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«Selection in Insurance Markets: Theory and Empirics in Pictures Liran Einav and Amy Finkelstein F rom the large-scale social insurance programs of ...»

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Journal of Economic Perspectives—Volume 25, Number 1—Winter 2011—Pages 115–138

Selection in Insurance Markets: Theory

and Empirics in Pictures

Liran Einav and Amy Finkelstein


rom the large-scale social insurance programs of Social Security and Medicare to the heavily regulated private markets for property and casualty

insurance, government intervention in insurance markets is ubiquitous. The

fundamental theoretical reason for such intervention, based on classic work from

the 1970s, is the problem of adverse selection. But despite the age and influence of the theory, systematic empirical examination of selection in actual insurance markets is a relatively recent development. Indeed, in awarding the 2001 Nobel Prize for the pioneering theoretical work on asymmetric information to George Akerlof, Michael Spence, and Joseph Stiglitz, the Nobel committee noted this paucity of empirical work (Nobelprize.org, 2001).

Over the last decade, however, empirical work on selection in insurance markets has gained considerable momentum, and a fairly extensive (and still growing) empirical literature on the topic has emerged. This research has found that adverse selection exists in some insurance markets but not in others. It has also uncovered examples of markets that exhibit “advantageous selection”—a phenomenon not considered by the original theory, and one that has different consequences for equilibrium insurance allocation and optimal public policy than the classical case of adverse selection. Researchers have also taken steps toward estimating the welfare consequences of detected selection and of potential public policy interventions.

Liran Einav is Associate Professor of Economics, Stanford University, Stanford, California.

■ Amy Finkelstein is Professor of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts. Both authors are also Research Associates, National Bureau of Economic Research, Cambridge, Massachusetts. Their e-mail addresses are 〈leinav@stanford.edu〉 and leinav@stanford.edu〉 〈afink@mit.edu〉.

nk@mit.edu〉 doi=10.1257/jep.25.1.115 116 Journal of Economic Perspectives In this essay, we present a graphical framework for analyzing both theoretical and empirical work on selection in insurance markets. This graphical approach, which draws heavily on a paper we wrote with Mark Cullen (Einav, Finkelstein, and Cullen, 2010), provides both a useful and intuitive depiction of the basic theory of selection and its implications for welfare and public policy, as well as a lens through which one can understand the ideas and limitations of existing empirical work on this topic.

We begin by using this framework to review the “textbook” adverse selection environment and its implications for insurance allocation, social welfare, and public policy. We then discuss several important extensions to this classic treatment that are necessitated by important real-world features of insurance markets and which can be easily incorporated in the basic framework. Finally, we use the same graphical approach to discuss the intuition behind recently developed empirical methods for testing for the existence of selection and examining its welfare consequences.

We conclude by discussing some important issues that are not well-handled by this framework and which, perhaps relatedly, have been little addressed by the existing empirical work; we consider these fruitful areas for additional research. Our essay does not aim at reviewing the burgeoning empirical literature on selection in insurance markets. However, at relevant points in our discussion we point the interested reader to recent papers that review or summarize recent findings.

Adverse and Advantageous Selection: A Graphical Framework

The Textbook Environment for Insurance Markets We start by considering the textbook case of insurance demand and cost, in which perfectly competitive, risk-neutral firms offer a single insurance contract that covers some probabilistic loss; risk-averse individuals differ only in their (privately-known) probability of incurring that loss; and there are no other frictions in providing insurance, such as administrative or claim-processing costs.

Thus, more in the spirit of Akerlof (1970) and unlike the well-known environment of Rothschild and Stiglitz (1976), firms compete in prices but do not compete on the coverage features of the insurance contract. We return to this important simplifying assumption later in this essay.

Figure 1 provides a graphical representation of this case and illustrates the resulting adverse selection as well as its consequences for insurance coverage and welfare. The figure considers the market for a specific insurance contract. Consumers in this market make a binary choice of whether or not to purchase this contract, and firms in this market compete only over what price to charge for the contract.

The vertical axis indicates the price (and expected cost) of that contract, and the horizontal axis indicates the quantity of insurance demand. Since individuals face a binary choice of whether or not to purchase the contract, the “quantity” of insurance is the fraction of insured individuals. With risk-neutral insurance providers and no additional frictions, the social (and firms’) costs associated with Liran Einav and Amy Finkelstein 117 Figure 1 Adverse Selection in the Textbook Setting

–  –  –

providing insurance are the expected insurance claims—that is, the expected payouts on policies.

Figure 1 shows the market demand curve for the insurance contract. Because individuals in this setting can only choose the contract or not, the market demand curve simply reflects the cumulative distribution of individuals’ willingness to pay for the contract. While this is a standard unit demand model that could apply to many traditional product markets, the textbook insurance context allows us to link willingness to pay to cost. In particular, a risk-averse individual’s willingness to pay for insurance is the sum of the expected cost and risk premium for that individual.

In the textbook environment, individuals are homogeneous in their risk aversion (and all other features of their utility function). Therefore, their willingness to pay for insurance is increasing in their risk type—that is, their probability of loss, or expected cost—which is privately known. This is illustrated in Figure 1 by plotting the marginal cost (MC) curve as downward sloping: those individuals who are willing to pay the most for coverage are those that have the highest expected cost. This downward-sloping MC curve represents the well-known adverse selection property of insurance markets: the individuals who have the highest willingness to pay for insurance are those who are expected to be the most costly for the firm to cover.

The link between the demand and cost curve is arguably the most important distinction of insurance markets (or selection markets more generally) from traditional 118 Journal of Economic Perspectives product markets. The shape of the cost curve is driven by the demand-side customer selection. In most other contexts, the demand curve and cost curve are independent objects; demand is determined by preferences and costs by the production technology.

The distinguishing feature of selection markets is that the demand and cost curves are tightly linked, because the individual’s risk type not only affects demand but also directly determines cost.

The risk premium is shown graphically in the figure as the vertical distance between expected cost (the MC curve) and the willingness to pay for insurance (the demand curve). In the textbook case, the risk premium is always positive, since all individuals are risk averse and there are no other market frictions. As a result, the demand curve is always above the MC curve, and it is therefore efficient for all individuals to be insured ( eff = Q max). Absent income effects, the welfare loss from (Q not insuring a given individual is the risk premium of that individual, or the vertical difference between the demand and MC curves.

When the individual-specific loss probability (or expected cost) is private information to the individual, firms must offer a single price for pools of observationally identical but in fact heterogeneous individuals. Of course, in practice firms may vary the price based on some observable individual characteristics (such as age or zip code). Thus, Figure 1 can be thought of as depicting the market for coverage among individuals who are treated identically by the firm.

The competitive equilibrium price will be equal to the firms’ average cost at that price. This is a zero-profit condition; offering a lower price will result in negative profits, and offering higher prices than competitors will not attract any buyers.

The relevant cost curve the firm faces is therefore the average cost (AC) curve, which is also shown in Figure 1. The (competitive) equilibrium price and quantity is given by the intersection of the demand curve and the AC curve (point C ).

The fundamental inefficiency created by adverse selection arises because the efficient allocation is determined by the relationship between marginal cost and demand, but the equilibrium allocation is determined by the relationship between average cost and demand. Because of adverse selection (downward sloping MC curve), the marginal buyer is always associated with a lower expected cost than that of infra-marginal buyers. Therefore, as drawn in Figure 1, the AC curve always lies above the MC curve and intersects the demand curve at a quantity lower than Q max. As a result, the equilibrium quantity of insurance will be less than the efficient quantity ( max) and the equilibrium price (Peqm) will be above the efficient price, (Q ( illustrating the classical result of under-insurance in the presence of adverse selection (Akerlof, 1970; Rothschild and Stiglitz, 1976). That is, it is efficient to insure every individual (MC is always below demand) but in equilibrium the Q max – Q eqm individuals who have the lowest expected costs remain uninsured because the AC curve is not always below the demand curve. These individuals value the insurance at more than their expected costs, but firms cannot insure these individuals and still break even.

The welfare cost of this under-insurance depends on the lost surplus (the risk premium) of those individuals who remain inefficiently uninsured in the Selection in Insurance Markets: Theory and Empirics in Pictures 119 Figure 2 Specific Examples of Extreme Cases A: Adverse Selection with No Efficiency Cost

–  –  –

competitive equilibrium. In Figure 1, these are the individuals whose willingness to pay is less than the equilibrium price, Peqm. Integrating over all these individuals’ risk premia, the welfare loss from adverse selection in this simple framework is given by the area of the deadweight loss trapezoid DCEF.

Even in the textbook environment, the amount of under-insurance generated by adverse selection, and its associated welfare loss, can vary greatly. Figure 2 illustrates this point by depicting two specific examples of the textbook adverse selection environment, one that produces the efficient insurance allocation and one that produces complete unraveling of insurance coverage. The efficient outcome is depicted in panel A. While the market is adversely selected (that is, the MC curve is downward sloping), the AC curve always lies below the demand curve. This leads to an equilibrium price Peqm, that, although it is higher than marginal cost, still produces the efficient allocation (Q eqm = Q eff = Q max). This situation can arise, for ( example, when individuals do not vary too much in their unobserved risk (that is, the MC and consequently AC curve is relatively flat) and/or individuals’ risk aversion is high (that is, the demand curve lies well above the MC curve).

120 Journal of Economic Perspectives Figure 2 (continued) B: Adverse Selection with Complete Unraveling

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The case of complete unraveling is illustrated in panel B of Figure 2. Here, the AC curve always lies above the demand curve even though the MC curve is always below it.1 As a result, the competitive equilibrium is that no individual in the market is insured, while the efficient outcome is for everyone to have insurance. One could also use panel B to illustrate the potential death spiral dynamics that may lead to such unraveling. For example, if insurance pricing is naively set but dynamically adjusted to reflect the average cost from the previous period (which is, in fact, a fairly common practice in many health insurance settings), the market will gradually shrink until it completely disappears. This convergent adjustment process is illustrated by the arrows in panel B. Cutler and Reber (1998) provide an empirical case study of a death spiral of this nature in the context of a health insurance plan offered to Harvard University employees.

Public Policy in the Textbook Case Our graphical framework can also be used to illustrate the consequences of common public policy interventions in insurance markets. The canonical solution to the inefficiency created by adverse selection is to mandate that everyone purchase insurance. In the textbook setting, this produces the efficient outcome in which everyone has insurance. However, the magnitude of the welfare benefit produced This can happen even within the textbook example if the individuals with the greatest risk are certain to incur a loss, so their risk premium is zero and their willingness to pay is the same as their expected costs.

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