Binary Endogenous Variable in a OLS regression

[Manos Avgerinos]

Hi,

As the title implies I have an endogenous binary variable in my OLS model. I have found two suggested solutions: First, follow Wooldridge (2002, p. 623, procedure 18.1)-also used by Adams et al. (2009)-and run a probit model to regress the endogenous variable on the instruments and exogenous variables, regress the endogenous variable using the predicted values and the exogenous variables and finally run an OLS on my dependent variable using the predicted values and other control variables (basically transform my endogenous binary in a continuous one using a probit model and then run a 2SLS as usual using the transformed variable). Second, run a probit model, calculate the inverse mills ratios and then run my original OLS including them (basically run a two-step Heckman selection model).

Any suggestions which one is better for hypotheses testing (or if there is any better alternative that I am not aware of)?

Kind Regards,

Manos

[Mark Schaffer]

Why not etregress? (Known as treatreg in Stata 12 and earlier.)

[Sergio Correia]

Dear Mark,

I have a related question. Is there an xt version of the estimator (user contributed or even on paper)? In the two-step estimator I'm guessing the -probit- step can be replaced with an -xtprobit- but AFAIK there is no consistent -xtprobit, fe- estimator, and even then (or if I use xtlogit,fe) I'm not sure of the properties of that. Any insights or references would be more than useful.

Thanks!
Sergio

[Mark Schaffer]

I can't recall seeing anything. I assume you've used findit etc. to look around for something user-written. The first reference I'd look in is Jeff Wooldridge's Econometric Analysis of Cross Section and Panel Data.

One thought - if you are in a small-n-large-T setting, then you can just include dummies for your fixed effects. The probit step will give you consistent estimates since you'll have many observations (large T) for each of the n dummies.

[Mark Schaffer]

I can't recall seeing anything. I assume you've used findit etc. to look around for something user-written. The first reference I'd look in is Jeff Wooldridge's Econometric Analysis of Cross Section and Panel Data.

One thought - if you are in a small-n-large-T setting, then you can just include dummies for your fixed effects. The probit step will give you consistent estimates since you'll have many observations (large T) for each of the n dummies.

[Manos Avgerinos]

Dear Mark,

Thank you for your reply. My main concern is which method is better (the one I described as first in my initial post or the one using etregress as you suggested). I have not found anyone in any forum replying this.

Many thanks.