IV regression with 2 endogenous variables (one is an indicator)

[urska.kosi]

Dear Statalist,

I have a question with respect to estimating an IV regression where I have two endogenous variables. One of them is a continuous variable and the other is a choice variable. The dependent variable (Y) is also continuous.
I thought that -ivreg2- would be a suitable command (I am using Stata 11.2); it allows two endogenous variables. However, I think -ivreg2- cannot estimate an OLS for one endogenous variable and logit/probit for the other one. Is this correct?
Could anyone help me with a different command that I could use in my case?

Alternatively, I was thinking to perform the IV regression “manually” as follows:
Original model: Y = a0 + a1X1 + a2X2 + a3X3 (X1 is continuous endogenous variable with instrument Z1; X2 is choice endogenous variable with instrument Z2; X3 are other exogenous variables).
1^st stage: reg X1 Z1 Z2 X3
predict X1hat, xb
1^st stage: logit X2 Z1 Z2 X3 –
predict X2hat, xb
2^nd stage: reg Y X1hat X2hat X3
Is this alternative suitable? Will I get unbiased coefficient estimates and correct standard errors?

Thank you for your help.
Best wishes, Urska Kosi

[Mark Schaffer]

Urska,

This question and variants of it come up on Statalist fairly regularly. A three-part answer:

1. ivreg2 (or ivregress) will give you consistent estimates. You do not need to model the first-stage as a a logit or probit because that's not what the IV estimator does. The classic IV estimator is a limited-information estimator and there is only one equation being estimated. The first stage doesn't necessarily has to have a structural interpretation. You can get more efficient estimates than the classic IV estimator will deliver, but the IV estimator is already consistent.

2. Your 2-step procedure won't work. It's an example of what's sometimes called the "forbidden regression". See http://www.stata.com/statalist/archi.../msg01130.html

3. Alternative procedures that are more efficient than classical IV and that do work are available. Here's a link to an old Statalist post with some suggestions: http://www.stata.com/statalist/archi.../msg00415.html

HTH,
Mark

[Bobby Wood]

Hi Mark, I have a related question. I estimate y=a1x1+a2x2. x1 and x2 are both endogeneous but I'm only interested in a1. My instrument for x1 is z1 and should in theory only affect x1, not x2. Will I get unbiased and consistent estimates for x1 if I only instrument for x1 but not for x2? Or would you recommend to drop x2 from the model? I really tried to find this out but could not find an answer on this. Thanks for your help.