Self-selection and direct estimation of across-regime correlation parameter

A direct maximum likelihood (ML) procedure to estimate the ‘generally unidentified’ across-regime correlation parameter in a tworegime endogenous switching model is here provided. The results of a Monte Carlo experiment confirm consistency of our direct ML procedure, and its relative efficiency over widely applied models and methods. As an empirical application, we estimate a two-regime simultaneous equation model of domestic work of Italian married women in which the two regimes are given by their working status (employed or unemployed).