Betting on a Long Life – the Role of Subjective Life Expectancy in the Demand for Private Pension Insurance of German Households

Doerr, Ulrike; Schulte, Katharina Article Betting on a Long Life – the Role of Subjective Life Expectancy in the Demand for Private Pension Insurance of German Households Schmollers Jahrbuch – Journal of Applied Social Science Studies. Zeitschrift für Wirtschaftsund Sozialwissenschaften Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Doerr, Ulrike; Schulte, Katharina (2012) : Betting on a Long Life – the Role of Subjective Life Expectancy in the Demand for Private Pension Insurance of German Households, Schmollers Jahrbuch – Journal of Applied Social Science Studies. Zeitschrift für Wirtschaftsund Sozialwissenschaften, ISSN 1865-5742, Duncker & Humblot, Berlin, Vol. 132, Iss. 2, pp. 233-263, https://doi.org/10.3790/schm.132.2.233 This Version is available at: https://hdl.handle.net/10419/292368 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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/ Betting on a Long Life – the Role of Subjective Life Expectancy in the Demand for Private Pension Insurance of German Households By Ulrike Doerr and Katharina Schulte* Abstract With a view to investigating the presence of adverse selection in the private pension insurance market, we analyze determinants of private pension insurance uptake of German households. Using the SAVE 2005 survey data on savings and old-age provision, we estimate a probit model of insurance holdings. We find that subjective life expectancy is positively related with the probability of having supplementary private pension insurance. This indicates that the German private pension insurance market is in fact characterized by adverse selection. As expected, pre-existing entitlements to benefits from the public pension system tend to be a substitute to private insurance. Furthermore, financial literacy enhances the uptake of private pension insurance. We also find evidence for a bequest motive in old-age provision, but see no indication for pooling longevity risk within couples. JEL Classification: D82, G22, D91, J26 1. Introduction The German welfare state comprises a public pay-as-you-go (PAYG) pension system designed to prevent old-age poverty and to maintain the standard of living after withdrawal from working life. In contrast to funded systems, a PAYG plan is directly financed from current contributions and therefore requires a nearly permanent balance of contributions and payments. Population aging and negative incentive effects have increasingly threatened the German system and triggered a reform process to keep its financing sustainable. This has been accompanied by a lively discussion of the system’s opportunities and limitations, Schmollers Jahrbuch 132 (2012), 233 –263 Duncker & Humblot, Berlin Schmollers Jahrbuch 132 (2012) 2 *We thank Ulrich Schmidt and Carsten Schröder as well as two anonymous referees for valuable comments. Research assistance by Jeremias Bekierman is gratefully acknowledged. All remaining errors are our own. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 that has created awareness of falling replacement rates from the public statutory system and the need for supplementary private old-age provision. In addition to pure accumulation of financial and non-financial assets, investment in private pension insurance policies presents one possible way to raise retirement income and concomitantly insures against outliving one’s wealth. Consequences of shifting substantial parts of old-age provision from the public to the private sector, however, depend on the efficiency of this market. A main concern over insurance markets raised by theoretical research, is the presence of information asymmetries between insurers and the insured that lead to market failure due to moral hazard and adverse selection. As pension insurance covers the financial risk related to longevity, moral hazard would be present if pension insurance coverage induced life-prolonging behavior that cannot be observed by the insurer. Adverse selection would be present if the length of life could be more accurately predicted by the insurant himself than by the insurer, and people expecting relatively long life systematically purchased larger pension insurance coverage. Concerning moral hazard, most people agree that in developed countries like Germany individual life-prolonging activities can be seen as independent of pension insurance coverage. Moral hazard is therefore reasonably assumed to be quantitatively negligible, if not non-existent.1In contrast, adverse selection in pension insurance markets is a concern. As a consequence of adverse selection, premiums rise and eventually become prohibitively high for low-risk individuals who are pushed out of the market. In an attempt to explain the observed low uptake of annuities –the annuity puzzle –related studies consistently provide evidence for adverse selection in the UK and the US annuities market (Finkelstein /Poterba, 2002, 2004 for the UK and Friedman/Warshawsky, 1990, Mitchell et al., 1999, Brown, 2001 and Brown et al., 2008a for the US). First empirical evidence by von Gaudecker/ Weber (2004) suggests that the German private pension market is also characterized by adverse selection. If this was the case, it might be too expensive for individuals who expect to die early to compensate public pension shortfalls by private pension insurance. Our work contributes to the literature on adverse selection in annuity markets. In contrast to most related studies that take the Money’s Worth approach introduced by Friedman/Warshawsky (1988), we investigate the existence of adverse selection on the micro level. Our main interest is the explanatory power of subjective life expectancy in the uptake of private pension insurance. According to previous research, subjective life expectancy is a remarkably good predictor of actual lifetime. In particular, it is superior to predictions based on mortality tables as made by the insurers (Hamermesh, 1985 and Hurd /McGarry, 234 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 1This view is shared in large parts of the literature; see among others Finkelstein/Poterba (2004) and Rothschild (2009). See, however, Philipson/Becker (1998) for a discussion of the existence of moral hazard effects in the market for annuities. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 1995, 2002). Expectations about lifetime therefore represent private information and give a risk selection opportunity to the insurants as return on investment of a pension insurance policy increases with lifetime. In the same vein, a study on formation and updating of subjective life expectancy by Steffen (2009) finds correlations of subjective life expectancy with private information like individual health behavior and health status as well as rational updating of expectations after e. g. adverse health shocks. Based on these findings, our work now seeks to answer the question whether people actually make use of their private information about lifetime when deciding about old-age provision. If, conditional on other relevant determinants, subjective life expectancy was positively associated with the probability of having supplementary private pension insurance, this would indicate adverse selection in this market. We will test this hypothesis using the German SAVE survey data on savings and old-age provision. Guided by the theory of savings and the life cycle with uncertain time of death beginning with Yaari (1965) and previous empirical studies, we provide an in-depth analysis of the determinants of pension insurance uptake of German households with a special focus on the role of subjective life expectancy. The remainder of this paper is organized as follows: Section 2 gives an overview of the related theoretical and empirical literature. The German Old-Age Pension System is presented in Section 3. Section 4 describes the data and methodology in use and contains estimation results. Section 5 concludes. 2. Related Literature Within an overall assessment of the determinants of pension insurance uptake, we specifically focus on the role of subjective life expectancy to understand whether the German private pension market is characterized by adverse selection. Our work thus mainly relates to two broad strands in the literature. First, we refer to the theoretical and empirical literature on life cycle savings and annuity demand dealing with optimal annuitization in portfolio choice and practically relevant determinants of the annuitization decision. Second, we refer to the theoretical and empirical discussion of adverse selection in insurance markets in general and in annuity markets in particular. Yaari (1965) was the first who incorporated uncertain lifetimes in the classical life cycle savings theory of Modigliani/Brumberg (1954). His model is a theoretical conjunction of mortality expectations and time and risk preference parameters in determining optimal annuitization. The main implication of his theory of consumption under the presence of longevity risk is that risk averse utility maximizing consumers who face actuarially fair insurance prices should fully annuitize their wealth, provided that they do not have any bequest motive. Davidoff et al. (2005) later confirmed the complete annuitization result within a more general framework. Betting on a Long Life 235 Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 Compared to the theoretical predictions of full or at least high annuitization, observed uptake of annuities is surprisingly low (Friedman /Warshawsky, 1990, Brown/ Poterba, 2000, James /Song, 2001 and James/Vittas, 2000). This gap between theory and reality has caused a large body of literature dedicated to resolve this so called annuity puzzle. Among potential explanations for the puzzle are adverse selection, administrative load factors, bequest motives, risksharing within families, pre-existing annuities from social security, financial illiteracy and precautionary savings for the event of unexpected expenditure shocks. In this context, Brown (2001) empirically investigates the behavioral relevance of Yaari’s life cycle model by relating a utility measure of annuity value to actual household decisions. Following the life cycle model, he calculates the utility measure –the annuity equivalent wealth –based on cohort mortality tables and survey data on risk aversion, marital status, and the presence of pre-existing annuity flows from social security. Brown (2001) finds that households for which the life cycle model predicts to have a higher valuation of annuities are in fact more likely to annuitize their retirement resources. However, in accordance with the annuity puzzle, much of the variation in the actual decision remains unexplained by the life cycle model. He therefore considers several additional factors that might influence the annuitization decision where he identifies individual health status and time horizon for financial decisionmaking to be the most relevant. Related to our research purpose, the importance of individual health status in explaining the actual annuitization decision conditional on average mortality from life tables is particularly interesting. It points to the fact that people use private information on health status and expected longevity in the old-age provision decision which would be consistent with the presence of adverse selection in annuity markets. A general theoretical framework of adverse selection was introduced by Akerlof (1970) which Rothschild / Stiglitz (1976) later applied to the insurance market. The basic idea is that private information about individual risk gives insurants an information advantage over the insurer which allows higher-risk individuals to self-select into insurance contracts. Pooled risks are then comparatively high, insurance premiums rise and crowd lowerrisk individuals out of the market. Thus, the theory of adverse selection predicts a positive correlation between insurance coverage and risk. A wide body of literature studies the empirical importance of adverse selection in insurance markets. Two markets that have been frequently studied are the automobile and the health insurance market. For the automobile insurance market, the early studies of Dahlby (1983) and Puelz/Snow (1994) suggest a positive coverage-risk correlation, which, however, was not reinforced by subsequent research (Chiappori/Salanié, 2000 and Dionne et al., 2001). Conflicting findings are also available for the health insurance market. While Cutler / Zeckhauser (1998) support the theoretical prediction of positive correlation, Cardon/Hendel (2001) and Fang et al. (2008) reject it. Available studies on the 236 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 market for life insurance (Cawley / Philipson, 1999 and McCarthy / Mitchell, 2010) so far consistently suggest absence of adverse selection.2 Concerning annuity markets, the empirical literature rather uniformly concludes that these are characterized by adverse selection. From a methodological point of view, two different strands of empirical investigations of adverse selection in the market for annuities can be distinguished. Roughly, the first strand compares mortality data of annuitants with mortality data of non-annuitants or the general population, respectively. This strand includes the large number of studies that apply the concept of Money’s Worth to identify how much of an insurance premium’s deviation from the actuarily fair premium can be attributed to selection effects. Friedman / Warshawsky (1988) introduced the money’s worth approach that was later refined by Mitchell et al. (1999). By now, the money’s worth is commonly understood as the expected net present value of payouts in relation to premium costs which is calculated separately using population and insurance mortality tables. Several studies applied this concept to investigate the extent of adverse selection in annuity markets in various countries. Most frequently studied are the markets in the US (Friedman / Warshawsky, 1990 and Mitchell et al., 1999) and in the UK (Finkelstein / Poterba, 2002, 2004). Further examinations have been done for Germany (von Gaudecker / Weber, 2004), Australia (Doyle et al., 2004) and Singapore (Doyle et al., 2004 and Fong, 2002), as well as for Canada, Chile, Israel and Switzerland (James / Song, 2001). McCarthy / Mitchell (2010) and Rothschild (2009) also compare mortality tables of policyholders with those of the general population, but do not explicitly calculate the money’s worth. All these studies find evidence for adverse selection which, however, can only partially explain the annuity puzzle due to its limited extent. The more recent second strand, where our study belongs to, analyzes adverse selection from the perspective of the policyholder using micro level data. While the focus of the first strand lies on a quantitative estimation of the effects of adverse selection on insurance premiums, the second strand is able to simultaneously assess the relevance of subjective life expectancy and other determinants of annuity uptake. In addition, the money’s worth does not allow to distinguish between active mortality selection based on asymmetric information about health and expected longevity and passive mortality selection reflecting other differences such as wealth and income that are also correlated with mortality (Finkelstein / Poterba, 2002). Due to data limitations, research on the micro level is less frequently done. Most closely related to our analysis, is the study by Brown et al. (2008a) who use data from the US Health and Retirement Study (HRS). They investigate self-reported willingness of the elderly population to exchange part of their social security inflation-inBetting on a Long Life 237 Schmollers Jahrbuch 132 (2012) 2 2See Cohen / Siegelman (2010) for a recent review of the empirical literature on adverse selection in insurance markets. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 dexed annuity benefit for an immediate lump-sum payment by self-reported health status and subjective survival probabilities relative to actuarial life tables. Their results are consistent with predictions of standard theoretical models of adverse selection, since individuals with poor health-status and pessimistic life expectations are less likely to annuitize, but tend to prefer lumpsum payments. Another related study by Inkmann et al. (2011) uses the English Longitudinal Study of Aging and investigates actual annuity uptake in the UK. In line with Brown et al. (2008a), they find that the subjective survival probabilities of annuitants are significantly higher than those of their non-policyholding counterparts which points to the presence of adverse selection in the UK’s annuity market as well. Our work differs from the existing studies in several aspects: Compared to the US and the UK, Germany is characterized by a dominant public statutory system which leaves a relatively smaller scope for supplementary private insurance. Consequently, selection effects in the private pension insurance market in Germany are likely to differ from those observed in the US and the UK. In contrast to Brown et al. (2008a) who consider stated intentions to annuitize retirement income, we are able to observe actual demand for private pension insurance of households. Compared to Inkmann et al. (2011), we dispose of a more comprehensive set of variables, as we are able to build proxies for preference parameters reflecting risk aversion and time preference that are not included in their data. Unlike Brown et al. (2008a) and Inkmann et al. (2011), we use subjective life expectancy in years instead of subjective survival probabilities in percent. This overcomes the difficulties respondents might have with thinking in probabilities, especially when it comes to very low or very large probabilities as suggested by prospect theory (Kahneman/Tversky, 1979). 3. The German Old-Age Pension System For our further analysis, it is instructive to briefly examine the German oldage pension system which consists of three coexisting pillars. Three things should be noted from the following description. First, the public first pillar is still by far the most important source of old-age income. Second, benefit levels from the first pillar differ for different population groups mainly depending on their type of employment. Third, the private pension insurance considered in our work is part of the third pillar and allows anyone to supplement pre-existing benefits. Introduced by Otto von Bismarck in 1889 as a fully funded system, the German public old-age pension system was gradually converted into a PAYG system from 1957 on. Generosity was a key characteristic of the German system after the 1972 reform in terms of both replacement rates and flexibility of retirement age. However, increasing life expectancy in times of low fertility and the 238 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 resulting population aging coupled with negative incentive effects as well as the additional financing need after the German reunification began to threaten the system. Starting with a major reform in 1992, benefit cuts were implemented in an effort to stabilize its functioning (Börsch-Supan /Wilke, 2004). Nowadays, the so-called first pillar of the three-pillar old-age provision system comprises statutory pension insurance for all employees covered by the German social security system, old-age security for farmers, professional provision for certain groups of self-employed like physicians, lawyers and architects as well as the civil-service pension scheme. Except for the self-employed who are at liberty to participate and some other occupational groups like farmers or soldiers who can apply for exemption from compulsory insurance, the whole work force is subject to mandatory coverage within the first pillar. Although the relative importance of the three pillars has changed in disfavor of the first pillar, it still constitutes the most important source of old-age income. In 2007, the public pension scheme covered about 92 % of the German elderly and accounted for about 76 % of total gross old-age income of all retirees (ASID 07, 2009). The various subsystems within the first pillar, like the old-age security for farmers or the civil-service pension scheme have neither historically been equally generous, nor have they undergone benefit cuts in an equal measure. In particular, in 2007, persons of age 65 and older whose last position was denoted as civil-servant, drew an average monthly gross pension of €2670 from the public system. This amounted to an average of €1195 for former blueand white-collar worker and to only €813 for former farmers and self-employed who were least secured by the public scheme (ASID 07, 2009). Employees in the private and the public sector are free to supplement their benefits from the mandatory statutory pension insurance by an occupational pension scheme within the capital funded second pillar. This is typically organized in form of deferred compensations, where employees waive part of their salary in favor of employer-provided retirement benefits. In 2007, benefits from occupational pension plans represented about 8% of total old-age income and accrued to 27% of the retirees (ASID 07, 2009). Private old-age provision as the third pillar involves additional accumulation of assets like investment funds, shares, real-estate, private pension insurance and life insurance that can be depleted during retirement. From 2002 and 2005 on, the third pillar also includes the state-subsidized Riesterand Rürup pension plans. Overall, the third pillar accounted for 10% of total old-age incomes in 2007 (ASID 07, 2009).3 Our analysis of adverse selection in pension insurance focuses on the uptake of private pension insurance within the third pillar because access to private pension insurance is open for everybody and the uptake is purely voluntary. In our definition, private pension insurance includes investment funds within the Betting on a Long Life 239 Schmollers Jahrbuch 132 (2012) 2 3The remaining part of total gross old-age income that is not accounted for by the three pillars is income from employment during retirement. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 so-called Altersvorsorge-Sondervermögen as their functioning is equivalent to regular private pension insurance. This type of investment fund that was introduced in 1998 is specifically designed for the provision of old age income and underlies a special regulation (see §§ 87 –90 of the German Investment Law). Riesterand Rürup pension plans are excluded because of the state subsidies that distort their uptake and the unability to fully control for eligibility for these subsidies with the data at hand.4 Anybody is at liberty to purchase a private pension policy to raise retirement income. Individual premiums are generally calculated based on insurance mortality tables by age and gender. While benefits are usually paid out as a monthly pension, most insurance companies offer the option of a single lump-sum payment, instead. In both cases, a minimum benefit is guaranteed, while any profit bonus is uncertain and depends on the development of the capital market. Insurance companies offer various supplemental agreements for the standard policy, mostly related to dependants’protection. In a standard contract, pensions are paid until the policyholder dies. In order to avoid highly negative returns of investment, guarantee periods, survivor’s pensions or contribution refund in case of early death can be agreed upon with the insurer. These additional agreements all come at some cost in the sense of lower pensions for a given monthly contribution. Finally, it should be noted that redemption of a purchased policy is financially highly disadvantageous, since contributions for the first years are used to cover broker remuneration and administrative expenses. 4. Empirical Analysis of Insurance Determinants We now investigate the determinants of private pension insurance demand of German households in a probit model. Section 4.1 describes the data and the derived variables. The methodology is explained in Section 4.2 that also contains estimation results. 240 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 4The coexistence of subsidized and non-subsidized private pension products raises the question why anybody takes up a non-subsidized product while a subsidized one is available. The main reasons are: (i) a number of people are not eligible for the Riester subsidies like e. g. most self-employed, marginally employed, students, social welfare recipients and people receiving disability benefits (see § 10a of the German Income Tax Act for the rather complex eligibility criteria), (ii) subsidies do not automatically imply a high rate of return if the general contract conditions are disadvantageous (Kleinlein, 2011) (iii) under the current legislation, Riester products are unattractive for those who intend to spend their retirement abroad as they would have to pay back the subsidies in that case and finally, (iv) in particular right after the introduction of the Riester pensions, the closing of a contract was accompanied by a heavy administrative burden for the insurant (Oehler, 2009). OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 Betting on a Long Life 247 Schmollers Jahrbuch 132 (2012) 2 Table 3 Correlations of the independent varaibles weighted by sampling weights and averaged over the five datasets AVSLE RISKAVERSE IMPATIENT FINLIT UNEMPL CIVSERV WORKER SELFEMPL AGE NRCHILD PARTNER AVSLE 1 RISKAVERSE –0.03 1 IMPATIENT –0.01 –0.07 1 FINLIT 0.07 –0.03 –0.12 1 UNEMPL –0.07 –0.04 0.16 –0.18 1 CIVSERV 0.00 0.01 –0.06 0.10 –0.13 1 WORKER 0.01 0.01 –0.11 0.07 –0.69 –0.32 1 SELFEMPL 0.08 0.03 –0.01 0.06 –0.17 –0.08 –0.42 1 AGE –0.06 0.10 –0.05 0.07 –0.11 0.08 0.02 0.07 1 NRCHILD –0.02 0.11 0.05 –0.01 –0.08 0.03 0.06 –0.01 0.42 1 PARTNER 0.02 0.06 –0.07 0.20 –0.31 0.05 0.17 0.12 0.22 0.34 1 MARRIED –0.04 0.09 –0.10 0.17 –0.27 0.05 0.17 0.05 0.31 0.36 0.78 EAST –0.06 –0.03 0.07 –0.11 0.14 –0.10 –0.06 –0.01 0.05 0.04 –0.09 FINWEALTHEQ 0.03 0.03 –0.03 0.14 0.01 0.01 –0-03 0.03 0.06 –0.02 0.05 FINWEALTH 0.02 0.03 –0.03 0.14 0.01 0.01 –0.03 0.03 0.06 –0.01 0.06 OTHWEALTHEQ 0.02 0.03 –0.04 0.09 –0.02 0.00 –0.04 0.09 0.05 0.02 0.06 OTHWEALTH 0.02 0.02 –0.03 0.09 –0.02 0.00 –0.04 0.09 0.06 0.03 0.08 INCOMEQ 0.02 –0.01 –0.09 0.19 –0.19 0.12 0.03 0.12 0.19 0.06 0.20 INCOME 0.02 0.00 –0.09 0.21 –0.21 0.11 0.05 0.13 0.18 0.18 0.33 OTHINSEQ 0.05 –0.03 –0.04 0.24 –0.11 –0.04 0.06 0.08 0.11 0.04 0.09 OTHINS 0.05 –0.03 –0.04 0.24 –0.11 –0.04 0.06 0.09 0.11 0.05 0.12 Continued next page OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 248 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 Continue Table 3 MARRIED EAST FINWEALTHEQ FINWEALTH OTHWEALTHEQ OTHWEALTH INCOMEEQ INCOME OTHINSEQ OTHINS MARRIED 1 EAST –0.09 1 FINWEALTHEQ 0.06 –0.05 1 FINWEALTH 0.07 –0.04 1.00 1 OTHWEALTHEQ 0.07 –0.07 0.62 0.63 1 OTHWEALTH 0.08 –0.07 0.64 0.64 0.99 1 INCOMEEQ 0.17 –0.14 0.14 0.12 0.11 0.12 1 INCOME 0.28 –0.15 0.14 0.13 0.13 0.14 0.94 1 OTHINSEQ 0.12 –0.10 0.13 0.12 0.13 0.14 0.31 0.30 1 OTHINS 0.14 –0.10 0.13 0.12 0.14 0.15 0.27 0.29 0.99 1 Source: The German SAVE study 2005. Own calculations. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 4.2 Estimation and Results To estimate determinants of private pension insurance uptake, we specify a probit model with the dichotomous dependent variable PPIifor all households i¼1...N.PPIitakes the value one for households holding a private pension insurance policy in 2005. As usual, we estimate the probit model by maximumlikelihood estimation. To deal with item non-response, we take advantage of the five multiply imputed data sets provided by MEA and combine the separate complete-data results by the method known as Rubin’s Rule. This method averages estimated coefficients across datasets and takes within-imputation and between-imputation variances into account when calculating standard errors of the estimates (Rubin, 1987). We distinguish between a model with purely theory-led explanatory variables and six different specifications where vectors of previously derived control variables Xiare included. The underlying latent model is thus specified as PPI i¼1þ2AVSLEiþ3RISKAVERSEiþ4IMPATIENTiðþXiÞþ"i:ð1Þ Table 4 displays average marginal effects calculated using Rubin’s Rules for multiply imputed data for the model without control variables and six different specifications with control variables.15 Let us first consider the model without control variables. As illustrated in the first column of Table 4, estimation results closely correspond to our expectations. In particular, average subjective life expectancy significantly positively influences the demand for private pension insurance. Other things being equal, households who expect to become old, are more likely to purchase supplementary private pension insurance than those who expect to die young. Quantitatively, the effect seems to be small, i. e. if subjective life expectancy increases by one year, the probability of having PPI increases by 0.3 percentage points, but it is statistically significant at a level of 1.3 percent. Risk averse individuals should be more willing to insure their longevity risk and thus exhibit a larger likelihood of having private pension insurance. Correspondingly, the marginal effect of risk aversion on private pension insurance uptake is positive, but insignificant. Since investment in pension insurance postpones today’s consumption to tomorrow, individuals with high time preference should buy private pension insurance less frequently than their patient counterparts. As expected, a high rate of time preference is associated with a low predicted probability of having private pension insurance. Betting on a Long Life 249 Schmollers Jahrbuch 132 (2012) 2 15 Marginal effects can be either evaluated at fixed values of the independent variables, typcially the means, or averaged over all observations. The first are called marginal effects at the mean (MEM), while the latter are referred to as average marginal effects (AME). The main argument in favor of AME is the fact that sample means used during the calculation of MEM might refer to either nonexistent or nonsensical observations (Bartus, 2005). For comparison, we also calculated the MEM which are almost identical to the AME (see Table 7 in the Appendix). OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 250 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 Table 4 Average marginal effects using Rubin’s Rule for multiply imputed data for the model without control variables and six different specifications of the model with a vector of control variables Without control variables With control variables (1) (2) (3) (4) (5) (6) dy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >z AVSLE 0.003** 0.013 0.003** 0.036 0.003** 0.043 0.003** 0.037 0.003** 0.044 0.003** 0.034 0.002* 0.091 RISKAVERSE 0.006 0.784 0.007 0.729 0.007 0.730 0.007 0.746 0.000 0.987 IMPATIENT –0.081*** 0.002 –0.0043 0.172 –0.042 0.175 –0.041 0.186 –0.042 0.181 FINLIT 0.097*** 0.000 0.099*** 0.000 0.096*** 0,000 0.098*** 0.000 0.099*** 0.000 0.090*** 0.001 CIVSERV 0.173** 0.011 0.185*** 0.007 0.175** 0.010 0.186*** 0.007 0.176** 0.010 0.187*** 0.007 WORKER 0.095*** 0.001 0.101*** 0.000 0.095*** 0.001 0.101*** 0.000 0.097*** 0.000 0.111*** 0.000 SELFEMPL 0.246** 0.000 0.255*** 0.000 0.245*** 0.000 0.254*** 0.000 0.253*** 0.000 0.260*** 0.000 AGE 0.024*** 0.002 0.024*** 0.001 0.025*** 0.001 0.025*** 0.001 0.025*** 0.001 AGE2 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 NRCHILD –0.017* 0.055 –0.018** 0.049 –0.018** 0.042 –0.019** 0.037 –0.016* 0.067 –0.017* 0.051 PARTNER 0.024 0.310 0.023 0.320 0.020 0.395 0.019 0.410 0.036 0.119 MARRIED 0.015 0.501 EAST 0.050** 0.027 0.050** 0.028 0.051** 0.027 0.050** 0.027 0.051** 0.027 0.050** 0.029 FINWEALTHEQ 0.001 0.433 0.001 0.424 0.001 0.434 0.005 0.157 FINWEALTHEQ2 0.000 0.964 FINWEALTH 0.001 0.476 0.001 0.467 OTHWEATHLEQ –0.000 0.527 –0.000 0.533 –0.000 0.531 0.001 0.339 OTHWEALTHEQ2 0.000 0.665 OTHWEALTH –0.000 0.545 –0.000 0.551 INCOMEEQ 0.000 0.315 0.000 0.299 0.000 0.302 0.000 0.868 INCOMEEQ2 0.000 0.696 INCOME 0.000 0.305 0.000 0.283 OTHINSEQ 0.000 0.252 0.000 0.259 0.000 0.267 0.000 0.823 OTHINS 0.000 0.206 0.000 0.214 Note: Dependent variable ¼PPI, sample size N¼1320 (non-retired households), * p<0.1, ** p<0.05, *** p<0.01. Source: The German SAVE study 2005. Own calculations. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 With a p-value of 0.002, this relationship is highly significant in the model without the vector of control variables. Now, let us direct our attention to the model specifications with control variables in columns three to eight of Table 4. Estimation results for this model prove to be robust across the six specifications. Compared to the model without control variables, our previous results remain qualitatively stable. As before, the probability of having private pension insurance significantly increases with average subjective life expectancy. We therefore conclude that people rationally take expectations about lifetime into account when deciding on old-age provision. Combined with the predictive power of subjective expectations of lifetime, this indicates risk-based selection due to private information. Hence, our investigation of the German annuity market confirms the common finding that annuity markets are in fact characterized by adverse selection. The impact of risk aversion on pension insurance is again estimated to be insignificantly positive. Thus, preference-driven selection based on risk aversion does not seem to play a major role in the annuitization decision. This conflicts the emerging literature on propitious or advantageous selection based on risk aversion that emphasizes selection effects driven by risk attitudes instead of riskiness (Hemenway, 1990 and De Meza / Webb, 2001). Besides the admittedly noisy proxy, a potential explanation is collinearity of risk aversion and subjective life expectancy. This would hold, if risk aversion increased life expectancy due to more cautious health behavior and if individuals rationally took this effect into account when building their expectations about lifetime. Simple crosscorrelation analysis as given in Table 3, however, throws doubt on this explanation because the correlation coefficient is close to zero and even slightly negative. Instead, we attribute insignificance of the marginal effect of risk aversion to a framing effect (Brown et al., 2008b). People might view private pension insurance policies as a type of investment rather than insurance. Due to its dependency on the ex ante unknown lifetime, return on investment in private pension insurance policies is relatively uncertain. In this regard, risk averse people should less frequently invest in pension insurance. Our result closely corresponds to Brown et al. (2008a) who use a similar proxy for risk aversion. In most of their specifications, more risk averse people do not exhibit a significantly higher likelihood of taking annuities instead of a lump-sum payment. In contrast, Cutler et al. (2008) find the expected relationship between risk-related behavior and annuitization. Smokers or individuals with risky jobs are less likely to be covered by annuities, whereas individuals that undertake preventive health activities or those who always wear seatbelts are more likely to be covered by annuities. While it is still estimated to be negative, the marginal effect of time preference on the probability of having private pension insurance becomes insignificant once the control variables are taken into consideration. Using an analogous proxy for time preference, Brown et al. (2008a) also do not detect a robust relaBetting on a Long Life 251 Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 tionship between time preference and annuity uptake. According to his result, patient individuals tend to be less likely to prefer the annuity over the lumpsum payment which, however, is significant at the 10 percent level in only two out of five specifications. We conclude that the effect is mainly attributed to other characteristics of the household than their time preference. A possible candidate is financial literacy which seems to play an outstanding role in the demand for private pension insurance. The probability of having private pension insurance is about 10 percentage points higher in financially literate than in financially illiterate households which is significant at the 1 percent level. This result is in line with the recent literature on the relationship between financial literacy, retirement planning ability and retirement saving (Lusardi/ Mitchell, 2006, 2007a, 2007b and van Rooji et al., 2007) and is also supported by Brown et al. (2008a) and Bucher-Koenen (2009). Benefit levels from the first pillar proxied by the type of employment also have substantial explanatory power. With the base category being the unemployed, the marginal effect of a self-employed main earner who is least covered by the public pension system is largest as expected. Thus, pre-existing annuities tend to crowd out private pension insurance uptake which ought to be the case according to Mitchell et al. (1999) and Dushi/ Webb (2004) and is empirically confirmed by Bernheim (1991). According to our results, the predicted probability also increases with being a worker or a civil servant. There, the marginal effect of being a civil servant exceeds that of being a worker. At first glance, this seems counterintuitive due to the relatively more generous benefit levels for civil servants. An explanation might be a more cautious and provident attitude of civil servants on average that is not covered by other regressors. On the one hand, wealth, in particular financial wealth, increases the afforability of private pension insurance. On the other hand, it works as a substitute to insurance. Rather surprisingly, the monetary variables of (equivalent) net wealth, balance in other insurance-type old-age provision and household income do not determine insurance demand. Wealthy households run a lower risk of depleting their assets before death so that wealth is theoretically supposed to negatively impact the probability of opting for supplementary private pension insurance. This effect should be particularly pronounced for illiquid assets like housing or business property that reduce the required replacement rate from pension insurance. In contrast, for liquid financial assets a positive impact might dominate due to the increasing affordability of private pension insurance. Actually, the signs of our estimated effects point into these directions. However, in accordance with Börsch-Supan et al. (2008b), Brown et al. (2008a) and Inkmann et al. (2011), we do not find any significant relationship in our data. A likely reason are the opposing effects of increased substitution and increased affordability with rising wealth. In a similar manner, other insurance-type old-age provision can be seen as a substitute to private pension insurance such that a 252 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 negative relationship is expected again. However, we again do not see evidence of substitution between different sources of old-age income. Instead, ahead thinking households tend to rely on several sources of old-age income. This finding is in line with other studies that also find a positive relationship between participation in alternative old-age provision and uptake of private pension plans (Börsch-Supan et al., 2008b and Inkmann et al., 2011).16 Finally, net (equivalent) household income also does not seem to play a role in the uptake of private pension insurance. While Börsch-Supan et al. (2008b) estimate a weakly significant positive impact of income on pension insurance uptake, our result corresponds to Brown et al. (2008a).17 As the average age of its members increases, a household’s probability to purchase private pension insurance increases, but at a decreasing rate. Aggravating population aging and raising awareness of decreasing replacement rates of the public pension system should lead to a larger probability of supplementary pension insurance in young households. The youngest households, however, possibly have not yet fully adressed the matter of old-age provion which explains the observed nonlinearity. Whether the respondent is married or lives in a partner household, does not seem to influence the insurance decision. Thus, we do not find evidence for intra-household risk pooling theoretically suggested by Kotlikoff / Spivak (1981). In contrast to Brown/Poterba (2000) who find higher annuity demand among singles than couples, our results correspond to Brown et al. (2008a). Households in Eastern Germany are more likely to purchase private pension insurance than their Western German counterparts. This might be explained by lower expected public pension replacement rates of the Eastern German population due to less continuous employment biographies and lower average income subject to contribution payments (Krenz/Nagl, 2009).18 Interestingly, if the number of children increases by one, the probability of having private pension insurance falls by about two percentage points. We interpret this statistically significant effect as evidence for a bequest motive or expected intergenerational transfer from children to their parents during retirement. As mentioned by Bernheim (1991), children’s altruism might function as a ‘safety net’ that makes pension insurance less needed. Our finding corresponds to the emBetting on a Long Life 253 Schmollers Jahrbuch 132 (2012) 2 16 Note, however, that Inkmann et al. (2011) only find this for a subsample of stockholders. 17 Presumably, household income is an important determinant of the amount of insurance purchased because of higher purchasing power and higher standard of living that needs to be insured. In principal, we could estimate a two-stage model with the amount as the dependent variable in the second stage. Unfortunately, data on private pension insurance premium in force and contributions to the scheme prove to be unreliable such that we restrict our attention to the binary variable PPI. 18 For a detailed income decomposition of the German elderly in the Old and New Laender see Bönke et al. (2010). OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 pirical results by Bernheim (1991). However, quite a number of studies does not find an empirical indication of bequest motives in old-age provision (Hurd, 1987, Brown, 2001, Börsch-Supan et al., 2008b, Brown et al., 2008a and Inkmann et al., 2011). 5. Conclusion We investigate determinants of private pension insurance uptake of German households using the 2005 SAVE survey on savings and old-age provision. In a comprehensive assessment of the relevant factors suggested by theory and previous empirical work, we simultaneously estimate their importance in a multivariate framework. Our main finding is that households take advantage of private information on expected lifetime in the pension insurance choice. Conditional on other relevant variables, households expecting to become old, are relatively more likely to take up supplementary private pension insurance. More precisely, the probability of having supplementary private pension insurance increases by about 0.3 percentage points with each additional year of expected lifetime. This indicates the presence of adverse selection in the German annuities market. We also find financial literacy and pre-existing annuities to play a prominent role in the insurance decision. Financially literate households, identified by their active participation in the stock market, are significantly more likely to hold private pension insurance policies. Pre-existing annuities from the quantitatively most important public pension system, tend to crowd out private insurance. Civil servants and workers are less likely to have supplementary private insurance than households with a self-employed main earner who are typically not covered by the public system, though this difference is significant only for the case of the workers. In addition, the number of children is negatively related to the probability of private pension insurance. This can be interpreted as an indication of bequest motives or expected intergenerational altruism. According to our results, uptake of private pension insurance does not differ between single and partner households. In addition, we only find very limited evidence for the theoretically suggested importance of risk aversion and time preference. Our measure of risk aversion has no explanatory power in the pension insurance choice. This might be explained by the fact that a pension policy cannot only be seen as insurance, but also as a type of investment. On the one hand, the insurance character of private pensions that protects the insurant from longevity risk should be appreciated by risk averse households. On the other hand, the relatively uncertain return on a pension policy that depends on the ex ante unknown length of life tends to retain risk averse households from purchase. These two opposing effects might therefore explain the lacking explanatory power of our measure of 254 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 risk aversion. Time preference has the expected negative coefficient, but it becomes insignificant as control variables are taken into account. This work contributes to the literature on adverse selection in annuities markets. Our result is in line with a number of related studies primarily focusing on the UK and US that also find evidence for adverse selection in annuities markets. While most of these studies make use of the money’s worth concept to detect adverse selection, we use micro level data and approach the issue from the perspective of the insurant. To our knowledge, we are the first to investigate adverse selection in the German annuities market at the household level. From the policy point of view, our work suggests that the private pension insurance market is in fact characterized by inefficiencies related to adverse selection. Difficulties arise for low risk individuals for whom insurance in the private pension market is prohibitively expensive. Policy makers should therefore keep in mind that privately insuring longevity risk is not without difficulty for part of the population. For future research, it would be meaningful to conduct a comparable analysis using panel data that allows to observe household characteristics directly at the time of annuity purchase. Since our indicators of risk and time preferences are rather rough, we additionally consider it worthwhile to construct more sophisticated measures of preferences in surveys. This would provide deeper insight in preference-driven selection in insurance markets. Finally, it would be interesting to follow the development of the German pension system and address to adverse selection in Riester pension plans. While cautiously demanded in the beginning, holding of these increased to about 14 million contracts in end of 2010. Possibly, the design of the subsidy scheme that strongly incentivizes specific parts of the population to take up Riester plans, outruns the importance of life expectancy for profitability of the policies and thus reduces adverse selection. References Agnew, J. / Anderson, L. / Gerlach, J. / Szykman, L. (2008): Who Chooses Annuities? An Experimental Investigation of the Role of Gender, Framing, and Defaults, American Economic Review 98, 418 –422. Akerlof, G. (1970): The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism, Quarterly Journal of Economics 84, 488 –500. ASID 07 (2009): Alterssicherung in Deutschland 2007 –Tabellenband 3: Deutschland, Kortmann, K. / Halbherr V., Bundesministerium für Arbeit und Soziales, Forschungsbericht F392/ D. Bartus, T. (2005): Estimation of Marginal Effects Using Margeff, Stata Journal 5, 309– 329. Betting on a Long Life 255 Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 Bernheim, B. (1991): How Strong are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities, Journal of Political Economy 99, 899–927. BMAS (2008): Ergänzender Bericht der Bundesregierung zum Rentenversicherungsbericht 2008 gemäß § 154 Abs. 2 SGB VI , Alterssicherungsbericht 2008. Bönke, T. / Schröder, C. / Schulte, K. (2010): Incomes and Inequality in the Long Run: The Case of German Elderly, German Economic Review 11, 487–510. Brown, J. (2001): Private Pensions, Mortality Risk, and the Decision to Annuitize, Journal of Public Economics 82, 29 –62. Brown, J. / Casey, M. / Mitchell, O. (2008a): Who Values the Social Security Annuity? New Evidence on the Annuity Puzzle, National Bureau of Economic Research Working Paper No. 13800. Brown, J. / Kling, J. / Mullainathan, S. / Wrobel, M. (2008b): Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle, American Economic Review 98, 304–309. Brown, J. / Poterba, J. (2000): Joint Life Annuities and the Demand for Annuitues for Married Couples, Journal of Risk and Insurance 67, 527 –553. Börsch-Supan, A. / Coppola, M. / Essig, L. / Eymann, A. / Schunk, D. (2008a): The German SAVE Study: Design and Results, Mannheim Research Institute for the Economics of Aging. Börsch-Supan, A. / Reil-Held, A. / Schunk, D. (2008b): Saving Incentives, Old-Age Provision and Displacement Effects: Evidence from the Recent German Pension Reform, Journal of Pension Economics and Finance 7, 295–319. Börsch-Supan, A. / Wilke, C. (2004): The German Public Pension System: How it Was, How it Will Be, National Bureau of Economic Research Working Paper No. 10525. Bucher-Koenen, T. (2009): Financial Literacy and Private Old-Age Provision in Germany –Evidence From SAVE 2008, Mannheim Research Institute for the Economics of Aging Discussion Paper No. 192-2009. Cardon, J. / Hendel, I. (2001): Asymmetric Information in Health Insurance: Evidence from the National Medical Expenditure Survey, RAND Journal of Economics 32, 408–427. Cawley, J. / Philipson, T. (1999): An Empirical Examination of Information Barriers to Trade in Insurance, American Economic Review 89, 827–846. Chiappori, P. / Salanié, B. (2000): Testing for Asymmetric Information in Insurance Markets, Journal of Political Economy 108, 56 –78. Cohen, A. /Siegelman, P. (2010): Testing for Adverse Selection in Insurance Markets, Journal of Risk and Insurance 77, 39 –84. Cutler, D. / Finkelstein, A. / McGarry, K. (2008): Preference Heterogeneity and Insurance Markets: Explaining a Puzzle of Insurance, American Economic Review 98, 157 – 162. 256 Ulrike Doerr und Katharina Schulte Schmollers Jahrbuch 132 (2012) 2 OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36 Betting on a Long Life 263 Schmollers Jahrbuch 132 (2012) 2 Table 8 Average marginal effects using Rubin’s Rule for multiply imputed data for the model without control variables and six different specifications of the model with a vector of control variables; sample includes observations with imputed dependent variable Without control variables With control variables (1) (2) (3) (4) (5) (6) dy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >zdy=dx P >z AVSLE 0.003** 0.034 0.003* 0.065 0.003* 0.067 0.003* 0.066 0.003* 0.069 0.003* 0.060 0.002 0.135 RISKAVERSE 0.003 0.887 0.001 0.972 0.001 0.979 0.000 0.994 –0.005 0.819 IMPATIENT –0.072*** 0.007 –0.035 0.263 –0.035 0.265 –0.034 0.279 –0.035 0.264 FINLIT 0.095*** 0.000 0.097*** 0.000 0.094*** 0.000 0.096*** 0.000 0.097*** 0.000 0.087*** 0.001 CIVSERV 0.175** 0.016 0.183** 0.011 0.176** 0.016 0.184** 0.010 0.178** 0.015 0.184** 0.013 WORKER 0.094*** 0.001 0.097*** 0.001 0.094*** 0.001 0.097*** 0.001 0.095*** 0.001 0.108*** 0.000 SELFEMPL 0.233** 0.000 0.238*** 0.000 0.232*** 0.000 0.237*** 0.000 0.240*** 0.000 0.249*** 0.000 AGE 0.023*** 0.002 0.024*** 0.002 0.024*** 0.002 0.024*** 0.002 0.024*** 0.002 AGE2 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 –0.000*** 0.001 NRCHILD –0.018* 0.062 –0.019* 0.058 –0.019** 0.043 –0.020** 0.039 –0.017* 0.073 –0.017** 0.043 PARTNER 0.027 0.255 0.027 0.257 0.023 0.343 0.022 0.348 0.037 0.107 MARRIED 0.018 0.462 EAST 0.051** 0.025 0.051** 0.025 0.051** 0.025 0.051** 0.025 0.051** 0.026 0.054** 0.016 FINWEALTHEQ 0.001 0.490 0.001 0.486 0.001 0.496 0.006 0.134 FINWEALTHEQ2 0.000 0.848 FINWEALTH 0.000 0.523 0.000 0.520 OTHWEALTHEQ –0.000 0.634 –0.000 0.640 –0.000 0.642 0.001 0.314 OTHWEALTHEQ2 0.000 0.617 OTHWEALTH –0.000 0.637 –0.000 0.642 INCOMEEQ 0.000 0.166 0.000 0.154 0.000 0.152 0.000 0.907 INCOMEEQ2 0.000 0.754 INCOME 0.000 0.166 0.000 0.153 OTHINSEQ 0.000 0.285 0.000 0.280 0.000 0.304 0.000 0.868 OTHINS 0.000 0.245 0.000 0.241 Note: Dependent variable ¼PPI, sample size N¼1320 (non-retired households including imputed dependent variables), * p<0.1, ** p<0.05, *** p<0.01. Source: The German SAVE study 2005. Own calculations. OPEN ACCESS | Licensed under | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.132.2.233 | Generated on 2023-01-16 13:36:36