The Two Conditions for Instrument Validity Are Corr(Z_i, X_i)≠ 0

question 47

Essay

The two conditions for instrument validity are corr(Z_i, X_i)≠ 0 and corr(Z_i, u_i)= 0. The reason for the inconsistency of OLS is that corr(X_i, u_i)≠ 0. But if X and Z are correlated, and X and u are also correlated, then how can Z and u not be correlated? Explain.

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