un an OLS regression of logarithm wage (lwage) on years of schooling (educ)

(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