Optimal deterrents to malingering : the role of incentives, attitudes and information costs in social insurance, especially sickness benefit and welfare

Abstract: In a sequence of four models which all generalize the single-period model of Diamond and Mirrlees (1978), we explain and optimize the structure of static social insurance against health-related disability in an economy where detected cheaters feel ashamed, where some of the workers are more honest than the others, and where the cost of ascertaining disease and disability varies. Given the insurance the workers report their disease to the insurer who benevolently chooses the consumption in each state and the probability with which to use his test of disease and disability. After analyzing insurance which tolerates malingering it is found that if a great enough proportion of the population is honest enough, the insurer needs no deterrents to malingering. The critical proportion of honest workers is found to increase with the exogenous weight of the honest in the social welfare function and, in a numerical example, to increase with risk aversion. Such a unique critical proportion may not exist if the social welfare weight depends on the proportion of honest workers. Given that honesty is not sufficiently common, a dual insurance structure is characterized. For disabilities with a screening cost lower than a critical level, the incomplete optimal insurance is of the sickness benefit type, i.e., it is characterized by a positive probability of screening, which, however, is strictly less than one. Both screening and extent of insurance are used here as deterrents to malingering. Moreover, given that the probability of screening is positive, the marginal cost of the test equals the cheater's gain from passing the test only if the shadow price of shame equals the shadow price of resources multiplied by the probability of sickness. In a numerical example the effects of variations in health, shame, screening cost, disutility of labour and risk aversion are studied. Disabilities with a screening cost higher than the critical level are insured by welfare, which is incomplete insurance and characterized by a zero probability of screening. The benefit is, given some additional conditions, lower than the sickness benefit, reflecting, also, that only the extent of insurance deters malingering. Not all diseases are insured by sickness benefit; in societies that are sufficiently poor, given some conditions, all diseases should be insured by welfare.