Question: onsider the structural equation and reduced form Yi = X2 i ei Xi = Zi ui with X2 i treated as endogenous so that E(X2

onsider the structural equation and reduced form Yi = X2 i ei Xi = Zi ui with X2 i treated as endogenous so that E(X2 i ei) 6 = 0. For simplicity assume no intercepts. Yi, Xi, Zi are scalar. Assume 6 = 0. Consider the following estimator. First, estimate by OLS of Xi on Zi and construct the fitted values Xi = Zi . Second, estimate by OLS of Yi on ( Xi )2 . Assume the fourth order moments of Xi and Zi are finite. And E (ei|Zi) = 0. 1

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