This exercise will empirically explore howwork experience affects hourly wage rates. We use the dataset which contains data on hourly wage rates (variable: wage), posteducationyears of experience (variable: exper) andother variables for 1000individuals. a. We generate the variable: lwage, which is defined as the logarithm of variable wage. Figure 1 shows the summary statistics (including mean, variance, skewness, kurtosis) for variables: wage, lwage and exper. Check whether these variables are normally distributed. You may use the 95% significance level for your hypotheses tests. (Advice: Clearly show null/alternative hypotheses, test statistics, rejection region, conclusion for each variable) b. Weestimatelinear,loglinearandlog-logmodel specifications toexaminetheeffect of experience on wage. These regression results are shown in Figure 2. i. Write down the fitted modes for each specification. ii. Obtain the 99% C.I. for the slope parameter in the linear specification. iii. Testthe null hypothesis that the intercept in the log-linear model is 0 against its right tail alternative. (Advice: Clearly write down the null/alternative hypotheses, test statistics, rejection region and conclusion. You may set the Type I error at α = 0.05.) c. UsingresultsfromFigure2,whatisthepredictedhourlywageforanindividualwith 10yearsof experience for eachmodel specification? Howdoyour results compare? 2 d. Using results from Figure 2, what is the elasticity of experience to wage for each specification? e. UsingresultsfromFigure2,comparetheR2 ofthelinearmodelwiththegeneralized R2 from the log-linear models? What can you conclude? (Advice: You need to calculate the generalized R2 using information from Figure 2). f. Figure 3shows the summary statistics ofthe residuals fromthe linearmodel(residlinear) and the residuals from the log-linear model (residuallogl). Check whether the residuals from the linear and log-linear model are normally distributed. You may use the 95% significance level for your hypotheses tests. (Advice: Clearly show null/alternative hypotheses, test statistics, rejection region, conclusion for each variable) g. Overall, which model specification would you choose? Justify your answer with findings from previous sections. 3 Figure 1: Summary statistics of wage, lwage and exper . sum wage, detail earnings per hour Percentiles Smallest 1% 3.895 2.03 5% 7.2 2.5 10% 8.275 2.83 Obs 1,000 25% 12 2.88 Sum of Wgt. 1,000 50% 16.5 Mean 20.20122 75% 25.4 Largest 72.13 Std. Dev. 12.1038 90% 36.96 72.13 Variance 146.5021 95% 45.175 72.13 Skewness 1.478395 99% 62.58 72.13 Kurtosis 5.475637 . sum lwage, detail lwage 1% Percentiles 1.359627 Smallest .7080358 5% 1.974081 .9162908 10% 2.113237 1.040277 Obs 1,000 25% 2.484907 1.05779 Sum of Wgt. 1,000 50% 2.80336 Mean 2.84477 75% 3.234744 Largest 4.27847 Std. Dev. .5710783 90% 3.609836 4.27847 Variance .3261304 95% 3.810542 4.27847 Skewness -.0561999 99% 4.136147 4.27847 Kurtosis 3.08314 . sum exper, detail post education years experience 1% Percentiles 5 Smallest 3 5% 7 3 10% 9 4 Obs 1,000 25% 15 4 Sum of Wgt. 1,000 50% 27 Mean 26.501 75% 36.5 Largest 58 Std. Dev. 12.99041 90% 43 59 Variance 168.7507 95% 47.5 63 Skewness .1219864 99% 55.5 64 Kurtosis 2.150823 . 4 Figure 2: Ordinary Least Squares regression Outputs . reg wage exper Source SS df MS Model 563.899211 1 563.899211 Residual 145791.662 998 146.08383 Total 146355.561 999 146.502063 . reg lwage exper Source SS df MS Model .892358779 1 .892358779 Residual 324.911879 998 .325563005 Total 325.804237 999 .326130368 . reg lwage lexper Source SS df MS Model 3.86415199 1 3.86415199 Residual 321.940085 998 .322585256 Total 325.804237 999 .326130368 . Number of obs = 1,000 F(1, 998) = 3.86 Prob > F = 0.0497 R-squared = 0.0039 Adj R-squared = 0.0029 Root MSE = 12.087 Number of obs = 1,000 F(1, 998) = 2.74 Prob > F = 0.0981 R-squared = 0.0027 Adj R-squared = 0.0017 Root MSE = .57058 Number of obs = 1,000 F(1, 998) = 11.98 Prob > F = 0.0006 R-squared = 0.0119 Adj R-squared = 0.0109 Root MSE = .56797 wage Coef. Std. Err. t P>|t| [95% Conf. Interval] exper .0578356 .0294371 1.96 0.050 .0000698 .1156014 _cons 18.66852 .8687121 21.49 0.000 16.96381 20.37323 lwage Coef. Std. Err. t P>|t| [95% Conf. Interval] exper .0023007 .0013897 1.66 0.098 -.0004263 .0050277 _cons 2.783798 .0410102 67.88 0.000 2.703322 2.864274 lwage Coef. Std. Err. t P>|t| [95% Conf. Interval] lexper .100985 .0291778 3.46 0.001 .0437282 .1582418 _cons 2.529811 .092757 27.27 0.000 2.34779 2.711832 5 Figure 3: Summary statistics of OLS residuals from linear model (residlinear) and loglinear model (residuallogl) . sum residlinear, detail residlinear 1% Percentiles -16.23426 Smallest -18.84381 5% -13.08766 -18.28813 10% -11.78101 -17.90359 Obs 1,000 25% -8.401573 -17.52359 Sum of Wgt. 1,000 50% -3.538217 Largest Mean Std. Dev. -1.84e-07 12.08046 75% 5.26518 51.20589 90% 16.52141 51.3794 Variance 145.9376 95% 24.71182 52.24693 Skewness 1.465559 99% 41.47007 52.94096 Kurtosis 5.456175 . . sum residuallogl, detail residuallogl 1% Percentiles -1.470989 Smallest -2.103371 5% -.8650622 -1.936529 10% -.7182188 -1.84448 Obs 1,000 25% -.3761723 -1.795029 Sum of Wgt. 1,000 50% -.0392261 Largest Mean Std. Dev. -3.46e-09 .5702956 75% .3922077 1.411846 90% .757394 1.415255 Variance .3252371 95% .9512334 1.446357 Skewness -.0662608 99% 1.263653 1.473965 Kurtosis 3.087397