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 along-side a public option, they may endanger the latter’s financial stability by cream-skimming good risks. This paper argues that two factors may contribute to the extentof cream-skimming: (i) degree of horizontal differentiation between public and privateoptions when preferences are heterogeneous; (ii) whether contract design encourageschoice of private insurance before information about risk is revealed. I explore therole of these factors empirically within the unique institutional setting of the Germanhealth insurance system. Using a fuzzy regression discontinuity design to disentangleadverse selection and moral hazard, I find no compelling support for extensive cream-skimming of public option by private insurers despite their ability to fully underwriterisk. A model of demand for private insurance supports the idea that heterogeneity innon-pecuniary preferences and long-term structure of private insurance contracts maybe muting cream-skimming in this setting.

JEL classification numbers: D12, I13, I18, G22, H44Keywords: 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 2012. I am indebted to AmyFinkelstein, Stephen Ryan, and two anonymous referees for their comments and suggestions. I also thankthe participants at the MIT Public Finance and Industrial Organization lunches, 15th IZA European SummerSchool 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.

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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 coun-

tervailing 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 long-

term annuity-style contracts.

Several key institutional features characterize the German market. First, private and

1See, for example, Halpin and Harbage (2010) and Washington Post for the discussion of the public optionas part of ACA Health Insurance Exchanges.

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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 under-

write 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 beconsidered 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.4In 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 expensesout of pocket and do not file claims are refunded a substantial fraction of annual premiums.

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constrained individuals. Moreover, anecdotally, private insurance is viewed as a “luxury”

good that provides better service, although does not necessarily lead to better medical out-

comes, 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 lit-

erature 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 cream-

skimming 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 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. For example,

Fang, Keane, and Silverman (2008) documented evidence consistent with the presence of ad-

vantageous selection into private Medicare add-on insurance, while Duggan (2004) studied

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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 empiri-

cal 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 hetero-

geneous 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 Bunnings 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

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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

5Statistisches Bundesamt, 2013 data

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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

6The income threshold in 2015 was EUR 54,900.7Civil 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 directpayments and have to cover 100% of the SHI premium out of pocket. The combinations of these policiesmake PHI coverage of the residual expenditures especially economically attractive for this group.

8For 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 anemployee is enrolled with the PHI, employers pay half of the PHI premiums up to a maximum contributionthat is equal to their maximum possible contribution in the SHI system.

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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 house-

hold survey panel SOEP.10 The raw data records information on 28,693 individuals. The

9Alternatively, one could define “good risks” as those with lifetime spending below lifetime contributions.10These 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 guidingcompetition between public and private insurers; hence I stop the analysis at 2009, assuming that 2009survey wave still reflects pre-reform decision-making. Robustness checks without year 2009 give very similarresults.

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survey offers a collection of answers to a rich set of demographic, employment, and health-

related 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 in-

stance 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 re-

strict the sample to include individuals aged 25-65. 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 self-

employed, 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

11For more detailed information on the statistical properties of SOEP panel sample please seehttp://panel.gsoep.de/

12The holiday allowances that I include are “Weihnachtsgeld” and “Urlaubsgeld.”

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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

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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:

E[Y outcomeit |.] = β0 + β1PHIit + β2Incomeit + β3Xit

The outcome variable Y outcome 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. PHI is an indicator variable

that is equal to one if individual i has private insurance in year t. The set of control covariates

Xit 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

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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 -0.008, 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. 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

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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 ma-

nipulate 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 his-

togram 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 non-

income observables between individuals below and above the cutoff. Table A1 in the Ap-

pendix 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

13Intuitively, the bunching around round numbers and hence around round thresholds is much starkerwhen I only consider baseline income, without 13th and 14th month payments and holiday allowances. Thissuggests that baseline salaries are very likely to be set at round numbers - specifically, 48,000 EUR a yearappears to be a common baseline salary in the sample close to the cutoff levels.

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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 school-

ing. 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, con-

trolling 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[PHIit|.] = γ1 + γ2Aboveit + γ3(Incomeit − Cutofft)+

+ γ4(Income− Cutofft)× Aboveit + γ5Xit

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

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 re-

duced 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 Xit:15

E[Y outcomeit |.] = α1 + α2Aboveit + α3(Incomeit − Cutofft)+

+ α4(Incomeit − Cutofft)× Aboveit + α5Xit

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

14The results remain similar in specifications with higher order polynomials; I do not test a non-parametricspecification with a small bandwidth around the cutoff due to scarcity of observations right around thethreshold. Moreover, considering the potential measurement error in income, local results right around thecutoff may be misleading, since the observations around the cutoff may have been misclassified. Note thatthe graphical evidence suggests that there are a number of observations very close to the cutoff that have afairly 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 misclassifythe individual’s eligibility. In addition, the German health insurance regulation allows individuals that optedout to the PHI at some point and then their income dropped below the current eligibility threshold, to signa waiver for the re-entry of the SHI.

15Appendix tables report specifications with richer controls. These reduce the sample size, since not allcontrol variables are available for all individuals. The conclusions from these alternative specifications remainthe same as in the baseline.

15

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 0.151 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 -4.005 with the

confidence interval of [-6.806, -1.204] as reported in Column (2). Using the point estimates,

we arrive at the implied extent of selection of −0.151 − (−4.005) = 3.854 or a third of

16

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 −0.858− (−1.204) = 0.346

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 −0.0199 with a confidence interval of [−0.0386, 0.00124]. The moral

hazard effect of having private insurance is reported in Column (2) as being 0.0176 more

visits [−0.0668, 0.102]. The 95% confidence interval for the moral hazard estimate is between

−0.0668 and 0.102. 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 −0.0199−0.0176 ≈ −0.04 at the point estimates. This suggests adverse

selection of individuals with expected 0.04 fewer hospital admissions into private insurance

off the mean of 0.095 admissions per year with a standard deviation of 0.419. 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

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 ei-

ther 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 con-

text 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:

uij = −αipij + βiφj + εij (1)

where pij is the premium that an individual i pays for choosing insurance option j, while

φj are the characteristics of the insurance choice. εij is a Type 1 extreme value that ac-

counts 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 termφj reduces to a insurance-system specific constant that

captures the average valuation for each type of insurance. To incorporate preference hetero-

16Baicker et al., 2013 discuss the ideas for the potential of such “basic” versus more generous coverage inthe context of Medicare, as way to efficiently sort beneficiaries according to their willingness to pay for moreconveneince or less cost-effective treatments.

18

geneity into the model, I let the coefficient on premium αi that measures the marginal utility

of income depend on whether individuals are employees or self-employed.17 Additionally, the

coefficient on insurance system choice βi depends on individual characteristics as follows:

βi = β0 + β1Xi

Xi are especially interesting in our setting, as they allow testing whether there are ob-

servable characteristics - for example, political or risk preferences - that are plausibly not

directly related to demand for healthcare, but increase the probability of choosing private

health insurance and thus capture some underlying preferences for this type of coverage. Xi

also includes demographic factors - for example, age, gender, sport affinity, smoking, BMI -

that we would expect to be directly associated with health outcomes.18

The key ingredient for the individual’s choice between the statutory and the private

insurance systems is the relative price that the individual faces on both markets. In the data,

I do not observe SHI premiums and can only observe PHI premiums for those individuals,

who chose to enroll into the PHI. Thus, before proceeding with the estimation of preferences,

I simulate public and private insurance premiums for all individuals that were eligible to

choose PHI. First, I calculate SHI-premiums for both the SHI and the PHI-insured using

the regulatory income percentages that determine premiums as a function of income. In the

next step, I use prices reported by individuals that chose private insurance to run a hedonic

pricing regression. Private health insurance underwriting is legally allowed to use information

on individual’s age, gender, and health. The real premium calculations are complex and

reflect the individual’s lifetime expected spending spread equally over the expected lifespan.

To construct hypothetical private insurance prices for publicly insured individuals, I use a

linear specification to approximate the conditional expectation function of premiums that

individuals face as a function of observable demographic factors and health conditions:

E[P PHIit |.] = α ·XDemographics

it + β ·XChronicConditionsit + γt

where the P PHI is the reported monthly private insurance premium in EUR paid by

individual i in year t, XDemographicsit is a set of demographic variables that in the richest spec-

17I have tried richer specifications of the model that allow the marginal utility of income to vary acrossmultiple demographic factors; they do not uncover substantial additional heterogeneity.

18Given the limitations of the data, the model simplifies the choice problem to a static decision. In reality,individuals face a dynamic decision, since in most cases they can only opt out of the SHI once, without theoption of returning to the SHI coverage later. See the discussion of the incentives stemming from long-termscontracts below.

19

ification include age, gender, self-employment status, income, number of children, whether

or not the individual is single, and whether or not he or she had any East German schooling.

XChronicConditionsit is a set of diagnosis indicators for chronic conditions and in the richest

specification includes indicators for diabetes, asthma, cardiac diseases, stroke, migrane, high

blood pressure, depression, obesity, and disability.

Table A3 in the Appendix reports the key coefficients for several specifications of the

pricing regression. The results imply that a 40-year old male that is a full-time employee

would pay about 400 EUR a month for his private health insurance. Reformulating the

regression in percentage terms by doing a log-transformation of the price variable, we get

that each additional year of life increases premiums by about 2%. Pricing is also sensitive

to the individual’s gender. It appears that women have both a different level and a different

age slope in the PHI pricing. Overall, the linear approximation of the PHI pricing accounts

for a substantial amount of variation in prices, with R2 equal to 0.3 in the specifications

with diagnosis-specific controls. Using this approximation of average PHI prices, I calculate

counterfactual PHI premiums for PHI-eligible individuals that chose SHI in 2004-2009. This

counterfactual calculation is based on a set of non-trivial assumptions. One of them is an

assumption that conditional on having the same observable characteristics, individuals who

didn’t switch to PHI would have faced the same prices as the individuals that did switch.

With the estimates of pij in hand, I proceed to the estimation of the choice model.

The estimation is done on the individuals in the baseline sample that are eligible for PHI

enrollment. That is, I consider only employees with income above the income threshold

and the self-employed. Table 4 reports the marginal effect estimates of the choice model.19 I

report several specifications that vary on the number of explanatory demographic and health-

related variables that are included in the utility function. The richest specification includes

a full set of demographics, as well as indicators for chronic conditions. All specifications

suggest that conditional on prices, there is significant heterogeneity in preferences for the

private insurance system. For example, older, self-employed, higher-income individuals are

more likely to get private health insurance conditional on prices. Since private insurance

covers family members not in the labor force at extra premiums (as opposed to“free”coverage

under public insurance), it is not surprising that single individuals, those with fewer children,

and those whose spouse works full-time are more likely to enroll into PHI.

19The non-linear logit transformation of the choice model in theory makes the inclusion of the simulatedprice variable problematic. Hence, I repeat the same specifications using a linear probability model that isrobust to the inclusion of the simulated variable as a regressor. The results are very close between the twomodels.

20

At the same time, there appears to be no specific tastes for private insurance based on

gender, BMI and risk aversion - individual characteristics that we would expect to be closely

linked to healthcare spending levels. Individuals with disability are less likely to enroll into

the PHI - this may be a reflection of tastes (e.g. aversion against deductibles) as well as

rejections by the PHI companies. Having diabetes is associated with a lower probability of

choosing the PHI, while other chronic conditions do not appear to be correlated with the

PHI choice.

Interesting taste heterogeneity is captured by the indicators for whether individuals em-

ploy household help. Supposing that household help variable may capture preferences for

convenience and high opportunity cost of time, the large magnitude and statistical signifi-

cance of this coefficient would suggest the importance of purely non-pecuniary and non-risk

related preferences in the choice of insurance plans.

Overall, I conclude that the data provides strong support for the presence of hetero-

geneous preferences for private insurance that in the German institutional context offers

shorter appointment wait times, better hospital rooms and more convenience in outpatient

visits on the one hand, and higher cost-sharing on the other. This heterogeneity in taste does

not appear to be directly related to the healthcare utilization margin or even individual’s

reported risk attitudes. The results of the choice model are thus consistent with the findings

of relatively little risk selection in the previous Section. They are also consistent with the

hypothesis that preferences other than expected healthcare utilization may guide individ-

ual’s decision for health insurance purchases. Moreover, the important role of seemingly

non-pecuniary preferences suggests that there is a lot of scope for “consumption” aspects

of healthcare utilization that may be valuable for individuals, but not emphasized in the

literature that usually treats insurance contracts as purely financial products.

Long-term contracts The second factor that could influence the extent of selection be-

tween the PHI and the SHI is the unique incentives scheme of the long-term contracts that

characterize the PHI. Given the data available, this factor is harder to capture empirically,

but it is still useful to consider it conceptually. The idea of risk selection or cream-skimming

assumes that insurers either have direct information on individual risk or can set up screen-

ing contracts that would indirectly sort high and low risk individuals. The latter type of

screening mechanisms in turn assume that individuals have information about whether they

are high or low risks.

When health insurance contracts, however, are set up as annuities or long-term contracts,

21

they have a built-in incentive for the individuals to try to enroll into these contracts as early

as possible in their lifetime. Since most of the healthcare spending occurs closer to retirement

age and individuals are paying for the PDV of life-long expenditures, it is important to enroll

into such contracts as early as possible, so as to have sufficient time to accumulate savings

that then cover expenses at later ages. While not strictly true, in some sense the PHI con-

tracts let an individual pool risk with her- or himself overtime. This strong incentive of early

enrollment may lead many individuals to choose insurance “behind the veil of ignorance”, or

in other words before a lot of information about their future health risk is revealed either to

them or to the insurer.

The level of informational uncertainty at the enrollment decision stage may be high

enough to significantly reduce the opportunities for meaningful cream-skimming or self-

selection. To see this, suppose all individuals were joining a private insurance plan right

at birth. At this point, assuming that the insurer cannot conduct genetic testing or collect

health information from parents, the insurer has very little information about individual-

specific risks for the vast majority of individuals. The insurer would then base the pricing

based on birth weight and gender, implying that most individuals will face similar premiums

that essentially correspond to the population averages of healthcare spending for their gender.

Several pieces of empirical evidence suggest that the incentives built into long-term PHI

contracts may be an important factor for selection dynamics. First, insurers charge sub-

stantially higher prices for older individuals, since even though the annual spending of a 50

and 55 year old may not be different, the 55 year old spreads the payment for the lifetime

expected spending over fewer years. Second, when conditioning on health status, but not

on premiums, younger individuals have a stronger preference for private insurance. In other

words, the probability of choosing to enroll in the private system falls with each additional

year of life. Once we condition on premiums, age does not have additional predictive power

for enrollment probability, suggesting that younger individuals face better prices and thus

have higher utility from private insurance conditional on the same observed health condi-

tions. Third, there exists a well-developed market for option contracts for private insurance

coverage. The idea is that individuals that are not yet eligible to opt out of the statutory

system, but expect to have high enough income to be eligible in the future, buy an option

for enrollment from a private insurer. This option “freezes” the health risk and thus the

underwriting basis for the individual at the time of option purchase. The fact that there

exists demand for freezing individual’s risk as early as possible, is consistent with the idea

that individuals would like to enroll in the PHI before their health risk is revealed.

22

In summary, if PHI observes all its applicants at a time when few health signals have

been revealed, it may be hard for the insurer to predict how healthcare utilization of a

specific individual will relate to the average in the plan or in the population. That is, in

this institutional setting the level of informational uncertainty may be so high that it may

prevent the insurers from successfully executing meaningful selection of good risks that we

would expect given that these insurers can fully underwrite applicants.

5 Conclusion

Conventional wisdom suggests that private health insurers operating in parallel to a public

option may endanger the latter’s financial stability by cream-skimming good risks. Despite

this concern, co-existing private-public arrangements are becoming ever more common in

health and other social insurance systems, raising the question of which policies and incentive

structures may be able to mute the cream-skimming dynamics.

In this paper I empirically explore this issue in the institutional environment of Germany;

several unique institutional features make the German market a fruitful laboratory for study-

ing the interaction of private and public health insurance. Germany has a well-developed

private non-group individual health insurance market in parallel to a statutory system. The

statutory system has many elements of a traditionally public option - public insurers are not

allowed to reject enrollment or to underwrite risks. Insurers in the private system, on the

other hand, can do both within annuity-like long-term insurance contracts.

I find no convincing evidence of extensive cream-skimming of better risks by private

insurers. To explore this puzzle, I first test whether demand for private insurance is affected

by preferences that are plausibly unrelated to health risk and could be muting the extent

of selection. I find empirical support for the presence of such “heterogeneous preferences.”

Private insurers in the German system offer more convenience and “luxury” in healthcare

utilization, including slightly broader provider networks, shorter waiting times, and access

to “star” physicians. Accordingly, I find that individuals that appear to exhibit preferences

for convenience and higher value of time, conditional on income, are more likely to enroll in

the private system.

These results suggests that if individual demand for, e.g., broader networks or shorter

wait times is related to the value of time rather than health risk directly, such preferences

may significantly mute the scope for risk selection in the system. These findings are in

general consistent with the idea that consumer choice in insurance may be efficient: there

23

is scope for horizontal rather than purely vertical or risk-protective differentiation of health

insurance contracts that is valuable for individuals.

In addition, I speculate that the long-term structure of private health insurance contracts

in this empirical setting may have an additional dampening effect on the degree of selection.

Instead of offering annual community-rated prices, private insurers offer an annuity-style

contract to each individual. Individual risk profiles are measured at the time of enrollment

and reclassification of risks is prohibited by the regulator. This type of insurance contracting

creates an incentive to enroll in insurance as early as possible or“behind the veil of ignorance,”

when little information about risk has been revealed and which hence leads to little scope

for meaningful risk-sorting.

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Figure 1: Income and characteristics of “public option” enrollees40

4550

55Y

ears

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Age

2526

2728

BM

I

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

BMI

0.0

5.1

.15

.2F

ract

ion

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Disabled

0.1

.2.3

.4.5

Fra

ctio

n

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Smoker

22.

12.

22.

32.

42.

5In

dex

1-3

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Worry about health

0.2

.4.6

Fra

ctio

n

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Health-related risk aversion

Baseline sample, employees only. The panels plot the relationship between monthly income (X-

axis, in deviations from the SHI mandate threshold in 100 EUR bins) and a set of six demographic

characteristics for individuals enrolled in the SHI system (Y-axis, calculated as averages within

each income bin). The vertical line marks income level at the mandate threshold. The fitted lines

are kernel-weighted local polynomials; the polynomials are fitted separately above and below the

threshold and are not weighted by bin size.

27

Figure 2: Empirical distribution of the running variable

0.0

1.0

2.0

3.0

4.0

5F

ract

ion

-1000 -500 0 500 1000Income relative to threshold

0.0

5.1

.15

Fra

ctio

n

3850 3900 3950 4000 4050 4100Income

Baseline sample, employees only. The top panel presents the distribution of deviations of themonthly income from the insurance mandate income cutoff. The plot is zoomed in to 1,000EUR around the cutoff. The bottom panel illustrates the distribution of monthly incomelevels close to mandate cutoffs in different years, which are marked with vertical lines.

28

Figure 3: First stage: relationship between insurance enrollment and income

0.2

.4.6

.8P

roba

bilit

y of

hav

ing

PH

I

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Employees

0.2

.4.6

.81

Pro

babi

lity

of h

avin

g P

HI

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Self-employed

Baseline sample. The top panel shows the probability of PHI-enrollment by income bins of 100

EUR for the sub-sample of employees. The vertical reference line marks the insurance mandate

threshold. The bottom panel shows PHI-enrollment probability by income bins of 100 EUR for the

sub-sample of self-employed individuals, who do not face a public option mandate at any income

level.

29

Fig

ure

4:R

educe

dfo

rm:

rela

tion

ship

bet

wee

nhea

lthca

reuti

liza

tion

and

inco

me

4681012Number of outpatient visits/year

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Out

patie

nt, n

umbe

r

.4.5.6.7.8Probability of an outpatient visit/year

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Out

patie

nt, p

roba

bilit

y

5101520Conditional number of outpatient visits/year

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Out

patie

nt, n

umbe

r co

nditi

onal

on

havi

ng h

ad a

ny

0.1.2.3Number of inpatient stays

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Inpa

tient

, num

ber

0.05.1.15.2Probability of inpatient stays

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Inpa

tient

, pro

babi

lity

11.522.5Conditional number of inpatient stays

-300

0--1

000-

1000

-30

00-

5000

-In

com

e re

lativ

e to

thre

shol

d

Inpa

tient

, num

ber

cond

ition

al o

n ha

ving

had

any

Bas

elin

esa

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le,

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rict

edto

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red

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nd

the

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ibilit

yth

resh

old

(ver

tica

lre

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nce

line)

and

div

ided

into

equally

spac

edbin

sof

100

EU

R.

For

each

bin

,th

eav

erag

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hea

lthca

reu

tiliza

tion

mea

sure

isp

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ed.

Outc

ome

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able

s-

top

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from

left

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ght:

nu

mb

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atie

nt

vis

its,

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bab

ilit

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ast

one

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nu

mb

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atie

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ional

on

hav

ing

had

atle

ast

one;

bot

tom

row

:sa

me

for

inpat

ient

adm

issi

ons.

30

Table 1: Summary statistics

Mean Std. Dev. Mean Std. Dev.

(1) (2) (3) (4)

Individual-years

No. unique individuals

Demographics

Age 43.43 9.82 42.95 9.83

Female (1/0) 0.32 0.47 0.33 0.47

Gross monthly income, EUR 3,339 2,432 3,155 1,921

Self-employed (1/0) 0.14 0.34 0 0

Has PHI (1/0) 0.14 0.35 0.08 0.28

Work time per week in hours 43.39 11.06 43.17 8.92

Years of education 12.75 2.71 12.6 2.65

Had GDR schooling (1/0) 0.25 0.43 0.25 0.43

Political party: SPD (1/0) 0.14 0.35 0.15 0.36

Political party: CDU (1/0) 0.18 0.38 0.16 0.37

Political party: FDP (1/0) 0.03 0.18 0.02 0.16

Has life insurance (1/0) 0.66 0.47 0.65 0.47

Household characteristics

Single or not married (1/0) 0.38 0.48 0.38 0.49

Spouse works full-time (1/0) 0.43 0.5 0.43 0.49

Number of children 0.53 0.9 0.51 0.88

House size in sqm 110.38 46.48 107.03 42.8

Employes household help (1/0) 0.09 0.28 0.07 0.25

Health-related characteristics

BMI 26.01 4.07 26.02 4.07

Would accept health risk (1/0) 0.27 0.45 0.27 0.44

No. outpatient visits annual 7.03 11.9 7.22 11.83

No. inpatient stays annual 0.09 0.42 0.09 0.42

Smoker (1/0) 0.33 0.47 0.33 0.47

Reports disability (1/0) 0.06 0.23 0.06 0.24

Asthma (1/0) 0.04 0.19 0.04 0.2

Cancer (1/0) 0.02 0.14 0.02 0.14

Cardiac (1/0) 0.04 0.19 0.04 0.19

Dementia (1/0) 0 0.01 0 0

Depression (1/0) 0.04 0.19 0.04 0.19

Diabetes (1/0) 0.04 0.19 0.04 0.19

High Blood Pressure (1/0) 0.17 0.38 0.18 0.38

Migraine (1/0) 0.04 0.2 0.04 0.2

Stroke (1/0) 0 0.07 0 0.07

10,725 9,454

Baseline sample Employees only

37,554 32,448

31

Table 2: Relationship between healthcare utilization and insurance type

OLS 2SLS Reduced Form Mean(s.d.)

Coefficient on: Coefficient on: Coefficient on: Outcome

Indicator for PHI Indicator for PHI Indicator for Above Cutoff Variable

(1) (2) (3) (4) (5)

Number Outpatient -0.151 -4.005** -0.674* 32,448 7.2 (11.8)

[-0.858, 0.556] [-6.806, -1.204] [-1.232, -0.116]

Probability Outpatient -0.0254 -0.0954 -0.00442 32,448 0.6 (0.5)

[-0.0538, 0.00292] [-0.214, 0.0236] [-0.0281, 0.0192]

Conditional Num. Out. 0.253 -4.906* -0.976* 19,820 11.8 (13.2)

[-0.714, 1.221] [-8.932, -0.880] [-1.725, -0.226]

Number Inpatient -0.0199* 0.0176 0.00275 32,395 0.09 (0.42)

[-0.0386, 0.00124] [-0.0668, 0.102] [-0.0150, 0.0205]

Probability Inpatient -0.00818 0.00520 0.000829 32,395 0.07 (0.26)

[-0.0204, 0.00401] [-0.0504, 0.0608] [-0.0107, 0.0123]

Conditional Num. Inpt. -0.141 0.187 0.0241 2,384 1.29 (0.91)

[-0.316, 0.0337] [-0.585, 0.959] [-0.119, 0.168]

The table reports point estimates and 95% Confidence Intervals of the coefficients on an indicator for

having private insurance (columns (1) and (2)) or for having income that crosses the mandate threshold

(column 3). The OLS, 2SLS and Reduced Form models are specified in the text. The estimation sample is

the baseline sample as described in the main text, excluding the self-employed. The specifications include,

but do not report, controls for income trend, age, gender, and year fixed effects.

Standard errors are clustered at the individual level.* p<0.05; **p<0.01; ***p<0.001

NOutcome variable

32

Table 3: First stage relationship between insurance type and income

Employees Employees Self-employed placebo Self-employed placebo

(1) (2) (3) (4)

Indicator for income above cutoff 0.216*** 0.216*** 0.0233 0.0386

(0.0135) (0.0135) (0.0337) (0.0331)

Cutoff deviation in '000 0.0145*** 0.0163*** 0.0956*** 0.0924***

(0.00180) (0.00191) (0.0145) (0.0141)

Cutoff deviation x above cutoff in '000 0.0244*** 0.0233*** -0.0859*** -0.0816***

(0.00541) (0.00547) (0.0150) (0.0146)

Age and gender controls No Yes No Yes

Year Fixed Effects No Yes No Yes

N 32448 32448 5106 5106

R-squared 0.250 0.251 0.0704 0.0931

Estimation sample is the baseline sample as described in the main text.

Standard errors clustered at the individual level.* p<0.05; **p<0.01; ***p<0.001

Dependent Variable: Indicator for Having PHI

33

Table 4: Preferences for private health insurance

(1) (2) (3) (4) (5)

Incremental PHI premium -0.00402*** -0.00658*** -0.00663*** -0.00653*** -0.00647***

(0.000236) (0.000670) (0.000696) (0.000783) (0.000824)

Age 0.00352 0.00383 0.00847 0.00894

(0.00654) (0.00685) (0.00769) (0.00823)

Female (1/0) -0.236 -0.246 -0.307 -0.314

(0.136) (0.141) (0.161) (0.171)

log (Income) 0.640*** 0.492*** 0.491*** 0.477***

(0.106) (0.109) (0.125) (0.132)

Single (1/0) 0.436*** 0.443*** 0.405** 0.433**

(0.125) (0.130) (0.148) (0.153)

Spouse full-time employed (1/0) 0.610*** 0.583*** 0.615*** 0.598***

(0.0960) (0.0994) (0.110) (0.115)

Number of children -0.0960* -0.0976* -0.0953 -0.0839

(0.0415) (0.0440) (0.0503) (0.0529)

Years of education 0.0822*** 0.0697*** 0.0629** 0.0613**

(0.0170) (0.0177) (0.0202) (0.0213)

Employ houshold help 0.612*** 0.728*** 0.751***

(0.123) (0.140) (0.146)

Political preference: SPD -0.413** -0.375** -0.325*

(0.131) (0.145) (0.154)

Political preference: FDP 0.619*** 0.671*** 0.714***

(0.177) (0.200) (0.207)

Year fixed effects Yes Yes Yes Yes Yes

Self-employment level shift No Yes Yes Yes Yes

Demographic characteristics^ No Some Yes Yes Yes

Health-related characteristics^^ No No No Yes Yes

Chronic conditions fixed effects No No No No Yes

N 11153 8835 8346 7108 6513

Estimation sample is the baseline sample as described in the main text, restricted to individuals that were eligible

to purchase PHI. The coefficients report parameters of the utility function and not marginal effects.

^Demographic characteristics included in the regressions, but not reported include: indicator for East German

schooling, having life insurance policy, CDU political preference, house size, weekly work hours

^^Health-related characteristics included in the regressions, but not reported include: BMI, smoking status,

attitude to high health risk, disability* p<0.05; **p<0.01; ***p<0.001

Dependent Variable: Indicator for having PHI

34

APPENDIX

“Risk Selection and Heterogeneous Preferences in HealthInsurance Markets with a Public Option”

Maria Polyakova

June 2016

35

Figure A1: Income and probability of chronic diagnoses among “public option” enrollees0

.05

.1.1

5F

ract

ion

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Asthma

0.1

.2.3

Fra

ctio

n

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Cancer

0.0

5.1

.15

.2F

ract

ion

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Cardiac

0.0

5.1

.15

.2.2

5F

ract

ion

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Diabetes

.1.2

.3.4

.5F

ract

ion

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

High Blood Pressure

0.0

2.0

4.0

6.0

8.1

Fra

ctio

n

-3000- -1000- 1000- 3000- 5000-Income relative to threshold

Migraine

Baseline sample, employees only. The panels plot the relationship between monthly income (X-

axis, in deviations from the SHI mandate threshold in 100 EUR bins) and prevalence of six chronic

diagnoses for individuals enrolled in the SHI system (Y-axis, calculated as probability within each

income bin). The vertical line marks income level at the mandate threshold. The fitted lines

are kernel-weighted local polynomials; the polynomials are fitted separately above and below the

threshold and are not weighted by bin size.

36

Table A1: Covariate levels around income threshold

below above p-value below above p-value

(1) (2) (3) (4) (5) (6)

Demographics

Age 44.36 44.12 0.54 45.12 43.22 0.12

Female (1/0) 0.26 0.26 0.74 0.23 0.23 0.91

Gross monthly income, EUR 3,811 4,029 0.00 3,918 3,906 0.52

Work time per week in hours 43.04 43.34 0.41 44.34 44.31 0.98

Years of education 13.1 13.6 0.00 13.3 13.9 0.09

Had GDR schooling (1/0) 0.18 0.19 0.72 0.15 0.21 0.30

Political party: SPD (1/0) 0.18 0.22 0.02 0.18 0.22 0.44

Political party: CDU (1/0) 0.21 0.18 0.10 0.26 0.16 0.10

Political party: FDP (1/0) 0.02 0.04 0.01 0.01 0.05 0.07

Has life insurance (1/0) 0.68 0.71 0.08 0.63 0.77 0.04

Household characteristics

Single or not married (1/0) 0.31 0.33 0.22 0.24 0.36 0.06

Spouse works full-time (1/0) 0.36 0.39 0.17 0.36 0.33 0.72

Number of children 0.56 0.57 0.97 0.64 0.47 0.17

House size in sqm 112.4 111.5 0.63 112.4 111.5 0.87

Employes household help (1/0) 0.06 0.08 0.08 0.04 0.08 0.31

Health-related characteristics

BMI 26.3 25.9 0.03 26.6 25.0 0.03

Would accept health risk (1/0) 0.26 0.29 0.15 0.29 0.24 0.46

Smoker (1/0) 0.32 0.28 0.09 0.35 0.3 0.49

Reports disability (1/0) 0.07 0.06 0.59 0.10 0.02 0.04

Asthma (1/0) 0.05 0.05 0.84 0.06 0.03 0.31

Cancer (1/0) 0.01 0.02 0.34 0.01 0.00 0.35

Cardiac (1/0) 0.05 0.04 0.41 0.06 0.14 0.13

Depression (1/0) 0.03 0.04 0.31 0.04 0.04 0.98

Diabetes (1/0) 0.05 0.03 0.05 0.09 0.00 0.01

High Blood Pressure (1/0) 0.19 0.20 0.81 0.24 0.16 0.18

Migraine (1/0) 0.04 0.04 0.82 0.04 0.06 0.66

Stroke (1/0) 0.002 0.005 0.24 0.00 0.00 -

Income within 25 EUR of cutoff

Baseline Sample, Employees Only

Income within 250 EUR of cutoff

37

Tab

leA

2:Sp

ecifi

cati

onch

ecks

for

OL

San

d2S

LS

rela

tion

ship

s

Ou

tco

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vari

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(2)

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(4)

(5)

(6)

(7)

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(9)

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)(1

1)

(12

)(1

3)

(14

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OLS

2

SLS

OLS

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SLS

OLS

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OLS

2

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OLS

2

SLS

OLS

2

SLS

OLS

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SLS

Nu

mb

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utp

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nt

-0.1

38

-3.1

63

*-0

.15

4-3

.90

3**

-0.1

51

-4.0

05

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4-4

.23

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0.3

90

-2.7

60

-0.3

54

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79

0.0

92

4-3

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1

(0.3

64

)(1

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7)

(0.3

60

)(1

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(0.3

61

)(1

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(0.3

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)(1

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6)

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(0.0

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ical

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ties

, siz

e o

f h

om

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rk h

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rs.

^^ S

pec

ific

atio

ns

wit

h "

som

e" c

on

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ls in

clu

de

year

s o

f ed

uca

tio

n, p

olit

ical

par

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, lif

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nce

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.

* p

<0.0

5;

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Bas

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ith

qu

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No

Co

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Bas

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fer

aro

un

d R

D t

hre

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ld

All

no

n-h

ealt

h

con

tro

ls

38

Table A3: Private health insurance pricing

PHI premium PHI premium PHI premium PHI premium Log PHI premium

(1) (2) (3) (4) (5)

Age 9.429*** 9.414*** 7.670*** 7.308*** 0.0191***

(0.584) (0.554) (0.531) (0.607) (0.00157)

Female (1/0) 101.5* 94.83* 84.46* 121.1* 0.373**

(45.97) (45.40) (42.35) (48.35) (0.130)

Self-employment (1/0) -79.44*** -55.08*** -60.26*** -0.139***

(9.026) (9.065) (10.10) (0.0245)

Age and gender controls Yes Yes Yes Yes Yes

Year fixed effects Yes Yes Yes Yes Yes

Self-employment level shift No Yes Yes Yes Yes

Demographic controls^ No No Yes Yes Yes

Chronic conditions fixed effects No No No Yes Yes

N 4861 4861 4861 3921 3921

R-squared 0.171 0.211 0.298 0.310 0.301

Y mean 417.5 417.5 417.5 416.8 5.925

Y std. dev. 197.9 197.9 197.9 193.8 0.480

Estimation sample is the baseline sample as described in the main text.

Standard errors clustered at the individual level.

^Demographic controls include number of children, log of monthly income, single status, East Germanschooling

* p<0.05; **p<0.01; ***p<0.001

Dependent Variable

39