Consider the following model:

• $wage_i=\beta_0+\beta_1after_i+\beta_2female_i+\beta_3after_ifemale_i+u_i$

where

• $after_i=1$ if date after gender-wage discrimination policy; $0$ if date before gender-wage discrimination policy.

• $female_i=1$ if female; $0$ if male.

The 'control group' is females.

This model measures the effect of a gender-wage discrimination policy on the average wage of women relative to men.

The affect of the policy is captured by $\beta_3$ which can be estimated as follows:

• $\hat{\beta_3}=(E[wage_i|after_i=female_i=1]-E[wage_i|after_i=1, female_i=0])-(E[wage_i|after_i=0, female_i=1]-E[wage_i|after_i=female_i=0])$

which is known 'difference-in-differences' estimator.

Questions:

1. If $\hat{\beta_3}>0$, then does this means that the policy caused women's earning to increase relative to mens?
2. For $\hat{\beta_3}$ to be interpreted as the causal effect of the policy on wages, does $E(u_i|female_i, after_i)=0$ have to be assumed?

Any guidance would be very much appreciated. Thank-you.