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In an applied econometrics paper, the author states the model to be estimated as:

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Why does the author claim homoscedasticity? This isn't making sense to me; can't the population variance-covariance have elements of the diagonal that are conditional upon $t$ if there's something like omitted variables?

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Sure it can, but it's going to be another method :) – Dmitry Laptev Aug 22 '12 at 3:36
@DmitryLaptev; I'm not sure what you mean? – user13253 Aug 22 '12 at 3:57
if you use the original version of OLS, and if you want to fit the model at once, then homoscedasity is required. What you can do is to fit P models at different times, and variance could differ in this case. But this is already a little different method. – Dmitry Laptev Aug 22 '12 at 4:07
O.K.. So the author is claiming that homoscedasticity is required, NOT that each element of the diagonal of the estimated variance covariance matrix of the residuals is equal to any other element? (even though this is the case in practice)? Is the way that the author has stated it standard practice in applied econometrics? – user13253 Aug 22 '12 at 4:20
I mis-spoke in my previous comment. I meant to say the "population variance covariance matrix" not the "estimated". – user13253 Aug 22 '12 at 4:26
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