III. Helmet Effectiveness Studies Using Regression Analysis Introduction
By Jonathan Goldstein
These studies use regression analysis -- a statistical technique that isolates the individual effect of each systematic determinant (independent variables) of a particular subject (dependent variable) -- to analyze motorcycle fatalities and fatality rates. With the exception of Goldstein (1986) who analyses accident victim data (Hurt data), regression studies have been confined to an analysis of the determinants of total motorcycle fatalities for the 50 states (Prinzinger (1982), deWolfe (1986), Watson et al. (1980) and Graham and Lee (1986). These studies focus on the effect of mandatory helmet use laws and typically find a 10%-38% increase in the fatality rate resulting from the repeal of a helmet law.
While regression analysis is a potentially superior statistical technique, it is not a panacea for the statistical deficiencies of correlation analysis. Unlike simpler techniques, regression analysis must be carefully implemented in order to derive more reliable (unbiased) statistical estimates. Failure to correctly specify (include all relevant (determinants) independent variables) in the regression equation can result in statistical estimates that are biased and thus unreliable. Thus, it is essential that all relevant factors are controlled for in the regression equation specification.
The studies reviewed all suffer from serious misspecification problems that lead to estimates of motorcycle helmet law effectiveness that are systematically overstated (biased upward). Goldstein (1985) proves theoretically that the Hatson et al. (1980) methodology
produces upwardly biased estimates of helmet effectiveness and proves empirically that Prinzinger's (1982) estimates are also upwardly biased. The criticism of the Prinzinger study also apply to the deWolf (1986) and Graham and Lee (1986) studies.
1. Prinzinger, J. M. (1982). "The Effect of the Repeal of Helmet Use Laws on Motorcycle Fatalities." Atlantic Economic Journal, 10:36-39.
This regression study explains the variation in the motorcycle fatality rate per capita (fatalities/population) across the 50 states by variations in: (1) helmet law status (law/no law); (2) alcohol consumption per capita; (3) personal income per capita; (4) the ratio of the number of males age 15-34 to the number of males age 35-65; (5) the average speed; and (6) a congestion index for each state. A separate equation is estimated for each year between 1975 and 1978. The study concludes that (1) a positive and statistically significant relation exists between alcohol consumption and fatalities; and (2) a negative relation exists between helmet use laws and fatalities -mandatory use laws reduce fatalities per capita by 25%.
In Goldstein (1985) it is shown that Prinzinger's use of fatalities/population rather than the more typical fatalities/ registrations results in a misspecification of the regression model and in estimates of helmet law effectiveness that are biased upward. Correcting for this misspecification, Goldstein (1985) shows that mandatory helmet use laws have no statistically significant effect on the number of fatalities and/or the fatalities per registration.
2. deWolfe, V. A (1986). "The Effect of Helmet Law Repeal on Motorcycle Fatalities." Contract DOT HS-807-065. NHTSA, Washington, DC.
This regression study cites problems in the consistency of the measured data across states to justify an alternative regression equation specification.
In this study both the specification of the equation (independent variables) and the dependent variable are different -- fatalities/ accident is used. deWolf explains variations in this fatality rate across the 50 states for the years 1975-1984 by variations in: (1) helmet law status (law/no law); (2) the number of motorcycle registrations; (3) 49 state "dummy" variables; and (4) 9 year "dummy" variables. Here the registration variable is used as a "proxy for economic conditions" and the state and time "dummy" variables are used to capture all other factors (i.e. the variables that affect fatalities but are not consistently measured across states). The state dummies "control" for how these factors vary across states in a given time period and the year dummies "control" for how these factors vary across time for all states. The study concludes that: (1) a negative and statistically significant relation exists between registrations (economic conditions) and fatalities/accident; and (2) a negative and statistically significant relation exists between helmet use laws and fatalities/accident. In particular, it is estimated that the repeal of mandatory helmet use laws results in a 10.4%-33.3% increase in fatalities/accident and a 3.6%-9.5% increase in fatalities.
The fundamental weakness of the de Wolf study is that the regression equation is misspecified on two levels: (1) the dependent variable -- fatalities/accidents -- is misspecified; and (2) the independent variables are misspecified. As a result of these misspecifications de Wolf's estimates of the effectiveness of helmet use laws are biased.
First, the choice of fatalities per accident implies that de Wolf's regression does not test the hypothesis that helmet laws decrease fatalities. Given that helmets potentially limit peripheral vision, increase noise distraction and result in driver fatigue, it is possible that they decrease the chance of accident avoidance and may even cause additional accidents. Thus helmet laws may increase accidents, particularly the type of accidents (low speed where accident avoidance techniques are most fruitful) that are less likely to result in fatalities. Given this scenario, a regression equation that shows that helmet laws reduce fatalities per accident is not capable of concluding that helmet laws save lives. The negative effect of helmet laws on fatalities per accident could result from an increase in accidents at the same time that fatalities remain constant (fatalities per accident decline). Thus' the statistically significant negative effect of helmet laws on fatalities per accident does not provide conclusive evidence that helmet laws save lives.
Second, de Wolf's use of state and year dummies to replace the "inconsistently measured" factors implies that the level of alcohol consumption, traffic density, etc. remain constant within each state over a ten year period. Thus, her specification fails to recognize within state changes in the non-measured variables (i.e. changes in alcohol consumption or average highway speed or age composition in a single state over a 10 year period (1975- 1984)) and thus does not consider the effects of such changes on fatalities per accident. If the influence of these changes on the fatality rate is not assigned to changes in the non-measured variables through the dummy variables it will be inappropriately assigned to other explanatory variables such as the helmet law variable. For example, if a state repeals a helmet law in 1976 at the same time that state backs off from the strict enforcement of the 55 MPH speed limit (instituted in 1973) the effect of higher speeds on the fatality rate (because they are not controlled for in de Wolf's equation) will incorrectly be assigned to the repeal of the helmet law and will incorrectly overstate the effectiveness of helmet laws. Thus de Wolf's results suffer from biased estimates of helmet law effectiveness. In contrast, this specification bias problem can be avoided by measuring the relevant variables (alcohol, speed, congestion, etc.) and incorporating them in the equation as in Goldstein (1985).
3. Graham, J. D., and Lee, Y. (1986). "Behavioral Response to Safety Regulation: The Case of Motorcycle Helmet-Wearing Legislation." Policy Sciences, 19:253-273.
This regression study employs the same methodology as the de Wolf study with the exception that the dependent variable is measured as fatalities/registrations and a different mix of independent variables is used. This study explains variations in fatalities/registrations across the 50 states for the years 1975 to 1984 by variations in: (1) helmet law status (law/no law); (2) a linear time trend beginning in the year after the repeal of a law in a particular state; (3) a linear time trend beginning in the year after adoption of the law in a particular state; (4) 49 state dummy variables; and (5) 9 year dummy variables. (4) and (5) are justified on the same grounds as in the de Wolf study. The inclusion of (2) and (3) , not found in the de Wolf equation, are used to test the risk compensation hypothesis (outlined below, Section VI) -- gradual compensating responses in behavior that offset the intent of the law. In addition no proxy for economic conditions is used, it is assumed that this determinant is captured in the dummy variables.
The study concludes that mandatory helmet use laws have: (1) a negative and statistically significant effect on fatalities and the fatality rate; and (2) a statistically significant gradual risk compensating effect that erodes the benefits of helmet laws in (1). In particular, repeal of helmet laws induces a 12% increase in the fatality rate but, this detrimental effect is eroded at a rate of roughly 2.5% per year, as motorcyclists adjust (compensate) their risky behavior downward.
The statistical estimates of this study suffer from the same specification problem as the de Wolf study: the dummy variable specification does not control for dynamic trends within states for the non-measured factors (speed, alcohol, etc.) between 1975-1984. Thus the effect of these dynamic trends are inappropriately assigned to helmet law repeal causing estimates of helmet effectiveness to be upwardly biased (see discussion in de Wolf review).
Finally the risk compensation estimates are also biased. These estimates are modeled as within state time trends after a law change. These within state time trends not only capture any risk compensation effects, but also partially (because they are only used for years after a law has changed) capture the within state dynamic trends in the non-measured variables. Thus these estimates are biased because they do not separate out the risk compensation effects from other dynamic effects.
Once again the problems inherent in this study could be resolved by measuring all relevant factors and including them in the equation.
4. Watson, G. S., Zador, P. L., and Wilks, A. (1980). "The Repeal of Helmet Use Laws and Increased Motorcyclist Mortality in the United States F 1975-1978." American Journal of Public Health, 70:6.
Based on the same premise that data on the multiple factors that influence motorcycle fatalities are either not available or not reliable, this study develops an alternative regression model that explains the number of fatalities in one state by the number of fatalities in a state in the same geographic region. The authors argue that this design overcomes data irregularities by assuming that "most factors affecting... motorcyclists fatalities... are likely to be similar... in states in the same geographic region." In other words, the determining factors in both states are hypothesized to be so similar that variations in the number of fatalities in one state can explain variations in the number of fatalities in another geographical similar state. Based on this premise an equation explaining monthly fatalities for each state that eventually repeals a helmet law by the monthly fatalities of a geographically similar state which does not repeal its helmet law is estimated for all 26 states that eventually repealed helmet use laws for a 48 month period prior to repeal. This equation is then used to forecast the number of fatalities that a repeal state should expect to experience if it had not repealed its law. This forecast is compared to the actual number of fatalities and it is concluded that in 23 of 26 states a - greater number of deaths than expected occurred. The typical percent increase in fatalities is estimated to be 38%.
Based on the underlying theoretical assumption used to justify the design of the regression equation -- that the factors influencing the number of fatalities are the same in the matched states -- it is theoretically proven in Goldstein (1985) that the predicted number of deaths in this study are biased. In the most relevant case the biased is signed and it is concluded that predicted fatalities from the regression equation are biased downward. Thus, comparisons of actual and predicted fatalities in post repeal years systematically overestimate the effectiveness of mandatory helmet use laws. The methodology employed to avoid "inconsistently measured" data , results in biased estimates and is thus not reliable.
In addition, Adams (1983) (reviewed below) argues that a downward bias in predicted deaths (upward bias in helmet law effectiveness) is induced by the smoothing technique employed by Waston et al. The critique offered in Goldstein (1985) is more general in that it focuses on the structure of the model rather than the transformation made to the data.
© Copyright Jonathan P. Goldstein Ph.D. 1986. All Rights Reserved.