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416 Chapter 10 Regression with Panel Data

The next four regressions in Table 10.1 include additional potential determi-
nants of fatality rates along with state and time effects. The base specification,
reported in column (4), includes variables related to drunk driving laws plus vari-
ables that control for the amount of driving and overall state economic conditions.
The first legal variables are the minimum legal drinking age, represented by three
binary variables for a minimum legal drinking age of 18, 19, and 20 (so the omitted
group is a minimum legal drinking age of 21 or older). The other legal variable is the
punishment associated with the first conviction for driving under the influence of
alcohol, either mandatory jail time or mandatory community service (the omitted
group is less severe punishment). The three measures of driving and economic condi-
tions are average vehicle miles per driver, the unemployment rate, and the logarithm
of real (1988 dollars) personal income per capita (using the logarithm of income
permits the coefficient to be interpreted in terms of percentage changes of income;
see Section 8.2). The final regression in Table 10.1 follows the “before and after”
approach of Section 10.2 and uses only data from 1982 and 1988; thus regression (7)
extends the regression in Equation (10.8) to include the additional regressors.

The regression in column (4) has four interesting results.

1. Including the additional variables reduces the estimated effect of the beer
tax from -0.64 in column (3) to -0.45 in column (4). One way to evaluate
the magnitude of this coefficient is to imagine a state with an average real
beer tax doubling its tax; because the average real beer tax in these data is
approximately $0.50 per case (in 1988 dollars), this entails increasing the
tax by $0.50 per case. The estimated effect of a $0.50 increase in the beer
tax is to decrease the expected fatality rate by 0.45 * 0.50 = 0.23 death
per 10,000. This estimated effect is large: Because the average fatality rate
is 2 per 10,000, a reduction of 0.23 corresponds to reducing traffic deaths
by nearly one-eighth. This said, the estimate is quite imprecise: Because
the standard error on this coefficient is 0.30, the 95% confidence interval
for this effect is -0.45 * 0.50 { 1.96 * 0.30 * 0.50 = ( -0.52, 0.07). This
wide 95% confidence interval includes zero, so the hypothesis that the beer
tax has no effect cannot be rejected at the 5% significance level.

2. The minimum legal drinking age is precisely estimated to have a small effect
on traffic fatalities. According to the regression in column (4), the 95% confi-
dence interval for the increase in the fatality rate in a state with a minimum
legal drinking age of 18, relative to age 21, is ( -0.11, 0.17).The joint hypothesis
that the coefficients on the minimum legal drinking age variables are zero can-
not be rejected at the 10% significance level: The F-statistic testing the joint
hypothesis that the three coefficients are zero is 0.35, with a p-value of 0.786.