Question #195481

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) 



1
Expert's answer
2021-05-21T11:40:47-0400

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

β2 is the coefficient of education than,

CI=β2ˆ±zα2S.D.(β2ˆ)CI = β_2ˆ ±\frac{zα}{2}S.D.( β_2ˆ)

CI=0.092±zα20.008CI = 0.092±\frac{zα}{2}0.008

CI=0.092±1.96×0.008CI = 0.092±1.96\times0.008

CI=0.092±0.01568CI = 0.092±0.01568

CI=(0.07632,0.10768)CI = (0.07632,0.10768)


b) If exp = 10

Log (earnings) =4.016+0.092.educi+0.079.10+0.002.100= 4.016 + 0.092 . educi + 0.079 .10 + 0.002 . 100

Log (earnings)=4.016+0.092.educi+0.79+0.2= 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= 4.016 + 0.092 . educi + 0.079 .11 + 0.002 . 121

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

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

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