latter models suffered from multicollinearity between the time trend and some of the
independent variables and thus the use of year dummy variables provided better estimates.
Table 3 presents two additional models. These are specified with the logarithm of the
ratio of total fatalities to total slight injuries as the dependent variable. This ratio has
declined over time and we would expect this sort of decline to be primarily due to medical
technology improvements. When these variables are not specified, in Model A, most
independent variables are not statistically significant. Two exceptions are the average age of
the car which has a negative sign and percent of households with no car which is positive.
More importantly we find that when the medical technology variables are included they are
all statistically significant at (or near) the 95% level with the expected signs.
This result is reinforced in models C and D where we correct for serial correlation in
the data. In this model the most significant variables appear to be the medical technology
proxies, again all with the expected sign. The level of significance is above 90%. GDP per
capita is also at a similar level of significance. The value of the autocorrelation parameter
∣p∣ < 1 indicates that serial correlation is present and needs to be taken into account in the
2
estimations.
Given that the medical technology variables are quite significant, we can evaluate the
relative magnitude of their effect. Table 4 calculates the estimated change in fatalities, using
elasticities from the NB model in Table 2 and from the ratio model that corrects for serial
correlation in Table 3. These are calculated by aggregating for the 9 regions for which we
had data (i.e, excluding London and Scotland). The average length of inpatient stay clearly
has had a large effect accounting for a reduction of 640 fatalities when estimated from model
2-B. The estimate using the ratio model produces a slightly larger value of 726. The other
2 Currently there are no methods available for adjusting for serial correlation in negative binomial models which
may suggest that the t-statistics in these models are biased upwards.
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