in the same regression model (referred 

to as multi-collinearity) can lead to biased results. Allison9 “begins to get concerned” with VIF 

values greater than 2.5, while Menard10 suggests that a VIF greater than 5 is a “cause for 

concern”, while a VIF greater than 10 “almost certainly indicates a serious collinearity problem”; 

however, O’Brien11 suggests that “values of VIF of 10, 20, 40 or even higher do not, by 

themselves, discount the results of regression analyses.” .

Figure 3.1 shows the correlation between curb weight and footprint by vehicle model in the 

NHTSA database; only the most popular 275 models, with at least 10 billion VMT or 100 

fatalities, are included in the figure (106 car models, 131 light truck models, and 38 

CUV/minivan models). The figure indicates that curb weight and footprint are more highly 

correlated for cars (Pearson correlation coefficient, or r, of 0.90) than for light trucks (r of 0.75) 

or CUVs/minivans (r of 0.78). Figure 3.2 shows the same data as Figure 3.1, but uses seven 

vehicle types. Here the correlation ranges from over 0.80 for 4-door cars, SUVs, small pickups, 

and CUVs to less than 0.80 for large pickups and 2-door cars, to only 0.49 for minivans. The 

correlation of 0.75 for all light trucks (pickups and SUVs) combined in Figure 3.1 is improved 

when the types of trucks are analyzed separately in Figure 3.2: 0.90 for SUVs and 0.86 for small 

pickups, but only 0.67 for large pickups. On the other hand, separating CUVs from minivans 

improves the correlation between curb weight and footprint for CUVs (0.86) but not for 

minivans (0.49). The correlation is so poor for minivans in part because of the Kia Sedona, 

which has a much higher weight (4,730 lbs) for its footprint (51.3 sq ft) than other minivans; 

removing this model improves the correlation for minivans to 0.63.

 9 Allison, P.D.. Logistic Regression Using SAS, Theory and Application. SAS Institute Inc., Cary NC, 1999.

10 Menard, S. Applied Logistic Regression Analysis, Second Edition. Sage Publications, Thousand Oaks CA, 2002.

11 O’Brien, R.M. “A Caution Regarding Rules of Thumb for Variance Inflation Factors,” Quality and Quantitiy, 

(41) 673-690, 2007.
34

Figure 3.1. Correlation between vehicle curb weight and footprint, by vehicle model and 

three vehicle types

Figure 3.2. Correlation between vehicle curb weight and footprint, by vehicle model and 

seven vehicle types

R! = 0.87 

R! = 0.65 

R! = 0.60 

34 

38 

42 

46 

50 

54 

58 

62 

66 

70 

74 

78 

2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 6400 6800 7200 7600 

Footprint (wheelbase x track width, sq ft) 

Curb weight (lbs) 

Average footprint and curb weight, by vehicle type and model 

Cars 

Light trucks 

CUVs and Minivans 

r = 0.90 

r = 0.75 

r = 0.78 

R! = 0.65 

R! = 0.89 

R! = 0.81 

R! = 0.43 

R! = 0.81 

R! = 0.66 

R! = 0.26 

34 

38 

42 

46 

50 

54 

58 

62 

66 

70 

74 

78 

2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 6400 6800 7200 7600 

Footprint (wheelbase x track width, sq ft) 

Curb weight (lbs) 

Average footprint and curb weight, by vehicle type and model 

2-dr cars 

4-dr cars 

Small pickups 

Large pickups 

SUVs 

CUVs 

Minivans 

r = 0.76 

r = 0.91 

r = 0.86 

r = 0.67 

r = 0.90 

r = 0.86 

r = 0.49 
35

Table 3.1 shows the correlation coefficients of curb weight with footprint, and variance inflation 

factors, by vehicle type. The values in the table are weighted by the VMT weights for individual 

makes and models. The table indicates that curb weight is most highly correlated with footprint 

for 4-door cars and SUVs (r over 0.90), followed by small pickups and CUVs (r of 0.80) and 2-

door cars (0.76). The correlation between weight and footprint is lowest for large pickups (0.67) 

and minivans (0.49); the low correlation between weight and footprint for minivans is strongly 

influenced by one model, the Kia Sedona, which is unusually heavy for its size. Removing this 

model from the analysis increases the correlation to 0.63. Table 3.1 also indicates that six of the 

seven vehicle types (all except minivans) have a VIF associated with curb weight greater than 

2.5, the point at which multi-collinearity becomes a concern.

Table 3.1. Correlation coefficients and variance inflation factors of curb weight with 

footprint, by vehicle type

Vehicle type

Correlation 

coefficient 

(r)

Variance inflation factor (VIF)

Accounting for vehicle and 

type variables

Accounting for all 

variables

CURBWT FOOTPRNT CURBWT FOOTPRNT

Cars 0.896 6.2 5.6 7.3 6.0

Light trucks 0.748 6.5 8.6 8.1 9.8

CUVs/minivans 0.781 3.8 6.7 4.7 8.7

2-dr cars 0.758 3.3 2.7 3.8 3.0

4-dr cars 0.910 6.8 6.2 8.6 6.8

Sm pickups 0.862 4.1 4.0 6.5 4.8

Lg pickups 0.673 2.0 1.9 3.6 2.3

SUVs 0.904 6.0 5.8 7.8 1.0

CUVs 0.863 5.1 4.4 7.9 6.4

Minivans 0.488 1.5 1.4 2.1 1.8

Figure 3.3 compares the results from the regression models for 13-state casualty risk per crash, in 

light green from Figure 2.5, with two alternative model specifications to test the sensitivity of the 

results. The first sensitivity, in dark purple, includes the weight variables in the regression model 

but excludes the footprint variable; this model tests the estimated effect of mass reduction while 

allowing footprint to vary with vehicle mass. This sensitivity slightly increases the risk from a 

100-lb mass reduction in lighter cars (from an estimated 0.09% to 0.25%) and CUVs/minivans 

(from an estimated 0.16% decrease in risk to an estimated 0.13% increase in risk), and reduces 

the beneficial effect of mass reduction in heavier cars (from an estimated 0.77% to a 0.61% 

reduction in risk). However, allowing light truck footprint to vary with mass is associated with a 

larger estimated reduction in casualty risk per crash in light trucks; from an estimated 0.11% 

reduction to an estimated 0.38% reduction in lighter-than-average light trucks, and from an 

estimated 0.62% reduction to an estimated 0.78% reduction in heavier-than-average light trucks. 

The estimated effects of mass reduction when footprint is allowed to vary with mass for casualty 

risk per crash are quite different from the effects for fatality risk per VMT. In an earlier analysis 

(Figure 3.3, LBNL, 2012), we showed that lower mass is associated with much larger increases 

in fatality risk per VMT when footprint is allowed to vary with mass, than when footprint is held 

constant, at least for cars and CUVs/minivans. Here, with risk measured as casualty risk per 
36

crash, lower mass is associated with only slightly larger increases in risk when car or 

CUV/minivan footprint is allowed to vary with mass (shown in dark purple), than when footprint 

is held constant (shown in green).

Figure 3.3. Estimated effect of reduction in mass or footprint on 13-state casualty risk per 

crash, by vehicle type: holding footprint constant, allowing footprint to vary with mass, 

and allowing mass to vary with footprint

The second sensitivity keeps footprint in the regression model, but removes mass, and is shown 

in light purple in Figure 3.3. Allowing vehicle mass to be reduced with footprint reduces the 

estimated effect of footprint reduction on casualty risk per crash in cars (from an estimated

0.23% increase to an estimated 0.10% decrease) and light trucks (from an estimated 0.25% 

decrease to an estimated 0.49% decrease); allowing CUV/minivan mass to vary with footprint 

has no effect on casualty risk per crash for CUVs/minivans. Figure 3.3 suggests that including 

both mass and footprint in the same regression model results in only slight changes in the effect 

of mass and footprint reductions on casualty risk per crash.

In its 2012 analysis NHTSA examined the relationship between curb weight and fatality risk for 

deciles of vehicles with roughly the same footprint. Figure 3.4 shows the range in curb weights 

for the footprint deciles NHTSA used for the three vehicle types. The figure shows that there is 

a large degree of overlap in the curb weights of vehicles with roughly the same footprint; this is 

an indication that the correlation between curb weight and footprint may be strong but is not 

absolute.

NHTSA ran a new regression model with all of the control variables except footprint, for each 

crash and vehicle type, and footprint decile, a total of 270 regression models; the two mass 

variables, UNDERWT00 and OVERWT00, originally used for cars and light trucks were 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.25% -0.61% -0.38% -0.78% 0.13% -0.10% -0.49% 0.56% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of reduction in weight or size on risk, by vehicle type

13-state casualties per crash 

Effect of mass reduction, allowing footprint to vary with mass 

Effect of footprint reduction, allowing mass to vary with footprint 

 100-lb reduction in weight 1-sq ft reduction in footprint 
37

replaced by a single mass variable LBS100. NHTSA listed the number of the regression models 

for the ten footprint deciles in which the regression coefficient on vehicle mass was positive; that 

is, where lower mass is associated with an increase in fatality risk. 

Figure 3.4. Range in curb weight for the footprint deciles, by vehicle type

We replicate this analysis for 13-state casualty risk in Table 3.2, which includes the number of 

footprint deciles in which the coefficient on vehicle mass is statistically significant. There are 

four columns for each vehicle type in Table 3.2; the first two indicate the number of footprint 

deciles in which lower vehicle mass is associated with higher casualty risk per crash, and the 

number that are statistically significant. Red print indicates cases in which three or more 

footprint deciles have significant coefficients. The second two columns for each vehicle type 

indicate the number of footprint deciles in which lower vehicle mass is associated with lower

casualty risk per crash, and the number that are statistically significant. For example, in car 

rollover crashes, mass reduction is associated with higher casualty risk in five footprint deciles, 

but only two of those associations are statistically significant. On the other hand, lower mass in 

light trucks is associated with higher casualty risk in rollover crashes in six footprint deciles, and 

four of those six are statistically significant. Table 3.2 indicates that lower mass is not 

consistently associated with increased casualty risk for vehicles with similar footprint. Lower 

mass is associated with higher casualty risk in a majority of footprint deciles for 9 of the 27 crash 

and vehicle combinations, but few of these increases are statistically significant. On the other 

hand, lower mass is associated with lower risk in a majority of footprint deciles for 12 of the 27 

crash and vehicle combinations, although few of these reductions are statistically significant. 

1600 2600 3600 4600 5600 6600 7600 

Footprint decile 

Curb weight (lbs) 

Range in curb weight for footprint deciles, by vehicle type 

Cars 

Light trucks 

CUVs/minivans 
38

Table 3.2. Number of footprint deciles in which lower mass is associated with increasing or 

decreasing 13-state casualty risk per crash, by vehicle and crash type 

Crash type

Cars Light trucks CUVs/Minivans

Number of deciles withincreasing riskNumber of deciles with estimates that are statistically significantNumber of deciles withdecreasing riskNumber of deciles with estimates that are statistically significantNumber of deciles withincreasing riskNumber of deciles with estimates that are statistically significantNumber of deciles withdecreasing riskNumber of deciles with estimates that are statistically significantNumber of deciles withincreasing riskNumber of deciles with estimates that are statistically significantNumber of deciles withdecreasing riskNumber of deciles with estimates that are statistically significant

1: Rollovers 5 2 5 2 6 4 4 2 5 0 5 2

2: w/object 2 1 8 2 6 2 4 0 5 0 5 0

3: w/ped etc. 4 0 6 1 3 0 7 1 4 1 6 2

4: w/HDT 2 2 8 1 6 2 4 0 6 1 4 0

5: w/lgt car 7 1 3 2 6 3 4 2 4 0 6 1

6: w/hvy car 4 0 6 3 3 1 7 3 7 1 3 0

7: w/lgt LT 5 1 5 2 1 0 9 3 8 0 2 1

8: w/hvy LT 5 1 5 2 8 3 2 2 3 2 7 2

9: Other 3 2 7 3 5 3 5 1 4 3 6 3

The data in Table 3.2 give no information on the size of the effect of mass reduction on casualty 

risk per crash in the footprint deciles. Figures 3.5 through 3.7 show the percent change in 

estimated casualty risk from mass reduction for each footprint decile, by vehicle type, for six of 

the nine crash types (rollovers, and crashes with stationary objects, cars, and light trucks). 

Figure 3.5 indicates that lower mass is associated with a larger than 5% increase in casualty risk 

in car rollover in deciles one, nine, and ten, but is associated with a larger than 25% decrease in 

casualty risk in decile eight. Figure 3.7 indicates that lower mass in CUVs/minivans is 

associated with reduced casualty risk in rollovers in five of the footprint deciles, and that these 

reductions are quite large (over 20%) for footprint deciles four, nine and ten. Figures 3.5 through 

3.7 suggest that there are no consistent trends in the estimated effect of mass reduction on risk 

when vehicles are grouped by footprint decile. 
39

Figure 3.5. Estimated effect of car mass reduction on 13-state casualty risk per crash, by 

footprint decile and crash type

Figure 3.6. Estimated effect of light truck mass reduction on 13-state casualty risk per 

crash, by footprint decile and crash type

-35% 

-25% 

-15% 

-5% 

5% 

15% 

0 1 2 3 4 5 6 7 8 9 10 

Percent change in casualty risk per crash 

from mass reduction 

Footprint decile (lowest to highest) 

Effect of mass reduction on car risk, by footprint decile and crash type 

Rollovers w/object 

w/lgt car w/hvy car 

w/lgt LT w/hvy LT 

-10% 

-5% 

0% 

5% 

10% 

15% 

0 1 2 3 4 5 6 7 8 9 10 

Percent change in casualty risk per crash 

from mass reduction 

Footprint decile (lowest to highest) 

Effect of mass reduction on LT risk, by footprint decile and crash type 

Rollovers w/object 

w/lgt car w/hvy car 

w/lgt LT w/hvy LT 
40

Figure 3.7. Estimated effect of CUV/minivan mass reduction on 13-state casualty risk per 

crash, by footprint decile and crash type

4. Casualty risk by vehicle model

In this section we examine the variation in societal casualty risk by average vehicle mass and by 

vehicle model, both before and after accounting for the vehicle, driver and crash variables 

NHTSA includes in its regression models of US fatality risk per VMT. Figure 4.1 plots 

unadjusted 13-state casualty risk per crash against average curb weight, with vehicles grouped 

into 100-lb increments of vehicle curb weight. Figure 4.1 indicates that casualty risk per crash 

increases slightly for cars, and decreases for light trucks and CUVs/minivans, as curb weight 

increases. There also is a large degree of variability for cars and light trucks, as indicated by the 

Pearson correlation coefficient (r) values below 0.20. 

Figures 4.2 through 4.4 show the relationship between unadjusted casualty risk per crash and 

mass by more detailed vehicle type. Figure 4.2 indicates that the relationship between curb 

weight and casualty risk per crash is weaker for 4-door cars than for 2-door cars, with risk 

actually increasing with increasing mass for 4-door cars between 3,700 and 4,100 lbs. Figure 4.3 

suggests that, while casualty risk decreases as the curb weight of small pickups and truck-based 

SUVs increases, for large pickups (3/4- and 1-ton pickups) casualty risk increases slightly as 

curb weight increases. And Figure 4.4 indicates that the relationship between casualty risk and 

curb weight is strong, with a dramatic reduction in casualty risk as mass increases and a high 

degree of correlation, for CUVs, and especially minivans.

-65% 

-45% 

-25% 

-5% 

15% 

35% 

0 1 2 3 4 5 6 7 8 9 10 

Percent change in casualty risk per crash 

from mass reduction 

Footprint decile (lowest to highest) 

Effect of mass reduction on CUV risk, by footprint decile and crash type 

Rollovers w/object 

w/lgt car w/hvy car 

w/lgt LT w/hvy LT 
41

Figure 4.1. Relationship between 13-state casualty risk per crash and curb weight, with 

vehicles grouped into 100-lb increments of curb weight, by vehicle type

Figure 4.2. Relationship between 13-state casualty risk per crash and curb weight, with 

vehicles grouped into 100-lb increments of curb weight, passenger cars

R! = 0.03 

R! = 0.02 

R! = 0.14 

0 

20 

40 

60 

80 

100 

120 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs/100) 

Casualty risk per crash, by curb weight andvehicle type 

Cars 

Light trucks 

CUVs and Minivans 

r = -0.17 

r = 0.16 

r = 0.38 

R! = 0.38 

R! = 0.00 

0 

20 

40 

60 

80 

100 

120 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs/100) 

Fatality risk per curb weight, passenger cars 

2-dr cars 

4-dr cars 

r = 0.61 

r = -0.04 
42

Figure 4.3. Relationship between 13-state casualty risk per crash and curb weight, with 

vehicles grouped into 100-lb increments of curb weight, light trucks

Figure 4.4. Relationship between 13-state casualty risk per crash and curb weight, with 

vehicles grouped into 100-lb increments of curb weight, CUVs and minivans

R! = 0.06 

R! = 0.01 

R! = 0.13 

0 

20 

40 

60 

80 

100 

120 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs/100) 

Fatality risk per curb weight, light trucks 

Small pickups 

Large pickups 

Truck-based SUVs 

r = 0.24 

r = -0.10 

r = 0.36 

R! = 0.34 

R! = 0.96 

0 

20 

40 

60 

80 

100 

120 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs/100) 

Fatality risk per curb weight, CUVs and minivans 

Crossover SUVs 

Minivans 

r = 0.58 

r = 0.98 
43

Figure 4.5 shows the danger of using the average risks of groups of individual models, such as 

by curb weight bins. The filled symbols in the figure represent the relationship between minivan 

casualty risk and curb weight when the data are grouped into bins of curb weight, from Figure 

4.4; this analysis shows a high correlation between risk and curb weight (R2 of 0.96). However, 

if the relationship between risk and curb weight of the 13 most popular individual minivan 

models, which represent over 90% of the minivan casualties and crashes, are plotted, the 

correlation is much lower, with the R2 dropping to 0.39.

12

Figure 4.5. Relationship between 13-state casualty risk per crash and curb weight for 

minivans, by average risk for 100-lb increments of curb weight and individual models

It is possible that the relationship between vehicle mass and casualty risk is stronger in certain 

types of crashes. Figure 4.6 presents the relationship between 100-lb increments in curb weight 

and casualty risk in one-vehicle crashes with a stationary object, the type of crash in which 

vehicle mass is thought to provide occupants the most protection. For all three types of vehicles, 

casualty risk per crash in crashes with stationary objects does decline as mass increases; the 

strength of this relationship is much greater in crashes with stationary objects than in all types of 

crashes (Figure 4.1). 

Note that, for a given vehicle weight, light trucks have a higher casualty risk per crash in crashes 

with stationary objects than cars or CUVs/minivans. Since there are no crash partner casualties in 

crashes with stationary objects, we suspect that light trucks have a higher risk than cars in Figure 

 12 Figure 4.5 actually excludes one additional popular minivan model, which has the highest casualty risk (67 per 

1,000 crashes) and weight (4,728 lbs) of the minivan models shown; including this model would make the 

correlation between casualty risk and curb weight even lower.

R! = 0.96 

R! = 0.39 

0 

10 

20 

30 

40 

50 

60 

70 

80 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs) 

Casualty risk per crash, minivans 

Curb weight bins 

Individual models 
44

4.6 because of their tendency to roll over, their increased use on more dangerous rural roads, and 

perhaps more passenger casualties in light trucks than in cars.

Figure 4.6. Relationship between 13-state casualty risk per crash in crashes with stationary 

objects and curb weight, by vehicle type

Table 4.1 summarizes the correlations between risk and a decrease in curb weight by 100-lb 

weight bins, by vehicle type, presented in Figures 4.1 through 4.6. 

Table 4.1. Correlation between risk and a decrease in curb weight, for vehicles grouped in 

100-lb curb weight bins

Vehicle type

US fatality risk, all crashes

US fatality risk, crashes with 

stationary objects

Estimate r R2 Estimate r R2

Cars -0.13% -0.17 0.03 0.09% * 0.70 0.49

Light trucks 0.23% 0.16 0.02 0.09% * 0.53 0.28

CUVs/minivans 0.84% 0.38 0.14 0.13% * 0.63 0.40

2-dr cars 0.59% * 0.61 0.38 0.12% 0.40 0.16

4-dr cars -0.04% -0.04 0.00 0.04% * 0.49 0.24

Sm pickups 0.40% 0.24 0.06 0.14% * 0.63 0.39

Lg pickups -0.17% -0.10 0.01 0.01% 0.04 0.00

SUVs 1.25% 0.36 0.13 0.23% * 0.59 0.35

CUVs 1.77% * 0.58 0.34 0.23% * 0.78 0.61

Minivans 2.75% * 0.98 0.96 0.18% * 0.90 0.80

R! = 0.49 

R! = 0.28 

R! = 0.40 

0 

2 

4 

6 

8 

10 

12 

20 24 28 32 36 40 44 48 52 56 60 64 68 72 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs/100) 

Fatality risk in crashes with objects per curb weight, by vehicle type 

Cars 

Light trucks 

CUVs and Minivans 

r = 0.70 

r = 0.53 

r = 0.63 
45

Figures 4.1 through 4.6 and Table 4.1 show that grouping vehicles into 100-lb mass increments 

indicates that, for some vehicle types, casualty risk per crash decreases as mass increases. Figure 

4.7 shows the relationship between vehicle mass and casualty risk by individual vehicle model. 

Only 275 models with at least 10 billion VMT, or at least 100 fatalities, based on the NHTSA 

2011 analysis, are included (106 car models, 131 light truck models, and 38 CUV/minivan 

models); these models represent over 90% of all casualties and crashes. Here we see that 

casualty risk declines slightly with increasing mass for cars, light trucks, and CUVs/minivans.

Although casualty risk gradually declines with increasing mass, the extremely low R2 values (all 

less than 0.10) indicate that there is essentially no relationship between mass and casualty risk 

per crash, for any of the three types of vehicles, and that there is a very large range in casualty 

risk for individual vehicle models at a given weight. For example, the vehicle model labeled A 

in the figure, which weighs 2,579 lbs, has a casualty risk of 86 per 1,000 crashes, while model B, 

which weighs slightly less (2,500 lbs), has a casualty risk of only 44.

Figure 4.7. 13-state casualty risk per crash and curb weight, by vehicle model

Of course, differences in vehicles (footprint, two- vs. four-doors, and presence of side impact air 

bags, automated braking systems, or electronic stability controls), drivers (age and gender), and 

crash characteristics (at night, on high-speed roads, or in rural vs. urban areas or high-casualty 

risk states) by vehicle model may explain some of the large range in casualty risk by vehicle 

weight. To account for these various variables, we reran the logistic regression models including 

all of the driver, crash, and vehicle control variables except vehicle mass and footprint, across all 

types of crashes for each of the three vehicle types. We then calculated the predicted casualty 

R! = 0.02 

R! = 0.00 

R! = 0.08 

0 

20 

40 

60 

80 

100 

120 

140 

160 

2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 6400 6800 7200 

13-state casualty risk (casualties per 1,000 crashes) 

Curb weight (lbs) 

Unadjusted US fatality risk per VMT and curb weight, by vehicle type 

Cars 

Light trucks 

CUVs and Minivans 

A 

B 
46

risk per crash for each vehicle in the 13-state crash database. We multiplied the logistic 

regression coefficients for all driver, crash, and vehicle variables except mass and footprint by 

the characteristics of each vehicle, to obtain the predicted number of casualties per vehicle, and 

then summed across vehicle make and model. We then divided the total number of predicted 

fatalities in each make and model by the number of crashes for that make and model, to obtain 

predicted risk, the number of predicted casualties per police-reported crash. We exclude footprint 

as well as mass in the predicted risks we calculate from the regression coefficients, as the two 

vehicle attributes are moderately correlated. 

While Figure 4.7 shows the unadjusted casualty risks by vehicle modes, Figure 4.8 shows the 

risks predicted by the regression model coefficients for all control variables except vehicle mass 

and footprint. Figure 4.8 indicates that, after controlling for the all of the driver, crash, and 

vehicle variables used in the logistic regression model except vehicle mass and footprint, there 

still is a large range in casualty risk per crash across vehicle models of similar weight, for all 

three vehicle types. Figure 4.9 shows the remaining residual, or unexplained, casualty risks after 

accounting for all variables except vehicle mass and footprint. In essence Figure 4.9 shows that 

there is no relationship between vehicle mass and the remaining, unexplained casualty risk after 

accounting for driver, crash and all other vehicle attributes.

Figure 4.8. Predicted 13-state casualty risk per crash after accounting for all driver, crash, 

and vehicle variables except mass and footprint, vs. curb weight

R! = 0.02 

R! = 0.00 

R! = 0.11 

0 

20 

40 

60 

80 

100 

120 

140 

160 

2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 6400 6800 7200 

Predicted 13-state risk (casualties per 1,000 crashes) 

Curb weight (lbs) 

Predicted risk, accntg for all variables except weight and footprint 

Cars 

Light trucks 

CUVs and Minivans 
47

Figure 4.9. Residual 13-state casualty risk per crash after accounting for all driver, crash, 

and vehicle variables except mass and footprint, vs. curb weight

Table 4.2 summarizes the relationships between predicted and residual casualty risk and vehicle 

curb weight that are presented in Figures 4.7 through 4.9. In addition to the correlation between 

casualty risk and curb weight, the table shows the slope of the linear regression line drawn 

through the risks by vehicle model, which represents the percent change in casualty risk per 100-

pound reduction in mass or 1-square foot reduction in footprint. The relationship for the three 

vehicle types is shown at the top of the table, followed by those for the seven detailed vehicle 

subtypes (with small, i.e. compact and 1⁄2-ton, pickups shown separately from heavy-duty, i.e. 3⁄4-

and 1-ton, pickups), and finally the five vehicle type and weight groups NHTSA used in its 

regression analyses. Cases where there is a positive relationship between casualty risk and 

vehicle mass reduction, i.e. where mass reduction leads to reduction in casualty risk, are shown 

in red in the table; there are no cases where the correlation between risk and weight by vehicle 

model exceeds 0.30. 

Table 4.2 indicates that casualty risk consistently increases with lower vehicle mass, for almost 

all vehicle types, although the correlation between casualty risk and weight is negligible in 

almost all cases. The exception is CUVs, where casualty risk increases by 1.6% for each 100-lbs 

of lower mass, with a moderate correlation between actual and predicted casualty risk with an R2

of 0.21. Table 4.3 presents the same information as Table 4.2, but for the relationship between 

casualty risk and vehicle footprint reduction, with the similar results: casualty risk increases 

slightly as footprint is reduced, with negligible correlation between casualty risk and footprint 

reduction.

R! = 0.00 

R! = 0.00 

R! = 0.13 

-50 

-40 

-30 

-20 

-10 

0 

10 

20 

2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000 6400 6800 7200 

Residual 13-state risk (casualties per 1,000 crashes) 

Curb weight (lbs) 

Residual risk accounting for all variables except weight and footprint 

Cars 

Light trucks 

CUVs and Minivans 
48

Table 4.2. Relationship between actual, predicted, and residual 13-state casualty risk per 

crash, and vehicle mass reduction, after accounting for all driver, crash, and vehicle 

variables except mass and footprint, by vehicle type and model

Vehicle type

Actual 13-state 

casualty risk per crash Predicted risk Residual risk

Estimate R2 Estimate R2 Estimate R2

Cars 0.28% 0.02 0.22% 0.02 0.03% 0.00

Light trucks 0.09% 0.00 0.15% 0.00 -0.01% 0.00

CUVs/minivans 0.93% 0.08 1.33% * 0.11 -0.25% 0.08

2-dr cars 0.25% 0.02 0.25% 0.02 0.04% 0.00

4-dr cars 0.29% 0.02 0.21% 0.01 0.05% 0.00

Small pickups 0.07% 0.00 0.62% 0.03 -0.49% 0.26

Heavy-duty pickups 0.09% 0.00 1.04% 0.03 -0.77% 0.11

SUVs 0.21% 0.00 0.38% 0.01 -0.10% 0.01

CUVs 1.63% 0.21 2.06% * 0.21 -0.25% 0.08

Minivans -0.39% 0.03 -0.19% 0.01 0.02% 0.00

Cars < 3106 0.95% * 0.07 0.58% 0.03 0.38% 0.03

Cars > 3106 -0.83% * 0.06 -0.82% 0.07 -0.28% 0.03

LTs < 4594 0.37% 0.00 0.62% 0.01 -0.25% 0.02

LTs > 4594 0.63% 0.01 0.72% 0.01 -0.07% 0.00

CUVs/ minivans 0.93% 0.08 1.33% * 0.11 -0.25% 0.08

* statistically significant at the 95% confidence level

Table 4.3. Relationship between actual, predicted, and residual 13-state casualty risk per 

crash, and vehicle footprint reduction, after accounting for all driver, crash, and vehicle 

variables except mass and footprint, by vehicle type and model

Vehicle type

Actual 13-state 

casualty risk per crash Predicted risk Residual risk

Estimate R2 Estimate R2 Estimate R2

Cars 0.34% 0.02 0.26% 0.01 0.06% 0.00

Light trucks -0.25% 0.01 -0.35% 0.01 0.08% 0.01

CUVs/minivans 0.03% 0.00 0.30% 0.00 -0.26% 0.07

2-dr cars 0.44% 0.03 0.11% 0.00 0.36% 0.03

4-dr cars 0.34% 0.02 0.26% 0.01 0.05% 0.00

Small pickups -0.51% 0.03 -0.19% 0.00 -0.36% 0.17

Heavy-duty pickups -1.65% 0.15 -2.19% 0.11 0.30% 0.01

SUVs -0.65% 0.01 -0.48% 0.01 -0.18% 0.02

CUVs 0.97% 0.04 1.29% 0.04 -0.31% 0.06

Minivans 1.24% * 0.14 1.34% * 0.31 -0.01% 0.00

Cars < 3106 1.39% * 0.10 0.63% 0.03 0.88% 0.11

Cars > 3106 -0.79% 0.05 -0.58% 0.03 -0.43% 0.07

LTs < 4594 -0.54% 0.01 -0.72% 0.02 0.06% 0.00

LTs > 4594 -0.31% 0.01 -0.57% 0.01 0.18% 0.02

CUVs/ minivans 0.03% 0.00 0.30% 0.00 -0.26% 0.07

* statistically significant at the 95% confidence level
49

In its 2012 report NHTSA notes that, despite their theoretical advantage in terms of handling, 

braking, and accelerating, small and light vehicles historically have had higher crash and 

insurance claim frequency per vehicle mile traveled. This discrepancy suggests that small and 

light vehicles have not been driven as well as larger, heavier ones, perhaps because less capable 

drivers tend to choose smaller and lighter vehicles. In their peer review, Kockelman and Chen 

(University of Texas) noted that low-income drivers tend to drive poorly, or in environments that 

are more dangerous than higher income drivers (SRA 2012). One indication of driving behavior 

is the frequency of one-vehicle, non-rollover crashes per VMT: one-vehicle crashes are most 

likely the fault of the driver of the crash-involved vehicle, while it is more difficult to assign fault 

to drivers in multi-vehicle crashes. 

The relationship between crash frequency in one-vehicle non-rollover crashes and household 

income, vehicle mass, and initial vehicle purchase price by vehicle make and model is shown in 

Table 4.4 by vehicle type. The first columns of the table indicate that the frequency of onevehicle crashes decreases as household income increases, for all vehicle types, and that the 

frequency of one-vehicle crashes in cars, and to a lesser extent in CUVs and minivans, is 

somewhat correlated with driver income, with an R2 of over 0.30. The middle columns of the 

table indicate that, while the frequency of one-vehicle crashes tends to decrease with increasing 

vehicle mass for most vehicle types, it is not strongly correlated with vehicle mass. The 

frequency of one-vehicle crashes involving full size pickups actually increases (by 2.3%) as full 

size pickup mass increases. NHTSA infers from its analysis of crash culpability that “small, 

light vehicles have not been driven as well as large, heavier ones;” Table 4.4 suggests that the 

higher frequency of one-vehicle crashes involving lighter cars is a function of poor driving 

behavior of the lower income households that tend to own these vehicles, and is unrelated to 

vehicle mass.

The ability of a vehicle to avoid a crash altogether may account for some of the correlation 

between car crash frequency and driver income; low-income drivers may not be able to afford 

vehicles that tend to have higher crash avoidance capabilities, such as improved handling and 

reduced braking distance. We use the initial purchase price by vehicle model as a proxy for the 

general quality of vehicle design; clearly other measures of vehicle handling and braking 

distance, such as vehicle tests conducted by Consumer’s Union, would be preferable measures of 

a vehicle’s crash avoidance capabilities. The last columns in Table 4.4 suggest that the 

frequency of one-vehicle non-rollover crashes does decline as initial purchase price increases for 

most vehicle types, but the relationship is not strong. However, crash frequency increases as the 

purchase price of fullsize pickups and minivans increases. 
50

Table 4.4. Relationship between frequency of one-vehicle non-rollover crashes and 

household income, vehicle mass, and initial vehicle purchase price, by vehicle type and 

model

Vehicle type

1-vehicle crash 

frequency and 

household income 

1-vehicle crash 

frequency and mass 

1-vehicle crash 

frequency and initial 

purchase price 

Estimate R2 Estimate R2 Estimate R2

Cars -6.0% * 0.36 -3.6% * 0.12 -2.3% * 0.23

Light trucks -3.0% 0.03 -1.3% * 0.06 -1.7% * 0.07

CUVs/minivans -4.0% * 0.40 0.0% 0.00 -1.0% 0.03

2-dr cars -10.6% * 0.42 -2.3% 0.02 -4.9% * 0.18

4-dr cars -5.1% * 0.52 -2.7% * 0.13 -1.8% * 0.30

Small pickups -7.0% 0.04 0.0% 0.00 0.3% 0.00

Heavy-duty pickups -4.4% 0.03 2.3% 0.09 5.3% * 0.28

SUVs -1.2% 0.01 -2.4% * 0.14 -2.2% * 0.14

CUVs -3.4% * 0.38 -0.6% 0.01 -1.8% * 0.17

Minivans -5.0% * 0.32 -2.7% 0.03 4.8% 0.19

Cars < 3106 -5.2% * 0.13 1.2% 0.00 -1.5% 0.01

Cars > 3106 -5.5% * 0.58 -4.0% * 0.07 -2.1% * 0.31

LTs < 4594 -3.5% 0.03 -1.7% 0.02 -1.0% 0.01

LTs > 4594 -1.8% 0.02 -0.1% 0.00 -1.4% 0.04

CUVs/ minivans -4.0% * 0.40 0.0% 0.00 -1.0% 0.03

* statistically significant at the 95% confidence level

We tested whether accounting for vehicle purchase price or household income in the regression 

models might change the unexpected relationship that crash frequency increases as vehicle mass 

decreases. For every $1,000 increase in purchase price, crash frequency is estimated to decline 

0.85% +/- 0.05% for cars, 1.18% +/- 0.07% for light trucks, and 1.22% +/- 0.13% for 

CUVs/minivans; similarly, for every $1,000 increase in driver household income, crash 

frequency is estimated to decline 0.80% +/- 0.06% for cars, 0.20% +/- 0.10% for light trucks, 

and 0.94% +/- 0.11% for CUVs/minivans.

Figure 4.10 compares the estimates for mass or footprint reduction on 13-state crash frequency 

per VMT, before and after adding the vehicle price and household income control variables to 

the regression models. Adding vehicle purchase price substantially reduces the estimated 

increase in crash frequency as vehicle mass decreases for all vehicle types; in the case of heavierthan-average cars, mass reduction is estimated to slightly decrease crash frequency. Adding 

household income has virtually no effect on the estimated relationship between vehicle mass and 

crash frequency for cars and light trucks, but reduces the estimated increase in crash frequency 

for CUVs/minivans. 
51

Figure 4.10. Estimated effect of mass or footprint reduction on 13-state crashes per VMT, 

after accounting for vehicle purchase price or median household income, by vehicle type

We examine the estimated effect of mass or footprint reductions on casualty risk per crash after 

accounting for initial vehicle purchase price and median household income in Sections 5.3 and 

Section 5.5, respectively. 2.00% 1.50% 

1.44% 

0.94% 

0.95% 

0.64% 

1.04% 

-0.55% 

1.41% 

-0.06% 

0.85% 

0.20% 

0.14% 

0.73% 

0.83% 

-0.87% 

1.95% 

1.33% 

1.52% 

0.94% 

0.59% 

0.92% 

1.03% 

-0.23% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

Percent change in crash frequency (crashes per VMT) 

minivans 

Effect of reduction in weight or size on risk, by vehicle type

13-state crashes per VMT 

Including vehicle purchase price 

Including median household income 

 100-lb reduction in weight 1-sq ft reduction in footprint 
52

5. Sensitivity of 13-state casualty risk per crash results to data used and model specification

In this section we examine the sensitivity of our results on the estimated effect of mass or 

footprint reduction on 13-state casualty risk per crash. We examine the effect of different 

methods of accounting for the state in which the crash occurred, and how the effect of mass or 

footprint reduction changes after accounting for vehicle manufacturer, after excluding the 

calendar year control variables, and after adding additional data to the analysis.

5.1. State control variables

As discussed above, we included 12 control variables to account for the different reporting 

requirements in each state, as well as other differences in risk per crash among states. Figure 5.1 

compares the effect of this approach with two other approaches: not accounting for state at all in 

the analysis, and using only two control variables, HIINJ and LOINJ, to identify states with 

relatively high (Alabama, Florida, Maryland, and Wyoming,) and relatively low (Michigan, New 

Jersey, and Washington) casualty risk per crash (see Figure 2.3, above). Figure 5.1 indicates that 

mass reduction has a much larger estimated beneficial effect, and footprint reduction a much 

more detrimental effect in cars and CUVs/minivans, when one excludes the state in which the 

crash occurred from the regression models (shown in blue). Including only the two variables to 

control for state, HIINJ and LOINJ, substantially reduces the estimated effect of mass and 

footprint reduction on casualty risk per crash (shown in red); including the 12 control variables 

for individual states reduces the estimated effect a little bit more (shown in green). 

Figure 5.1. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash by vehicle type, under two methods of controlling for the state in which the crash 

occurred

-0.64% 

-1.68% 

-0.21% 

-1.84% 

-2.09% 

1.52% 

-1.05% 

3.79% 

-0.13% 

-1.19% 

-0.15% 

-0.75% 

-0.47% 

0.45% 

-0.30% 

0.69% 

0.09% 

-0.77% 

-0.11% 

-0.62% 

-0.16% 

0.23% 

-0.25% 

0.56% 

-3.0% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

5.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability) 

Effect of reduction in weight or size on risk, by vehicle type

No state variables 

Including HIINJ and LOINJ 

Including 12 state variables 

 100-lb reduction in weight 1-sq ft reduction in footprint 
53

5.2. Alternative measure of risk

Figure 5.2 compares the estimated effect of mass and footprint reduction on the risk of a casualty 

crash, rather than the risk of all casualties that occurred in the crash; in other words, the casualty 

crash cases are not weighted by the total number of casualties, either in the case vehicle or in its 

crash partner. In his review of the previous NHTSA studies, Paul Green suggested that 

analyzing risk at the crash, rather than person, level might be a better approach; each fatal case 

would be a single independent observation, and may serve to increase any under-estimation of 

the uncertainty around the parameter estimates. As shown in Figure 5.2, this alternative measure 

of risk, the risk of a casualty crash per all police-reported crashes (shown in dark orange) slightly 

increases the estimated detrimental effect of mass reduction on risk in lighter-than-average cars,

slightly reduces the estimated beneficial effect of mass reduction in heavier cars, and has little 

effect on risk in light-duty trucks and CUVs/minivans. Footprint reduction is associated with 

more detrimental estimated risk of casualty crash per police-reported crash than risk of casualties 

per crash, for all three types of vehicles. 

Figure 5.2. Estimated effect of mass or footprint reduction on 13-state casualties and 

casualty crashes per crash, by vehicle type

5.3. Vehicle manufacturer

The analysis by vehicle model in Section 4 indicates that the variables included in the regression 

models account for only a fraction of the variability in risk. We suspect that other, more subtle 

differences in vehicle models, or driver behavior, may explain the large remaining variability in 

risk. We tested that assumption by adding 14 dummy variables based on the vehicle nameplate 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.30% -0.63% -0.04% -0.61% -0.21% 0.34% -0.05% 0.80% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

13-state casualty crashes per crash 

 100-lb reduction in weight 1-sq ft reduction in footprint 
54

manufacturer. 13 GM brands (Buick, Cadillac, Chevrolet, GMC, Oldsmobile, Pontiac, and 

Saturn) are treated as the default value, since combined they represent the most vehicles by 

manufacturer, in terms of both casualties and police-reported crashes. The five Chrysler brands 

(Jeep, Chrysler, Dodge, Plymouth, and Sprinter) were combined in a single Chrysler category, 

while the three Ford brands (Ford, Lincoln, Mercury) were combined in a single Ford category. 

Ten low-volume manufacturers were grouped into a separate Other manufacturer category. 14

Figure 5.3 compares the effect of adding variables for each of the 14 manufacturers (shown in 

red) to the regression models estimating casualty risk per crash from the thirteen states in Figure 

2.5 above (shown in light green). Accounting for vehicle manufacturer results in a large

estimated increase in the harmful effect of mass reduction for cars, slightly increases the

estimated beneficial effect of mass reduction in light trucks, and slightly decreases the estimated 

beneficial effect in CUVs/minivans. Accounting for vehicle manufacturer has the opposite result 

on the effect of footprint reduction on risk: the estimated effect of footprint reduction becomes 

beneficial for cars, less beneficial for light trucks, and more detrimental for CUVs/minivans. 

Figure 5.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash by vehicle type, after controlling for vehicle manufacturer

Figure 5.3 also shows a second case in which five additional control variables are included for 

five luxury brands (Cadillac, Lincoln, Acura, Infiniti, and Lexus). Including the five luxury 

brands in the regression models (shown in light orange) results in little change in the estimated 

 13 The 14 manufacturers are: Chrysler, Ford, BMW, Honda, Hyundai, Kia, Mazda, Mercedes-Benz, Mitsubishi, 

Nissan, Subaru, Toyota, Volkswagen, and Volvo.

14 The manufacturers included in the Other category are: AM General, Audi, Daewoo, Isuzu, Jaguar, Land Rover, 

Mini, Porsche, Saab, and Suzuki. 0.09% -0.77% 

-0.11% 

-0.62% 

-0.16% 

0.23% 

-0.25% 

0.56% 

0.85% 

0.78% 

-0.24% 

-0.65% 

-0.05% 

-0.52% 

-0.09% 

0.88% 

0.96% 

0.76% 

-0.24% 

-0.60% 

-0.40% 

-0.60% 

-0.11% 

1.16% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (fatality probability per 1010 VMT) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

Including 14 vehicle makes 

Plus 5 luxury brands 

 100-lb reduction in weight 1-sq ft reduction in footprint 
55

effect of mass or footprint reduction on risk in cars and light trucks, but increases the estimated 

beneficial effect of mass reduction, and increases the estimated detrimental effect of footprint 

reduction, in CUVs/minivans.

Initial vehicle purchase price, rather than manufacturer nameplate, is another proxy for the 

general quality of vehicle design. We obtained the initial purchase price from the Polk VIN 

decoder, using 2010 California registration data from the state Department of Motor Vehicles. 

Every $1,000 increase in initial purchase price is estimated to reduce casualty risk per crash in all 

three types of vehicles: by 0.52% +/- 0.13% in cars, 0.28% +/- 0.15% in light trucks, and 0.52% 

+/- 0.31% in CUVs/minivans. Figure 5.4 shows how accounting for vehicle purchase price 

changes the estimated effect of mass or footprint reduction on casualty risk per crash, compared 

to the control variables for vehicle manufacturer. In contrast with the manufacturer variables, 

including vehicle purchase price increases the estimated beneficial effect of mass reduction, 

especially in cars and CUVs/minivans. Accounting for initial vehicle purchase price makes the 

estimated effect of footprint reduction slightly more detrimental in cars, more beneficial in lightduty trucks, and less detrimental in CUVs/minivans.

Figure 5.4. Estimated effect of mass or footprint reduction on US fatalities per VMT, after 

controlling for vehicle manufacturer or for initial vehicle purchase price, by vehicle type

The control variables for vehicle manufacturer and initial purchase price attempt to account for 

differences in vehicle models not controlled for in the NHTSA regression models. Other vehicle 

attributes which could explain the remaining unexplained risk include:

• relatively low bumper height, which increases the extent to which a vehicle’s front bumper 

overlaps the bumper or door sill of a crash partner, may reduce risk in two-vehicle crashes; 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.85% 0.78% -0.24% -0.65% -0.05% -0.52% -0.09% 0.88% 0.96% 0.76% -0.24% -0.60% -0.40% -0.60% -0.11% 1.16% -0.35% -1.72% -0.14% -0.71% -0.64% 0.29% -0.40% 0.41% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (fatality probability per 1010 VMT) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

Including 14 vehicle makes 

Plus 5 luxury brands 

Initial purchase price 

 100-lb reduction in weight 1-sq ft reduction in footprint 
56

• lower center of gravity, or static stability factor, may reduce the tendency of a vehicle to

roll over; 

• high engine power-to-weight ratio may increase crash frequency, and

• measures of braking distance and handling capabilities which may affect the ability of 

vehicles to avoid crashes;

LBNL may estimate the effect of accounting for these vehicle attributes in future analyses.

5.4. Calendar year variables

One interesting effect of the regression models is the reduction in casualty risk per crash over 

time, as indicated by the coefficients for the calendar year control variables. The reduction is 

consistent, and of roughly the same magnitude, for each vehicle type, as shown in Figure 5.5. 

The calendar year variables account for changes in both case vehicles and their crash partners, as 

well as the crash environment, over time, changes that are not explicitly included as other control 

variables in the regression models. In its 2011 report NHTSA interprets the trend of reduced risk 

over time as a reflection of general improvements in vehicle and roadway safety, increase in curb 

weight of crash partners, and, in particular, improvement in light truck design to reduce their 

tendency to rollover. 

Figure 5.6 shows the estimated effect on light truck casualty risk per crash, by type of crash, over 

time; for the most part, these results are consistent with fatality risk per VMT over time, reported 

in LBNL 2012. The figure indicates that the estimated effect of the calendar year variables on 

light truck risk is strong for crashes with lighter-than-average cars and lighter-than-average lightduty trucks. NHTSA believes that this may be the result of the removal over time of very light 

and unsafe cars and light trucks as potential crash partners for light trucks. However, there also 

are consistent decreases over time in light truck risk in crashes with heavy-duty trucks, and other 

(mostly multi-vehicle) crashes, as well as in crashes with heavier cars, although the effect is not 

as large. NHTSA suspects that the risk associated with light trucks involved in crashes with 

heavy-duty trucks has decreased over time because heavy-duty truck activity decreases as the 

economy has faltered; the economic recession in 2008 may have reduced the number of heavyduty trucks traveling roadways, and thus available as potential crash partners with light-duty 

vehicles. 

Note that there is a fairly consistent trend in light truck casualty risk per crash in rollover crashes 

in Figure 5.6; NHTSA believes that the decline in light truck rollover fatality risk per VMT over 

time (reported in LBNL 2012) may be the result of manufacturers increasing static stability 

factor or other aspects of light truck design to reduce their likelihood to rollover. These changes 

would not be expected to reduce risk of casualty (or fatality) in light trucks once a rollover has 

occurred, however Figure 5.6 does suggest that a consistent reduction in rollover risk per crash. 
57

Figure 5.5. Estimated effect of calendar year variables on 13-state casualty risk per crash, 

by vehicle type

Figure 5.6. Estimated effect of calendar year variables on light truck risk, by crash type

-20% 

-15% 

-10% 

-5% 

0% 

5% 

10% 

15% 

20% 

CY2002 CY2003 

CY2004 

CY2005 CY2007 CY2008 CY2002 CY2003 

CY2004 

CY2005 CY2007 CY2008 CY2002 CY2003 

CY2004 

CY2005 CY2007 CY2008 

Percent change in risk (casualtyy probability per crash) 

Effect of control variables on risk, CUVs and minivans 

Cars Light Trucks CUVs/Minivans 

-40% 

-30% 

-20% 

-10% 

0% 

10% 

20% 

30% 

40% 

CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 CY2002 CY2003 CY2004 

CY2005 

CY2007 CY2008 

Percent change in risk (casualty probability per crash) 

Effect of control variables on risk, light trucks 

 Rollover w/obj w/ped w/HDT w/lgt car w/hvy car w/lgt LT w/hvy LT Other 
58

Figures 5.7 through 5.10 show the effect of removing the calendar year variables from the 

regression model of 13-state casualty risk per crash (shown in white). Figure 5.7 indicates that 

excluding the calendar year variables has little impact on the estimated effect of mass reduction 

in cars, or for footprint reduction in CUVs/minivans. However, removing the calendar year 

variables reduces the estimated beneficial effect of mass reduction in trucks and CUVs/minivans; 

and increases the estimated detrimental effect of footprint reduction in cars but increases the 

estimated beneficial effect of footprint reduction in light trucks. 

Figure 5.7. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash by vehicle type, including and excluding calendar year variables

Figures 5.8 through 5.10 show what effect removing the calendar year variables has on the 

vehicle control variables; there is little to no effect on the driver or crash control variables (not 

shown). Figures 5.8 through 5.10 indicate that removing the calendar year variables has a large 

effect on the curtain airbag variable in cars and CUVs/minivans, the SUV, HD pickup, 

BLOCKER2, and ESC variables in light trucks, and the minivan variable in CUVs/minivans. In 

addition, the figures indicate that removing the calendar year variables reduces the estimated 

detrimental effect of vehicle age, and whether a vehicle is brand new, on casualty risk per crash

in all three vehicle types. Figures 5.7 through 5.10 suggest that inclusion of the calendar year 

variables in the regression models dilutes the effect of airbag technologies in cars and CUVs and 

minivans, the added risk in SUVs and heavy-duty pickups, and the beneficial effect of ESC in 

light trucks in general, while over-stating the effect of vehicle age in all three vehicle types. 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.00% -0.99% 0.43% -0.20% 0.28% 0.69% -0.49% 0.47% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

Excluding CY variables 

 100-lb reduction in weight 1-sq ft reduction in footprint 
59

Figure 5.8. Estimated effect of selected control variables on car risk, including and 

excluding calendar year variables

Figure 5.9. Estimated effect of selected control variables on light truck risk, including and 

excluding calendar year variables

-25% 

-20% 

-15% 

-10% 

-5% 

0% 

5% 

10% 

15% 

20% 

25% 

TWODOOR 

ROLLCURT 

CURTAIN 

COMBO 

TORSO 

ABS 

ESC 

VEHAGE 

BRANDNEW 

Percent change in risk (casualty probability per crash) 

Effect of control variables on risk, passenger cars 

13-state casualties per crash 

Excluding CY variables 

-25% 

-20% 

-15% 

-10% 

-5% 

0% 

5% 

10% 

15% 

20% 

25% 

SUV 

HD_PKP 

BLOCKER1 BLOCKER2 

ESC 

AWD 

VEHAGE 

BRANDNEW 

Percent change in risk (casualty probability per crash) 

Effect of control variables on risk, light trucks 

13-state casualties per crash 

Excluding CY variables 
60

Figure 5.10. Estimated effect of selected control variables on CUV/minivan risk, including 

and excluding calendar year variables

5.5. Effect of household income

Unlike in FARS, details on the driver’s condition or behavior are not consistently reported in the 

state crash data; therefore, we cannot account for the behavior of individual drivers in our 

estimates of the effect of mass or footprint reduction on casualty risk per crash. One possible 

surrogate for the behavior of drivers who tend to select certain vehicle models is driver 

household income. There is a fairly strong correlation between household income and predicted 

fatality risk, with risk decreasing as income increases. And crash frequency decreases as 

household income increases, particularly for cars and CUVs/minivans, as discussed in Section 4. 

Every $1,000 increase in household income is estimated to reduce 13-state casualty risk per 

crash in all three types of vehicles: by 1.51% +/- 0.15% in cars, 0.99% +/- 0.21% in light trucks, 

and 1.34% +/- 0.31% in CUVs/minivans. 

Figure 5.11 shows the effect of including household income on the relationship between lower

mass or footprint and casualty risk per crash (shown in light violet). Accounting for household 

income substantially increases the estimated beneficial effect of mass reduction in heavier-thanaverage cars and CUVs/minivans, but has little effect on other types of vehicles. Adding 

household income to the regression models substantially increases the estimated detrimental 

effect of footprint reduction in cars and CUVs/minivans, but has little effect on the estimated 

effect of footprint reduction in light trucks. 

-25% 

-20% 

-15% 

-10% 

-5% 

0% 

5% 

10% 

15% 

20% 

25% 

MINIVAN 

ROLLCURT 

CURTAIN 

COMBO 

TORSO 

ABS 

ESC 

AWD 

VEHAGE 

BRANDNEW 

Percent change in risk (casualty probability per crash) 

Effect of control variables on risk, CUVs and minivans 

13-state casualties per crash 

Excluding CY variables 
61

Figure 5.11. Estimated effect of mass or footprint reduction on 13-state casualties per 

crash, after controlling for median household income, by vehicle type

5.6. Effect of including sports, police, and all-wheel drive cars, and fullsize vans

In its analysis of US fatality risk per VMT, NHTSA excluded three types of cars (models used as 

sports cars, police cars, and models with all-wheel drive), all Ford Crown Victorias, and fullsize 

passenger and cargo vans. Including these vehicles in the analysis, and adding control variables 

for the four additional vehicle types, has essentially no effect on the relationship between lower

mass and 13-state casualty risk per crash in either cars or light trucks, as shown in Figure 5.12. 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% -0.04% -1.12% -0.05% -0.68% -0.65% 0.69% -0.26% 1.01% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (fatality probability per 1010 VMT) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

Including household income 

 100-lb reduction in weight 1-sq ft reduction in footprint 
62

Figure 5.12. Estimated effect of mass and footprint reduction on 13-state casualty risk per 

crash by vehicle type, after including sports, police, and all-wheel drive cars, and fullsize

passenger and cargo vans

5.7. Effect of adding additional data

As mentioned above, we excluded certain data that NHTSA did not include in their regression 

analyses:

• vehicles from 2000 to 2008 for three states (Georgia, Illinois, and New Mexico) that 

NHTSA did not include in its analysis because those states did not report the posted 

speed limit at the crash site (Georgia data are available only through 2007). NHTSA 

included IL in its 2003 and 2010 analyses, using the fraction of FARS crashes 

occurring on roads with a posted limit 55 mph or over, by roadway classification; we 

used this same method to assign posted speed limits to these three states in this 

analysis;

• vehicles whose model year was not reported in the state crash data (except all crash 

records from Washington, which were included in the above analysis); 

• vehicles involved in police-reported crashes in 2000 and 2001, from all states but 

Michigan, New Jersey, and Washington);

• vehicles that had apparent VIN transcription errors that we corrected so that the model 

year reported in the state crash data matched the VIN model year. The method to 

make these corrections for VIN errors is described in LBNL 2011a.

We analyzed the effect of adding all of these data on the regression coefficients for vehicle mass 

and footprint; we added five new control variables for the additional calendar years 2000 and 

2001, and for the three additional states, GA, IL, and NM. Figure 5.13 shows that including all 

of the additional data increases the number of vehicle records by nearly 40%. 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 

0.56% 

0.10% 

-0.76% 

-0.09% 

-0.64% 

-0.16% 

0.25% 

-0.27% 

0.56% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of increase in weight or size on risk, by vehicle type

13-state casualties per crash 

Including all cars and fullsize vans 

 100-lb reduction in weight 1-sq ft reduction in footprint 
63

Figure 5.13. Number of vehicles involved in casualty crashes by vehicle type, using 

additional state crash data

Figure 5.14 indicates that adding the data results in little change in the estimated effect of mass 

or footprint reduction on casualty risk per crash, for all vehicle types. Note in Figure 5.14 that the 

last column (in light orange), which represents the effect from increasing the sample size by 

about 40%, reduces the uncertainty of the estimates of the effect of mass or footprint on risk by 

only a small amount. This suggests that the uncertainty is a function of the variability in the 

effect of mass or footprint reduction on risk by vehicle, and not a function of relatively small 

sample sizes. 

0 

20,000 

40,000 

60,000 

80,000 

100,000 

120,000 

140,000 

160,000 

180,000 

200,000 

Cars Light trucks CUVs/minivans 

Number of vehicles involved in casualty crashes 

Effect of increase in weight or size on risk, by vehicle type

13-states 

16-states plus missing MY, corrected VINs, and CY00, CY01 
64

Figure 5.14. Estimated effect of mass or footprint reduction on casualty risk per crash by 

vehicle type, using additional state crash data

5.8. Effect of changes suggested by NHTSA peer reviewers

In its review of the preliminary NHTSA 2011 study, DRI suggested that NHTSA account for the 

two components of vehicle footprint, wheelbase and track width, separately in the regression 

models; in previous analyses DRI found that these two changes to the regression models tended 

to reduce the estimated detrimental effect of mass reduction on risk (Van Auken and Zellner, 

2005b). Figure 5.15 shows that replacing vehicle footprint with track width and wheelbase

increases the estimated beneficial effect of mass reduction on casualties per crash (shown in 

olive); in addition, a one-inch reduction in track width is associated with a large increase in 

casualty risk per crash, particularly for cars and CUVs/minivans, while a one-inch reduction in 

wheelbase is associated with a small reduction in risk for all three types of vehicles. 

Other reviewers suggested that NHTSA conduct two additional sensitivities: reweighting the 

casualties of CUVs and minivans by their market shares in 2010 (Paul Green); and removing the 

non-significant control variables from the 27 regression models for the three vehicle types and 

nine crash types (Charles Farmer). Figure 5.16 shows the sensitivity of our estimates to these 

changes. Weighting the distribution of casualties in CUVs and minivans by their respective 

shares of sales in 2010 (which reflects more CUVs and fewer minivans) has very little effect on 

the relationship between lower mass or footprint and casualty risk per crash in CUVs and 

minivans (shown in orange). Removing non-significant control variables from each of the 

regression models results in slightly more detrimental effects of reduced mass estimated for cars

and CUVs/minivans, and slightly more beneficial effects estimated for light trucks. 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 

0.56% 

0.19% 

-0.54% 

-0.02% 

-0.64% 

-0.34% 

0.02% 

-0.30% 

0.44% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of increase in weight or size on risk, by vehicle type

13-states 

16-states plus missing MY, corrected VINs, and CY00, CY01 

 100-lb reduction in weight 1-sq ft reduction in footprint 
65

Figure 5.15. Estimated effect of mass or footprint reduction on casualty risk per crash by 

vehicle type, replacing footprint with track width and wheelbase

Figure 5.16. Estimated effect of mass and footprint reduction on casualty risk per crash, 

after reweighting CUV/minivan fatalities to 2010 sales and excluding non-significant 

control variables, by vehicle type 0.09% -0.77% -0.11% -0.62% 

-0.16% 

0.23% 

-0.25% 

0.56% 

-0.37% 

-1.05% 

-0.40% 

-0.75% 

-0.34% 

2.58% 

0.40% 

2.10% 

-0.59% 

-0.15% 

-0.33% 

-2% 

-1% 

0% 

1% 

2% 

3% 

Cars < 

3106 

Cars > 

3106 

LTs < 

4594 

LTs > 

4594 

CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Cars LTs CUVs/ 

Percent change in risk (casualty probability per crash) 

minivans 

13-state casualty risk per crash 

Replace footprint with track width and wheelbase 

 100-lb reduction 1-sq ft reduction 1-inch reduction 1-inch reduction 

 in weight in footprint in track width in wheelbase 0.09% -0.77% -0.11% -0.62% -0.16% 0.23% -0.25% 0.56% 0.09% -0.77% -0.11% -0.62% -0.24% 0.23% -0.25% 0.53% 0.17% -0.58% -0.24% -0.68% -0.03% 0.11% -0.15% 

0.64% 

-2.0% 

-1.0% 

0.0% 

1.0% 

2.0% 

Cars < 3106 Cars > 3106 LTs < 4594 LTs > 4594 CUVs/ 

minivans 

Cars LTs CUVs/ 

minivans 

Percent change in risk (casualty probability per crash) 

Effect of reduction in weight or size on risk, by vehicle type

13-state casualties per crash 

Reweighting CUV/minivans to 2010 sales 

Excluding non-significant control variables 

 100-lb reduction in weight 1-sq ft reduction in footprint 
66

6. Conclusions

NHTSA recently completed a logistic regression analysis (Kahane 2012) updating its 2003 and 

2010 studies of the relationship between vehicle mass and US fatality risk per vehicle mile 

traveled (VMT). The new study updates the previous analyses in several ways: updated FARS 

data for 2002 to 2008 involving MY00 to MY07 vehicles are used; induced exposure data from 

police reported crashes in several additional states are added; a new vehicle category for carbased crossover utility vehicles (CUVs) and minivans is created; crashes with other light-duty 

vehicles are divided into two groups based on the crash partner vehicle’s weight, and a category 

for all other fatal crashes is added; and new control variables for new safety technologies and 

designs, such as electronic stability controls (ESC), side airbags, and methods to meet voluntary 

agreement to improve light truck compatibility with cars, are included.

In a companion report (Wenzel 2012b), we use the updated databases NHTSA has created to 

replicate their findings on the relationship between vehicle weight, size (actually footprint, or 

vehicle wheelbase times track width), and US fatality risk per vehicle miles traveled (VMT), for 

model year 2000 to 2007 light-duty vehicles involved in fatal crashes between 2002 and 2008. 

The data are examined in slightly different ways, to get a deeper understanding of the 

relationship between reductions in vehicle mass and footprint, and overall safety. 

This report compares the logistic regression results of the NHTSA analysis of US fatality risk per 

VMT with an analysis of 13-state fatality risk and casualty risk per crash. This final report 

incorporates revisions from the preliminary report released in November 2011, including revised 

estimates of national weights for vehicle miles traveled, inclusion of 2008 police-reported crash 

data from eight additional states, and responses to reviewers’ comments. 

Our analysis differs from the NHTSA analysis in two respects: first, it analyzes risk per crash, 

using data on all police-reported crashes from thirteen states, rather than risk per estimated 

VMT; and second, it analyzes casualty (fatality plus serious injury) risk, as opposed to just

fatality risk. There are several good reasons to investigate the effect of mass and footprint 

reduction on casualty risk per crash. First, risk per VMT, includes two effects that influence 

whether a person is killed or seriously injured in a crash: how well a vehicle can be, or actually 

is, driven (based on its handling, acceleration, and braking capabilities) to avoid being involved 

in a serious crash (crash avoidance), and, once a serious crash has occurred, how well a vehicle 

protects its occupants from fatality or serious injury (crashworthiness) as well as the occupants of 

any crash partner (compatibility). By encompassing both of these aspects of vehicle design, risk 

per VMT gives a complete picture of how vehicle design can promote, or reduce, road user 

safety. On the other hand, risk per crash isolates the second of these two safety effects, 

crashworthiness/compatibility, by examining the effect of mass and footprint reduction on how 

well a vehicle protects its occupants once a crash occurs. 

Second, estimating risk on a per crash basis only requires using data on police-reported crashes 

from states, and does not require combining them with data from other sources, such as vehicle 

registration data and VMT information, as in NHTSA 2012. Because only sixteen states 

currently record the vehicle identification number of vehicles involved in police-reported 

crashes, which is necessary to determine vehicle characteristics, and only thirteen states also 
67

report the posted speed limit of the roadway on which the crash occurred, extending the analysis 

to casualties (fatalities plus serious/incapacitating injuries; i.e. level “K” and “A” injuries in 

police reports) reduces the statistical uncertainty of analyzing just fatalities per crash. Finally, a 

serious incapacitating injury can be just as traumatic to the victim and her family, and costly 

from an economic perspective, as a fatality. Limiting the analysis to the risk of fatality, which is 

an extremely rare event, ignores the effect vehicle design may have on reducing the large number 

of incapacitating injuries that occur each year on the nation’s roadways. All risks in this report 

are societal risk, including fatalities and serious injuries in the case vehicle and any crash 

partners, and include not only driver casualties but passenger and non-occupant casualties as 

well.

However, the frequency of police-reported crashes per VMT and of casualties per policereported crash can both be influenced, in opposite directions, by the probability that a collision 

event becomes a police-reported crash. If collisions of certain vehicles are slightly less likely to 

be reported, because these vehicles are either somewhat less damage-prone or are uninsured, this 

would tend to increase the observed detrimental effect of mass reduction on reported crashes per 

VMT and conversely decrease its detrimental effect on casualties per reported crash. By 

contrast, fatalities or casualties per VMT would be not be affected by crash-reporting rates, 

because the crash-reporting rate is not part of the formula for calculating risk. The extent to 

which any reporting bias of non-injury crashes exists, the observed effects for police-reported 

crashes per VMT might not correspond exactly to the “effect of mass reduction on crash 

avoidance” and the observed effects for casualties per police-reported crash might not 

correspond exactly to the “effect of mass reduction on crashworthiness/compatibility.” We 

suspect that large pickups are less likely to suffer damage in non-injury crashes than other 

vehicle types; and that older, less expensive, or uninsured vehicles are less likely to report crash 

damage to police. In addition, one vehicle crashes are more likely to suffer from this reporting 

bias, as there is no crash partner who may file an insurance claim. 

Table 6.1 summarizes the results of our analysis of the effect of vehicle mass or footprint 

reduction on the two components of risk per VMT, crash frequency (number of crashes per 

VMT) and crashworthiness/compatibility (risk per crash), for both fatality and casualty risk, 

using data from 13 states. We convert the percent change in the log-odds of casualty or fatality

per crash output from the SAS LOGIST procedure to the percent change in the probability of 

casualty or fatality per crash. This conversion has no effect on the output regression coefficients 

when the change in the log-odds of casualty is small, but substantially increases the percent 

change for explanatory variables that have a large effect on the log-odds of casualty. Effects that 

are statistically significant are shown in red in the table; significance is based on the 95% 

confidence interval derived from the standard error of the output of the SAS LOGIST procedure, 

converted to a percent probability interval.

Table 6.1 indicates that for cars and light trucks, the effects from the two components, crash 

frequency and crashworthiness/compatibility, roughly add together to result in the overall effect 

on fatality risk per VMT. For example, the models estimate that 100-lb lower mass in lighterthan-average cars is associated with a 2.00% increase in crash frequency (column B), while 

lower mass is associated with a 0.54% decrease in the number of fatalities per crash (column C); 

the net effect is only a 1.42% increase in the risk of fatality per VMT (column D), which is 
68

roughly the sum of the crash frequency and crashworthiness/compatibility effects (2.00% -

0.54% = 1.45%). For CUVs/minivans, the relationship is different; lower mass is associated 

with a 0.95% increase in crash frequency, as well as a 0.98% increase in the number of fatalities 

per crash; however, the net result, an estimated 1.60% increase in the number of fatalities per 

VMT, is less than the sum of the two components (0.95% + 0.98% = 1.92%). Solving the three 

equations (crashes per VMT, risk per crash, and risk per VMT) simultaneously, as DRI has done, 

forces the estimates for the first two-stages of the regression (crashes per VMT and risk per 

crash) to equal that of the third state of the regression (risk per VMT).

The regression results in Table 6.1 estimate that mass reduction increases crash frequency 

(columns B and E) in all five vehicle types, with larger estimated increases in lighter-thanaverage cars and light-duty trucks. As a result, mass reduction is estimated to have a more 

beneficial effect on crashworthiness/compatibility, or casualty risk per crash (column F), than on 

casualty risk per VMT (column G), and on fatality risk per crash (column C) than on fatality risk 

per VMT (column D). Mass reduction is associated with decreases in casualty risk per crash 

(column F) in all vehicles except lighter cars; in two of the four cases these estimated reductions 

are statistically significant, albeit small. Footprint reduction is associated with increases in crash 

frequency (columns B and E) in cars and light trucks, but with a small decrease in crash 

frequency in CUVs/minivans; footprint reduction does not have a statistically-significant effect 

on fatality risk per crash (column C), and only for casualty risk per crash (column F) for light 

trucks. For cars and light trucks, lower mass is associated with a more beneficial effect on 

fatality risk per crash (column C) than on casualty risk per crash (column F), while lower 

footprint is associated with slightly more detrimental effects. For CUVs/minivans Table ES.1 

shows the opposite: lower mass is associated with a more beneficial effect, while lower footprint 

is associated with a more detrimental effect, on casualty than fatality risk per crash.

Table 6.1. Estimated effect of mass or footprint reduction on two components of 13- state 

fatality and casualty risk per VMT: crash frequency (crashes per VMT) and 

crashworthiness/compatibility (risk per crash)

Variable

Case vehicle 

type

A. NHTSA US fatalities per VMT

B. 13-state crashesper VMT

C. 13-state fatalitiesper crashD. 13-state fatalities per VMTE. 13-state crashes 

per VMT

F. 13-state casualties per crashG. 13-state casualties per VMT

Mass

reduction

Cars < 3106 lbs 1.55%* 2.00% -0.54% 1.42% 2.00% 0.09% 1.86%

Cars > 3106 lbs 0.51% 1.50% -2.39% -1.07% 1.50% -0.77% 0.73%

LTs < 4594 lbs 0.52% 1.44% -1.61% -0.13% 1.44% -0.11% 1.55%

LTs > 4594 lbs -0.34% 0.94% -1.25% -0.34% 0.94% -0.62% -0.04%

CUV/ minivan -0.38% 0.95% 0.98% 1.60% 0.95% -0.16% 0.10%

Footprint

reduction

Cars 1.87% 0.64% 0.92% 2.11% 0.64% 0.23% 1.54%

LTs -0.07% 1.04% 0.48% 1.64% 1.04% -0.25% 0.94%

CUV/ minivan 1.72% -0.55% -1.67% -1.24% -0.55% 0.56% 1.54%

* Based on NHTSA’s estimation of uncertainty using a jack-knife method, only mass reduction in cars less than 

3,106 lbs has a statistically significant effect on US fatality risk.

Estimates that are statistically significant at the 95% level are shown in red.
69

It is unclear why lower vehicle mass is associated with higher crash frequency, but lower risk per 

crash, in the regression models. It is possible that including variables that more accurately 

account for important differences among vehicles and driver behavior would reverse this 

relationship. For example, adding vehicle purchase price substantially reduces the estimated 

increase in crash frequency as vehicle mass decreases, for all vehicle types; in the case of 

heavier-than-average cars, mass reduction is estimated to slightly decrease crash frequency. On 

the other hand, it is also possible that over thirty years of improvements in vehicle design to 

achieve high crash test ratings have enabled manufacturers to use clever vehicle design to 

mitigate the hypothetical safety penalty of low mass vehicles.

The association of mass reduction with 13-state casualty risk per VMT (column G) is quite 

consistent with that NHTSA estimated for US fatality risk per VMT (column A), although we 

estimate the effects on casualty risk to be more detrimental than the effects on fatality risk, for all 

vehicle types. The association of footprint reduction also is similar, with 13-state casualty risk 

per VMT slightly more beneficial than US fatality risk per VMT for cars and CUVs/minivans, 

while 13-state casualty risk is substantially more detrimental than US casualty risk for light-duty 

trucks.

In contrast with NHTSA’s estimates on US fatality risk per VMT (column A), mass reduction is 

estimated to reduce casualty risk per crash (column F) for four of the five vehicle types, with two 

of these four reductions estimated to be statistically significant. Mass reduction is associated 

with a small but insignificant increase in casualty risk per crash for lighter cars. And footprint 

reduction is associated with much smaller, and not statistically significant, estimated increases in 

casualty risk per crash (column F) than in US fatality risk per VMT (column A).

Many of the control variables included in the logistic regressions are statistically significant, and 

have a large effect on fatality or casualty risk per crash, in some cases one to two orders of 

magnitude larger. However, the estimated association of these variables with risks per crash are 

not as large as their estimated association with fatality risk per VMT. While the estimated effect

of mass reduction may result in a statistically-significant increase in risk in certain cases, the 

increase is small and is overwhelmed by other known vehicle, driver, and crash factors.

ABS and ESC in cars are estimated to reduce crash frequency more than risk per crash, as 

expected, while AWD in light trucks and CUVs/minivans is estimated to increase crash 

frequency more than risk per crash. Two-door cars and the side airbag variables in cars have a 

larger effect on risk given a crash than on crash frequency; two-door cars increase risks per 

crash, while side airbags decrease risks per crash. The driver age variables estimate that crash 

frequency consistently increases for the youngest and oldest drivers, and that risk per crash 

consistently increases for the two oldest groups of drivers (over 50 years old). All of these 

results are expected. 

On the other hand, there are several unexpected results: side airbags in light trucks and 

CUVs/minivans are estimated to reduce crash frequency; ESC and ABS are estimated to reduce 

risk once a crash has occurred; and AWD and brand new vehicles are estimated to increase risk 

once a crash has occurred. In addition, male drivers are estimated to have essentially no effect on 

crash frequency, but are associated with a statistically significant increase in fatality risk once a 
70

crash occurs. And driving at night, on high-speed or rural roads, are associated with higher 

increases in risk per crash than on crash frequency. These unexpected results suggest that 

important control variables are not being included in the regression models. For example, 

crashes involving male drivers, in vehicles equipped with AWD, or that occur at night on rural or 

high-speed roads, may not be more frequent but rather more severe than other crashes, and thus 

lead to greater fatality or casualty risk. And drivers who select vehicles with certain safety 

features may tend to drive more carefully, resulting in vehicle safety features designed to 

improve crashworthiness or compatibility, such as side airbags, being also associated with lower 

crash frequency. 

In contrast with NHTSA’s results for US fatalities per VMT, allowing footprint to vary along 

with weight results in little change in the estimated effect of mass reduction on casualty risk per 

crash than when footprint is held constant; however, the estimated detrimental effect of mass 

reduction on casualty risk per crash in lighter cars is increased just enough to make it statistically 

significant. When mass is allowed to vary along with footprint, footprint reduction is estimated 

to be slightly more beneficial for cars and light trucks (Alternative 3 in Table 6.2; further 

addressed in Section 3 of this report). As with NHTSA’s analysis of fatality risk per VMT, mass 

reduction is not consistently associated with increased casualty risk per crash across all footprint 

deciles for any combination of vehicle type and crash type. Lower mass is associated with 

increased casualty risk per crash in a majority of footprint deciles for 9 of the 27 crash and 

vehicle combinations, but few of these increases are statistically significant. On the other hand, 

lower mass is associated with decreased risk in a majority of footprint deciles for 12 of the 27 

crash and vehicle combinations.

Similar to our findings on US fatality risk per VMT, after accounting for all of the control 

variables in the logistic regression model, except for vehicle mass and footprint, we find that the 

correlation between mass and the casualty risk per crash by vehicle model is very low. There 

also is no significant correlation between the residual, unexplained risk and vehicle weight. 

These results corroborate our earlier finding that, even after accounting for many vehicle, driver, 

and crash factors, the variation in risk by vehicle model is quite large and unrelated to vehicle 

weight (addressed in more detail in Section 4). The large remaining unexplained variation in risk 

by vehicle model could be attributable to other differences in vehicle design, or how drivers who 

select certain vehicles drive them. It is possible that including variables that account for these 

factors in the regression models would change the estimated relationship between mass or 

footprint and risk.

Other changes in the data and variables used in the regression models result in changes in the 

estimated effect of mass or footprint reductions on casualty risk per crash, as summarized in 

Tables 6.2 and 6.3. For example:

• Regression analyses using police-reported crash data from states must use control variables 

to account for differences in definitions of “serious” or “incapacitating” injuries, and 

reporting requirements, across states. Removing the 12 state control variables results in a 

large reduction in estimated casualty risk per crash from mass reduction in all five vehicle 

types, a large increase in estimated risk from footprint reduction in cars and 

CUVs/minivans, and a small reduction in estimated risk from footprint reduction in light 
71

trucks (Alternative 4 in Table 6.2). Including only two variables to control for states with 

high and low casualty risk per crash substantially reduces the estimated effect of mass and 

footprint reduction on casualty risk (Alternative 5 in Table 6.2), while including the 12 

control variables for individual states reduces the estimated effect a little bit more. These 

results indicate that excluding control variables for the state in which a crash occurred from 

a regression model using state police-reported crash data can give inaccurate estimates of 

the effect of mass or footprint reduction on casualty risk per crash (addressed in Section 

5.1).

• Calculating risk as casualty crashes, rather than total casualties, per crash results in little 

change in the association between mass or footprint and risk, but does increase the small 

estimated detrimental effect of footprint reduction in cars on risk, and makes it statistically 

significant (Alternative 6 in Table 6.2; addressed in Section 5.2). 

• Adding control variables for vehicle manufacturer estimates that lower mass is associated 

with higher casualty risk per crash for cars, with little effect on the estimates for light 

trucks and CUVs/minivans. Accounting for vehicle manufacturer turns the small estimated 

increase in casualty risk per crash from footprint reduction in cars to a small decrease in 

risk, and slightly increases the estimated casualty risk per crash in light trucks and 

CUVs/minivans (Alternative 7 in Table 6.3). Also including control variables for five 

luxury vehicle makes has little effect on the estimated relationships between mass or 

footprint and casualty risk per crash (Alternative 8 in Table 6.3; addressed in Section 5.3).

Table 6.2. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, under alternative regression model specifications

Variable

Case vehicle 

type

LBNL 13-state casualties per policereported crash

1. Single regression model for all crash types

2. Weighted by current distribution of fatalities3. Excluding footprint

or weight

4. Excluding state control variables5. Including only two state control variables6. Casualty crashes per crash

Mass

reduction

Cars < 3106 lbs 0.09% 0.07% 0.08% 0.25% -0.64% -0.13% 0.30%

Cars > 3106 lbs -0.77% -0.87% -0.86% -0.61% -1.68% -1.19% -0.63%

LTs < 4594 lbs -0.11% -0.11% -0.09% -0.38% -0.21% -0.15% -0.04%

LTs > 4594 lbs -0.62% -0.74% -0.67% -0.78% -1.84% -0.75% -0.61%

CUV/ minivan -0.16% -0.31% -0.26% 0.13% -2.09% -0.47% -0.21%

Footprint

reduction

Cars 0.23% 0.50% 0.41% -0.10% 1.52% 0.45% 0.34%

LTs -0.25% 0.05% -0.13% -0.49% -1.05% -0.30% -0.05%

CUV/ minivan 0.56% 0.68% 0.75% 0.56% 3.79% 0.69% 0.80%

Estimates that are statistically significant at the 95% level are shown in red.

• An alternative to control variables for vehicle manufacturers is a single continuous variable 

for the vehicle’s initial purchase price; purchase price may better account for other 

differences in vehicle design that may influence traffic safety. Adding this single variable 

turns the estimated small increase in casualty risk per crash from mass reduction into an 

estimated small decrease in risk for lighter-than-average cars, and increases the estimated 

beneficial effect from mass reduction for other vehicles, particularly heavier-than-average 
72

cars and CUVs/minivans; the price variable makes the estimated effect of footprint 

reduction slightly more detrimental in cars, more beneficial in light-duty trucks, and less 

detrimental in CUVs/minivans (Alternative 9 in Table 6.3; also addressed in Section 5.3).

• As we found in our assessment of NHTSA’s analysis of US fatality risk per VMT, 

including calendar year variables in the regression models appears to weaken the benefit of 

side air bags in cars and CUVs/minivans, and compatibility measures and ESC in light 

trucks. These variables also appear to minimize the increased risk of SUVs and heavy-duty 

pickup trucks. Excluding the calendar year variables from the regression models slightly 

reduces the beneficial effect of mass reduction on casualty risk per crash in light trucks and 

CUVs/minivans, and slightly increases the detrimental effect of footprint reduction on 

casualty risk per crash in cars (Alternative 10 in Table 6.3; addressed in Section 5.4).

• Because details on the driver’s condition or behavior are not consistently reported in the 

state crash data, we cannot account for the behavior of individual drivers in our estimates. 

One possible surrogate for the behavior of drivers who tend to select certain vehicle models 

is driver household income. Including a measure of household income by vehicle model 

makes the estimated effect of mass reduction on casualty risk per crash more beneficial, 

and the estimated effect of footprint reduction more detrimental, for cars and 

CUVs/minivans, but has little effect on the estimates for light trucks (Alternative 11 in 

Table 6.3). 

• Including all-wheel-drive, sports, and police cars, and fullsize vans results in virtually no 

change in the estimated effect of mass or footprint reduction on casualty risk per crash for 

cars or light trucks (Alternative 12 in Table 6.3; addressed in Section 5.5). 

Table 6.3. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, excluding certain data or using different control variables

Variable

Case vehicle 

type

LBNL 13-state casualties per policereported crash7. Accounting for vehicle manufacturer8.Accounting for vehicle manufacturer plus five luxury brands 9. Accounting for initial vehicle purchase price10. Excluding CY variables11. Accounting for median household income12. Including sports, squad, AWD cars and fullsize vans13. Including all additional data

Mass

reduction

Cars < 3106 lbs 0.09% 0.85% 0.96% -0.35% 0.00% -0.04% 0.10% 0.19%

Cars > 3106 lbs -0.77% 0.78% 0.76% -1.72% -0.99% -1.12% -0.76% -0.54%

LTs < 4594 lbs -0.11% -0.24% -0.24% -0.14% 0.43% -0.05% -0.09% -0.02%

LTs > 4594 lbs -0.62% -0.65% -0.60% -0.71% -0.20% -0.68% -0.64% -0.64%

CUV/ minivan -0.16% -0.05% -0.40% -0.64% 0.28% -0.65% -0.16% -0.34%

Footprint

reduction

Cars 0.23% -0.52% -0.60% 0.29% 0.69% 0.69% 0.25% 0.02%

LTs -0.25% -0.09% -0.11% -0.40% -0.49% -0.26% -0.27% -0.30%

CUV/ minivan 0.56% 0.88% 1.16% 0.41% 0.47% 1.01% 0.56% 0.44%

Estimates that are statistically significant at the 95% level are shown in red.

• Adding data from three additional states, including vehicles with unreported model year, 

correcting VIN transcription errors, and expanding the analysis to calendar years 2000, 
73

2001, and 2008, increases the number of state crash records by about 40 percent. Including 

these data in the regression analyses makes the estimated effect of mass reduction in cars 

and lighter light trucks more detrimental, and in CUVs/minivans more beneficial. 

Including these data slightly reduces the estimated detrimental effect of footprint reduction

on casualty risk per crash in cars and CUVs/minivans. However, increasing the sample 

size included in the regression analysis by 40% does not noticeably reduce the confidence 

intervals around the point estimates (Alternative 13 in Table 6.3; addressed in Section 5.6).

Table 6.4 shows the results of additional sensitivity tests NHTSA conducted in response to 

comments from peer reviewers of its preliminary 2011 report. Replacing vehicle footprint with 

its two components, track width and wheelbase, increases the estimated beneficial effect of mass 

reduction on casualty risk per crash, making it statistically significant for four of the five vehicle 

types, as shown in Alternative 14. Decreasing track width is associated with a significant 

increase in casualty risk per crash, while decreasing wheelbase is associated with a small 

decrease in risk. Weighting the distribution of fatalities in CUVs and minivans by their 

respective shares of sales in 2010 (which reflects more CUVs and fewer minivans) has little 

effect on the estimated effects (Alternative 15). Alternative 16 removes non-significant control 

variables from each of the regression models, which results in only small changes in the 

estimated effects.

Table 6.4. Estimated effect of mass or footprint reduction on 13-state casualty risk per 

crash, alternative regression model specifications suggested by NHTSA peer reviewers

Variable

Case vehicle 

type

LBNL 13-state casualties per police-reported crash

14. Including track width and wheelbase instead of footprint

15. Reweighting CUVs and minivans by 2010 sales16. Excluding nonsignificant control variables

Mass

reduction

Cars < 3106 lbs 0.09% -0.37% 0.09% 0.17%

Cars > 3106 lbs -0.77% -1.05% -0.77% -0.58%

LTs < 4594 lbs -0.11% -0.40% -0.11% -0.24%

LTs > 4594 lbs -0.62% -0.75% -0.62% -0.68%

CUV/ minivan -0.16% -0.34% -0.24% -0.03%

Footprint

reduction

Cars 0.23% — 0.23% 0.11%

LTs -0.25% — -0.25% -0.15%

CUV/ minivan 0.56% — 0.53% 0.64%

Track 

width 

reduction

Cars — 2.58% — —

LTs — 0.40% — —

CUV/ minivan — 2.10% — —

Wheel 

base 

reduction

Cars — -0.59% — —

LTs — -0.15% — —

CUV/ minivan — -0.33% — —

Estimates that are statistically significant at the 95% level are shown in red.

In conclusion, casualty risk per crash is not necessarily a better metric than fatality risk per VMT 

for evaluating the effect of mass or footprint reduction on risk; rather, it provides a different 
74

perspective in assessing the benefits or drawbacks of mass and footprint reduction on safety in 

vehicles. However, it does allow the risk per VMT to be separated into its two components, 

crash frequency and risk per crash. Our analysis indicates that much of the estimated detrimental 

effect of mass or footprint reduction on risk can be attributed to the tendency for crash 

frequency, rather than crashworthiness/compatibility (risk once a crash has occurred), to increase 

as vehicle mass or footprint decreases.

As with our analysis of US fatalities per VMT, this report concludes that the estimated effect of 

mass reduction on casualty risk per crash is small, and is overwhelmed by other control 

variables, such as vehicle type, specific safety technologies, and crash conditions such as 

whether the crash occurred at night, in a rural county, or on a high-speed road. This report 

indicates that the effects are sensitive to what variables and data are included in the regression 

analysis. Finally, as in our analysis of US fatality risk per VMT, this report shows that after 

accounting for many vehicle, driver, and crash variables there remains a wide variation in 

casualty risk per crash by vehicle make and model, and this variation is unrelated to vehicle 

mass.

Although the purpose of the NHTSA and LBNL reports is to estimate the effect of vehicle mass 

reduction on societal risk, this is not exactly what the regression models are estimating. Rather, 

they are estimating the recent historical relationship between mass and risk, after accounting for 

most measurable differences between vehicles, drivers, and crash times and locations. In essence, 

the regression models are comparing the risk of a 2600-lb Dodge Neon with that of a 2500-lb 

Honda Civic, after attempting to account for all other differences between the two vehicles. The 

models are not estimating the effect of literally removing 100 lbs from the Neon, leaving 

everything else unchanged. 

In addition, the analyses are based on the relationship of vehicle mass and footprint on risk for 

recent vehicle designs (model year 2000 to 2007). These relationships may or may not continue 

into the future as manufacturers utilize new vehicle designs and incorporate new technologies, 

such as more extensive use of strong lightweight materials and specific safety technologies. 

Therefore, throughout this report we use the phrase “the estimated effect of mass (or footprint) 

reduction on risk” as shorthand for “the estimated change in risk as a function of its relationship 

to mass (or footprint) for vehicle models of recent design.”
75

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