Suppose that you have panel data with two periods (t =1, 2). Let the treatment b

Question

Suppose that you have panel data with two periods (t =1, 2). Let the treatment be binary, so that X_it = 1 for t = 2 for the individuals in the treatment group and let X_it = 0 otherwise. Note that at t =1, no one is in the treatment. Consider the regression model Y_it = alpha_i + beta_1 X_it + beta_0 D_t + v_it, where alpha_i are individual fixed effects, D_t is the binary variable that equals 1 if t = 2 and 0 otherwise. Explain why it is important to include D_t. What problems might occur if it is left out? Explain why it is important to include alpha_i. Explain in detail how to estimate beta_1 and beta_0. Be specific about the assumptions you are making.

Explanation / Answer

(a) Dt being the binary variable will represent group/period t=2 as in its coefficient beta0 will get added to intercept alpha to reflect the phenomenon of group 2.

(b) It will get changed as group changes from 1 to 2. It is the commom intercept to all models.

(b) To estimate betas, assign binary variables Dt & Xit 1 & 0 as per period of data considered and then run a multiple linear regression model

Assumptions:

1) data is iid

2) Normal dist

3) Homoskeadasticity

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