Because information on the intensity of bicycle use is not available, Viscusi examined injuries per bicycle in use as a "second-best" measure of injuries controlled for use. He assumed a seven year operating life for bicycles.(77) The National Safety Council assumes a ten year life.(78) Senior Economist Gregory Rodgers of the Consumer Product Safety Commission criticizes both simple formulations and calculates the number of bicycles in use by using the CPSC Product Life Model.(79) The use of bicycles as a control for bicycle use, regardless of whether a seven or ten year life is assumed, fails to account for whether or not bicycle owners are consistent bicycle users.(80) If a significant proportion of people buy bicycles, use them for a while and then store them away without further use, even a seven year operating life may be inaccurate. The analysis presented here hopes to provide a more accurate measure of bicycle use by estimating the number of active bicyclists for each year. These estimates are based on consumer surveys and industry estimates.(81)

A number of variables are postulated as likely to have an effect on bicycling related injuries or fatalities. Since bicycling is popular among young people and they are less likely to wear helmets than adults, some control for the proportion of youth in the population is needed. Two such measures were used: the proportion of population below the ages of thirteen and twenty-four. In each case tested, the proportion of population under the age of twenty-four proved to be a slightly better predictor. The proportion of the population with health insurance coverage also was used to see if bicyclists are more likely to ride recklessly if they have insurance.

Other studies have looked at consumption or income based on the hypothesis that consumers with more income will purchase more safe goods. However, with bicycles it is not clear that more expensive bicycles are necessarily safer. In fact, expensive, lightweight bicycles may be more apt to fail than their less expensive counterparts. Therefore, no income or consumption measure was used in this study. This study also does not control for product liability lawsuits. Although the number of such lawsuits is generally believed to have increased dramatically in recent years, the bicycle industry has faced relatively few product liability lawsuits.(82)

The principal independent variables of this study are whether the CPSC standard is in effect and the proportion of bicyclists who own (and presumably use) helmets. Because there is some disagreement concerning the operating life of a bicycle, the proportion of bicycles in use which satisfy the CPSC standard was calculated using the CPSC model and a simple model, assuming alternately seven and ten year lives. As noted previously, the author estimated the number of helmets in use based on industry figures to obtain helmets per bicyclist. Rodgers' study suggests two other variables. First, he uses a dummy variable to control for a change of the NEISS sample in 1979. Although he suggests that the change should not have much effect, the variable is significant in some of his results.(83) It therefore is also adopted here.

The second additional variable used by Rodgers is pedestrian fatalities. He argues that if drivers are more careful, perhaps due to tougher law enforcement or reduced drunk driving, both pedestrian and bicycle fatalities should be reduced. This variable was found to be significant for fatalities, so it too was used here.(84) However, it is important to realize that such a variable would also encompass any other trends that would affect pedestrian fatalities such as the age composition of the population, the proportion with health insurance, etc.

The causal hypotheses to be tested are straightforward. The CPSC safety standard may cause a reduction in bicycling related injuries. Helmet use may cause a reduction in fatalities or head injuries. There is no reason to believe that the CPSC standard will reduce fatalities directly except through a reduction of total injuries. In addition, there is no reason to expect that helmet use will significantly affect the number of overall injuries, except to reduce the number of head injuries.

A simple linear model is tested here since there is no reason to assume a more complex relationship between the variables. Although Viscusi recommends using the lagged dependent variable as the first independent variable to control for the stock of pre-existing consumer products and avoid possible serial correlation effects, lagged variables were not used here.(85) Lagged variables were not needed here because the CPSC dummy variable controls for the stock of bicycles in use and intensity of use was controlled using participation rather than products currently owned. Thus, the equations to be estimated are:(86)

[1] IR = a + b₁CPSC + b₂POP + b₃INS + b₄NEISS

[2] FR = a + b₁HEL + b₂POP + b₃INS + b₄PED

[3] PH = a + b₁1HEL + b₂2POP + b₃3INS + b₄4NEISS +b₅PED

Estimates of these equations using least squares multiple regression analysis are:(87)

[1] IR = 4.65 + 1.57CPSC + 0.80POP + 0.72INS - 0.42NEISS,(88) with 0.012, 0.01, 0.063, and 0.244 significance.

[2] FR = -3.34 + 0.35HEL + 0.07POP + 0.049INS + 1.15PED,(89) with 0.062, 0.512, 0.69 and 0 significance.

[3] PH = 14.17 - 1.12HEL - 0.76POP - 0.19INS - 0.34NEISS + 0.16PED,(90) with 0.079, 0.045, 0.62, 0.139 and 0.586 significance.

The results for equation [1] fail to confirm the causal hypothesis. It is statistically significant at the 97% level, and the CPSC variable is also highly significant.(91) However, the positive coefficient of the CPSC variable suggests that the CPSC safety standard is associated with increasing rather than decreasing the injury rate.(92)

In equation [2], an incredibly significant relationship is found, but the PED variable overwhelms all the other variables and almost completely explains the bicyclist fatality rate. Thus, traffic factors that affect pedestrian fatalities appear to affect bicyclist fatalities as well.

Helmet use is significant at the 90% level, but its coefficient is much smaller than that of PED. The helmet use coefficient is however positive, which is contrary to the causal hypothesis. It suggests that the fatality rate increases as helmet use increases. Dropping the overwhelming PED variable from the analysis reduces the amount of variance explained to only 50%, and, although the regression equation itself is significant at the 95% level, none of the individual variables are significant even at the 90% level. The insignificant coefficient for helmets does become negative in the modified equation.

This result is curious for two reasons. First, the simple correlation between fatality rate and helmet usage is -0.64, significant at the 99% level. However, helmet usage is strongly negatively correlated with pedestrian fatality rates, health insurance coverage and both alternative population variables. The correlation coefficients range from -0.77 to -0.89, all significant at the 99.9% level. Thus, increased helmet usage may be associated with decreased fatality rates, but the effect may be masked by other trends.

The latter explanation is supported by equation [3] which uses the proportion of head injuries as the dependent variable. There, both helmet use and the proportion of young people in the population are significantly associated with the proportion of head injuries. Moreover, the helmet use coefficient is negative, indicating that, as usage increases, the proportion of head injuries decreases. Thus, it is the only equation to confirm a causal hypothesis.

As indicated, earlier, most fatalities are caused by head injuries.(93) Why then does helmet usage appear to affect head injuries but not fatalities? One explanation is that other factors besides head injuries influence fatality rates. This is suggested by the simple correlation between fatality rate and proportion of head injuries -- a weak 0.27 that is significant only at the 70% level. Alternatively, annual head injuries are approximately 70 times the number of bicyclist fatalities. Perhaps changes in the latter are too small to be accurately predicted by this data.

It should also be noted that the Durbin Watson d statistics frequently appear noticeably different from 2.0, suggesting the possibility of first order autocorrelation.(94)