23-04-21 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
23-04-21 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
23-04-21 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
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