Linking retirement age to life expectancy does not lessen ... · LINKING RETIREMENT AGES TO LIFE...

LINKING RETIREMENT AGES TO LIFE EXPECTANCYDOES NOT LESSEN THE CONSEQUENCES OF

UNEQUAL LIFESPANS

Jesus-Adrian AlvarezMalene Kallestrup-LambSøren KjærgaadJames W. Vaupel

[email protected]

mailto:[email protected]

best practice life expectancy at birth

40

50

60

70

80

90

1840 '60 '80 1900 '20 '40 '60 '80 2000

Year

Life

exp

ecta

ncy

at b

irth

(in y

ears

)

1

so what?

1

Challenges for pension systems

challenges for pension systems

• More and more people survive to retirement ages,

• Individuals from more recent cohorts spend more time inretirement than those from previous cohorts,

• Exacerbates inter-cohort inequality of the pension system(Sanderson and Scherbov, 2013),

• Put preassure on national finances.

2


• More and more people survive to retirement ages,• Individuals from more recent cohorts spend more time in

retirement than those from previous cohorts,

• Exacerbates inter-cohort inequality of the pension system(Sanderson and Scherbov, 2013),


2



retirement than those from previous cohorts,• Exacerbates inter-cohort inequality of the pension system

(Sanderson and Scherbov, 2013),


2



retirement than those from previous cohorts,• Exacerbates inter-cohort inequality of the pension system

(Sanderson and Scherbov, 2013),• Put preassure on national finances.

2

What to do?

what to do?

In many countries (Denmark, the Netherlands, Finland,...),retirement age will be linked to life expectancy (OECD, 2015).

In Denmark• current retirement age is 65 years• gradually increase and in 2022, linked to a target retirement

age r

e(r) = 14.5In the long run, it is expected that the indexation rule will alleviatethe burden of increased longevity.

3

what to do?


In Denmark• current retirement age is 65 years

• gradually increase and in 2022, linked to a target retirementage r


3

what to do?



age r


3

what to do?



age r

e(r) = 14.5

In the long run, it is expected that the indexation rule will alleviatethe burden of increased longevity.

3

what to do?



age r


3

distribution of lifespans for danish females, 1985

65 70 80 90 100 1100.00

0.02

0.04

0.06

Lifespan

Pro

babi

lity

lowest SES highest SES4


65 70 80 90 100 1100.00

0.02

0.04

0.06

Lifespan

Pro

babi

lity



65 70 80 90 100 1100.00

0.02

0.04

0.06

Lifespan

Pro

babi

lity



65 70 80 90 100 1100.00

0.02

0.04

0.06

Lifespan

Pro

babi

lity

lowest SES highest SES

83%

7

Measuring the implications ofe(r) = 14.5

measuring the implications of e(r) = 14.5

• How fast is the target retirement age r increasing?

• How unequal are lifespans a�er age r?• How does the indexation rule a�ect the pension payments for

the di�erent socio-economic (SES) groups?

8


• How fast is the target retirement age r increasing?• How unequal are lifespans a�er age r?

• How does the indexation rule a�ect the pension payments forthe di�erent socio-economic (SES) groups?

8


• How fast is the target retirement age r increasing?• How unequal are lifespans a�er age r?• How does the indexation rule a�ect the pension payments for

the di�erent socio-economic (SES) groups?

8


• Register data from 1985 to 2016

• Socio-economic (SES) groups• A�uence index based on individuals’ income and wealth (Cairns et.

al, 2019),• Lock-down at age 67,• 5 equally sized groups (quintiles) over time.

9


• Register data from 1985 to 2016• Socio-economic (SES) groups

• A�uence index based on individuals’ income and wealth (Cairns et.al, 2019),

• Lock-down at age 67,• 5 equally sized groups (quintiles) over time.

9





9




• Lock-down at age 67,

• 5 equally sized groups (quintiles) over time.

9





9

demographic measures

Life expectancy

e(x) =∫ ∞x l(y)dyl(x)

Lifespan inequality: Population Entropy

H(x) =∫ ∞x e(y)d(y)dy

e(x)”Elasticity of e(x) due to changes in death rates (Keyfitz, 1977)”

10


Life expectancy




e(x)

”Elasticity of e(x) due to changes in death rates (Keyfitz, 1977)”

10


Life expectancy




e(x)”Elasticity of e(x) due to changes in death rates (Keyfitz, 1977)”

10

actuarial measures

Cost of a pension: life annuity

a(x) =∫ ∞x l(y)eδydy

l(x)

Actuarial entropy

H(x, δ) =∫ ∞y a(y)d(y)eδydy

a(x)At a given interest rate δ:

”Elasticity of a(x) due to changes in death rates (Haberman et. al, 2010)”

If δ = 0, then a(x) = e(x) and H(x, δ = 0) = H(x).

11

actuarial measures



l(x)Actuarial entropy


a(x)

At a given interest rate δ:



11

actuarial measures








11

actuarial measures







If δ = 0, then a(x) = e(x) and H(x, δ = 0) = H(x).11


Compute demographic and actuarial measures:

• over time,• by SES and for the total population,• at age 65 and at age r.

12



• over time,

• by SES and for the total population,• at age 65 and at age r.

12



• over time,• by SES and for the total population,

• at age 65 and at age r.

12



• over time,• by SES and for the total population,• at age 65 and at age r.

12

Demographic panorama, δ = 0%

target retirement age, r

A BFemales Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '1559

61

63

65

67

69

71

73

75

Year

Tar

get r

etire

men

t age

(in

yea

rs)

SES quintile

First

Second

Third

Fourth

Fifth

Target retirement age,rsuch that e(r)=14.5 years.Calculated for thetotal population

13

remaining life expectancy at age 65 (current retirement age)

A BFemales Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '1510

12

14

16

18

20

22

24

Year

at a

ge 6

5

SES quintile

First

Second

Third

Fourth

Fifth

19.3 years

14

remaining life expectancy at age r (target retirement age)

C DFemales Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '1510

12

14

16

18

20

22

24

Year

at a

ge r

SES quintile

First

Second

Third

Fourth

Fifth

15

population entropy at age 65 (current retirement age)

A BFemales Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Year

at a

ge 6

5

SES quintile

First

Second

Third

Fourth

Fifth

0.39 in 2016

16

population entropy at age r (target retirement age)

Females MalesSES quintile

First

Second

Third

Fourth

Fifth

C D

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Year

at a

ge r

0.46 in 2016

17

Actuarial perspective, δ > 0%

life annuity at age 65, δ = 1%

Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '155

6

7

8

9

10

11

Year

a(65

) w

ith δ

= 1

% SES quintile

First

Second

Third

Fourth

Fifth

18


Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '152

3

4

5

6

Year

a(65

) w

ith δ

= 2

% SES quintile

First

Second

Third

Fourth

Fifth

19


Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.0

0.2

0.4

0.6

0.8

1.0

Year

a(65

) w

ith δ

= 5

% SES quintile

First

Second

Third

Fourth

Fifth

20

life annuity at age r, δ = 5%

Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.0

0.2

0.4

0.6

0.8

1.0

Year

a(r)

with

δ=

5% SES quintile

First

Second

Third

Fourth

Fifth

21

actuarial entropy at age 65 with δ = 1%

Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.25

0.30

0.35

0.40

0.45

0.50

0.55

Year

H(r

,δ)

with

δ=

1% SES quintile

First

Second

Third

Fourth

Fifth

22

actuarial entropy at age 65 with δ = 5%

Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Year

H(r

,δ)

with

δ=

5% SES quintile

First

Second

Third

Fourth

Fifth

23

actuarial entropy at age r with δ = 5%

Females Males

1985 '90 '95 2000 '05 '10 '15 1985 '90 '95 2000 '05 '10 '150.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Year

H(r

,δ)

with

δ=

5% SES quintile

First

Second

Third

Fourth

Fifth

24

Implications

a different demographic panorama

By increasing the retirement age, the demographic panoramachanges:

• The increasing pattern of life expectancy is o�set by the targetretirement age r,

• Inequalities across SES• Gap between higher and lower SES prevails over time and in all

longevity measures,• Males are in disadvantaged with respect to females.

25






25





longevity measures,

• Males are in disadvantaged with respect to females.

25






25

demographic balance

Intergenerational balance is achieved: equilibrium between theneeds of previous and current generations, without placing anunfair burden on either (Willets, 2017).

Disruption on the intragenerational balance: Those from lower SESwill struggle more to cope with changes in retirement ages.

26

demographic balance

Intergenerational balance is achieved: equilibrium between theneeds of previous and current generations, without placing anunfair burden on either (Willets, 2017).

Disruption on the intragenerational balance: Those from lower SESwill struggle more to cope with changes in retirement ages.

26

unequal lifespans and ineffective planning

Retirement is one of the most important events of the life course.

Individuals require to plan the number of years they expect tospend in retirement:

• prepare the financial conditions in which they will experience it,• plan their consumption path for post-retirement years.

Higher lifespan inequality a�er retirement→ Higher uncertainty about the age at death:

• More di�cult to plan their future (Aronsson, 2018; Van Raalte, 2018),• Important financial decisions can be taken up lightly.

Ine�ective planning a�ects directly the financial stability ofpension systems.

27








27




• prepare the financial conditions in which they will experience it,

• plan their consumption path for post-retirement years.




27








27








27






• More di�cult to plan their future (Aronsson, 2018; Van Raalte, 2018),

• Important financial decisions can be taken up lightly.


27








27








27

actuarial perspective

High δ alleviate the e�ect of the demographic inequalities:

• a(x) and H(x, δ) go down.

However...

28




However...

28




However...

28




However...

28

a neglected dimension of longevity risk

In Denmark, interest rates are at their lowest levels (Pedersen, 2019):

a(x) = e(x)H(x, δ = 0) = H(x)

The cost of a pension is highly susceptible to changes in mortality.

This pattern is exacerbated by raising retirement age from 65 to r.

This reflects the importance of longevity risk management (Haberman

et. al, 2011; Blake et. al, 2019).

29



a(x) = e(x)H(x, δ = 0) = H(x)




et. al, 2011; Blake et. al, 2019).

29



a(x) = e(x)H(x, δ = 0) = H(x)




et. al, 2011; Blake et. al, 2019).

29



a(x) = e(x)H(x, δ = 0) = H(x)




et. al, 2011; Blake et. al, 2019).

29



a(x) = e(x)H(x, δ = 0) = H(x)




et. al, 2011; Blake et. al, 2019).

29

INCREASINGLIFE EXPECTANCY

& UNEQUAL LIFESPANS

↓I M B A L A N C E DPENSION SYSTEMS

29

LINKING RETIREMENT AGES TO LIFE EXPECTANCYDOES NOT LESSEN THE CONSEQUENCES OF

UNEQUAL LIFESPANS

Jesus-Adrian AlvarezMalene Kallestrup-LambSøren KjærgaadJames W. Vaupel

[email protected]

mailto:[email protected]

Date post:	10-Oct-2020
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Linking retirement age to life expectancy does not lessen ... · LINKING RETIREMENT AGES TO LIFE...

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