We leverage two unique natural experiments to show that, in public drug insurance for the low-income elderly in the U.S., defaults have large and persistent effects on plan enrollment and beneficiary drug utilization. We estimate that when a beneficiary’s default is exogenously changed from one year to the next, over 90% of beneficiaries follow that default. We then develop a general framework for choice under costly cognition that allows for the possibility that either paternalistic defaults that steer consumers to plans that suit them (Thaler and Sunstein 2008) or ‘shocking’ defaults that trigger consumers to make active choices (Carroll et al. 2009) could be optimal. We show that optimal default design depends on a previously-overlooked parameter: The elasticity of active choice propensity with respect to the value of the default. Leveraging variation in the match value of randomly-assigned default plans, we estimate an elasticity close to zero: There is little difference in the probability of active choice between beneficiaries assigned a well-matched default versus beneficiaries assigned a poorly-matched default. We also show that this passivity has real consequences, with beneficiaries assigned poorly-matched defaults experiencing large declines in drug consumption relative to those assigned well-matched defaults. This suggests that any potential welfare gains from an active choice response induced by a poorly-matched default are likely to be small and outweighed by the welfare losses due to reductions in drug consumption among beneficiaries who follow the poorly-matched default. Using a third natural experiment and a structural model of attention, we find that the little active choice that is present in this market appears to be largely random, with two-thirds of the variation in active choice coming from within-beneficiary transitory shocks to attention. Our results show that default rules are an integral part of insurance market design and that beneficiaries are likely to benefit from paternalistic defaults rather than be hurt by them.