This study considers the small sample performance of approximate but simple two-stage estimators for probit models with two endogenous binary covariates. Monte Carlo simulations showthat all the considered estimators, including the simulated maximum-likelihood (SML) estimation, of the trivariate probit model are biased in very small samples (N = 100). With moderately small samples (N = 500), some of the approximations perform as well as the SML estimator when the degree of endogeneity is not very large. Some of the approximations seem robust with higher correlations and are also promising for testing the exogeneity of binary covariates. The methods are used to estimate the impact of employment-based health insurance and health care (HC) on HC use, where the approximations seem to work at least as well as the SML and in some cases better.
Journal of Statistical Computation and Simulation, 2013, Vol 83, Issue 6, p. 1156-1178