Mind the Gap! Consumer Perceptions and Choices of Medicare Part D Prescription Drug Plans

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1 Conference version, preliminary and incomplete Mind the Gap! Consumer Perceptions and Choices of Medicare Part D Prescription Drug Plans Florian Heiss University of Munich florian.heiss@lrz.uni-muenchen.de Daniel McFadden University of California, Berkeley mcfadden@econ.berkeley.edu Joachim Winter University of Munich joachim.winter@lrz.uni-muenchen.de This version: May 7, 2007 Abstract: Medicare Part D provides prescription drug coverage through Medicareapproved plans offered by private insurance companies and HMOs. In this paper, we study the role of current prescription drug use and health risks, related expectations, and subjective factors in the demand for prescription drug insurance. To characterize rational behavior in the complex Part D environment, we develop an intertemporal optimization model of enroll decisions. We generally find that seniors choices respond to the incentives provided by their own health status and to the institutional environment as predicted by the normative model. However, there is also evidence that seniors over-react to some salient features of the choice situation and do not take account of future benefits and costs implied by their decisions. The proportion of individuals who do not attain the optimal choice is small, but this is mostly due to the fact enrollment is optimal for most eligible seniors in the first place so the the margin for error is small. Keywords: Medicare; prescription drugs; insurance demand; health production; dynamic discrete choice. JEL classification: C25; C61; C81; D12; D91; H51; I10; I12; I18. We thank Carol Kelly and Audrey McDowell of CMS and Richard Suzman of NIA for information and comments. Helpful comments were also obtained from Amy Finkelstein and other participants of the session Consumer-Directed Health Care: A Wise Choice? at the 2007 AEA Annual Meeting in Chicago and by seminar participants at the University of Mannheim and the ifo Institute, Munich. Dedicated research assistance was provided by Byung-hill Jun and Carlos Noton. This research was supported by the Behavioral and Social Research program of the National Institute on Aging (grants P01 AG and R56 AG A1), with additional support from the E. Morris Cox Fund at the University of California, Berkeley. The authors are solely responsible for the results and conclusions offered in this paper.

2 1 Introduction Medicare Part D provides prescription drug coverage through Medicare-approved plans offered by private insurance companies and HMOs. This new program is part of the current trend towards consumer-directed health care. However, making optimal, or even just reasonable, decisions is difficult for seniors. They face uncertainty with respect to their future health status and drug costs, a rather complicated payment schedule and other peculiar institutional features of the Part D program, as well as a large number of available plans with features that vary along several dimensions. How seniors decide whether to enroll in Medicare Part D, and what plan to select, is therefore not only of crucial importance for public policy, but also for our understanding of choice behavior in real-world decision situations with a highly complicated structure and also high stakes. In the week before Medicare Part D enrollment began in November 2005, we conducted a survey of Americans aged 65 and above (the Retirement Perspectives Survey, RPS) to study information, perceptions, and preferences regarding prescription drug use, cost, and insurance. After the initial enrollment period closed on May 15, 2006, we re-interviewed the same respondents to elicit their actual Medicare Part D decisions. In addition, we presented hypothetical choice tasks with experimental variation of plan features. In a third wave of our survey, we re-interviewed our respondents once more in March and April 2007 to collect data about their experiences in the first year of Medicare Part D. 1 When we first interview eligible seniors in November 2005, we found that despite the complexity of the program s competing plans, which can differ in premiums and coverage, a majority of the Medicare population have at least some knowledge of Part D and intend to enroll. However, low-income, less educated elderly with poor health or some cognitive impairment were significantly less informed, and we concluded at that time that they may fail to take advantage of the new program; see Winter et al. (2006). In our second survey, conducted in May 2006 just after the initial enrollment period had ended, we confirmed that Medicare has met its target of 90% coverage; see Heiss et al. (2006b). However, we also found that sizable numbers of elderly people remain uncovered. Consumer opinions about Part D were mixed just after the initial enrollment period. Majorities are troubled by the deductible and gap provisions of Standard Part D coverage, and found it difficult to determine the current and future formularies of the plans they evaluate. This raises a more general issue: Consumers are often skeptical about markets, and suspicious of their organizers (McFadden, 2006). This seems to be the case for Part D. Asked the question Does your experience with Medicare Part D leave you more satisfied or less satisfied with the Medicare program?, 58.1% said they were less satisfied. Asked the question Does your experience with Medicare Part D leave 1 In what follows, the three waves of the Retirement Perspectives Survey are referred to as RPS 2005, RPS 2006, and RPS 2007, respectively. 1

3 you more satisfied or less satisfied with the political process in Washington that produced this program?, 74.7% said they were less satisfied. These responses indicate substantial dissatisfaction with the design and administration of the program. In this paper, we study the actual enrollment decisions made in the initial enrollment period of the Medicare Part D program. In most of our analysis, we concentrate on active deciders. These are those eligible individuals in our sample who did not have any other prescription drug coverage in November 2005 (including automatic coverage, for instance through their current or former employer s health program). The first part of our analysis is descriptive; its intention is to investigate whether decisions are related to the salient features of the program and the economic incentives they provided by the institutional arrangements. We look at whether active deciders enrolled in Part D or not, at the timing of enrollment, and at the choice of plans. We stress the role of of current prescription drug use and health risks, related expectations, and subjective factors in the demand for prescription drug insurance. In the second part, we develop a stylized intertemporal optimization problem faced by an individual without other prescription drug coverage during the initial enrollment period. We calibrate, solve and simulate this model using data on the dynamics of health status and chronic conditions as well as drug use and expenditure taken from the Medicare Current Beneficiary Survey (MCBS). This normative analysis allows us to infer who optimal individual decisions would have looked. We then combine these results with our own data to study the rationality of decision in the Medicare Part D initial enrollment period formally. We generally find that seniors choices respond to the incentives provided by their own health status and the institutional environment as predicted by a normative of intertemporal optimization model. However, there is also evidence that seniors over-react to salient features of the choice situation and to present costs and benefits, while they are not sensitive to future costs and benefits implied by their current decisions. We find that the proportion of individuals who do not attain the optimal choice is relatively small, but much of this is due to the fact that enrollment was optimal for more than XX%. Given the structure of the program, there was little margin for error in the first place. The remainder of this paper is structured as follows. In section 2, we describe the new Medicare Part D prescription drug benefit and the plans offered by private insurers during the initial enrollment period from November 2005 through May The existing literature on Medicare Part D, and on the demand for health insurance plans more generally, is reviewed briefly in section 3. We then introduce our primary source of data, the Retirement Perspectives Survey (section 4). Section 5 contains our descriptive analysis of decisions in the initial enrollment period. In section 6, we develop, calibrate, and simulate an intertemporal optimization model of the Medicare Part D enrollment decision, and we evaluate the rationality of observed decisions. Section 7 takes a preliminary look at the 2

4 data from the final wave of our survey to characterize first-year experiences with Part D. Section 8 contains some concluding remarks. 2 The Medicare Part D prescription drug benefit The Medicare Modernization Act of 2003 (MMA) was enacted to extend coverage for prescription drugs to the Medicare population. Beginning in 2006, the new Medicare Part D benefit would reduce the financial burden of prescription drug spending for beneficiaries, especially those with low incomes or extraordinarily high ( catastrophic ) out-of-pocket drug expenses. Under this new benefit, Medicare pays for outpatient prescription drug coverage through private drug plans, giving beneficiaries access to a standard prescription drug benefit. In 2006, the standard Medicare Part D benefit has a deductible of $250 in total drug costs. Medicare then pays 75% of costs between $250 and an initial coverage limit of $2,250; 0% of costs between $2,250 and $5,100 (with beneficiaries paying 100% of costs in this coverage gap, also known as the doughnut hole ); and 95% after total costs exceed $5,100. Figure 1 shows the payment schedule as a function mapping the total yearly drug bill into out-of-pocket (OOP) cost (excluding the annual premium). The Medicare Part D plans offered by private insurance firms differ in their premiums, and also in other plan features (as long as they are at least as good as the standard benefit just described). The private insurers who provide drug coverage within the Plan D framework may offer coverage enhancements to the Standard plan, at higher premiums. Enhancements may include coverage for the $250 deductible, and for the gap in the standard plan, which pays no added benefits for pharmacy bills above $2,250 and below $5,100. These enhancements may result in restrictions in plan formularies in order to keep the actuarial value identical to that of the standard plan (but all approved plans must have formularies that include at least two drugs in each therapeutic category). CMS classifies the stand-alone prescription plans that are available under Medicare Part D in four categories, see Back and McClellan (2006, p. 2313): The standard benefit is a plan with the statutorily defined coverage of deductibles, doughnut hole, and cost sharing. An actuarially equivalent plan is one that adheres to the statutorily defined coverage with respect to deductibles and doughnut hole but has different cost sharing (such as reduced copayments for preferred drugs and generic drugs). A basic alternative plan is actuarially equivalent to the statutorily defined benefit, but both the deductible and cost sharing can be altered. (Most of these plans have no deductible.) 3

5 An enhanced alternative plan exceeds the defined standard coverage - for example, by offering coverage in the doughnut hole. A database available on the CMS website 2 lists 2166 plans that were available in (41.9%) out of these plans provide the standard Part D benefit. One important feature of Medicare Part D is the penalty for late enrollment. Individuals who enroll after May 15, 2006 and do not have creditable coverage from another source face a late enrollment penalty fee of 1% a month for every month that they wait to join. The penalty is computed based on the average monthly premium of Part D standard plans in a given year. This rule was put in place to reduce adverse selection as our analysis in section 6 confirms, it provides a strong incentive for eligible consumers to enroll at the beginning of the program rather than wait to join when health problems develop and drug costs rise. More details on the Medicare part D prescription drug benefit can be found on the CMS website and in Bach and McClellan (2005). The political controversy surrounding its introduction is reflected in two back-to-back papers in the New England Journal of Medicine, Bach and McClellan (2006) and Slaughter (2006). 3 Related literature The new Medicare Part D prescription drug benefit, and choice of health plans more generally, have been studied by numerous authors. In this section, we briefly review those papers that are more directly related to our analysis. Hall (2004) provides an empirical analysis of how much Medicare beneficiaries value prescription drug benefits. Using a nested logit specification and data from the Medicare HMO program, she estimates parameters of demand for drug benefits and calculate estimates of consumer surplus and marginal cost. The premium elasticity is estimated to be 0.15 to Further, her results indicate that Medicare beneficiaries are willing to pay about $20 per month on average for prescription drug benefits and are willing to pay $28 to increase their brand-name coverage by $100. Her study also provides empirical evidence for adverse selection and moral hazard effects. She finds that adding a prescription drug benefit raises HMO costs by $146 per person per month, and raising brand-name coverage by $100 costs $100. These cost estimates are higher than the corresponding welfare estimates. Hall argues that this discrepancy is probably due to either the HMOs 2 The Centers for Medicare and Medicaid Services (CMS) within the U.S. Department of Health and Human Services administer health insurance coverage for older Americans via the Medicare program. CMS is the agency responsible for the administration of Medicare Part D. 3 This number includes some double counting since the plans were listed by state, but some plans are offered identically in more than one state. 4

6 experiencing adverse selection or regulation of the HMOs that lead them to offer benefits inefficiently combined with moral hazard on the part of beneficiaries. Huskamp, et al. (2003, 2005) provide empirical analysis of the effects of three-tier prescription drug formularies which have been adopted by health plans and employers in an effort to control rising prescription drug costs. Huskamp et al. (2003) examine the impact of changes in two employer-sponsored health plans on the use of three specific drugs. They find that different changes in formulary administration may have dramatically different effects on drug use and spending; in some cases patients even discontinue therapy. Huskamp et al. (2005) estimate econometric models of the probability of selecting drugs assigned to the third tier (with the highest co-payment requirement) of a three-tier plan and compute changes in out-of-pocket spending. They find that implementation of the three-tier formulary resulted in some shifting of costs from the plan to patients. They argue that the savings from increased bargaining power from plans may well be substantial. Joyce et al. (2002) analyze the impact of pharmacy benefit changes implemented by employers and health insurance providers, using data on a large cross-section of employers with different pharmacy benefit designs. Joyce et al. find that moving from a two-tier to a three-tier formulary, increasing existing co-payments or coinsurance rates, and requiring mandatory generic substitution, all would result in a reduction in plan payments and total pharmacy spending. Goldman et al. (2004) investigate the effects of such plan changes on the demand for specific drug classes. They find that a doubling of co-payments was associated with reductions in the use of eight classes. The largest decreases occurred for non-steroidal anti-inflammatory drugs and antihistamines which are both often used intermittently to treat symptoms. The reduction in use of medications for individuals in ongoing care was more modest. Moran and Simon (2006) estimate how retirees use of prescription medications responds to changes in their incomes. They find that lower-income retirees exhibit considerable income sensitivity in their use of prescription drugs, using data from the 1993 wave of the Study of Asset and Health Dynamics Among the Oldest Old (AHEAD). Their estimates indicate that a $1000 increase in post-retirement income (in 1993 dollars) for those in the low-education and lower-income group would increase the number of prescription medications used in a typical month by approximately 0.55 prescriptions per household. Yang et al. (2004) investigate how insurance affects medical care utilization, and subsequently, health outcomes over time. They develop a dynamic model of these variables, and use longitudinal individual-level data from the Medicare Current Beneficiary Survey provide to estimate these effects. Their simulations indicate that over five years, expanding prescription drug coverage would increase drug expenditures by between 12% and 17%. However, other health care expenditures would only increase slightly, and their results suggest that the mortality rate would improve. 5

7 Several studies look at the economic incentives provided by the new Medicare Part D prescription drug benefit, including Lucarelli (2006) and McAdams and Schwarz (2006). Frakt and Pizer (2006) and Simon and Lucarelli (2006) describe the plans that were available in The latter also contains a hedonic regression that relates plan premiums to plan features. There are also several papers that discuss whether Medicare Part D provides sufficient coverage to all older Americans, and in particular the effect of the coverage gap. Stuart et al. (2005) argue that discontinuities in the drug benefit will affect people with greater-than-average medical need disproportionately (which by itself is not surprising). More interestingly, they argue that those affected by the coverage gap will reduce their medication us and spending. Donohue (2006) discusses the potential impact of Medicare Part D on the demand for drugs that are used persistently at high expected cost, such as certain psychotropic medications. Her study stresses the close relation between known chronic conditions (and the medications taken for them) and plan choice. We are aware of only a few empirical studies of individuals actual behavior during the Part D initial enrollment period. 4 The Health and Retirement Study (HRS) contained questions on prescription drug use, expenditure, and Part D decisions in several of its surveys in 2005 and 2006, but results are not yet available. Hurd et al. (2007) conducted hypothetical choice experiments with a sample of individuals from the American Life Panel. 5 They obtain the ranking of several hypothetical prescription drug plans with varying cost and payment schedules. Using data on the respondent s actual drug expenditure, they can also calculate the expected out-of-pocket costs for each of the hypothetical plans. They find that the correspondence between the preference and cost rankings is low. They speculate that respondents do not know the full cost of their drugs and so cannot know what the out-of-pocket cost would be. Another explanation they give for the stated preferences is that respondents anticipate that with some probability their prescription drug requirements will change and take into account the insurance aspects of the plans. Another important issue that we do not address in the current version of this paper is potential moral hazard following enrollment in Medicare Part D. Several recent empirical studies address adverse selection and/or moral hazard in health insurance markets and the difficult problem of how to distinguish among these two effects in observed market data, in particular, Abbring et al. (2003), Bajari et al. (2006), Fang et al. (2006). 4 Health insurance and health plan choices have of course been studied in many other situations. Buchmueller (2006) presents estimated the premium (price) elasticity of health plan demand and reviews other papers on the effect of price on health plan choice. 5 The American Life Panel is an internet panel maintained by RAND, Santa Monica, and in many respects similar to the Knowledge Networks Panel we used to collect the data for the Retirement Perspectives Survey. 6

8 4 The Retirement Perspectives Survey (RPS) The three waves of the Retirement Perspectives Survey were administered to a panel of individuals maintained by Knowledge Networks, a commercial survey firm. The members of the KN Panel are enrolled using traditional random-digit-dialing (RDD) sampling methods; thus they are initially representative of the U.S. resident population in terms of demographics and socioeconomic status. Sample weighting is used to adjust for subsequent nonresponse. The RPS respondents are somewhat more computer-literate than the underlying population: About half the panel members use the internet, compared with about a third in the corresponding population. The KN Panel members are interviewed using supplied web TV hardware at regular intervals. These surveys come from both commercial and academic clients, but they are all designed and administered by Knowledge Networks. KN Panel members are compensated for participation. The first wave of our study, RPS 2005, was conducted in the Fall of 2005, just before the initial enrollment period for the new Medicare Part D prescription drug benefit began. This survey focused on prescription drug use and intentions to enroll in the new Medicare Part D program. Additional questions focused on long-term care, and a sequence of questions was designed to obtain simple measures of respondents risk attitude. The RPS 2005 questionnaire also contained some embedded experiments on information processing and response behavior in consumer surveys (see McFadden, et al., 2006, for a discussion of these experiments). In May 2006, after the initial enrollment period had ended, we administered the second wave (RPS 2006). For this survey, we re-contacted the Medicare eligible respondents of RPS 2005 and elicited their prescription drug insurance status as well as their Part D decisions, including plan choice. RPS 2007 was conducted in March and April 2007; its sample consisted of both re-interviews of earlier RPS respondents and refreshment cases. The RPS interviews required about 30 minutes for completion in 2005 and 2007, and about 20 minutes in Most socioeconomic and demographic variables were provided by Knowledge Networks as background on panel members so we did not need to include them in the RPS questionnaires. Table 1 contains sample sizes and cooperation rates for the various RPS waves and segments. Cooperation rates were generally rather high. For the first wave (RPS 2005), we contacted almost 6000 KN Panel members aged 50 and older. 80.6% of those KN Panel members that were invited to participate completed the questionnaire. For RPS 2006, we contacted only KN members who had completed RPS 2005 and were aged 63 years or older at the time of the interview (or who were younger but already on Medicare, but these are only a few cases). The cooperation rate was again rather high at 82.3%. Finally, for RPS 2007 we used two samples: re-interviews of earlier RPS respondents (i. e., those who had completed either RPS 2005 only or both RPS 2005 and RPS 2006), and a refreshment sample of KN Panel members who had not participate in any prior RPS wave. The cooperation rate among these groups was the highest for those who had completed 7

9 both RPS 2005 and RPS 2006 (89.6%) and slightly below the other rates for those who had completed RPS 2005 but missed RPS 2006 (76.6%). The cooperation rate for the refreshment sample was 81.5% and thus well in line with that in the comparable RPS 2005 sample. In private correspondence, KN indicated that the cooperation rates that were achieved for the RPS surveys were slightly above those typically observed in other studies that use the KN Panel; this is attributed to the highly topical subject of the surveys. In sections 5 and 6, we use data from the RPS 2006 core sample. This sample consists of 1573 respondents who were 65 or older in May 2006, eligible for Part D, interviewed in both RPS 2005 and RPS 2006, and had no item nonresponse on key variables. (Item nonresponse rates are generally very low in the KN Panel (less than 5% for most questions considered in this paper.) Most variables used in our analysis are based directly on the corresponding survey question. One important variable, current (i. e., 2005) total drug cost is constructed. This is a measure of what the annual out-of-pocket drug cost would be for a person without any prescription drug insurance. Details on how we constructed this variable can be found in Winter et al. (2006). Descriptive statistics of key variables in the various RPS samples are reported in table 2. 5 Consumers decisions in the initial enrollment period In this section, we describe the enrollment decisions of the active deciders among the RPS 2006 respondents. We classify those RPS 2006 core respondents as active deciders who either enrolled in a Part D stand-alone plane during the initial enrollment period or still did not have prescription drug coverage after the end of the initial enrollment period. We look at three aspects of these respondents decisions: Whether they enrolled or not, when they enrolled, and what plan they chose. The nature of this analysis is descriptive, but it nevertheless sheds light on how consumer s behavior responds to the salient economic incentives that the Medicare Part D market provides. In the RPS 2006 core sample of 1573 respondents, 443 respondents are classified as active deciders. Among those, 349 (78.6%) enrolled in a Part D stand-alone plan; 94 (21.4%) remain uncovered. Table 3 summarized the enrollment status of all 1753 core respondents, along with breakdowns along various demographic dimensions as well as current (2005) drug use and expenditure. Of those who enrolled, 319 provided the exact name of their plan so that we can determine such plan features as premium and gap coverage from the official list of plans provided by CMS. The expected payoff of enrolling in a Part D stand-alone plan consists of two components, the expected immediate benefit (defined as expected 2006 benefits less 2006 premiums) and the expected present value of benefit of avoiding premium penalties in case of future 8

10 enrollment. The second component is more difficult to evaluate and requires an intertemporal optimization model (see section 6. However, a positive expected immediate benefit is already a sufficient condition for enrollment for risk-neutral or risk-averse consumers, so it is useful to see whether enrollment reacts to factors that influence the expected immediate benefit. As noted before, the initial enrollment period began on November 15, 2005 and ended on May 15, Coverage in the initial enrollment period began in the month after enrollment (in January 2006 if already enrolled in 2005). Thus, decisions in the initial enrollment period have a second dimension consumers did not only have to decide whether to sign up for a Part D stand-alone plan, they had also a choice about when they should sign up. To characterize the timing dimension of the decision problem, we consider a stylized description of the decision problem. An individual decides at the beginning of the enrollment period whether to enroll early (Nov/Dec 2005), late (May 2006), or not at all. Let p denote the yearly premium and EP the expected present value of avoiding the penalty for not being enrolled in 2006 which remains unspecified for the purpose of our simple descriptive analysis (EP will be fully specified in the intertemporal optimization model presented in section 6, of course). The function b(c) denotes the benefits given the drug bill c. With c 2006 denoting drug costs in 2006, the payoff for early enrollment is U early = E[b(c 2006 )] p + EP. When an individual enrolls at the end of the initial enrollment period, only drugs used between June and December are covered, denote that cost by c 6:06 12:06. Thus, late enrollment is associated with a utility of U late = E[b(c 6:06 12:06 )] 7 p + EP. A rational individual enrolls early if 12 U early > 0 and U early > U late. To abstract from the nonlinearities of the benefit schedule of the standard plan and unequal monthly drug costs over the year, consider a plan which pays benefits b proportional to drug costs c. Since EP is positive, these simplifications ensure that U early > U late implies U early > 0. Thus, we obtain the following decision rule: Enroll early if you expect immediate benefits in 2006, i. e., if E[b(c 2006 )] p > 0. Enroll late if you expect immediate losses in 2006, but if these losses are compensated by the present value of avoided penalty: 0 < p E[b(c 2006 )] < EP. Do not enroll if immediate losses in 2006 are larger than the present value of avoided penalty: p E[b(c 2006 )] > EP. Thus, in this simple model the decision whether to enroll early is straightforward and depends only on expected drug costs in 2006 (which should be highly predictable by 2005 drug costs). The decision whether to enroll late given early enrollment is not beneficial is complicated since it depends on the present value of avoided penalty. Note that the nonlinearities in the benefit schedule (especially the coverage gap of the standard plan) or unequal distributions of drug costs over the year (e. g., all 2006 drug costs are expected 9

11 in January through May or in June through December) can lead to cases in which this simplified decision rule has to be modified. But the bottom line remains: Early enrollment is mainly driven by 2006 drug costs, while the decision between late and no enrollment is complicated since it depends on the present value calculations. When allowing individuals to decide month by month whether to enroll or delay enrollment, new information may make enrollment beneficial in the middle of the enrollment period. Since there won t be that much new information within a few months, one would expect peaks of enrollment at the beginning of the enrollment period (for people who immediately benefit) and at the end where the penalty becomes relevant. The distribution of months in which the sample of RPS respondents enrolled is shown in Figure 2. It shows peaks at the beginning and at the end of the initial enrollment period (even though Nov 05 and May 06 only had 15 enrollment days ). For further analysis, the sample is split into four groups of respondents. Details can be found in table 4. As argued above, individuals with high drug costs should sign up early, those with intermediate drug costs or high present value of the penalty should sign up late and for the others, it might be rational not to sign up at all. The distribution of drug costs differs significantly between the four groups. Conditional means, medians, 10th and 90th percentiles are also presented in table 4. For the empirical CDFs (together with p-values of Kolmogorov-Smirnov tests of equal distributions) please refer to figure 3. Current drug costs appear to have a strong impact on enrollment, especially on early enrollment by December 2005 and additional enrollment by March Additional late enrollment in April or May does not seem to strongly depend on 2005 drug costs. Next, we present results from logit models for enrollment with dummies for categories of drug costs. A specification with splines or linear models with an additive non-parametric function of drug costs essentially gives the same results. A few socio-economic variables are added. Odds ratios for enrollment are presented in the first column of Table 5. Drug costs in 2005 are very strong predictors of enrollment. The younger (under 70 years of age) are more likely to enroll. As might be expected, those in excellent SRHS are less likely to enroll even though drug costs are controlled for. Somewhat surprisingly, poor or fair SRHS also decreases the enrollment probability relative to the intermediate SRHS category. The other two columns show results from logit estimates which look at the timing of enrollment. As argued above, the rational decision whether to enroll early mainly depends on whether the individual expects immediate benefits in 2006 since delaying enrollment to the deadline in May is not penalized. So the decision only depends on expected drug costs in 2006 which are highly correlated with drug costs in The second column of table 5 shows logit results for early enrollment (defined as being enrolled by March 2006). The results are as expected for rational individuals: Drug costs in 2005 are a very strong predictor of early enrollment while the socio-demographic variables have no 10

12 significant impact. Late enrollment within the initial enrollment period is rational for individuals who don t expect immediate benefits in 2006 but want to avoid the penalty. The present value of avoiding the penalty depends on the whole trajectory of future drug costs. Those are also correlated with 2005 drug costs but weaker than 2006 costs. In addition to that, individual expectations, tastes, and the understanding of the penalty and its expected present value drive the decision whether to enroll late or not at all given that early enrollment is not beneficial. The third column of table 5 shows logit results for whether individuals enroll late (April or May 2006) for those who were not enrolled early (by March 2006). Note that this is not a structural behavioral model since it ignores self-selection. The results show that among those not enrolled early, 2005 drug costs do predict late enrollment, but only weakly. On the other hand, socio-economic variables become important predictors. They may reflect health and other expectations, information, and/or tastes. Taken together, table 5 shows that the strong predictive power of drug costs for total enrollment (column 1) is mainly driven by early enrollers (column 2), while the enrollment differentials by socio-economic variables are mainly driven by late enrollers (column 3). This is consistent with a view that the individuals understood at least the de-sign of the initial enrollment period and its incentives. Next, we turn to plan choice of those core respondents who enrolled in a Medicare Part D stand-alone plan. The plan information we use comes from two sources: We asked the RPS respondents what plan they chose using a two-stage procedure during which they were first presented with a list of plan providers active in their state, and then with a list of plans offered by that firm. Information on all available plans features comes from a database available on the CMS website. The number of plans offered in each state differs between 17 and 52 with the median respondent having 43 plans to choose from. The monthly premium varies between $1.87 and $ and the plan designs vastly differ. 58% of all offered plans remove the deductible and/or the coverage gap (at least for generic drugs) and the formularies, authorization rules and other features differ significantly. So the individuals face a choice from a complex choice set. On the other hand, plan can be switched annually without any costs (except for hassle). So the plan choice mainly depends on expected benefits in For 316 of the 349 respondents with individual stand-lone insurance (92%), we can identify which plan they chose from the plan name look up questions. Table 6 shows the distribution of drug costs by enrollment status and plan features. Cheapest plan indicates whether the individual enrolled into the plan with the lowest premium available in her state. Figure 4 shows the distribution of the premiums of all 2166 plans that were available for 2006, stratified into four coverage classes: standard plans, actuarily equivalent plans, and two types of enhanced plans (one with gap coverage only for generic drugs, the other 11

13 with gap coverage for generic and brand drugs). As expected, premiums are higher for the enhanced plans. More importantly, there is considerable variation in plan premiums. Figure 5 shows similar distributions, but now for those plans that were chosen by the RPS respondents. A comparison of the two figures shows that RPS respondents tended to choose cheaper plans in each of the categories, and also to concentrate on a few plans in each category, in particular among the equivalent plans. The plan that was in highest demand in this group was the AARP plan which had a 30% share among RPS respondents who enrolled in a stand-alone plan (table 7). Table 8 shows results from OLS and quantile regressions of the premium of the chosen plan on the same covariates as in table 5. Higher drug costs substantially increase the premiums of chosen plans, especially the lower part of the distribution. The socio-economic variables have hardly any explanatory power. Table 9 presents odds ratios from two logit regressions where the dependent variables are two alternative definitions of cheap plans : In the first column, a cheap plan is defined as one with a premium less than $10/month (which holds for 11.1% of the sample). In the second column, the dependent variable is equal to one if the respondents chose the cheapest of all available plans in the respective state (which holds for 20.9% of the sample). High drug bills substantially decrease the probability to enroll into a cheap plan. Individuals who enrolled in order to avoid the penalty but do not expect immediate benefits would rationally be more likely to enroll into cheap plans since switching plans is costless (except for hassle). For a more detailed look at the features of the chosen plans, we present estimates of both the implicit price and the willingness to pay for those features. The attributes we study are: No deductible: Plan offers benefits without the $250 deductible of the standard plan. Gap coverage (generics): Generic drugs are covered in the coverage gap of the standard plan. Gap coverage (all drugs): All drugs in the formulary are covered in coverage gap of the standard plan. Top 100 drugs uncovered: Number of top 100 drugs missing in the formulary. Top 100 with authorization: Number of top 100 drugs only covered after authorization or step therapy. Drug tiers: Plan divides drugs into tiers with differing co-pays. 12

14 We estimate the implicit prices of these attributes are based on a hedonic regression for the 2166 plans offered in the 51 states. 6 For state s, company c, and plan p, the premium pr scp is specified as pr scp = α sc + x scp β + u scp, (1) with x scp denoting the vector of plan attributes listed above. The regression includes fixed effects for state/company combinations so that the implicit prices β are identified by plans with different features offered by the same company in the same state. Results are reported in the first column of table 10. The estimates of the willingness to pay (WTP) of these attributes are based on simple conditional logit model of observed choices. An individual i chooses between the J plans offered in her state. The utility of a plan depends on plan attributes and the premium, U ij = x j γ + pr j δ + e ij, j = 1,..., J. (2) The error terms e ij are specified as i.i.d. Extreme Value Type 1 random variables, leading to a standard conditional logit model of choice. The WTP is defined as the amount the premium has to be increased to exactly offset the increase of an attribute is by one unit so that the total utility (and therefore the choice probability) remains unaffected and is calculated as bγ. This model is first estimated for the sample of the 316 individuals for bδ whom we can identify the chosen plan assuming identical WTP. Then, the same model is estimated adding full interactions between the attributes and an indicator for drug costs above the median. The results for the WTP and implicit price estimates are shown in table 10 as well. A plan without deductible has a premium which is, ceteris paribus, higher by $7.42/month compared to a plan with the deductible. Gap coverage for generic drugs costs $8.29 and coverage for all drugs additionally $31.09 per month. For each of the top 100 drugs not on the formulary, the premium is decreased by 95 cents. Authorization or step therapy does not significantly decrease the premium. Offering drug tiers appears to be almost as costly as having no deductible. These six attributes explain 74% of the variance of the premium within companies and states. The variance of the company/state fixed effects is more than three times the variance of the remaining i.i.d. error. Interestingly, the correlation between these fixed effects and the explained premiums is negative, so plans offered by expensive companies in expensive states tend to have inferior measured attributes. The willingness to pay for removing the deductible is $19.44 for individuals with drug costs below the median and lower for individuals with high drug costs. On the other hand, unlike those with high drug costs, individuals with low costs have no willingness to pay for removing the coverage gap for generic drugs. Attributes which make the plan more 6 Simon and Lucarelli (2006) present a hedonic analysis of Part D plans that uses a different database, collected by the authors, that contains various plan characteristics that are not part of the publicly available CMS database we use. 13

15 complicated are disliked by our respondents: Drugs available only after authorization or step therapy are valued almost as poorly as drugs not available at all. And while plans offering tiers are more expensive, especially individuals with low drug costs have a negative WTP for this attribute. 6 The utility option value of enrolling in Medicare Part D In this section, we consider the dynamic stochastic programming problem faced by an individual with the option of enrolling now in a Medicare Part D prescription drug plan, or delaying enrollment. An individual who enrolls now gains current insurance coverage, and preserves the option value of later coverage at a non-penalized premium. An individual who delays loses current insurance coverage, and faces a premium penalty if he or she enrolls later, but may still come out ahead by waiting until health conditions warrant. We ask whether observed enrollment decisions are rational in the sense of behaving consistently with optimization of the dynamic stochastic program, noting that irrationalities may result if the individual fails to act in her self-interest given her beliefs, if she fails to have rational expectations, or if our specification of the dynamic model is inaccurate. Medicare Part D embeds a substantial government subsidy, so that it is actuarially favorable for the average senior. As a consequence, all risk-averse seniors with above average current prescription drug costs will find immediate enrollment in the money. Seniors meeting this criterion are clearly irrational if they fail to enroll. 7 However, healthy seniors with sufficiently low current drug costs face a more difficult choice, weighing the expected net cost of immediate enrollment against the likelihood of future health problems and drug needs, and the expected present value of penalized premiums from delayed enrollment. Elements of a rational decision on enrollment for these individuals will be socioeconomic status, age, gender, the degree of risk aversion, their discount rates, and their beliefs about future health, mortality, and prescription drug needs and costs, given current health. An individual who enrolls in Part D may also face choices among alternative plans that differ in premiums, coverage, and degree of risk protection. It is possible to embed the Part D enrollment decision in a more general framework for modeling dynamic decisions on health, including decisions on the use of optional preventative or palliative drugs, and the effects of drug use on health outcomes. We will outline of this modeling framework, but will not implement all its elements in our current analysis. The major pieces of this analysis are a dynamic stochastic programming model for the enrollment decision, and an econometric hidden Markov model for the dynamics of health 7 In principle, an individual could be risk-loving and rationally decline actuarially favorable insurance. We have not formally tested this possibility, but believe that as an explanation of Part D enrollment choices it would be inconsistent with other behavior and with stated preferences among hypothetical lotteries. Consequently, we classify rejection of actuarially favorable insurance as irrational behavior. 14

16 and drug use status. Section 6.1 provides a general framework for studying consumers lifecycle economic and health decision problems. Section 6.2 describes the hidden Markov model we specify and estimate for health and drug cost dynamics. In section 6.3, we describe the dynamic programming model we use to study the rationality of Part D enrollment decisions, and we present the results of a simulation study of rational decisions. Section 6.4 contrasts rational and observed Part D enrollment decisions of RPS respondents. 6.1 Life-cycle economic and health decisions Consumer Dynamics The life-cycle of a consumer can be described as a series of periods (e.g., years) at which economic and health states are realized, and economic and health choices are made. Broadly, the consumers problem is to make these choices to maximize well-being, subject to the impact of choices on the evolution of economic and health states. In general, economic and health states and choices influence both utility and the technology that determines the dynamic evolution of states. Let s t denote a vector of observed and latent economic and health state variables in period t, x t a vector of current policy choices from a feasible set X(s t ), z t a vector of observed exogenous variables, and ɛ t a vector of disturbances. Also, let d t denote an indicator that is one if the consumer is alive, and zero otherwise, p t = (p 1t,..., p Jt ) denote a vector of prices of market goods, c t denote expenditure on inputs to health maintenance, and y t denote consumption expenditure on market goods. The expenditures c t and y t are policy choices, and could have alternately been treated as components of x t. The survival indicator d t could alternately have been treated as a component of s t. Equations of motion s t+1 = h(s t, d t, x t, y t, c t, p t, z t, ɛ t ) (3) determine the evolution of the system. The rational consumer makes choices at each period t to maximize the expected present value from t forward, given the information available at t and accounting for the equations of motion, of the payoff function j u = β j [ d t+i ]U(s t+j, x t+j, y t+j, p t+j, z t+j, ɛ t+j ), (4) j=0 i=0 where β is a discount rate determined by impatience and U(s t, x t, y t, p t, z t, ɛ t ) is a felicity or instantaneous utility function. Feedbacks between health and wealth are captured in the equations of motion, and interactions of health and consumption of economic market goods in the determination of well-being appear in the felicity function. The final component of this general setup is a description of what the consumer knows at t, understands about the equations of motion and her own preferences, and believes about the distribution of 15

17 future exogenous variables and disturbances. Strict rationality requires the consumer to have full understanding of her environment, and objective or rational expectations. Characterization of the equations of motion of the system as a first-order Markov process is not restrictive when the state vector includes latent components, as this is then a hidden Markov model (HMM). Any stationary stochastic process can be approximated as closely as one pleases by an HMM; see Künsch et al. (1995) and Ribeiro (2005). We can apply this result by first embedding consumers in a stationary population, and then as necessary allowing drift in the distributions of exogenous variables z t. Note that it is primarily a question of modeling convenience whether exogenous forcing variables are listed separately, or included in the state vector, and whether exogenous variables and disturbances are distinguished. At the time consumer policy decisions are made, some exogenous variables and disturbances may be known to the consumer, while others will be revealed later or not at all. Further, some variables may be known to the consumer but not the observer, and vice versa. These distinctions will be important in specifying exclusion restrictions on behavioral response functions and in econometric identification. Life-cycle health Consider application of the general model of dynamic consumer decision-making to the question of Part D enrollment, and use of prescription drugs. We specify a model that includes more interactions and feedbacks than we can incorporate in the current empirical analysis; these are placeholders for future research. The state of an individual at the time of an enrollment decision is described by her demographic and socioeconomic status (e.g., age, gender, education, wealth), her existing health financing arrangements (e.g., status of employer-provided insurance), her observed objective and self-reported descriptors of health (e.g., inventory of medical conditions, bio-markers such as blood pressure, medical episodes such as hospitalizations and doctor visits, prescriptions, pharmacy bill), behavioral indicators such as smoking status and BMI, and latent state variables that describe health capital. Exogenous variables include current income and prices of market goods, particularly insurance premiums, and prices and co-pay rates for medical services and drugs. Policy variables include expenditures on economic market goods for consumption and as inputs to health maintenance, health insurance enrollment decisions, and choices on utilization of health services. Utilization choices include specifically choice among prescription drug therapies for existing health conditions (e.g., brand-name or generic), whether to adhere to prescribed drug therapies, and whether to use preventative drugs (e.g., statins) and palliative drugs (e.g., pain-killers). Note that our distinctions between therapeutic, preventative, and palliative drugs have only a rough correspondence in medical practice, where drug often have multiple effects, but are important in the model specification - therapeutic drugs for existing conditions and preventative drugs for potential conditions enter the technology for health maintenance, and hence the equations of motion, while palliative drugs enter the felicity function. 16

18 Health capital We view the dynamics of health in terms of latent health capital whose evolution depends on the technology for health maintenance, incidence of health problems, behavior, and inputs of resources that treat or prevent problems. Just as the concept of skill or human capital informed the economic analysis of education as a life cycle decision, the concept of health capital, and life-cycle decision-making on health maintenance, offer useful insights into the interactions of human biology, medical technology, and individual behavior. The concept of health capital was introduced by?, who pictured investmentdepreciation dynamics for health capital that mimic the conventional treatment of economic capital. This model with a depreciation rate that increases with age captures some of the life-cycle dynamics of health, but McFadden (2004) suggests that health capital may be more like the stock of water in a reservoir, so that (1) early in life the body s self-repair and replenishment mechanisms are usually adequate to maintain the stock near capacity, (2) with age natural replenishment diminishes and more budgeted investment is needed to maintain the stock, and (3) the technology of depreciation may induce losses that are not proportional to stock, and are relatively larger when the stock is small, old, and worn. This analogy provides a simple explanation as to why health expenditures can be low when we are young and health capital is high, and can rise sharply as we age and the remaining stock of health capital diminishes. Preventative maintenance is important, and hard use hurts, but hazard rates for various failures are largely beyond our control. We work around some failures, and repair others, until the system fails. Objective and self-rated health measures are indicators of health capital. Specifically, self-rated health status (SRHS), a five-point semantic differential from poor to excellent, the presence or absence of specific health conditions such as diabetes and high blood pressure (HBP), and scores on activities of daily living (ADL s) and instrumental activities of daily living (IADL s) may be included as indicators. For some modeling purposes, a one-dimensional measure of health capital may suffice. However, in general we can expect health capital to be fundamentally multi-dimensional, requiring more work to identify and measure its components, but also inviting new analysis; e.g.: Are cardio-vascular, gastro-intestinal, crystalized and fluid mental, respiratory, and skeletal-muscular capital complements or substitutes, and can our portfolio of health capital stocks be re-balanced through the life cycle to minimize risk? Can individuals give self-rated cardio-vascular or respiratory health status with comparable or better consistency and predictive power than a single overall self-rated health status? Do various indicators load differently on health capital components? For example, one might expect IADL s and indicators for cognitive function to load heavily on mental capital, ADL s and some health conditions to load heavily on cardio-vascular capital or skeletal/muscular capital, and so forth. In general, the mappings from health capital to indicators can be non-linear, capturing the sharply increasing probabilities of some health conditions or death when health capital, scaled to other indicators, nears exhaustion. 17

19 It may be fruitful to look to failure time models for description of the dynamics of health capital. There is ample precedent for this in both physical and biological applications, and in the epidemiology of aging. Multiple hazard models such as accelerated failure time models with hazard rates influenced by exposure to various risk factors and by preventative and restorative investments, may work to describe the evolution of health capital. When considering life cycle models with health capital, a few questions arise that parallel issues that appear in the dynamics of financial capital. We know that optimal lifecycle expenditure jumps at retirement due to regime change in the consumption of leisure, and upon the death of a spouse due to regime change in household equivalents. Does these regime changes also affect the productivity of health expenditures; e.g., are leisure and spousal consumption-sharing substitutes or complements for health expenditures? Can we as a result expect to see structural breaks in medical expenditures at the times of retirement and changes in family composition? Health technology The equations of motion s t+1 = h(s t, d t, x t, y t, c t, p t, z t, ɛ t ) are determined by the available technologies for economic and health maintenance, and by behavioral choices of levels of inputs, including use of therapeutic and preventative drugs. A useful economic characterization of this technology is in terms of input costs, described by a cost function c t = C(s t+1, s t, d t, x t, y t, p t, z t, ɛ t ), (5) interpreted as the minimum out-of-pocket expenditure c t required to achieve the transition from s t to s t+1. Given c t, this equation implicitly determines the equations of motion; i.e., c t C(h(s t, d t, x t, y t, c t, p t, z t, ɛ t ), s t, d t, x t, y t, p t, z t, ɛ t ). Input demands G k (p t ) are given by Shephard s identity, G k (s t+1, s t, d t, x t, y t, p t, z t, ɛ t ) = C(s t+1, s t, d t, x t, y t, p t, z t, ɛ t )/ p kt. (6) Suppose, for example, one specifies C(s t+1, s t, d t, x t, y t, p t, z t, ɛ t ) to be trans-log, log C = J K it log p it i=0 J i=0 J λ it log p it log p jt, (7) j=0 with price-homogeneity imposing the parameter restrictions J J J K it = 1 and λ ij = λ ij = 0, (8) i=0 i=0 j=0 where the K i t are functions of the remaining cost function arguments, s t+1,s t,d t,x t,y t,z t,ɛ t. The input demand shares in cost then satisfy J µ k (p t ) = p kt G kt /c t = K kt + λ kj log p jt, (9) j=0 18

20 implying own and cross price elasticities of demand Felicity log G k (p t, y t )/ log p jt = 1(j = k) + µ j (p t ) + λ kj /µ k (p t ). (10) The felicity function U(s t, x t, z t, ɛ t ) is an indirect utility function of current consumption expenditures and prices of market goods. Then, demands for economic market goods are given by Roy s identity. In particular, demands for prescription drugs will be determined in this manner. There is a potential complication when commodities are priced nonlinearly, as is the case for prescription drugs under the Part D standard plan. Then, to apply Roy s identity, it is necessary to identify the marginal cost of the commodity as its price, to subtract the infra-marginal net cost of the commodity from expenditure, and to determine the final consumption level implicitly; see Hausman (????). An example of a parametric felicity function that could be adapted to empirical analysis of prescription drugs is the Almost Ideal Demand System (AIDS) specification U(s t, x t, z t, ɛ t ) = [log y t J α it log p it 1 2 i=0 J i=0 J γ ij log p it log p jt ]/ j=0 J i=0 p β i it, (11) where p st = (p 0t,..., p Jt ) is a vector of commodity prices that is a component of z t, y st is expenditure on market goods net of expenditures on inputs to the technology for health maintenance, a component of x t, and the parameters α it, γ ij, and β j may in general depend on health state and disturbances. In particular, enrollment in Part D and choice of a prescription drug insurance plan will influence net expenditure (through deduction of the insurance premium) and the price component that applies for drugs under the chosen plan, and α it will depend on health condition. Price homogeneity requires the restrictions 1 = J α it and 0 = i=0 For shorthand, define and log Y t = log y t P t = J i=0 p β i it, J γ ij = i=0 J γ ij = j=0 J α it log p ist 1 2 i=0 J i=0 J β i. (12) i=0 J γ ij log p it log p jt, (13) and interpret Y t as discretionary per capita income and P t as a relative price index. Roy s identity gives the market demand functions, j=0 D k (p t, y t ) = V(p t, y t )/ p kt V(p t, y t )/ y t. (15) (14) 19

21 Expressed in terms of logarithmic derivatives, this identity gives expenditure shares, θ k (p t, y t ) p kt D k (p t, y t )/y t = V(p t, y t )/ log p kt J = α kt + γ ki log p it +β k log Y t.(16) V(p t, y t )/ log y t This specification allows a general pattern of income and substitution effects. The own and cross price elasticities and income elasticities are J log D k (p t, y t )/ log p jt = 1(j = k)+γ kj /θ k (p t, y t )+[β k /θ k (p t, y t )][α kt + γ ki log p it ](17) log D k (p t, y t )/ log y t = 1 + β k /θ k (p t, y t ). (18) Applied to prescription drugs, this system will imply price and income effects for palliative drugs whose consumption influences felicity directly. There may also be price and income effects on demand for therapeutic and preventative drugs that come indirectly from the impact of their cost on the net expenditure appearing in the felicity function, and from input substitution in the medical maintenance technology. A limitation of the AIDS specification in a model of intertemporal choice behavior is that it will not necessarily correctly represent risk preferences. However, to the extent that risk appears as randomness in uncommitted expenditure, its appearance as a log term in the felicity function implies a Bernoulli evaluation of risk, which may be a reasonable first approximation. Part D enrollment decisions Individuals who do not enroll in Part D when they are initially eligible have the opportunity to enroll later. This opportunity is continuing for individuals with sufficiently low income, and is available to others during open enrollment periods held annually in November and December. No individual can be refused enrollment, but late enrollees are penalized one percent of the national average premium for each month of delay beyond the open enrollment period in which they were initially eligible. (Gaps in enrollment are also penalized one percent per month.) Enrolled individuals may switch plans each year without penalty or qualifying conditions, an important feature of the organization of the Part D market. We model health dynamics as an annual process with the timing convention that at the end of a year an individual either dies, or survives for another 12 months. Then, at the beginning of the new year events for a survivor unfold in the following sequence: (1) if the individual has not previously enrolled, an enrollment decision is made; (2) if there are plan choices, the individual decides whether to switch to a new plan; (3) a new health status is determined for the following 12 months, (4) a new number of medications or pharmacy bill is determined for the following 12 months, (5) net out-of-pocket pharmacy costs are calculated taking into account insurance coverage and plan, and (6) utility for the year is determined. The decision tree of the respondent is illustrated in figure i=0 i=0

22 In this schematic, health status is latent and not observed directly, but an indicator for it, self-reported health status (SRHS), is observed. An inventory of health conditions, and ADL and IADL scores, are also observed, and can also be used as indicators. Random elements enter the determination of survival, and innovations in health status and pharmacy bills. We will assume in the current model that health capital is one-dimensional, and leave multi-dimensional generalizations for future research. The evidence from Heiss (2006) is that persistent unobserved components are present in the evolution of health capital; thus, we anticipate a high degree of persistence in levels of health capital for each individual. It is possible that there is heterogeneity across individuals in the technologies available for health maintenance and in initial endowments of health capital; these individual differences reflect what is often designated as the latent robustness or frailty of the individual. In the current model, we assume that all such differences are captured by latent health capital. We use SRHS as an indicator for health capital. A preliminary question is the reliability of this indicator. In analysis of AHEAD data, an indicator for Poor/Fair SRHS is predictive of future incidence of health conditions and of mortality, but the Good/Very Good/Excellent gradient is not predictive; see Adams et al. (2003). This may be a reporting effect, or if SRHS is a good indicator of health capital, may reflect sharply diminishing productivity of health capital above a threshold. Baker et al. (2004) find in Canada over-reporting of health impairments among the unemployed, using medical records as a benchmark, a justification effect. Thus, SRHS may be susceptible to justification effects. In AHEAD, Poor/Fair SRHS is strongly associated with clinical depression, and strongly associated with a dwelling rated Poor/Fair, even with statistical control for overall socioeconomic status. This again suggests that reporting effects may influence SRHS. Strong behavioral regularities appear in recall of past experiences - compared with instantaneous reports of experience, recall weighs heavily recent experience and changes in experience, and adapts to long-run experience. Stated in statistical terms, recall over-weights recent, high-frequency components of history and under-weights low-frequency components of history. These regularities are likely to be present in subjective judgments of health capital, e. g., SRHS. In Adams et al. (2003), probit models are estimated for prevalence and for incidence of Poor/Fair SRHS, given objective health status indicators and a variety of measures of socioeconomic status. Tables 1 and 2 below reproduce these models for the AHEAD panel. Consider first the explanation of prevalence in Table 1. For both females and males, prevalence of cancer, heart disease, stroke, lung disease, diabetes, arthritis, cognitive impairment, depression, ADL limitations, and IADL limitations are associated with Poor/Fair SRHS. In addition, high blood pressure for females and low Body Mass Index (BMI) for males are associated with Poor/Fair SRHS. Thus, Poor/Fair SRHS appears to correlate well with objective health impairments. The very strong association of de- 21

23 pression and Poor/Fair SRHS may reflect, in addition, a perception or reporting effect that could reduce the reliability of SRHS as an overall measure of health capital. Socioeconomic variables show some association with SRHS, with the prevalence of Poor/Fair SRHS higher when SES is lower for both females and males. The measurement problem is to disentangle true links between SES and health capital coming out of life cycle planning and use of medical technology, and spurious associations arising from reporting effects. Table 2 is a model for incidence of new Poor/Fair SRHS between waves one and three of the AHEAD panel, a period of about five years, as a function of pre-existing SES and health status, and of incidence of new objective health impairments between the waves. In this model, at least some spurious reporting effects are controlled, and the model can be interpreted more plausibly as giving structural, causal effects of incidence of new objective health conditions or changes in SES. The pattern that emerges is that for both females and males, some pre-existing chronic conditions, such as lung disease, and some new acute conditions, such as cancer, heart disease, and ADL impairment, appear to induce a transition into Poor/Fair SRHS. In addition, for females, pre-existing hip fracture and depression, and new stroke, induce Poor/Fair SRHS, while for males, pre-existing high blood pressure and arthritis induce Poor/Fair SRHS. The fact that all serious health impairments are not significantly related to incidence of Poor/Fair SRHS is probably a consequence of the modest frequency with which various detailed impairments appear over a five-year period. There are weak impacts of SES on incidence of Poor/Fair SRHS, notable primarily because these impacts are absent for incidence of most objective health impairments. The good news to be drawn from these models is that SRHS relates strongly to objective health conditions, meeting one criterion for a measure of health capital that it be predictive for objectively measured health status. The bad news is that the strong dependence of Poor/Fair SRHS on depression, and to a lesser extent on SES, may reflect reporting effects as well as the interdependence of health and financial status that life-cycle decisions on health investment would induce. Careful measurement and analysis will be needed to isolate reporting effects and construct health capital variables that capture the real health-wealth interactions embedded in the dynamics of life-cycle behavior. 6.2 A hidden Markov model for health dynamics We adapt the econometric specification of Heiss (2006, 2007) for the dynamics of health capital. Heiss et al. (2006a) for an application of a similar model. Assume that health capital is defined by a latent variable H (n, t) for subject n in period t that follows an AR1 process, H (n, t) = ρh (n, t 1) + (1 ρ 2 ) 1 2 u(n.t), (19) 22

24 where the u(i, t) are i.i.d. standard normal. In the stationary solution, H is also standard normal, with EH (n, t)h (n, t j) = ρ j. If one directly observed H (n, t) in two or more periods without censoring, then the off-diagonal covariances would identify the parameter ρ. Suppose that one observes mortality/morbidity status d(n, t), and for survivors with d(n, t) = 1 observes SRHS and pharmacy bill (PB) category. These satisfy the mappings, d(n, t) = 1(α 1 x(n, t) + γ 1 H (n, t) + u 1 (n, t) > θ 1,0 ), (20) SRHS(n, t) = m 2 if θ 2,m 1 < α 2 x(n, t)+γ 2 H (n, t)+u 2 (n, t) < θ 2,m for m = 1,..., 5,(21) P B(n, t) = m 3 if θ 3,m 1 < α 3 x(n, t)+γ 3 H (n, t)+u3(n, t) < θ 3,m for m = 1,..., 12,(22) where x(n, t) is a vector of exogenous variables such as age and gender, the u j (n, t) are i.i.d. logistic disturbances, and the threshold parameters satisfy θ 1,0 = 0, θ 2,0 = θ 3,0 =, and θ 2,5 = θ 3,12 = +. The model (20) (22) is substantially simpler than the general setup for health dynamics outlined earlier. Medical conditions, ADL s, and IADL s are not used as indicators of health capital. The evolution of health capital is strictly exogenous and autonomous, uninfluenced by exogenous variables such as age and drug prices, or behavioral variables such as prescription drug expenditures. There is no autocorrelation in the disturbances entering the equations for SRHS and pharmacy bills. This is a strong restriction that forces latent health capital to account for persistence effects, such as permanent random reporting effects in SRHS. One consequence of these restrictions is that the model cannot currently account for feedbacks from prescription drug use to health outcomes, which in any case are very difficult to measure in short panels. Estimation Method The model (17)-(20) can be estimated by maximum likelihood or generalized method of moments. Note that as specified this system does not depend on behavior such as the Part D enrollment choice, so that issues of endogeneity do not arise. (More generally, if the model included feedbacks from behavior to the evolution of health status, it would be necessary to account for endogeneity. In this case, the consumer s dynamic stochastic program could be used to identify suitable instrumental or control variables.) While it is possible to carry out simulated maximum likelihood estimation directly in a short panel, a more practical and stable method that also works in long panels is to solve a nested sequence of partial likelihood problems for the first transition, the first two transitions, and so forth; see Heiss (2007). Given the value of H (n, t), the outcomes are independent and their probabilities can be easily computed they are binary and ordered logit probabilities. Let Pr(y(n, t) H (n, t)) 23

25 denote this joint conditional probability. The likelihood contribution of individual i can then be expressed as T l(n) = Pr(y(n, t) H (n, t)) f(h (n, 1),..., H (n, T )) dh (n, 1) dh (n, T ).(23) t=1 As discussed by Heiss (2007), the structure of models like this allows to rewrite this likelihood contribution as l(n) = Pr(y(n, 1) H (n, 1))f(H (n, 1))dH (n, 1) (24) T t=2 Pr(y(n, t) H (n, t)) f(h (n, t) y(n, 1),..., y(n, t 1)) dh (n, t). This allows a sequential approximation of the likelihood contribution in the spirit of the Kalman filter and provides computational advantages over the simulation of the full sequence dh (n, 1) dh (n, T ) in (23). The actual estimation of this model was performed using a sequential Gaussian quadrature algorithm for (24), see Heiss (2007). The health state H is specified to be standard normal and independent of explanatory variables at age 65. Because mortality depends on H, its distribution at higher ages is adjusted according to the model. Data and estimation results The data used to estimate the model of health and drug expenditure dynamics come from the Medicare Current Beneficiary Survey (MCBS), in particular, the Cost and Use files for years 2000 to The MCBS is conducted by the Centers for Medicare and Medicaid Services (CMS). The MCBS is based on a stratified random sample of about 12,000 Medicare beneficiaries. It is a rotating panel, and an individual is observed for at most three years (together with a preliminary interview, resulting in at most four observations). The MCBS includes information on demographics, socioeconomic status, health status, and utilization as well as cost of medical care (including physician services, inpatient hospital services, and prescription drugs). Self-reported events are validated by Medicare claims. A study by Poisal (2003) suggests that there is some underreporting in self-reported prescription drug expenditure in the MCBS. We do not address this issue here. Table 11 shows the maximum likelihood parameter estimates of the full model. It includes age splines, a dummy variable for high education (more than high school) and a dummy variable for non-caucasian respondents in all equations. The model is estimated separately by gender. Ceteris paribus, non-white females use less drugs than white females. Independent of gender, highly educated respondents use less drugs and report better selfrated health. The latent component enters all equations significantly and its correlation from one year to the next is high (.97 for males and.96 for females). 24

26 Simulation of health trajectories Since the model parameters are difficult to interpret directly, a few simulations of the trajectories help to understand the model and its implications. All results are for white males with a high school degree or less unless stated otherwise. Figure 7 illustrates the dynamic features of the latent health level H. It shows its mean for the surviving population given starting values at the mean, the 25th, and 75th percentile. While the distance of the three lines becomes smaller over age, they never really converge. Technically, this is because H is not constant over time. Intuitively it means that someone who is very healthy at age 65 will be relatively healthy at age 90 compared to someone who was in worse health at 65. Mortality shifts the distribution down markedly at higher ages. This is because individuals with negative health shocks are more likely to die earlier. Figure 8 shows the survival probability for the same hypothetical individuals with initial latent health at the mean, the 25th, and 75th percentile. The differences are strong. While half of the unhealthy only survive to age 70, half of the average individuals make it to age 80 and almost half of the healthy are still alive at age 90. Figure 8 shows the aaverage drug bill over age. The thick black line represents crosssectional averages in the MCBS sample. If anything, the average drug bill decreases over age. The thick blue line shows the simulation results from the estimated model. It represents the average simulated drug bill for the surviving population. The model interprets the decline over time mostly as a selection effect: The healthy use less drugs and are more likely to survive to a higher age. This effect is illustrated by the thin lines. They show the simulated drug bill of the population surving to age 70, 75, 80, 85, 90, and 95. Those who survive to a high age are also likely to have used fewer drugs when they were 65 than the average population alive at The consumer s dynamic stochastic program Consumers decide at the end of each year whether to enroll into a Part D plan. The simple structure of the model of health and drug use dynamics allows to simulate an optimal decision strategy in a relatively straightforward way. A main ingredient of the model is the latent health state Ht which is assumed to follow an AR(1) process. We assume that individual decision makers know the current value of Ht when they make a decision but not the future shocks to it. Use the following notation: 25

27 t = 1,..., T a t Ht b t e t n t B t (b t, n t ) Ct e (Ht, n t ) Ct n (Ht, n t ) C t (Ht, n t ) Time. At year T, the individual is 100 years old. Age at time t latent health state at time t drug bill at t enrollment status at t. E t = 1 if enrolled, =0 otherwise accumulated years of non-enrollment. NE t = t 1 s=1 (1 E t) immediate net benefit of enrollment with drug bill b t and accumulated years of non-enrollment n t expected present value of total costs at t if enrolled in t expected present value of total costs at t if not enrolled in t expected present value of total costs at t V t (Ht, n t ) expected total costs at t given Ht and n t s t survival status in year ahead, s = 1 if alive, s = 0 if deceased δ discount factor Let P r(b t H t ) denote the probability of drug bill b t conditional on H t, the age, and other sociodemographic variables. It is known by the model assumption and corresponds to an ordered logit outcome probability. Likewise, P r(s t H t ) denotes the survival probability conditional on the same information which is a binary logit probability by assumption. Discretize the distribution of the health state with R nodes, so Ht {H 1,..., H R }. These nodes can be thought of as a draw from the marginal distribution of H. The AR(1) assumption on Ht translates into transition probabilities P (Ht = H r Ht 1 = H s ) for any r = 1,..., R and s = 1,..., R. Assume that in each year, first the health state Ht is realized. The individual observes this value and decides about enrollment e t. Finally the drug bill b t and survival s t are realized. The individual is risk neutral and enrolls if the expected present value of the net benefits is positive. Given the current health status Ht, the expected drug bill is E(b t H t, n t ) = b t b t P r(b t H t ). (25) The immediate benefit of being enrolled at time t (that is the benefits minus the insurance premium) given a drug bill b t is denoted as B t (b t, n t ). Given the current health status H t, its expected value is E(B t H t, n t ) = b t B(b t, n t )P r(b t H t ). (26) The complication arises from the fact that the current enrollment decision affects all future expenditures and decision since the net benefit of enrollment depends on the accumulated years of non-enrollment due to the penalty. The decision problem can be solved using backward induction. Start with t = T, so at the age of 100. There is no future so the decision only depends on the current net benefit of 26

28 enrollment B(b T, n T ). The individual does not know b T but the health state H T = Hr for some r = 1,..., R, so she can easily calculate the expected benefit of enrollment according to (26). The expected present value of costs without and with enrollment at T are simply C n T (H T, n T ) = E(b T H T, n T ) (27) C e T (H T, n T ) = E(b T H T, n T ) + E(B T H T, n T ) (28) In general, the individual enrolls at age t if the expected costs with enrollment are smaller than those without: e t (H t, n t ) = 1[C n t (H t, n t ) > C e t (H t, n t )], (29) with 1[ ] denoting the indicator function. The expected total costs at t given the information at the beginning of the year Ht and n t are simply C t (H t, n t ) = min{c n t (H t, n t ), C e t (H t, n t )}. (30) These values can be easily calculated for the final year t = T for all r = 1,..., R and n T = 0,..., T 1. This gives a decision rule and expected costs for all situations the individual could face at the age of 100. Now go backwards in time and do all calculations for some t assuming the calculations for t + 1 are done. The expectations for the drug bill and immediate benefits can be easily done using (25) and (26), respectively. But now the present value of the total costs is different from the last year because they include future costs. With a probability of 1 P r(s t Ht ), the individual will die after this year implying no future costs or benefits. The discounted expected present value of future costs given today s value of the latent health state Ht and next year s number of accumulated non-enrollment years n t+1 is R C f t (Ht, n t+1 ) = δp r(s t Ht ) P (Ht+1 = H s Ht )C t+1 (H s, n t+1 ). (31) s=1 Now the total present value in t without and with enrollment at T is C n t (H t, n t ) = E(b t H t, n t ) + C f t (H t, n t + 1) (32) C e t (H t, n t ) = E(b t H t, n t ) + E(B t H t, n t ) + C f t (H t, n t ) (33) The main point here is that without enrollment, the number of accumulated years in the future is increased by 1. These calculations are again done for all r = 1,..., R and n t = 0,..., t 1. At the first year, n 1 = 0 because everybody starts without accumulated years of non-enrollment. Simulation results This simulation can be run for all combinations of socioeconomic characteristics. Below, simulation results are shown for illustrative cases. Figure 10 shows net benefits of enrollment for for 65 year old caucasian males with a high school degree or less. They choose 27

29 whether to enroll into a standard plan which costs $240 a year. The discount rate is set to 5% per year. The abscissa represents the relative value of H. On the left, the very healthy and on the right the very unhealthy are located. The green lower upward sloping line shows the expected immediate net benefit of enrollment. It is negative for the healthiest 14% of this population. The red line shows the expected present value of penalty savings. It is driven by two effects: worse health increases the probability of future enrollment and decreases further life expectancy. These two effects have offsetting effects regarding the expected present value of penalty savings. In the simulation, the extremely healthy have a low present value of future penalty savings because they have a good chance never to enroll. It increases as health gets worse. The 10th percentile already has a very high probability of future enrollment and with worse health, life expectancy and therefore also the present value of penalty savings decreases markedly. The top blue line is the total net benefit of enrollment which is the sum of the other two lines. It is positive for all but the healthiest two percent. So 98% of this population should enroll. Figure 11 shows the same graph as Figure 10 for the same population but with the additional restriction that in the previous year, the individual did not use any drugs. This population only has an 8 percent chance that they will end up with a drug bill that makes enrollment immediately beneficial. But at the same time, the further life expectancy is quite high for this group and there is a good chance that they will eventually end up with a sizable drug bill, the expected present value of the penalty savings is high enough to make enrollment beneficial for more than 80%. Figure 12 shows the simulation results for the population as Figure 11, but for the age 80 instead of 65. The expected immediate benefits are similar to those of the 65 years old, but due to the lower further life expectancy, the present value of future benefit savings is lower, resulting in a rational enrollment rate of only 60%. 6.4 Rational and observed Part D enrollment decisions of RPS respondents We have run the same simulation presented for illustrative individuals in section 6.3 for all active deciders in RPS. The result is a probability that enrollment is rational according to our model which represents the share of people with the same age, previous year s drug bill, SRHS, and demographics who have a positive net benefit. Furthermore, we impute the enrollment share if individuals only look at the next year s outcome and the expected benefit of enrollment, split into the immediate benefit and the present value of saved penalties. Table 12 shows the overall descriptives of these values. In total, 97.5% should enroll if they are fully rational, and for 81.7% this is even immediatedly beneficial. On average, the immediate benefit is $1116 and the present value of future benefit savings is $299. In Table 28

30 13, these averages are shown by the actual enrollment decisions of the RPS respondents. Enrolled is defined as all individuals who bought either a Part D stand-alone plan or a Medicare Advantage plan with Part D prescription drug coverage. Respondents who have a larger probability that enrollment is rational actually have a higher enrollment rate. But using the fully rational rule, even 93.4% of those who did not enroll should have enrolled according to our model. Table 14 shows actual and simulated enrollment by health and socio-demographic and health variables. Only respondents who have not used any drugs in 2005 have a reasonable probability to be better off not enrolling according to the rational model. The myopic decision rule implies only 12.7% enrollment with a zero previous drug bill. The actual enrollment in this group is with 64.1% between the rational and the myopic rule. For higher drug bills, the probability that enrollment is rational is numerically indistinguishable from 1. Also myopic and actual enrollment clearly increase by the previous drug bill. Table 15 compares estimates from reduced-form models of actual and rational enrollment. The previous drug bill is the most important determinant of both. Also, both are lower for respondents with excellent SRHS. The other predictors are hardly significant for actual enrollment. Rational enrollment is lower for the older because of the lower life expectancy over which the present value of avoided penalties accumulate. Highly educated individuals have a higher life expectancy. The same is true for females and they tend to use more drugs. Race does not play any role. Table 16 shows parameter estimates from more logit models of enrollment. Specification (1) only includes the simulated rational enrollment probability as an explanatory variable. Its coefficient is highly significantly positive - on average, respondents who have a high enrollment probability in our model are more likely to actually enroll. Specification (2) adds the dollar-value of enrollment, split into immediate and future benefits. High immediate benefits increase the enrollment probability, whereas future benefits do not seems to have an effect. Specification (3) also includes the simulated enrollment probability if respondents only care about the immediate benefits. Its coefficient comes out highly significantly and all other variables lose their explanatory power. Adding socio-demographic variables in Specification (4) does not qualitatively change the results. Adding the 2005 drug bill in addition leads to a bad collinearity problem: the four simulated values and the 2005 drug bill are to highly dependent to statistically decide which of the groups of variables drive the results. While single t-tests of these nine variables do not reject the hypothesis that they are equal to zero, a Wald test of the hypothesis that they are all zero is clearly rejected (test statistic = a χ 2 [9], p < ). 29

31 Overall, the results indicate that respondents are very well aware of the (simple) fact that enrollment is more beneficial with a higher drug bill, but do not seem to understand the (complicated) consequences of the penalty for late enrollment. 7 Plan satisfaction and switching: First results from RPS 2007 To be completed. 8 Conclusions To be completed. References Abbring, J. H., P.-A. Chiappori, J. J. Heckman, and J. Pinquet (2003): Adverse selection and moral hazard in insurance: Can dynamic data help to distinguish? 1(2-3), Adams, P., M. D. Hurd, D. McFadden, A. Merrill, and T. Ribeiro (2003): Healthy, wealthy, and wise? Tests for direct causal paths between health and socioeconomic status. Journal of Econometrics, 112, Bach, P. B. and M. B. McClellan (2005): A prescription of a modern Medicare program. New England Journal of Medicine, 353, Bach, P. B. and M. B. McClellan (2006): The first months of the prescription-drug benefit: A CMS update. New England Journal of Medicine, 354, Bajari, P., H. Hong, and A. Khwaja (2006): Moral hazard, adverse selection and health expenditures: A semiparametric analysis. NBER Working Paper No Baker, M., M. Stabile, and C. Deri (2004): What do self-reported, objective, measures of health measure? Journal of Human Resources, 39(4), Buchmueller, T. (2006): Price and the health plan choices of retirees. Journal of Public Economics, 25, Donohue, J. (2006): Mental health in the Medicare Part D drug benefit: A new regulatory model? Health Affairs, 25(3), Fang, H., M. P. Keane, and D. Silverman (2006): Sources of advantageous selection: Evidence from the Medigap insurance market. NBER Working Paper No Frakt, A. B. and S. D. Pizer (2006): A first look at the new Medicare prescription drug plans. Health Affairs, 25, w252 w

32 Goldman, D. P., G. F. Joyce, J. J. Escarce, J. E. Pace, M. D. Solomon, M. Laouri, P. B. Landsman, and S. M. Teutsch (2004): Pharmacy benefits and the use of drugs by the chronically ill. Journal of the American Medical Association, 291(19), Hall, A. E. (2004): Estimating the demand for precription drug benefits by Medicare beneficiaries. Unpublished manuscript, MIT and NBER. Heiss, F. (2006): Health as a latent process. Unpublished manuscript, University of Munich. Heiss, F. (2007): Sequential numerical integration in nonlinear state-space models for microeconometric panel data. Journal of Applied Econometrics, forthcoming. Heiss, F., A. Börsch-Supan, M. Hurd, and D. Wise (2006a): Pathways to disability: Predicting health trajectories. In D. Cutler and D. A. Wise (Eds.), Health in Older Ages: The Causes and Consequences of Declining Disability Among the Elderly, forthcoming. Chicago and London: University of Chicago Press. Heiss, F., D. McFadden, and J. Winter (2006b): Early results: Who failed to enroll in Medicare Part D, and why? Health Affairs, 25, w344 w354. Hurd, M., A. Kapteyn, S. Rohwedder, and A. van Soest (2007): Knowledge of drug costs and insurance plan choice. Paper presented at the AEA Annual Meeting, Chicago, January. Huskamp, H. A., P. A. Deverka, A. M. Epstein, R. S. Epstein, K. A. McGuigan, and R. G. Frank (2003): The effect of incentive-based formularies on prescription-drug utilization and spending. New England Journal of Medicine, 349(23), Huskamp, H. A., R. G. Frank, K. A. McGuigan, and Y. Zhang (2005): The impact of a three-tier formulary on demand response for prescription drugs. Journal of Economics and Managment Strategy, 14(3), Joyce, G. F., J. J. Escarce, M. D. Solomon, and D. P. Goldman (2002): Employer drug benefit plans and spending on prescription drugs. Journal of the American Medical Association, 288(14), Künsch, H., S. Geman, and A. Kehagias (1995): Hidden markov random fields. Annals of Applied Probability, 5(3), Lucarelli, C. (2006): An analysis of the Medicare prescription drug benefit. Unpublished manuscript, Cornell University. McAdams, D. and M. Schwarz (2006): Perverse incentives in the Medicare prescription drug benefit. NBER Working Paper No McFadden, D. (2004):??? McFadden, D. (2006): Free markets and fettered consumers. American Economic Review, 96(1), Moran, J. R. and K. I. Simon (2006): Income and the use of prescription drugs by the elderly: Evidence from the notch cohorts. Journal of Human Resources, 41(2),

33 Poisal, J. A. (2003): Reporting of drug expenditures in the MCBS. Health Care Financing Review, 25(2), Ribeiro, T. (2005): Discrete dynamic models in panel settings: Approximations using hidden markov chains. Unpublished manuscript, University of California, Berkeley. Simon, K. I. and C. Lucarelli (2006): What drove first year premiums in stand-alone Medicare drug plans? NBER Working Paper No Slaughter, L. M. (2006): Medicare Part D: The product of a broken process. New England Journal of Medicine, 354, Stuart, B., L. Simoni-Wastila, and D. Chauncey (2005): Assessing the impact of coverage gaps in the Medicare Part D drug benefit. Health Affairs, W5, Winter, J., R. Balza, F. Caro, F. Heiss, B. Jun, R. Matzkin, and D. McFadden (2006): Medicare prescription drug coverage: Consumer information and preferences. Proceedings of the National Academy of Sciences of the United States of America, 103(20), Yang, Z., D. B. Gilleskie, and E. C. Norton (2004): Prescription drugs, medical care, and health outcomes: A model of elderly health dynamics. NBER Working Paper, No

34 Table 1: Sample selection criteria and response rates, RPS RPS 2005 RPS 2006 RPS 2007 Age selection criteria 50 and older 63 and older 64 and older re-interview refreshment total Completed RPS 2005 n/a yes yes no n/a Completed RPS 2006 n/a n/a no yes no n/a KN members contacted Completed interviews Cooperation rate (%) Notes: In addition, RPS 2005 respondents younger than 63 years were contacted for RPS 2006 if they said that they are on Medicare. Completion of RPS 2005 was required for this subsample. The cooperation rate is defined as the number of completed interviews as a proportion of the number of KN Panel members contacted. Table 2: Descriptive statistics, RPS To be completed. 33

35 Table 3: Prescription drug insurance status after the initial enrollment period Automatic Private Part D No coverage Total Col % Observations % drug costs (dollars) Mean st quartile Median rd quartile Total prescription drug cost in 2005 (row %) $ $1 to $ $251 to $ $1001 to $ $2251 to $ $5101 or more Total number of prescription drugs taken in 2005 (row %) No drugs or 2 drugs or more drugs Self-reported health status (row %) Excellent Very good or good Poor or fair Age class (row %) 70 years or younger to 75 years years or more Sex (row %) Male Female Education class (row %) High school or less More than high school Income class (row %) $20,000 or less $20,001 to $60, $60,001 or more Notes: Private includes prescription drug coverage as part of a Medicare Advantage program. Part D includes only Part D stand-alone plans. 34

36 Table 4: Distribution of the month of Part D enrollment among active deciders Nov Dec Jan Mar Apr May Not enrolled Total Observations % drug costs (dollars) Mean st decile Median th decile Table 5: Logit analysis of the active enrollment decision 2005 drug costs (reference category is $0) Late enrollment given Enrollment Enrollment by March 06 not enrolled by March 06 $1 to $ ** 1.06 $251 to $ *** 5.84 *** 2.65 * $1001 to $ *** *** 2.42 * $2251 to $ *** *** 4.62 *** $5101 or more 9.74 *** *** 2.55 p-value for F -test < < Socio-economic variables 71 to 75 years 0.45 ** * 76 years or more Female ** High school or less Income $30,000 or less SRHS excellent 0.37 ** *** SRHS poor or fair 0.45 ** ** p-value for F -test Observations Notes: Coefficients reported in this table are odds ratios; all covariates are coded as dummy variables. denotes p <.1, denotes p <.05, and denotes p <.01 for a two-sided t-test. 35

37 Table 6: Enrollment decisions, plan attributes, and 2005 drug costs 2005 drug costs Column % Mean Median Total Enrollment No *** Yes Cheapest plan Yes ** No Monthly premium $20 or less *** $21 to $ $31 or more Deductible Yes No Gap coverage No *** Yes Notes: denotes p <.1, denotes p <.05, and denotes p <.01 for a test of equal medians. Table 7: Top five plans purchased by RPS 2006 respondents Share Mean premium Rank Plan name N (%) (dollars) Plan type 1 AARP Medicare Rx Plan Equivalent 2 Humana PDP Standard Standard 3 Humana PDP Enhanced Equivalent 4 Humana PDP Complete Enhanced (G & B) 5 Pacificare Saver Plan Equivalent Other plans Total

38 Table 8: Regression analysis of premiums of chosen Part D plans OLS Quantile regressions 2005 drug costs (reference category is $0) Median 20th percentile 80th percentile $1 to $ * 9.18 *** $251 to $ ** $1001 to $ *** 9.8 *** 9.99 ** 2.62 $2251 to $ *** *** *** *** $5101 or more *** *** 12.5 ** 2.91 Socio-economic variables 71 to 75 years years or more Female * High school or less Income less than $30, SRHS excellent * 2.78 SRHS poor or fair Constant *** *** *** Observations Notes: All covariates are coded as dummy variables. denotes p <.1, denotes p <.05, and denotes p <.01 for a two-sided t-test. 37

39 Table 9: Logit analysis of choosing a cheap plan Low monthly premium (less than $10) 2005 drug costs (reference category is $0) Cheapest plane available $1 to $ * 0.45 $251 to $ $1001 to $ *** 0.28 *** $2251 to $ *** 0.12 *** $5101 or more 0.21 ** 0.22 ** Socio-economic variables 71 to 75 years years or more Female High school or less Income less than $30, SRHS excellent SRHS poor or fair Observations Notes: Coefficients reported in this table are odds ratios; all covariates are coded as dummy variables. denotes p <.1, denotes p <.05, and denotes p <.01 for a two-sided t-test. Table 10: Implicit prices of, and willingness-to-pay for, Part D stand-alone plan attributes Implicit price Willingness to pay all low costs high costs No deductible 7.42 *** *** *** * Gap coverage (generics) 8.29 *** ** Gap coverage (all drugs) *** *** *** Top 100 drugs uncovered *** -1.4 *** *** Top 100 with authorization *** *** 0.34 Drug tiers 6.63 *** *** *** ** R 2 (within) 0.74 var(α)/var(u) 3.11 corr(α, xβ) Notes: See text for definition of plan attributes and explanation of regressions. denotes p <.1, denotes p <.05, and denotes p <.01 for a two-sided t-test. 38

40 Table 11: Parameter estimates male female Mortality: non-white 0.309* (0.127) (0.117) high education ** (0.094) ** (0.089) latent health (γ 1 ) 1.336** (0.061) 1.728** (0.057) Drug bill: non-white (0.301) ** (0.246) high education ** (0.209) ** (0.185) latent health (γ 2 ) 6.124** (0.175) 6.228** (0.150) SRHS: non-white 0.370** (0.065) 0.465** (0.052) high education ** (0.044) ** (0.039) latent health (γ 3 ) 0.877** (0.025) 0.910** (0.022) ρ 0.967** (0.004) 0.963** (0.003) Std. errors in parentheses. */**: different from 0 at 5%/1% significance level. All equations also include age splines. Table 12: Simulation results: descriptives mean 5th 95th enrollment share: Fully rational Myopic benefit of enrollment [$1000]: Total Immediate Future

41 Table 13: Simulated vs. actual enrollment Actually Enrollment share Benefit of enrollment [$1000] enrolled? Obs. Fully rational Myopic Total Immediate Future Total Yes No Table 14: Simulation results: descriptives Enrollment share Benefit [$1000] Obs [%] Actual Rational Myopic Immediate Future 2005 drug bill bill= <bill <bill <bill <bill bill> SRHS Excellent Very good Good Fair Poor Age <age > Gender Male Female Education High school or less More than high school Race White Other

42 Table 15: Reduced-form regressions: actual and rational enrollment Logit model OLS on log odds 1 actual enrollment rational enrollment 0<bill (0.3799) *** (0.2070) 250<bill *** (0.4167) *** (0.1054) 1000<bill *** (0.3229) *** (0.0829) 2250<bill *** (0.4717) *** (0.0816) bill> *** (0.5482) *** (0.0886) SRHS excellent ** (0.3352) *** (0.1159) SRHS fair/poor (0.3589) * (0.0453) 70<age * (0.2832) *** (0.0458) age> (0.3082) *** (0.0787) Female (0.2551) *** (0.0540) More than high school (0.2517) *** (0.0504) Non-White (0.4256) (0.0700) 1 dependent variable = log(p/(1 P )), where P represents the rational enrollment probability, trimmed at Standard errors in parentheses */**/***: different from 0 at 10%/5%/1% significance level. 41

43 Table 16: Logit models for actual enrollment (1) (2) (3) (4) (5) Rational enrollment 5.530*** 3.877*** (1.155) (1.494) (1.873) (2.002) (2.053) Immediate benefits 0.468** (0.212) (0.177) (0.203) (0.244) Future Benefits (1.724) (1.775) (2.898) (3.200) Myopic enrollment 1.894*** 2.160*** (0.514) (0.530) (1.645) SRHS excellent ** ** (0.353) (0.369) SRHS fair/poor (0.337) (0.344) 70<age ** * (0.322) (0.336) age> * (0.496) (0.547) Female (0.270) (0.285) > High school (0.254) (0.286) Non-White (0.447) (0.450) 0<bill (0.940) 250<bill (1.318) 1000<bill (1.456) 2250<bill (1.522) bill> (1.708) Observations Log-Likelihood Standard errors in parentheses */**/***: different from 0 at 10%/5%/1% significance level. 42

44 Figure 1: Benefit schedule of the Part D standard plan Figure 2: Distribution of active enrollment by month 43