Solow model: Convergence

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1 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

2 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

3 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

4 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)

5 Baumol (1986) cited in De long (1988)

6 All once-rich countries: De long (1988)

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

8 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,

9 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 = α s = average of investment-gdp ratios over the period y = per capita GDP in the year 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 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 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

10 3 Human Capital and Growth pp 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

11 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 pp 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

12 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

13 Case: Growth accounting and the East Asian economic miracle

14 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)

15 Asian economic miracle: annual growth of output/capita (60-85) 1 Botswana Turkey Kenya Taiwan Algeria Guatemala Hong Kong Sweden Jamaica Singapore Ecuador Peru S. Korea Ireland Saudi Arabia Japan Mexico Nepal Malta Suriname Ethiopia Lesotho Iran Chile Egypt Swaziland Argentina Cyprus Barbados Sierra Leone Gabon Mauritius Uganda Greece Luxembourg Burundi Brazil Pakistan Guinea Syria Tanzania India Portugal Gambia Bangladesh Malaysia Colombia Nicaragua Yugoslavia Australia Niger China Dom. Rep Uruguay Thailand U.S.A Benin Norway U.K Senegal Cameroon Costa Rica Haiti Congo Togo Mauritania -0, Italy Cape Verde Liberia Panama Trin. & Tob Sudan Spain Switzerland Somalia Finland Zimbabwe Zaire Morocco Fiji Nigeria Israel Philippines Afghanistan Austria South Africa Mali Tunisia PNG CAR Iceland Venezuela Ghana France Ivory Coast Guyana Jordan Sri Lanka Madagascar Denmark N. Zealand Chad Belgium Honduras Zambia -' Netherlands Bolivia Angola Paraguay Malawi Mozambique Canada Rwanda Kuwait Burma Iraq W. Germany El Salvador 0.012

16 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.)

17 Participation rates & growth ( )

18 Annual growth of output/worker (60-85) 1 Botswana Yugoslavia Israel Gabon Spain Morocco Lesotho Thailand Finland Taiwan Italy France Japan Brazil Tunisia Egypt Austria Ecuador South Korea Swaziland Norway Hong Kong Portugal Tanzania Greece Malaysia Burma Syria Jordan Pakistan Cameroon Turkey Ivory Coast Congo Panama Ireland Cyprus Gambia Paraguay Singapore Algeria W. Germany Malta China Belgium 0.025

19 Investments in the NICs

20 I/GDP ratios

21 Annual Growth of Total Factor Productivity ( ) 1 Egypt Guinea Turkey Pakistan South Korea Netherlands Botswana 0, Iran Ethiopia Congo Burma Austria Malta Mauritius Australia Hong Kong China Spain Syria 0, Denmark Kenya Zimbabwe Israel France Gabon Greece Liberia Tunisia Japan Paraguay Cameroon Luxembourg Honduras Lesotho Yugoslavia Portugal Uganda Tanzania U.S.A Cyprus Colombia Belgium Thailand Sweden Canada Bangladesh 0, Malaysia Algeria Iceland 0, Malawi CAR Italy Brazil India Norway Panama Singapore Finland U.K Sri Lanka Taiwan W. Germany Fiji Ecuador Mali Switzerland The TFP growths of the four tigers were not miraculous any more!!

22 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 = *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.

23 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.

24 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

Supplementary Appendix for. Version: February 3, 2014

Supplementary Appendix for. Version: February 3, 2014 Supplementary Appendix for When Do Governments Resort to Election Violence? Version: February 3, 2014 This appendix provides supplementary information not included in the published draft. Supplementary