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

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050

Year

Italy

Spain

Germany

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

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

1980 1985 1990 1995 2000

Year

child

ren

Italy

Spain

West G.

East G.

Germany

Life expectancy at age 65 Italy, Spain (women)

13

14

15

16

17

18

19

20

21

1980 1985 1990 1995 2000

Year

year

s

Italy Spain

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 medium- short-term solutions

Net migration rate (% of the population) Italy, Spain

-1.0

-0.5

0.0

0.5

1.0

1980 1985 1990 1995 2000

Year

%

Italy 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

A.D.2000

A.D.1000

A.D.1

1000B.C.

2000B.C.

3000B.C.

4000B.C.

5000B.C.

6000B.C.

7000B.C.

1+ million years

8

7

6

5

2

1

4

3

OldStoneAge New Stone Age

BronzeAge

IronAge

MiddleAges

ModernAge

Black Death — The Plague

9

10

11

12

A.D.3000

A.D.4000

A.D.5000

18001900

1950

1975

2000

2100

Future

Billions

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 (1766-1834)

• 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”

0

11

r

PrrPPP tttt

Exponential growth

Popolazione

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 100 200 300 400 500 600

015.0

100

r

P

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)

KP

r

K

PPrPP tttt

0

1

0

1

Logistic growth (discrete time)

Popolazione

0

500

1000

1500

2000

2500

0 100 200 300 400 500 600

2000

05.0

100

K

r

P

Logistic growth with time-varyingcarrying capacity

• The realism of the model can be improved, including ‘demographic transitions’

• K may vary over time because e.g. of innovation

t

tttt K

PPrPP 11

Logistic growth with time-varyingcarrying capacity

Popolazione

0

200

400

600

800

1000

1200

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

P

YPI

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: 849-865