my problem is from the following book on page 94 (http://www.development.wne.uw.edu.pl/uploads/Main/recrut_econometrics.pdf).
They say the covariance between a single dummy instrument variable (z), which is one with probability p, and the dependent variable (y) is: Cov(y,z) = (E(y I z=1) - E(y I z=0))p(1-p). They say this is easy to show, but i cant figure it out. I tried using the usual covariance formulas, but it didnt help. Does anybody know an answer?