# About Identification in a 3 equation SEM

I got this example and I was wondering about a certain statement: \begin{aligned} y_1 &= \alpha_{12}y_2 + \alpha_{13}y_3 + \beta_{11}z_1 + u_1 \\ y_2 &= \alpha_{21}y_1 + \beta_{21}z_1 + \beta_{22}z_2 + \beta_{23}z_3 u_2 \\ y_3 &= \alpha_{32}y_2 + \beta_{31}z_1 + \beta_{32}z_2 + \beta_{33}z_3 + \beta_{34}z_4 + u_3 \end{aligned}

It is written that in the first equation of the model we could use all the excluded exogenous variables i.e. $z_2, z_3, z_4$ as instruments for the two endogenous regressors $y_2,y_3$.

But as I remembered I can't use $z_2$ nor $z_3$ for $y_2$ because these variables already appear in equation 2. In the same sense I cannot use any of those z's for $y_3$.

In my understanding I could use $z_2, z_3, z_4$ for $y_1$ but not for $y_2, y_3$ right?

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