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This is taken from Hansen's econometrics textbook.

Take the linear model:

$$Y = Z\beta + e $$

Let the residuals in an IV regression be $\tilde e$ and in an OLS regression $\hat e$. If X is indeed endogeneous, will IV fit better than OLS in the sense that $\tilde e' \tilde e$ < $\hat e' \hat e$?

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  • $\begingroup$ I am guessing from context that "IV" refers to instrument variables rather than independent variables. $\endgroup$
    – Galen
    Commented Apr 24, 2022 at 3:29
  • $\begingroup$ Yes, sorry I wasn't being clear $\endgroup$
    – Rainroad
    Commented Apr 24, 2022 at 19:25

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