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 two-regime 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).