Solow model: Convergence

Solow model: Convergence Per capita income k(0)>k* Assume same s, δ, & n, but no technical progress y* k(0)=k* k(0)<k* time

Solow model: Convergence (log) Per capita income k 0 > k Assume same s, δ, & n, same technical progress k 0 =k k 0 < k time

Per capita income along steady state (log) Per capita income Assume same E(0), having steady state at time 0 Same π, different δ, s, n time The two dashed lines correspond to the same π, higher that the one with the two solid lines

convergence Assume same technology E(0) Unconditional convergence: if all countries have same π, δ, s, n Conditional convergence: otherwise Empirical testing of convergence Baumol (1986); De Long (1988); Barro (1991); and Mankiw, Romer, Weil (1992)

Baumol (1986) cited in De long (1988)

All once-rich countries: De long (1988)

per capita GDP in 1960-85 versus per capita income in 1960; Barro (1991)

1 Convergence (pp74-84) 2 Mankiw, Romer, and Weil (1992): (pp84-90) in the steady state (1 + n) (1 + π) k = (1 δ) k + sŷ (1) k ŷ = s (1 + n) (1 + π) (1 δ) k ŷ Cobb-Douglas production function s n + π + δ (2) rearranging Y = K α L 1 α ) α k α ŷ Y L = ( K L hence k ŷ = ŷ(1 α)/α [ ] α/(1 α) ŷ s (3) n + π + δ express this in logarithmic form ln ŷ ŷ = α 1 α ln s α ln (n + π + δ) 1 α Y (t) P (t) E (0) (1 + π) t = 1 y (t) E (0) (1 + π) t,

Hence ln y (t) A + where A = ln E (0) + t ln (1 + π). from other research α = 1/3 so Mankiw, Romer, and Weil (1992) Heston-Summers data set π + δ = 0.05 α 1 α ln s α ln (n + π + δ) (4) 1 α α = 0.5. 1 α s = average of investment-gdp ratios over the period 1965-85 y = per capita GDP in the year 1985. 2.0.1 what to expect: the coeffi cient on the term ln s is positive, the coeffi cient on the term ln (n + π + δ) is negative; the two coeffi cients should be equal in size 2.0.2 results more than half the worldwide variation in per capita GDP in 1985 can be explained by the two variables s and n. The correlation coeffi cent of the regression is 0.59. the coeffi cient of ln s is significant and positive, whereas that of ln (n + π + δ) is significant and negative both coeffi cients are too large to be close to 0.5; the coeffi cint on savings is 1.42 and that on population is -1.97. 2

3 Human Capital and Growth pp99-107 production function y = k α h 1 α (4.1) no population growth, no depreciation (for simplicity, nothing is lost) saving to accumulate physical capital saving to accumulate human capital k(t + 1) k(t) = sy(t) (4.2) h(t + 1) h(t) = qy(t) (4.3) define r(t) h(t)/k(t), equations (4.2) and (4.3) become k(t + 1) k(t) k(t) h(t + 1) h(t) h(t) if both k and h grow at the same rate = sr 1 α = qr α sr 1 α = qr α = r = q s (4.4) then r = h/k ratio must be constant over time, and the time argument can be omitted In this case, physical capital grows at a rate of s α q 1 α because sr 1 α = s ( ) q 1 α s Note that y (t + 1) = k (t + 1) α h (t + 1) 1 α = ( 1 + s α q 1 α) α k (t) α ( 1 + s α q 1 α) 1 α h (t) 1 α = ( 1 + s α q 1 α) k (t) α h (t) 1 α = ( 1 + s α q 1 α) y (t) In other words, long run growth rate for all variables is given by s α q 1 α. 3

3.1 Comments diminishing returns to physical capital, yet no convergence in per capita income: initial conditions matter=>even with similar savings and technological parameters, no tendency for two countries per capita incomes to come together both s and q have growth rate effects, not just level effects as in the Solow model constancy of returns to physical and human capital combined relation to Mankiw, Romer, and Weil (1992): saving rate in the paper, as it is computed, captures only savings in physical capital, an increase in growth rate of population lowers per capita income, cutting into both forms of savings (physical and human capital) hence, the coeffi cient on population growth is likely to exceed the coeffi cient on physical savings. 4 Total Factor Productivity pp117-123 also due to Solow, in another paper published also in 1957 The production function Y (t) = F (K(t), P (t), E(t)) Imagine the term E(t) does not exist. Approximation shows that From (4.11) Y (t) = MP K K(t) + MP L P (t) (4.11) Y (t) Y (t) = MP K K(t) K(t) Y (t) K(t) MP L P (t) P (t) + Y (t) P (t) 4

output elasticities: σ K (t) MP K K(t) ; σ P (t) Y (t) MP L P (t) Y (t) : Y (t) Y (t) = σ K (t) K(t) K(t) + σ P (t) P (t) P (t) = σ K (t) K(t) K(t) + σ P (t) P (t) P (t) + T F P G(t) T F P G(t) stands for TFP growth over the period t and t + 1. If we have data about how Y, K, and P change, we can compute the total-factorproductivity growth. TFP growth is also known as the Solow residual the part of growth that cannot be explained by growth in factors of production. 5

Case: Growth accounting and the East Asian economic miracle

Growth Accounting Long run growth matters. A 7% increase each year means that the GDP will double in 10 years, while a 3.5% increase each year means 20 years. (rule of 70) Is growth due to inspiration (technology growth) or perspiration (input increases)? Three eye-catching episodes The case of Asian economic miracle from 50s to early 90s (we postpone the discussion of Chinese growth until later classes)

Asian economic miracle: annual growth of output/capita (60-85) 1 Botswana 0.067 41 Turkey 0.026 81 Kenya 0.011 2 Taiwan 0.062 42 Algeria 0.026 82 Guatemala 0.011 3 Hong Kong 0.059 43 Sweden 0.026 83 Jamaica 0.011 4 Singapore 0.059 44 Ecuador 0.026 84 Peru 0.010 5. S. Korea 0.057 45 Ireland 0.025 85 Saudi Arabia 0.009 6 Japan 0.055 46 Mexico 0.025 86 Nepal 0.009 7 Malta 0.053 47 Suriname 0.024 87 Ethiopia 0.009 8 Lesotho 0.051 48 Iran 0.023 88 Chile 0.008 9 Egypt 0.050 49 Swaziland 0.023 89 Argentina 0.007 10 Cyprus 0.049 50 Barbados 0.023 90 Sierra Leone 0.006 11 Gabon 0.045 51 Mauritius 0.023 91 Uganda 0.006 12 Greece 0.044 52 Luxembourg 0.023 92 Burundi 0.005 13 Brazil 0.042 53 Pakistan 0.023 93 Guinea 0.005 14 Syria 0.041 54 Tanzania 0.023 94 India 0.005 15 Portugal 0.041 55 Gambia 0.023 95 Bangladesh 0.005 16 Malaysia 0.039 56 Colombia 0.023 96 Nicaragua 0.003 17 Yugoslavia 0.039 57 Australia 0.022 97 Niger 0.001 18 China 0.038 58 Dom. Rep. 0.022 98 Uruguay 0.001 19 Thailand 0.038 59 U.S.A. 0.021 99 Benin 0.001 20 Norway 0.036 60 U.K. 0.021 100 Senegal 0.001 21 Cameroon 0.036 61 Costa Rica 0.021 101 Haiti 0.000 22 Congo 0.035 62 Togo 0.019 102 Mauritania -0,000 23 Italy 0.035 63 Cape Verde 0.019 103 Liberia -0.001 24 Panama 0.035 64 Trin. & Tob. 0.018 104 Sudan -0.001 25 Spain 0.035 65 Switzerland 0.017 105 Somalia -0.002 26 Finland 0.035 66 Zimbabwe 0.017 106 Zaire -0.002 27 Morocco 0.034 67 Fiji 0.016 107 Nigeria -0.002 28 Israel 0.034 68 Philippines 0.016 108 Afghanistan -0.003 29 Austria 0.033 69 South Africa 0.016 109 Mali -0.004 30 Tunisia 0.032 70 PNG 0.015 110 CAR -0.006 31 Iceland 0.032 71 Venezuela 0.015 111 Ghana -0.008 32 France 0.030 72 Ivory Coast 0.014 112 Guyana -0.010 33 Jordan 0.029 73 Sri Lanka 0.014 113 Madagascar -0.016 34 Denmark 0.028 74 N. Zealand 0.014 114 Chad -0.017 35 Belgium 0.028 75 Honduras 0.013 115 Zambia -'0.017 36 Netherlands 0.027 76 Bolivia 0.013 116 Angola -0.018 37 Paraguay 0.027 77 Malawi 0.012 117 Mozambique -0.020 38 Canada 0.026 78 Rwanda 0.012 118 Kuwait -0.080 39 Burma 0.026 79 Iraq 0.012 40 W. Germany 0.026 80 El Salvador 0.012

Was the Asian economic miracle really a miracle? No! said Krugman in his famous 1994 Foreign Affairs article, which made him famous to the world outside the economic profession. Relying on work by Young and Lau, he argued that the growth of the four tigers was largely due to increase in inputs (perspiration) rather than to increase in technology (inspiration). Now let s turn to the so called Asian miracle. (The following figures are taken from a paper by A. Young 1994, European Economic Review.)

Participation rates & growth (1960-85)

Annual growth of output/worker (60-85) 1 Botswana 0.076 16 Yugoslavia 0.039 31 Israel 0.032 2 Gabon 0.069 17 Spain 0.037 32 Morocco 0.031 3 Lesotho 0.057 18 Thailand 0.037 33 Finland 0.031 4 Taiwan 0.055 19 Italy 0.037 34 France 0.029 5 Japan 0.054 20 Brazil 0.037 35 Tunisia 0.028 6 Egypt 0.053 21 Austria 0.035 36 Ecuador 0.027 7 South Korea 0.050 22 Swaziland 0.035 37 Norway 0.027 8 Hong Kong 0.047 23 Portugal 0.035 38 Tanzania 0.027 9 Greece 0.047 24 Malaysia 0.034 39 Burma 0.027 10 Syria 0.046 25 Jordan 0.034 40 Pakistan 0.027 11 Cameroon 0.045 26 Turkey 0.033 41 Ivory Coast 0.026 12 Congo 0.043 27 Panama 0.033 42 Ireland 0.026 13 Cyprus 0.043 28 Gambia 0.033 43 Paraguay 0.025 14 Singapore 0.043 29 Algeria 0.033 44 W. Germany 0.025 15 Malta 0.040 30 China 0.033 45 Belgium 0.025

Investments in the NICs

I/GDP ratios

Annual Growth of Total Factor Productivity (1970-1985) 1 Egypt 0.035 23 Guinea 0.014 45 Turkey 0.008 2 Pakistan 0.030 24 South Korea 0.014 46 Netherlands 0.008 3 Botswana 0,029 25 Iran 0.014 47 Ethiopia 0.007 4 Congo 0.028 26 Burma 0.014 48 Austria 0.007 5 Malta 0.026 27 Mauritius 0.013 49 Australia 0.007 6 Hong Kong 0.025 28 China 0.013 50 Spain 0.006 7 Syria 0,025 29 Denmark 0.013 51 Kenya 0.006 8 Zimbabwe 0.024 30 Israel 0.012 52 France 0.005 9 Gabon 0.024 31 Greece 0.012 53 Liberia 0.004 10 Tunisia 0.024 32 Japan 0.012 54 Paraguay 0.004 11 Cameroon 0.024 33 Luxembourg 0.012 55 Honduras 0.004 12 Lesotho 0.022 34 Yugoslavia 0.011 56 Portugal 0.004 13 Uganda 0.021 35 Tanzania 0.011 57 U.S.A. 0.004 14 Cyprus 0.021 36 Colombia 0.011 58 Belgium 0.004 15 Thailand 0.019 37 Sweden 0.010 59 Canada 0.003 16 Bangladesh 0,019 38 Malaysia 0.010 60 Algeria 0.003 17 Iceland 0,018 39 Malawi 0.010 61 CAR 0.002 18 Italy 0.018 40 Brazil 0.010 62 India 0.001 19 Norway 0.017 41 Panama 0.009 63 Singapore 0.001 20 Finland 0.015 42 U.K. 0.009 64 Sri Lanka 0.001 21 Taiwan 0.015 43 W. Germany 0.009 65 Fiji 0.001 22 Ecuador 0.014 44 Mali 0.008 66 Switzerland 0.000 The TFP growths of the four tigers were not miraculous any more!!

What is TFP? Essentially, TFP is a measure of our ignorance (growth that cannot be explained otherwise) Solow (1957) found that, for the US during the period 1909 to 1949, the annual output growth rate=2.75%; labor growth rate=1% ; capital growth rate=1.75% ; MPL=0.65; and MPK=0.35 Hence, G A =2.75 0.65*1 0.35*1.75 =1.50% That is, more than half of the growth in real output could be attributed to technical change rather than to growth in the physical quantities of inputs.

More complicated production functions can be used... For instance, production function: Y=AF(L,K,H,N) where H is human capital and N is natural resources. Young (1995, Quarterly Journal of Economics) still finds similar results of TFP growth as previous slide shows. Kim and Lau (1994, J of J&IE) find that the hypothesis TFP growth rates of 4 little dragons equal to zero cannot be rejected. A reminder: some authorities in the area (Jorgenson and Griliches (1967)) have argued that TFP is a result of mismeasurement of factor inputs and therefore does not really exist.

Despite difference, the following are agreed between both sides of the debate A moderate conclusion: four tigers growth was not a miracle, but not completely due to perspiration as well. Hong Kong people should not be too pessimistic about the findings. Growth relies solely on input increase is bound to diminishing (marginal) returns Less developed countries can usually grow at a greater rate than their more developed counterparts due to the catch-up effect