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Retirement Age around which explanations in letters are framed. Moreover, I discuss potentialalternative mechanisms. On the one hand, firm responses do not seem to drive much of the results.For instance, self-employed workers and those in small firms below the employment protectionthreshold also bunch strongly at statutory ages. On the other hand, liquidity constraints couldexplain at least part of the response to the Early Retirement Age, although this remains hardto verify directly in the absence of data on assets. Hence, the behavioral interpretation in theremainder of the paper focuses on Full or Normal Retirement Ages.The third part of the paper turns to an interpretation of the empirical findings in a simple modelof retirement with reference dependence. The reference point is given by a salient threshold in theform of a Full or Normal Retirement Age, for instance because workers perceive it as a normaltime to retire. Reference dependence is modeled as a change in marginal disutility from continuingwork at the reference point. Incorporating this standard formulation into a bunching frameworkyields predictions consistent with the empirical patterns, namely sharp bunching at statutory agesirrespectively of financial incentives.Reference dependence may not be the only possible behavioral explanation for bunching atstatutory ages, but I argue that it provides a parsimonious model which fits the data well. Inparticular, the shape of the empirical retirement age distribution around statutory ages is consistentwith an asymmetric density shift as predicted by reference dependence with loss aversion. On theother hand, the empirical density does not exhibit missing mass in the neighborhood of statutoryages, as would be predicted by alternative models where individuals derive a fixed utility premiumfrom retiring at this age. Such a discrete utility gain is one way to represent alternative behavioralmechanisms where individuals perceive retiring exactly at statutory ages as implicit advice by thegovernment, or as a social norm. Moreover, if workers follow a suggestion by the government, onemay expect that responses to statutory ages are concentrated among less financially sophisticatedworkers who find it difficult to make optimal retirement decisions. However, I do not find a negativerelationship between bunching at statutory ages and proxies for financial literacy.Based on the model, the magnitude of observed bunching can be directly related to parametersgoverning the strength of reference dependence, and these parameters can be straightforwardly recovered via structural bunching estimation. The estimation exploits the same variation in statutoryages and financial incentives across discontinuities used in the reduced-form analysis. Estimatedlocal utility kinks at Full and Normal Retirement Ages are large and significant, with magnitudesequivalent to variation in the implicit tax rate of at least 51%.Finally, counterfactual simulations highlight an important policy implication: Reforms shiftingstatutory ages are effective in influencing retirement behavior and can generate a positive fiscalimpact, which would be more difficult to achieve via financial incentives. First, I simulate anincrease in the Normal Retirement Age from 65 to 66. This leads to an increase in average actualretirement ages by 3 months. The second simulated reform provides stronger financial incentivesfor late retirement in the form of a “delayed retirement credit”. In order to match the effect onretirement behavior from the first scenario, financial rewards would have to be more than doubled3

from their current level. Although both policies have the same effect on average retirement ages,the fiscal impact is very different: A back-of-the-envelope calculation suggests that the NormalRetirement Age increase entails a long-term annual fiscal gain e1.1bn, whereas the financialrewards leads to a net fiscal loss of e1.2bn. The difference in fiscal effects arises because workerspay contributions for longer in both scenarios, but in contrast to the second scenario, shiftingstatutory ages can induce workers to retire later without having to increase pension benefits atolder retirement ages.This paper contributes to three strands of literature. First, I contribute to the empirical literature on retirement behavior. A number of studies estimate the effects of pension reforms involvingstatutory retirement ages, but evidence on the direct effect of statutory ages is scarce. For instance, Staubli and Zweimüller (2013) and Manoli and Weber (2018) find sizeable effects of anEarly Retirement Age increase using Austrian administrative data. Importantly, this type of reform simultaneously changes statutory ages and the financial incentives linked to them, such thatthe total reform effect is a mixture of the two.2 Most closely related to this paper, Mastrobuoni(2009) documents sizeable responses to a change in the Full Retirement Age using U.S. surveydata, and Behaghel and Blau (2012) argue that loss aversion is a potential explanation for benefitclaiming spikes.3 In this paper, I leverage a unique setting combining rich, independent variation instatutory ages and financial incentives and full-population administrative data over two decades. Iobtain compelling and precise estimates of the large direct effect of statutory retirement ages on jobexit behavior, and provide new evidence on behavioral mechanisms. To my knowledge, this paperis the first to jointly quantify reference point effects and standard elasticities, which allows me tosimulate and explicitly compare the effects of statutory age reforms to pure financial incentives.Second, I contribute to a growing literature on the role of reference points in field settings. Inparticular, Allen et al. (2017) and Rees-Jones (2018) investigate bunching at reference points amongmarathon runners and income tax filers, respectively. Building on these approaches, I take the use ofbunching methods further and estimate underlying reference dependence parameters by exploitingvariation in financial incentives and statutory retirement ages across multiple discontinuities.4 Thebunching approach is complementary to full structural approaches such as DellaVigna et al. (2017)and Thakral and Tô (2019). In addition, the results in this paper highlight the empirical relevanceof salient thresholds as reference points,5 and contribute to a broader literature on the importanceof individuals’ perception of incentives set by policy (e.g. Duflo et al. 2006).2Similar recent studies estimating the total effects of pension reforms involving statutory ages and financialincentives include Lalive and Staubli (2015), Cribb et al. (2016), and Fetter and Lockwood (2018). Moreover, Brown(2013) and Manoli and Weber (2016) analyze retirement responses to pure financial incentives.3In addition, some studies present survey and experimental evidence in favor of framing effects or referencedependence in intended retirement behavior, including Brown et al. (2013), Merkle et al. (2017) and Shoven et al.(2017).4Existing bunching approaches including Allen et al. (2017) and Rees-Jones (2018) are unable to recover underlying reference dependence parameters, as suitable variation to estimate the curvature of the cost of effort functionis not available in those settings (see DellaVigna 2018).5This contributes to an ongoing debate about the relevance of salient/backward-looking reference points vs.forward-looking reference points (see O’Donoghue and Sprenger 2018).4

Third, this paper builds on and contributes to the literature on bunching methods (Saez 2010;Chetty et al. 2011; Kleven 2016). Studies such as Kleven and Waseem (2013), Bastani and Selin(2014) and Gelber et al. (2020) emphasize the importance of contextual factors in determiningresponses, mostly focusing on optimization frictions. Estimating bunching at many discontinuities,this paper shows that reference point effects can magnify bunching responses and highlights thatbunching methods can be used to estimate related preference parameters.The remainder of this paper is organized as follows. Section 2 outlines context and data, section3 describes the empirical methodology, section 4 presents reduced-form evidence, section 5 discussesmechanisms behind the statutory age effect, section 6 develops the conceptual framework, section7 presents the estimation and counterfactuals, and finally, section 8 concludes.2Context and Data2.1The German Public Pension SystemGermany has a pay-as-you-go pension system that covers the vast majority of workers in the country(86% of the labor force in 2014). Enrolment is mandatory for private-sector employees, but mostself-employed workers and civil servants are exempt. Contributions are levied as a payroll tax ongross earnings. Benefits are defined according to a pension formula based on a worker’s lifetimecontribution history.6 Hence, pensions are roughly proportional to lifetime income and there isrelatively little redistribution. The average net replacement rate is just over 50% (OECD 2019).Public pensions are the main source of income for most recipients.7 Moreover, there is an earningstest for pension recipients where earnings above e450 per month lead to reductions in benefitpayments. Only 2.5% of workers in the data have any income from employment while receiving apension, making retirement an absorbing state for most.The system features three types of statutory retirement ages. First, the Early Retirement Age(ERA) is the earliest age from which a pension can be claimed. Second, the Full Retirement Age(FRA) is the age from which workers can claim their full pension. Third, the Normal RetirementAge (NRA) is the age from which workers can get more than their full pension.8Discontinuous Benefit Rules. The key advantage of the empirical setting is that thereare more than 600 pension discontinuities. Three types of discontinuous pension benefit rules areat their source. First, marginal pension adjustment changes at statutory retirement ages. A fullmonthly benefit level is defined at the FRA, and there are permanent benefit reductions for workersclaiming before the FRA as well as permanent benefit increases for claiming after the NRA. The6Appendix B provides additional details on benefit calculation and other aspects of the institutional setting.In a 2003 survey, 11% of retirees reported to receive any income from employer pension schemes and only 1%had a private pension. Among retirees with any employer or private pension, the average income from that sourcecorresponds to 34% and 23% of their public pension, respectively (Heien et al. 2005).8The distinction between the Full and Normal Retirement Age is somewhat peculiar to the German pensionsystem. Historically, FRAs were introduced in some pathways to allow certain workers to claim a full pension beforethe NRA. However, late claiming rewards are only available after the NRA for all workers.75

benefit adjustment function follows a kinked schedule, with a penalty of 0.3% for each month ofretirement before the FRA, no adjustment between the FRA and the NRA, and a reward of 0.5%per month after the NRA.9Second, workers become eligible for discontinuously higher pensions at some contribution thresholds, where they qualify for more generous pathways into retirement. Pathways are summarizedin Table 1. The regular pathway requires just 5 years of contributions, but pensions can only beclaimed from the NRA. At 15 and 35 years of contributions, workers become eligible for pathwayswith ERAs between 60 and 63, and FRAs between 60 and 65. Thus, they can receive a pensionfor more years and/or the benefit level is higher at any given age due to more favorable adjustment, which implies a discontinuous increase in pension wealth. Some pathways have additionalrequirements including gender, disability and periods of unemployment. Finally, the third type ofdiscontinuous pension rule occurs in a pathway without statutory retirement ages where pensionscan be claimed at any age. The disability pathway has a low contribution requirement of 5 years,but a relatively strict disability requirement. In this pathway, benefits are increased by 0.3% permonth for retiring between 60 and 63, with no further adjustment when claiming before 60 or after63.10Framing of Statutory Retirement Ages. Statutory ages are one source of pension discontinuities, but the way they are presented to workers differs fundamentally from other, “pure”financial incentives. Figure 2 provides an example of the framing of statutory ages from a leafletdesigned to inform workers about a future pension reform that increases the NRA to 67. First,statutory ages are saliently featured as normal retirement dates. The title “Retirement at 67” refersto the post-reform NRA. In fact, this title is a commonly used name for the reform in the mediaand public discourse. Using a hypothetical worker (“Maria F.”), readers are then told that if theywant to retire “as early as possible” they can retire at the ERA, but if they wish a full pension,they should retire at the FRA. Furthermore, workers are warned of losses if they retire before theFRA (“the penalty will remain for her entire retirement”).The example illustrates how statutory ages are framed as reference points. By invoking notionssuch as a “normal” retirement age, statutory ages are presented as reference ages, and “early” and“late” retirement is defined relative to them. Moreover, pension adjustment is framed as a loss(penalty) or gain (reward) relative to a “full” reference level linked to a statutory age.11 Suchframing of retirement ages has been shown to affect reported retirement plans in experimentalsettings (e.g. Brown et al. 2013, Merkle et al. 2017).9In contrast to the U.S., there is no discontinuity in the availability of public health insurance at statutory ages.Moreover, contribution points are credited in the disability pathway as if the individual had continued workinguntil age 60, making benefits less dependent on their contribution history.11More generally, statutory ages play a crucial role in the way pensions and retirement are presented to workers.For instance, pension reforms tend to be presented as changes to statutory ages rather than changes to benefit levelsthey might effectively entail.106

2.2Lifetime Budget Constraint DiscontinuitiesIn order to see how the pension system affects incentives for the timing of retirement, the netpresent value of a worker i’s net lifetime income can be written as a function of her retirement (jobexit) age Ri :N P Vi (Ri ) Ri 1 δ t wit (1 τ̃it ) t 0Ti δ t Bi (Ri )(1)t max(Ri ,ERA)The worker earns a gross wage w from starting age 0 to the period before retirement, which is subjectto payroll tax τ̃ . Pension benefits B depend on R both via contributions paid until retirement andvia pension adjustment. Benefits can be claimed from the job exit age if the worker has alreadyreached her ERA, and from the ERA otherwise, and are paid until time of death T , which isassumed to be known for simplicity. Finally, all payments are discounted at factor δ.The slope of the budget constraint, that is the marginal gain in lifetime consumption possibilitiesC from delaying retirement by one period, defines the implicit net wage wnet dC/dR. Expressingthe consumption gain as a fraction of the gross wage, the implicit net-of-tax rate is 1 τ wnet /w. Delaying retirement generally affects consumption in three ways. First, the worker gainsan additional period of wage earnings. Second, she sees a permanent change in her benefit eligibilitydB/dR. In the German case dB/dR is always strictly positive, since later retirement implies bothmore favorable pension adjustment and a larger sum of contribution points. Third, if she is alreadyeligible to claim benefits, there is an opportunity cost of work in terms of foregoing one period ofbenefits.Panel B of Figure 1 shows a stylized version of the lifetime budget constraint. The discontinuousbenefit rules described in section 2.1 introduce discontinuities into the budget constraint:Kinks at Statutory Retirement Ages. There are kinks at all statutory ages, but their signand magnitudes differ. Kinks at the ERA and the FRA are convex, i.e. the marginal net-of-taxrate is reduced. Moreover, there is a non-convex kink, i.e. an increase in the marginal return towork, at the NRA.12 The kinks at the FRA and NRA are a direct consequence of discontinuouspension adjustment, where marginal adjustment decreases from 3.6% p.a. to 0 at the FRA andincreases from 0 to 6% p.a. at the NRA. The kink at the ERA arises due to a combination ofpension adjustment and an additional opportunity cost of working, since workers start foregoingbenefits from the ERA onwards.13Pure Financial Incentive Discontinuities:Contribution Notches and DisabilityKinks. There are two sources of pure financial incentive discontinuities. First, contributionrequirements of different pathways create budget constraint discontinuities in the form of notches,i.e. jumps in the average net-of-tax rate. In Panel B of Figure 1, for instance, the worker reaches12An exception is the regular pathway where pensions can only be claimed from the NRA, in which case there isa convex kink at the NRA.13The ERA kink could be smoothed out by actuarially fair adjustment of pensions. However, the adjustment of3.6% annually is less than actuarially fair (see Börsch-Supan and Wilke 2004).7

35 years of contributions when working until age 58, where he becomes eligible for the long-terminsured pathway with higher implied pension wealth. Similarly, workers face notches in all mainpathways where eligibility requires 5, 15 or 35 years of contributions.14 Note that the age locationof these notches is worker-specific since it depends on the individual career starting age. As asecond source of pure financial incentive discontinuities, the kinks in the benefit schedule of thedisability pathway imply budget constraint kinks, where the marginal net-of-tax rate changes dueto changes in marginal pension adjustment.2.3644 DiscontinuitiesTwo sources of variation generate more than 600 budget constraint discontinuities.15 First, the sixpathways described in Table 1 vary in statutory ages and contribution requirements. Second, aseries of cohort-based pension reforms have been enacted since the early 1990s. Appendix Figure A2shows the evolution of ERAs and FRAs for birth cohorts 1933 to 1949. In addition to cross-sectionalvariation, statutory ages were changed in different pathways at different times. For instance, thewomen’s FRA was gradually increased from 60 to 65 for cohorts 1940 to 1944, such that eachmonthly birth cohort faces a one-month change in the FRA. Similar gradual changes to the FRAor ERA were also implemented in the other pathways.In total, this yields 386 budget constraint kinks linked to statutory ages. Contribution notchesand disability kinks amount to 258 pure financial incentive discontinuities. Combining variationacross pathways, cohorts and age groups yields a total of 180 contribution notches. Includinga gradual introduction period, there are 78 disability pension kinks. To illustrate the variation,Appendix Figure A3 provides some examples of lifetime budget constraints, where workers facedifferent statutory ages and pure financial incentive discontinuities depending on their month ofbirth, gender, contribution history and disability status.Panel A of Table 3 summarizes the 644 budget constraint discontinuities. At statutory retirement ages, there is strong heterogeneity in underlying kink sizes. At ERAs and FRAs, the averagekink size is between 0.22 and 0.25, i.e. the net-of-tax rate decreases between 22% and 25% at thethreshold. On the other hand, NRAs feature sizeable non-convex kinks of average size -0.50. Theaverage change in the net-of-tax rate is 0.32 at pure financial incentive kinks, and 0.44 at contribution notches. The figure at notches is obtained from the approximation as a kink for the marginalbuncher following Kleven and Waseem (2013). A further advantage of the setting is that there issubstantial variation in kink sizes across discontinuities of a given type. For instance, the standarddeviation of kink sizes across statutory ages is 0.39. There is also some within-group variation ineffective kink sizes due to different individual earnings histories, but the within-group standarddeviations are relatively small. The average retirement age at which statutory ages are located is14The notches at 5 years of contributions are not used in the a

Reference Points for Retirement Behavior: Evidence From German Pension Discontinuities Arthur Seibold 1 October 2020 1 University of Mannheim, [email protected] Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through CRC TR 224 is gratefully acknowledged. Discussion Paper Series - CRC TR 224