This article introduces a new method for testing asymmetric information in insurance markets using a multivariate ordered logit regression model. The traditional "Positive Correlation" (PC) test, which checks for a positive correlation between insurance coverage and risk, is extended to account for more complex relationships when multiple ordered response variables are involved. The authors apply this method to the Medigap health insurance market in the United States, where individuals can purchase additional coverage to fill gaps left by Medicare. Results show that the relationship between risk and coverage is not uniform across different categories of coverage and risk, and depends on individual socioeconomic and risk preference characteristics. The study finds that the association between insurance coverage and risk is not homogeneous across different categories of coverage and risk. For example, the association between Medigap plan purchase and health care utilization varies depending on how high/low claim/coverage is defined. The authors also find that the direction and strength of association differ depending on the specific categories considered. This suggests that the presence of asymmetric information is not uniform across different types of insurance and risk. The multivariate ordered logit model allows for a more detailed analysis of the association structure between multiple ordered response variables. This model is more flexible and computationally efficient than the traditional bivariate probit model used in previous studies. The authors also find that the association between insurance coverage and risk can be influenced by individual characteristics such as education, income, and preventive care behavior. The study provides evidence of positive and statistically significant risk-coverage association in the Medigap market, and finds that this effect is not homogeneous across categories of insurance coverage and health care utilization. The results suggest that price differentiation could be used to reduce selection in insurance markets. The authors conclude that the proposed method offers a more comprehensive approach to analyzing asymmetric information in insurance markets compared to traditional methods.This article introduces a new method for testing asymmetric information in insurance markets using a multivariate ordered logit regression model. The traditional "Positive Correlation" (PC) test, which checks for a positive correlation between insurance coverage and risk, is extended to account for more complex relationships when multiple ordered response variables are involved. The authors apply this method to the Medigap health insurance market in the United States, where individuals can purchase additional coverage to fill gaps left by Medicare. Results show that the relationship between risk and coverage is not uniform across different categories of coverage and risk, and depends on individual socioeconomic and risk preference characteristics. The study finds that the association between insurance coverage and risk is not homogeneous across different categories of coverage and risk. For example, the association between Medigap plan purchase and health care utilization varies depending on how high/low claim/coverage is defined. The authors also find that the direction and strength of association differ depending on the specific categories considered. This suggests that the presence of asymmetric information is not uniform across different types of insurance and risk. The multivariate ordered logit model allows for a more detailed analysis of the association structure between multiple ordered response variables. This model is more flexible and computationally efficient than the traditional bivariate probit model used in previous studies. The authors also find that the association between insurance coverage and risk can be influenced by individual characteristics such as education, income, and preventive care behavior. The study provides evidence of positive and statistically significant risk-coverage association in the Medigap market, and finds that this effect is not homogeneous across categories of insurance coverage and health care utilization. The results suggest that price differentiation could be used to reduce selection in insurance markets. The authors conclude that the proposed method offers a more comprehensive approach to analyzing asymmetric information in insurance markets compared to traditional methods.