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414 Chapter 10 Regression with Panel Data

coefficient in Equation (10.21) is 0.25, substantially smaller than the clustered stan-
dard error, 0.36, and the respective t-statistics testing b1 = 0 are -2.51 and -1.78.
The reason we report the clustered standard error is that it allows for serial correla-
tion of uit within an entity, whereas the usual heteroskedasticity-robust standard
error does not. The formula for clustered standard errors is given in Appendix 10.2.

10.6 Drunk Driving Laws and Traffic Deaths

Alcohol taxes are only one way to discourage drinking and driving. States differ
in their punishments for drunk driving, and a state that cracks down on drunk
driving could do so by toughening driving laws as well as raising taxes. If so, omit-
ting these laws could produce omitted variable bias in the OLS estimator of the
effect of real beer taxes on traffic fatalities, even in regressions with state and time
fixed effects. In addition, because vehicle use depends in part on whether drivers
have jobs and because tax changes can reflect economic conditions (a state budget
deficit can lead to tax hikes), omitting state economic conditions also could result
in omitted variable bias. In this section, we therefore extend the preceding analy-
sis of traffic fatalities to include other driving laws and economic conditions.

The results are summarized in Table 10.1. The format of the table is the same
as that of the tables of regression results in Chapters 7 through 9: Each column
reports a different regression, and each row reports a coefficient estimate and
standard error, F-statistic and p-value, or other information about the regression.

Column (1) in Table 10.1 presents results for the OLS regression of the fatal-
ity rate on the real beer tax without state and time fixed effects. As in the cross-
sectional regressions for 1982 and 1988 [Equations (10.2) and (10.3)], the
coefficient on the real beer tax is positive (0.36): According to this estimate,
increasing beer taxes increases traffic fatalities! However, the regression in col-
umn (2) [reported previously as Equation (10.15)], which includes state fixed
effects, suggests that the positive coefficient in regression (1) is the result of omit-
ted variable bias (the coefficient on the real beer tax is -0.66). The regression R 2
jumps from 0.091 to 0.889 when fixed effects are included; evidently, the state
fixed effects account for a large amount of the variation in the data.

Little changes when time effects are added, as reported in column (3)
[reported previously as Equation (10.21)], except that the beer tax coefficient is
now estimated less precisely. The results in columns (1) through (3) are consistent
with the omitted fixed factors—historical and cultural factors, general road condi-
tions, population density, attitudes toward drinking and driving, and so forth—
being important determinants of the variation in traffic fatalities across states.