Addressing Endogeneity Using a Two-stage Copula Generated Regressor Approach

A prominent challenge when drawing causal inference using observational data is the ubiquitous presence of endogenous regressors. The classical econometric method to handle regressor endogeneity requires IVs that must satisfy the stringent condition of exclusion restriction, making it infeasible to use in many settings. We propose a new IV-free method using copulas to address the endogeneity problem. Existing copula correction methods require nonnormal endogenous regressors: normally or nearly normally distributed endogenous regressors cause model non-identification or significant finite-sample bias. Furthermore, existing copula control function methods presume the independence of exogenous regressors and the copula control function. Our proposed two-stage copula endogeneity correction (2sCOPE) method simultaneously relaxes the two key identification requirements, and we prove that 2sCOPE yields consistent causal-effect estimates with correlated endogenous and exogenous regressors as well as normally distributed endogenous regressors. Besides relaxing identification requirements, 2sCOPE has superior finite-sample performance and addresses the significant finite-sample bias problem due to insufficient regressor nonnormality. Moreover, 2sCOPE employs generated regressors derived from existing regressors to control for endogeneity, and thus can greatly increase the ease and broaden the applicability of using IV-free methods to handle regressor endogeneity. We further demonstrate the performance of 2sCOPE via simulation studies and illustrate its use in an empirical application.