While the critical role of imperfect information has become axiomatic in explaining health care market failure, the theory is backed by little empirical evidence. In this paper we use a unique panel data set with explicit measures of information and an educational intervention to investigate the role of uncertain information about health insurance benefits on the demand for supplemental Medicare insurance that allows imperfect information to affect both the mean and the variance of the expected benefits distribution. The empirical specification is a structural panel multinomial probit with an unrestricted variance-covariance, including heteroskedasticity and random effects to control for unobserved heterogeneity. The model is computationally complex and is estimated by simulated maximum likelihood. The empirical results indicate that imperfect information affects the demand for supplement Medicare insurance by increasing the variance of the expected benefits distribution rather than by systematically shifting the mean of the distribution. Since the majority of people already purchase insurance, an increase in variance due to imperfect information reduces demand. We estimate that if everyone has perfect information, then the proportion of individuals not purchasing insurance would fall 23% from .096 to .074. We also found that controlling for unobserved heterogeneity was important. The goodness of fit increased by about 25% and the precision of the estimated effect of information on the variance of the expected benefits distribution increased dramatically.