Mortality Inequality Sam Peltzman Booth School of Business University of Chicago 1

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? 2

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) 3 C = annual income or Consumption X = number of years lived

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 = c+x V=variance, S=standard 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 4

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 > 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 5

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) << S(c) in developed world But remains important in less developed countries Gender inequality: long cycles, but no long trend The Soviet/Russian anomaly 6

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 7

Life Table for England,

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 = - ΔF = deaths between age t and t+1 Expected value of the distribution of mortality is “life expectancy at birth” (c. 70+ years today) Measure dispersion around expected value 9

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+ 10

Prologue: How Large is Income Inequality Historically? If y = c+x 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 < S(log income) < 1 Since c.1900 upper bound ~ 1 Compare Sweden & US (i.e., high and low equality) 11

Standard Deviation of Log Household Income: US and Sweden 12

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 13

Expected Years of Life at Birth: 10 Countries 14

What has Happened to S(x) since 1750? Overall Measure (incl Infant mortality) ~1.5 up to c Declines substantially throughout 20 th Century Now ~.3 (i.e., << income inequality measures) 15

Standard Deviation Log Life at Birth: 10 Countries 16

What has Happened to S(x) since 1750? Overall Measure (incl Infant mortality) ~1.5 up to c Declines substantially throughout 20 th Century Now ~.3 (i.e., << income inequality measures) Excluding Infant Mortality (S(log life/x ≥ 5) Similar pattern (accelerated decline after 1900) Goes from before 1900 to ~.25 today 17

SD Log Life for Survivors to Age 5: 10 Countries 18

What has Happened to S(x) since 1750? Overall Measure (incl Infant mortality) ~1.5 up to c Declines substantially throughout 20 th Century Now ~.3 (i.e., << income inequality measures) Excluding Infant Mortality (S(log life/x ≥ 5) Similar pattern (accelerated decline after 1900) Goes from before 1900 to ~.25 today Both measures converge across countries S(x) historically important component of inequality Much less so today 19

Why did Inequality Improvement Lag? 1.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

Mortality Data for England/Wales Year Percentage Surviving Past 80 Average Age at Death of Those Dying Ratio of Old to Young of Birthsif Alive at 5Before 80After 80Life Expectancy All Alive at 5 (1)(2)(3)(4)(5)(5)/(3)(5)/(4) % 13.0%

Why did Inequality Improvement Lag? 1.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 This uneven progress  conflicting effects on inequality Reducing mortality at ‘young’ ages  reduced inequality BUT increased odds of surviving to old age  greater inequality 22

Medical Progress & Inequality (continued) Decompose X as X= expected life, A 1 (A 2 ) =years lived if you die before (after) 80 P = probability of living to 80 Then the trend in V(log X) is D= log (A 2 /A 1 ) Second term is a “Kuznets curve” in mortality If progress means “more people survive to old age” Then progress  more inequality as long as p<1/2 Actual progress is a mix of strictly declining first term and Kuznets effect Kuznets effect still important in less developed world 23

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 24

What About Less-Developed Countries Mostly 20 th century data And few very poor countries Progress in E(x) and S(x) But << convergence than rich countries And ‘Kuznets effect’ – lag between E(x) and S(x) – seems more important 25

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 26

Expected Life & SD Log Life: 5 Countries Expected Life Standard Deviation Log Life at Birth 27 Heavy line is average of 10 rich countries shown earlier

Russian Anomaly Every country (in range from US to India) has increased LE since c 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 28

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

Russian Anomaly Every country (in range from US to India) has increased LE since c 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 > 50 since : LE for 50 yr old male = 18.3 yrs 2002: LE for 50 yr old male = 17.6 yrs 30

Male to Female LE at 50. FSU/RU, since

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 20 th century: inverted U Antibiotics (favors females) then Heart Disease (favors males) 32

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

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 20 th 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 34

Female to Male LE: 4 Largest Countries,

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 20 th 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 36

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 >.5 Prob of 80 yr old surviving to 95 ~.1 But that kind of change could reverse long decline in mortality inequality 37