Chapter 10
Regression with Panel Data
±
Solutions to Exercises
1.
(a) With a $1 increase in the beer tax, the expected number of lives that would be saved is 0.45 per
10,000 people. Since New Jersey has a population of 8.1 million, the expected number of lives
saved is 0.45
×
810
=
364.5. The 95% confidence interval is (0.45
±
1.96
×
0.22)
×
810
=
[15.228, 713.77].
(b) When New Jersey lowers its drinking age from 21 to 18, the expected fatality rate increases by
0.028 deaths per 10,000. The 95% confidence interval for the change in death rate is 0.028
±
1.96
×
0.066
=
[
−
0.1014, 0.1574]. With a population of 8.1 million, the number of fatalities will
increase by 0.028
×
810
=
22.68 with a 95% confidence interval [
−
0.1014, 0.1574]
×
810
=
[
−
82.134, 127.49].
(c) When real income per capita in new Jersey increases by 1%, the expected fatality rate increases
by 1.81 deaths per 10,000. The 90% confidence interval for the change in death rate is 1.81
±
1.64
×
0.47
=
[1.04, 2.58]. With a population of 8.1 million, the number of fatalities will increase
by 1.81
×
810
=
1466.1 with a 90% confidence interval [1.04, 2.58]
×
810
=
[840, 2092].
(d) The low
p
value (or high
F
statistic) associated with the
F
test on the assumption that time
effects are zero suggests that the time effects should be included in the regression.
(e) The difference in the significance levels arises primarily because the estimated coefficient is
higher in (5) than in (4). However, (5) leaves out two variables (unemployment rate and real
income per capita) that are statistically significant. Thus, the estimated coefficient on
Beer Tax
in
(5) may suffer from omitted variable bias. The results from (4) seem more reliable. In general,
statistical significance should be used to measure reliability only if the regression is well
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 Spring '09
 Smith
 Statistics, Regression Analysis, Statistical hypothesis testing, Statistical significance, fatality rate increases

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