We study optimal risk adjustment in imperfectly competitive health insurance markets when high-risk consumers are less likely to switch insurer than low-risk consumers. First, we find that insurers still have an incentive to select even if risk adjustment perfectly corrects for cost differences among consumers. Consequently, the outcome is not efficient even if cost differences are fully compensated. To achieve first best, risk adjustment should overcompensate for serving high-risk agents to take into account the difference in mark- ups among the two types. Second, the difference in switching behavior creates a trade off between efficiency and consumer welfare. Reducing the difference in risk adjustment subsidies to high and low types increases consumer welfare by leveraging competition from the elastic low-risk market to the less elastic high-risk market. Finally, mandatory pooling can increase consumer surplus even further, at the cost of efficiency.
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