ivreg2 with interaction term

[Jacob Collier]

Dear Statalist,


I face problems in running a 2SLS regression with an endogeneous variable that is interacted.

Here's the OLS setting :

Y = X1 + X2 + X1*X2

reghdfe Y c.X1##c.X2

With X2 the endogenous variable, that with be instrumented by Z2
Thus, I've got to instrument both the interaction term and the endogeneous variable.

So I think the Stata code should look like this:

gen X1_X2 = X1 * X2
gen X1_Z2 = X1 * Z2

ivreg2 Y X1 (X2 X1_X2 = Z2 X1_Z2)

But:

1. I'm not sure whether this is the correct code.

2. I'm confused about the first stage – is it a simple OLS for each instrument?

3. I don't know which tests, like the F-stat, to perform.

Thank you for your help !

[George Ford]

https://www.statalist.org/forums/forum/general-stata-discussion/general/1533191-iv-regression-with-interaction-terms-and-2-instruments

[Jacob Collier]

https://www.statalist.org/forums/forum/general-stata-discussion/general/1533191-iv-regression-with-interaction-terms-and-2-instruments

Thank you, George, it reassures me that this is the correct code. However, I still haven't found answers regarding the first stage and the tests/F-stat. Could you please provide some guidance on these aspects?

[George Ford]

I think it's just the X2 regression F-stat. The other is just an interaction.

I also think a control function is the better option. In that case, there is only 1 first stage regression, and the approach is well suited to interactions.