Lectures 2, 3

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Lectures 2, 3 Variance in Death and Mortality
Decline Shripad Tuljapurkar Ryan D.
Edwards Queens College Grad Center CUNY
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MORTALITY LEVELS, DECLINES ARE ASSESSED IN TERMS
OF e0 e0 LIFE EXPECTANCY AT BIRTH
AVERAGE AGE AT DEATH E(T) where T
Random age at death Density of T is
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• MORTALITY CHANGE
• THE DETAILS ARE MESSY
• Year to year decline irregular
• Persistent, puzzling differentials
• Cause of death structure difficult to understand
  to predict
• Poor understanding of causal relationship to
  driving forces
• Startling reversibility -- the Former Soviet
  Union

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BUT IN THE AGGREGATE (i.e., age/sex) OVER THE
LONG-TERM ( gt40 years) IN HIGHLY INDUSTRIALIZED
NATIONS THERE APPEARS TO BE A Simple, general
(?) pattern of decline
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log m(x,t) s a(x) k(t) r b(x) g(t)
Singular Values s gt r gt gt 0 IF s gtgt r gt
THEN DOMINANT TEMPORAL PATTERN IS k(t)
VARIANCE EXPLAINED IS s2/(s2 r2 )
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Lee Carter (US) Tulja, Li , Boe (G7) In every
G-7 country ONE TEMPORAL COMPONENT EXPLAINS OVER
92 OF CHANGE IN log m(x,t) m(x,t) central
death rate G-7 Canada, France, Germany,
Italy, Japan, UK, US Period 1950 TO 1994
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• LEE CARTER MORTALITY

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OEPPEN-VAUPEL Best-in-world life expectancy has
risen in a straight line for 160 years, as shown
by
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1875
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Death young death before age A, adult
death after age A
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Most death adult death after age A
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Variance in age at death young death, adult
death
From adult death
From young death
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Most variance in death variance in adult death
after age A
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Infant Mortality leave out
Mode
S10 Variance of Age at Death if Die after Age 10
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• ADULT DEATHS AGES gt 10 YEARS
• CAPTURES MOST VARIANCE IN AGE OF DEATH
• V(10)
• VAR (AGE AT DEATH DIE AT AGE gt 10)
• S(10) v V(10)
• STANDARD DEVIATION IN AGE AT ADULT DEATH.

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US
Japan
Sweden
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Conditional distribution --- die after age 10
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Did ß change through history? Is it still
changing?
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s DECREASED and ß INCREASED through the first
half of the 20th century everywhere s is still
DECREASING and ß INCREASING in Sweden
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Forecasting Models
Bongaarts
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Forecasting Models
Lee-Carter
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Shape of b(x) at ages past mode could reverse
this case of Japan
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• Role of T and V(T) (adult death)
• Annuities, Life insurance
• Longevity bonds
• Risk life cycle savings and consumption
• Risk societal pension risk
• Optimization without constant environments
  economic models

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Can racial differentials explain high U.S. S10?
S10 in the U.S. by race compare Canada, France
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African Americans Whites
Log mortality
Ages at death
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WHAT ELSE MAKES US SPECIAL?
EXTERNAL CAUSES OF DEATH (Homicide, suicide,
violence, other)
SEPARATE OUT EXTERNAL DEATHS, FIND S10 FOR
WHATS LEFT
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FACT Education Income affect Mortality Risk
USUAL Q how much Mortality ? when Educ ?
BUT Variance within educational/income groups??
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HH income and age at death using the NLMS
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Education and age at death using the NLMS
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WHAT ABOUT AGGREGATE INEQUALITY? DOES ? INCOME
INEQUALITY IMPLY ? INEQUALITY IN AGE AT DEATH?
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• Risk factors?
• Epidemics of risk factors (obesity, smoking,
  alcohol)?
• Comparative analysis

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