# Solved – Difference-in-differences estimator

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 'treatment 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.

Contents