# A doubt on FIML assumptions

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.

• 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 – Alecos Papadopoulos Mar 20 '15 at 18:35
• @AlecosPapadopoulos Thanks, it's not typo. I think I've got it... The notation in Hayashi is not always intuitive... – An old man in the sea. Mar 20 '15 at 18:38
• Indeed it is not. Get the .pdf – Alecos Papadopoulos Mar 20 '15 at 18:41
• @AlecosPapadopoulos Got it. ;) – An old man in the sea. Mar 20 '15 at 22:15

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.