January 2022.

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 new instrument-free methods using copulas to address the endogeneity problem. The existing copula correction method focuses only on the endogenous regressors and may yield biased estimates when exogenous and endogenous regressors are correlated. Furthermore, (nearly) normally distributed endogenous regressors cause model non-identification or finite-sample poor performance. Our proposed two-stage copula endogeneity correction (2sCOPE) method simultaneously overcomes the two key limitations and yields consistent causal-effect estimates with correlated endogenous and exogenous regressors as well as normally distributed endogenous regressors. 2sCOPE employs generated regressors derived from existing regressors to control for endogeneity, and is straightforward to use and broadly applicable. Moreover, we prove that exploiting correlated exogenous regressors can address the problem of insufficient regressor non-normality, relax identification requirements and improve estimation precision (by as much as ∼50% in empirical evaluation). Overall, 2sCOPE can greatly increase the ease of and broaden the applicability of instrument-free methods for dealing with regressor endogeneity. We demonstrate the performance of 2sCOPE via simulation studies and an empirical application.

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