Question

8. A regression of wage (log(wage) is run on a set of following variables: female (-1 if female), educ (years of education), exper (years of experience) and tenure (years with current employer). The regression results are listed as follows. Coefficients: Estimate Std. Error tvalue Pr(Itl) (Intercept) -1.56794 0.72455 -2.164 0.0309 female -1.81085 0.26483 -6.838 2.26e-11*** educ 0.57150 0.04934 11.584 <2e-16*** 0.02540 0.01157 2.195 0.0286 exper 0.14101 0.02116 6.663 6.83e-11*** tenure Signif. codes:0.0010.010.050.1'"1 Residual standard error: 2.958 on 521 degrees of freedom Multiple R-squared: 0.3635, Adjusted R-squared: 0.3587 F-statistic: 74.4 on 4 and 521 DF, p-value: < 2.2e-16

Answer 1

(1)
The difference in log(wage) between male and female is 1.81085
or, the average wage of male is exp(1.81085) = 6.115644 times than the that of female.

(2)
The coefficient estimates would not change because heteroskedasticity would not affect your parameter estimates but it does make them less precise. Lower precision increases the likelihood that the coefficient estimates are further from the correct population value. Heteroskedasticity increases the variance of the coefficient estimates and thus the standard errors will be different in the next run, Consequently, OLS calculates the t-values and F-values using an underestimated amount of variance. This problem can lead you to conclude that a model term is statistically significant when it is actually not significant.