Selection in Insurance Markets: Theory and Empirics in

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

FF rom the large-scale social insurance programs of Social Security and Medi-rom the large-scale social insurance programs of Social Security and Medi-care to the heavily regulated private markets for property and casualty care to the heavily regulated private markets for property and casualty insurance, government intervention in insurance markets is ubiquitous. The insurance, government intervention in insurance markets is ubiquitous. The

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

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

Selection in Insurance Markets: Theory and Empirics in Pictures

■ ■ Liran Einav is Associate Professor of Economics, Stanford University, Stanford, California. Liran Einav is Associate Professor of Economics, Stanford University, Stanford, California. Amy Finkelstein is Professor of Economics, Massachusetts Institute of Technology, Cambridge, Amy Finkelstein is Professor of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts. Both authors are also Research Associates, National Bureau of Economic Massachusetts. Both authors are also Research Associates, National Bureau of Economic Research, Cambridge, Massachusetts. Their e-mail addresses are Research, Cambridge, Massachusetts. Their e-mail addresses are ⟨⟨[email protected]@stanford.edu⟩⟩ and and ⟨⟨afi [email protected] [email protected]⟩⟩..

doi=10.1257/jep.25.1.115

Liran Einav and Amy Finkelstein

116 Journal of Economic Perspectives

In this essay, we present a graphical framework for analyzing both theoretical In this essay, we present a graphical framework for analyzing both theoretical and empirical work on selection in insurance markets. This graphical approach, 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 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 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 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 which one can understand the ideas and limitations of existing empirical work on this topic.this topic.

We begin by using this framework to review the “textbook” adverse selection We begin by using this framework to review the “textbook” adverse selection environment and its implications for insurance allocation, social welfare, and public environment and its implications for insurance allocation, social welfare, and public policy. We then discuss several important extensions to this classic treatment that are 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 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 be easily incorporated in the basic framework. Finally, we use the same graphical approach to discuss the intuition behind recently developed empirical methods approach to discuss the intuition behind recently developed empirical methods for testing for the existence of selection and examining its welfare consequences. 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 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 framework and which, perhaps relatedly, have been little addressed by the existing empirical work; we consider these fruitful areas for additional research. Our essay empirical work; we consider these fruitful areas for additional research. Our essay does not aim at reviewing the burgeoning empirical literature on selection in insur-does not aim at reviewing the burgeoning empirical literature on selection in insur-ance markets. However, at relevant points in our discussion we point the interested ance markets. However, at relevant points in our discussion we point the interested reader to recent papers that review or summarize recent fi ndings.reader to recent papers that review or summarize recent fi ndings.

Adverse and Advantageous Selection: A Graphical FrameworkAdverse and Advantageous Selection: A Graphical Framework

The Textbook Environment for Insurance MarketsThe Textbook Environment for Insurance MarketsWe start by considering the textbook case of insurance demand and cost, in We start by considering the textbook case of insurance demand and cost, in

which perfectly competitive, risk-neutral fi rms offer a single insurance contract which perfectly competitive, risk-neutral fi rms offer a single insurance contract that covers some probabilistic loss; risk-averse individuals differ only in their that covers some probabilistic loss; risk-averse individuals differ only in their (privately-known) probability of incurring that loss; and there are no other fric-(privately-known) probability of incurring that loss; and there are no other fric-tions in providing insurance, such as administrative or claim-processing costs. tions in providing insurance, such as administrative or claim-processing costs. Thus, more in the spirit of Akerlof (1970) and unlike the well-known environment Thus, more in the spirit of Akerlof (1970) and unlike the well-known environment of Rothschild and Stiglitz (1976), fi rms compete in prices but do not compete of Rothschild and Stiglitz (1976), fi rms compete in prices but do not compete on the coverage features of the insurance contract. We return to this important on the coverage features of the insurance contract. We return to this important simplifying assumption later in this essay.simplifying assumption later in this essay.

Figure 1 provides a graphical representation of this case and illustrates the Figure 1 provides a graphical representation of this case and illustrates the resulting adverse selection as well as its consequences for insurance coverage and resulting adverse selection as well as its consequences for insurance coverage and welfare. The fi gure considers the market for a specifi c insurance contract. Consumers welfare. The fi gure considers the market for a specifi c insurance contract. Consumers in this market make a binary choice of whether or not to purchase this contract, and in this market make a binary choice of whether or not to purchase this contract, and fi rms in this market compete only over what price to charge for the contract.fi rms 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 vertical axis indicates the price (and expected cost) of that contract, and the horizontal axis indicates the quantity of insurance demand. Since individuals 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” 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 of insurance is the fraction of insured individuals. With risk-neutral insurance providers and no additional frictions, the social (and fi rms’) costs associated with providers and no additional frictions, the social (and fi rms’) costs associated with

Liran Einav and Amy Finkelstein 117

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

Figure 1 shows the market demand curve for the insurance contract. Because 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 individuals in this setting can only choose the contract or not, the market demand curve simply refl ects the cumulative distribution of individuals’ willingness to pay curve simply refl ects the cumulative distribution of individuals’ willingness to pay for the contract. While this is a standard unit demand model that could apply to 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 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 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.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 aver-In the textbook environment, individuals are homogeneous in their risk aver-sion (and all other features of their utility function). Therefore, their willingness to sion (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 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 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 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 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 downward-sloping MC curve represents the well-known adverse selection property of insurance markets: the individuals who have the highest willingness to pay for insur-insurance markets: the individuals who have the highest willingness to pay for insur-ance are those who are expected to be the most costly for the fi rm to cover.ance are those who are expected to be the most costly for the fi rm to cover.

The link between the demand and cost curve is arguably the most important The link between the demand and cost curve is arguably the most important distinction of insurance markets (or selection markets more generally) from traditional distinction of insurance markets (or selection markets more generally) from traditional

Figure 1Adverse Selection in the Textbook Setting

Quantity

Pric

e

Demand curve

MC curve

A

B

C

DE

F

GJPeqm

AC curve

Q eqm Q max


product markets. The shape of the cost curve is driven by the demand-side customer 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 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. 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 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 are tightly linked, because the individual’s risk type not only affects demand but also directly determines cost.directly determines cost.

The risk premium is shown graphically in the fi gure as the vertical distance The risk premium is shown graphically in the fi gure as the vertical distance between expected cost (the MC curve) and the willingness to pay for insurance 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 (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, 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 effi cient for all the demand curve is always above the MC curve, and it is therefore effi cient for all individuals to be insured (individuals to be insured (Q effeff == Q maxmax). Absent income effects, the welfare loss from ). Absent income effects, the welfare loss from not insuring a given individual is the risk premium of that individual, or the vertical not insuring a given individual is the risk premium of that individual, or the vertical difference between the demand and MC curves.difference between the demand and MC curves.

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

The competitive equilibrium price will be equal to the fi rms’ average cost at The competitive equilibrium price will be equal to the fi rms’ average cost at that price. This is a zero-profi t condition; offering a lower price will result in nega-that price. This is a zero-profi t condition; offering a lower price will result in nega-tive profi ts, and offering higher prices than competitors will not attract any buyers. tive profi ts, and offering higher prices than competitors will not attract any buyers. The relevant cost curve the fi rm faces is therefore the average cost (AC) curve, The relevant cost curve the fi rm faces is therefore the average cost (AC) curve, which is also shown in Figure 1. The (competitive) equilibrium price and quantity is 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 given by the intersection of the demand curve and the AC curve (point C ).).

The fundamental ineffi ciency created by adverse selection arises because The fundamental ineffi ciency created by adverse selection arises because the effi cient allocation is determined by the relationship between the effi cient allocation is determined by the relationship between marginal cost cost and demand, but the equilibrium allocation is determined by the relationship and demand, but the equilibrium allocation is determined by the relationship between between average cost and demand. Because of adverse selection (downward sloping cost and demand. Because of adverse selection (downward sloping MC curve), the marginal buyer is always associated with a lower expected cost than 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 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 lies above the MC curve and intersects the demand curve at a quantity lower than Q maxmax. As a result, the equilibrium quantity of insurance will be less than the effi cient . As a result, the equilibrium quantity of insurance will be less than the effi cient quantity (quantity (Q maxmax) and the equilibrium price () and the equilibrium price (Peqmeqm) will be above the effi cient price, ) will be above the effi cient price, illustrating the classical result of under-insurance in the presence of adverse selec-illustrating the classical result of under-insurance in the presence of adverse selec-tion (Akerlof, 1970; Rothschild and Stiglitz, 1976). That is, it is effi cient to insure tion (Akerlof, 1970; Rothschild and Stiglitz, 1976). That is, it is effi cient to insure every individual (MC is always below demand) but in equilibrium the every individual (MC is always below demand) but in equilibrium the Q maxmax – – Q eqmeqm individuals who have the lowest expected costs remain uninsured because the individuals who have the lowest expected costs remain uninsured because the AC curve is not always below the demand curve. These individuals value the insur-AC curve is not always below the demand curve. These individuals value the insur-ance at more than their expected costs, but fi rms cannot insure these individuals ance at more than their expected costs, but fi rms cannot insure these individuals and still break even.and still break even.

The welfare cost of this under-insurance depends on the lost surplus (the The welfare cost of this under-insurance depends on the lost surplus (the risk premium) of those individuals who remain ineffi ciently uninsured in the risk premium) of those individuals who remain ineffi ciently uninsured in the

Selection in Insurance Markets: Theory and Empirics in Pictures 119

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

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

Figure 2Specifi c Examples of Extreme Cases

A: Adverse Selection with No Efficiency Cost

Quantity

Pric

e

Demand curve

MC curve

AC curve

Peqm

Q max

C

(continued on next page)


The case of complete unraveling is illustrated in panel B of Figure 2. Here, the 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 AC curve always lies above the demand curve even though the MC curve is always below it.below it.11 As a result, the competitive equilibrium is that no individual in the market As a result, the competitive equilibrium is that no individual in the market is insured, while the effi cient outcome is for everyone to have insurance. One could is insured, while the effi cient outcome is for everyone to have insurance. One could also use panel B to illustrate the potential death spiral dynamics that may lead to 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 such unraveling. For example, if insurance pricing is naively set but dynamically adjusted to refl ect the average cost from the previous period (which is, in fact, a adjusted to refl ect the average cost from the previous period (which is, in fact, a fairly common practice in many health insurance settings), the market will gradu-fairly common practice in many health insurance settings), the market will gradu-ally shrink until it completely disappears. This convergent adjustment process is ally shrink until it completely disappears. This convergent adjustment process is illustrated by the arrows in panel B. Cutler and Reber (1998) provide an empirical 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 case study of a death spiral of this nature in the context of a health insurance plan offered to Harvard University employees.offered to Harvard University employees.

Public Policy in the Textbook CasePublic Policy in the Textbook CaseOur graphical framework can also be used to illustrate the consequences of Our graphical framework can also be used to illustrate the consequences of

common public policy interventions in insurance markets. The canonical solution common public policy interventions in insurance markets. The canonical solution to the ineffi ciency created by adverse selection is to mandate that everyone purchase to the ineffi ciency created by adverse selection is to mandate that everyone purchase insurance. In the textbook setting, this produces the effi cient outcome in which insurance. In the textbook setting, this produces the effi cient outcome in which everyone has insurance. However, the magnitude of the welfare benefi t produced everyone has insurance. However, the magnitude of the welfare benefi t produced

1 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.

Figure 2 (continued)

B: Adverse Selection with Complete UnravelingPr

ice

QuantityQ max

Demand curve

MC curve

AC curve


by an insurance purchase requirement can vary dramatically depending on the by an insurance purchase requirement can vary dramatically depending on the specifi cs of the market. The two extreme examples presented in Figure 2 illustrate specifi cs of the market. The two extreme examples presented in Figure 2 illustrate this point, but even in intermediate cases captured by Figure 1, the magnitude of this point, but even in intermediate cases captured by Figure 1, the magnitude of the welfare loss (area the welfare loss (area CDEF ) is highly sensitive to the shape and location of the cost ) is highly sensitive to the shape and location of the cost and demand curves and is therefore ultimately an empirical question.and demand curves and is therefore ultimately an empirical question.22

Another commonly discussed policy remedy for adverse selection is to subsi-Another commonly discussed policy remedy for adverse selection is to subsi-dize insurance coverage. We can use Figure 1 to illustrate. Consider, for example, dize insurance coverage. We can use Figure 1 to illustrate. Consider, for example, a lump sum subsidy toward the price of coverage. This would shift demand out, a lump sum subsidy toward the price of coverage. This would shift demand out, leading to a higher equilibrium quantity and less under-insurance. The welfare loss leading to a higher equilibrium quantity and less under-insurance. The welfare loss would still be associated with the area between the original (pre-subsidy) demand would still be associated with the area between the original (pre-subsidy) demand curve and the MC curve, and would therefore unambiguously decline with any posi-curve and the MC curve, and would therefore unambiguously decline with any posi-tive subsidy. A large enough subsidy (greater than the line segment tive subsidy. A large enough subsidy (greater than the line segment GE in Figure 1) in Figure 1) would lead to the effi cient outcome, with everybody insured.would lead to the effi cient outcome, with everybody insured.

A fi nal common form of public policy intervention is regulation that imposes A fi nal common form of public policy intervention is regulation that imposes restrictions on the characteristics of consumers over which fi rms can price discrimi-restrictions on the characteristics of consumers over which fi rms can price discrimi-nate. Some regulations require “community rates” that are uniform across all nate. Some regulations require “community rates” that are uniform across all individuals, while others prohibit insurance companies from making prices contin-individuals, while others prohibit insurance companies from making prices contin-gent on certain observable risk factors, such as race or gender. For concreteness, gent on certain observable risk factors, such as race or gender. For concreteness, consider the case of a regulation that prohibits pricing on the basis of gender. Recall consider the case of a regulation that prohibits pricing on the basis of gender. Recall that Figure 1 can be interpreted as applying to a group of individuals who must that Figure 1 can be interpreted as applying to a group of individuals who must be treated the same by the insurance company. When pricing based on gender is be treated the same by the insurance company. When pricing based on gender is prohibited, males and females are pooled into the same market, with a variant of prohibited, males and females are pooled into the same market, with a variant of Figure 1 describing that market. When pricing on gender is allowed, there are now Figure 1 describing that market. When pricing on gender is allowed, there are now two distinct insurance markets—described by two distinct variants of Figure 1—one two distinct insurance markets—described by two distinct variants of Figure 1—one for women and one for men, each of which can be analyzed separately. A central for women and one for men, each of which can be analyzed separately. A central issue for welfare analysis is whether, when insurance companies are allowed to price issue for welfare analysis is whether, when insurance companies are allowed to price on gender, consumers still have residual private information about their expected on gender, consumers still have residual private information about their expected costs. If they do not, then the insurance market within each gender-specifi c segment costs. If they do not, then the insurance market within each gender-specifi c segment of the market will exhibit a constant (fl at) MC curve and the equilibrium in each of the market will exhibit a constant (fl at) MC curve and the equilibrium in each market will be effi cient. In this case, policies that restrict pricing on gender are market will be effi cient. In this case, policies that restrict pricing on gender are unambiguously welfare decreasing since they create adverse selection where unambiguously welfare decreasing since they create adverse selection where none existed before. However, in the more likely case that individuals have some none existed before. However, in the more likely case that individuals have some residual private information about their risk that is not captured by their gender, residual private information about their risk that is not captured by their gender, each gender-specifi c market segment would look qualitatively the same as Figure 1 each gender-specifi c market segment would look qualitatively the same as Figure 1 (with downward sloping MC and AC curves). In such cases, the welfare implica-(with downward sloping MC and AC curves). In such cases, the welfare implica-tions of restricting pricing on gender could go in either direction; depending on tions of restricting pricing on gender could go in either direction; depending on the shape and position of the gender-specifi c demand and cost curves relative to the shape and position of the gender-specifi c demand and cost curves relative to the gender-pooled ones, the sum of the areas of the deadweight loss trapezoids in the gender-pooled ones, the sum of the areas of the deadweight loss trapezoids in

2 Although in the specifi c examples in Figure 2, the welfare cost of adverse selection is increasing with the amount of under-insurance it creates, this does not have to be the case in general.


the gender-specifi c markets could be larger or smaller than the area of the single the gender-specifi c markets could be larger or smaller than the area of the single deadweight loss trapezoid in the gender-pooled market.deadweight loss trapezoid in the gender-pooled market.33

Departures from the Textbook EnvironmentDepartures from the Textbook EnvironmentAlthough the textbook treatment of insurance markets may give rise to dramat-Although the textbook treatment of insurance markets may give rise to dramat-

ically different magnitudes of the welfare costs arising from adverse selection, the ically different magnitudes of the welfare costs arising from adverse selection, the qualitative fi ndings are robust. Under the textbook assumptions, private informa-qualitative fi ndings are robust. Under the textbook assumptions, private informa-tion about risk never produces over-insurance relative to the effi cient outcome, tion about risk never produces over-insurance relative to the effi cient outcome, and mandatory insurance coverage is always a (weakly) welfare-improving policy and mandatory insurance coverage is always a (weakly) welfare-improving policy intervention. However, these robust qualitative results only hold in this textbook intervention. However, these robust qualitative results only hold in this textbook case. They may be reversed with the introduction of two important features of actual case. They may be reversed with the introduction of two important features of actual insurance markets: 1) insurance “loads” or administrative costs of providing insur-insurance markets: 1) insurance “loads” or administrative costs of providing insur-ance, and 2) preference heterogeneity.ance, and 2) preference heterogeneity.

Consider fi rst a loading factor on insurance, for example in the form of addi-Consider fi rst a loading factor on insurance, for example in the form of addi-tional administrative cost associated with selling and servicing insurance, perhaps tional administrative cost associated with selling and servicing insurance, perhaps due to costs associated with advertising and marketing, or with verifying and due to costs associated with advertising and marketing, or with verifying and processing claims. Many insurance markets display evidence of nontrivial loading processing claims. Many insurance markets display evidence of nontrivial loading factors, including markets for long-term care insurance (Brown and Finkelstein, factors, including markets for long-term care insurance (Brown and Finkelstein, 2007), annuities (Friedman and Warshawsky, 1990; Mitchell, Poterba, Warshawsky, 2007), annuities (Friedman and Warshawsky, 1990; Mitchell, Poterba, Warshawsky, and Brown, 1999; Finkelstein and Poterba, 2002), health insurance (Newhouse, and Brown, 1999; Finkelstein and Poterba, 2002), health insurance (Newhouse, 2002), and automobile insurance (Chiappori, Jullien, Salanié, and Salanié, 2006).2002), and automobile insurance (Chiappori, Jullien, Salanié, and Salanié, 2006).44

The key implication of such loads is that it is now not necessarily effi cient to The key implication of such loads is that it is now not necessarily effi cient to allocate insurance coverage to all individuals. Even if all individuals are risk averse, allocate insurance coverage to all individuals. Even if all individuals are risk averse, the additional cost of providing an individual with insurance may be greater than the additional cost of providing an individual with insurance may be greater than the risk premium for certain individuals, making it socially effi cient to leave such the risk premium for certain individuals, making it socially effi cient to leave such individuals uninsured. This case is illustrated in Figure 3, which is similar to Figure 1, individuals uninsured. This case is illustrated in Figure 3, which is similar to Figure 1, except that the cost curves are shifted upward refl ecting the additional cost of insur-except that the cost curves are shifted upward refl ecting the additional cost of insur-ance provision.ance provision.55

Figure 3 is drawn in a way that the MC curve crosses the demand curve “inter-Figure 3 is drawn in a way that the MC curve crosses the demand curve “inter-nally” (that is, at a quantity lower than nally” (that is, at a quantity lower than Qmaxmax), at point ), at point E , which depicts the socially , which depicts the socially effi cient insurance allocation. It is effi cient to insure everyone to the left of point effi cient insurance allocation. It is effi cient to insure everyone to the left of point E (because their willingness to pay for insurance exceeds their expected cost), but (because their willingness to pay for insurance exceeds their expected cost), but

3 An example illustrates how pricing on gender can increase deadweight loss. Consider three types of individuals. Type 1 individuals (representing 10 percent of the population) have expected cost of 20 and willingness to pay for insurance of 30. Type 2 individuals (60 percent) have expected cost of 5 and willingness to pay of 20, and type 3 (30 percent) have expected cost of 4 and willingness to pay of 7.5. The competitive (zero-profi t) price in this market is 6.2, leading to an effi cient allocation in which everyone is insured (this case is similar to that of panel A in Figure 2). Suppose now that type 2 individuals are all females and type 1 and 3 individuals are all males, and gender can be priced. In this case, the competitive price for women is 5 and they are all insured. However, the competitive price for men is 8, leaving all type 3 individuals ineffi ciently uninsured.4 Admittedly, most of these papers lack the data to distinguish between loading factors arising from administrative costs to the insurance company and those arising from market power (insurance company profi ts). Still, it seems a reasonable assumption that it is not costless to run an insurance company.5 We note that Figure 3 could also describe a market with no frictions, but in which a fraction of the individuals are risk loving.


socially ineffi cient to insure anyone to the right of point socially ineffi cient to insure anyone to the right of point E (because their willing- (because their willing-ness to pay is less than their expected cost). In this situation, it is effi cient to keep ness to pay is less than their expected cost). In this situation, it is effi cient to keep Q maxmax – – Q effeff individuals uninsured. individuals uninsured.

The introduction of loads does not affect the basic analysis of adverse selection, The introduction of loads does not affect the basic analysis of adverse selection, but it does have important implications for its standard public policy remedies. but it does have important implications for its standard public policy remedies. The competitive equilibrium is still determined by the zero profi t condition, or the The competitive equilibrium is still determined by the zero profi t condition, or the intersection of the demand curve and the AC curve (point intersection of the demand curve and the AC curve (point C in Figure 3), and in in Figure 3), and in the presence of adverse selection (and thus a downward sloping MC curve), this the presence of adverse selection (and thus a downward sloping MC curve), this leads to under-insurance relative to the social optimum (leads to under-insurance relative to the social optimum (Q eqmeqm << Q effeff), and to a ), and to a familiar deadweight loss triangle familiar deadweight loss triangle CDE ..

However, with insurance loads, the textbook result of an unambiguous welfare However, with insurance loads, the textbook result of an unambiguous welfare gain from mandatory coverage no longer obtains. As Figure 3 shows, while a mandate gain from mandatory coverage no longer obtains. As Figure 3 shows, while a mandate that everyone be insured “regains” the welfare loss associated with under-insurance that everyone be insured “regains” the welfare loss associated with under-insurance (triangle (triangle CDE ), it also leads to over-insurance by covering individuals whom it is ), it also leads to over-insurance by covering individuals whom it is socially ineffi cient to insure (that is, whose expected costs are above their willingness socially ineffi cient to insure (that is, whose expected costs are above their willingness to pay). This latter effect leads to a welfare loss given by the area to pay). This latter effect leads to a welfare loss given by the area EGH in Figure 3. in Figure 3. Therefore whether a mandate improves welfare over the competitive allocation Therefore whether a mandate improves welfare over the competitive allocation depends on the relative sizes of triangles depends on the relative sizes of triangles CDE and and EGH ; this in turn depends on the ; this in turn depends on the specifi c market’s demand and cost curves and is therefore an empirical question.specifi c market’s demand and cost curves and is therefore an empirical question.

Figure 3Adverse Selection with Additional Cost of Providing Insurance

Source: Einav, Finkelstein, and Cullen (2010), fi gure 1.

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A second important feature of real-world insurance markets not captured by A second important feature of real-world insurance markets not captured by the textbook treatment is preference heterogeneity: that is, the possibility that the textbook treatment is preference heterogeneity: that is, the possibility that individuals may differ not only in their risk but also in their preferences, such as individuals may differ not only in their risk but also in their preferences, such as their willingness to bear risk (risk aversion). The classical models (like Rothschild their willingness to bear risk (risk aversion). The classical models (like Rothschild and Stiglitz, 1976) make the simplifying and theoretically attractive assumption that and Stiglitz, 1976) make the simplifying and theoretically attractive assumption that individuals have the same preferences and may vary only in their (privately known) individuals have the same preferences and may vary only in their (privately known) expected costs. As a result, willingness to pay for insurance is an increasing function expected costs. As a result, willingness to pay for insurance is an increasing function of expected costs.of expected costs.

In practice, of course, individuals may differ not only in their expected cost but In practice, of course, individuals may differ not only in their expected cost but also in their preferences. Indeed, recent empirical work has documented substan-also in their preferences. Indeed, recent empirical work has documented substan-tial preference heterogeneity in different insurance markets, including automobile tial preference heterogeneity in different insurance markets, including automobile insurance (Cohen and Einav, 2007), reverse mortgages (Davidoff and Welke, 2007), insurance (Cohen and Einav, 2007), reverse mortgages (Davidoff and Welke, 2007), health insurance (Fang, Keane, and Silverman, 2008), and long-term care insur-health insurance (Fang, Keane, and Silverman, 2008), and long-term care insur-ance (Finkelstein and McGarry, 2006). The existence of unobserved preference ance (Finkelstein and McGarry, 2006). The existence of unobserved preference heterogeneity opens up the possibility of heterogeneity opens up the possibility of advantageous selection, which produces selection, which produces opposite results to the opposite results to the adverse selection results just discussed. selection results just discussed.66

Consider for example heterogeneity in risk aversion in addition to the original Consider for example heterogeneity in risk aversion in addition to the original heterogeneity in risk (expected cost). All else equal, willingness to pay for insurance heterogeneity in risk (expected cost). All else equal, willingness to pay for insurance is increasing in risk aversion and in risk. If heterogeneity in risk aversion is small, is increasing in risk aversion and in risk. If heterogeneity in risk aversion is small, or if those individuals who are high risk are also more risk averse, the main insights or if those individuals who are high risk are also more risk averse, the main insights from the textbook analysis remain. But if high-risk individuals are less risk averse from the textbook analysis remain. But if high-risk individuals are less risk averse and the heterogeneity in risk aversion is suffi ciently large, advantageous selection and the heterogeneity in risk aversion is suffi ciently large, advantageous selection may emerge. Namely, the individuals who are willing to pay the most for insurance may emerge. Namely, the individuals who are willing to pay the most for insurance are those who are the most risk averse, and in the case described, these are also are those who are the most risk averse, and in the case described, these are also those individuals associated with the lowest (rather than the highest) expected cost. those individuals associated with the lowest (rather than the highest) expected cost. Indeed, it is natural to think that in many instances individuals who value insurance Indeed, it is natural to think that in many instances individuals who value insurance more may also take action to lower their expected costs: drive more carefully, invest more may also take action to lower their expected costs: drive more carefully, invest in preventive health care, and so on.in preventive health care, and so on.

Figure 4 provides our graphical illustration of such advantageous selection and Figure 4 provides our graphical illustration of such advantageous selection and its consequences for insurance coverage and welfare. In contrast to adverse selection, its consequences for insurance coverage and welfare. In contrast to adverse selection, advantageous selection is defi ned by an advantageous selection is defi ned by an upward sloping MC (and AC) curve. sloping MC (and AC) curve.77 As price As price is lowered and more individuals opt into the market, the marginal individual opting is lowered and more individuals opt into the market, the marginal individual opting in has higher expected cost than infra-marginal individuals. Since the MC curve is in has higher expected cost than infra-marginal individuals. Since the MC curve is

6 Another important (and more nuanced) aspect of preference heterogeneity is that it complicates the notion of effi ciency. With preference heterogeneity, the mapping from expected cost to willingness to pay need no longer be unique. That is, two individuals with the same expected cost may have different valuations for the same coverage, or two individual with the same willingness to pay for the coverage may have different underlying expected costs. This possibility does not affect our earlier and subsequent analysis, except that one needs to recognize that it requires a weaker sense of effi ciency. Specifi cally, it requires us to think of a constrained effi cient allocation that maximizes welfare subject to a uniform price. In such cases, the (constrained) effi cient allocation need not coincide with the fi rst-best allocation. Bundorf, Levin, and Mahoney (2010) discuss and empirically analyze this issue in more detail.7 More generally, once we allow for preference heterogeneity, the marginal cost curve needs not be monotone. However, for simplicity and clarity we focus our discussion on the polar cases of monotone cost curves.


upward sloping, the AC curve will lie everywhere below it. If there were no insurance upward sloping, the AC curve will lie everywhere below it. If there were no insurance loads (as in the textbook situation), advantageous selection would not lead to any loads (as in the textbook situation), advantageous selection would not lead to any ineffi ciency; the MC and AC curves would always lie below the demand curve, and in ineffi ciency; the MC and AC curves would always lie below the demand curve, and in equilibrium all individuals in the market would be covered, which would be effi cient.equilibrium all individuals in the market would be covered, which would be effi cient.

With insurance loads, however, advantageous selection generates the mirror With insurance loads, however, advantageous selection generates the mirror image of the adverse selection case, also leading to ineffi ciency, but this time due to image of the adverse selection case, also leading to ineffi ciency, but this time due to over-insurance rather than under-insurance. Figure 4 depicts this case. The effi cient over-insurance rather than under-insurance. Figure 4 depicts this case. The effi cient allocation calls for providing insurance to all individuals whose expected cost is allocation calls for providing insurance to all individuals whose expected cost is lower than their willingness to pay—that is, all those who are to the left of point lower than their willingness to pay—that is, all those who are to the left of point E(where the MC curve intersects the demand curve) in Figure 4. Competitive equilib-(where the MC curve intersects the demand curve) in Figure 4. Competitive equilib-rium, as before, is determined by the intersection of the AC curve and the demand rium, as before, is determined by the intersection of the AC curve and the demand curve (point curve (point C in Figure 4). But since the AC curve now lies below the MC curve, in Figure 4). But since the AC curve now lies below the MC curve, equilibrium implies that too many individuals are provided insurance, leading to equilibrium implies that too many individuals are provided insurance, leading to over-insurance: there are over-insurance: there are Q eqmeqm – – Q effeff individuals who are ineffi ciently provided individuals who are ineffi ciently provided insurance in equilibrium. These individuals value the insurance at less than their insurance in equilibrium. These individuals value the insurance at less than their expected costs, but competitive forces make fi rms reduce the price, thus attracting expected costs, but competitive forces make fi rms reduce the price, thus attracting these individuals together with more profi table infra-marginal individuals. Again, these individuals together with more profi table infra-marginal individuals. Again, the area of the deadweight loss triangle the area of the deadweight loss triangle EDC quantifi es the extent of the welfare loss quantifi es the extent of the welfare loss from this over-insurance.from this over-insurance.

Figure 4Advantageous Selection

Source: Einav, Finkelstein, and Cullen (2010), fi gure 2.

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From a public policy perspective, advantageous selection calls for the opposite From a public policy perspective, advantageous selection calls for the opposite solutions relative to the tools used to combat adverse selection. For example, given solutions relative to the tools used to combat adverse selection. For example, given that advantageous selection produces “too much” insurance relative to the effi cient that advantageous selection produces “too much” insurance relative to the effi cient outcome, public policies that tax existing insurance policies (and therefore raise outcome, public policies that tax existing insurance policies (and therefore raise Peqmeqm toward toward Peffeff) or outlaw insurance coverage (mandate no coverage) could be ) or outlaw insurance coverage (mandate no coverage) could be welfare-improving. Although there are certainly taxes levied on insurance policies, welfare-improving. Although there are certainly taxes levied on insurance policies, to our knowledge advantageous selection has not yet been invoked as a rationale to our knowledge advantageous selection has not yet been invoked as a rationale in public policy discourse, perhaps refl ecting the relative newness of both the theo-in public policy discourse, perhaps refl ecting the relative newness of both the theo-retical work and empirical evidence. To our knowledge, advantageous selection was retical work and empirical evidence. To our knowledge, advantageous selection was fi rst discussed by Hemenway (1990), who termed it “propitious” selection. De Meza fi rst discussed by Hemenway (1990), who termed it “propitious” selection. De Meza and Webb (2001) provide a theoretical treatment of advantageous selection and its and Webb (2001) provide a theoretical treatment of advantageous selection and its implications for insurance coverage and public policy.implications for insurance coverage and public policy.

Advantageous selection is not merely a theoretical possibility. It has recently Advantageous selection is not merely a theoretical possibility. It has recently been documented in several insurance markets, with different sources of been documented in several insurance markets, with different sources of individual heterogeneity that give rise to it. Finkelstein and McGarry (2006) individual heterogeneity that give rise to it. Finkelstein and McGarry (2006) document advantageous selection in the market for long-term care insurance and document advantageous selection in the market for long-term care insurance and provide evidence that more cautious individuals invest more in precautionary provide evidence that more cautious individuals invest more in precautionary behavior and are less likely to use a nursing home but at the same time are more behavior and are less likely to use a nursing home but at the same time are more likely to purchase long-term care insurance. Fang, Keane, and Silverman (2008) likely to purchase long-term care insurance. Fang, Keane, and Silverman (2008) document advantageous selection in the market for Medigap coverage, which document advantageous selection in the market for Medigap coverage, which provides private health insurance that supplements Medicare for the elderly, but provides private health insurance that supplements Medicare for the elderly, but show that in the case of Medigap, cognition may be the driving force: individuals show that in the case of Medigap, cognition may be the driving force: individuals with higher cognitive ability are often able to make better decisions, which can with higher cognitive ability are often able to make better decisions, which can translate into both greater coverage and at the same time lower healthcare translate into both greater coverage and at the same time lower healthcare expenditures.expenditures.

Advantageous selection provides a nice example of the interplay in the selec-Advantageous selection provides a nice example of the interplay in the selec-tion literature between theory and empirical work. The original adverse selection tion literature between theory and empirical work. The original adverse selection theory motivated empirical work testing for the existence of adverse selection. This theory motivated empirical work testing for the existence of adverse selection. This empirical work in turn provided examples of advantageous selection (which the empirical work in turn provided examples of advantageous selection (which the original theory had precluded), suggesting the need for important extensions to original theory had precluded), suggesting the need for important extensions to the theory. We now turn to a more detailed discussion of how the existing empirical the theory. We now turn to a more detailed discussion of how the existing empirical work can be viewed through the graphical framework we have developed.work can be viewed through the graphical framework we have developed.

Empirical Work on SelectionEmpirical Work on Selection

Empirical research on selection in insurance markets has fl ourished over the Empirical research on selection in insurance markets has fl ourished over the last decade. This empirical literature began, quite naturally, by asking how we can last decade. This empirical literature began, quite naturally, by asking how we can test for whether the classic adverse selection models apply in real-world insurance test for whether the classic adverse selection models apply in real-world insurance markets. In other words, what would selection look like in the data, when or if it markets. In other words, what would selection look like in the data, when or if it exists? Empirical research has now progressed from trying to detect the existence exists? Empirical research has now progressed from trying to detect the existence (and nature) of selection toward attempts to quantify its welfare consequences and (and nature) of selection toward attempts to quantify its welfare consequences and those of potential public policy interventions. We can use our graphical framework those of potential public policy interventions. We can use our graphical framework to understand the intuition and limitations of this research program.to understand the intuition and limitations of this research program.


“Positive Correlation” Tests for Adverse Selection“Positive Correlation” Tests for Adverse SelectionUsing our graphical framework, testing for adverse selection essentially requires Using our graphical framework, testing for adverse selection essentially requires

us to test whether the MC curve is downward sloping. Making inferences about us to test whether the MC curve is downward sloping. Making inferences about marginal individuals is diffi cult, however. As a result, the early empirical approaches marginal individuals is diffi cult, however. As a result, the early empirical approaches developed strategies that attempt to get around this diffi culty by, instead, focusing developed strategies that attempt to get around this diffi culty by, instead, focusing on comparing averages.on comparing averages.

The graphical depictions of adverse selection in Figure 1 (or Figure 3) suggest The graphical depictions of adverse selection in Figure 1 (or Figure 3) suggest one way to examine whether adverse selection is present in a particular insurance one way to examine whether adverse selection is present in a particular insurance market: compare the expected cost of those with insurance to the expected cost market: compare the expected cost of those with insurance to the expected cost of those without (or compare those with more insurance coverage to those with of those without (or compare those with more insurance coverage to those with less coverage).less coverage).

To see this idea more clearly, consider Figure 5. Here we start with the adverse To see this idea more clearly, consider Figure 5. Here we start with the adverse selection situation already depicted in Figure 3, denoting the AC curve shown in selection situation already depicted in Figure 3, denoting the AC curve shown in previous fi gures by AC previous fi gures by AC insuredinsured to refl ect the fact that it averages over those individuals to refl ect the fact that it averages over those individuals with insurance, and adding one more line: the AC with insurance, and adding one more line: the AC uninsureduninsured curve. The AC curve. The AC uninsureduninsured curve represents the average expected cost of those individuals who do not have curve represents the average expected cost of those individuals who do not have insurance. That is, the AC insurance. That is, the AC insuredinsured curve is derived by averaging over the expected costs curve is derived by averaging over the expected costs of the insured (averaging “from the left,” starting at of the insured (averaging “from the left,” starting at Q == 0) while the AC 0) while the AC uninsureduninsured curve is produced by averaging over the expected costs of the uninsured (averaging curve is produced by averaging over the expected costs of the uninsured (averaging “from the right,” starting at “from the right,” starting at Q == Q maxmax). A downward-sloping MC curve implies that ). A downward-sloping MC curve implies that

Figure 5The “Positive Correlation” Test for Selection

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AC AC insuredinsured is always above AC is always above AC uninsured uninsured , with the average costs of the insured at , with the average costs of the insured at Q maxmax equal to the average costs of the uninsured at equal to the average costs of the uninsured at Q == 0 (because both represent the 0 (because both represent the average costs of the full population) and with the marginal cost curve intersecting average costs of the full population) and with the marginal cost curve intersecting AC AC insuredinsured at at Q == 0 and AC 0 and AC uninsureduninsured at at Q == Qmaxmax..

Thus, at any given insurance price, and in particular at the equilibrium price, Thus, at any given insurance price, and in particular at the equilibrium price, adverse selection implies that the average cost of insured individuals is higher than adverse selection implies that the average cost of insured individuals is higher than the average cost of uninsured, and the difference in these averages is given by line the average cost of uninsured, and the difference in these averages is given by line segment segment CF in Figure 5 (the thick arrowed line in the fi gure). This basic insight in Figure 5 (the thick arrowed line in the fi gure). This basic insight underlies the widely used “positive correlation” test for asymmetric information. This underlies the widely used “positive correlation” test for asymmetric information. This positive correlation (between insurance coverage and expected costs) is analogous positive correlation (between insurance coverage and expected costs) is analogous to the distance between point to the distance between point C (average costs of those who in equilibrium are (average costs of those who in equilibrium are insured) and point insured) and point F (average costs of those who in equilibrium are not insured). (average costs of those who in equilibrium are not insured). The results are consistent with the existence of adverse selection if the average cost The results are consistent with the existence of adverse selection if the average cost of the insured (point of the insured (point C ) is statistically greater than those of the uninsured (point ) is statistically greater than those of the uninsured (point F ). ).

The test has typically been implemented by comparing proxies for expected The test has typically been implemented by comparing proxies for expected costs across individuals with different insurance coverage, controlling as needed costs across individuals with different insurance coverage, controlling as needed for important confounding factors (as we discuss below). Many of these empirical for important confounding factors (as we discuss below). Many of these empirical papers use data from a single company and examine average claims across individ-papers use data from a single company and examine average claims across individ-uals who are offered the same contracts but who choose more or less coverage. Our uals who are offered the same contracts but who choose more or less coverage. Our graphical framework naturally extends to the choice of more versus less coverage graphical framework naturally extends to the choice of more versus less coverage (as opposed to any insurance versus no insurance). Indeed, the recent burgeoning (as opposed to any insurance versus no insurance). Indeed, the recent burgeoning of empirical work on selection likely refl ects at least in part researchers’ increasing of empirical work on selection likely refl ects at least in part researchers’ increasing success in obtaining access to insurance company data, which has greatly improved success in obtaining access to insurance company data, which has greatly improved their ability to examine questions of private information empirically.their ability to examine questions of private information empirically.

Perhaps due in part to its not-so-demanding data requirement, variants of the Perhaps due in part to its not-so-demanding data requirement, variants of the positive correlation test have been quite popular; the test requires “only” that one positive correlation test have been quite popular; the test requires “only” that one observe the average expected costs of individuals (who are observationally identical observe the average expected costs of individuals (who are observationally identical to the fi rm) with different amounts of insurance coverage. There is now a large liter-to the fi rm) with different amounts of insurance coverage. There is now a large liter-ature studying how average costs vary across different coverage options in a broad ature studying how average costs vary across different coverage options in a broad range of insurance markets, including health, life, automobile, and homeowner range of insurance markets, including health, life, automobile, and homeowner insurance. The results have been mixed. In some markets, researchers have found insurance. The results have been mixed. In some markets, researchers have found evidence consistent with adverse selection—that is, higher average costs for indi-evidence consistent with adverse selection—that is, higher average costs for indi-viduals with greater insurance coverage—while in others they have found evidence viduals with greater insurance coverage—while in others they have found evidence of advantageous selection—defi ned by a negative relationship between insurance of advantageous selection—defi ned by a negative relationship between insurance coverage and average costs—or have been unable to reject the null hypothesis coverage and average costs—or have been unable to reject the null hypothesis of symmetric information, meaning no difference in average costs. Cohen and of symmetric information, meaning no difference in average costs. Cohen and Siegelman (2010) provide a recent review of this literature.Siegelman (2010) provide a recent review of this literature.

Challenges in Applying the Positive Correlation TestChallenges in Applying the Positive Correlation TestAlthough applying the simple positive correlation test is reasonably straight-Although applying the simple positive correlation test is reasonably straight-

forward, one must confront certain challenges. Researchers have generally been forward, one must confront certain challenges. Researchers have generally been quite careful to acknowledge these issues and in some cases to fi nd creative ways quite careful to acknowledge these issues and in some cases to fi nd creative ways that get around them. We mention here three common issues that often come up that get around them. We mention here three common issues that often come up in applications.in applications.


A fi rst important limitation of the positive correlation test is that comparing A fi rst important limitation of the positive correlation test is that comparing expected costs across individuals with and without insurance may confound adverse expected costs across individuals with and without insurance may confound adverse selection and moral hazard. Both adverse selection and moral hazard can generate selection and moral hazard. Both adverse selection and moral hazard can generate a positive correlation between insurance coverage and claims, but these are two a positive correlation between insurance coverage and claims, but these are two very different forms of asymmetric information with very different implications very different forms of asymmetric information with very different implications for public policy. With adverse selection, individuals who have private information for public policy. With adverse selection, individuals who have private information that they are at higher risk self-select into the insurance market, generating the that they are at higher risk self-select into the insurance market, generating the positive correlation between insurance coverage and observed claims. As already positive correlation between insurance coverage and observed claims. As already discussed, the government has several potential welfare-improving policy tools discussed, the government has several potential welfare-improving policy tools to possibly address such selection. With moral hazard, individuals are identical to possibly address such selection. With moral hazard, individuals are identical before they purchase insurance, but have incentives to behave differently after. before they purchase insurance, but have incentives to behave differently after. Those with greater coverage have less incentive to take actions that reduce their Those with greater coverage have less incentive to take actions that reduce their expected costs, which will generate a relationship between insurance coverage expected costs, which will generate a relationship between insurance coverage and observed claims. Unlike in the case of adverse selection, the government typi-and observed claims. Unlike in the case of adverse selection, the government typi-cally has no advantage over the private sector at reducing the welfare costs of cally has no advantage over the private sector at reducing the welfare costs of moral hazard.moral hazard.

Figure 6 shows how moral hazard can produce the same “positive correlation” Figure 6 shows how moral hazard can produce the same “positive correlation” property as adverse selection produces in Figure 5. Specifi cally, Figure 6 provides a property as adverse selection produces in Figure 5. Specifi cally, Figure 6 provides a graphical representation of an insurance market with moral hazard but no selection. graphical representation of an insurance market with moral hazard but no selection. The lack of selection is captured by the fl at MC curves. Moral hazard is captured The lack of selection is captured by the fl at MC curves. Moral hazard is captured

Figure 6The “Positive Correlation” Test for Moral Hazard

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by drawing two different MC curves, as opposed to the single MC curve we have by drawing two different MC curves, as opposed to the single MC curve we have drawn in the fi gures so far. The MC drawn in the fi gures so far. The MC insuredinsured curve represents the expected cost of curve represents the expected cost of insured individuals, and corresponds to the MC curves we have been drawing in all insured individuals, and corresponds to the MC curves we have been drawing in all previous fi gures. The MC previous fi gures. The MC uninsureduninsured curve represents the expected cost of these curve represents the expected cost of these same individuals, if they were uninsured. Moral hazard, which takes the form of greater individuals, if they were uninsured. Moral hazard, which takes the form of greater expected costs when a given individual has insurance than when the individual does expected costs when a given individual has insurance than when the individual does not, implies that MC not, implies that MC insuredinsured is greater than MC is greater than MC uninsureduninsured for each individual (or, graphi- for each individual (or, graphi-cally, point-by-point).cally, point-by-point).88 The vertical difference between MC The vertical difference between MC insuredinsured and MC and MC uninsureduninsured is a is a graphical way to quantify moral hazard in terms of expected cost.graphical way to quantify moral hazard in terms of expected cost.

Figure 6 is drawn for a case in which there is no adverse selection: individuals Figure 6 is drawn for a case in which there is no adverse selection: individuals have the same expected cost, the MC curves are fl at, and the demand curve is down-have the same expected cost, the MC curves are fl at, and the demand curve is down-ward sloping due to other factors (for example, heterogeneity in risk aversion). Yet, ward sloping due to other factors (for example, heterogeneity in risk aversion). Yet, a comparison of expected costs between the “insureds” and “uninsureds” would lead a comparison of expected costs between the “insureds” and “uninsureds” would lead to the same quantity (line segment to the same quantity (line segment CF ) as in Figure 5. However, while in Figure 5 ) as in Figure 5. However, while in Figure 5 the positive correlation arose due to adverse selection, in Figure 6 this same positive the positive correlation arose due to adverse selection, in Figure 6 this same positive correlation is generated entirely by moral hazard.correlation is generated entirely by moral hazard.99

Therefore, in situations where moral hazard could be an important factor, the Therefore, in situations where moral hazard could be an important factor, the positive correlation test is a joint test of either adverse selection or moral hazard. positive correlation test is a joint test of either adverse selection or moral hazard. Finding a positive correlation between insurance coverage and expected costs would Finding a positive correlation between insurance coverage and expected costs would force us to reject the null hypothesis (of symmetric information) either due to the force us to reject the null hypothesis (of symmetric information) either due to the presence of adverse selection or moral hazard (or both). Moreover, a fi nding of no presence of adverse selection or moral hazard (or both). Moreover, a fi nding of no correlation could either be due to no asymmetric information or to the existence of correlation could either be due to no asymmetric information or to the existence of both moral hazard and advantageous selection, which offset each other. On the other both moral hazard and advantageous selection, which offset each other. On the other hand, a convincing fi nding of a negative correlation is still informative, as it would be hand, a convincing fi nding of a negative correlation is still informative, as it would be consistent with advantageous selection, even in the presence of moral hazard.consistent with advantageous selection, even in the presence of moral hazard.

A second important consideration in applying the positive correlation test is A second important consideration in applying the positive correlation test is the set of covariates that are being conditioned out. As a starting point, one must the set of covariates that are being conditioned out. As a starting point, one must condition on the consumer characteristics that determine the prices offered to each condition on the consumer characteristics that determine the prices offered to each individual. That is, a proper implementation of the positive correlation test requires individual. That is, a proper implementation of the positive correlation test requires that we examine whether, among a set of individuals who are offered coverage that we examine whether, among a set of individuals who are offered coverage options at options at identical prices, those who buy more insurance have higher expected prices, those who buy more insurance have higher expected costs than those who do not. In the absence of such conditioning, it is impossible to costs than those who do not. In the absence of such conditioning, it is impossible to know whether a correlation arises due to demand (different individuals self-select know whether a correlation arises due to demand (different individuals self-select

8 For simplicity, we have drawn Figure 6 so that the MC uninsured curve is parallel to the MC insured curve, thus assuming that the cost effect associated with moral hazard is homogeneous across individuals. The discussion would be the same for a richer situation, in which the moral hazard effect is heterogeneous (so that the vertical distance between the MC insured and MC uninsured varies).9 Naturally, one could consider an environment in which both selection and moral hazard were present. The issues and discussion would be similar; we focused on the extreme case to simplify the graphical presentation. In particular, with no selection (fl at MC curves) we do not need to draw the corresponding AC curves since they are identical to the MC curves. In an environment with both selection (as shown by non-fl at MC curves) and moral hazard (MC insured > MC uninsured) each MC curve would have a corre-sponding AC curve. As in Figure 5, AC insured would be constructed by averaging “from the left” over the marginal costs of those with insurance (MC insured), while AC uninsured would be constructed by averaging “from the right” over the marginal costs of those without insurance (MC uninsured).


into different contracts) or supply (different individuals are offered the contracts into different contracts) or supply (different individuals are offered the contracts at different prices by the insurance company). Only the former is evidence of at different prices by the insurance company). Only the former is evidence of selection. As a result, some of the most convincing tests are those carried out using selection. As a result, some of the most convincing tests are those carried out using insurance company data, where the researcher knows (rather than assumes) the insurance company data, where the researcher knows (rather than assumes) the full set of characteristics that the insurance company uses for pricing. Absent data full set of characteristics that the insurance company uses for pricing. Absent data on individually customized prices, which is sometimes diffi cult to obtain, one may on individually customized prices, which is sometimes diffi cult to obtain, one may instead try to control in a fl exible manner for all individual characteristics that instead try to control in a fl exible manner for all individual characteristics that affect pricing (Chiappori and Salanie, 2000).affect pricing (Chiappori and Salanie, 2000).

A yet-more-nuanced decision is whether one should control for a larger set of A yet-more-nuanced decision is whether one should control for a larger set of covariates (when available). In addition to the consumer characteristics that deter-covariates (when available). In addition to the consumer characteristics that deter-mine their choice set—that is, the specifi c contracts and their prices—one could mine their choice set—that is, the specifi c contracts and their prices—one could attempt to control for other observed variables that are not used by the fi rm (due to attempt to control for other observed variables that are not used by the fi rm (due to regulation or any other reason), for other observable variables that are not observed regulation or any other reason), for other observable variables that are not observed by the fi rm (some may be observable to the fi rm with additional cost, others may by the fi rm (some may be observable to the fi rm with additional cost, others may be observable only to the researcher), and so on. Whether such variables should be be observable only to the researcher), and so on. Whether such variables should be used as covariates is less obvious and is likely to depend on the question that one used as covariates is less obvious and is likely to depend on the question that one would like to answer. One needs to recognize that the interpretation of a positive would like to answer. One needs to recognize that the interpretation of a positive correlation can vary depending on such decision. For example, one may fi nd a posi-correlation can vary depending on such decision. For example, one may fi nd a posi-tive correlation between insurance coverage and expected costs only because fi rms tive correlation between insurance coverage and expected costs only because fi rms are not allowed to incorporate race into pricing. If this positive correlation disap-are not allowed to incorporate race into pricing. If this positive correlation disap-pears when race is included as a control variable, one may want to be careful about pears when race is included as a control variable, one may want to be careful about the precise meaning of the term “asymmetric information” (since race is known to the precise meaning of the term “asymmetric information” (since race is known to the insurance company even if not used in pricing) even though the implications the insurance company even if not used in pricing) even though the implications for market equilibrium and ineffi ciency may be the same.for market equilibrium and ineffi ciency may be the same.

A fi nal important consideration in applying the test concerns the measurement A fi nal important consideration in applying the test concerns the measurement of costs. Figure 5 suggests that the theoretical object one would like to observe is of costs. Figure 5 suggests that the theoretical object one would like to observe is that of expected cost. Expectations are, of course, diffi cult to observe, so researchers that of expected cost. Expectations are, of course, diffi cult to observe, so researchers often use proxies.often use proxies.

The most direct proxy would use the average realized costs. With enough data, The most direct proxy would use the average realized costs. With enough data, realized costs of the insured converge to the expected costs, precisely capturing the realized costs of the insured converge to the expected costs, precisely capturing the theoretical object. In practice, however, realized costs may be tricky. For example, theoretical object. In practice, however, realized costs may be tricky. For example, when comparing insured to uninsured individuals, one obviously does not observe when comparing insured to uninsured individuals, one obviously does not observe the “claims” of the uninsured. Even when comparing claims of individuals who the “claims” of the uninsured. Even when comparing claims of individuals who choose more or less coverage within a given company, certain realized (social) costs choose more or less coverage within a given company, certain realized (social) costs are less likely to be claimed by individuals with less coverage. For example, there is are less likely to be claimed by individuals with less coverage. For example, there is a range of possible claim amounts that are worth claiming under low deductible, a range of possible claim amounts that are worth claiming under low deductible, but would not provide any benefi ts for (and are unlikely to be fi led by) individuals but would not provide any benefi ts for (and are unlikely to be fi led by) individuals covered by a higher deductible.covered by a higher deductible.

There are several potential strategies for trying to detect differences in real There are several potential strategies for trying to detect differences in real behavior as opposed to differences in claiming behavior. One option is to focus on behavior as opposed to differences in claiming behavior. One option is to focus on a subset of realized claims that are less prone to insurance coverage infl uencing a subset of realized claims that are less prone to insurance coverage infl uencing decisions to fi le a claim: for example, one could focus on multiple-car accidents in decisions to fi le a claim: for example, one could focus on multiple-car accidents in the context of automobile insurance. Alternatively, one might use data external to the context of automobile insurance. Alternatively, one might use data external to the fi rm: for example, by examining mortality certifi cates in the context of annuities the fi rm: for example, by examining mortality certifi cates in the context of annuities


or life insurance. The latter has the ancillary benefi t that such “external” data are or life insurance. The latter has the ancillary benefi t that such “external” data are observed for the uninsured population as well.observed for the uninsured population as well.

Another approach is to identify individual characteristics that are not priced Another approach is to identify individual characteristics that are not priced by insurance companies but are known to be associated with expected cost, such as by insurance companies but are known to be associated with expected cost, such as age or gender in the context of employer-provided health insurance. An ancillary age or gender in the context of employer-provided health insurance. An ancillary benefi t of this approach is that it also gets around the issue of moral hazard. A benefi t of this approach is that it also gets around the issue of moral hazard. A limitation of this approach, however, is that it can only be applied in situations in limitation of this approach, however, is that it can only be applied in situations in which—in confl ict with textbook economics—pricing is not affected by an impor-which—in confl ict with textbook economics—pricing is not affected by an impor-tant risk factor. In such settings, one might reasonably wonder whether the original tant risk factor. In such settings, one might reasonably wonder whether the original concerns about the effi ciency loss from adverse selection and the potential public concerns about the effi ciency loss from adverse selection and the potential public policy remedies are all that relevant.policy remedies are all that relevant.

Beyond Testing: Quantifying Selection EffectsBeyond Testing: Quantifying Selection EffectsThe importance and infl uence of the seminal theoretical work on selection The importance and infl uence of the seminal theoretical work on selection

in insurance markets stemmed in large part from its fi ndings that selection could in insurance markets stemmed in large part from its fi ndings that selection could impair the effi cient operation of competitive insurance markets and potentially impair the effi cient operation of competitive insurance markets and potentially open up scope for welfare-improving government intervention. Detecting selection open up scope for welfare-improving government intervention. Detecting selection is therefore only a fi rst step. If selection is empirically detected, it is natural to ask is therefore only a fi rst step. If selection is empirically detected, it is natural to ask whether the welfare costs it generates are large or small, and what might be the whether the welfare costs it generates are large or small, and what might be the welfare consequences of specifi c government policies. These are fundamentally welfare consequences of specifi c government policies. These are fundamentally empirical questions, and our graphical framework is useful for guiding attempts to empirical questions, and our graphical framework is useful for guiding attempts to quantify these welfare constructs.quantify these welfare constructs.

We begin by debunking a common (mis)perception that the very same We begin by debunking a common (mis)perception that the very same empirical objects that are used for the positive correlation test (described earlier) empirical objects that are used for the positive correlation test (described earlier) can also be informative about the welfare costs associated with selection. It may be can also be informative about the welfare costs associated with selection. It may be appealing to imagine that markets that appear “more adversely selected”—that is, appealing to imagine that markets that appear “more adversely selected”—that is, ones in which there is a larger difference between the expected costs of the insureds ones in which there is a larger difference between the expected costs of the insureds and uninsureds—experience greater welfare loss associated with that selection. and uninsureds—experience greater welfare loss associated with that selection. Unfortunately, Figure 7 illustrates that without additional assumptions, compari-Unfortunately, Figure 7 illustrates that without additional assumptions, compari-sons of expected costs are not that informative about underlying effi ciency costs. sons of expected costs are not that informative about underlying effi ciency costs. Figure 7 starts with the situation depicted in Figure 3. Once again, the equilibrium Figure 7 starts with the situation depicted in Figure 3. Once again, the equilibrium difference in expected costs between the insureds and uninsureds is given by the difference in expected costs between the insureds and uninsureds is given by the distance between points distance between points C and and F , and the welfare loss from adverse selection is , and the welfare loss from adverse selection is given by the area of the deadweight loss triangle given by the area of the deadweight loss triangle CDE . However, here we have drawn . However, here we have drawn two possible demand curves, each of which give rise to the same equilibrium point two possible demand curves, each of which give rise to the same equilibrium point (point (point C ), while keeping the MC and AC curves unchanged.), while keeping the MC and AC curves unchanged.1010 By design, the two By design, the two demand curves generate the same equilibrium point, thereby producing the same demand curves generate the same equilibrium point, thereby producing the same difference in expected costs between the insureds and uninsureds (line segment difference in expected costs between the insureds and uninsureds (line segment CF

10 Linear demand curves (as in Figure 7) allow us to rotate the demand curve without altering the rela-tionship between the MC curve and the AC curve. If demand was nonlinear, changes to demand would have triggered shifts in the AC curve (holding the MC curve constant). The basic point that the welfare cost of adverse selection can vary across markets with the same difference in expected costs between the uninsured and insured would still apply in cases with a nonlinear demand curve, but the fi gure would be messier to draw.


in Figure 7). However, these demand curves generate different effi cient outcomes, in Figure 7). However, these demand curves generate different effi cient outcomes, meaning different points at which the two demand curves intersect the MC curve, meaning different points at which the two demand curves intersect the MC curve, denoted in the fi gure by points denoted in the fi gure by points E11 and and E22..

1111 As a result, they produce different-sized As a result, they produce different-sized welfare losses, given by the corresponding triangles welfare losses, given by the corresponding triangles CDE 11 and and CDE 22. This example . This example thus illustrates how deadweight loss triangles of different sizes can be generated thus illustrates how deadweight loss triangles of different sizes can be generated even though the “extent of adverse selection” as measured by the difference in even though the “extent of adverse selection” as measured by the difference in average costs is the same.average costs is the same.

One way to make some progress in quantifying the welfare consequences of One way to make some progress in quantifying the welfare consequences of selection or of potential public policy is to use bounds that are based on easily selection or of potential public policy is to use bounds that are based on easily observable objects. For example, suppose we would like to bound the welfare cost observable objects. For example, suppose we would like to bound the welfare cost of selection. We use Figure 1 (adverse selection) for this discussion, but it is easy to of selection. We use Figure 1 (adverse selection) for this discussion, but it is easy to imagine an analogous discussion for the advantageous selection shown in Figure 4. imagine an analogous discussion for the advantageous selection shown in Figure 4. Suppose fi rst that we observe only the price of the insurance sold in the market. If Suppose fi rst that we observe only the price of the insurance sold in the market. If we are willing to assume that we observe the competitive equilibrium price (we are willing to assume that we observe the competitive equilibrium price (Peqmeqm), ), we can obtain a (presumably not very tight) upper bound of the welfare cost of we can obtain a (presumably not very tight) upper bound of the welfare cost of

11 As we emphasize throughout, the demand and cost curves are tightly linked. Thus, many changes in primitives will shift both demand and cost curves at the same time. It is still possible, however, to think of changes in the environment that could change demand without affecting the cost curves. For example, in the textbook case such changes would require preferences (but not loss probabilities) to change while preserving the ranking of willingness to pay for insurance across individuals.

Figure 7The “Positive Correlation” and Its (Non)relation to Welfare Costs of Selection

Quantity

Pric

e

Possible demand curves

MC curve

A

B

C

D

E2F

Peqm

ACinsured curve

Q eqm Q max

ACuninsured curve

E1


selection, given by selection, given by Peqmeqm ×× Q maxmax. Intuitively, because adverse selection leads to under-. Intuitively, because adverse selection leads to under-insurance, the worst possible scenario is when nobody is insured but everybody insurance, the worst possible scenario is when nobody is insured but everybody should be insured. Since the equilibrium price must exceed the willingness to pay should be insured. Since the equilibrium price must exceed the willingness to pay for insurance by the uninsureds (otherwise they would have purchased insurance), for insurance by the uninsureds (otherwise they would have purchased insurance), the price provides an upper bound on the per-individual welfare loss.the price provides an upper bound on the per-individual welfare loss.

Additional data may help tighten the bound. If we also observe the (equilib-Additional data may help tighten the bound. If we also observe the (equilib-rium) share of uninsured individuals (that is, rium) share of uninsured individuals (that is, Q maxmax – – Q eqmeqm), the upper bound for ), the upper bound for the welfare loss can be tightened to the welfare loss can be tightened to Peqmeqm((Q maxmax – – Q eqmeqm). Finally, if we also have all ). Finally, if we also have all the data elements needed for the positive correlation test—so that we also observe the data elements needed for the positive correlation test—so that we also observe the expected costs of the uninsureds and denote it by X—we can further tighten the expected costs of the uninsureds and denote it by X—we can further tighten this upper bound to (this upper bound to (Peqmeqm – – X )()(Q maxmax – – Q eqmeqm) (which is equal to area ) (which is equal to area CDFJ in in Figure 1.)Figure 1.)1212

Substantially more progress can be made in estimating the welfare conse-Substantially more progress can be made in estimating the welfare conse-quence of selection (or of potential public policy interventions) if we have one quence of selection (or of potential public policy interventions) if we have one additional data element beyond what is required for the positive correlation test. additional data element beyond what is required for the positive correlation test. This additional element, which is so heavily used in other subfi elds of applied This additional element, which is so heavily used in other subfi elds of applied microeconomics, is identifying variation in insurance prices.microeconomics, is identifying variation in insurance prices.

To see how useful price variation may be for welfare analysis, one can imagine To see how useful price variation may be for welfare analysis, one can imagine the ideal experiment of randomly varying the price at which insurance is offered the ideal experiment of randomly varying the price at which insurance is offered to large pools of otherwise identical individuals. For each pool, we would then to large pools of otherwise identical individuals. For each pool, we would then observe the fraction of individuals who bought insurance and the average realized observe the fraction of individuals who bought insurance and the average realized costs of insured individuals. In such an ideal situation, we can use the data gener-costs of insured individuals. In such an ideal situation, we can use the data gener-ated to “trace out” the demand curve and the AC curve in our graphical analysis, ated to “trace out” the demand curve and the AC curve in our graphical analysis, and to derive the MC curve, thus producing the three essential curves behind all of and to derive the MC curve, thus producing the three essential curves behind all of the welfare analysis in our graphical framework.the welfare analysis in our graphical framework.1313

Observing the MC curve arguably addresses the key challenge for empirically Observing the MC curve arguably addresses the key challenge for empirically analyzing insurance markets which, as noted earlier, is to identify the marginal indi-analyzing insurance markets which, as noted earlier, is to identify the marginal indi-viduals. Indeed, with knowledge of the MC curve, AC curve, and demand curve, it is viduals. Indeed, with knowledge of the MC curve, AC curve, and demand curve, it is straightforward to compute the welfare loss of adverse selection or any other object straightforward to compute the welfare loss of adverse selection or any other object of interest within the graphical framework we propose, such as the welfare effects of interest within the graphical framework we propose, such as the welfare effects of the various public policy interventions we analyzed earlier. This is the basic point of the various public policy interventions we analyzed earlier. This is the basic point we advance in Einav, Finkelstein, and Cullen (2010), where we empirically illustrate we advance in Einav, Finkelstein, and Cullen (2010), where we empirically illustrate this idea in the context of employer-provided health insurance. We also provide this idea in the context of employer-provided health insurance. We also provide some discussion of possible sources of such identifying pricing variation, including some discussion of possible sources of such identifying pricing variation, including fi eld experiments, experimentation by fi rms, and pricing variation driven by various fi eld experiments, experimentation by fi rms, and pricing variation driven by various common forms of insurance regulation.common forms of insurance regulation.

Such pricing variation has two related ancillary benefi ts. First, it provides a Such pricing variation has two related ancillary benefi ts. First, it provides a direct test of both the existence and nature of selection based on the slope of the direct test of both the existence and nature of selection based on the slope of the

12 To see this, note that Peqm(Q max – Q eqm) is equal to the area below line CJ, while X (Q max – Q eqm) is equal to the area below line DF because X is the average value of the MC curve between Q eqm and Q max.13 Note that the AC curve and the MC curve are linked through the demand curve, so that knowledge of two of the three curves allows us to obtain the third. To see this, note that marginal costs at point p, MC( p), can be computed by evaluating the difference in total costs TC( p) – TC(p′ ) for p′ just above p, where TC( p) is simply the product of average cost AC( p) and demand Q( p).


estimated MC curve. We can reject the null hypothesis of symmetric information estimated MC curve. We can reject the null hypothesis of symmetric information if we can reject the null hypothesis of a constant MC curve. Moreover, a fi nding if we can reject the null hypothesis of a constant MC curve. Moreover, a fi nding that the MC curve is downward sloping suggests the existence of adverse selection; that the MC curve is downward sloping suggests the existence of adverse selection; conversely, a fi nding that the MC curve is upward sloping suggests the existence of conversely, a fi nding that the MC curve is upward sloping suggests the existence of advantageous selection. Unlike the “positive correlation” test, this “cost curve” test advantageous selection. Unlike the “positive correlation” test, this “cost curve” test of selection is not affected by the existence (or lack thereof) of moral hazard. To of selection is not affected by the existence (or lack thereof) of moral hazard. To see why this is true, recall that the AC curve from which the MC curve is derived see why this is true, recall that the AC curve from which the MC curve is derived is defi ned as the average costs of all those individuals who buy a specifi c insurance is defi ned as the average costs of all those individuals who buy a specifi c insurance contract. Because the cost curves are defi ned over a sample of individuals who all contract. Because the cost curves are defi ned over a sample of individuals who all have the have the same insurance contract, differences in the shape of the cost curve are not insurance contract, differences in the shape of the cost curve are not directly affected by moral hazard.directly affected by moral hazard.1414

This insight suggests a step-by-step approach to analysis of selection in insurance This insight suggests a step-by-step approach to analysis of selection in insurance markets if one has access to identifying pricing variation in addition to the data on markets if one has access to identifying pricing variation in addition to the data on average costs of those with different insurance coverage. In the fi rst step, the simple average costs of those with different insurance coverage. In the fi rst step, the simple correlation test can be used to see if one can reject the null of symmetric informa-correlation test can be used to see if one can reject the null of symmetric informa-tion (in favor of either a positive or negative correlation). In the second step, if the tion (in favor of either a positive or negative correlation). In the second step, if the null of symmetric information is rejected, the identifying pricing variation can then null of symmetric information is rejected, the identifying pricing variation can then be used to estimate the cost curves and thus detect whether selection—as distinct be used to estimate the cost curves and thus detect whether selection—as distinct from moral hazard—exists and whether it is adverse or advantageous. Finally, if from moral hazard—exists and whether it is adverse or advantageous. Finally, if selection is detected, then its welfare cost can be estimated, and the welfare conse-selection is detected, then its welfare cost can be estimated, and the welfare conse-quences of potential public policy interventions weighed, by bringing the estimated quences of potential public policy interventions weighed, by bringing the estimated demand curve into the analysis as well.demand curve into the analysis as well.

There is yet another important benefi t from identifying pricing variation There is yet another important benefi t from identifying pricing variation (although it is not the focus of this essay), which is that it allows one to test for and (although it is not the focus of this essay), which is that it allows one to test for and quantify moral hazard. To see this, we can again consider what the ideal experiment quantify moral hazard. To see this, we can again consider what the ideal experiment might be. To analyze moral hazard, one would randomly allocate insurance to some might be. To analyze moral hazard, one would randomly allocate insurance to some individuals and allocate no insurance to others. But this is essentially the experiment individuals and allocate no insurance to others. But this is essentially the experiment generated by identifying pricing variation: those individuals who are assigned high generated by identifying pricing variation: those individuals who are assigned high prices are less likely to have insurance, while those who are assigned low prices are prices are less likely to have insurance, while those who are assigned low prices are more likely to be insured. One can then test and quantify the moral hazard effect of more likely to be insured. One can then test and quantify the moral hazard effect of insurance by regressing any observed behavior of interest on whether an individual insurance by regressing any observed behavior of interest on whether an individual is insured or not, using the identifying source of price variation as an instrument for is insured or not, using the identifying source of price variation as an instrument for insurance coverage. Moreover, one can go further and, instead of only quantifying insurance coverage. Moreover, one can go further and, instead of only quantifying the average moral hazard effect, use the estimated demand curve for insurance to the average moral hazard effect, use the estimated demand curve for insurance to quantify the heterogeneity of moral hazard as a function of the individual’s willing-quantify the heterogeneity of moral hazard as a function of the individual’s willing-ness to pay for insurance. Such analysis may address important questions that go ness to pay for insurance. Such analysis may address important questions that go well beyond the current state of the empirical literature on average moral hazard well beyond the current state of the empirical literature on average moral hazard effects in insurance markets to examine whether high-risk individuals are such effects in insurance markets to examine whether high-risk individuals are such because their underlying risk is higher—for example, because they are chronically because their underlying risk is higher—for example, because they are chronically

14 Of course, it is possible that the moral hazard effect of insurance is greater for some individuals than others and that, anticipating this, individuals whose behavior is more responsive to insurance may be more likely to buy insurance. We would still view this as selection, however, in the sense that individuals are selecting insurance on the basis of their anticipated behavioral response to it.


ill—or because their behavioral response to insurance is greater—for example, they ill—or because their behavioral response to insurance is greater—for example, they are deterred from seeing a doctor unless their out-of-pocket cost is suffi ciently low. are deterred from seeing a doctor unless their out-of-pocket cost is suffi ciently low. Indeed, we investigate this question empirically in some of our current work (Einav, Indeed, we investigate this question empirically in some of our current work (Einav, Finkelstein, Ryan, Schrimpf, and Cullen, 2010).Finkelstein, Ryan, Schrimpf, and Cullen, 2010).

Finally, we note that an attractive feature of our graphical framework is that it Finally, we note that an attractive feature of our graphical framework is that it provides a transparent way to assess the relative contribution of the data and of any provides a transparent way to assess the relative contribution of the data and of any underlying theoretical or statistical assumptions in giving rise to the empirical esti-underlying theoretical or statistical assumptions in giving rise to the empirical esti-mates. An example may be useful. Consider Figure 3, and suppose we are interested mates. An example may be useful. Consider Figure 3, and suppose we are interested in estimating the area of the deadweight loss triangle in estimating the area of the deadweight loss triangle CDE . For this particular object . For this particular object of interest, we require estimates of the demand curve and cost curves at the range of interest, we require estimates of the demand curve and cost curves at the range that is between that is between Q eqmeqm and and Q effeff , while other parts of the curves are less important. , while other parts of the curves are less important. A researcher who has excellent price variation that identifi es the curves for infra-A researcher who has excellent price variation that identifi es the curves for infra-marginal buyers (to the left of marginal buyers (to the left of Q eqmeqm) would need to rely heavily on theoretical or ) would need to rely heavily on theoretical or statistical assumptions to extrapolate the curves to the relevant region and would statistical assumptions to extrapolate the curves to the relevant region and would need to perform robustness checks to evaluate alternative models that may imply need to perform robustness checks to evaluate alternative models that may imply different extrapolations. In contrast, if the price variation spans the relevant region, different extrapolations. In contrast, if the price variation spans the relevant region, sensitivity to modeling assumptions may be less of a concern.sensitivity to modeling assumptions may be less of a concern.

To the extent that more limited (or nonexistent) pricing variation requires To the extent that more limited (or nonexistent) pricing variation requires greater modeling assumptions for the welfare analysis, one nice feature of insur-greater modeling assumptions for the welfare analysis, one nice feature of insur-ance markets is that the theory underlying individual choices of insurance coverage ance markets is that the theory underlying individual choices of insurance coverage is well developed and much tested (in the laboratory and in the fi eld). Thus, this is well developed and much tested (in the laboratory and in the fi eld). Thus, this is a context where perhaps more than others, relying on theoretical restrictions is a context where perhaps more than others, relying on theoretical restrictions may be quite credible. In Einav, Finkelstein, and Levin (2010), we provide a review may be quite credible. In Einav, Finkelstein, and Levin (2010), we provide a review of modeling approaches to welfare analysis in insurance markets and some of the of modeling approaches to welfare analysis in insurance markets and some of the recent fi ndings.recent fi ndings.

Concluding CommentsConcluding Comments

The graphical framework we have presented provides a unifi ed approach for The graphical framework we have presented provides a unifi ed approach for understanding both the conceptual welfare issues posed by selection in insurance understanding both the conceptual welfare issues posed by selection in insurance markets and potential government intervention, as well as the existing empirical markets and potential government intervention, as well as the existing empirical efforts to detect selection and measure its welfare consequences. However, this efforts to detect selection and measure its welfare consequences. However, this framework has abstracted from several constructs that are potentially of interest. framework has abstracted from several constructs that are potentially of interest. Some are very easily handled by simple extensions of the framework, others less so.Some are very easily handled by simple extensions of the framework, others less so.

We start with the easier issues. Although for expositional simplicity we focused on We start with the easier issues. Although for expositional simplicity we focused on the binary choice of “whether or not to buy insurance,” the same graphical analysis the binary choice of “whether or not to buy insurance,” the same graphical analysis can easily be applied to a choice between more or less coverage. It can also be used to can easily be applied to a choice between more or less coverage. It can also be used to analyze choices across more than two contracts, although a multidimensional graph-analyze choices across more than two contracts, although a multidimensional graph-ical approach is less appealing. Finally, it is straightforward to relax our maintained ical approach is less appealing. Finally, it is straightforward to relax our maintained assumption of perfectly competitive insurance markets—which in many markets may assumption of perfectly competitive insurance markets—which in many markets may not bear much resemblance to reality. One could carry out a similar analysis using not bear much resemblance to reality. One could carry out a similar analysis using alternative pricing assumptions which lead to a different equilibrium point (instead alternative pricing assumptions which lead to a different equilibrium point (instead of the average cost pricing arising from perfect competition). Welfare could then of the average cost pricing arising from perfect competition). Welfare could then


be analyzed by comparing the new equilibrium point with the effi cient allocation, be analyzed by comparing the new equilibrium point with the effi cient allocation, although of course now it must be recognized that any welfare cost confl ates both although of course now it must be recognized that any welfare cost confl ates both those costs created by selection and those created by imperfect competition.those costs created by selection and those created by imperfect competition.

A more serious issue is that we have focused on pricing distortions arising from A more serious issue is that we have focused on pricing distortions arising from selection while abstracting from the possibility that selection can distort the set of selection while abstracting from the possibility that selection can distort the set of insurance contracts that are offered. In other words, we have assumed that insurance insurance contracts that are offered. In other words, we have assumed that insurance companies compete over the price of a given set of insurance contracts. In practice, companies compete over the price of a given set of insurance contracts. In practice, insurance companies also set the coverage features of the insurance contract (like insurance companies also set the coverage features of the insurance contract (like deductibles, covered events, and so on) and selection pressures may well affect the set deductibles, covered events, and so on) and selection pressures may well affect the set of contract features offered in equilibrium. Admittedly, abstracting from this potential of contract features offered in equilibrium. Admittedly, abstracting from this potential consequence of selection may miss a substantial component of its welfare implications consequence of selection may miss a substantial component of its welfare implications and may explain why most of the empirical work to date on the welfare costs of selec-and may explain why most of the empirical work to date on the welfare costs of selec-tion has tended to fi nd relatively modest welfare effects. In Einav, Finkelstein, and tion has tended to fi nd relatively modest welfare effects. In Einav, Finkelstein, and Levin (2010), we provide more discussion and description of this point.Levin (2010), we provide more discussion and description of this point.

Allowing the contract space to be determined endogenously in a selection Allowing the contract space to be determined endogenously in a selection market raises challenges on both the theoretical and empirical front. On the theo-market raises challenges on both the theoretical and empirical front. On the theo-retical front, we currently lack clear characterizations of the equilibrium in a market retical front, we currently lack clear characterizations of the equilibrium in a market in which fi rms compete over contract dimensions as well as price, and in which in which fi rms compete over contract dimensions as well as price, and in which consumers may have multiple dimensions of private information (like expected consumers may have multiple dimensions of private information (like expected cost and risk preferences). From an empirical standpoint, the challenge is that if cost and risk preferences). From an empirical standpoint, the challenge is that if adverse selection greatly reduces the set of offered contracts, estimating the welfare adverse selection greatly reduces the set of offered contracts, estimating the welfare loss from the contracts not offered may require the researcher to go quite far out of loss from the contracts not offered may require the researcher to go quite far out of sample. While these challenges are far from trivial and may explain why there has sample. While these challenges are far from trivial and may explain why there has been relatively little work of either type on this topic to date, we view this direction been relatively little work of either type on this topic to date, we view this direction as an extremely important—and likely fruitful—topic for further research. As with as an extremely important—and likely fruitful—topic for further research. As with the research to date on selection in insurance markets, we expect that there will be a the research to date on selection in insurance markets, we expect that there will be a useful complementarity between theoretical and empirical progress moving forward.useful complementarity between theoretical and empirical progress moving forward.

■ We are grateful to David Autor, Seema Jayachandran, Chad Jones, Casey Rothschild, Dan Silverman, and Timothy Taylor for helpful comments, and to the National Institute of Aging (Grant No. R01 AG032449) for fi nancial support.

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