Economic Growth, Population, and Human Capital

Gary S. BeckerUniversity of Chicago

June 4, 2005

Beijing, China

China Center for Economic Research

GDP per CapitaChina, France, Japan, Germany, United Kingdom and United States1820 - 2000

Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

0

5,000

10,000

15,000

20,000

25,000

30,000

1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

1990

Inte

rnat

ion

al G

eary

-Kh

amis

Do

llars

France Germany United Kingdom United States China Japan

Gross School Enrolment in Secondary and Tertiary EducationChina1990, 2001

1990 2001

Secondary Education 48.7 67.2

Tertiary Education 2.9 12.7Source: World Development Indicators, The World Bank.

The China/West European Dichotomy1–2001 AD

Population

(millions)

Per Capita GDP

(1990 int. $)

GDP

(billions 1990 int. $)

China West Europe

China West Europe

China West Europe

1 59.6 24.7 450 450 26.8 11.1

1000 59 25.4 450 400 26.6 10.2

1300 100 58.4 600 593 60 34.6

1400 72 41.5 600 676 43.2 28.1

1500 103 57.3 600 771 61.8 44.2

1820 381 133 600 1,204 228.6 160.1

1913 437.1 261 552 3,458 241.3 902.3

1950 546.8 304.9 439 4,579 239.9 1,396.2

2001 1,275.4 392.1 3,583 19,256 4,569.8 7,550.3Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

Malthusian Economy

Income per Capita

Population GrowthPopulation

I*

N’

S

S

D

D’

D’D

N* 0

ln n(t) = a + b ln w(t)

ln w(t) = α - β ln N(t)

SS: ln n(t) = 0, n* = 1

ln w* = - a/b

ln N* = α/β + a/(bβ)

Dynamics

ln n(t) = ln N(t+1) – ln N(t) = a + b ln w(t)

... ln N(t+1) = a + bα + (1 – bβ) ln N(t)

Since, b, β > 0, 1 – bβ < 1

Stable, although requires also bβ < 2

β << 1, so sufficient if b < 2

Malthusian Model

Total Fertility RateChina, England and Wales, France, Japan, Sweden and United States1800 - 2000

Sources: Chesnais, Jean Claude. The Demographic Transition. Oxford: Oxford University Press, 1992. World Development Indicators, World Bank, 2004. The Reader's companion to American history. http://college.hmco.com/history/readerscomp/rcah/html/ah_009701_fertilityand.htm, 2005.

0

1

2

3

4

5

6

7

8

1800

1820

1840

1856

-186

0

1866

-187

0

1876

-188

0

1886

-189

0

1896

-190

0

1906

-191

0

1916

-192

0

1926

-193

0

1936

-194

0

1946

-195

0

1956

-196

0

1966

-197

0

1976

-198

0

1986

-199

0

1996

-200

0

Bir

ths

per

Wo

man

England and Wales France Sweden United States China Japan

1970 1980 1990 2000 1970 1980 1990 2000Armenia 3.24 2.31 2.62 1.28 Kazakhstan 3.35 2.9 2.72 1.88Australia 2.86 1.9 1.91 1.75 Korea, Rep 4.27 2.56 1.77 1.43Austria 2.29 1.62 1.45 1.34 Latvia 1.96 1.86 2.02 1.16Barbados 3.02 2.03 1.74 1.75 Lithuania 2.37 2.03 2.03 1.27Belarus 2.31 2.03 1.91 1.29 Luxembourg 1.98 1.5 1.62 1.78Belgium 2.2 1.67 1.62 1.61 Macao 3.12 2.3 1.75 1.15Bosnia 2.85 2.09 1.7 1.6 Macedonia 3.1 2.51 2.06 1.76Bulgaria 2.17 2.05 1.81 1.27 Malta 2.03 2.05 2.05 1.81Canada 2.26 1.74 1.83 1.55 Moldova 2.58 2.39 2.39 1.4Channel Isl. N/A 1.41 1.71 1.75 Netherlands 2.57 1.6 1.62 1.72China 5.78 2.54 2.1 1.9 Norway 2.5 1.72 1.93 1.85Croatia N/A N/A 1.63 1.39 Poland 2.2 2.28 2.04 1.34Cuba 3.85 1.95 1.69 1.58 Portugal 2.76 2.19 1.43 1.51Cyprus 2.6 2.46 2.42 1.91 Puerto Rico 3.15 2.55 2.2 1.9Czech Rep. 1.93 2.07 1.89 1.15 Romania 2.89 2.43 1.84 1.31Denmark 1.95 1.55 1.67 1.77 Russia 1.99 1.89 1.89 1.21Dominica N/A 3.92 2.7 1.9 Singapore 3.09 1.74 1.87 1.45Estonia 2.16 2.02 2.04 1.24 Slovak Rep. 2.39 2.31 2.09 1.34Finland 1.83 1.63 1.78 1.73 Slovenia 2.24 2.08 1.46 1.22France 2.48 1.95 1.78 1.88 Spain 2.84 2.22 1.33 1.24Georgia 2.65 2.25 2.21 1.08 Sweden 1.94 1.68 2.13 1.55Germany 2.03 1.44 1.45 1.35 Switzerland 2.09 1.55 1.59 1.46Greece 2.34 2.23 1.4 1.32 Thailand 5.44 3.48 2.27 1.84Hong Kong 3.34 2 1.27 1.02 Trinidad 3.59 3.3 2.36 1.75Hungary 1.97 1.91 1.84 1.29 Ukraine 2.09 1.95 1.85 1.2Iceland 2.79 2.48 2.31 1.98 United Kingdom 2.44 1.89 1.83 1.68Ireland 3.93 3.23 2.12 1.87 United States 2.48 1.84 2.08 2.13Italy 2.43 1.64 1.26 1.23 Yugoslavia 2.28 2.26 2.08 1.71Japan 2.14 1.75 1.54 1.36

Source: World Development Indicators, The World Bank.

Fertility Rates for Nations with below Replacement Fertility1970 – 2000

Knowledge Revolution: Modern Economy

Per Capita Income Growth(ΔI)

Population GrowthPopulation N’

S

S

D

D

N*

ΔI*

ΔI’

0

p(t) = ln [N(t+1)/N(t)] = a – b ln[I(t+1)/I(t)] + c(I(t)) ln I(t)

with c(I) → 0 as I → ∞

ln[I(t+1)/I(t)] = α + β ln N(t) + γ ln I(t)

if γ = 0,

SS: p(t) = p* = 0

ln [I(t+1)/I(t)] = g* = a/b

ln N* = (a/bβ) – (α/β)

if γ ≠ 0,

differentiate growth equation at SS

0 = β p* + γ g*

or p* = - γ g*/β < 0 as γ g* > 0

= 0 as γ g* = 0

> 0 as γ g* < 0

a – b g* = p*, or g* = a / (b - γ/β)

Modern Model

ln N(t+1) – ln N(t) = a – b [α + β ln N(t) + γ ln I(t)] + c ln I(t)

ln N(t+1) = ln N(t) = a – b α + (1-bβ) ln N(t) + (c-bγ) ln I(t)

if c > bγ, force raising population over time

if c = γ ≈ 0

Stability bβ > 0, same as Malthusian

although now have growth in income and change over time in population

Stability of Growth