Incentives of agency theory – Knight, Arrow, Pauly: Incentives in Insurance

The notion of moral hazard, i.e., the ability of insured agents to affect the proba- bilities of insured events, was well known in the insurance profession.15 However, the insurance writers tended to look upon this phenomenon as a moral or ethical problem affecting their business.

Arrow (1963b) introduced this concept in the economic literature and argued that it led to a market failure because some insurance markets would not emerge due to moral hazard. Arrow was quite influenced by the moral connotation of the concept and looked for solutions involving changes of ethical attitudes. Pauly (1968) rejected this approach, by arguing that it was quite natural for agents to react to zero price—like demanding more health care if treatment was free— and that the noninsurability of some risks did not imply a market failure in that no proof was given of the superiority of public intervention faced with the same informational problems. Pauly (1974) and Helpman and Laffont (1975) showed that competitive insurance markets (with linear prices) were inefficient in the sense that an uninformed government could improve upon the free market outcome.

Spence and Zeckhauser (1971) looked for more sophisticated contracts (non- linear prices). They solved the maximization of the welfare of a representative agent with a break-even constraint for the insurance company and the moral haz- ard constraint that each agent chooses his level of self-protection optimally. When the self-protection variable is chosen before nature selects the states of nature (i.e., who has an accident, who does not), they obtained the moral hazard model with a continuum of agents and a break-even constraint. When the self-protection vari- able is chosen after nature selects the states of nature, they have both moral hazard and adverse selection, making the problem quite close to the Mirrlees optimal income tax problem (as already noted by Zeckhauser 1970).

Ross (1973) expressed the pure principal-agent model with only moral hazard and an individual rationality constraint for the agent before it received its modern treatment in Mirrlees (1975), Guesnerie and Laffont (1979), Holmström (1979), Shavell (1979), and later in Grossman and Hart (1983).

The Pareto inefficiency of competitive insurance markets (with linear prices) with adverse selection was shown in Rothschild and Stiglitz (1976),18 and their successors studied various forms of competition in nonlinear tariffs. As in the case of moral hazard, one can also study the optimal nonlinear tariff, which maximizes the expected welfare of a population of agents having private information about their own risk characteristics.19 However, this problem was encountered earlier in the literature on price discrimination with quality replacing quantity.

Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.

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