Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard
Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard

Author: Joseph E. Stiglitz

Publisher:

Published: 2013

Total Pages:

ISBN-13:

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This paper analyzes optimal and equilibrium insurance contracts under adverse selection and moral hazard, comparing them with those under a single informational asymmetry. The complex interactions of self-selection and moral hazard constraints have important consequences. We develop an analytic approach that allows a characterization of equilibrium and optimal (Pareto Optimal (PO), and Utilitarian optimal (UO)) allocations. Among the results : (i) a PO allocation may involve "shirking" (not only less care in accident avoidance than is possible, but less care compared to the case of pure moral hazard) either by high risk individuals in the case of single-crossing preference or by one or both types in the case of multi-crossing preference (as may naturally be the case under the double informational asymmetry); and (ii) while an equilibrium, which is unique (even under multi-crossing preferences) if it exists, is more likely to exist as the non-shirking constraint for low-risk type gets more stringent (i.e. when low risk individuals shirk with lower levels of insurance). We also show that a pooling equilibrium, which is not feasible under pure adverse selection, may exist when individuals differ in risk aversion (as well as in accident probability) or when the provision of insurance is non-exclusive (i.e. individuals can purchase insurance from more than one firm). Furthermore, while with pure adverse selection, UO always entails pooling with complete insurance (in the standard model), with adverse selection and moral hazard, all PO allocations may entail separation and the UO may entail incomplete insurance. We show further that, in general, any PO allocation can be implemented by a basic pooling insurance provided by the government and a supplemental separating contracts that can be offered by the market, although, in the presence of moral hazard, a tax needs to be imposed upon the market provision. The analysis suggests that two commonly obser.

Price Equilibrium, Efficiency, and Decentralizability in Insurance Markets
Price Equilibrium, Efficiency, and Decentralizability in Insurance Markets

Author: Richard Arnott

Publisher:

Published: 1991

Total Pages: 80

ISBN-13:

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In this paper, we investigate the descriptive and normative properties of competitive equilibrium with moral hazard when firms offer "price contracts" which allow clients to purchase as much insurance as they wish at the quoted prices. We show that a price equilibrium always exists and is one of three types: i) zero profit price equilibrium - zero profit, zero effort, full insurance ii) positive profit price equilibrium - positive profit, positive effort, partial insurance iii) zero insurance price equilibrium - zero insurance, zero profit, positive effort. We also demonstrate circumstances under which the linear taxation of price insurance allows decentralization of the social optimum (conditional on the unobservability of effort), and when it, does not, whether it is at least utility-improving

Moral Hazard in Health Insurance
Moral Hazard in Health Insurance

Author: Amy Finkelstein

Publisher: Columbia University Press

Published: 2014-12-02

Total Pages: 161

ISBN-13: 0231538685

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Addressing the challenge of covering heath care expenses—while minimizing economic risks. Moral hazard—the tendency to change behavior when the cost of that behavior will be borne by others—is a particularly tricky question when considering health care. Kenneth J. Arrow’s seminal 1963 paper on this topic (included in this volume) was one of the first to explore the implication of moral hazard for health care, and Amy Finkelstein—recognized as one of the world’s foremost experts on the topic—here examines this issue in the context of contemporary American health care policy. Drawing on research from both the original RAND Health Insurance Experiment and her own research, including a 2008 Health Insurance Experiment in Oregon, Finkelstein presents compelling evidence that health insurance does indeed affect medical spending and encourages policy solutions that acknowledge and account for this. The volume also features commentaries and insights from other renowned economists, including an introduction by Joseph P. Newhouse that provides context for the discussion, a commentary from Jonathan Gruber that considers provider-side moral hazard, and reflections from Joseph E. Stiglitz and Kenneth J. Arrow. “Reads like a fireside chat among a group of distinguished, articulate health economists.” —Choice

Existence of Equilibria in Competitive Insurance Markets
Existence of Equilibria in Competitive Insurance Markets

Author: Peter S. Faynzilberg

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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Under the conditions conjectured by Rothschild and Stiglitz (1976)as leading to market failure, we demonstrate the existence of a uniqueequilibrium in a risk-sharing economy with adverse selection. This equilibrium may be separating or partially pooling: in an economy withthree types, for instance, the low- and the medium-risk buyer segmentsmay be offered the same insurance policy.In equilibrium, buyers' indirect utility decreases with their propensityfor accident. When low-risk buyers are prevalent, sellers subsidizetheir operations across segments: they derive a positive profit in thelow-risk segment and incur a loss of equal magnitude in the rest ofthe economy. This leaves high-risk buyers better off than under thefirst-best policy they purchase when sellers are perfectly informed.In contrast to the putative equilibrium of the Rothschild-Stiglitzmodel, the second-best equilibrium depends on the structure of thebuyer population and converges to the first-best of the correspondinghomogeneous population as low- risk buyers become increasingly prevalentin the economy.

Insurance Contracting with the Coexistence of Adverse Selection and Moral Hazard
Insurance Contracting with the Coexistence of Adverse Selection and Moral Hazard

Author: Zhiqiang Yan

Publisher:

Published: 2014

Total Pages: 40

ISBN-13:

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The asymmetric information problem has been widely discussed in the context of insurance markets. Most of previous research usually treats adverse selection and moral hazard separately, though it is quite possible that they may coexist and interact with each other. In this paper, we build a principal-agent model to examine optimal contracts in a competitive insurance market facing adverse selection and moral hazard simultaneously. We apply the change-of-variable method and the Kuhn-Tucker conditions to solve the optimization programs and find that there are several forms of separating Nash equilibria, although separating Nash equilibria may not exist. Our model brings richer equilibria and retains some properties in the benchmark models of pure adverse selection and pure moral hazard. For example, no agent is offered full insurance, and the positive correlation between insurance coverage and risk type still holds. Our study on comparative statics indicates that, under some conditions, the optimal indemnity and premium, in general, decrease with the disutility, increase with the potential loss and decrease with the intial wealth of the insured.