Insurer Pricing and Consumer Welfare: Evidence from Medigap

Transcription

1 Insurer Pricing and Consumer Welfare: Evidence from Medigap Amanda Starc y November 9, 2010 Abstract While adverse selection is often blamed for ine ciently high insurance premiums, imperfect competition is also a pervasive feature of many health insurance markets. In Medicare Supplement insurance (Medigap), two rms control nearly three-fourths of the market and premiums exceed claims by thirty percent. Motivated by these facts, I model the demand and supply side of the market. Rather than harming consumers, adverse selection actually restrains markups, resulting in a seven percent increase of total surplus. However, a low price elasticity and consumers brand preferences incentivize rms to engage in substantial marketing of their products and price above cost. Policies limiting marketing by insurers could reduce premiums signi cantly. I conclude that the strategic behavior of insurers facing relatively inelastic demand is far more important than adverse selection in explaining poor market performance and loss of consumer surplus. I am grateful to Susan Athey, Michael Dickstein, Greg Lewis, Julie Mortimer, Chris Nosko, Dennis Yao, and especially David Cutler and Ariel Pakes for helpful comments. All errors are my own. y Harvard University, 420E Baker Library, Harvard Business School, Boston, MA 02163, astarc@hbs.edu 1

2 1 Introduction The Patient Protection and A ordable Care Act, signed in March 2010, represents a substantial expansion in health insurance coverage. The legislation relies on the creation of exchanges and regulation of individual insurance markets to accompany an individual mandate. Underlying these exchanges is the idea that comparison shopping by consumers will lead to more e cient outcomes. However, there is little empirical evidence on the nature of consumer demand for di erentiated insurance markets or the operation of individual health insurance markets 1. Indeed, many such markets are characterized by high concentration, high premiums, and poor outcomes for consumers. The market for Medicare Supplement (Medigap) insurance is one example; in this market, consumers face dramatic price di erences for contractually identical policies, two rms control nearly three-fourths of the market, and the markup of premiums over claims is nearly thirty percent - a full fteen percent higher than the guidelines in the heath reform bill. These features are not unique to Medigap insurance. In the past decade, the growth in health insurance premiums has rapidly outpaced in ation, and this combination of rising premiums, pro ts, and concentration has led to arguments for increased antitrust enforcement and stricter regulation from the left, as well as counter-arguments questioning the e cacy and prudence of such policies from the right. In this paper, I will use a structural model to describe and analyze the Medigap market. This insurance is designed to cover the cost-sharing provisions associated with Medicare, the public health insurance program for elderly Americans. The market is of considerable policy interest in its own right, covering over one-fourth of Medicare-eligible seniors in my dataset. The policies in the Medigap market are standardized, and there are a large set of potential suppliers. Rather than experiencing adverse selection, Fang, Keane, and Silverman (2008) argue that Medigap policies are purchased by relatively healthy consumers. The market is heavily regulated: rms may only o er standardized policies and are required to pay out sixty- ve percent of the premiums they collect. Under many circumstances, they cannot price based on an individual s health status. Despite a concerted policy e ort to ensure a well-functioning market, the market does not seem to lead to e cient outcomes for consumers. I consider a number of explanations for the structure of the Medigap market. First, asymmetric information in the form of adverse selection - a classic and well-studied market failure - could lead to higher premiums or an underprovision of insurance. However, in addition to asymmetric information, a low 1 As noted by Dafny, Ho, and Varela (2010), most non-elderly Americans purchase policies through an employer, who mediates the exchange and typically o ers a small number of choices. They argue that this reduction in the set of choices available to consumers creates substantial deadweight loss. 2

3 demand elasticity coupled with brand preferences may cause welfare losses for consumers. Insurance policies are complicated nancial products and it is extremely di cult for average Americans, let alone a potentially vulnerable and less technology-savvy group of elderly Americans, to understand all of the contractual details. The stakes are high; therefore, consumers are willing to pay more for insurance from a "trusted name," potentially driving up premiums as consumers trade-o brand preferences and price. In turn, insurers will compete to be such a "trusted name," often incurring large marketing expenditures. This paper contributes to the literature by jointly addressing the asymmetrical information problem and the role of insurer market power in an equilibrium model. Certain features of the Medigap market, such as standardized policies, make this market ideal for such a study. However, the paper also contains more general insights; methodologically, I show how the standard analysis of demand systems and imperfect competition can be modi ed to incorporate asymmetric information. Conceptually, the paper shows that the interaction between asymmetric information and imperfect competition is important for consumer welfare: if rms have market power, adverse selection can increase consumer welfare. I model demand using a discrete choice framework that allows for the calculation of elasticities and estimation of the relationship between premiums and claims. I incorporate consumer heterogeneity in preferences to allow for adverse selection. Importantly, estimates of consumer preferences and the relationship between consumer characteristics and claims are used in a model of pro t maximizing rm behavior. The moments generated by the supply side assumptions allow for the estimation of any marginal administrative costs that rms incur in addition to claims 2. Finally, assumptions about entry behavior determine xed costs of advertising and operation for the two largest insurers. The results show that demand for Medigap insurance is best characterized by a low demand elasticity and very strong brand preferences. This elasticity, at -1.1, allows insurers to price far above marginal cost, while the strong brand preferences provide big incentives for insurers to invest in brand-promoting activity, such as marketing. The Not all of the rents are captured by insurers: many of these rents are realized by other participants in the market, such as the American Association of Retired Persons (AARP), while other rents are dissipated through the payout of commissions to insurance brokers. Using these estimates and the equilibrium model, I show that the presence of selection holds down markups: adverse selection is, in this case, good for consumers. This is not simply a transfer: the presence of adverse selection increases total surplus by nearly seven percent 3. Public policy that focuses on adverse selection will have limited positive impact 2 The combination of claims data and assumptions that rms pro t maximize pro ts allows me to separate pro ts from administrative loads, and, in turn, estimate xed and sunk costs. 3 Unsuprisingly, marginal and average cost pricing rules lead to big price reductions and large gains in 3

4 because adverse selection is not the cause of high premiums. In contrast, policies that focus on the provision of information to consumers have great potential for improving consumer welfare. For example, limiting the extent to which insurers can di erentiate their products with marketing leads to sti er price competition associated with an nine percent fall in premiums. Subsidizing a rm to compete direct with UnitedHealth reduces premiums by twenty percent. The paper is organized as follows. Section 2 describes the Medicare Supplemental Insurance market in greater detail. Section 3 outlines the demand system, focusing on the potential for adverse selection. Section 4 describes the model of supplier behavior. Section 5 provides an analysis of the interaction between asymmetric information and imperfect competition. Section 6 describes the role of marketing in shaping consumer welfare, and section 7 concludes. 2 The Medigap Market Medicare, the federally run health insurance for the elderly, has signi cant cost sharing provisions. The program was largely designed to resemble private insurance available at the time of its inception and, as a result, the cost-sharing provisions left Medicare bene ciaries exposed to a large degree of risk. Part A, which covers hospitalization and is free to all those who are eligible, has a deductible of approximately one day of inpatient care, or around $1000. Part B, which covers outpatient services, requires 20% copayments for services with no stoploss. As a result, over half of all seniors have some form of "wrap-around" (supplemental) insurance; despite the prevalence of additional coverage, out of pocket costs are substantial 4. Medigap insurance arose to meet the demand for wrap-around coverage. Due to allegations of insurer fraud, consumer confusion, and duplicate coverage, minimum standards were introduced in various states in the 1970s and in 1980, these minimum standards were implemented nationally 5. The plans were standardized in 1990; additional plans have been added and prescription drug coverage eliminated since that time. Today, consumers may only choose from a federally mandated menu of Medigap policies. These plans are described in Table 1, which also shows the distribution of consumers across policies. With the exceptions of policies K and L, which have substantial cost sharing arrangements, the plans are fairly similar. Plans A-J cover the Part A hospital deductible and plans B-J cover the coinsurance on Part B outpatient services. Plan F is by far the most popular, covering both consumer and total surplus. 4 This is especially true for the near-poor. See Gross et al (1999) for a discussion. 5 Finkelstein (2004) discusses the reasons for and impact of the implementation of minimum standards. 4

5 nearly half of the Medigap population, and plans C and J capture signi cant portions of the market as well. In addition to supplemental coverage through a previous employer or Medigap, seniors can choose a Medicare HMO or a prescription drug plan; some seniors are also eligible for additional bene ts from Medicaid or the Veterans Administration. After turning sixty- ve and enrolling in Medicare Part B, consumers have six months to choose a Medigap policy without being subjected to medical underwriting, in which insurers can ask about, and price to, pre-existing conditions and current health status. During this period, insurers can only price based on age, gender, and smoking status. Evidence from Robst (2001) indicates that most consumers are not subject to medical underwriting; premiums are a function of state of residence, age, and gender. The individual level sample will be constructed to take account of this fact. In addition to standardization and medical underwriting regulation, loss ratio regulation is important in this market and especially important to the formulation of the supply side model. Federal regulation requires a minimum loss ratio, de ned as the ratio of claims paid out in a market to premiums collected, of 65% for individual plans. If plans violate this regulation, they are required to pay transfers to policyholders such that at least 65% of the premiums collected are paid back out to policyholders. However, the regulation is violated in the data for over 48% of policies and the mean pro t rate in this market is 29%. 2.1 Data Market level data from the National Association of Insurance Commissioners (NAICS), a regulatory administrative database, contains premiums, quantities of new policies sold, and claims at the state-insurer-policy level. The data are aggregated into three year periods: the 2006 data contains new policies sold from , the 2007 data contains new policies sold from , and the 2008 data contains new policies sole from treat each state in each of these three year sets within a state as a separate market 6. I will The data contains information about new policies sold; there are a few advantages this measure. First, I observe consumers the rst time they purchase a given policy, which makes it less likely that they are being subjected to medical underwriting. This limits the ability of the insurer to price to individual risk, making the examination of selection more interesting. Furthermore, because they have no history in this market, consumer inertia or 6 This also masks any within-state price variation. Maestras, Schroeder, and Goldman document that within-state price dispersion is dwarfed by cross-state price dispersion. Furthermore, the market shares are adjusted to account for consumers that appear in multiple cross-sections, and the standard errors are corrected using the method described by Bhattacharya (2005). 5

6 switching costs will not bias my demand estimates, allowing me to abstract away from the potentially dynamic problem facing consumers and rms 7. Therefore, a market is de ned as the pool of rst-time enrollees (assumed to be in the open-enrollment period) in a state-year combination. Individual level data from the Medicare Current Bene ciary Survey (MCBS) is used to augment the NAIC market level data. The MCBS is a survey of a nationally representative panel of Medicare bene ciaries that is linked to administrative records from Medicare. provides information both on expenditures, coverage, and a wide variety of demographic characteristics. I will use several variables from this data, including demographic characteristics such as age and income, Medicare expenditures as a proxy for health, and a dummy for having any Medigap coverage (constructed as in Fang, Keane, and Silverman (2008)). This will provide me with a set of consumers to simulate characteristics without making any assumptions about the joint distribution of consumer characteristics. The data highlights the potential for both asymmetric information and imperfect information in this market. Medigap is no exception. First, health insurance is a highly concentrated industry, and In 2008, the American Medical Association reported that nearly all acute care health insurance markets quali ed as "highly concentrated" by the standards of the Department of Justice 8. Figure 1 plots the Her ndahl index across markets; not only are the vast majority "highly concentrated", but the majority have Her ndahl indices over Still, concentration is even higher in Medigap insurance, in which only two markets have a Her ndahl index below As seen in Table 2, the national four rm concentration ratio for Medigap insurance is a staggering 82%. This stands in direct contrast to other lines, or types, of insurance; for example, commercial auto insurance, purchased by most Americans, has a four rm concentration ratio of only 21%. It Despite the high level of market concentration, the federal government has not challenged the mergers and acquisitions that have led to massive consolidation, largely leaving the role of regulation to states 9. Table 3 shows Medigap market share data at both the national and state level. United- Health is the dominant rm in the market, capturing 46% of the national market and nearly 50% of each state s market on average. Mutual of Omaha sells nearly a fourth of all policies sold nationwide; taken together, two rms sell nearly three-fourths of all Medigap policies. Market share declines quickly; beyond the top ten rms, no insurer captures more than 1% of the market. Additionally, among the small and mid-sized rms, there are some recognizable companies. For example, State Farm - a rm normally associated with property and 7 This is addressed in the discussion of the game played by insurers in Section 3. 8 See "Competition in Health Insurance: A Comprehensive Study of U.S. Markets" 9 See Dafny et al s (2010) discussion of the UnitedHealth-Paci Care, UnitedHealth-Sierra, and, in particular, Aetna-Prudential mergers. 6

7 casualty - captures approximately 2% of the market, while Nationwide, another property and casualty company, is a very small player. HMOs, capture a negligible part of the market as well. Furthermore, Wellpoint and Humana, large In the Medigap market, the rms are highly asymmetrical, with a few large rms that capture the majority of the market, driving the high concentration ratios 10. Marketing insurance is a di cult and expensive task; search costs may be high and employing insurance brokers may be costly (Cebul et al 2010). Furthermore, this problem is likely to be exacerbated with an elderly population that is not technologically savvy enough to search e ectively on the internet and may be experiencing cognitive declines 11. Ultimately, search costs are not the only feature of this market that leads to the existing market structure; consumer anxiety and preferences for a "trusted name" are important even for contractually identical policies 12. a number of potential channels. Facing the task of marketing their policies, insurers may choose one of They can sell their policies directly, through independent brokers, who sell a variety of insurance and nancial products of a variety of di erent rms, or proprietary agents. The second largest rm in the Medigap market, Mutual of Omaha, pays 16% of premiums of Medigap policies to agents in the form of commissions 13. largest rm, UnitedHealth, is both a large player in other lines of health insurance and has purchased the brand of the American Association of Retired Persons (AARP), which, according to Bloomberg, collected nearly ve hundred million dollars in royalties and fees in 2007 and $222 million from UnitedHealth alone in The The AARP brand name allows it to capture a large proportion of the Medigap market by selling their policies directly to consumers 14. Table 4 shows prices, claims, and pro t rates, de ned as the percent markup over claims. 10 Sutton (1992) suggests that the sunk costs (potentially of marketing) can lead to asymmetric rm sizes similar to those seen in this market. Ultimately, I will measure xed and sunk cost of entry and argue that only an entrant who incurs such large costs can have a positive impact on the market. 11 See Fang, Keane, and Silverman (2008) for a discussion of cognitive ability and insurance purchasing behavior. 12 Alexcih et al indicate that insurers attempt to di erentiate themselves along this dimension. Simple logit models of demand show that elasticities are not statistically di erent from one another if brand e ects are included or not. However, signi cantly more of the variation in jm is explain when brand dummies are included. 13 Brand e ects are critical in explaining consumer behavior on the demand side, and are drivers of consumer behavior. The commission is taken from a Mutual of Omaha Agent Guide. 14 The strategies of the rms with a small market presence are often to be a niche player, capturing consumers who happen to prefer their brand. Often, these rms, such as Aetna, specialize in other lines of insurance, but will engage in direct sales of Medigap on their website or over the phone. As a result, they do not sell many policies, but also do not need to pay brokers commissions on the policies they sell. They can choose to incur low costs - both variable and xed - knowing that they will sell very few policies. The next section formalizes the game played by insurers calculates costs that correspond to these marketing strategies. 7

8 There is both substantial variation in prices across policies and a sizable gap between prices and claims. This gap is the largest among the more popular policies. The average enrollment weighted premium for Plan C is $1729 and the average enrollment weighted claim is only $1399; implying a pro t rate of almost 24%. For Plans F and J, load or margin before administrative costs, average 32% and 35%, respectively. Figure 2 shows the relationship between prices and market concentration. Average enrollment-weighted premiums are plotted against the two- rm concentration ratio, which, in the vast majority of markets will capture the size of UnitedHealth and Mutual of Omaha. Higher concentration is associated with higher premiums; a 1% increase in two- rm concentration rate is associated with an approximately 0.26% increase in premiums. In addition to market structure, adverse selection could negatively impact market outcomes for consumers. Consumers may sort non-randomly into Medigap insurance and between policies because their preferences for holding insurance and for insurance contract characteristics, including price, are correlated with their eventual claims. Figure 3 shows the relationship between premiums charged and average claims for Policy C 15. There is a strong positive relationship between the two: the correlation is 0.54 over all policies. This provides some evidence that consumer preferences are correlated with underlying risk (perhaps because higher risk individuals are less price sensitive); this could lead to distortions in pricing. The potential for welfare losses due to adverse selection is well documented in the theoretical and empirical literature. Chiappori and Salanie (2000) propose a positive correlation test: in the presence of either adverse selection or moral hazard, insurance coverage and claims will be positively correlated. A number of studies use this framework, and some fail to nd evidence of imperfect information (Cawley and Philipson (1999), Cardon and Hendel (2001)). Cutler, Finkelstein, and McGarry (2006) explain these con icting results as the result of multidimensional consumer characteristics; a consumer with a low risk ex ante may also be extremely risk adverse (the "worried well"). A more recent literature has attempted to quantify the welfare e ects of selection. However, these papers ignore strategic insurer pricing decisions, and rely on the benchmark of average claim pricing (Einav, Finkelstein, and Cullen 2010), while this paper will focus on the interaction between imperfect competition and asymmetric information. This interaction is crucial: if insurers have market power, adverse selection can be an e ective check on markups. By contrast to the extensive literature on adverse selection, less attention has been paid to the structure of insurance markets. Cebul et al (2010) draw attention to the extensive use of marketing and brokers in employer-sponsored health insurance, showing that search costs 15 Policy C was chosen because it popular, but never contain prescription drug coverage before Part D insurance became available. Anecdotally, the policies with drug coverage faced severe adverse selection. 8

9 create frictions in the market. Dafny et al (2010) show that a portion of the rapid increase in claims can be attributed to changes in market structure. However, these studies have not analyzed the impact of selection and insurer behavior in an equilibrium model. Therefore, this study is a natural complement to these two strains of the literature; I will draw on a fair amount of institutional detail and show how market structure, strategic rm decisions, and consumer welfare are linked when asymmetric information a ects demand for insurance. The analysis will highlight the importance of marketing costs and strategic insurer behavior in driving market outcomes. It will show that adverse selection can reduce markups, and, therefore, bene t consumers. Finally, it will show how policy remedies depend critically on the impact of advertising on consumer preferences. 3 Demand In order to understand how insurer behavior is related to the problem of imperfect information as well as how consumer behavior a ects welfare, it is important to analyze an equilibrium model that incorporates consumer demand and insurer pricing. This section will rst describe the model of consumer preferences for insurance products and insurer claims. Conditional on these estimates, assumptions about rm pro t-maximizing behavior will identify marketing and administrative costs. After describing the game played by insurers, I will describe the joint estimation of consumer preferences and claims in sections 3.1 and 3.2. Section 4 describes the estimation of administrative costs and the market-speci c xed or national sunk costs of marketing. The game is played by insurers in four stages as follows: 1. Firms simultaneously decide which markets to enter, and incur a xed or sunk cost of marketing and chose which subset of plans to o er Firms simultaneously set prices, knowing that the equilibrium distribution of prices a ect the allocation of consumers and, therefore, shares and claims. 3. Consumers choose between available plans and incur claims. (Firms are passive at this stage.) 16 Eventually, xed and sunk costs will be estimated. The estimation relies on Mazzeo s model of entry, in which rms decide to enter and on a product type (here, a marketing type). Mazzeo s game can be formalized using a number of di erent equilibrium concepts, though a number of restrictions are necessary to guarantee a unique equilibrium. The avor of the estimation I describe (and the market itself) is much closer to a Stackelberg game in which an entrant decides whether or not enter conditional on the current market structure. 9

10 4. Regulator possibly nes rms who do not meet the required loss ratio. Firms know this when pricing and incorporate it into their pricing decision. In order to estimate administrative cost, I explicitly model the pricing game in Stage 2. Conditional on demand and cost estimates, I form moment inequalities conditional on variable pro ts, which require positive pro ts for active rms and negative for an additional rm replicating the strategy of a currently existing rm. These assumptions (partially) identify xed or sunk costs, which can be compared to gains in consumer surplus from increased competition. The game described above and the demand system are both static simpli cations of a dynamic problem. However, the market level data provides information on new policies sold, which allows me to abstract away from issues related to plan switching or cancellation 17. Additionally, rms may rate their policies di erently, choosing to base premiums on the age at which the policy was issued (issue-age) or the current age of the consumer (attainedage) or based on a community rating. The attained-age policies have a steeper pro le of premiums over time, but may initially be cheaper. The data do not contain information on the rating method, so the unobserved pro le of future premiums is part of the unobserved characteristic in the demand system. Therefore, I will model demand as static and the game described above as being played once in each market, where a market is de ned as the pool of new enrollees in a state-year. Firms must compete for this new pool every year. 3.1 Consumer Preferences In this market, the signi cant cost-sharing provisions of basic Medicare create demand for insurance coverage. In the most basic model of insurance, consumers value both their health status and consumption c i. health status and may, in turn, improve health. The two are linked because medical expenditures depend on To simplify, consider the choice between supplement coverage and no supplemental coverage in a model in which consumers have utility over income! i and health which is a function of underlying status z i and medical expenditure m (z i ). If the consumer chooses no supplemental coverage, they face the cost of their medical expenditure, while if the consumer chooses supplemental coverage, they simply pay the policy s premium regardless of the state of the world. Let the states of the world be indexed by s with probability (s; z i ), which vary with individual health status, and 17 From the consumer s perspective, the insurance policy is not simply a one year contract at a speci ed price, but also the option to purchase in the future. Because consumers are subject to medical underwriting after the open enrollment period, they may be "locked in" to the policy they purchase, which is guaranteed renewable. Therefore, they should consider not only the current premium, but also the expected future stream of premiums. 10

11 expenditure by m (s; z i ) where j = 1 if the consumer purchases insurance. Consumer utility is given by: Z V (c i ; z i ) = (U (z;! i p j ) 1 (j = 1) + U (z i ;! i m (s; z i )) 1 (j = 0)) d (s; z i ) and with su ciently restrictive functional forms on the utility over consumption and health and knowledge of the potential states of the world s, the econometrician can estimate coef- cients of interest, such as a coe cient of absolute risk aversion and the consumer s (potentially subjective) probabilities (s). However, this model is already a simpli cation (full insurance, a single policy) and still cannot be estimated in this context. Except for binary cases or extremely detailed data, it is nearly impossible to even innumerate the states of the world due to data limitations 18. Furthermore, insurers in individuals markets o er a wide range of di erentiated products; even within Medigap s standardized policies, consumers choose from a wide range of vertically and horizontally di erentiated options. Therefore, one can consider a simpli cation of this model where the consumer has a valuation over insurance contracts j. In such a model, the valuation, which may be contingent on health status or income! i, is denoted by v j ; z i ;! i ; d = f E m j ; z i ; zi ; d (! ; z i ) p j, where consumers value their expected medical expenditure under the contract, and utility over insurance depends on health status and price sensitivity is also individual-speci c. As a result, I will use variation in prices and coverage levels to estimate the distribution of a set of random coe cients d that a ect utility for insurance and disutility for price. coe cients and claims govern selection. The interaction of the random Price dispersion exists even within individual contracts, indicating that consumers either have brand preferences or incur search costs, or both. I will model consumers as having preferences over individual brands; therefore, a consumer could obtain higher utility from an AARP-sponsored policy A than a Mutual of Omaha branded policy A, even if the latter has lower premiums 19. The standardization has limited the ability of insurers to o er di erentiated contracts, and this leads companies to compete based on level of service and "company reputation" 20. As a result, following the discrete choice literature, contracts are de ned as a bundle of characteristics: the lettered policy x jm and brand b jm such that 18 This is the approach taken, for example, in Cohen and Einav (2007) and Handel (2009). In the rst case, the authors model deductible choice (high or low), while Handel considers an employer-sponsored context and has extensive data on claims and out-of-pocket costs under various policies. 19 While the plans are identical and claims are largely automated, some rms, such as UnitedHealth, o er services, such as a nurse call line. 20 Alexcih et al (1997) note that the regulations allow individual states to approval "innovative bene ts"; however, in practice, companies choose to compete on brand reputation rather than product di erentiation. 11

12 j = g (x jm ; b jm ). I will allow consumers to vary along two dimensions, a proxy for health status z i and income! i, but no unobserved characteristics. Consumer preferences over health and income drive the value consumers place on di erent insurance contracts. Income is likely to a ect willingness-to-pay for insurance through price sensitivity. Therefore, the model will allow to depend on income. Furthermore, if expenditure depends on severity of illness, the trade-o between facing a sure premium and an uncertain expenditure varies by health status. Therefore, the model will allow to depend on a proxy for health status that captures expected expenditure. Finally, health status also a ects the probability of needing medical care; therefore, the utility of holding any insurance policy will depend on health status. The trade-o that governs both interactions is the same: those with higher expected expenditure prefer a product that reduces their own nancial exposure or are willing to trade o more certain income for reduced exposure to uncertain payments. Formally, a set of products J, de ned by the contract letters above, are o ered by a set of rms F in a set of markets M, where a market is de ned as a state-year. The consumer chooses one such policy (or the outside option) in order to maximize their indirect utility function. Consumer i 0 s valuation from product j in market m is given by: v ijm x jm ; jt ; p jm ;! i ; z i ; d = x 0 jm 1 + b 0 jm 2 + jm + p jm + ijm + " ijm ijm =! p jm! k i + z p jm z k i + k z k i The unobserved product characteristic is denoted by jm. The estimates of! and z capture the impact of consumer characteristics on price sensitivity. Finally, k allows consumers to vary in their preference for holding any Medigap policy. The error in the utility function is an IID type-i extreme value " ijm. Summary statistics describing consumers are found in Table 5 and 5a. About 30% of the sample purchases Medigap insurance, which is representative of the Medicare eligible population as a whole. The sample is restricted to those who are likely to be purchasing Medigap insurance for the rst time, those younger than 72 with Part B charges. The income variable indicates an average income of $36,803, with a substantial amount of variation 21. The mean of private health insurance expenditure is low because it is equal to zero for those consumers without private health insurance, including Medigap. Therefore, I form an expectation of insured expenditure that conditions on having insurance, as well as income, demographic characteristics, and self-reported health status, and extrapolate to the whole sample. The regression used is detailed in Table 5c; the expectation depends heavily on the 21 Income is truncated above at $200,000 in the MCBS. 12

13 consumer s own perception of their health as well as demographic characteristics, including income, which may a ect utilization of health care services. This measure, which is assumed to proxy for Medigap claims, averages $ , which is slightly higher than the average claim in the market-level data, which may re ect overlap between Medigap and other private insurance plans 22. checks. The error term implies that, conditional on consumer characteristics, shares can be written as: Appendix A contains alternative demand speci cations and robustness s ijmj! x jm ; jt ; p jm ;! i ; i ; d = exp x 0 jm 1 + b 0 jm 2 + jt + p jm + ijm 1 + J l=1 exp x0 jm 1 + b 0 jm 2 + lt + p lm + ilm Income and health are jointly distributed; given the joint distribution F (!; ), market shares can be written as: Z s jm = exp x 0 jm 1 + b 0 jm 2 + jt + p jm + ijm 1 + J l=1 exp x0 jm 1 + b 0 jm 2 + lt + p lm + ilm df (!; ) The parameters d can be estimated using the methodology proposed by Berry, Levinsohn, and Pakes (1995). However, price is likely to be correlated with the unobserved characteristic; if brokers differentially "push" certain policies within a companies line of products or insurers very their rating methods across policies, these characteristics will both be correlated with consumer demand and price. problem. Two sets of price instruments are used to correct for the endogeneity First, retaliatory tax regimes, in which states can levy taxes on premiums di erently depending on an insurer s state of incorporation, are used. Retaliatory taxes work as follows: suppose insurance company A is incorporated in Illinois, with a 1% premium tax, while company B is incorporated in Indiana, with a 4% premium tax. Illinois charges company B a retaliatory tax of 4% on the premiums it collects in Illinois. Therefore, di erent companies in the same state face di erent tax rates 23. The instrument is valid if the state of incorporation is uncorrelated with the jm. If rms were incorporated before the Medigap insurance market existed and did not change their state of incorporation in response to their activity in the Medigap market, which seems like a reasonable assumption, the exclusion 22 In practice and for computational simplicity, I divide the income variable by $1000 and demean the expected expenditure variable such that it is orthogonal to income. 23 This has two distinct e ects. The rst is an entry e ect: a company only enters a market in which it will face higher than average taxes if it is a low cost provider who can compete in terms of price. The second e ect is a pure price e ect, where some of the additional tax is passed on to consumers in the form of higher premiums; the functional form used takes account of both e ects. 13

14 restriction is satis ed. The second set of instruments the average premiums of policies in other markets 24. The exclusion restriction requires that, conditional on the variation at the state-company level captured by the retaliatory taxes, the prices in other markets re ect cost shocks rather than demand shocks. The unobserved characteristic contains anything about the insurance product that is not captured by plan and brand dummies. Therefore, the exclusion restriction could be violated if, for example, rms used di erent rating methods in di erent markets based on local demand. However, this instrument is necessary for estimation premiums vary at the state-company-policy level and the retaliatory taxes only vary at the state-company level. Micro-moments improve the t of the model. For the consumers drawn from the MCBS data, I construct the probability of purchasing any Medigap plan, as well as the premiums paid conditional on purchase. Following the intuition of Imbens and Lancaster (1994) and Petrin (2002), I construct the probability of purchase given consumer characteristics in the model and compare it to the expectation of purchase given consumer characteristics in the micro-level MCBS data. Furthermore, I compare premiums paid in the MCBS data and the model. The estimation strategy assumes these are equal in expectation. The model predicts the probability that individual i purchases a Medigap policy is 1 s i0m and that the premium paid by any individual is j2m p ijm s ijm. If i is an indicator variable that takes on a one if individual i purchases Medigap insurance in the MCBS data and p i is the premium paid by individual i, the micro-moments are given by: E ( i j! i ) E ((1 s i0m ) j! i ) = 0 E (p i j! i ; i ) E ( j2m p ijm s ijm j! i ; i ) = 0 for any consumer characteristic! of interest. A similar micro-moment can be constructed for the level of premiums paid conditional on purchase. The GMM routine chooses the random coe cients to help match this information from the individual level data along with moments from the demand and claims functions; thus, while the mean price coe cient is identi ed by the assumption of the exogeneity of the price coe cients and variation in choice sets (and, by extension, prices) across markets, micro-moments help identify the random coe cients. 24 Hausman (1999) 14

15 3.2 Claims Function In the demand estimation literature, incorporating consumer heterogeneity is key to avoiding undesirable features of logit demand speci cations, such as the independence of irrelevant alternatives. However, in the speci c case of insurance demand, consumer heterogeneity is a key feature of the broader asymmetric information problem. As rms change their prices or contract characteristics, they are likely to attract a di erent subset of consumers. In insurance markets, consumer heterogeneity is also a key feature of the asymmetric information problem: rms care about the types of consumers they attract because di erent types of consumers will incur higher or lower claims. Therefore, both the elasticity of demand and the degree of selection, measured by the shape of the claims function, will a ect equilibrium prices. The joint estimation of claims and demand is also the key modi cation in the model that accounts for the possibility of asymmetric information. Therefore, it is important to estimate the relationship between choice variables, such as price and coverage, and claims, which are the largest component of costs. When this relationship between price and claims is positive, we typically refer to it as adverse selection; the critical feature of adverse selection is that consumers with the highest willingness to pay for insurance are the highest risk. The claims function relates claims to plan and consumer characteristics. Let ijm be the claim of individual i under policy j in market m and write: ijm = 0 + x 0 jm 1 +! 0 i 2 + z 0 i 3 + # ijm where the error # ijm is a function of both an individual level and plan level error # ijm = " jm + i : Therefore, while claims may depend on the observed characteristics in a plan and the plan s characteristics, the unexplained part of an individuals claim does not depend on the plan chosen, which implies that E i ( i jj = j) = 0; this speci cation assumes no moral hazard. However, claims are not observed at the individual level, and I must take expectations over individuals in a given plan. The plan level claims jm are given by: jm = E i ijm jj = j = 0 + x 0 jm 1 + E i [! i jj = j] E i [z i jj = j] " jm and this equation can be estimated using the rm level claims data and information from the demand system. The goal of this paper is to examine the impact of supplier decisions in the presence of selection. In this market, the key supplier decision is pricing, and insurers must consider selection on two margins. First, some types of consumers may have a higher (lower) utility for insurance. As the price of a given policy rises, these consumers are less (more) likely to 15

16 switch to the outside option and more (less) likely to switch to one of the other J 1 inside alternatives. Therefore, the claims of any given policy are a function of the entire vector of prices. However, this if only one margin that may a ect rm pricing. Di erent consumers may have a higher (lower) distaste for price, and the consumer characteristics that drive preferences over price may be correlated with claims. If this is the case, an increase in price will attract a di erent group of consumers not only because consumers with a lower preference for insurance are more likely to substitute to the outside option but also because some consumers with a higher distaste for price will be more likely to substitute to a lower priced option. Furthermore, it is possible that these forces work in opposite directions - sicker consumers may have a higher preference for insurance but also a higher distaste for price (because they are, for example, poorer on average). As a policy increases its price, the mix of consumers it retains (or new consumers it attracts) will depend on the balance of those two forces. If jm is the average claim of policy j in market m, p jm is the associated premium, and! jm and z jm are the average consumer characteristics, the derivative of claims with respect to price can be written jm jm jm where the derivatives of consumer characteristics with respect to price depend on consumer heterogeneity in preferences for holding insurance and price 25. In order to account for any correlation in the error in the aggregate claims function and the structural error in the demand system, I will estimate the two jointly. The estimation consists of three sets of moments: the macro-moments from the demand system, the micro-moments from the demand system, and the moments from the claims function. estimation routine picks the random coe cients that minimize the error in the moments. Therefore, allowing Z jm to denote demand instruments and X jm to be a matrix of individual and plan characteristics, the moments are: The E Z jm jm = 0 E [X jm " jm ] = 0 E ( i j! i ) E ((1 s i0m ) j! i ) = 0 E (p i j! i ; i ) E ( j2m p ijm s ijm j! i ; i ) = 0 25 Write! jm = i! is ijm s jm =ns. Individual shares and derivatives with respect to price are functions of the parameters of the demand system. 16

17 3.3 Estimates Table 6 shows the demand system estimates. The average elasticity is , indicating that a $100 increase in price results in an 7.5% reduction in market share. Given that the coverage of lettered contracts is identical and they are likely to be close substitutes, I interpret this as a relatively small price sensitivity. The main e ects show that consumers dislike policies K and L, which provide more limited coverage and, unsuprisingly, the popular plans yield high utility for consumers. The elasticity is similar across speci cations that allow for di erent types of consumer heterogeneity: in column 1, consumers are only allowed to vary by income, and in the second speci cation, expected claim is only allowed to a ect preference for insurance, not price sensitivity. The rst speci cation shows that high income consumers are especially price insensitive: a 1% increase in income leads to a 0.35% decrease in this elasticity. The second speci cation allows consumers with di erent expected claims to value insurance di erently in addition to allowing consumers with di erent incomes to vary in their price sensitivity. Conditional on income-varying price sensitivity, consumers with higher expected claims gain higher utility for holding insurance. In the nal, preferred speci cation, the random coe cient on the interaction between price and income is , which is signi cantly di erent from zero; again, this indicates that richer consumers are less price sensitive that their poorer counterparts. However, sicker consumers are also more price sensitive, even conditional on income, while the preference for holding insurance does not vary with health status 26. The bottom panel shows the e ect on this sorting of consumers on claims. In the rst speci cation, the regression of logged claims on consumer and plan characteristics, which is estimated jointly, shows that a 1% increase in income leads to a 0.15% increase in expected claim, conditional on health. consumers on price by health status. However, this speci cation does not capture the sorting of In the preferred speci cation, the coe cients imply that a $100 increase in expected claim leads to a 14% increase in claims. Given that the median average claim across policies is $944, this estimate implies that, at the median, a $100 increase in the proxy for health status given by average expected private insurance claims (from the individual level data) leads to a $131 increase in average Medigap claim (in the market level data). in claims, conditional on health status 27. Furthermore, a $1000 increase in income leads to a.05% increase The demand estimates imply a number of things. First, demand for Medigap insurance 26 While allowing consumer preferences to vary with expected claim, whether this characteristic a ects preference for insurance or price sensitivity is less important. 27 This captures that the expected private health insurance expenditure in the MCBS tends to be slightly higher than the average claim in the NAIC data; the private health insurance expenditure variable includes other forms of private insurance, including employer-sponsored plans. 17

18 is very insensitive to price because consumers are very concerned with the brand name of their insurance. In addition, because consumers have heterogeneous preferences over price, and these preferences are correlated with claims, the price insurers charge is related to their claims. Taken together, these e ects imply that a $100 increase in premium leads to a $15 increase in average claims and a 7% reduction in market share. The selection e ect is due almost exclusively to the fact that elasticities are correlated with claims, rather than the fact that claims are correlated with preference for holding insurance. 4 Supply 4.1 Insurer Pro ts and Variable Costs In addition to claims, rms face an administrative cost of marketing and administering an insurance policy. Firms set prices p jfm for all J fm policies in order to maximize variable pro ts, cognizant of the fact that the vector of market prices p m a ect not only shares, but also claims and potentially administrative costs (if the administrative cost is a percentage commission, for example). Additionally, when setting prices, rms are subject to minimum loss ratios. This potential ne a ects how the rm sets prices, as well as the rm s pro t from any given policy. Let the econometrician s approximation to rm f 0 s variable pro ts from policy j in market m with market size M be equal to: jfm = p jfm jfm (p m ) a jfm (p m ) s jfm (p m ) M where a jfm denotes the administrative cost of policy j o ered by rm f in market m. In order to get rm level pro ts, jfm is summed over the policies the rm o ers, subtracting any xed or sunk costs of operation. Conditional on being active in a market, there may be a cost of o ering an additional policy, jm due to additional underwriting or time spent explaining di erences among policies to consumer. Additionally, there may be a xed cost of operating in a market, Jm due to the cost of registering with a state insurance commissioner or organizing a eet of agents to sell policies. Finally, there may be a sunk cost of national operation, such as payments to an organization like AARP.; I will denote these costs by J. The rm s total pro t in market m, fm is given by: fm = X j2j f p jfm jfm (p m ) a jfm (p m ) s jfm (p m ) M jm Jm Total pro ts in year t can be obtained by summing over markets in which a rm is active in 18

19 year t, J mt, and subtracting any sunk costs; therefore, total rm pro ts f are given by: ft = X m2j mt ( fm ) While I will assume a Nash in prices equilibrium in this market, minimum loss ratio regulation, as described in Section 2, will play an important role in the estimation. policy violates the requirement that sixty- ve percent of premiums be paid out in claims, the insurance regulator could ultimately force the rm to rebate the di erence to consumers. In practice, the insurer often contests the potential ne and the rates are allowed to stand (a fact which is obvious in the data). Nearly half of all policies violate minimum loss ratio regulation. I will remain not take a stand on about the exact impact of regulation on the pro t function; the model simply assumes that rms cannot increase pro ts by lowering the price of policies which currently violate the minimum loss ratio regulation. The estimation is based on Kuhn-Tucker conditions for pro t maximization, where the rm s problem is written as: max p jfm fm s:t: jfm :65p jfm Due to the assumption that regulation need not bind exactly, the complementary slackness condition is relaxed such that jm :65p jfm jfm 0 while jm 0. In this case, if minimum loss ratio regulation is violated, it must be jfm ( fm ) 0, while if the ratio regulation is not violated, jm = 0 jfm ( fm ) = In words, if minimum loss ratio regulation binds, the estimation routine allows the derivative to be positive, as rms may prefer to raise their price in the absence of regulation. all policies were subject to regulation, this would be equivalent to minimizing the negative of the function - estimation based on moment inequalities. J If a If If all policies were not subject to regulation, this would be equivalent to the more standard method of moments, the estimation routine would simply pick the variable administrative costs that minimized the expectation of the moments 29. The marginal administrative cost is the cost of adding one consumer conditional on the policies o ered by an active rm in a market. What composes variable administrative 28 The results of a counterfactual in which loss ratio regulation is lifted are in Appendix B. In the absence of regulation, premiums would rise by 14%; the regulation does manage to restrain premiums. 29 Additionally, I could potentially improve the e ciency of the estimating by jointly estimating administrative costs and the demand and claim moments. However, for computational simplicity and because I will need to subsample to obtain the standard errors of the variable cost estimates, I will do the estimation separately, taking the demand estimates as given. The current standard errors were obtained using a bootstrap. 19

20 costs? These costs must be truly marginal, in the sense that they are incurred for each additional consumer. Claims processing is automated and done in conjunction with traditional Medicare billing. Therefore, the marginal costs that are not associated with claims must largely be marketing costs - the costs of generating an additional policyholder. The main component of variable administration cost in this market is sales commissions and will assume that variable administrative costs are a percentage of the price charged; that is, a jfm = p jfm. 4.2 Fixed Costs and Sunk Costs There are a large number of potential entrants in the Medigap market, and variable pro ts indicate the possibility of a pro table challenge to the current market structure. An additional large rm may be able to both be pro table and improve consumer surplus. I will consider the potential for a rm to duplicate the strategy of either UnitedHealth or Mutual of Omaha by o ering the same mix of products with the same brand preferences induced by similar marketing expenditures. I will estimate the xed or sunk cost of such a strategy. However, this analysis will require a number of additional assumptions. I will not be able to separately identify all of the xed and sunk costs. However, institutional detail can focus my analysis and allow for reasonable assumptions that capture the costs most relevant to insurers. First, I assume that the xed cost of o ering an additional policy conditional on being active in a market, jm is zero or small 30. of entry or marketing in an additional market, denoted by jm. Furthermore, rms may incur a xed cost This may encapsulate the cost of setting up a network of agents in a given geographic area to sell policies or the cost of being certi ed by the state insurance commissioner to sell Medigap insurance. The degree to which insurers choose to enter markets and o er policies is likely to impact pricing and consumer surplus. Because of Mutual of Omaha s strategy of employing brokers to sell their policies, this is likely to be the most relevant cost they face. UnitedHealth, however, faces one large sunk cost J - the cost of the AARP endorsement - that is likely to dwarf any market level xed costs. Therefore, while I cannot separately identify xed cost of entry into a speci c geographic market and sunk costs of national operation, I will focus on the xed costs of Mutual of Omaha s strategy and the sunk cost of UnitedHealth s strategy. Conditional on this set of potential entrants, the assumption identifying xed or sunk costs follows Mazzeo s model of entry 31, modi ed to incorporate an inequality approach. This will require the 30 See Iyengar et al (2000) for a discussion of the negative impacts of additional choice. 31 Mazzeo analyzes a game in which hotels choose a di erentiated type (low, middle, or high quality) and whether or not to enter a speci c market. I will consider two types based on presumed cost structure rather 20