4th HMD Symposium - mortality.org · 4th HMD Symposium Aburto et al. 2017 Life Expectancy and Lifespan Equality 17. Introduction Methods & Data Results Include the age dimension Reducing

4th HMD Symposium

Life Expectancy and Lifespan Equality:A Dynamic Long run Relationship

Jose Manuel Aburto, Ugofilippo Basellini, Søren Kjærgaard& James W. Vaupel

23rd May 2017

IntroductionMethods & Data

Results

Introduction

I Background:I Life expectancy at birth (e0) is one of the most widely used

measures to summarize population health.I Most countries have improved in this indicator. Record e0 has

steadily increased by 2.5 years every decade.I However, it conceals variation in lifespans or lifespan equality.

I What is lifespan equality?

I Dimension that expresses a fundamental difference insurvivorship among individuals.

I It addresses the growing interest in health inequalities and itslinkage with social behavior.

4th HMD Symposium Aburto et al. 2017 Life Expectancy and Lifespan Equality 2


Results

Introduction




I What is lifespan equality?

I Dimension that expresses a fundamental difference insurvivorship among individuals.




Results

Introduction




I What is lifespan equality?I Dimension that expresses a fundamental difference in

survivorship among individuals.




Results

Introduction




I What is lifespan equality?I Dimension that expresses a fundamental difference in

survivorship among individuals.I It addresses the growing interest in health inequalities and its

linkage with social behavior.



Results

Why studying lifespan equality is important?

Ages

Danish Females

0 20 40 60 80 100

0

1000

2000

3000

4000

d(x)

e0

67.281.33

IQR

19.9914.66

Ω0

89.9997.33

1945 2010

Source: HMD4th HMD Symposium Aburto et al. 2017 Life Expectancy and Lifespan Equality 3


Results

Strong association between life expectancy and lifespan equality

0.0

0.5

1.0

1.5

2.0

20 40 60 80Life expectancy

Life

span

equ

ality

Period1900−19211921−19591960 onwards

Life expectancy (e0) vs lifespan equality (η)

Japan

Pearson correlation coefficient > .95



Results

Non-stationary seriesLife expectancy

Year

Year

s

30

40

50

60

70

80

1900 1920 1940 1960 1980 2000 2020

SexFemalesMales

Lifespan equality (η)

Year

0.5

1.0

1.5

2.0

1900 1920 1940 1960 1980 2000 2020



Results

If non-stationarity −→ risk of misleading resultsLife expectancy (e0) vs lifespan equality (η)

Durbin−Watson statistic

R s

quar

ed

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

78 %

SexFemalesMales



Results

Stochastic properties suggest analyzing both in first differences

R square = 0.704

−0.50

−0.25

0.00

0.25

0.50

−10 −5 0 5 10

(∆e0)

(∆η)

Period1900−19211921−19591960 onwards

Changes in life expectancy and lifespan equality



Results

General idea of the model

0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality




Results


0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality




Results


0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality


Long

term

equ

ilibriu

m



Results


0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality


Japan

Russia

''Mortality forces''''Mortality forces''



Results


0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality


Japan

Russia




Results


0.0

0.5

1.0

1.5

2.0


Life

span

equ

ality



β'x1994

β'x2000

x∞|t



Results

Cointegration analysis

Two-dimensional VAR model in its equilibrium correction (VECM)form:

∆Zt =k−1∑i=1

Γ∆Zt−i + αβ′Zt−1 + µ+ ΨDt + εt

where:

I ∆ first difference operator

I Zt vector of stochastic variables, e0 and η

I Dt vector of deterministic variables (e.g. linear trends)

Data comes from HMD, over 8 500 lifetables for 44 countries



Results

Lifespan equality measuresThree measures were used:

η = − log

(− ∫ ω0 `(x) ln `(x)dx∫ ω0 `(x)dx

)= − log

(e†

eo0

), (1)

η based on Keyfitz’ entropy used in Colchero et al 2016.

¯ = − log

(1−−∫ ω0 `2(x)dx∫ ω0 `(x)dx

)= − log (G ) , (2)

¯ a variant of the Gini coefficient.

cv = − log

√∫ ω

0 (x − eo0 )2f (x)dx∫ ω0 `(x)dx

= − log

(σ

eo0

), (3)

cv a variant of the coefficient of variation.



Results

Long run relationship [Johansen’s trace test]

New ZealandLithuania

BelarusWest Germany

BulgariaGreece

LatviaEstonia

SloveniaBelgiumUkraineFrance

Czech RepublicFinlandIceland

GermanyIreland

DenmarkU.S.A.

U.K.RussiaAustria

New Zealand (Maori)Hungary

PolandNorthern Ireland

IsraelCanada

ScotlandTaiwan

ItalyNetherlands

AustraliaSlovakia

East GermanyEngland & Wales

NorwayNew Zealand (Non Maori)

PortugalSweden

LuxembourgSwitzerland

SpainJapan

Distance from 95% critical value

0 20 40 60 80

0 20 40 60 80

Females

0 20 40 60 80

BelarusBelgium

LithuaniaLatvia

BulgariaEstoniaIceland

Northern IrelandNew Zealand (Maori)

East GermanyHungary

IrelandUkrainePoland

ScotlandWest Germany

RussiaAustriaTaiwan

England & WalesSlovakia

Czech RepublicLuxembourg

DenmarkJapan

GermanySloveniaCanadaGreece

AustraliaU.K.Italy

IsraelNetherlands

New Zealand (Non Maori)Norway

New ZealandSpain

U.S.A.Finland

PortugalSwedenFrance

Switzerland

0 20 40 60 80

Males



Results

Speed of adjustment towards long term equilibrium

Speed of adjustment

−1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 1 1.25

PolandEast Germany

U.K.Hungary

Northern IrelandUkraineRussia

EstoniaLatvia

ScotlandU.S.A.

England & WalesDenmark

ItalyFrance

Czech RepublicAustria

AustraliaNorway

New Zealand (Non Maori)FinlandTaiwanJapan

SwedenGreece

NetherlandsSwitzerland

SpainCanada

New Zealand (Maori)Bulgaria

LuxembourgSlovenia

West GermanyGermanySlovakia

IsraelIreland

PortugalIceland

−1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 1 1.25

Life expectancy

−1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 1 1.25

FranceItaly

FinlandLuxembourg

SwedenNew Zealand (Maori)

NetherlandsCanadaPortugalAustralia

U.K.IrelandAustria

Czech RepublicSwitzerland

U.S.A.Slovenia

JapanScotland

England & WalesNorthern Ireland

DenmarkBulgariaGreeceUkraineRussiaTaiwan

East GermanyNew Zealand (Non Maori)

IsraelSpain

West GermanyLatvia

NorwayPolandIceland

SlovakiaGermanyHungaryEstonia

−1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 1 1.25

Lifespan equality

SexFemalesMales



Results

Include the age dimension Reducing deaths at any age increasese0; for η, it depends whether deaths occur before or after ai

Age

−0.8

−0.6

−0.4

−0.2

0.0

0 20 40 60 80 100

Sens

itivity

of l

ifesp

an e

qual

ity

Threshold age

Sen

sitivi

tyImprovements below increase lifespan equality

Improvements above decrease equality



Results

Threshold age aη

Year

Year

s

20

40

60

80

1900 1920 1940 1960 1980 2000 2020

SexFemalesMales



Results

Decomposition method

Model of continuous change: analysis based on the assumptionthat covariates change continuously along an actual orhypothetical dimension.[Horiuchi et al 2008 Demography; Caswell 2010 Journal of Ecology]

The effect of the i-th age group death rate on the change in e0and η from period t to t + 1 can be calculated as

ci =

∫ mi (t+1)

mi (t)

∂e0(t)

∂mi (t)dmi (t) (4)

Then we calculated contributions below and above the thresholdage to changes in life expectancy and lifespan equality.



Results

Age-specific contributions

−0.2

0.0

0.2

−4 0 4

(∆e0)

(∆η)

Period1900−19211921−19591960 onwards

Changes below the threshold age

−0.2

0.0

0.2

−4 0 4

(∆e0)

(∆η)

Period1900−19211921−19591960 onwards

Changes above the threshold age



Results

Summary and conclusions

I Strong association between changes in e0 and η.

I We found evidence of a long term equilibrium.

I Even if in the short term they diverge from each other, thereis a correction mechanism that bring them together again.

I To some extent mortality improvements below threshold ageare driving the relationship.



Results

Thanks for your attention.

Comments and/or questions?



Results

Normalized (η = 1) long run coefficient for e0

Long run relationship

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

RussiaBulgaria

TaiwanUkraineU.S.A.

SloveniaEast Germany

Czech RepublicScotland

U.K.Norway

LuxembourgGermany

New Zealand (Non Maori)

West GermanyPolandFranceAustria

HungaryIsraelLatvia

Northern IrelandSpain

EstoniaSlovakiaGreeceIceland

CanadaFinland

DenmarkNetherlands

SwedenItaly

New Zealand (Maori)Portugal

SwitzerlandAustralia

Ireland

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Females

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

England & WalesNetherlands

IrelandSlovakia

RussiaUkraineBulgaria

TaiwanCzech Republic

JapanEast Germany

U.S.A.West Germany

AustriaPoland

GermanyPortugal

IsraelSwitzerland

EstoniaLuxembourg

AustraliaCanada

SloveniaSpain

HungaryScotland

FranceNew Zealand (Non Maori)

IcelandFinland

DenmarkItaly

Northern IrelandNorway

U.K.Latvia

SwedenNew Zealand (Maori)

Greece

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Males



Results

Can we talk about causality?

I Granger causality −→ Because e0 and η cointegrate at leastGranger causality exists in one direction.[Caution!]

I Just a potential causality, does not take into account latentvariables.

I Temporal precedence: a cause precedes its effects in time

I Instantaneous causality: test non-zero correlation betweenerror processes of the cause and effect variables.In 90% of the cases we reject the H0 = no instantaneouscausality



Results

long run relationship

Distance from 95% critical value

−20 0 20 40 60 80

LatviaIsrael

West GermanyNorwayUkraineTaiwan

CanadaBelarus

DenmarkLithuania

SwitzerlandFinland

AustraliaGreece

SloveniaEstonia

ItalyBelgium

GermanyNetherlands

RussiaU.K.

IcelandNorthern Ireland

England & WalesSpain

New ZealandScotland

New Zealand (Non Maori)Sweden

New Zealand (Maori)Austria

East GermanyPortugal

PolandFrance

HungaryLuxembourg

U.S.A.Czech Republic

BulgariaIreland

SlovakiaJapan

−20 0 20 40 60 80

Females

−20 0 20 40 60 80

Northern IrelandWest Germany

GreeceTaiwan

New Zealand (Non Maori)LithuaniaSlovenia

GermanyLatvia

DenmarkEstonia

England & WalesU.K.

SpainNew Zealand (Maori)

BelarusBelgium

IsraelNorwaySwedenCanadaRussia

ItalyUkraine

NetherlandsPortugalAustralia

FinlandNew Zealand

ScotlandFranceIceland

SwitzerlandLuxembourg

HungaryEast Germany

U.S.A.PolandAustria

BulgariaIreland

Czech RepublicJapan

Slovakia

−20 0 20 40 60 80

Males

Measure(1−G)log(inv(H))log(inv(CV))


Documents

4th HMD Symposium - mortality.org · 4th HMD Symposium Aburto et al. 2017 Life Expectancy and Lifespan Equality 17. Introduction Methods & Data Results Include the age dimension Reducing