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In Hayashi's Econometrics, page 529, he states one of the assumptions we need for the FIML estimator.

My doubt is in the third line of point 1). He says that the vector $(y_{t1},...,y_{tM},\mathbf{z}_{t1},...,\mathbf{z}_{t1})$ are elements of $(\mathbf{y}_t,\mathbf{x}_t) $. How is that possible? If $\mathbf{y}_t=(y_{t1},...,y_{tM})'$, then it means that $\mathbf{x}_t=(\mathbf{z}_{t1},...,\mathbf{z}_{t1})$.

I don't think I'm understanding the 'english' here.

Any help would be appreciated.

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    $\begingroup$ In any case, I hope you have downloaded the .pdf with the various mistakes to be corrected in the book. fhayashi.fc2web.com/hayashi_econometrics.htm "Known typos and errors" .pdf $\endgroup$ Mar 20, 2015 at 18:35
  • $\begingroup$ @AlecosPapadopoulos Thanks, it's not typo. I think I've got it... The notation in Hayashi is not always intuitive... $\endgroup$ Mar 20, 2015 at 18:38
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    $\begingroup$ Indeed it is not. Get the .pdf $\endgroup$ Mar 20, 2015 at 18:41
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    $\begingroup$ @AlecosPapadopoulos Got it. ;) $\endgroup$ Mar 20, 2015 at 22:15

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I think I understand now. If we look at example 8.1 on the previous page, the $y_{tm}$ variables may be the same, which would allow for some of the $\mathbf{z}_{tm}$ variables to be endogenous. And we pool all those endogenous variables (both the $y_{tm}$ and of the $\mathbf{z}_{tm}$) in one vector, $\mathbf{y}_{t}$, and all the remaining ones (exogenous) in the $\mathbf{x}_{t}$ vector.

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