The standard Medicare Part D drug insurance contract is nonlinear – with reduced subsidies in a coverage gap – resulting in a dynamic purchase problem. We consider enrollees who arrived near the gap early in the year and show that they should expect to enter the gap with high probability, implying that, under a benchmark model with neoclassical preferences, the gap should impact them very little. We find that these enrollees have flat spending in a period before the doughnut hole and a large spending drop in the gap, providing evidence against the benchmark model. We structurally estimate behavioral dynamic drug purchase models and find that a price salience model where enrollees do not incorporate future prices into their decision making at all fits the data best. For a nationally representative sample, full price salience would decrease enrollee spending by 31%. Entirely eliminating the gap would increase insurer spending 27%, compared to 7% for generic-drug-only gap coverage.