Regression of a continuous variable on three binary endogenous variables and other covariates

[Johannes Tabi]

I wish to run a regression of wages on three distinct training choices. These training choices are binary endogenous variables which are independent as an individual may have been trained in one aspect and later in another at different point in time. I am dealing with past training. I thought of using a two-step econometrics estimation procedure. First an estimation of a multinomial probit model of training choice while computing the inverse mills and in the second step, a structural wage equation that corrects for selection into training. But my worry is that, am loosing observations because we at times obtain (1 1 1), (101), (110), etc, by building a multinomial setting.
What other method, can be used. I am thinking of a control function approach which in each first stage, considers the different training dummies as simple endogenous regressors that rely on a set of instruments. Is that Ok?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

You might consider a simultaneous equation model using GSEM.