Cross-Price Moral Hazard: Evidence from Diabetics' Insulin Usage Before and After Medicare Part D

Cross-Price Moral Hazard: Evidence from Diabetics' Insulin Usage Before and After Medicare Part D Daniel Kaliski February 14, 2018 Abstract I document evidence that diabetics previously reliant on insulin stopped using insulin to a signicant extent once they became eligible for Medicare in 1998-2006. This pattern only ends in 2006 when Medicare Part D is established, which subsidises Medicare recipients' purchases of diabetic medication and insulin. I interpret these results as evidence for the relative strength of cross-price moral hazard on preventive medicine usage before and after Part D. When individuals don't bear the costs of hospitalisation, but have to pay for preventive care, they will take fewer precautions than is optimal for holding down the cost of publicly provided health care. By contrast, a subsidy for preventive care can reduce this eect by making it less expensive to reduce the probability of a future hospitalisation from a given individual's point of view. I conclude that Medicare Part D signicantly increased insulin usage among elderly diabetics.the rst piece of evidence is from a regression-discontinuity design using the 1998 wave of the Health and Retirement Study (HRS), which nds a large and statistically signicant eect of Medicare eligibility on insulin usage - 10.77% fewer individuals above 65 manage their condition using insulin than those who are under 65. Additional evidence to support the regression-discontinuity design comes from following those who were under 65 in 1998 as they cross the eligibility threshold in subsequent survey years in 2000, 2002, 2004 and 2006. In 2000-2004, signicantly more of those who were ineligible for Medicare in 1998 stop using insulin than start using insulin once they become eligible; in 2006, this pattern is reversed. This is in contrast with previous studies which have either Nueld College, University of Oxford. A previous version of this paper was circulated under the title Did Medicare Decrease Insulin Usage Among Diabetics Until the Advent of Part D?. This paper has been improved by the helpful comments and advice of my discussant at the National Tax Association meetings, David Powell, participants in the Munich Risk and Insurance Center's Risk and Management seminar, as well as Johannes Abeler, Steve Bond, Ian Crawford, Johannes Jaspersen, Ian Jewitt, Olivia Mitchell, Michael Keane, Paul Klemperer, Sophie Roth, Hanna Wang and Peter Zweifel. All correspondence to be addressed to daniel.kaliski@nueld.ox.ac.uk. Any remaining mistakes and/or omissions are my own. 1

focused on own-price moral hazard (increased coverage leads to increased utilization) or found negligible eects of coverage on preventive medicine usage. 1 Introduction This article nds evidence of cross-price moral hazard, in contrast with most of the economics literature, which has focused on own-price moral hazard. In classic studies such as the RAND health insurance experiment(aron-dine et al., 2013), the price of health care utilization decreases due to expanded coverage, and so individuals use more health services than when they were uninsured. In the setting studied in this paper, coverage is a subsitute for a subset of health care spending: spending on preventive medicine. Preventive care is a form of self-insurance: individuals reduce their expected medical costs by maintaining their health. Since self-insurance ex ante and coverage for losses ex post are substitutes, when the price of medical intervention due to ill health decreases, utilization of preventive medicine also decreases. It is in this sense that the type of moral hazard studied here is cross-price moral hazard, whereas increased usage of medical services whose own costs decrease under a new insurance regime is own-price moral hazard. I use this distinction instead of the traditional distinction between ex ante and ex post moral hazard to emphasise the second key empirical result found in this paper: once subsidies are provided for preventive medicine, cross-price moral hazard can be oset entirely given a large enough subsidy. As in standard price theory, the eect of reducing the price of a substitute on demand can be eliminated for a large enough decrease in the price of the good for which it is a substitute. This is in sharp contrast to a previous literature which nds negligible or positive eects of coverage on usage of preventive care (Baicker et al., 2013; Simon et al., 2017). In this paper, I nd that there is a discontinuous decrease of 17.6% in the proportion of diabetics who report using insulin to maintain their health when they get Medicare coverage at age 65 in the pre-part D era. Other studies on preventive care tended to focus on the eects of Medicaid expansion rather than Medicare. One potential explanation for the dierence between the ndings here and in other studies could be the subsidization of preventive care measures alongside coverage for treatment provided under the state Medicaid programs studied previously. As found in the results from the post-part D era in this study, these subsidies can act so as to oset moral hazard eects on the use of preventive care that would otherwise accompany the expansion of coverage for treatment. In fact, I nd that the subsidies provided for preventive care in 2006 under Medicare Part D oset these eects completely. The eect of universal health coverage on usage of preventive care is important for assessing the overall costs of the provision of health care (Aron-Dine 2

et al., 2013). Strong moral hazard eects on the use of preventive care, where individuals decrease self-protection due to not having to bear the costs of their eventual ill health, will tend to increase the burden on the health care system. This article nds evidence that these eects are present among diabetics, but also nds that these eects can be mitigated or even completely oset by subsidising preventive care as well as treatment. Diabetics who became eligible for Medicare before Part D was introduced, all else equal, were less likely to use insulin to manage their condition than diabetics who were younger than 65 and hence ineligible. However, after Part D was introduced, the proportion of diabetics who stopped using insulin around the age-eligibility threshold declined signicantly and the proportion who began using it after age 65 increased signicantly. Since diabetes is both widespread and necessitates a great deal of preventive care, diabetics are an ideal group among whom to study cross-price moral hazard. Diabetes is the most prevalent chronic condition in the United States, aecting between 12 and 14 percent of the U.S. population in 2011-2012 (Menke et al., 2015). Until the introduction of long-acting insulin in 2005 with the FDA approval of Levemir, diabetics recommended insulin for managing their condition had to self-administer insulin at least twice per day. Some bolus insulin regimens require doses of insulin before each meal to prevent blood sugar levels from climbing at too fast a rate. Even with long-acting insulin available, avoiding the complications of diabetes may require a great deal of self-maintenance by diabetics, which introduces indirect costs (via sacrices of time) over and above the direct costs of purchasing insulin. Diabetics are therefore a group among whom we should expect both a large degree of cross-price moral hazard in usage of preventive care and high responsiveness to subsidies of insulin, given the direct (monetary) and indirect costs involved. I use two strategies to recover the results in this paper: rstly, a regressiondiscontinuity design that uses the age of Medicare eligibility as the threshold, and secondly, a dierence-in-discontinuities regression. The rst set of results demonstrates a discontinuous decrease in 1998 in the proportion of diabetics reporting that they use insulin to manage their condition at age 65, a result which is robust to several dierent modications of the sample. The second set of results shows that there are signicant dierences in the strength and sign of this eect pre- and post-2006, the year in which Medicare Part D came into eect. These results are robust to a wide range of assumptions regarding the eect of past histories of usage on current usage. This paper contributes to the literature in three ways. First, it adds to the literature on social insurance crowding out self-insurance, dating back at least to the seminal paper by Hubbard et al. (1995). That paper found that means testing, rather than the provision of insurance itself, reduced precautionary saving: Medicaid's asset thresholds discouraged buer stocks of saving since individuals valued access to health insurance to a greater extent than the self- 3

insurance they could provide for themselves via saving. Here, coverage directly discourages self-insurance via preventive medicine since the two are substitutes regarding the reduction of expected future health care costs. Other papers in this vein have included, among others, Low and Pistaferri (2015); Gruber and Yelowitz (1999), and Fout and Gilleskie (2015). Second, it adds to the moral hazard literature, as mentioned above, as in papers such as Aron-Dine et al. (2015); Baicker et al. (2013), and Card et al. (2008). Third, it contributes to the literature specically on the impact of Medicare Part D on health outcomes which includes papers such as Einav et al. (2015) and Madden et al. (2008). The remainder of this paper is structured as follows. Section 2 details the features of both Medicare and diabetes that are relevant for this paper. Section 3 describes the subset of the data from the HRS and RAND HRS on diabetics used to obtain the empirical results in Sections 4 and 5. Section 4 outlines the empirical strategies for the regression-discontinuity and dynamic panel data results. Section 5 discusses the results and several tests of the specications used. Section 6 concludes. 2 Institutional and Medical Background Consider a diabetic eligible for coverage through Medicare Parts A and B in 1998. Her doctor may recommend that she uses an insulin pump attached to her body which delivers insulin that she cannot produce herself. In that case, her Part B coverage will pay for 80% of the cost of the pump, but will not cover the insulin itself. The insulin itself will be a much larger fraction of the total cost of using insulin to manage her diabetes (see footnote 1, above). In addition, knowing whether the insulin is in fact eective at keeping her blood sugar at a healthy level requires regular self-administered blood-sugar tests. In order to maximise the eectiveness of the insulin, she may have to make radical changes to her diet, which may have had too many foods that raise blood sugar levels at too quick a rate. Without exploring further possibilities for this scenario, the diabetic in question faces large monetary costs as well as non-monetary costs in terms of time and cognitive bandwidth. In light of this, low adherence to insulin among diabetics (Weinger and Beverly, 2010) is perhaps not that surprising, despite its adverse consequences in the longer term (Rydall et al., 1997). Diabetics who forgo insulin recommended for their condition are most likely to have Type II diabetes, which typically develops later in life, rather than Type I, since the adverse health consequences of forgoing insulin among Type I diabetics are more severe and immediate. The adverse health consequences that are specic to diabetics whose condition is poorly managed tend to result from deterioration of the small blood vessels (capillaries). These include damage to the retinas 4

which induces blindness (retinopathy), damage to nerves that can necessitate amputation of appendages (neuropathy) and damage to the kidneys which can eventually necessitate the use of dialysis in order to keep the person in question alive (nephropathy). For a large subset of diabetics, the decision of whether or not to use insulin is essentially a trade-o between the immediate costs in terms of time and forgone consumption and longer-term benets paid out in better health and lower medical expenses. In 2006, this situation is dierent in two main ways. The rst is that in 2003, the Bush administration approved the expansion of Medicare to include subsidies that partially or wholly cover the costs of medication and insulin (Medicare Part D), which came into eect in 2006. The subsidies available under these plans could vary widely depending on the individual coverage plan chosen after enrolling in Part D. In the case of insulin, between 20% and 100% of the monthly costs of insulin could be covered under Part D depending on the individual plan. The second is that in 2005, the FDA approved the rst long-acting insulin, Levemir, for use in the United States. This form of insulin could be administered once per day, reducing the potential complexity of an insulin-based health maintenance regime. As noted in Section 5, I will be unable to account for the reduction in non-monetary costs resulting from the availability of long-acting insulin. To attribute the dierence in behavior seen from 2006 onwards to Levemir rather than Part D, one must have a strong prior belief that non-monetary costs are more signicant than monetary costs of insulin. Given the already high and rising costs of insulin in the 2000s, this seems relatively unlikely 1. 3 Data The Health and Retirement Study (HRS) is a nationally representative longitudinal survey administered by the Institute for Social Research at the University of Michigan. I use both the Public Use subset of the data made publicly available for registered users on the HRS website as well as a cleaned version of a subset of the data called the RAND HRS dataset (Chien et al., 2013). Attention is restricted to 3 043 individuals diagnosed with diabetes from the 1998 wave of the HRS. In 1998, the individuals are drawn from four birth cohorts: the Oldest Old (born pre-1924), the Children of the Depression (born 1924-31), the original cohort from 1992 (born 1931-41) and the War Babies (born 1942-47), plus their co-habitants in the households in which they resided at the time of the survey. The HRS followed up respondents every two years, and so I also 1 For example, Eli Lilly's fast-acting insulin, Humalog, cost $34.81 per vial (which would typically contain a month's worth of insulin) in 2001. This would amount to a yearly cost of $416.72. This is a modest estimate since many diabetics will require more than one vial's worth of insulin per month. 5

have data on surviving individuals from the 1998 wave in 2000, 2002, 2004, and 2006. The characteristics of the sample are summarised in Table 1 (below). Table 1: Characteristics of the Sample at Baseline Age < 65 Age 65 Characteristic (N = 1 308) (N = 1 735) Age - Mean±S.d. - yr 57.99±4.77 74.40±6.78 BMI - Mean±S.d. 30.73±6.39 27.86±5.40 Male - no. (%) 593 (45.34) 795 (45.82) High school graduate - no. (%) 611 (46.71) 715 (41.11) College graduate - no. (%) 182 (13.91) 169 (9.74) Caucasian - no. (%) 857 (65.62) 1 334 (76.89) Black - no. (%) 367 (28.10) 329 (18.96) Married - no. (%) 892 (68.46) 946 (54.56) Medical History - no.(%) Current Smoker 260 (19.88) 142 (8.18) Cancer 94 (7.19) 251 (14.50) Heart Disease 335 (25.61) 681 (39.32) Stroke 111 (8.49) 282 (16.26) Using - no. (%) Insulin 381 (29.13) 451 (25.99) Medication 775 (59.22) 1080 (62.32) Diet 822 (62.84) 1 025 (59.18) Vigorous Exercise 480 (36.73) 485 (27.95) Fewer individuals remain in each additional year of the survey. Dierential mortality is not as great a concern in this context, however, as the probability of surviving until at least age 65 will determine the regression-discontinuity estimand in any study that uses age as the running variable for an older population. This is because in this context the propensity score is equivalent to the probability of surviving until 65; therefore, to the extent that those not observed in subsequent years are not observed since they died before becoming eligible for Medicare, this is reected in the original estimate in 1998 before attrition from the sample begins. 6

4 Empirical Strategy I use a regression discontinuity design to compare individuals who are just above the age cuto of 65 for Medicare eligibility with individuals who fall just below that cuto. An important assumption behind the use of this method is that the unobservable characteristics of these individuals that aect their usage of insulin do not vary discontinuously with the age of Medicare eligibility; equivalently, there should be no latent discontinuous changes at 65 that can explain the decrease in the use of insulin. An important implication of this paper's results will be for the overall eect on the long-term health of diabetics of enrolling in Medicare; if they substitute towards other less costly methods of maintaining their health, such as diet or exercise, then the net eect on long-run health outocomes may be zero or positive (if, for example, discontinuing insulin use prompts greater caution in those who forgo it). I therefore also report regression-discontinuity results for alternative methods of health maintenance - diet, exercise and diabetes medication. In addition, I can follow the diabetics in the original sample in 1998 every two years in the HRS data up to and including 2006, the year that Medicare Part D came into eect. I record the proportions of insulin users who stop using insulin once eligible for Medicare, at ages 65-66 (some individuals will have had their 65th birthdays in between waves of the survey, which was administered every two years), as well as the proportion of non-users who take up insulin after turning 65. To test whether there was a signicant dierence between the insulin usage of diabetics who turned 65 before Part D was made available and that of those who turned 65 within two years of 2006, I estimate the equation I it = αi it 1 + β1[age [63, 67]] + γ1[t = 2006] + δ1[age [63, 67]] 1[t = 2006] + φx it + ωτ t + η i + ξ it where X it is a vector of individual-specic xed eects, τ t is a vector of time dummies to absorb common time trends, η i is unobserved time-invariant heterogeneity, and ξ it is an idiosyncratic error term, assumed to be i.i.d. The coecient on the lagged dependent variable, α, cannot be consistently estimated via OLS (Nickell, 1981), since the specication implies that it contains the unobserved xed eect, η i. In Tables 3 and 4 (below), I only report the results for the regressions that exclude the xed eects and time dummies. This is for conciseness' sake; their inclusion barely changes the estimates of the coecients of interest, and the only signicant variable among them is the indicator for 2004, which may pick up the increasing necessity of insulin usage the longer an individual has diabetes (given that the individuals who survive from 1998 to 2004 have already lived for 6 years with the disease). 7

We may worry that the estimates of the other coecients in this regression are contaminated by this bias as a result. However, most estimation methods that naively dierence out the latent xed eects in the regression via rst dierencing or the within-groups transformation will result in estimators with serious eciency losses (Keane and Runkle, 1992), and will introduce endogeneity through the correlation between the rst dierence of the lagged dependent variable and the lagged time-varying component of the error term, which it contains by construction. While the OLS estimator of the lagged dependent variable is biased upward, the within-groups estimator is biased downward; I report both estimates in order to bound the true value of the autoregressive parameter. In Appendix C, I report the details of Arellano-Bond estimation of equation (1), which proves problematic for a variety of reasons detailed there. We may nonetheless be concerned that the coecient on the interaction term between the 2006 indicator variable and the threshold indicator is imprecisely estimated by any model that eliminates time-invariant individual-specic variation, since this amounts to triple dierencing - it is the result of (i) dierences between those around the threshold and those away from the threshold, (ii) differences between observations from before and after 2006, and (iii) dierences between adjacent time periods. The amount of variability left over in the key variable of interest is therefore unlikely to be large, which would weaken standard tests' ability to reject the null hypothesis of no eect. To deal with this concern, I also include the results of a random-eects dynamic Probit estimation as implemented in Wooldridge (2005). This involves conditioning on the initial values of the dependent variable I i0 and assuming that the unobserved individual-specic eects are Normally distributed. That is, I assume that η i = φ 0 + φ 1 I io + ε i ε i I i0 N(0, σ 2 ε) which implies that I it given (I it 1,..., I i0, 1[age [63, 67]], 1[t = 2006], ε i ), follows a Probit model with response probability Φ(φ 0 + αi it 1 + β1[age [63, 67]] + γ1[t = 2006] + δ1[age [63, 67]] 1[t = 2006] + φ 1I io + ε i + ξ it) The advantage of this method is that I can re-estimate the model and constrain the coecient on the lagged dependent variable to any of a number of pre-specied values, which in turn changes the other coecients and the estimated variance of the individual-specic eects. Intuitively, more variation 8

has to be attributed to unobserved inter-individual dierences in insulin usage trajectories the less variation is explained by state dependence in insulin usage. These inter-individual dierences may be due to (among other things) cohort eects: those who are 65 or older in 1998 were born in 1933 or earlier, while those who are 65 or older in 2006 were born in 1941 at the latest. While the discontinuous decrease itself around the threshold of 65 years is harder to explain via cohort eects, since it requires a signicant cohort dierence between individuals aged 65-67 and those aged 62-64 2, the magnitude of this eect may dier across cohorts due to cohort-specic dierences in (for example) early life circumstances. This method allows me to explore the range of true values of the coecient on the lagged dependent variable that are consistent with a statistically signicant dierence-in-discontinuities eect, and how large the unobserved individual-specic variance has to be in order to be consistent with that hypothesised true value and the remaining estimated coecients. As will be seen, a wide range of values for the coecient on the lagged dependent variable are consistent with a statistically signicant interaction eect between being within two years of the Medicare eligibility threshold and the period eect associated with the year 2006. The main drawback of this method is that if the error term is not Normally distributed, this will lead to inconsistent estimators of the parameters. The similarity of the conclusions obtained to those obtained using OLS, which does not rely on the Normality assumption for consistency, are relatively reassuring on this point. 5 Results Figure 1 (below) shows a statistically signicant decline in insulin usage at age 65 in 1998. 29.13% of under-65s report using insulin to manage their diabetes, compared with 25.99% of over-65s, a relative dierence of 10.77%. At the cuto, the estimated relative dierence is 17.7%. I nd no similar evidence of a statistically signicant discontinuity in three other health behaviors: diet, exercise and adherence to diabetic medication (see Appendix B, below). Examination of Figure 1 reveals an increasing incidence of take-up before 65 and a decreasing incidence of take-up after age 75 or so; the former is likely explained by the positive association between the length of time a person has lived with diabetes and insulin usage, and the latter by the increasing probability of death (and hence inability to benet from the gains from maintaining one's health). The analogy with an experiment is imperfect, since individuals who receive Social Security Disability Insurance benets also have access to Medicare, but there are only 10 such individuals in the sample, and their exclusion does not alter the results. One potential threat to the inference that the drop in the proportion us- 2 As well as requiring a large number of cohort eects, since this would imply one cohortspecic eect every four to ve years 9

ing insulin is due to Medicare eligibility would be the coincidence of retirement at 65 with Medicare eligibility, as the designers of Medicare intended. However, since the abolition of mandatory retirement in 1986 in the United States, the spike in retirement status has almost entirely disappeared (Card et al., 2008; Von Wachter, 2002) 3, so a discontinuity in retirement status is unlikely to be able to explain the results. Figure 1: Regression Discontinuity Plot - Proportion of Diabetics Reporting Insulin Usage in 1998 N = 3 043, p = 0.006. Separate results not shown above indicate a signicant discontinuity at age 65 for the sub-sample excluding smokers and those with a history of cancer (N = 2 322, p = 0.006), and no discontinuity in other behaviors such as diet (p = 0.07), exercise (p = 0.784) or medication adherence (p = 0.422). There are two further potential complications to the analysis due to the presence of smokers and individuals with a history of cancer in the sample. Smokers are known to have a diminished response to insulin, and cancer suerers' and survivors' metabolism diers from those with no history of cancer. To exclude the possibility that these anomalous groups are driving the results, I re-run the analysis with them excluded from the sample, reducing the sample size to 2 322 3 In Appendix D, I document evidence that this is also true for the sample used in this study. There is a spike in retirement status at age 62, the earliest age at which it is possible to claim Social Security benets, but there is no discontinuity in insulin usage rates at this age (see Appendix A). 10

Table 2: Incidents (No. (%)) of First Insulin Use vs. Insulin Cessation, Ages 65-66 2000 2002 2004 2006 Ceased 64 (12.50) 41 (17.07) 42 (11.90) 53 (1.99) Began 139 (4.31) 112 (6.25) 100 (9.00) 81 (13.58) Table 3: Dierence-in-Discontinuities: Insulin Uptake and Cessation, 1998-2006 Dep. Var.: Using Insulin Coecient (t-stat.) OLS WG Probit Constant.078** 0.275*** -1.423*** (19.50) (40.70) (-48.67) Insulin Used Two Years Prior 0.831*** 0.146*** 2.770*** (106.01) (6.55) (61.22) Aged 63-67 -0.017* -0.016-0.118* (-2.13) (-1.59) (-1.98) 2006 0.026** 0.069*** 0.170** (2.99) (8.13) (2.89) 2006*Aged 63-67 0.048* 0.030 0.312* (2.47) (1.53) (2.43) N = 7631 signicant at 5%; ** signicant at 1%; *** signicant at 0.1% Standard errors are robust to arbitrary heteroskedasticity and autocorrelation and clustered at the individual level 11

individuals. The results are remarkably close to those obtained with the full sample. Another potential confounder is that becoming eligible for Medicare may increase the probability of being diagnosed with previously undiagnosed diabetes (see Appendix F). In Appendix F, I discuss how this could spuriously produce the results observed in 1998 and 2006 (see below). In that same Appendix I provide evidence that there is no discontinuity in the probability of being diagnosed with diabetes at age 65, which is reassuring on this point. When following up individuals who are below the threshold in 1998 and who are subsequently eligible for coverage through Medicare in 2000, 2002, 2004 and 2006, a pattern emerges - in most years, the proportion of individuals who use insulin at ages 63-64 in a previous wave of the survey who then stop reporting using insulin to manage their diabetes in the subsequent wave when they are 65-66 is larger than the proportion of individuals who take up insulin when they become eligible (Table 2, above). However, this dierence is reversed in 2006, which is when Medicare Part D comes into eect, and access to subsidies for the purchase of insulin become available through the Medicare program. There is a steady upward increase in the number of individuals who rst start using insulin when they turn 65 and become eligible for Medicare coverage, from 4.31% in 2000 to 13.58% in 2006. At the same time, there is a relatively steady percentage of individuals each year who stop reporting that they use insulin when they become eligible for Medicare coverage at age 65 until 2006, when there is a precipitous decline from 11.9% to 1.99% of individuals aged 63-64 in 2004 who were using insulin to manage their condition. While this is highly suggestive of the role Part D played in dampening a pre-existing moral hazard eect, it is not by itself enough to infer a statistically signicant dierence in behavior. I therefore include regressions which pool the years 1998-2006 together to examine whether there is a structural break in the eect of Medicare eligibility on insulin usage in 2006 (Table 3), conditional on diabetics' past usage of insulin - hence I include a lagged dependent variable among the regressors to control for individual-specic histories of past insulin usage. As is standard practice in dierence-in-dierence specications, I also cluster the standard errors at the individual level to mop up any remaining serial correlation in the error term, which is known to increase the Type I error rate in these settings (Bertrand et al., 2004). From the patterns of statistical signicance it seems that 2006 represents a signicant regime change from previous years in the relative rates of insulin cessation and take-up among diabetics who become eligible for Medicare - the interaction eect between being within a two-year interval of eligibility and a dummy variable for the year 2006 is positive and statistically signicant while for all other years the eect of being in the interval 63-67 has a statistically signicant negative eect on usage which is oset completely in 2006. This is not true when the Within-Groups estimator is used, but this is likely due to some combination of the eciency losses due to 12

dierencing out time-invariant variation and inconsistency (see the discussion in Section 3 above). The random-eects dynamic Probit results (Table 4) show that in order to get the dierence-in-discontinuities eect to no longer be statistically signicant, we need the strong assumption that there is no state dependence in insulin usage (i.e. the coecient on the lagged dependent variable is zero). This is implausible in this case for two reasons. Firstly, on medical grounds, we should expect at least some state dependence in the usage of insulin in the absence of any exogenous regime changes due to either the increasing necessity of insulin usage for the management of Type II diabetes as the disease progresses, or persistence in the prescription of insulin by physicians. If we assume that there is no state dependence whatsoever, then we are forced to attribute both changes in insulin usage and the persistence of insulin usage to unobservable exogenous regime changes such as cohort eects. This is a less parsimonious explanation than one that includes past insulin usage as a predictor of future insulin usage. Secondly, the within-groups estimator of the coecient on the lagged dependent variable is known to be biased downward (Nickell, 1981), and the estimate in this case is still statistically signicant and positive, so no consistent estimator of the coecient on the lagged dependent variable should nd that there is no state dependence. In sum, on both statistical and theoretical grounds, we can reject the specication that assumes no state dependence. All the specications that assume some state dependence in the random-eects Probit model nd that the moral hazard eect found in 1998 is present in years prior to 2006 and is reversed in 2006. Moreover, the absence of the cross-price moral hazard eect found in years prior to 2006 appears to persist after 2006 (see Appendix E, below). One limitation of the analysis is that I lack a comprehensive measure of overall health maintenance by diabetics; it may be that other methods not recorded in the HRS survey are used in preference to insulin other than the ones ruled out in the data (medication adherence, dietary restrictions, and exercise). Future work that is able to address these limitations will need to explain why the decrease in insulin usage happens discontinuously at age 65 rather than continuously decreasing towards the end of the life cycle. 13

Table 4: Dierence-in-Discontinuities: Random Eects Dynamic Probit Results Dep. Var.: Using Insulin Coecient (t-stat) ˆα u ˆα = 0 ˆα = 0.1ˆα u α = 0.5ˆα u Constant -1.724*** -2.703*** -2.576*** -2.150*** (-21.52) (-25.82) (-24.88) (-24.04) Insulin Used Two Years Prior 1.939*** 0 0.194 0.970 (17.08) (.) (.) (.) Insulin Used in 1998 1.497*** 5.230*** 4.800*** 3.244*** (6.45) (26.56) (24.59) (19.23) Aged 63-67 -0.171* -0.202* -0.201* -0.194* (-2.28) (-2.00) (-2.03) (-2.17) 2006 0.318*** 0.764*** 0.713*** 0.527*** (4.27) (9.06) (8.55) (6.68) 2006*Aged 63-67 0.362* 0.375 0.378* 0.384* (2.36) (1.95) (2.00) (2.18) ˆσ u 0.737 2.027 1.871 1.351 ˆρ 0.352 0.803 0.778 0.646 N = 7 631 * signicant at 5%; ** signicant at 1%; *** signicant at 0.1% A further complication arises from other changes to the insulin treatment regimen options available to diabetics over the period 1998-2006. In 2005, the rst long-acting insulin (insulin detemir, marketed under the trade name Levemir) was approved for use by diabetics by the FDA. This allowed diabetics to follow a less demanding once-daily dose of long-acting insulin, as compared with twice-daily basal insulin regimens. Without data on the relative implicit costs of following a more demanding insulin regimen, I cannot distinguish whether the increased uptake in 2006 owes more to the lower direct costs of purchasing insulin or the lower indirect costs (via lower necessary investments of time and cognitive eort) of administering insulin in an outpatient setting. One avenue for future work would be to exploit data on individuals' self-reports of diculties they experience in managing chronic conditions. This would allow for a comparison of the relative sizes of the implicit costs of patient self-management and the direct monetary costs of the medications needed for their treatment 14

regimens. It is possible that for some individuals, being freed to implement a simpler treatment regimen may be a stronger form of encouragement towards investing in their health than receiving subsidies for the medications necessary for that regimen. It seems likely that this is a relatively small fraction of the population, however. 6 Conclusion If individuals' usage of preventive care is not subsidised, but the costs of ill health are, then it is more likely than otherwise that they will decrease their usage of preventive care. This is a distinct form of moral hazard from the type most commonly studied in the literature. This article has provided evidence that this eect can be oset by subsidising prevention as well as treatment. The reasoning is the same as that for substitution across dierent goods; when the price of a substitute goes down, individuals consume less of a good than they would otherwise, and increase their consumption if that good's price is in turn reduced. This adds to the evidence that Medicare Part D increased the usage of the medications and preventive treatments it subsidised, but also adds to the evidence that this eect osets what would otherwise be signicant moral hazard eects that lead individuals - and diabetics in particular - to reduce their usage of preventive care when enrolling in Medicare. References Manuel Arellano and Stephen Bond. Some Tests of Specication for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. The Review of Economic Studies, 58(2):277297, 1991. Aviva Aron-Dine, Liran Einav, and Amy Finkelstein. The RAND Health Insurance Experiment, Three Decades Later. Journal of Economic Perspectives, 27(1):197222, 2013. Aviva Aron-Dine, Liran Einav, Amy Finkelstein, and Mark Cullen. Moral Hazard in Health Insurance: Do Dynamic Incentives Matter? Review of Economics and Statistics, 97(4):725741, 2015. Katherine Baicker, Sarah L Taubman, Heidi L Allen, et al. The Oregon ExperimentEects of Medicaid on Clinical Outcomes. New England Journal of Medicine, 368(18):17131722, 2013. Marianne Bertrand, Esther Duo, and Sendhil Mullainathan. How Much Should We Trust Dierences-in-Dierences Estimates? The Quarterly Journal of Economics, 119(1):249275, 2004. 15

MJG Bun, V Saradis, and BH Baltagi. Dynamic Panel Data Models. Oxford Handbook of Panel Data, pages 76110, 2015. The David Card, Carlos Dobkin, and Nicole Maestas. The Impact of Nearly Universal Insurance Coverage on Health Care Utilization and Health: Evidence from Medicare. American Economic Review, 98(5):22422258, 2008. Sandy Chien, Nancy Campbell, Orla Hayden, et al. RAND HRS Data Documentation, Version M. Santa Monica, CA: RAND Center for the Study of Aging, 2013. Liran Einav, Amy Finkelstein, and Paul Schrimpf. The Response of Drug Expenditure to Nonlinear Contract Design: Evidence from Medicare Part D. The quarterly journal of economics, 130(2):841899, 2015. Betty Tao Fout and Donna B Gilleskie. Does Health Insurance Encourage or Crowd Out Benecial Nonmedical Care? a Dynamic Analysis of Insurance, Health Inputs, and Health Production. American Journal of Health Economics, 2015. Jonathan Gruber and Aaron Yelowitz. Public Health insurance and Private Savings. Journal of Political Economy, 107(6):12491274, 1999. R Glenn Hubbard, Jonathan Skinner, and Stephen P Zeldes. Precautionary Saving and Social Insurance. Journal of Political Economy, 103(2):360399, 1995. Guido W Imbens and Donald B Rubin. Causal Inference in Statistics, Social, and Biomedical Sciences. Cambridge University Press, 2015. Michael P Keane and David E Runkle. On the Estimation of Panel-Data Models with Serial Correlation When Instruments are not Strictly Exogenous. Journal of Business & Economic Statistics, 10(1):19, 1992. Hamish Low and Luigi Pistaferri. Disability Insurance and the Dynamics of the Incentive Insurance Trade-O. The American Economic Review, 105(10): 29863029, 2015. Jeanne M Madden, Amy J Graves, Fang Zhang, Alyce S Adams, Becky A Briesacher, Dennis Ross-Degnan, Jerry H Gurwitz, Marsha Pierre-Jacques, Dana Gelb Safran, Gerald S Adler, et al. Cost-Related Medication Nonadherence and Spending on Basic Needs Following Implementation of Medicare Part D. JAMA, 299(16):19221928, 2008. Andy Menke, Sarah Casagrande, Linda Geiss, and Catherine C Cowie. Prevalence of and Trends in Diabetes among Adults in the United States, 1988-2012. JAMA, 314(10):10211029, 2015. Stephen Nickell. Biases in Dynamic Models with Fixed Eects. Econometrica: Journal of the Econometric Society, pages 14171426, 1981. 16

David Roodman. How to do xtabond2: An Introduction to Dierence and System GMM in Stata. Stata Journal, 9(1):86136, 2009a. David Roodman. A Note on the Theme of Too Many Instruments. Oxford Bulletin of Economics and statistics, 71(1):135158, 2009b. Anne C Rydall, Gary M Rodin, Marion P Olmsted, Robert G Devenyi, and Denis Daneman. Disordered Eating Behavior and Microvascular Complications in Young Women with Insulin-Dependent Diabetes Mellitus. New England Journal of Medicine, 336(26):18491854, 1997. Kosali Simon, Aparna Soni, and John Cawley. The Impact of Health Insurance on Preventive Care and Health Behaviors: Evidence from the First Two Years of the ACA Medicaid Expansions. Journal of Policy Analysis and Management, 36(2):390417, 2017. Till Von Wachter. The End of Mandatory Retirement in the US: Eects on Retirement and Implicit Contracts. Center for Labor Economics, University of California, Berkeley, 2002. Katie Weinger and Elizabeth A Beverly. Barriers to Achieving Glycemic Targets: Who Omits Insulin and Why?, 2010. Jerey M Wooldridge. Simple Solutions to the Initial Conditions Problem in Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity. Journal of Applied Econometrics, 20(1):3954, 2005. 17

Appendix A: Robustness to Alternative Cutos In this Appendix, I test whether I can replicate the results in the main body of the paper with three alternative thresholds. First I test whether there really is a discontinuous change at 65 by using placebo cutos of 64 and 66 (Imbens and Rubin, 2015). Secondly, I use a cuto of 62 - the earliest age by which Americans can claim Social Security benets - to check whether the discontinuity can be explained by discontinuous changes in retirement status. None of the three tests (see Figures 2-4, below) nd discontinuities in insulin usage at these alternative cutos. Figure 2: Regression Discontinuity Plot - Cuto of 62 18

Figure 3: Regression Discontinuity Plot - Cuto of 64 Figure 4: Regression Discontinuity Plot - Cuto of 66 19

Appendix B: Evidence on Other Health Behaviors As reported in the main body of the text, the individuals in the data set are asked to report whether they (i) are on a special diet to manage their diabetes, (ii) exercise vigorously at least three times per week, and/or (iii) swallow antidiabetes medication. Figures 5-7 (below) show that there are no discontinuities in these health maintenance behaviors at 65. This supports the explanation for the main results in the text that the reduciton in insulin at 65 represents a lower overall level of health maintenance by diabetics after that age threshold, rather than a substitution away from insulin towards less expensive methods of managing diabetes. Figure 5: Regression Discontinuity Plot - Proportion of Diabetics Reporting Dieting in 1998 20

Figure 6: Regression Discontinuity Plot - Proportion of Diabetics Reporting Regular Vigorous Exercise in 1998 Figure 7: Regression Discontinuity Plot - Proportion of Diabetics Reporting Use of Diabetic Medication in 1998 21

Appendix C: Arellano-Bond Estimates of the Difference in Discontinuities The dierence-in-discontinuties regression (Table 3, above) conditions on the previous usage of insulin by including a lagged dependent variable among the regressors. The coecient on the lagged dependent variable cannot be consistently estimated via OLS (Nickell, 1981), since the specication implies that it contains any unobserved time-invariant inter-individua heterogeneity. We may worry that the estimates of the other coecients in this regression are contaminated by this bias as a result. However, most estimation methods that naively dierence out the latent xed eects in the regression via rst dierencing or the within-groups transformation will result in estimators with serious eciency losses (Keane and Runkle, 1992), and will introduce endogeneity through the correlation between the rst dierence of the lagged dependent variable and the lagged time-varying component of the error term, which it contains by construction. While the OLS estimator of the lagged dependent variable is biased upward, the within-groups estimator is biased downward; I report both estimates in order to bound the true value of the autoregressive parameter. I therefore re-estimate the equation using the Arellano-Bond estimator (Arellano and Bond, 1991). Recently this estimator has been subject to the criticism that at suciently long lags, the lagged levels of the variables that are used as instruments introduce a many weak instruments problem (Roodman, 2009b). I therefore also use recent methods proposed for mitigating this problem - restricting the number of lags used as instruments, and collapsing the set of instruments. All of the foregoing was implemented using the xtabond2 command in Stata (Roodman, 2009a). Of the four specications used, we have reason to believe that three of the four's estimators are inconsistent. Without collapsing the set of instruments, the Sargan Test rejects the null that the instruments are orthogonal to the error term. Somewhat mysteriously, the Sargan test fails to reject the null when the same instruments are combined into smaller sets via collapsing, but it is unclear under what conditions this procedure should avoid endogeneity where the non-collapsed instruments do not (an issue which has not, to the author's knowledge, been addressed explicitly in the prior literature). Since the Within-Groups estimator of the coecient on the lagged dependent variable is biased downwards, and the estimate in column (4) of Table 5 lies below it (see above), there are reasons to believe that the specication that restricts the instruments to the second and third lags of the variables and collapses the resulting instrument set suers from inconsistency as well. This casts doubt on the results in column (3) as well - as in column (4), the Sargan test fails to reject the null, but it uses at least as many instruments as in column (4) (though the latter's results may properly be attributed to weak instruments, which are 22

Table 5: Dierence-in-Discontinuities: Arellano-Bond Results Dep. Var.: Using Insulin Coecient (t-stat.) (1) (2) (3) (4) Lags (Collapsed?) 1-3 (No) 2-3 (No) 1-3 (Yes) 2-3 (Yes) No. Instruments 14 8 6 4 Insulin Used Two Years Prior 0.362*** 0.444 0.406*** -0.0227 (5.03) (1.93) (5.20) (-0.07) Aged 63-67 -0.0786*** -0.0659** -0.0826*** -0.103** (-4.70) (-3.00) (-3.86) (-3.26) 2006 0.0149 0.0222 0.0407* 0.0844*** (1.34) (1.49) (2.57) (3.72) 2006*Aged 63-67 0.0535* 0.0325-0.0220-0.274* (2.05) (0.53) (-0.39) (-2.48) Sargan Test p-value 0.005 0.045 0.068 1.00 N = 5 150 * signicant at 5%; ** signicant at 1%; *** signicant at 0.1% known to weaken the power of the Sargan test (Bun et al., 2015) and a collapsed version of the instruments in column (1), both of which exhibit evidence of inconsistency in the estimators. The results in column (3) are therefore to be regarded with scepticism in the absence of arguments as to how collapsing a matrix of instruments that previously resulted in inconsistent estimators can be used to obtain a consistent GMM estimator of the parameter vector. The argument that this is due to weak instruments does not do the necessary work in this case since in that instance we should expect the Sargan test to have low power to detect a violation of the orthogonality conditions necessary for the set of included instruments to be valid (Bun et al., 2015). 23

Appendix D: Distribution of the Proportion Retired in the Sample by Age To add to the evidence that the discontinuous change at age 65 is not due to retirement status, Figure 8 (below) displays the distribution of the proportion reporting that they are retired in the sample between age 50 and age 70. While there does not appear to be a large discontinuity in retirement status at age 65, there is a larger increase in the proportion of individuals who are retired at age 62, the age of eligibility for claiming Social Security benets. As documented in Appendix A (above), there is no discontinuity in insulin usage at age 62, so discontinuous changes in retirement status are unlikely to be able to explain the results. Figure 8: Distribution of Proportion Retired in Sample in 1998, Ages 50-70 24

Appendix E: Persistence of the Part D Eect in 2008-2010 Figure 9: Regression Discontinuity Plot - Proportion of Diabetics Reporting Insulin Usage in 2008 25

Figure 10: Regression Discontinuity Plot - Proportion of Diabetics Reporting Insulin Usage in 2010 26

Appendix F: Absence of Changes in Diabetes Diagnosis Frequency, 1998 & 2006 One potential threat to the inferences regarding insulin usage in 1998 and 2006 comes from the potential for more frequent diagnosis of diabetes to occur at the cuto. If individuals with better coverage are seen by medical professionals more often, there may be more opportunity for the onset of diabetes to be detected. This may drive the results for insulin usage among diabetics in two ways. First, those who have had Type II diabetes for a short period of time are less likely to need to use insulin; if there is a spike at 65 in recently diagnosed diabetics with recent onset, they will articially drive a downward spike in the numbers of diabetics using insulin. Second, those diagnosed as diabetic who have not been assessed by a medical professional but who have had longstanding but undiagosed diabetes will be more likely to have to use insulin immediately, and so they would drive a spurious upward spike in the usage of insulin after becoming eligible for Medicare coverage and being diagnosed. Figures 11 and 12 show that these worries are misplaced - the results cannot be explained by changes in the numbers of diabetics in the sample at the cuto age of 65. Figure 11: Regression Discontinuity Plot - Proportion of Sample Diabetic in 1998 27

Figure 12: Regression Discontinuity Plot - Proportion of Sample Diabetic in 2006 28