This paper studies imperfectly-perceived private information in insurance markets when contracts endogenously respond. Equilibrium contracts, pooling and welfare depend on the joint distribution of risk and misperception. In the Health and Retirement Study (HRS), I show that misperceptions typically co-vary with (medical, long-term care, disability and mortality) risk type: high types under-perceive their risk, low types over-perceive. I develop a general model and algorithm to estimate the equilibrium contracts, pooling and welfare impact of misperceptions that is applicable in many settings. I offer suggestive evidence from US annuity markets that contracts are distorted due to misperceptions, with welfare likely increasing.