Gaussian Copula Regression in the Presence of Thresholds

Park and Gupta’s (2012) introduction of the Gaussian Copula (GC) approach to deal with endogeneity has made a significant impact on empirical marketing research with many papers using this approach. Recent studies have however started to explore and examine the approach and its underlying assumptions more closely, resulting in a more critical picture of it. A particular challenge is the non-testable assumption that the dependency structure between the endogenous regressor and the error term should be described by a Gaussian copula. In general, there exists a limited understanding of what this assumption implies, what causes its violation, and potential remedies. Our study addresses this explicitly. We provide a detailed discussion of the dependency structure assumption and how thresholds in the data can lead to its violation and biased results. We use real and simulated data to show how threshold detection before applying the GC approach can overcome this problem and thereby provide researchers with a useful tool to increase the likelihood of the GC approach’s assumptions being met.