Question

5.4 Consider the rudimentary educational attainment model S = B. + B, MALE+ Demonstrate that, if it were fitted with a sample of observations, ß = 5, and B2 = 5x -5F where 5p and 5 are mean years of schooling of females and males in the sample. Hint: use the normal equations from the simple regression analysis (1.27) and (1.28).

Answer 1

MALE is the indicator whether the student is a male or a female. Based on the gender of the student, the model becomes the following:

1) For Females, MALE=0

$S_F=\beta_1+u_F$

using OLS, we have

$\hat{\beta}_1= \sum_F{S_F*1}/\sum_F{1*1}= \bar{S}_F$

i.e., it is just the mean schooling for all the girls.

2) For Males: MALE=1,

SM = B1 + B2 + UM

using

$S_M-\beta_1=\beta_2+u_M\\\\ \hat{\beta}_2= \sum_M({(S_M-\hat{\beta}_1)*1})/\sum_M{(1*1)}\\\\ =\sum_M{(S_M*1)}/\sum_M{(1*1)}-\sum_M{(\hat{\beta}_1*1)}/\sum_M{(1*1)} \\\\ =\bar{S}_M - \hat{\beta}_1\\\\ =\bar{S}_M-\bar{S}_F$