Consider the simple regression model
yi = bo+ b1zi + ei
and let xi be a binary instrumental variable for zi.
(a) Show that the IV estimator b1 can be written as b1 = (mean(y1) - mean(y0)) /(mean(z1)-mean(z0))
where mean(y0) and mean(z0) are the sample averages of yi and zi over the part of the sample
with xi = 0, and mean(y1) and mean(z1) are the sample averages of yi and zi over the part
of the sample with xi = 1. (20 points)
(b) What is the interpretation of b1 if zi is also binary, for example, repre-
senting participation in a social program? (20 points)