Adverse selection in health insurance: are first best contracts impossible ? (original) (raw)

Adverse selection and moral hazard in health insurance

In this paper, we want to characterize the optimal health insurance contract with adverse selection and moral hazard. We assume that policyholders di¤er by the permanent health status loss and choose an unobservable preventive e¤ort in order to reduce the probability of illness which is ex-ante identical. The di¤erence in illness'after-e¤ect modi…es policyholders' preventive actions. By the way, they di¤er in probabilities of illness leading to a situation close to Rothschild and Stiglitz 'model. In this case, we show that the optimal contract exhibits a deductible for the high health risk type since a higher after e¤ect implies a higher preventive e¤ort and then a lower probability of illness rather than for the low health risk type.

Optimal insurance contracts with adverse selection and comonotonic background risk

In this note, we consider an adverse selection problem involving an insurance market à la Rothschild-Stiglitz. We assume that part of the loss is uninsurable as in the case with health care or environmental risk. We characterize su¢ cient conditions such that adverse selection by itself does not distort competitive insurance contracts. A su¢ ciently large uninsurable loss provides an incentive to high-risk policyholders not to mimic low-risk policyholders without distorting the optimal coverage.

Adverse Selection in Insurance Markets

2000

In this survey we present some of the more signi…cant results in the literature on adverse selection in insurance markets. Sections 1 and 2 introduce the subject and section 3 discusses the monopoly model developed by for the case of single-period contracts and extended by many authors to the multiperiod case. The introduction of multi-period contracts raises many issues that are discussed in detail : time horizon, discounting, commitment of the parties, contract renegotiation and accidents underreporting. Section 4 covers the literature on competitive contracts. The analysis becomes more complicated since insurance companies must take into account competitive pressures when they set incentives contracts. As pointed out by , there is not necessarily a Cournot-Nash equilibrium in presence of adverse selection. However, market equilibrium can be sustained when principals anticipate competitive reactions to their behaviour or when they adopt strategies that di¤er from the pure Nash strategy. Multi-period contracting is discussed. We show that di¤erent predictions on the evolution of insurer pro…ts over time can be obtained from di¤erent assumptions concerning the sharing of information between insurers about individual's choice of contracts and accidents experience. The roles of commitment and renegotiation between the parties to the contract are important. Section 5 introduces models that consider moral hazard and adverse selection simultaneously and section 6 treats adverse selection when people can choose their risk status. Section 7 discusses many extensions to the basic models such as risk categorization, di¤erent risk aversion, symmetric imperfect information, multiple risks, principals more informed than agents and uberrima …des.

Adverse Selection in Insurance Contracting

SSRN Electronic Journal, 2012

In this survey we present some of the more signi…cant results in the literature on adverse selection in insurance markets. Sections 1 and 2 introduce the subject and Section 3 discusses the monopoly model developed by Stiglitz (1977) for the case of single-period contracts extended by many authors to the multi-period case. The introduction of multi-period contracts raises many issues that are discussed in detail; time horizon, discounting, commitment of the parties, contract renegotiation and accidents underreporting. Section 4 covers the literature on competitive contracts. The analysis is more complicated because insurance companies must take into account competitive pressures when they set incentive contracts. As pointed out by Rothschild and Stiglitz (1976), there is not necessarily a Cournot-Nash equilibrium in the presence of adverse selection. However, market equilibrium can be sustained when principals anticipate competitive reactions to their behavior or when they adopt strategies that di¤er from the pure Nash strategy. Multi-period contracting is discussed. We show that di¤erent predictions on the evolution of insurer pro…ts over time can be obtained from di¤erent assumptions concerning the sharing of information between insurers about individual's choice of contracts and accident experience. The roles of commitment and renegotiation between the parties to the contract are important. Section 5 introduces models that consider moral hazard and adverse selection simultaneously and Section 6 covers adverse selection when people can choose their risk status. Section 7 discusses many extensions to the basic models such as risk categorization, multidimensional adverse selection, symmetric imperfect information, reversed or double-sided adverse selection, principals more informed than agents, uberrima …des and participating contracts.

Optimal health insurance contract : can moral hazard increase indemnity ?

2006

In this note, we generalize the results obtained by Barday and Lesur (2005) by considering a bivariated non separable utility function. We characterize optimal health insurance contracts. Moreover, we show that under moral hazard a sufficiently high risk aversion implies that the optimal coverage and the optimal preventive effort are higher than with perfect information.

Optimal insurance with adverse selection and comonotonic background risk

2007

In this note, we consider an adverse selection problem involving an insurance market a la Rothschild-Stiglitz. We assume that part of the loss is uninsurable as in the case with health care or environmental risk. We characterize sufficient conditions such that adverse selection by itself does not distort competitive insurance contracts. A sufficiently large uninsurable loss provides an incentive to high-risk policy holders not to mimic low-risk policy holders without distorting the optimal coverage.

Guaranteed renewability uniquely prevents adverse selection in individual health insurance

Journal of Risk and Uncertainty, 2011

New models of multi-period insurance show that health insurance buyers can be protected against changes in premiums from health shocks associated with chronic conditions by the addition of "guaranteed renewability" provisions. These models assume that a buyer's risk level in every time period is observed by all insurers. They also require a premium sequence that is "front-loaded," which may be costly to buyers if capital markets are imperfect. We relax the common knowledge feature of the model by assuming that a person's risk in any time period is known only by that individual and the current insurer. One might suspect that a premium sequence with higher later period premiums would be incentive compatible because low risks will have less desirable offerings from alternative insurers. However, we show that generally, only the original premium schedule is incentive compatible, and attempts to alter front-loading will not be an equilibrium.

(Neutrally) Optimal Mechanism Under Adverse Selection: The Canonical Insurance Problem

SSRN Electronic Journal, 2000

This paper revisits the problem of adverse selection in the insurance market of Rothschild and Stiglitz [35]. We extend the three-stage game in Hellwig [19] by allowing firms to endogenously choose whether or not to pre-commit on their contractual offers (menus). We show how this mechanism can deliver the Miyazaki-Wilson-Spence allocation as the unique perfect-Bayesian equilibrium. This allocation is the unique incentive-efficient and individually-rational maximizer of the utility of the most profitable type. In fact, given that the informed player has only two types, it is the unique core allocation and thus the unique neutral optimum in the sense of Myerson [29].

Insurance under moral hazard and adverse selection: The case of pure competition

1997

We consider a model of pure competition between insurers a la Rothschild-Stiglitz, where two types of agents privately choose an effort level, and where the effort costs and the resulting accident probabilities differ across agents. We characterize the set of possible separating equilibria, with a special emphasis on the case where the Spence-Mirrlees condition is not satisfied. We show, in particular, that several equilibria a la Rothschild-Stiglitz may coexist; that they are Pareto-ranked, only the best of them being an equilibrium in the sense of Hahn (1978); and that equilibria may take original forms (for instance, both revelation constraints may then be binding). Finally, we discuss the existence of an equilibrium in this context, and show that, though equilibria may fail to exist, conditions for existence may differ from those in the initial Rothschild-Stiglitz setting.