Coherency and estimation in simultaneous models with censored or qualitative dependent variables

Abstract

This paper concerns estimation and inference in simultaneous limited dependent variable or simultaneous qualitative dependent variable models. We discuss the implications of the coherency condition which is required to ensure a unique implicit reduced form in such nonlinear models. A number of model specifications are examined, including the Simultaneous Prohit, Simultaneous Tohit, and Simultaneous Generalised Selectivity models, and we consider the usefulness of a conditional maximum likelihood (CML) methodology. We obtain a simple consistent estimator which is a natural counterpart to the CML estimator for standard simultaneous models. An application to a structural model of household labour supply is presented.