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How to log linearize an equation that has a conditional expectation? Any reference or example would be appreciated.

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You need to remember two properties of derivatives and expectations. Everything else stays the same.

  • $E(f(x))$ is not equal to $f(E(x))$ unless f is linear.

  • $\partial E(f(x)) / \partial x$ is equal to $E(\partial f(x) / \partial x)$.

Also remember that as a result, linearizing models with uncertainty reduces them to their certainty equivalent version. This may or may not matter for what you are doing.

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    $\begingroup$ The second bullet point is true only when you impose some regularity conditions on $f(x)$. That being said, you'll almost always get away with assuming said conditions are satisfied when doing economics. $\endgroup$
    – Theoretical Economist
    Jan 12, 2017 at 23:25
  • $\begingroup$ Theoretical Economist - Thank you for your answer. Do you know of any book or journal paper that has some work on the above? $\endgroup$
    – user11751
    Jan 13, 2017 at 12:05

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