Lectures 2, 3 Variance in Death and Mortality Decline Shripad Tuljapurkar Ryan D. Edwards

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

2. 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

5. 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

6. 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

7. 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 s2/(s2 + r2 + …)

8. 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

10. LEE CARTER MORTALITY

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

13. 1875

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

18. Most death – adult death after age A

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

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

22. Infant Mortality – leave out Mode S10 – Variance of Age at Death if Die after Age 10

23. “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.

24. US Japan Sweden

25. Conditional distribution --- die after age 10

28. Did β change through history? Is it still changing?

32. σDECREASED and βINCREASED through the first half of the 20th century everywhere* σ is still DECREASING and β INCREASING in Sweden

33. Forecasting Models Bongaarts

34. Forecasting Models Lee-Carter

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

38. 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

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

42. 0.04 Whites m(10+) = 75.8 0.03 S (10) = 15.2 African Americans m(10+) = 70.7 0.02 S (10) = 17.4 0.01 0 0 10 20 30 40 50 60 70 80 90 100 110 African Americans & Whites Log mortality Ages at death

43. WHAT ELSE MAKES US SPECIAL? “EXTERNAL CAUSES OF DEATH” (Homicide, suicide, violence, other) SEPARATE OUT EXTERNAL DEATHS, FIND S10 FOR WHAT’S LEFT

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

46. HH income and age at death using the NLMS

47. Education and age at death using the NLMS

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