The identification of information problems in different markets is a challenging issue in the economic literature. In this paper, we study the identification of moral hazard from adverse selection and learning about risk within the context of a multi‐period dynamic model. We extend the model of Abbring, Chiappori, and Pinquet (2003, Journal of the European Economic Association, 1, 767–820) to include learning about risk and insurance coverage choice over time. We derive testable empirical implications for panel data. We then perform tests using longitudinal data from France during the period 1995–1997. We find evidence of moral hazard among a sub‐group of policyholders with less driving experience (less than 15 years). Policyholders with fewer than five years of experience have a combination of learning about risk and moral hazard, whereas no residual information problem is found for policyholders with more than 15 years of experience.