Paper presented at the Séminaire Scientifique 2010, Caisse des depots, Bordeaux ,

What are the driving forces behind trends in inequality among pensioners?

(Lessons from a stylized model)

Paper presented at the Séminaire Scientifique 2010, Caisse des depots, Bordeaux,

March 29th, 2010

Gijs DekkersFederal Planning Bureau &CESO, K.U.Leuven

FederalPlanning Bureau

Economic analyses and forecasts

What are the driving forces behind trends in inequality among pensioners?

Starting point: Future trends in inequality are usually simulated using large

microsimulation models. Yet simulation results are often explained using “common

sense” reasonings, using only a few parameters

Theses: 1. It should be possible to build a simple, stylized model that

simulates trends in inequality.2. The results of this stylized model could then be compared to

the simulation results of a dynamic microsimulation model.



Overview of this presentation

A base stylized model for the inequality of pensions

Simulate a change of the indexation parameter, and the impact of the retirement age

Apply two ‘forms’ of demographic ageing- A ‘baby boom’ generation- Increasing longevity

Comparison with results of the Belgian MIDAS modelFederalPlanning Bureau


The base model Suppose

1. 100 individuals in time t≥0, each of a different age (so, aget=[0,…, 100], t=[0, …, 100].

2. everybody retires at 60 and dies at 100, 3. the pension benefit at 60 equals € 100. 4. The model is expressed relative to wage growth, and pensions lag behind the

development of wages with a constant fraction Ψ.

Thenp0,age =100(1- Ψ)age-60 when t=0

Pt,age=

)60&60,)1(100)60,)1(

0)60()(

0)(

00 ageageif

ageifpaget

t

(1)

100,60,60, ,...,,..., tagettt PPPFGini (3)



age 60.000 100.000

pension benefit p

60.500

100.000

year t

100.000

0.000

.01

.06

.11

.16

.21

.26

.31

.36

Gin

i

0 20 40 60 80 100simulation year

psi=5% psi=2.5% psi=1.25% psi=0.5%

base model (Ψ=1.25%)



Pt,age=

)(&))60((&)60(&)60(,)1(100

)(&))60((&)60&60,)1(

)1()1(100)(&))60((&)60(&)60(,)1(100

)(&)60(,)1()1()(&)60(,)1(

00)60()(

2

00)60(1

)(2

)(1

00)60()(

1

0)(

2)(

10

0)(

10

0

0

0

chttchtageageageif

chttchtageageageif

chttchtageageageifchttageifp

chttageifp

aget

age

chttcht

aget

chttcht

t

(

A change of the indexation parameter ψ in the period cht



age 60.000 100.000

pension benefit p

48.410

99.998

year t

100.000

0.000Ψ decreases from 1.8% to 1.25% in t=20

1.12

1.14

1.16

1.18

1.2

1.22

Rat

io

.06

.08

.1.1

2.1

4G

ini


Gini, retirement age 55 Gini, retirement age 60Gini, retirement age 65 Gini, retirement age 70ratio of Gini '55' and '60' ratio of Gini '60' and '65'ratio of Gini '65' and '70'



Demographic ageing I: a ‘baby boom generation’ Write the base model as

tF with 100,60,60, ...... tagettt PPP or

1.0.0.....0.1.0.....0.0.1

...... 100,60,60, tagettt PPP

A special case is

Wt

Wt FGini

And

100,

60,

60,

100,60,60,

.0.0.....0..0.....0.0.

......

t

aget

t

tagettWt

w

w

w

PPP

with w0,age0~N(43,23) and wt,age=w0,(age-t)



Demographic ageing I: a ‘baby boom generation’KDE of age at t≤50

.004

.006

.008

.01

.012

.014

Den

sity

0 20 40 60 80 100Age

t=0 t=10 t=20 t=30 t=40 t=50

Source: PSBH, MIDAS starting dataset in 2002, and own calculations.

.005

.01

.015

.02

kden

sity

age

0 20 40 60 80 100x

t=0 t=30 t=60 t=90

KDE of age at t≤90



.01

.06

.11

.16

.21

.26

.31

.36

Gin

i


psi=5% psi=2.5% psi=1.25% psi=0.5%

Demographic ageing I: a ‘baby boom generation’



Demographic ageing II: increasing longevity xtagettt PPPFGini ,60,60, ,...,,..., (5)

With x=g(t) t=[0, …, 100].

age of death x increases by 10 years , from 90 in period 0 to 100 in period 100.

age 60.000 100.000

pension benefit p

60.500

100.000

year t

100.000

0.000

.01

.06

.11

.16

.21

.26

.31

.36

Gin

i


psi=5% psi=2.5% psi=1.25% psi=0.5%



Demographic ageing: impact of ageing on pension inequality: the compound effect of fertility shock and increasing life expectancy

.01

.06

.11

.16

.21

.26

.31

.36

Gin

i


psi=5% psi=2.5% psi=1.25% psi=0.5%



MIDAS Belgium

An acronym for ‘Microsimulation for the Development of Adequacy and Sustainability’ A dynamic microsimulation model with cross-sectional ageing Developed in the FP6 project AIM The aim is to simulate the consequences of the assumptions and projections of the

AWG on the adequacy of pensions.• MIDAS was simultaneously developed for Belgium, Germany and Italy, by teams

from the FPB, DIW and ISAE.• The starting dataset of MIDAS_BE is the PSBH cross-sectional dataset representing a

population of all ages in 2002 (8,488 individuals) MIDAS simulates• demographics: fertility, mortality, education• labour market: work, unemployment, disability, retirement, private & public

sector, ...• pension module, 1st pillar: employees’ pensions, civil servants’ pensions, self-

employed minimum pensions, CELS, IGO



Validation of the results of MIDAS_Belgium

.075

.08

.085

.09

.095

.1G

ini S

tyliz

ed m

odel

.2.2

2.2

4.2

6.2

8G

ini e

quiv

alen

t pen

sion

inco

mes

MID

AS

_Bel

gium

1980 2000 2020 2040 2060 2080simulation year

Gini MIDAS_Belgium Gini Stylized model



Conclusions The more pensions lag with the development of wages, the higher

inequality of pensions at any point in time. The lower the retirement age, the higher the inequality of

pensions. The lower the retirement age, the slower inequality of pensions

reacts to changes of the indexation regime. The two underlying causes of demographic ageing each have a

different impact on the inequality of pensions.



These findings obviously are not surprising. However, they are generated by a very rudimentary model so there is no black box

Besides a difference in base levels and a sluggish reaction of inequality on a change in the indexation parameter , the results of the stylized model seems to resemble those of MIDAS_BE.

Documents

Paper presented at the Séminaire Scientifique 2010, Caisse des depots, Bordeaux ,