This article introduces a new method to test for asymmetric information in insurance markets, extending the standard Positive Correlation (PC) test. The authors propose using multivariate ordered logit regression models to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. They apply this extension to the Medigap health insurance market in the United States, finding that the risk-coverage association is not homogeneous across coverage and risk categories and depends on individual socioeconomic and risk preference characteristics. The study highlights the importance of considering multidimensional private information and provides a flexible framework for analyzing complex data structures in insurance markets.This article introduces a new method to test for asymmetric information in insurance markets, extending the standard Positive Correlation (PC) test. The authors propose using multivariate ordered logit regression models to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. They apply this extension to the Medigap health insurance market in the United States, finding that the risk-coverage association is not homogeneous across coverage and risk categories and depends on individual socioeconomic and risk preference characteristics. The study highlights the importance of considering multidimensional private information and provides a flexible framework for analyzing complex data structures in insurance markets.