reg3 for non-linear (binary dependent variables) simultaneous equation model

[teenug kaur]

I have a non-linear triangular system of equations where dependent variables are binary. What is the reg3 analogous for a non-linear set-up?

y = x1 + y' + x2

y' = x1 + y

x2 is an endogenous variable here for which I have an instrument variable.

Thank You!

[Joro Kolev]

This is not a triangular system because both y depends on y' and y' depends on y.

I am not aware of existence of a fully simultaneous probit.

[Jeff Wooldridge]

Agree with Joro and I wonder if that’s the model you really mean. It looks like an SEM with an additional endogenous variable x2. If it’s what you want it would be very difficult to estimate, and even interpret.

[teenug kaur]

Joro Kolev apologies for the error in my equations. Here is the correct one:

y = x1 + x2

y' = x1 + y

x2 is an endogenous variable here for which I have an instrument variable.

Jeff Wooldridge , if I use gsem command in stata, what exactly is the issue? Can you please elaborate?

[teenug kaur]

https://www.stata.com/meeting/german...ukker_gsem.pdf

I am trying to follow procedure mentioned in these slides.

[Joro Kolev]

What you have described below is a triangular system indeed.

I think that both the native -biprobit- and the user written -cmp- are appropriate estimators in this case.

You can try them both and compare the results, the results should be numerically equivalent.

Joro Kolev apologies for the error in my equations. Here is the correct one:

y = x1 + x2

y' = x1 + y

x2 is an endogenous variable here for which I have an instrument variable.

Jeff Wooldridge , if I use gsem command in stata, what exactly is the issue? Can you please elaborate?

[teenug kaur]

Joro Kolev , I thought that cmp can only fit "recursive" models with clearly defined stages, not ones with simultaneous causation. In my case, there is a possibility of simultaneous causation as well.