The positive correlation (PC) test is the standard procedure used in the empirical literature to detect the existence of asymmetric information in insurance markets. This article describes a new tool to implement an extension of the PC test based on a new family of regression models, the multivariate ordered logit, designed to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. We present an application of our proposed extension of the PC test to the Medigap health insurance market in the United States. Results reveal that the risk–coverage association is not homogeneous across coverage and risk categories, and depends on individual socioeconomic and risk preference characteristics.