Economic Growth, Population, and Human Capital

1. Economic Growth, Population, and Human Capital June 4, 2005 Beijing, China China Center for Economic Research Gary S. Becker University of Chicago

2. GDP per CapitaChina, France, Japan, Germany, United Kingdom and United States1820 - 2000 Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

3. Gross School Enrolment in Secondary and Tertiary EducationChina1990, 2001 Source: World Development Indicators, The World Bank.

4. The China/West European Dichotomy1–2001 AD Source: Madison, Angus. The World Economy: Historical Statistics. OECD, 2003.

5. Malthusian Economy Income per Capita D D’ S I* S D’ D N* N’ 0 Population Population Growth

6. Malthusian Model 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

7. 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.

8. Fertility Rates for Nations with below Replacement Fertility1970 – 2000 Source: World Development Indicators, The World Bank.

9. Knowledge Revolution: Modern Economy Per Capita Income Growth (ΔI) D ΔI’ S ΔI* D S N* N’ 0 Population Population Growth

10. Modern Model 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)

11. Stability of Growth 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