Chapter 3, Exercise Solutions, Principles of Econometrics, 3e46EXERCISE 3.9(a) We set up the hypotheses H0: 20β =versus H1: 20β >. The alternative 20β >is chosen because we assume that growth, if it does influence the vote, will do so in a positive way. The test statistic, given H0is true, is 2(29)2~se()bttb=The rejection region is (0.95,29)1.699tt>=. The value of the test statistic is 0.65994.04600.1631t==Since t= 4.0460 > 1.699, we reject the null hypothesis that β2= 0 and accept the alternative that 20β >. We conclude that economic growth has a positive effect on the percentage vote. (b) A 95% interval estimate for 2βfrom the regression in part (a) is: 2(0.975,29)2se()btb±=0.6599 ±2.045 ×0.1631 = (0.3264, 0.9934) This interval estimate suggests that, with 95% confidence, the true value of 2βis between 0.3264 and 0.9934. Since 2βrepresents the change in percentage vote due to economic growth, we expect that a 1% increase in the growth rate will increase the percentage vote by an amount between 0.3264 to 0.9934 percent.
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