comparing the OLS and 2SLS estimators for the effect of education on wages, using father’s years of schooling as the instrument variable.

(a) Run an OLS regression of logarithm wage (lwage) on years of schooling (educ), i.e.,
lwagei = α + βeduci + ui.
Use a sentence to interpret βˆOLS.
(b) Use ivreg command to run a Two Stage Least Squares (2SLS) regression. Use father’s years of
schooling (fatheduc) as the instrument variable. Use a sentence to interpret βˆ
2SLS.
(c) Check the F-statistics from the first-stage regression. How large it is? Is the instrument variable
weak?
(d) Perform a Hausman’s test to compare OLS with 2SLS estimators. Write down your test hypoth-
esis, p-value and conclusion.
(e) Discuss if father’s years of schooling (fatheduc) is a solid instrument variable, i.e., satisfies con-
ditions of instrument variables.