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. Building on the model, we develop a two-stage nonparametric copula control function approach (2sCOPEnp) for endogeneity correction without relying on instrumental variables. The method relaxes the restrictive assumption of the Gaussian copula regressor-error dependence structure and eliminates the need to model regressors. It unifies and generalizes existing copula-based endogeneity correction methods, while minimizing assumptions about the first-stage auxiliary dependence structures among regressors. Specifically, 2sCOPEnp constructs control functions using nonparametric estimates of the conditional cumulative distribution functions (CDFs) of endogenous regressors given exogenous variables, enhancing the accuracy and robustness of endogeneity correction. Unlike existing copula control function methods, 2sCOPE-np applies to broader dependence structures and can handle discrete endogenous regressors (e.g., binary or count) by leveraging relevant exogenous control variables to smooth discrete conditional CDFs. We demonstrate the robustness and broad applicability of the proposed method compared to existing copula-based endogeneity correction methods. Simulation studies demonstrate that the proposed method outperforms existing methods. We illustrate its usage and advantages in two empirical examples: store sales estimation and return to education.