On the Role of Patience in an Insurance Market With Asymmetric Information

We analyze a two-period competitive insurance market that is characterized by the simultaneous presence of moral hazard and adverse selection with regard to consumer time preferences. It is shown that there exists an equilibrium in which patient consumers use high effort and buy an insurance contract with high coverage, whereas impatient consumers use low effort and buy a contract with low coverage or even remain uninsured. This finding may help to explain why the opposite of adverse selection with regard to risk types can sometimes be observed empirically.     

First-Best Equilibrium in Insurance Markets With Transaction Costs and Heterogeneity

We investigate extensions of the classic Rothschild and Stiglitz (1976) (RS) model of adverse selection under asymmetric information. In RS, low‐risk customers are worse off owing to an externality created by high‐risk buyers in the market. We find critical changes in insurance buyers' behavior under the joint assumptions of transaction costs and buyer heterogeneity with respect to either risk aversion or wealth. Combining transaction costs and heterogeneity, we find a separating equilibrium in which neither high‐risk nor low‐risk individuals are penalized due to information asymmetry.     

An Insurance Market Simulation With Both Adverse and Advantageous Selection

The theory of adverse selection predicts that high‐risk individuals are more likely to buy insurance than low‐risk individuals if asymmetric information regarding individuals’ risk type is present in the market. The theory of advantageous selection predicts the opposite—a negative relationship between insurance coverage and risk type can be obtained when hidden knowledge in other dimensions (e.g., the degree of risk aversion) is present in addition to the risk type. Using the heterogeneity of insurance buyers in either risk type or risk aversion, we first introduce a classroom‐based insurance market simulation game to show that adverse selection and advantageous selection can coexist. We then explain the underlying concepts using two methods: a mathematical framework based on expected utility theory and an empirical framework based on the results of the game itself. The game is easy to implement, reinforces textbook concepts by providing students a hands‐on experience, and supplements current textbooks by bringing their content up to date with current research.     

Background Risk and the Performance of Insurance Markets under Adverse Selection

Background risk can influence the performance of insurance markets that must deal with adverse selection when applicants are risk vulnerable, since they are more averse to bearing the insurable risk as a result of their exposures to background risk. We show that background risk always results in a lower deductible for the incentive constrained contract, and that a broader range of markets attains the stable sequential equilibrium cross-subsidized pair of separating contracts. We conclude that background risk always improves the performance of markets for coverage against (insurable) foreground risks that must deal with adverse selection. We also find, however, that these improvements are never sufficient to offset the cost to insureds of bearing the background risk.     

A Theory of the Demand for Underwriting

We examine the demand for underwriting and its effect on equilibrium in an insurance market in which insureds know their risk type, but insurers do not. Our analysis indicates that a set of policies including one that requires buyers to take an underwriting test can constitute a full coverage Nash equilibrium when perfect classification is possible. We also find that underwriting equilibria, in which low risks obtain greater coverage than they would without underwriting, widely exist in a Wilsonian market with nonmyopic insurers. Our findings provide a potential explanation for why empirical evidence on adverse selection is mixed.     

Testing for Asymmetric Information in the Automobile Insurance Market Under Rate Regulation

This article examines whether adverse selection or moral hazard could be induced by rate regulation, which prohibits insurance companies from considering some attributes of drivers in setting premiums. Using an individual data set from a heavily regulated automobile insurance market, we arrived at several conclusions, as follows. First, no evidence of adverse selection or moral hazard is found in general: conditional on all the variables observed by insurer, the null hypothesis of independence between risk and coverage is not rejected at reasonable levels of statistical significance. Second, this result is robust in the sense that it holds under several empirical procedures and different definitions of risk and coverage. Third, we find that unobserved variables do not induce adverse selection: the null hypothesis that consumers in risky regions are more likely to purchase insurance is tested against the alternative and rejected. Our study supports the view that the adverse selection phenomenon exists only to a very limited extent in this market.     

Competitive Insurance Markets and Adverse Selection in the Lab

We provide an experimental analysis of competitive insurance markets with adverse selection. Our parameterised version of the lemons’ model of Akerlof in the insurance context predicts total crowding-out of low risks when insurers offer a single full insurance contract. The therapy proposed by Rothschild and Stiglitz consists of adding a partial insurance contract so as to obtain self-selection of risks. We test the theoretical predictions of these two models in two experiments. A clean test is obtained by matching the parameters of these experiments and by controlling for the risk neutrality of insurers and the common risk aversion of their clients by means of the binary lottery procedure. The results reveal a partial crowding-out of low risks in the first experiment. Crowding-out is not eliminated in the second experiment and it is not even significantly reduced. Finally, instead of the predicted separating equilibrium, we find pooling equilibria. The latter can be sustained because insureds who objectively differ in their risk level do not perceive themselves as being so much different.     

Time Deductibles as Screening Devices: Competitive Markets

Seminal papers on asymmetric information in competitive insurance markets, analyzing the monetary deductible as a screening device, show that any existing equilibrium is of a separating type. High risks buy complete insurance, whereas low risks buy partial insurance—and this result holds for the Nash behavior as well as for the Wilson foresight. In this article, we analyze the strength of screening based on limitations to the period of coverage of the contract. We show that in this case (1) the Nash equilibrium may entail low risks not purchasing any insurance at all, and (2) under the Wilson foresight, a pooling equilibrium may exist.     

Testing Adverse Selection With Two‐Dimensional Information: Evidence From the Singapore Auto Insurance Market

This article examines adverse selection in insurance markets with two‐dimensional information: policyholders’ riskiness and degree of risk aversion. We build a theoretical model to make equilibrium predictions on competitive insurance screening. We study several variations on the pattern of information asymmetry. The outcomes range from full separation to partial separation, and complete pooling of risk types. Next, we propose a copula approach to jointly examine policyholders’ coverage choice and accident occurrence in the Singapore automobile insurance market. Furthermore, we invoke the theory to identify subgroups of policyholders for whom one may expect the risk–coverage correlation and adverse selection to arise.     

The Probationary Period as a Screening Device: The Monopolistic Insurer

Stiglitz [1977], considering asymmetry of information in a monopolistic insurance market and the monetary deductible as a screening device, shows that an equilibrium is always of a separating type. High risks buy complete insurance whilst low risks buy partial insurance. In this paper, we show that a pooling equilibrium may exist if a probationary period, rather than the partial coverage in monetary terms, is used as a screening device.JEL Classification No.: D42, D82     

Explaining Insurance Policy Provisions via Adverse Selection

In this article, we show that common insurance policy provisions—namely, deductibles, coinsurance, and maximum limits–can arise as a result of adverse selection in a competitive insurance market. Research on adverse selection typically builds on the assumption that different risk types suffer the same size loss and differ only in their probability of loss. In this study, we allow the severity of the insurance loss to be random and, thus, generalize the results of Rothschild and Stiglitz [1976] and Wilson [1977]. We characterize the separating equilibrium contracts in a Rothschild-Stiglitz competitive market. By further assuming a Wilson competitive market, we show that an anticipatory equilibrium might be achieved by pooling, and we characterize the optimal pooling contract.     

On the Possibility of Profitable Self-Selection Contracts in Competitive Insurance Markets

Several studies extend the Rothschild–Stiglitz model of competitive insurance contracting with adverse selection by incorporating additional dimensions of private information and conclude that some insurers may earn positive profit in a separating, self-selection equilibrium, provided each insurer is restricted to making a single contract offer. The main result of this article is that these profitable configurations are not sustainable when individual insurers can offer multiple contracts. It is also shown that the ability to offer multiple contracts overturns equilibria that have applicants from different risk classes pooled as well as those where profits are dissipated by a fixed entry cost.     

Full Insurance, Bayesian Updated Premiums, and Adverse Selection

In the classic Rothschild-Stiglitz model of adverse selection in a competitive environment, we analyse a no-claims bonus type contract (bonus-malus). We show that, under full insurance coverage, if the insurance company applies Bayes's rule to learn about client probability types over time and uses this information in premium calculations for contract renewals, then there exist conditions under which all client types strictly prefer the Bayesian updating contract to the classic Rothschild-Stiglitz separating equilibrium.     

Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk

Under Yaari's dual theory of risk, we determine the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. Also, we determine the pooling equilibrium contract when insurers are assumed non-myopic. Expected utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, we show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.     

保险市场逆向选择的信号传递博弈研究

在保险市场中,投保人比保险人更了解自己的风险状况,保险双方之间的这种信息不对称难以避免地会产生逆向选择问题,于是在保险人混同定价的情形下,低风险投保人要承受过高的费率而受损,高风险投保人因保险成本过低而削弱控制风险的激励,导致整个市场资源配置低效甚至因逆向选择螺旋而崩溃。通过引入信号传递机制来实现保险市场的分离定价,从...     

Bank credit default swaps and deposit insurance around the world

We investigate the impact of deposit insurance schemes on banks' credit risk – a predictor of failure and a key element in the current financial crisis. Unlike most studies, which use balance sheet measurements of risk, we adopt a forward-looking and market-based measure of bank credit risk: the credit default swap (CDS) spread. We find that banks in countries with explicit deposit insurance systems have higher CDS spreads, supporting the “moral hazard” view. The results suggest that deposit insurance design features that lessen the adverse impact are risk-adjusted premium, coinsurance systems, government-established systems, “risk-minimizing” systems, and systems with dual-funding sources. Full coverage appears to stabilize bank risk only during the financial crisis period. More stringent bank regulation, such as capital adequacy regulation and independent supervision, could reduce the undesirable impact of deposit insurance. Deposit insurance seems to help stabilize volatile markets, as evidenced during the financial crisis and in countries with greater market volatility. In addition, we find that the adverse impact of deposit insurance on bank credit risk is more pronounced for banks with low asset quality and low liquidity.     

Insurance loss coverage and social welfare

Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome, both for insurers and for society. However, a social benefit of modest adverse selection is that it can lead to an increase in ‘loss coverage’, defined as expected losses compensated by insurance for the whole population. We reconcile the concept of loss coverage to a utilitarian concept of social welfare commonly found in the economic literature on risk classification. For iso-elastic insurance demand, ranking risk classification schemes by (observable) loss coverage always give the same ordering as ranking by (unobservable) social welfare.     

Voluntary versus mandatory disclosure of liability insurance coverage limit

This article analyzes the disclosure of the liability insurance coverage limit and the impact of mandating disclosure of the coverage limit in a setting where voluntary disclosure of a firm’s cash flow information is subject to litigation risk and the firm has directors’ and officers’ (D&O) liability insurance. Disclosure of cash flow information is costly, but disclosure of the insurance coverage limit features no direct disclosure friction. We find that, when the litigation environment is weak, the usual unraveling argument applies, and the manager always voluntarily discloses the coverage limit in equilibrium. However, when the litigation environment is strong, either no coverage limit is disclosed or only sufficiently high coverage limits are disclosed in equilibrium. Further analysis shows that mandatory disclosure of the coverage limit increases the voluntary disclosure of cash flow information.     

How Country and Safety-Net Characteristics Affect Bank Risk-Shifting

Risk-shifting occurs when creditors or guarantors are exposed to loss without receiving adequate compensation. This paper seeks to measure and compare how well authorities in 56 countries controlled bank risk shifting during the 1990s. Although significant risk-shifting occurs on average, substantial variation exists in the effectiveness of risk control across countries. We find that the tendency for explicit deposit insurance to exacerbate risk shifting is tempered by incorporating loss-control features such as risk-sensitive premiums, coverage limits, and coinsurance. Introducing explicit deposit insurance has had adverse effects in environments that are low in political and economic freedom and high in corruption.     

Testing for Adverse Selection in Insurance Markets

This article reviews and evaluates the empirical literature on adverse selection in insurance markets. We focus on empirical work that seeks to test the basic coverage–risk prediction of adverse selection theory—that is, that policyholders who purchase more insurance coverage tend to be riskier. The analysis of this body of work, we argue, indicates that whether such a correlation exists varies across insurance markets and pools of insurance policies. We discuss various reasons why a coverage–risk correlation may not be found in some pools of insurance policies. The presence of a coverage–risk correlation can be explained either by moral hazard or adverse selection, and we discuss methods for distinguishing between them. Finally, we review the evidence on learning by policyholders and insurers.