On “forbidden regression” and ivprobit

[Marcos Almeida]

Dear members,
I wonder whether this model is correct (I mean, statistically speaking):
The outcome variable is binary (“death”) and there are two binary predictors that I believe need to be “instrumented”. I started with standard probit models, starting with the “crude” model and going forward.

Then, I decided to use the ivprobit.
Below, the command, for a sample of 550 observations:

. ivprobit binoutcome continuousvar1 continuousvar2 binvar1 binvar2 binvar3  (bin_inst1 bin_inst2  = binvar4 continuousvar3), vce(robust)

Contrary to the output under standard probit, the output for ivprobit, in terms of rationale, seemed quite appropriate. What is more, the model converged with few iterations (6). This probit model with endogenous regressors presented:

Wald test of exogeneity: chi2(2) = 9.47                   Prob > chi2 = 0.0088

The output with vce(jackknife) showed an increase of around 12% in the SEs, but gave similar results in terms of p-values.

Theoretically speaking, I’m confident these 2 binary variables shall be instrumented, or at least somewhat “adjusted” in terms
of bias towards the outcome.

By the way, I also used a couple of propensity score methods (including the inverse- probability weighted regression adjustment), but the results of the ivprobit seemed to me the most convincing in terms of biological rationale.

As a matter of fact, that is not the case of “fishing” good results, but conceiving that the previous models provided information that defies the logic and biology at once.

In short, my question is: is this “forbidden regression”? If so, shall it be “allowed” in this particular case? If not, I wonder whether there is an alternative in Stata.

Thank you in advance.

[Marcos Almeida]

I'm still struggling with an appropriate method to cope with a binary outcome (in the first equation) and 2 binary instrumented variables (in the second).

The - ivprobit - provided results that can be taken as quite reasonable in logical as well as biological terms.

In this thread, particularly in #3, Jeff Wooldridge provided an insightful approach to the matter, even though 2SLS was the main issue. Also, - biprobit - was recommended.

With regards to the use of p_hat of separated probit models, then adding them as instruments (I guess, if I got it right, this what is called "forbidden regression"), the model didn't improve at all.

Again, with - biprobit - I found at least two cons : most (biologically reasonable) models provided a nonsignificant rho, and those with p <0.05 had only one endogenous regressor. Second, I believe I should use two instrumented variables, theoretically speaking, as shared in #1.

In short, I wonder whether "my" ivprobit model, "forbidden" or not, must be taken as "wrong" (under statistical terms). Shall there be a chance to check its assumptions, I'd be very happy to know as well.