= Bat Bo tr We are concerned that is endogenous, that is, Elulz] 0. To solve the endogeneity issue, we find an instrumental variable z which is binary (taking values of 0 and 1 only). Suppose that we have a random sample {(,2): 1 i n}. The size of the group with 2 = 1 is n = Ei=1, and the size of the group with 2=0 is no =(1-2). Show that the instrumental variable estimator can be written as = in Consider the simple regression model: 91 - 90 To 721 where 9 90 6:2,=1 no 1 721 no (=1 In words, yo and I are the sample averages of y, and z, over the part of the sample with z = 0, and where 1 and 1 are the sample averages of y, and r, over the part of the sample with 2, = 1. 1:0