ps8_sol

# ps8_sol - Introduction to Econometrics Professor Alexei...

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Introduction to Econometrics Professor Alexei Onatski Problem Set 8 – November 23 Problem 1) [ Stock and Watson 10.1 ] (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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## This note was uploaded on 12/20/2009 for the course ECON 1300 taught by Professor Natski during the Fall '09 term at Columbia.

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ps8_sol - Introduction to Econometrics Professor Alexei...

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