Correcting Endogeneity via Nonparametric Copula Control Functions

We propose a new framework that addresses endogenous regressors using a novel conditional copula endogeneity model to capture the regressor-error dependence unexplained by exogenous regressors. Under the model, we develop a two-stage nonparametric copula control function approach (2sCOPE-np) for endogeneity correction without relying on instrumental variables. The 2sCOPE-np relaxes the key assumption of the Gaussian copula regressor-error dependence structure and eliminates modeling of regressors. It generalizes and unifies existing copula-based methods for correcting endogeneity while minimizing assumptions about the first-stage auxiliary model for the regressors. Specifically, 2sCOPE-np constructs control functions using nonparametric estimates of the conditional cumulative distribution functions of endogenous regressors given exogenous variables, enhancing both the accuracy and robustness of endogeneity correction. Unlike existing copula control function methods, the 2sCOPE-np is capable of handling discrete endogenous regressors (e.g., binary or count) by leveraging relevant exogenous control variables to overcome plateaus in the discrete CDFs. We elucidate the robustness and broad applicability of 2sCOPE-np, compared to existing copula endogeneity correction methods. Simulation studies further demonstrate that 2sCOPE-np outperforms existing methods. We illustrate the usage of 2sCOPE-np in two empirical examples: the store sales estimation and the return on education.