Question: Suppose that you have the same data as in given Exercise (panel data with two periods, n observations), but ignore the W regressor. Consider the alter-native regression model
where Gi =1 if the individual is in the treatment group and Gi = 0 if the individual is in the control group. Show that the OLS estimator of β1 is the differences-in-differences estimator in Equation (13.4). (Hint: See Section 8.3).
Exercise: Suppose that you have panel data from an experiment with T = 2 periods (so t = 1, 2). Consider the panel data regression model with fixed individual and time effects and individual characteristics Wi that do not change over time, such as gender. Let the treatment be binary, so that Xit = 1 for t = 2 for the individuals in the treatment group and let Xit = 0 otherwise. Consider the population regression model
