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1 Selection in Employer Health Plans: Homogeneous Prices and Heterogeneous Preferences Michael Geruso February 21, 2013 (most recent version here) Abstract I extend a standard adverse selection model to show that if groups of consumers such as men and women or the young and old have systematically different tastes for insurance, then the standard regulatory responses to adverse selection, which include subsidies and risk adjustment, are no longer optimal. I show that the optimal policy, subject to the constraint of private information about risk, is to price insurance on the basis of tastes, even if tastes bear no relation to risk. To assess the empirical relevance of the model, I analyze administrative health claims from a large US employer, and show a previously undocumented pattern of selection: Demand for more complete health insurance increases dramatically in age, even after controlling for expected healthcare expenditures. I estimate a structural model of plan choice to quantify the efficiency gains that would result if pricing were allowed to vary with age. The results indicate that the welfare gains from introducing even naive, minimal-information agespecific prices are similar in magnitude to recent estimates of the welfare gains from constrained optimal uniform prices. I would like to thank Anne Case, Ben Handel, David Lee, John Papp, Harvey Rosen, Dean Spears, and Tom Vogl, and seminar participants at Princeton University and ASHECON for useful feedback. I gratefully acknowledge financial support from the Princeton Center for Health and Wellbeing. University of Texas at Austin and Harvard University. Web: 1

2 1 Introduction Selection on private information poses an important regulatory challenge in any insurance market, and in health insurance in particular. Adverse selection was widely cited as a motivating factor for state and federal involvement in the health insurance exchanges established under the Affordable Care Act. Adverse selection is also of long-standing interest in the non-market setting of employer health plans. The problem of adverse selection and its solution are well known: Consumers with the highest privately-known health risks select the most generous insurance contracts, driving up the price of full insurance and driving out the lower-risk consumers in equilibrium (Akerlof 1970 and Rothschild and Stiglitz 1976). Because the distortionary effect of adverse selection is to raise prices above marginal cost, fixing the price can correct the market failure and result in allocative efficiency. Thus the solution to this problem, discussed in the context of health insurance by Feldman and Dowd (1982), Cutler and Reber (1998), Glazer and McGuire (2000), Einav et al. (2010a), and others, is an intervention that subsidizes the adversely selected contract, either directly or via risk adjustment payments to insurers. This intuition has been incredibly influential in guiding policy. Nonetheless, the analyses on which this insight is based have tended to ignore the possibility that consumers have heterogeneous tastes for insurance. In this paper, I show that the standard policy response to adverse selection is not the welfare-maximizing feasible policy when different groups of consumers have systematically different preferences over insurance. In most markets, preference heterogeneity is completely ignorable. If different groups of consumers (male and female, older and younger, richer and poorer) have systematically different demand for a good, it may affect how products are marketed and the ways in which firms behave under imperfect competition, but it does not affect the the socially optimal price, which occurs when all consumers, regardless of tastes, face prices equal to the 2

3 producer s marginal cost. In fact, in most markets heterogeneity in consumer preferences helps to ensure efficient outcomes by creating thick demand across a range of prices. I argue that in insurance markets, heterogeneity plays a fundamentally different role. The distinguishing feature of insurance markets is that marginal costs depend on the buyer s characteristics, rather than some production technology of the producer. This relationship creates a link between marginal cost and demand at the level of the individual consumer, and its consequences have not yet been fully explored. While several recent papers have begun to examine heterogeneity in insurance markets, in most cases they have introduced heterogeneity as a means to explain empirical patterns of selection that diverged from the prediction of adverse selection. For instance, heterogeneity is discussed in the context of advantageous selection in life insurance (Cutler et al. 2008) and Medigap coverage (Fang et al. 2008), and to explain the finding of no net selection in in long term care insurance (Finkelstein and McGarry 2006). Here, I examine a subtler implication of heterogeneity. While it is true that any patterns of selection are possible once arbitrary heterogeneity is introduced, the goal here is to point out that even under the benchmark case of adverse selection, acknowledging heterogeneity changes intuitions about the optimal policy response. The empirical setting in which I demonstrate this kind of preference heterogeneity is an employer health plan. Overall, the sicker and more costly employees choose the most generous insurance, consistent with adverse selection. But younger and older employees reveal different demand for insurance, even after conditioning on their objective health risk. A younger and older employee facing the same expected medical spending in the coming year will make systematically different plan choices. I show that this type of selection pattern implies younger and older consumers should face different prices. This is not because they have different privately-known health risk. That problem can be solved with subsidy or risk adjustment. Instead, they should face different prices because they have different preferences. Although the result is unusual, the allocative 3

4 efficiency condition on which it is based is the same condition considered in the classic adverse selection literature: a person should purchase an insurance contract if and only if his willingness to pay exceeds the insurer s expected cost of providing the insurance. To shed light on this idea and its potential importance, I proceed in the spirit of a sufficient statistics approach. First, I develop the simple model that lays out the conditions under which this particular type of heterogeneity leads to uniform prices being inefficient among the feasible options. The model extends the canonical model of adverse selection to allow for preferences over insurance contracts that are independent of the consumer s insurable risk, but correlated with some observable characteristic, such as age, income, geographic location, gender, or other readily identifiable variables. Under these conditions, I show that the optimal feasible allocation (subject to the constraint of private information) requires that consumers face prices based on the observable marker that correlates with their preferences, even if that marker bears no relation to risk or expected costs. The intuition is straightforward: Efficient prices are determined by the intersection of the demand and marginal cost curves. But different groups may have systematically different willingness-to-pay, for any fixed level of the costs they generate. Therefore, inducing efficient sorting via prices requires setting different prices for different groups. My model is closely related to the theoretical frameworks of Bundorf et al. (2012) and Einav and Finkelstein (2011). Both note that in the face of demand heterogeneity, first-best pricing would require price discrimination on the basis of unobserved (privately-known) expected costs. In contrast, the insight and focus of the model here is that welfare-improving price discrimination on the basis of observables is possible, even when the observables are signals only of willingness-to-pay and not of expected costs. Next, to show evidence of this kind of selection, I analyze the administrative health plan enrollment and claims data from a single large employer. The setting is one in which employees choose from two vertically differentiated health insurance contracts that differ 4

5 only in their financials. I find that older employees tend to choose more generous insurance contracts. Because health risk generally increases with age, this unsurprising pattern implies adverse selection. However, using a detailed measure of expected medical spending derived from each enrollee s history of medical events and diagnoses, I show that even after controlling for expected spending, the older consumers tend to choose more generous plans. For instance, year-old workers in my employer dataset are 50% more likely than year-old workers to choose more comprehensive insurance, conditional on generating the same costs to the insurer. In this way, age is a marker for insurance plan preference above and beyond its correlation with the enrollee s cost to insure. Comparing the choices of younger and older employees in this way requires minimal econometric assumptions. The key requirement for identification is that age is not predicting plan choice merely because the health risk variable fails to adequately control for each individual s expected costs. Fortunately, the panel nature of the data permit a direct test of this criterion: I show that while age predicts plan choice conditional on my measure of expected health risk, age does not predict realized health spending conditional on that same measure of health risk. To quantify the welfare losses of uniform pricing and explore counterfactuals, I estimate a structural model of plan selection that characterizes the choice between insurance contracts as a choice between money lotteries in a standard expected utility framework following Einav et al. (2010b). Doing so requires abandoning the transparency and simplicity of the sufficient statistics approach and making stronger assumptions about the utility function and information set of consumers. But subject to those caveats, it allows estimation of deeper parameters for use in evaluating counterfactual pricing regimes. Those counterfactuals reveal that, consistent with my extension to the standard model, optimal age-specific prices differ from the optimal uniform price, with the older enrollees facing a larger contribution for more comprehensive insurance. These age-adjusted prices yield a welfare improvement beyond the optimal uniform prices, though the dollar gain is small in 5

6 magnitude. A more significant and practical result emerges when I apply typical employer subsidy rules separately to each age group, rather than jointly to the pool of all employees. This counterfactual is relevant because the informational requirements needed to implement it are much weaker than for optimal pricing, which requires tracing the demand and cost curves. I find that most (95%) of the welfare gain from switching from uniform prices based on typical employer subsidies to optimal uniform prices can be achieved by applying the same typical subsidy rules separately to each age group. This is precisely because within most age groups, adverse selection is relatively weak. Examining only pooled selection or assuming that young and old differ in insurance demand only insofar as they differ in health risk would mask this fact. The main theoretical contribution of the paper is to develop a sufficient condition that indicates a welfare gain for taste-based pricing under adverse selection. The sufficient condition is the existence of any characteristic that has a residual impact on demand after holding expected costs fixed. While the empirical analysis of selection patterns is specific to the employer health plan setting I examine, this general principle is broadly applicable in selection markets. The finding builds on Bundorf et al. (2012), who established that uniform pricing leads to allocative inefficiency when there are heterogeneous preferences in insurance markets, but did not explore taste-based pricing. The model here is also closely related to Glazer and McGuire (2011), who do consider optimal pricing on the basis of consumer tastes. The most important difference between this paper and Glazer and McGuire (2011) is that by construction, health status in their model does not affect the optimal health plan for an individual. This assumption, while useful in their setting, is at odds with other classic and recent work on adverse selection as summarized in Einav and Finkelstein (2011). Allowing that some plans might be more efficient for delivering care to higher risk consumers and others more efficient for lower risk consumers creates a more difficult (but I argue relevant) sorting problem that this paper addresses: The optimal 6

7 allocation here depends on both tastes and costs. In the classic literature it depends only on costs. In Glazer and McGuire (2011) it depends only on tastes. The main empirical contribution of this paper is to document large and robust differences in tastes for insurance that vary systematically with age. Glazer and McGuire (2011) discuss such potential tastes, but their analysis is entirely theoretical. Ericson and Starc (2012) offer some empirical evidence of age-based heterogeneity in the context of imperfect insurer competition and analyze incentives for insurers to set markups that exploit demand elasticity differences across age groups. However, Ericson and Starc (2012) are forced to impute costs from a different population and data source than the population used to observe demand. I complement these papers by providing the strongest empirical evidence to date of tastes for insurance differing systematically with observable characteristics, conditional on the insurer s cost. The remainder of the paper is organized as follows. Section 2 explains intuitively why prohibiting price discrimination can cause an inefficiency when willingness-to-pay for insurance is correlated with observable characteristics independently of risk, and that this inefficiency cannot be corrected by even an omniscient social planner (or health insurance providing employer) free to set any uniform price. Section 3 describes the data, and Section 4 presents a set of reduced form empirical results that demonstrate that willingness-to-pay for insurance varies with age, conditional on the risk people face. Section 5 presents a structural model of plan choice that builds on the basic reduced-form findings. The structural estimates are used to calculate the welfare changes under alternative pricing policies in Section 6. The conclusion discusses broader implications of the findings. 2 Heterogeneity and Adverse Selection The goal of this paper is to demonstrate the potentially important interaction between preference heterogeneity and adverse selection. Maximizing allocative efficiency under adverse 7

8 selection with heterogeneity cannot be achieved by the well-established policy responses of risk adjustment or direct subsidy to the adversely selected contract. To show this, I begin by briefly reviewing the standard model of adverse selection as well as the variant developed in Bundorf et al. (2012) that allows for pure, unobserved preference heterogeneity. The framework follows in the spirit of Akerlof (1970) in that contract prices, but not the features of contracts, respond endogenously to the selection patterns of consumers. 1 Building on that framework, I introduce the feature that heterogeneity in preferences might be correlated with some observable characteristic. This condition which I show below is empirically relevant implies that uniform pricing is not the socially optimal pricing scheme among the feasible alternatives. This is true even when a social planner is free to set any uniform price, or when selection is perfectly risk adjusted in a regulated market. A sufficient condition for this kind of distortion is observing any characteristic that has a residual impact on demand conditional on its correlation with expected loss. This result, which contrasts with Cutler and Reber (1998), Feldman and Dowd (2000) and other treatments of adverse selection, is unusual because it implies that in markets with adverse selection on risk, socially optimally prices might be differ across consumers as a function of observable characteristics, even if those characteristics have no correlation with risk. Consider risk averse agents facing a choice between two health insurance options, a high coverage plan (H) and a low coverage plan (L). The restriction to exactly two options both simplifies the graphical analysis and parallels the menu of options in the empirical exercise that follows, but the restriction is otherwise unimportant. As a starting point, let agents differ only in their private information regarding health status. Specifically, they differ in expected healthcare spending, s. Health status here may be private information either in the sense that health state is unobservable or in the sense that contracts cannot be priced on observable correlates of risk because of regulations. 1 This is in line with most of the recent literature (see, for example, Einav and Finkelstein 2011) 8

9 Efficient sorting into insurance contracts depends on an agent s valuation of the contracts relative to her expected cost to insure. Denote the agent s difference in valuation between plans H and L as v(s). It is a function of r because people with different health status will value more generous insurance differently. Denote the difference in expected costs of enrolling a type-r in plan H rather than L as MC(s). MC(s) reflects differences in the insurer s expected payouts to medical service providers between the two plans. These payouts can differ between plans because of differences in case management or in covered services, and/or because the plans shift different shares of the total bill to the consumer. Efficient allocation requires that v(s) MC(s) for all agents that choose plan H, and v(s) < MC(s) for all agents that choose plan L. In other words, the efficiency condition is that an agent chooses the fuller coverage contract if and only if her valuation of the contract exceeds the insurer s cost of insuring her. More generally, the efficient choice j among the available plans is the one for which: v(s) j MC(s) j v(s) j MC(s) j j J. (1) In contrast to the efficiency condition, which relates valuation to cost, the agent s choice problem relates valuation to price. In the two plan setting, the agent chooses plan H if v(s) > P, that is if her relative valuation of the high plan exceeds the difference in price. In the standard model, consumers with the highest privately known risk have the highest valuation for the generous plan, so that the marginal enrollee in the generous plan is lower risk than the average enrollee in that plan. The competitive equilibrium results in average cost pricing, with the well-known adverse selection result that lower risk consumers are underinsured. 2 (See Einav and Finkelstein 2011 for a through review of the canonical 2 In a competitive pricing environment with no loads and an interior solution, a zero profit condition 9

10 model.) Figure 1, which closely follows Cutler and Reber (1998) and Feldman and Dowd (2000), illustrates the problem. [Figure 1 around here.] In the figure, health status is drawn along the horizontal axis, with higher expected costs to the right. Willingness-to-pay is increasing in s. MC(s) is also assumed to be increasing in s, indicating that as health worsens, the insurer s costs of enrolling the agent grow faster in the more generous plan. Average costs, AC(s), are a function of s only in the sense that the marginal s-type selecting plan H determines the composition of the risk pools in L and H in equilibrium. As drawn, MC(s) and v(s) exhibit single crossing at point D, leading to the efficient price P and cuttoff risk level s. An efficient allocation requires agents with s < s be in plan L, and those with s s be in plan H. Prices set to P induce this efficient allocation. Neither competitive pricing in the non-group markets nor employee contribution rates in group markets naturally deliver the optimum allocation, since prices in both settings are tied to average costs via competitive equilibrium in the non-group market, and via convention in the group market. However, employers can in principle set an efficient price for their group plans with some knowledge of the demand and cost curves. The efficient pricing rule simply sets the price consumers face in moving from plan L to H equal to P*. This solution has long been observed (e.g. Cutler and Reber 1998; Feldman and Dowd 2000; Pauly and Herring 2000), and recent empirical work like Einav et al. (2010a) has sought to quantify the welfare loss of non-optimal uniform pricing in employer settings. In non-group markets where prices are determined in equilibrium, such as health insurance exchanges, another body of work has focused on the possibility of risk adjustment to mitigate adverse selection by compensating insurers for the bad risks they attract. In all cases, it is important to note that these policy responses involve a single, uniform price for all consumers. requires that the price difference would simply be equal to the full difference in average costs between plans, following the AC(s) curve. 10

11 Bundorf et al. (2012) add pure heterogeneity to the standard model in the form of idiosyncratic preferences (µ i ) over insurance. Agents choose plan H if v(s i ) + µ i > P, where µ i expresses heterogeneity. Figure 2 illustrates the idea, showing a cloud of demand values that represent v(s i ) + µ i, replacing the v(s) curve from the top panel. For any value of health risk, there is a distribution of plan valuations. Importantly, the authors show that no price can induce all consumers to select efficiently. allocation in their model requires pricing on person-specific costs. Inducing an efficient But of course, the special feature of selection markets is precisely that such costs are unobserved. Therefore, the disconcerting implication is that there is no way to induce an efficient allocation so long as cost information is private and people have heterogeneous preferences. 3 [Figure 2 around here.] The idea that consumers might have heterogeneous prefs over insurance is not new. Spence (1978) observed. Not only may individuals differ in the expected costs they impose upon the insurer, the may also differ in their preferences with respect to insurance coverage. Nonetheless, the basic theory of adverse selection has not fully incorporated this simple fact. Now I turn to a more systematic form of heterogeneity to show that so long as taste is correlated with some observable characteristic, welfare improvements are possible beyond the risk adjustment and subsidy policies, even if perfect sorting is not achievable. In Figure 3, I extend the case in Figure 1 to a setting in which two groups, A and B, have different willingness-to-pay for plan H, holding constant expected health spending. Assume that which group an individual is a part of is identifiable to the econometrician or policy maker, even though individual health risk remains private information. In the figure, the marginal cost curve depends only on risk, not preferences, and so is necessarily identical for the two groups. 3 Bundorf et al. (2012) point out that one case in which private information on risk could be priced is when the private information is artificial in the sense of being observable but prohibited from use in pricing by the regulatory environment. The policy implication is to remove the pricing restriction. 11

12 [Figure 3 around here.] Group B has a higher relative valuation of plan H at all risk levels. The innovation in the model is that this heterogeneity in insurance valuation is systematic, rather than random. A number of phenomena could generate this pattern, including differences in income or wealth or greater risk aversion among group B. For the purpose of the present analysis, the existence of differential willingness-to-pay, rather than its source, is the salient feature. Nonetheless, it is important to note that the scenario in Figure 3 is very inclusive: The pattern could be generated simply because group B faces a mean-preserving spread of the same risks faced by group A. The canonical model includes only a unidimensional health risk or health status index, and so by construction ignores this possibility. This may be the broadest application of the model: It describes a situation in which individuals that may have identical preferences and identical expected losses have different valuations of insurance because of different dispersions of risk. In Figure 3, the intersections of the marginal cost curve and the willingness-to-pay curves generate two separate efficient prices for the two groups, P A and P B, and two separate efficient risk cutoffs. From an efficiency standpoint, Group A members should choose plan H if and only if their risk exceeds r A. Group B members should choose plan H if and only if their risk exceeds r B. No single price can simultaneously achieve efficient allocations in both groups. 4 The bottom panel in the figure highlights this result. In the bottom panel, Group A achieves an efficient allocation at the pictured common price, but Group B does not. Group B members with risk types between r B and re B should be sorted 4 A numerical example may be helpful. Consider 4 people inhabiting the same community-rated insurance pool. The {WTP, Cost} pairs for persons 1 through 4 are {19, 18}, {15, 16}, {9, 8}, and {5, 6}, respectively. It is efficient only for persons 1 and 3 to take up insurance, since only their willingness-to-pay exceeds their costs of insuring. Note that no single community price can induce this allocation: Prices must be > 15 to keep out person 2, but must also be < 9 to induce in person 3. This is not the typical adverse selection problem because it does not arise solely from the feedback between the cost of providing insurance and the price charged. (Indeed, assume that prices can be set arbitrarily.) Call persons 1 and 2 old and 3 and 4 young. If young and old can be priced separately, even competitive (average cost) pricing creates efficient allocations, with the competitive price among old being set at 18, and among the young at 8. 12

13 into plan H rather than plan L because they value plan H above their costs of enrolling in it. For the example in Figure 3, even a social planner with full information and arbitrary price setting power could not induce allocations through uniform pricing that are efficient relative to optimal group-specific prices. This is because no single horizontal price line could intersect both point D A and point D B. More generally, in a model that includes both systematic and random preference heterogeneity, the efficiency condition is that v(s ig )+δ g +µ i > P i.f.f. v(s ig )+δ g +µ i > C(s ig ), where δ g denotes group g-specific demand shifters. In this more general case, it is not possible to satisfy this condition without setting individual-specific prices that condition on private information (s ig ). Nonetheless, allocative efficiency can be improved when prices are set as a function of the group g. To see why, note that all else equal, under adverse selection, both C(s) and v(s) are increasing in s, so a shift up of v(s) must mean that the crossing point is further to the left. In other words, the optimal allocation includes more insured consumers among groups with a high δ ig. The intuition is that that people who value the good more highly (for any fixed level of marginal cost of the good) should be at least as likely to obtain it as those who value it less. If the members of groups A and B were unidentifiable in practice, then there would be little hope of achieving a more efficient allocation than what is possible under uniform pricing. Of course, it is an empirical question whether in health insurance it is possible to identify groups with different insurance demand, conditional on risk. The finding that groups with different willingness-to-pay should optimally face different prices is special to insurance markets (or selection markets, more generally), because unlike with other goods, the cost of production depends on who purchases the good rather than on some production technology of the supplier. In a typical goods market, a social planner could always achieve efficient allocations by setting price equal to marginal cost. 13

14 3 Data and Measurement of Health Status Data on health plan selection and medical risk come from the administrative health claims of a single large employer. 5 Around 40,000 employees enrolled in this employer s plans annually, and the data span Over the period studied, employees could choose between two PPO (preferred provider organization) plans. The firm is a manufacturer of consumer non-durables, with plant locations throughout the US. Workers at all locations were offered the same set of plan options. Employees are traceable over time, and their plan elections each year are known. The claims files are line-item billing records listing prices and quantities. All contacts with medical service providers are observed, as well as all prescription drug purchases. Most records include one or more diagnosis or procedure codes, providing rich clinical information on health status. This clinical information is used to construct a measure of expected healthcare spending that corresponds to s in the model. The main estimation sample is limited to the roughly one third of employees who do not enroll any other family members in their plan. Analyzing family-level enrollment is illsuited to search for evidence that plan choice differs systematically by the age of the enrollee, because families are mixed demographic groups that must make a single, common health plan choice for all members. Focusing on the single-enrolled may be particularly informative for selection patterns in the exchanges introduced by the Affordable Care Act. Experience with Massachusetts has shown that the majority of plans sold in the MA exchange were for single coverage (Ericson and Starc 2012). Health plan data exist for enrollees up to age 64, though to avoid the complication of enrollees aging into Medicare and out of the sample over the panel, the sample is capped at age 59. Table 1 displays worker characteristics. Because aggregate statistics vary little from year to year, three years of data ( ) are averaged for the sake of parsimony. The 5 These claims files were collected and purged of identifying information by Medstat. 14

15 first column includes all employees who are enrolled in a health plan. The second column is limited to employees who enroll no dependents. Workers are predominately male. Most are hourly workers. The row labeled enrolled t 1 gives the fraction of current-year enrollees who were also enrolled in the previous year in any health plan offered by the firm. Employment records, as distinct from enrollment records, are unavailable, but it is likely that turnover in health plan enrollment is largely driven by turnover in employment. Although no information is known regarding employees who waive coverage, data from the Kaiser Family Foundation (2007) Survey of Employer Health Benefits indicates that 15% of workers in firms of similar size and in the same industry waived coverage around this time. [Table 1 around here.] Employees were offered two PPO options that differed in their cost-sharing rules that is, the degree of consumption smoothing they provided against health spending shocks. Call these options L and H for low and high coverage. Contract H had a lower deductible, lower coinsurance, and a lower out-of-pocket maximum. Plan characteristics are listed in Table 2. 6 The coinsurance rate the marginal price of medical consumption once the deductible has been met is 10% in plan H and 20% in plan L. Plan L, which had lower monthly premiums, is cost minimizing for employees with low levels of utilization, while plan H is cost minimizing for employees with higher utilization. Both plans have an allowance for well-visits at no out-of-pocket cost to the enrollee. Prescription drug benefits are the same between plans and across time over the study period, except for a temporary change to drug copays in The employee contributions to plan premiums are not available in the data, so the prices 6 The cost sharing rules in Table 2 apply only to in-network services. Out-of-network services involve higher cost sharing in both plans, but these types of claims comprise a small minority of all claims. No direct evidence is available on the physician networks associated with each plan, but the networks appear to be similar or the same: Comparison of physician IDs in the claims data reveal that most (70%) of the primary care physicians visited by at least one Plan H enrollee were also visited by at least one Plan L enrollee. 15

16 employees face to enroll in these plans are not known. Average plan costs, in contrast, can be directly and precisely calculated by aggregating the total health plan payouts. When prices are needed in the choice model below, they are constructed by applying typical employee contribution formulas to average plan costs. Fortunately, identifying demand differences across groups, which is the main empirical goal of this paper, hinges only on observing the plan choices of employees who face the same prices, regardless of what those prices are. ERISA rules governing employee benefit plans ensure that younger and older employees face the same premium contributions. Table 3 provides a high-level summary of employees plan choices and healthcare consumption. The first column tallies the fraction of enrollees who choose plan H. Healthcare consumption in columns (2) through (4) is measured as the total bill paid to service providers. Column (2) gives the average overall expenditure. Columns (3) and (4) are conditional on the plan chosen. Column (5) simply takes the difference between columns (3) and (4) in order to show the magnitude of the adverse selection effect. The first row lists these aggregate statistics for the entire estimation sample, pooling years [Table 3 around here.] It is immediately apparent that adverse selection is reflected in the plan choices: Overall, 32% of enrollees choose plan H, and these enrollees consume twice as much healthcare on average as plan L enrollees. Moving down the table, the statistics are repeated for different demographic sub-groups. The same general pattern of adverse selection exists within each group as it does in the sample overall, but the level of costs vary widely across the groups. Table 3 provides the first suggestive evidence that younger and older enrollees are making systematically different plan choices as a function of the expected medical spending they face. Older enrollees, 50-59, are less likely to select plan L, but conditional on selecting L (which is optimal for low risks), their costs are relatively high. In fact, their realized costs in the low plan are dramatically higher than the costs of year olds in the high 16

17 plan. These patterns suggest that while the probability of selecting plan H increases in age, this is not simply due to the fact that risk increases in age. Instead, it appears that older enrollees, as a group, are more likely to choose plan H at all levels of risk. Second, the magnitude of selection is different within each age group than it is overall. This is evident by comparing the first row of column (5) to those below it. For most age groups, adverse selection is weaker within the age group than overall. In the policy simulations below, I return to the implications of this pattern. The summary statistics are merely suggestive about differences in insurance valuation. Evaluating demand heterogeneity that corresponds to the model above requires comparing plan choices between a younger and an older enrollee who face the same ex-ante level of expected healthcare costs. To form the appropriate comparison, I create a measure of expected healthcare costs using the Johns Hopkins Adjusted Clinical Grouper (ACG). The ACG aggregates rich cost and clinical information into a person-level risk index. Past studies of plan choice in health insurance have often proxied for health risk by age, gender, and limited or self-reported information on health status. Here, the claims records include all diagnoses, every contact with a physician or hospital, and all prescription drug purchases, enabling a more precise measure of risk to be constructed. 7 Precise controls for risk are important here, in part because a finding of this study is that there are large differences in insurance demand across age, conditional on health risk. This pattern has necessarily been missed in studies that proxy for risk with age and gender. The ACG tool is widely used by insurers and managed care organizations to predict future spending, to flag high-cost patients for intensive management, and to monitor drug adherence. Here, it is used solely to predict expected medical consumption, in dollars, on the basis of past episodes of care. The prediction is consistent with s in the model above, 7 Inputs into the ACG from my data include age, gender, pharmacy spending, medical (non-pharmacy) spending, inpatient stays, outpatient visits, ER visits, all ICD-10 diagnosis codes, all CPT procedure codes, national drug codes of all prescriptions filled, and places of service. 17

18 and represents total payments to providers and pharmacies made on behalf of the enrollee (insurer plus enrollee share). The panel data permit a direct test of the ACG prediction by comparing the predictions to the ex-post realized claims for the same individual. In the next section, I show that the ACG predictor accurately forecasts future expenditure: a regression of actual use on predicted use has a coefficient near one and an unconstrained intercept not different from zero. Alternative risk measures, including the predicted values from my own regressions of current expenditure on past expenditure (run separately by age), produce similar results to those shown in the next section. However, less of the variance in realized healthcare costs is explained by these alternative predictors. 4 Reduced Form Results 4.1 Demand Differences Across Age In this section, I present evidence that willingness-to-pay for insurance varies strongly with age. The analysis imposes minimal economic and econometric assumptions, asking only if age has residual power to predict plan choice once expected costs are controlled for. Figures 4 plot local regressions of plan choice versus health risk, estimated separately by age and gender. Expected healthcare spending, predicted by the Johns Hopkins ACG tool, runs along the horizontal axis. The dependent variable is an indicator for choosing plan H. Health risk is measured as expected healthcare consumption in dollars, and the axis is scaled in logs. Both panels include data from years 2005 through 2007, and the sample is limited to the 1st through 99th percentiles of predicted cost within each group. [Figure 4 around here] The top panel shows that conditional on health risk, take-up of plan H increases fairly monotonically in age. By taking any vertical slice in the top plot, one can compare the average choices of employees of different ages who face the same prices and carry the same 18

19 expected costs. For instance, at $1500 of expected healthcare consumption, which is near the median for year-olds, the take up of plan H differs by 13 percentage points (54%) between the oldest and youngest groups, with year-olds falling roughly in the middle. Another way to see these dramatic differences is to consider that while take up rates reach 40% at $2000 of predicted health expenditure for year-olds, take up reaches 40% only at $8000 of predicted expenditure among year-olds. The bottom panel shows that women appear to have a slight preference for more comprehensive insurance, though the difference is less dramatic. Interpreting these results in terms of willingness-to-pay is straightforward: For any level of health risk, the take up rate is just the fraction of employees for whom willingness-topay for plan H over plan L exceeds the difference in employee contributions to premiums between plans L and H. The figures parallel the earlier theoretical analysis in Figure 3, which plotted willingness-to-pay against health risk. Since at all levels of health risk, a greater fraction of older employees choose plan H, the figures suggest that willingnessto-pay for plan H increases in age, after controlling for the cost of insuring the enrollee. Although rational expectations of the insurer s costs are the theoretically relevant variable (RS), results included in an Appendix show that these patterns are robust to conditioning on alternative measures of health risk along the x-axis. These include last period s total claims which may capture a relevant heuristic and ex-post realized healthcare claims that occur in the period for which the plan choice is made. To better differentiate age and gender effects and control for other covariates, Table 4 reports results from a series of plan choice regressions that parallel the figures, where the dependent variable is an indicator for choosing plan H. The specification here is a linear probability model for ease of interpretation. Since multiple years are included, standard errors are clustered at the person level, and year effects are also included in the control variables. Columns (1) and (2) regress plan choice on expected healthcare consumption. 19

20 Columns (3) and (4) regress plan choice of the natural log of expected healthcare consumption. Consistent with the figures, the regressions confirm there is a large plan choice gradient in age. Coefficients on the age indicators are the percentage point differences in take-up rates relative to the excluded category, 18 to 29 year-olds. Because the base take up rates are low, these correspond to large effects. Demand for more comprehensive insurance increases monotonically with age in both specifications, although the non-parametric plots in the figures indicate that the log transformation in columns (3) and (4) is the correct specification. [Table 4 around here.] Columns (2) and (4) of Table 4 include controls for worker characteristics, including union status, whether full time or part time, whether paid hourly, and state of residence. These controls are potentially important though in practice they don t materially alter the results because regulations require only that similarly-situated workers face the same prices and plan options, which means that employee contributions to premiums may differ by pay status, union status, or plant location, for example. Gender differences in willingness-to-pay are smaller, but indicate that women have a preference for more comprehensive insurance. Interactions of age and gender, not included in the table, were found to be insignificant. The analysis thus far has conditioned only on objective measures of health risk. It has ignored other variables that are presumably important in the consumer s decision process, such as subjective risk assessment, risk aversion, or liquidity constraints. This is because these regressions are not intended to represent the consumer s choice problem. The point of view is rather one of a social planner or risk-neutral insurer, both of whom are concerned with plan choice as a function of cost to insure, but not necessarily with the preferences or budget constraints that generate demand. Einav et al. (2010a) summarize this point about sufficient statistics in welfare analysis in the following way: Different underlying 20

21 primitives (i.e. preferences and private information...) have the same welfare implications if they generate the same demand and cost curves. Here, age is merely a stand-in for a variety of unobserved parameters and decision factors that influence willingness-to-pay, consistent with the model in Section Robustness of Expected Costs The main identifying assumption in the plan choice regressions is that the ACG variable adequately controls for expected spending. Validity would be threatened, for instance, if ACG under-predicted health risk for the young and over-predicted it for the old. Measurement error could also pose a problem: age coefficients could be simply reflecting correlation between age and the unmeasured portion of expected costs. The regressions in Table 4 are intended to determine whether age has residual power to predict plan choice once insurer s expected costs controlled for. Of course, age is not exogenous in the regression, as it is likely correlated with many unobserved preferences that are incorporated into the error term of the regression. Nonetheless, the sufficient condition that the regressions are seeking to establish is merely whether conditional on expected costs, the old are more likely to choose plan H than the young. Validity threatened only if the ACG variable fails to adequately control for expected spending. For instance, the observed age effects in the plan choice regression could be generated spuriously if the ACG under-predicted health risk for the young and over-predicted it for the old. Measurement error could also pose a problem: if the ACG were a noisy measure of expected costs, then the coefficients on age could simply be reflecting correlation between age and true expected costs. Fortunately, the data allow a direct test for these kinds of bias. The ACG predicts expenditure in the plan period based on expenditure in the previous period. For example, predicted expenditure for 2006 is based on utilization in Since actual expenditure 21

22 corresponding to the prediction is observed, the fit of the ACG prediction can be assessed directly by regressing the actual expenditure in any period t on the ACG prediction of expenditure for based on the t 1 information. If the ACG were unbiased overall, regressing the realized costs on predicted costs should yield a slope of one and an unconstrained intercept of zero. Further, if age contained no residual correlation with realized costs after conditioning on the ACG, then coefficients on age dummies added to that regression should be jointly insignificant. Table 5 displays the results from a series of regressions of actual healthcare spending on ACG predicted spending. The regression in column (1) includes all enrollees in the main estimation sample for whom I observe information in t and t 1. No controls are included, other than an unconstrained intercept. The coefficient on expected spending (ACG) is close to one and the intercept is zero. Column (2) adds age-specific intercepts, which are found to be jointly insignificant. The unit of these intercepts is dollars. Taken together, these coefficients indicate that differential bias by age is not likely driving results. Columns (3) and (4) repeat the exercise in logs rather than levels. Here column (4) shows significant coefficients on some age indicators, although the sign of these results would indicate a bias against the findings of the paper. Increasingly negative coefficients at higher ages implies that the ACG may overestimate risk for the old. This biases against finding that valuation for plan H increases with age, holding fixed expected costs because it says that an older enrollee who already appears to value P P O H above and beyond this objective risk may actually be lower risk than the ACG estimate implies. Columns (5) and (6) attempt to provide insight on whether the variance varies with age, conditional on expected costs. The dependent variable is a log transformation of the prediction error (actual health spending minus expected spending) squared. This measure of variance appears to increase with expected spending, and there is some evidence that the variance of risk increases with age, even after conditioning on expected spending. The 22

23 potential for differential variance to explain demand differences by age is explored in more detail in the next subsection. The importance of the set of regressions in Table 5 is that they argue against a large set of stories in which the observed relationship between age and plan choice is driven by some artifact of the risk variable. Overall, Table 5 suggests that expected costs are appropriately controlled for by the ACG predictor, so that the age coefficients are not reflecting unobserved components of risk. In other words, conditional on predicted costs, age predicts preference for more generous insurance, but conditional on predicted costs, age does not predict higher realized healthcare spending. 4.3 What Drives Demand Differences? Determining the origin of taste differences is not the goal of this paper, nor is it critical for welfare analysis. Nonetheless, the differential patterns of health plan selection by age beg the question of what drives demand these differences. One candidate explanation is that older enrollees face wider dispersions of risk, even for the same level of expected costs. Estimates from the structural model below directly control for the full distribution of health spending risk in each age group, yet still produce a preference for greater coverage that increases with age. This is evidence that higher moments of risk are not solely responsible for the demand differences is corroborated by additional reduced form results in an Appendix, which show that although variance does appear to increase somewhat with age conditional on expected costs, the magnitude is not sufficient to rationalize the choice patterns. Differences in risk preferences and income are also plausible explanations. Unfortunately, there is very little scope to differentiate between these alternatives with the data at hand. I can, however, rule out another class of plausible explanations. I briefly present evidence here that demand differences are not due default options and/or inertia in plan choice because this class of behavior would have somewhat different welfare implications 23

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