23-04-20 1

Cohort and Period Mortality in Sweden

A nearly 150 year perspective and projection strategies

Hans LundströmStatistics Sweden

Joint Eurostat/UNECE Work Session on Demographic Projections

Lisbon, 28-30 April 2010

Available mortality data

2

• Mortality rates by sex in one year age classes

• 1861 to 2009

• Age is calculated based on registered data

• Quality of data is high

Mortality rates by calendar year and year of birth

3

0

1

Year

Age

P(1)D(1)M(1)

P(0)

Age

Year

D(0)M(0)

P(0)

B

Age

0

Cohort and period perspective

4

1861 1862 1863 1864 1865

0

1

2

3

4

Year

Period Cohort

Age

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Female mortalityAge 30-100

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

3035404550556065707580859095100

Year

Age

Apart from stochastic fluctuations mortality rate is closely related to mortality rate for next higher/lower age

and to mortality rate in preceding/following year. Stable pattern

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Male mortalityAge 30-100

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

3035404550556065707580859095100

Year

Age

23-04-20 7

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

3035404550556065707580859095100

Year

Age

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

3035404550556065707580859095100

Year

Age

Females Males

Mortality show a smooth and gradual change over time and age.

Mortality projection

8

To sum it all up:

• The Lee-Carter model for the last 15 to 20 years fits nicely to male and female mortality

Problem

9

• Male mortality is declining more rapidly then female mortality

• Lee-Carter method results in a cross-over after some years

• Is a situation with lower mortality for males than for females likely?

Male excess mortality for nearly all ages and years 1861-2008

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Age 1861 1950 2008 0

100

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Using Lee-Carter Age-Period model the projection results in lower mortality for males than for females in a 30 year perspective

Likely?

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

f40

m40

f50

m50

f60

m60

f70

m70

f80

m80

f90

m90

Year

Age

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A new model is needed

To the two-factor model Age & Period

we must add Sex to the model

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An observation ..

A more rapid mortality decline for females started in the 1950s. For males we had a 30 year lag before mortality started to decline.

Present rate of progress for males similar to that for females in the 1950s

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

f40

m40

f50

m50

f60

m60

f70

m70

f80

m80

f90

m90

Year

Age

14

Male mortality shifted back 30 years in time for ages 40,50,60,70, 80 and 90

0,0001

0,001

0,01

0,1

1

1950 1970 1990 2010

f40

m40

f50

m50

f60

m60

f70

m70

f80

m80

f90

m90

Year

Age

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The cohort perspective

Mortality show a smooth and gradual change over time and age in a cohort perspective too

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For ages above 50 nearly parallell shift of mortality curve from one cohort to the next.

Female mortality. Cohorts 1770-2005

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Male mortality. Cohorts 1770-2005

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A new model is needed

•So far we have used the Lee-Carter Age & Period model

•The Lee-Carter model has lately been extended to incorporate cohort effects too. This model is worth a closer look

•Probably we still have to add Sex as a fourth factor to the model

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Alternative future approach

• We must gain better insight into the causes and predictors of mortality

• For that we must know the ”risk profile” for cohorts and know the relationship between”risk factors” and mortality

• Much remains to be done

• A first step is look into cohort cause-of-death data

Thank you for your attention

20

A cohort-based extension to the Lee–Carter model for mortality reduction factors. A.E. Renshaw, S. Haberman Cass Business School, City University, London, EC1Y 8TZ, UK

21

AbstractThe Lee–Carter modelling framework is extended through the introduction of a wider class of generalised, parametric, non-linear models. This permits the modelling and extrapolation of age-specific cohort effects as well as the more familiar age-specific periodeffects. The choice of error distribution is generalised.

Insurance: Mathematics and Economics 38 (2006) 556–570

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Life expectancy 1861-2009

30

40

50

60

70

80

90

1860 1880 1900 1920 1940 1960 1980 2000 Year

Males

Females

83,3

79,3

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Remaining life expectancy at age 65, 75 and 85. 1861-2009

0

2

4

6

8

10

12

14

16

18

20

22

1860 1880 1900 1920 1940 1960 1980 2000

Age 65

Age 75

Age 85

Year

Males

Females

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Female mortality rate. Age 0-9

0,00001

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

0

1

2

3

4

5

6

7

8

9

Year

Age

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Male mortality rate. Age 0-9

0,00001

0,0001

0,001

0,01

0,1

1

1860 1880 1900 1920 1940 1960 1980 2000

0

1

2

3

4

5

6

7

8

9

Year

Age

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Female mortality rate. Age 10-19

0,00001

0,0001

0,001

0,01

1860 1880 1900 1920 1940 1960 1980 2000

10111213141516171819

Year

Age

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Male mortality rate. Age 10-19

0,00001

0,0001

0,001

0,01

1860 1880 1900 1920 1940 1960 1980 2000

10111213141516171819

Year

Age

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Female mortality rate. Age 20-29

0,0001

0,001

0,01

0,1

1860 1880 1900 1920 1940 1960 1980 2000

20

21

22

23

24

25

26

27

28

29

Year

Age

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Male mortality rate. Age 20-29

0,0001

0,001

0,01

0,1

1860 1880 1900 1920 1940 1960 1980 2000

20

21

22

23

24

25

26

27

28

29

Year

Age

23-04-20 30

Cohort mortality in Sweden - Mortality statistics since 1861

http://www.scb.se/Pages/PublishingCalendarViewInfo____259924.aspx?PublObjId=12788

Cohort life tables in Excel format:

http://www.scb.se/Pages/ProductTables____55370.aspx

The future population of Sweden 2009-2060 publication

http://www.scb.se/Pages/PublishingCalendarViewInfo____259924.aspx?PublObjId=11386

The future population of Sweden 2010-2060 publication

http://www.scb.se/Pages/PublishingCalendarViewInfo____259924.aspx?PublObjId=11928