Question

suppose that you have data on many (say 1,000) randomly selected employed country's  residents. FURTHER DETAILS GIVEN IN THE END OF THE QUESTIONS

a) Explain how you would test whether, holding everything else constant, females earn less than males.

b) Explain how you would measure the payoff to someone becoming bilingual if her mother tongue is i) French, ii) English.

c) Does including both X₃ and X₄ in this regression model have the potential to show any "problems" when estimating your regression model? Explain. Would eliminating one of them potentially cause other problems? Explain

d) Can you use this model to test if the influence of on-the-job experience is greater for males than females? Why or why not? If not, how would you need to change the model to test whether the influence of on the job experience is greater for males than females?

FURTHER DETAILS:

Consider the following linear regression model "explaining" salaries in the Country:

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + β₅D₁ + β₆D₂ + β₇D₃ + µ

where: Y = salary,

X₁ = years of education,

X₂ = innate ability (proxied by IQ test results)

X₃ = years of on the job experience

X₄ = age

D₁ = a dummy variable for gender (= 1 for males, 0 for females)

D₂ = 1 for uni-lingual French speakers

D₃ = 1 for uni-lingual English speakers

Answer 1

a)

To test whether holding everything else constant that females earn less than males, we have to test the null hypothesis H0 : beta5 ( coefficient for dummy variable for gender) = 0 vs the alternative hypothesis H1: beta5 > 0

If alternative hypothesis is that males earn more than females, it would imply that salary is higher for males, that is coefficient for males is greater than 0.

Thus, if the null hypothesis is rejected then it would imply that based on the data, females would earn less than males.

b)

If someone’s mother tongue is French, then becoming bilingual would mean learning English which would mean a payoff of learning English that is, an increase in salary by beta7.

If someone’s mother tongue is English, then becoming bilingual would mean learning French which would mean a payoff of learning French that is, an increase in salary by beta6.

c)

Including age and years on the job experience together might lead to problem of multi collinearity.

As years on the job experience is related to the age, with an increase in the latter leading to an increase in the former without loss of generality. And multicollinearity would lead inconsistent model results.

If one of the variables is removed however, it might reduce the predictive power of the model, in addition to the fact that all the variables that came significant previously might not come significant in the new model.

d)

This model can’t be used to test the influence of on the job experience being greater for males or females.

That is because both the variables are present as explanatory variables and there is no interaction term in the model as well to test the interaction between the variables on the job experience and gender.

One way in to test the influence of experience being greater for males than females or not is to use an interaction term in the regression model, that would help in understanding in which direction the salary goes for males or females when taken together with the on the job experience.