Correcting Endogeneity via Instrument-Free Two-Stage Nonparametric Copula Control Functions

Given the ubiquitous presence of endogenous regressors and the challenges in finding good instruments to overcome the endogeneity problem, a forefront of recent research is the development and application of endogeneity correction methods without requiring instruments. In this article, we formulate the regressor endogeneity problem using a novel conditional copula endogeneity model to capture the regressor-error dependence unexplained by exogenous regressors. The model relaxes the key assumption of Gaussian copula regressor-error dependence structure and eliminates unnecessary modeling of regressors. Under the model, we develop an instrument-free two-stage nonparametric copula endogeneity control function approach (2sCOPE-np), which generalizes existing copula endogeneity correction methods and minimizes the assumptions in the first-stage auxiliary model for endogenous regressors. Specifically, the 2sCOPE-np employs robust model-free kernel estimates of copula control functions. We elucidate and demonstrate 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 an empirical application of the store sales demand estimation.