Lingfeng Lyu, Michael Sherris and Mengyi Xu

Means tests reserve public support, care included, for retirees of limited means: income tests reduce it as income rises; an asset test stops it above a wealth threshold. Yet even wealthier retirees, seemingly beyond these tests, rarely buy long-term care insurance. Such insurance is penalised by an implicit tax: the support lost because payouts count as income. We show that the tax lowers coverage even for retirees far above the threshold: with no public support above it, consumption and risk can run wealth below it, where payouts reduce support. We derive this in a model where a healthy retiree buys coverage once, consumes and invests, may need care and may value bequests. Merton’s solution does not apply: support stops abruptly at the threshold, and wealth cannot go negative. Without a bequest motive, convex duality solves the care phase explicitly up to two scalars, and the rest is numerical. In our calibration, a retiree below the threshold keeps under half of each payout, so the premium is over twice what they expect to keep. For wealth up to five times the threshold, optimal coverage is below a third of the cost of care, and a bequest motive can bring it near zero. Exempting payouts from income tests raises coverage at all these wealth levels, even with a bequest motive, at little extra public cost. Without a bequest motive, abolishing the asset test lowers coverage for all but the poorest, mainly because everyone then qualifies for support and payouts reduce it.