ivprobit, cmp, and marginal effects

[Sam Rawlings]

Hello,

I am currently estimating a linear IV (2SLS) regression in which both the dependent and endogenous variable are binary. I am using Stata version 13.1.

My 2SLS specification looks like this:

ivreg2 y (x1 = x2 x3) $controls, robust

both y and x1 are binary variables (and renamed here for simplicity).

I would like to check robustness of my results to estimating this using the probit model i.e. an IV probit, but with a binary endogenous variable. The stata command ivprobit is unsuitable for this type of regression, and I am trying to use the cmp command. I have read both the help file and Roodman's 2011 article in the Stata Journal. However, I am a little confused regarding two issues:

1. The correct specification to estimate through cmp

2. Estimation of the marginal effect of the endogenous variable and instruments

Regarding issue (1) above, I *think* the correct specification in cmp is to use the ‘two stage’ (bivariate) probit (given as example 3 in Roodman’s article), which in cmp would be:

cmp (y = $controls x1) (x1 = x2 x3 $controls) , ind($cmp_probit $cmp_probit) robust

Is this correct? In any case, I am currently using this command, and to calculate average marginal effects afterwards:

margins, force dydx(*) predict(pr)

however, when I do this, the marginal effects for x2 and x3 are omitted (the output is below):

Average marginal effects                          Number of obs   =      27777
Model VCE    : Robust

Expression   : Pr(y), predict(pr)
dy/dx w.r.t. : x1 x2 x3

--------------------------------------------------------------------------------
               |            Delta-method
               |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
            x1 |   .0311537   .0219898     1.42   0.157    -.0119455    .0742529
            x2 |          0  (omitted)
            x3 |          0  (omitted)
--------------------------------------------------------------------------------

Does anyone have any advice on whether I am doing (1) or (2) (or both!) incorrectly, and how I might be able to calculate the average marginal effect of x2 and x3 on x1 in this model?

Thanks in advance!

[David Roodman]

Hi Sam,
That cmp command line looks right.

What you're trying to do with the marginal effects is hard. To my knowledge, margins is not good at linking equations. It doesn't "know" that x3 affects x1 via x2. And even if it did, it would have trouble getting what it needs to do the computation out of cmp. In principle, I could write a special package that would do cross-equation margins in cmp in this way, but that would be a lot of work.

That said, if this really is an IV estimate, then I'm not what you're trying to do makes sense. In general in IV, we don't assume that the first-stage equation is structurally correct, only that the excluded instruments have some explanatory power.

--David