Artifacts in Population DataNick Owen, Chris ReynoldsPartnerRe

15 April 2023

15 April 2023 2

Disclaimer

The following presentation is for general information, education and discussion purposes only.

Views or opinions expressed, whether oral or in writing do not necessarily reflect those of PartnerRe nor do they constitute legal or professional advice.

15 April 2023 3

© Fotolia.com

15 April 2023 4

Artifact (or should it be Artefact?)

“an unintentional pattern in data, arising from processes

of collection and management”

© Fotolia.com

15 April 2023 5

Where have all the men gone?

© Fotolia.comhttp://news.bbc.co.uk/2/hi/uk_news/magazine/3601493.stm

15 April 2023 6

Discussion Topics

• Projection Basics

• Smoothing

• Basis Risk

• Migration Impact

• International Comparison

• External Factors and Volatility

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

Mortality Projections 101

15 April 2023 8

The Basics

Risk toExposure

DeathsRateDeath

15 April 2023 9

The Basics

Death Rate

© Fotolia.com

15 April 2023 10

The Basics

Future Death Rates

© Fotolia.com

15 April 2023 11

Heat Map

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

92

96

100

1991 2001 2011 2021 2031 2041 2051 2061

4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%

ProjectedActual

Source: CMI 2013

15 April 2023 12

Heat Map

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

92

96

100

1991 2001 2011 2021 2031 2041 2051 2061

4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%

ProjectedActual

Source: CMI 2013

Cohort Effect

15 April 2023 13

Heat Map

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

92

96

100

1991 2001 2011 2021 2031 2041 2051 2061

4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%

ProjectedActual

Source: CMI 2013

Cohort Effect

PeriodEffect

15 April 2023 14

)1,(),(5.0

21

txPtxP

x, tPE(x,t)

Potential Complications

15 April 2023 15

)1,(),(5.0

21

txPtxP

x, tPE(x,t)

Potential Complications

15 April 2023 16

Potential Complications

What assumptions are we making here?

)1,(),(5.0

21

txPtxP

x, tPE(x,t)

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

To Smooth or not to Smooth?

15 April 2023 18

Potential Complications

© Fotolia.com

Toomuch

smoothing???

15 April 2023 19

Russia Smoothed

Source of Data: Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de.

PartnerRe Own Calculations

15 April 2023 20

Russia Smoothed

Source of Data: Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de.

PartnerRe Own Calculations

15 April 2023 21

Russia – No Smoothing

Source: HMD (own calculations)

15 April 2023 22

UK - Smoothed

Source: HMD (own calculations)

15 April 2023 23

UK – No Smoothing

Source: HMD (own calculations)

15 April 2023 24

UK – No Smoothing

See Andrew Cairns’ talk and paper for more on this

Source: HMD (own calculations)

15 April 2023 25

Longevity Portfolio

• Over 1 million lives

• Gender differentiated

• Full date of birth available

How are dates of birth distributed?

15 April 2023 26

Longevity Portfolio

Source: PartnerRe

15 April 2023 27

Longevity Portfolio

Source: PartnerRe

15 April 2023 28

Longevity Portfolio

Source: PartnerRe

First World War Ends

Nov 11, 1918

15 April 2023 29

Longevity Portfolio

Source: PartnerRe

First World War Ends

Nov 11, 1918

Second World War Ends Sep

2, 1945

15 April 2023 30

Longevity Portfolio

Source: PartnerRe

15 April 2023 31

Longevity Portfolio

Source: PartnerRe

First World War Ends

Nov 11, 1918

Second World War Ends Sep

2, 1945

15 April 2023 32

Longevity Portfolio

Source: PartnerRe

First World War Ends

Nov 11, 1918

Second World War Ends Sep

2, 1945

Downwards trend???

15 April 2023 33

Longevity Portfolio

Source: PartnerRe

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

Basis Risk

15 April 2023 39

Basis Risk

© Fotolia.com

vs

Population Portfolio

15 April 2023 40

U.S. Example

• Consider data from the Centers for Disease Control and Prevention (CDC)

• Gender differentiated

• Individual Age

• Calendar Years 1999 – 2011

• … also includes ethnic origin

15 April 2023 41

U.S. Example

Source: CDC - Accessed Oct 2014

15 April 2023 42

U.S. Example

Source: CDC - Accessed Oct 2014

15 April 2023 43

U.S. Example

Source: CDC - Accessed Oct 2014

~ 2.2% per annum

~ 1.9% per annum

15 April 2023 44

U.S. Example

Source: CDC - Accessed Oct 2014

15 April 2023 45

U.S. Example

Source: CDC - Accessed Oct 2014

15 April 2023 46

U.S. Example

Source: CDC - Accessed Oct 2014

~ 2.5% p.a

~ 2.2% p.a

15 April 2023 47

U.S. Example

Source: CDC - Accessed Oct 2014

~ 2.5% p.a

~ 2.2% p.a~ 1.5% p.a

~ 1.1% p.a

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

Migrations

15 April 2023 49

2 Populations

Cat LandNo mortality improvement

© Fotolia.com

15 April 2023 50

2 Populations

Cat LandNo mortality improvement

Dog LandNo mortality improvement

© Fotolia.com

15 April 2023 51

2 Populations

Cat LandNo mortality improvement

Dog LandNo mortality improvementq(x) is 900% of that in Cat Land

© Fotolia.com

15 April 2023 52

Example 1

• Residents of Dog Land migrate to Cat Land

• 1% population growth – Per annum

– Over 4 years

– Over the age range 30 – 50

• Dogs don’t trend to local mortality experience

15 April 2023 53

Example 1

15 April 2023 54

Example 1

Period Effect over 4 years

15 April 2023 55

Example 1

Leading edge cohort effect

15 April 2023 56

Example 1

Trailing edge cohort effect

15 April 2023 57

Improvements by Calendar YearA

nn

ua

l Im

pro

vem

en

t

Calendar Years

354555

15 April 2023 58

Improvements by Age

15 April 2023 59

Example 2

• Residents of Dog Land migrate to Cat Land

• 1% population growth – Per annum

– Over 4 years

– Over the age range 30 – 50

• Dogs take on cat characteristics over 10 years

15 April 2023 60

Example 2

15 April 2023 61

Example 2

15 April 2023 62

Example 2

Fully Integrated

15 April 2023 63

Real examples?

15 April 2023 64

The Polish Example

Source: HMD (own calculations)

15 April 2023 65

The Polish Example

Source: HMD (own calculations)

15 April 2023 66

The Polish Example

Source: HMD (own calculations)

15 April 2023 67

Low Immigrant Mortality or Data Artifact?

• Low mortality for most immigrant groups compared to natives in the host country1

• Often attributed to beneficial health selection processes

• Could it be data artifacts?

• Explored in recent paper by Wallace and Kulu2

1NZ - Hajat et al., 2010, U.S. - Abraido-Lanza et al., 1999; Palloni and Arias, 20042Wallace and Kulu, 2014

15 April 2023 68

Potential Data Artifacts

Misreporting of Age

Misclassifying Nationality

Emigrations under-

registered

Deaths undercounted

Mobility Bias

15 April 2023 69

Potential Data Artifacts

Misreporting of Age

Misclassifying Nationality

Emigrations under-

registered

Deaths undercounted

Mobility Bias

“This study supports low mortality among immigrants … results are not a

data artefact.” (Wallace and Kulu)

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

One True History?

15 April 2023 71

UK Population

Source: HMD (own calculations)

15 April 2023 72

France Population

Source: Human Mortality Database

15 April 2023 73

Ireland Population

Source: HMD (own calculations)

15 April 2023 74

Belgium Population

Source: Human Mortality Database

15 April 2023 75

Italy Population

Source: HMD (own calculations)

15 April 2023 76

Netherlands Population

Source: Human Mortality Database

15 April 2023 77

Denmark Population

Source: Human Mortality Database

15 April 2023 78

Portugal Population

Source: Human Mortality Database

15 April 2023 79

Sweden Population

Source: Human Mortality Database

15 April 2023 80

Austria Population

Source: Human Mortality Database

15 April 2023 81

Czech Republic Population

Source: Human Mortality Database

15 April 2023 82

Spain Population

Source: Human Mortality Database

15 April 2023 83

Norway Population

Source: Human Mortality Database

15 April 2023 84

Iceland Population

Source: Human Mortality Database

15 April 2023 85

Poland Population

Source: Human Mortality Database

15 April 2023 86

Canada Population

Source: Human Mortality Database

15 April 2023 87

Japan Population

Source: Human Mortality Database

88

One true history?

Source: HMD (own calculations)

UK IRE FR

BEL ITA POR

NL DMK AUT

JA CAN

Progr

ess

Comm

unity

Sessio

nal M

eetin

gs

Educa

tion

Wor

king

parti

es

Volunt

eerin

g

Resea

rch

Shapin

g th

e fu

ture

Networ

king

Profe

ssion

al su

ppor

t

Enter

prise

and

risk

Lear

ned

socie

ty

Oppor

tunit

y

Inte

rnat

ional

prof

ile

Jour

nals

Suppo

rting

Exper

tise

Spons

orsh

ip

Thoug

ht le

ader

ship

15 April 2023

The Changing Seasons

15 April 2023 90

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

2008/9 Flu epidemic

Seasonality – weekly death registrations

Source: ONS

1999/2000 Flu epidemic

15 April 2023 91

-

1,000

2,000

3,000

4,000

5,000

6,000

2010 2011 2012 2013 2014

Seasonality – Age 85+ (CMI)

Source: CMI

15 April 2023 92

-

1,000

2,000

3,000

4,000

5,000

6,000

2010 2011 2012 2013 2014

Seasonality – bank holiday effect

Source: CMIQueen’s Jubilee

3 day week

August bank holiday

Christmas

Royal wedding

15 April 2023 93

Seasonality – weekly death registrations

Source: ONS & MetOffice4 week moving average

Deaths

Temperature

-40

-30

-20

-10

-

10

20

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

2000 2001 2002 2003 2004 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Deaths Temperature

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

15 April 2023 94

Seasonality – conventional approach

• Seasonality normally ignored

• Deaths by calendar year

• Mid-year population estimates

Interval Average improvement in

mortality

Standard deviation in

annual improvement

12 months ending December

2.3% 2.3%

Ten year time series

15 April 2023 95

Seasonality – choice of interval

Source: ONS data & own calculations

Conventional methodVol = 2.3%

12 months ending 30 SeptemberVol = 1.5%

15 April 2023 96

Seasonality – choice of interval

Interval Average improvement

Standard deviation in annual improvement

12 months ending December

2.3% 2.3%

12 months ending September

2.3% 1.5%

• Calendar year interval overstates underlying volatility

• Stochastic models - Lee Carter, CBD, RH etc

Source: ONS data & own calculations

15 April 2023 97

Final Thoughts

© Fotolia.com

15 April 2023 98

Standardized mortality rate

Source: Wikipedia

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1

10

100

1000

10000

10000019

1919

2119

2319

2519

2719

2919

3119

3319

3519

3719

3919

4119

4319

4519

4719

4919

5119

5319

5519

5719

5919

6119

6319

6519

6719

6919

7119

7319

7519

7719

7919

8119

8319

8519

8719

8919

9119

9319

9519

9719

9920

0120

0320

0520

0720

0920

11

number of pirates SMR (UK)

15 April 2023 99

Standardized mortality rate

Source: Wikipedia

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1

10

100

1000

10000

10000019

1919

2119

2319

2519

2719

2919

3119

3319

3519

3719

3919

4119

4319

4519

4719

4919

5119

5319

5519

5719

5919

6119

6319

6519

6719

6919

7119

7319

7519

7719

7919

8119

8319

8519

8719

8919

9119

9319

9519

9719

9920

0120

0320

0520

0720

0920

11

number of pirates SMR (UK)

15 April 2023 100

Expressions of individual views by members of the Institute and Faculty of Actuaries and its staff are encouraged.

The views expressed in this presentation are those of the presenter.

Questions Comments

15 April 2023

Artifacts in Population DataNick Owen nicholas.owen@partnerre.comChris Reynolds christopher.reynolds@partnerre.com