Hello, I hope you could help me with this.

I need to estimate three separate equations with -ivreg2- where I have three endogenous variables, three instruments, and an exogenous variable that needs to interact with each of the three endogenous variables; one interaction in each equation. For subsequent interpretation, I would like to figure out which instrument needs to interact with which endogenous variable.

To start with, in the below equation X is an endogenous variable, T is an exogenous variable, Z1 is an instrument for X, and Y is the DV.

Y = b1*X + b2*T

To account for endogeneity, I understand I could do:

ivreg2 Y T (X X*T = Z1 Z1*T)

In my case, X is a count of experience and I would like to break it down to theoretically meaningful parts such that:

X = X1 + X2 + X3

Since X is endogenous, X1, X2, and X3 are endogenous too. I have three instruments, Z1, Z2, Z3. Now, how do I match X1, X2, X3 with Z1, Z2, Z3 when constructing instruments for interaction terms. In casual language, what do I write within the brackets that will allow a meaningful interpretation? Theoretically, each instrument is equally suitable for each endogenous variable. Could I randomly match instruments to endogenous variables?

Thank you for your help,