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Impact of the New Zealand seat belt law.


Offsetting consumer behavior may have reduced the effectiveness of a mandatory seat belt law in reducing fatalities in New Zealand. It appears that the favorable effect on automobile occupants may be offset partially, or in some models perhaps completely, by deaths among cyclists and pedestrians that may be caused by more dangerous driving by drivers who feel safer. Furthermore, the improvement in safety found for occupants is smaller than generally reported in the literature. A caveat is that speed may be endogenous for some models.


This paper tests empirically, with data on New Zealand from 1960-85, whether seat belts reduce highway mortality rates once one allows for the possibility of more reckless driving behavior by seat belt users. New Zealand has required the installation of seat belts in new automobiles and light vehicles since 1965. In 1972, legislation was passed requiring front seat occupants over the age of fifteen years traveling in automobiles and light vehicles registered after 1964 to wear seat belts. As of 1975, seat belt fitting and wearing was extended to motor vehicles registered after 1954. The age for compulsory seat belt use was lowered to eight years in 1979. Other than a twice yearly vehicle safety inspection, there are no government-mandated safety design requirements for light vehicles. This may allow the impact of the seat belt law on traffic fatalities to be more easily isolated.(1)

Lave and Weber [1970] first suggested the possibility that mandated safety features might lead to faster driving and that this could offset some of their beneficial effects. Peltzman [1975] tested this question of offsetting consumer behavior with regard to automobile safety equipment and design that was first required in the 1960s. Peltzman argued that drivers might offset some or all of the mandated safety by driving more dangerously. It might be possible, he suggested, to have a fall in occupant deaths or injuries and a concomitant rise in non-occupant deaths and injuries as vehicles collide more frequently or more seriously with motorcyclists, cyclists and pedestrians. On the empirical results from a double log model of fatality rates, that incorporated most of the essential explanatory variables (alcohol, youth, speed, income, accident cost, trend), Peltzman concluded that there is strong support for the concept of offsetting behavior.

Swan [1984], in a pooled model for Australian states and territories plus New Zealand, found a strong reduction in fatalities due to seat belt fitting of automobiles. However, McEwin [1986] found no effect for a similar variable. Hurst [1979] found for New Zealand that voluntary seat belt usage (observed rate of 20 percent) reduces fatalities by 5 percent, while compulsory seat belt usage, (observed rate of 65 percent) reduces fatalities by 16 percent. Assuming 100 percent usage, he estimated that fatalities would fall by 40 percent. However, he analyzed only one year of data before and after the introduction of the seat belt law.


I estimate fatality and fatality rate models for total traffic fatalities, occupant fatalities (drivers plus passengers) and non-occupant fatalities (motorcyclists, cyclists, and pedestrians). The fatality models include independent variables for seat belt usage, income, speed, alcohol, distance traveled and a time trend. Table I lists variable definitions and sources. Ordinarily a youthful driver variable would be included in the model to take account of the greater accident frequency associated with inexperience. However, in the New Zealand case, this variable has almost no variation. Also, accident price would usually be included, but New Zealand has a missing data problem in this case. The fatality rate models delete distance traveled from the right-hand-side variables. Fatality rate is calculated as the appropriate fatality group divided by distance traveled (per 100 billion kilometers). The basic model is TOTAL = [[Alpha].sub.0] + [[Alpha].sub.1] NOBELT

+ [[Alpha].sub.2] INCOME + [[Alpha].sub.3] [SPEED.sub.t]

+ [[Alpha].sub.4] [ALCOHOL.sub.t] + [[Alpha].sub.5] [DISTANCE.sub.t ]

+ [[Alpha].sub.6] [TREND.sub.t] + [u.sub.n].

The model is estimated via ordinary least squares in logarithmic and linear form for the three fatality categories. Each of the models is estimated with and without SPEED following the suggestion of MacAvoy [1976] that SPEED may be an endogenous variable. If offsetting behavior is the result of automobile safety regulation, then risky driving is a function of the known highway death rate. To properly account for these relationships, a simultaneous set of equations is required. Risky driving may be measured by behavioral changes in SPEED, drunk driving and reckless driving. Some argue that SPEED is the only one of these that may be directly measurable. However, the data for SPEED may be unreliable or unavailable (properly measured) to allow estimation of a simultaneous equation model (Graham [1983]). A compromise solution is to estimate the fatalities model in reduced form. This basically means that SPEED is dropped from the model. Since there is no way to determine directly the endogenous nature of SPEED, the sensitivity of the model is tested with and without SPEED. If model results for critical coefficients are not changed much, then it can be assumed that endogeneity is not important. However, if the coefficients change significantly, then SPEED may be endogenous, and then it is not clear how to resolve the issue.

The predicted signs of the coefficients are as follows. NOBELT is constructed so that it measures seat belts not in use. The observed fraction of front seat belt use is subtracted from 1.0 beginning in 1972. This variable does not distinguish between voluntary and enforced usage. The coefficient for NOBELT should have a positive sign in the OCCUPANT equation, a negative sign in the NON-OCCUPANT equation (if offsetting behavior is present) and an undetermined sign in the TOTAL equation, since the prevalence of offsetting behavior is not clear.

As INCOME (in this case a proxy for permanent income) rises, the value of time rises. Drivers may increase speed and take chances in order to cut the cost of travel. However, on the other side, as INCOME rises, the value of life rises. More caution may be exercised as a consequence of higher INCOME. The predicted sign on the coefficient is an empirical question, though most time series studies have found a positive sign.

As Lave [1985] has shown, it is not speed that contributes to traffic deaths, but speed variation. The appropriate speed variable is one that measures the variation. In other words, slow drivers are as dangerous as fast drivers. It is safer if everyone is traveling at about the same pace. Therefore, the appropriate speed variable is some speed differentiated between fast and slow drivers. Recent papers by Fowles and Loeb [1989], Levy and Asch [1989], Snyder [1989], and Garber and Gadirau [1988] look at this issue again. All these papers find speed variance to be important. Lave [1989] persuasively argues that any difference between his results, which find speed variance to be statistically important and the new results that find average speed to be statistically significant as well, are due to the difference between aggregate data and his more appropriate disaggregate data.

The variable used here is the speed of traffic at the 85th percentile (measured open road speed).(2) The coefficient should have a positive sign.

ALCOHOL is alcohol consumption per capita and is assumed to be a proxy for driving while intoxicated. Is ALCOHOL closely related to drunk driving? Since it is not known how much drunk driving exposure there is, either from time series or cross-sectional data, it is difficult to answer this question. Nevertheless, it is generally assumed that the coefficient should carry a positive sign.

A recent study by Asch and Levy [1987] presents a convincing argument that the legal drinking age has no measurable influence on fatalities and that drinking experience is a risk factor independent of age. If so, the general rise in the legal drinking age may not be as effective as advertised. Efforts should perhaps be concentrated on drinking education and responsible behavior.

DISTANCE is the estimated kilometers traveled by the vehicle fleet.(3) The more travel, the more accident exposure; however, it does not follow necessarily that there is a one-to-one relationship between travel and fatalities. It is of some interest to determine the exposure impact on fatalities. To do this, DISTANCE must be entered as an independent variable. On the other hand, rate models may provide information not otherwise available as a result of adjusting for exposure.

A time trend (linear form) is also included to take account of permanent income that may not be captured by INCOME. This may be reflected in improved safety design of both roads and vehicles. Remember that New Zealand does not have any legislation dealing with automobile safety design. Therefore, the time trend might possibly identify improved safety due to market forces. TREND is entered in linear form in all the models. The coefficient sign should be negative.


I performed a simple Box-Cox transformation to test for appropriate functional form. Logarithmic and linear models were compared for all the possibilities. The transformed residual sums of squares were very close to one another without exception. The d statistic was less than the critical value of 2.706 at the 90 percent level of confidence and the null hypothesis that the two functions are empirically equivalent is accepted in all cases. (See Rao and Miller [1971, 107-11] for details of this test).

Table II reports the results for the logarithmic death models with and without TREND. Summary tables are available from the author reporting the results of all fourteen equations including death and death rate models, with and without SPEED, with and without TREND in both logarithmic and linear functional form. For the logarithmic models with SPEED and TREND, there appears to be a complete offsetting effect. Positive results in the OCCUPANT equations are offset by negative results in the NON-OCCUPANT equations. The positive results of the TOTAL equations are very small and are not statistically significant. In the death model without SPEED (Table II), there again appears to be an offsetting effect, since the NOBELT estimates for the TOTAL models are only about half the size of the estimates in the OCCUPANT models, but now the NON-OCCUPANT equations have NOBELT coefficients that are not statistically significant. This suggests that SPEED may be an endogenous variable.

Models were also estimated in linear form for deaths and death rates with and without SPEED. In the models with SPEED and TREND and in the death rate model without SPEED, there is substantial offsetting behavior between OCCUPANT and NON-OCCUPANT models. The TOTAL models have a NOBELT coefficient that is not statistically significant. However, in the case of the death model without SPEED, I found a net favorable effect between OCCUPANT and NON-OCCUPANT models that is carried over into the TOTAL model (an elasticity of about 0.155). This last result also suggests the possibility of an endogenous SPEED variable.

The other elasticity estimates perform in general as expected. The INCOME estimates are only significant in a few of the OCCUPANT equations.(4) The estimates fall in the range of 1.0-1.4 suggesting that the value of time is the important factor influencing the model. The SPEED elasticity generally falls around 1.0 across all models, though it is sometimes not significant in the NON-OCCUPANT models. ALCOHOL elasticity ranges from about 0.7-1.3 across TOTAL and OCCUPANT models. It has a negative sign throughout in the NON-OCCUPANT models and is not significant.

Since models of this type are usually estimated for fatality rates, it is interesting to compare results from this study with the other available estimates of the impact of DISTANCE on deaths. The estimate for the logarithmic OCCUPANT model has an elasticity of 1.64. This compares with Zlatoper's [1984] estimate of about 1.48 and the Crandall et al. [1986] estimate of 0.4 (not significant), both for the United States. A t-test indicates, however, that my estimated coefficient is not significantly different from 1 for the logarithmic model.

The TREND coefficient is negative and significant in all the models except for some NON-OCCUPANT death models and one TOTAL death model. Estimates are quite similar across all models. It is obvious that TREND has a powerful effect. On the one hand, the models are receiving valuable information from TREND. It may identify improved safety brought about by market forces. On the other hand, the precise nature of the information that the variable is picking up is vague.

Each of the models was also estimated without TREND. As might be expected, the models performed differently without TREND. The results reported in Table II are illustrative. INCOME (still with a positive coefficient) and ALCOHOL become more important explanatory variables and the estimate for the DISTANCE coefficient falls by more than half. The elasticity for NOBELT with TREND is [0.109.sup.*], [0.217.sup.*] and -0.116 for TOTAL, OCCUPANT and NON-OCCUPANT models (starred figures are significant at the .05 level). Without TREND, the estimates for the NOBELT coefficient are [0.165.sup.*], [0.286.sup.*] and -0.071, respectively. The net effects for NOBELT are small and similar in both cases.

If TOTAL, OCCUPANT and NON-OCCUPANT models with SPEED, but without TREND, are compared with models that omit both of these variables, the results are also similar for NOBELT. These results suggest that SPEED may not be an endogenous variable.

The question is not whether the models will perform differently with or without TREND, but whether it is appropriate to enter TREND in the model to account for the general long-term downward trend in accidents. Peltzman [1975; 1976] argues strongly for the inclusion of TREND. Graham [1983] questions the use of TREND, but has not been able to find an adequate alternative. Crandall et al. [1986] suggest that TREND is inappropriate. However, if they have the correct permanent income variable, then it should be incorporated into their key models. While TREND is not the ideal proxy, it is not clear how to otherwise account for long-run effects. In the present case, a better variable is unavailable.

The model may require cross-sectional data or some way to adjust for possible variation in pedestrian or motorcycle exposure that may be independent of occupant activity. In lieu of cross-sectional data which, of course, are not adequate to estimate a model for New Zealand, I added two variables, population in millions and registered motorcycles in thousands, to the logarithmic NON-OCCUPANT rate model to take account of pedestrian and motorcycle exposure. The NOBELT coefficient remains the same and neither of the new variables is significant at the .05 level.(5)


Logarithmic and linear death and death rate models with and without SPEED and with and without TREND generally suggest support for the concept of offsetting consumer behavior. Also, the estimates of favorable effects from seat belt usage are generally smaller than previously reported. However, an important caveat should be taken into account. Some of the results suggest the possibility that SPEED is an endogenous variable even though the differences between the equations with and without SPEED are usually small and offsetting effects tend to show up either way. [Tabular Data 1 and 2 Omitted]

(1)While improved safety design may partially be made available through imports to countries that do not require it, this possibility is limited by the manufacturers' desire to minimize production costs by providing the vehicle with only the mandated safety features. Japan produces different versions of the same automobile to meet the safety requirements of different markets. (2)A speed variation variable would be useful but the data are not available. (3)DISTANCE has been indirectly estimated by a consulting firm. It is believed to be an underestimate (Scott et al. [1987]). (4)The poor performance of INCOME may be partly due to a lack of variation. (5)Garbacz [1990] has developed a cross-sectional economics model of seat belt usage effectiveness for the United States. Results suggest that offsetting behavior is present.


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Policy Analysis and Management 6(2), 1987, 180-92. Crandall, Robert W., H. K. Gruenspecht, T. E. Keeler, and L. B. Lave. Regulating the Automobile.

Washington, D.C.: The Brookings Institution, 1986. Fowles, Richard and Peter D. Loeb. "Speeding, Coordination, and the 55-MPH Limit: Comment." American

Economic Review, September 1989, 916-21. Garbacz, Christopher. "Estimating Seat Belt Effectiveness with Seat Belt Usage Data from the Centers

for Disease Control." Economic Letters, 34(1), 1990, 83-8. Garber, Nicholas J. and Ravi Gadirau. "Speed Variance and Its Influence on Accidents." Unpublished

manuscript, AAA Foundation for Traffic Safety, Washington, D.C., July 1988. Graham, John D. "Automobile Safety: An Investigation of Occupant Protection Policies." Ph.D.

dissertation, Carnegie-Mellon University, 1983. Hurst, Paul M. "Compulsory Seatbelt Use: Further Inferences." Accident Analysis and Prevention,

11(1), 1979, 27-33. Lave, Charles A. "Speeding, Coordination and the 55-MPH Limit." American Economic Review, December

1985, 1159-64. _____. "Speeding, Coordination and the 55-MPH Limit: Reply." American Economic Review, September

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Economic Review, September 1989, 79, 913-15. MacAvoy, Paul W. "Comment" 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, 96-98. McEwin, R. I. No Fault and Motor Vehicle Accidents, Centre of Policy Studies, Monash University,

D105, September 1986, 1-30. Peltzman, Sam. "The Effects of Automobile Safety Regulations." Journal of Political Economy, August

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edited by H. G. Manne and R. L. Miller. Glen Ridge, N.J.: Thomas Horton, 1976, 1-52. Rao, R. and R. L. Miller. Applied Econometrics. Belmont: Wadsworth Publishing Company, 1971. Scott, Graeme, Grant Pittams and Nigel Derby. "Regression Models of New Zealand Road Casualty Data:

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CHRISTOPHER GARBACZ, Professor of Economics, University of Missouri-Rolla. For helpful discussions at the New Zealand Ministry of Transport headquarters in Wellington, thanks go to John Toomath, William Frith, Bill Steed, Graeme Scott, Nigel Derby, William White and Wayne Jones. Grant Pittams kindly provided time series data on distance, speed and seat belt usage. Also, Anatole Sergejew, in the Auckland Office of the Ministry of Transport, provided valuable help in clarifying the data base. This work was undertaken while the author was Visiting Professor of Economics at the University of Auckland. Robin Court, department chair, provided the resources and environment that made the initial work possible. This is a revised version of a paper presented at the session on "Automobile Safety Legislation" at the American Economic Association meetings in Chicago, December 30, 1987. Sam Peltzman provided insightful comments as a discussant and on a revised version of the paper. Two anonymous referees and the editor, Frank C. Wykoff, gave the author helpful suggestions for improvement.
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Author:Garbacz, Christopher
Publication:Economic Inquiry
Date:Apr 1, 1991
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