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.     

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.     

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.     

Multidimensional Screening in Insurance Markets with Adverse Selection

Bundled coverage of different losses and distinct perils, along with differential deductibles and policy limits, are common features of insurance contracts. We show that, through these practices, insurers can implement multidimensional screening of insurance applicants who possess hidden knowledge of their risks, and thereby reduce the externality cost of adverse selection. Competitive forces drive insurers to exploit multidimensional screening, enhancing the efficiency of insurance contracting. Moreover, multidimensional screening allows competitive insurance markets to attain pure strategy Nash equilibria over a wider range of applicant pools, resolving completely the Rothschild–Stiglitz nonexistence puzzle in markets where the perils space is sufficiently divisible.     

Mandatory Pensions and the Intensity of Adverse Selection in Life Insurance Markets

This article examines the impact of varying mandatory pensions on saving, life insurance, and annuity markets in an adverse selection economy. Under reasonable restrictions, we find unambiguous effects on market size, participation rates, and equilibrium prices. The degree of adverse selection, whether a market is active or inactive, and social welfare are analyzed.     

Pooling and Separating Equilibria in Insurance Markets with Adverse Selection and Distribution Costs

In the Rothschild-Stiglitz [1976] model of a competitive insurance market with adverse selection, pooling equilibria cannot exist. However in practice, pooling contracts are frequent, notably in health insurance and life insurance. This is due to the fact that distribution costs are nonnegligible and increase rapidly when more contracts are offered. We modify accordingly the Rothschild-Stiglitz model by introducing such distribution costs. We find that, however small these costs may be, they entail possible existence of pooling equilibria. Moreover, in these pooling equilibria, it is the high-risk individuals who are rationed, in the sense that they would be willing to buy more insurance at the current premium/insurance ratio.     

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.     

Adverse Selection in Reinsurance Markets

This paper looks for evidence of adverse selection in the relationship between primary insurers and reinsurers. We test the implications of a model in which informational asymmetry—and therefore, its negative consequences—decline over time. Our tests involve a data panel consisting of U.S. property-liability insurance firms that reported to the National Association of Insurance Commissioners during the period 1993–2012. We find that the amount of reinsurance, insurer profitability, and insurer credit quality all increase with the tenure of the insurer–reinsurer relationship.     

Dynamic Insurance Contracts and Adverse Selection

We take a dynamic perspective on insurance markets under adverse selection and study a dynamic version of the Rothschild and Stiglitz model. We investigate the nature of dynamic insurance contracts by considering both conditional and unconditional dynamic contracts. An unconditional dynamic contract has insurance companies offering contracts where the terms of the contract depend on time, but not on the occurrence of past accidents. Conditional dynamic contracts make the actual contract also depend on individual past performance (such as in car insurances). We show that dynamic insurance contracts yield a welfare improvement only if they are conditional on past performance. With conditional contracts, the first‐best can be approximated if the contract lasts long. Moreover, this is true for any fraction of low‐risk agents in the population.     

Complete Versus Incomplete Insurance Contracts under Adverse Selection with Multiple Risks

This article extends the standard adverse-selection model for competitive insurance markets, which assumes a single source of risk, to the case where individuals are subject to multiple risks. We compare the following market situations—the case where insurers can offer comprehensive policies against all sources or risks (complete contracts) and the case where different risks are covered by separate policies (incomplete contracts). In the latter case, we consider whether the insurer of a particular risk has perfect information regarding an individual's coverage against other sources of risks. The analysis emphasizes the informational role of bundling in multidimensional screening. When the market situation allows bundling, it is shown that in equilibrium the low-risk type with respect to a particular source of risk does not necessarily obtain partial coverage against that particular risk.     

Risk Mutualization and Competition in Insurance Markets

The aim of this paper is to analyze the impact of mutual firms on competition in the insurance market. We distinguish two actors in this market: mutual firms, which belong to their pooled members, and traditional companies, which belong to their shareholders. Our approach differs from the literature by one crucial assumption: the expected utility of the consumers depends on the size of their insurance firm, which generates network externalities in this market. Thus, the choice of a contract results in a trade-off between the premium level and the probability of that premium being ex-post adjusted. The optimal contract offered by a mutual firm involves a systematic ex-post adjustment (negative or positive), while the contracts a company offers imply a fixed premium that is possibly negatively adjusted at the end of the contractual period. In an oligopoly game, we show that three types of configurations are possible at equilibrium: either one mutual firm or insurance company is active, or a mixed structure emerges in which two or more companies share the market with or without a mutual firm.     

Risk Aversion and the Willingness to Pay for Insurance: A Cautionary Discussion of Adverse Selection

Textbooks frequently describe adverse selection as an almost inevitable feature of insurance markets with heterogeneous buyers and asymmetric information. But if low-risk applicants are more risk averse than their high-risk counterparts, the former may be as willing or more willing than the latter to purchase insurance at any given price. The present article discusses this possibility in several forms suitable for different levels of instruction, to help bridge the gap between insurance education and current research on this topic.     

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.     

Changes in Background Risk and the Demand for Insurance

The demand for insurance against loss from a particular risky asset is likely to depend on other risks the decision-maker faces. For independently distributed other risks, referred to as background risk, Eeckhoudt and Kimball [1992] determine the effect on insurance demand of introducing background risk. Recently, Eeckhoudt, Gollier, and Schlesinger [1996] determine conditions on preferences such that first- and second-degree stochastic deteriorations in background risk lead to a decrease in the decision-maker's willingness to accept other risks. These results, although formulated in a general decision model, also apply to insurance demand. This article continues analysis of this question by determining the effect on insurance demand of several other general changes in background risk.     

逆向选择条件下带甄别期的最优保险设计

为了改善信息不对称对保险市场交易效率的影响,分投保人为两种及两种以上风险类型建立了带甄别期的保险契约模型,指出可以利用投保人在甄别期的风险发生情况来推断投保人的风险类型.带甄别期的保险契约是指:自保险合同生效之日起的一段时间内(甄别期),如果投保人发生风险,保险公司将给予一定的赔偿,甄别期过后,如果投保人再次发生风险,保险公司将不再给予任何赔偿;如果投保人在甄别期未发生风险,而在甄别期之后的剩余保险期发生风险,保险公司仍然给予与上述情况相同的赔偿.证明指出效用最优时带甄别期的保险契约不比R-S传统部分保险契约差,并给出了前者是后者严格帕累托改进的充分条件.此外,对于两种以上风险类型情形,证明了满足对次低风险投保人的激励相容约束是满足对其余高风险投保人激励相容约束的一个充分不必要条件,并给出了相应的充分条件,进一步指出该充分条件的集合恰是带甄别期的保险契约能够产生分离均衡的一个充分条件.最后,以一个算例说明确实存在效用最优时带甄别期的保险契约是R-S传统部分保险契约的严格帕累托改进情形.     

An Examination of Adverse Selection in the Public Provision of Insurance

Using a unique data set from Florida's residual property insurer, we test for adverse selection in the public provision of homeowners’ insurance in Florida. We find a significant relationship between the losses and deductible choices of insureds in Florida's residual homeowners’ insurance market. This relationship provides strong evidence of the existence of an adverse selection problem in Florida's residual property insurance market. While this relationship is important to Florida regulators (and taxpayers) specifically, a finding of an adverse selection problem in residual markets in general has implications more broadly for government providers of insurance as an adverse selection problem in these settings will impact the public policy debates and decisions involving these markets.     

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.