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# st: RE: Endogenous interaction terms in 2SLS

 From "Wooldridge, Jeffrey" To Subject st: RE: Endogenous interaction terms in 2SLS Date Thu, 3 Mar 2011 07:21:04 -0500

```Let me modestly (:-)) suggest the solution in Chapter 20 of 2e of my MIT Press book. It takes advantage of the binary nature of Y1 but is fully robust to the probit model being misspecified.

1. Estimate a reduced form probit for Y1 using ALL exogenous variables. Get the fitted probabilities, say phat.

2. Construct instruments (NOT regressors!) phat*X1, phat*X1*X2

3. Estimate the equation

Y2 = b0+ b1*Y1 +b2* Y1*X1 + b3*Y1*X1*X2

Using IVs phat, phat*X1, phat*X1*X2.

No need to adjust the standard errors asymptotically, but you can bootstrap if you have a smaller sample.

One comment: Many get nervous -- me included -- when variables that show up as interactions do not show up in level form. How come X1 and X2 don't appear by themselves (and act as their own IVs)? Leaving the level terms out can result in the interactions being spuriously significant.

JW

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Rene Algesheimer
Sent: Thursday, March 03, 2011 4:52 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Endogenous interaction terms in 2SLS

Dear Statalisters,

I have a very specific Stata question that I wasn't able to solve with the Statalist. I would therefore highly appreciate to hear your advice on this.

I would like to estimate the following model:

Y2 = b0+ b1*Y1 +b2* Y1*X1 + b3*Y1*X1*X2

Y1 is a dummy variable and endogenous,

X1 is another dummy variable and the instrument for Y1.

The situation therefore is similar to http://www.stata.com/statalist/archive/2008-10/msg01239.html with endogenous interaction terms. However, in my case one interaction is between the instrumented and the instrumental variable.

Any advice how to deal with this situation is highly appreciated.

best wishes,

René
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