Lecture Notes on Retirement

8/19/2019 Lecture Notes on Retirement

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Lecture notes Microeconomics of Household Behaviour,lecture 7

Microeconomics of Household Behaviour (Rijksuniversiteit Groningen)

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The retirement decision: lecture 7

Coordinator: prof. dr. Rob Alessieemail: [email protected]

office: DUI 727 tel: 050-3637240Lecturer: Viola Angelini email: [email protected]

office: DUI 854 tel: 050-3633852

February 24, 2014

Literature

• Lecture notes

• Kapteyn, A., and K. De Vos (1998). Social security and labor-force par-

ticipation in the Netherlands. The American Economic Review , 88(2),164-167.

http://www.jstor.org/discover/10.2307/116912?uid=3738736&uid=2&uid=4&

• Stock, J. H., and D. A. Wise (1990): Pensions, the Option Value of Work,and Retirement,” Econometrica , 58, 1151-1180.

see Nestor• Belloni, M., and R. Alessie (2009), The importance of financial incentives

on retirement choices: New evidence for Italy, Labour Economics , Vol 16(5),Pages 578-588.

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AIM:

• Studying models and approaches that analyze the decision to retire

• Theoretical background: labor supply and life cycle models (see lecture

notes: Labour Supply)• Most economic models of retirement come from empirical literature: study-

ing a particular pension system, policy effects of changes in the system

• Degree of complication: models are difficult to solve

• Consequence: none of the approaches in the literature is complete

• Theory important for understanding the underlying mechanisms

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This class

• The option value of retirement: basic idea

• Financial incentives of retirement: Kapteyn & De Vos (1998)

• Example reduced form model: Belloni and Alessie (2009)

• The option value model of Stock and Wise (1990)

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1 The option value of retirement: basic idea

• Individual is employed at date (or age) τ .

• Decision to retire at date s ≥ τ .

What are the implications of retirement?

(i) Retirement is an ’absorbing’ state, i.e. a retired person does not returnto to the labor force.

(ii) Implications for income: retirement benefit: Bt(s) for t ≥ s: incomeat date t if someone retired at date s.

Note: pension benefit systems are usually such that Bt(s + 1)≥

Bt(s)for t ≥ s + 1.

(iii) No labor income received anymore, full leisure: Lt = 1 for t ≥ s.

(iv) Wealth accumulation (denote Bt(0) the non-labour income while work-ing):

At = (1 + rt)At−1 + Bt(0) + wt(1 − Lt) − cet, if τ ≤ t ≤ s − 1

At = (1 + rt)At−1 + Bt(s) − crt, if s ≤ t ≤ T (1)

Note: the financial consequences of retirement, determined by the re-tirement system, are an important determinant of the retirement deci-sion.

(v) Utility maximization becomes:

maxcet,crt,Lt

s−1t=τ

u(cet, Lt, t) +T t=s

u(crt, 1, t)

subject to the asset accumulation constraints (1).

• Note: the utility maximization function is formulated conditional on s l OM o RP


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• The solution gives the optimal retirement age s∗ from the perspective of someone at age τ .

Decision rule:

Retire at age τ if s∗ = τ

Stay on the job if s∗ > τ (and solve the problem again at age τ + 1)

• Option value of retirement = V tau(s∗) − V τ (τ ): value of keeping the option

open to retire later If retirement is irreversible, this option is lost once thedecision to retire has been taken.

• Continue working if V tau

(s∗) − V τ

(τ ) > 0. Then the option to retire laterhas larger utility than the option to retire now.

• Option value model by Stock and Wise.

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2 Financial Incentives to Retire and Alternative Exit routes

• Empirical models of retirement:

– Many models for retirement are developed from the empirical/econometric

literature– Theory and empirics:

∗ All models in the literature solve only part of the puzzle, e.g. Noprivate savings, or only public pension system modeled.

∗ Why? (i) Data limitations, (ii) Large degree of complexity in model-ing the retirement decision: future, uncertainty, dynamic program-ming required.

– Empirical models:

∗ Structural models : try to implement the economic theory in theempirical model. Option value model, dynamic programming mod-els. Suitable for doing policy simulations.

∗ Reduced form models: measuring the impact of explanatoryvariables on the decision to retire. E.g. specify a Probit modelfor the retirement probability, or a hazard rate model. Suitablefor finding out which factors influence (or: are correlated with)retirement.

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Figure 1:

2.1 Kapteyn en De Vos (1998)

• In both structural and reduced form models of retirement the financialconsequences of retirement play an important role: (see also the Option

Value).

• Two concerns in the development of labour market participation of theelderly:

1. Increase in percentage of population older than 65:

1950: 8 percent; 1995: 13 percent; 2050: 21 percent, see figure 1.

2. Low participation of workers in age range 55-65.

• ad 1: Aging problem

a) Retirement of the baby-boom generation

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Figure 2:

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In addition:

– Due to longer period of education young workers enter the labour mar-ket at later age

– Decrease in labour-market participation of older workers

Ratio of people with age 65+ to people with age 20-64 (grijze druk) willincrease from 22 % now to 43 % in 2040.

Consequence:

– Increase in expenditures on Social Security (AOW), the Dutch statepension

– Social Security is financed as pay-as-you-go

– Properties:

∗ 50 % of minimum wage for each spouse in a couple

∗ 70 % of minimum wage for singles

∗ Supplement for single parents with dependent child 40 %

∗ Independent of earnings history, not means tested, mostly receivedon top of employer pension plan.

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• ad 2: Low participation of workers in age range 55-65.

Development labor force participation of older workers, see table above

Financial incentives to withdraw from the labor market before age 65?

Various exit routes:

(a) Disability Insurance, WAO (DI)

(b) Unemployment Insurance, WW (UI)

(c) Early Retirement, VUT (ER)

Ad (a). Disability Insurance (WAO):

– Level: 70 % previous wage

– Eligible if ’disabled’ according to medical examination

– ’Consensus’ between worker and employer: convenient for both, ”loose” l OM o RP


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Ad (b). Unemployment Insurance

– 70 % of previous wage (gross)

– Eligibility and duration depend on labor market history, job tenure

– Maximum duration: 5 years. E.g. someone aged 60 will receive it till65.

– From age 57 on: no obligation to apply for job. (changed now)

Ad (c). Early Retirement

– Employer provided: difference per employer/sector (collective bargain-

ing agreement– Level ranges from 70 to 80 % previous wage

– Average age is 60 (depending on employer, sector)

– Rights to ER are lost is one stops working before

– Due to some policy reform, the ’ER exit route’ has become less attrac-tive (a reform in 2006 is especially important)

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How to quantify the financial incentives to withdraw from the labourforce?

• Definition Social Security Wealth (SSW ) :

SSW = actuarially discounted sum of [current and future benefits minuscurrent and future contributions]

In formula: SSW for a worker of age a who evaluates retirement at age h(h ≥ a):

SSW a,h =

Ω

∑s=h+1

ρ(s)Bh(s) if h = a

Ω∑s=h+1

ρ(s)Bh(s) −h∑

s=a+1ρ′(s)c(s) if h > a

where

Ω:= Life span

Bh(s):= Pension benefit received at age s if one retires at age h

c(s):= Contributions paid at age s

ρ(s):= Discount factor at age s, which includes a real interest rate andconditional survival probabilities

• Factors that influence SSW (by working another year, from t to t+1):

– Premium contributions for UI, ER, SS and DI. negative influence of working.

– The benefit payment forgone of working at age t. Negative influenceorking l OM o RP


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• Marginal Incentive (MI) measures

1. Accrual rateACC a = SSW a,a+1 − SS W a,a

2. Implicit tax rate τ a

τ a = −ACC a

wa

where wa denotes labor earnings.

3. Peak value P V a

P V a = maxh

(SSW a,h − SSW a,a)

4. Option value

• Kapteyn en De Vos (1998) compute the values of SS W a,h, AAa and τ a forvarious cases.

– Constant real benefits after 1995

– Mortality rates independent between worker and spouse

– Real interest rate is 3 percent

– Tax system remains the same from 1995 on

– Wage development same as minimum wage

– Men with median earnings, born in 1930 (a = 54, spouse withoutincome

– Entitled to Early Retirement (ER) benefits: from age 60 on

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• Case A. Worker who is participating in Early Retirement scheme.

Results, see figure 2.1.

Comments, (see Panel A of table below)

– ER Benefits 80 % of previous earnings, after tax 90 % (replacementrate)

– Age 55-58: τ a > 0, but τ a 1: for all ages 55-64 ⇒ strong incentive to exit workforce by WAO

if possible.

• Overall conclusion: various social insurance systems provide strong fi-nancial incentives to withdraw from the labour market at an age below

65.

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The Importance of Financial Incentives onRetirement Choices: New Evidence for Italy

Michele BelloniCeRP - Collegio Carlo Alberto

Rob Alessie

University of Groningen, Netspar and Tinbergen Institute

ICEEE 2009 CongressAncona,30th January 2009

Verspreiden niet toegestaan | Gedownload door Celine van Essen ([email protected])

O i

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Overview

Aim: use a panel dataset covering the period 1985-2001 to analyzethe impact of financial incentives provided by the social securitysystem on retirement choices in Italy

Motivation: a good understanding of the role of financial incentivesis crucial for the design of effective reforms which aim to increase

the average retirement age Method: following Gruber and Wise (2004), we estimate a probit

model in which the probability for a worker to retire is explained byfinancial incentives, in addition to personal characteristics.Identification exploits the time variation in financial incentives which

stems from a series of social security reforms introduced in Italy inthe 1990s


The basic idea fo a d looki g o ke

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The basic idea: forward-looking worker

At age a he computes:

his current social security wealth: SSW a his SSW associated with retiring at alternative future ages:

SSW a+1,SSW a+2...

MI variables: ACC a = SSW a+1 − SSW a orPV a = max (SSW h − SSW a) h = a + 1, . . . , R .

two key variables in the model: SSW and MI (ACC or PV)

the higher her SSW a the higher her retirement probability (incomeeffect);

the higher her ACC a (or PV a) the lower her retirement probability(substitution effect);

The model is dynamic: worker reconsiders retirement next year if he didnot retire at age a, since new information affecting his expectations areavailable. Retirement is an absorbing state.


Literature: main references and contribution 1

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Literature: main references and contribution 1 Gruber and Wise (2004): collects 12 recent country studies,

common econometric approach. General finding: strong causaleffect of financial incentives on retirement

Brugiavini and Peracchi (2004): contribution for Italy in the book.Weak evidence for SSW and MI

Other studies for Italy (Brugiavini and Peracchi, 2003 and 2007;Ranzani 2006) confirm the weak evidence

Is Italy a puzzling exception?

previous studies exploit various versions of the INPS-O1M archive, which doesnot provide info on seniority. Seniority:

is crucial to define eligibility and to compute pensions in Italy

needed to be imputed, under strong hp on the unobserved part of thecareer; consequence is possible measurement error in SSW

is observed in our data

to what extent does having better data help explain differences in results

across countries?Verspreiden niet toegestaan | Gedownload door Celine van Essen ([email protected])

Literature: main references and contribution 2

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Literature: main references and contribution 2Most studies on retirement (e.g. Gruber and Wise, 2004) do not accountfor individual unobserved heterogeneity:

Individuals might differ in their preferences (e.g. for leisure) forreasons not observed by the econometrician

possible dynamic sample selection bias: work-loving individuals staylonger in the sample

Individual effects and financial incentive variables can be correlated(Chan and Stevens, 2004; Coile and Gruber, 2000): e.g. work-lovingindividuals tend to have higher SSW and low retirement probability

Wooldridge (2002) describes how to account for a correlationbetween individual effects and r.h.s. vars in probit models

we extend the random effects probit model explaining the retirementprobability by including, as extra regressors, financial incentives inthe first year in which each worker is observed. As a result, financialincentive parameters are identified exploiting within-individualvariation


Institutional framework: overview

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Institutional framework: overview

we model the rules of private sector employees: INPS-FPLD fund

two main exit routes o.l.f.: old-age and seniority pensions

Several laws and three main reforms, in 1992, 1995 and 1997, affectedeligibility (see table) and DB formula

Old-Age pension Seniority pensionYear age seniority age+seniority seniority only

males females1985-1992 60 55 15 - 351993 60 55 16 - 351994 61 56 16 - 351995 61 56 17 - 351996 62 57 17 52+35 361997 63 58 18 52+35 361998 63 58 18 54+35 36

1999 64 59 19 55+35 372000 65 60 19 55+35 372001 65 60 20 56+35 372002-2003 65 60 20 57+35 372004-2005 65 60 20 57+35 382006-2007 65 60 20 58+35 39> 2007 65 60 20 58+35 40


Data and sample selection

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Data and sample selectionData: WHIP + additional INPS pension file

WHIP: random sample drawn from INPS archive. Unbalanced panel:1/90 of private sector, non agricultural workforce in 1985-2001. O1M files: data on working careers (wages, weeks worked,

occupation). Exploited in previous studies complementary files: data on spells of self-employment (artisans and

traders), atypical work, unemployment, and mobility main weaknesses: no public, nor agricultural sectors; few individual

characteristics (gender, date and region of birth) additional INPS pension file: data on pensions paid (dates of

payments, amounts, type of pension) and seniority

Sample selection:

workers aged 50-70, cohorts 1935-1941 workers with long interruptions in the career or contributions mainlyto other schemes automatically excluded

retirement through disability, unemployment or mobility isconsidered involuntary

employee is defined retired if permanently leaves the O1M archive

and does not then work as a self-employed or atypical workerVerspreiden niet toegestaan | Gedownload door Celine van Essen ([email protected])

Financial incentives

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Financial incentives

definition:

SSW a,h =

Ωs =h+1

ρ(s )B h(s ) if h = a

Ωs =h+1

ρ(s )B h(s ) −h

s =a+1

ρ(s )c (s ) if h > a

ACC a = SSW a,a+1 − SSW a,a

PV a = max (SSW a,h − SSW a,a) h = a + 1, . . . ,R

computation:

expected wages: prediction from AR(1) fixed-effects model for log-wages

estimated on O1M data

individuals know the pension formulae and hold static expectations

ρ(s ) is evaluated allowing for variation by age, gender, region and cohortin conditional survival probabilities


The retirement model

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e et e e t ode

We consider the following latent variable retirement model for worker i inperiod t (t = 1, . . . ,T )

y ∗

it = w

it θ + c i + it (1)

where we observe

y it = 1 if y ∗

it > 0 (retires)

y it = 0 otherwise

due to the absorbing state assumption, y it = 0 implies y is = 0 for each s


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we make the following standard assumption for it

it |wit θ, c i ∼ NID (0, 1)

equation (1) contains an individual effect c i which captures unobserveddifferences across individuals in, for example, taste for work. The individualeffects and financial incentive variables can be correlated.

Following Wooldridge(2002) we model it as follows:

c i

= z

i 1γ + α

i

c i

|wit

, θ ∼ NID (z

i 1γ , σ

2

α)where zi 1 ≡ (SSW i 1,MI i 1, x

1i 1)

. γ measures the correlation between financialincentives and the individual unobserved effect (no clear economicinterpretations can be given to its estimates)

The likelihood contribution of individual i who retires in period T is:

L i (θ,γ |yi ,wi , zi 1, αi ) =

T t =1

Φ

(2y it − 1)

w

it θ + z

i 1γ + αi

where αi is integrated-out in the standard way


Results: males

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Results (other)

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( )

policy simulations as in Gruber and Wise (2004): “three yearreform” increases the average retirement age by up to 1.5 years

females react stronger to financial incentives than males

results robust to alternative assumptions on expected future wagesand specifications for age


Discussion

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Is Italy a puzzling exception? To what extent does having better data

help explain differences in results across countries?Controlled experiment: suppose we do not observe seniority in the data

1. impute the variable ‘seniority’ as in previous studies: from SHIW data compute average age of entry into the l.m. by

gender and occupation for similar cohorts impute this average to each worker according to her characteristics assuming a continuous career, compute seniority as the difference

between age and the imputed age of entry into the l.m.

2. compute SSW and MI according to the imputed seniority:considerable overestimation of SSW

3. estimate a pooled probit model using our dataset and replacingactual SSW and MI with their imputed counterparts


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Figure: Country studies in Gruber and Wise(2004) and this paper: estimated sign for PVand SSW and quality of the data

results based on imputed seniority (BA-i)are qualitatively similar to ITA

The quality of the SSW and MI variablesdiffers across countries because of data

limitations. Data requirements may becountry-specific because pension systemsdiffer. We construct a quality index

country studies which dispose of ‘good’() data, report correct signs for thePV and SSW coefficients, with theexception of Belgium and Spain

In countries with incomplete () data,one generally obtains the wrong sign forSSW and the correct one for PV

These findings are in line with those of the controlled experiment, suggestingthat measurement error in SSW explainsthe pattern observed in the table

caution: to our knowledge, the statisticalproperties of the probit model taking intoaccount the non-classical measurementerror problem have not been formallyderived yet


Conclusions

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We quantify the effects of financial incentives on retirement in Italy

we exploit a dataset which - for the first time in Italy - provides info

on seniority our methodology takes into account correlated unobserved

heterogeneity

Main findings:

in accordance with Gruber and Wise (2004), financial incentives havean effect on retirement, this effect goes in the expected direction

the procedure used in previous Italian studies to impute seniorityleads to a considerable overestimation of that variable and of SSW.

We show that, due to these measurement errors, the estimate of theSSW coefficient takes the wrong sign

comparison of retirement studies across countries provides primafacie evidence that a lack of good quality data often leads towrongly signed estimates of the SSW coefficient


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4. The option value model of Stock and Wise (1990)

A.

The option value model: Stock and Wise (1990)

B. Three models of retirement: Computational Complexity versus Predictive Validity

Lumsdaine, Stock an Wise (1992): Next week


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A. The option value model: Stock and Wise (1990)

Stock and Wise (1990) use data on employees of large Fortune 500 firm. Pension

scheme:

- Regular pension benefit from the age of 65 on

- Age 55-64: entitled to Early Retirement (VUT). Reduction of normal pension benefits:

actuarially beneficial (about 3% per year).

- Age 50-54: retirement possible, but based on regular pension benefit spread over 10

additional years: benefit reduced actuarially (about 7% a year)

- From age 62: entitled to Social Security (comparable to AOW)

-

From age 65: Social Security subtracted


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Type of benefit: Defined benefit, depending on

- age

- tenure, tenure > 10

-

final wage

B = k x (#years served) x (final wage)


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Retirement:

- absorbing state

- pension scheme determines financial incentives

Financial incentives: retirement leads to

-

stop of wage as source of income

-

stop of pension accruel

- obtaining income out of pension (if eligible)

Trade-off between these financial consequences:

-

At each possible retirement age (50-68) determine the present value of income

At which age is this present value highest?


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Definitions:

-

Y s: wage income at age s (yearly basis)

- Bs(r ): pension benefit if worker with age s retires at age r

For a worker of age 50 who retires at age r we have:

Present value of wage (“earnings”):

Y

i

r

50

1

50

1

1

(with i = 5%)

Present value pensions (“retirement benefits”):

)(

1

150

r B

i

S

r

(with S end of life)

Table 1: figures in US dollars


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The optional value model for retirement

- Behavioural model, not only financial incentives

- Decision rule for retirement

A.

Definition of utility and value

Utility function: U w(Y s) : utility for someone who works with income Y s

U r ( Bs(r )) : utility for someone retired with benefit Bs(r )

Note: even if Y s = Bs(r ) the utility levels may be different due to differences in

preferences for working and not.

“Value” for someone with age t who retires at age r :

S

r s sr

t sr

t s sw

t s

t r BU Y U r V ))(()()(1

with a discount factor measuring time preference. V t (t ) is the value of retiring now.


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B. Decision rule

Uncertain future: base decision on expected value:

E tV t(r )

-

Determine the maximum expected present value of retiring in future:

)()(max*

},...,1{

r V E r V E t t t t

S t r

(so maximum at r *).

-

Determine E tV t(t ): value of pensioning now.

-

Expected return at time t of postponing retirement to r *: Gt(r *) = E tV t(r *) – E tV t(t )

- Gt(r *) measures the ‘gain’ from retiring in the future

- Retire NOW if Gt(r *) 0

- Continue working if Gt(r *) > 0


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C. Specification

U w(Y s) = Y s + s

With a parameter and s a ‘random’ proxy for unobserved determinant of utility.

U r (Bs) = (kBs) + s

With k a parameter that determines the difference in the marginal utility of income in

different labour market states:

k > 1: (marginal) utility retirement > (marginal) utility work (at same income)

k = 1: only income itself matters, indifferent between states

k < 1: ‘disutility’ of retirement

s: random variable.


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Interpretation of s and s :

Unobserved (or unobservable) factors that influence utility like

-

individual preferences

-

health status

- private savings

Expected Values for different retirement ages are compared: Uncertainty:

- In preferences: A stochastic process for s and s is specified (as an AR(1) process,

Normally distributed disturbances, see Stock and Wise for details)

-

Income: an equation for income is specified to be able to determine the expected future

value of income, and to incorporate income uncertainty: Income is specified as a

function of Age and Tenure, Dynamic process (see Stock and Wise for details).


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D. The retirement probability can be specified :

Two variants:

1 year model: cross section data:

Probability of retirement of someone aged t = P(Gt(r *) 0)Multiple years: uses multiple observations for 1 individual:

Probability of retirement at age :

P(Gt(r *) > 0, Gt+1(r *) > 0,…, G -1(r *) > 0, G (r *) 0)

(retirement at , no retirement previous years).


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E. Results

Sample of 1500 workers of Fortune 500

- aged 50 or older

-

at least 3 years of tenureTable IV: Multiple year model, 6 variants estimated:

- variant 1: same retirement probability for everyone (simplification, lowerbound on

model fit)

-

variant 2: retirement probability the same for everybody with the same age

-

variant 4: the complete model

Note:

< 1: Decreasing marginal utility of income, some risk aversionk > 1: Higher utility of retirement ( at equal income)


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Variant 5: Extension: utility is made dependent on age.

1

550

k

agek k

Why?

-

Variant 4: Age only enters through the income process and the pension system.

- Can the income process and the pension system (that determine utility) completely

describe the retirement decision or are there age effects that cannot be described?

- Thus, variant 5 serves as a ‘test’ of the model

-

Outcome: k 0 = 0.950, k 1 = 4.87 > 1: Utility of retirement rises with age.


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‘Fit’ of the model: Table V

Compare observed retirement rate with the predicted

- Model is able to fit the early retirement peak at age 55

-

Hard to predict retirement rates above age 64 due to low number of observations.

-

There may be a “customary retirement age” effect not associated with monetary gain at

age 65


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F. Policy Simulations

Use the model and the estimated parameter values to simulate the effects of changes in

the pension scheme.

a). Increase of early retirement age from 55 to 60.

b). From ‘defined benefit’ to ‘defined contribution’:ad a). effects: Table VI.

-

Early Retirement age of 55: before age 60 65% has already retired

-

Early Retirement age of 60: before age 60 only 42% retired

- Note also higher retirement rates before age 55: individuals who before waited with

retirement until age 55 to become eligible don’t want to wait until age 60 and retire

earlier than before.

Ad b). Towards defined contribution: no large peaks in retirement any longer: Table VII

- higher retirement rates before and after the age of 55. “Actuarially Fair”.


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C.


Lecture Notes on Retirement

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