Lingfeng Lyu, Michael Sherris and Mengyi Xu

Means tests reserve public support, including care, for retirees of limited means. Income tests reduce it as income rises, and assets tests stop it above a wealth cut-off. Buyers of private long-term care insurance face an implicit tax, the share of each payout lost to reduced support. We find that the tax lowers coverage even for retirees who start far above the cut-off. Although no payout is taxed above it, consumption and risk can later push wealth below it. In the model a retiree buys coverage once while healthy, consumes and invests, may need care and may value bequests. Support stops at the cut-off and wealth cannot go negative, so Merton’s solution does not apply. Without a bequest motive, we use convex duality to solve the care phase. In our calibration a retiree below the cut-off keeps under half of each payout, so the premium is over twice what they expect to keep. With unbounded leverage, coverage stays under a third of the cost of care up to five times the cut-off. With a bequest motive added, the tax almost removes coverage. Even then, weakening income tests enough raises coverage at all these wealths for little extra public cost. A leverage cap lowers coverage, but exempting payouts from income tests still raises it. Lowering the cut-off raises coverage a little, with a bequest motive only at higher wealth. Yet retirees above the present cut-off lose more than the government saves, since the support removed comes only when they are poorer.