st: IV: endogenous interaction regressor and interaction instrument

[Olivia Bertelli <olivia.bertelli@gmail.com>]

Dear Statalists,

I want to estimate the following regression with an IV 2SLS method,
having two endogenous regressors:

1st stage:

X1 = b1*Z1 + b2*(Z1 x Z2)

and

X1 x Z2 = b1*Z1 + b2*(Z1 x Z2)

where, Z1 and Z1 x Z2 are the excluded instruments, X1 is endogenous,
and both X1 x Z2 and Z1 x Z2 are interaction terms

2nd stage:

Y = a1*X1 + a2 *(X1 x Z2)

My question is: how to I handle endogenous interaction terms
instrumented with exogenous interactions? should I include also a3*Z2
alone in the 2nd stage? Or rather in the first stage? Neither of the
two?

Thank you very much for any help or reference you may provide,
Best regards,
Olivia Bertelli
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