Dealing with regression models’ endogeneity by means of an adjusted estimator for the Gaussian copula approach
Liengaard, Benjamin D., Becker, Jan Michael, Bennedsen, Mikkel, Heiler, Phillip, Taylor, Luke N., and Ringle, Christian M. (2024) Dealing with regression models’ endogeneity by means of an adjusted estimator for the Gaussian copula approach. Journal of the Academy of Marketing Science, 53. pp. 279-299.
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Abstract
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.
| Item ID: | 87485 |
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| Item Type: | Article (Research - C1) |
| ISSN: | 1552-7824 |
| Keywords: | Bias, Endogeneity, Estimator, Gaussian copula, Guidelines, Intercept, Regression model |
| Copyright Information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
| Date Deposited: | 09 Dec 2025 00:51 |
| FoR Codes: | 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490599 Statistics not elsewhere classified @ 70% 35 COMMERCE, MANAGEMENT, TOURISM AND SERVICES > 3506 Marketing > 350606 Marketing research methodology @ 30% |
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