2SLS regression with interaction term

[Johnny YANG]

Dear all,
I'm currently building a model with two variables plus their interaction term, to be instrumented. One of the two variables is exogenous, the other is endogenous. I'm wondering how to use instrumental variables.
The first variable is multinationality, which is the number of countries a company has expanded into. The second variable is the institutional stringency of the home country of the firm. The dependent variable is firm's performance. And I have found 2 valid instrumental variables for multinationality. For institutional stringency, since it is an exogenous variable, I think I don't need to add instrumental variables for it. And I need to add the interaction term of multinationality and institutional stringency. In my case, how can I use 2SLS regression model?
For the model without interaction term, the code is as follows,
ivreg2 ROA (multinationality =RDint Marketing) FirmSize FirmAge Solvency lagROA
All the tests for instrumental variables are good.

For the model with interaction term, my current code is
ivreg2 ROA (multinationality multinationality*InstitutionScore=RDint Marketing) InstitutionScore FirmSize FirmAge Solvency lagROA

The thing is the results does not have Sargan statistic, and the other test results are bad too.

Thank you very much for your help in advance!

[Andrew Musau]

ivreg2 ROA (multinationality =RDint Marketing) FirmSize FirmAge Solvency lagROA

Interact the instruments as well for the endogenous interaction and see how you fare.

ivreg2 ROA (multinationality c.multinationality#c.InstitutionScore=RDint Marketing ///
c.RDint#c.InstitutionScore c.Marketing#c.InstitutionScore) FirmSize FirmAge Solvency lagROA

[Jeff Wooldridge]

Two small addendums to Andrew’s helpful suggestion. First, include InstitutionScore on its own. Second, to get coefficients with better interpretations and to study the weak IV problem, you might center the variables around their means before interacting.