# Log linearization and Conditional Expectation [duplicate]

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

## marked as duplicate by BKay, emeryville, luchonacho, Kitsune Cavalry♦, EnergyNumbersFeb 5 '17 at 7:44

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.

• 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. – Theoretical Economist Jan 12 '17 at 23:25
• Theoretical Economist - Thank you for your answer. Do you know of any book or journal paper that has some work on the above? – user11751 Jan 13 '17 at 12:05