A Practical Guide to Endogeneity Correction Using Copulas

Causal inference is of central interest in many empirical applications, yet often challenging because of the presence of endogenous regressors. The classical approach to the problem requires using instrumental variables that must satisfy the stringent condition of exclusion restriction. In recent research, instrument-free copula methods have been increasingly used to handle endogenous regressors. This article aims to provide a practical guide for how to handle endogeneity using copulas. The authors give an overview of copula endogeneity correction, outlining its theoretical rationales, advantages, and limitations for empirical research. They also discuss recent advances that enhance the understanding, applicability, and robustness of copula correction, and address implementation aspects of copula correction such as constructing proper and robust copula control functions, handling higher-order terms of endogenous regressors and noncontinuous endogenous regressors, choosing between control function and likelihood-based joint estimation methods, and extending the approach to panel data and nonlinear models. To facilitate the appropriate usage of copula correction in order to realize its full potential, the authors detail a process of checking data requirements and identification assumptions to determine when and how to use copula correction methods, and illustrate its usage using empirical examples.