How To Understand The Cost Of A Private Health Care Plan

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1 Can Health Insurance Competition Work?: The US Medicare Advantage Program Vilsa Curto, Liran Einav, Jonathan Levin, and Jay Bhattacharya March 2014 Abstract. We study health plan costs, risk selection and pricing incentives under the competitive bidding mechanism introduced into Medicare Advantage in We present a model of plan bidding and consumer choice that allows for market power and risk selection. Using data on the universe of Medicare beneficiaries, we find that private plan costs are lower on average and only weakly correlated with traditional Medicare claims costs. Moreover, although private plans attract relatively healthy enrollees, bidding higher does not result in more favorable risk selection. However, we find that the incentives for plans to reduce their bids to increase market share are relatively weak. We attribute this to a combination of consumer decision-making and concentrated market structure. Finally, we combine our model and empirical estimates to examine program changes that might enhance plan competition. Acknowledge Acumen... Department of Economics, Stanford University (Curto, Einav, Levin), School of Medicine, Stanford University (Bhattacharya), and NBER (Bhattacharya, Einav, Levin). vcurto@stanford.edu, leinav@stanford.edu, jdlevin@stanford.edu, and jay@stanford.edu.

2 1 Introduction Introducing managed competition into healthcare has long been an alluring idea to economists and policy-makers. Proponents have argued for more than forty years that effectively designed market mechanisms are the most effective way to avoid the inefficiencies of an administrative price system. et despite many examples of managed competition in the US and abroad, there is little consensus on how well it can work in practice. One reason is that many competitive systems do not look much like the proposed ideals. But perhaps more importantly, in most cases there is no clear benchmark against which to compare a competitive system. Over the last decade, the US Medicare program has undertaken a fairly dramatic experiment with managed competition. Almost thirty percent of US seniors are now enrolled in private insurance plans through the Medicare Advantage program (Figure 1). Under the program, plans receive capitated payments for each enrollee. Historically, the payments were set administratively, but starting in 2006, Medicare introduced competitive bidding to encourage plans to accept payments below a maximum benchmark rate. It also introduced a system of risk adjustment designed to reduce the incentives for cream-skimming. As a result, Medicare Advantage now looks similar to the types of proposals advanced by advocates of managed competition. And because it operates side by side with the traditional fee-for-service Medicare system, it provides an opportunity to study managed competition against a natural control. Medicare Advantage was set up to save taxpayer money, but it generally costs taxpayers more if a beneficiary opts out of traditional Medicare to enroll in a private plan (MedPAC (2009)). An important question is whether this extra cost translates into increased benefits for seniors, or is due to inefficiencies in the way private plans operate, or to problems in program implementation or competition. The potential problems are several. The insurance market is highly concentrated, especially at the local level, so effective competition is not guaranteed. The program relies on beneficiaries making informed and price-sensitive choices among private plans, again not a given. And despite Medicare s efforts to risk-adjust payments, plans may have an incentive to quote high prices to maintain a favorable risk pool. We set out in this paper to disentangle these possibilities. Our basic finding is that 2

3 the high costs of Medicare Advantage are not due to inherent cost disadvantages of private plans, but rather to a combination of limited competition and benefits passed to seniors. In a typical private plan enrollment, taxpayers incur an additional cost of around $1,540 per year. We estimate that the enrollee obtains an additional dollar benefit of around $869, and the plan surplus is around $672. In short, the gains from trade appear to be substantial relative to the current structure of fee-for-service Medicare (note that we do not ask if feefor-service Medicare could be made more efficient), but much of the gains appears to accrue to the insurers. We attribute the latter finding to a combination of consumer choice behavior and concentrated market structure that weakens competitive incentives. We assemble several pieces of evidence to support this argument. On the issue of relative costs, a first observation is that a large majority of Medicare Advantage beneficiaries are enrolled in plans that have offered to provide basic Medicare benefits at lower cost than CMS would provide them. This is true even after accounting for the fact that private plans generally enroll healthier enrollees. Moreover, we estimate that underlying plan costs are lower still after accounting for mark-ups. It is also the case, perhaps surprisingly, that plan bids and costs correlate only weakly with Medicare fee-for-service costs. The weak relationship between private plan bids and fee-for-service costs has been observed earlier, notably in a recent Institute of Medicine study on regional cost variation (MaCurdy et al. (2013)). We find that the correlation is even lower after accounting for benchmark rates or using our cost estimates. Our interpretation is that private plans in fact have quite different cost structures, with more ability to control utilization, but less ability to impose standardized prices. The weak correlation, coupled with wide dispersion in both private and public fee-for-service costs, and lower on average costs for private plans, suggests that effective plan competition could indeed have benefits. This leads us to explore the potential frictions in competition. To do this, we set out a model that accounts for three salient issues: consumer choice, risk selection, and market power. We find that risk selection per se does not preclude competitive bidding. While it is true that private plans systematically enroll healthier beneficiaries, and Medicare s risk adjustment formula does not appear to perfectly adjust for the differential, plans do not have an incentive to submit high bids to avoid high-cost enrollees. We estimate that plan bids have a relatively small effect on plan costs, and if anything, submitting a lower bid appears to improve a plan s risk selection. As a result, it is possible to think of favorable selection 3

4 effects as a cost advantage for private plans that does not in itself encourage non-competitive bidding. Our results on consumer choice and market power are less encouraging. We find that plan enrollments respond only modestly to reductions in plan bids, so that plans face relatively limited competitive pressure to submit bids close to their costs. Depending on our exact specification, we estimate that plans have an incentive to set markups on the order of $ per enrollee-month. We base our estimates on a nested logit model of plan demand, so that we can distinguish how much plans are competing amongst themselves, or instead against traditional Medicare. We find that most of the competition is with traditional Medicare. Our back-of-the-envelope calculation suggests that a $100 decrease in the Medicare benchmark payment rate would cause a plan to reduce its bid by $50 and margin by 8 percentage points, whereas a $100 decrease in rival plan bids would lead to a reduction of only $4. Interestingly, a further implication is that promoting entry to reduce the high degree of insurer concentration might not yield large reductions in plan bids. 1 These findings have implications for thinking about ways to improve the design of competitive bidding. The two most obvious levers available to CMS are the local benchmark rates against which plans compete, and the rebate formula that specifies how bid savings below the benchmark are divided between taxpayers and enrollees. Under the current rules, when a plan bids below its benchmark rate, CMS retains 25% of the difference and mandates that the other 75% be passed on to consumers. One way to limit taxpayer costs would be to increase the retention rate from 25%, something that would be effective if enrollee demand were highly elastic, but might be less effective given our estimates. Instead, benchmark reductions appear to be a more effective instrument for reducing plan bids and reducing plan costs. We estimate that a $100 dollar decrease in the benchmark per enrollee-month would save taxpayers around $16 billion annually, and would reduce the effective benefits to enrollees by only $47 per enrollee-month, while having relatively slight effects on enrollment. Our analysis builds on a small but growing literature assessing different elements of the reformed MA program. Song, Landrum, and Chernew (2012) argue that the relationship between plan bids and benchmark rates is inconsistent with perfect competition, indicating the presence of insurer market power. Duggan, Starc, and Vabson (2014) estimate that 1 We run cross-market regressions and estimate that a $100 decrease in the Medicare benchmark payment would induce the exit of 3.5 plans on average, which would lead to an increase in bids of less than $5. 4

5 only about one-fifth of additional reimbursement in the form of higher benchmark rates is passed on to consumers in the form of rebates, which is also indicative of a lack of perfect competition. Song, Cutler, and Chernew (2012) suggest that the particular bidding rules may be partly to blame for high costs, and discuss alternative bidding mechanisms. There is also a debate about whether Medicare s risk adjustment policy has managed to mitigate risk selection (Brown et al. (2011); Newhouse et al. (2012)). The paper proceeds as follows. Section 2 describes the (fairly intricate) institutional background and how the program and the competitive bidding system works. Section 3 provides some preliminary evidence on enrollment patterns, risk selection, and plan competition. Section 4 presents the theoretical model that we use to frame our analysis of bidding competition. Sections 5-7 provide evidence on plan bidding patterns, plan choice by beneficiaries, and the relationship between bids and risk selection. Section 8 provides estimates of plan costs obtained using our demand estimates and an optimal mark-up formula, and relates them to fee-for-service costs. Section 9 discusses alternative ways to promote plan competition. Section 10 concludes. 2 Medicare Advantage and Competitive Bidding 2.1 Background Medicare Advantage (MA) began operating in The program was established with two objectives: to expand the choices available to Medicare beneficiaries, and to capture cost savings from private sector managed care. McGuire, Newhouse, and Sinaiko s (2011) history of Medicare Advantage highlights the difficulty of satisfying these objectives. One challenge is that they are to some extent contradictory. A natural way to encourage plan entry and expand access is to raise plan payments, which obviously runs counter to the goal of achieving cost savings. Risk selection is a second challenge. Private plans historically have had an incentive to operate selectively in areas where reimbursement rates are high, and to enroll relatively healthy beneficiaries within a given area. 2 The reforms of the last decade can be seen as attempts to address these problems. 3 Under 2 As an empirical matter, plans have tended to enjoy very advantageous risk selection (Eggers (1980); Eggers and Prihoda (1982)), and as recently as 2005, only around 67 percent of Medicare beneficiaries had access to an HMO or local PPO MA plan (MedPAC (2009)). 3 The reforms originate in the Balanced Budget Act of 1997 (risk scoring) and the Medicare Modernization 5

6 the risk adjustment system phased in between 2003 and 2006, CMS compensates plans based on the health of their enrollees, which in principle limits incentives for cream-skimming. 4 The competitive bidding system introduced in 2006 attempts to sidestep the difficulty of choosing a reimbursement rate that might be either too high (raising taxpayer costs) or too low (limiting access). These reforms, combined with an increase in maximum capitation rates set by CMS, have coincided with the expansion of plan offerings and enrollment in Figure 1. In recent years, Medicare Advantage has become one of the largest government programs, accounting for $123 billion in federal spending in Program Operation Medicare Advantage plans are offered by private insurers that enter into contracts with CMS. During our sample period, around 130 insurers participated in the program in any given year. 5 A contract between an insurer and CMS may include several plans with different benefit levels, but with the same provider network and a plan type (e.g. HMO, PPO). Plan benefits consist of cost-sharing requirements, monthly premiums, and potentially supplemental coverage for dental, vision, or prescription drugs. A given plan is available in a specified set of counties, known as the plan s service area. Larger insurers enter into multiple contracts with CMS and in this way are able to offer different plan types and provider networks in different areas. Beneficiaries can enroll in private plans during a fall open enrollment period, and have access to any plan that is offered in their counties. A primary attraction of private plans is that they generally provide more generous cost-sharing than standard Medicare. 6 Medicare beneficiaries can easily accumulate several thousand dollars in out-of-pocket costs each year, and to avoid this around sixty percent of beneficiaries pay an additional premium to purchase Act of 2003 (competitive bidding and more detailed risk scoring). 4 The risk scores are based on a formula that give weights to chronic disease diagnoses. At the same time, CMS also reformed the enrollment process, so that beneficiaries must enroll in MA plans during a fixed period, rather than being able to switch in and out of private plans on a monthly basis. 5 A few offer plans nearly nationwide. For instance, UnitedHealth and Humana offer plans in around 95 percent of US counties. These insurers have 20 and 16 percent of Medicare Advantage enrollees respectively. Other insurers operate in more limited geographic regions. In some cases, these insurers may have significant market share in their home areas. For instance, Kaiser offers plans in only 2.5 percent of US counties but has a 24 percent share of Medicare Advantage enrollees in their markets. Table A1 in the Appendix shows the insurers with the largest share of enrollees and their geographic coverage. 6 Medicare private plans also may include drug, dental, and vision benefits. While plans charge an additional premium for these benefits, beneficiaries may value the convenience of having a single plan. 6

7 either employer-sponsored or Medigap supplemental insurance. 7 Medicare private plans are required to offer coverage that is at least as generous as standard Medicare, but in our sample period, around 95 percent of private plan enrollees were in plans that offered strictly more generous coverage but charged no additional premium over the standard Medicare premium. 8 The trade-off for beneficiaries is that private plans typically restrict access to a limited set of providers. Around 80 percent of Medicare Advantage enrollees are in HMOs or PPOs with restricted networks. So-called private fee-for-service (PFFS) plans are an exception. These plans offer the same broad provider access as standard Medicare, and pay providers per service at standard Medicare rates. They proliferated in the mid-2000s, taking advantage of relatively generous capitation rates that in effect created an arbitrage opportunity for insurers, but shrunk by 2011 to less than an 18 percent share of Medicare Advantage enrollees. 2.3 Competitive Bidding Historically, private plans were compensated according to administrative rates that varied geographically. Under competitive bidding, plans are reimbursed based on their bids and local benchmark rates set by CMS. There is a separate benchmark rate for each county. These rates originally were based on plan payments prior to 2006, which themselves were intended to reflect the cost of providing fee-for-service coverage to a representative Medicare beneficiary in a given county. In practice, most of the benchmark rates as of 2006 were at one of two floors established in earlier Congressional legislation: an urban floor that applies to major metropolitan areas, and a general (or rural) floor. Figure 2 shows the distribution of county benchmarks in 2006, with a high degree of clustering at the floors, and also the distribution in 2011, after five years of benchmark increases. CMS updates the local benchmark rates each year according to a statutory formula. All local benchmarks are adjusted upward by the minimum of 2% and the average national 7 In 2014 beneficiaries faced a yearly deductible of $147 and twenty percent coinsurance for physician services, as well as a $1,216 deductible for hospital stays, and additional coinsurance payments for long stays. The hospital deductible must be paid for each benefit period, which begins the day a beneficiary is admitted for inpatient hospital care and ends once a beneficiary goes sixty full days without receiving any inpatient hospital care. Approximately 23 percent of beneficiaries were enrolled in Medigap insurance in 2010; Medigap insurance compensates for out-of-pockets costs but generally requires paying an additional monthly premium, which averaged $183 per month in 2010 (Huang et al. (2013)). 8 All Medicare beneficiaries pay a Part B monthly premium regardless of whether they are enrolled in TM or MA. In 2014, this monthly premium is $ per month for married couples with incomes up to $170,000; wealthier couples or individuals pay slightly more. 7

8 increase in fee-for-service Medicare costs (MMCM, chapter 8). In addition, CMS is required to rebase each county payment rate at least once every three years. In rebasing years, CMS calculates per-capita Medicare spending in the county based on a five-year moving average. If this exceeds the minimum update, it becomes the new benchmark. Insurers submit their plan bids after the county benchmarks are published. A given plan then receives payments based on its bid b and its benchmark B, which is defined as the average benchmark across counties that the plan serves. The average is taken using projected plan enrollment in the relevant counties. The payment formula works as follows. If a plan submits a bid b above the plan benchmark B, CMS pays the plan a base amount b for each enrollee, and scales this to reflect the likely cost of the enrollee and the county, minus an amount b B, which is the premium an enrollee is required to pay. So if the enrollee has risk score r, and lives in a county with benchmark B k, the plan receives revenue: b r (B k /B) = B k r. If the plan bid b is less than the plan benchmark B, CMS pays the plan a base amount b for each enrollee, again risk-adjusting the base amount to reflect the likely cost of the enrollee and his or her county. In addition, CMS pays the plan a rebate equal to 0.75 (B b). The plan is require to pass on the rebate to the beneficiary in the form of additional benefits. The beneficiary pays no additional premium. It is easiest to see the implications of this scheme if one ignores risk adjustment and assumes, as we do below, that plans pass on rebate payments to enrollees as required. In this case, a plan always receives per enrollee its bid b in (unallocated) revenue, and the enrollee either pays b B if the bid is above B, or receives a benefit with actuarial value 0.75 (B b) if the bid is below B. Despite the somewhat complicated details, the result is that plans face a standard trade-off: a lower bid makes a plan more attractive to beneficiaries, but reduces its per-enrollee revenue. We expand this observation into a theory of bidding competition in Section 4. 3 Data and Prelimary Evidence In this section, we provide some preliminary evidence on private plan enrollment and the characteristics of Medicare Advantage enrollees. We then describe the market structure of private insurers, and patterns of plan bidding. Finally, we discuss the commonly cited 8

9 observation that CMS costs are higher when individuals enroll in private plans. We rely on two main datasets constructed using Medicare administrative data from 2006 to Our source data includes all Medicare payment claims from , the enrollment and risk-score information for all Medicare beneficiaries from , and all private plan payments from It also includes plan characteristics, including type of plan and benefits offered, as well as the five-star plan quality rating that was introduced by CMS in The first dataset we construct is an individual-level panel that includes all aged Medicare beneficiaries not enrolled in employer-sponsored plans and not dually eligible for Medicare and Medicaid. This dataset contains 149,952,912 individual-year observations on 31,547,924 unique individuals. The second dataset is a plan-level panel that contains observations on each non-employer-sponsored private plan targeted at the aged Medicare population. It contains 12,317 observations at the plan-year level, on 4,931 unique MA plans. Both datasets cover Details of the dataset construction are reported in the Appendix. 3.1 Private Plan Enrollment and Risk Selection The enrollment rate in Medicare Advantage grew over our sample period from 7 million in 2006 to 12.2 million in Most of the movement between private plans and traditional Medicare were primarily one way. Around 2 percent of Medicare beneficiaries switched into Medicare Advantage in each year of our sample, while only around 0.7 percent switched back. Private plan enrollees do not differ much from traditional Medicare enrollees in terms of age or gender (Table 1), but they do tend to be more heavily concentrated in urban areas. An important difference between private plan enrollees and fee-for-service beneficiaries is that private plan enrollees are healthier. The average risk score of private plan enrollees was 0.939, compared to for traditional Medicare. So based on risk score, a private plan enrollee had expected costs that were about 0.939/0.975 = 96.7 percent those of a traditional Medicare beneficiary. 9 Figure 5a provides more detail, showing the relationship between risk scores and Medicare Advantage enrollment rates. The enrollment share is slightly higher 9 Risk scores are constructed so that an individual with a score of 2 has twice the expected health costs of an individual with a score of 1. The risk score is calibrated to have a mean of 1 on a subsample of several million Traditional Medicare enrollees. We have already dropped two high-risk groups Medicaid recipients and individuals with Disability insurance from our sample, so risk scores are slightly lower than in the entire population. 9

10 for beneficiaries with low risk scores, and much lower for beneficiaries with very high risk scores. 10 It is challenging to quantify exactly how well Medicare s risk adjustment formula corrects for health differences between private plan and fee-for-service beneficiaries, in part because we lack detailed claims data from private plans. 11 However, we can compare the two populations using proxy measures that might be correlated with healthcare needs. Figure 5b provides evidence on one such proxy: the one-year mortality rate of Medicare Advantage enrollees, compared to the same measures for enrollees in traditional Medicare, conditional on being in the same risk score bin. The figure shows that even conditional on risk score, private plan enrollees appear to be healthier. Their mortality rate is around 8 percent lower than would be expected based on risk score. 3.2 Private Plan Market Structure and Bids The market structure of Medicare Advantage is characterized by two basic features: a large number of plans and a high degree of insurer concentration. The average county has 3 HMO plans, 1 PPO plan and 14 PFFS plans. The HMO and PPO plans are the most important: they account for around 80 percent of Medicare Advantage enrollment nationally. Despite the large number of plans, most local markets have relatively high insurer concentration. Appendix Table A2 shows that in more than 75 percent of US counties, the top two insurers had over 66 percent of Medicare Advantage enrollees. The top three had over 59 percent of enrollees in 90 percent of counties. Both insurer and plan concentration levels are lower in urban areas and in areas with high benchmark rates. To get a sense of this, we divide counties in each year by whether their benchmark rate is above or below the national median. In our sample, counties with benchmarks above the median had on average 20 plans and an insurer Herfindahl of 0.493, 10 We are not aware of very good evidence on exactly why this pattern arises. One interpretation (consistent with the modeling approach in Brown et al. (2013)) is that MA plans actively try to avoid high-cost enrollees through plan design or service quality. A more benign interpretation is that chronically ill individuals are simply less likely to search for a suitable MA plan, or prefer the wide choice of providers offered by TM to the narrower networks of MA plans. 11 Private plans do submit disease diagnoses for use in risk scoring. As of 2013, CMS has started to require MA plans to submit complete claims data, which eventually should allow for a comparison of relative utilization rates. Table 2 does provide information on MA and TM inpatient days, which are recorded as part of hospital reporting requirements. The general view is that inpatient days are probably understated for private plans, although Landon et al. (2012) estimate that even after correcting for measurement issues, private plan enrollees seem to have around 20 to 25 percent fewer inpatient days. 10

11 compared to 17 plans and a Herfindahl of for counties with benchmarks below the median. It also is important to recognize that the degree of insurer concentration looks different if we account for the presence of traditional Medicare as an alternative insurer. This suggests that in thinking about competition, it is important to assess the extent to which private plans compete with each other, or with traditional Medicare. We observed earlier that for beneficiaries considering a private plan, the relevant price depends on how the plan s bid compares to its benchmark rate. Figure 3 plots the distribution of plan bids relative to plan benchmarks for all the plan-years in our sample. Ninety-three percent of plan bids are below the benchmark, meaning that these plans receive rebate payments. As a result, the average private plan enrollee receives additional insurance benefits of around $73 compared to standard Medicare. Figure 4 shows how plans convert rebate dollars into benefits. The two main uses are improved cost-sharing and subsidized Part D drug benefits, although some plans provide other benefits or try to attract enrollees by reducing the standard Medicare premium. 3.3 Comparing Private Plan and FFS Costs A main criticism of Medicare Advantage is that it costs CMS more to have a beneficiary enroll in a private plan than to cover that beneficiary under traditional Medicare (MedPAC (2012)). A point that this masks is that at least on average, Medicare Advantage plans are very likely to have lower costs of providing basic Medicare insurance benefits. To make this point, we first adjust the data on private plan payments and fee-for-service costs to account for differences between the two populations. To do this, we start with our full sample of fee-for-service beneficiaries and regress their annual claims on risk score, county fixed effects, and year fixed effects. We use the estimated regression coefficients to compute an expected fee-for-service cost for individuals enrolled in fee-for-service Medicare and those in private plans. This gives us a risk-adjusted, county-adjusted, and year-adjusted estimate of expected fee-for-service cost for each Medicare beneficiary. Based on this calculation, private plan enrollees in our sample period had an average expected fee-for-service claims cost of $7,071. The average plan bid weighted by enrollment was significantly lower, just $7,742 per year. Taking plan bids as an upper bound on plan costs, this suggests at least a 10% cost advantage for private plans. Of course with the rebate payments, the lower plan bids do not translate into lower government cost. Including 11

12 the rebates, the total government payment per MA enrollee increases to $8,611, about 22 percent higher than what it would have cost CMS to cover the MA enrollees under traditional Medicare. It is worth noting a few caveats to these numbers. First, it is conceivable that private plans are bidding below cost and losing money on basic coverage. Second, we already have seen that private plan enrollees probably are less costly even after controlling for risk score, county and year. So the expected fee-for-service costs of these beneficiaries likely are somewhat overstated. At the same time, the expected fee-for-service costs do not include administrative costs of managing the claims process, something that should be factored into the MA bids. These factors notwithstanding, it seems hard to avoid the conclusion that private plans do manage to achieve a degree of cost savings relative to traditional Medicare for their current enrollee population. 4 A Model of Bidding Competition In this section we develop a bidding model of insurer competition. We start with a streamlined version of the model, and then consider some elaborations that potentially are relevant for matching the theory to the data. 4.1 A Baseline Model For simplicity, we consider a single market with beneficiaries who vary in their risk type r. There are J plans, indexed by j = 1,..., J. Plan j has cost rc j of covering an individual with risk r. There is also traditional Medicare, which has cost rc 0. Bidding competition follows the rules described earlier. Let B denote the benchmark rate, and b j the bid of plan j. If b j > B, CMS pays the plan r i b (b j B) for covering individual i, and i must pay a premium b j B, so the plan receives r i B if i enrolls. If b j B, CMS pays the plan r i b j, and a rebate equal to α (B b j ), where α = The plan passes the rebate to the enrollee in the form of extra benefits. Plan Demand. Beneficiaries choose among plans taking into account a plan s fixed characteristics (its provider network, brand name, etc.), and the premium or extra rebate benefits that result from the plan s bid, or more precisely the plan s excess bid p j b j B. We there- 12

13 fore write the demand for plan j among beneficiaries with risk type r as D jr (p 1,..., p J ). 12 A natural assumption is that D jr will be decreasing in a plan s own excess bid, and increasing in the excess bids of rival plans. The total enrollment of plan j is Q j (p 1,..., p J ) D jr (p 1,..., p J ) dg (r), (1) and it is useful to define a plan s risk-weighted enrollment Q w j (p 1,..., p J ) rd jr (p 1,..., p J ) dg (r). (2) In addition, we can define a plan s average risk as r j Q w j (p 1,..., p J ) /Q j (p 1,..., p J ) (3) Here we suppress the dependence of r j on the plan bids. We will show below that empirically the average risk of an MA plan does not appear to vary much with a plan s bid, and hence there is little if any incentive to change a plan bid to affect the plan s risk composition. Plan Profits. Next we consider plan profits. A plan always receives rb j for enrolling an individual with risk r, and incurs cost rc j. Therefore plan j s profit given a set of plan bids p 1,..., p J is π j (p 1,..., p J ) = Q w j (p 1,..., p J ) (p j + B c j ). (4) The plan s risk composition matters only insofar as if affects the risk-weighted enrollment. This is because the effects of risk composition on costs are perfectly compensated by the risk-adjustment formula. adjustment is imperfect. We discuss below how plan incentives might be skewed if risk Equilibrium bids. We assume that bids are generated in a complete information Nash Equilibrium. This is of course a simplification, as actual bids are made without complete 12 Below we use a nested logit structure to model individual demand, and aggregate up to a market-level demand, but here we focus directly on the market-level demand since this is what is relevant to the individual plans. 13

14 knowledge of rivals bids, but it maintains the key features of competition, and avoids the complication of modeling an incomplete information bidding game. A full information bidding equilibrium is given by a vector of bids p 1,..., p J, such that each insurer is maximizing profits given rival bids. 13 For an insurer that offers a set of plans J, the optimal bid for plan j J satisfies: 0 = k J (p k + B c k ) Qw k p j + Q w j (p 1,..., p J ), (5) where the insurer accounts for the fact that raising the bid for plan j may affect enrollment in the insurer s other plans. In the simpler case where an insurer offers only a single plan j, we can re-write the formula for the optimal excess bid as ( ln Q w j p j = c j B + p j ) 1. (6) Adding B to both sides reveals that an optimal bid b j equals the plan s marginal cost c j plus a mark-up term that depends on the semi-elasticity of the risk-weighted plan demand. 4.2 Expanding the Baseline Model We now consider some implications of the model, and potential elaborations. Plan Choice and Bidding Incentives. In the model, plans bids and markups are related to the elasticity of plan demand. To see this, it is useful to express the formula for equilibrium bidding in terms of the actual (rather than excess) bids. Substituting p j = b j B, and realizing that Q w j / p j = Q w j / b j, we can write condition (6) as b j = c j + ( ln Q w j / b j ) 1. The last term multiplied by b j is the residual plan demand elasticity. If plans are bidding above the benchmark, the plan demand elasticity is directly related to the price sensitivity of individual beneficiaries. there is a $1 increase in the premium required to enroll. For every $1 increase in a plan s bid, If plans are bidding below the benchmark, however, the relationship is less direct. A $1 increase in a plan s bid increases the rebate by α = 0.75, but whether the effect is analogous to a $0.75 premium reduction 13 Conditions under which such an equilibrium will exist are laid out in Caplin and Nalebuff (1991), for instance assuming each Q w j is continuous and ρ-concave in p j with ρ 1. 14

15 is an empirical question. However, it is worth noting that all else equal an increase in α should make plan demand more sensitive to plan bids, therefore reducing margins (although potentially increasing taxpayer costs). Effect of the Benchmark Rates. From equation (6), it is clear that changes in the benchmark rate have a parallel effect to uniform changes in plan costs. To see this, suppose plan demands are symmetric, have equivalent unit costs c, and are each controlled by a separate insurer. Let p = b B be the equilibrium excess bid and b the equilibrium bid. Then from (6), we have dp/db = dp/d( c). Therefore it follows that: db db = 1 + dp db = 1 dp dc = 1 db dc. (7) If the market is perfectly competitive, so that b = c, it follows that changes in the benchmark will have no effect on plan bids. More generally, if a uniform $10 increase in plan costs leads to equilibrium bids being $6 higher, a $10 increase in the benchmark rate will lead to bids that are $4 higher. The pass-through rate of benchmark increases will be one minus the pass-through rate on uniform cost increases. We will return to this point below when we consider the relationship between plan bids, benchmarks and FFS costs in Section 6. Competition between Plans versus Competition with TM. A loose way to interpret the model is to think of TM as being a Stackelberg competitor that moves first and sets a premium equal to B, following which the plans set bids b 1,..., b J, so that by giving up TM and moving to a private plan j, a beneficiary obtains a subsidy B to offset the plan bid b j. In this sense, a lower benchmark B makes TM a more formidable competitor. An important empirical question therefore, is whether the incentive to reduce plan bids comes primarily from competition with other private plans so that for instance, the entry of new plans and insurers will lead to a large reduction in bids or competition from TM, in which case the most effective way to reduce plan margins will be to reduce benchmark rates. This distinction motivates our use of a nested logit demand specification below, in order to allow for TM to compete with plans in a different way than they compete amongst themselves. Incentives for Risk Selection. We have seen above that MA plans appear to enroll individuals who are relatively low risk. In the model, any variation in a plan s risk composition 15

16 is fully compensated so long as the plan bids below the benchmark. 14 Let s consider what happens when this assumption is relaxed. A simple way to capture this is to assume that individuals with risk score r who enroll in plan j have actual risk λ (r, p j, p j ) r. Case 1: Suppose λ (r, p j, p j ) = λr, with λ < 1. In this case, MA plans have favorable selection conditional on observed risk score (we will see below that this is indeed a feature of the data), and the effect on bidding incentives is straightforward. In particular, it is as if the cost of MA plan j per enrollee risk unit is λc j, so equation (6) becomes ( ln Q w j p j = λc j B + p j ) 1 (8) with the mark-up of bid over cost again depending on the elasticity of risk-weighted demand. Case 2: A more complicated case is that λ( ) depends on p j either because p j affects observed risk composition and λ ( ) is not proportional to r so for instance unobserved selection is more important for high or low risk enrollees, or because p j affects risk composition conditional on r. In this case, equation (6) becomes ( ln Q w j p j = c j B + p j ) 1 Qjr p j [r λ ( )] dg (r) Q w j / p j c j, (9) where the last term reflects the fact that changes in p j potentially affect the plan s (observed or unobserved) risk composition. In particular, if an increase (decrease) in p j leads to a risk composition for plan j that is relatively overcompensated, then the insurer will want to increase (decrease) its bid, and competitive incentives will be distorted by the desire to affect risk composition. 4.3 Empirical Strategy To assess the efficacy of the bidding mechanism, we want to understand what determines plan bids, and also how plan bids affect plan enrollment. This calls for estimates of how plan bids respond to changes in costs or CMS benchmarks, and of how enrollment changes with plan bids. We therefore face a common challenge in industry studies of locating plausibly 14 If p j > 0, a plan would prefer lower risk individuals for a given risk-weighted demand because they will pay more per risk unit in individual premium. But given the actual distribution of plan bids, this latter effect cannot be very important. 16

17 exogenous sources of variation in costs, benchmarks and bids. For instance, an obvious concern in looking at the relationship between plan bids and plan enrollment is that there might be significant differences in plan quality (even accounting for the CMS quality scores) that drive both bids and enrollment. Our solution is to rely on the panel structure of the data. We mainly use a differencein-differences framework that relies on variation within a plan or contract, either over time or across counties, or both. This approach has some limitations, but has the benefit that it utilizes the large scale of the program and its structure. To see how it works, consider estimating how plan bids affect plan enrollment, where we are concerned about plan quality being imperfectly measured. Here we can rely on three sources of variation. First, because we typically observe the same plan for several consecutive years, we include a plan fixed effect in some of our specifications. This will capture unobserved plan quality that is constant over time. Second, in a given year we observe the same plan being offered in multiple counties. The typical HMO or Local PPO plan is offered in 8 counties, so we are able to include county fixed effects, or even countyyear fixed effects, in some of our specifications, and still identify demand parameters using variation in benchmarks across multiple counties in which the plan is offered. Third, we make use of an important institutional detail related to the structure of plan offerings. A contract between an insurer and CMS defines the plan type and provider network, and there are typically several plan offerings within the same contract. These plan offerings vary in terms of the exact package of benefits that is offered (i.e., the monthly premium, whether the plan includes Part D benefits, and so on). However, they are associated with the same insurer and same provider network. Thus, another way in which we control for unobserved plan quality is to include contract (but not plan) fixed effects. In some specifications we include contract-county fixed effects in order to account for the fact that the value of the provider network may vary across different counties within the same service area. We report a number of alternative specifications for each of our empirical exercises, partly because readers may find some sources of variation more convincing than others. For instance, a specification that includes plan-county fixed effects provides a very tight control for fixed plan quality, but relies only on time-series variation, whereas with contract-county fixed effects, we can also compare plans in the same year, controlling for the provider network, 17

18 which may be the most important hard-to-measure aspect of plan quality. We discuss some of the trade-offs in the various identification strategies in the context of each exercise. 5 Determinants of Plan Bids We next turn to the relationship between plan bids, benchmark rates and FFS costs. As noted above, Song, Landrum, and Chernew (2012) and Song, Cutler, and Chernew (2012) have reported a relatively strong connection between benchmark rates and plan bids, interpreting this relationship as evidence of imperfect competition. In a perfectly competitive environment where plans submitted bids at their per-enrollee cost, we would find no effect of exogenous changes in the benchmark. In the model above that allows for market power, we have seen that changes in the benchmark rate will be passed through into plan bids at the same rate as uniform reductions in plan costs. Therefore, it is natural to look at the bid-benchmark relationship at the same time as we look at the bid-ffs cost relationship. Table 4 reports results from regression specifications in which the unit of observation is a plan-year, and the dependent variable is the excess bid, p jt. The key regressors are the associated benchmark and the associated (risk-adjusted) cost of traditional Medicare in the plan s service area. The empirical model is: b jt = ρb jt + γc T M jt + µ j + ν t + ε jt. (10) Our preferred specification includes both year and plan dummies, so that identification comes from comparing the bid changes of plans that received smaller or larger benchmark increases from one year to the next. However, the results are fairly similar across different specifications. We start by discussing the pooled results in Columns (1)-(3). Consistent with the findings of Song, Landrum, and Chernew (2012), we find that each $1 increase in a plan s benchmark rate leads to an increase in the plan s bid of around $0.55, so that the plan s excess bid decreases by around $0.45. The more surprising result in Table 4 is that FFS costs are only weakly correlated with plan bids conditional on the benchmark rate. As noted above, even under imperfect competition, we expect the relationship between uniform cost decreases and benchmark increases 18

19 to be essentially the same. However, rather than estimating a coefficient of around 0.5 (we would expect 1.0 under perfect competition), we obtain coefficients on the order of 0 and What can explain this? In the context of our theoretical model, one possibilitiy is that realized FFS costs in a plan s service area are a very noisy measure of a plan s ex-ante cost expectations, and this attenuates the estimated coefficient toward zero. However, in the appendix we report additional specifications that attempt to resolve the measurement error concern by focusing on larger counties (where idiosyncratic cost shocks are more likely to average out), by averaging costs over multiple years, etc. and our basic finding remains stable: observed FFS costs bear little relationship to plan bids. We therefore consider an alternative hypotheses, which is that the cost structure of MA plans is in fact quite different from that of traditional, fee-for service Medicare. As we have discussed, most MA plans are either HMOs or PPOs that negotiate prices with providers, so their unit costs need not be identical to CMS across the country, and their utilization management practices may also differ from those of fee-for-service Medicare. Indeed, several recent papers (Aizcorbe et al. (2012); Baker, Bundorf, and Kessler (2010); MaCurdy et al. (2013)) have noted that Medicare FFS costs and the costs of employer-provided private health insurance are not strongly correlated across regions. The structure of most MA plans is probably more similar to employer-sponsored health plans for non-seniors than it is to FFS Medicare. To support this hypothesis, the second panel of Table 4 reports results from a similar set of regressions, where we estimate our excess bid model separately for the three types of MA plans: HMO plans, PPO plans and private FFS plans. As noted above, the private FFS plans are Medicare Advntage plans that operate as an indemnity plan, just like traditional Medicare, and pay CMS-negotiated rates to providers. The results from these regressions are strikingly different. The estimates for the HMO plans are similar to our pooled estimates: pass-through rates of around 0.5 for benchmark changes, and close to zero relationship between bids and FFS costs. The estimates for Private FFS plans have a slightly higher rate of benchmark pass-through into bids (0.62, so that a $1 benchmark increase reduces the excess bid by $0.38), and a coefficient estimate on FFS costs that is exactly as the optimal bidding model above predicts that is, dp/db = dp/dc. The estimates for PPO plans are in between the HMO and PFFS estimates, with the cost estimates arguably more similar to 19

20 the HMO numbers. In light of this, we conclude that the theoretical model may in fact be an appropriate model for thinking about bidding incentives, but that Medicare FFS costs may not be an ideal proxy for the cost structure of most MA plans (with the exception of private FFS plans). For this reason, we turn in Section 6 to using estimates of plan demand, coupled with the conditions for optimal bidding above, to back out alternative estimates of MA plan costs. 6 Estimating Plan Demand In this section we consider how plan bids affect plan enrollment. We adopt a nested logit specification for plan demand, altering the demand model slightly to capture the fact that plan revenue and costs depend on risk-weighted demand. We consider each county-year as a separate market, indexed by m. We divide the plans into two exhaustive and mutually exclusive categories indexed by g: the outside good (traditional Medicare), j = 0, is the only member of group g = 0, and all MA plans belong to the other group g = With this setting and specification, the utility of beneficiary i from plan j in market m is given by where δ j u ijm = δ j + η m + ζ ig + (1 σ)ɛ ijm (11) = x jmβ αp jm + ξ j + ξ jm. We use x jm to denote a K-dimensional vector of observable plan characteristics, which include variables capturing the allocation of the plan rebate, 16 an indicator for whether the plan is bundled with Part C supplemental benefits, This is an oversimplification for the sake of exposition. A beneficiary who chooses traditional Medicare could also choose to purchase a supplemental insurance (Medigap) policy (a beneficiary is not permitted to purchase Medigap coverage if he is enrolled in a Medicare Advantage plan). In addition, the beneficiary could choose to enroll in a stand-alone Part D plan. We lump all of these possibilities together and call this the outside good. In our estimation, we include a market fixed effect in order to explicitly allow for the possibility that the mean utility of MA relative to the outside good may vary across markets. 16 Each plan is required to return rebate dollars to beneficiaries in the form of higher benefits. Plans can choose to allocate these dollars across the following four categories: reduction in cost sharing, reduction of the Part B premium, increase in Part D benefits, and other mandatory benefits. We include three covariates that capture the proportion of rebate dollars spent on each of the first three categories (the other mandatory benefits category is omitted). 17 Each plan has the option to offer supplemental benefits, which are benefits that are not part of the standard package of benefits included in Medicare Parts A and B, e.g., vision and dental care. These plans must charge beneficiaries a separate Part C supplemental premium to cover the cost of these additional benefits. Since these benefits are priced separately, we abstract away from beneficiaries valuations of these benefits and simply include an indicator to capture beneficiaries valuations for bundling these benefits with 20