ECON 104 Lecture Notes - Lecture 43: Conditional Expectation, Internal Validity, Instrumental Variable
Document Summary
Nb nonlinear least squares, ols, probit, logit, mle. Procedure that tells you what to do with data to get good guess of beta 1. First: isolate part of x uncorrelated with u, by regressing x on z (instrumental variable) using. Since being z is uncorrelated with u, then pi0 + pi1z1 should be uncorrelated with u. Don"t know pi 0 and pi 1 but we come up with estimates of them. Predicted values of x are thus pi0 hat + pi1 hat z1. Get predicted values of x, which is important, because original x is useless to begin with. Predicted values of x doesn"t suffer from ovb, because new x hat is uncorrelated with ui. Second: use x hat that is the predicted x from previous regression, doesn"t suffer from ovb anymore, x hat is a conditional expectation of x. Expectation of xi hat is = pi0 + pi1zi, so on expectation x = xi hat.
