Safety and Fuel Economy of Passenger Cars
Masayoshi Tanishita
Hiroaki Miyoshi
ITEC Working Paper Series
07-03
March 2007

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Safety and Fuel Economy of Passenger Cars


Institute for Technology, Enterprise and Competitiveness, Doshisha University
Working Paper 07-03



Masayoshi Tanishita
Associate Professor
Department of Civil Engineering, Faculty of Science and Engineering
Chuo University
1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan 112-8551
Tel: 03-3817-1810
Fax: 03-3817-1803
E-mail: tanishi@civil.chuo-u.ac.jp
and COE Visiting Fellow
Institute for Technology, Enterprise and Competitiveness (ITEC)
Doshisha University


Hiroaki Miyoshi
COE Research Fellow
Institute for Technology, Enterprise and Competitiveness (ITEC)
Doshisha University
Karasuma Imadegawa, Kamigyo-ku, Kyoto, Japan 602-8580
Tel: 075-251-3837
Fax: 075-251-3139
E-mail: hmiyoshi@mail.doshisha.ac.jp

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Abstract:
In the United States, while there exists a result of analysis that shows tighter fuel
efficiency requirements leading to lighter vehicle bodies would increase the number of
fatal accidents, other recent works argue that fuel economy is not relevant to the
occurrence rate of fatal accidents. This research is aimed at examining the relationship
between fuel economy and the occurrence rates of accidents in Japan.
Traditionally, the safety of passenger cars has been assessed through the use of
laboratory data from the viewpoint of risk of death and injury under the assumption that
accidents have already occurred and results have been published in New Car
Assessment. On the other hand, we examined safety by vehicle type from the
perspective of the occurrence rates of accidents resulting in death (fatal accidents) and
accidents resulting in injury or death (hereinafter accidents”). We conducted negative
binominal regression analyses of the occurrence rates of fatal accidents and accidents,
taking into consideration the influence of driver-related factors, vehicle characteristics
on these occurrence rates. The results of our analysis demonstrate that there is no
important difference in the adjusted occurrence rates of fatal accidents and accidents,
which excludes the effects of driver-related characteristics, among vehicle types other
than minivans and sport and specialty cars; further, it has been clarified that the
adjusted occurrence rate of fatal accidents is not necessarily strongly correlated with the
score in New Car Assessment. While the adjusted occurrence rate of fatal accidents
exhibited a tendency to decrease inversely with the increase in the weight of the vehicle,
we obtained an opposite result for sport and specialty cars, which have a high adjusted
occurrence rate of fatal accidents. There is a possibility that the interior volume or the
vehicle shape would have a greater influence on the occurrence rate of fatal accidents.
Keywords: safety, accident, fatal accident, fuel economy, negative binominal regression
JEL codes: K29, R49
Acknowledgements:
This paper is a modified version of our paper presented at the 34th Conference of
Infrastructure Planning (Takamatsu-city); it is also part of Doshisha University’s ITEC
21st Century COE (Centre of Excellence) Program titled “Synthetic Studies on
Technology, Enterprise and Competitiveness.” The idea of this paper emerged during
a discussion with Tom Wenzel (Lawrence Berkeley National Laboratory) and Marc
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Ross (University of Michigan). In compiling the database for analysis, we gained the
cooperation of Mr. Hiroshi Takahashi (who graduated from Chuo University in 2005)
and received valuable advice from Mr. Hisashi Imanaga (Japan Automobile Research
Institute), the participants of the above conference, and anonymous referees. I would
like to take this opportunity to extend a special thanks to all of them.
ITEC Working Paper 07-03

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Safety and Fuel Economy of Passenger Cars
Masayoshi Tanishita/ Hiroaki Miyoshi


1. Introduction
In connection with the restriction of the Corporate Average Fuel Economy (CAFE)
in the United States, while Crandall and Graham (1989) show that tighter fuel efficiency
requirements leading to lighter vehicle bodies would increase the number of fatal
accidents, other recent works (Ahmad and Greene, 2005; Noland, 2005; Wenzel and
Ross, 2003) argue that fuel economy is not relevant to the occurrence rate of fatal
accidents. This research is aimed at examining the relationship between fuel economy
and the occurrence rate of accidents resulting in death (fatal accidents) and accidents
resulting in injury or death (hereinafter “accidents”) in Japan. It would also be
important to clarify the relationship between vehicle characteristics and the occurrence
rates of fatal accidents or accidents for the future examination of fuel efficiency
requirements or safety regulations in Japan. Three factors—vehicle characteristics,
driver-related characteristics, and the driving environment (the road structure, the traffic
volume, etc.)—are relevant to traffic accidents, and a number of research studies have
been carried out on the relationship between each factor and traffic accidents. In this
paper, we will focus on the characteristics of vehicles and drivers. With regard to
vehicle characteristics, factors such as the engine size and the weight of the vehicle
affect the acceleration performance, while factors such as the interior volume or the
center of gravity have an impact on the ease of driving, the risk of overturn, and the ease
of engaging in avoidance behaviors. These factors are relevant to the occurrence rates
of accidents and the gravity of damage in accidents. On the other hand, with regard to
driver-related characteristics, experience and character are said to influence the
occurrence rates of accidents.
As concrete indicators of safety related to vehicle characteristics, the Ministry of
Land, Infrastructure and Transport and the National Agency for Automotive Safety &
Victims’ Aid evaluated the collision safety performance of each type of vehicle through
collision tests and published the results in New Car Assessment. In addition, Japan
Automobile Research Institute examined the relationship between the score presented in
New Car Assessment and the mortality and serious injury rates in actual accidents; it
concluded that while there is a correlation between these factors, the statistical
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significance is low (Tominaga et al., 2004). While they have examined safety on the
presupposition that accidents have already occurred, we can also consider the
occurrence rate of accidents, which is calculated by dividing the number of accidents
that have occurred by the number of vehicles as one of indicators for evaluating vehicle
safety. Thus, this paper will focus on the occurrence of “actual” accidents as the
indicator for safety.
The data on the number of actual accidents is published by Institute for Traffic
Research and Data Analysis. However, the values in this data do not exclude driver-
related characteristics and the influences of the driving environment; further, they do
not directly reflect the safety of the vehicle itself. In addition, it should also be noted
that there is a possibility that drivers’ overestimation of safe vehicles caused a moral
hazard for them and increased the number of accidents.
This paper is aimed at estimating the safety of passenger cars from the viewpoint
of the probability of accidents, by controlling for driver-related factors, such as the rate
at which the seatbelt is worn and the rate of alcohol consumption, and analyzing the
relationship between the results of our estimation and those of the evaluation in New
Car Assessment or the fuel economy.
In this paper, we will first explain the data and method used in the next section.
With regard to the method, we show that it would be inappropriate to apply the ordinary
regression analysis as we intend to deal with a rare phenomenon, namely, accidents;
thus, we use the negative binominal regression that further generalizes the Poisson
regression. In the third section, we present the regression results obtained using the
abovementioned method. In the fourth section, we discuss the regression results and
demonstrate the following: (i) the level of safety is the highest in the case of minivans
and the lowest in the case of sport and specialty cars, but there is no important
difference among other types of vehicle; (ii) the occurrence rate of actual fatal accidents
is not necessarily strongly correlated with the assessment score in New Car Assessment;
and (iii) while the rate of fatal accidents tends to decrease inversely with the increase in
the weight of the vehicle, we have obtained the opposite result for sport and specialty
cars, which have a high occurrence rate of fatal accidents; further, there is a possibility
that the interior volume, which is a variable representative of the number of passengers,
or the vehicle shape would have a greater influence on the occurrence rate of fatal
accidents. Finally, in the concluding section, we explain the importance of promoting
the development of technologies for improving both fuel economy and safety.
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2．Data and Methods
2.1. Data
We have used the integral data on traffic accidents prepared and managed by
Institute for Traffic Research and Data Analysis for a period of six years in total—from
1996 to 1998 and from 1999 to 2001—to extract the following statistics: the number of
vehicles by common name, the number of vehicles in which passengers were killed, the
number of vehicles involved in accidents, the rate of alcohol consumption, the accident
history, and the rate at which the seatbelt is worn in vehicles involved in fatal accidents
and accidents. In this case, the number of vehicles involved in accidents implies the
cases in which the passenger(s) of the vehicle concerned was (were) killed or injured.
With respect to the number of vehicles in which passengers were killed, we counted as
one car when at least one of the passengers of the vehicles involved in an accident was
killed even if several passengers were killed. While we are aware that in order to
describe the vehicle characteristics, it may be more appropriate to deal with fatal
accidents and accidents in which the vehicle concerned has the maximum rating blame,
we did not consider this in this study; it remains as a challenge for future research.
By doing so, we obtained macro data on these items by common names (names
used in catalogs, such as “Corolla” or “Crown,” which can be different from those
appearing on vehicle inspection certificates). 8 types of vehicles, 238 common names,
and 363 samples. We excluded vehicles with less than 50 thousand registered number
from the samples to ensure reliability. Vehicle Types and the number of common names
considered in the analysis are presented in Table 1 (the names within parentheses
represent the common names of the relevant vehicle type).

Table 1 Vehicle Types and the number of common names considered in the analysis
Vehicle type
Number of common names

Light family cars (Wagon R) 30


Sedan A (Engine size of less than 1500 cc: March)
28

Sedan B (Engine size of less than 2000 cc: Corona)
36

Sedan C (Engine size of more than 2000 cc: Mark II)
28

Sport and Specialty (Celica)
23

Wagon (Corolla Wagon)
42
Minivan
(Estima)
30
RV/SUV
(Pajero)
21
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For the above samples, using the Japanese Motor Vehicles Guidebook, we have
also compiled data such as the price, the weight of the vehicle, fuel economy, the
interior volume (= length of the vehicle * width of the vehicle * height of the vehicle),
as well as the degree of instability (= height of the vehicle / (width of the vehicle *
length of the vehicle)) in view of the risk of overturn during collision. As the weight
of the vehicle may alleviate the acceleration performance or the impact at the time of
collision, it is expected to have a negative influence on the occurrence rate of fatal
accidents and accidents. Likewise, fuel economy will have a positive correlation with
the occurrence rates of fatal accidents and accidents because it decreases as the weight
of the vehicle increases. These are the arguments of automakers in the discussion
related to tighter restrictions on fuel economy in the United States. While we have
employed the interior volume as one of indicators showing the ease of driving due to
our belief that drivers can derive greater relaxation in spacious cars, we should also be
aware of its effect as a representative indicator of the number of passengers. In other
words, the driver will become more safety conscious when he or she has one or more
fellow passengers, thereby reducing the occurrence rates of fatal accidents and accidents.
(In contrast, we can assume that the possibility that passengers sustained injuries in the
accident will increase in the case of a greater number of fellow passengers). While
elements such as the engine size, the horsepower/weight, and the brake performance are
also important variables, in this paper, we consider them as dummy variables for vehicle
types. With regard to the data on the performance indicator of passenger cars, we have
employed the median value in the case where one common name of vehicle has several
models. The descriptive statistics related to the abovementioned variables are listed in
Table 2.
Table 2 Summary statistics for the key variables
Variables
Min.
Mean
Max.
Variance
a. # of vehicles involved in fatal accidents
0
17.9
147
464.5
b. # of vehicles involved in accidents
563
4595
55055
6.72E+07
c. # of registered vehicles
51000
417240
2683000
1.92E+11
Occurrence rate of fatal accidents (= a / c)
0
0.0035
0.028
1.34E-05
Occurrence rate of accidents (= b / c)
1.05
1.84
2.94
1.00E-01
Weight (kg)
6.30E+02
1.25E+03
2.13E+03
1.04E+04
Interior volume (m3)
0.99
3.25
5.71
9.70E-01
Degree of instability (= height / (width*length)) (m–1)
2.60E-04
4.60E-04
1.02E-03
1.29E-08
Fuel economy (l/km)
6
12.68
28
1.60E+01
Drinking rate (%)
0
2.17E+01
1.00E+02
331.07
Accident history rate (%)
0
9.9
50
1.34E+02
Seatbelt wearing rate (%)
84.4
93.58
98
8.47
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2.2. Method
With respect to the occurrence rate of fatal accidents (= the number of accidents in
which passengers were killed / the number of vehicles registered) and the occurrence
rate of accidents (= the number of vehicles involved in accidents resulting in injury or
death / the number of vehicles registered), we will conduct regression analyses with
four categories of variables as the explanatory variables. The first is driver-related
characteristics that comprise the rate of alcohol consumption, accident history, and the
rate at which the seatbelt is worn. The second is vehicle characteristics that span the
weight of the vehicle, the interior volume, the degree of instability, and the dummy
variables for vehicle types (we set recreational vehicle (RV) as zero). The third is the
dummy variable for the time points that reflect the technological improvement between
the periods 1996–1998 and 1999–2001 as well as the changes in the driving
environment. As indicated in Figure 1, it should be noted that fuel economy has a
strong correlation with the weight of the vehicle. Therefore, in order to avoid the
problem of multicollinearity, we will not consider fuel economy as an explanatory
variable at this stage, but we examine this in section 4.
30
25
20
fe
15
10
5
0
0
500
1000
1500
2000
2500


weight

Note 1) “Fe” denotes “Fuel economy.”
2) The result of the single regression is as follows:
ln (Fe) = 9.40 – 0.97 ln (Weight) 2
R = 0.71
(40.43)
(–29.75)
The values within parentheses are t-values.
Figure 1 Correlation between the weight of the vehicle and fuel economy
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As the frequency of accidents is limited, it is not appropriate to apply the ordinary
least squares (OLS) method that presupposes the homogeneous dispersion and normal
distribution of the error term. Namawa and Shimamura (1998) conducted a Poisson
regression analysis that presupposes that the average and the dispersion of the error term
are equal. Initially, we attempted to adopt the Poisson regression as well. However,
because the dispersion of the error item greatly exceeded its average, we decided to
conduct a negative binominal regression analysis that further generalizes the Poisson
regression (when the parameter of the Poisson distribution follows the gamma
distribution, the Poisson distribution will correspond to the negative binominal
distribution.) In this case, it can be described as the generalized linear model, and the
parameters will be estimated by the maximum likelihood method.
We now briefly explain the negative binomial regression. Let us assume that
Y —the number of accidents (the number of fatal accidents)—follows the negative
binominal distribution. If three covariates ( X ) affects Y , the probability that we can
obtain Y = y will be indicated as below:
k
y
Γ( + ) ⎛
⎞ ⎛ μ ⎞
P ( Y = y |
y
k
k
X , X , X , k ) =
y = 0, 1, 2… (1)
1
2
3
⎜
⎜
⎟
⎟ ⎜⎜
⎟
⎟
Γ(k)Γ( y) ⎝ k + μ ⎠ ⎝ k + μ ⎠
In this case, Γ is expressed as a gamma function, μ = E (Y ) (the expectation of Y ),
and k is a parameter related to the dispersion. The dispersion of Y can be
expressed as V ( Y ) = μ + 2
μ k (in the Poisson distribution, k = ∞). Thus,
assuming that the following link function η = g ( μ ) can be explained as the linear
sum of the covariate ( X ), we estimate parameter β 3 as follows.

η = g ( μ ) = log ( μ ) = 'x β
μ = exp ( 'x β )
⎡β0 ⎤
⎢ ⎥
where
'
x = [1,
β
X ,
1
X ,
2
X ] and β = ⎢ 1 ⎥ …(2)
3
⎢β ⎥
⎢ 2 ⎥
⎣β3 ⎦

While Y denotes the number of targeted vehicles, we obtain the occurrence rates of
fatal accidents and accidents by using the number of vehicles registered as the offset
variable (denominator).


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Document Outline

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