The National Safety Council estimates that the expected reduction in occupant death rates due to usage of lap seat belts would be 7-8.5 percent (see Peltzman |1975~). In addition, Campbell and Campbell |1988~ estimate that fatalities in the twenty-five states with seat belt laws were 6.6 percent lower than forecast for these states. This improvement amounts to approximately 1,300 lives saved. Swan |1984~ reports that seat belts are negatively correlated with the number of traffic fatalities. This conclusion is based on a pooled cross-section, time-series model for Australia and New Zealand. Finally, McEwin |1986~ estimates on the basis of his empirical model that a 100 percent usage of seat belts would reduce fatalities by 40 percent.
However, a number of studies have pointed out that, contrary to conventional wisdom, seat belt laws may not reduce the total number of fatalities. Their argument is that use of the safety belt provides the driver with an additional sense of security which translates into relatively more reckless driving. There is a potential for offsetting or compensating behavior on the part of the driver of the automobile. This notion is referred to as the "compensating-behavior hypothesis."
Compensating behavior is justified on both theoretical and empirical grounds. Blomquist |1986~ finds that compensating behavior is utility maximizing if an individual's safety effort and exogenous safety measures (e.g., government regulations) are substitutes in determining the probability of and loss from an automobile accident.
Peltzman |1975; 1976~ tested the impact of automobile safety regulation on both occupant and non-occupant deaths. He found evidence from aggregate time-series and cross-section data that occupants' lives are saved at the expense of pedestrian deaths and a larger number of nonfatal accidents. Recently, Garbacz |1991a~ tested this hypothesis using aggregate time-series data for New Zealand. He found that a mandatory seat belt law, enacted in 1972, was negatively correlated with the deaths of automobile occupants and positively associated with deaths of cyclists and pedestrians. In fact, the Garbacz study indicated complete offsetting in that total deaths showed no relationship to seat belt use (savings in occupant deaths were just offset by the increase in non-occupant deaths). In other work Garbacz |1990; 1991b; 1992~ provides further evidence of offsetting behavior, demonstrating that both non-occupants and rear-seat passengers are more at risk when seat belt laws are in effect. A final example of offsetting behavior was provided in a recent Wall Street Journal article (10 October 1991) that showed that air bags seem to reduce fatalities, but accidents and other associated injuries have increased.
One concern in the Garbacz |1991a~ work was the sensitivity of the results to the "speed variable" (average open-road speed for the 85th percentile of vehicles). He concluded that this variable could be endogenous to the estimation process. Thus, the compensating-behavior hypothesis would imply more risk taking (including speeding) after the imposition of the seat belt law. In fact, Lave and Weber |1970~ first suggested the possibility that mandated safety devices might lead to faster driving, offsetting some or all of the beneficial effect of the safety device.
In this paper we re-examine the issue of compensating behavior when individuals use seat belts. Our investigation has a number of significant departures from previous studies. First, since compensating behavior is a hypothesis of individual action, we test the hypothesis using individual-specific observations. The studies discussed above employed aggregate time-series or cross-section data. At the aggregate level, the statistical regularities could conceivably be caused by other confounding factors.
Second, we test the compensating-behavior hypothesis after accounting for tastes in risks (as manifested by precautionary steps individuals have taken to reduce everyday risks). The notion of an individual who wears a seat belt taking more or less risk is obviously tied to his/her risk preference. For example, Blomquist |1991~ has found that individuals seem to consider relative risk when making safety equipment decisions; that is, individuals are not risk incompetent. Testing the compensating hypothesis at an aggregate level without controlling for the risk preferences of specific individuals could result in specification error. One would expect a priori that the compensating-behavior hypothesis holds for individuals who have a low regard for various risks. On the other hand, risk averse individuals may not compensate (for the additional safety provided by a seat belt) by driving more recklessly. Clearly, tastes for risk are an important dimension of the compensating behavior hypothesis.
Third, this study employs a more sensitive indicator of compensating behavior. As discussed above, past studies have analyzed the impact of safety belts or safety belt laws on the number of fatalities and/or the number of accidents. We analyze the impact of an individual's seat belt usage on the number of moving violations (tickets).(1) If seat belt wearing drivers are taking additional risks, then such behavior will result in a larger number of moving violations, ceteris paribus.
Finally, our empirical model controls for other individual-specific variables (besides seat belt use) which may affect driving performance. These confounding factors include the number of years individuals have worn seat belts, age, miles driven to work, education level, sex, and annual income.
The remainder of the paper is organized as follows. In the next section we present a theoretical model of individual behavior. In section III the data and the basic empirical model are discussed. Results are presented in section IV. Concluding remarks and some caveats are offered in section V.
II. THEORETICAL BASIS
Blomquist |1986~ demonstrated that compensating behavior is utility maximizing if individual and exogenous safety measures are substitutes in the production of a specific accident risk level. However, Blomquist did not address the possibility that individual and exogenous measures could be combined in a complementary manner (i.e. exogenous safety measures would enhance individual efforts). In this latter case compensating behavior cannot be predicted a priori. In this paper the manner in which individuals combine safety measures, and the consequent effect on compensating behavior, is taken to be an empirical question.
The model presented herein utilizes the Blomquist framework. Let
e = individual safety measures;
g = exogenous safety measures beyond control of the individual;
P = P(e,g) = probability that an individual is involved in an automobile accident where probability is influenced by individual actions (|P.sub.e~ |is less than~ 0, |P.sub.ee~ |is greater than~ 0) and exogenous factors |P.sub.g~ |is less than~ 0, |P.sub.gg~ |is greater than~ 0);
L = L(e,g) = loss associated with an accident where loss is influenced by individual actions (|L.sub.e~ |is less than~ 0, |L.sub.ee~ |is greater than~ 0) and exogenous safety measures (|L.sub.g~ |is less than~ 0, |L.sub.gg~ |is greater than~ 0);
D = D(e,g) = disutility associated with driver safety (|D.sub.e~ |is greater than~ 0, |D.sub.ee~ |is greater than~ 0) and exogenous safety factors (|D.sub.g~ |is greater than~ 0, |D.sub.gg~ |is greater than~ 0). Disutility may result from the interaction of individual and exogenous actions (|D.sub.eg~ |is greater than~ 0).
Also note that we have made no assumption concerning the relationship between e and g in either the production function P or the loss function L. If |P.sub.eg~ and |L.sub.eg~ are non-negative, then individual and exogenous actions are substitutes in production (see Blomquist |1986~). However, if these values are negative, then individuals perceive e and g as complementary goods.
The individual is assumed to maximize expected utility, constrained by income (I). Thus
(1) U = P (e,g)|I - D(e,g) - L(e,g)~ + |1 - P(e,g)~ |I - D(e,g)~
U = I - D(e,g) - P(e,g)L(e,g).
The individual will take safety measures until the benefits of additional action (benefits of reduction in expected loss) are just offset by the additional disutility. Thus, optimal driver safety effort will conform to
(2) -|D.sub.e~ = |P.sub.e~L + P|L.sub.e~.
The relationship between individual and exogenous safety measures can be determined by treating equation (2) as an implicit function and using the implicit function rule to solve for de/dg.
(3) de/dg = (|D.sub.eg~ + |P.sub.eg~L + |P.sub.e~|L.sub.g~ + |P.sub.g~|L.sub.e~ + P|L.sub.eg~) / (-|D.sub.ee~ - |P.sub.ee~L - 2|P.sub.e~|L.sub.e~ - P|L.sub.ee~)
Following Blomquist |1986~, de/dg |is less than~ 0 if individual and exogenous actions are assumed to be substitutes in the production and loss functions. This is the formula for compensating behavior. However, the sign of de/dg is indeterminate if e and g are assumed to be complementary in reducing risk and loss. In this case compensating behavior does not always occur and will depend on the extent that complementarity produces additional safety that offsets the extra disutility of any exogenous safety measure.
The manner in which individuals treat individual and exogenous safety measures is an empirical question. A priori one would expect that relatively risk averse individuals would demonstrate the least amount of compensating behavior. That is, exogenous safety measures might not be offset by reductions in individual carefulness. Likewise, risk preferrers or risk lovers would be relatively strong candidates for compensating behavior. In the next section we present the data and empirical model that allows this hypothesis to be tested.
III. DATA SPECIFICS AND EMPIRICAL MODEL
The data was collected through a mail survey sent to residents in six San Francisco Bay area counties: Alameda, Contra Costa, Marin, San Francisco, San Mateo and Santa Clara. Potential respondents were selected at random from a master data tape of homeowners. We employed the Dillman |1978~ Total Design Method (TDM) in order to maximize the response rate. This procedure requires complete personalization of the correspondence and multiple attempts to convince respondents to participate in the survey.
Approximately 3,000 surveys were distributed and 1,092 surveys were eventually returned. The response rate was 37.13 percent. This is considered a satisfactory response rate for a mail survey that was extensive, provided no compensation for respondents, and did not utilize all of the TDM approach (we did not follow our mail correspondence with a telephone call due to limited funds).(2)
The survey obtained information concerning seat belt usage, years of seat belt use, number of moving violations over the previous three years, risk preferences, and several control variables including income, sex, age, and education. A detailed definition of each variable is provided in Table I.
Four variables require further discussion. First, the dependent variable in the empirical analysis is the number of moving violations the respondent has received in the previous three years.(3) Moving violations include exceeding posted speed limits, failure to stop at stop sign or traffic light, reckless driving, etc. Second, the seat belt use variable is used to test the compensating-behavior hypothesis by examining its relationship to the number of moving violations. Third, the independent variable for years of seat belt use allows a determination of the magnitude of learning concerning compensating behavior. Finally, the risk index variable, formed by summing the responses to questions concerning six different revealed preferences about risk behavior (presence of smoke alarm, burglar alarm, car alarm, earthquake home insurance, emergency equipment, and emergency food items), is used to measure relative risk aversion.(4) That is, if the individual's risk index is close to the maximum value (6) then he/she is considered relatively risk averse. On the other hand, if the individuals' risk index is near zero then this individual is considered a risk lover since relatively few precautions are taken.
Number of Tickets Number of traffic citations for moving
violations in the past three years.
Moving violations include speeding,
red light, stop sign, reckless driving
Seat Belt Use Discrete variable for seat belt use:
(0) no seat belt use; (1) yes, but
rarely; (2) yes, some of the time; (3)
yes, all the time.
Years of Seat Belt Use Number of years individual has worn a
Education Discrete variable for education
completed: (1) 0-5 grades; (2) 6-8
grades; (3) 8-11 grades; (4) finished
high school; (5) trade school; (6)
some college; (7) college degree; (8)
some graduate work; (9) advanced
college degree/professional degree.
Sex Discrete variable: (0) female; (1)
Age Number of years.
Distance to Work Distance to work site in miles.
Income Discrete variable for annual income:
(1) less than $5,000; (2)
$5,000-$9,999; (3) $10,000-$19,999;
(4) $20,000-$29,999; (5)
$30,000-$39,999; (6) $40,000-$49,999;
(7) $50,000-$59,999; (8)
$60,000-$79,999; (9) $80,000-$99,999;
(10) over $100,000.
Risk Index Sum of responses to six yes/no
questions concerning revealed
preferences about risk. Categories
were smoke alarm, burglar alarm, car
alarm, earthquake insurance, emergency
equipment, and emergency supplies. In
all cases "zero" indicates no whereas
"one" indicates yes.
Underage Children Number of children under the age of
In the empirical analysis we define the risk averse group as those individuals with risk index values of 5 or 6. Those individuals that prefer risk (risk lovers) have index values of 0, 1 or 2. The remaining individuals are considered risk neutral. These division values are arbitrary. However, the significance pattern of the results remains basically the same if other groupings are used. For instance, we used six categories, conforming to the values one through six. The basic results were unchanged. However, the problem with six categories is that risk index values of one and six have only thirteen and thirty observations, respectively. Consequently, the three-tier demarcation defined above is preferred because of a relatively more symmetric distribution of the number of observations in each category.
Descriptive statistics for each of the variables used in the empirical analysis are presented in Table II. The data are presented for each of the three risk preference groups defined above. As is illustrated, risk lovers have received more moving violations than the other groups. In addition, risk lovers use seat belts less often, have used seat belts for a shorter length of time, have lower incomes, and are less educated and younger than the other groups.
It should also be noted that our sample consists of resident owners of single-family homes. Thus, the sample is not necessarily representative of the general population. In particular, our sample is relatively older, better educated, and has greater income than the general population. For example, the sample contains only three respondents less than the age of 25. Since the age group 16-24 generally comprises approximately 20 percent of the drivers, our sample is not representative. Thus, our sample likely receives fewer moving violations and wears seat belts more frequently than the general population. In other words we expect our sample to be relatively more risk averse.
IV. EMPIRICAL RESULTS
The empirical analysis is based on 690 complete data points. The basic model attempts to explain the number of moving violations (Number of Tickets) as a function of the independent variables Seat Belt Use, Years of Seat Belt Use, Risk Index, Education, Income, Age, Distance to Work, Sex, and Number of Underage Children. The model is estimated via ordinary least squares.
The results for the model in which all risk groups are pooled are presented in Table III. A dummy variable is used to define the separate groups. This variable, interacted with seat belt use, allows interpretation of the relationship between seat belt use and number of tickets by group. Note also that the constant term is suppressed.
A number of aspects of the estimated equation are noteworthy. First, the overall significance of the regression is relatively low. This is not uncommon with individual-level data. Further, this problem is alleviated somewhat in later estimation procedures.
Second, the results are reported after White's |1980~ heteroscedastic correction. The Park-Glejser test statistic for heteroscedasticity (t-value = 17.24) indicated that White's correction was needed.
Third, the control variables (Income, Sex, Education, Distance to Work, and Number of Underage Children) are generally not significantly different from zero. The exception is the Age variable that shows that age reduces ticket frequency; that is, older respondents receive fewer tickets. We also experimented with other functional forms for the control variables. For instance, we added an Age Squared term to the equation. However, performance of the control variables was unchanged; the Age variable continued to be negative and significant whereas the Age Squared variable and the other control variables were not significantly different from zero.
Fourth, the impact of seat belt use varies according to the risk index. Seat belt use is positive and significant for risk lovers (Risk Index of two or less). This result is indicative of strong compensating behavior; that is, seat belt use is strongly related to an increase in the number of moving violations for members of this group. Compensating behavior is also demonstrated to a lesser extent in the risk TABULAR DATA OMITTED neutral group, although the estimated coefficient is significantly different from zero only at the 10 percent level. The behavior of the risk averse group is counter to these results. Compensating behavior does not occur among members of this group. In fact, the opposite is true. The seat belt wearing members of the risk averse respondents receive fewer moving violations than those that do not wear a seat belt. This is evidence that risk averse individuals combine personal and exogenous safety measures in a complementary fashion.
Finally, the Years of Seat Belt Use variable is negative and significantly different from zero. Thus, the number of moving violations declines in all groups the longer one wears a seat belt. This is an indication of learning, which results in less compensating behavior over time.
Impact of Seat Belt Use on Number of Tickets Pooled Estimates
Variables Coefficients t-statistics
Risk Lover Group -.005 -.017
Risk Lover*Seat Belt Use .327 4.28
Risk Neutral Group .487 1.64
Risk Neutral*Seat Belt Use .136 1.62
Risk Averse Group 3.68 2.23
Risk Averse*Seat Belt Use -.935 -1.69
Years of Seat Belt Use -.011 -3.65
Education .0003 .02
Income .007 .40
Sex .048 .83
Age -.011 -3.78
Distance to Work -.0005 -.57
Underage Children .012 .47
Number of Observations 690
In Table IV an alternative empirical specification is presented. We performed an F-test to determine the efficacy of including the three groups, distinguished by the risk index, in a single equation. The F-statistic for the unrestricted specification (three separate equations) compared to the restricted specification (single equation) is 2.20 versus the critical value of 2.10 (at 1 percent level). This implies that the three equations may be analytically distinct. Thus, in Table IV we present three separate estimated equations.
As in the previous pooled model all results are reported with White's heteroscedastic correction. The test statistics for the three equations (risk lovers, risk neutral, risk averse) are 2.16, 2.49, and 2.47, respectively. All exceed the 5 percent significance level, indicating that White's correction is needed.
As is illustrated, the overall significance of the individual regressions for the risk lover and risk averse groups are markedly improved. However, the conclusions drawn above for the single-equation model generally remain in effect. The control variables continue to perform poorly. Moreover, the pattern for Seat Belt Use and Years Wearing Seat Belt remains the same. The risk lover group demonstrates strong compensating behavior whereas the risk TABULAR DATA OMITTED averse group does not compensate. Learning (illustrated by the Years of Seat Belt Use variable) continues to be significantly different from zero for the risk neutral and risk averse groups. However, this variable is not significant among the risk lover group, implying that this group shows minimal learning. Thus, compensating behavior is not offset over time in this group.
Since the control variables do not perform as expected, we eliminated them as a final test of the stability of the estimated coefficients. Our conclusions regarding Seat Belt Use and Years Wearing Seat Belt are unchanged. The estimated coefficients (t-statistics in parentheses) on Seat Belt Use were .29 (3.71), .10 (1.22), and -.89 (-1.61) for the three groups (risk lovers, risk neutral, risk averse), respectively. In addition, the pattern of learning established above remains the same.
V. CONCLUDING REMARKS AND CAVEATS
Models based on individual-specific survey data are estimated to investigate the relationship between seat belt usage and the number of citations for moving violations. The analysis incorporates risk tastes of individuals as revealed by the degree of precaution exhibited against everyday risks. The results indicate that the compensating-behavior hypothesis applies only to those individuals who are not strongly risk averse. Conversely, seat belt use is associated with relatively fewer moving violations for the individuals who exhibit risk aversion. Taken together, the results imply that individual risk preferences are an important dimension which should be considered when testing the compensating-behavior hypothesis. Aggregate models which do not make this distinction may be suspect.
Three caveats about our analysis are in order. First, the investigation is based on survey data which is generally less preferred than revealed preference data. However, note that respondents had no incentive to misrepresent preferences since they were assured of complete anonymity. Second, our sample is not representative of the general population since it consists entirely of resident owners of single-family homes. Further analysis with other segments of the population is needed to verify our results. Third, proxy variables for evaluating risk preferences may not have accurately discerned the underlying risk state of each individual. The risk preference demarcations are developed on the basis of revealed choices regarding everyday exposure to different types of risks such as theft, fire and earthquakes. All these risky events entail potential for bodily harm to self and/or family. Since the risk of an automobile accident has a similar dimension, one would expect consistent risk behavior across similar risks. However, further tests of the compensating-behavior hypothesis based on individual-specific analysis and risk preferences developed from other data sources need to be attempted.
1. We do not presume any relationship between the number of moving violations and traffic accidents and/or fatalities. This relationship is currently poorly understood and should be the focus of future research.
2. Dillman |1978~ routinely gets in excess of 70 percent response rates for mail surveys. However, these are obtained for surveys that (1) target specific groups with an interest in the primary issue and (2) utilize the entire Total Design Method, which requires multiple correspondence procedures, including telephone follow-up. Our response rate is considered satisfactory in this context.
3. We utilize the previous three-year time period for two reasons. First, this is the usual time period that insurance companies use when evaluating insurance risk and premiums. Thus, respondents are familiar with this measure and will likely respond with little error. Second, most individuals do not receive moving violations yearly (approximately 65 percent of the sample had none in the previous three years) so using three years generates the necessary variation in the dependent variable. However, using the previous three-year period may cause some inconsistency with seat belt use since the latter may not be stable over the previous three years.
4. Blomquist |1991~ and McCarthy |1986~ examine the relationship between risk and seat belt usage. Thus, they concentrate on risk as it relates to the driving trips (road conditions, length of trip, etc). However, we are not trying to predict seat belt usage. Rather, we concentrate on the individual's general notion of risk as portrayed in response to a set of everyday risks.
Blomquist, G. "A Utility Maximization Model of Driver Traffic Safety Behavior." Accident Analysis and Prevention 18 (5), 1986, 371-75.
-----. "Motorist Use of Safety Equipment: Expected Benefits or Risk Incompetence?" Journal of Risk and Uncertainty 4(2), 1991, 135-52.
Campbell, B., and F. Campbell. "Injury Reduction and Belt Use Associated with Occupant Restraint Laws," in Preventing Automobile Injury: New Findings from Evaluation Research, edited by J. Graham. Dover, Massachusetts: Auburn House Publishing Company, 1988, 24-50.
Dillman, D. Mail and Telephone Surveys: The Total Design Method. New York: John Wiley and Sons, 1978.
Garbacz, Christopher. "Estimating Seat Belt Effectiveness with Seat Belt Usage Data from the Centers for Disease Control." Economic Letters 34(1), 1990, 83-88.
-----. "Impact of the New Zealand Seat Belt Law." Economic Inquiry, April, 1991a, 310-16.
-----. "Are Rear Seat Passengers and Non-Occupants More at Risk Due to Seat Belt Laws?" Unpublished manuscript, University of Missouri-Rolla, 1991b.
-----. "More Evidence on the Effectiveness of Seat Belt Laws." Applied Economics, forthcoming, 1992.
Lave, L., and W. Weber. "A Benefit-Cost Analysis of Auto Safety Features." Applied Economics 4(1), 1970, 265-75.
McCarthy, P. "Seat Belt Usage Rates: A Test of Peltzman's Hypothesis." Accident Analysis and Prevention 18(5), 1986, 425-38.
McEwin, R. No Fault and Motor Vehicle Accidents, Working Paper D105, Center for Policy Studies, Monash University, September, 1986, 1-30.
Peltzman, Sam. "The Effect of Automobile Safety Regulations." Journal of Political Economy, August 1975, 677-726.
-----. "The Regulation of Automobile Safety," in Auto Safety Regulation: The Cure or the Problem?, edited by H. G. Manne and R. L. Miller. Glen Ridge, N.J.: Thomas Horton, 1976, 1-52.
Swan, P. "The Economics of Law: Economic Imperialism in Negligence Law, No Fault Insurance, Occupational Licensing and Criminology." Australian Economic Review, 3rd Quarter 1984, 92-108.
White, Halbert. "A Heteroscedasticity-Consistent Covariance Matrix and A Direct Test for Heteroscedasticity." Econometrica 48, May 1980, 821-46.