Across a wide set of non-group insurance markets, applicants are rejected based on observable, often high-risk, characteristics. This paper argues private information, held by the potential applicant pool, explains rejections. I formulate this argument by developing and testing a model in which agents may have private information about their risk.

I first derive a new no-trade result that theoretically explains how private information could cause rejections. I then develop a new empirical methodology to test whether this no-trade condition can explain rejections. The methodology uses subjective probability elicitations as noisy measures of agents beliefs. I apply this approach to three non-group markets: long-term care, disability, and life insurance.

Consistent with the predictions of the theory, in all three settings I find significant amounts of private information held by those who would be rejected; I find generally more private information for those who would be rejected relative to those who can purchase insurance; and I show it is enough private information to explain a complete absence of trade for those who would be rejected. The results suggest private information prevents the existence of large segments of these three major insurance markets.