A Practical Guide to Endogeneity Correction Using Copulas

Causal inference is of central interests 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. At the forefront of 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 and its usage in marketing research, discuss recent advances that broaden the understanding, applicability, and robustness of copula correction, and examine implementation challenges of copula correction such as construction of copula control functions and handling of higher-order terms of endogenous regressors. To facilitate the appropriate usage of copula correction, 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.