Biprobit assumptions

[Ale Olivera]

Hi everyone!
I have some questions about the basic assumptions for work with biprobit.
Before I start, I have a dependent binary variable and an independent binary endogenous var so I use an IV to solve the endogenous problem.
My questions are:
1) I know that is important to see the Wald test with rho=0, but I am not sure about what it is mean. If the test is significant the error of the two regressions are correlated?
2) I read that is important to see Murphy's score test and I use the scoregof command in stata, but I am not sure about the meaning of the test. What is the null hypothesis? Do I need to reject it or not? I understand that is for see the normal distribution of the error which is an important assumption to know for unbiased bivariate probit but I read Murphys and Chiburis work again and is not clear to me.

If you are thinking that why I don't use and OLS (MPL) and Ivreg2 is because I want to contrast the results with them.

Thank you for your response!

[Mustafa Coban]

Hi Ale,

from your post I assume that you want to estimate a recursive bivariate probit model, i.e. both dependent variables are binary and one dependent variable is an endogenous explanatoray variable of the other one.

In that case, I would recommend to switch to rbiprobit instead of using biprobit, You can install it from SSC by typing

ssc install rbiprobit

This package enables the estimation of recursive bivariate probit models and the calculation of various treatment effects afterwards. For example, here the estimation of a model and the calculation of the average treatment effect of y2

rbiprobit y1 = x1 x2 x3, endog(y2 = x2 x3 x4)
rbiprobit tmeffects, tmeffect(ate)

For more background:

Just check out the repo of the rbiprobit package on Github and current presentation slides from the Italian Stata Conference.


Some notes to your questions:

1) If the p-value of the Wald test is "small enough", you can reject the null hypothesis that the error terms of the outcome and treatment equation are uncorrelated. In a nutshell, the error terms are in fact correlated.
2) I wouldn't recommend to use scoregof. This command has some bugs once used for recursive bivariate probit models.

If you are not sure whether your data follows a bivariate normal distribution you could run the same regression using alternative distributional assumption by applying the new package rbicopula. You can install the package from the GitHub repo

net install rbicopula, from("https://cobanomics.github.io/rbicopula/")

A short reminder:

The base assumption of ivreg2 is that your outcome y1 is continuous. Instead, rbiprobit accounts for the fact that both endogenous variables are binary.

[Ale Olivera]

Thank you for your reply, Mustafa!

I have another question. I’m working with instrumental variables. Can this be included in the bivariate recursive probit model? What would be the post estimate?

[Mustafa Coban]

You can include IVs on the right-hand side of the treatment equation, e.g.

rbiprobit y1 = x1 x2 x3, endog(y2 = x1 x2 x4)

In this case, x4 is the instrumental variable. But, there is no weak IV-test available for bivariate nonlinear estimations. So, I would recommend to use ivreg2 or ivprobit to test the validity of your instrumental variable.

[Lucas Smith]

Hi Mustafa Coban, Thank you so much for your contributions! I have a quick question. Is it possible to recuperate or calculate a LATE instead of ATET? In my case, I want to see the effect on the compliers only, not on compliers + always treated. I really appreciate any help you can provide.

[Mustafa Coban]

Hi Lucas,

I would recommend to use Hasebe's new package edbinary to estimate LATE. You can download the package from SSC and there is also a paper published in the Stata Journal. Unfortunately, rbiprobit and rbicopula don't include the estimation of LATE currently.

[Michael Zuze]

Hi Mustafa Coban please assist, how do i test for the bivariate normality of the error terms in a recursive bivariate probit.