Mortality Inequality

1
Mortality Inequality

• Sam Peltzman
• Booth School of Business
• University of Chicago

2
Overview

• Economists interested in inequality
• Usually income inequality
• Focus here years of life
• Several Questions
• How can we measure this kind of inequality?
• In a metric comparable to income inequality
  measures?
• What has happened over time?
• And how does this compare to income inequality
  trends?
• How does inequality of lifetimes vary
• Across countries?
• Across genders?
• What can we say about future trends?

3
Mortality Inequality Income Inequality

• Income inequality is one dimension of overall
  inequality
• Potentially misleading as measure of personal
  welfare
• Income measured at a moment (year)
• Number of years over which income enjoyed is also
  important
• Think of lifetime income (consumption) (Y)

C annual income or Consumption X number of
years lived
4
Inequality of Mortality as a Component of
Inequality of Lifetime Income

• Variability of Y across individuals in a
  population
• c, x are logs, so y cx
• Vvariance, Sstandard deviation, r correlation
• S(c) is a standard measure of income inequality
• This talk focuses on S(x) (or V(x))
• Entirely descriptive
• How important is inequality of lifetimes compared
  to inequality of income?
• Historically? Today?
• Gender Cross-Country Aspects

5
How Has Broad Topic Been Treated in Past?

• Most attention to cross-country comparisons
• Correlation of average c and average x
• Correlation is positive, but becomes weak beyond
  low level (Preston)
• Change over time in average c and average x
• Both increasing everywhere
• But, increase in x for low income countries gt
  for high income
• Reverse may be true for income
• So Widening North-South divide is exaggerated
  (Becker et al)
• This talk is entirely about within country
  comparisons
• S(x) measures does someone born today live to
  age 1? 25? 85?
• How has this changed over time?
• Gender differences

6
Some Broad Conclusions

• Historically (since c.1750) S(x) has been
  important component of total inequality
• More important than S(c), by some measures
• S(x) has declined over time as E(x) has increased
• But relation between longevity and inequality is
  not necessarily monotonic
• Kuznets curve for mortality
• Today S(x) ltlt S(c) in developed world
• But remains important in less developed countries
• Gender inequality long cycles, but no long trend
• The Soviet/Russian anomaly

7
Measuring Mortality Inequality

• Start with Life Table
• Survivors F(age), F(0)100,000 and F(110)0
• Period v Cohort
• Period LT just summarizes contemporary mortality
• No productivity adjustment
• Example

8
Life Table for England, 1850
9
Measuring Mortality Inequality

• Start with Life Table
• Survivors F(age), F(0)100,000 and F(110)0
• Period v Cohort
• Period LT just summarizes contemporary mortality
• No productivity adjustment
• Example
• Take first difference mortality - ?F deaths
  between age t and t1
• Expected value of the distribution of mortality
  is life expectancy at birth (c. 70 years
  today)
• Measure dispersion around expected value

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Measurement Issues

• Distribution of mortality is skewed left
• S(log age) dominated by infant mortality
• But directly comparable to S(log income)
• Show S(log age), but also take out infant
  mortality
• E.g., age 5

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Prologue How Large is Income Inequality
Historically?

• If y cx
• What is V(c) (or S(c)) within a country?
• In principle, c should be present value of future
  consumption at birth
• In practice, all we have is per capita or per
  household income
• V of income probably overstates V(c)
• And, poor data on income distributions until
  recently
• Rough estimates
• Today .6 lt S(log income) lt 1
• Since c.1900 upper bound 1
• Compare Sweden US (i.e., high and low equality)

12
Standard Deviation of Log Household Income US
and Sweden
13
Prologue 2 What has Happened to Average
Longevity?

• Increasing
• But Where? And When did this Start?
• Everywhere in the Developed World since c.1850
• Steady Convergence
• Will show data for 10 countries with life tables
  from 1850 or before
• Scandinavia Large European US

14
Expected Years of Life at Birth 10 Countries
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What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)
• 1.5 up to c. 1900
• Declines substantially throughout 20th Century
• Now .3 (i.e., ltlt income inequality measures)

16
Standard Deviation Log Life at Birth 10 Countries
17
What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)
• 1.5 up to c. 1900
• Declines substantially throughout 20th Century
• Now .3 (i.e., ltlt income inequality measures)
• Excluding Infant Mortality (S(log life/x 5)
• Similar pattern (accelerated decline after 1900)
• Goes from .6 - .7 before 1900 to .25 today

18
SD Log Life for Survivors to Age 5 10 Countries
19
What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)
• 1.5 up to c. 1900
• Declines substantially throughout 20th Century
• Now .3 (i.e., ltlt income inequality measures)
• Excluding Infant Mortality (S(log life/x 5)
• Similar pattern (accelerated decline after 1900)
• Goes from .6 - .7 before 1900 to .25 today
• Both measures converge across countries
• S(x) historically important component of
  inequality
• Much less so today

20
Why did Inequality Improvement Lag?

• Medical Progress (as we have so far known it) is
  uneven
• Most of the progress is getting people to live
  into their 80s
• Relatively little progress in extending upper
  limit
• Example England 1842-2002

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Mortality Data for England/Wales 1842-2002
Year Percentage Surviving Past 80 Percentage Surviving Past 80 Average Age at Death of Those Dying Average Age at Death of Those Dying Average Age at Death of Those Dying Ratio of Old to Young Ratio of Old to Young
  of Births if Alive at 5 Before 80 Before 80 After 80 Life Expectancy Life Expectancy
      All Alive at 5      
  (1) (2) (3) (4) (5) (5)/(3) (5)/(4)
1842 9.6 13.0 36.5 50.7 85.0 2.33 1.68
1902 11.9 15.1 43.2 56.3 84.6 1.96 1.50
1952 30.1 31.1 62.2 65.1 85.3 1.37 1.31
2002 54.8 55.2 66.3 67.2 87.7 1.31 1.31
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Why did Inequality Improvement Lag?

• Medical Progress (as we have so far known it) is
  uneven
• Most of the progress is getting people to live
  into their 80s
• Relatively little progress in extending upper
  limit
• Example England 1842-2002
• This uneven progress ? conflicting effects on
  inequality
• Reducing mortality at young ages? reduced
  inequality
• BUT increased odds of surviving to old age?
  greater inequality

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Medical Progress Inequality (continued)

• Decompose X as
• X expected life,
• A1 (A2) years lived if you die before (after)
  80
• P probability of living to 80
• Then the trend in V(log X) is
• D log (A2/A1)
• Second term is a Kuznets curve in mortality
• If progress means more people survive to old
  age
• Then progress ? more inequality as long as plt1/2
• Actual progress is a mix of strictly declining
  first term and Kuznets effect
• Kuznets effect still important in less developed
  world

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Summary So Far

• Improvement in Mortality Inequality is an
  Important Part of any Increase in Social Equality
• Ex-infant mortality S(x) improves .3 to .4
  since 1850 or 1900
• Matches plausible decline in S(c) in advanced
  welfare states
• Accounts for all improvement in US
• Convergence in longevity equality across
  developed countries
• May suggest reduction in income-longevity
  correlation
• But incomes have also converged

25
What About Less-Developed Countries

• Mostly 20th century data
• And few very poor countries
• Progress in E(x) and S(x)
• But ltlt convergence than rich countries
• And Kuznets effect lag between E(x) and S(x)
  seems more important

26
The Third World (Then Now)?

• 5 poor (c.1900 or now) countries
• 3 Latin America (Argentina, Brazil, Chile)
• 2 Asia (Japan, India)
• Progress in both expected life inequality
• But more inter-country variability than first
  world
• In levels at any point in time
• Less or no convergence
• In lag of inequality behind expected life

27
Expected Life SD Log Life 5 Countries

• Expected Life

• Standard Deviation Log Life at Birth

Heavy line is average of 10 rich countries shown
earlier
28
Russian Anomaly

• Every country (in range from US to India) has
  increased LE since c. 1950
• Except FSU/Russia
• LE - 4 yrs beginning in 1950s, accelerates in
  1990s
• Reverses previous relative progress
• Gap now 10 (females) to 20 (males) years at birth
• Occurs despite continued reduction in infant
  mortality
• Similar Anomalies in Inequality Measures

29
LE at Birth. FSU/Russia Relative to 18 OECD
Countries
30
Russian Anomaly

• Every country (in range from US to India) has
  increased LE since c. 1950
• Except FSU/Russia
• LE - 4 yrs beginning in 1950s, accelerates in
  1990s
• Reverses previous relative progress
• Gap now 10 (females) to 20 (males) years at birth
• Occurs despite continued reduction in infant
  mortality
• Similar Anomalies in Inequality Measures
• Major effects on Males gt 50 since 1990
• 1896 LE for 50 yr old male 18.3 yrs
• 2002 LE for 50 yr old male 17.6 yrs

31
Male to Female LE at 50. FSU/RU, since 1950
32
The Female Advantage

• Today Female life expectancy 1.07 x Male LE
• C. 1750 Female LE 1.07 Male LE
• But considerable variation in between
• 20th century inverted U
• Antibiotics (favors females) then Heart Disease
  (favors males)

33
Female to Male Life Expectancy at Birth(average
across countries, wars removed)
34
The Female Advantage

• Today Female life expectancy 1.07 x Male LE
• C. 1750 Female LE 1.07 Male LE
• But considerable variation in between
• 20th century inverted U
• Antibiotics (favors females) then Heart Disease
  (favors males)
• Also considerable variation across countries
• Post WW2 average peaks at 1980
• But 1970 in US/UK, 1980 in FR and 1990 in GE

35
Female to Male LE 4 Largest Countries, 1950-2002
36
The Female Advantage

• Today Female life expectancy 1.07 x Male LE
• C. 1750 Female LE 1.07 Male LE
• But considerable variation in between
• 20th century inverted U
• Antibiotics (favors females) then Heart Disease
  (favors males)
• Also considerable variation across countries
• Post WW2 average peaks at 1980
• But 1970 in US/UK, 1980 in FR and 1990 in GE
• Conclusion Female advantage mitigates lower
  market income
• But no clear trends over very long periods

37
In Conclusion

• Economists study income inequality intensively
• Also study the value of life
• Missing a key linkage improvement in mortality
  has done more for social equality than all the
  explicit redistribution.
• But further substantial change in (developed
  world) inequality unlikely
• Without increase in maximum life span
• Prob of surviving to 80 gt .5
• Prob of 80 yr old surviving to 95 .1
• But that kind of change could reverse long
  decline in mortality inequality