The Longevity of Famous People from Hammurabi to Einstein David de - - PowerPoint PPT Presentation

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The Longevity of Famous People from Hammurabi to Einstein

David de la Croix

IRES and CORE, Universit´ e catholique de Louvain

Omar Licandro

IAE-CSIC and Barcelona GSE

UCLA, February 24, 2015

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Why should economists bother with longevity ?

Adult longevity matters for economic choices and growth Transmission of ideas Lucas (2009): “A productive idea needs to be in use by a living person to be acquired by someone else, so what one person learns is available to others only as long as he remains alive. If lives are too short or too dull, sustained growth at a positive rate is impossible.” Incentive to invest Galor and Weil (1999): “The effect of lower mortality in raising the expected rate of return to human capital investments will nonetheless be present, leading to more schooling and eventually to a higher rate of technological progress. This will in turn raise income and further lower mortality...”.

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Research Question

Adult longevity is expected to display no trend in the Malthusian stagnation We know it increased widely from the beginning of the 19th century (Human mortality database) Earlier for English aristocrats (Cummins, 2014) When did it start to increase ? for whom ? where ? why ? Did it lead the increase in income per capita?

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Beliefs at the time of the industrial revolution: For Malthus (1798): “With regard to the duration of human life, there does not appear to have existed from the earliest ages of the world to the present moment the smallest permanent symptom or indication of increasing prolongation.” For Condorcet (1794): “One feels that transmissible diseases will slowly disappear with the progresses of medicine, which becomes more effective through the progress of reason and social

• rder, ... and that a time will

come where death will only be the consequence of extraordinary accidents, or of the increasingly slower destruction of vital forces.”

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What we do

Build a new dataset of around 300,000 famous people born from the 24th century BCE (Hammurabi) to 1879 CE, Einstein’s birth. Data taken from the Index Bio-bibliographicus Notorum Hominum (IBN), which contains information on vital dates + some individual characteristics. Characteristics are used to control for selection and composition biases. Allows us to go beyond the current state of knowledge and provide a global picture.

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Contribution

1 Adult mean lifetime shows no trend over most of history. It is

equal to 59.7 ± 0.19 years during four millennia. ֒ → confirms the existence of a Malthusian era.

2 Permanent improvements in longevity precede the Industrial

• Revolution. Steady increase starting with generations born

1640-9, reaching 68 years for Einstein’s cohort. ֒ → lends credence to hypothesis that human capital was important for take-off to modern growth

3 Occurred almost everywhere over Europe, not only in the

leading countries, and for all observed (famous) occupations.

4 Reasons to be found in age-dependent shifts in the survival

• law. → early tendency of the survival law to rectangularize.

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The IBN

Index Biobibliographicus Notorum Hominum, aimed to easily access existing biographical sources. Compiled from around 3000 biographical sources (dictionaries and encyclopedias); Europeans are overrepresented. Famous People: ≡ included in a biographical dictionary or encyclopedia.

Hammurapi; 1792-1750 (1728-1686) ante chr.; ... ; Babylonischer k¨

• nig aus der dynastie der Amorer; Internationale Bibliographie de

Zeitschriftenliteratur aus allen Gebieten des Wissens. Einstein, Albert; 1879-1955; Ulm (Germany) - Princeton (N.J.); German physicist, professor and scientific writer, Nobel Prize winner (1921), Swiss and American citizen; Internationale Personal Bibliographie 1800-1943.

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Biographical Sources

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825 1850 1875 1900 1925 1950 1975

Time Distribution of the 2,781 Biographical Sources. Dashed - frequency (left axis), solid - cumulative (right axis)

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Sources - examples

Four haphazard examples of sources written in English language:

A Dictionary of Actors and of Other Persons Associated with the Public Representation of Plays in England before 1642. London: Humphrey Milford / Oxford, New Haven, New York, 1929. A Biographical Dictionary of Freethinkers of all Ages and Nations. London: Progressive Publishing Company, 1889. Portraits of Eminent Mathematicians with Brief Biographical

• Sketches. New York: Scripta-Mathematica, 1936.

Who Was Who in America. Historical volume (1607-1896). A complement volume of Who’s Who in American History. Chicago: The A. N. Marquis Company, 1963.

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Number of observations

1 10 100 1000 10000 100000 1 10 100 1000 10000 100000 1000000

• 2450 -2150 -1850 -1550 -1250 -950 -650 -350
• 50

250 550 850 1150 1450 1750

Number of Observations by Decade, density (dots) and cumulative (solid)

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Our database

The digital version of the IBN contains around one million famous people whom last names begin with letters A to L. The retained database includes 297,651 individuals: born before 1880 known years of both birth and death lifespan smaller than 15 or larger than 100 years were excluded, (729 and 872 respectively).

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Control variables

From birth and death places: 77 cities with at least 300 observations – as either birth or death place From description: all relevant words with at least 300 observations: 171 occupations, 65 nationalities and 10 religions Source publication date → distance with birth of person Precision dummy, Migration dummy, +8 other characteristics Gender, with the help of a name database Note: took care of translations in 22 languages.

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The universe

Upper class – top 10% of society

< 1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

Religion 16.7% 22.3% 20.8% 15.6% 9.3% 7.4% 4.9% Army 3.4% 5.3% 7.1% 8.7% 12.1% 7.5% 4.4% Education 18.7% 24.0% 23.0% 22.6% 20.9% 23.4% 26.5% Art 10.9% 11.7% 11.2% 11.5% 10.9% 13.2% 14.5% Law 12.4% 12.8% 12.1% 14.1% 16.6% 14.2% 12.7% Humanities 4.6% 3.6% 3.4% 3.6% 4.0% 6.7% 8.7% Science 4.8% 4.2% 4.7% 6.2% 7.8% 10.2% 12.3% Business 2.8% 3.3% 4.5% 6.0% 7.6% 9.7% 10.0% Nobility 11.0% 4.9% 4.2% 3.2% 2.5% 1.0% 0.4% Unknown 14.7% 8.2% 9.0% 8.6% 8.2% 6.7% 5.7% Women 1.4% 2.2% 2.5% 2.5% 3.3% 3.4% 4.0%

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Unconditional mean lifetime

Descriptive statistics: mean lifetime by ten-year cohorts without any control Smoothing: when nt < x λt = (nt/x) lt + (1 − nt/x)λt−1

• therwise,

λt = lt lt and λt are the actual and smoothed mean lifetimes, nt the actual cohort size, and x is an arbitrary representative size (set to 400) Initial condition: λ−∞ = 60.8, from Clark (2007) for hunter-gatherers

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Unconditional mean lifetime

15 25 35 45 55 65 75 85 95

• 2460
• 2160
• 1860
• 1560
• 1260
• 960
• 660
• 360
• 60

240 540 840 1140 1440 1740

Unconditional Mean Lifetime. Note: sample mean for individuals born before 1640 = 60.9.

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The notoriety bias

To compute the life expectancy at age a of a population: Ea =

T

• s=a

(s − a) age × death rate

• ds

Ns × Ss,a

• survival function

Ss,a is the probability of reaching age s if one has reached age a: Ss+1,a = Ss,a ×

• 1 − ds

Ns

• Problem:

Ns is the population at risk. That is, the population of people already famous at age s. Unobserved.

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The notoriety bias (2)

Measuring Ns by the population of all people that will become famous leads to underestimate mortality rates. This is a kind of selection bias, our measure of longevity (lifespan)

• verestimate life expectancy.

Worry: if age at notoriety changes over time, lifespan may change while life expectancy is in fact constant Solution: two out-of-sample tests, with populations for which we can compute both measures

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The Cardinals of the catholic church

50 55 60 65 70 75 80 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

Longevity at 25 (black) and Life expectancy at 25 (gray) of cardinals

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The Knights of the Golden Fleece

45 50 55 60 65 70 75 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

Longevity at 25 (black) and Life expectancy at 25 (gray) of Knights of the Golden Fleece

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Longevity and life expectancy

Longevity is informative about life expectancy Both measures move in the same direction Common tipping point at the second half of the 17th century Despite changes in the standards to enter the sample (e.g. mean age at elevation of cardinals rose from 40 to 50).

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Other biases

Source Bias. Celebrities in the IBN still alive at the publication of a biographical dictionary or encyclopedia are excluded from database Occupation Bias. Weight of some occupations may have change substantially over time (e.g. nobility, martyrs) Location Bias. Changes over time in the location of individuals in the sample Gender Bias.

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Model

mi,t = m + dt + α xi,t + εi,t (1) mi,t: lifespan of individual i belonging to cohort t m: conditional mean lifetime of a representative individual born before 1430 without known city, nationality and occupation, and with precise vital dates dt: difference between the conditional mean lifetime of cohort t and m xi,t: individual controls including city, occupation and nationality, precision and migration dummies, and age at publication dummies estimated using Ordinary Least Squares

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Main result

The estimated constant is 59.04 years (sd 0.19)

• 2

2 4 6 8 10 1430 1470 1510 1550 1590 1630 1670 1710 1750 1790 1830 1870

Figure: Conditional Mean Life: Cohort dummies and 95% conf. interval

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Notoriety bias

religious

• 0.03

military

• 3.02

education 0.74

rabbi

4.51

admiral

8.21

dean

4.07

bishop

3.87

general

7.04

academician

3.22

archbishop

3.47

marshal

6.74

professor

1.36

abbot

3.44

colonel

4.33

rector

1.22

archdeacon

2.38

major

2.17

writer

0.95

cardinal

1.58

• fficer

0.96

teacher

0.25

theologian

1.18

commander

0.73

scholar

0.15

clergyman

1.16

military

• 0.54

lecturer

• 0.86

priest

0.84

captain

• 0.77

student

• 10.03

pastor

0.82

lieutenant

• 1.23

vicar

0.13

soldier

• 2.40

preacher

• 0.27

fighter

• 4.23

missionary

• 1.26

deacon

• 4.98

martyr

• 14.62

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Source bias - estimation of the dummies

• 50
• 40
• 30
• 20
• 10

15-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99

Figure: Cohort age at publication dummies

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Source bias - effect on mean lifetime

1.5 3 4.5 1430 1530 1630 1730 1830

Figure: Source bias. Estimation (solid), 2× std cohort dummies (dots)

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Looking for special events

53 55 57 59 61 63 65 67 69 1550 1600 1650 1700 1750 1800 1850 1900

Mean Lifetime per Year of Death

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Robustness

Does any of the occupational groups lead the results? Does any of the nationalities lead the results? mi,t = m + dt + ˜ dt + α xi,t + εi,t (2) ˜ dt measures the additional effect of birth decade for the people with the suspected characteristic.

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Robustness - occupations

Add interaction between cohort dummies and each occupation

57 59 61 63 65 67 69 1430 1470 1510 1550 1590 1630 1670 1710 1750 1790 1830 1870

Figure: Robustness: Occupational groups

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Robustness - Do leading countries determine the results?

Add interaction between cohort dummies and leading countries citizenship

57 59 61 63 65 67 69 1430 1470 1510 1550 1590 1630 1670 1710 1750 1790 1830 1870

Figure: Robustness: British, leading nations and leading cities

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Conditional survival laws - idea

How to interpret the rise in longevity? For each individual i belonging to cohort t, let us define ˆ ri,t ≡ ˆ m + ˆ dt + ˆ εi,t ri,t = int(ˆ ri,t + 0.5) the conditional lifespan of individual i belonging to cohort t It represents the lifespan of individual i after controlling for all individual i observed characteristics Then compute conditional survival laws for cohorts of minimum 1600 individuals (1600-cohorts)

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Conditional survival laws - results

0.5 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Figure: Conditional Survivals for some 1600-cohorts: From deep black to clear gray are cohorts 1535-1546, 1665-1669, 1787-1788, 1807-1808, 1816, 1879.

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Gompertz-Makeham law of mortality

We estimate and interpret the evolution of the survival law using Gompertz-Makeham law of mortality and the Compensation Effect Death rates as a function of age a: δ(a) = A + eρ+αa. (3) Age-dependent component, the Gompertz function eρ+αa; Age-independent component, the Makeham constant A, A > 0. We estimate by non-linear least squares the Gompertz-Makeham law (3) (in logs) for each of the 1600-cohorts.

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Estimation results (1)

Consistently with Gavrilov and Gravilova (1991), the estimated Gompertz parameter ρ is decreasing over time. These parameter changes take place as early as for the cohort born in 1640, i.e. more than one century earlier than in GG.

50 100 150 −10 −9 −8 −7 −6 −5

Estimated ˆ ρ

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Compensation Effect of Mortality

The Compensation Effect of Mortality states that any drop in ρ, has to be compensated by an increase in α, following the relation ρ = M − Tα, (4) where M and T, T > 0, are constant parameters, the same for all human populations. Under the Compensation Effect, the survival tends to rectangularize when A = 0 and α goes to infinity; in this case, the maximum life span of humanity is constant at T.

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Compensation Effect of Mortality holds

The life span parameter T is 80.4 years(std dev 0.57)

• ●
• ●
• ●
• ●
• ●
• ●
• ●
• 0.04

0.05 0.06 0.07 0.08 0.09 0.10 −10 −9 −8 −7 −6 −5 y = −1.937 −80.191 x

Figure: The Compensation Effect of Mortality: ρ (Y-axis), α (X-axis)

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Open questions

Are the survival probabilities we estimate for the famous people informative about the survival probabilities of the whole population? → compare our estimates with the English data based on family reconstruction (1550-1820), and the Swedish census data (1750-). Do we provide a different message from the various studies which have analyzed specific groups of famous people? → comparison with aristocrats, and cities Remember that our survival probabilities are computed from a measure of conditional lifespan for each individual

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English Family Reconstitution Data 1580-1820

55 60 65 70 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

England: Life Expectancy at 25 (Wrigley’s data, gray) vs Longevity at 25 (IBN, black)

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Comparison with Nobility

50 55 60 65 70 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

British Nobles: Life Expectancy at 25 (Hollingsworth’s data, gray) vs Longevity at 25 (IBN, black)

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Comparison with Cities - Geneva, 1625-1825

50 55 60 65 70 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

Geneva: Life Expectancy at 25 (Perrenoud’s data, gray) vs Longevity at 25 (IBN, black)

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Three conclusions from these comparisons

In England & Sweden, famous adult people are forerunners in mortality decline Mortality reductions for nobility take place in the 17th century in the three databases (IBN, Hollingsworth, Vandenbroucke) In Geneva, improvement of longevity over 1625-1774 in both famous and non-famous samples

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Criteria

Our analysis has pointed out several necessary conditions any credible explanation should display.

• Selectivity. Not to affect the mean lifetime of the general

population. Regional Independence. Not to be related to a particular location, it takes place at least all around Europe. Occupation Independence. To affect all occupations of famous people similarly, from Nobility to Religion Ministers, from Scientists to Artists. Age Dependence & Life Span Constancy. To reduce the mortality of the working age adults more. Urban Character. May also affect ordinary people living in cities.

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Explanations

Possible candidates Receding pandemics: last plague in England in 1666. May benefit the rich more, the poor being hit by infections anyhow Medical progress: better practise and habits benefitting the rich & the cities Increase in inequality (+ childhood development): high social classes are become richer before the industrial revolution.

consistent with Galor Moav (2002)

Excluded candidates Military revolution, Potatoes

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Data Precision - imprecise observations

With “c.”, for circa, or “?”, or when more than one date reported.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2450-2459 a.chr. 510-519 a.chr. 220-229 a.chr. 60-69 350-359 640-649 930-939 1230-1239 1520-1529 1810-1819

Figure: Frequency of Imprecise Observations

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Data Precision - heaping index

Frequency of observations with vital dates finishing in 0 o 5.

0.50 1.00 1.50 2.00 2.50 3.00 3.50 1000-1009 1120-1129 1240-1249 1360-1369 1480-1489 1600-1609 1720-1729 1840-1849

Figure: Heaping Index (solid - birth year, dashed - death year)

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Occupation bias: 9 categories + 171 occupations

278,084 individuals have at least one occupation (94.4%)

• 4
• 3
• 2
• 1

1 2 military arts and metiers nobility religious humanities education business law and government sciences

Figure: Conditional Mean Life: Main occupational groups

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Some tests

−60 −40 −20 20 40 60 0.000 0.005 0.010 0.015 0.020 0.025 0.030

Kernel Density of the Residuals (solid) and Normal density (dashes)

12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 1430 1470 1510 1550 1590 1630 1670 1710 1750 1790 1830 1870

Standard Deviation of Residuals by Decade, and 95% confidence interval

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Why the Makeham constant is nil - notoriety bias

0.00100 0.01000 0.10000 1.00000 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89

Figure: Mortality Rates 1871-79: Ages 30 to 90 (X-axis) and dead probabilities in log scale (Y-axis). Swedish from Human Mortality Database (solid), IBN (dashed)

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Death rates and the notoriety bias

Denote by δp(a) the mortality rates of the population of potentially famous people Φ(a) the probability that potentially famous people achieve notoriety before age a Observed mortality is the product of those that die conditional on being already famous: δ(a) = Φ(a)δp(a),

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One correction

Take the case of princes and kings. A prince has to wait until his father’s death to become king. Then, Φ(a) = 1 − Sp(a + b) Sp(b) , where a is the age of the prince and a + b is the age of his father. Sp(a + b) depends on the same parameters as the Gomperzt-Makeham function δp(a): can be estimated together: δ(a) = 1 − exp{−A(a + b) − (eα(a+b) − 1)eρ/α} exp{−Ab − (eαb − 1)eρ/α}

• Φ(a)
• A + eρ+αa
• δp(a)

(5)

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The corrected compensation law with b = 26

Makeham constant now positive, but constant.

• ●
• ●
• ●
• ●
• ●
• ●
• ●
• 0.04

0.05 0.06 0.07 0.08 0.09 0.10 −10 −9 −8 −7 −6 −5 y = −1.985 −80.192 x

Figure: The Compensation Effect of Mortality of potentially Famous People: ρ (Y-axis), α (X-axis)

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Simulation of the notoriety bias

0.001 0.01 0.1 1 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89

Figure: Simulated Mortality Rates 1871-79 for IBN people: Ages 30 to 90 (X-axis) and dead probabilities in log scale (Y-axis). δp(a) (solid), δ(a) (dashed)

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Swedish Records, 1750-1879

As for England: systematic underestimation of young adult survivals and catching-up, 50 years later than in England.

50 55 60 65 70 <1550 1550-1649 1650-1699 1700-1749 1750-1799 1800-1849 1850-1879

?

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