Part (a Preferred Final Specification Source | SS df MS Number of obs = 1192 ————-+—————————— F( 10, 1181) = 68.06 Model | 160.34744 10 16.034744 Prob gt. F = 0.0000 Residual | 278.231651 1181 .235589882 R-squared = 0.3656 ————-+—————————— Adj R-squared = 0.3602 Total | 438.579091 1191 .368244409 Root MSE = .48538 —————————————————————————— logearnings | Coef. Std. Err. t Pgt.|t| [95% Conf. Interval] ————-+—————————————————————- ls | .9932233 .0983202 10.10 0.000 .8003217 1.186125 lsf | .1169449 .0451264 2.59 0.010 .0284081 .2054817 lasvabc | .5227557 .0876052 5.97 0.000 .3508765 .6946349 lweight02 | -.1928427 .0676438 -2.85 0.004 -.3255582 -.0601272 lexp | .096436 .0445005 2.17 0.030 .0091272 .1837448 ltenure | .0840076 .011747 7.15 0.000 .0609602 .107055 lhours | .2658989 .0535023 4.97 0.000 .1609288 .3708689 catgov | -.0469187 .034193 -1.37 0.170 -.1140045 .0201672 female | -.2666817 .033851 -7.88 0.000 -.3330966 -.2002669 region | -.0327165 .012845 -2.55 0.011 -.0579181 -.007515 _cons | -2.270849 .4863924 -4.67 0.000 -3.225139 -1.31656 —————————————————————————— 2. Explanation of Constructed Variables logearnings = log(earnings) the ‘l’ prefixes on the independent variables indicate natural logs. For example, ls = log(s), ltenure = log(tenure), etc1. 3. Interpretation Conditional on the other characteristics that influence earnings, ‘catgov’, i.e., the indicator variable for whether an individual is employed by the government sector or not has a negative but insignificant coefficient. Therefore, there is no evidence that working for the government leads to systematically different mean hourly earnings compared to not working for the government sector. From the signs and magnitudes of the other estimated coefficients, the following noteworthy points emerge. A one percent increase in own schooling years leads to a 0.99 percent increase in mean hourly earnings. Additionally, a one percent increase in father’s years of schooling leads to a 0.11 percent increase in mean hourly earnings. Similarly, ability, tenure, experience and hours all have positive and significant effects. Weight in 2002 however, has a negative impact on hourly earnings. Similarly, being a female leads to a systematically lower mean wage, as does being employed in a major US region. The final model was chosen on the basis of the following aspects. First, the R-squared and adjusted R-squared were found to be highest under this specification. Note from the table above the R-squared is approximately 0.36 implying that 36 percent of the variability in the natural logarithm of earnings is explained by the variability of the included independent variables. For a cross-sectional model, this is a pretty decent performance. Secondly, the included variables are the only ones that had statistically significant impacts. Finally, hours and tenure are likely to depend on hourly earnings – higher hourly earnings are likely to motivate an individual to work longer and try to retain higher tenure. As a result of this possible endogeneity, these variables are not included as regressors. 4. Diagnostic tests for normality and heteroskedasticity The variable ‘earnings’ in levels is much more asymmetric and thus farther away from a normal distribution compared to earnings in natural logarithms. This is shown in figure 1 and figure 2 below. Figure 1 represents the histogram of earnings in levels. Figure 2 presents the histogram of earnings in natural logs. Evidently the second figure is a much closer approximation to a normal distribution. Figure 1: Distribution of earnings in levels Figure 2: Histogram of earnings in natural logs However, even the logarithm of earnings is not entirely normally distributed. A test based on skewness and kurtosis (‘sktest’ in stata) rejects the null hypothesis of a normal distribution. A Breusch-Pagan test of heteroskedasticity (‘estat hettest’ in stata) rejects the null hypothesis of constant variance. However, it should be noted that even if heteroskedastic disturbances imply the point estimates are not efficient, they are still unbiased and consistent. Part (b) 1. Preferred Final specification Source | SS df MS Number of obs = 1192 ————-+—————————— F( 14, 1177) = 50.28 Model | 164.136337 14 11.7240241 Prob gt. F = 0.0000 Residual | 274.442754 1177 .233171414 R-squared = 0.3742 ————-+—————————— Adj R-squared = 0.3668 Total | 438.579091 1191 .368244409 Root MSE = .48288 —————————————————————————— logearnings | Coef. Std. Err. t Pgt.|t| [95% Conf. Interval] ————-+—————————————————————- ls | .3138573 .413471 0.76 0.448 -.4973652 1.12508 lsf | .1226065 .0449431 2.73 0.006 .0344289 .2107841 lasvabc | 1.188378 .3973633 2.99 0.003 .4087581 1.967997 lweight02 | -.2095736 .0674643 -3.11 0.002 -.3419372 -.07721 lexp | .0894088 .0444351 2.01 0.044 .0022279 .1765897 ltenure | .0833685 .0117213 7.11 0.000 .0603715 .1063654 lhours | .2591345 .0534606 4.85 0.000 .1542457 .3640232 ability_gov | -.0227416 .0088423 -2.57 0.010 -.0400899 -.0053932 ability_pri | -.0114904 .0085438 -1.34 0.179 -.0282531 .0052723 s_gov | .0487331 .0315916 1.54 0.123 -.013249 .1107152 s_pri | .0526783 .0316882 1.66 0.097 -.0094933 .1148499 catgov | .5837549 .2096278 2.78 0.005 .1724691 .9950407 female | -.2668284 .0336893 -7.92 0.000 -.3329261 -.2007307 region | -.0346761 .0128164 -2.71 0.007 -.0598217 -.0095305 _cons | -3.113162 .7133313 -4.36 0.000 -4.512705 -1.713619 —————————————————————————— 2. Explanation of constructed variables ability_gov = asvabc*catgov ability_pri = asvabc*catpri s_gov = s*catgov s_pri = s*catpri The variables above are interaction variables. The first two are interactions of ability with categorical indicators of whether the employer is the government sector or the private sector. The second two are interactions of years of schooling with the same categorical indicators used in the first two. 3. Interpretation The coefficient on the interaction between ability and the dummy variable for government employment is negative and significant. This implies the returns to ability is lower in government sector employment. That is, an increase in ability leads to a lower increase in hourly earnings in the government sector compared to the non-government sectors. The interaction between ability and the dummy for private sector employment has a smaller negative coefficient, but it is not significant statistically. Therefore, changes in ability in the private sector have no meaningful effects. The interaction between schooling and government employment is insignificant, but the interaction between schooling and private-sector employment is positive and significant at the 10 percent level. Therefore, we can conclude that while ability has a negative effect in the government sector jobs, schooling has a positive effect in private sector employment. The other important point to note from the table above is that now, catgov has a significant and positive coefficient. This implies when we control for how ability and years of schooling work through employment in government and private sectors, mean log earnings are higher in the government sector.