Bivariate Logit Models with Dummy Endogenous Regressors Using Copulas

Measuring the impact of a binary treatment on a binary response variable is of great interest in many medical, social and economic applications. Estimating such effect is very important when the endogeneity problem occurs. This research proposes a bivariate logit model to control endogeneity when the structural errors of the two equations are correlated. The copula approach will be applied to estimate the dependence between the binary treatment and the binary response; and hence, the joint normality assumption of the structural error is irrelevant. For estimation, the maximum likelihood method will be applied to estimate the model parameters. The performance of the copula bivariate logit model in estimating the dependence between the binary treatment variable and the binary response variable is assessed by the Average Treatment Effect (ATE) criterion in both simulation study and real medical data.