Question

Suppose you want to investigate the differences in earnings between men and women. Consider the following model:

ln(WAGE) = β1 + β2 EDUC + β3 EXPER + β4 MALE + β5 (EDUC*MALE) + β6 (EXPER*MALE) + e

where EDUC = years of education, EXPER = years of work experience, and MALE = an indicator variable that = 1 for males and = 0 for females. Then the effect of being male (select the best answer)

a) depends on the male’s level of education

b) depends on the male’s level of experience

c) depends on the male’s level of education and experience

d) is given by β4+ β5+ β6

e)If males and females have the same average experience, then the male ef- fect is given by β1+ β2+ β4+ β5 .

Answer 1

ln(WAGE) = β1 + β2 EDUC + β3 EXPER + β4 MALE + β5 (EDUC*MALE) + β6 (EXPER*MALE) + e

For male,  MALE = 1

ln(WAGE) = β1 + β2 EDUC + β3 EXPER + β4 * 1 + β5 (EDUC*1) + β6 (EXPER*1) + e

ln(WAGE) = β1 + β4 + (β2 + β5) EDUC + (β3 + β6) EXPER + e ---(1)

For female,  MALE = 0

ln(WAGE) = β1 + β2 EDUC + β3 EXPER + β4 * 0 + β5 (EDUC*0) + β6 (EXPER*0) + e

ln(WAGE) = β1 + β2 EDUC + β3 EXPER + e --(2)

From (1) and (2), the difference between males and females ln(WAGE) is,

β4 + β5 EDUC + β6EXPER

Thus, the effect of being male is,

c) depends on the male’s level of education and experience