Some time ago I wrote about a paper by Arthur Lewbel in the Journal of Business & Economic Statistics in which he develops a method to do two-stage least squares regressions without actually having an exclusion restrictions in the model. The approach relies on higher moment restrictions in the error matrix and works well for linear or partly linear models. Back then, I expressed concerns that the estimator does not seem to work when an endogenous regressor is binary though; at least not in the simulations I have carried out.
After a bit of email back-and-forth we were able to settle the debate now. Continue reading Follow-up on “IV regressions without instruments” (technical)