2SLS With Interaction Terms

[Jordan Wenham]

Hello, Sorry I've seen similar posts like this before however, I have been unable to find an answer that satisfies my needs. I am looking to run a 2SLS regression in which I interact the predicted term with another variable in my data set to see the effect this has on the instruments effect on y. Something like:

y = x₁ + z₁ + z₁ . x₁ + x₂

With z₁ representing the instrument for x₃ regressed on x₄, x₁ being an exogenous variable and x₂ representing some other exogenous control variables. Sorry if there is anything wrong with this post this is my first one. Thank you!

[Phil Bromiley]

Welcome to Stata list. You will increase the chances of a useful answer by following the FAQ on asking questions – provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Think about the original model, not the one with the instrument in it. Create the interaction before the model using a generate statement. Then, include both the endogenous variable and the interaction in the instrumentation part of an ivreg.

That is:
g x1x2=x1*x2
ivreg y x2 (x1 x1x2 = z1 z2 )

You'll need a second exogenous variable since you're now handling two endogenous variables. However, you might also look at
Bun MJG, Harrison TD. 2019. OLS and IV Estimation of Regression Models Including Endogenous Interaction Terms. Econometric Reviews. 2017 38(7): 814–827.