2 page report on a paper (due soon)

Inconsistent Retirement Timing∗

Christoph Merkle†, Philipp Schreiber‡, and Martin Weber§

Abstract

In an online experiment with more than 3,000 participants, we measure time

preference consistency and study actual and planned retirement timing decisions.

Theory predicts that hyperbolic time preferences can lead to dynamically incon-

sistent retirement timing. We find that time inconsistent participants retire on

average up to 2.2 years earlier than time consistent participants. Participants,

who are not yet retired, decrease their planned retirement age as they grow

older. This negative effect of age is about twice as strong for time inconsistent

participants. The temptation of early retirement seems to rise as participants

approach retirement. As a consequence, time inconsistent participants have a

higher probability of regretting their retirement decision. In addition, they do

not compensate for the loss of social security benefits by buying private pension

insurance. Using data from a representative household survey (German SAVE

panel), we find similar results.

JEL classification: D14, D15, D91, H55, J18, J22, J26.

Keywords: Retirement Timing, Time Preferences, Hyperbolic Discounting, Social Security.

∗We are grateful to the Frankfurter Allgemeine Zeitung for conducting the study with us. Intensive dis- cussion with two journalists, Anne-Christin Sievers and Patrick Bernau, helped to considerably improve the questionnaire. We further thank Shlomo Benartzi, participants of the 8thAlhambra meets Colosseo Workshop, the HeiKaMaX 2013 Workshop, and seminar participants in Mannheim for their valuable suggestions. †Department of Management and Economics, Kuehne Logistics University, Hamburg (corresponding au-

thor: Grosser Grasbrook 17, 20457 Hamburg, Germany, +49-40-328707-234, [email protected].) ‡zeb.Management Consulting, Frankfurt a.M. §Department of Banking and Finance, University of Mannheim; CEPR, London.

1. Introduction

When to retire is one of the most important financial decisions in later life that almost

everyone has to face. Income during retirement highly depends on retirement timing. In

most countries, social security benefits are paid according to years of work and income

during employment. In these systems, earlier retirement results in lower retirement benefits.

The retirement timing decision is becoming even more important as life expectancy increases.

For example, the average number of years spent in retirement by men in the United States

has increased from eight years in 1950 to almost twenty years in 2017. Accepting a reduction

in retirement benefits, therefore, affects the financial well-being of a retiree for a substantial

period of time.

Early retirement does not only have consequences on a personal level, but also affects

the pension system as a whole. Increasing life expectancy combined with low birth rates

put the pay-as-you-go social security systems of many developed countries under pressure.

Retirement timing is an important determinant of the ratio between contributors and re-

cipients within the system. Policy attention to this issue has grown recently. The European

Commission (2012) in a white paper on adequate, safe and sustainable pensions highlights

the importance of creating an environment that encourages older workers to remain in the

workforce. To develop appropriate strategies in this regard, it is necessary to understand the

drivers of individual retirement timing.

There is a broad literature on retirement timing (for a detailed review see Beehr and

Bennett, 2015; Fisher et al., 2016). Among the analyzed factors that influence retirement

timing are health (van Rijn et al., 2013), economic status (Kim and Feldman, 1998; Madero-

Cabib et al., 2015), gender (Finch, 2014), education (DePreter et al., 2015), subjective life

expectancy (Griffin et al., 2012), marital status (Gustman and Steinmeier, 2000), and job

characteristics (Wang and Shultz, 2010; Earl and Taylor, 2015). Besides these individual

factors, the macroeconomic situation has been identified as another important predictor of

retirement timing (God et al., 2011; Hairault et al., 2015). These factors have in common

that they can be categorized as rational considerations to delay or speed up retirement.

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Behavioral economics has identified further determinants, which exert an influence on

retirement savings and planning (Benartzi and Thaler, 2007). Framing and its impact on

retirement timing is perhaps the phenomenon studied most extensively, with the common

finding that the retirement decision is strongly affected by how information is presented

(Fetherstonhaugh and Ross, 1999; Brown et al., 2011; Shu et al., 2014; Merkle et al., 2017).

This opens up potential for policy makers to alter public choice architecture. Other behavioral

influences on the retirement timing decisions are loss aversion and the ability to forecast

future happiness (for an overview see Knoll, 2011). We contribute to the behavioral strand

of the retirement literature by experimentally measuring individuals’ time preferences and

analyzing their impact on actual retirement timing.

The retirement timing decision is an intertemporal consumption decision under uncer-

tainty for which time preferences play an important role. They can be interpreted as indi-

viduals’ valuation of a good at an earlier date compared to its valuation on a later date

(Frederick et al., 2002). We examine the relation between the consistency of time prefer-

ences and the decision when to retire. A decision maker with hyperbolic time preferences

exhibits higher discount rates in the near future and lower rates in the more distant future.

Such preferences can lead to dynamically inconsistent decisions. A dynamically inconsistent

decision maker will evaluate an optimal plan at some point in time, but re-evaluate that

plan at a later point in time and not necessarily stick to it. For example, DellaVigna and

Malmendier (2006) analyze gym membership contracts and find that the majority of gym

members plan to attend on a regular basis when signing the membership contract. However,

actual attendance over the lifetime of the contract is much lower.

In the retirement context, a dynamically inconsistent decision maker schedules an op-

timal retirement age during work life. However, when the retirement age approaches, she

might re-evaluate that plan and choose to retire earlier (or later). In the case of unplanned

early retirement, this can have undesirable financial consequences. Monthly income in retire-

ment will be lower due to a reduction in social security benefits. Since the retirement date

changes on relatively short notice, also the private savings plan may not match the needs in

retirement.

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The question of how time preferences affect retirement timing has been addressed in re-

cent theoretical work (Diamond and Köszegi, 2003; Holmes, 2010; Zhang, 2013; Findley and

Feigenbaum, 2013; Findley and Caliendo, 2015). These studies model the savings and retire-

ment timing decision of hyperbolic agents when retirement is endogenous, and allow us to

derive predictions for retirement timing. Hyperbolic discounting (in contrast to exponential

discounting) can lead to dynamically inconsistent early retirement. The decision maker ini-

tially plans to retire on a certain date, but by putting too much weight on the near future will

prefer to retire early when the retirement date approaches. Future consumption is in this

case traded against immediate leisure. However, hyperbolic discounting at the same time

predicts undersaving. A hyperbolic decision maker might not have accumulated sufficient

wealth to afford early retirement and is forced to retire later (Diamond and Köszegi, 2003).

The direction of the effect is therefore an empirical question.

We conduct a large online experiment in cooperation with the German newspaper Frank-

furter Allgemeine Zeitung (FAZ). The FAZ is one of Germany’s most widely circulated daily

newspapers and promoted the experiment in the print edition and by posting a link to the

survey on their website. Through these channels 3,077 participants are recruited. They an-

swer a series of questions regarding their retirement plans and expectations. They indicate

their planned retirement age if they are not yet retired, or their actual retirement age if they

are already retired. In addition, we experimentally elicit participants’ time preferences. The

survey also includes questions regarding risk preferences, loss aversion, financial literacy, and

subjective life expectancy.

In a first step, we classify participants as time consistent or time inconsistent based on an

intertemporal choice task. Using the example of a tax refund, participants are offered several

choices of a smaller sooner or later larger amount. We then examine for the subsample of

retired participants the relation between their time preferences and their reported actual

retirement age. We find that retirees, who can be classified as time inconsistent, retired on

average 2.2 years earlier than time consistent participants. This demonstrates that incon-

sistent time preferences may have severe consequences for retirement timing. Moreover, we

find that time inconsistent participants are on average 16% points more likely to regret their

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retirement timing decision. 32% of time inconsistent participants state that they would retire

later, if they could decide again.

We also explore the financial consequences of the dynamically inconsistent retirement de-

cision. The German social security system allows contributors to retire earlier with reduced

monthly benefits. We find that participants, who plan to retire early from the beginning,

compensate this reduction by buying private pension insurance. For time inconsistent partic-

ipants however, early retirement is unplanned and does not increase the likelihood of owning

private pension insurance. Therefore, the reduction in social security benefits remains largely

uncompensated. In the German social security system, this results in a 13% lower level of

monthly retirement benefits. The result suggests that the nature of individual time prefer-

ences strongly influences participants’ financial budget in retirement.

For the larger subsample of not yet retired participants, we focus on the relation between

time preferences and their planned retirement age. Inconsistent time preferences may lead to

a decreasing planned retirement age with advancing age of the decision maker (Diamond and

Köszegi, 2003; Zhang, 2013; Findley and Caliendo, 2015). The argument for this effect is an

increasing temptation to retire as the planned retirement date approaches. We find evidence

for this prediction in the data. Participants’ age has a highly significant and economically

strong negative effect on the planned retirement age. The older participants are, the earlier

they plan to retire. Time inconsistent participants on average plan to retire about 0.7 months

earlier by each year they get older. While this may have numerous reasons, we find that this

negative age effect is between 1.5 and 3 times larger than for time consistent participants.

Moreover, participants who are closer to retirement exhibit a stronger negative effect of age.

Both results are specific to hyperbolic discounting suggesting a role of hyperbolic preferences

in adapting retirement plans.

To test the robustness of these results, we use a German household survey (SAVE panel),

which includes questions on planned and actual retirement. It complements the FAZ survey

data as it provides a representative sample and the opportunity to analyze the dynamics of

planned retirement with panel data. The panel structure of SAVE allows to rule out possible

cohort effects. The analysis of participants in at least two of the SAVE waves in 2008, 2009,

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and 2010 shows that they significantly decrease their planned retirement age over time.1

As the SAVE data lacks a direct measure of time preferences, we use smoking habits as a

proxy. With the help of this proxy we can confirm the previous results for planned and actual

retirement age (controlling for health effects).

2. Time Preferences and the Retirement Decision

2.1. Time Preferences: Hyperbolic Discounting

Time preferences can be described as the relative preference for a good at an earlier date

compared to a later date (Frederick et al., 2002). A discount function is commonly used to

formalize how individuals value consumption or money at different points in time (i.e., to

describe their time preferences). Since Samuelson (1937) introduced the discounted-utility

model, a standard assumption is that discount functions are stationary. The only discount

function fulfilling this assumption is the exponential discount function. Stationarity implies

a constant discount rate between two consecutive time periods. However, empirical and

experimental studies find that discount rates are not constant and individuals exhibit higher

discount rates for outcomes in the near future and lower discount rates for outcomes in the

more distant future (Thaler, 1981; Laibson, 1997; Frederick et al., 2002). Such preferences

can lead to dynamically inconsistent decisions. For example, as explained by Laibson et al.

(1998), someone might prefer a 30-minute break in 101 days over a 15-minute break in 100

days, but as time passes reverse the decision in favor of a 15-minute break today instead of

a 30-minute break tomorrow.

Impatient behavior in the short-run and more patient behavior in the long run can be

described by a hyperbolic discount function. A functional form of the hyperbolic discount

function is DF(t) = (1 + αt)− γ α with parameters α,γ > 0 (Loewenstein and Prelec, 1992).

Compared to the exponential function, the hyperbolic function discounts the immediate

future more strongly and becomes rather flat for the distant future. Dynamic inconsistency

1Waves before 2007 are not included, as with the reform of the German pension system in 2007, the full retirement age has been increased to 67. This change represents a structural break in the panel.

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arises, as a decision maker chooses an optimal plan at a point in time t, but re-evaluates this

plan at a later point in time t + 1 and may not stick to it. Hereby, it is important whether

the decision maker is aware of the hyperbolic preferences or not (sophisticated vs. näıve,

O’Donoghue and Rabin, 1999). The näıve hyperbolic decision maker does not anticipate the

urge to change the original plan in later periods. In contrast, the sophisticated decision maker

anticipates a lack of self-control and tries to pre-commit to a course of action if possible

(Strotz, 1955; Thaler, 1981; Sorger, 2007). Commitment devices can help a sophisticated

decision maker to stick to a plan identified as optimal. Examples for financial commitment

devices are savings accounts with low liquidity like savings clubs or long-term deposits.

2.2. The Retirement Decision

The decision of when to retire and to claim social security benefits is one of the most

important financial decisions in later life. For example in Germany, retiring at the earliest

age possible (63) instead of the full retirement age (67) results in a permanent decrease of

about 28% in monthly social security benefits for the remaining lifespan (Merkle et al., 2017).

In addition, the time in retirement is increasing due to life expectancy increasing faster than

the effective retirement age.

We first provide an overview on how hyperbolic time preferences influence retirement

timing in theory. Hyperbolic decision makers pay much attention to the near future. In

the retirement context, this can have two opposing effects: On the one hand, hyperbolic

decision makers prefer instantaneous consumption and save less during their work life. As a

consequence, they might have to work longer before they can afford to retire than exponential

decision makers (Laibson, 1997). On the other hand, the retirement timing decision itself

represents a trade-off between immediate leisure and future consumption. Hyperbolic decision

makers are tempted to retire early since they weight the utility gained from immediate leisure

highly relative to the utility loss due to reduced future consumption. For a given level of

accumulated wealth, the hyperbolic decision maker is thus more likely to retire early. We

highlight three of the most prominent models studying the savings and retirement timing

decisions under hyperbolic discounting.

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Diamond and Köszegi (2003) examine the effect of endogenous retirement decisions on

prior savings behavior in a model with sophisticated quasi-hyperbolic agents.2 In a three-

period setting, the agent works in period −1, decides whether to work or to retire in period

0, and is retired in period 1. Working in period −1 provides income, which can be consumed

or saved. As a result of saving, the agent holds wealth W0 ≥ 0 in period 0.

Working in period 0 produces additional wealth of ∆, but costs effort of e > 0. For

consumption in periods 0 and 1, there thus is W0, if the agent retires, and W0 + ∆ otherwise.

Diamond and Köszegi (2003) show that there are wealth levels, W0, for which the agent

initially (in period −1) plans to retire late (in period 1) but, with ongoing time, reevaluates

this plan and chooses to retire early (in period 0), displaying a dynamic inconsistency. As

sophisticated quasi-hyperbolic agents anticipate this future behavior, they can incorporate

it into the initial retirement plan. This allows for two outcomes: Either the savings in period

−1 can be reduced so that W0 is sufficiently low to force the period-0-self to work (“strategic

undersaving”), or savings can be increased that both the self in period −1 and 0 prefer

to retire early. Whether or not hyperbolic discounting leads to early retirement, therefore,

depends on the level of accumulated wealth.

Two extensions to the model have been proposed. Holmes (2010) shows that, in a

three-period model, dynamic inconsistency in the retirement decision will never occur. An

agent with hyperbolic time preferences would not save an amount sufficiently high to cause

unplanned early retirement. However, Findley and Feigenbaum (2013) show that time-

inconsistent retirement can exist with a slight generalization of the underlying assumptions.

Again, depending on accumulated wealth, agents plan to retire late but actually retire early.

Zhang (2013) argues that empirically both undersaving and early retirement is observed.

For example in the U.S., the majority of employees choose to retire earlier than the full

retirement age (Behaghel and Blau, 2012; Gruber and Wise, 2004). Simultaneously, the

aggregated U.S. savings rate has been declining since the 1980s (Laibson, 1997). Zhang (2013)

studies a three-period model that differs from the Diamond and Köszegi (2003) model in three

2The concept of quasi-hyperbolic discounting has been introduced by Laibson (1997). The quasi- hyperbolic discount function is a discrete time function DF(t) = βδt and DF(0) = 1, with δ and β between 0 and 1. It combines most features of the general hyperbolic function with a good analytical tractability.

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ways: 1) The decision maker chooses an amount of labor supply l in period 0. Therefore, the

decision whether to work or to retire is continuous. 2) Both näıve and sophisticated hyperbolic

agents are taken into account and 3) early retirement and undersaving are defined relative

to a decision maker who discounts exponentially. As a result, she shows that hyperbolic

discounting can lead to a co-existence of undersaving and early retirement. This holds for

näıve as well as for sophisticated decision makers.

Findley and Caliendo (2015) also study the effect of hyperbolic discounting on savings be-

havior in a continuous-time model with endogenous retirement. They focus on näıve decision

makers and compare them to exponential discounters. They find that hyperbolic discounters

plan to retire early but then delay retirement, which is caused by insufficient savings. The

hyperbolic discounter fails to stick to previous savings plans and, therefore, has to delay

retirement.

2.3. Hypotheses

According to the presented theory, hyperbolic discounting can have a direct and an indi-

rect effect on retirement timing. The direct effect predicts earlier retirement as hyperbolic

discounters are tempted to trade future consumption against immediate leisure. The indi-

rect effect, however, goes in the opposite direction. Hyperbolic discounters might not have

sufficient savings to finance early retirement and therefore need to work longer.

We study the empirical relation between inconsistent time preferences (probably due

to hyperbolic discounting) and the retirement decision in Germany. Since the theoretical

predictions are conflicting, we derive two pairs of hypotheses. In our first pair of hypotheses,

we consider the influence of inconsistent time preferences on actual retirement age. Taking

into account the direct and indirect effect, we hypothesize:

H1a: Time inconsistent decision makers will retire earlier than time consistent

decision makers.

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H1b: Time inconsistent decision makers will retire later than time consistent

decision makers.

Inconsistent time preferences do not only influence the final retirement decision, but also

ongoing retirement plans. A hyperbolic agent, who approaches retirement, walks up the

discount function and becomes more and more tempted to retire early, expressed by reducing

the planned retirement age. However, agents might also become increasingly aware of their

insufficient savings and postpone retirement. Therefore, the direct and indirect effect of

inconsistent time preferences lead to Hypotheses 2a and 2b:

H2a: The planned retirement age of time inconsistent decision makers will de-

crease with increasing age.

H2b: The planned retirement age of time inconsistent decision makers will in-

crease with increasing age.

There are of course many other factors that might have an effect on planned retirement age.

For example, older individuals have less uncertainty about their future life expectancy. If they

have previously overestimated (underestimated) their life expectancy, they would revise their

retirement plans accordingly. In our analysis, we control for subjective life expectancy. We

further control for demographics, risk aversion, loss aversion, and many other variables. To

establish a stronger link between time inconsistent retirement and hyperbolic discounting,

we derive two additional hypotheses.

If results regarding H2 are driven by time inconsistent preferences, there should be no

age-effect for time consistent decision makers. In the analysis, we compare both groups. We

hypothesize:

H3: The negative or positive effect of age on planned retirement age will only be

present for time inconsistent decision makers.

The idea of time inconsistent retirement plans is also supported by Bidewell et al. (2006),

who conduct an experiment in which participants choose between early and late retirement

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depending on hypothetical savings, enjoyment of retirement, and chances of good health

during retirement. They find that participants, who are closer to their planned or expected

retirement age, are more impatient and are willing to give up more of their future retirement

income in order to retire early. This is in line with hyperbolic time preferences, as a hyperbolic

decision maker is more impatient with regard to the immediate future. For the observed age

effect, we therefore hypothesize:

H4: The negative or positive effect of age on the planned retirement age will be

stronger for decision makers closer to retirement.

3. Survey Design and Data, Summary Statistics, and Estimation

Strategy

3.1. Survey Design and Data

We conduct an online experiment in cooperation with a large and well-circulated German

newspaper, the Frankfurter Allgemeine Zeitung (FAZ). Participants are recruited via a link

on the newspaper’s website and two announcements in the print edition. In total, 3,077

participants complete the 21 survey questions, which takes them on average 11 minutes.

Participants answer hypothetical questions about retirement planning, demographics, their

risk preferences, time preferences, and financial literacy. A number of observations have to

be excluded, as there are missing values in variables necessary for the analysis (e.g., not

all participants complete the time preference questions). In addition, some participants are

assigned to different treatments, which are analyzed in two papers that use data from the

same survey (Schreiber and Weber, 2016; Merkle et al., 2017). The final sample for this study

consists of 218 retired participants and 2,049 non-retired participants.

The main dependent variables are the actual or planned retirement age. First, participants

are asked whether or not they already retired. Depending on their response, the subsequent

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question elicits the planned or actual retirement age. We ask participants “At what age do

you plan to retire?” or “At what age did you retire?”, respectively.

To distinguish between time inconsistent and time consistent participants, we follow a

standard eliciting procedure from the decision analysis literature (Sayman and Oencueler,

2009; Meier and Sprenger, 2013). Participants make six choices on when to receive a tax

refund. The choices always offer a smaller sooner refund and a later larger refund. Half of

the choices involve decisions between a refund today and in ten months, while the other half

is between a refund in 18 months and 28 months. The three questions within each set differ

in the annual interest rate i, which takes the values 3.3%, 11.3%, and 31.3%. Figure 1 shows

a (translated) screenshot of the time preference questions.

If participants have time consistent preferences, only the time difference between the two

options should matter, which is the same for all questions (10 months). Time consistent

participants make the same decision (earlier or later payment) independent of whether the

earlier payment takes place today or in 18 months. Hyperbolic decision makers, however,

value the immediate payment more highly relative to the payment in 10 months than they

do if all payments are delayed by 18 months. It is likely that a hyperbolic discounter will

switch decisions for at least one interest rate level. In Online Appedix B, we discuss the

occurrence of such switches depending on the discount function. Participants’ choices are

thus classified as inconsistent if they prefer the earlier payment in the choice involving the

immediate payment and the later payment in the delayed choice. We define a proxy for time

preferences that counts the number of inconsistent answers ranging from 0 to 3.

In the experiment, we use hypothetical choices. The non-incentivized design allows us

to recruit a large sample of participants including employees of all ages and retirees. In

contrast to a laboratory experiment with students, for many participants the decision when

to retire lies in the nearer future. We expect the participants to give more relevant answers to

retirement-related questions compared to a student sample. There are two additional reasons

why we did not incentivize the survey. First, using real incentives in an intertemporal choice

can provoke participants to view future payments as uncertain; in particular, when the time

distance between the experiment and the actual payoff is large (e.g., up to 28 months in our

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survey). Therefore, a present bias or hyperbolic discounting pattern can be generated even

for participants with time consistent preferences (Read, 2005; Sutter et al., 2013). Second,

if real money is paid, this could create a self-selection problem by attracting participants

who are in immediate need of money. This again would introduce a bias in the direction

of hyperbolic discounting (Noor, 2009; Sutter et al., 2013). In addition, Rubinstein (2001)

replicates more than 40 experiments without monetary rewards and in almost all cases finds

no qualitative differences in results compared to incentivized experiments.

A set of eight control variables includes measures of risk and loss aversion, financial

literacy, subjective life expectancy, ownership of private pension insurance, trust in the social

security system, the time needed to complete the survey, and the full retirement age. Risk and

loss aversion are both self-reported and elicited on a seven-point scale. Participants indicate

whether they agree to the statements “I am very afraid of losses” and “I am a risk-averse

person.” There is evidence that self-reported risk and loss preferences are good predictors of

choices (Nosic and Weber, 2010; van Rooij et al., 2011; Merkle et al., 2017).3

Participants also answer a set of six financial literacy questions. Since the FAZ newspaper

focuses on financial markets, only one of the basic questions and three of the advanced ques-

tions by (van Rooij et al., 2011) are used. We introduce two even more advanced questions

(see Online Appendix A). Additional controls are participants’ subjective life expectancy

(elicited directly), an indicator variable that equals one if a participants owns private pen-

sion insurance, and a measure of trust in the German social security system (on a scale from

1-7). If a participant is not retired, we ask for the current monthly after tax income. Retired

participants instead report their retirement benefits, provided by the social security system

and private pension insurance. Additional demographics (age, gender, number of children,

education, and marital status) are elicited, and the time needed to complete the survey is

recorded.

3Simple scales might currently be the best available measurement, as lottery-based approaches, such as Holt and Laury (2002), have mostly proved unsuccessful in predicting behavior in non-lottery tasks. In addition, Erner et al. (2013) show that elicited prospect theory parameters including loss aversion have low predictive power out of sample. An additional disadvantage of lottery tasks is the demanding and lengthy elicitation procedure.

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3.2. Summary Statistics

Table 1 displays summary statistics and a short description of all variables. The average

planned retirement age is close to the former full retirement age in Germany (65). The actual

retirement age of retirees in the survey is 61.5. If we consider men and women separately, the

actual retirement age is 61.6 for men and 60.6 for women. In the year of the survey (2012),

the average retirement age in Germany was 61.14, which is not significantly different from

the mean in the experiment.

The average age in the sample is 43 years. Men are overrepresented (85% male), reflecting

the fact that the majority of FAZ readers are male (62%). Moreover, the FAZ sample can

be classified as a high education and high income sample. Participants report a monthly

net income of EUR 3,449, which is about 50% higher than the German average at the time

of the survey.5 Education is measured by the fraction of participants who obtained a high

school diploma or university degree; 91% of participants received the German equivalent to

a high school diploma and 66% graduated from a university. About half of the participants

are married. In Section 5, we test the robustness of the results with a representative German

Household Panel (SAVE Panel).

The average number of inconsistent answers to the three pairs of tax refund questions

is 0.68. More than 50% of participants always answer consistently (number of inconsistent

answers = 0). These participants are classified as “time consistent participants.”6. About

9% of participants always answer inconsistently. In the quasi-hyperbolic model, these would

be people with a high present bias (low beta), but moderate discount rate (see also Online

Appendix B).

4Average age at which a person first received an old-age pension. Source: Eurostat, (http://appsso. eurostat.ec.europa.eu/nui/show.do?dataset=lfso_12agepens&lang=en); retrieved 11/22/2017.

5Source: German Federal Statistical Office (www.destatis.de/DE/ZahlenFakten/ GesamtwirtschaftUmwelt/VerdiensteArbeitskosten/VerdiensteVerdienstunterschiede/Tabellen/

Bruttomonatsverdienste.html); retrieved 11/27/2017. EUR 3,391 is the average gross income (2012), net income is about 6070% of this value depending on personal tax rate.

6The three questions cannot perfectly identify time inconsistent preferences. There exist parameter com- binations for the hyperbolic and quasi-hyperbolic discount functions that also produce zero switching. Our measure is thus conservative and may understate the prevalence of time inconsistent preferences

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The survey includes eight control variables. The questions for risk-aversion and loss aver-

sion on a seven-point scale result in average ratings of 3.9 and 4.3, respectively. As expected,

participants do well in the financial literacy task with an average of 4.1 correct answers (out

of six). Participants estimate their life expectancy on average to be 83.6 years, and about

60% own private pension insurance. The trust in the social security system is on average

rated 3.1 on a seven-point scale. Participants completed the survey on average in 11 minutes.

3.3. Estimation Strategy

The full sample can be naturally split into two subsamples: participants who are already

retired and those who are not yet retired. To test Hypothesis 1, we use the retired subsample,

and the actual retirement age of participants as dependent variable. To test Hypotheses 2-4,

the non-retired subsample and their planned retirement age is used as dependent variable.

A complication arises due to the reform of the German pension system in 2007. A stepwise

increase of the full retirement age (FRA) was implemented in this reform depending on the

year of birth. Contributors born before 1947 could still claim full retirement benefits at age

65, while the FRA was raised to 67 for those born after 1963. In between, the FRA increases

by one to two months for each year of birth.

The variation in full retirement age is problematic for the following reason: if participants

make plans relative to their FRA, then retiring one year earlier than the FRA will result in

a higher planned retirement age for young participants. Regressing planned retirement age

on current age would result in a negative age effect even if all participants had the same plan

(retiring one year prior to the FRA). To account for this, we use survey participants current

age to calculate the FRA per participant. On average, the full retirement age in the sample is

66.6 years (see Table 1). To control for the FRA, the variable full retirement age is included

in all regressions in which the planned retirement age is used as dependent variable.7

7In addition, taking only non-retired participants into account results in a conservative estimate of the age effect, as the planned retirement age of all participants in the sample has to be greater than their current age. A participant of age 63 remains in the sample only when expressing a relatively high planned retirement age.

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In the first regression specification, the actual retirement age (ARA) is the dependent

variable. In Hypotheses 1a and 1b, we posit that time inconsistent participants retire earlier

or later than time consistent participants. The effect of time preferences on the ARA is

estimated with the following regression model:

ARA = β0 + β1Inconsistent Answers + βDD + βCC + ε. (1)

β1 is the coefficient of interest and measures the effect of the number of inconsistent answers

on the actual retirement age. A significant and negative coefficient would provide evidence in

favor of H1a. Participants who make time inconsistent decisions more often would on average

retire earlier. In contrast, a significant and positive coefficient would provide evidence in favor

of H1b. In Equation (4.1), D is the vector of demographic variables and C is the vector of

the additional control variables. ε is the error term.

In a second regression specification, Hypotheses 2a, 2b, and 3 are tested. The effect of

time preferences and age on the dependent variable planned retirement age (PRA) is assessed

in the following way:

PRA = β0 + β1Inconsistent Answers + β2Age + β3(Age · Inconsistent Answers)

+ βDD + βCC + ε. (2)

In Equation (2), the number of inconsistent answers again serves as measure of time prefer-

ences. We include Age, the mean centered age, as explanatory variable for which β2 measures

its effect on planned retirement age. Centering the age variable is necessary as otherwise the

baseline effect of number of inconsistent answers would be the effect for an age equal to zero

(Spiller et al., 2013). A significant and negative (positive) coefficient β2 provides evidence for

Hypothesis 2a (2b). In addition, the interaction of the number of inconsistent answers with

Age is included. Hypothesis 3 predicts that the magnitude of the age effect increases with

hyperbolic discounting. Therefore, we expect β3 to be significant and in the same direction

as the age effect.

15

In a final regression specification, we test Hypothesis 4. It states that the age effect

will be stronger for participants closer to retirement. To test for this non-linearity in the

age effect, we include three additional explanatory variables in Equation (2). We add age

squared Age2 to asses the nonlinearity. However, age is mean centered, which generates high

squared values for participants who are older or younger than the mean age. As we are

mainly interested in participants who are close to retirement, we include an indicator for age

above the mean (Age>Mean). We study the interaction of this indicator with age squared

to test whether there is a nonlinearity in the age effect for older participants. The following

model is estimated:

PRA = β0 + β1Inconsistent Answers + β2Age + β3(Age · Inconsistent Answers)

+ β4Age 2 + β5Age>Mean + β6(Age

2 ·Age>Mean) + βDD + βCC + ε. (3)

In addition to these main regressions, we analyze further variables such as the ex-post sat-

isfaction with the retirement timing decision and the purchase of private pension insurance.

4. Results

4.1. Results for Actual Retirement Age

We examine the relation between time preferences and the actual retirement age of retired

participants. In total, 218 retired participants answer the time preference questions com-

pletely. The results of a simple cross-tabulation are presented in Figure 2. The number of

inconsistent answers is important for retirement timing: answering more time preference

questions inconsistently leads is associated with a lower actual retirement age. Participants

who answer all three tax questions inconsistently retired on average 2.2 years earlier than

those with zero inconsistent answers. This difference is significant at the 1%-level.

Table 2 reports results of the multivariate ordinary least squares (OLS) regression analysis

outlined in Equation . In column (1), we include the number of inconsistent answers as

an explanatory variable. In columns (2) and (3), demographics and control variables are

16

added subsequently. In all three regressions, the number of inconsistent answers has a highly

significant and negative effect on the actual retirement age of retired participants. In the full

specification of column (3), the actual retirement age decreases by 0.76 years per inconsistent

answer. The most inconsistent participants (number of inconsistent answers = 3) retire on

average about 3 · 0.76 = 2.3 years earlier compared to participants with zero inconsistent

answers. The significance and magnitude of the effect presented in Figure 2 is thus robust

to the inclusion of demographic and control variables.

In summary, we find evidence in support of Hypothesis 1a. Time inconsistent participants

on average retire earlier than time consistent participants. The contrary Hypothesis 1b can be

rejected. The predominant direct effect of hyperbolic discounting may be due to the nature of

Germany’s social security system. As mandatory contributions are a fixed fraction of income,

there is no room for undersaving within the system. Given that social security benefits still

represent the main source of retirement income (about 75% according to a report of the

German government)8, undersaving outside the system may be of limited consequence; time

inconsistent employees might still be able to afford early retirement. One can interpret the

social security system as a commitment device for these people.

In addition to the number of inconsistent answers, two demographic variables and one

control variable are significant predictors of the actual retirement age in column (3) of Table

2. Participants who earn higher income (in this case after retirement income) retire earlier.

Moreover, male participants on average retire 2.3 years later compared to female participants.

Both patterns are often observed (van Solinge and Henkens, 2010; Moen and Flood, 2013).

In addition, we find that financial literacy, measured by the number of correct responses to

the financial literacy questions, reduces the actual retirement age. This effect is puzzling, but

mainly driven by few retirees who answer only one or two out of the six questions correctly.

8Source: Alterssicherungsbericht 2012, Bundesministerium für Arbeit und Soziales, (http: //www.bmas.de/SharedDocs/Downloads/DE/PDF-Gesetze/alterssicherungsbericht-2012.html); retrieved 11/28/2017.

17

4.2. Ex Post Satisfaction with Retirement Timing

When people follow their preferences it is not immediately obvious whether this is harmful,

even if these preferences are inconsistent. We thus next examine whether time inconsistent

participants are satisfied with their decision ex post. A decision in which immediate leisure

is weighted to highly relative to future consumption, might be regretted afterward. The FAZ

survey data allows to analyze this questions. Retired participants are asked how they would

decide if they could make the retirement decision again. They can choose whether they would

retire later with higher social security benefits, retire earlier with reduced social security

benefits, or make the same retirement decision again. To analyze satisfaction with retirement

timing, we create an indicator variable Retired Too Early. It equals 1 if participants indicate

that they retired too early and would retire later from today’s perspective. The indicator

equals 0 for participants who would not change their decision or would retire earlier.

Figure 3 shows a cross-tabulation of results for the number of inconsistent answers and

the fraction of participants who indicate that they retired too early. Time preferences seem to

matter: The fraction of participants stating they retired too early is significantly increasing

with the number of inconsistent answers. In the group of retirees who are classified as time

consistent, 15.6% indicate that they would now choose to retire later. This fraction increases

almost monotonously to 34.9% in the group with three inconsistent answers. The difference

is significant at the 1%-Level.

In Table 3, we present results of the corresponding OLS regression analysis. The depen-

dent variable is the indicator variable Retired Too Early. We apply OLS regressions through-

out the paper as coefficients and interaction effects can be interpreted directly. All results

with a binary variable as the dependent variable are confirmed using logistic regressions (see

Online Appendix C). In column (1), we include the time preference measure (Inconsistent

Answers ) as an explanatory variable, in column (2) actual retirement age and demographic

variables are added, and in column (3) additional controls are included.

The effect of the time preference measure is significant and positive in all three specifica-

tions. In the full model (column (3)), the probability of judging the own retirement timing

18

as too early increases by about 7% per inconsistent answer. In addition, the number of in-

consistent answers is the only variable that has a strongly statistically significant effect in all

three specifications. In particular, the age participants actually retired does not matter for

the propensity to regret the decision. The only other variable with a significant effect is the

indicator for holding a high school degree. Participants with a high school degree are more

likely to wish they had retired later. In sum, the results provide evidence that time incon-

sistent decision makers are ex post more likely to regret their retirement decision. This can

be a result of the unplanned decision which is inconsistent with prior as well as subsequent

preferences.

4.3. Results for Planned Retirement Age

We next examine the planned retirement age of all participants who are not yet retired. With

2,062 observations, this subsample is much larger than the sample of retired participants.

Using this data, we test Hypotheses 2a, 2b, 3, and 4 on the influence of time preferences

on the planed retirement age. For easier interpretation of the coefficients, we use planned

retirement age in months (not years).

Hypothesis 2a (2b) predicts a negative (positive) effect of age on planned retirement

age. Regression specification (1) of Table 4 includes mean centered age, demographics, and

controls as explanatory variables. The effect of age is highly significant and negative. Per year

of age, participants reduce their planned retirement age on average by about 0.5 months.

As the age range in the sample of non-retirees is about 40 years, this implies a difference

in planned retirement age of about 1.7 years from the youngest to the oldest participants.

We control for individual full retirement age to avoid picking up the legal increase in full

retirement age. While other cohort effects are possible, in robustness tests we confirm this

finding in a panel (see section 5).

In addition, coefficients for income and university degree are statistically significant.

Participants with a higher income plan to retire earlier, which is in line with Munnell et al.

(2004) and Li et al. (2008), who also find a negative relation between income (or wealth)

19

and retirement age. Participants with a university degree plan to retire on average about

seven months later than participants without a university degree. This effect could be driven

by higher job satisfaction (Helman et al., 2008). Additionally, education could enable a

better understanding of the impact of retirement age on social security benefits, which could

motivate a later planned retirement age (Coile et al., 2002).

Of the control variables, loss aversion, subjective life expectancy, and owning private pen-

sion insurance significantly affect the planned retirement age. More loss averse participants

plan to retire earlier, which might be driven by an endowment effect. Shu and Payne (2015)

find that loss aversion is a significant predictor of preference for early versus later retirement.

We further find that participants who indicate a higher subjective life expectancy plan to

retire later, which seems reasonable as they expect to spend a longer time in retirement.

They expect to receive social security benefits for a longer period of time, which makes

early retirement more costly. Finally, owning a private pension plan reduces the planned

retirement age by about six months. Private pensions substitute for social security benefits,

making early retirement more affordable (Bidewell et al., 2006).

We find evidence in support of Hypothesis 2a. However, a negative effect of age on the

planned retirement age can be driven by other factors besides time preferences. Therefore,

we test two additional hypotheses that are specific to hyperbolic discounting to empirically

rule out other possible explanations.

Hypothesis 3 states that the negative effect of age on the planned retirement age will be

stronger for more time inconsistent participants. To test this hypothesis, we use the vari-

able Inconsistent Answers and its interaction term with (mean centered) age as expressed

in equation 2. The coefficient β2 measures the baseline age effect for time consistent par-

ticipants. Coefficient β3 allows us to assess to what extend the negative age effect is driven

by inconsistent preferences. Results in column (2) of Table 4 reveal that β2 is negative and

marginally significant, meaning that the age effect is present for time consistent participants.

However, its economic magnitude is smaller compared to the results in column (1). More

importantly, the coefficient β3 for the interaction term is negative and strongly significant.

The age effect increases for more time inconsistent participants; per inconsistent answer by

20

−0.26. For example, in the extreme case of three inconsistent answers, the average negative

age effect is −1.17 (−0.39 + 3 ·−0.26).

The result provides evidence that hyperbolic discounting contributes to an inconsistent

retirement decision, as the age effect is much stronger for participants with time inconsistent

preferences (in line with Hypothesis 3). However, we also find a negative age effect for

time consistent participants. There are two potential explanation for this finding. First, our

measure for time preferences does not capture all forms of time inconsistency. It remains

possible that participants, who are falsely classified as time consistent, drive the age effect

in this group. Secondly, other factors besides time preferences may cause an age effect.

For example, health effects are only measured indirectly by controlling for life expectancy.

However, it could be that some participants develop health issues that are curable but

nevertheless require earlier retirement. These participants would update their retirement

plans but not their life expectancy. But as such factors should affect both groups equally,

the between group difference speaks for a strong role of inconsistent time preferences for

planned retirement.

The functional form of hyperbolic time preferences implies that the negative effect of

age on the planned retirement age will be stronger for decision makers closer to retirement

(Hypothesis 4). Impatience is particularly strong for the present or near future. As partici-

pants approach retirement, they are more tempted to retire early and to trade future income

for immediate leisure. Column (3) in Table 4 shows the results of a regression estimating

the model presented in Equation (4.1). The variable Age2, the indicator variable Age Above

Mean, and their interaction are introduced to test Hypothesis 4. Squared age accounts for a

non-linear age effect. The indicator variable is added as this effect is only expected for the

upper part of the age distribution.

In this regression, the baseline effect of age becomes insignificant, although it is still neg-

ative. The interaction effect between age and inconsistent time preferences remains negative

and significant. The age effect appears more robust for participants with time inconsistent

preferences. In addition, the effect of Age2 as well as its interaction with the indicator variable

are significant. For participants below the mean age, Age2 has a positive sign. This means

21

the younger participants are, the later they plan to retire. The opposite effect is observed

for participants older than the mean age. The coefficient for interaction of Age2 with the

Age Above Mean indicator term is −0.12 and significant. The closer the participants are to

reaching retirement, the stronger the negative effect of age becomes. This lends support to

Hypothesis 4.

4.4. Sophisticated vs. Näıve Hyperbolic Decision Makers

In the literature, an important distinction is made between sophisticated and näıve hy-

perbolic discounters (Laibson, 1997; Diamond and Köszegi, 2003). Sophisticated hyperbolic

discounters are aware of their preferences and anticipate that they might reverse their deci-

sions in the future. To overcome this time inconsistency, sophisticated decision makers try

to make a binding decision. In the retirement context, sophisticated hyperbolic discounters

would anticipate the urge to retire early and would seek to lock in the late retirement deci-

sion. However in the German social security system, a commitment device that would allow

for a binding decision is not available. Therefore, our hypotheses for actual retirement age

hold for sophisticated and näıve hyperbolic discounters.

In this subsection, we analyze whether hyperbolic discounters buy private pension in-

surance to compensate for an anticipated reduction in social security benefits due to early

retirement. If participants who plan to retire earlier are more likely to own private pension

insurance, this would be evidence for a planned decision and against näıve hyperbolic dis-

counting. Table 5 presents the results of three OLS regressions with an indicator variable

that equals 1 if a participant owns private pension insurance as the dependent variable (see

Online Appendix C for the corresponding logistic regressions). Column (1) presents results

for the full sample. Columns (2) and (3) show results for subsamples of younger and older

participants using a median split of age.

In specification (1), the planned retirement age has a highly significant and negative

effect on the probability of owning private pension insurance. Participants who plan to

retire earlier are more likely to own private pension insurance. This savings behavior seems

22

rational as earlier retirement reduces social security benefits and private pension insurance

can compensate for this reduction. The effect of the number of inconsistent answers is also

negative and significant. Consistent with the idea that hyperbolic discounters find it harder to

save, they are less likely to own private pension insurance (by 2.5% per inconsistent answer).

However, some of the more sophisticated hyperbolic discounters might use a private pension

contract as a commitment device.

When we compare the effect of the planned retirement age on the likelihood to own

private pension insurance in column (1) with the subsamples displayed in columns (2) and

(3), we find that the effect is significant and stronger for younger participants. This means

that participants who plan far ahead to retire early incorporate this retirement plan into

their savings decision. However, participants above median age show less inclination to com-

pensate for early retirement by private pension insurance. One reason could be that they

adapted their retirement plans over time (as shown before). They would then confront an

unanticipated gap in their retirement provisions. Again, participants with inconsistent time

preferences are less likely to own private pension insurance (not significant).9

Retiring early without sufficient replacement by other means of savings has severe finan-

cial consequences. Not only do retirees incur a deduction on their social security benefits by

each month they retire earlier, but they also forgo additional contributions they would be

making when retiring later. In Online Appendix D, we provide a calculation of the financial

impact of the on average 2.2 years of earlier retirement we observe for the most time incon-

sistent participants. In the German social security system, this would result in 13% lower

social security benefits. These lower benefits are permanent, which is why retirement entry

should be well-considered.

9The results are robust to splits at other ages. In particular, for participants very close to retirement, the coefficient for planned retirement age even changes sign. This means that those opting for early retirement are less prepared than those who retire later. However, as the sample size becomes rather small, this result has to be interpreted with caution.

23

5. Robustness

5.1. The SAVE Dataset

For robustness tests, we use a representative German household panel (SAVE). The SAVE

panel survey has been conducted since 2001 by the Munich Center for the Economics of

Aging (MEA). It focuses on savings behavior, financial assets, and old-age provision (for a

detailed description see Börsch-Supan et al., 2009). We use the survey waves of 2008, 2009,

and 2010 in these robustness tests. Waves before 2007 are not included as, with the reform

of the German pension system, the full retirement age increased to 67. In line with Behaghel

and Blau (2012), we find that participants use the full retirement age as an anchor for their

planned retirement age. Therefore, the change in the full retirement age presents a structural

break in the data.

The two dependent variables, planned retirement age and actual retirement age, as well

as the demographics are similar to the ones used in the FAZ experiment. The datasets are

complements, as the SAVE survey provides a more diverse sample of respondents and, due

to the panel structure, allows to study changes within person. However, none of the survey

waves in the SAVE panel includes an explicit measure for time preferences or hyperbolic

discounting. Therefore, we have to use participants’ cigarette smoking habits, which have

been shown to be related to time preferences, as a proxy. Smokers tend to be more impulsive

and impatient than non-smokers, which also extends to behavior not related to smoking

(Bickel et al., 1999; Baker et al., 2003; Reynolds and Fields, 2012). In prior literature, smoking

habits have been frequently used as a proxy for time preferences (Munasinghe and Sicherman,

2006; Kan, 2007; Khwajaa et al., 2007; Grignon, 2009). All waves of SAVE survey provide

information about the smoking habits of participants.

Smoking as a time preference proxy has the disadvantage that it might influence retire-

ment timing due to health effects. Non-smokers are usually found to be in better health

compared to smokers. We thus have to control for health to overcome a potential omitted

variable bias. In the analysis, we include three variables regarding the health status of SAVE

24

participants: 1) the self-assessed health status on a five-point scale; 2) the satisfaction with

the current health status on a ten-point scale; and 3) whether or not the participant suf-

fers (or has suffered) from a prolonged illness. Additional control variables in the SAVE

survey include a financial literacy score, the subjective life expectancy of participants, and

whether or not participants own private pension insurance. The financial literacy score is

based on nine questions from van Rooij et al. (2011) (see Online Appendix A.2). Subjective

life expectancy is elicited in a two-step procedure. First, participants estimate the average

life expectancy for a person of their age and gender. They then indicate by how many years

they expect to live longer or shorter than the average person.10

Table 6 shows summary statistics for the 2010 wave of the SAVE survey. The planned

retirement age of SAVE participants is comparable to the FAZ sample, while the actual

retirement age is lower. The datasets further differ in average income, education, and in the

fraction of female participants. This reflects the educated, more affluent, and predominantly

male readership of the FAZ business section. Some of the differences also arise from the fact

that SAVE participants are much older with a higher fraction of retirees. The SAVE results

will thus provide robustness against selection effects.

5.2. SAVE: Results for Actual Retirement Age

In a first robustness test, we repeat the analysis of actual retirement age with data from the

SAVE 2010 cross-section.11 In the SAVE survey about 907 participants indicate that they

are already retired. We proxy for time preferences by smoking habits (15% are smokers). As

smoking has negative effects on health, we include variables on participants’ health status

in the analysis. A second concern is a potential survivorship bias. Studies that analyze the

effect of regular cigarette smoking find that it on average reduces life expectancy by ten

years (Doll et al., 2004; Sakata et al., 2012; Jha et al., 2013). Consequently, the health status

of the surviving smokers in the dataset is biased upward. However, observing more healthy

10This procedure prevents the responses to be overly affected by misperceptions of general live expectancy. 11We use the cross-section in this analysis, as the number of new retirees in each wave is small.

25

smokers is an advantage as we are interested in the component of the smoking variable that

is correlated with time preferences, not health.

Table 7 presents the results of three OLS regressions with the actual retirement age

as the dependent variable. In column (1), only the time preference proxy is included in

the regression. In the regression for column (2), control variables on participants’ health

status are added. The regression for column (3) includes demographics, health controls, and

other control variables. In all three specifications, the coefficient for smoking indicator is

negatively related to retirement age. The average difference in the actual retirement age

between smokers and non smoker is 3.6 years (column (1)). Adding health variables (column

(2)) does not change the magnitude and significance of the effect much. In the full model

with all controls (column (3)), the coefficient for the smoking indicator is somewhat reduced

but still negative and strongly significant. As we control for health variables, life expectancy,

and other personal characteristics, the unobservable difference between smokers and non-

smokers can be at least partly attributed to time preferences. We conclude that inconsistent

time preferences proxied by smoking habits contribute to earlier retirement (in line with

Hypothesis 1a).

Besides the time preference proxy, poor health is predictive of early retirement. The

self-assessed health status is significant at the 1%-level; a one point higher value on the five-

point scale is associated with a 1.5 year reduction in retirement age. This variable seems to

subsume the other health variables as they remain insignificant. In the full model (column

(3)), age, gender, income, and education show the same effects as in Table 2. In addition,

life expectancy and owning a private pension insurance obtain statistical significance. Quite

intuitively, participants with longer life expectancy retire later, while those who own private

pension insurance retire earlier.

5.3. SAVE: Results for Planned Retirement Age

In a second robustness test, we make use of the panel structure of the SAVE data. The

analysis is restricted to 1,653 participants who participated in at least two waves of the

26

SAVE survey in 2008, 2009, and 2010. In the panel the time preference proxy is defined as

indicator variable as before, on average about 35% of the participants smoke. Smoking is

thus much more common in the non-retired subsample than in the retired subsample. We

obtain similar results, if we classify all participants as smokers, who at least smoke at one

survey date.

We run a fixed effects panel regressions with the planned retirement age in months as

dependent variable. The fixed-effects model is used, as a Hausman test rejects the null

hypothesis of no difference between random and fixed effects estimates. The SAVE data

are multiply imputed and all five imputations are used. Coefficients and standard errors for

imputed data are calculated according to Rubin (1987). The main explanatory variable is

the current age of participants. While the age effect identified in the prior analysis could be

due to a cohort effect, the passage of time in the panel identifies aging on a within subject

level. Many of the control variables included in Table 6 cannot be used in the regressions

as they are not elicited in all three waves. Other variables such as gender are constant and

subsumed by the fixed effect.12

Table 8 presents the results of the panel regressions. The regression in column (1) in-

cludes only age for which the coefficient is negative and significant at the 5%-level. On

average, participants decrease their planned retirement age by about 1 months per year.

The economic magnitude of the age effect is larger compared to the cross-sectional analysis.

This might reflect that the SAVE population is older on average and the effect becomes

stronger when people approach retirement (in line with Hypothesis 4). In columns (2) and

(3), we include the time preference proxy and its interaction with age. The age effect seems

to be almost completely driven by the time inconsistent (smoking) subsample. They decrease

their retirement age by about 2.5 months per year, while the effect becomes insignificant for

non-smokers. We interpret the results as further evidence for H2a and H3.

The positive coefficient for the time preference proxy itself is hard to interpret as smoking

habits are mostly constant. In the fixed effect regression it will pick up only changes in

12Variables such as “Married” or “High School Degree” are almost constant. However, as some participants newly marry and others complete a degree as adults, we include the variables for completeness.

27

smoking behavior. Among the control variables, income exhibits a negative effect on planned

retirement as seen before. For health, only satisfaction with health is available as a panel

variable. It remains insignificant, which suggests that it is not declining health that explains

the reduction in planned retirement age among smokers. In addition, general health status

will be captured by the fixed effect.

6. Conclusion

In an experiment on choices within the social security system, we relate the decision of

when to retire to participants’ time preferences. In cooperation with FAZ, a large and well-

circulated German newspaper, more than 3,000 participants are recruited. The experiment

includes questions on the preferred time to receive a tax refund which allow to measure time

preferences of participants. We use this measure to analyze the effect of inconsistent time

preferences on the actual and planned retirement age. We find that participants behaving in

line with hyperbolic discounting are more likely to show inconsistent retirement planning.

The typical pattern is that time inconsistent participants decrease their planned retirement

age as they age. The temptation of early retirement seems to get stronger, as retirement

approaches. This age effect is much less strong for (time-consistent) exponential discounters.

Moreover, as predicted for hyperbolic discounters, the effect gets stronger for participants

who are closer to retirement. For this group the present bias is particularly relevant.

While plans might change a lot, the time preference effect can be confirmed for the

actual retirement age of participants who are already retired. On average, time inconsistent

participants retire 2.2 years earlier than time consistent participants. This behavior has severe

financial consequences during retirement as it results in a decrease in monthly retirement

benefits of about 13% (in the German social security system. In addition, time inconsistent

participants are more likely to regret their retirement decision. A third of retired participants

who are classified as time inconsistent indicate that they would retire later if they could make

the retirement timing decision again. This suggests that they retire rather spontaneously and

not in line with their prior and later preferences.

28

A policy implication that can be derived from our results is that it would be beneficial

to offer a commitment device within the social security system. At least for sophisticated

hyperbolic discounters, this would provide the opportunity to tie themselves to the mast.

Such a commitment device could work by allowing contributors to lock in a specific retirement

age ex ante. Changes would then only be possible in exceptional circumstances (e.g., severe

health decline or job loss). Alternatively, a waiting period of several months between claiming

and receiving benefits would protect both näıve and sophisticated hyperbolic discounters

from the most immediate impact of present bias. Time consistent contributors would be

(largely) unaffected from these changes as their retirement plans are stable over time.

29

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Table 1. Summary statistics and description. The table presents summary statistics (mean and standard deviation) of all variables and a description of how they were elicited in the FAZ survey.

Variable Mean Description / Survey Questions (Std. dev)

Dependent variables Planned Retirement Age 64.96 Planned retirement age in years

(3.75) (at what age do you plan to retire?). Actual Retirement Age 61.49 Actual retirement age in years

(4.48) (at what age did you retire?).

Demographics Age 43.00 Date of the survey – date of birth.

(14.25) Male 0.85 0=female, 1=male.

(0.36) Married 0.51 0=no, 1=yes.

(0.50) Number of Children 0.87 Number of children.

(1.21) High School Degree 0.91 0=no, 1=yes.

(0.29) University Degree 0.67 0=no, 1=yes.

(0.47) Income 3415.37 Net monthly income in EUR.

(3131.90) Retired 0.10 0=no, 1=yes.

(0.31)

Time preferences Inconsistent Answers 0.68 Number of inconsistent answers (0-3)

(0.98) within three pairs of tax refund questions.

Controls Risk Aversion 3.89 Risk aversion from 1-7

(1.47) (1=not at all, 7=very risk averse). Loss Aversion 4.28 Loss aversion from 1-7

(1.60) (1=not at all, 7=very loss averse). Financial Literacy Score 4.11 Number of correct responses out of 6 financial

(1.14) literacy questions (see online appendix A). Life Expectancy 83.62 Subjective life expectancy in years

(7.73) (how old do you think you are going to get?). Private Pension Insurance 0.62 0=no, 1=yes

(0.49) (do you own a private pension insurance?). Certainty of Social Security 3.10 Safety of social security benefits from 1-7

(1.84) (1=not safe at all, 7=very safe). Time Taken 10.98 Minutes needed to complete the survey.

(2.87) Full Retirement Age 66.75 Full retirement age depending on year of birth.

(0.48)

34

Table 2. Test of Hypothesis 1a and 1b. The table presents the results of three OLS regressions with Actual Retirement Age as the dependent variable. Specification (1) includes the time preference proxy (Inconsistent An- swers ); in specification (2) demographic variables are included; and in specification (3) ad- ditional controls are included. ***, **, and * indicate statistical significance at the 1%, 5%, and 10%-level, respectively. Robust standard errors are displayed in parentheses.

(1) (2) (3)

Time Preferences Inconsistent Answers −0.758 *** −0.843 *** -0.761 **

(0.282) (0.271) (0.308)

Demographics Age 0.328 *** 0.318 ***

(0.064) (0.073) Male 1.554 2.366 *

(1.233) (1.259) Married −0.313 −0.653

(0.853) (0.942) Number of Children −0.216 −0.149

(0.278) (0.300) High School Degree 1.501 1.441

(0.980) (1.011) University Degree −0.166 −0.440

(0.553) (0.577) Income (log) −0.597 * −0.489 *

(0.308) (0.288)

Controls Risk Aversion −0.226

(0.225) Loss Aversion −0.109

(0.201) Financial Literacy Score −0.732 **

(0.353) Life Expectancy −0.046

(0.048) Private Pension Insurance −0.013

(0.563) Certainty of Social Security 0.170

(0.182) Time Taken 0.153

(0.099) Constant 62.153 *** 43.155 *** 48.223 ***

(0.334) (4.359) (6.854)

Number of Observations 218 200 186 Adjusted R2 0.034 0.228 0.246

35

Table 3. Evaluation of the retirement decision. This table presents the results of three OLS regressions with the indicator Retired Too Early as the dependent variable. The indicator equals 1 for participants who state that they retired too early and 0 otherwise. Specification (1) includes the time preference proxy (Inconsistent Answers ); in specification (2), demographic variables are added; and in specification (3) additional controls are added. ***, **, and * indicate statistical significance at the 1%, 5% and 10%-level, respectively. Robust standard errors are displayed in parentheses.

(1) (2) (3)

Time Preferences Inconsistent Answers 0.067 *** 0.068 ** 0.074 **

(0.025) (0.028) (0.030) Actual Retirement Age −0.002 −0.005

(0.009) (0.009)

Demographics Age 0.001 0.002

(0.006) (0.007) Male −0.082 −0.051

(0.119) (0.133) Married −0.013 −0.051

(0.093) (0.106) Number of Children −0.017 −0.014

(0.026) (0.029) High School Degree 0.146 0.212 **

(0.101) (0.105) University Degree −0.125 −0.148

(0.084) (0.092) Income (log) 0.008 0.008

(0.020) (0.020)

Controls Risk Aversion −0.005

(0.023) Loss Aversion 0.012

(0.024) Financial Literacy Score −0.033

(0.036) Life Expectancy 0.002

(0.005) Private Pension Insurance −0.060

(0.066) Certainty of Social Security 0.002

(0.016) Time Taken −0.006

(0.012) Constant 0.171 *** 0.205 0.331

(0.032) (0.546) (0.753)

Number of Observations 217 197 184 Adjusted R2 0.031 0.008 0.000

36

Table 4. Test of Hypotheses 2a, 2b, 3, and 4. This table presents results of three OLS regressions with Planned Retirement Age (in months) as the dependent variable. In column (1), (mean-centered) age is considered; in column (2), the time preference proxy and its interaction with age are included; and in column (3), Age2, Age>Mean, and their interaction. ***, **, and * indicate statistical significance at the 1%, 5% and 10%-level, respectively. Robust standard errors are displayed in parentheses.

(1) (2) (3) Age and Time Preferences Age −0.529 *** −0.387 *4 −0.746

(0.189) (0.198) (0.634) Inconsistent Answers −1.905 * −2.249 **

(1.043) (1.063) Age x Inconsistent Answers −0.255 *** −0.283 ***

(0.084) (0.084) Age2 −0.059 *

(0.030) Age>Mean −7.432

(6.308) Age>Mean x Age2 −0.124 **

(0.058) Demographics Male 1.289 0.850 0.260

(2.829) (2.826) (2.815) Married −3.970 −3.913 −4.439 *

(2.504) (2.506) (2.493) Number of Children 0.326 0.465 0.743

(1.680) (1.677) (1.659) High School Degree 2.865 2.580 4.355

(3.891) (3.909) (3.943) University Degree 7.308 *** 7.818 *** 5.275 **

(2.462) (2.478) (2.634) Income (log) −5.295 *** −5.391 *** −6.855 ***

(1.645) (1.655) (1.738) Controls Risk Aversion 1.370 1.319 1.187

(0.902) (0.906) (0.909) Loss Aversion −1.969 ** −1.990 ** −1.858 **

(0.839) (0.843) (0.847) Financial Literacy Score −1.260 −1.491 −1.478

(0.994) (1.012) (1.008) Life Expectancy 0.503 ** 0.496 ** 0.500 **

(0.251) (0.252) (0.255) Private Pension Insurance −6.157 *** −6.563 *** −6.582 ***

(2.111) (2.113) (2.107) Certainty of Social Security −0.188 −0.266 −0.259

(0.564) (0.566) (0.564) Full Retirement Age −0.429 −0.571 ** 0.237

(0.266) (0.277) (0.798) Time Taken 0.114 0.052 0.047

(0.357) (0.358) (0.359) Constant 1127.245 *** 1245.848 *** 614.318

(210.433) (220.007) (643.318) Number of Observations 2,062 2,049 2,049 Adjusted R2 0.053 0.057 0.064

37

Table 5. Effect of time preferences on private pension insurance. The table presents the results of three OLS regressions with the indicator Private Pension Insurance (see Table 1) as the dependent variable. Column (1) presents results for the full sample. In columns (2) and (3), the results for a sample split by age (at median age 43) are presented. ***, **, and * indicate statistical significance at the 1%, 5% and 10%-level, respectively. Standard errors are displayed in parentheses.

Full sample Age≤43 Age>43 (1) (2) (3)

Time Preferences Planned Retirement Age −0.009 *** −0.011 *** −0.006

(0.003) (0.004) (0.005) Inconsistent Answers −0.025 ** −0.019 −0.025

(0.011) (0.016) (0.017)

Demographics Age 0.000 0.005 * −0.002

(0.001) (0.003) (0.003) Male −0.016 −0.006 −0.041

(0.032) (0.040) (0.056) Married 0.060 ** 0.060 * 0.044

(0.026) (0.035) (0.039) Number of Children −0.010 −0.020 −0.005

(0.010) (0.018) (0.014) High School Degree −0.012 0.063 −0.069

(0.044) (0.075) (0.059) University Degree 0.032 0.016 0.050 *

(0.027) (0.036) (0.043) Income (log) 0.062 *** 0.055 *** 0.057 ***

(0.014) (0.021) (0.021)

Controls Risk Aversion −0.017 * −0.019 −0.017

(0.009) (0.012) (0.015) Loss Aversion −0.008 −0.005 −0.008

(0.009) (0.011) (0.013) Financial Literacy Score −0.007 −0.019 0.019

(0.010) (0.013) (0.017) Life Expectancy 0.003 ** 0.003 * 0.003

(0.001) (0.002) (0.002) Certainty of Social Security −0.001 0.011 −0.013

(0.006) (0.008) (0.009) Time Taken −0.005 −0.004 −0.004

(0.004) (0.005) (0.006) Constant 0.680 ** 0.641 * 0.603

(0.267) (0.359) (0.429)

Number of Observations 2,049 1,196 853 Adjusted R2 0.034 0.043 0.019

38

Table 6. Summary Statistics for SAVE 2010. The table presents summary statistics for the 2010 SAVE survey. The number of observations indicates the maximum number of observations across variable. The SAVE data are multiply imputed with five different imputations. All five imputations are used. Means and standard deviations (in parentheses) displayed in this table are calculated as the average over all five imputations.

Variable Mean Description / Survey Questions (std. dev)

Dependent variables Planned retirement age 64.93 Planned retirement age in years

(2.98) (At what age are you going to retire?). Actual retirement age 58.88 Actual retirement age in years

(7.15) (In which year did you enter retirement?).

Demographics Age 56.68 Year of the survey − year of birth.

(15.20) Male 0.48 0=female, 1=male.

(0.50) Married 0.62 0=no, 1=yes.

(0.49) Number of Children 0.57 Number of children.

(0.90) High School Degree 0.19 0=no, 1=yes.

(0.39) University Degree 0.11 0=no, 1=yes.

(0.31) Income 1520.76 Net monthly income in EUR.

(1017.67) Retired 0.43 0=no, 1=yes.

(0.49)

Time preferences (proxy) Smoker 0.24 0=no, 1=yes

(0.43) (Do you smoke regularly?).

Controls Financial Literacy Score 2.93 Number of correct responses out of 9 financial

(1.07) literacy questions (see online appendix A). Life Expectancy 79.41 Life expectancy for average person

(7.92) + personal relative life expectancy. Private Pension Insurance 0.28 0=no, 1=yes

(0.46) (do you have a private pension insurance?).

Health Health Status 2.61 Health status from very good to very bad

(0.84) (Would you say your health status is... [1-5]). Satisfaction Health 6.03 Satisfaction with personal health

(2.42) (How satisfied are you with your health? [1-10]). Prolonged Illness 0.55 0=no, 1=yes. (Do you have prolonged

(0.50) health problems/illnesses/disabilities?).

Number of Observations 2,047

39

Table 7. Robustness Test Actual Retirement Age. This table shows the results of an OLS regression with the Actual Retirement Age as the dependent variable for the subsample of already retired participants. Standard errors are displayed in parentheses. Data used for the cross-sectional analysis come from the 2010 wave of the SAVE survey. ***, ** and * indicate statistical significance on the 1%, 5% and 10%- level, respectively. The SAVE data is multiply imputed with five different imputations. All five imputations are used. Coefficients and standard errors are calculated according to Rubin (1987).

(1) (2) (3)

Time Preferences (Proxy) Smoker −3.604 *** −3.548 *** −2.532 ***

(0.709) (0.700) (0.708)

Health Health Status −1.577 *** −0.904 *

(0.503) (0.497) Satisfaction Health 0.017 0.075

(0.162) (0.160) Prolonged Illness 0.397 0.535

(0.661) (0.636)

Demographics Male 1.354 ***

(0.460) Married −0.369

(0.485) Number of Children −2.778 ***

(0.423) High School Degree 1.732 **

(0.811) University Degree −0.211

(0.894) Income (log) −0.264 ***

(0.068)

Controls Financial Literacy Score −0.077

(0.221) Life Expectancy 0.131 ***

(0.035) Private Pension Insurance −3.389 ***

(0.820) Constant 59.395 *** 63.506 *** 51.554 ***

(0.259) (2.062) (3.506)

Number of Observations 907 907 905 Adjusted R2 0.033 0.062 0.190

40

Table 8. Robustness Test Planned Retirement Age. This table shows the results of three fixed effects panel regressions with Planned Retirement Age in months as the dependent variable. Standard errors are displayed in parentheses. Data used for the analysis come from SAVE 2008, 2009, and 2010. ***, ** and * indicate statistical significance on the 1%, 5% and 10%-level, respectively. The SAVE data is multiply imputed with five different imputations. All five imputations are used. Coefficients and standard errors are calculated according to Rubin (1987).

Full Sample Time Inconsistent Time Consistent (1) (2) (3)

Age and Time Preferences Age −1.151 ** −0.368 −0.116

(0.556) (0.664) (0.667) Smoker 6.776 * 6.710 *

(3.598) (3.596) Age x Smoker −2.448 ** −2.574 **

(1.241) (1.230)

Health Satisfaction Health 0.011

(0.364) Demographics Married 1.125

(3.099) Number of Children 0.137

(1.693) High School Degree 3.810

(4.380) University Degree −3.058

(4.630) Income (log) −4.828 ***

(1.580) Constant 833.984 *** 796.836 *** 820.728 ***

(25.351) (30.230) (31.506)

Number of Observations 4,043 4,043 4,043 Overall R2 0.022 0.014 0.015

41

Figure 1. Time preference survey questions. Screenshot of the survey question used to elicit time preferences. Displayed are six choices between a smaller sooner amount and a later larger amount.

42

62.20

61.18

60.46

59.98

59

60

61

62

63

0 1 2 3

A V

E R

A G

E R

E T

IR E

M E

N T

A G

E

NUMBER OF INCONSISTENT ANSWERS

–2.23***–1.74*–1.03*

Figure 2. Average actual retirement age by number of inconsistent answers. The solid line shows the average actual retirement age for participants with 0, 1, 2 or 3 inconsistent answers. The number in the dashed box is the difference between the actual retirement age of participants with 0 inconsistent answers and participants with 1, 2 or 3 inconsistent answers, respectively. ***, **, and * indicate statistical significance at the 1%, 5%, and 10%-level of a t-test.

43

15.57%

30.77% 30.77%

34.88%

10%

20%

30%

40%

50%

0 1 2 3

R E

T IR

E D

T O

O E

A R

LY

NUMBER OF INCONSISTENT ANSWERS

+19.31%***+15.20%*+15.20%**

Figure 3. Participants indicating they retired too early by number of inconsistent answers. The solid line shows the fraction of participants who (self-reportedly) retired too early de- pending on the number of inconsistent answers (0, 1, 2, or 3) . The number in the dashed box is the difference between this fraction of participants with 0 inconsistent answers and par- ticipants with 1, 2, or 3 inconsistent answers, respectively. ***, **, and * indicate statistical significance at the 1%, 5%, and 10%-level of a t-test.

44

Online Appendix A. Financial Literacy Questions

The financial literacy questions of the FAZ survey and the SAVE survey are presented in this

appendix. Correct answers to the financial literacy questions are in bold.

A.1. FAZ Survey

1. Suppose you had EUR 100 in a savings account and the interest rate was 4% per year. After

10 years, how much do you think you would have in the account if you left the money to

grow?

(i) More than EUR 140; (ii) Exactly EUR 140; (iii) Less than EUR 140; (iv) Do not

know/Refusal.

2. Normally, which asset described below display the highest fluctuations over time:

(i) Savings accounts; (ii) Bonds; (iii) Stocks; (iv) Do not know/Refusal.

3. Which of the following statements is correct?

(i) Once one invests in a mutual fund, one cannot withdraw the money in the first year;

(ii) Mutual funds can invest in several assets, for example invest in both stocks

and bonds; (iii) Mutual funds pay a guaranteed rate of return which depends on their past

performance; (iv) None of the above; (v) Do not know/Refusal.

4. Consider a call-option with a stock as underlying. Please judge the following statement: “The

price of the call-option should increase if the volatility of the underlying stock increases”

(i) True; (ii) False; (iii) The statement cannot be judge with the information given; (iv) Do

not know/Refusal.

5. If the interest rate falls, what should happen to bond prices:

(i) Rise; (ii) Fall; (iii) Stay the same; (iv) None of the above; (v) Do not know/Refusal.

6. What is measured by a stocks “beta”?

(i) The stocks book to market value; (ii) The stocks volatility; (iii) The sensitivity of the

stock price to price changes of a benchmark index; (iv) None of the above; (v) Do

not know/Refusal.

45

A.2. SAVE Survey

1. Suppose you had EUR 100 in a savings account and the interest rate was 2% per year. After

5 years, how much do you think you would have in the account if you left the money to

grow?

(i) More than EUR 102; (ii) Exactly EUR 102; (iii) Less than EUR 102; (iv) Do not

know/Refusal.

2. Suppose you had EUR 100 in a savings account and the interest rate was 20% per year.

After 5 years, how much do you think you would have in the account if you left the money

to grow?

(i) More than EUR 200; (ii) Exactly EUR 200; (iii) Less than EUR 200; (iv) Do not

know/Refusal.

3. Imagine that the interest rate on your savings account was 1% per year and inflation was 2%

per year. After 1 year, how much would you be able to buy with the money in this account?

(i) More than today; (ii) Exactly the same; (iii) Less than today; (iv) Do not know/Refusal.

4. Suppose that in the year 2012, your income has doubled and prices of all goods have doubled

too. In 2012, how much will you be able to buy with your income?

(i) More than today; (ii) The same; (iii) Less than today; (iv) Do not know/Refusal.

5. Normally, which asset described below displays the highest fluctuations over time:

(i) Savings accounts; (ii) Bonds; (iii) Stocks; (iv) Do not know/Refusal.

6. Which of the following statements describes the main function of the stock market?

(i) The stock market helps to predict stock earnings; (ii) The stock market results in an

increase in the price of stocks; (iii)The stock market brings people who want to buy

stocks together with those who want to sell stocks; (iv) None of the above; (v) Do

not know/Refusal.

7. Buying a company stock usually provides a safer return than a stock mutual fund?

(i) True; (ii) False; (iii) Do not know/Refusal.

46

8. Which of the following statements is correct?

(i) Once one invests in a mutual fund, one cannot withdraw the money in the first year;

(ii) Mutual funds can invest in several assets, for example invest in both stocks

and bonds; (iii) Mutual funds pay a guaranteed rate of return which depends on their past

performance; (iv) None of the above; (v) Do not know/Refusal.

9. If the interest rate falls, what should happen to bond prices:

(i) Rise; (ii) Fall; (iii) Stay the same; (iv) None of the above; (v) Do not know/Refusal.

47

Online Appendix B. The Time Preference Measure

In this appendix, we show how an agent with quasi-hyperbolic preferences would respond to the

tax refund choices illustrated in Figure 1. The quasi-hyperbolic discount factor is DF(t) = βδt and

DF(0) = 1, with δ and β between 0 and 1. Figure B.1 shows the number of inconsistent choices

depending on the parameters of the discount function.

Delta

Beta 1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.90 0.89 0.88 0.87 0.86 0.85 0.84 0.83 0.82 0.81 0.80 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.72 0.71 0.70

1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.99 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

0.98 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0

0.97 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0

0.96 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0

0.95 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0

0.94 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0

0.93 1 1 2 2 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.92 1 2 2 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.91 2 2 2 2 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.90 2 2 2 2 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.89 2 2 2 2 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.88 2 2 2 2 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.87 2 2 2 2 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.86 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.85 2 2 2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.84 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.83 2 2 2 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.82 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.81 2 2 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.80 2 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.79 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.78 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.77 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.76 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.75 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.74 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.73 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.72 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.71 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

0.70 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

Figure B.1. Number of inconsistent choices. The figure shows the number of inconsistent choices by a quasi-hyperbolic agent depending on the parameters δ = and β.

For δ < 0.77, an agent would always prefer the sooner option independent of the initial delay.

However, such low values of delta imply very strong time discounting. For higher values of δ, the

number of inconsistent choices depends on β and increases with lower beta (higher present bias).

The most inconsistent choices occur when β is very low, but δ is close to one. Such time preferences

discriminate strongly between the present and the future, but not so much between two dates in the

future. This is why a choice involving an immediate payout will be viewed differently from a choice

involving two payouts in the future. Importantly, we observe at least one time inconsistent choice

for most parameter combinations. To capture all forms of time inconsistent preferences, a higher

number of questions would be needed (e.g., using an interest rate between the chosen values).

48

Online Appendix C. Robustness Tests

In this appendix, the regressions with binary dependent variables of Table 3 and 5 are re-estimated

using a logistic model.

Table C.1 shows marginal effects of logistic regressions with retirement regret (Retired Too

Early ) as the dependent variable. The results confirm those of the linear regression. The number

of inconsistent answers is a strong predictor of regret. Earlier retirement per se, however, appears

not to be a reason for regret.

Table C.2 shows marginal effects of logistic regressions with ownership of a private pension

insurance (Private Pension Insurance) as the dependent variable. The results again confirm those

of the linear regression. Planned retirement age has a negative effect on owning private pension in-

surance, which means that those who plan to retire earlier compensate for this by buying insurance.

However, participants with time inconsistent preferences are less likely to own insurance.

49

Table C.1. Robustness for Table 3. This table presents marginal effects of three logistic regressions with the indicator Retired Too Early as the dependent variable. The indicator equals 1 for participants who state that they retired too early and 0 otherwise. Specification (1) includes the time preference proxy (Inconsistent Answers ); in specification (2), demographic variables are added; and in spec- ification (3) additional controls are added. ***, **, and * indicate statistical significance at the 1%, 5% and 10%-level, respectively. Robust standard errors are displayed in parentheses.

(1) (2) (3)

Time Preferences Inconsistent Answers 0.061 *** 0.062 ** 0.068 ***

(0.022) (0.024) (0.026) Actual Retirement Age −0.002 −0.005

(0.008) (0.008)

Demographics Age 0.001 0.002

(0.006) (0.006) Gender −0.085 −0.054

(0.125) (0.130) Married −0.014 −0.054

(0.093) (0.106) Number of Children −0.018 −0.015

(0.027) (0.031) High School Degree 0.117 * 0.161 **

(0.068) (0.062) University Degree −0.123 −0.147 *

(0.081) (0.088) Income (log) 0.011 0.015

(0.020) (0.020)

Controls Risk Aversion −0.003

(0.024) Loss Aversion 0.011

(0.024) Financial Literacy Score −0.027

(0.033) Life Expectancy 0.002

(0.005) Private Pension Insurance −0.066

(0.063) Certainty of Social Security 0.003

(0.015) Time Taken −0.007

(0.011)

Number of Observations 217 197 184 Pseudo R2 0.031 0.048 0.078

50

Table C.2. Robustness for Table 5. The table presents marginal effects of three logistic regressions with the indicator Private Pension Insurance as the dependent variable. Column (1) presents results for the full sample. In columns (2) and (3), the results for a sample split by age (at median age 43) are presented. ***, **, and * indicate statistical significance at the 1%, 5% and 10%-level, respectively. Standard errors are displayed in parentheses.

Full sample Age≤43 Age>43 (1) (2) (3)

Time Preferences Planned Retirement Age −0.010 *** −0.013 *** −0.007

(0.003) (0.004) (0.005) Inconsistent Answers −0.026 ** −0.019 −0.025

(0.011) (0.016) (0.017)

Demographics Age 0.000 0.005 * −0.002

(0.001) (0.003) (0.003) Male −0.017 −0.005 −0.040

(0.032) (0.041) (0.053) Married 0.062 ** 0.065 * 0.045

(0.026) (0.038) (0.040) Number of Children −0.010 −0.019 −0.005

(0.011) (0.022) (0.013) High School Degree −0.011 0.070 −0.066

(0.043) (0.078) (0.053) University Degree 0.031 0.014 0.051 *

(0.027) (0.037) (0.043) Income (log) 0.062 *** 0.055 ** 0.057 **

(0.015) (0.022) (0.022)

Controls Risk Aversion −0.018 * −0.019 −0.017

(0.010) (0.013) (0.015) Loss Aversion −0.008 −0.005 −0.008

(0.009) (0.012) (0.013) Financial Literacy Score −0.007 −0.020 0.020

(0.010) (0.013) (0.017) Life Expectancy 0.004 ** 0.004 * 0.004

(0.002) (0.002) (0.002) Certainty of Social Security −0.001 0.010 −0.014

(0.006) (0.009) (0.009) Time Taken −0.005 −0.004 −0.004

(0.004) (0.005) (0.006)

Number of Observations 2,049 1,196 853 Pseudo R2 0.033 0.044 0.029

51

Online Appendix D. Financial Impact of Inconsistent Retirement

Timing

Evaluating the main results within the institutional settings of the German social security system

allows us to assess the financial consequences of the inconsistent retirement decisions. Social security

benefits in Germany are determined according to the following formula13, presented in equation

(4).

Monthly retirement benefits = EP ·EC ·CPV (4)

The retirement system is based on earnings points (EP ), which employees earn relative to their

yearly gross income. For each year t, they accumulate EPt = Gross Incomet

Average Gross Income in Germanyt . When

claiming social security benefits, the sum of all accumulated earning points EP enters Equation (4).

The second factor is the entry coefficient (EC ). It equals one for someone, who claims retirement

benefits at full retirement age and decreases by 0.3% for each month of claiming early. Delayed

claiming, however, increases the entry coefficient by 0.5% per month. The last factor, the current

pension value (CPV ), is adjusted each year by the government. In 2012, the year of the survey, it

amounts to EUR 28.07 (EUR 24.92 for East Germany).

The decision to retire early affects the accumulated earnings points (EP ), as well as the entry

coefficient (EC). We can thus calculate the reduction in monthly benefits due to early retirement

for the experimental data. The most time inconsistent participants retire on average 26 months

earlier than time consistent participants. This results in a reduction of the entry coefficient by

7.8% (0.003 · 26). To estimate the reduction in earning points we have to make two assumptions.

First, a person is assumed to have contributed for 40 years when entering retirement. Second, the

forgone income is assumed to be equal to the average income of that person. Since the income

usually increases with years of employment, the second assumption results in a conservative es-

timate of the forgone contributions. The reduction in earning points can then be calculated as

Number of Years Retired Earlier 40+Number of Years Retired Earlier

. In the example, this leads to a reduction of 2.2 42.2

= 5.2%.

In sum, monthly social security benefits are reduced by about 13% (7.8% + 5.2%). Time incon-

sistent participants confront a considerable loss in monthly pension benefits due to early retirement.

For a näıve hyperbolic discounter, this loss comes unanticipated. The result indicates that having

13The pension formula is explained in detail in the following legal text: §64, Sozial Gesetzbuch (SGB) VI.

52

less time consistent preferences strongly influences financial well being in retirement. As we use

the multivariate estimate, this is after controlling for differences in demographics and personal

characteristics, such as risk and loss aversion, financial literacy, and subjective life expectancy.

53