The country level:
sustainability and age structure
• The most important issue that links age
structure to potential problems of
sustainability is the pension system
• The equilibrium of a pay-as-you-go pension
system depends on the fact that the total
amount of contributions is equal to the total
amount of pensions paid in any given year
The country level:
sustainability and age structure
• Demographically, this depends on the stability
of the ratio between population in working age
and population in retirement age
• ‘Support ratio’: how many persons aged 15-64
are there for a person aged 65 and over?
‘Support ratio’ Italy, Germany,
Spain,UN projections 2002
5.0
4.5
4.0
Italy
3.5
Spain
Germany
3.0
2.5
2.0
1.5
1.0
2000
2005
2010
2015
2020
2025
Year
2030
2035
2040
2045
2050
The country level:
sustainability and age structure
• If the support ratio decreases, solutions:
– Increase retirement age
– Increase labour force participation (i.e. of
women)
– Decrease level of pensions
– Increase level of contributions
• At the level seen, the development is not
sustainable
The country level:
sustainability and age structure
• The main reason is the decrease in fertility
• Second reason the increase in longevity
TFR (number of children per
woman) Italy, Germany, Spain
2.2
Italy
2.0
Spain
West G.
1.8
East G.
Germany
children
1.6
1.4
1.2
1.0
0.8
0.6
1980
1985
1990
1995
Year
2000
Life expectancy at age 65
Italy, Spain (women)
21
20
19
years
18
17
16
Italy
Spain
15
14
13
1980
1985
1990
1995
Year
2000
The country level:
sustainability and age structure
• “Lowest-low” fertility, defined when the
average number of children per woman in a
year (“period” TFR) drops below 1.3 has
emerged in Europe in the 1990s (Kohler,
Billari, Ortega, 2002)
• Forerunners: Italy & Spain. Then Central &
Eastern Europe, Former USSR
The country level:
sustainability and age structure
• Long-term sustainable solution:
– Increase in fertility combined with
– Increase in immigration
• To be in equilibrium, TFR should be close
to 2.1 (e.g. 1.8) and immigration
compensate for the difference (close to
U.K., U.S. solution)
• Of course, in the meanwhile mediumshort-term solutions
Net migration rate (% of the
population) Italy, Spain
1.0
%
0.5
0.0
1980
1985
1990
1995
2000
-0.5
Italy
-1.0
Year
Spain
The global level
• World’s population is at a level that has
never been reached in the past
• Today’s counts are pretty close to 6.4 billion
individuals (U.S. Census Bureau World
Population Clock)
• Is population a “bomb”?
The global level
Billions
12
11
2100
10
9
Old
Stone
7 Age
8
New Stone Age
Bronze
Age
Iron
Age
6
Modern
Age
Middle
Ages
2000
Future
5
4
1975
3
1950
2
1
Black Death —The Plague
1+ million 7000 6000 5000
years
B.C. B.C. B.C.
4000
B.C.
1900
1800
3000 2000 1000 A.D. A.D. A.D. A.D. A.D. A.D.
B.C. B.C. B.C. 1 1000 2000 3000 4000 5000
The global level
• Maybe pure growth problems are not the
most relevant ones for the future
• The demographer Wolfgang Lutz and
colleagues in 2001 (‘Nature’) proclaimed
‘The end of world population growth’
The global level
Modeling population dynamics
• Population dynamics can be modeled in
simple but meaningful and didactical ways
• Exponential growth
• Logistic growth
• Logistic growth with time-varying carrying
capacity
Exponential growth
• T.R. Malthus (17661834)
• 1798: An Essay on the
Principle of Population
• “…the human species would
increase in the ratio of -- 1,
2, 4, 8, 16, 32, 64, 128, 256,
512, etc. and subsistence as
-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
etc.”
Exponential growth
• The “Population
Bomb”
Pt 1  Pt  rPt  1  r Pt
r 0
Exponential growth
P0  10
r  0.015
Popolazione
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0
100
200
300
400
500
600
Logistic growth
• Back to Malthus (a
different reading):
• “…That population cannot
increase without the means of
subsistence is a proposition
so evident that it needs no
illustration...”
• Pierre Verhulst (1845):
logistic growth.
Population cannot grow
above a certain level
(‘carrying capacity’)
Logistic growth (discrete time)
• Explicit modeling of
the carrying capacity
(K)
• Limits to growth
• K is an asymptote
• Note: potential
chaotic dynamics
(Robert May, ‘Nature’,
1976)
 Pt 
Pt 1  Pt  r  Pt 1  
 K
r 0
P0  K
Logistic growth (discrete time)
Popolazione
P0  10
2500
r  0.05
K  2000
2000
1500
1000
500
0
0
100
200
300
400
500
600
Logistic growth with time-varying
carrying capacity
• The realism of the
model can be
improved, including
‘demographic
transitions’
• K may vary over
time because e.g. of
innovation
 Pt 
Pt 1  Pt  r  Pt 1  
 Kt 
Logistic growth with time-varying
carrying capacity
Popolazione
1200
1000
800
600
400
200
0
0
100
200
300
400
500
600
Deevey’s (1960) graph
(Scientific American – note the
log scale)
…real data on the log, log scale
Modeling environmental impact
and population
• Paul Ehrlich and John Holdren
(1971), “Impact of Population
Growth”, Science; also Barry
Commoner
• IPAT Model
I=PAT
• Environmental impact (I) is a
function of:
– Population (P)
– Affluence (A)
– Technology (T)
• In fact,
– A is usually expressed as production per
capita (Y/P)
– T is usually expressed as impact per unit
of production (I/Y)
Y I
I  P 
P Y
I=PAT
• This model can be used to decompose
the role of the three factors (P, A, T) in
shaping environmental impact
• E.g. Energy use
• Technology (& technology transfers) are
the keys to reduce environmental impact!
I=PAT (McKellar et al., 1995)
Bibliography
• Joseph A. McFalls Jr., 2003, Population: a lively
introduction, Population Bulletin, 58, 3, Population
Reference Bureau, Washington D.C.
• Massimo Livi Bacci, 2001, A Concise History of World
Population, Blackwell Publishing, Malden
• World Commission on Environment and Development,
1987, Our Common Future, Oxford University Press,
Oxford
• Luis Rosero-Bixby & Alberto Palloni, 1998, Population
and Deforestation in Costa Rica, Population and
Environment, 20: 149-185
• Richard Jackson & Neil Howe, 2003, The 2003 Aging
Vulnerability Index, Center for Strategic and International
Studies and Watson Wyatt Worldwide, Washington, D.C.
Bibliography
• Kohler, Hans-Peter, Francesco C. Billari & José Antonio
Ortega, 2002, The Emergence of Lowest-Low Fertility in
Europe During the 1990s, Population and Development
Review 28: 641-680
• Wolfgang Lutz, Warren Sanderson & Sergei Scherbov,
2001, The end of world population growth, Nature 412:
543-545
• Robert May, 1976, Simple mathematical models with
very complicated dynamics, Nature 261: 459-467
• Edward S. Deevey Jr., 1960, The Human Population,
Scientific American 203: 194-204
• Paul R. Ehrlich & John P. Holdren, 1971, Impact of
population growth, Science 171: 1212-1217
• F. Landis MacKellar, Wolfgang Lutz, Christopher Prinz &
Anne Goujon, 1995, Population, Households and CO2
Emissions, Population and Development Review 21: