Lectures 2, 3 Variance in Death and Mortality Decline Shripad Tuljapurkar Ryan D. Edwards Queens College & Grad Center CUNY

MORTALITY LEVELS, DECLINES ARE ASSESSED IN TERMS OF e 0 e 0 = LIFE EXPECTANCY AT BIRTH = AVERAGE AGE AT DEATH = E(T) where T = Random age at death Density of T is

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

BUT… IN THE AGGREGATE (i.e., age/sex) OVER THE LONG-TERM ( >40 years) IN HIGHLY INDUSTRIALIZED NATIONS THERE APPEARS TO BE A Simple, general (?) pattern of decline

log m(x,t) = s a(x) k(t) + r b(x) g(t) + … Singular Values s > r > … > 0 IF s >> r > … THEN DOMINANT TEMPORAL PATTERN IS k(t) % VARIANCE EXPLAINED IS s 2 /(s 2 + r 2 + …)

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

LEE CARTER MORTALITY

OEPPEN-VAUPEL Best-in-world life expectancy has risen in a straight line for 160 years, as shown by

1875

Death – young death before age A, – adult death after age A

Most death – adult death after age A

Variance in age at death – young death, adult death From young death From adult death

Most variance in death – variance in adult death after age A

Infant Mortality – leave out Mode S 10 – Variance of Age at Death if Die after Age 10

“ADULT” DEATHS AGES > 10 YEARS CAPTURES MOST VARIANCE IN AGE OF DEATH V(10) = VAR (AGE AT DEATH | DIE AT AGE > 10) S(10) = √ V(10) = STANDARD DEVIATION IN AGE AT ADULT DEATH.

US Japan Sweden

Conditional distribution --- die after age 10

Did β change through history? Is it still changing?

σ DECREASED and β INCREASED through the first half of the 20 th century everywhere* σ is still DECREASING and β INCREASING in Sweden

Forecasting Models Bongaarts

Forecasting Models Lee-Carter

Shape of b(x) at ages past mode could reverse this – case of Japan

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

Can racial differentials explain high U.S. S10? S10 in the U.S. by race; compare Canada, Franc e

African Americans & Whites Log mortality Ages at death

WHAT ELSE MAKES US SPECIAL? “ EXTERNAL CAUSES OF DEATH ” (Homicide, suicide, violence, other) SEPARATE OUT EXTERNAL DEATHS, FIND S 10 FOR WHAT ’ S LEFT

FACT: Education & Income affect Mortality Risk BUT: Variance within educational/income groups?? USUAL Q: how much Mortality  when Educ 

HH income and age at death using the NLMS

Education and age at death using the NLMS

WHAT ABOUT AGGREGATE INEQUALITY? DOES  INCOME INEQUALITY IMPLY  INEQUALITY IN AGE AT DEATH?

Risk factors? Epidemics of risk factors (obesity, smoking, alcohol)? Comparative analysis