Reexamining Gaussian copula endogeneity correction with noncontinuous endogenous regressors

In recent years, the instrumental variable-free Gaussian copula (GC) model has gained traction among researchers as a tool for correcting endogeneity bias. This paper offers new theoretical insights showing that, although Gaussian copula control function (GC-CF) estimators are not suitable for noncontinuous endogenous regressors (e.g., binary regressors), the parameters of the GC model remain uniquely identified and can be reliably estimated using alternative estimators. For researchers developing GC models, these findings highlight the need to create estimators beyond the popular GC-CF estimators to extend the model’s applicability to empirical settings involving noncontinuous endogenous regressors, which are common in marketing. For researchers interested in using GC models to correct endogeneity bias with noncontinuous regressors, the authors provide a Bayesian software implementation of GC models and demonstrate its effectiveness through simulation studies.