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The Two Conditions for Instrument Validity Are Corr(Zi, Xi)≠ 0

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The two conditions for instrument validity are corr(Zi, Xi)≠ 0 and corr(Zi, ui)= 0. The reason for the inconsistency of OLS is that corr(Xi, ui)≠ 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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