Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models

Lagrange multiplier and Wald tests for the hypothesis of absence of unobserved confounding are extended to the context of semiparametric recursive and sample selection bivariate probit models. The finite sample size properties of the tests are examined through a Monte Carlo study using several scenarios: correct model specification, distributional and functional misspecification, with and without an exclusion restriction. The simulation results provide some guidelines which may be important for empirical analysis. The tests are illustrated using two datasets in which the issue of unobserved confounding arises.