Unformatted text preview: ECO321 by H. Morita Economic Statistics II Solution  HW2 Use the same data growth.dta as the homework assignment, but exclude country Malta from regression. Then, run three regressions of growth(= Y ) on: Regression (1) tradeshare(= X1 ) and yearsschool(= X2 ) Regression (2) tradeshare(= X1 ), yearsschool(= X2 ), rev coup(= X3 ) Regression (3) tradeshare(= X1 ), yearsschool(= X2 ), rev coup(= X3 ), assassinations(= X4 ) Assume that the error term is heteroskedastic. Note: To exclude Malta, remember that you add the following command at the end of regress command: if country name = "Malta" The results of regressions are reported in Appendix along with Stata's commands. a. Which regression has the best fit to the sample? Using adjusted R2 , explain. Answer: R = .1331 in (1), R = .1336 in (2), and R = .1209 in (1). Thus, Regression (2) has the best fit to the sample. b. In Regression (2), find a 90% confidence interval of the coefficient of tradeshare(= X1 ). Answer: .153 and 3.156 c. In Regression (3), find the predicted value of growth when tradeshare is 1.2, yearsschool is 6.2, rev coup is 0.12, assassinations is 0.05. Answer: growth = .2364 + 1.761(1.2) + .2106(6.2)  1.233(.12) + .1898(.05) %] d. In Regression (2), is rev coup statistically significant at the 5% level? Answer: In the hypothesis test of H0 : 3 = 0 against H1 : 3 = 0, the pvalue is .182, or 18.2%. Since the pvalue is greater than the level of significance () of 5%, we cannot reject the null hypothesis. Thus, rev coup is not statistically significant at the 5% level. (Alternative Solution) In the same hypothesis test above, tstatistic is 1.35. The critical value at the 5% level is 1.96. Since t < CV , we cannot reject the null hypothesis. Thus, rev coup is not statistically significant at the 5% level. e. Is Regression (3), is asassinations statistically significant at the 5% level? Answer: In the hypothesis test of H0 : 4 = 0 against H1 : 4 = 0, the pvalue is .662, or 66.2%. Since the pvalue is greater than the level of significance () of 5%, we cannot reject the null hypothesis. Thus, asassinations is not statistically significant at the 5% level.
1 2 2 2 3.52 [Annual (Alternative Solution) In the same hypothesis test above, tstatistic is .44. The critical value at the 5% level is 1.96. Since t < CV , we cannot reject the null hypothesis. Thus, asassinations is not statistically significant at the 5% level. f. Which regression (1), (2) or (3) is the most preferable to predict growth? Based on your conclusion in d and e, explain. Answer: The regressor rev coup is not statistically significant in (2), indicating that (1) is better model than (2). The regressor asassinations is not statistically significant in (3), indicating that (2) is better model than (3). Overall, (1) is the best model to predict growth. g. Do you agree with the idea that political instabilities prevent nations' economies from growing. Based on the results of the regression, explain. Sample Answer: I agree with the idea that political instabilities prevent nations' economies from growing. Yet, the results of the regression above show that the regressors rev coup and asassinations are not statistically significant. Even if they are statistically significant, the coefficient of asassinations is a positive value, implying that economic growth and the number of political assassinations are positively correlated. This points to the opposite direction. Although political instabilities might prevent nations' economies from growing, measuring political instabilities is a challenging task. Extracredit Question Using the estimates and their standard errors obtained from Stata, manually compute for b, d, and e. Answer: (b) 90% confidence interval of 1 in (2) = 1 CV SE(1 ) = 1.6545 1.645(.8990) .176 and 3.133. Note that those numbers are slightly different from Stata's output because Stata use CV from t instead of Z, and then makes a correction for small sample. (d) t = (1.052  0)/.7786 lution above. (e) t = (.1898  0)/.4320 above. 1.35. The rest of process is the same as the alternative so .44. The rest of process is the same as the alternative solution 2 Appendix: Stata Outputs . r e g g r o w t h t r a d e s h a r e y e a r s s c h o o l i f c o u n t r y _ n a m e ~=" M a l t a " , r Linear regression N u m b e r of obs F( 2, 61) Prob > F Rs q u a r e d Root MSE = = = = = 64 6.40 0.0030 0.1606 1.691                                                                                Robust growth  Coef . Std . Err . t P >t  [95% C o n f . I n t e r v a l ]       +                                                                       tradeshare  1.897823 .8655411 2.19 0.032 .1670666 3.628579 yearsschool  .2429753 .0758919 3.20 0.002 .0912201 .3947305 _ cons  .1222363 .691165 0.18 0.860 1.504306 1.259833                                                                               Adjusted Rsquared = .13309102 . r e g g r o w t h t r a d e s h a r e y e a r s s c h o o l r e v _ c o u p s i f c o u n t r y _ n a m e ~=" M a l t a " , r l e v e l ( 9 0 ) Linear regression N u m b e r of obs F( 3, 60) Prob > F Rs q u a r e d Root MSE = = = = = 64 5.79 0.0015 0.1749 1.6905                                                                                Robust growth  Coef . Std . Err . t P >t  [90% C o n f . I n t e r v a l ]       +                                                                       tradeshare  1.654549 .8990022 1.84 0.071 .1526319 3.156466 yearsschool  .2106772 .0836441 2.52 0.014 .0709373 .3504171 rev_ coups  1.052122 .7786461 1.35 0.182 2.352966 .248722 _ cons  .3165196 .8245622 0.38 0.702 1.061034 1.694073                                                                               Adjusted Rsquared = .13363915 . r e g g r o w t h t r a d e s h a r e y e a r s s c h o o l r e v _ c o u p s a s s a s i n a t i o n s i f c o u n t r y _ n a m e ~=" M a l t a " , r Linear regression N u m b e r of obs F( 4, 59) Prob > F Rs q u a r e d Root MSE = = = = = 64 5.02 0.0015 0.1768 1.7028                                                                                Robust growth  Coef . Std . Err . t P >t  [95% C o n f . I n t e r v a l ]       +                                                                       tradeshare  1.760786 .9841691 1.79 0.079 .2085315 3.730104 yearsschool  .2105987 .0830399 2.54 0.014 .0444363 .3767611 rev_ coups  1.232778 .9383476 1.31 0.194 3.110407 .6448511 assasinati ~s  .1898288 .4320358 0.44 0.662 .6746729 1.054331 _ cons  .2364186 .9003265 0.26 0.794 1.56513 2.037968                                                                               Adjusted Rsquared = .12094555 . 3 ...
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 Spring '11
 HiroshiMorita
 Statistics, Statistical hypothesis testing, Malta, Rev Coup

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