Title: Optimal Demand Management Policies With Probability Weighting
Abstract: Received theory of insurance (Pauly (1968) and Zeckhauser (1970)) suggest that demand management policies (i.e. deductibles or coinsurance rates) allow to strike the right balance between the consumer's desire to insure and the incentives problem created by insurance; since insurance gives access to health services without having to face their full financial cost, it results in overexpenditure if the state of health is not fully contractible (ex-post moral hazard). Optimal insurance policies are calculated so as to maximize consumer's expected utility, taking into account how the fraction of cost born by consumers affects demand after the purchase of insurance. However, the theoretical literature on decision under risk is ripe with experimental and empirical observations of systematic violations of the axioms underlying expected utility. Promising alternative theories that fare better, at least in the description of how choices under risk are actually taken, are rankdependent theories like the theory of anticipated utility (Quiggin (1982)) and cumulative prospect theory (Tversky and Kahneman (1992)). These theories distinguish between attitudes towards risk, features of utility functions that measure sensitivity towards outcomes, and attitudes towards probability, that substitute objective probabilities with so called decision weights in calculating the value of a prospect. An early paper pointing to the relevance of prospect theory considerations in the choice of health plans is Ellis (1989). The present paper reviews the optimality of partial insurance for individuals affected by probability weighting. We consider a simple model of health insurance where illness comes in two severity levels; a fixed-cost treatment that fully eliminates the consequences of illness should be applied in the severe state only. Our model is a simplified version of the one in Ma and Riordan (2002). If severity were observable to the insurer, individuals should be exactly compensated for the financial losses incurred when ill. Otherwise, it is optimal ex-ante to purchase partial insurance, if the difference between the cost of treatment and the losses due to low severity is large enough. The introduction of decision weights changes the value of insurance ex-ante. As a result, the optimality of partial insurance depends on the probability of illness. We show that full insurance is preferred more often for low illness probability, whereas partial insurance is preferred more often for high illness probability. We then illustrate with examples, how consumers affected by probability weighting may react when they are offered objectively optimal second-best contracts (those that maximize expected utility instead of the subjective value of insurance). In particular, in the presence of moderate optimism, when the consequences of severe illness are overweighted but the consequences of illness in general are underweighted, consumers who would like to insure partially may find the classical second-best contracts too expensive and, thus, choose not to insure. This points to the desirability of a minimum compulsory level of insurance for important losses that are typically underweighted.
Publication Year: 2006
Publication Date: 2006-02-01
Language: en
Type: article
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