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Borrowing randomness, the idea behind instruments

Asked at AQR

You want the causal effect of a variable xx on an outcome yy, but xx is endogenous, correlated with the error term because of confounding or reverse causation, so OLS is biased. A colleague mentions using an "instrument."

Explain what an instrumental variable is, the conditions it must satisfy, and how it recovers the causal effect.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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