The Future of Death in America - GARY KINGgking.harvard.edu/files/gking/files/mort-hupop.pdf · The...
Transcript of The Future of Death in America - GARY KINGgking.harvard.edu/files/gking/files/mort-hupop.pdf · The...
The Future of Death in America
Gary KingInstitute for Quantitative Social Science
Harvard University
joint work with Samir Soneji
(talk at the Center for Population and Development Studies, Harvard University, 12/15/08)
()(talk at the Center for Population and Development Studies, Harvard University, 12/15/08) 1
/ 65
Citations
Gary King and Samir Soneji. 2008. “The Future of Death in America”
Gary King and Samir Soneji. 2008. “Eating Away Social Security’sFinancial Problems”
Gary King and Federico Girosi. 2008. Demographic Forecasting,Princeton University Press.
copies at http://gking.harvard.edu
Gary King (Harvard, IQSS) The Future of Death 2 / 65
Citations
Gary King and Samir Soneji. 2008. “The Future of Death in America”
Gary King and Samir Soneji. 2008. “Eating Away Social Security’sFinancial Problems”
Gary King and Federico Girosi. 2008. Demographic Forecasting,Princeton University Press.
copies at http://gking.harvard.edu
Gary King (Harvard, IQSS) The Future of Death 2 / 65
Citations
Gary King and Samir Soneji. 2008. “The Future of Death in America”
Gary King and Samir Soneji. 2008. “Eating Away Social Security’sFinancial Problems”
Gary King and Federico Girosi. 2008. Demographic Forecasting,Princeton University Press.
copies at http://gking.harvard.edu
Gary King (Harvard, IQSS) The Future of Death 2 / 65
Citations
Gary King and Samir Soneji. 2008. “The Future of Death in America”
Gary King and Samir Soneji. 2008. “Eating Away Social Security’sFinancial Problems”
Gary King and Federico Girosi. 2008. Demographic Forecasting,Princeton University Press.
copies at http://gking.harvard.edu
Gary King (Harvard, IQSS) The Future of Death 2 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sections
Including demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)
Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
The Forecasting Task
Time series: 25-50 annual mortality rates
Cross-sections: 1 time series for each age, country, cause, sex, etc.
Goal: Forecast each time series 25 years
Challenges: reducing error by:
Pooling cross-sectionsIncluding demographic knowledge (smooth over time and age)Including biological knowledge (smoking, obesity)
Gary King (Harvard, IQSS) The Future of Death 3 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
How (Some) Existing Mortality Forecasts Work
Procedures:
Develop private forecasts qualitatively (i.e., informally)
Adopt a ‘toy’ statistical model
Get data; produce tentative forecasts with the model
Adjust model until forecasts fit private views
Present forecasts, with statistical model as your “method”
Meaning of procedures
Forecasts use qualitative information (good!)
Statistical models add little (bad!)
Method is invulnerable to being proven wrong
We bring statistics to demography
Gary King (Harvard, IQSS) The Future of Death 4 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20
Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20
Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)
Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)
Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Existing Method 1: Parameterize the Age Profile
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
All Causes (m)
Age
ln(m
orta
lity)
Japan
Turkey
Bolivia
Gompertz (1825): log-mortality is linear in age after age 20Reduce age-specific rates to 2 parameters (µage = γ1 + γ2 × age)Forecast only these 2 parameters (γ1, γ2)Reduces variance, constrains forecasts
Dozens of more general functional forms proposed since 1825
But does it fit anything else?
Gary King (Harvard, IQSS) The Future of Death 5 / 65
Mortality Age Profile: The Same Pattern?
−12
−10
−8
−6
−4
−2
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Cardiovascular Disease (m)
Age
ln(m
orta
lity)
France
USA
Brazil
Gary King (Harvard, IQSS) The Future of Death 6 / 65
Mortality Age Profile: The Same Pattern?
−16
−14
−12
−10
−8
−6
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Breast Cancer (f)
Age
ln(m
orta
lity)
Japan
Venezuela
New Zealand
Gary King (Harvard, IQSS) The Future of Death 7 / 65
Mortality Age Profile: The Same Pattern?
−12
−10
−8
−6
−4
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Other Infectious Diseases (f)
Age
ln(m
orta
lity)
Italy
Barbados
Sri Lanka
Thailand
Gary King (Harvard, IQSS) The Future of Death 8 / 65
Mortality Age Profile: The Same Pattern?
−10
−9
−8
−7
−6
15 20 25 30 35 40 45 50 55 60 65 70 75 80
Suicide (m)
Age
ln(m
orta
lity)
Sri Lanka
Colombia
Canada
Hungary
Gary King (Harvard, IQSS) The Future of Death 9 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality rates
Age profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger ages
We don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Parameterizing Age Profiles Does Not Work
No mathematical form fits all or even most age profiles
Out-of-sample age profiles often unrealistic
The key empirical patterns are qualitative:
Adjacent age groups have similar mortality ratesAge profiles are more variable for younger agesWe don’t know much about levels or exact shapes
Ignores covariate information
Gary King (Harvard, IQSS) The Future of Death 10 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates
; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates
; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates
; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates
; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates; forecasts fan out
;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
Existing Method 2: Deterministic Projections
1960 1980 2000 2020 2040 2060
−10
−8−6
−4−2
All Causes (m) USA
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520253035 404550
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4−2
All Causes (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Random walk with drift; Lee-Carter; least squares on linear trend
Pros: simple, fast, works well in appropriate data
Cons: omits covariates; forecasts fan out;age profile becomes less smooth
Does it fit elsewhere?
Gary King (Harvard, IQSS) The Future of Death 11 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Time
Dat
a an
d Fo
reca
sts
1520
25
30
35
40
45
50 5560
65
70
75
80
20 30 40 50 60 70 80
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Gary King (Harvard, IQSS) The Future of Death 12 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Time
Dat
a an
d Fo
reca
sts
1520
25
30
35
40
45
50 5560
65
70
75
80
20 30 40 50 60 70 80
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Gary King (Harvard, IQSS) The Future of Death 12 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Time
Dat
a an
d Fo
reca
sts
1520
25
30
35
40
45
50 5560
65
70
75
80
20 30 40 50 60 70 80
−10.
5−1
0.0
−9.5
−9.0
−8.5
−8.0
−7.5
−7.0
Suicide (m) USA
Age
Dat
a an
d Fo
reca
sts
1950 2060
Gary King (Harvard, IQSS) The Future of Death 12 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Time
Dat
a an
d Fo
reca
sts
05
10
15
20
253035 40455055 60
65 70
7580
0 20 40 60 80
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Age
Dat
a an
d Fo
reca
sts
1955 2060
Gary King (Harvard, IQSS) The Future of Death 13 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Time
Dat
a an
d Fo
reca
sts
05
10
15
20
253035 40455055 60
65 70
7580
0 20 40 60 80
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Age
Dat
a an
d Fo
reca
sts
1955 2060
Gary King (Harvard, IQSS) The Future of Death 13 / 65
The same pattern?Random Walk with Drift ≈ Lee-Carter ≈ Least Squares
1960 1980 2000 2020 2040 2060
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Time
Dat
a an
d Fo
reca
sts
05
10
15
20
253035 40455055 60
65 70
7580
0 20 40 60 80
−10.
0−9
.5−9
.0−8
.5−8
.0−7
.5−7
.0−6
.5
Transportation Accidents (m) Portugal
Age
Dat
a an
d Fo
reca
sts
1955 2060
Gary King (Harvard, IQSS) The Future of Death 13 / 65
Deterministic Projections Do Not Work
Linearity does not fit most time series data
Out-of-sample age profiles become unrealistic over time
Gary King (Harvard, IQSS) The Future of Death 14 / 65
Deterministic Projections Do Not Work
Linearity does not fit most time series data
Out-of-sample age profiles become unrealistic over time
Gary King (Harvard, IQSS) The Future of Death 14 / 65
Existing Method 3: Stacked Regression
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)
large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),
considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)
same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
Existing Method 3: Stacked Regression(Murray and Lopez, 1996)
Model mortality over countries (c) and ages (a) as:
mcat = Zca,t−`βca + εcat , t = 1, . . . ,T
Zca,t−` : covariates lagged ` years.
βca : coefficients to be estimated
Equation by equation estimation: huge variances
Pool over countries: βca ⇒ βa
Small variance (due to large n)large biases (due to restrictive pooling over countries),considerable information lost (due to no pooling over ages)same covariates required in all cross-sections
(It always seems ok to pool over variables outside your own field.)
Gary King (Harvard, IQSS) The Future of Death 15 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
The New Approach
Start with separate equation-by-equation regressions
Use Bayesian priors to smooth across age, time, age×time, etc.
Put priors on E(mortality), not coefficients
No arbitrary normalizations
Different covariates allowed in each regression
Only one smoothing parameter to represent demographic information
An easy-to-use software program, YourCast
Gary King (Harvard, IQSS) The Future of Death 16 / 65
Formalizing (Prior) Indifference (so no cooking the books)equal color = equal probability
Level indifference
0 20 40 60 80
−10
−8
−6
−4
−2
0
All Causes (m) , n = 1
Age
Log−
mor
talit
y
Level and slope indifference
0 20 40 60 80
−8
−6
−4
−2
02
All Causes (m) , n = 2
Age
Log−
mor
talit
y
Gary King (Harvard, IQSS) The Future of Death 17 / 65
Formalizing (Prior) Indifference (so no cooking the books)equal color = equal probability
Level indifference
0 20 40 60 80
−10
−8
−6
−4
−2
0
All Causes (m) , n = 1
Age
Log−
mor
talit
y
Level and slope indifference
0 20 40 60 80
−8
−6
−4
−2
02
All Causes (m) , n = 2
Age
Log−
mor
talit
y
Gary King (Harvard, IQSS) The Future of Death 17 / 65
Formalizing (Prior) Indifference (so no cooking the books)equal color = equal probability
Level indifference
0 20 40 60 80
−10
−8
−6
−4
−2
0
All Causes (m) , n = 1
Age
Log−
mor
talit
y
Level and slope indifference
0 20 40 60 80
−8
−6
−4
−2
02
All Causes (m) , n = 2
Age
Log−
mor
talit
y
Gary King (Harvard, IQSS) The Future of Death 17 / 65
Mortality from Respiratory Infections, MalesLeast Squares
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 18 / 65
Mortality from Respiratory Infections, males, σ = 2.00Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 19 / 65
Mortality from Respiratory Infections, males, σ = 1.51Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 20 / 65
Mortality from Respiratory Infections, males, σ = 1.15Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 21 / 65
Mortality from Respiratory Infections, males, σ = 0.87Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 22 / 65
Mortality from Respiratory Infections, males, σ = 0.66Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 23 / 65
Mortality from Respiratory Infections, males, σ = 0.50Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 24 / 65
Mortality from Respiratory Infections, males, σ = 0.38Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 25 / 65
Mortality from Respiratory Infections, males, σ = 0.28Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 26 / 65
Mortality from Respiratory Infections, males, σ = 0.21Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 27 / 65
Mortality from Respiratory Infections, males, σ = 0.16Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 28 / 65
Mortality from Respiratory Infections, males, σ = 0.12Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 29 / 65
Mortality from Respiratory Infections, males, σ = 0.09Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 30 / 65
Mortality from Respiratory Infections, males, σ = 0.07Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 31 / 65
Mortality from Respiratory Infections, males, σ = 0.05Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 32 / 65
Mortality from Respiratory Infections, males, σ = 0.04Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 33 / 65
Mortality from Respiratory Infections, males, σ = 0.03Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 34 / 65
Mortality from Respiratory Infections, males, σ = 0.02Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 35 / 65
Mortality from Respiratory Infections, males, σ = 0.01Smoothing over Age Groups
0 20 40 60 80
−12
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d F
orec
asts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 36 / 65
Mortality from Respiratory Infections, malesLeast Squares
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
20
25
30 35
4045
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 37 / 65
Mortality from Respiratory Infections, males, σ = 2.00Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
2025
30 3540 4550 55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 38 / 65
Mortality from Respiratory Infections, males, σ = 1.51Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
2025
30 3540 4550
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 39 / 65
Mortality from Respiratory Infections, males, σ = 1.15Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
2025
30 3540 4550
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 40 / 65
Mortality from Respiratory Infections, males, σ = 0.87Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
2025
30 3540 4550
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 41 / 65
Mortality from Respiratory Infections, males, σ = 0.66Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
5
10
15
2025
30354045
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 42 / 65
Mortality from Respiratory Infections, males, σ = 0.50Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
15
2025
3035
4045
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 43 / 65
Mortality from Respiratory Infections, males, σ = 0.38Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
15
2025
3035
4045
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 44 / 65
Mortality from Respiratory Infections, males, σ = 0.28Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
15
2025
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 45 / 65
Mortality from Respiratory Infections, males, σ = 0.21Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 46 / 65
Mortality from Respiratory Infections, males, σ = 0.16Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 47 / 65
Mortality from Respiratory Infections, males, σ = 0.12Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 48 / 65
Mortality from Respiratory Infections, males, σ = 0.09Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 49 / 65
Mortality from Respiratory Infections, males, σ = 0.07Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 50 / 65
Mortality from Respiratory Infections, males, σ = 0.05Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 51 / 65
Mortality from Respiratory Infections, males, σ = 0.04Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 52 / 65
Mortality from Respiratory Infections, males, σ = 0.03Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 53 / 65
Mortality from Respiratory Infections, males, σ = 0.02Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 54 / 65
Mortality from Respiratory Infections, males, σ = 0.01Smoothing over Age Groups
1970 1980 1990 2000 2010 2020 2030
−12
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d F
orec
asts
0
510
1520
25
30
35
40
45
50
55
60
65
70
75
80
Gary King (Harvard, IQSS) The Future of Death 55 / 65
Smoothing Trends over Age Groups
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age GroupsLog-mortality in Belize males from respiratory infections
Least Squares
1970 1980 1990 2000 2010 2020 2030
−10
−9−8
−7−6
−5−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
SmoothingAge Groups
1970 1980 1990 2000 2010 2020 2030
−10
−8−6
−4
(m) Belize
Time
Dat
a an
d Fo
reca
sts
0
510
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0 20 40 60 80
−10
−8−6
−4
(m) Belize
Age
Dat
a an
d Fo
reca
sts
1970 2030
Gary King (Harvard, IQSS) The Future of Death 56 / 65
Smoothing Trends over Age Groups and Time
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Smoothing Trends over Age Groups and TimeLog-Mortality in Bulgarian males from respiratory infections
Least Squares
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
4045
50 5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
SmoothingAge and Time
1970 1990 2010 2030
−11
−10
−9−8
−7−6
−5−4
(m) Bulgaria
Time
Dat
a an
d Fo
reca
sts
0
5
10
1520
25
30
35
40
4550
5560
65
70
75
80
0 20 40 60 80
−12
−10
−8−6
−4
(m) Bulgaria
Age
Dat
a an
d Fo
reca
sts
1964 2030
Gary King (Harvard, IQSS) The Future of Death 57 / 65
Using Covariates (GDP, tobacco, trend, log trend)
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Korean Males
Least Squares
1990 2000 2010 2020 2030
−10
−50
5
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
3540
45
50
5560 65
70
7580
30 40 50 60 70 80
−10
−50
5
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Smooth over age,time, age/time
1990 2000 2010 2020 2030
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
−14
−12
−10
−8−6
−4
(m) Republic of Korea
Age
Dat
a an
d F
orec
asts
1985 2030
Gary King (Harvard, IQSS) The Future of Death 58 / 65
Using Covariates (GDP, tobacco, trend, log trend)
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
Using Covariates (GDP, tobacco, trend, log trend)Lung cancer in Males, Singapore
Least Squares
1970 1990 2010 2030
−20
−15
−10
−50
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
4550
55
60
65
707580
30 40 50 60 70 80
−20
−15
−10
−50
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Smooth over age,time, age/time
1970 1990 2010 2030
−14
−12
−10
−8−6
(m) Singapore
Time
Dat
a an
d F
orec
asts
30
35
40
45
50
55
60
65
70
7580
30 40 50 60 70 80
−14
−12
−10
−8−6
(m) Singapore
Age
Dat
a an
d F
orec
asts
1963 2030
Gary King (Harvard, IQSS) The Future of Death 59 / 65
U.S. Male Mortality over Age and TimeDemographic Facts: Smoothness in both dimensions
0 20 40 60 80 100
−8
−6
−4
−2
●
●
●●
●●●●●●●●
●●
●
●
●●●●●
●●●●●●●●●●●●●●●●
●●●●
●●●●
●●●●●
●●●●
●●●
●●●
●●●●
●●●
●●●●●
●●●●
●●●●●●
●●●●
●●●●
●●●●
●●●●●
●●
●
●
●
●●●●
●●●●●●
●
●
●
●
●
●●●●●●●●●●●●●●
●●●●●●●
●●●●●
●●●●
●●●
●●●
●●●●
●●●●
●●●●
●●●
●●●
●●●
●●●●
●●●●
●●●●
●●●●
●●●●
●●●●
●●
19802005
1980 1985 1990 1995 2000 2005
−8
−6
−4
−2
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
0
● ●● ● ● ● ● ● ●
● ● ●● ● ● ● ● ● ● ● ● ● ● ●
● ●
10
●● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
20 ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●
● ● ● ● ●● ● ● ● ●
30
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●
40
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●
50
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
60
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
70
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
80
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
90
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●100
Ages
Age Year
log
(mx)
Gary King (Harvard, IQSS) The Future of Death 60 / 65
Biological Risk Factors in U.S. Data
1960 1970 1980 1990 2000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
● ●
●
● ●●
●
●
●
●
●●
●
●
●
●●
●●
20 ● ●
●
●
●
●
●
●●
●
●
●●●
●
●
●●
●
40
● ●
●
● ●
●
●
●
●●
●
●●
●
●●
●●
●
60
● ●
●
●
● ●
●
●
●
●●
●
●●
●●
●
● ●
80
Age
1960 1970 1980 1990 2000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
● ●●
●
●
●●
●
●
●
● ●
●
●
●
●●●
●
20● ●
● ●
●
●
●●
●●●●●
●
●●
●●
●
40
● ●
●
●
●
●
●●
●●
●
●●
●
●
●●●
●60
● ●
●●
●●
●
●
●
●●
●●
●
●●
●●
●
80
1960 1970 1980 1990 2000
0.00
0.10
0.20
0.30
● ● ●●●●
●●●
●●
●●
●
●
●
●
●
●
●
●
●●●●
●
●
20
● ● ● ●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
40● ● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
● ●
60
● ● ●
●
●●
●
●
●
●
●
●●
●
●●
●●
●●
●
●
●
●
●
●
●
80
1960 1970 1980 1990 2000
0.00
0.10
0.20
0.30
● ● ● ●●● ●
●●●
●
●●
●●
●
●●
●
●●●
●
●
●
●
●
20
● ● ● ●
●●
●
●
●
●●
●●
●
●
●●●
●
●
●
●●
●
●
● ●
40● ● ●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●●
●
60
● ● ●●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
80
Year Year
Sm
okin
g P
reva
lenc
eO
besi
ty P
reva
lenc
e
Male Female
Gary King (Harvard, IQSS) The Future of Death 61 / 65
Linear Models: Biology vs. Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●●
●●●●●●●●
●●●●●●●●●
5●●
●●●●●●●●●●
●●●●●●●●●●●●
●●
10
●●●●●●
●●●●●●●●●
●●●●●●●●●●●
15
●●●●●●
●●●●●●●●●●●
●●●●●●●●●
20 ●●●●●●●●●●●●●●●●●●●●●●●●●●
25 ●●●●●●●●●●●●●●●●
●●●●●
●●●●●
30●●●●●●
●●●●●●●●●●●●●●●●●●●●
35
●●●●●●●
●●●●●●●●●●●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
45
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
55
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
65
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
75
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
85
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●●
95●●●●●●●
●●●●●●●●●●●●●●●●●●●
100
Age
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●●
●●●●●●●●
●●●●●●●●●
5●●
●●●●●●●●●●
●●●●●●●●●●●●
●●
10
●●●●●●
●●●●●●●●●
●●●●●●●●●●●
15
●●●●●●
●●●●●●●●●●●
●●●●●●●●●
20 ●●●●●●●●●●●●●●●●●●●●●●●●●●
25 ●●●●●●●●●●●●●●●●
●●●●●
●●●●●
30●●●●●●
●●●●●●●●●●●●●●●●●●●●
35
●●●●●●●
●●●●●●●●●●●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
45
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
55
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
65
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
75
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
85
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●●
95●●●●●●●
●●●●●●●●●●●●●●●●●●●
100
1980 1990 2000 2010 2020 2030−
10−
8−
6−
4−
2Year
●●●●●●●●●
●●●●●●●●
●●●●●●●●●
5●●
●●●●●●●●●●
●●●●●●●●●●●●
●●
10
●●●●●●
●●●●●●●●●
●●●●●●●●●●●
15
●●●●●●
●●●●●●●●●●●
●●●●●●●●●
20 ●●●●●●●●●●●●●●●●●●●●●●●●●●
25 ●●●●●●●●●●●●●●●●
●●●●●
●●●●●
30●●●●●●
●●●●●●●●●●●●●●●●●●●●
35
●●●●●●●
●●●●●●●●●●●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
45
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
55
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
65
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
75
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
85
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●●
95●●●●●●●
●●●●●●●●●●●●●●●●●●●
100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
log(
mx)
log(
mx)
Linear Model: Time
Linear Model: Time+Smoking
Linear Model: Time+Smoking+Obesity
Gary King (Harvard, IQSS) The Future of Death 62 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Forecasts: Biology and Demography
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●●●●●●
●●
●●●●●
●●●●●●●●●
●●
10
●●
●●●●●●●
●●●●●●●●●●●●●●●●●
20●●●●●●●●●●●●●●●●
●●
●●●●●●
●●
30
●●●●●●●
●●●●●●●●●●
●●●●●●●●●
40
●●●●●●●●●●●●●●●●●●●●●●●●●●
50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●
70
●●●●●●●●●●●●●●●●●●●●●●●●●●
80
●●●●●●●●●●●●●●●●●●●●●●●●●●
90
●●●●●●●●●●●●●●●●●●●●●●●●●
●100
Time+Smoking+Obesity
Time+Smoking
1980 1990 2000 2010 2020 2030
−10
−8
−6
−4
−2
Year
●●●
●●
●●
●
●●●●
●●●●
●●
●●
●●●●
●●
10
●●●●●●
●●●●●●●●●●●●●●●●●●●●
20●●
●●●●●●●●●●
●●●●●●●●●
●●●●●
30
●●●●●●●●
●●●●●●●●●●●●●●●●●●40
●●●●●●●●●●●●●●●●
●●●●●●●●●●50
●●●●●●●●●●●●●●●●●●●●●●●●●●
60
●●●●●●●●●●●●●●●●●●●●●●●●●●70
●●●●●●●●●●●●●●●●●●●●●●●●●●80
●●●●●●●●●●●●●●●●●●●●●●●●●●90
●●●●●●●●●●●●●●●●●●●●●●●●
●●100
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
Time+Smoking+ObesityTime+Smoking
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Year 2030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
198019902000201020202030
0 20 40 60 80 100
−10
−8
−6
−4
−2
Age
Time+Smoking+Obesity
log(
mx)
log(
mx)
log(
mx)
Male Female
Forecasts retainsmoothness over age andtime
After age 50, age-specificmortality increases whenadding obesity.
2030 forecast for70-year-olds (per100, 000PYs). Males:2, 290 deaths with obesity;1, 775 without; Females:1, 558 with, 1, 144without.
At ages over 90, modelforecasts converge fasterfor females than males.
Gary King (Harvard, IQSS) The Future of Death 63 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)
Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)
Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2
Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)
Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)
Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)
Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)
Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)
Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)Past: +2.7 years 80.4
Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)
Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
Life Expectancy and Aged Dependency Ratios
1980 1990 2000 2010 2020 2030
7075
8085
Exp
ecte
d A
ge a
t Dea
th
Time+Smoking
Time+Smoking+Obesity
Age 0
Age 65
observed
1980 1990 2000 2010 2020 203070
7580
85E
xpec
ted
Age
at D
eath
Age 0
Age 65
1980 1990 2000 2010 2020 2030
3032
3436
3840
4244
Rat
io o
f Eld
ery
per
100
Wor
king
Age
Year Year Year
Male Female Aged Dependency Ratio
Male Life Expectancy (±25 years)Past: +5.1 years 75.2Future: +5.7 years 80.9 (excluding obesity)Future: +3.5 years 78.7 (a 35% drop)
Female Life Expectancy (±25 years)Past: +2.7 years 80.4Future: +3.9 years 84.4 (excluding obesity)Future: +1.8 years 81.9 (a 53% drop)
1/2 trillion dollar difference for Social Security
Gary King (Harvard, IQSS) The Future of Death 64 / 65
For papers, software, etc.
http://GKing.Harvard.edu
Gary King (Harvard, IQSS) The Future of Death 65 / 65