Within an asymmetric information set-up in which individuals differ in terms of their risk aversion and can choose whether or not to take preventative action, we illustrate in a unified framework the equilibrium possibilities with stand-alone long-term care insurance and annuity contracts. With costs of administering insurance, so that insurance is unfair, we show the existence of an equilibrium in which the risk averse type, who take more preventative action, obtain more of both types of insurance, even though their probability of using long-tern care coverage is lower than the less risk averse. Hence, we show that the empirical observations of Finkelstein and Poterba (2004) and Finkelstein and McGarry (2003) are consistent with simultaneous separating equilibria in the two markets. A key finding of the paper is that as individuals who take care will be relatively low risk in the long-term care insurance market but high risk in the annuities market, with the opposite being the case for those who take less preventative action, an equilibrium exists in bundled contracts that Pareto dominates the outcome with stand-alone contracts.
Also included in: UBS Pensions Series 034.