Consider the following model Yoi = xo +uoi Y₁ = x3₁+un D = 1 if z0+v> 0 = 0 if x0+v0 ()--(0)79)) Yi = ₁, D₁ + Yoi (1 - D

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Consider The Following Model Yoi Xo Uoi Y X3 Un D 1 If Z0 V 0 0 If X0 V0 0 79 Yi D Yoi 1 D 1 (73.85 KiB) Viewed 31 times

Consider the following model Yoi = xo +uoi Y₁ = x3₁+un D = 1 if z0+v> 0 = 0 if x0+v0 ()--(0)79)) Yi = ₁, D₁ + Yoi (1 - D₂). N We have a random sample {(ri, yi, Di)}1 I (a) What is E[yoili, D₁ = 0] ? (b) Use (a) to construct a consistent estimator of 8o and show its influence function under some additional conditions. (c) Given 30 and 3₁, obtain the moment condition of Ely₁ - yol- (d) Use (c) and (b) (and an analogous estimator for 3₁) to obtain a 2-step estimator of Ely₁ - yo]. (e) What is the influence function for the 2-step estimator you defined in (d) ? (f) How will you improve efficiency of the 2-step estimator your proposed in (d) ?