Abstract
This paper analyzes the choice of deductible in insurance contracts that insure against a risk that, as is common, might materialize more than once during the life of the policy. As was established by Arrow (1963), from the perspective of risk-bearing costs, the optimal contract is one that uses an aggregate deductible that applies to the aggregate losses incurred over the life of the policy. Aggregate deductibles, however, are uncommon in practice. This paper identifies two disadvantages that aggregate deductibles have. Aggregate deductibles are shown to produce higher expected verification costs and moral hazard costs than contracts that apply a per-loss deductible to each loss that occurs. I further show that each of these disadvantages can make an aggregate deductible contact inferior to a contract with per loss deductibles. The results of the analysis can help explain the rare use of aggregate deductibles and, in addition, might explain why umbrella policies that cover all types of losses are rarely used.
On the design of optimal health insurance contracts under ex post moral hazard
