Risk selection and heterogeneous preferences in health insurance markets with a public option

Transcription

1 Risk selection and heterogeneous preferences in health insurance markets with a public option Maria Polyakova June 17, 2016 Abstract Conventional wisdom suggests that if private health insurance plans compete alongside a public option, they may endanger the latter s financial stability by creamskimming good risks. This paper argues that two factors may contribute to the extent of cream-skimming: (i) degree of horizontal differentiation between public and private options when preferences are heterogeneous; (ii) whether contract design encourages choice of private insurance before information about risk is revealed. I explore the role of these factors empirically within the unique institutional setting of the German health insurance system. Using a fuzzy regression discontinuity design to disentangle adverse selection and moral hazard, I find no compelling support for extensive creamskimming of public option by private insurers despite their ability to fully underwrite risk. A model of demand for private insurance supports the idea that heterogeneity in non-pecuniary preferences and long-term structure of private insurance contracts may be muting cream-skimming in this setting. JEL classification numbers: D12, I13, I18, G22, H44 Keywords: Health Insurance, Public Option, Adverse Selection, Individual Mandate Department of Health Research and Policy, Stanford University, and NBER, mpolyak@stanford.edu. This paper is a revised chapter of my MIT dissertation. First draft: May I am indebted to Amy Finkelstein, Stephen Ryan, and two anonymous referees for their comments and suggestions. I also thank the participants at the MIT Public Finance and Industrial Organization lunches, 15th IZA European Summer School in Labor Economics, MEA Seminar at the Max Planck Institute for Social Law and Social Policy, and Stanford HRP for their feedback. Data for this project - the Scientific Use Files of the German Socio- Economic Panel - were provided by DIW Berlin and Cornell Department of Policy Analysis and Management, which I gratefully acknowledge. 1

2 1 Introduction A ubiquitous feature of health insurance markets is that insurers costs depend on who their enrollees are and how they behave. This feature has traditionally raised concerns about the feasibility of efficiency-improving competition, and has served as a common rational for the extensive role of government in health insurance. Increasingly, however, public policies in health insurance attempt to find a balance between selection concerns and potential efficiency gains from competition by reorganizing purely public or purely private health insurance systems into mixtures of the two. A central question in such arrangements, where a private health insurance system may exist in parallel to a public one, is whether private insurers may harm the public option by disproportionately enrolling good risks. The debate about how best to design mixed public-private insurance environments is not settled, and it has recently gained new momentum in the academic and policy discussion in light of the health insurance landscape reforms in the United States under the 2010 Affordable Care Act. 1 This paper offers empirical insights into the workings of an insurance system in which private insurers compete alongside a public option and are allowed to fully underwrite risk. The empirical setting is the institutional environment of German health insurance. Taking advantage of several unique features of this environment, the paper attempts to quantify the extent of selection between the public option and private insurers and explore which factors may affect the degree of selection. I first use a fuzzy regression discontinuity design to decompose selection and moral hazard. Finding surprisingly limited evidence for better risks being enrolled in private insurance, I consider two potential forces that may be countervailing cream-skimming in this setting. First, heterogeneous preferences for convenience in healthcare consumption, and second, the long-term structure of private contracts that incentivizes enrollment before information about risk type is revealed. Utilizing the German empirical setting offers several advantages. First, a discontinuity in the rule that determines access to private insurance allows for an effective way of separating adverse selection and moral hazard, which has been a well known challenge in documenting selection between private and public insurance. Second, the type of differences that exist between public and private insurance in Germany allow evaluating the role of non-pecuniary preferences in the choice of health insurance, and exploring the incentives offered by longterm annuity-style contracts. Several key institutional features characterize the German market. First, private and 1 See, for example, Halpin and Harbage (2010) and Washington Post for the discussion of the public option as part of ACA Health Insurance Exchanges. 2

3 public insurers follow different pricing regimes. 2 In the so-called statutory system, there is guaranteed issue and premiums are equal to a percentage of pre-tax income set by the regulator to ensure the solvency of the system. 3 Private insurers, on the other hand, can reject enrollment, and are allowed to carry out extensive underwriting of individual risk (including that of family members) at the time of enrollment. Private insurers use long-term contracts that are rare in health insurance - the contracts are life-long and premium underwriting principles are similar to annuities. Second, public insurers offer very low levels of consumer cost-sharing. Private insurers, however, typically offer contracts with higher cost-sharing levels. 4 At the same time, private insurers typically cover more comfortable hospital facilities, allow extra fees that may be charged by star physicians, and provide shorter appointment wait times (Lungen et al., 2008). Finally, the market is strongly influenced by a policy that mandates enrollment in the statutory system for all employees with income below an annually set threshold of about 50,000 USD. The enrollment mandate creates a discontinuity in the probability of individuals enrolling with private insurers, which I use to disentangle adverse selection and moral hazard. The idea is that OLS estimates that relate measures of healthcare utilization to the type of insurance that individuals contain both the selection and treatment (or moral hazard ) effects. Using the income-based mandate as an instrument for enrollment into the private system, I estimate the degree of moral hazard and then calculate the selection effect as the residual between these estimates and the OLS results. The estimates suggest that private insurers enroll individuals that are likely to incur more outpatient visits, while having private insurance leads individuals to significantly reduce the number of visits. My estimates cannot reject a reverse effect on inpatient admissions. Overall, the estimates cast doubt on the prior that private insurers extensively cherry-pick low healthcare utilizers that would have likely been good risks in the public system. These findings appear surprising given that private insurers are allowed to fully underwrite risks and reject enrollment. I discuss two possible (albeit certainly non-exhaustive) explanations for this result. The first possible explanation is the presence of heterogeneous preferences for private insurance that are uncorrelated with health risk. Private insurance allows for higher cost-sharing and may thus be attractive to less risk-averse or less liquidity- 2 Public insurance here refers to the system of sickness funds that are heavily regulated and can be considered as a unity for the purposes of analyzing selection on the extensive margin. 3 Adult family members not in the labor force and children are covered at no extra charge. 4 In addition to familiar cost-sharing methods such as deductibles and co-insurance, private insurers in Germany use a different way of combating moral hazard. Typically, individuals that pay for smaller expenses out of pocket and do not file claims are refunded a substantial fraction of annual premiums. 3

4 constrained individuals. Moreover, anecdotally, private insurance is viewed as a luxury good that provides better service, although does not necessarily lead to better medical outcomes, so it may attract individuals with stronger preferences for convenience, irrespective of their health status. Using a simple model of demand for private health insurance, I find empirical support for this hypothesis. Preferences for convenience in healthcare consumption are rarely considered in the literature on insurance contracts, which are typically viewed as purely financial instruments. The presence of convenience preferences, however, may imply that plan features such as wait times and location of in-network physicians and hospitals may be key drivers of individual choices of insurance. The presence of such non-pecuniary taste heterogeneity also introduces opportunities for horizontal differentiation across insurance plans that may help insurers soften price competition. The policy implication of these results, which is applicable beyond the specifics of the German institutional setting, is that allowing private plans that exist in parallel to a public option to provide products that are sufficiently horizontally differentiated from the public option, may soften selection concerns at the extensive margin between the two systems. The second hypothesis concerns the design of private contracts. I argue that muted creamskimming across the two systems may be the outcome of incentives created by dynamic contracts of private insurers. The annuity structure of these contracts creates a strong incentive for an individual to enroll into the private system as early as possible in his or her lifetime to freeze the health risk at a point in time at which both the individual and the insurer have only very noisy information about individual-specific expected risks. Thus, in many cases, private insurers are likely to have relatively limited scope for underwriting and cream-skimming. Indeed, this hypothesis is strongly supported by the existence of a market for options on private insurance contracts. Individuals that are not yet eligible to enroll because their income is too low, but expect to have higher income and be able to enroll in the future, can buy an option contract that freezes their health underwriting at the time of option purchase rather than at the time when they actually buy private coverage. This paper is related to several strands of literature. First, it is related to the broad literature that tests for the presence of adverse selection in insurance markets. Einav, Finkelstein, and Levin (2010) provide a recent survey. One strand of this literature has specifically focused on the question of selection between public and private health insurance. For example, Fang, Keane, and Silverman (2008) documented evidence consistent with the presence of advantageous selection into private Medicare add-on insurance, while Duggan (2004) studied 4

5 the efficiency implication of having Medicaid provided by private insurers. More recently, Brown, Duggan, Kuziemko, and Woolston (2014), Cabral, Geruso, and Mahoney (2014), and Newhouse et al. (2015) explored the selection of risks between the Medicare fee-for-service and the Medicare Advantage program. The present paper contributes to this literature in two ways. First, it illustrates how a combination of OLS and treatment effect estimates can be used to quantify the degree of adverse selection. Second, the paper provides an empirical example of tests for adverse selection in a public-private insurance environment that is not distorted by risk-adjusted subsidies to private insurers, which is typically the case in Medicare markets. Second, the paper is related to the literature on the role of heterogeneous preference in health insurance markets. Cutler, Finkelstein, and McGarry (2008) discuss the role of heterogeneous preferences in determining the degree and direction of selection in health insurance. There has been relatively little work exploring the sources of heterogeneous preferences in health insurance empirically. Finkelstein and McGarry (2006) have proposed the presence of heterogeneous preferences in long-term care insurance. More recently, Geruso (2013) found that older individuals enroll in more comprehensive plans than younger individuals with the same healthcare expenditure risk. Ericson and Starc (2015) studied the implications of age-related heterogeneity in the context of the Massachusetts Health Insurance Exchange, while Shepard (2015) considered the role of preferences for star hospitals. The current paper suggests that in addition, individuals may have heterogeneous preferences for what one can broadly think of as convenience or time-efficiency in the consumption of healthcare services, and that these preferences may be important drivers of health insurance choices, as well as provide scope for horizontal differentiation of insurance plans. Finally, the paper is closely related to the literature that has specifically studied the German health insurance system, such as Nuscheler and Knaus (2005), Bauhoff (2012), Hofmann and Browne (2013), and Bünnings and Tauchmann (2015). Hullegie and Klein (2010) use an RD design like the one I exploit in the current paper to assess the impact of private insurance on health utilization. They similarly estimate that holding a private insurance policy decreases the number of doctoral visits and doesn t affect the number of hospital stays. While their results already provided the estimates of moral hazard, they were done on a different sample, so that they could not be directly used as an input in the current study. Grunow and Nuscheler (2014) study the issue of selection patterns between the private and statutory systems in Germany, arguing that private insurers are unable to select good risks at the enrollment stage, but manage to return high-risk individuals back to the public 5

6 system later. Relative to that study, I take into account the concern about moral hazard, and also empirically investigate which factors may be contributing to the muted selection across the two systems. Concurrent work by Panthoefer (2016) revisits the question of selection on the extensive margin between the two systems, and, assuming no moral hazard, tests for the presence of asymmetric information in the context of inpatient admissions and private health insurance choice using the unused observables test (Finkelstein and Poterba, 2014). The main contribution of the current paper to this literature is an attempt to quantify selection separately from moral hazard, and to consider which factors at the enrollment stage may have a muting effect on cream-skimming. Moreover, combining the analysis of selection and insurance choice helps to link the findings from the unique institutional environment in Germany to the broader literature on the role of heterogeneous preferences, horizontally differentiated contracts, and the design of mixed public-private health insurance systems that has often focused on the US Medicare program. The rest of the paper is structured as follows. Section 2 outlines the key market forces within the German institutional setting and describes the data. Section 3 presents the descriptive evidence on the allocation of risks across the two systems as well as the regression discontinuity analysis. Section 4 explores potential explanations for the empirical results by documenting heterogeneous preferences for convenience in healthcare consumption and the possibility that long-term insurance contracts increase informational uncertainty and thus decrease the opportunity for selection. Section 5 briefly concludes. 2 Data and economic environment 2.1 Institutional Environment Germany spends 11% of its GDP on healthcare, amounting to around $5,000 per capita or roughly $400 billion total in annual healthcare expenditures. 5 A large fraction of these expenditures - 58% - are paid by insurers, which are part of the so-called Statutory Health Insurance (henceforth SHI ) system. The SHI differs from conventional public coverage, as there are multiple independent non-profit mutual insurance funds operating within the system. The government does not directly carry the actuarial risk or administer the plans. Similarly to a traditional public option, however, SHI insurers cannot deny coverage, cannot underwrite risk, and the amount of coverage they provide as well as premiums are almost 5 Statistisches Bundesamt, 2013 data 6

7 completely determined by the government. The next largest payer in the German healthcare sysem (after individual out of pocket expenditures) is private health insurance (henceforth PHI ) that covers 8% of total spending. Independent commercial insurers that are part of the PHI system offer individual health insurance packages in a robust non-group market. These insurers are free to decide whether to enroll an individual or to deny coverage, and enjoy substantial freedom in their decision about the extent of coverage and premiums. There are several key public policies that shape the German health insurance setting. First, there exists an individual mandate policy, according to which employees with income below an annually set regulatory threshold (about $58,000 in 2015) 6 have to enroll in the SHI. Only a selected group of individuals may choose to enroll in the private system - primarily, employees with sufficiently high income, self-employed individuals, and civil servants. 7 Those choosing to forego the public option and enroll in the PHI, are restricted in their ability to return to the public system later. Second, the government sets redistributive premiums for the public option - premiums differ by individual s income, but not by risk. In 2015, non-self-employed enrollees paid 7.3% of their income in SHI premiums. There is a cap to the amount of income that is subject to SHI premium withholding. This amount is close, but not necessarily equal, to the mandate income threshold. As a result, individuals that are eligible to choose between the SHI and PHI systems face the highest premiums in the SHI. Third, private insurers are allowed to fully underwrite individual s health risk when an individual enrolls with a PHI insurer for the first time; in return, insurers have to offer renewable long-term contracts (similar to annuities) without the re-classification risk. 8 The SHI and PHI plans differ on many dimensions. In addition to the differences in premiums as outlined above, there are often substantial differences in cost-sharing. While SHI plans typically have low or even just nominal cost-sharing, PHI plans may offer significant deductibles and may have some co-insurance, although consumers have a lot of choice in the design of the PHI plans and can trade-off premiums and cost-sharing. PHI plans require more financial liquidity from their enrollees, as outpatient services are first paid by patients out of pocket and are later reimbursed by the PHI insurer if the patient submits the claim. SHI 6 The income threshold in 2015 was EUR 54, Civil servants have a portion (typically 50-70% depending on the family structure) of their healthcare expenditures paid by the government directly. If civil servants enroll with the SHI, they loose these direct payments and have to cover 100% of the SHI premium out of pocket. The combinations of these policies make PHI coverage of the residual expenditures especially economically attractive for this group. 8 For non-civil cervant employees, employers match (almost equally) the health insurance contribution. Hence, in reality the premium collected by SHI is, e.g. in 2015, 14.6% of individual s gross income. If an employee is enrolled with the PHI, employers pay half of the PHI premiums up to a maximum contribution that is equal to their maximum possible contribution in the SHI system. 7

8 plans offer more generous family coverage for families with children or spouses that are not in the labor force - the latter two groups are covered at no extra charge under the SHI, while they have to pay full premiums under the PHI. At the same time, PHI plans often provide access to more convenience in healthcare consumption, covering more comfortable rooms for in-patient admissions, providing faster inpatient and outpatient appointments (Lungen et al., 2008), and covering extra fees for seeing star physicians. Physicians can charge much higher fee-for-service rates to private insurers than they can in the SHI system, which may improve the care provided, but may also induce excess utilization in the PHI system. Given this multitude of differences between the two systems, different types of individuals may be considered good or bad risks by the private insurers and the public system. Consider the SHI. The employees with income above the mandate income threshold all pay the same fixed premium to the SHI, as their income is above the withholding cap. Thus - in a given year - the good risks for the SHI are simply those individuals whose healthcare expenditures in a given year are lower than what they pay into the system. 9 Let us call these individuals net payers and the individuals that are expected to spend more on their healthcare than they pay, net receivers. Then, we can define selection in this market as follows. There is adverse selection into the private system if the individuals that opt out of the public system would have been predominantly net payers. There is advantageous selection into the private market if the individuals that opt out would have been net receivers in the public system. And finally there is no selection if the switchers are a random mix of risks. The conventional intuition suggests that competition alongside private insurers may harm the public option, because private insurers may disproportionally cream-skim net payers out of the public system. In Section 3, I proxy expected healthcare spending by healthcare utilization and test empirically whether the PHI system appears to cherry-pick relatively lower utilizers from the public system. 2.2 Data Throughout the empirical analysis, I use data from years 2004 to 2009 of the German household survey panel SOEP. 10 The raw data records information on 28,693 individuals. The 9 Alternatively, one could define good risks as those with lifetime spending below lifetime contributions. 10 These years of the data fall in between reform years, allowing for analysis within a relatively stable institutional environment. Specifically, a 2009 reform significantly changed the policy landscape guiding competition between public and private insurers; hence I stop the analysis at 2009, assuming that 2009 survey wave still reflects pre-reform decision-making. Robustness checks without year 2009 give very similar results. 8

9 survey offers a collection of answers to a rich set of demographic, employment, and healthrelated questions for a representative sample of the German population. 11 The survey has multiple questions related to health and health insurance that I utilize in this paper. First, SOEP records whether an individual is enrolled within the statutory or the private health instance system. For those individuals that are enrolled in the PHI, the survey asks for the level of monthly premiums. Second, SOEP contains several questions about healthcare utilization and health conditions. It also includes a rich set of potentially private information that is not necessarily used for pricing by private insurers, such as questions about risk aversion in various domains, information about other insurance products that the household holds (e.g. life insurance), as well several variables that plausibly reveal individuals preferences for convenience or value of time. The baseline analytic sample imposes several restrictions on the raw data. First, I restrict the sample to include individuals aged This age restriction primarily excludes children, students, and retirees, who likely either do not make active decisions about their health insurance, or face a different set of incentives in their choices. Second, I restrict the sample to include individuals working full-time, either as non-public-sector employees or selfemployed, with gross income at or above 400 EUR per month. This excludes those working part-time and civil servants, who may face a different set of incentives. This also excludes individuals that report being unemployed or out of the labor force, as they are typically not making their own insurance choices, being insured either as dependents or through welfare programs. These restrictions leave us with 37,554 individual-year observations on 10,725 unique individuals, out of whom 9,454 are employees and 1,271 are self-employed. Table 1 reports summary statistics for this baseline sample. Individuals in the sample are on average 43 years old, 32 percent female, with average gross monthly income of 3,339 EUR. The gross monthly income includes regular monthly income, as well as (a twelfth) of 13th and 14th month payments and holiday allowances if individuals reported those in the survey. 12 These additional payments are a common component of the German compensation schemes and qualify as regular income that is taken into account when determining whether or not someone crosses the income threshold of the SHI enrollment mandate. The average individual has almost 13 years of schooling and works 43 hours per week. 38% are not married. The survey respondents report visiting a doctor in an outpatient setting about 7 times a year, while only about 10 in a hundred have one inpatient admission. Individuals report being 11 For more detailed information on the statistical properties of SOEP panel sample please see 12 The holiday allowances that I include are Weihnachtsgeld and Urlaubsgeld. 9

10 slightly overweight with an average BMI of 26; 33% report being smokers. 17% have high blood pressure, about 4% report asthma, cardiac conditions, depression, or diabetes. In the baseline sample, 14% have private health insurance. This fraction is much lower - at 8% - for the sub-sample of employees, who are only eligible to purchase PHI if their income is high enough. In general, the sub-sample of employees has slightly lower average gross income at 3,155 EUR per month, but other socio-demographic characteristics and health-related indicators are very similar to the overall sample. 3 Empirical evidence: selection and moral hazard 3.1 Descriptive evidence I start my investigation of risk selection between public and private insurers in the German system with model-free evidence. If PHI disproportionately enrolled healthier individuals, we would expect this to be reflected in the compositional changes of SHI demographics, diagnoses, and utilization around the income threshold. For example, suppose PHI only accepted individuals that are younger than 40, then we would expect the average age of SHI enrollees to the right of the threshold to increase disproportionately relative to the average age in the SHI to the left of the threshold. Hence, we are interested in whether there are breaks in the observable demographics of SHI enrollees at the income threshold above which individuals may leave the SHI system and enroll with a private insurer. I compare the average age, BMI, fraction of smokers, fraction of disabled individuals, as well as self-reported worry about health and risk attitude towards health, of SHI enrollees around the income eligibility threshold. Figure 1 illustrates these comparisons. The graphs uncover few if any changes in individual characteristics around the income cutoff. Figure A1 in the Appendix reports the outcomes of a similar exercise, looking at the probability of six chronic diagnoses - asthma, cancer, cardiac conditions, migraine, diabetes, and high blood pressure - around the income threshold. There are no discernible breaks in the prevalence of these conditions. Overall, this descriptive evidence suggests that individuals that leave the SHI around the income threshold have similar observable characteristics as those that stay. 3.2 Disentangling adverse selection and moral hazard The key challenge for the empirical identification of selection between the two insurance systems is the need to disentangle the ex ante selection into the PHI system from the ex post 10

11 causal effects of PHI enrollment, or moral hazard. To address this identification concern, I rely on a combination of OLS and IV estimates. The idea is that an ordinary least squares regression of health care utilization on the indicator of insurance type combines the treatment (i.e. PHI changing individuals utilization) and the selection effect (i.e. PHI selecting or being selected by lower risk individuals). An instrumental variables strategy - in this case based on a fuzzy regression discontinuity design - allows us to estimate the treatment effect, or the moral hazard component. The difference between the OLS and IV estimates should then allow us to capture the selection effect of interest. This approach is similar in spirit to the ideas in Chandra and Staiger (2007); McClellan et al. (1994). I proceed in three steps. First, I estimate an OLS regression that captures both selection and moral hazard. Second, I use a instrumental variables specification to estimate the extent of moral hazard. And third, I compare the two sets of estimates, to quantify the extent of selection by subtracting the instrumental variables coefficients from the OLS results. Healthcare utilization and insurance type: OLS I first use an OLS specification to estimate the relationship between insurance type and healthcare utilization: The outcome variable Y outcome E[Yit outcome.] = β 0 + β 1 P HI it + β 2 Income it + β 3 X it is one of the following outcome variables observed in the data: the unconditional annual number of inpatient and outpatient visits, the number of inpatient and outpatient visits conditional on having at least one visit, as well as the probability of having at least one inpatient or outpatient visit. P HI is an indicator variable that is equal to one if individual i has private insurance in year t. The set of control covariates X it includes age, gender, and year fixed effects. Column (1) of Table 2 reports the results of this regression on the full baseline sample of employees for all six outcome variables. The coefficients for outpatient outcomes are not different from zero at a 5% confidence level with point estimates close to zeros relative to the mean of the outcome variables in the data. The estimates are more precise for the inpatient admissions outcomes, suggesting fewer inpatient admissions for those with PHI insurance. This result appears to be driven both by the negative correlation between having a private insurance and reporting fewer hospital stays conditional on having had at least one. For the latter outcome variable, individuals are likely to have on average 0.14 fewer (95% CI [-0.32, 0.03]) hospital stays, while the mean number 11

12 of hospital stays conditional on having any is 1.3 with a standard deviation of 0.9. The probability of having any hospital stay is similarly lower by about 10% relative to the mean - the point estimate is , as compared to the mean probability of inpatient admission in the sample of Overall, these results suggest that there is little if any difference in the frequency of outpatient visits for PHI-insured individuals. At the same time, privately insured individuals appear to have meaningfully fewer hospital stays in a year conditional on having been hospitalized at least once, and somewhat lower probability of being hospitalized. The estimated correlation between the PHI enrollment and the utilization of healthcare includes the effects of selection and moral hazard that we try to disentangle in the next step. Before moving to this next step, it is important to put these results into the institutional context. Given the multiplicity of differences between the PHI and the SHI, both the causal or moral hazard and the selection effects in this setting themselves include a multitude of potentially countervailing forces. The selection effect could be a combination of strategic cream-skimming by private insurers, as well as selection on individual preferences that lead different individuals to apply for PHI contracts. The causal effect of the PHI may include the classic moral hazard argument, according to which the higher degree of cost-sharing should decrease the demand for healthcare. At the same time, the causal effect of the PHI could also include the physician-induced demand argument, whereby physicians, whose remuneration is substantially higher under the PHI, induce more demand from patients. Yet a third causal channel could arise if PHI-insured are treated better and thus need fewer healthcare services. Lastly, if PHI patients face shorter waiting times and more convenient service, they could be inclined to more utilization of healthcare. The available data will not allow me to cleanly disentangle any of these forces; therefore, it is useful to keep in mind that my empirical findings of selection and moral hazard will necessarily reflect the net of all these channels. Measuring moral hazard To identify the effect that private insurance may have on healthcare utilization, I exploit the regulatory break in the PHI eligibility as an instrument for private insurance enrollment. Only employees whose income crosses an annually set eligibility threshold may choose to opt out of the SHI system in favor of a private insurance plan. Hence, we would expect a change in the probability of enrolling into the PHI at the income eligibility cutoff. This set-up renders itself well to a fuzzy regression discontinuity design, where the change in the probability of treatment can be used as an instrument for treatment status. The discontinuity design is fuzzy, since the crossing of the eligibility threshold only gives the individual the choice to 12

13 take up the PHI treatment, rather than imposing a switch to the PHI. The key identifying assumption in this setting is that individuals cannot precisely manipulate which side of the cutoff they are on. To explore the plausibility of this assumption, I plot two histograms of income distribution in Figure 2. The top histogram zooms in to 1,000 EUR income around the cutoff and plots income relative to the cutoff. The bottom histogram zooms in even closer around the cutoff points in different years of the data and plots levels of income. The patterns in both histograms have to be interpreted with care. First, income may be reported with measurement error, so any lack of bunching in the histograms around the cutoff may be a reflection of the data imprecision. Second, since employees may report wages with rounding and, more importantly, since employers tend to set rounded wages or use the insurance income cutoff as a wage benchmark, bunching around the cutoff may not necessarily represent evidence of manipulation. Finally, since I have added various additional income allowances (like extra months of income and holiday allowances), baseline income that would tend to bunch at round numbers would be affected by these additions. With these limitations in mind, we observe that the top histogram uncovers no evidence of bunching around the threshold. The bottom histogram that uses the levels of income rather than the deviations from the cutoff and zooms in closer to the cutoff values, suggests that in general income tends to bunch at or close to round numbers. In this more nuanced histogram we observe that in those years where the threshold was close to round numbers, there is some bunching close to the cutoff. 13 There is, however, no evidence that bunching occurs close to cutoff levels when they are further away from round numbers. Hence, overall, the empirical income distribution does not suggest systematic manipulation of the running variable. Further covariate balance checks around the cutoff reveal few differences along the nonincome observables between individuals below and above the cutoff. Table A1 in the Appendix records several demographic measures, such as age gender, schooling, hours of work, marriage status, number of children, housing arrangements, and political preferences, as well as several health-related measures, such as smoking status, BMI, disability and prevalence of chronic conditions, 250 EUR and narrower 25 EUR to the left and right of the cutoff. By definition of the cutoff, income is different across the two groups, with monthly income averaging at 3,811 EUR below the cutoff, and 4,029 EUR above the cutoff (for the 250 EUR comparison window). As many of the listed characteristics have a sharp income gradient, we 13 Intuitively, the bunching around round numbers and hence around round thresholds is much starker when I only consider baseline income, without 13th and 14th month payments and holiday allowances. This suggests that baseline salaries are very likely to be set at round numbers - specifically, 48,000 EUR a year appears to be a common baseline salary in the sample close to the cutoff levels. 13

14 would expect to observe some differences between the two groups, since there is not enough power in the data to zoom in literally one euro below and above the cutoff, where would expect no differences. In practice, I find that the vast majority of the non-income measures are smooth around the threshold at both the larger the and tighter income windows. For the 250 EUR window I find statistically significant (at 5% or less) differences in the years of education, political choices, BMI, and (borderline) prevalence of diabetes. While statistically significant, the economic differences of these measures apart from the education measure are not large. The fact that individuals with higher income have 0.5 years more education on average, is not surprising given the well-known gradient between income and years of schooling. At the smaller income window, the data is quite sparse; at this window the statistically significant differences occur for BMI, disability, diabetes and ownership of life insurance. In the specification checks in the Appendix A2, I repeat all of the fuzzy RD analyses, controlling for the few demographic variables that appear to be slightly different around the cutoff; the results are somewhat noisier, but the qualitative conclusions are not sensitive the these specifications. In general, the smoothness of the majority of non-income observables, even of those that we would expect to be strongly correlated with income, corroborates the plausibility of assuming that whether individuals end up slightly above or slightly below the public insurance mandate is close to being as good as randomly assigned. I continue with the estimation of a first stage relationship that tests for the existence of a strong link between the instrument and the PHI enrollment. I use a linear specification that allows for a break in levels at the cutoff and for different slopes before and after the threshold. The income running variable is centered at the cutoff, which allows combining observations from different years that had different threshold levels. The outcome variable is the indicator of whether an individual has PHI: E[P HI it.] = γ 1 + γ 2 Above it + γ 3 (Income it Cutoff t )+ + γ 4 (Income Cutoff t ) Above it + γ 5 X it Figure 3 presents a graphical illustration of the first stage. The first scatterplot uses the baseline analytic sample of full-time employees. We see a clear change in the probability of having the PHI after individuals cross the income threshold marked with a vertical line. The second scatterplot also plots the probability of enrolling with the PHI at different income levels, but it uses the sub-sample of self-employed individuals only. These individuals do not fall under the SHI mandate at any income level and thus we would not expect a first stage 14

15 for this sample. Indeed, there is no visual break in trend or jump in the probability of PHI enrollment for the self-employed at any income level. 14 The regression results for the first stage are reported in Table 3. The probability of PHI enrollment is estimated to be 22 percentage points higher after the threshold. The estimates are precise, with the F-statistic of 168 in the specification that includes age and gender, and year fixed effects. Having established the presence of a first-stage relationship, I proceed with the analysis of the reduced form specification. Figure 4 provides a graphical representation of the reduced form for six outcomes of healthcare utilization: total outpatient and inpatient visits; probability of having at least one inpatient or outpatient visit; and the number of visits conditional on having had at least one. The graphical representation shows some evidence of a discontinuity in the number, although not the probability, of outpatient visits and no discernible change in the level or trend for the inpatient outcomes. I test for the presence of a statistically significant discontinuity formally using the following linear specification. The specification is similar to the first stage - the income variable is centered at the cutoff and it allows for different income trend slopes before and after the cutoff. I include only basic demographic controls (age and gender) in X it : 15 E[Y outcome it.] = α 1 + α 2 Above it + α 3 (Income it Cutoff t )+ + α 4 (Income it Cutoff t ) Above it + α 5 X it Column (3) of Table 2 summarizes the reduced form coefficients. The estimates broadly confirm the intuition from the graphical evidence. I find that individuals with income above the threshold are not less likely to visit an outpatient physician, but conditional on the visit they are likely to have one fewer visit (relative to the mean of 11.8), leading to -0.7 overall 14 The results remain similar in specifications with higher order polynomials; I do not test a non-parametric specification with a small bandwidth around the cutoff due to scarcity of observations right around the threshold. Moreover, considering the potential measurement error in income, local results right around the cutoff may be misleading, since the observations around the cutoff may have been misclassified. Note that the graphical evidence suggests that there are a number of observations very close to the cutoff that have a fairly high probability of PHI enrollment, even if their income is reported to be below the eligibility level. The first reason for such observations may be a measurement error in income that leads me to misclassify the individual s eligibility. In addition, the German health insurance regulation allows individuals that opted out to the PHI at some point and then their income dropped below the current eligibility threshold, to sign a waiver for the re-entry of the SHI. 15 Appendix tables report specifications with richer controls. These reduce the sample size, since not all control variables are available for all individuals. The conclusions from these alternative specifications remain the same as in the baseline. 15

16 visits off the base of 7.2. There are no economically or statistically significant jumps in the average utilization of the inpatient services. Column (2) of Table 2 reports the coefficients of a 2SLS specification that is similar to the reduced form regression, except that I instrument for PHI enrollment with an indicator for being above the income threshold. The point estimates suggest that PHI induces individuals to have 4 fewer outpatient visits per year, which is about a third of the standard deviation. Most of this effect appears to stem from individuals having fewer visits conditional on having had at least one rather than from having a substantially lower probability of a visit. The probability of having at least one visit is only slightly smaller for the PHI enrollees; the imprecisely estimated coefficient suggests 0.09 lower probability of a visit off the mean of 0.6. The measures on inpatient admission effects are estimated imprecisely. Taken at face value, the point estimates suggest that enrolling with PHI leads individuals to have 0.19 more admissions (0.2 standard deviations) conditional on having experienced at least one. The patterns just described would be consistent with several underlying mechanisms. For instance, they would be consistent with PHI offering nicer hospital facilities and thus inducing less deterrence of inpatient treatment, or inducing inpatient demand through reimbursement of head and star physicians. At the same time, the PHI may be more effective at managing moral hazard on the outpatient dimension by reducing the number of visits, potentially through the deductible feature of the contracts. Overall, the data suggest that PHI leads to fewer outpatient visits, while the effect on inpatient admissions is likely to be slightly positive. Measuring selection In the last step, I combine the OLS and IV estimates to bound the extent of selection between the public and the private insurance systems that is supported by the data. The idea is to subtract the IV estimates of moral hazard from the OLS estimates that combine selection and treatment effects. While many of the OLS and 2SLS estimates are imprecise zeros, we can still use the confidence intervals to learn about the potential extent of risk selection. Consider first the outpatient visit frequency as a measure of utilization. In Column (1) of Table 2, I estimate that individuals with private insurance report fewer physician visits than SHI-insured individuals. The confidence interval on this estimate is [-0.858, 0.556]. The moral hazard component in outpatient visits is estimated at with the confidence interval of [-6.806, ] as reported in Column (2). Using the point estimates, we arrive at the implied extent of selection of ( 4.005) = or a third of 16

17 the standard deviation in the number of physician visits. This implies that individuals who selected into the PHI would have inherently had 3.8 more outpatient physician visits as compared to individuals that stayed in the public system. In other words, these point estimates suggest the selection of higher outpatient care utilizers into the PHI system. Next, I use the confidence intervals to bound the maximum amount of adverse selection that the data would be consistent with. The maximum level of adverse selection would occur at the left hand side of the OLS confidence interval together with the right hand side of the moral hazard confidence interval, leading to a selection effect of ( 1.204) = of outpatient visits per year. Hence, the data would be consistent with a much smaller selection effect, however, the direction would still be such that individuals switching to PHI are slightly higher outpatient utilizers. We next consider the inpatient admissions. The OLS results for the total number of annual hospital stays, reported in Column (1) in Table2, suggest a combined effect of selection and moral hazard at with a confidence interval of [ , ]. The moral hazard effect of having private insurance is reported in Column (2) as being more visits [ , 0.102]. The 95% confidence interval for the moral hazard estimate is between and Applying the same logic as in the previous paragraph and subtracting the IV estimates from OLS, we conclude that the extent of selection on the inpatient admissions dimension is around at the point estimates. This suggests adverse selection of individuals with expected 0.04 fewer hospital admissions into private insurance off the mean of admissions per year with a standard deviation of The confidence intervals are wide and would be consistent with higher adverse selection, as well as the reverse result of higher inpatient utilizers exiting the public system. Thus, overall the data is consistent with selection of worse risks into the PHI on the outpatient utilization dimension, and selection of slightly better risks on the inpatient utilization dimension. Given the noisiness of the estimates, I cannot reject that the selection effects of the PHI are zero on the inpatient dimension. These results cast doubt on the prior that private insurers manage to select individuals with substantially lower expected healthcare utilization, who would have very likely been good risks in the public system. In the next section I discuss several possible explanations for this result. 17

18 4 Preferences for privately provided health insurance Many factors may be limiting the extent of risk selection between the PHI and the SHI. One possible factor is the presence of taste preferences for private insurance that are either unrelated to the risk profile of individuals or are negatively correlated with risk. The idea of heterogeneous preferences for insurance has been discussed in Hemenway (1990) and empirically corroborated in the context of annuity insurance in Finkelstein and McGarry (2006), as well as in the context of Medicare supplementary insurance - Medigap - in Fang, Keane, and Silverman (2008). More recently, Geruso (2013) has documented age-specific preferences for insurance that go beyond the predicted age-specific health risk in the context of US employer-sponsored insurance plans, while Shepard (2015) has documented the importance of selection across insurance plans based on individuals preferences for having access to star hospitals. In the German institutional environment, the PHI provides not only a different financial product with different premiums and cost-sharing, but also renders access to more convenience in healthcare (shorter waiting times, single hospital rooms, etc.) and potentially easier access to star physicians. Such convenience preferences are not necessarily correlated with risk, and hence, there is substantial scope for choices between the PHI and the SHI on non-risk-related dimensions. 16 To empirically test for the presence of such heterogeneous preferences for private health insurance, I estimate a discrete choice model of demand for private health insurance. The model takes advantage of the survey data, which allows observing many characteristics of the individuals that are not related to their consumption of healthcare and thus would not typically be observed in healthcare claims data. I let the utility of individual i from choosing insurance j take the following form: u ij = α i p ij + β i φ j + ɛ ij (1) where p ij is the premium that an individual i pays for choosing insurance option j, while φ j are the characteristics of the insurance choice. ɛ ij is a Type 1 extreme value that accounts for the unobservable part of utility. Individual i chooses insurance j that maximizes her utility. Since in our case j is binary (private or public insurance), the model simplifies significantly. The characteristics termφ j reduces to a insurance-system specific constant that captures the average valuation for each type of insurance. To incorporate preference hetero- 16 Baicker et al., 2013 discuss the ideas for the potential of such basic versus more generous coverage in the context of Medicare, as way to efficiently sort beneficiaries according to their willingness to pay for more conveneince or less cost-effective treatments. 18