I have two treatments (decisions) Y1 and Y2 which are two binary variables coded (1,0). They have some common explanatory variables and can occur at the same time.
I want to test the causality between the two treatments to see if Y1 causes Y1 or the opposite?
So I used a recursive bivariate probit with the same control variables considering that the two treatments have common antecedents.
Is it possible to test this causality using the recursive bivariate probit?
I believe so using R. See the attached screenshot search for more information. Best wishes David Booth
You are asking about the causality, and using a correlation estimation method.
Correlation does not imply causation.
So, decide what you want to estimate. If it is causation, then, information theory tools is a better choice for you.
Thank you Abd AlRahman Rasheed AlMomani for your response. Yes, it is indeed a causality!
I estimate the two models jointly (two probit equations) and this allows the error terms to be correlated, and the binary dependent variable in the first equation is an endogenous regressor in the second equation.
I see. Then you are practically using some version of Granger Causality. Very nice direction.