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EMAC 2023 Annual

Addressing Endogeneity using a Two-stage Copula Generated Regressor Approach

Published: May 24, 2023


Fan Yang, NEOMA Business School; Yi Qian, University of British Columbia; Hui Xie, Simon Fraser University


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 instrumental variables that must satisfy the stringent condition of exclusion restriction, making it infeasible to use in many settings. We propose a new instrument-free method using copula to address the endogeneity problem. Existing copula correction methods require sufficiently nonnormal endogenous regressors. Furthermore, existing copula control function methods presume the independence of exogenous regressors and the endogenous regressor. Our proposed two-stage copula endogeneity correction (2sCOPE) method simultaneously relaxes the two key identification requirements, and we theoretically 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 non-normality. 2sCOPE employs generated regressors derived from existing regressors to control for endogeneity, and is straightforward to use and broadly applicable. Overall, 2sCOPE can greatly increase the ease and broaden the applicability of using instrument-free methods to handle regressor endogeneity. We further demonstrate the performance of 2sCOPE via simulation studies and an empirical application. Our paper is intended for the 'Methods, Modelling & Marketing Analytics' track.