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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