Can private insurers fail to cream-skim the public option? Evidence from the individual mandate in Germany.

 
Can private insurers fail to cream-skim the public option? Evidence
                    from the individual mandate in Germany.

                                          Maria Polyakova∗

                                          February 4, 2015

                                                Abstract

       Conventional wisdom suggests that if private health insurance plans compete alongside
       a public option, they may endanger the latter’s financial stability by cream-skimming
       good risks. Documenting cream-skimming in dual insurance systems is challenging
       because of the co-existence of selection and moral hazard. I use a fuzzy regression
       discontinuity design based on exogenous variation in the propensity of choosing private
       health insurance to address this challenge. The empirical setting is Germany, where
       there exists an unsubsidized non-group for-profit private health insurance market in
       parallel to a statutory alternative. Federal regulation mandates individuals with in-
       come below an annually set threshold to enroll into the statutory system. I do not
       find compelling support for concerns of cream-skimming by private insurers. Using a
       discrete choice model of demand for private insurance, I explore heterogeneous prefer-
       ences and long-term contract design of private insurers as potential explanations for
       this optimistic result about insurance design.

       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, maria.polyakova@stanford.edu. This
paper is a revised chapter of my MIT dissertation. First draft: May 2012. I am indebted to Amy Finkelstein
and Stephen Ryan for their guidance throughout this project. I also thank the participants at the MIT Public
Finance and Industrial Organization lunches, 15th IZA European Summer School in Labor Economics of
2012, and MEA Seminar at the Max Planck Institute for Social Law and Social Policy 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
1       Introduction
The ubiquitous feature of health insurance markets is that insurers’ costs depend on who their
enrollees are and how they behave. This characteristic of selection markets raises concerns
about the feasibility of efficiency-improving competition, and has served as a traditional ra-
tional for extensive government intervention in health insurance. Increasingly, public policies
in health insurance attempt to strike a balance between selection and competitive efficiency
by reorganizing purely public or purely private insurance systems into different mixtures of
the two. A central question in such arrangements, where a private health insurance system
exists in parallel to a public one, is whether private insurers may harm the public system by
successfully cream-skimming good risks out of the public option. This debate is not settled
and has recently gained new momentum in the academic and policy discussion in light of a
proposal for a “public option” as part of the Affordable Care Act reforms. Similar discussions
have played a key role in the analysis of Medicare and Medicaid programs that are both ex-
periencing growing enrollment in private managed care plans that co-exist with the fee for
service public option. These discussions have also seen debates about an array of potential
fundamental changes in insurance system design that could alter the risk allocation dynamics
in the US. One such debate included a speculation of potential effects of the introduction of
long-term or life-long contracts into the health insurance system.1 The current paper will
offer empirical insights into a system where such contracts exist in practice.
    In this paper, I empirically investigate the question of cream-skimming between a public
and a private health insurance system within the unique institutional setting in Germany.
Utilizing the German empirical setting offers several new angles to the ongoing debate.
First, we gain insights into a public-private health insurance market for a representative
sample of ages and income levels in the population, which has been a traditional gap in the
literature that has mostly focused on the retirees in Medicare. Second, private insurers in
Germany are not paid by the government, so there are no risk-adjustment distortions that
have been documented to affect the allocation of risks across private and public Medicare
and Medicaid programs. Finally, individual mandate policies that govern which individuals
are allowed to select which types of coverage in Germany, allow to isolate exogenous variation
in the individual’s propensity to select private insurance and thus separate selection from
the treatment effects of private coverage. Disentangling the latter two effects has been a well
known challenge to documenting cream-skimming of public insurance systems. I do not find
compelling evidence of cream-skimming from the public option, which is often voiced as a
    1
    See, for example, http://johnhcochrane.blogspot.com/2012/10/after-aca-freeing-market-for-health-
care.html for policy debate and Cochrane (1995) for early theoretical analysis.

                                                 2
policy concern in Germany,2 and discuss potential features of the market design that could
have aided to the sustained co-existence of the two systems.
    There are three key institutional features that characterize the German market. First,
private and public insurers3 follow different pricing regimes. 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 at levels that would ensure the solvency of the system. Statutory insurance
is run by independent non-profit sickness funds and have to be self-solvent, as they do not
directly depend on financing from the federal or state budgets.4 Private insurers, on the other
hand, are mostly for-profit corporations, can reject enrollment, and are allowed to carry out
practically unrestricted underwriting of individual risk at the time of enrollment.5 Private
insurers use long-term rather than annual contracts - the contracts are life-long and premium
underwriting principles are similar to annuities. Second, public insurers offer very low, if
any, levels of consumer cost-sharing. Private insurers (and there is substantial heterogeneity
among them) typically offer contracts with higher cost-sharing levels,6 but broader coverage
networks, more comfortable hospital facilities and, anecdotally, shorter appointment wait
times.7 Finally, the market is strongly influenced by a policy that mandates enrollment in
   2
      In the latest election cycle, there was an upsurge of debate around the duality of the Germa
health insurance system. The Minester of Health suggested a repeal of the income restriction for
enrollment in the private system, motivating his arguement by providing more choice to the conus-
mers. (See e.g. http://www.spiegel.de/wirtschaft/soziales/bahr-will-private-krankenkassen-fuer-alle-oeffnen-
a-918754.html.) At the same time, a lot of popular debate around the dual system focuses on the arguement
of “cherry-picking” from the statutory pool. (See e.g. Jacobs, Klauber, Leinert “Fairer Wettbewerb oder
Risikoselektion? Analysen zur gesetzlichen und privaten Krankenversicherung” Wisseschaftliches Institut
der AOK)
    3
      Throughout the paper I will be referring to the German public or statutory health insurance system as
a unity. It is important to note that, in reality, the system has more than 130 separate so-called “sickness
funds” that are essentially non-profit insurers that largely follow federal standards in pricing and coverage.
The insurance is thus not directly administered by the government and in principle the funds have some small
latitude in their pricing and coverage decisions, and thus there exists competition for enrollees within the
public system. For the purposes of thinking about the extensive margin between the statutory and private
systems, I consider it appropriate to treat both systems as collective objects.
    4
      If individuals do not have a regular source of income, the premiums are typically set at some average or
minimum levels and are carried by the government.
    5
      The issue of risk-reclassification is somewhat unsettled. On the one hand, by law, the insurers cannot
re-classify individual’s risks after enrollment. In practice, however, premiums do increase over time, which
typically is justified by adjustments to the premium calculations due to population-wide growth in life
expectancy and healthcare costs. At the same time, the government imposes consumer commitment to the
long-term contracts of private insurers by not allowing those, who opted out of the public system, to return
back, unless they fall under the income threshold.
    6
      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 do not file any claims
during the year - or in other words pay for smaller expenses out of pocket - are refunded a substantial fraction
of annual premiums.
    7
      Additional institutional differences include the fact that dependents without income are covered without
additional cost to the enrollee in the statutory system, and have to be carried in the private system. The

                                                       3
the statutory system for all employees with income below an annually set threshold of about
50,000 USD. I extensively utilize this enrollment mandate in my empirical analysis.
    I start my investigation of cream-skimming in the German system with several pieces of
non-parametric evidence. First, I look for breaks in the observable demographics, diagnoses,
and healthcare utilization of statutory system enrollees at the income threshold. Using survey
data, I compare average age, fraction of young and old enrollees, average BMI, fraction
of smokers, self-reported risk attitudes, sport affinity, health satisfaction, and outpatient
and inpatient utilization of public option enrollees around the income eligibility threshold.
If cream-skimming were present, we would expect relatively higher risks to remain in the
statutory system, and this should be reflected in the demographics that are typically strongly
correlated with health risks, as well as in utilization intensity. However, I find no meaningful
differences in individual characteristics to the left and to the right of the income cutoff, even
though to the right of the cutoff, about 25% (at the cutoff) to 50% (overall) of individuals
leave the public system.
    I next report the outcomes of a similar exercise that looks at differences in diagnostic
probabilities rather than demographic factors for eight diagnoses - asthma, cancer, stroke,
migraine, depression, diabetes, high blood pressure, and cardiovascular conditions. I compare
probabilities of having these diagnoses for public and private insurance enrollees.8 I find that
individuals with private insurance are less likely to report having diabetes; however, there
are no meaningful differences in incidence across the other seven diagnoses. The two pieces
of evidence presented so far suggest at the first sight that there is little difference in risks
across the two systems. It is possible, however, that private insurers cream-skim individuals
that look the same in terms of their demographics and diagnoses, but are nevertheless likely
to utilize less healthcare. To explore this possibility I use data on health care utilization -
the number of self-reported outpatient and inpatient visits9 - to do a conditional comparison
of means between the privately and publicly insured individuals that were all eligible to
choose a private plan. This comparison suggests that individuals with private insurance, but
otherwise observationally similar, report lower incidence of healthcare utilization.
    This evidence of lower healthcare utilization in the private system, however, faces the
classic challenge of the need to distinguish selection from moral hazard. Put differently, in-
insurance choice model in Section 4 of the paper will attempt to account for this difference. This difference
may also constitute one of underlying channels for the allocation of risks that will be captured in the positive
exercise in Section 3.
    8
      I implement this comparison on the whole range of incomes rather than only at the threshold, since
self-employed individuals are exempt from the statutory system mandate and thus provide information on
the incidence of diagnoses for income levels below the income cutoff.
    9
      Naturally, a more compelling comparison would have used data on healthcare expenditures rather than
utilization; such data, however, to the best of my knowledge, is not systematically available for Germany.

                                                       4
dividuals that end up insured in the private system are not a randomly assigned group and
moreover, being in the private system may lead to a change in one’s healthcare consumption.
Thus, merely comparing healthcare utilization of enrollees in the public and in the private
systems will always confound the presence of the causal effect of private insurance (“moral
hazard”) and the ex ante selection or a cream-skimming effect. In this paper, I address the
challenge of distinguishing selection from moral hazard by using a fuzzy regression disconti-
nuity design. The idea of this identification strategy is to estimate the moral hazard effect
using an income-based mandate for enrollment into the statutory system, and then calcu-
late the cream-skimming effect as the residual that explains the difference between the OLS
estimates and the moral hazard estimates.
    In the first step, I estimate an OLS regression that documents that having private insur-
ance is associated with a lower number of outpatient visits and hospital admissions. In the
next step, I utilize the fact that only individuals whose income lies above a government-set
income threshold can enroll in the private system. Empirically, the probability of enrollment
in the private system at the threshold jumps from nearly zero to about 25%. Since individuals
are not forced into private insurance if they cross the threshold, the regression discontinuity
design is fuzzy, and crossing the income threshold is used as an instrument for enrollment
in the private system. The fuzzy RD point estimates suggest that having private insurance
induces fewer outpatient visits, while the results are close to zero for inpatient admissions.
Combining the point estimates and confidence intervals from the RD estimation with OLS
results, I calculate plausibility bounds on the extent of cream-skimming. My results suggest
that private insurers enroll individuals that are likely to incur more physician visits, while
having private insurance causes individuals to significantly reduce the number of visits. My
estimates cannot reject a similar effect on inpatient admissions. Using confidence interval
bounds, the estimates suggest that the upper bound for cream-skimming by private insurers
is to enroll individuals with about 0.1 fewer annual inpatient admissions.
    Thus, overall the econometric analysis is consistent with negative selection into the PHI on
the outpatient utilization dimension and cannot reject that both the causal and the selection
effects of the PHI on inpatient utilization are zero. These results are strong enough to cast
doubt on the prior - which is common in German public debate - that private insurers manage
to successfully cherry-pick a lot of individuals with low expected healthcare utilization that
would have likely been better risks in the public system. How could this be the case if the
private insurers can reject individuals and are allowed to collect lots of information about
them for full risk-underwriting? I discuss two possible (albeit certainly non-exhaustive)
explanations for this result.
    The literature that has analyzed selection in insurance markets has argued that the

                                               5
presence of heterogeneous preferences, such as risk aversion, may imply that there is no clear
relationship between the insurance contract chosen and the individual’s risk type (Finkelstein
and McGarry, 2006). To test whether a version of this hypothesis could apply to my empirical
setting, I take advantage of the detailed survey data and estimate individual preferences for
different types of insurance using a discrete choice model. In terms of contract structure,
private insurance allows for higher cost-sharing and may thus be attractive to less risk-
averse or wealthier individuals. Moreover, anecdotally, private insurance in Germany is
viewed as a “luxury” good that provides better service, although does not necessarily lead
to better medical outcomes. My estimates of preferences support both of these arguments.
First, I find that individuals with higher income are more likely to choose private insurance.
Moreover, conditional on income, individuals that employ household help, which I interpret
as a reasonable proxy for valuing convenience and service, are also much more likely to opt
out of the statutory system. Such preferences for convenience in healthcare consumption
are not typically central in the literature on insurance contracts that are viewed purely as
financial instruments. At the same time, the presence of convenience preferences may imply
that plan features such as wait times and location of in-network physicians and hospitals,
which have become prominent in the Affordable Care Act debate, may be the 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, softens the selection concerns at the extensive margin
between the two systems.
    The second hypothesis concerns the supply-side of the market. I argue that the lack of
evident differences in risks across the two systems may be the outcome of incentives created
by dynamic contracts of the private insurers. The annuity structure of these contracts
implies that beneficiaries pay in equal monthly installments their expected lifetime spending
on healthcare.10 The insurers assess this expectation at the time of individual’s enrollment
and are not allowed by the regulator to re-classify risk or to drop coverage in response to
information about the individual’s health being revealed over time. Consequently, individuals
have a strong incentive to enroll into the private system as early as possible in their lifetime
to “freeze” their health risk at a point in time at which both the individual and the insurer
  10
    De facto, premiums do not stay constant over the life cycle. Indeed, there has been a lot of public debate
about growing premiums for private health insurance contracts. The growth in premiums, however, is by
statue related to the overall costs in the healthcare system. This growth in premiums is not individual-specific
and does not constitute a re-classification risk.

                                                       6
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 with a private
insurer 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.11
    This paper is related to several strands of literature. First, it is related to the broad litera-
ture 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 fo-
cused on the question of selection between public and private health insurance. Brown,
Duggan, Kuziemko, and Woolston (2014) is a recent contribution that explores the selection
of risks between the Medicare fee-for-service and the Medicare Advantage program. The
paper finds that private insurers that participate in the Medicare Advantage program select
risks even in the presence of risk adjustment mechanisms. Cabral, Geruso, and Mahoney
(2014) also study the Medicare Advantage market and find little evidence of advantageous
selection into the privatized Medicare along the margin of payment variation exploited in
the paper. Newhouse et al. (2014) study a reform of risk-adjustment in Medicare Advantage
and document that there is still some scope remaining for concerns about selection into the
program from Medicare’s public option. Fang, Keane, and Silverman (2008) document evi-
dence consistent with the presence of advantageous selection into Medigap, which is a private
Medicare add-on insurance. Duggan (2004) studied the efficiency implication of outsourcing
Medicaid to private insurers know as Medicaid managed care.
    A related strand of literature studies selection within the private markets that compete
alongside a public option. Lustig (2011) studies the interaction of adverse selection and
imperfect competition on the Medicare+C HMOs market. Kuziemko, Meckel, and Rossin-
Slater (2013) explore whether health insurance companies compete on risk in the context
of Medicaid managed care market, finding that insurers try to retain low-cost enrollees and
pass high-cost risks to competitors. Bauhoff (2012) conducts an audit study in Germany,
documenting how insurers within the statutory system screen risks. The audit study design
allows the paper to disentangle demand-driven self-selection from cream-skimming.
    Cutler, Finkelstein, and McGarry (2008) discuss the role of heterogeneous preferences in
determining the degree and direction of selection in health insurance markets. The idea is
that individual preferences, such as the degree of risk aversion, may reverse the relationship
  11
    Unfortunately, to the best of my knowledge there is no systematic data on prices and enrollment in
private option contracts that is availbale to researchers.

                                                  7
between the risk type and the selected level of coverage. Only few papers have explored the
sources of heterogeneous preferences in health insurance empirically. Geruso (2013) focuses
on the theme of heterogeneous preferences in employer-provided health insurance and finds
that older individuals enroll in more comprehensive plans than younger individuals with the
same healthcare expenditure risk. Ericson and Starc (forthcoming) study the implications of
age-related heterogeneity in the context of the Massachusetts Health Insurance Exchange.
    Finally, this paper is closely related to the literature that has specifically studied the Ger-
man health insurance system. Nuscheler and Knaus (2005) explore the issue of risk selection
among different sickness funds within the statutory system, arguing that the observed differ-
ences in risk pools are due to the consumers’ switching costs rather than cherry-picking by
plans. Hullegie and Klein (2010) use an RD design similar to the one I exploit in the current
paper and estimate that holding a private insurance policy decreases the number of doctoral
visits, doesn’t affect the number of hospital stays and improves self-assessed health. Grunow
and Nuscheler (2013) study the issue of selection patterns between the private and statutory
systems in Germany, arguing that the private insurers are unable to select good risks at
the enrollment stage, but manage to return high-risk individuals back to the public system
later. Hofmann and Browne (2013) study the German private insurance market from the
perspective of the dynamic contracts theory with one-sided commitment, outlining several
channels for selection within the private system. Bünnings and Tauchmann (2014) explore
what determines the choice of enrolling with the private insurance system.
    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 the 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    Environment
To conceptualize the key features of the empirical setting, consider a non-group health insur-
ance market where a private insurer competes with a “public option.” Suppose the defining
feature of the public option is not the degree of government ownership, but the idea that
any individual can enroll into the public system and there is no risk underwriting. The

                                                8
private insurer, in contrast, can deny enrollment and can set individual-specific premiums
after unrestricted underwriting. Within the German health insurance system, the “public
option” is the so-called Statutory Health Insurance (henceforth SHI). The SHI differs from
conventional public coverage, as there are multiple independent non-profit mutual insurance
funds operating within the system, so there there is no direct actuarial role of the govern-
ment. Similarly to a traditional “public option,” however, SHI insurers cannot deny coverage,
cannot underwrite risk, and their quality as well as prices are largely dictated by local and
federal governments. Independent for-profit insurers that are part of the Private Health
Insurance system (henceforth PHI) offer competing individual health insurance packages in
a well-functioning non-group market. These insurers are free to decide whether to enroll an
individual and enjoy substantial freedom in their decision about the extent of coverage and
premiums. In particular, private insurers are allowed to underwrite risk.
    There are three key public policies that shape this market in our empirical setting. First,
the regulator allows access to the private system only to a subset of the population with
sufficiently high income. Individuals with income below an annually set regulatory threshold
have to enroll in the SHI and do not have access to the PHI.12 Second, the regulator sets
redistributive premiums for the public option - premiums differ by individual’s income, but
not by risk. Thus, individuals that are eligible to enroll with the PHI face the highest
premiums in the SHI. Third, private insurers can fully underwrite individual risk, but they
have to offer renewable long-term contracts without re-classification risk (which, however,
does not imply that prices do not increase over the individual’s lifetime, it only implies that
prices can increase in the whole system, so that increases are not individual-specific). These
contracts underwrite the life-time risk similarly to annuity pricing.
    With these key institutional features in mind, I next discuss a stylized model of the
market forces and selection incentives in the empirical setting at hand. This description
abstracts from the intricate institutional details and terminology of the system and instead
serves to highlight the economic forces of interest.
    Consider a set of beneficiaries that can be characterized by type θi , distributed in the
population with θi ∼ F (θ). The individual’s type is a vector of characteristics that includes
expected healthcare utilization costs, risk preferences and other potential sources of hetero-
geneous preferences for different insurance systems. The latter may include preferences for
better customer service or convenience in healthcare consumption, such as preferences for a
larger physician network, shorter waiting times, and more comfortable hospital rooms. Indi-
  12
     Interestingly, because of concerns for dynamic selection, according to which individuals in the private
system may want to switch back to the public system if their healthcare costs or relative premiums increase
(if PHI premiums go up, or income goes down triggering a lower potential SHI premium), the government
restricts the SHI vs PHI system choice to a one in a lifetime decision.

                                                     9
vidual’s money-valued utility from purchasing an insurance contract from a private insurer
or in the public system is then:

                                    Uij = uij (θi ) − pij (θi )

Here, individual i gets some value uij (θi ) from enrolling into an insurance plan j ∈ {SHI, P HI}
that depends on the individual’s type θi and the type of an insurance plan. The difference in
the valuation of the private and public plans comes from heterogeneous preferences for the
quality of services, coverage benefits, and cost-sharing. The individual has to pay premium
pij that varies by the type of plan j, but also by the individual’s characteristics within a
plan type. That is, unlike in many standard consumer goods markets, the price for the
insurance contract is allowed to depend on the individual’s type, to represent the possibility
of individual-specific risk underwriting in the private system. Individuals with sufficiently
high income that are allowed to choose between the two systems, choose insurance product
j, so as to maximize utility.
    Now consider the supply side of the market. A stylized description of the health insurance
market in our empirical setting involves two firms j = P HI and j = SHI. The firms
sell health insurance products that are horizontally differentiated. While private insurers
typically offer higher quality services and shorter waiting times than the statutory system,
they also offer different cost-sharing arrangements. Therefore, the consumer ranking of the
contracts may disagree depending on individual preferences. Assume that both firms have no
administrative cost, so that their only cost are the expenses caused by consumers’ healthcare
utilization. In this setting, the cost that each firm experiences for covering consumer i
with characteristics θi depends on consumer’s health risk and the type of contract that
the consumer chose. In our institutional setting, private insurers pay higher reimbursement
rates to providers than the statutory system for the same services; consequently, for any given
amount of service, private insurers will experience higher costs. At the same time, private
insurers typically have stronger cost-sharing incentives to combat moral hazard. Thus, the
total difference in costs per year for an individual between the two systems is ambiguous:

                                    cP HI (θi ) R cSHI (θi ) ∀i

Although the comparison of costs between the two insurance providers for a given individual
is ambiguous, each firm has information about its own expected costs and can use this
information to set premiums and coverage quality strategically in an attempt to attract
more profitable enrollees. In practice, the pricing strategies and quality choices available to
insurers are constrained by regulation.

                                                10
Insurer SHI that offers the “public option” coverage has practically no latitude in the
setting of its premiums (pSHI ) or its coverage terms (qSHI ). Both are set directly by the
social planner, so that the premiums reflect the average costs of providing coverage level qSHI
in the population, adjusted for income weights ωi . That is, the premium that individual i
faces for policy SHI can be expressed as:
                                                 ˆ
                  pSHI
                   i     = ωi                                           cSHI (θ, qSHI )dθ
                                {θ|(incomeUP HI )}

Firm P HI gets to choose premiums (pP HI ) and coverage levels (qP HI ) after it has observed
the regulated price and quality of firm SHI and can respond strategically. In particular,
if firm P HI competes with firm SHI by cream-skimming, then it would set its premium
and coverage levels so as to attract the most profitable risks. Importantly, firm P HI can
fully price-discriminate on any observable consumer characteristics, which makes the strate-
gic response to the social planner’s pricing of firm SHI easier to execute if the observed
characteristics provide sufficient information about individual’s expected risk. Thus, firm
P HI will set quality and individual pricing functions so as to maximize profit conditional
on the quality and price of the SHI system:

                           (q P HI , pPi HI ) = f (θiobservable , pSHI , qSHI )

    In this paper, I empirically investigate whether the strategic price and quality choices
by the P HI insurers result in the cream-skimming of “good risks” out of the SHI system.
Note that given the differences in the pricing methods, different types of individuals may be
considered “good” or “bad” risks by the private insurers and the public system. Specifically,
for the employees above the income threshold, the SHI charges a fixed premium. Thus, the
“good risks” for the SHI are simply those individuals whose healthcare utilization expendi-
tures in this year are lower than what they pay into the system. 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, I 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 sys-
tem 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. Note,
importantly, that in the empirical application, on the margin, there will be no selection on
income - all individuals that are eligible to enroll into the private system in Germany are
paying the same maximum contributions to the statutory system. The conventional wisdom

                                                     11
is that private competition may harm the public option by cream-skimming the “net payers”
out of the public system. In Section 3, I proxy expected healthcare spending by healthcare
utilization records and test empirically whether overall the private system ends up cherry-
picking the lower utilizers from the public system. Given differences in the pricing methods
of the two systems, the direction of selection is a priori ambiguous.
    Understanding if and what kind of selection occurs at the intersection of the systems
is policy-relevant in light of the regulatory restrictions on the access to the PHI through
mandated SHI enrollment, and the political debate in Germany about the potential repeal
of the restrictions.13 Suppose that despite the theoretical ambiguity, we were to find empir-
ically that there is adverse selection from the SHI to the PHI. Then, the access restriction
policy in place would be ensuring that no Akerlof (1970) style unraveling can occur in the
SHI structure, since the majority of individuals under this insurance coverage are in the
non-selected risk pool.14 The welfare-improving case of the access restriction would be sig-
nificantly weaker, if advantageous selection were occurring. Lastly, consider the case of no
selection. Suppose we believed that the reason for selection not occurring were indeed the
pricing nature of the PHI, which induces individuals to switch to the PHI at as young age
as possible. In that case, removing high-income eligibility threshold would allow individuals
to apply for the PHI when they are even younger (assuming that most employees need some
time to get to the high-earner status). This would make selection even harder for the PHI
insurers, since they will face even less information about the applicant’s expected risks. In
this scenario, the current presence of the access restriction would again appear ceteris paribus
welfare-decreasing.15 To shed some light on the issue, Section 3 considers whether healthcare
utilization data reveals any distinct selection patterns between the insurance systems.

2.2     Data
Throughout the empirical analysis, I use data from years 2005-2009 of the German household
survey panel SOEP. The cross-sectional sample size is about 20,000 individuals. The survey
offers a collection of answers to a rich set of demographic, employment, and health-related
  13
     In 2013, the head of the Ministry of Health suggested a repeal of the income restriction to enter the pri-
vate system. http://www.spiegel.de/wirtschaft/soziales/bahr-will-private-krankenkassen-fuer-alle-oeffnen-a-
918754.html
  14
     Granted, unraveling could well occur within the SHI system, since we must not forget that SHI is actually
comprised of more than 100 companies that do have some minimal leeway in the manipulation of their risk
pool. In fact, Bauhoff (2012) finds that SHI firms try to select customers on the basis of their geographic
location. However, the argument here relates to the risk pool in the SHI system as a whole.
  15
     It is important to note that this logic assumes no substantial changes in the pricing policies or contract
space. A full welfare analysis would require predictions about the changes in the behavior of firms in response
to any regulatory access changes.

                                                      12
questions for a representative sample of the German population.16 Importantly for this paper,
the survey offers information on the status of the individual’s health insurance coverage,
including whether an individual is enrolled within the statutory or the private health instance
system, and in the case of the latter - how much is paid for it in premiums. I also utilize
information on which other types of insurance policies exist in the household (for example,
life insurance), indicators of existing chronic diagnosis, BMI, self-reported information on
the number of outpatient visits and hospital stays, as well as the self-reported level of risk
affinity in different settings.
    I construct several sub-samples of the survey respondents for the analysis in this paper.
For the central analytic sample that is used to explore the distribution of risks across the two
insurance systems, I select the group of individuals in their prime employment age 25-65 that
report to be currently employed, but not as either civil servants or self-employed individuals.
The latter two restrictions are necessary because self-employed individuals and civil servants
face a different regulatory regime for health insurance choices. I do not include individuals
that report being unemployed or out of the labor force, as they are typically not making their
own insurance choices and are insured either as dependents or through welfare programs.
In the last section of the paper, where I evaluate individual preferences for purchasing the
private insurance, I add self-employed individuals and civil servants to the sample to increase
the statistical power,17 as all these individuals typically have the option of enrolling into the
private system.
    Table 1 records the basic summary statistics for the main analytic sample of employees.
Individuals in the sample on average had about 3000 EUR in gross monthly income. 33%
of the individuals in the sample are female and are on average 43 years old. The survey
respondents report visiting a doctor in an outpatient setting about 2 times a year, while
only about 10 in a hundred have one inpatient admission. Individuals report being slightly
overweight with an average BMI of 26 (over 25 is typically classified as overweight); 34%
report being smokers. 58% have no diagnosed chronic conditions, while 17% have high blood
pressure.
    In the analytic sample, 8% report enrollment in the private health insurance system. Only
in 20% of individual-year cases, individuals are actually eligible to purchase private insurance,
as they have income high enough to be exempt from the individual mandate. Among these
20% of individual-year observations, the fraction of private insurance enrollment is much
higher than for the whole sample, at 36%.
  16
    For more detailed information on the SOEP panel please see http://panel.gsoep.de/
  17
    As described in Section 4, the regression allows for a rich set of fixed effects and interactions to allow
for unobserved differences across the employment groups.

                                                     13
3      Empirical evidence: selection and moral hazard
3.1     Descriptive evidence
I start my investigation of cream-skimming by private insurers in the German system with
several pieces of descriptive evidence. First, I look for 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. The idea is that if cream-skimming were present and PHI
disproportionately selected individuals with lower health risks, we would expect relatively
higher risks to remain in the statutory system, and this mechanism to be reflected in the
change of SHI demographics, diagnoses, and utilization around the income threshold. To
test this hypothesis, I use survey data to compare average age, fraction of young and old
enrollees, average BMI, fraction of smokers, self-reported risk attitudes, sport affinity, health
satisfaction, and array of diagnoses, as well as outpatient and inpatient utilization frequences
of SHI enrollees around the income eligibility threshold. Figures 1 and 2 illustrate these
comparisons. To detrend the development of the outcome variables from the relationship
with income, the figures plot the residuals from the regression of the outcome varianles on
income using the sample to the left of the cutoff and calculating out-of-sample residuals to
the right of the cutoff. The graphs suggest no evidence of a change in the demographic or
health-related composition of the SHI system at the income eligibility threshold. I find no
meaningful differences in individual characteristics to the left and to the right of the income
cutoff, even though to the right of the cutoff, about 25% (at the cutoff) to 50% (overall) of
individuals leave the public system. Importantly, this descriptive result on the lack of stark
differences in outpatient and inpatient utilization in SHI around the cutoff will be consistent
with the instrumental variable exercise in the following section.
    I next report the outcomes of a similar exercise that looks at differences in diagnostic
probabilities rather than demographic factors for eight diagnoses - asthma, cancer, stroke,
migraine, depression, diabetes, high blood pressure, and cardiovascular conditions. I compare
probabilities of having these diagnoses for public and private insurance enrollees.18 These
comparisons are illustrated in Figure 3. I find that individuals with private insurance are
systematically less likely to report having diabetes; however, there are no meaningful differ-
ences in incidence across the other seven diagnoses. If one believes that diagnoses such as
asthma, cancer or heart problems, cannot be meaningfully related to whether an individual
has statutory or private insurance, then these graphs would suggest that PHI companies do
  18
     I implement this comparison on the whole range of incomes rather than only at the threshold, since
self-employed individuals are exempt from the statutory system mandate and thus provide information on
the incidence of diagnoses for income levels below the income cutoff.

                                                  14
not manage to differentially select individuals that will not have chronic/expensive illnesses.
    These two pieces of evidence suggest at first sight that there is little if any difference in
risks across the two systems. It is possible, however, that private insurers cream-skim indi-
viduals that look the same in terms of their demographics and diagnoses, but are nevertheless
likely to utilize less healthcare. In the next section I explore this possibility.

3.2    Disentangling adverse selection and moral hazard
The key challenge for the empirical identification of selection between the two insurance
systems along the healthcare utilization rather than the demographic margin is the need
to disentangle the ex ante selection into the PHI system from the ex post causal effects of
PHI enrollment, or moral hazard. To address this identification challenge, I rely on a fuzzy
regression discontinuity design. Specifically, I employ the income-based eligibility threshold
below which individuals have to enroll into SHI, as an instrument for the individuals’ en-
rollment into the PHI. This allows me to identify the causal effect of the PHI enrollment on
healthcare utilization and separate it from selection.

Correlation between healthcare utilization and private insurance enrollment

I first use a linear specification to summarize the prima facie evidence on the relationship
between the type of insurance and the amount of healthcare utilization. The conditional
expectation function for a set of healthcare utilization outcomes is approximated by a linear
index:
                              E[Y outcome |X, P HI] = αP HI + βX

    The outcome variables Y outcome include the number of inpatient visits, the number of
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.
The set of control covariates includes age, gender and income. Table 2 reports the results
of this regression on the full baseline sample of employees as well as on the PHI-eligible
subsample of employees with income above the threshold. The results are similar across
these two samples. Most coefficients 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, driven primarily by the
strong negative correlation of having a private insurance and reporting fewer hospital stays
conditional on having had at least one. For this outcome variable, individuals are likely to
have on average 0.24 fewer hospital stays, while the mean number of hospital stays conditional
on having any is 1.3. The probability of having any hospital stay is not meaningfully larger

                                               15
or smaller for individuals with private insurance - the point estimate is -0.007, as compared
to the mean probability of inpatient admission in the sample of 0.07. Overall, these results
suggest that there is little if any difference in the frequency of outpatient visits for PHI-
insured individuals and there is also little if any difference in the probability of experiencing
a hospital admission. At the same time, privately insured individuals are likely to have fewer
hospital stays in a year if they had at least one.
    The association between the PHI enrollment and the utilization of healthcare, warrants
further analysis, as the observed correlations confound selection and moral hazard. Even
though the regression conditions on important determinants of healthcare consumption such
as age and gender, there may be taste characteristics of individuals that both induce the
choice of the PHI and lesser or more significant healthcare utilization. For example, if an
individual likes to go to a physician a lot for preventive care, then this individual may choose
to buy private insurance that provides better “consumer” experience in the healthcare system.
This would be an example of selection. At the same time, the PHI utilizes more aggressive
cost-sharing mechanisms than the SHI and thus we could expect less moral hazard in the
PHI system, which could lead to the individual making fewer preventive visits.
    Thus, to characterize the nature of selection between the public and the private sys-
tems, we need to disentangle the causal effects of having the PHI on the level of healthcare
utilization from the ex ante selection. In the next section I propose an empirical strategy
that allows to identify the moral hazard effect of PHI. As the OLS results in this section
can be thought of as a sum of the moral hazard and selection effect, subtracting the moral
hazard estimates of the next section from the OLS results will give me an estimate of net
cream-skimming by private insurers from the public system. It is important to emphasize
that both the causal or “moral hazard” and selection effects in this setting themselves include
a multitude of potentially countervailing forces. Specifically, the selection effect could be a
combination of any strategic cream-skimming by the private insurers as well as 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, PHI causal-
ity could also include the physician-induced demand argument, whereby physicians, whose
remuneration is substantially higher under the PHI, induce more demand from patients. A
countervailing causal force would exist if PHI-insured are treated better and thus need less
healthcare service. Lastly, if PHI patients face shorter waiting times and more convenient
service, they could be inclined to more utilization of healthcare. The available data does not
allow me to disentangle any of these forces separately; therefore, it is useful to keep in mind
that my empirical findings of selection and moral hazard will necessarily reflect the net of

                                               16
all these channels.

Fuzzy regression discontinuity analysis of moral hazard in healthcare utilization

To identify the causal effects of having a private insurance plan on healthcare utilization,
I need an instrumental variable that would be highly predictive of whether an individual
enrolls in a private insurance plan, but at the same time not related to the unobserved
characteristics that may influence both the individual’s utilization of healthcare and the
choice of the PHI conditional on observed covariates. I exploit the regulatory break in the
PHI eligibility as an instrument for private insurance enrollment. In the German health
insurance system, the access to the choice between the SHI and the PHI for employees is
restricted by the government. Employees whose income lies below the threshold are subject
to mandated enrollment into the public system. 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. If the income eligibility boundary is binding, we would expect that there is
a discontinuity in the probability of enrolling into the PHI at the income eligibility cutoff.
In other words,
                            
                            g (income ) if income ≥ cutof f
                              1       i           i
           P r(P HIi = 1) =                                  , where g1 (·) 6= g2 (·)
                            g (income ) if income < cutof f
                              2       i           i

    This setting corresponds to a fuzzy regression discontinuity design, where I use the dis-
continuity in the probability of treatment as the instrument for the treatment status.19 The
discontinuity design is fuzzy, since the crossing of the eligibility threshold only gives the
individual the choice to 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 manip-
ulate on which side of the cutoff they are to gain the treatment. To explore the plausibility
of this assumption, I plot several histograms of income distribution in the data. Figure 6
shows four histograms. Two of these represent income distribution in levels and as deviations
from income threshold in respective years. The other two zoom in to the distribution within
1000 EUR around the cutoff. Given that income is likely reported with measurement error
the lack of heaping in the histograms around the cutoff should be interpreted with care. At
the same time, since employees may report wages with rounding or since employers tend
to set rounded wages or use the insurance income cutoff as a wage benchmark, bunching
around the cutoff may not necessarily present evidence of manipulation. The histograms in
 19
      The fuzzy RD discussion here follows Angrist and Pischke (2009)

                                                    17
Figure 6 that include the full distribution of income do not have any strong visual evidence
of bunching at the cutoff. Zooming in around the cutoff, there appears to be some bunching
around zero in the histogram that uses centered income variable. The analogous histogram
that uses the levels of income rather than the deviations from the cutoff, however, suggests
that the bunching occurs at the round 4,000 EUR mark. The income thresholds for years
2005-2009 are illustrated with vertical bars and they are all close to the 4,000 EUR mark.
Looking closer around the vertical bars that represent the exact cutoff amounts, we see no
evidence that bunching occurs at those levels if they are slightly further away from 4,000
EUR. Overall, the histogram analysis of the density of the running variable does not seem
to present evidence for a systematic manipulation of the running variable.
    Further covariate balance around the cutoff does not reveal any differences along the non-
income observables between individuals below and above the cutoff. Table 3 records average
age, gender, health status, healthcare utilization, BMI, smoking propensity, disability and
risk attitudes for individual-years observed 250 EUR below and 250 EUR above the cutoff.
None of these observables have statistically significant differences in means across the two
samples. By definition of the cutoff, income is significantly different across the two groups,
with monthly income averaging at 3,819 EUR below the cutoff, and 4,032 EUR above the
cutoff. The smoothness of the non-income observables, even of those that we would expect to
be correlated with income, such as gender and age, corroborates the plausibility of assuming
that whether individuals end up slightly above or slightly below the public insurance mandate
is as good as randomly assigned.
    I continue with the estimation of the first stage regression that tests for the existence of
a strong relationship between the instrument and the endogenous decision to enroll into a
private plan. I use a linear specification that allows for a break in levels at the cutoff an 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 cutoff
levels. The outcome variable is the indicator of whether an individual enrolled into a private
insurance plan:

                     E[P HI|.] = γ1 + γ2 Above + β(Income − Cutof f )+
                               + δ(Income − Cutof f ) × Above + γX

   Figure 4 presents a graphical illustration of the first stage. The left-hand side scatter-
plot uses the baseline analytic sample of full-time employees. We see a clear jump in the
probability of enrolling with the PHI right after individuals cross the threshold of SHI man-
date. The right-hand side scatterplot also plots the probability of enrolling with the PHI

                                               18
at different income levels, but it uses an auxiliary sample of self-employed individuals only.
These individuals do not fall under the SHI mandate at any income levels and thus we would
not expect a first stage 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. The latter
evidence strengthens the conclusion that the SHI mandate is binding and crossing the income
threshold induces a substantial fraction of employees to opt out of the SHI. 20 The regression
results for the first stage are reported in Table 4. The regression results quantify the jump
in the probability of PHI enrollment to be 24 percentage points, from the baseline of essen-
tially zero. As we have seen in the graphical representation, the jump is stark and thus the
estimates are very precise, with the F-statistic of 162 in the specification with demographic
controls X that include age and gender.
    Having established the presence of the first-stage relationship, I proceed with the anal-
ysis of the reduced form specifications. Figure 5 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 no evidence of
a discontinuity or change in trend in all health utilization outcome variables at the income
threshold or at any other income levels. Moreover, unlike in the incidence of chronic diag-
noses illustrated in Figure 3, we observe very little correlation between the levels of income
and the intensity of healthcare utilization. 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, and I include age and gender as demographic
controls in X:

                      E[Y outcome |.] = α1 + α2 Above + β(Income − Cutof f )+
                                       + δ(Income − Cutof f ) × Above + γX

       Table 5 summarizes the reduced form coefficients. The estimates are imprecise, but
  20
     The results remain similar in specifications with higher order polynomials; I do not test a non-parametric
specification in a small bandwidth around the cutoff due to scarcity of observations right aroud 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. Secondly, 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.

                                                        19
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