<p>It appears correct to me.
The relevant Wikipedia page is here,
<a href="https://en.wikipedia.org/wiki/Law_of_total_expectation" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Law_of_total_expectation</a></p>

CC BY-SA 4.0
2022-07-08T10:35:32.207Z
2022-07-08T10:35:32.207Z
Michael Gmeiner
<p>Is this procedure correct?
<span class="math-container">$$E[y_{t-1}\epsilon_t]$$</span>
<span class="math-container">$$= E[E[y_{t-1}\epsilon_t|y_{t-1}]]$$</span>
<span class="math-container">$$=E[y_{t-1}E[\epsilon_t|y_{t-1}]]$$</span></p>

CC BY-SA 4.0
2022-07-07T17:05:00.380Z
A time index for the expectations operator would help.
BrsG
CC BY-SA 4.0
2022-07-08T08:02:44.413Z
Unfortunately I don’t know it.
tryingtogetsmth
<econometrics>
Iterated Expectations problem
tryingtogetsmth
# Iterated Expectations problem

(Asked by: username_0 on 2022-07-07)

Is this procedure correct?
$$E[y\_{t-1}\epsilon\_t]$$
$$= E[E[y\_{t-1}\epsilon\_t|y\_{t-1}]]$$
$$=E[y\_{t-1}E[\epsilon\_t|y\_{t-1}]]$$

**Tags:** econometrics

> **Comments:**
> **username_1**: A time index for the expectations operator would help.  
> **username_0**: Unfortunately I don’t know it.  

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## 1 answers

### Answer by username_2 on 2022-07-08. Score: 2

It appears correct to me.
The relevant Wikipedia page is here,
<https://en.wikipedia.org/wiki/Law_of_total_expectation>


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