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I was working through Bruce Hansen's Econometrics book/notes and got tripped up over something that should be very simple. See the snapshot below, which comes from page 25 of his book Econometrics.

enter image description here

With regards to the variance of e conditional on X, here's how I thought of it: $$ Var(e|X)=E[e^2|X]-E[e|X]^2= E[e^2|X] = E[X^2u^2|X]=E[X^2u^2]=E[X^2]E[u^2]=1\times 1=1$$

Wondering where I made a mistake and why he wrote the variance to equal $X^2$.

Xi'an
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Guinness
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1 Answers1

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Almost correct:

$$E[X^2u^2|X] = X^2E[u^2|X] = X^2 E[u^2] = X^2$$

Because $X$ becomes a constant once you condition on it.

Ale
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