Single-year and multi-year insurance policies in a competitive market

This paper examines the demand and supply of annual and multi-year insurance contracts with respect to protection against a catastrophic risk in a competitive market. Insurers who offer annual policies can cancel policies at the end of each year and change the premium in the following year. Multi-year insurance has a fixed annual price for each year and no cancellations are permitted at the end of any given year. Homeowners are identical with respect to their exposure to the hazard. Each homeowner determines whether or not to purchase an annual or multi-year contract so as to maximize her expected utility. The competitive equilibrium consists of a set of prices where homeowners who are not very risk averse decide to be uninsured. Other individuals demand either single-year or multi-year policies depending on their degree of risk aversion and the premiums charged by insurers for each type of policy.     

Optimal insurance without expected utility: The dual theory and the linearity of insurance contracts

Models of the insurance markets and institutions are routinely based on expected utility. Since EU is being challenged by an increasing number of decision models, we examine whether EU-based models are robust in their predictions. To do so, we rework some basic models of optimal insurance contracts and equilibrium using the “dual” theory to EU of Yaari. When there is a single, insurable source of risk, dual theory permits only corner solutions if the contract itself is linear. This contrasts sharply with EU. Nonlinearity, and thereby the possibility of interior solutions, is introduced in two ways. First, the contract itself is nonlinear, i.e., a deductible insurance policy. Or second, the decision maker is subject to some background risk such as uninsurable risky assets or default of the insurer. When decision problems are subject to nonlinearity, the predictions on optimal insurance are more similar to, though not identical with, those generated with EU.     

Experimental markets for insurance

This article extends the large amount of research on double-oral auction markets to hazards that produce only losses. We report results from a series of experiments in which subjects endowed with low-probability losses can pay a premium for insurance protection. Insurers specify the price at which they are willing to assume the risk of a loss. Insurance prices approach expected value for a large range of probabilities and loss amounts. Subjects seem to realize losses are statistically independent. Prices are not affected by ambiguity about the probability of loss.     

Choice of purchasing arrangements in insurance markets

A simple dynamic model helps explain why risk-pooling purchasing arrangements evolved for health, disability, and term life insurance but not for property, automobile, or homeowners' insurance, and why whole-life policies typify life insurance purchased on an individual basis. We show that risk-pooling purchases facilitate insurance against unpredictable changes in one's risk type, but such contracts prevail in competitive equilibrium only when the loss probabilities increase with age, as they do for health, disability, and life insurance. In contrast, when the loss probability declines with age (as it does for automobile insurance), then competitive equilibrium entails separating insurance contracts.     

Guaranteed renewability uniquely prevents adverse selection in individual health insurance

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.     

Choosing a gambling partner: testing a model of mutual insurance in the lab

In this study, we investigate how economic agents choose gambling partners and how paired risky choices differ from individual ones. To this aim, we develop a simple model and design a laboratory experiment that allows us to compare individual versus paired decisions across two treatments, where pairs are, respectively, exogenously and endogenously formed. In both treatments, paired subjects decide individually and independently how to allocate their wealth over a portfolio of lotteries and fully commit to share any winnings. The main result from our experiment is that whenever agents are allowed to choose a gambling partner they decide to team up with other agents who display the same degree of risk aversion as themselves. Moreover, paired choices consistently involve higher risk taking than individual choices. This finding is more evident when information on subjects’ risk attitudes is made available and when subjects team up in homogeneous pairs, thereby confirming that subjects successfully exploit the benefits of mutual insurance.     

Guaranteed renewability in insurance

We propose a guaranteed renewability (GR) insurance in which a sequence of premiums would enable insurers to break even and would be chosen by both low- and high-risk buyers, whether or not they had suffered a loss. The premium schedule would continually decline over time, as the insurer collects more information to determine who the low-risk buyers are. The highest premiums are charged initially to protect the insurer if low-risk individuals leave for the spot market. The concluding portion of the article discusses the limitations of a GR policy in the health and environmental liability area, the most serious being instability in estimates of underlying loss trends.     

Does insurance fraud in automobile theft insurance fluctuate with the business cycle?

Financial institutions face various cyclical risks, but very few studies have analyzed the cyclicality of operational risk. External fraud is an important operational risk faced by insurers. In this research, we analyze the empirical relationship between insurance fraud and the business cycle and we concentrate our study on two insurance contracts that may create an incentive to defraud. We find that residual insurance fraud exists both in the contract with replacement cost endorsement and the contract with no-deductible endorsement in the Taiwan automobile theft insurance market. These results are consistent with previous literature on the relationship between fraud activity and non-optimal insurance contracting. We also show that the severity of insurance fraud is countercyclical. Fraud is stimulated during periods of recession and mitigated during periods of expansion. Although this last result seems intuitive, our contribution is the first to measure its significance.     

Premium Risk and Managed Care

This paper analyzes how individuals can insure premium risk and obtain high quality health insurance in a managed care environment. Insurers choose health care providers. Only a fraction of high risk individuals is unambiguously identifiable in front of a court. Premium insurance is not able to reach a first-best risk allocation while health insurers have an incentive to stint on quality under guaranteed renewable contracts. It is shown that a contract exists which can implement the first-best. This contract specifies payments to individuals and a third party upon switching to create a credible self-commitment by the insurer to provide high quality.     

Probabilistic Insurance

Probabilistic insurance is an insurance policy involving a small probability that the consumer will not be reimbursed. Survey data suggest that people dislike probabilistic insurance and demand more than a 20% reduction in the premium to compensate for a 1% default risk. While these preferences are intuitively appealing they are difficult to reconcile with expected utility theory. Under highly plausible assumptions about the utility function, willingness to pay for probabilistic insurance should be very close to willingness to pay for standard insurance less the default risk. However, the reluctance to buy probabilistic insurance is predicted by the weighting function of prospect theory. This finding highlights the potential role of the weighting function to explain insurance.     

Voluntary social insurance for Vietnamese laborers in the informal economic sector

Voluntary social insurance (VSI), a type of social insurance organized by the Government, allows participants, who work in the informal sector with unstable jobs and income, to choose the premium and payment methods in accordance with their income for their retirement plan. The rate of Vietnamese laborers participating in VSI is low. This study aims to examine the current situation of VSI participation of laborers, as well as their perception of VSI visibility and assessment of VSI policies and utilization. Results from survey with 293 laborers, including 144 VSI participants and 149 VSI non‐participants, and semi‐structured interviews with 60 stakeholders in two districts in Northern Vietnam show the lack of awareness of VSI existence among non‐VSI participants, and limited knowledge of VSI policies among VSI participants. Although participants endorsed beneficiaries and premium in the retirement plan, they were concerned about the long 20‐year premium payment duration in the situation of unstable jobs and income, and the lack of other benefits, for example, maternity leave and unemployment benefit. Results recommend better propagandas, distributed documents, and educational sessions on VSI policies on mass and social media, as well as at VSI conferences and their workplace.     

An Experiment on Rational Insurance Decisions

We describe the results of an experiment on decision making in an insurance context. The experiment was designed to test for the underlying rationality of insurance consumers, where rationality is understood in usual economic terms. In particular, using expected utility as the preference function, we test for positive marginal utility, risk aversion, and decreasing absolute risk aversion, all of which are normal postulates for any microeconomic decision context under uncertainty or risk. We find that there the discrepancy from rational decision making increases with the sophistication of the rationality criteria, that irrationality concerning fair premium contracts is uncharacteristically high, and that the slope of absolute risk aversion seems to depend on the format of the insurance contract. This revised version was published online in June 2006 with corrections to the Cover Date.     

The risky business of insurance pricing

The factors influencing insurance pricing decisions are assessed using the ISO product liability ratemaking files for 1980–1984. The mean loss level has a strong positive effect on manual rates and premium rates/exposure. Evidence on a variety of ambiguity measures is more mixed. As a broad generalization, risk ambiguity lowers manual rates, which may reflect exclusion of large loss outliers as being unrepresentative. Risk ambiguity tends to have a positive effect on actual pricing decisions for particular policies, especially bodily injury lines and the interactive risk-ambiguity model.     

Availability Crises in Insurance Markets: Optimal Contracts with Asymmetric Information and Capacity Constraints

Insurance markets sometimes exhibit "crises" in which prices rise dramatically and coverage is unavailable or is rationed at the new prices. A recent explanation for such crises is the "capacity constraint" model of Gron and Winter. Crises usually follow sudden and large depletions in insurers' equity or surplus. The capacity constraint model argues that frictional costs in replacing surplus, and limited liability, give rise to a kinked insurance supply function and that crises arise from discontinuous short term adjustments around the kink. While this model explains much about liability insurance crises, it still leaves unexplained their most prominent feature; that insurance is rationed or unavailable. We follow their insight in looking to equity shocks and capital market frictions to explain crises and combine this with a model of optimal risk sharing contracts under the information conditions characteristic of this market. We use implicit long term contracts with truth telling constraints to address information asymmetries and this allows us to model crises that exhibit rationing. Our model is tested in the market most dramatically affected by such crises in the 1980‘s, the general liability insurance market.     

Precarious workers' choices about unemployment insurance membership after the Ghent system reform: The Finnish experience

The literature on the Ghent system has focused on the link between voluntary unemployment insurance and union membership in terms of industrial relations. Less attention has been paid to unemployment benefits and employees' decision‐making concerning unemployment insurance, even though the core function of the Ghent system is to provide unemployment insurance. This paper examines both of the options that precarious workers (i.e., part‐timers, temporary employees, and low‐skilled service employees) choose regarding unemployment insurance membership and the change in union density after the Ghent system reform in Finland. First, the results show that the growth of the independent unemployment insurance fund was the main reason for declining union density in the 2000s and early 2010s. Second, in terms of precarious workers, we find that the emergence of the independent fund has affected their choices about unemployment insurance membership and that their choices depend on the type of precarious employment they have. Moreover, part‐timers and temporary employees younger than 35 years of age are much less likely to enroll in unemployment insurance than older employees who have the same types of employment contracts.     

Adverse selection and equilibrium in liability insurance markets

Models of asymmetric information in insurance markets typically consider insurance buyers with Bernoulli loss distributions differing in expected loss. This article analyzes markets where buyer loss distributions are characterized by mean-preserving spreads and insurers can classify applicants in terms of expected values but not by risk. Because liability losses are characterized by skewed continuous probability distributions, both discrete and continuous loss distributions are considered. In contrast to the single separating equilibrium in the classic Rothschild-Stiglitz insurance market, multiple separating equilibria are identified in this article: three in the discrete case and four in the continuous case. The possibility of extreme discontinuities in insurer policy offers provides a new explanation for crises in liability insurance markets.The support of the National Association of Insurance Commissioners is gratefully acknowledged.     

Insurance supply with capacity constraints and endogenous insolvency risk

Negative shocks to industry capital and significant capital adjustment costs have been offered as an explanation of periodic “crises” in the property-liability insurance market. According to these capacity constraint models, in which post-shock production must meet a solvency constraint, increases in price can cause some or perhaps all of the cost of a negative shock to capital to be shifted to policyholders. This article develops a model of insurance supply with capacity constraints and endogenous insolvency risk that incorporates limited liability and potential loss of insurer intangible capital. If industry demand is inelastic with respect to price and capital, the model predicts that price will increase following a negative shock to capital, but by less than the amount needed to fully offset the shock. Equity value and the expected recovery by policyholders for post-shock production are predicted to decline. Elastic demand mitigates shock-induced price increases.     

Excluded losses and the demand for insurance

The demand for insurance is examined when the insured asset can incur losses that are excluded from insurance coverage. These losses are negatively correlated with covered losses and hence cannot be treated as background risk. Excluded losses have strikingly different effects on the demand for insurance than does background risk and lead to a modification of many standard insurance demand results. A number of new theorems concerning the effects of excluded losses are also presented. Risk-averse and prudent decision makers reduce their demand for insurance when excluded losses increase in size or riskiness. Excluded losses are a possible explanation for why many decision makers fail to take up insurance when it is offered.     

Macroeconomic and financing determinants of out of pocket payments in health care: Evidence from selected OECD countries

In this paper, we examine the impact of macroeconomic, as well public and private health insurance financing (PHI) factors on out of pocket (OOP) healthcare expenditures, by using fixed/random effects and dynamic panel data methodology to a dataset of 26 EU and OECD countries for a period lasting from 1995 to 2013. The existing empirical literature has focused on testing the hypothesis that several macroeconomic and health financing determinants have an effect on OOP healthcare expenditures. Nevertheless, the related articles have not well tested the hypothesis concerning the potential impact of PHI financing on OOP spending. We find that public and PHI financing have a significant countervailing effect on OOP spending. Moreover, we show that unemployment rate has a significant positive impact on OOP expenditures. Sensitivity tests with variation of specifications and samples show that our findings are robust. We argue that policy-makers should give serious consideration to PHI institution; our results indicate that there is an inverse effect on OOP spending. We suggest that our examined countries have to provide financial risk protection to their citizens against OOP payments, rather than only attending health budgetary retrenchments in order to adjust public finances.     

The impact of governmental assistance on insurance demand under ambiguity: a theoretical model and an experimental test

This article deals with the impact of governmental assistance on insurance demand under ambiguity, i.e., in situations where probabilities are uncertain. First, using a model of insurance demand under ambiguity, we derive theoretical predictions about the impact of several governmental assistance programmes on optimal insurance demand. For example, governmental assistance through a fixed public support scheme implies that partial insurance is always optimal under fair insurance with ambiguity. Second, we present the results of an experiment designed to test these predictions. We find support for several of our theoretical predictions. For example, the presence of governmental assistance through a fixed public support scheme decreases individuals’ willingness to pay to be fully insured. Finally, we compare these results with those obtained for a risk situation. We find that, regardless of the form of governmental assistance, participants in the ambiguity context are consistently willing to pay more to be fully insured than participants in the risk situation.