# Chapter 10 Answers - Chapter 10 Answers 1(a With a \$1...

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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- specified (no important omitted variable bias, correct functional form, no simultaneous causality or selection bias, and so forth.) (f) Define a binary variable west which equals 1 for the western states and 0 for the other states. Include the interaction term between the binary variable west and the unemployment rate, west × (unemployment rate), in the regression equation corresponding to column (4). Suppose the coefficient associated with unemployment rate is β , and the coefficient associated with west × (unemployment rate) is γ . Then β captures the effect of the unemployment rate in the eastern states, and β + γ captures the effect of the unemployment rate in the western states.
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