LBNL-xxxxx

                        Assessment of NHTSA's Report
"Relationships Between Fatality Risk, Mass, and Footprint in Model Year 2000-2007 Passenger Cars and LTVs"

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

                                  Prepared by

                                  Tom Wenzel
                          Energy Analysis Department
                  Environmental Energy Technologies Division
                     Lawrence Berkeley National Laboratory
                              Berkeley, CA 94720

                                 November 2011

         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.

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.

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.

Executive Summary

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).  The new study updates the previous analyses in several ways: updated FARS data from 2002 to 2008 for MY00 to MY07 vehicles are used; induced exposure data from police reported crashes in several additional states are added; a new vehicle category for car-based 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.

Using the updated NHTSA databases, our analysis finds that reducing vehicle mass by 100 lbs while holding footprint fixed would increase fatality risk per VMT by 1.44% for lighter than average cars, and 0.52% for lighter than average light-duty trucks.  However, mass reduction in heavier than average light-duty trucks, while holding footprint constant, would reduce risk by 0.40%.  The effect of mass reduction on heavier cars and CUVs and minivans are not statistically significant.  (Using a different method to estimate the uncertainty around these point estimates, NHTSA found that only the effect of mass reduction on lighter than average cars is statistically significant.)  NHTSA concludes that, when footprint is held fixed, "no judicious combination of mass reductions in the various classes of vehicles results in a statistically significant fatality increase and many potential combinations are safety-neutral as point estimates".

The effect of mass reduction on risk that NHTSA calculated in 2011 is much smaller than in its 2003 and 2010 studies, particularly for cars.  NHTSA attributes this reduction in the importance of mass reduction on safety to the phase-out of relatively light cars that had unusually high fatality risk, an observed improvement in how light, small cars are driven which reduces their tendency to be involved in serious crashes, and voluntary improvements made to light trucks to improve their compatibility with other vehicles.  The 2011 NHTSA analysis finds that reducing vehicle footprint by one square foot while holding mass fixed would increase fatality risk per VMT by 1.89% in cars and 1.73% in CUVs and minivans (the effect on risk in light trucks is small and not statistically significant).

Rather than relying on the confidence intervals output by the logistic regression models, NHTSA estimates the uncertainty around its point estimates using a jack-knife technique that accounts for the sampling error in the FARS fatality and state crash data.  These uncertainty estimates are larger than the confidence intervals output by the logistic regression models included in this report.  As a result, in its report NHTSA finds that only the 1.44% increase in risk from mass reduction in lighter than average cars is statistically significant.

This report replicates the 2011 NHTSA analysis, and examines the data in slightly different ways to get a deeper understanding of the relationship between vehicle weight/footprint and safety.  The results of these alternative analyses are summarized in Table ES.1; statistically significant results, based on the confidence intervals output by the logistic regression models, are shown in red in the table.  In particular, we found that:

   :: NHTSA's (reasonable) assumption that all vehicles will have ESC installed by 2017 slightly increases the detrimental effect of mass reduction, but slightly decreases the detrimental effect of footprint reduction, on risk in cars, CUVs and minivans (Alternative 1 in Table ES.1; explained in more detail in Section 2.1 of this report). This is because NHTSA projects ESC to substantially reduce the number of fatalities in rollovers and crashes with stationary objects, and mass reduction reduces risk, while footprint reduction increases risk, in these types of crashes, particularly in cars and CUVs/minivans.

   :: Many of the control variables NHTSA includes in its logistic regressions are statistically significant, and have a large effect on fatality risk.  For example, a car's mass could be reduced by 800 lbs while adding ESC without increasing its fatality risk.  And increasing the amount of vehicle travel on highways with speed limits greater than 55 miles per hour by 0.35% would result in the same increase in risk as reducing the mass of all cars by 100 lbs.  While the 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.

   :: Vehicle mass and footprint are correlated, but only strongly for passenger cars. NHTSA includes both variables in their regression models, introducing the possibility that multi-collinearity may create biased results.  When footprint is allowed to vary along with weight, mass reduction results in a larger increase in risk than when footprint is held constant.  Similarly, when mass is allowed to vary along with footprint, footprint reduction results in larger increases in risk (Alternative 2 in Table ES.1, further addressed in Section 3 of this report). To isolate the effect of mass reduction from footprint reduction on risk, NHTSA estimates the effect of mass reduction on risk for deciles of vehicles with similar footprint.  Mass reduction does not consistently increase risk across all footprint deciles for any combination of vehicle type and crash type.  Mass reduction increases risk in a majority of footprint deciles for 13 of the 27 crash and vehicle combinations, but few of these increases are statistically significant (the increases are statistically significant only for light-duty trucks in rollovers).  On the other hand, mass reduction decreases risk in a majority of footprint deciles for 9 of the 27 crash and vehicle combinations.  In some cases these risk reductions are large and statistically significant (such as in cars in rollovers and crashes with stationary objects; light-duty trucks in crashes with light and heavy cars; and CUVs and minivans in crashes with heavy cars).

   :: Logistic regression does not allow a statistic, such as the model R[2] in a linear regression model, to measure how much variability in risk by vehicle model is explained by the control variables included in the model.  Analysis of pseudo-R[2] and R[2] from a linear regression model suggests that much of the variance in risk remains unexplained, even after accounting for many important vehicle, driver, and crash variables.  After accounting for all of the variables in NHTSA's logistic regression model, except for vehicle mass and footprint, we find that the correlation between fatality risk by vehicle model and mass is very low.  There also is no significant correlation between the residual, unexplained risk and vehicle weight.  These results indicate that, even after accounting for many vehicle, driver, and crash factors, the variance in risk by vehicle model is quite large and unrelated to vehicle weight (addressed in more detail in Section 4).

   :: Changes in the data and variables NHTSA used in its regression models have only slight changes on NHTSA's results.  Calculating risk as fatal crashes, rather than total fatalities, per vehicle mile traveled, as suggested by one of the independent reviewers of the previous NHTSA reports, increases the detrimental effect of mass reduction on risk in cars, but has no effect on mass reduction in light trucks or CUVs/minivans, or on footprint reduction in any vehicle type (Alternative 3 in Table ES.1).  Calculating risk as total fatalities per induced exposure crash, rather than per vehicle mile traveled, reverses the sign of the effect of mass reductions on risk in cars and the lighter light trucks, with mass reduction leading to a reduction in risk in all vehicle types.  Footprint reduction continues to result in large increases in risk per induced exposure crash for cars and CUVs/minivans, but leads to a large reduction in fatality risk per induced exposure crash for light trucks (Alternative 4 in Table ES.1; further addressed in Section 5.1).

   :: Adding control variables for vehicle manufacturer tends to increase the effect of mass reduction, but decrease the effect of footprint reduction, on risk for cars and light trucks, and makes mass reduction detrimental, and footprint reduction slightly beneficial, for CUVs/minivans (Alternative 5 in Table ES.1).

   :: NHTSA included control variables for the calendar year in which the crash occurred, to reflect reducing risk from changes to vehicles, driver behavior and driving conditions over time.  However, including these calendar year variables in the regression models appear to weaken the benefit of curtain side air bags in cars, CUVs, and 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 these calendar year variables from the regression models increases the detrimental effect of mass reduction on risk in light trucks (Alternative 6 in Table ES.1, addressed in Section 5.3).

   :: Excluding crashes involving alcohol or drugs, or drivers with poor driving records, also increases the detrimental effect of mass reduction on risk, but reduces the detrimental effect of footprint reduction on risk (Alternatives 7 and 8 in Table ES.1, Section 5.4).  Including all-wheel-drive, sports, and police cars increases the effect of mass reduction, but reduces the effect of footprint reduction, on risk for cars; while including fullsize vans reduces the effect of mass reduction, and increases the effect of footprint reduction, on risk for light trucks (Alternative 9 in Table ES.1, Section 5.5).

   :: As mentioned above, for its baseline fatalities NHTSA assumes that all vehicles will have ESC installed by 2017, which will reduce the fraction of fatalities in rollovers and crashes with stationary objects, and thus will increase the detrimental overall effect of mass reduction, but decrease the detrimental overall effect of footprint reduction, on risk.  However, other recent trends that are likely to continue through 2017 may also affect the distribution of crashes in that year.  For example, side airbags in cars will likely reduce the fraction of fatalities in side-impact crashes (Section 6.1), and better alignment of light truck bumpers with those of other vehicles appears to reduce the risk imposed on car occupants, at least in side impact crashes (Section 6.2).  However, it appears that mass reduction has less of a detrimental effect on risk when cars are struck in the side than when they are involved in frontal or rear-end crashes, so any future reduction in fatalities in car side impact crashes will not necessarily influence the effect of mass reduction on risk.  And it is not clear whether full adoption of side airbags or compatibility measures for light trucks will reduce fatality risk when light-duty trucks, CUVs or minivans are struck in the side.

   :: Finally, in part because of high gas prices and the poor economy, households have been purchasing smaller and lighter vehicles in the last decade.  For example, the explosion of CUVs appears to have led to a reduction in the market share of minivans, cars, and in recent years (MY05 to MY07) SUVs and pickups.  It is likely that these trends would continue, even in the absence of stronger CAFE and GHG emission standards. Any future market shifts from SUVs or pickups to cars or car-based CUVs and minivans will result in much larger reductions in fatality risk than the relatively small increases in risk expected from mass or footprint reduction.  For example, we estimate that a large-scale shift in the market share of pickups and SUVs to CUVs, minivans, and cars will reduce overall fatalities by nearly 4% (Section 6.3).

Table ES.2 compares the results from NHTSA's 2003, 2010, and 2011 analyses with the alternative model specifications examined in this report (again, results that are statistically significant are shown in red in the table). The first two columns of the table indicate that NHTSA's 2011 analysis of a simultaneous reduction in mass and footprint (i.e. excluding a control variable for footprint in the regression model) results in a smaller increase in fatalities than in NHTSA's 2003 analysis, particularly for lighter cars (a 2.64% increase rather than a 4.39% increase) and light trucks (a 0.52% increase rather than a 2.90% increase).  The third and fourth columns of the table indicate a similar reduction in additional fatalities for cars when footprint is held constant (i.e. when a control variable for footprint is included in the regression model).  However, holding footprint constant increases the effect of mass reduction slightly in light trucks (a 0.52% increase rather than a 0.17% increase in fatalities for lighter light trucks, and a 0.40% reduction rather than a 1.90% reduction in fatalities for the heavier light trucks). This small increase in light truck risk may be due to NHTSA analyzing crossover utility vehicles and minivans as a separate vehicle class, rather than as light trucks, in the 2011 analysis.

The last column in Table ES.2 shows that the results of the alternative model specifications examined in this report are, in all cases, lower than the results of the 2003 NHTSA report, and often lower than the results of the 2010 and 2011 analyses.

The 2011 NHTSA study, and this report, conclude that the effect of mass reduction on US fatality risk is small.  This report indicates that although the effect is sensitive to what variables and data are included in the regression analysis, in nearly all cases the effect is less, in some cases dramatically less, than reported in the 2003 NHTSA study.  This report also finds that the effect of 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, on risk is much larger than the effect of mass or footprint reduction on risk.  Finally, this report shows that after accounting for the many vehicle, driver, and crash variables NHTSA used in its regression analyses, there remains a wide variation in risk by vehicle make and model, and this variation is unrelated to vehicle mass.

The results of the NHTSA study and this assessment of it 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.

Table ES.1.  Effect of mass and footprint reduction on fatality risk, under alternative regression model specifications
Variable
Case vehicle type
NHTSA preferred model (fatalities per VMT)
1. Using current distribution of fatalities
2. Excluding. mass or footprint variable
3. Fatal crashes per
VMT
4. Fatalities per induced exposure crash
5. Accounting for vehicle manufacturer
6. Excluding CY variables
7. Excluding crashes with alcohol/drugs
8. Excluding. bad drivers
9. Including sports, squad, AWD cars and fullsize vans
Mass
reduction
Cars < 3106 lbs
                                    1.43%*
                                     1.18%
                                     2.64%
                                     1.84%
                                    -0.24%
                                     1.81%
                                     1.39%
                                     1.66%
                                     2.03%
                                     1.64%

Cars > 3106 lbs
                                     0.48%
                                     0.30%
                                     1.94%
                                     0.86%
                                    -1.43%
                                     0.67%
                                     0.39%
                                     0.77%
                                     1.04%
                                     0.73%

LTs < 4594 lbs
                                     0.52%
                                     0.38%
                                     0.52%
                                     0.54%
                                    -1.14%
                                     0.60%
                                     1.22%
                                     0.75%
                                     0.97%
                                     0.34%

LTs > 4594 lbs
                                    -0.40%
                                    -0.44%
                                    -0.41%
                                    -0.48%
                                    -0.75%
                                    -0.21%
                                     0.25%
                                    -0.40%
                                    -0.16%
                                    -0.95%

CUV/ minivan
                                    -0.47%
                                    -0.77%
                                     0.52%
                                    -0.56%
                                    -0.69%
                                     0.92%
                                    -0.06%
                                    -0.28%
                                    -0.20%
                                    -0.47%
Footprint
reduction
Cars
                                     1.89%
                                     2.22%
                                     2.92%
                                     1.85%
                                     2.20%
                                     1.72%
                                     2.14%
                                     1.77%
                                     1.52%
                                     1.65%

LTs
                                    -0.02%
                                     0.25%
                                     0.10%
                                     0.19%
                                    -1.28%
                                    -0.24%
                                    -0.38%
                                    -0.17%
                                    -0.29%
                                     0.16%

CUV/ minivan
                                     1.73%
                                     2.26%
                                     1.26%
                                     1.82%
                                     1.97%
                                    -0.09%
                                     1.63%
                                     1.43%
                                     1.26%
                                     1.73%
* 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.

Table ES.2.  Previous NHTSA results of the effect of mass and footprint reduction on fatality risk compared with different scenarios analyzed in this report
Variable
Case vehicle type
                       NHTSA (2003) excluding footprint

                       NHTSA (2011) excluding footprint
                       NHTSA (2010) including footprint
                       NHTSA (2011) including footprint
             Range of different scenarios analyzed in this report
Mass
reduction
Cars < 3106 lbs
                                     4.39%
                                     2.64%
                                     2.21%
                                     1.43%
                                -0.24% to 2.64%

Cars > 3106 lbs
                                     1.98%
                                     1.94%
                                     0.89%
                                     0.48%
                                -1.43% to 1.94%

LTs < 4594 lbs
                                     2.90%
                                     0.52%
                                     0.17%
                                     0.52%
                                -1.14% to 1.22%

LTs > 4594 lbs
                                     0.48%
                                    -0.41%
                                    -1.90%
                                    -0.40%
                                -0.95% to 0.25%

CUV/ minivan

                                     0.52%

                                    -0.47%
                                -0.77% to 0.92%
Footprint
reduction
Cars

                                     1.89%
                                1.52% to 2.92%

LTs

                                    -0.02%
                                -1.28% to 0.25%

CUV/ minivan

                                     1.73%
                                -0.09% to 2.26%

                               Table of Contents

Acknowledgements	i
Executive Summary	iii
1. Introduction	1
2. NHTSA results	1
2.1. Data and methods	2
3. Multi-collinearity between vehicle mass and footprint	14
4. Fatality risk by vehicle model	22
5. Sensitivity of NHTSA results to data used and model specification	37
5.1. Alternative measures of exposure	37
5.2. Vehicle manufacturer	38
5.3. CY variables	39
5.4. Effect of alcohol/drug use and driving behavior	46
5.5. Effect of including sports, police, and all-wheel drive cars, and fullsize vans	48
6. Influence of recent trends on the expected effect of mass reduction on risk in 2017-2025	49
6.1 Effect of electronic stability control (ESC)	49
6.2 Effect of side airbags	50
6.3 Effect of measures to increase light truck compatibility	57
6.4 Effect of sales shift from SUVs and other light trucks to CUVs and other car-based vehicles	58
7. Conclusions	64

                          List of Tables and Figures

Table ES.1.  Effect of mass and footprint reduction on fatality risk, under alternative regression model specifications	viii
Table ES.2.  Previous NHTSA results of the effect of mass and footprint reduction on fatality risk compared with different scenarios analyzed in this report	viii
Table 2.1. Control variables used in regression models, by subject vehicle type	3
Table 2.2.  Baseline fatal crash involvements, by case vehicle type and crash type	4
Figure 2.1. Effect of mass and size variables on risk, across all crash types and weighted average effect in each type of crash, by vehicle type	6
Figure 2.2. Effect of mass and footprint reduction on risk in cars, by type of crash	7
Figure 2.3. Effect of mass and footprint reduction on risk in light trucks, by type of crash	8
Figure 2.4. Effect of mass and footprint reduction on risk in CUVs/minivans, by type of crash	9
Figure 2.5. Effect of selected control variables on risk, passenger cars	10
Figure 2.6. Effect of selected control variables on risk, passenger cars	10
Figure 2.7. Effect of selected control variables on risk, light trucks	12
Figure 2.8. Effect of selected control variables on risk, light trucks	12
Figure 2.9. Effect of selected control variables on risk, CUVs and minivans	13
Figure 2.10. Effect of selected control variables on risk, CUVs and minivans	13
Figure 3.1. Correlation between vehicle curb weight and footprint, by vehicle model and three vehicle types	14
Figure 3.2. Correlation between vehicle curb weight and footprint, by vehicle model and seven vehicle types	15
Figure 3.3. Effect of reduction in mass or footprint on US fatality risk per VMT, by vehicle type: mass only, footprint only, and both	16
Figure 3.4. Effect of reduction in car mass or footprint on US fatality risk per VMT, by crash type	17
Figure 3.5. Effect of reduction in light-duty truck mass or footprint on US fatality risk per VMT, by crash type	17
Figure 3.6. Effect of reduction in CUV/minivan mass or footprint on US fatality risk per VMT, by crash type	18
Figure 3.7. Range in curb weight for the footprint deciles, by vehicle type	19
Table 3.1. Number of footprint deciles in which mass reduction increases or decreases fatality risk, by vehicle and crash type	20
Figure 3.8. Effect of car mass reduction on fatality risk, by footprint decile and crash type	21
Figure 3.9. Effect of light truck mass reduction on fatality risk, by footprint decile and crash type	21
Figure 3.10. Effect of CUV/minivan mass reduction on fatality risk, by footprint decile and crash type	22
Figure 4.1. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, by vehicle type	23
Figure 4.2. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, passenger cars	23
Figure 4.3. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, light trucks	24
Figure 4.4. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, CUVs and minivans	24
Figure 4.5. Relationship between US fatality risk in crashes with stationary objects and curb weight, by vehicle type	25
Figure 4.6. US fatality risk per VMT and curb weight, by vehicle model	27
Figure 4.7. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint, vs. curb weight	27
Figure 4.8. Residual US fatality risk after accounting for all driver, crash, and vehicle variables except mass and footprint, vs. curb weight	28
Figure 4.9. US fatality risk per VMT vs. curb weight, car models	29
Figure 4.10. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, car models	29
Figure 4.11. Residual US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, car models	30
Figure 4.12. US fatality risk per VMT vs. curb weight, light truck models	31
Figure 4.13. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, light truck models	32
Figure 4.14. Residual US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, light truck models	32
Figure 4.15. US fatality risk per VMT vs. curb weight, CUV/Minivan models	33
Figure 4.16. Predicted US fatality risk per VMT after accounting for all driver, crash and vehicle variables except mass and footprint vs. curb weight, CUV/Minivan models	33
Figure 4.17. Residual US fatality risk per VMT after accounting for all driver, crash and vehicle variables except mass and footprint vs. curb weight, CUV/Minivan models	34
Table 4.1. Relationship between actual, predicted, and residual fatality risk, and vehicle mass reduction, after accounting for all driver, crash, and vehicle variables except mass and footprint, by vehicle type and model	35
Table 4.2. Relationship between actual, predicted, and residual fatality risk, and vehicle footprint reduction, after accounting for all driver, crash, and vehicle variables except mass and footprint, by vehicle type and model	36
Figure 5.1. Effect of mass and footprint reduction on US fatalities per VMT, fatal crashes per VMT, and fatalities per induced exposure crash, by vehicle type	37
Figure 5.2. Effect of mass and footprint reduction on US fatality risk per VMT, after controlling for vehicle manufacturer, by vehicle type	39
Figure 5.3. Effect of calendar year variables on risk, by vehicle type	40
Figure 5.4. Effect of calendar year variables on light truck risk, by crash type	40
Figure 5.5. NHTSA 2003 effect of calendar year variables on risk, by vehicle type	41
Figure 5.6. NHTSA 2003 effect of calendar year variables on light truck risk, by crash type	42
Figure 5.7. US fatality risk per VMT, by vehicle type and calendar year	43
Figure 5.8. Total US VMT for MY2002 vehicles, by vehicle type and calendar year	43
Figure 5.9. Effect of increasing weight or size on risk, including and excluding calendar year variables	44
Figure 5.10. Effect of selected control variables on car risk, including and excluding calendar year variables	45
Figure 5.11. Effect of selected control variables on light truck risk, including and excluding calendar year variables	45
Figure 5.12. Effect of selected control variables on CUV/minivan risk, including and excluding calendar year variables	46
Figure 5.13. Effect of mass and footprint reduction on US fatality risk per VMT, after excluding case vehicles whose driver was suspected of drinking or using drugs, or exhibited bad driving behavior, by vehicle type	47
Figure 5.14. Effect of mass and footprint reduction on US fatality risk per VMT, after including sports, police, and all-wheel drive cars, and fullsize vans, by vehicle type	48
Figure 6.1. Market penetration of ESC, by vehicle type and model year	49
Figure 6.2. Effect of ESC on fatality risk, by vehicle type and crash type	50
Figure 6.3. Market penetration of side impact airbags, by vehicle type and model year	51
Figure 6.4. Effect of side airbags on risk to car occupants only, when struck in the side by another light-duty vehicle, by crash partner vehicle type	52
Figure 6.5. Effect of side airbags on risk to CUV/minivan occupants only, when struck in the side by another light-duty vehicle, by crash partner vehicle type	52
Figure 6.6. Effect of side airbags on risk to light truck occupants only, when struck in the side by another light-duty vehicle, by crash partner vehicle type	54
Figure 6.7. Effect of mass reduction on risk to car occupants only in two-vehicle crashes, by crash partner vehicle type and crash configuration	55
Figure 6.8. Effect of mass reduction on risk to CUV/minivan occupants only in two-vehicle crashes, by crash partner vehicle type and crash configuration	56
Figure 6.9. Effect of mass reduction on risk to light truck occupants only in two-vehicle crashes, by crash partner vehicle type and crash configuration	56
Figure 6.10. Market penetration of compatibility measures in light trucks, by light truck type and model year	57
Figure 6.11. Effect of compatibility measures on risk imposed by light trucks on other light-duty vehicles, by crash partner vehicle type and crash configuration	58
Figure 6.12. US registrations of new vehicles, by vehicle type and year	59
Figure 6.13. Effect of mass and footprint reductions across all vehicle types, and a comparison of fatality risk by vehicle type compared to four-door sedans	60
Table 6.1. Average driver characteristics and crash times and locations, by vehicle type	61
Table 6.2. Actual risk per billion VMT, and risk adjusted to the average driver and crash time/location in a four-door sedan, all-wheel-drive car, CUV, and minivan, by vehicle type	61
Table 6.3. Average annual fatalities and VMT in model year 2000 to 2007 light-duty vehicles between 2004 and 2008, by vehicle type	62
Table 6.4. Estimated change in annual fatalities from four scenarios of shifts among vehicle types	63
Table 7.1.  Effect of mass and footprint reduction on fatality risk, under alternative regression model specifications	68
Table 7.2.  Previous NHTSA results of the effect of mass and footprint reduction on fatality risk compared with different scenarios analyzed in this report	68

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).  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 car-based 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.

This report uses 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.  In addition, we examine the data in slightly different ways, to get a deeper understanding of the relationship between reductions in vehicle mass and footprint, and overall safety.

Section 2 of this report replicates NHTSA's results, and analyzes the control variables NHTSA includes in their preferred regression models.  Section 3 examines in more detail the multi-collinearity between vehicle mass and footprint, and the methods NHTSA took to address that multi-collinearity,  In Section 4 we examine the relationship between vehicle mass and risk by vehicle model, before and after accounting for differences in driver characteristics, crash locations, and other vehicle attributes by vehicle model.  In Section 5 we test alternative specifications of the regression models developed by NHTSA, in order to examine the sensitivity of their results to the assumptions they used and different model specifications.  Finally in Section 6 we examine the influence of recent trends in vehicle market share on the expected effect of mass reduction on risk in 2017 to 2025.

2. NHTSA results

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 13 states; NHTSA refers to this 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 NHTSA 2011.

In this section we replicate the logistic regression results NHTSA obtained using the database they constructed.  We also test the effect certain changes in the regression model specifications have on the coefficients for the independent variables of interest, vehicle mass and footprint.

2.1. Data and methods

For this new analysis NHTSA used FARS data on fatal crashes, and police-reported crash data from 13 states, for MY00 to MY07 light-duty vehicles between 2002 and 2008.  NHTSA used a subset of nonculpable vehicles in two-vehicle crashes as a measure of 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 vehicle miles traveled (VMT).

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 all-wheel 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 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.

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
                                       C
                                       C
                                       C
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
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.

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.  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.

Table 2.2.  Baseline fatal crash involvements, by case vehicle type and crash type
Crash type
                      Baseline fatal crash involvements:
                          MY04-07 vehicles in CY04-08
                     Adjusted for full penetration of ESC
                              Percent difference

                                                                           Cars
                                                                           LTVs
                                                                 CUVs/ minivans
                                                                           Cars
                                                                           LTVs
                                                                 CUVs/ minivans
                                                                           Cars
                                                                           LTVs
                                                                 CUVs/ minivans
1: Rollovers
                                                                            937
                                                                          1,626
                                                                            277
                                                                            453
                                                                            507
                                                                            100
                                                                           -52%
                                                                           -69%
                                                                           -64%
2: w/object
                                                                          3,496
                                                                          2,090
                                                                            571
                                                                          2,076
                                                                          1,253
                                                                            373
                                                                           -41%
                                                                           -40%
                                                                           -35%
3: Ped etc.
                                                                          2,259
                                                                          2,192
                                                                            812
                                                                          2,259
                                                                          2,192
                                                                            812
                                                                             0%
                                                                             0%
                                                                             0%
4: w/HDT
                                                                          1,248
                                                                            838
                                                                            316
                                                                          1,158
                                                                            779
                                                                            297
                                                                            -7%
                                                                            -7%
                                                                            -6%
5: w/lgt car
                                                                          1,474
                                                                          1,890
                                                                            525
                                                                          1,375
                                                                          1,761
                                                                            494
                                                                            -7%
                                                                            -7%
                                                                            -6%
6: w/hvy car
                                                                          1,441
                                                                          1,364
                                                                            477
                                                                          1,341
                                                                          1,272
                                                                            449
                                                                            -7%
                                                                            -7%
                                                                            -6%
7: w/lgt LT
                                                                          1,385
                                                                          1,220
                                                                            366
                                                                          1,286
                                                                          1,135
                                                                            345
                                                                            -7%
                                                                            -7%
                                                                            -6%
8: w/hvy LT
                                                                          1,418
                                                                            890
                                                                            330
                                                                          1,315
                                                                            829
                                                                            311
                                                                            -7%
                                                                            -7%
                                                                            -6%
9: Other
                                                                          4,431
                                                                          3,663
                                                                          1,469
                                                                          4,134
                                                                          3,427
                                                                          1,389
                                                                            -7%
                                                                            -6%
                                                                            -5%
Total
                                                                         18,089
                                                                         15,773
                                                                          5,143
                                                                         15,397
                                                                         13,155
                                                                          4,570
                                                                           -15%
                                                                           -17%
                                                                           -11%

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 that they reflect the effect of a decrease in vehicle mass or footprint; we use the same convention throughout this report).  The output from the SAS LOGIST procedure reflect the percent change in the log-odds of fatality per billion VMT for a one-unit increase in the explanatory variable.  In order to obtain the percent change in the probability of fatality, the SAS outputs need to be converted from log-space to linear space, and from odds to probabilities.  We use the equation 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 fatality is small; however it substantially increases the percent change for explanatory variables that have a large effect on the log-odds of fatality (such as the crash location variables).  For example, the fatality risk from a rollover crash involving a car has a 2.20 times higher log-odds of fatality if it occurs in a rural county; after conversion, this crash has a 802 percent higher probability of fatality if it occurs in a rural county (EXP(2.20) - 1 = 8.02).  Unless noted otherwise, the 95% confidence intervals shown in this report are calculated the same way, using the standard error of the log-odds output by the SAS LOGIST procedure.

Figure 2.1 presents the regression coefficients from the NHTSA report (in light blue); the coefficients for each of the 9 crash types are weighted by the distribution of 2016 baseline fatal crash involvements, after adjustment for full ESC penetration, from Table 2.2.  (The coefficients are slightly different from those provided in the 2011 NHTSA report, perhaps because of rounding errors and our reporting of percent changes in risk as probabilities rather than as log-odds.)  The figure indicates that mass reduction increases societal 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.  As a result, NHTSA's 2011 report indicates that only the 1.43% increase in risk from mass reduction for the lighter cars is statistically significant.

Figure 2.1. Effect of mass and size variables on risk, across all crash types and weighted average effect in each type of crash, by vehicle type

Figure 2.1 also shows that reduction in footprint consistently increases risk for all three types of vehicles, and has a larger effect on risk than reduction in mass for cars and CUVs/minivans.  A 1-square foot reduction in footprint increases fatality risk in cars and CUVs/minivans by close to 2 percent, but has no effect on risk in light trucks.

Results from a single regression analysis across all crash types are also shown in Figure 2.1 (in dark turquoise), as are the results of the nine regression models by crash type weighted by the current distribution of fatalities (light turquoise), not the distribution NHTSA assumes for 2017-2025 based on full ESC penetration.  Full penetration of ESC in the on-road fleet slightly increases the safety penalty from mass reduction, as the NHTSA weighted values (in light blue) are all higher than the unweighted values (in light turquoise).  On the other hand, full ESC penetration reduces the safety penalty from a reduction in footprint, for all vehicle types.

Figures 2.2 through 2.4 show the effect of changes in mass or footprint on risk, by type of crash.  For cars, mass reduction increases risk in all crash types except rollovers and crashes with stationary objects, as shown in Figure 2.2.  A possible explanation for why mass reduction reduces risk in rollovers is that once a vehicle rolls over, a lighter vehicle applies less force on its roof than a heavier vehicle.  It is less clear why mass reduction would reduce risk in crashes with stationary objects.  Because NHTSA assumes that by 2017 ESC will have eliminated many of the fatalities in rollovers and crashes with stationary objects, and these are the only types of crashes in which mass reduction reduces risk, NHTSA's weighted regression results for 2017-2025 show a larger increase in overall risk than the results based on recent crashes (in Figure 2.1).  On the other hand, footprint reduction results in the largest risk increases in rollovers and crashes with stationary objects (Figure 2.2), so removing fatalities in these types of crashes by 2017 will reduce the detrimental effects of footprint reduction (as shown in the light blue columns in Figure 2.1).

Mass reduction in the lighter cars has the biggest increase in risk (5.80%) in crashes with a heavy light truck.  For heavier cars, mass reduction results in generally smaller increases in risk for most types of crashes.  A reduction in car footprint increases risk in all types of crashes, including rollovers and crashes with stationary objects.  In fact, footprint reduction leads to the largest increases in risk in these two crash types (7.79% and 3.99%), followed by crashes with a lighter light-duty truck (3.88%) and with a heavy-duty truck (2.96%).

Figure 2.3 shows the effect of mass and footprint reductions on risk in light trucks.  In general, the effects on risk are smaller for light trucks than for cars, and there are more cases in which mass reduction reduces risk, although the effects are often small and not statistically-significant.  Mass reduction leads to a statistically-significant reduction in risk in lighter truck crashes with objects, and heavier truck rollovers; but (statistically-insignificant) increases in risk in lighter truck rollovers and heaver truck crashes with objects.  As with light cars, the biggest effect of weight reduction in lighter trucks is in crashes with a heavier light truck, with a 4.37% increase in risk.  A reduction in light truck footprint tends to increase risk, although the increases are small and often not statistically-significant.  However, contrary to cars, footprint reduction in light trucks significantly reduces fatality risk in crashes with pedestrians and cyclists, and with heavier light trucks.

Figure 2.2. Effect of mass and footprint reduction on risk in cars, by type of crash

Figure 2.3. Effect of mass and footprint reduction on risk in light trucks, by type of crash

The effect of reductions in mass and footprint on risk in crashes involving CUVs and minivans are shown in Figure 2.4.  The effects from mass reduction tend to be larger in CUVs and minivans than in cars or light trucks, with a greater than 7% reduction in risk in rollovers and a 3.77% reduction in risk in crashes with objects.  Mass reduction in CUVs/minivans has the most detrimental effect on risk in crashes with a light light-duty truck, a 3.69% increase.  The effect of reductions in footprint in CUVs and minivans is similar to that for cars, with a larger, statistically-significant increase in risk in rollovers (10.48%) and crashes with objects (7.34%).  As with cars, NHTSA's assumption of fewer fatalities in rollovers and crashes with stationary objects due to full adoption of ESC by 2017 results in an increase in the effect of mass reduction, but a decrease in the effect of footprint reduction, on risk in CUVs and minivans (light blue columns in Figure 2.1).

Figure 2.4. Effect of mass and footprint reduction on risk in CUVs/minivans, by type of crash

Figures 2.5 and 2.6 compare the effect of mass and footprint reduction on risk with that of the other control variables, for cars.  In terms of other car characteristics, Figure 2.5 indicates that two-door cars increase US fatality risk per VMT by 8%, while TORSO side airbags, automated braking systems (ABS), and electronic stability control (ESC), reduce risk by about 10%.  The driver age variables tend to increase risk, with young male and elderly drivers (male and female) increasing US fatality risk per VMT from 5% to 8%.  Car age causes a small increase in risk, while a brand new car increases risk by 10%, presumably because the driver is unfamiliar with a new car's controls, handling, and/or braking capabilities.  The calendar year variables have a decreasing effect on risk over time, declining from a 6% increase in risk in 2002 to a 13% reduction in risk in 2008.  The calendar year variables are examined in more detail in Section 5.3.

Figure 2.5. Effect of selected control variables on risk, passenger cars

Figure 2.6. Effect of selected control variables on risk, passenger cars

Note that the three vehicle variables of interest, UNDRWT, OVERWT, and FOOTPRINT, all have a much lower effect on risk than almost all of the control variables in Figure 2.5.  For instance, a 100-lb reduction in curb weight for an underweight car is expected to increase risk by 1.4%, while installing ESC would reduce risk by 11.4%.  Therefore, the mass of a lighter car could be reduced by 800 lbs while adding ESC, without increasing fatality risk.

The control variables in Figure 2.6 have a much bigger effect on risk than the mass or footprint reduction variables, or the control variables presented in Figure 2.5.  Male drivers increase US fatality risk per VMT by over 25%, while the three control variables for crash environment, NITE, RURAL, and SPDLIM55, more than triple fatality risk per VMT.  A crash occurring in a high-fatality state carries a 25% higher fatality risk per VMT than a crash in other states.  Since driving on a roadway with a posted speed limit greater than 55 miles per hour increases risk by over 400%, a 0.35% increase in driving on high-speed roads would result in the same increase in fatalities as a 100-lb mass reduction in all cars (1.4% / 400%  = 0.35%).

Figures 2.7 and 2.8 present the effect of the control variables on fatality risk in crashes involving light trucks.  SUVs, and to a lesser extent heavy-duty pickups, have a higher fatality risk than regular pickups.  NHTSA includes two variables identifying approaches to comply with voluntary measures to reduce light truck aggressivity towards cars: BLOCKER1, vertical alignment of bumpers, and BLOCKER2, employment of an additional blocker beam behind the bumper.  These two approaches have about the same effect on reducing risk.  As with cars, risk is higher with young males and elderly drivers.  Brand new light trucks have a lower risk than brand new cars, which is surprising as one would think unfamiliarity with the handling of a light truck would increase the chance of it rolling over.  As with cars, the calendar year variables have a decreasing effect on risk over time, but the decline is much greater, from 22% increase in risk in 2002 to a 16% decrease in risk in 2008.  The calendar year variables are discussed in more depth in Section 5.3.

ESC reduces risk by 18% in light trucks (Figure 2.8) as opposed to only 11% in cars (Figure 2.5), while male drivers increase risk in trucks only 18% but 40% in cars (Figure 2.6).  All-wheel drive (AWD) reduces risk in pickups by nearly 15%.  As in cars, driving at night, in rural areas, and on roadways with high speed limits more than triple the risk in trucks, while driving in high fatality states has a similar increase in risk as in cars (25%).

Figure 2.9 indicates that minivans have a slightly lower fatality risk than CUVs.  For CUVs and minivans, combination airbags result in a larger reduction in risk than side curtain airbags, while torso airbags result in a slight, non-significant increase in risk.  As there is no logical explanation of why torso air bags could increase risk, this result indicates the lack of precision in the regression coefficients for some of the safety technologies, especially in regressions limited to relatively small subsets of the data.  ABS has a bigger reduction in risk (15%) than ESC (4%) for CUVs and minivans, opposite to the results seen for cars in Figure 2.5.  In terms of driver characteristics, young and elderly drivers have the highest increase in risk. The coefficients on the calendar year control variables are smaller than those for light trucks (with the exception of CY2008); these are discussed in more detail in Section 5.3.

The control variables for CUVs and minivans presented in Figure 2.10 are similar to those for cars (Figure 2.6) and light trucks (Figure 2.8).  For all vehicle types, many of the control variables shown in Figures 2.3 through 2.8 have a much greater effect on fatality risk than reductions in vehicle mass or footprint.
Figure 2.7. Effect of selected control variables on risk, light trucks

Figure 2.8. Effect of selected control variables on risk, light trucks

Figure 2.9. Effect of selected control variables on risk, CUVs and minivans

Figure 2.10. Effect of selected control variables on risk, CUVs and minivans

3. Multi-collinearity between vehicle mass and footprint

In the 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.  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 (R[2] of 0.87) than for light trucks (R[2] of  0.65) or CUVs/minivans (R[2] of  0.60).  Figure 3.2 shows the same data as Figure 2.12, but uses six vehicle types.  Here the correlation ranges from over 0.80 for 4-door cars, pickups, and SUVs, to less than 0.70 for CUVs and 2-door cars, to only 0.26 for minivans.  The correlation of 0.65 for all light trucks (pickups and SUVs) combined in Figure 3.1 is improved when these two types of trucks are analyzed separately in Figure 3.2: 0.86 for pickups and 0.81 for SUVs in Figure 3.2.  On the other hand, separating CUVs from minivans improves the correlation between curb weight and footprint for CUVs (0.66) but not for minivans (0.26).  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 0.78.

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

Figure 3.3 compares NHTSA's preferred model, in light blue from Figure 2.1, with two alternative model specifications to test the sensitivity of the results from the preferred model.  The first sensitivity, in dark purple, includes the weight variables in the regression model but excludes the footprint variable; this model tests the effect of mass reduction while allowing footprint to vary with vehicle mass.  This sensitivity increases the risk from a 100-lb mass reduction in cars (from 1.43% to 2.64% for lighter cars, and from 0.48% to 1.94% for heavier cars) and CUVs/minivans (from a 0.47% decrease in risk to a 0.52% increase in risk; however, there is no change in fatality risk in light-duty trucks.  These results are quite similar to those reported by NHTSA in Section 3.7 of the 2011 report; the slight differences are likely due to rounding errors, as well as our reporting of percent changes in risk as probabilities rather than as log-odds, as described above.

Figure 3.3. Effect of reduction in mass or footprint on US fatality risk per VMT, by vehicle type: mass only, footprint only, and both

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 increases the effect of a reduction in footprint on car risk, from a 1.89% increase to a 2.92% increase, but decreases the effect of footprint reduction on CUV/minivan risk, from a 1.73% increase to a 1.26% increase.  Allowing light truck mass to be reduced along with footprint does not change the effect of a reduction in footprint on risk in light trucks.  Figure 3.3 suggests that including both mass and footprint reductions in the same regression model somewhat reduces the effect of both variables in cars and CUVs/minivans, but has no effect on the variables for light trucks.

Figures 3.4 through 3.6 show the effect of these two sensitivities by crash type; in contrast to Figures 2.2 through 2.4, the figures indicate that including only mass or footprint in the regression models reduces or eliminates any reduction in risk in a particular crash type, particularly for mass reductions in car rollover and object crashes, and for mass or footprint reductions in CUV/minivan crashes.

Figure 3.4. Effect of reduction in car mass or footprint on US fatality risk per VMT, by crash type

Figure 3.5. Effect of reduction in light-duty truck mass or footprint on US fatality risk per VMT, by crash type

Figure 3.6. Effect of reduction in CUV/minivan mass or footprint on US fatality risk per VMT, by crash type

In its 2011 analysis NHTSA examined the relationship between curb weight and fatality risk for deciles of vehicles with roughly the same footprint.  Figure 3.7 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 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 a mass reduction would be harmful and increase fatality risk.

Figure 3.7. Range in curb weight for the footprint deciles, by vehicle type

Table 3.1 replicates this analysis and results, and includes the number of footprint deciles in which the coefficient on vehicle mass is statistically significant, for each combination of vehicle and crash type.  There are four columns for each vehicle type in Table 3.1; the first two indicate the number of footprint deciles in which a reduction in vehicle mass increases risk, 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 a reduction in vehicle mass reduces risk, and the number that are statistically significant.  For example, in car rollover crashes, mass reduction increases risk in only three footprint deciles, and none of those increases is statistically significant.  However, mass reduction reduces risk in seven footprint deciles in car rollover crashes, and four of those seven are statistically significant.  Table 3.1 indicates that mass reduction increases risk in only a small number of car rollover crashes and crashes with a stationary object.  On the other hand, mass reduction reduces risk in light truck crashes with cars for seven of the footprint deciles, and several of these reductions (four in crashes with light cars, three in crashes with heavy cars) are statistically significant.  For CUVs and minivan crashes with heavy cars, mass reduction increases risk in eight deciles, with three of those increases being statistically significant.

Table 3.1. Number of footprint deciles in which mass reduction increases or decreases fatality risk, by vehicle and crash type
Crash type
                                     Cars
                                 Light trucks
                                 CUVs/Minivans

Number of deciles with increasing risk
Number of deciles with estimates that are statistically significant
Number of deciles with decreasing risk
Number of deciles with estimates that are statistically significant
Number of deciles with increasing risk
Number of deciles with estimates that are statistically significant
Number of deciles with decreasing risk
Number of deciles with estimates that are statistically significant
Number of deciles with increasing risk
Number of deciles with estimates that are statistically significant
Number of deciles with decreasing risk
Number of deciles with estimates
that are statistically significant
1: Rollovers
                                       3
                                       0
                                       7
                                       4
                                       6
                                       3
                                       4
                                       2
                                       4
                                       0
                                       6
                                       2
2: w/object
                                       4
                                       0
                                       6
                                       3
                                       5
                                       0
                                       5
                                       0
                                       6
                                       0
                                       4
                                       1
3: w/ped etc.
                                       6
                                       2
                                       4
                                       2
                                       5
                                       1
                                       5
                                       1
                                       4
                                       0
                                       6
                                       0
4: w/HDT
                                       7
                                       0
                                       3
                                       0
                                       6
                                       2
                                       4
                                       0
                                       6
                                       2
                                       4
                                       0
5: w/lgt car
                                       4
                                       0
                                       6
                                       0
                                       3
                                       1
                                       7
                                       4
                                       4
                                       1
                                       6
                                       0
6: w/hvy car
                                       5
                                       1
                                       5
                                       0
                                       3
                                       0
                                       7
                                       3
                                       8
                                       3
                                       2
                                       1
7: w/lgt LT
                                       5
                                       1
                                       5
                                       1
                                       6
                                       0
                                       4
                                       0
                                       7
                                       0
                                       3
                                       0
8: w/hvy LT
                                       7
                                       1
                                       3
                                       0
                                       9
                                       2
                                       1
                                       0
                                       4
                                       0
                                       6
                                       2
9: Other
                                       7
                                       1
                                       3
                                       1
                                       5
                                       1
                                       5
                                       1
                                       6
                                       1
                                       4
                                       1

The data in Table 3.1 give no information on the size of the effect of mass reduction on risk in the footprint deciles.  Figures 3.8 through 3.10 show the percent change in 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 3.8 indicates that mass reduction reduces risk in car rollover crashes (shown as blue diamonds) in seven deciles, by over 10% in footprint deciles six and seven, and by over 20% in footprint decile eight.  Figure 3.10 indicates that mass reduction in CUVs/minivans reduces risk in crashes with a heavy light-duty truck (shown as purple circles) in five of the footprint deciles, and that these reductions are quite large (over 45%), and statistically significant, for the largest two deciles of CUVs/minivans.  Figures 3.8 through 3.10 suggest that there are no consistent trends in the effect of mass reduction on risk when vehicles are grouped by footprint decile.

Figure 3.8. Effect of car mass reduction on fatality risk, by footprint decile and crash type

Figure 3.9. Effect of light truck mass reduction on fatality risk, by footprint decile and crash type

Figure 3.10. Effect of CUV/minivan mass reduction on fatality risk, by footprint decile and crash type

4. Fatality risk by vehicle model

Unless noted otherwise, all fatality risks in this report are societal risk, including fatalities in the case vehicle and any crash partners, and include not only driver fatalities but passenger fatalities as well.  In this section we examine the variance in societal fatality risk by vehicle model, both before and after accounting for the vehicle, driver and crash variables NHTSA includes in its regression models. Figure 4.1 plots unadjusted US fatality risk per VMT against average curb weight, with vehicles grouped into 100-lb increments of vehicle curb weight.  Figure 4.1 indicates that, although risk does tend to decrease linearly as curb weight increases, there remains a fair degree of variability, particularly for trucks and CUVs/minivans, as indicated by the R[2] values below 0.50.  Note that the relationship between mass and fatality risk for light trucks changes above 5,900 lbs, where risk begins to increase as mass increases; we plot these heavier trucks, which are predominately (3/4)- and 1-ton pickups, separately in Figure 4.1.

Figures 4.2 through 4.4 show the relationship between unadjusted risk and mass by more detailed vehicle type.  Figure 4.2 indicates that the relationship between curb weight and fatality risk is weaker for 4-door cars than for 2-door cars.  Figure 4.3 suggests that for large pickups risk increases as curb weight increases.  And Figure 4.4 indicates that the relationship between risk and curb weight is strongest for minivans.

Figure 4.1. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, by vehicle type

Figure 4.2. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, passenger cars

Figure 4.3. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, light trucks

Figure 4.4. Relationship between US fatality risk and curb weight, with vehicles grouped into 100-lb increments of curb weight, CUVs and minivans

It is possible that the relationship between vehicle mass and fatality risk is greater in certain types of crashes.  Figure 4.5 presents the relationship by vehicle type for fatality 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.  Although the relationship between vehicle mass and risk is quite consistent among vehicle types, the strength of this relationship is no greater in crashes with stationary objects than in all types of crashes (Figure 4.1), and in the case of light trucks, the relationship is weaker in crashes with stationary objects.

Note that, for a given vehicle weight, light trucks have a higher fatality risk in crashes with stationary objects than cars, and an even higher rate than CUVs and minivans. Since there are no crash partner fatalities in crashes with stationary objects, we suspect that light trucks have a higher risk than cars in Figure 4.5 because of their tendency to rollover, their increased use on more dangerous rural roads, and perhaps more passenger fatalities in light trucks than in cars.

Figure 4.5. Relationship between US fatality risk in crashes with stationary objects and curb weight, by vehicle type

Figures 4.1 through 4.5 show that grouping vehicles into 100-lb mass increments suggests that fatality risk decreases as mass increases, for most vehicle types (the exceptions are large pickups and fullsize vans).  Figure 4.6 shows the relationship between vehicle mass and unadjusted fatality risk by vehicle model.  Only 275 models with at least 10 billion VMT, or at least 100 fatalities, are included (106 car models, 131 light truck models, and 38 CUV/minivan models); these models represent about 90% of all fatalities, vehicle registration-years, and VMT.  Here we see that fatality risk declines with increasing mass for cars, and at a smaller rate for CUVs and minivans, while risk increases as mass increases for light trucks.  However, although risk declines with increasing car weight, the relatively low R[2] (0.18) indicates that this is not a very strong relationship; there is a large range in risk for individual vehicle models at a given weight.  For example, the model labeled as A in the figure, which weighs 2,879 lbs, has a fatality risk of 331 per 10 billion VMT, while model B, which weighs essentially the same (2,870 lbs) has a fatality risk of only 96.

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-fatality states) by vehicle model may explain some of the large range in risk by vehicle weight.  To account for these various variables, we reran NHTSA's 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 risk for each induced exposure vehicle from the 13 state crash databases.  We first 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 log odds of fatality per vehicle.  We then multiplied these odds by the VMT weighting each induced exposure vehicle represents, to obtain the number of predicted fatalities in each induced exposure vehicle, and summed across vehicle make and model.  Finally we divided the total number of predicted fatalities in each make and model by their total VMT, to obtain predicted risk, the number of predicted fatalities per ten billion VMT. We exclude footprint as well as mass in the predicted risks we calculate from the NHTSA regressions, as the two vehicle attributes are moderately correlated.

Figure 4.7 shows the risks predicted by the regression model coefficients for all control variables except vehicle mass and footprint. Figure 4.7 indicates that, even after controlling for the all of the driver, crash, and vehicle variables NHTSA used in their logistic regression model, except vehicle mass and footprint, there still is a large range in fatality risk across vehicle models of similar weight, for all three vehicle types.

Figures 4.8 shows the remaining residual, or unexplained, risks after accounting for all variables except vehicle mass and footprint.  In essence Figure 4.8 shows that there is no relationship between vehicle mass and risk, after accounting for driver, crash and all other vehicle attributes.

Figure 4.6. US fatality risk per VMT and curb weight, by vehicle model

Figure 4.7. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint, vs. curb weight

Figure 4.8. Residual US fatality risk after accounting for all driver, crash, and vehicle variables except mass and footprint, vs. curb weight

Figures 4.9 through 4.11 show similar plots for 106 car models, with 2- and 4-door cars shown separately.  The figures indicated that two-door car models tend to have higher risk than 4-door models. The model labeled C provides an example of the values shown in Figures 4.9 through 4.11.  This model has an actual risk of 272 fatalities per ten billion VMT, while the NHTSA regression model predicts that a vehicle with the same driver, crash location, and vehicle attributes (except mass and footprint) would have a risk of only 248 fatalities per ten billion VMT.  In other words, after accounting for all of the variables except vehicle mass and footprint, this vehicle model has a higher actual risk than predicted by the NHTSA regression model.  This remaining residual risk, 24 fatalities per ten billion VMT, can be attributed to the model's mass and footprint relative to other car models, as well as other, unexplained differences among vehicles.

Figure 4.10 indicates that some vehicles on the road today have the same, or lower, risk than models that weigh substantially more, and are substantially larger in terms of footprint.  For example, after accounting for differences in driver age and gender, safety features installed, and crash times and locations, model D, which weighs 3,367 lbs and has a footprint of 46.6 square feet, has an expected fatality risk over twice that of model E, which weighs 3,346 lbs and has a footprint of 43.8 square feet (248 vs. 106 fatalities per ten billion VMT).  Similarly, model F (3,107 lbs, 43.9 sq ft, 196 fatalities per VMT) has a predicted fatality risk nearly twice that of model G (3,111 lbs, 41.4 sq ft, 111 fatalities per VMT), while model H (2,599 lbs, 42.3 sq ft, 219 fatalities per VMT) has a predicted risk 50% higher than that that of model I (2,500 lbs 41.8 sq ft, 141 fatalities per VMT).  Models E, G, and I all have risk similar to or lower than that of
Figure 4.9. US fatality risk per VMT vs. curb weight, car models

Figure 4.10. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, car models

Figure 4.11. Residual US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, car models

models J and K, which are both substantially larger and heavier (J: 3,909 lbs, 52.5 sq ft, 126 fatalities per ten billion VMT; K: 3,990 lbs, 48.7 sq ft, 135 fatalities per ten billion VMT).  Clearly differences in vehicle design can, and already do, mitigate any theoretical safety penalty from reduced mass.  The fact that NHTSA attributes the change in its regression results between the 2003 study and the 2011 study in part to the redesign or removal of certain smaller and lighter models of poor design confirms that vehicle design can overcome any perceived safety penalty in lightweight or small vehicles.  Figure 4.10 suggests that manufacturers can continue to design vehicles that overcome any theoretical safety penalty from reducing mass in order to improve fuel economy and reduce greenhouse gas emissions.

Figure 11 indicates that, after accounting for all variables except mass and footprint, there is no correlation between the remaining residual risk and curb weight.

Figures 4.12 and 4.13 show the actual and predicted risks vs. curb weight for pickup trucks and truck-based SUV models.  Risk declines with increasing curb weight for SUVs, but increases with increasing weight for pickups.  However, the correlations between fatality risk and curb weight are weak, even after accounting for all of the driver, crash, and other vehicle variables in the NHTSA logistic regression model.  Figure 4.14 indicates that there is no correlation between the residual risk and weight, after accounting for all variables except for mass and footprint.

Risk, predicted risk, and residual risk for CUV and minivan models are shown in Figures 4.15 through 4.17.  There is a reasonable correlation between risk and mass for CUVs (Figure 4.15); however, the correlation decreases after accounting for all variables except mass and footprint (Figure 4.16).  After accounting for all variables except vehicle mass and footprint, there is no correlation between residual risk and CUV curb weight, while residual risk increases with increasing minivan weight, as shown in Figure 4.17.

It is possible that other differences in vehicle models, particularly other aspects of vehicle design or subtle differences in driver behavior, explain some of the remaining variation in risk for vehicles of similar weight.

Figure 4.12. US fatality risk per VMT vs. curb weight, light truck models

Figure 4.13. Predicted US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, light truck models

Figure 4.14. Residual US fatality risk per VMT after accounting for all driver, crash, and vehicle variables except mass and footprint vs. curb weight, light truck models

Figure 4.15. US fatality risk per VMT vs. curb weight, CUV/Minivan models

Figure 4.16. Predicted US fatality risk per VMT after accounting for all driver, crash and vehicle variables except mass and footprint vs. curb weight, CUV/Minivan models

Figure 4.17. Residual US fatality risk per VMT after accounting for all driver, crash and vehicle variables except mass and footprint vs. curb weight, CUV/Minivan models

Table 4.1 summarizes the relationships between predicted and residual fatality risk and vehicle curb weight that are presented in Figures 4.6 through 4.17.  In addition to the correlation between fatality 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 fatality 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 fatality risk and vehicle weight, i.e. where risk decreases as weight decreases, are shown in red in the table. Cases where the correlation between risk and weight by vehicle model exceeds 0.30 are shown in blue.  Table 4.1 indicates that fatality risk consistently increases as weight increases for heavy-duty pickups, and that in some cases the correlation between risk and weight is rather high (R[2] of 0.62 for actual fatality risk, and 0.43 for predicted risk after accounting for all variables except vehicle mass and footprint).  In these two cases the slope of the regression line is also high, between 7% and 11%.  For CUVs, the correlation between actual and predicted fatality risk and mass is moderate, with an R[2] of over 0.30, with risk increasing about 3% for every 100-lb reduction in mass.

Table 4.1. Relationship between actual, predicted, and residual fatality risk, 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 US fatality risk
                                Predicted risk
                                 Residual risk

                                                                           R[2]
                                                                          Slope
                                                                           R[2]
                                                                          Slope
                                                                           R[2]
                                                                          Slope
Cars
                                                                           0.16
                                                                           4.7%
                                                                           0.09
                                                                           2.9%
                                                                           0.05
                                                                           1.7%
Light trucks
                                                                           0.01
                                                                          -0.5%
                                                                           0.06
                                                                          -1.4%
                                                                           0.03
                                                                           0.7%
CUVs/minivans
                                                                           0.11
                                                                           2.0%
                                                                           0.13
                                                                           2.1%
                                                                           0.00
                                                                          -0.1%
2-dr cars
                                                                           0.16
                                                                           6.5%
                                                                           0.12
                                                                           3.9%
                                                                           0.03
                                                                           2.4%
4-dr cars
                                                                           0.12
                                                                           3.4%
                                                                           0.04
                                                                           1.6%
                                                                           0.07
                                                                           1.7%
Small pickups
                                                                           0.03
                                                                           1.1%
                                                                           0.00
                                                                          -0.2%
                                                                           0.03
                                                                           0.8%
Heavy-duty pickups
                                                                           0.62
                                                                         -10.9%
                                                                           0.43
                                                                          -6.7%
                                                                           0.12
                                                                          -4.2%
SUVs
                                                                           0.08
                                                                           2.1%
                                                                           0.05
                                                                           1.1%
                                                                           0.04
                                                                           1.0%
CUVs
                                                                           0.37
                                                                           3.5%
                                                                           0.33
                                                                           3.1%
                                                                           0.01
                                                                           0.4%
Minivans
                                                                           0.00
                                                                           0.1%
                                                                           0.09
                                                                           2.9%
                                                                           0.13
                                                                          -2.8%
Cars < 3106
                                                                           0.05
                                                                           4.4%
                                                                           0.02
                                                                           2.3%
                                                                           0.02
                                                                           2.1%
Cars > 3106
                                                                           0.16
                                                                           4.7%
                                                                           0.09
                                                                           2.9%
                                                                           0.05
                                                                           1.7%
LTs < 4594
                                                                           0.01
                                                                          -0.5%
                                                                           0.06
                                                                          -1.4%
                                                                           0.03
                                                                           0.7%
LTs > 4594
                                                                           0.11
                                                                           2.0%
                                                                           0.13
                                                                           2.1%
                                                                           0.00
                                                                          -0.1%
CUVs/ minivans
                                                                           0.16
                                                                           6.5%
                                                                           0.12
                                                                           3.9%
                                                                           0.03
                                                                           2.4%

Table 4.2 presents the same information as Table 4.1, but for the relationship between risks and vehicle footprint.  As in Table 4.1, fatality risks for heavy-duty pickups consistently increase as footprint increases, between 5% and 10%.  However, the correlation between actual risk and footprint by heavy-duty pickup model (0.43) is not as high as with mass (0.62 in Table 4.1).  And the correlations between actual and predicted risk and CUV/minivan footprint (0.08 and 0.06, respectively) are much lower than the correlations with mass (0.37 and 0.33 in Table 4.1).  This is somewhat surprising, as Figure 3.3 indicates that footprint reduction has a relatively large (detrimental) effect on CUV and minivan fatality risk, while mass reduction has a smaller, beneficial effect.  However, the correlation between footprint and risk for CUVs and minivans shown in Table 4.2 is quite low.

Table 4.2. Relationship between actual, predicted, and residual fatality risk, 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 US fatality risk
                                Predicted risk
                                 Residual risk

                                                                           R[2]
                                                                          Slope
                                                                           R[2]
                                                                          Slope
                                                                           R[2]
                                                                          Slope
Cars
                                                                           0.11
                                                                           5.2%
                                                                           0.04
                                                                           2.6%
                                                                           0.07
                                                                           2.6%
Light trucks
                                                                           0.08
                                                                          -1.7%
                                                                           0.24
                                                                          -2.7%
                                                                           0.05
                                                                           0.9%
CUV/minivans
                                                                           0.00
                                                                           0.1%
                                                                           0.00
                                                                           0.0%
                                                                           0.00
                                                                           0.1%
2-door cars
                                                                           0.12
                                                                           8.5%
                                                                           0.04
                                                                           3.1%
                                                                           0.07
                                                                           5.3%
4-door cars
                                                                           0.06
                                                                           3.2%
                                                                           0.01
                                                                           0.8%
                                                                           0.08
                                                                           2.4%
Small pickups
                                                                           0.02
                                                                           0.8%
                                                                           0.00
                                                                          -0.3%
                                                                           0.07
                                                                           1.1%
Heavy-duty pickups
                                                                           0.43
                                                                         -10.2%
                                                                           0.19
                                                                          -5.0%
                                                                           0.16
                                                                          -5.2%
SUVs
                                                                           0.05
                                                                           2.1%
                                                                           0.00
                                                                           0.3%
                                                                           0.07
                                                                           1.7%
CUVs
                                                                           0.08
                                                                           2.2%
                                                                           0.06
                                                                           1.9%
                                                                           0.01
                                                                           0.4%
Minivans
                                                                           0.17
                                                                           4.3%
                                                                           0.06
                                                                           3.1%
                                                                           0.02
                                                                           1.2%
Cars < 3106
                                                                           0.05
                                                                           5.8%
                                                                           0.01
                                                                           1.8%
                                                                           0.05
                                                                           4.0%
Cars > 3106
                                                                           0.02
                                                                          -2.5%
                                                                           0.02
                                                                          -2.4%
                                                                           0.00
                                                                          -0.1%
LTs < 4594
                                                                           0.04
                                                                          -1.8%
                                                                           0.22
                                                                          -3.0%
                                                                           0.04
                                                                           1.3%
LTs > 4594
                                                                           0.40
                                                                          -5.6%
                                                                           0.53
                                                                          -6.0%
                                                                           0.00
                                                                           0.4%
CUVs/ minivans
                                                                           0.00
                                                                           0.1%
                                                                           0.00
                                                                           0.0%
                                                                           0.00
                                                                           0.1%

5. Sensitivity of NHTSA results to data used and model specification

In this section we examine the sensitivity of the NHTSA results on the effect of mass and footprint on US fatality risk per VMT.  We examine the effect of calculating risk of a fatal crash (as opposed to risk of fatality), and risk of fatality per non-culpable vehicle; and how the effect of mass or footprint reduction changes after accounting for vehicle manufacturer, after excluding the calendar year control variables, and after excluding crashes involving alcohol or drug use, or otherwise bad driving behavior.

5.1. Alternative measures of exposure

Figure 5.1 compares the results for US fatality risk per VMT using NHTSA's preferred regression model specification (in light blue) with two other measures of US fatality risk.  The first measure is the risk of a fatal crash, rather than the risk of all fatalities that occurred in the crash. In other words, the fatal crash cases are not weighted by the total number of fatalities, either in the case vehicle or in its crash partner, as they are in NHTSA's preferred model.  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 5.1, this alternative measure of risk, the risk of a fatal crash per ten billion VMT (shown in dark orange) increases the detrimental effect of mass reduction on risk in cars, from 1.43% to 1.84% for lighter than average cars, and from 0.48% to 0.86% for heavier cars.  On the other hand, analyzing risk of fatal crash per VMT has essentially no impact on the effect of mass reduction in light trucks or CUVs/minivans.

Figure 5.1. Effect of mass and footprint reduction on US fatalities per VMT, fatal crashes per VMT, and fatalities per induced exposure crash, by vehicle type

The statistical uncertainties around the point estimates of the effect of mass reduction on risk per fatal crash in Figure 5.1 are only slightly higher than the uncertainties around the risk per fatality point estimates, in part because on average there are only 1.16 fatalities per fatal crash (123,324 fatalities in 106,613 fatal crashes).

We also investigate the effect NHTSA's weighting of the induced exposure crashes has on its regression results.  NHTSA uses the non-culpable vehicle in two-vehicle crashes from the 13 states as its measure of induced exposure.  It then creates weights so that the crashes from the 13 states can first be scaled up to represent national vehicle registration-years, and then multiplied by average annual VMT by vehicle age and type to arrive at national VMT.  In the light orange columns in Figure 5.1 we exclude these two calculations, and examine US fatality risk per induced exposure crash from the 13 states (rather than VMT).  Using induced exposure crashes as the measure of exposure changes the sign of the effect of car mass reduction, and light truck mass and footprint reduction, on risk; for all vehicle types, mass reduction actually reduces fatality risk given that a crash occurs.  Footprint reduction in light trucks similarly reduces fatality risk per crash, while it slightly increases risk per crash in cars and CUVs/minivans.

The effect of analyzing fatality risk per crash shown in Figure 5.1 is approximate, as total U.S. fatalities are combined with induced exposure crashes for only 13 states.  A more exact analysis would utilize both fatalities and crashes from the same states.  We will perform just such an analysis in the near future, using fatality, serious injury, and crash data from the same source, the police-reported crashes from 13 states.

5.2. Vehicle manufacturer

The analysis by vehicle model in Section 4 indicates that the variables included in the NHTSA preferred model only account for 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 18 dummy variables based on the vehicle nameplate manufacturer. 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, both in fatalities and VMT.  The six Chrysler brands (Jeep, Chrysler, Dodge, Plymouth, AM General and Sprinter) and the three Ford brands (Ford, Lincoln, Mercury) were combined in a single Chrysler and Ford category.  The luxury brands of Toyota, Honda, and Nissan (Lexus, Acura, and Infiniti, respectively) were treated as separate manufacturers.  A small number of low-volume manufacturers were grouped into a separate Other manufacturer category.

Figure 5.2 compares the effect of adding variables for each of the 18 manufacturers (shown in red) in NHTSA's preferred regression model specification (shown in light blue).  For cars and light trucks, accounting for vehicle manufacturer increases the effect of mass reduction, but decreases the effect of footprint reduction, on risk.  Accounting for vehicle manufacturer in the CUV/minivan regression models makes mass reduction detrimental, and footprint reduction slightly beneficial.

Figure 5.2. Effect of mass and footprint reduction on US fatality risk per VMT, after controlling for vehicle manufacturer, by vehicle type

5.3. CY variables

One interesting effect is the reduction in risk over time, as indicated in the calendar year control variables.  This is consistent for each vehicle type, but largest for light trucks, as shown in Figure 5.3.  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.  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 5.4 indicates that the effect of the calendar year variables on light truck risk is strongest for crashes with light cars and lighter light-duty 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 (although not as large) decreases over time in light truck risk in rollovers, crashes with heavy-duty trucks and heavy cars, and other (mostly multi-vehicle) crashes.  NHTSA believes that the decline in light truck rollover risk over time may be the result of manufacturers increasing static stability factor or other aspects of light truck design to reduce their likelihood to rollover.  However, cars and CUVs/minivans show a similar trend in reduced rollover risk over time (cars and CUVs/minivans also show similarly large reductions in risk over time in crashes with light cars and light LTVs).  NHTSA suspects that the risk associated with light trucks involved in crashes with heavy-duty trucks decreases over time because heavy-duty truck activity decreases as the economy falters.  The economic recession in 2008 may have reduced the number of heavy-duty trucks traveling roadways, and thus available as potential crash partners with light-duty vehicles.

Figure 5.3. Effect of calendar year variables on risk, by vehicle type

Figure 5.4. Effect of calendar year variables on light truck risk, by crash type

In its 2003 report, NHTSA included calendar year variables for light trucks, but not for cars, because "light trucks grew in weight throughout the 1990's but cars did not" (NHTSA did not analyze CUVs/minivans as a separate vehicle class in the 2003 study).  Figure 5.5 shows the weighted average coefficients on the calendar year variables from the 2003 analysis (taken from the tables in Section 4.3 of that report).  Note that the effect of the calendar year variables on risk is much smaller than in the 2011 analysis, and there is not the consistent decrease of the effect of calendar year on risk in later years as in the 2011 analysis.

Figure 5.5. NHTSA 2003 effect of calendar year variables on risk, by vehicle type

The calendar year effect for light trucks is strongest on crashes with cars and other light trucks in the 2003 NHTSA analysis, as shown in Figure 5.6.  However, calendar year increases the risk in crashes with cars, but decreases the risk in crashes with another light truck.  In addition, there is no consistent trend in the variables over time.

Figure 5.6. NHTSA 2003 effect of calendar year variables on light truck risk, by crash type