Topic : Establishing Causal Interference

Question: Suppose you have assumed the following data-generating process: Y= + 1 X1i + 2 X2i + Ui. You further assume that U is uncorrelated with X1 and X2 . For each of the four possibilities below, determine whether you can get consistent estimates of the parameters for the determining function using regression if your sample of Y, X1 , and X2 is selected according to:

a. X1 > 100

b. 80 < X1 < 150 and 40 < X2 < 205

c. Y < 200

d. 50 < X1 < 150 and Y > 75