Penalty mandates are used in many countries to encourage people to purchase health insurance. But are they effective? We use a large administrative dataset for a 10% random sample of all Australian tax-filers to study how people respond to a step-wise age-based mandate, and whether this has changed over time. The mandate creates discontinuities in the incentive to insure by age, which we exploit to estimate causal effects. People who do not insure before the penalty dates face higher premiums in the future, which should encourage them to bring forward purchases. We find that people respond as expected to the initial age-penalty, but not to subsequent penalties. The 2% premium loading results in a 1-4% increase in take-up, with effects increasing after an annual government letter campaign that reminds people approaching the penalty deadline about the policy. We discuss the impact of the mandate on the overall efficiency of the market, and implications of potential reforms.