The Longevity of Famous People from Hammurabi
to Einstein
David de la Croix
IRES and CORE, Université catholique de Louvain
Omar Licandro
IAE-CSIC and Barcelona GSE
UCLA, February 24, 2015
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
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?
3 / 53
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Additional
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
order, ... 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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Additional
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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Additional
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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Introduction
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Survival Laws
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Additional
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
könig 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.
7 / 53
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Additional
Biographical Sources
80
70
1
0.9
0.8
60
0.7
50
40
30
0.6
0.5
0.4
0.3
20
0.2
10
0.1
0
0
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)
8 / 53
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Additional
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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Additional
Number of observations
1000000
100000
100000
10000
10000
1000
1000
100
100
10
10
1
-2450 -2150 -1850 -1550 -1250 -950
1
-650
-350
-50
250
550
850
1150 1450 1750
Number of Observations by Decade, density (dots) and cumulative
(solid)
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Additional
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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Additional
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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Additional
The universe
Upper class – top 10% of society
Religion
Army
Education
Art
Law
Humanities
Science
Business
Nobility
Unknown
Women
< 1550
1550-1649
1650-1699
1700-1749
1750-1799
1800-1849
1850-1879
16.7%
3.4%
18.7%
10.9%
12.4%
4.6%
4.8%
2.8%
11.0%
14.7%
1.4%
22.3%
5.3%
24.0%
11.7%
12.8%
3.6%
4.2%
3.3%
4.9%
8.2%
2.2%
20.8%
7.1%
23.0%
11.2%
12.1%
3.4%
4.7%
4.5%
4.2%
9.0%
2.5%
15.6%
8.7%
22.6%
11.5%
14.1%
3.6%
6.2%
6.0%
3.2%
8.6%
2.5%
9.3%
12.1%
20.9%
10.9%
16.6%
4.0%
7.8%
7.6%
2.5%
8.2%
3.3%
7.4%
7.5%
23.4%
13.2%
14.2%
6.7%
10.2%
9.7%
1.0%
6.7%
3.4%
4.9%
4.4%
26.5%
14.5%
12.7%
8.7%
12.3%
10.0%
0.4%
5.7%
4.0%
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Additional
Unconditional mean lifetime
Descriptive statistics: mean lifetime by ten-year cohorts without
any control
Smoothing:
when nt < x
otherwise,
λt = (nt /x) lt + (1 − nt /x)λt−1
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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Additional
Unconditional mean lifetime
95
85
75
65
55
45
35
25
15
-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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Additional
The notoriety bias
To compute the life expectancy at age a of a population:
Ea =
T
X
s=a
death rate
z}|{
ds
(s − a) ×
×
Ss,a
| {z }
Ns
|{z}
age
survival function
Ss,a is the probability of reaching age s if one has reached age a:
ds
Ss+1,a = Ss,a × 1 −
Ns
Problem: Ns is the population at risk. That is, the population of
people already famous at age s. Unobserved.
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Introduction
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Additional
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)
overestimate 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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Additional
The Cardinals of the catholic church
80
75
70
65
60
55
50
<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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Additional
The Knights of the Golden Fleece
75
70
65
60
55
50
45
<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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Additional
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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Additional
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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Introduction
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Conditional Mean Lifetime
Survival Laws
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Additional
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)
10
8
6
4
2
0
1430
1470
1510
1550
1590
1630
1670
1710
1750
1790
1830
1870
-2
Figure: Conditional Mean Life: Cohort dummies and 95% conf. interval
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Introduction
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Additional
Notoriety bias
religious
rabbi
bishop
archbishop
abbot
archdeacon
cardinal
theologian
clergyman
priest
pastor
vicar
preacher
missionary
deacon
martyr
-0.03
4.51
3.87
3.47
3.44
2.38
1.58
1.18
1.16
0.84
0.82
0.13
-0.27
-1.26
-4.98
-14.62
military
admiral
general
marshal
colonel
major
officer
commander
military
captain
lieutenant
soldier
fighter
-3.02
8.21
7.04
6.74
4.33
2.17
0.96
0.73
-0.54
-0.77
-1.23
-2.40
-4.23
education
dean
academician
professor
rector
writer
teacher
scholar
lecturer
student
0.74
4.07
3.22
1.36
1.22
0.95
0.25
0.15
-0.86
-10.03
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Additional
Source bias - estimation of the dummies
0
15-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
-10
-20
-30
-40
-50
Figure: Cohort age at publication dummies
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Additional
Source bias - effect on mean lifetime
4.5
3
1.5
0
1430
1530
1630
1730
1830
Figure: Source bias. Estimation (solid), 2× std cohort dummies (dots)
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Additional
Looking for special events
69
67
65
63
61
59
57
55
53
1550
1600
1650
1700
1750
1800
1850
1900
Mean Lifetime per Year of Death
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Additional
Robustness
Does any of the occupational groups lead the results?
Does any of the nationalities lead the results?
mi,t = m + dt + d˜t + α xi,t + εi,t
(2)
d˜t measures the additional effect of birth decade for the people
with the suspected characteristic.
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Additional
Robustness - occupations
Add interaction between cohort dummies and each occupation
69
67
65
63
61
59
57
1430
1470
1510
1550
1590
1630
1670
1710
1750
1790
1830
1870
Figure: Robustness: Occupational groups
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Additional
Robustness - Do leading countries determine the results?
Add interaction between cohort dummies and leading countries
citizenship
69
67
65
63
61
59
57
1430
1470
1510
1550
1590
1630
1670
1710
1750
1790
1830
1870
Figure: Robustness: British, leading nations and leading cities
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Additional
Conditional survival laws - idea
How to interpret the rise in longevity?
For each individual i belonging to cohort t, let us define
rˆi,t ≡ m̂ + dˆt + ε̂i,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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Additional
Conditional survival laws - results
1
0.5
0
0
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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Additional
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 + e ρ+αa .
(3)
Age-dependent component, the Gompertz function e ρ+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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Additional
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.
−5
−6
−7
−8
−9
−10
0
50
100
150
Estimated ρ̂
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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 − T α,
(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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Additional
Compensation Effect of Mortality holds
The life span parameter T is 80.4 years(std dev 0.57)
−5
●
●
−6
● ●● ●
●
●
●
−7
●●
● ●●
●●
●●
●●●●
●
●
●
●
●● ●
●●
●
●●
●●●●
●
●●●●●●
●●
●●
−8
−9
−10
● ●
●●
●
●
●
●●
●●
●
●●
●
●●
●
●
●
●●
●●
●
●
●●
●
●●
●
●
●
●●● ●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●●● ●
●●
●● ●
●●
●
●● ●
●
●●●
●
●
●
●
●●
●
●●
●
●●
●
y = −1.937 −80.191 x
0.04
0.05
0.06
0.07
0.08
0.09
0.10
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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Additional
English Family Reconstitution Data 1580-1820
70
65
60
55
<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
70
65
60
55
50
<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
70
65
60
55
50
<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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Additional
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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Additional
Data Precision - imprecise observations
With “c.”, for circa, or “?”, or when more than one date reported.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
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.
3.50
3.00
2.50
2.00
1.50
1.00
0.50
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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Additional
Occupation bias: 9 categories + 171 occupations
278,084 individuals have at least one occupation (94.4%)
2
1
0
military
arts and
metiers
nobility
religious
humanities
education
business
law and
government
sciences
-1
-2
-3
-4
Figure: Conditional Mean Life: Main occupational groups
46 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
Some tests
0.030
17
16.5
0.025
16
0.020
15.5
0.015
14.5
15
14
0.010
13.5
13
0.005
12.5
12
0.000
1430
−60
−40
−20
0
20
40
1470
1510
1550
1590
1630
1670
1710
1750
1790
1830
1870
60
Kernel Density of the Residuals (solid) Standard Deviation of Residuals by
Decade, and 95% confidence interval
and Normal density (dashes)
47 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
Why the Makeham constant is nil - notoriety bias
1.00000
0.10000
0.01000
0.00100
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)
48 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
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),
49 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
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) − (e α(a+b) − 1)e ρ /α}
A + e ρ+αa
αb
ρ
exp{−Ab − (e − 1)e /α}
|
{z
}
|
{z
}
δp (a)
Φ(a)
(5)
50 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
The corrected compensation law with b = 26
Makeham constant now positive, but constant.
−5
●
●
●
−6
● ●
●● ●●
●
●
−7
−8
−9
−10
●
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●
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● ●●● ●
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●
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●
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● ●
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●
●●
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●
●
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●
●
●
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●
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●
●
●
●
●
●
●
●
●
●
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●
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●●
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● ● ●●●
●●●●●●
●
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●
●
●
y = −1.985 −80.192 x
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Figure: The Compensation Effect of Mortality of potentially Famous
People: ρ (Y-axis), α (X-axis)
51 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
Simulation of the notoriety bias
1
0.1
0.01
0.001
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)
52 / 53
Introduction
Data
Biases
Conditional Mean Lifetime
Survival Laws
Comparisons
Interpretations
Additional
Swedish Records, 1750-1879
As for England: systematic underestimation of young adult
survivals and catching-up, 50 years later than in England.
70
65
?
60
55
50
<1550
1550-1649
1650-1699
1700-1749
1750-1799
1800-1849
1850-1879
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