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