if the dependent var and the endogenous independent var are both binary, biprobit or eprobit or something else?

[kangoh lee]

Dear All,

The dependent var and the endogenous independent var are both binary, and it appears that I can use biprobit or eprobit:
biprobit (y = x1 x2 x3) (x1 = z x2 x3), robust
or
eprobit y x2 x3, endogenous(x1 = z x2 x3, probit) robust

Estimation results are different so much.

I am especially interested in the marginal effect of x1, so
margins, dydx(x1)
or
margins, dydx(x1) predict(pr fix(x1))
or
margins, dydx(x1) predict(pr)

The marginal effects are again different so much.

I would appreciate your opinion about if I should use biprobit or eprobit or something else such as Coban's rbiprobit,
and possibly why the results are so different between biprobit estimates and eprobit estimates.

Thanks,
Kangoh

[George Ford]

biprobit typically gets the nod here.

[Frode Andre]

I am wondering whether you are answering two different research questions in the eprobit and biprobit cases? In the biprobit case, you have two dependent variables. This contrasts the eprobit case, where there is one dependent variable and an endogenously determined independent variable.

In the biprobit case, your x1 variable is both dependent and independent. Can you create a reproducible example using the datafiles from either the eprobit or biprobit help files. I am not able to get convergence using the biprobit model when x1 is both an independent variable (your first equation) and also a dependent variable (in your second equation).

[kangoh lee]

biprobit is not specifically designed for endogeneity but estimates seemingly unrelated bivariate probit,
which I think can be interpreted to take into account endogeneity via errors of two probit regressions.

So, I expect that biprobit results and eprobit results would not be exactly the same but would not be different much, either.

All these issues arise because ivprobit cannot handle the case with binary endogenous independent variables.
Stata 19 introduces cfprobit (control-function approach to endogeneity), but I am not inclined to use it yet.

[kangoh lee]

Hi Frode,

I forgot to respond to the second part.
convergence is not achieved, not because x1 is in both equations.
Rather, biprobit or eprobit is based on max likelihood, so the results are sensitive to controls.
As such, if you drop or change some of your controls, convergence will be achieved.

[Jeff Wooldridge]

From a “structural” perspective, biprobit is preferred because it can be derived from two latent variable modes. The eprobit command uses an approximation based on the control function approach—something I discussed in my 2014 Journal of Econometrics paper. It rarely has convergence problems because it’s a two-step probit. One needs to average out the CF when computing the average partial effect.

another possibility is to estimate a full endogenous switching model. This can be done estimating two heckprobit commands, one when x1 = 0, the other when x1 = 1. I’ve done this using the Catholic high school attendance data in my Journal of Human Resources survey (2015).

[kangoh lee]

Hi Jeff,

Thanks for your explanation.
I have an additional question.
biprobit displays Wald test of rho = 0, which I interpret as a test of endogeneity.
eprobit displays only corr(e.dep var, e.endogenous treatment), and I wonder if it can be interpreted as a test of endogeneity,
or if there is any way to ask Stata to display some test statistics or if I can calculate some test statistics manually?

Thanks,
Kangoh