In regression (18.1) with T 2 and N 2 suppose the time variable is omitted. Thus the estimating equation is Yi t

In regression (18.1) with T Æ 2 and N Æ 2 suppose the time variable is omitted. Thus the estimating equation is Yi t Æ ¯0 ů1Statei ŵDi t Å"i t .

where Di t ÆStateiTimet is the treatment indicator.

(a) Find an algebraic expression for the least squares estimator bµ.

(b) Show that bµ is a function only of the treated sub-sample and is not a function of the untreated sub-sample.

(c) Is bµ a difference-in-difference estimator?

(d) Under which assumptions might bµ be an appropriate estimator of the treatment effect?