Question 2 Consider the following panel data model: yu = B'Tu tut fiten, i=1,..., n; t = 1,...,T, where ya is the scalar outcome variable, To is the K x 1 vector of regressors, 4 and fe are the unobserved individual effects and time effects. Define the unit- specific average over time as G. = + 2 Tu. Define the time-specific average over the cross section as D = , my Ta. The overall average is defined as i= a Etz Et Tu. Define the grand-difference as in = In - 1 - 1 + 1. (a) Show that the fixed-effects estimator AFF can be obtained by OLS regression of yu on int- (b) Show that the fixed-effects estimator AFF can be obtained by OLS regression of ya on 1, In, 1, it- (c) Suppose we observe a time-variant regressor z, and a common time effect wy. Show that in the OLS regression of ya on 1, In, , It, 2, we, the OLS estimates for the coefficients on z, and w are both zero. (d) Consider a policy intervention that occurred in period To. Let D, be a dummy variable indicating whether unit i is subject to the policy intervention. Let Fe denote the time dummy such that F, = 1 ift > To. Define the interaction term Xit = D: x Fi. Let AFE denote the fixed-effects estimator in the regression yit = BXu+ Hit fetei. Let pop denote the difference-in-differences estimator in the regression yu = Bo + pXu+yDi +4Fi + wi. Show that BFE = PDD