Correcting Endogeneity via Nonparametric Copula Control Functions

We propose a new framework to address endogenous regressors using a novel conditional copula endogeneity model. Endogenous regressor models are nonparametric and agnostic to the functions that determine the values of endogenous regressors from exogenous regressors and unobservables. To capture the regressor-error dependence unexplained by exogenous regressors, conditional Gaussian copulas are used to link the structural error terms and the nonparametric models for endogenous regressors. Building on the model, we develop a two-stage nonparametric control function approach for endogeneity correction without relying on instrumental variables. Specifically, the approach constructs control functions using nonparametric estimates of the conditional cumulative distribution functions of endogenous regressors given exogenous regressors. The method relaxes the assumption of regressors and error jointly following Gaussian copula dependence structure and eliminates the need to model regressors. It unifies and generalizes existing copula-based endogeneity correction methods, while minimizing assumptions about how endogenous regressors are determined. Unlike existing copula control function methods, it can handle discrete endogenous regressors (e.g., binary or low-count) by leveraging variation in relevant exogenous control regressors. We demonstrate the robustness and broad applicability of the proposed method compared to existing copula-based endogeneity correction methods in simulation studies and empirical applications.