The positive correlation test for asymmetric information developed by Chiappori and Salanie (2000) has been applied in many insurance markets. Most of the literature focuses on the special case of constant correlation
it also relies on restrictive parametric specifications for the choice of coverage and the occurrence of claims. We relax these restrictions by estimating conditional covariances and correlations using deep learning methods. We test the positive correlation property by using the intersection test of Chernozhukov, Lee, and Rosen (2013) and the "sorted groups" test of Chernozhukov, Demirer, Duflo, and Fernandez-Val (2023). Our results confirm earlier findings that the correlation between risk and coverage is small. Random forests and gradient boosting trees produce similar results to neural networks.