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.     

Cream Skimming: Innovations in Insurance Risk Classification and Adverse Selection

We demonstrate how innovations in insurance risk classification can lead to adverse selection, or cream skimming, against insurers that are slow to adopt such pricing innovations. Using a model in which insurers with insufficient pricing data cannot differentiate between low‐ and high‐risk policyholders and therefore charge both the same premium, we show how innovative insurers develop new risk classification data to identify overcharged low‐risk policyholders and attract them from rival insurers with reduced prices. Less innovative insurers thus insure a growing percentage of high‐risk customers, resulting in adverse selection attributable to their informational disadvantage. Next, we examine two cases in which “Big Data” innovations in risk classification led to concerns about cream skimming among U.S. auto insurers. First, we track the rapid adoption of credit‐based insurance scores as pricing variables in personal auto insurance markets. Second, we examine the growing popularity of usage‐based insurance programs like telematics, plans in which insurers use data on policyholders’ actual driving behavior to set prices that attract low‐risk customers. Issues associated with the execution of such pricing strategies are discussed. In both cases, we document how rival insurers quickly adopt successful innovations to reduce their exposure to adverse selection.     

Consumer risk perceptions and information in insurance markets with adverse selection

Standard models of adverse selection in insurance markets assume policyholders know their loss distributions. This study examines the nature of equilibrium and the equilibrium value of information in competitive insurance markets where consumers lack complete information regarding their loss probabilities. We show that additional private information is privately and socially valuable. When the equilibrium policies separate types, policyholders can deduce the underlying probabilities from the contracts, so it is information on risk type, rather than loss probability per se, that is valuable. We show that the equilibrium is “as if” policyholders were endowed with complete knowledge if, and only if, information is noiseless and costless. If information is noisy, the equilibrium depends on policyholders' prior beliefs and the amount of noise in the information they acquire.     

中国健康险市场逆向选择和正向选择并存现象的研究

本文以中国的健康险市场为例,考察不对称信息的影响。通过考察投保人投保金额以及附加险选择和索赔情况的相关关系,论文发现事后出现索赔的投保人,事前往往会选择购买附加险,但是投保金额却相对较低。结合理论模型分析,论文认为投保人在财富、风险偏好等方面的异质性以及信息不对称的存在是导致市场同时出现逆向选择和正向选择的主要原因。     

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.     

On the design of optimal health insurance contracts under ex post moral hazard

We analyze the design of optimal medical insurance under ex post moral hazard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-off between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when insurers’ rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.     

Adverse Selection With Frequency and Severity Risk: Alternative Risk‐Sharing Provisions

The analysis considers an insurance market with adverse selection where individuals' loss distributions may differ with respect to both the frequency and severity of loss. We show that the combination of deductibles and coinsurance can be used to sort rationed policyholders. Because of their screening properties, coinsurance and deductibles may both be equilibrium forms of risk sharing for a particular insurer facing asymmetric information, with different rationed consumers choosing different risk‐sharing provisions.     

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.     

Understanding Basis Risk in Insurance Contracts

There is a tremendous amount of resources being tied up in litigation between insurance companies and policyholders over things like the extent of coverage for various loss scenarios or allegedly bad faith delays in settlement payments. The fact that policyholders formally dispute insurer coverage positions or claims payment strategies gives credibility to the idea that mismatches exist between what policyholders expect insurance policies to cover and what the insurance contracts actually provide as loss indemnification. This mismatch essentially represents insurance basis risk, the analysis of which can more accurately reflect the value and overall efficiency of insurance contracts and suggest factors that may influence policyholder dissatisfaction and consequently insurance contract disputes. This article takes a detailed look at insurance basis risk and finds that subjectivity plays a prominent role in its definition. Using Bayesian inference, it is shown how factors can affect the magnitude of insurance basis risk depending on the individual situation in which the mismatch between losses and coverage exists.     

Markttransparenz durch Versicherungsaufsicht — Informationsökonomische Begründung der dritten Säule von Solvency II

The paper shows that there will be the possibility of adverse selection in insurance markets, if policyholders are inadequate informed about the solvency of the insurance companies. We analyse potential methods of resolution of the insurance market itself to overcome the informational disadvantages of the policyholders. While screening and signalling by the original market participants do not seem to be successful, transparency of solvency may be obtained by a regulating authority. However the actual instruments of the German regulating authority BAFin do not turn out to be satisfactory in this point. Hence the paper gives chapter for a statement for the third pillar of the Solvency II project. Finally we point out additional demand of research concerning the detailed design of the disclosure requirements.     

Optimal Insurance Policy Indemnity Schedules With Policyholders’ Limited Liability and Background Risk

This article makes two contributions to the insurance literature by studying optimal insurance policy indemnity schedules with policyholders’ limited liability and background risk. First, generalizing a prominent approach by Huberman, Mayers, and Smith (1983), it is shown that a welfare subsidy in the case of a ruinous loss may make the insurance premium “overly fair” for nonbankrupting losses and full insurance for this event becomes optimal. Second, introducing correlated background risk into this limited liability framework relativizes or even turns results by Doherty and Schlesinger (1983) as to the impact of background risk on optimal coverage into its opposite.     

The Effect of Risk Aversion and Loss Aversion on Equity-Linked Life Insurance With Surrender Guarantees

We price equity-linked life insurance with surrender guarantees and account for risk preferences in the form of risk-averse and loss-averse policyholders in continuous time. Risk-averse policyholders surrender their policy for higher equity index values. Compared to optimally surrendered policies, this behavior creates substantial policy value losses. In contrast, loss-averse policyholders surrender once the surrender benefit realizes a gain but keep under-performing policies. This disposition effect reduces the policy value relative to both optimally surrendered policies and policies surrendered by risk-averse policyholders. Insurers in competitive markets need to estimate their policyholders’ risk preferences accurately.     

Flood Insurance Coverage in the Coastal Zone

We explore determinants of flood insurance demand in the coastal zone using micro‐data for nine Southeastern counties. Overall estimates indicate price inelastic demand, though subsidized policyholders have greater coverage and are more price sensitive. Mortgage borrowers exhibit no greater coverage; only 12 percent in 100‐year flood zone indicate flood insurance was required by their lender. Flood insurance demand is increasing in the levels of flood and erosion risk. We find a positive correlation between household income and coverage, but the effect is not monotonic. Community‐level erosion hazard mitigation projects influence flood insurance coverage, with beach replenishment acting as a complement.     

Multidimensional private information,market structure,and insurance markets

We investigate whether selection based on multidimensional private information in risks and risk preferences can, under different market structures, result in a negative correlation between insurance coverage and ex post realization of risk. We show that, under perfect competition, selection based on multidimensional private information does not result in the negative correlation property, unless there is a sufficiently high loading factor. However, it is possible to generate the negative correlation property under monopoly when risk and risk preference types are sufficiently negative dependent. We also clarify the connections between important concepts such as adverse/advantageous selection and positive/negative correlation property.     

Überlegungen zu einem fairen Risikomanagement-Mix in Versicherungsunternehmen

This article deals with the question of how a ?fair risk management mix“ that does not lead to a wealth transfer between shareholders and policyholders can be achieved in a joint-stock insurance company. In our financial model of an insurer, the ?fair“ situation, it is assumed that there is no wealth transfer between shareholders and policyholders when both parties receive a net present value of zero on their investments. Taking the default risk of the insurance company into account, we first model a ?fair“ situation for the insurer’s existing portfolio. Surprisingly, closing a new insurance contract that has been priced on a fair basis and then included in the insurer’s existing portfolio leads to a disequilibrium situation because the net present value for the shareholders is no longer zero. This new net present value can be viewed as the fair price of any risk management measure the insurer must take so as to reestablish an equilibrium for both parties, the shareholders and the policyholders.     

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.     

Hidden Overconfidence and Advantageous Selection

Theories of adverse selection and moral hazard predict the occurrence of the risk and the coverage of the insurance should be positively correlated, whereas empirical researches find little support of it. This paper provides a theoretical model of hidden overconfidence and demonstrates that a competitive insurance market may settle on separating equilibrium with advantageous selection predicting a negative relationship between risk and coverage. By assuming heterogeneity in risk perception and hidden action on self-protection, we find that, in equilibrium, the rational type of individual takes precautions to reduce the loss probability, whereas the overconfident type of individual will not make any effort. In the separating equilibrium, the insurer provides a product with high coverage to attract rational type of individual (low risk), and a product with low coverage for overconfident type of individual (high risk). In addition, other types of equilibrium such as adverse selection or linear premium rate are also found.     

Insurance Markets With Differential Information

This article attempts to understand the outcomes when each party of an insurance contract simultaneously has superior information. I assume that policyholders have superior information about specific risks while insurers have superior information about general risks. I find that low-general-risk policyholders purchase insurance, while high-general-risk policyholders are self-insured. Among the low-general-risk policyholders, high-specific-risk policyholders purchase full insurance, while low-specific-risk policyholders purchase partial insurance. When insurers can strategically publicize their information, efficiency is improved because high-general-risk policyholders purchase actuarially fair insurance. The market segmentation is also found based on the general-risk type and the publicizing of information.     

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.     

保险公司偿付能力风险信息对称性与市场供求

保险公司偿付能力充足性是保险监管的内容之一,但是这一信息却往往不被投保人所获知,造成保险供给(保险公司)和保险需求(投保人)两方信息的不对称.本文以保险公司存在偿付能力风险为基本假定,以累积性预期理论和风险调整资本收益率构建保险需求和供给模型,分析在信息对称条件下和信息不对称条件下保险需求的变化及其对保险供给和保险公司...