TY - JOUR
T1 - Dealing with regression models’ endogeneity by means of an adjusted estimator for the Gaussian copula approach
AU - Liengaard, Benjamin Dybro
AU - Becker, Jan-Michael
AU - Bennedsen, Mikkel
AU - Heiler, Phillip
AU - Taylor, Luke Nicholas
AU - Ringle, Christian M.
PY - 2025/1
Y1 - 2025/1
N2 - Endogeneity in regression models is a key marketing research concern. The Gaussian copula approach offers an instrumental variable (IV)-free technique to mitigate endogeneity bias in regression models. Previous research revealed substantial finite sample bias when applying this method to regression models with an intercept. This is particularly problematic as models in marketing studies almost always require an intercept. To resolve this limitation, our research determines the bias’s sources, making several methodological advances in the process. First, we show that the cumulative distribution function estimation’s quality strongly affects the Gaussian copula approach’s performance. Second, we use this insight to develop an adjusted estimator that improves the Gaussian copula approach’s finite sample performance in regression models with (and without) an intercept. Third, as a broader contribution, we extend the framework for copula estimation to models with multiple endogenous variables on continuous scales and exogenous variables on discrete and continuous scales, and non-linearities such as interaction terms. Fourth, simulation studies confirm that the new adjusted estimator outperforms the established ones. Further simulations also underscore that our extended framework allows researchers to validly deal with multiple endogenous and exogenous regressors, and the interactions between them. Fifth, we demonstrate the adjusted estimator and the general framework’s systematic application, using an empirical marketing example with real-world data. These contributions enable researchers in marketing and other disciplines to effectively address endogeneity problems in their models by using the improved Gaussian copula approach.
AB - Endogeneity in regression models is a key marketing research concern. The Gaussian copula approach offers an instrumental variable (IV)-free technique to mitigate endogeneity bias in regression models. Previous research revealed substantial finite sample bias when applying this method to regression models with an intercept. This is particularly problematic as models in marketing studies almost always require an intercept. To resolve this limitation, our research determines the bias’s sources, making several methodological advances in the process. First, we show that the cumulative distribution function estimation’s quality strongly affects the Gaussian copula approach’s performance. Second, we use this insight to develop an adjusted estimator that improves the Gaussian copula approach’s finite sample performance in regression models with (and without) an intercept. Third, as a broader contribution, we extend the framework for copula estimation to models with multiple endogenous variables on continuous scales and exogenous variables on discrete and continuous scales, and non-linearities such as interaction terms. Fourth, simulation studies confirm that the new adjusted estimator outperforms the established ones. Further simulations also underscore that our extended framework allows researchers to validly deal with multiple endogenous and exogenous regressors, and the interactions between them. Fifth, we demonstrate the adjusted estimator and the general framework’s systematic application, using an empirical marketing example with real-world data. These contributions enable researchers in marketing and other disciplines to effectively address endogeneity problems in their models by using the improved Gaussian copula approach.
KW - Bias
KW - Endogeneity
KW - Estimator
KW - Gaussian Copula
KW - Guidelines
KW - Intercept
KW - Regression model
UR - https://www.scopus.com/pages/publications/85208052758
U2 - 10.1007/s11747-024-01055-4
DO - 10.1007/s11747-024-01055-4
M3 - Journal article
SN - 0092-0703
VL - 53
SP - 279
EP - 299
JO - Journal of the Academy of Marketing Science
JF - Journal of the Academy of Marketing Science
ER -