A voluntary deductible in health insurance: the more years you opt for it, the lower your premium?

Adverse selection regarding a voluntary deductible (VD) in health insurance implies that insured only opt for a VD if they expect no (or few) healthcare expenses. This paper investigates two potential strategies to reduce adverse selection: (1) differentiating the premium to the duration of the contract for which the VD holds (ex-ante approach) and (2) differentiating the premium to the number of years for which insured have opted for a VD (ex-post approach). It can be hypothesized that premiums will decrease with the duration of the contract or the number of years for which insured have opted for a VD, providing an incentive to insured to opt for a deductible also in (incidental) years they expect relatively high expenses. To test this hypothesis, we examine which premium patterns would occur under these strategies using data on healthcare expenses and risk characteristics of over 750,000 insured from 6 years. Our results show that, under the assumptions made, only without risk equalization the premiums could decrease with the duration of the contract or the number of years for which insured have opted for a VD. With (sophisticated) risk equalization, decreasing premiums seem unfeasible, both under the ex-ante and ex-post approach. Given these findings, we are sceptical about the feasibility of these strategies to counteract adverse selection.