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Quantitative analysis of policy decisions
Accid. Anal. & Prey.Vol.12,pp.41-53 © PergamonPressLtd. 1980.Printedin GreatBritain
0001--457518010301-00411502.0010
QUANTITATIVE ANALYSIS OF POLICY DECISIONS WILLIAM L . CARLSON Department of Economics, St. OLaf College, Northfield, MN 55057, U.S.A. (Received 26 January 1979; in revised [orm 15 July 1979)
Abstraet--The use of quantitative models for highway safety policy analysis is discussed. The importance of interaction between managers and model analysts is emphasized for the development and application of these models. Two examples are presented. First, the trade-off between injury cost and fuel savings as a function of vehicle weight reduction is analyzed. Second, passive restraint effectiveness and its interaction with vehicle size is studied. INTRODUCTION
Public policy decisions can be guided by a comprehensive structured analysis of specific policy questions. Essentially such an analysis would utilize a model that includes relationships between variables that are important for policy analysis. Models may be developed using a variety of methodologies. Models and the process of their development assist policy makers by focusing attention on important variables. The model analysis should be conducted with policy decision makers taking an active role in formulating questions and providing critical evaluation of the results. Such a process requires open communication between the model analyst and the policy maker. Policy makers need to discuss openly the political and the nonquantifiable issues associated with a policy decision. Model analysts must attempt to structure the quantitative results given these other issues. Thus, the process requires acceptance and active involvement by policy makers and an awareness of the problem context by model analysts. The need for involvement of policy makers and for problem oriented model analyses cannot be over emphasized. There is a clear analogy to the experience in the private sector. An excellent paper by Hayes and Nolan (1974), which appeared in the Harvard Business Review, presents an overview of the corporate experience with models for analysis and decision making. During the late 1950s and early 1960s, operations researchers worked on small models directed toward specific management problems. These efforts were reasonably successful. Based upon the early success management scientists began to develop very large corporate models that were expected to provide comprehensive analysis for a wide variety of corporate problems. Unfortunately the models tended to be developed by modelers with little input from operating management. These mathematically elegant models became difficult for managers to understand. In addition, the models required large expensive data bases to provide necessary inputs. Communications between analysts and managers broke down. The manager was left with promises that additional research and finetuning would produce the ideal model. Answers that came from the model were often too late or were conditional on narrow assumptions about the operating environment. As a result many firms abandoned large modeling efforts. A third generation approach, that is evolving, is based upon the previous experiences and a more realistic view from managers and analysts. Smaller models are developed for solving specific problems. Models are developed by ad hoc project teams that include managers, systems analysts, and management scientists. Team members tend to have broad experience in both operating management positions and analyst positions. This integrated approach has led to useable problem solutions and to a better understanding of the corporate subsystems by managers. In many cases the most important benefit from the process was ~ better understanding by management. This paper presents examples of analyses based upon a crash injury prediction model (Carlson, 1979) that can be used to guide automobile safety policy. The injury prediction model was developed using data from in depth crash investigations and technical inputs from persons 41
42
W . L . CARLSON
who understand crash injury mechanisms. There are two important objectives of this paper. First, the benefits of utilizing an analysis process that is based upon a comprehensive model are demonstrated. Second, the results of two analyses are presented as contributions to the highway safety research literature. The methodology presented here can be used with other comprehensive models. Analyses of the same question using other models make important contributions to the total information available for policy analysis. Every model includes certain assumptions and simplifications. Therefore, analyses based upon several different models would tend to reduce any biases that might be associated with a given model.
INJURY PREDICTION MODEL
The model used in this study was presented in detail by Carlson (1979). Variables and their functional form used in the model were specified using a broad base of previous crash injury research. Coefficients in the model were estimated using two stage least squares applied to data in the Crash Performance Injury Report (CPIR) file maintained by the Highway Safety Research Institute at the University of Michigan. The data used for the model includes crashes involving passenger cars, pickups, and vans for model years 1969-75. Interested readers are referred to the previous paper for a detailed discussion of the model development process. The model has two phases. In the first phase the expected Abbreviated Injury Score (AIS) is estimated, for a vehicle occupant, using a set of crash variables. The second phase uses the expected AIS to estimate the severe injury rate and the death rate given a towaway crash. The final phase 1 model, which assumed that 8.4% of the occupants were restrained, is: 17"= - 0.80 + 0.093A V~ + 0.014A + 0.24D + 0.28RF - 0.16A W5 - 0.22A W6 - 0.33A W7 - 0.40A W8 (0.0028)
(0.00095)(0.044) (0.047) (0.058)
(0.053)
(0.054)
(0.063). (I)
Where the numbers below the coefficients ( ) are the coefficient standard errors and f" is the expected AIS, A V1 is the change in velocity at impact, A is the occupant age, D is 1 if the occupant is the driver and 0 otherwise, RF is I if the occupant is a front seat passenger and zero otherwise, and A Wr indicates the vehicle weight group according to the following ranges:
A W5 = 1 A W6 = 1 A W7 = 1 A W8 = 1 A WK = 0
Vehicle weight range 2200-2899 lb. 2900-3599 lb. 360(04299 lb. greater than 4299 lb. else (K = 5. . . . . 8).
A key variable for predicting injury severity was crash severity measured, in two vehicle crashes,
W2
A V1 - W1 +--~2 ~/( Vl2 + V22 + 2 V, V2 cos a). Where, W1 is the weight of the case vehicle, W2 is the weight of the other vehicle, VI is the impact velocity of the case vehicle, V2 is the impact velocity of the other vehicle, and a = Ol- 02.
(2)
Quantitative analysis of policy decisions
43
Where
01 is the reported direction of the principal impact for vehicle 1 and, 02 is the reported direction of the principal impact for vehicle 2. Notice that when vehicles of unequal weight collide the lighter vehicle absorbs a higher A V that is inversely related to the relative vehicle weights. The model contains two components, one for unrestrained occupants, and the other for occupants with seat belts. The model for occupants wearing seat belts is, 1~"-- - 0.79 + 0.094A ~', + 0.0083A + 0.11D + 0.32R¢ - 0.08A W5 - 0.15A W6 - 0.18A W7 - 0.28A W8, (0.0055)
(0.002)
(0.13)
(0.14)
(0.12)
(0.11)
(0.11)
(0.13) (3)
and for occupants not wearing seat belts the model is, 17 = - 0.80 + 0.0932~ ~', + 0.015A + 0.25D + 0.28R s - 0.17A W5 - 0.23A W6 - 0.34A W7 - 0.41A W8 (0.0030)
(0.001)
(0.047)
(0.050)
(0.062)
(0.057)
(0.058)
(0.067). (4)
Equations (3) and (4) are linear combinations of injury prediction equations fitted for each of the crash configurations defined in Table 1. Readers interested in the equations by crash configuration should see Carlson (1979). The relative weights for each crash configuration were obtained from the National Crash Severity Study (NCSS) data file and are presented in Table 1. Equation (1) is a linear combination of eqns (3) and (4). The 8.4% restrained occupants was obtained from the NCSS data (Hedlund, 1979).
Table 1. Percentageof vehicles in crashes Crash Configuration
Percent of Vehicles (~i)
1.
Head-on
12.7%
2.
Side-impact--striking
22.4Z
3.
Side-impact--struck right
ii.2%
4.
Side-lmpact--struck left
11.2%
5.
Rear-impact--striking
I0.7%
6.
Rear-impact--struck
I0.7%
7.
Single-vehlcle--ro ii over
8.
Single-vehicle--fixed object
2.9% 18.3% I00.0%
These percentageswere obtainedfrom the NationalCrash SeverityStudyas of March, 1979(Hedlund, 1979).Tha assistanceof Dr. James Hedlundof NHTSA in providing these data is gratefully acknowledged.
Alternative forms for eqns (1), (3), and (4) could be obtained by using different weights. For example, models were also obtained using proportions by crash configuration for United States fatal crashes and for North Carolina accidents. In both of those cases the final models (eqns (1), (3) and (4)) were essentially unchanged and therefore the alternative models are not presented. In phase 2 the expected AIS is used as input to models which compute estimated fatality
44
W . L . CARLSON
and severe injury rates. The probability of a fatality is estimated using, Z, = O;
(17 <_ 1.38) (1.38 < 12 < 5.62)
2, : 0.031 - 0.086 12 + 0.046 I22; (0.O4O) ZI = 1.0;
(O.042)
(5)
(O.Oll)
( 12 _>5.62).
Where, 2, is the estimated probability of a fatality for a towaway crash given Y, 12 is the estimated expected AIS from phase 1, and the numbers below the coefficients are the coefficient standard errors. Similarly the probability of a serious injury, overall AIS > 2, is estimated using, 22=0;
(17-<0.78) (6)
22 : - 0.054 + 0.038 12 + 0.040 I;'2; (0.78 < 12 < 4.67) (0.063)
(0.067)
(0.017)
22 = 1.0; (12 -> 4.67). Where Z2 is the estimated probability of a serious injury for a towaway crash given 12, and the other quantities are as defined above. Examination of eqns (5) and (6) indicates that fatal and serious injuries increase quadratically with expected AIS. The probability of injuries with overall AIS equal to 1 or 2 did not change with I7. This occurred because increased 17 was associated with AIS 1 or 2 injuries moving to AIS greater than 2 and these were "replaced" by non injured occupants who suffered AIS 1 or 2 injuries. Since 17 is a linear function of variables such as A V, occupant age, vehicle weight, etc. we see that severe injuries vary quadratically with the crash injury predictor variables in eqn (1). Policy decisions that operate on the injury prediction variables in the model operate to increase or decrease serious injury and death rates. Other analyses would be necessary for policy decisions that influence property damage. Before policy analysis begins it is necessary to verify that the model adequately represents reality with respect to the variables of interest. The model presented here was validated by first comparing the predicted effect of model variables with other research. Next the model was used to predict severe injury and death rates for a new accident population. That exercise demonstrated that the model does predict correctly. Details of the verification procedure are contained in Carlson (1979). A second test of the model was conducted by using more recent data from the NCSS data file discussed previously. Table 2 presents a comparison of predicted and observed fatality and Table 2. Driver fatal and severe injury prediction for national crash severity study (NCSSI sampler SEVERE INJURY AV
!'h'dian
Subgroup 0 -
AV
Probability of AV
Expl,ctcJ A]5
(\)
PA]ALIIY Predicted
P~\TI[
(ZI)
Observed
(A]S Predicted
(Z2)
RATE
> 2) Observed
6
3.5
0.207
0
0
(!
0.0
0.002
lfi
9.5
0.4AI
(1.46
~
0.0008
0.0
0,GI2
13 - 18
~5.5
0.219
1.02
0
0,0035
0.0274
0.034
1 ~ - 2~
21.5
0.076
1,57
0.0094
0.0109
0.1058
0.0S!
25 - 30
27.5
0.032
2,13
0.0565
0.0510
0.2105
0.165
> 30
37.5
0.(/24
3.06
0.1986
0.1913
0.4399
0.3Q9
0.69
0.0073
0.0081
0.031
0.034
7
E×pected Value
11.7
fThe observed probability distribution of A V and the observed fatality and injury rates were obtained for NCSS file on March, 1979. Data is regularly added to the file and therefore observed values are expected to vary slightly depending on when the sample was obtained. The sample contained about 8600 automobiles when these results were obtained.
Quantitativeanalysisof policydecisions
45
severe injury rates as a function of delta V. As can be seen, the model predictions are close to the observed values. This test, which was performed with more extensive data provides further support for the model. The following sections contain two examples of analyses related to policy questions. The analyses were performed in response to questions asked by policy makers within the National Highway Tralfic Safety Adminstration. These examples are presented to indicate typical analyses that could be performed in response to questions presented by policy makers. Both examples are related to vehicle size and crash injury severity. The first example indicates the economic tradeoff between crash injury and fuel economy associated with reductions in vehicle weight. The second example examines the potential interaction between vehicle size and passive restraints. In the first example substantial savings from fuel economy are indicated. A portion of these savings could be used for building additional occupant protection into vehicles. The second example indicates that passive restraints are not likely to provide greater injury reduction in cars under 3600 lb compared to the reduction in larger cars. However, cars under 2200 lb receive greater benefits from passive restraints compared to larger cars. That conclusion was influenced in part by the result that large car occupants are older and thus more injury prone. VEHICLE SIZE AND WEIGHT An important policy question is associated with United States fuel economy standards. To achieve the standards auto manufacturers are substantially reducing vehicle weight. Each 1000 Ib reduction in vehicle weight reduces fuel cost by $0.01 per mile driven when fuel price is $0.55 per gallon (McGillivray; 1976). At present $0.90 per gallon the savings is $0.016 per mile. Thus, the potential reduction in operating cost is substantial. However, various accident studies indicate that the occupants of smaller cars suffer crash injuries of higher severity (for example; O'Day et al. 1973; Mela, 1974; O'Neill et al. 1974; and Reinfurt and Dutt, 1977). Therefore, an important policy question concerns that tradeoff between fuel consumption and crash injury. The question of vehicle size reduction for fuel economy cannot be treated as a narrow technical problem. The entire U.S. economy is greatly influenced by world wide energy shortages and the associated high price of oil produced by OPEC countries. Thus, the political arguments in favor of automobile fuel economy are likely to be stronger than any narrow technical arguments. The arguments presented previously against global models that attempt to include "all" variables are particularly relevant in this problem. There are too many poorly defined variables in the energy problem. No rational national policy maker or federal adminstrator would base policy decisions only on a large poorly understood model. Therefore, we believe that analysis of sub-problems using small problem oriented models can provide useful inputs to the information used to develop national energy policy. In this section we present an example of such an analysis. To understand the problem of vehicle weight and injury the reader needs to be aware of an important condept. In the present automobile population there is a high positve correlation between vehicle weight and measures of vehicle volume, such as wheelbase, overall weight, overall width, etc. For this reason vehicle size often refers to either vehicle weight or vehicle volume. Vehicle size has two effects on crash injury; these effects influence injury in opposite directions. In a two-vehicle crash, the heavier vehicle imposes larger decelerations on the smaller vehicle. These larger decelerations cause injuries of higher severity for occupants of the smaller vehicle. In addition, a vehicle with greater volume is able to absorb greater deformations. This results in injuries of lower severity to occupants of the larger car. Thus, when a large car strikes a small car, the occupants of the large car obtain the benefit of greater vehicle volume and avoid the penalty of lower vehicle weight. Occupants of smaller vehicles experience the negative of both of these effects. Thus, direct comparison of occupant injuries for small versus large cars in the present vehicle population results in overstating the injury severity of small car occupants when all cars are smaller. If all vehicles are reduced in size proportionally, the occupant-protection capability associated with vehicle volume will be reduced. But the injury component associated with differences in vehicle weight would not change. Therefore, any attempt to determine the relationship between vehicle weight and crash injury for the vehicle population must isolate these two components.
46
W.L. CARLSON
AS indicated above, this problem requires isolation of the separate effects of vehicle size. Therefore, the crash injury model described above provides an excellent structure for the analysis. The "hostile" effect of differences in vehicle weight are included in the coefficient of A V while the "protective" effects of vehicle volume are included in the coefficients of the A WK terms. Analyses have been conducted by merely computing the present injury severity by vehicle size. Of course, that approach is incorrect for estimating the injury severity for small cars in the future. Future vehicle populations will contain fewer large cars and thus occupants of small cars will experience smaller hostile effects in crashes. The injury analysis was conducted by comparing the average injury severity for a 30 yr old driver in the 1976 vehicle population with the average injury severity in a hypothetical future population. In this way, an absolute measure of injury severity difference as a function of vehicle weight change was estimated. Fuel consumption differences for the two vehicle populations were also estimated. Finally, the injury and fuel consumption differences were compared in economic terms. Injury severities were computed using the model tiescribed previously. The analysis began by computing the expected Abbreviated Injury Score, I?, fatality rate, Z1, and severe injury rate, Z2, for each vehicle size group using eqns (1), (5), and (6). For each weight group the same probability distribution of AV was used. In this way differences in crash severity associated with the "hostile" effect of large vehicles were excluded. The probability distribution used was obtained from the National Crash Severity Study and is shown in Table 2. Values of Y, Z,, and Z2 were computed separately for each value of A V and then these results were combined using the probabilities shown in Table 2. This procedure gives more accurate predictions because of the quadratic relationship between A V and fatal or severe injuries. Table 3 summarizes the important results of the injury analysis. Columns 2-4 contain the expected AIS, probability of fatality, and probability of severe injury by vehicle size group. Estimated injury rates per towaway crash were then computed using the 1976 distribution of vehicles by size group (Column 5). That distribution was computed by the Department of Transportation using data obtained from R. L. Polk and Company [Jatras, Carlson; 1978]. A hypothetical future population was constructed (Column 6) to represent the result of reducing vehicle size. The hypothetical population was arbitrarily specified to obtain a substantial reduction in average automobile weight. The reader could easily substitute a different hypothetical population and repeat the analysis presented here. The injury effect of a change in vehicle size mix was obtained by comparing the 1976 and the hypothetical vehicle populations. Table 3 contains the average vehicle weight and average injury rates for each population. These numbers were computed as the linear combination of estimates by vehicle size. To provide a comparison between vehicle weight change and injury change the injury and weight differences between the two populations are expressed as a percentage of the 1976 population values. Table 3. Crashinjuryseverityand vehiclesize distribution VE~ICLE SIZE GROUP
(i) MEDIAN WEIGHT
(2) EXPECTED AIS (YI)
(3) FATALITY PATE (ZI)
(4) SEVERE INJURY (AIS > 2) (Z2)
(5) PROPORTION 1976 VEHICLE POPULATION (fll
(6) PROPORTIC~[ HYPOTHETICAl FUTURE POPULAIfON (f2~__
2200 ibs.
1850
.95
.0113
.047
.086
.!9
2.
2200-2900 Ibs.
2550
.79
.0089
.038
.~35
.35
3.
2900-3600 ibs.
3250
,74
.0080
.035
.247
.25
4.
3600-4300 lbs.
3950
.65
.0067
,029
.330
.19
4650
.59
.0059
.025
.201
.02
Mean for 1976 Population (Col. 5)
3544
.70
.0075
.032
Mean for Hypothetical Population (Column 6)
2900
.78
.0087
.037
- 644
+,08
+.00[2
~.O05
+11.4%
+16.0%
+15.6~
-.61
-.88
-.86
I.
5.
•
>
4300 ibs.
Difference (Hypothetical)(1976) Percent Change Elaoti¢ity with Reopeet to Vehicle Weight
18.2%
Quantitativeanalysisof policydecisions
47
The relationship between weight change and injury change can be standardized by computing the elasticity of injury with respect to average vehicle weight. Elasticity, e, in this situation is defined as the percentage change of injury rate given a crash divided by the percentage change of average vehicle weight, Ay y e=AW W where,
Ay AW
W Y
W is the vehicle weight for the present population Y is the average injury for the present population n W is the change in vehicle weight, and A y is the injury rate change.
Equation (7) was used with the numbers contained in Table 3 to compute the following elasticities, 1. Elasticity of Average AIS,
ev
(0.08)/(0.70)_ (644)/(3544)
0.63
2. Elasticity of Fatality Rate,
eF=
(0.0012)/(0.0075) = _ 0.88, and, (644)/(3544)
3. Elasticity of Severe Injury Rate, es : (0.005)/(0.032) _
0.86.
(644)/(3544) Comparison of the elasticities indicates that higher severity injury rates increase more for a given weight reduction. The elasticities computed above can also be used to estimate the increased injury cost that results from average vehicle weight reduction. However, the resulting estimates can only be made if an acceptable cost for fatal and severe injuries is available. In addition, an estimate of fatal and severe injury rate per mile is also required if a comparison between fuel and injury costs is to be made. Defining the cost for death and severe injury accidental injury is extremely difficult. Using economic theory we could define the utility of avoiding death and severe injury and then assign a price to that utility. However, such an assignment requires a market which is difficult to conceive. Most ethical models assign maximum utility to the preservation of life. Thus, one might argue that no dollar value can be assigned to death and severe injury. The recent public and legal protests against the use of cost benefit analysis by the Ford Motor Company to guide the design of Pintos clearly supports that position. However, society does not in practice actually assign an infinite cost to human life. The courts are filled with litigation which attempts to set appropriate compensation for accident victims. Similarly individuals voluntarily participate in hazardous recreational activities (e.g. skydiving, motorcycle racing, snowmobiling, etc.). These later activities contain a probability rather than a certainty of death. Thus, individuals have decided that the utility of participating exceeds the utility associated with an increased probability of death or severe injury. Similarly most people have decided that the utility of not using active restraint systems exceeds the utility of increased probability of death. Thus, avoidance of death or severe injury has a finite utility. Extension of this result to conclude that a finite cost exists is subject to much greater criticism.
48
W.L. CARLSON
Given the above problems this study used costs that have been used previously for analysis by the Department of Transportation. That approach provided a comparative link to other economic evaluations. Therefore, the economic analysis presented here has the same advantages and shortcomings as those other studies that use death and injury costs developed by the Department of Transportation. The injury and fatality costs were derived by combining average direct costs with expected lost contribution to Gross National Product associated with death or injury for an average victim (Fagin, 1976). Table 4 presents an economic analysis of the relationship of injury cost to vehicle weight. Average cost per occurrence for minor, severe, and fatal injuries were obtained from Fagin (1976). Rates of occurrence per million miles were obtained from the 1977 Fatal Accident Reporting System (FARS). Analysis injuries were obtained from Fagin (1976). Rates of occurrence per million miles were obtained from the 1977 Fatal Accident Reporting System (FARS). Analysis of the CPIR File indicated that there were 1.55 occupants per vehicle involved in crashes. The elasticities for severe and fatal crashes are those computed above. Analysis of the data indicated that the minor injury rate did not increase with vehicle weight change. Instead, some non-injury occupants receive minor injuries while some occupants with minor injuries receive severe injuries. As a result of the computations it can be seen that injury cost is about $18,000 per million miles or 1.8 cents per mile. In addition, each one percent reduction of vehicle weight increases injury cost by approximately $131 per million miles. The fuel cost analysis was based upon the method presented by McGillioray (1976). In this analysis the marginal cost of fuel as a function of vehicle weight change is $0.0016 per mile per 100 lb. This result assumes an average price of $0.90 per gallon and an average consumption of 1/16 gallons per mile (16 mg). The elasticity, ei, of fuel cost with respect to vehicle weight is,
~C/C er=iW/W
AC W ,~W ~-
(7)
where AC C W
is the change in fuel cost per 100 Ib change in vehicle weight per mile, is the average fuel cost per mile, and is the average vehicle weight in pounds.
By using the previously stated values, we found that, 0,0016
3544
et = 100 "0.09/16
-
1.03.
Fuel cost per million miles was, (0.55/14) × 106 = $56,250, or approximately 5.6 cents per mile compared to 1.8 cents per mile for injury cost. The change in fuel cost per million miles for each one percent reduction in vehicle weight was therefore, (1.03) (-0.01) (56,250)=- $579. Thus the difference between fuel cost reduction in injury cost increase is, $579-$131 = $448 per million miles of vehicle travel for each one percent reduction in vehicle weight. These results can also be expressed in terms of an individual vehicle life. If a vehicle life is Table 4. Economicanalysisof injury cost and change in averagevehicleweight¢ INJURY SEVERITY
AVLRA(;E COST PEK OCCURREHCE
b!Inor (A!S = 1,2)
$
Severe (AIS > 2) Fatal
2,9g6"
DRIVER IN.TUI~Y RF,~E PER NILLION MILES
0.670
OV}[IK~LL INJL:R! RAql }'El), VLHICLI PER HILLI01; MILES
!.838
COST PER MILLION blILES
$ 3,258
ELASTICITY
0
36,282
0.126
0.195
7,094
-.86
244,107
0.016
0.0231
7r949
-.88
$18,101
COST PER i% VEHICLE WEIGHT R~DUCTION
561 70 $131
tThese costs were adjusted from the 1975 costs reported by Fagin (1976) by using the implicit price deflator (President's rep. 1979).
Quantitative analysis of policy decisions
49
assumed to be 100,000 miles then a 20% reduction in vehicle weight would result in a net savings of $8%. The analysis above has several important policy implications. In terms of overall societal costs, vehicle weight reduction has a positive benefit. Unfortunately that result is clouded by the fact that the cost analysis includes the controversial procedure of assigning a dollar value to human life. One possible solution to that problem is to spend additional money for improved occupant protection. Given proper selection of technology it is likely that increased occupant injury could be avoided. Thus, some of the above cost saving could be used to purchase additional occupant protection. For example, design concepts from the research safety vehicle and passive restraints are likely candidates for improved occupant protection. Other alternatives could be explored using the above approach. By using the estimated potential injury severity reduction and cost for new occupant protection devices a less controversial analysis could be performed. The cost of reducing to zero the injury severity increase that results from reduced vehicle size could then be determined. By using that approach the controversial use of a dollar cost of death and severe injury could be avoided. Then the economic comparison would involve fuel cost savings versus increased cost for occupant protection hardware. At this point, interaction between policy makers and the analysis process would be desirable. P A S S I V E R E S T R A I N T S AND V E H I C L E SIZE I N T E R A C T I O N
The Department of Transportation has ruled that the air bag or other passive restraints will become mandatory on all new cars beginning with the 1982 model year. Passive restraints avoid the need for drivers or passengers to actively buckle seat belt and shoulder harnesses. Passive restraints are expected to provide occupant injury protection in frontal but not side or rear impacts. The mandatory requirement is motivated by the fact that only about one in five vehicle occupants presently use active restraints. Thus, passive restraints will benefit only those people who are presently unwilling to use the presently available seat belts and shoulder harnesses. This raises important ethical and political questions. Should society protect those who are unwilling to protect themselves? Should persons who presently use active restraints be forced to pay an additional cost for protection that they now obtain by voluntary use of restraints? These questions were debated by both the Department of Transportation and Congress and were part of the decision process. Thus in a strictly legal sense these "ethical" questions have been answered. Our concern here is with their relative effectiveness in large vs small cars. The introduction of passive restraints will begin with large automobiles in the first year and proceed to include smaller automobiles in subsequent years. The decision to introduce passive restraints first in large cars was based primarily on the present level of design and production technology. Recently this phasing decision has been criticized by consumer groups. Their criticism was based on the fact that injury severity is greater for occupants of small cars compared to occupants of large cars. This paper presents the results of a study to determine whether the effectiveness of passive restraints are related to vehicle size. To estimate the comparative effectiveness of restraints in large and small cars it was necessary to first consider their design objectives and crash dynamics. Passive restraints are designed to reduce occupant injuries in frontal crashes over a range of crash severity. Passive restraints will not reduce injuries in low severity crashes because occupants are typically not injured without them. Passive restraints will not reduce injuries in high severity crashes because of crash forces that exceed both vehicle structure and restraint design characteristics. Thus, there is a critical range of crash severity.t Within this range passive restraints can be expected to reduce injuries. From other studies we know that small cars will have fewer crashes below the critical range and more crashes above the critical range compared to large cars. This phenomenon complicates the analysis. Based upon the above discussion we anticipated that passive restraints reduce small car occupant injuries more in low speed crashes and reduce large car occupant injuries more in high speed crashes. The model presented in this paper does not include the effect of passive restraints. Thus, if the injury prediction model is to be used it is necessary to specify a surrogate for passive restraints. This analysis has used seat belts in frontal crashes as a surrogate for passive tFor this study crash severity was measured by A V the change in velocity at impact. AAP Vol. 12, No. I--D
50
W.L. CARLSON
restraints. That approach has the disadvantage of not using data from the actual occupant protection mechanism that is being analyzed. Direct use of passive restraint performance data from crashes is hampered by the limited number of observations. This reduces the precision of injury reduction estimates and minimizes the possibility of considering passive restraint interactions with other crash variables. Thus our analysis has the advantage of considering restraint effectiveness over a wide range of crash conditions. The NCSS data indicates that restraint usage in accident involved vehicles does not vary substantially by size of car. Specifically the observed restraint usage was:
Vehicle Size < 2200 lb 2200-2900 lb 2900-3600 lb 3600--4300 lb > 4300 lb
Per cent Restraint Usage 9.9% 13.2% 7.9% 6.5% 10.1%
Comparison of the age coefficient for the belted and the unbelted injury prediction models (eqns (3) and (4)) indicates an important interaction. Injury severity increases faster with increasing age for belted compared to unbelted occupants. Thus, greater overall injury reduction would occur if older persons received the benefits of passive restraints before younger persons. Analysis of the Restraint System Evaluation Project (RSEP) data indicates that in the accident population the mean driver age by vehicle size was: subcompacts, 28.0, compacts, 30.5; intermediates, 33.0; and full sized, 38.9. A frontal crash restraint system effectiveness model was developed from the overall injury prediction model. This was done by first obtaining a separate effectiveness model for head on, side impact-striking, rear impact-striking and single vehicle-struck fixed object crash configurations. Restraint system effectiveness models for each crash configuration were obtained by subtracting the restrained occupant model from the unrestrained occupant model. The result is an equation which predicts reduction in expected AIS for each crash configuration. A positive difference indicated a positive injury reduction. The following restraint effectiveness models by crash configuration resulted, 1. Head on crashes A y = - 0.0095 V + 0.006A + 0.44X1 + 0.52)(2 + 0.20)(3 -0.06X4 + 0.19X~
(8)
2. Side Impact--striking car A y = - 0.031A V + 0.008A + 0.77X1 + 0.38)(2 + 0.44X~ + 0.29)(4 + 0.42X5
(9)
3. Rear Impact--striking car A y = - 0.012A V - 0.001A - 0.37X1 + 0.13)(2 + 0.13X3 + 0.25X4 + 0.34Xs
(lO)
4. Single Vehicle--struck fixed object A Y = 0.0235 V + 0.014A - 0.15)(1 - 1.04X2 - 0.68X3 - 0.63)(4 - 0.84X5
(11)
where Ay
is the estimated difference in expected AIS between unrestrained and restrained drivers, A V is the estimated change in velocity at impact in mph (This variable is used to control for differences in crash severity). A is the occupant age,
Quantitativeanalysisof policydecisions :(1 :(2 :(3 X4
X5
51
is 1 for cars under 2200 lb 0 otherwise, is 1 for cars in the weight range 2200-2900 lb 0 otherwise, is 1 for cars in the weight range 2900-3600 lb 0 otherwise, is 1 for cars in the weight range 360(0300 lb 0 otherwise, is 1 for cars above 4300 lb 0 otherwise.
The driver and right front passenger coefficients were eliminated from these equations because they do not affect the comparison. Examination of these separate models revealed several important conclusions concerning restraint effectiveness in frontal crashes, 1. Restraint effectiveness increases with increasing occupant age. 2. Restraint effectiveness for cars under 2200 lb is generally higher compared to larger cars, 3. The model for single vehicle crashes has strange coefficients for the vehicle weight vffects. From the NCSS data file it was determined that cars are involved in crashes with the following proportions:
Crash Configuration Head on Side Impact--striking Rear Impact--striking Single Vehicle--Struck Fixed Object
Percent of All Crash Involvements 12.7% 22.4% 10.7%
Percent of Frontal Crash Involvements 19.8% 34.9% 16.7%
18.3% 64.1%
28.5% 100.0 .
The four restraint effectiveness models were then combined using the above percentages of frontal crash involvements as weights. In this way the following overall model of restraint effectiveness was estimated, A y = - 0.00005A V + 0.008A + 0.25X1 + - 0.04X2 + 0.02X3 + 0.05X4 + 0.0X5
(12)
where the variables are as defined above. The large coefficient for Xt indicates that restraint effectiveness, unadjusted for restraint usage and occupant age, is greatest for cars under 2200 lb. Equation (12) was used to obtain adjusted measures of restraint effectiveness. To do this it was necessary to estimate the average occupant age and the average change in velocity at impact for each vehicle size. Average occupant age was obtained from the NCSS data file. To obtain an average change in velocity at impact, A V, we assumed that all vehicles in each weight group had a single weight and that they collided with a vehicle whose weight was equal to the average weight for the entire vehicle population. An average velocity at impact was also determined from both the CPIR and the NCSS files. This velocity was used with the relative weights of colliding vehicles to compute an average, A V, for each vehicle size. This process assigned a higher A V to lighter vehicles, which is consistent with crash dynamics. Finally, the restraint effectiveness measures were adjusted by the fraction of the drivers who do not use restraints. Using the data described above and eqn (12) a net effectiveness measure was computed for each vehicle size. Net effectiveness is the reduction is expected AIS that results from using restraints. The data and the results of this process are presented in Table 5. Examination of the net effectiveness by vehicle size indicated that the effectiveness is greatest for cars under 2200 lb. However, the effectiveness is approximately the same for all other vehicle sizes.
W. L. CARLSON
52
Table 5. Computationof net restrainteffectivenessby vehicle size Vehicle Size
Percent Unrestrained
Net Restraint Effectiveness
AV
Ase
14.9
28.0
.901
.43
2200-2900 pounds
]3.4
30.5
.868
.18
2900-3600 ')cur:ds
12.(I
33.0
.921
.26
3600-4300
]6).8
33.0
.935
.20
>4300 pounds
]0.1
38.9
.899
.28
<2200
pounds
Table 6. Injuryseverityfor belted vs unbeltedoccupantsby vehicle size in towawaycrashes (Proportion AIS ~ 2) Injury Reduction (Unbelted-Belted)
Unbelted
Belted
Subcompact
0.131
0.094
0.035
Compact
0.111
0.082
0.029
Intermediate
0.118
0.068
0.050
Full ~ize
0.120
0.048
0.072
The injury reduction for full size cars is significantly
(~ < .05) larger
than the redu~=ion for subcompact cars
Table 7. Injuryseverityfor belted vs unbeltedoccupantsby vehicle size in towawaycrashes (Proportion AIS > 3) Injury R~ductlon (Unbelted-Belted)
Unbelted
Belted
Subcompact
0.033
0.022
0.011
Compact
0.029
0.010
0.019
Intermediate
0.032
0.014
0.0}8
Full Size
0.035
0.013
0.022
This analysis revealed the complexity of the restraint effectiveness question. The analysis began with models that estimated expected injury as a function of several important variables. These models were then used with observed characteristics of the driving and crashing population to obtain measures of net restraint effectiveness. An important result of this analysis is the interactive effect of occupant age and restraint usage on restraint effectiveness. Thus, passive restraints will reduce injury severity more in large cars in part because large car occupants tend to be older. A number of political arguments could be developed based on these effects. However, it is the opinion of this writer that programs to reduce injuries should not discriminate against older people. Thus it is not reasonable to argue against the conclusion because of the interaction effects. Additional support for the result presented here was obtained from the results of a recent study of restraint system effectiveness (Reinfurt, Silva, Seila, 1976). That study used data from the RSEP data file to conduct an extensive analysis of restraint system effectiveness. Table 6 compares the proportion injured (AIS-> 2) for unrestrained and lap belted vehicle occupants. Examination of the data indicates that the injury reduction for lap belts was largest for full size cars. The same result occurred for severe injuries (AIS-> 3) as shown in Table 7.
Quantitative analysis of policy decisions
53
These comparisons differ somewhat from the analysis which used the injury prediction model. First the comparisons were not restricted to frontal crashes. Thus, lap belted occupants cannot be used as surrogates for occupants with passive restraints. A specific adjustment was not made for occupant age. However, the RSEP data file included different age groups in proportion to their occurrence in crashes. Thus the age adjustment was included in the injury rates presented in Tables 6 and 7. In addition, the injury rate differences were not adjusted for differences in restraint usage. However, that adjustment would increase the margin in favor of large cars even more. REFERENCES Carlson W. L., Crash injury prediction model, Accid. Anal. & Prey. 11,137-153. Dutt A. and Reinfurt D., Accident involvement and crash injury rates by make, model, and year of car, a follow-up. Highway Safety Research Center, The University of North Carolina, Chapel Hill, North Carolina, June 1977. Fagin B. M., 1975 Societal Costs of Motor Vehicle Accidents, U.S. Department of Transportation, Washington, D.C., December, 1976. Hayes R. H. and Nolan R. L., What kind of corporate modeling functions best, Harvard Business Review, May-June, 102-112, 1974. Hedlund James H., The national crash severity study and its relationships to ESV design criteria. Proc. of 7th Int. Conf. on Experimental Safety Vehicle, Paris, June 5-8, 1979. Highway Statistics 1976, Federal Highway Administration. Jatras K., and Carlson W., Frequency distributions of passenger cars by weight and wheelbase by state: July I, 1976. U.S. Department of Transportation, Washington, D.C., May, 1978. Kahane C., and Mungenast J., Restraint systems evaluation project codebook, Rep. No. DOT-HS-8020285, U.S. Department of Transportation, Washington, D.C., March, 1977. Kahane C. and Mungenast J., Survey of trafficpopulation (August 1976-March, 1977),Krischner Associates, Washington, D.C., DOT-HS-6-O1340, December, 1977. McGillivray R., Automobile gasoline conservation, Rep. No. 708-01, Urban Institute, Washington, D.C., April, 1976. Mela D., How safe can we be in small cars. Proc. of the 3rd Int. Cong. on Automotive Safety, Vol. II. San Francisco, California, July, 1974. O'Day J., Golomb H. and Cooley P., A statistical description of large and small car involvement in accidents, Hit. Lab Rep., Vol. 3, No. 9, Highway Safety Research Institute, University of Michigan, Ann Arbor, Michigan, May, 1973. O'Neil B., Joksch G. and Haddon W., Empirical relationships between car size, car weight and crash injuries in car-to-car crashes. 5th Int. Tech. Conf. on Experimental Safety Vehicles, London, England, June, 1974. Reinfurt D. W., Silva C. Z., and Seila A. F., A statistical analysis of seat belt effectiveness in 1973-1975 model cars involved in towaway crashes, Highway Safety Research Center, The University of North Carolina, Chapel Hill, N.C., May, 1976.
0001--457518010301-00411502.0010
QUANTITATIVE ANALYSIS OF POLICY DECISIONS WILLIAM L . CARLSON Department of Economics, St. OLaf College, Northfield, MN 55057, U.S.A. (Received 26 January 1979; in revised [orm 15 July 1979)
Abstraet--The use of quantitative models for highway safety policy analysis is discussed. The importance of interaction between managers and model analysts is emphasized for the development and application of these models. Two examples are presented. First, the trade-off between injury cost and fuel savings as a function of vehicle weight reduction is analyzed. Second, passive restraint effectiveness and its interaction with vehicle size is studied. INTRODUCTION
Public policy decisions can be guided by a comprehensive structured analysis of specific policy questions. Essentially such an analysis would utilize a model that includes relationships between variables that are important for policy analysis. Models may be developed using a variety of methodologies. Models and the process of their development assist policy makers by focusing attention on important variables. The model analysis should be conducted with policy decision makers taking an active role in formulating questions and providing critical evaluation of the results. Such a process requires open communication between the model analyst and the policy maker. Policy makers need to discuss openly the political and the nonquantifiable issues associated with a policy decision. Model analysts must attempt to structure the quantitative results given these other issues. Thus, the process requires acceptance and active involvement by policy makers and an awareness of the problem context by model analysts. The need for involvement of policy makers and for problem oriented model analyses cannot be over emphasized. There is a clear analogy to the experience in the private sector. An excellent paper by Hayes and Nolan (1974), which appeared in the Harvard Business Review, presents an overview of the corporate experience with models for analysis and decision making. During the late 1950s and early 1960s, operations researchers worked on small models directed toward specific management problems. These efforts were reasonably successful. Based upon the early success management scientists began to develop very large corporate models that were expected to provide comprehensive analysis for a wide variety of corporate problems. Unfortunately the models tended to be developed by modelers with little input from operating management. These mathematically elegant models became difficult for managers to understand. In addition, the models required large expensive data bases to provide necessary inputs. Communications between analysts and managers broke down. The manager was left with promises that additional research and finetuning would produce the ideal model. Answers that came from the model were often too late or were conditional on narrow assumptions about the operating environment. As a result many firms abandoned large modeling efforts. A third generation approach, that is evolving, is based upon the previous experiences and a more realistic view from managers and analysts. Smaller models are developed for solving specific problems. Models are developed by ad hoc project teams that include managers, systems analysts, and management scientists. Team members tend to have broad experience in both operating management positions and analyst positions. This integrated approach has led to useable problem solutions and to a better understanding of the corporate subsystems by managers. In many cases the most important benefit from the process was ~ better understanding by management. This paper presents examples of analyses based upon a crash injury prediction model (Carlson, 1979) that can be used to guide automobile safety policy. The injury prediction model was developed using data from in depth crash investigations and technical inputs from persons 41
42
W . L . CARLSON
who understand crash injury mechanisms. There are two important objectives of this paper. First, the benefits of utilizing an analysis process that is based upon a comprehensive model are demonstrated. Second, the results of two analyses are presented as contributions to the highway safety research literature. The methodology presented here can be used with other comprehensive models. Analyses of the same question using other models make important contributions to the total information available for policy analysis. Every model includes certain assumptions and simplifications. Therefore, analyses based upon several different models would tend to reduce any biases that might be associated with a given model.
INJURY PREDICTION MODEL
The model used in this study was presented in detail by Carlson (1979). Variables and their functional form used in the model were specified using a broad base of previous crash injury research. Coefficients in the model were estimated using two stage least squares applied to data in the Crash Performance Injury Report (CPIR) file maintained by the Highway Safety Research Institute at the University of Michigan. The data used for the model includes crashes involving passenger cars, pickups, and vans for model years 1969-75. Interested readers are referred to the previous paper for a detailed discussion of the model development process. The model has two phases. In the first phase the expected Abbreviated Injury Score (AIS) is estimated, for a vehicle occupant, using a set of crash variables. The second phase uses the expected AIS to estimate the severe injury rate and the death rate given a towaway crash. The final phase 1 model, which assumed that 8.4% of the occupants were restrained, is: 17"= - 0.80 + 0.093A V~ + 0.014A + 0.24D + 0.28RF - 0.16A W5 - 0.22A W6 - 0.33A W7 - 0.40A W8 (0.0028)
(0.00095)(0.044) (0.047) (0.058)
(0.053)
(0.054)
(0.063). (I)
Where the numbers below the coefficients ( ) are the coefficient standard errors and f" is the expected AIS, A V1 is the change in velocity at impact, A is the occupant age, D is 1 if the occupant is the driver and 0 otherwise, RF is I if the occupant is a front seat passenger and zero otherwise, and A Wr indicates the vehicle weight group according to the following ranges:
A W5 = 1 A W6 = 1 A W7 = 1 A W8 = 1 A WK = 0
Vehicle weight range 2200-2899 lb. 2900-3599 lb. 360(04299 lb. greater than 4299 lb. else (K = 5. . . . . 8).
A key variable for predicting injury severity was crash severity measured, in two vehicle crashes,
W2
A V1 - W1 +--~2 ~/( Vl2 + V22 + 2 V, V2 cos a). Where, W1 is the weight of the case vehicle, W2 is the weight of the other vehicle, VI is the impact velocity of the case vehicle, V2 is the impact velocity of the other vehicle, and a = Ol- 02.
(2)
Quantitative analysis of policy decisions
43
Where
01 is the reported direction of the principal impact for vehicle 1 and, 02 is the reported direction of the principal impact for vehicle 2. Notice that when vehicles of unequal weight collide the lighter vehicle absorbs a higher A V that is inversely related to the relative vehicle weights. The model contains two components, one for unrestrained occupants, and the other for occupants with seat belts. The model for occupants wearing seat belts is, 1~"-- - 0.79 + 0.094A ~', + 0.0083A + 0.11D + 0.32R¢ - 0.08A W5 - 0.15A W6 - 0.18A W7 - 0.28A W8, (0.0055)
(0.002)
(0.13)
(0.14)
(0.12)
(0.11)
(0.11)
(0.13) (3)
and for occupants not wearing seat belts the model is, 17 = - 0.80 + 0.0932~ ~', + 0.015A + 0.25D + 0.28R s - 0.17A W5 - 0.23A W6 - 0.34A W7 - 0.41A W8 (0.0030)
(0.001)
(0.047)
(0.050)
(0.062)
(0.057)
(0.058)
(0.067). (4)
Equations (3) and (4) are linear combinations of injury prediction equations fitted for each of the crash configurations defined in Table 1. Readers interested in the equations by crash configuration should see Carlson (1979). The relative weights for each crash configuration were obtained from the National Crash Severity Study (NCSS) data file and are presented in Table 1. Equation (1) is a linear combination of eqns (3) and (4). The 8.4% restrained occupants was obtained from the NCSS data (Hedlund, 1979).
Table 1. Percentageof vehicles in crashes Crash Configuration
Percent of Vehicles (~i)
1.
Head-on
12.7%
2.
Side-impact--striking
22.4Z
3.
Side-impact--struck right
ii.2%
4.
Side-lmpact--struck left
11.2%
5.
Rear-impact--striking
I0.7%
6.
Rear-impact--struck
I0.7%
7.
Single-vehlcle--ro ii over
8.
Single-vehicle--fixed object
2.9% 18.3% I00.0%
These percentageswere obtainedfrom the NationalCrash SeverityStudyas of March, 1979(Hedlund, 1979).Tha assistanceof Dr. James Hedlundof NHTSA in providing these data is gratefully acknowledged.
Alternative forms for eqns (1), (3), and (4) could be obtained by using different weights. For example, models were also obtained using proportions by crash configuration for United States fatal crashes and for North Carolina accidents. In both of those cases the final models (eqns (1), (3) and (4)) were essentially unchanged and therefore the alternative models are not presented. In phase 2 the expected AIS is used as input to models which compute estimated fatality
44
W . L . CARLSON
and severe injury rates. The probability of a fatality is estimated using, Z, = O;
(17 <_ 1.38) (1.38 < 12 < 5.62)
2, : 0.031 - 0.086 12 + 0.046 I22; (0.O4O) ZI = 1.0;
(O.042)
(5)
(O.Oll)
( 12 _>5.62).
Where, 2, is the estimated probability of a fatality for a towaway crash given Y, 12 is the estimated expected AIS from phase 1, and the numbers below the coefficients are the coefficient standard errors. Similarly the probability of a serious injury, overall AIS > 2, is estimated using, 22=0;
(17-<0.78) (6)
22 : - 0.054 + 0.038 12 + 0.040 I;'2; (0.78 < 12 < 4.67) (0.063)
(0.067)
(0.017)
22 = 1.0; (12 -> 4.67). Where Z2 is the estimated probability of a serious injury for a towaway crash given 12, and the other quantities are as defined above. Examination of eqns (5) and (6) indicates that fatal and serious injuries increase quadratically with expected AIS. The probability of injuries with overall AIS equal to 1 or 2 did not change with I7. This occurred because increased 17 was associated with AIS 1 or 2 injuries moving to AIS greater than 2 and these were "replaced" by non injured occupants who suffered AIS 1 or 2 injuries. Since 17 is a linear function of variables such as A V, occupant age, vehicle weight, etc. we see that severe injuries vary quadratically with the crash injury predictor variables in eqn (1). Policy decisions that operate on the injury prediction variables in the model operate to increase or decrease serious injury and death rates. Other analyses would be necessary for policy decisions that influence property damage. Before policy analysis begins it is necessary to verify that the model adequately represents reality with respect to the variables of interest. The model presented here was validated by first comparing the predicted effect of model variables with other research. Next the model was used to predict severe injury and death rates for a new accident population. That exercise demonstrated that the model does predict correctly. Details of the verification procedure are contained in Carlson (1979). A second test of the model was conducted by using more recent data from the NCSS data file discussed previously. Table 2 presents a comparison of predicted and observed fatality and Table 2. Driver fatal and severe injury prediction for national crash severity study (NCSSI sampler SEVERE INJURY AV
!'h'dian
Subgroup 0 -
AV
Probability of AV
Expl,ctcJ A]5
(\)
PA]ALIIY Predicted
P~\TI[
(ZI)
Observed
(A]S Predicted
(Z2)
RATE
> 2) Observed
6
3.5
0.207
0
0
(!
0.0
0.002
lfi
9.5
0.4AI
(1.46
~
0.0008
0.0
0,GI2
13 - 18
~5.5
0.219
1.02
0
0,0035
0.0274
0.034
1 ~ - 2~
21.5
0.076
1,57
0.0094
0.0109
0.1058
0.0S!
25 - 30
27.5
0.032
2,13
0.0565
0.0510
0.2105
0.165
> 30
37.5
0.(/24
3.06
0.1986
0.1913
0.4399
0.3Q9
0.69
0.0073
0.0081
0.031
0.034
7
E×pected Value
11.7
fThe observed probability distribution of A V and the observed fatality and injury rates were obtained for NCSS file on March, 1979. Data is regularly added to the file and therefore observed values are expected to vary slightly depending on when the sample was obtained. The sample contained about 8600 automobiles when these results were obtained.
Quantitativeanalysisof policydecisions
45
severe injury rates as a function of delta V. As can be seen, the model predictions are close to the observed values. This test, which was performed with more extensive data provides further support for the model. The following sections contain two examples of analyses related to policy questions. The analyses were performed in response to questions asked by policy makers within the National Highway Tralfic Safety Adminstration. These examples are presented to indicate typical analyses that could be performed in response to questions presented by policy makers. Both examples are related to vehicle size and crash injury severity. The first example indicates the economic tradeoff between crash injury and fuel economy associated with reductions in vehicle weight. The second example examines the potential interaction between vehicle size and passive restraints. In the first example substantial savings from fuel economy are indicated. A portion of these savings could be used for building additional occupant protection into vehicles. The second example indicates that passive restraints are not likely to provide greater injury reduction in cars under 3600 lb compared to the reduction in larger cars. However, cars under 2200 lb receive greater benefits from passive restraints compared to larger cars. That conclusion was influenced in part by the result that large car occupants are older and thus more injury prone. VEHICLE SIZE AND WEIGHT An important policy question is associated with United States fuel economy standards. To achieve the standards auto manufacturers are substantially reducing vehicle weight. Each 1000 Ib reduction in vehicle weight reduces fuel cost by $0.01 per mile driven when fuel price is $0.55 per gallon (McGillivray; 1976). At present $0.90 per gallon the savings is $0.016 per mile. Thus, the potential reduction in operating cost is substantial. However, various accident studies indicate that the occupants of smaller cars suffer crash injuries of higher severity (for example; O'Day et al. 1973; Mela, 1974; O'Neill et al. 1974; and Reinfurt and Dutt, 1977). Therefore, an important policy question concerns that tradeoff between fuel consumption and crash injury. The question of vehicle size reduction for fuel economy cannot be treated as a narrow technical problem. The entire U.S. economy is greatly influenced by world wide energy shortages and the associated high price of oil produced by OPEC countries. Thus, the political arguments in favor of automobile fuel economy are likely to be stronger than any narrow technical arguments. The arguments presented previously against global models that attempt to include "all" variables are particularly relevant in this problem. There are too many poorly defined variables in the energy problem. No rational national policy maker or federal adminstrator would base policy decisions only on a large poorly understood model. Therefore, we believe that analysis of sub-problems using small problem oriented models can provide useful inputs to the information used to develop national energy policy. In this section we present an example of such an analysis. To understand the problem of vehicle weight and injury the reader needs to be aware of an important condept. In the present automobile population there is a high positve correlation between vehicle weight and measures of vehicle volume, such as wheelbase, overall weight, overall width, etc. For this reason vehicle size often refers to either vehicle weight or vehicle volume. Vehicle size has two effects on crash injury; these effects influence injury in opposite directions. In a two-vehicle crash, the heavier vehicle imposes larger decelerations on the smaller vehicle. These larger decelerations cause injuries of higher severity for occupants of the smaller vehicle. In addition, a vehicle with greater volume is able to absorb greater deformations. This results in injuries of lower severity to occupants of the larger car. Thus, when a large car strikes a small car, the occupants of the large car obtain the benefit of greater vehicle volume and avoid the penalty of lower vehicle weight. Occupants of smaller vehicles experience the negative of both of these effects. Thus, direct comparison of occupant injuries for small versus large cars in the present vehicle population results in overstating the injury severity of small car occupants when all cars are smaller. If all vehicles are reduced in size proportionally, the occupant-protection capability associated with vehicle volume will be reduced. But the injury component associated with differences in vehicle weight would not change. Therefore, any attempt to determine the relationship between vehicle weight and crash injury for the vehicle population must isolate these two components.
46
W.L. CARLSON
AS indicated above, this problem requires isolation of the separate effects of vehicle size. Therefore, the crash injury model described above provides an excellent structure for the analysis. The "hostile" effect of differences in vehicle weight are included in the coefficient of A V while the "protective" effects of vehicle volume are included in the coefficients of the A WK terms. Analyses have been conducted by merely computing the present injury severity by vehicle size. Of course, that approach is incorrect for estimating the injury severity for small cars in the future. Future vehicle populations will contain fewer large cars and thus occupants of small cars will experience smaller hostile effects in crashes. The injury analysis was conducted by comparing the average injury severity for a 30 yr old driver in the 1976 vehicle population with the average injury severity in a hypothetical future population. In this way, an absolute measure of injury severity difference as a function of vehicle weight change was estimated. Fuel consumption differences for the two vehicle populations were also estimated. Finally, the injury and fuel consumption differences were compared in economic terms. Injury severities were computed using the model tiescribed previously. The analysis began by computing the expected Abbreviated Injury Score, I?, fatality rate, Z1, and severe injury rate, Z2, for each vehicle size group using eqns (1), (5), and (6). For each weight group the same probability distribution of AV was used. In this way differences in crash severity associated with the "hostile" effect of large vehicles were excluded. The probability distribution used was obtained from the National Crash Severity Study and is shown in Table 2. Values of Y, Z,, and Z2 were computed separately for each value of A V and then these results were combined using the probabilities shown in Table 2. This procedure gives more accurate predictions because of the quadratic relationship between A V and fatal or severe injuries. Table 3 summarizes the important results of the injury analysis. Columns 2-4 contain the expected AIS, probability of fatality, and probability of severe injury by vehicle size group. Estimated injury rates per towaway crash were then computed using the 1976 distribution of vehicles by size group (Column 5). That distribution was computed by the Department of Transportation using data obtained from R. L. Polk and Company [Jatras, Carlson; 1978]. A hypothetical future population was constructed (Column 6) to represent the result of reducing vehicle size. The hypothetical population was arbitrarily specified to obtain a substantial reduction in average automobile weight. The reader could easily substitute a different hypothetical population and repeat the analysis presented here. The injury effect of a change in vehicle size mix was obtained by comparing the 1976 and the hypothetical vehicle populations. Table 3 contains the average vehicle weight and average injury rates for each population. These numbers were computed as the linear combination of estimates by vehicle size. To provide a comparison between vehicle weight change and injury change the injury and weight differences between the two populations are expressed as a percentage of the 1976 population values. Table 3. Crashinjuryseverityand vehiclesize distribution VE~ICLE SIZE GROUP
(i) MEDIAN WEIGHT
(2) EXPECTED AIS (YI)
(3) FATALITY PATE (ZI)
(4) SEVERE INJURY (AIS > 2) (Z2)
(5) PROPORTION 1976 VEHICLE POPULATION (fll
(6) PROPORTIC~[ HYPOTHETICAl FUTURE POPULAIfON (f2~__
2200 ibs.
1850
.95
.0113
.047
.086
.!9
2.
2200-2900 Ibs.
2550
.79
.0089
.038
.~35
.35
3.
2900-3600 ibs.
3250
,74
.0080
.035
.247
.25
4.
3600-4300 lbs.
3950
.65
.0067
,029
.330
.19
4650
.59
.0059
.025
.201
.02
Mean for 1976 Population (Col. 5)
3544
.70
.0075
.032
Mean for Hypothetical Population (Column 6)
2900
.78
.0087
.037
- 644
+,08
+.00[2
~.O05
+11.4%
+16.0%
+15.6~
-.61
-.88
-.86
I.
5.
•
>
4300 ibs.
Difference (Hypothetical)(1976) Percent Change Elaoti¢ity with Reopeet to Vehicle Weight
18.2%
Quantitativeanalysisof policydecisions
47
The relationship between weight change and injury change can be standardized by computing the elasticity of injury with respect to average vehicle weight. Elasticity, e, in this situation is defined as the percentage change of injury rate given a crash divided by the percentage change of average vehicle weight, Ay y e=AW W where,
Ay AW
W Y
W is the vehicle weight for the present population Y is the average injury for the present population n W is the change in vehicle weight, and A y is the injury rate change.
Equation (7) was used with the numbers contained in Table 3 to compute the following elasticities, 1. Elasticity of Average AIS,
ev
(0.08)/(0.70)_ (644)/(3544)
0.63
2. Elasticity of Fatality Rate,
eF=
(0.0012)/(0.0075) = _ 0.88, and, (644)/(3544)
3. Elasticity of Severe Injury Rate, es : (0.005)/(0.032) _
0.86.
(644)/(3544) Comparison of the elasticities indicates that higher severity injury rates increase more for a given weight reduction. The elasticities computed above can also be used to estimate the increased injury cost that results from average vehicle weight reduction. However, the resulting estimates can only be made if an acceptable cost for fatal and severe injuries is available. In addition, an estimate of fatal and severe injury rate per mile is also required if a comparison between fuel and injury costs is to be made. Defining the cost for death and severe injury accidental injury is extremely difficult. Using economic theory we could define the utility of avoiding death and severe injury and then assign a price to that utility. However, such an assignment requires a market which is difficult to conceive. Most ethical models assign maximum utility to the preservation of life. Thus, one might argue that no dollar value can be assigned to death and severe injury. The recent public and legal protests against the use of cost benefit analysis by the Ford Motor Company to guide the design of Pintos clearly supports that position. However, society does not in practice actually assign an infinite cost to human life. The courts are filled with litigation which attempts to set appropriate compensation for accident victims. Similarly individuals voluntarily participate in hazardous recreational activities (e.g. skydiving, motorcycle racing, snowmobiling, etc.). These later activities contain a probability rather than a certainty of death. Thus, individuals have decided that the utility of participating exceeds the utility associated with an increased probability of death or severe injury. Similarly most people have decided that the utility of not using active restraint systems exceeds the utility of increased probability of death. Thus, avoidance of death or severe injury has a finite utility. Extension of this result to conclude that a finite cost exists is subject to much greater criticism.
48
W.L. CARLSON
Given the above problems this study used costs that have been used previously for analysis by the Department of Transportation. That approach provided a comparative link to other economic evaluations. Therefore, the economic analysis presented here has the same advantages and shortcomings as those other studies that use death and injury costs developed by the Department of Transportation. The injury and fatality costs were derived by combining average direct costs with expected lost contribution to Gross National Product associated with death or injury for an average victim (Fagin, 1976). Table 4 presents an economic analysis of the relationship of injury cost to vehicle weight. Average cost per occurrence for minor, severe, and fatal injuries were obtained from Fagin (1976). Rates of occurrence per million miles were obtained from the 1977 Fatal Accident Reporting System (FARS). Analysis injuries were obtained from Fagin (1976). Rates of occurrence per million miles were obtained from the 1977 Fatal Accident Reporting System (FARS). Analysis of the CPIR File indicated that there were 1.55 occupants per vehicle involved in crashes. The elasticities for severe and fatal crashes are those computed above. Analysis of the data indicated that the minor injury rate did not increase with vehicle weight change. Instead, some non-injury occupants receive minor injuries while some occupants with minor injuries receive severe injuries. As a result of the computations it can be seen that injury cost is about $18,000 per million miles or 1.8 cents per mile. In addition, each one percent reduction of vehicle weight increases injury cost by approximately $131 per million miles. The fuel cost analysis was based upon the method presented by McGillioray (1976). In this analysis the marginal cost of fuel as a function of vehicle weight change is $0.0016 per mile per 100 lb. This result assumes an average price of $0.90 per gallon and an average consumption of 1/16 gallons per mile (16 mg). The elasticity, ei, of fuel cost with respect to vehicle weight is,
~C/C er=iW/W
AC W ,~W ~-
(7)
where AC C W
is the change in fuel cost per 100 Ib change in vehicle weight per mile, is the average fuel cost per mile, and is the average vehicle weight in pounds.
By using the previously stated values, we found that, 0,0016
3544
et = 100 "0.09/16
-
1.03.
Fuel cost per million miles was, (0.55/14) × 106 = $56,250, or approximately 5.6 cents per mile compared to 1.8 cents per mile for injury cost. The change in fuel cost per million miles for each one percent reduction in vehicle weight was therefore, (1.03) (-0.01) (56,250)=- $579. Thus the difference between fuel cost reduction in injury cost increase is, $579-$131 = $448 per million miles of vehicle travel for each one percent reduction in vehicle weight. These results can also be expressed in terms of an individual vehicle life. If a vehicle life is Table 4. Economicanalysisof injury cost and change in averagevehicleweight¢ INJURY SEVERITY
AVLRA(;E COST PEK OCCURREHCE
b!Inor (A!S = 1,2)
$
Severe (AIS > 2) Fatal
2,9g6"
DRIVER IN.TUI~Y RF,~E PER NILLION MILES
0.670
OV}[IK~LL INJL:R! RAql }'El), VLHICLI PER HILLI01; MILES
!.838
COST PER MILLION blILES
$ 3,258
ELASTICITY
0
36,282
0.126
0.195
7,094
-.86
244,107
0.016
0.0231
7r949
-.88
$18,101
COST PER i% VEHICLE WEIGHT R~DUCTION
561 70 $131
tThese costs were adjusted from the 1975 costs reported by Fagin (1976) by using the implicit price deflator (President's rep. 1979).
Quantitative analysis of policy decisions
49
assumed to be 100,000 miles then a 20% reduction in vehicle weight would result in a net savings of $8%. The analysis above has several important policy implications. In terms of overall societal costs, vehicle weight reduction has a positive benefit. Unfortunately that result is clouded by the fact that the cost analysis includes the controversial procedure of assigning a dollar value to human life. One possible solution to that problem is to spend additional money for improved occupant protection. Given proper selection of technology it is likely that increased occupant injury could be avoided. Thus, some of the above cost saving could be used to purchase additional occupant protection. For example, design concepts from the research safety vehicle and passive restraints are likely candidates for improved occupant protection. Other alternatives could be explored using the above approach. By using the estimated potential injury severity reduction and cost for new occupant protection devices a less controversial analysis could be performed. The cost of reducing to zero the injury severity increase that results from reduced vehicle size could then be determined. By using that approach the controversial use of a dollar cost of death and severe injury could be avoided. Then the economic comparison would involve fuel cost savings versus increased cost for occupant protection hardware. At this point, interaction between policy makers and the analysis process would be desirable. P A S S I V E R E S T R A I N T S AND V E H I C L E SIZE I N T E R A C T I O N
The Department of Transportation has ruled that the air bag or other passive restraints will become mandatory on all new cars beginning with the 1982 model year. Passive restraints avoid the need for drivers or passengers to actively buckle seat belt and shoulder harnesses. Passive restraints are expected to provide occupant injury protection in frontal but not side or rear impacts. The mandatory requirement is motivated by the fact that only about one in five vehicle occupants presently use active restraints. Thus, passive restraints will benefit only those people who are presently unwilling to use the presently available seat belts and shoulder harnesses. This raises important ethical and political questions. Should society protect those who are unwilling to protect themselves? Should persons who presently use active restraints be forced to pay an additional cost for protection that they now obtain by voluntary use of restraints? These questions were debated by both the Department of Transportation and Congress and were part of the decision process. Thus in a strictly legal sense these "ethical" questions have been answered. Our concern here is with their relative effectiveness in large vs small cars. The introduction of passive restraints will begin with large automobiles in the first year and proceed to include smaller automobiles in subsequent years. The decision to introduce passive restraints first in large cars was based primarily on the present level of design and production technology. Recently this phasing decision has been criticized by consumer groups. Their criticism was based on the fact that injury severity is greater for occupants of small cars compared to occupants of large cars. This paper presents the results of a study to determine whether the effectiveness of passive restraints are related to vehicle size. To estimate the comparative effectiveness of restraints in large and small cars it was necessary to first consider their design objectives and crash dynamics. Passive restraints are designed to reduce occupant injuries in frontal crashes over a range of crash severity. Passive restraints will not reduce injuries in low severity crashes because occupants are typically not injured without them. Passive restraints will not reduce injuries in high severity crashes because of crash forces that exceed both vehicle structure and restraint design characteristics. Thus, there is a critical range of crash severity.t Within this range passive restraints can be expected to reduce injuries. From other studies we know that small cars will have fewer crashes below the critical range and more crashes above the critical range compared to large cars. This phenomenon complicates the analysis. Based upon the above discussion we anticipated that passive restraints reduce small car occupant injuries more in low speed crashes and reduce large car occupant injuries more in high speed crashes. The model presented in this paper does not include the effect of passive restraints. Thus, if the injury prediction model is to be used it is necessary to specify a surrogate for passive restraints. This analysis has used seat belts in frontal crashes as a surrogate for passive tFor this study crash severity was measured by A V the change in velocity at impact. AAP Vol. 12, No. I--D
50
W.L. CARLSON
restraints. That approach has the disadvantage of not using data from the actual occupant protection mechanism that is being analyzed. Direct use of passive restraint performance data from crashes is hampered by the limited number of observations. This reduces the precision of injury reduction estimates and minimizes the possibility of considering passive restraint interactions with other crash variables. Thus our analysis has the advantage of considering restraint effectiveness over a wide range of crash conditions. The NCSS data indicates that restraint usage in accident involved vehicles does not vary substantially by size of car. Specifically the observed restraint usage was:
Vehicle Size < 2200 lb 2200-2900 lb 2900-3600 lb 3600--4300 lb > 4300 lb
Per cent Restraint Usage 9.9% 13.2% 7.9% 6.5% 10.1%
Comparison of the age coefficient for the belted and the unbelted injury prediction models (eqns (3) and (4)) indicates an important interaction. Injury severity increases faster with increasing age for belted compared to unbelted occupants. Thus, greater overall injury reduction would occur if older persons received the benefits of passive restraints before younger persons. Analysis of the Restraint System Evaluation Project (RSEP) data indicates that in the accident population the mean driver age by vehicle size was: subcompacts, 28.0, compacts, 30.5; intermediates, 33.0; and full sized, 38.9. A frontal crash restraint system effectiveness model was developed from the overall injury prediction model. This was done by first obtaining a separate effectiveness model for head on, side impact-striking, rear impact-striking and single vehicle-struck fixed object crash configurations. Restraint system effectiveness models for each crash configuration were obtained by subtracting the restrained occupant model from the unrestrained occupant model. The result is an equation which predicts reduction in expected AIS for each crash configuration. A positive difference indicated a positive injury reduction. The following restraint effectiveness models by crash configuration resulted, 1. Head on crashes A y = - 0.0095 V + 0.006A + 0.44X1 + 0.52)(2 + 0.20)(3 -0.06X4 + 0.19X~
(8)
2. Side Impact--striking car A y = - 0.031A V + 0.008A + 0.77X1 + 0.38)(2 + 0.44X~ + 0.29)(4 + 0.42X5
(9)
3. Rear Impact--striking car A y = - 0.012A V - 0.001A - 0.37X1 + 0.13)(2 + 0.13X3 + 0.25X4 + 0.34Xs
(lO)
4. Single Vehicle--struck fixed object A Y = 0.0235 V + 0.014A - 0.15)(1 - 1.04X2 - 0.68X3 - 0.63)(4 - 0.84X5
(11)
where Ay
is the estimated difference in expected AIS between unrestrained and restrained drivers, A V is the estimated change in velocity at impact in mph (This variable is used to control for differences in crash severity). A is the occupant age,
Quantitativeanalysisof policydecisions :(1 :(2 :(3 X4
X5
51
is 1 for cars under 2200 lb 0 otherwise, is 1 for cars in the weight range 2200-2900 lb 0 otherwise, is 1 for cars in the weight range 2900-3600 lb 0 otherwise, is 1 for cars in the weight range 360(0300 lb 0 otherwise, is 1 for cars above 4300 lb 0 otherwise.
The driver and right front passenger coefficients were eliminated from these equations because they do not affect the comparison. Examination of these separate models revealed several important conclusions concerning restraint effectiveness in frontal crashes, 1. Restraint effectiveness increases with increasing occupant age. 2. Restraint effectiveness for cars under 2200 lb is generally higher compared to larger cars, 3. The model for single vehicle crashes has strange coefficients for the vehicle weight vffects. From the NCSS data file it was determined that cars are involved in crashes with the following proportions:
Crash Configuration Head on Side Impact--striking Rear Impact--striking Single Vehicle--Struck Fixed Object
Percent of All Crash Involvements 12.7% 22.4% 10.7%
Percent of Frontal Crash Involvements 19.8% 34.9% 16.7%
18.3% 64.1%
28.5% 100.0 .
The four restraint effectiveness models were then combined using the above percentages of frontal crash involvements as weights. In this way the following overall model of restraint effectiveness was estimated, A y = - 0.00005A V + 0.008A + 0.25X1 + - 0.04X2 + 0.02X3 + 0.05X4 + 0.0X5
(12)
where the variables are as defined above. The large coefficient for Xt indicates that restraint effectiveness, unadjusted for restraint usage and occupant age, is greatest for cars under 2200 lb. Equation (12) was used to obtain adjusted measures of restraint effectiveness. To do this it was necessary to estimate the average occupant age and the average change in velocity at impact for each vehicle size. Average occupant age was obtained from the NCSS data file. To obtain an average change in velocity at impact, A V, we assumed that all vehicles in each weight group had a single weight and that they collided with a vehicle whose weight was equal to the average weight for the entire vehicle population. An average velocity at impact was also determined from both the CPIR and the NCSS files. This velocity was used with the relative weights of colliding vehicles to compute an average, A V, for each vehicle size. This process assigned a higher A V to lighter vehicles, which is consistent with crash dynamics. Finally, the restraint effectiveness measures were adjusted by the fraction of the drivers who do not use restraints. Using the data described above and eqn (12) a net effectiveness measure was computed for each vehicle size. Net effectiveness is the reduction is expected AIS that results from using restraints. The data and the results of this process are presented in Table 5. Examination of the net effectiveness by vehicle size indicated that the effectiveness is greatest for cars under 2200 lb. However, the effectiveness is approximately the same for all other vehicle sizes.
W. L. CARLSON
52
Table 5. Computationof net restrainteffectivenessby vehicle size Vehicle Size
Percent Unrestrained
Net Restraint Effectiveness
AV
Ase
14.9
28.0
.901
.43
2200-2900 pounds
]3.4
30.5
.868
.18
2900-3600 ')cur:ds
12.(I
33.0
.921
.26
3600-4300
]6).8
33.0
.935
.20
>4300 pounds
]0.1
38.9
.899
.28
<2200
pounds
Table 6. Injuryseverityfor belted vs unbeltedoccupantsby vehicle size in towawaycrashes (Proportion AIS ~ 2) Injury Reduction (Unbelted-Belted)
Unbelted
Belted
Subcompact
0.131
0.094
0.035
Compact
0.111
0.082
0.029
Intermediate
0.118
0.068
0.050
Full ~ize
0.120
0.048
0.072
The injury reduction for full size cars is significantly
(~ < .05) larger
than the redu~=ion for subcompact cars
Table 7. Injuryseverityfor belted vs unbeltedoccupantsby vehicle size in towawaycrashes (Proportion AIS > 3) Injury R~ductlon (Unbelted-Belted)
Unbelted
Belted
Subcompact
0.033
0.022
0.011
Compact
0.029
0.010
0.019
Intermediate
0.032
0.014
0.0}8
Full Size
0.035
0.013
0.022
This analysis revealed the complexity of the restraint effectiveness question. The analysis began with models that estimated expected injury as a function of several important variables. These models were then used with observed characteristics of the driving and crashing population to obtain measures of net restraint effectiveness. An important result of this analysis is the interactive effect of occupant age and restraint usage on restraint effectiveness. Thus, passive restraints will reduce injury severity more in large cars in part because large car occupants tend to be older. A number of political arguments could be developed based on these effects. However, it is the opinion of this writer that programs to reduce injuries should not discriminate against older people. Thus it is not reasonable to argue against the conclusion because of the interaction effects. Additional support for the result presented here was obtained from the results of a recent study of restraint system effectiveness (Reinfurt, Silva, Seila, 1976). That study used data from the RSEP data file to conduct an extensive analysis of restraint system effectiveness. Table 6 compares the proportion injured (AIS-> 2) for unrestrained and lap belted vehicle occupants. Examination of the data indicates that the injury reduction for lap belts was largest for full size cars. The same result occurred for severe injuries (AIS-> 3) as shown in Table 7.
Quantitative analysis of policy decisions
53
These comparisons differ somewhat from the analysis which used the injury prediction model. First the comparisons were not restricted to frontal crashes. Thus, lap belted occupants cannot be used as surrogates for occupants with passive restraints. A specific adjustment was not made for occupant age. However, the RSEP data file included different age groups in proportion to their occurrence in crashes. Thus the age adjustment was included in the injury rates presented in Tables 6 and 7. In addition, the injury rate differences were not adjusted for differences in restraint usage. However, that adjustment would increase the margin in favor of large cars even more. REFERENCES Carlson W. L., Crash injury prediction model, Accid. Anal. & Prey. 11,137-153. Dutt A. and Reinfurt D., Accident involvement and crash injury rates by make, model, and year of car, a follow-up. Highway Safety Research Center, The University of North Carolina, Chapel Hill, North Carolina, June 1977. Fagin B. M., 1975 Societal Costs of Motor Vehicle Accidents, U.S. Department of Transportation, Washington, D.C., December, 1976. Hayes R. H. and Nolan R. L., What kind of corporate modeling functions best, Harvard Business Review, May-June, 102-112, 1974. Hedlund James H., The national crash severity study and its relationships to ESV design criteria. Proc. of 7th Int. Conf. on Experimental Safety Vehicle, Paris, June 5-8, 1979. Highway Statistics 1976, Federal Highway Administration. Jatras K., and Carlson W., Frequency distributions of passenger cars by weight and wheelbase by state: July I, 1976. U.S. Department of Transportation, Washington, D.C., May, 1978. Kahane C., and Mungenast J., Restraint systems evaluation project codebook, Rep. No. DOT-HS-8020285, U.S. Department of Transportation, Washington, D.C., March, 1977. Kahane C. and Mungenast J., Survey of trafficpopulation (August 1976-March, 1977),Krischner Associates, Washington, D.C., DOT-HS-6-O1340, December, 1977. McGillivray R., Automobile gasoline conservation, Rep. No. 708-01, Urban Institute, Washington, D.C., April, 1976. Mela D., How safe can we be in small cars. Proc. of the 3rd Int. Cong. on Automotive Safety, Vol. II. San Francisco, California, July, 1974. O'Day J., Golomb H. and Cooley P., A statistical description of large and small car involvement in accidents, Hit. Lab Rep., Vol. 3, No. 9, Highway Safety Research Institute, University of Michigan, Ann Arbor, Michigan, May, 1973. O'Neil B., Joksch G. and Haddon W., Empirical relationships between car size, car weight and crash injuries in car-to-car crashes. 5th Int. Tech. Conf. on Experimental Safety Vehicles, London, England, June, 1974. Reinfurt D. W., Silva C. Z., and Seila A. F., A statistical analysis of seat belt effectiveness in 1973-1975 model cars involved in towaway crashes, Highway Safety Research Center, The University of North Carolina, Chapel Hill, N.C., May, 1976.