cmp command

[Dang Le]

Dear,

Now, I would like to investigated the mediation effect of A on B and C. There is potentially endogenous among A, B and C. Could I use cmp (B= A C X1) (C= A B X2), because I found that A could be affected by B and C as well, and afraid that the system does not cover that problem.
Hope to have your help.

Thanks

[Joro Kolev]

No, -cmp- does not cover this case, because what you have written is a fully simultaneous system. -cmp- deals with recursive/triangular systems.

If you have enough instruments for the endogenous variables, -reg3- is appropriate for fully simultaneous systems.

[Dang Le]

Thanks so much Joro Kolev. But my matters are (1) not enough instruments (2) C is binary, and (C= A B X2) needs to be done with probit. Could you help any suggestions pls?

[Joro Kolev]

I am afraid you do not have many options, except to assume that your system is recursive/triangular.

(B= A C X1) (C= A X2)

there is no fully simultaneous probit in Stata, neither as a native nor as a user contributed command (to the best of my knowledge).

Thanks so much Joro Kolev. But my matters are (1) not enough instruments (2) C is binary, and (C= A B X2) needs to be done with probit. Could you help any suggestions pls?

[Dang Le]

Thank you so much Joro Kolev. I will try with the system again.

[David Roodman]

Actually, cmp can fit this model. It can handle simultaneous systems as long as the references to censored variables such as C are recursive/triangular. This would be done with something like

cmp (B= A C X1) (C = A B# X2), ind($cmp_cont $cmp_probit)

The key is the "#" symbol. In general, you use # to refer a latent predictor "behind" a variable that is modeled as censored, such as a probit. But since B is not censored, B# means the same things as B. However, adding the # tells cmp that this is a simultaneous system, so it can handle it properly.

You could also do

cmp (B= A C# X1) (C = A B# X2), ind($cmp_cont $cmp_probit)

But that is a different model. It says that B depends not on C as observed (binary), but on the linear linear predictor behind C.

There are examples of simultaneous models in the help file. I added this functionality after writing the paper about cmp.

What you cannot do is a full, simultaneous probit model:

cmp (B= A C X1) (C = A B X2), ind($cmp_probit $cmp_probit)

That is logically impossible, as explained in the paper about cmp.

[Dang Le]

Oh Thanks so much David. I read your paper on the Stata Journal.
Yep, it would be cont and probit.
Another in my question is concerned about A. Because A is potentially affected by B and C. So, I just employ the mentioned system or do I need to add anything more? Appreciating your help!

[David Roodman]

In principle, you can add a third equation for that--an A equation, which expresses the dependence of A on B C. But in general you will need some kind of instrument. Exactly what you do depends on what variables you have and what you believe about them, so I can't tell you exactly what to do. But something like this might make sense:

 cmp (A = B# C# X3) (B= A C X1) (C = A B# X2), ind($cmp_cont $cmp_cont $cmp_probit)

Notice that all the references to other endogenous variables that do not have a # together form a triangular recursive system: B = A C..., C = A... There is no circularity among them.

Meanwhile, the # references are either to the linear predictor inside of the probit variable C (C#) or to the uncensored linear predictor B#, which is actually the same as B.

[Dang Le]

Thank you so much David. I will try with it. Your reply is really worth for me.
Best wishes,

[Rhys Thomas]

I'm just picking up not his.

So let's say I have an instrument (Z) for a variable A, and I would like to analyse the mediation effect of A and B on C. I have a structure such that:

(1) Z -> A
(2) A(hat) B - > C
(3) A(hat) C - > B

What I really want to know is the impact of A and B on C (point (2) above), but the relationship between B and C is not unidirectional. How would I go about estimating this system? Is it possible?

Am I correct in thinking it would be:

 cmp (C = A# B X3) (B = A# C X2) (A = Z X1), ind($cmp_cont $cmp_cont $cmp_cont)

Where the first set of parentheses above is what I really want to know.

[David Roodman]

The rule is that references to other equations that lack # suffixes must not be circular. Here I see B in the C equation and C in the B equation, so that won't work.
But since these equations are apparently all uncensored--I just see $cmp_cont in the ind() option--you can easily fix that by adding more # suffixes. It doesn't change the mathematical meaning but it matters to the cmp program. These should all work and give the same results (though I can't guarantee convergence):

cmp (C = A# B  X3) (B = A# C# X2) (A = Z X1), ind($cmp_cont $cmp_cont $cmp_cont)
cmp (C = A# B# X3) (B = A# C  X2) (A = Z X1), ind($cmp_cont $cmp_cont $cmp_cont)
cmp (C = A# B# X3) (B = A# C# X2) (A = Z X1), ind($cmp_cont $cmp_cont $cmp_cont)