A doubt on SUR model On page 279, Hayashi begin by defining the SUR model. See picture below.

If I compare with these slide-notes(slide number 34), we define the instrument vector $x_i$ equal not only to the union of all regressors(of all the equations), and also to a $z_i$, which I have no idea what it means, but if I had to guess it would mean that I'm determining every regressor vector to be the same in all equations.This type of assumption I have found on more than one set of slides-notes
So, are these two definitions/assumptions equivalent? Which one implies the other?
Any help would be appreciated.
 A: I can of course not say for sure what Eric Zivot had in mind when using this notation, but I am fairly sure the "two" definitions really are to mean the exact same thing. 
The reason I guess he writes $x_i=\bigcup_m z_{im}=z_i$ is, in slightly modified notation of mine, $x_i=\bigcup_m z_{im}=:z_i$. That is, the SUR assumption says that the set of instruments is simply the set of all regressors that may be found somewhere in the system, i.e. $x_i=\bigcup_m z_{im}$. In other words, the regressors are no longer endogenous. Hence, it is OK to denote the set of instruments by $z_i$, i.e. we need no "outside" instruments that yield exogenous variation, as the regressors of the equations are enough to identify the coefficients.
Note this is not to say that the regressors are the same in each equation. See further below (slide 38) that equations may be overidentified in SUR. The multivariate regression case in which each equation has the same regressors is studied at the end of the lecture slides. 
