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LINKING RETIREMENT AGES TO LIFE EXPECTANCYDOES NOT LESSEN THE CONSEQUENCES OF
UNEQUAL LIFESPANS
Jesus-Adrian AlvarezMalene Kallestrup-LambSøren KjærgaadJames W. Vaupel
alvarez@sdu.dk
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
challenges for pension systems
• 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),
• Put preassure on national finances.
2
challenges for pension systems
• 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),
• Put preassure on national finances.
2
challenges for pension systems
• 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),• 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 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 retirementage 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 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 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) = 14.5
In the long run, it is expected that the indexation rule will alleviatethe burden of increased longevity.
3
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
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
distribution of lifespans for danish females, 1995
65 70 80 90 100 1100.00
0.02
0.04
0.06
Lifespan
Pro
babi
lity
lowest SES highest SES5
distribution of lifespans for danish females, 2005
65 70 80 90 100 1100.00
0.02
0.04
0.06
Lifespan
Pro
babi
lity
lowest SES highest SES6
distribution of lifespans for danish females, 2016
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
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 forthe di�erent socio-economic (SES) groups?
8
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
measuring the implications of e(r) = 14.5
• 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
measuring the implications of e(r) = 14.5
• 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
measuring the implications of e(r) = 14.5
• 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
measuring the implications of e(r) = 14.5
• 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
measuring the implications of e(r) = 14.5
• 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
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
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
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
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
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
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
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
measuring the implications of e(r) = 14.5
Compute demographic and actuarial measures:
• over time,• by SES and for the total population,• at age 65 and at age r.
12
measuring the implications of e(r) = 14.5
Compute demographic and actuarial measures:
• over time,
• by SES and for the total population,• at age 65 and at age r.
12
measuring the implications of e(r) = 14.5
Compute demographic and actuarial measures:
• over time,• by SES and for the total population,
• at age 65 and at age r.
12
measuring the implications of e(r) = 14.5
Compute demographic and actuarial measures:
• 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
life annuity at age 65, δ = 2%
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
life annuity at age 65, 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(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
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
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
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
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
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
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
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
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
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
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
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
actuarial perspective
High δ alleviate the e�ect of the demographic inequalities:
• a(x) and H(x, δ) go down.
However...
28
actuarial perspective
High δ alleviate the e�ect of the demographic inequalities:
• a(x) and H(x, δ) go down.
However...
28
actuarial perspective
High δ alleviate the e�ect of the demographic inequalities:
• a(x) and H(x, δ) go down.
However...
28
actuarial perspective
High δ alleviate the e�ect of the demographic inequalities:
• a(x) and H(x, δ) go down.
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 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 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 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 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
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
alvarez@sdu.dk
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