We extend the nonparametric literature on partially identified probability distributions and use our analytical results to provide sharp bounds on the impact of universal health insurance on provider visits and medical expenditures. Our approach accounts for uncertainty about the reliability of self-reported insurance status as well as uncertainty created by unknown counterfactuals. We construct health insurance validation data using detailed information from the Medical Expenditure Panel Survey. Imposing relatively weak nonparametric assumptions, we estimate that under universal coverage monthly per capita provider visits and expenditures would rise by less than 8 percent and 16 percent, respectively, across the nonelderly population.