Exploiting Between-Regressor Correlation to Robustify Copula Correction Models for Handling Endogeneity

Abstract

This paper proposes a generalisation of the joint copula modelling approach by Park and Gupta (Marketing Science, 2012, 32(4), 567-586) with an endogeneity correction that involves the exogenous variables. Seeing that related studies require the strong assumption of independence between the endogenous and the exogenous regressors, we first show that the estimator by Park and Gupta suffers from an omitted variables bias when this assumption is violated. The distinguishing characteristic of the proposed approach is that we use a first-stage auxiliary regression to generate copula correction functions by exploiting the informational content of the exogenous variables in a similar spirit as IV-based identification. As this first-stage regression does not generate an additional identification problem, model identification remains subject to the same requirements as within the Park and Gupta model. The approach is least-squares-based and thus does neither require numerical optimisation nor the search for starting values. Monte Carlo simulations reveal that the proposed approach performs well in finite samples. We demonstrate the practical applicability by reassessing the empirical example in Park and Gupta using the proposed approach.

Keywords: Endogeneity, copula function, two-stage least squares, instrumental variables, linear regression model

JEL Classification: C14, C18, C21, C36