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

<ul>
<li><p>$E(f(x))$ is not equal to $f(E(x))$ unless f is linear.</p></li>
<li><p>$\partial E(f(x)) / \partial x$  is equal to $E(\partial f(x) / \partial x)$.</p></li>
</ul>

<p>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.</p>

CC BY-SA 3.0
2017-01-12T23:25:44.040Z
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
CC BY-SA 3.0
2017-01-13T12:05:24.090Z
Theoretical Economist - Thank you for your answer. Do you know of any book or journal paper that has some work on the above?
user11751
CC BY-SA 3.0
2017-01-12T16:57:17.770Z
2017-01-12T16:57:17.770Z
Tobias
<p>How to log linearize an equation that has a conditional expectation? Any reference or example would be appreciated.</p>

<macroeconomics><mathematical-economics><statistics>
Log linearization and Conditional Expectation
user11751
# Log linearization and Conditional Expectation

(Asked by: username_0 on 2017-01-12)

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

**Tags:** macroeconomics, mathematical-economics, statistics


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## 1 answers

### Answer by username_1 on 2017-01-12. Score: 0

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.

> **Comments:**
> **username_2**: 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.  
> **username_0**: username_2 - Thank you for your answer. Do you know of any book or journal paper that has some work on the above?  

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