2SLS (Probit First Stage & OLS Second Stage)

[hussein bataineh]

Hi,

I need to run a 2SLS regression, where the first stage is a probit model and the second stage is OLS. However, I'm unsure of the appropriate code for this.

Could you advise me on the correct approach and code for implementing this?

Thanks in advance!

[Seungmin Lee]

Running non-linear first stage (i.e.) and OLS second stage could be problematic, as it is often called as "forbidden regression."
You can find more of this on Section 4.6.1 on the Mostly Harmless Econometrics (MHE), and I also found this page (link)

An alternative MHE suggests in the same section is to run probit of endogenous binary variable on an instrument, and use its predicted value as an instrument and run classic OLS 2SLS.

[Devra Golbe]

If you are using StataNow, cfregress can estimate a linear equation with a first-stage probit.

[hussein bataineh]

actually i have three endogenous variable and there IV . i need to run first stage for three endogenous variable (these three endogenous variable are binary so we need to use probit

in the second stage we use OLS

can you advice me what to do

[Seungmin Lee]

It's not strictly necessary to run a non-linear regression for a binary dependent variable. Linear probability model (LMP) often works well in many cases for binary dependent variables.
I suggest running LPM for your binary dependent variables, and check whether your fitted values from LPM are largely outside [0,1]. If most of your fitted values is within [0,1] range, then I would go for LPM.