Binary Endogenous Variable Help?!

[Priscilla Gowero]

Hi,

Can anyone guide me on how I should proceed?

All my variables are binary or ordinal, so I have been running probit regressions and have included fixed effects and clustered standard errors.. With further research I have realized that I have a binary endogenous variable so I have identified a potential instrumental variable . Most of the reading that I have done on instrumental variables says that I cannot use ivprobit on Stata with a binary endogenous variable as it needs to be continuous. I am unsure of what to use at this point in order to mitigate endogeneity. Any guidance would be appreciated.

Thank you in advance!

[Joro Kolev]

The most appropriate model in this case is probably [R] biprobit -- Bivariate probit regression.

You can also do linear analysis, 2SLS.

[Parul Gupta]

Does 2sls help if both the dependent and endogenous regressors are binary? Is there any advantage of biprobit over 2sls?

[Mustafa Coban]

Hi Parul,

if the assumption of bivariate normal distributed errors is true, then coefficient estimates of a recursive bivariate probit model are more efficient than 2sls coefficient. By the way, there is the package rbiprobit suited for your case

ssc install rbiprobit

[Puneet Sachdeva]

Hi Parul,

if the assumption of bivariate normal distributed errors is true, then coefficient estimates of a recursive bivariate probit model are more efficient than 2sls coefficient. By the way, there is the package rbiprobit suited for your case

ssc install rbiprobit

Dear Mustafa,
Please would you help me with a query about rbiprobit.

I read a paper where authors tested a 3-way interaction involving an endogenous treatment. So, the model is:
Y_binary ~ A*B*Z_endogenous_binary + controls
Z_endogenous_binary ~ W + controls
A and B are continuous.

They use rbiprobit

They report separate coefficients (for A*B and controls) for the two cases:

Case 1: when Z_endogenous_binary = 1 and
Case 2: when Z_endogenous_binary = 0 and

They do a chow test to compare whether the coefficients for A*B are equal in two cases.

So, my question is how to do this using rbiprobit. The core of their argument is that the average treatment effect on the treated group is different from the average treatment effects on the control group. I tried the following commands:

rbiprobit tmeffects, tmeffect(atet) and
rbiprobit tmeffects, tmeffect(atec)

I get the overall treatment effect, but I do not get separate coefficients for all regressors (including control variables)