Answer to Question #201197 in Statistics and Probability for Biniyam yirgalem

Question

Problem 3 In this question we look at the relation between the logarithm of weakly earnings and years of education. Using data from the national longitudinal study of youth, we find the following results for a regression of log weekly earnings and years of education, experience, experience squared and an intercept:Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2 ( 0.222) ( 0.008) ( 0.025) (0.001) a).Construct a 95% confidence interval for the effect of years of education on log weakly earnings. (2 point) b).Consider an individual with 10 year of experience. What would you expect to be the return to an additional year of experience for such an individual (the effect on log weakly earnings)? (3 point) c).

Answer 1

a) 95% confidence interval for the effects of years of education is given as follows:

β₂ is the coefficient of education than,

$CI = β_2ˆ ±z_{\frac{α}{2}}S.D.( β_2ˆ)$

$CI = 0.092±z_{\frac{α}{2}}0.008$

$CI = 0.092±1.96\times0.008$

$CI = 0.092±0.01568$

$CI = (0.07632,0.10768)$

b) If exp = 10

Log (earnings) $= 4.016 + 0.092 . educi + 0.079 .10 + 0.002 . 100$

Log (earnings)$= 4.016 + 0.092 . educi + 0.79 + 0.2$

If exp = 11 (1 year added)

Log (earnings) $= 4.016 + 0.092 . educi + 0.079 .11 + 0.002 . 121$

Log (earnings) $= 4.016 + 0.092 . educi + 0.869 + 0.242$

Effect of Log (earnings) $= (0.869 + 0.242) -( 0.79 + 0.2 ) = 0.121$