Privatizing Disability Insurance
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Seibold, Arthur; Seitz, Sebastian; Siegloch, Sebastian Article — Published Version Privatizing Disability Insurance Econometrica Provided in Cooperation with: John Wiley & Sons Suggested Citation: Seibold, Arthur; Seitz, Sebastian; Siegloch, Sebastian (2025) : Privatizing Disability Insurance, Econometrica, ISSN 1468-0262, Wiley, Hoboken, NJ, Vol. 93, Iss. 5, pp. 1697-1737, https://doi.org/10.3982/ECTA22113 This Version is available at: https://hdl.handle.net/10419/329806 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/
Econometrica, Vol. 93, No. 5 (September, 2025), 1697–1737 PRIVATIZING DISABILITY INSURANCE ARTHUR SEIBOLD Department of Economics, Ludwig-Maximilians University Munich and CEPR SEBASTIAN SEITZ Department of Economics, University of Manchester and ZEW SEBASTIAN SIEGLOCH Department of Economics, University of Cologne, CEPR, and ZEW Public disability insurance (DI) programs in many countries face growing fiscal pressures, prompting efforts to reduce spending. In this paper, we investigate the welfare effects of expanding the role of private insurance markets in the face of public DI cuts. We exploit a reform that abolished one part of German public DI and use unique data from a large insurer. We document modest crowding-out effects of the reform, such that private DI take-up remains incomplete. We find no adverse selection in the private DI market. Instead, private DI tends to attract individuals with high income, high education, and low disability risk. Using a revealed preference approach, we estimate individual insurance valuations. Our welfare analysis finds that partial DI provision via the voluntary private market can improve welfare. However, distributional concerns may justify a full public DI mandate. KEYWORDS: Disability insurance, social insurance, privatization, risk-based selection. 1. INTRODUCTION ACROSS THE DEVELOPED WORLD, the number of individuals receiving public disability insurance (DI) benefits has risen rapidly over the past decades. This has made DI one of the largest social insurance programs in OECD countries (OECD (2024)). Due to the increasing fiscal burden, governments face pressure to enact reforms reducing the generosity of public DI programs. While such reforms help improve fiscal sustainability, they naturally come at the cost of providing less insurance to individuals at risk of disability. As a consequence, some economists and policymakers have proposed a larger role of private DI (e.g., GAO (2018)). Sizable private DI markets already exist in many countries, including the U.S. and Germany. However, private DI provision faces several potential problems, including market failures due to adverse selection and equity concerns Arthur Seibold: [email protected] Sebastian Seitz: [email protected] Sebastian Siegloch: [email protected] We thank Marika Cabral, Andreas Haller, David Koll, Camille Landais, Christina Meyer, Johannes Spinnewijn, Derek Wu, Josef Zweimüller as well as seminar participants at Oxford, LSE, CREST, LMU Munich, Manchester, St. Andrews, Tinbergen Institute Amsterdam, Stockholm, Copenhagen, FU Berlin, Frankfurt School of Finance/Goethe, Hohenheim, KIT, the NBER Summer Institute, the CEPR Public Economics Symposium, NHH, ZEW, CESifo, the Bocconi-CEPR Social Security Workshop, Bonn-Mannheim CRC, NTA, IIPF, EEA, and Bonn-Cologne ECONtribute for helpful comments and suggestions. We especially thank Eckhard Janeba for his support in obtaining the data used in this paper. Arthur Seibold gratefully acknowledges financial support from the Daimler and Benz Foundation and the German Research Foundation (DFG) through CRC TR 224 (Project C01). Sebastian Siegloch gratefully acknowledges financial support from the DFG under the Excellence Strategy—EXC 2126/1-390838866. © 2025 The Authors. Econometrica published by John Wiley & Sons Ltd on behalf of The Econometric Society. Arthur Seibold is the corresponding author on this paper. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
1698 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH (Liebman (2015)). Despite the significance of this policy debate, there is remarkably little empirical evidence on the functioning of private DI markets.1 In this paper, we break new empirical ground on these issues. We investigate key features of private DI markets and study the welfare consequences of expanding the role of private DI. We exploit a unique reform that abolished one part of public DI for German workers. Our analysis is based on novel microdata from a large private insurer and administrative data on the universe of public DI claims. This setting and data allow us to obtain three pieces of empirical evidence that govern the welfare impact of private DI provision. First, we estimate crowding-out effects between public and private DI. Second, we document substantial heterogeneity in private DI take-up, which raises distributional concerns. Third, we carefully test for risk-based selection, which provides crucial information about the efficiency of the private DI market. We adopt a revealed preference approach to estimate individual insurance valuations based on these empirical facts. Our welfare analysis shows that partly privatizing DI can improve welfare. However, a full public DI mandate could be justified by equity concerns. Assessing the potential of private DI to complement public DI is challenging for two reasons. First, suitable variation in public DI coverage is needed. Second, comprehensive and reliable data on private insurance is necessary to quantify the interaction between public and private DI. This paper is the first to overcome both of these challenges. We exploit exogenous variation induced by a reform that removed one part of German public DI and replaced it with a voluntary private DI market. Specifically, the reform of 2001 privatized own-occupation DI for younger workers. Receiving own-occupation DI benefits requires workers to be unable to work in their previous occupation. In contrast, general DI benefits are based on stricter eligibility criteria: being unable to work in any occupation. Before the reform, both own-occupation and general DI were part of the social insurance system. The reform completely removed public own-occupation DI for birth cohorts 1961 and younger. Importantly, the German private DI market offers contracts including own-occupation DI coverage, for which workers can opt if they wish to compensate for the loss of public DI coverage. To address the second challenge, we obtained a novel data set on all private DI contracts issued by a top-10 insurer in the German private DI market. This data contains highquality information on private DI coverage, prices, and individual characteristics, which are critical inputs into our empirical analysis. We demonstrate that the insurer microdata is representative of the overall private DI market in key dimensions using aggregate data on the entire private DI market from a leading rating agency and representative household survey data. Complementing the data on private DI, we use administrative data on the universe of public DI claims. We provide three pieces of empirical evidence on the private DI market. First, we study crowding-out effects of the reform, that is, the impact of public DI cuts on private DI takeup. On aggregate, we find substantial growth in the private DI market after the reform. To identify a causal effect, we use a difference-in-difference strategy exploiting the cohort cutoff of the reform. We find that treated individuals born above the cutoff significantly increase private DI purchases compared to control cohorts below the cutoff. Yet, even 15 years after the reform, overall take-up remains modest, as only 26% of workers have private DI. Thus, crowding-out is far from complete. 1For instance, in their report to Congress, the U.S. Government Accountability Office (GAO (2018)) concludes that the implications of various proposals to expand private DI cannot be fully assessed due to “an array of complex factors that could influence private DI expansions and SSDI cost savings—factors for which data, methods, and assumptions [...] are either unreliable, unsupported, or unavailable.”
PRIVATIZING DISABILITY INSURANCE 1699 Second, we document substantial heterogeneity in private DI take-up. Modest overall private DI take-up is mainly driven by low take-up among individuals with low income and low education. For instance, take-up is 65% in the top income quintile but only 7% to 12% in the bottom three quintiles. Moreover, there is important heterogeneity in take-up by priced risk groups, which insurers assign to workers based on occupations. Individuals in high-risk groups facing higher premiums are much less likely to take up insurance. These patterns indicate potential equity issues in the private DI market. Third, we carefully investigate risk-based selection into private DI using two complementary empirical strategies. The first strategy is a “positive correlation test” (Chiappori and Salanié (2000)), regressing private DI take-up on disability risk at the level of finegrained occupations. As a second strategy, we conduct a “cost curve test” (Einav, Finkelstein, and Cullen (2010)), which exploits variation in private DI premiums over time to test for differences in risk across individuals. We do not find any evidence of adverse selection. In both empirical designs, risk-based selection is of a small and insignificant degree. At first glance, the lack of adverse selection may be surprising, as insurance should, in principle, be more valuable to higher-risk individuals. We discuss several potential explanations for this result. For instance, there could be heterogeneous preferences for insurance that are negatively correlated with risk. In particular, the fact that individuals with high education and high income are more likely to purchase private DI seems to counter adverse selection. We also explore the possibility of heterogeneous earnings losses upon disability that could make private DI more valuable for workers in high-skill occupations. We then turn to the welfare consequences of privatizing DI provision. The analysis builds on Einav, Finkelstein, and Cullen (2010), who show that insurance demand and cost curves are sufficient statistics to assess welfare in insurance markets. Our setting with insurance choice provides a unique opportunity to implement a revealed preference approach and directly estimate individuals’ willingness to pay for the DI coverage offered by the private market. To trace out the slope of the private DI demand curve, we implement an event study design around occupation reclassifications, which entail large changes in private DI premiums. This estimation yields a demand elasticity of −1.06. Our counterfactual analysis compares the post-reform status quo, where DI is partly provided via the private market, to a full public DI mandate, including this extra coverage. We consider two welfare measures: (i) the net value of DI, which expresses the value of DI relative to its direct cost, and (ii) the marginal value of public funds (Hendren and Sprung-Keyser (2020)). For the latter, we calibrate additional indirect fiscal effects based on our data and estimates from the literature. Our main net value estimate implies that revealed insurance valuations among individuals receiving extra coverage amount to only 70.5% of the direct cost of insurance. Similarly, the marginal value of public funds of a mandate is 0.617. This initial welfare analysis ignores distributional concerns. In an extension, we incorporate welfare weights based on a Utilitarian social welfare function. We find that a full public DI mandate has a social value exceeding its costs, even under small degrees of equity concern. Importantly, redistributive effects hinge on the design of social insurance. Aprivate DI mandate does not increase social welfare since insurance benefits to highrisk groups are counteracted by risk-rated premiums. In contrast, a public DI mandate financed by income-based social insurance contributions effectively redistributes to lowincome, high-risk individuals. Overall, this paper shows that several market failures discussed in prior literature cannot justify mandating extra DI coverage in this context. Most importantly, we do not find any evidence of adverse selection in the private DI market, which is often considered
1700 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH the canonical rationale for a public DI mandate. We also account for market power and administrative costs, which contribute to low take-up in other private insurance markets (Braun, Kopecky, and Koreshkova (2019)), and we calibrate several potential externalities. We find that none of these factors warrant a mandate in our setting. Hence, the private market covers the majority of individuals with a sufficiently high willingness to pay, and a mandate would predominantly enroll those with valuations below marginal cost. It is important to note that our welfare analysis follows existing literature and maintains the assumptions of the revealed preference approach, which abstracts from behavioral biases. Studying such biases is beyond the scope of this paper. We argue that our findings are relevant beyond the German context for two main reasons. First, our systematic review of DI systems across countries reveals that both the German public DI system and the German private DI market share key characteristics with other countries, making our setting a broadly representative case study of privatizing DI. We also provide evidence that our results are not driven by specific institutional features, such as means-tested social assistance. Second, own-occupation disability risk—the subrisk our setting centers on—is strongly positively correlated with overall disability risk in the data. Hence, the types of individuals who would benefit from private DI tend to be those who would benefit from DI more generally. One may therefore expect similar patterns to emerge in other settings, including those where the details of DI coverage differ. Indeed, the limited existing evidence on private DI take-up from other countries points in this direction.2 This paper contributes to a large and growing literature on DI (see Low and Pistaferri (2020), for a review). Much of this literature focuses on public DI and its effect on labor supply and claiming decisions (Bound (1989), Gruber (2000), Autor and Duggan (2003, 2006,2007), Chen and van der Klaauw (2008), Autor, Duggan, and Lyle (2011), Staubli (2011), von Wachter, Song, and Manchester (2011), Marie and Vall Castello (2012), Maestas, Mullen, and Strand (2013), French and Song (2014), Kostol and Mogstad (2014), Borghans, Gielen, and Luttmer (2014), Koning and Lindeboom (2015), Liebman (2015), Autor, Duggan, Greenberg, and Lyle (2016), Burkhauser, Daly, and Ziebarth (2016), Deshpande (2016a,b), Mullen and Staubli (2016), Gelber, Moore, and Strand (2017), Autor, Kostol, Mogstad, and Setzler (2019), Ruh and Staubli (2019)). In contrast, there is much less prior work on private DI markets. Exceptions include Autor, Duggan, and Gruber (2014), Stepner (2021), and Seitz (2021), who analyze moral hazard effects of private DI. A recent working paper by Fischer, Geyer, and Ziebarth (2024) also investigates the German reform of 2001. Their approach is complementary to ours, combining survey data with a general equilibrium model of the private DI market. Similar to our results, they find modest private DI take-up after the reform, particularly among low-income groups. While our welfare analysis focuses on the trade-off between private and public DI provision, they emphasize the role of supply-side factors for take-up and welfare within the private DI market. We make three main contributions to this literature. First, exploiting our unique data and setting, we provide novel empirical evidence on crowding-out and selection in private DI markets. Our findings constitute the first direct empirical evidence on these issues, which are key in assessing the welfare impact of policies expanding the role of private markets and choice in DI. Second, we further exploit our setting with insurance choice to estimate willingness to pay for DI in a revealed preference approach. So far, little is 2For instance, Autor, Duggan, and Gruber (2014)andGAO (2018) report that private DI take-up increases with income in U.S. data, similar to our findings.
PRIVATIZING DISABILITY INSURANCE 1701 known about how individuals value DI. One exception is Cabral and Cullen (2019), who estimate willingness to pay for supplemental DI coverage within a U.S. firm and derive a lower bound on public DI valuations.3Our third contribution is to assess the welfare consequences of partial private DI provision vs. a full public mandate. This complements and extends existing work analyzing welfare and the insurance-incentive trade-off within public DI (Diamond and Sheshinski (1995), Low and Pistaferri (2015), Meyer and Mok (2019), Haller, Staubli, and Zweimüller (2024)). More broadly, our work builds on a rich literature testing for risk-based selection in social insurance settings. In Supplemental Appendix D (Seibold, Seitz, and Siegloch (2025)), we provide a more detailed review of this literature and conduct a meta-analysis of studies on risk-based selection published in leading economics journals since 2000. A large majority of existing work focuses on health insurance. Several papers have examined long-term care insurance (LTCI), pension annuities, and unemployment insurance. Evidence on risk-based selection in DI is particularly scarce. The only exception is Hendren (2013), who provides indirect evidence on potential risk-based selection in DI by documenting that individuals have private information about their disability risk. While prior work on health insurance, pension annuities, and unemployment insurance tends to find evidence of adverse selection, our analysis of DI shows some interesting parallels to LTCI. DI and LTCI share several features, including risks predominantly occurring later in life, strong risk-rating in the private market, and the coexistence of public and private schemes. Like us, Finkelstein and McGarry (2006)andBoyer, De Donder, Fluet, Leroux, and Michaud (2020) find no adverse selection in private LTCI, with point estimates indicating advantageous selection. Braun, Kopecky, and Koreshkova (2019)investigate the interplay of asymmetric information, market power on the supply side, and other transfer programs in explaining low observed LTCI take-up. Finally, this paper contributes to a nascent literature investigating the welfare effects of universal mandates versus voluntary markets in social insurance settings. Existing studies on these issues include work on health insurance (e.g., Einav, Finkelstein, and Cullen (2010), Finkelstein, Hendren, and Shepard (2019)), unemployment insurance (Landais, Nekoei, Nilsson, Seim, and Spinnewijn (2021), Hendren, Landais, and Spinnewijn (2021)), and workers’ compensation (Cabral, Cui, and Dworsky (2022)). Our main contribution to this wider literature is that we provide the first welfare analysis of a private market with choice versus a full public mandate in the context of DI, one of the most important social insurance programs. The remainder of this paper is organized as follows. Section 2outlines context and data, Section 3presents evidence on crowding-out, Section 4discusses heterogeneity in private DI take-up, Section 5tests for risk-based selection, Section 6presents the demand and cost estimation, Section 7shows the welfare analysis, and finally Section 8concludes. 2. INSTITUTIONAL BACKGROUND AND DATA 2.1. Disability Insurance in Germany Public Disability Insurance. In Germany, public disability insurance (DI) is administered by the State Pension Fund. Enrollment is mandatory for all employed individuals, while most self-employed workers and civil servants are exempt. DI contributions are 3In addition, a few studies use indirect consumption-based methods to quantify the insurance value of public DI (e.g., Meyer and Mok (2019), Deshpande and Lockwood (2022)).
1702 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH levied as payroll taxes together with old-age pension contributions. Enrolled workers become eligible for DI benefits in the event of a long-term disability limiting their work capacity. Moreover, eligibility requires having contributed for at least 5 years in total and at least 3 out of the 5 years before the onset of disability. Upon application, a medical and work capacity assessment is carried out by the Pension Fund. Benefits are a function of workers’ contributions, assuming they would have kept contributing according to their average predisability earnings until age 63. Public DI benefits are thus roughly proportional to individuals’ predisability earnings, with an average gross replacement rate of 39%. Benefits can be paid until a worker reaches the normal retirement age, when they are converted into an old-age pension. According to our administrative data, 25.1% of German workers become disabled and claim public DI throughout their lifetime. Crucially for our purposes, the public DI system consists of two separate tiers, general DI and own-occupation DI. The first tier pays benefits to workers suffering from a general disability (Erwerbsunfähigkeit), such that they are unable to work in any occupation for more than 3 hours per day. Common conditions leading to general disability include degenerative disc disease or severe depression/burn-out. The second tier, on the other hand, requires an own-occupation disability (Berufsunfähigkeit), defined as being unable to work in one’s previous occupation. For instance, a bus driver suffering from vision impairment is unable to work in their occupation but may be able to work in other jobs. The two DI tiers require separate applications. Workers on own-occupation DI receive two-thirds of general DI benefits but face a less stringent earnings test.4Own-occupation DI cases make up 13.2% of all public DI claims. The Reform of 2001. Before 2001, all workers were covered both by general and ownoccupation DI as part of the public DI mandate. However, rising expenditure on DI benefits stoked concerns about the fiscal sustainability of the program in the 1990s. This motivated a major reform in 2001 aimed at reducing public DI spending. Most importantly, the reform featured a sharp, cohort-based change in the scope of public DI: own-occupation DI coverage was completely removed for birth cohorts 1961 and younger from 2001 onward. Besides this main element, the reform featured further changes equally affecting all cohorts, including gradually phased-in changes to benefit calculation.5 The timing of the reform was noteworthy. Initially, the reform was announced in December 1997 to take effect in January 1999. The initial reform proposal intended to abolish own-occupation DI for all workers, not only for younger cohorts. After a change of federal government, the reform was retracted in late 1998. However, in December 2000, the reform was reannounced in its final form featuring the cohort cutoff, and the changes took effect in January 2001. Private Disability Insurance. According to our rating agency data, at least 73 insurance companies offer private DI contracts. In 2015, the top 3 providers had a combined market 4General DI benefits are reduced for monthly earnings above EUR 400, whereas workers on ownoccupation DI are allowed to earn at least EUR 700, depending on their prior earnings. Note that these earnings test thresholds are adjusted every few years. The aforementioned figures apply between 2008 and 2017. 5More precisely, the reform altered two elements of benefit calculation. First, an adjustment factor was gradually introduced, featuring negative benefit adjustments similar to penalties for early old-age pension claims. Second, the hypothetical contribution period used for benefit calculation was gradually extended, somewhat counteracting the new penalties. In addition, the reform introduced the possibility of claiming partial DI benefits for individuals with a general disability who can work between 3 and 6 hours per day. Finally, work capacity reassessments were introduced, but in practice, most beneficiaries still receive benefits permanently.
PRIVATIZING DISABILITY INSURANCE 1703 share of 34.2%, and the top 10 providers had a market share of 62.7%. Crucially, private DI always includes coverage of own-occupation disability risk, closely mirroring the prereform public DI system. Thus, workers affected by the reform can choose to purchase private DI in order to compensate for the removal of public own-occupation DI. Private DI payouts are independent of the public DI system, such that they can also serve as a top-up in case a worker is awarded public DI benefits. Before 2001, private DI purely served as such top-up insurance. An important difference to the public DI system is that private DI premiums are riskbased. The primary determinant of private DI premiums are individuals’ occupations, whereby insurers map occupations into a discrete number of risk groups (see below). Furthermore, insurance premiums can be adjusted for preexisting medical conditions and risky leisure activities, but this occurs infrequently.6Finally, monthly premiums are actuarially adjusted to the individual’s contract start and end date. This pricing practice has remained largely unchanged throughout our sample period and applies to all buyers. Private DI contracts typically specify a fixed amount of insured benefits, which can be set individually. In practice, monthly private DI payouts are of a similar magnitude to public DI benefits (see Section 2.3). German private DI is largely a nongroup market: the majority of 85% of contracts are purchased individually, and the remainder are obtained via employers (FAZ (2012)). Except a few niche providers, insurers generally offer contracts to all occupations. According to official statistics, only 3% of contract applications are denied by insurers (GDV (2023)).7In terms of primary features, including the definition of disability, benefit levels, and contract duration, private DI contracts are quite homogenous across providers.8Private DI can be bought either as a stand-alone product or bundled with other types of insurance, most commonly life insurance. Table Iprovides summary information about private DI premiums and risk groups. The average monthly premium to insure EUR 1000 of monthly benefits is around EUR 73 for a contract start age of 25 and EUR 98 for a start age of 45. Following standard practice in the industry, the insurer from which our microdata originates uses five risk groups to price DI contracts. Appendix Table A1 shows frequent occupations in each risk group. Examples of occupations classified as low-risk include medical doctors, computer scientists, and accountants. Medium-risk occupations include high-school teachers, secretaries, and electrical engineers; high-risk occupations include bakers, firefighters, and warehouse workers. Private DI premiums differ strongly across risk groups: for instance, an individual in the lowest-risk group 1 is charged EUR 32 at age 25, while premiums rise up to EUR 155 for the highest-risk group 5. This variation in premiums is roughly in line with differences in disability risk across occupations. According to our administrative data, the lifetime disability risk of individuals in risk group 1 is less than 5%, while it is 24% in risk 6Premiums are adjusted beyond risk-group specific prices in only 4% of private DI contracts (GDV (2023)). 7This includes a few extremely risky occupations such as circus artists and explosives workers, as well as rejections due to preexisting conditions or risky leisure activities. Besides coverage denials, another 12% of private DI contracts feature exclusion clauses for preexisting conditions. The relatively low denial and exclusion rates are an important difference to U.S. nongroup insurance markets, where these are more frequent and can affect broader sets of occupations and income groups (Hendren (2013), Braun, Kopecky, and Koreshkova (2019)). 8The well-known consumer advice organization Stiftung Warentest (2024) finds in their latest report that contracts offered by 67 private DI providers are essentially homogenous in these primary characteristics. Even on secondary characteristics such as waiting periods, retroactive benefit adjustments, and rules on occupation switches, contracts are quite similar: the average provider satisfies 86% of secondary criteria set by the report. Ultimately, 85% of providers receive the highest (“very good”) or second-highest (“good”) rating.
1704 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH TABLE I RISK GROUPS,DISABILITY RISK,AND PRIVATE DI PREMIUMS. (1) (2) (3) (4) (5) (6) Risk group Share of labor force Lifetime disability risk Share of own-occupation DI claims Monthly insurance premium for contract start at... age 25 age 35 age 45 All 10000% 2506% 1320% 7284 8354 9815 Risk Group 1 972% 481% 1085% 3161 3595 4322 Risk Group 2 1699% 1535% 806% 4172 4908 5749 Risk Group 3 3512% 2377% 1256% 6814 7990 9373 Risk Group 4 3756% 3101% 1574% 10060 11331 13303 Risk Group 5 062% 3992% 3194% 15524 17578 21068 Note: The table shows information on disability risk and private DI premiums by risk group. Risk groups are assigned by the insurer to individuals based on their occupations. See Appendix Table A1 for frequent occupations in each risk group. Column (1) shows the share of each risk group out of the labor force. Column (2) shows the fraction of individuals ever claiming public DI benefits in each group. Column (3) shows the share of own-occupation DI claims out of all DI claims. Columns (4) to (6) show the monthly premium (in EUR) charged to an individual insuring EUR 1000 of monthly benefits by contract start age, for a fixed contract end age of 65. The information in columns (1) to (3) is from our administrative data, and premiums are based on the insurer microdata. group 3, and 40% in risk group 5.9Own-occupation disability risk is strongly positively correlated with overall disability risk and increases even faster across risk groups. For instance, 8% to 11% of all disability cases in risk groups 1 and 2 are due to own-occupation disability, but the share increases to 32% for risk group 5. Finally, we note that risk groups differ in size, where risk group 1 and especially risk group 5 make up a smaller share of the labor force than the middle groups. Other Safety Net Programs. In the German context, a number of other safety net programs are potentially available to individuals who are unable to work. Most importantly, means-tested social assistance (Arbeitslosengeld II) pays a flat benefit to individuals at risk of poverty, which could provide an alternative to DI benefits for some workers. Other transfer programs, including unemployment, sickness, and accident insurance, have a maximum benefit duration of up to 2 years, and thus cannot substitute DI for permanently disabled workers. Since a large welfare reform in 2005, social assistance benefits have been relatively low; for instance, the average beneficiary received EUR 469 per month in 2015. Social assistance is also subject to a strict means test at the household level: households owning any assets worth more than EUR 10k are ineligible, and transfers are withdrawn at a rate of 80% for household income exceeding EUR 100 per month. Moreover, benefit receipt requires actively searching for a job. Thus, social assistance is unlikely to be a meaningful substitute for DI for most workers, except perhaps for those in very low-income, low-asset households. We return to this discussion in Sections 3.2 and 4.2, where we show that the availability of social assistance cannot explain much of our results. 9Note that we calculate disability risk among cohorts 1960 and older, who are observed under full public DI coverage, including own-occupation DI. Thus, our risk measure is not confounded by endogenous claiming responses to the 2001 reform (see also Section 5).
PRIVATIZING DISABILITY INSURANCE 1711 the reform cutoff. Only our baseline control group exhibits a very small increase relative to older cohorts, but there are no differential trends in insurance purchases between cohorts further below the cutoff. Quantifying Crowding-out. Our difference-in-difference analysis reveals a significant impact of the 2001 reform on private DI purchases. To understand how this maps into crowding-out effects on the level of private DI take-up, we can perform a simple back-ofthe-envelope calculation. We compute the predicted number of contracts held by cohorts 1961–1962 in 2015 based on pre-reform mean purchases and add the cumulative causal impact over the post-reform period implied by our estimates. This results in a 26% increase in the stock of private DI contracts held by the baseline treatment group who were treated at ages 39 to 40. Performing a similar calculation among the full set of treated cohorts from Figure 3suggests a substantially larger rise in average private DI take-up by 194%. Applying this estimate to the pre-reform take-up rate from Figure 1yields a crowding-out effect of 18 percentage points, similar to the observed increase in overall take-up. This implies that much of the growth of the private market can be attributed to a causal effect of the reform, while confirming that the magnitude of crowding-out between public and private DI is modest. Alternative Strategy: Regression Discontinuity Design. As an alternative empirical strategy, the cohort cutoff of the reform could be exploited to implement a regression discontinuity design (RDD). Our difference-in-difference strategy has the advantage of providing higher statistical power, particularly for subgroup analyses. Nevertheless, Appendix Figure A2 shows that an RDD would yield results similar to our main specification. The figure depicts a sharp jump in the number of private DI contracts held by individuals precisely at the January 1961 cutoff. The RDD estimate is highly significant and corresponds to an increase of 25% relative to average take-up among control cohorts. This is almost perfectly in line with the 26% increase in the stock of private DI contracts implied by our baseline difference-in-difference result. The Welfare Reform of 2005. As we explained in Section 2.1, another important safety net reform occurred in 2005. The reform made social assistance substantially less generous, replacing the prior income-dependent welfare system with a lower, flat benefit. Moreover, strict means testing was introduced, and benefit receipt was made conditional on active job search (see, e.g., Bradley and Kuegler (2019)). For our purposes, the 2005 reform presents a valuable opportunity to test the potential role of social assistance in determining private DI take-up. If social assistance served as a substitute for private DI, one might expect private DI take-up to increase after 2005, when benefit levels were reduced and many workers became ineligible for social assistance. However, Figure 1suggests that much of the growth in private DI take-up occurs right around 2001, with no further change after 2005. Similarly, Figure 2provides no indication that treated cohorts increase private DI purchases after 2005. To test this more formally, Appendix Table A5 performs a difference-in-difference estimation around the 2005 reform, resulting in a small and insignificant effect on private DI purchases. This suggests that the generosity of social assistance is not a major driver of private DI take-up. 4. HETEROGENEITY IN PRIVATE DI TAKE-UP In this section, we study which types of individuals take up private DI. The main challenge in doing so is that comprehensive microdata on the overall private DI market is not
1712 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH available. This challenge is faced by much of the literature investigating private insurance markets, which often uses data from a specific insurer or employer (e.g., Finkelstein and Poterba (2004,2014), Einav, Finkelstein, and Cullen (2010), Autor, Duggan, and Gruber (2014), Cabral and Cullen (2019)). We follow a similar approach and resort to the insurer microdata. Supplemental Appendix B.1 describes in detail how we use this data in combination with administrative data and official social insurance statistics to calculate private DI take-up of subgroups. Importantly, our approach requires the assumption that the market share of the insurer is constant across subgroups (within contract type and year). This assumption is not innocuous and its validity hinges on how representative the insurer is for the overall market. In Section 2.3, we argued that the insurer reflects the market well in terms of contract design, pricing, occupational coverage, and geographic coverage. Moreover, we present comprehensive validation checks of the resulting take-up rates using representative household survey data and other independent data sources in Section 4.3. 4.1. Private DI Take-up Across Groups In Figure 4, we begin by providing descriptive evidence on heterogeneity in private DI take-up in 2015. Panel (a) displays a strong positive correlation between private DI takeup and income. In the top income quintile, almost two-thirds (65%) of individuals have private DI. Private DI take-up is 30% in the fourth quintile, 11% to 12% in the second and third quintiles, and only 7% in the bottom quintile. Panel (b) shows a similar gradient of private DI take-up by education. 80% of individuals in the highest education quintile have private DI, while take-up is 26% in the fourth quintile and only 5% to 8% in the bottom three quintiles. Panel (c) depicts private DI take-up by type of occupation. We use the task-based classification by Dengler, Matthes, and Paulus (2014) who adapt the method of Autor, Levy, and Murnane (2003) and distinguish between cognitive (analytical or interactive) versus manual tasks and routine versus nonroutine tasks. With 77% and 45%, respectively, workers in occupations performing analytical or interactive nonroutine tasks display the highest private DI take-up rates. In cognitive routine occupations, 20% of individuals have private DI, while take-up in manual occupations is only 8%. Panel (d) finally investigates private DI take-up by risk group. Recall that the insurer assigns individuals to one of five risk groups based on occupations, and these risk groups are the primary determinant of private DI premiums. We find that lower-risk workers facing lower insurance premiums are much more likely to purchase private DI. In the lowest-risk groups 1 and 2, 58% and 56% of individuals have private DI, respectively. Among risk group 3, private DI take-up is 20%, and only 7% to 8% of individuals in risk groups 4 and 5 have private DI. Heterogeneous Impact of the 2001 Reform. To understand how the 2001 reform affects private DI take-up across groups, we provide two additional pieces of evidence. First, Appendix Figure A3 shows private DI take-up rates before the reform (in 1997). Differences in take-up before the reform are qualitatively similar to Figure 4, but much less pronounced. For instance, 17% to 18% of individuals in the top two income quintiles have private DI, compared to 6% to 9% in the bottom three quintiles. Second, Appendix Figure A4 shows results from a causal analysis estimating heterogeneous effects of the 2001 reform. For this purpose, we repeat the difference-in-difference estimation from equation (1) separately for each subgroup. To increase statistical power, we extend the
PRIVATIZING DISABILITY INSURANCE 1713 FIGURE 4.—Private DI Take-Up across Groups. Notes: The figure shows private DI take-up rates in 2015 by income quintile (panel a), education quintile (panel b), type of occupation (panel c), and risk group (panel d). In panel (b), education is defined as years of schooling. In panel (c), we use the task-based classification by Dengler, Matthes, and Paulus (2014) to group occupations. Take-up rates are calculated among all cohorts; see Supplemental Appendix B.1 for details. cohort window used in the estimation to 1957–1964. The relative effects by subgroup are very similar to the descriptive patterns from Figure 4. For instance, we estimate that the impact on private DI purchases of the top income quintile is about double that for the fourth quintile, while effects for the bottom three quintiles are very small. The impact of the reform on take-up also strongly increases with education and nonroutine occupations, but decreases with risk groups. These results suggest that the causal impact of the 2001 reform by subgroup is closely in line with the observed post-reform heterogeneity in private DI take-up.19 Multivariate Heterogeneity. Our main heterogeneity analysis shows that private DI take-up exhibits strong unconditional correlations with income, education, type of oc19In addition, Appendix Table A2 shows summary statistics of private DI contracts by time of purchase. Characteristics of preversus post-reform buyers align with the heterogeneity analysis presented here. Individuals who took up private DI between the first reform announcement and its final implementation (1998 to 2000) display similar characteristics to prereform buyers more broadly.
1714 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH FIGURE 5.—Determinants of Private DI Take-Up. Notes: The figure displays results from regressions of private DI take-up rates on individual characteristics at the three-digit occupation level. The coefficients show the estimated impact of the respective variable with 95% confidence intervals. “Basic controls” are the set of characteristics from the figure, that is, log income, education (years), indicators for cognitive and non-routine occupations, and risk groups. “Extended controls” include these variables plus gender, marital status, an indicator for economic training and residence in East Germany. See Appendix Table A7 for full regression results. cupation, and priced risk groups. To further unpack this heterogeneity, Figure 5displays results from regressions of private DI take-up on these characteristics, controlling for varying sets of individual and occupational characteristics. One key result from these multivariate specifications is that income is not a significant determinant of private DI take-up once education and other characteristics are controlled for. Thus, while the unconditional take-up gradient by income is important for distributional considerations (see Section 7.2), income per se does not seem to drive heterogeneous private DI demand. On the contrary, Figure 5shows that private DI take-up remains significantly correlated with education, risk groups, and working in a nonroutine occupation in all specifications. 4.2. Private DI Take-up, Disability Risk, and Risk Protection Benefit Both descriptive patterns and difference-in-difference results suggest that private DI take-up decreases with risk groups. This raises a potential puzzle, as, in principle, one would expect higher-risk individuals to place a higher valuation on insurance. Note that risk-rated premiums alone cannot explain this finding. Private DI premiums increase across risk groups in a manner not far from actuarially fair. Thus, while one may not necessarily expect private DI take-up to increase with risk groups, the pricing scheme cannot explain the decreasing pattern.20 To explore what could explain low private DI take-up among high-risk workers, we calibrate a comprehensive measure of the potential insurance value of private DI. Our risk protection benefit measure takes into account a variety 20This point is closely related to our test for risk-based selection in Section 5.Oncewecontrolforinsurance prices, we find that the correlation between private DI take-up and disability risk becomes flat but does not turn positive, as one would expect under standard models of adverse selection.
PRIVATIZING DISABILITY INSURANCE 1715 of factors beyond lifetime disability risk, including heterogeneity in the timing and subrisk composition of disability events, other safety net programs, and consumption drops upon disability. Building on existing approaches in the insurance literature, particularly Mitchell, Poterba, Warshawsky, and Brown (1999)andFinkelstein and McKnight (2008), we set out an expected lifetime utility framework in Supplemental Appendix B.3. In this framework, individuals face some risk of disability in each period, and they may qualify for public DI benefits or social assistance in case of disability. We use the model to calibrate the certainty equivalent utility gain that risk-averse individuals would derive from private DI. To perform the calibrations, we combine the information on dynamic disability risk paths, income, and private DI parameters contained in our various data sources, and we rely on a range of assumptions about consumption drops upon disability and the probability of receiving public DI benefits.21 In all specifications, individuals can receive basic social assistance if their income is sufficiently low. We initially assume that consumption losses and risk preferences are homogeneous across groups, but relax these assumptions later. Figure 6displays the calibrated risk protection benefit by risk group under selected specifications, along with private DI take-up and lifetime disability risk. Full calibration results are shown in Appendix Table A8. FIGURE 6.—Private DI Take-Up, Disability Risk, and Risk Protection Benefit. Notes: The figure shows private DI take-up rates, disability risk, and the risk protection benefit of private DI by risk group. The vertical bars depict private DI take-up rates for each group, calculated among all cohorts in 2015. The solid line shows lifetime disability risk by group. The dashed lines show the risk protection benefit of private DI as a fraction of income under three selected calibration scenarios, namely (i) under our baseline assumptions, (ii) in a scenario where income losses upon own-occupation disability increase somewhat progressively with income, and (iii) in a scenario with extremely progressive income losses. See Appendix Table A8 for detailed calibration results. 21Since no estimates of consumption losses upon disability are available in the German context, we rely on results from the U.S. by Meyer and Mok (2019) and results from Denmark by Humlum, Munch, and Plato (2025) in the calibration.
1716 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH Under the baseline calibration scenario, which assumes a coefficient of relative risk aversion of three, we find that the expected utility gain from private DI increases monotonically from 3.2% of income for risk group 1 to 19% for risk group 5. These relative magnitudes are roughly aligned with the simple risk measure, which implies that taking into account full dynamic disability risk paths and the composition of claims does not substantially change the relative utility gain from private DI.22 In Appendix Table A8, the gradient of the risk protection benefit across groups remains similar under alternative assumptions about risk aversion, public DI rejections, and the size of consumption losses. Next, the availability of other safety net programs has been shown to play a role for insurance choices, for example, in long-term care insurance (Braun, Kopecky, and Koreshkova (2019)). In our setting, two key programs could matter for private DI take-up. First, basic social assistance pays a flat benefit, which could provide some implicit insurance particularly for high-risk groups, given their lower average income (see Fischer, Geyer, and Ziebarth (2024)). In Figure 6, the calibrated risk protection benefit indeed increases less steeply than the simple risk measure for the highest risk groups 4 and 5, but this effect is quantitatively small. A limited role of social assistance is in line with the low implicit replacement rate of the program and with the evidence from Section 3.2,where we show that a large welfare reform hardly affects private DI take-up. Second, the availability of public DI benefits could influence private DI take-up. However, post-reform public DI only covers general disability risk and pays an approximately constant replacement rate to all groups. Thus, it is unlikely to induce differential private DI demand. This is confirmed by Appendix Table A8, where varying the probability of qualifying for public DI (rejection rates) hardly impacts the relative benefit of private DI across risk groups. Our baseline calibration assumes that consumption losses upon disability are a constant percentage of income for all risk groups. However, the consequences of own-occupation disability may vary. In particular, low-risk occupations are more likely to perform cognitive nonroutine tasks, which tend to require specialized skills (see Dengler, Matthes, and Paulus (2014)). It is thus possible that workers in low-risk groups experience larger earnings losses if an own-occupation disability necessitates switching to a different occupation.23 Unfortunately, we do not know of any existing estimates of heterogeneous consumption losses upon disability across occupations or risk groups. Hence, we consider two calibration scenarios to examine this channel. As a benchmark, we make the extreme assumption that in the event of own-occupation disability, all individuals are only able to work in a basic low-skill occupation where they earn the average bottom-quintile income. We also consider an intermediate scenario in between this extreme case and our baseline specification. Figure 6shows that such “progressive” earnings losses can substantially modify the relative benefit of private DI. Under the intermediate scenario, the risk protection benefit increases less steeply with risk groups, and under the extreme scenario, it becomes virtually flat. Finally, observed private DI take-up patterns could be explained by heterogeneous risk preferences. In particular, high-risk workers may have lower risk aversion. One potential reason behind a negative correlation between disability risk and risk aversion could be that workers select into more or less risky occupations based on their risk tolerance. To 22Two key calibration inputs illustrate why this occurs. Appendix Figure A5 shows that the timing of disability events is similar across risk groups. Table Ishows that, in addition to overall disability risk, the share of ownoccupation claims also increases with risk groups. 23This would be consistent with evidence from the literature on earnings losses upon job displacement. For instance, Huckfeldt (2022) documents particularly large losses for workers with specific human capital who find reemployment in a different occupation with lower skill requirements.
PRIVATIZING DISABILITY INSURANCE 1717 assess whether plausible variation in risk preferences could explain heterogeneous private DI take-up, we calibrate the degree of risk aversion that would make individuals indifferent between lifetime expected utility with and without private DI at market premiums. This yields an implied coefficient of relative risk aversion for the marginal buyer in each risk group. Details of the calibration are shown in Supplemental Appendix B.4, and results are displayed in Appendix Table A8. Across calibration scenarios with proportional consumption drops, the implied coefficient of risk aversion is between 1.09 and 4.96 for risk group 1 and between 0.66 and 2.87 for risk groups 4 and 5. Even when allowing for progressive earnings losses, implied risk aversion of higher-risk groups remains below that of risk group 1.24 This suggests that lower risk aversion among high-risk groups could indeed explain their lack of private DI demand. Our risk aversion estimates for these groups are low but not implausibly far from results in the literature.25 Implications for Welfare Analysis. Our baseline calibrations suggest that, given the size and structure of disability risk and the low level of social assistance in the German context, workers in high-risk groups should benefit substantially from private DI. However, low take-up among these workers could be explained by heterogeneous earnings losses upon own-occupation disability or by heterogeneous risk preferences. A key advantage of the revealed preference approach we follow later on is that the underlying reasons behind individual choices will not matter for the welfare implications, as long as observed private DI take-up reflects workers’ true insurance valuations. Besides the factors discussed above, behavioral biases could be another potential reason for low insurance takeup among certain groups. Studying such biases is outside the scope of this paper. We briefly return to this discussion in our conclusion. 4.3. Validation Checks Our empirical results on heterogeneity rely on the insurer microdata, as individuallevel data on the entire market is not available. As we discussed before, the validity of these findings depends on how representative the insurer is of the overall market. In this section, we present several validation checks using additional, independent data sources. To begin with, overall private DI take-up in our data is very similar to estimates from other sources. A survey conducted by TNS Infratest (2015), a private survey company, finds that 26% of working adults had private DI in 2015, corresponding precisely to our main take-up rate estimate for the same year from Section 3.1. In the representative EVS survey data, overall private DI take-up by German households was 31% in 2013. Household-level take-up is naturally higher than our individual-level estimate since the average household has around two members (see Appendix Table A4). Other data sources also suggest qualitatively similar private DI take-up patterns by subgroups. Appendix Figure A6 shows that take-up rates clearly increase with income in the household survey, albeit with a somewhat flatter gradient. We match take-up rates by gender well, considering that the survey figures are at the household level. To validate 24Interestingly, calibrated risk aversion does not decrease monotonically with risk groups. In particular, risk aversion of the marginal buyer in group 5 tends to be higher than in groups 2 to 4. This likely occurs due to a combination of social assistance providing more sizable implicit insurance and relatively high private DI premiums charged to this group. 25Studies on insurance choices typically yield estimates of relative risk aversion ranging between 1 and 8 (e.g., French (2005), Lockwood (2018), Jacobs (2023), Landais and Spinnewijn (2021)). Some work implies larger values (e.g., Cohen and Einav (2007), Sydnor (2010)).
1718 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH private DI take-up rates by risk group, we use the rating agency data, which includes a breakdown by “harmonized” risk groups for the entire market. This information is based on insurers reporting the number of contracts in four risk groups defined by the rating agency. Harmonized groups correspond roughly to the risk groups used by the insurer providing our microdata, but the insurer additionally differentiates among the highest risks. Our main take-up estimates for the largest risk groups 2 and 3 are virtually the same as those from the rating agency data. For the lowest and highest-risk groups, the rating agency data displays even stronger heterogeneity in take-up than our main results. Finally, as an additional piece of evidence, we present a comparison of private DI pricing by different insurers. For this exercise, we collect data on prices charged to the 10 most frequent occupations in each risk group for those of the top 10 insurers offering online price calculators. Appendix Figure A6 plots the average monthly premium by risk group for the insurer providing our microdata and four large competitors. Relative prices charged to different occupations are fairly similar across insurers. This suggests that different risk groups should have little reason to select specifically into the insurer providing our microdata, as its pricing reflects the overall market. 5. RISK-BASED SELECTION: POSITIVE CORRELATION TEST A crucial question for the efficient functioning of private DI markets is whether and how individuals select into purchasing insurance based on their disability risk. Standard adverse selection models predict that high-risk individuals are more likely to purchase insurance, which can lead to underprovision of insurance or even complete market unraveling (Akerlof (1970), Rothschild and Stiglitz (1976)). To formally test for risk-based selection, we implement a positive correlation test (Chiappori and Salanié (2000)) in this section. Later, we provide additional evidence from a cost curve test (see Section 6.2). Our aim is to test for a positive correlation between private DI take-up and disability risk, which would indicate adverse selection. Specifically, we run the following regression: Qj=β0+β1πj+ 5 ∑︂ k=2 γk1(risk groupj=k)+ϵj(2) where Qjdenotes private DI take-up of individuals in three-digit occupation jin 2015, πjis lifetime disability risk measured in administrative data, and 1(risk groupj=k)isan indicator for occupation jbeing assigned to risk group kby the insurer.26 Note that we define πjas total risk (including both own-occupation DI and general DI top-up payouts), as this is the relevant risk measure from the perspective of insurer cost. Our setting and data enable us to address two key challenges often faced by similar positive correlation tests in the literature. First, in assessing whether there is adverse selection, it is important to estimate the correlation between private DI take-up and risk within groups of individuals facing the same insurance prices. Indeed, we found a strong negative correlation between private DI take-up and risk groups in the previous section. Risk groups reflect an observed component of risk based on which insurance contracts are priced. In equation (2), we control flexibly for prices by including a set of risk group dummies, such that we can interpret β1as capturing selection on unpriced risk. Second, 26More precisely, we measure risk groupjas the modal risk group in an occupation. Risk groups are not necessarily the same for all individuals within a three-digit occupation in the data because the insurer sometimes changes risk group assignment over time (see Section 6.2).
PRIVATIZING DISABILITY INSURANCE 1719 FIGURE 7.—Risk-Based Selection: Positive Correlation Test. Notes: The figure shows a binned scatterplot depicting the correlation between private DI take-up and residual (unpriced) disability risk, controlling for private DI premiums. We run the regression at the level of three-digit occupations. As explained in Section 5, take-up rates are calculated among treated cohorts in 2015, while disability risk is measured only among control cohorts. The figure also includes the estimated slope coefficient bwith its standard error in parentheses. See Appendix Table A9 for details of the corresponding regression results. a well-known difficulty with the positive correlation test is that ex post measures of risk based on observed insurance claims may confound selection on ex ante risk and moral hazard responses (see, e.g., Landais et al. 2021). A correlation of DI take-up and ex post claiming probabilities may be driven by certain risk types selecting into insurance (selection) or those with more insurance coverage becoming more likely to claim (moral hazard). To address this challenge and isolate risk-based selection, we calculate take-up among the treated cohorts 1961 and younger but measure disability risk πjas the fraction claiming DI only among the control cohorts 1960 and older. This risk measure should not be confounded by moral hazard responses to differential take-up among treated cohorts since all individuals in the control cohorts are observed under full public DI coverage. Figure 7depicts the estimation results in a binned scatter plot. There is considerable residual unpriced variation in disability risk along the horizontal axis. Crucially, the estimated relationship between occupation-level private DI take-up and unpriced risk is quite flat, and the estimated slope coefficient corresponding to β1in equation (2)issmall and statistically insignificant. In other words, we do not find any adverse selection from the point of view of the insurer: within priced risk groups, individuals with higher risk are no more likely to select into purchasing insurance. The point estimate on risk is negative, which would imply slightly advantageous selection into private DI, if anything. At first glance, the lack of adverse selection may seem surprising, as insurance should in principle be more valuable to higher-risk individuals. However, some of the factors we discussed in Section 4.2 could explain this empirical finding. Evidence from other insurance markets points to heterogeneity in nonrisk related components of individual insurance valuations. If these correlate negatively with underlying risk, they can undo potential adverse selection (e.g., Finkelstein and McGarry 2006,Cutler, Finkelstein, and McGarry 2008). Our finding that high-income and highly educated individuals are more likely to purchase private DI could, for instance, reflect heterogeneous risk aversion or earnings
1720 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH losses that are negatively correlated with risk. Appendix Table A9 presents further suggestive evidence along these lines by exploring how risk-based selection changes conditional on different sets of observables. In particular, we find that the coefficient turns positive (but remains insignificant) once we control for education. This suggests that not conditioning prices on education induces some advantageous selection, countering potential adverse selection within risk groups. Hence, even though it is somewhat coarse, the pricing scheme devised by insurers seems to be an important factor in preventing adverse selection.27 6. VALUE AND COST OF DI 6.1. Basic Conceptual Framework Next, our aim is to quantify the value and cost of the DI coverage offered by the private market. These two are the main components entering our welfare analysis later on. Our conceptual approach builds on Einav, Finkelstein, and Cullen (2010), who show that in order to evaluate welfare in insurance markets, the key sufficient statistics are given by insurance demand and cost curves. Similar frameworks have been used in a number of social insurance settings (Hendren, Landais, and Spinnewijn (2021), Einav and Finkelstein (2023)). We consider a population of heterogeneous individuals indexed by θi,whereF(θi)denotes the distribution of types. Heterogeneity may include variation both in individual disability risk and in other factors influencing DI valuations, such as risk aversion. The first key component for our welfare analysis is demand for DI. Denote by v(θi) the utility of consumer ifrom DI, and by pkthe insurance premium charged to individuals in risk group k. In a private market with insurance choice, the individual purchases DI if their willingness to pay exceeds the premium, v(θi)≥pk. Aggregate demand for private DI in group kcan be written as Dk(pk)=∫︂1(︁v(θ)≥pk)︁dFk(θ)=Prk(︁v(θi)≥pk)︁ The second component we require is the cost of providing DI. We denote by c(θi) the expected cost of insuring individual i’s risk. The average cost at price pkis ACk(pk)=1 Dk(pk)∫︂c(θ)1(︁v(θ)≥pk)︁dFk(θ)=𝔼k(︁c(θi)|v(θi)≥pk)︁ In addition, we can write marginal cost as MCk(pk)=𝔼k(c(θi)|v(θi)=pk). Before we proceed to the empirical implementation, three aspects are worth noting. First, we assume that individuals make a discrete choice whether to buy insurance, and we abstract from the choice of insured benefit amounts in private DI contracts. This assumption is motivated by our results from Section 3.2, which suggest that this extensive margin is the empirically relevant dimension of insurance choice. Second, our main analysis follows the literature regarding the cost of providing DI and abstracts from any other cost incurred by insurers. We discuss the potential role of administrative cost in Section 7.3. Third, since insurance prices depend on risk groups to which insurers assign individuals 27In line with this argument, Bundorf, Levin, and Mahoney (2012) show that risk-rated premiums can improve efficiency by limiting risk-based selection into health insurance.
PRIVATIZING DISABILITY INSURANCE 1727 the insured relative to the cost to the insurer. Net value in the private market is NVpriv =∑︂ k nk[︃∫︂v(θ)1(︁v(θ)≥pk)︁dFk(θ)]︃ ∑︂ k nk[︃∫︂c(θ)1(︁v(θ)≥pk)︁dFk(θ)]︃(6) where nkdenotes the size of risk group k. In the private market, the net value is given by the value to those who choose to purchase DI, that is, for whom v(θ)≥pk, divided by the cost of providing DI to them. Since we estimate private DI valuations in the presence of baseline public DI coverage, NVpriv shouldbe interpreted as the net value of the additional coverage offered by the private market. Our main counterfactual of interest is the introduction of an insurance mandate providing the coverage offered by private DI to all workers.33 Starting from the private market equilibrium, the net value of introducing the mandate is NVmand =∑︂ k nk[︃∫︂v(θ)1(︁v(θ)<p k)︁dFk(θ)]︃ ∑︂ k nk[︃∫︂c(θ)1(︁v(θ)<p k)︁dFk(θ)]︃(7) Individuals with willingness to pay above the market price already purchased private DI when they had the choice. Thus, a mandate expands coverage to those individuals whose willingness to pay is below the price. Based on this welfare measure, a reform is welfare-improving if its net value is greater than one; that is, it generates value exceeding its cost. For our counterfactual, NVmand > 1 would imply that mandating private DI coverage is welfare-improving. In contrast, NVmand <1 would mean that leaving this coverage to the voluntary private market is preferable. Our baseline welfare analysis follows Einav, Finkelstein, and Cullen (2010)andfocuses on the direct value and cost of providing extra DI. However, various types of indirect effects could be associated with DI provision. To account for these as much as possible, we also calculate a marginal value of public funds (MVPF) measure (Hendren and Sprung-Keyser (2020), Finkelstein and Hendren (2020)). To do this, we augmentequation(7) and include relevant fiscal externalities in the denominator.34 As a first externality, mandating private DI coverage is likely to impose indirect moral hazard costs onto public DI, since top-up insurance in case the worker also qualifies for 33While there might be alternative policies of interest, for example, mandating parts of private DI coverage, we focus on this counterfactual for two reasons. First, the fairest comparison is arguably between two policies providing the same insurance coverage, so it is natural to consider a mandate of actual private DI coverage. Second, our empirical estimates are directly related to this counterfactual since we quantify selection, insurance demand, and cost for the coverage provided by the private DI market. Thus, we consider a counterfactual based on actual private DI coverage the most empirically credible. 34We continue using the entire estimated demand and cost curves when calculating the MVPF, as in equations (6)and(7). This is important because our counterfactual is a large reform moving insurance take-up to 100%, such that the approximation of willingness to pay based on the envelope theorem often used in MVPF calculations would not be appropriate.
1728 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH public (general) DI benefits is included. To quantify this channel, we use the estimate of Seitz (2021), who finds that private DI increases public DI claims by 8.6%. Second, a fiscal externality may arise because additional DI claims entail reductions in labor supply, which in turn lower tax revenue. Unfortunately, empirical estimates of the labor supply effects of DI are not available in the German context, so we use an average of estimates from the literature. Third, covering all workers with private DI may reduce their propensity to claim social assistance if they become unable to work, implying a positive fiscal externality. Supplemental Appendix B.5 provides full details on how we calibrate each channel based on our data and estimates from the literature. Welfare in the private DI market can be graphically illustrated using our estimated demand and cost curves. Panel (a) of Figure 10 depicts net value in the private DI market for the case of risk group 3. The total area under the demand curve up to equilibrium take-up corresponds to the numerator in equation (6), and the area under the marginal cost curve corresponds to the denominator. In addition, the figure shows a decomposition of willingness to pay into consumer surplus (area A), producer surplus (B), and cost (C). Appendix Figure A8 shows analogous graphs for all risk groups. Overall, the private DI market generates a large surplus, as individuals with the highest willingness to pay choose to purchase private DI. Consumer surplus is particularly sizable in risk groups 1 and 2, where individuals exhibit the highest insurance valuations. Producers receive the largest surplus from risk groups 1, 4, and 5, where markups over marginal cost are highest (see Section 7.3). FIGURE 10.—Welfare Calculations. Notes: The figure illustrates our welfare calculations for the case of risk group 3. Panel (a) depicts welfare in the private DI market, where the net value is given by the total area under the demand curve (A+B+C) divided by the area under the cost curve (C). Panel (b) illustrates the net value of a reform mandating private DI coverage. The mandate increases DI take-up from the market equilibrium to 1. The net value of the reform is given by the additional area under the demand curve (D+G) divided by the additional cost (F+G). In both panels, the net value can be further decomposed, as explained in the respective legend. Appendix Figures A8 and A9 show corresponding graphs for all risk groups.
PRIVATIZING DISABILITY INSURANCE 1729 TABLE IV WELFARE EFFECTS OF INSURANCE MANDATES. (1) (2) (3) (4) Private DI Mandate (Risk-Based Premiums) Public DI Mandate (Income-Based Contributions) Net Value MVPF Net Value MVPF Baseline value 0.705 0.617 0.705 0.617 Social value by risk aversion σ σ=1 0.634 0.553 1.215 1.057 σ=2 0.575 0.499 1.547 1.343 σ=3 0.527 0.455 1.749 1.518 σ=5 0.459 0.393 1.936 1.678 σ=8 0.395 0.333 2.010 1.742 Note: The table shows the welfare effects of mandating the DI coverage offered by the private insurance market. Column (1) presents net value estimates for a private DI mandate and column (3) presents estimates for a full public DI mandate financed by income-based social insurance contributions. Columns (2) and (4) present marginal value of public funds (MVPF) estimates for the same mandates, taking into account fiscal externalities. The first row shows the baseline value calculated as in equation (7). The remaining rows show the social value calculated as in equations (8)and(9), using welfare weights from a Utilitarian social welfare function under different values of the coefficient of relative risk aversion σ. Panel (b) of Figure 10 illustrates the welfare effects of a mandate, again for the case of risk group 3. Starting from the private market status quo, insuring all individuals entails additional costs given by the area under the cost curve between equilibrium take-up and mandated take-up of 100% (areas F+G). Expanding insurance yields additional value (D+G), but this is exceeded by additional premium payments (D+E+F+G), implying a net loss in consumer surplus. Insurers, on the other hand, gain surplus (D+E). Thus, the overall net value of the mandate is given by D+Gover F+G, which is clearly below one. Appendix Figure A9 shows that the net value of a mandate is below one for all risk groups except group 1. The first row of Table IV quantifies these welfare results. We find an overall net value of introducing a private DI mandate of 0.705. This implies that partial DI privatization, similar to the 2001 reform, is welfare-improving compared to a full public DI mandate. Similarly, we find an MVPF of a mandate of 0.617. This reflects that the joint effect of fiscal externalities increases the net cost of providing extra DI, reinforcing our conclusion that the private DI market is welfare-improving.35 7.2. The Social Value of a DI Mandate As an extension of the welfare analysis, we introduce distributional concerns. Recall that the private DI market disproportionately covers high-income and low-risk individuals. A mandate would thus extend coverage to more low-income and high-risk individuals, on whom a social planner concerned with equity would place particular weight. We write 35As a point of comparison, Hendren and Sprung-Keyser (2020) report similar MVPF estimates for marginal reforms providing additional DI benefits between 0.74 and 0.96.
1730 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH the social net value of introducing a mandate as SNVmand =∑︂ k nk[︃λk Consumer surplus ⏟⏞⏞ ⏟ ∫︂(︁v(θ)−pk)︁1(︁v(θ)<p k)︁dFk(θ)+ Insurer revenue ⏟⏞⏞ ⏟ ∫︂pk1(︁v(θ)<p k)︁dFk(θ)]︃ ∑︂ k nk[︃∫︂c(θ)1(︁v(θ)<p k)︁dFk(θ)]︃(8) The first term in the numerator captures the additional net utility individuals in risk group kderive under a mandate, corresponding to their valuation minus the price of extra DI. The change in consumer surplus among risk group kis multiplied by λk, the social welfare weight of individuals in this group. The second term in the numerator reflects additional revenue to the insurer. The social net value then relates the sum of these two terms to the additional cost of providing insurance.36 Equation (8) considers a private insurance mandate where individuals are compelled to purchase private DI at market prices. However, in our setting, extra DI coverage was provided via the social insurance system before the 2001 reform, where individuals are mandated to participate and pay social insurance contributions. To evaluate such a public DI mandate, we have to consider that contributions can differ from risk-rated private DI premiums pk. Formally, the social net value of a public DI mandate is given by SNVpub =(︃∑︂ k nk{︃λk[︃∫︂(︁v(θ)−pk)︁1(︁v(θ)<p k)︁dFk(θ)+ Pricing effect ⏟⏞⏞ ⏟ ∫︂(︁pk−ppub k)︁dFk(θ)]︃ +∫︂ppub k1(︁v(θ)<p k)︁dFk(θ)}︃)︃/︂(︃∑︂ k nk[︃∫︂c(θ)1(︁v(θ)<p k)︁dFk(θ)]︃)︃(9) where ppub kdenotes contributions paid by individuals in risk group k.Comparedtoequation (8), a public DI mandate thus entails an additional pricing effect entering consumer surplus. Specifically, we suppose that contributions are levied as a proportion of an individual’s gross income, as is the case in our setting and other social insurance systems. We calculate the required contribution rate such that total contributions equal the cost of providing the extra coverage to all individuals. In order to obtain welfare weights, we require a social welfare function. As is common in the literature, we assume Utilitarian social welfare, such that welfare weights are given by marginal utility from consumption. Moreover, we assume constant relative risk aversion utility. We calculate social welfare weights for each risk group based on expected lifetime income. Appendix Table A12 shows information on income and resulting social welfare weights by group. Expected income decreases monotonically with risk groups. On average, individuals in risk group 1 earn more than double the income of those in risk 36Insurer revenue and cost carry a weight of one, corresponding to the average social welfare weight in the population.
PRIVATIZING DISABILITY INSURANCE 1731 group 5. We consider a range of values of the coefficient of relative risk aversion σbetween 1 and 8, where a higher σimplies stronger equity concern, and thus larger welfare weights on higher-risk groups. Results from the social net value calculations are shown in Table IV. Column (1) suggests that a private DI mandate would lower welfare under any degree of equity concern. Stronger equity concern decreases the social net value, indicating that a private DI mandate would be a regressive policy. As can be seen in Appendix Figure A9, forcing all individuals to purchase insurance at market prices entails larger reductions in consumer surplus among higher-risk groups, since they have to pay higher prices relative to a low willingness to pay. Column (3) shows the welfare effects of a public DI mandate with income-based contributions. In our baseline net value calculations shown in the first row of the table, the welfare impact of a public DI mandate is the same as that of a private DI mandate because the difference in pricing does not affect total surplus. However, in the presence of equity concerns, a public DI mandate improves welfare relative to the private market. Intuitively, the social insurance system with income-based contributions raises revenue from low-risk, high-income groups and redistributes towards high-risk, low-income groups by providing them with additional insurance at prices below risk-rated premiums. This redistribution is highly valued by the social planner. Even under low risk aversion of σ=1, the social net value is already 1.215. As expected, the social net value rises with the degree of equity concern; for instance, it becomes 1.749 under σ=3 and 2.010 under σ=8. We also calculate an analogous “social” MVPF measure. To this end, we augment equations (8)and(9) and include the various fiscal externalities described in Section 7.1.Table IV shows that the social MVPF is generally somewhat lower than the social net value. As before, this occurs because the joint effect of fiscal externalities increases net cost. However, our main welfare results remain similar: the social MVPF of a private DI mandate is far below one, whereas the social MVPF of a public DI mandate is between 1.057 and 1.742. Extensions and Robustness. Appendix Table A13 shows results from three extensions to our welfare analysis. First, we separate the effects of the different types of indirect costs included in our MVPF calculations. As expected, moral hazard spillovers onto public DI and the fiscal externality due to reduced labor supply lower the value of a mandate, but the positive externality due to reduced social assistance claims increases its value. Second, we check whether our results are robust to relaxing the assumption of a constant demand elasticity across risk groups. We find that results are qualitatively unaffected when using the point estimates for each risk group instead. Third, we allow for some risk-based selection in the private DI market. To quantify the potential range of cost curve slopes, we use the 95% confidence interval around the claim effect from panel (b) of Figure 8.Converted into lifetime claiming probabilities, the confidence interval ranges from adverse selection with a 6.9% difference in costs between insured and uninsured individuals to advantageous selection with a −11.1% difference. Adverse selection somewhat increases the net value of a mandate, and advantageous selection somewhat decreases it, but again, results remain similar. 7.3. Supply-Side Factors: Market Power and Administrative Costs Our welfare analysis relies on the sufficient-statistics framework by Einav, Finkelstein, and Cullen (2010), which takes insurance supply and the characteristics of insurance con-
1732 A. SEIBOLD, S. SEITZ, AND S. SIEGLOCH tracts as given. Evidence from other insurance markets, in particular long-term care insurance, suggests that the supply side can matter for take-up and welfare (Braun, Kopecky, and Koreshkova (2019)). Key supply-side factors emphasized by prior literature include the degree of market power and the extent of administrative costs. Several empirical observations suggest that both market power and administrative costs are less critical issues in our setting. First, the German private DI market is relatively competitive: the top 3 providers have a combined market share of 34.2%. This is substantially lower than in other markets, for example, Braun, Kopecky, and Koreshkova (2019) report a top-3 market share of 66% in U.S. long-term care insurance. Second, administrative costs are modest in German private DI. According to Fischer, Geyer, and Ziebarth (2024), fixed and variable administrative costs amount to 3% and 10% of premiums, respectively, compared to 20% and 13% in Braun, Kopecky, and Koreshkova (2019). Third, coverage denials, which can result from administrative costs, are infrequent in our setting. The overall denial rate is only 3% (see Section 2.1), versus 56% in U.S. long-term care insurance (Braun, Kopecky, and Koreshkova (2019)) and up to 64% in U.S. private DI (Hendren (2013)). These empirical facts translate into modest insurance loads, a commonly used metric combining insurer profits and administrative costs.37 Across all risk groups, we find an average load of 0.27, implying that insured individuals can expect to receive 73% of premiums in benefits. This is considerably lower than the average load of 0.42 reported in Braun, Kopecky, and Koreshkova (2019). Note that these loads are already implicitly incorporated in our main welfare analysis. Market power and administrative costs can lead to inefficiently low private DI take-up, which policy interventions aimed at increasing take-up such as a mandate can address. However, our welfare results imply empirical insurance loads are not sufficiently large to justify a mandate. To shed more light on the role of administrative costs for private DI take-up and welfare, we nonetheless perform an additional counterfactual simulation building on Braun, Kopecky, and Koreshkova (2019)andFischer, Geyer, and Ziebarth (2024). Some proponents of regulatory tools such as minimum benefit ratios argue that these could reduce administrative costs. In the counterfactual, we set administrative costs to zero and assume that this cost reduction is fully passed through to consumers. As it is unlikely that such an extreme reduction can be achieved in practice, we interpret the results from this simulation as an upper bound on the potential impact of administrative costs. Appendix Table A14 shows that the decrease in private DI premiums due to the removal of administrative costs leads to a modest rise in private DI take-up to 33%. The positive impact on consumer surplus and insurer profits exceeds the additional (direct) costs of providing DI, such that the net value of the counterfactual is 1.359, indicating an improvement in overall welfare. While these results are qualitatively unsurprising, they confirm that the impact of administrative costs is limited in our setting. 8. CONCLUSION In this paper, we provide novel empirical evidence on the functioning of private DI markets. We document significant crowding-out after a reform that cut public DI coverage. Yet, private DI take-up remains far from complete, especially among low-income, 37We follow Brown and Finkelstein (2008) and calculate insurance loads as 1 −(𝔼(cik )/𝔼(pik )), where cik are expected DI benefits (corresponding to the direct cost of providing insurance) from equation (5)andpik are expected insurance premium payments from equation (4).
PRIVATIZING DISABILITY INSURANCE 1733 low-educated, and high-risk individuals. Our welfare analysis highlights the policy implications of these findings. Our baseline welfare result is that leaving private DI coverage to the voluntary market is welfare-improving. This is closely related to our main empirical findings. First, we do not find adverse selection, which would lead to inefficiently low insurance take-up in the private market and which would be the canonical rationale for a mandate. Second, the value of extra DI coverage revealed by insurance choices is low for many individuals, especially in higher-risk groups, and our sizable demand elasticity estimates imply that insurance valuations decline fast among the uninsured. Third, market power and administrative costs are of insufficient magnitude to justify a mandate. In other words, the private DI market covers the majority of individuals whose willingness to pay is above marginal cost. However, equity concerns can provide a rationale for including the DI coverage currently offered by the private market in the public DI mandate. For such a reform to improve social welfare, it is crucial to implement income-based contributions as in realworld social insurance systems. Such a mandate redistributes not only from highto lowincome groups but also from lowto high-risk groups. Importantly, this analysis takes the design of other tax and transfer schemes as given. If the government aims at redistributing across income levels, there are likely more efficient ways to achieve equity gains. Nevertheless, redistribution across disability risk types is a distinctive feature of public DI. It would be worthwhile for future research to explore these trade-offs further. Throughout the welfare analysis, we follow the literature on mandates versus markets in social insurance settings and maintain the assumptions of the revealed preference approach (Einav, Finkelstein, and Cullen (2010), Finkelstein, Hendren, and Shepard (2019), Landais et al. (2021), Cabral, Cui, and Dworsky (2022)). Crucially, this includes the assumption that individuals make optimal private DI purchase decisions, such that observed demand reflects individuals’ true insurance valuations. As discussed in Section 4.2,observed private DI take-up could be explained by several factors consistent with revealed preferences. However, if behavioral biases lead to inefficient underinsurance for some workers, this could potentially provide an alternative rationale for a mandate beyond the classic market failures considered by the revealed preference approach. Studying such biases is outside the scope of this paper, but this may be another area where future work is needed to inform policy.38 REFERENCES AKERLOF,GEORGE A. (1970): “The Market for “Lemons”: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics, 84 (3), 488–500. [1718] ANONYMOUS FIRM (2019): “Data on Private Disability Insurance Contracts,” Unpublished data, accessed 3001-2019. [1705] AUTOR,DAVID,MARK DUGGAN,KYLE GREENBERG,AND DAVID S. LYLE (2016): “The Impact of Disability Benefits on Labor Supply: Evidence From the VA’s Disability Compensation Program,” American Economic Journal: Applied Economics, 8 (3), 31–68. [1700] AUTOR,DAVID,MARK DUGGAN,AND JONATHAN GRUBER (2014): “Moral Hazard and Claims Deterrence in Private Disability Insurance,” American Economic Journal: Applied Economics, 6 (4), 110–141. [1700, 1712] AUTOR,DAVID,ANDREAS RAVNDAL KOSTOL,MAGNE MOGSTAD,AND BRADLEY SETZLER (2019): “Disability Benefits, Consumption Insurance, and Household Labor Supply,” American Economic Review, 109 (7), 2613–2654. [1700] 38In an earlier version of this paper (Seibold, Seitz, and Siegloch (2022)), we considered behavioral biases as an alternative rationale for a mandate more explicitly. As it is difficult to directly quantify such biases in our data, we defer this topic to future work.
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