Consider a model where the return to education depends upon the amount of work experience (and vice versa): log(wage) = β0 + β1educ + β2exper + β3educ ∗ exper + u.

Question

Formally state and test the hypothesis that the wage does not depend on education.

Answer 1

Hope the below helps. Let me know if you have follow-up questions.

Let M=conditional mean of log(wage)

Let C=conditional mean of educ

H0: M-C=0

Ha: M-C!=0

In a bivariate model, you would examine the p-value on B1 or conduct a t-test.

The multiple regression model is simply an extension of this, and in the regression you would examine the p-value on the B1 coefficient.