Working Paper: NBER ID: w29708
Authors: Fan Yang; Yi Qian; Hui Xie
Abstract: The ubiquitous presence of endogenous regressors presents a significant challenge when drawing causal inference using observational data. The classical econometric method used to handle regressor endogeneity requires IVs that must satisfy the stringent condition of exclusion restriction, rendering it unfeasible in many settings. Herein, we propose a new IV-free method that uses 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. Assuming a Gaussian copula dependence structure for all regressors and a normally distributed structural error, we prove that 2sCOPE yields consistent causal-effect estimates with correlated endogenous and exogenous regressors as well as normally distributed endogenous regressors. In addition to relaxing the 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 can thus considerably increase the ease and broaden the applicability of IV-free methods for handling regressor endogeneity. We further demonstrate 2sCOPE’s performance using simulation studies and illustrate its use in an empirical application.
Keywords: endogeneity; causal inference; copula; instrumental variables; regression
JEL Codes: C01; C1; C13; C18; C4
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| 2scope (Y20) | consistent causal effect estimates (C22) |
| endogenous regressors correlated with exogenous ones (C32) | consistent causal effect estimates (C22) |
| 2scope (Y20) | improvement over traditional IV methods (C36) |
| 2scope (Y20) | handles normally distributed endogenous regressors (C51) |
| 2scope (Y20) | improves finite sample performance (C51) |
| 2scope (Y20) | addresses biases associated with insufficient regressor nonnormality (C20) |
| 2scope (Y20) | broadens applicability of IV-free methods (C36) |