A note on the parametric three step estimator in structural labor supply models

In the estimation of structural models of labor supply, simultaneous equation systems are frequently used. Often, these systems are estimated by three step methods that are based on the ideas developed by Heckman [Econometrica 47 (1979) 153–161]. Although for the first two steps the statistical theory for the resulting estimators is well established, the same cannot be said for the third step. As a consequence, most of those empirical inferences rely simply in incorrect statistics. In this article we give the theory and a brief example for a fully parametric three step estimator.