Dear Stata users,

This is my first post here and I hope I am doing it properly, according the forum rules.

The situation is the following: I am working on a panel of Spanish firms and I would like to implement a IV regression. The point is to test the learning by internationalization hypothesis. In particular, we want to see if firms that undertake internationalization strategies (three in my case: Y1 export, Y2 outsourcing and Y3 FDI), have returns in terms of innovation of two types (X1 product and X2 process). There are, then, other regressors (Zs).

In my dataset, both the innovation variables (dependent, Xs) and internationalization variables (independent, Ys) are binary and I would like to implement an IV strategy with some instruments (Is) that I have built following related literature.

I have read through the forum and I found several examples in which the endogenous variable is only one and the solution suggested was to estimate the model in the form of a bivariate probit model, estimating a model of the joint determination of two dependent variables, the outcome variable, and the endogenous binary regressor.

So, the Stata command suggested was the biprobit

biprobit (Xs = Ys Zs) (Y = Is Zs)

But, as long as I understood, there is no possibility to implement it with more than one endogenous (binary) variable with a mvprobit at first stage.

One way could be, if I am right, implementing a three-step approach as in Wooldridge (2002: 623-625)

1) a probit regression of the endogenous dummy variable on the exogenous variables and the exclusion restrictions.
2) a least squares regression of the endogenous treatment variable on the exogenous variables and the predicted probabilities from Step 1.
3) a least squares regression of the outcome variable on the exogenous variables and the predicted values from Step 2.

"The procedure begins no differently from the probit model of selection, and hence exclusion restrictions must be found. The second step uses first-step predicted probabilities as its exclusion restrictions; the intermediate step allows the researcher to employ a non-linear probability for the assignment of the treatment but does not impose a specific distributional assumption for the probability model." (Basinger, S. J., & Ensley, M. J. (2010). Endogeneity problems with binary treatments: A comparison of models. Technical report: 11-12)

My questions are:
1) Could it be a suitable solutions?
2) Could you help to sketch the command?

Thank you to anyone could help!
Amato