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402 Chapter 10 Regression with Panel Data

Figure 10.2 Changes in Fatality Rates and Beer Taxes, 1982–1988

This is a scatterplot Change in fatality rate FatalityRate 1988 – FatalityRate1982 = –0.072 – 1.04( BeerTax1988 – BeerTax1982 )
of the change in (fatalities per 10,000)
the traffic fatality
rate and the change 1.0
in real beer taxes
between 1982 and 0.5
1988 for 48 states.
There is a nega- 0.0
tive relationship
between changes – 0.5
in the fatality rate
and changes in the –1.0
beer tax.

–1.5 0.0 0.2 0.4 0.6
–0.6 –0.4 –0.2 Change in beer tax

(dollars per case $1988)

In contrast to the cross-sectional regression results, the estimated effect of a
change in the real beer tax is negative, as predicted by economic theory. The hypoth-
esis that the population slope coefficient is zero is rejected at the 5% significance level.
According to this estimated coefficient, an increase in the real beer tax by $1 per case
reduces the traffic fatality rate by 1.04 deaths per 10,000 people. This estimated effect
is very large: The average fatality rate is approximately 2 in these data (that is, 2 fatal-
ities per year per 10,000 members of the population), so the estimate suggests that traf-
fic fatalities can be cut in half merely by increasing the real tax on beer by $1 per case.

By examining changes in the fatality rate over time, the regression in Equa-
tion (10.8) controls for fixed factors such as cultural attitudes toward drinking and
driving. But there are many factors that influence traffic safety, and if they change
over time and are correlated with the real beer tax, then their omission will pro-
duce omitted variable bias. In Section 10.5, we undertake a more careful analysis
that controls for several such factors, so for now it is best to refrain from drawing
any substantive conclusions about the effect of real beer taxes on traffic fatalities.

This “before and after” analysis works when the data are observed in two dif-
ferent years. Our data set, however, contains observations for seven different years,
and it seems foolish to discard those potentially useful additional data. But the
“before and after” method does not apply directly when T 7 2. To analyze all the
observations in our panel data set, we use the method of fixed effects regression.