Binary endogenous regressor, binary outcome, and fixed effects

[Michael Lachanski]

Hello,

I have a binary endogenous regressor X and binary outcome Y. My instrument is a set of exogeneous Z that take on values 1, 2, 3, 4. I also want to include region by time "fixed effects" or "dummies" D_1 through D_n. Is STATA's ivprobit command the way to do this?

At first, I believed this regression was forbidden or would yield inconsistent results, but reading the forum post below leads me to believe that I was mistaken.

Can this be run as

 ivprobit Y X [Z D_1 D_2...D_n-1]

Thank you,

[Andrew Musau]

The post that you link deals with the inclusion of regional dummies in a probit model. ivprobit allows for a binary outcome, but the endogenous variables need to be continuous.

Description

ivprobit fits models for binary dependent variables where one or more of the covariates are endogenous and errors are normally distributed. By default, ivprobit
uses maximum likelihood estimation, but Newey's (1987) minimum chi-squared (two-step) estimator can be requested. Both estimators assume that the endogenous
covariates are continuous and so are not appropriate for use with discrete endogenous covariates.

See

help ivprobit

[Michael Lachanski]

Thanks. So is it still the case that for binary outcome and binary endogenous regressor, we have no way to consistently include dummies?

[Andrew Musau]

You should start with the primary problem of estimating a binary dependent variable model with a non-continuous endogenous explanatory variable. The inclusion of dummies on the right-hand side is a secondary issue and will depend on what estimation method you end up settling on. I recommend that you start a new thread with the primary problem in the title, but you could also wait and see whether anyone will give you suggestions here.

ADDED IN EDIT: Actually, your title conveys your primary problem. Ignore the suggestion of starting a new thread. Hopefully, you will get suggestions on how to proceed, but ivprobit is not the way.

[Michael Lachanski]

According to this thread, if you are willing to accept the linear probability model for a binary endogenous regressor, then this problem can be handled by ivregress if you are willing to dichotomize your exogenous first stage regressors.

In my case, that is a suitable solution. Of course, this is not generalizable.

https://www.statalist.org/forums/for...nary-variables