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Major Currents in Contemporary Economics New Developments in Growth Theory Mariusz Próchniak Department of Economics II Warsaw School of Economics 1 Time Models of economic growth: An overview Models of economic growth Neoclassical models The Solow model (1956) The Ramsey model (1928, 1965) The Diamond model (1965) Endogenous models The Romer learning-by-doing model (1986) The Lucas model (1988) R&D models Neoclassical revival: the Mankiw-Romer-Weil (augmented Solow) model (1992) 2 Time The Harrod-Domar model (1939, 1946) Harrod (1939) and Domar (1946) tried to combine the Keynesian analysis with the elements of economic growth. Economic growth is proportional to the investment rate (equal to the savings rate) and inversely depending on the marginal capital intensity of production. The growth rate of GDP is described by the following equation: s gy k where: gy – real GDP growth rate, s – the investment rate (the savings rate), k – the capital intensity of production (investment outlays per unit increase in national income). 3 Time The neoclassical growth theory: General characteristics The neoclassical production function: constant returns to scale, diminishing marginal product of capital. Neoclassical models do not explain well the long-run economic growth. Long-run economic growth depends on technological progress which is exogenous. The desired property would be to endogenize technical progress, so that economic growth could be explained within the model. 4 Time The neoclassical growth theory: General characteristics (cont.) Neoclassical models confirm the existence of conditional convergence. Convergence (-type) means that less developed countries (with lower GDP per capita) tend to grow faster than more developed ones. The catching-up process confirmed by neoclassical models is conditional because it only occurs if the economies tend to reach the same steady-state. 5 Time The Solow model The Solow model, also called the Solow-Swan model: Robert Solow (1956), Trevor Swan (1956). (1) Assumptions F – the production function. Inputs to production: physical capital K(t), effective labour A(t)L(t): the product of the level of technology A(t) and population (labour force) L(t). F K t , A t L t 6 Time The Solow model (cont.) The production function exhibits: constant returns to both inputs (capital and effective labour), diminishing marginal product of capital. One of the functions satisfying these assumptions is the Cobb-Douglas production function: F K t , A t L t K t A t L t 1 where 0 < < 1. 7 Time The Solow model (cont.) Technology and population both grow at constant exogenous rates: L t L t n A t A t a The increase in capital stock equals investment (savings) minus depreciation: K t sF K t , A t L t K t s – the exogenous savings rate, – the capital depreciation rate. 8 Time The Solow model (cont.) (2) Dynamics The dynamics of the economy is analysed in terms of capital and output per unit of effective labour: K k AL f k F K , AL AL K AL F , F k ,1 f k AL AL To find the equation describing the dynamics of the economy, we differentiate the definition of k with respect to time: k sf k n a k 9 Time The Solow model (cont.) k sf k n a k The above equation is the basic formula describing the dynamics of the economy in the Solow model. The increase in capital per unit of effective labour equals actual investment sf(k) minus replacement investment (n + a + )k. 10 Time The Solow model (cont.) (3) Steady-state f k f k* c* n a k sf k f k 0 k k k k 0 sf k* k 1 k 2 k* k Figure 1 The transition period and the steady-state in the Solow model The long-run equilibrium (steady-state) occurs at the point of intersection between sf(k) and (n + a + )k. In the steady-state, output and capital per unit of effective labour are constant over time. 11 Time The Solow model (cont.) What is the growth rate of total GDP (Y = F(K,AL)) and GDP per capita (Y/L) in the steady-state? We have to differentiate Y ≡ f(k)AL and Y/L ≡ f(k)A with respect to time: Y f k A L Y f k A L Y / L f k A Y / L f k A In the steady-state, output per unit of effective labour is constant, while technology and population both grow at constant rates (a and n). 12 Time The Solow model (cont.) We have obtained two important implications of the Solow model. In the steady-state (long-run equilibrium): the growth rate of GDP equals technological progress plus population growth, the growth rate of per capita GDP equals technological progress. 13 Time The Solow model (cont.) The steady-state in the Solow model is stable: regardless of the initial capital stock, the economy always tends towards the steady-state. During the transition period, economic growth is higher than in the steady-state because capital and output per unit of effective labour both increase. The Solow model confirms the existence of conditional convergence. 14 Time The Solow model (cont.) The steady-state may be dynamically inefficient: long-run equilibrium needn’t be Pareto optimal. This results from the exogenous savings rate. Too high savings rate leads to excessive capital accumulation. The savings rate does not affect the pace of economic growth in the steady-state, but it influences the equilibrium level of income (higher savings rate means a higher position of sf(k) function and consequently a higher level of k*). The impact of a change in the savings rate on GDP growth is temporary – higher savings rate accelerates economic growth during the transition period. 15 Time The Ramsey model The Ramsey-Cass-Koopmans model: Frank Ramsey (1928), David Cass (1965), Tjalling Koopmans (1965). The main difference: the savings rate. In the Ramsey model, it is endogenous and results from optimal decisions made by utility-maximizing individuals. Similarities as compared with the Solow model: In the steady-state, GDP growth rate equals the sum of technological progress and population growth (the variables exogenously given) while the growth rate of per capita GDP equals technological progress. The Ramsey model confirms the conditional convergence. Differences as compared with the Solow model: The Ramsey model is Pareto optimal. Endogenous savings prevent excessive accumulation of physical capital dynamic inefficiency does not appear. 16 Time Endogenous models of economic growth Endogenous models explain the economic growth in an endogenous manner, i.e. within the model. This feature contrasts with neoclassical growth theory where long-run growth depended on exogenous technological progress, introduced along with other assumptions. Achieving endogenous growth is possible due to abandoning the neoclassical production function which assumes diminishing returns to accumulable inputs and constant returns to scale. Endogenous models assume that there are at least constant returns to accumulable inputs. 17 Time The AK model The mechanism of endogenous growth can be explained by introducing into the Solow model the production function: Y t AK t This function exhibits constant returns to capital, the only accumulable factor of production. Given (Y = C + I = C + dK/dt) and (I = sY), the economic growth rate is: Y sA Y The economy is continuously growing at the rate of sA. The increase in the savings rate is sufficient to accelerate permanently the long-run rate of economic growth. 18 Time Endogenous models of economic growth Endogenous growth occurs by eliminating the assumption of diminishing returns to accumulable inputs. Introduction of (at least) constant returns takes various forms. The Romer learning-by-doing model: a one-sector model, in which long-run growth is achieved due to increasing returns to accumulable factors at the whole economy level. The Rebelo and Lucas models: endogenous growth is possible due to the existence of two sectors, each of which exhibiting constant returns. Models with an expanding variety of products and models with an improving quality of products are known as R&D models: long-run economic growth is obtained by endogenizing technical progress, which is the output of the R&D sector. 19 Time The Romer learning-by-doing model Romer (1986) Knowledge, which is the only accumulable factor of production, exhibits increasing returns at the social (whole economy) level. Knowledge, being created through investment of individual firms, can spread freely throughout the economy and can be used by all firms without incurring additional costs (learning-by-doing). Due to increasing returns, the Romer model reveals an accelerating and permanent economic growth without introducing exogenous variables. 20 Time The Romer learning-by-doing model (cont.) The production function of an individual firm: fi ai , ki , A ai – the level of knowledge of an individual firm, ki – other factors of production (capital, labour, etc.), A – the general level of knowledge in the economy. Other inputs are constant (ki = const.) knowledge is the only accumulable factor of production. The production function exhibits increasing returns with respect to all inputs (a, k, A) and constant returns with respect to a and k: f a, k , A f a, k , A f a, k , A f a, k , A The marginal product of knowledge at the social level is increasing while from the firm’s point of view it is decreasing or constant. 21 Time The Romer learning-by-doing model (cont.) There is no steady-state in the Romer model. At the optimal trajectory, a perfectly competitive economy reveals a permanent and accelerating economic growth. The Romer model does not confirm the existence of convergence. It suggests rather divergence trends: the rate of economic growth increases with income meaning that more developed countries grow faster than less developed ones. Perfectly competitive economy is not Pareto optimal. This is because investments in knowledge made by a single firm lead to the increase of the overall level of knowledge. But a single company in its investment decisions does not take into account these positive externalities. 22 Time The Lucas model Also: Uzawa-Lucas model (Lucas, 1988; Uzawa, 1964, 1965). A two-sector model: physical capital and human capital. Endogenous growth is achieved due to the existence of two sectors that both exhibit constant returns. The Lucas model explains well the differences in income levels between countries. The economies, which at a starting point are capital scarce, achieve long-run equilibrium with low level of capital. The economies which are initially richer tend to steady-state characterized by higher capital level. The Lucas model does not confirm the convergence – in terms of both the comparison of various steady-states and the comparison of transition periods. Steady-states: GDP growth rate does not depend on income level. Transition periods: less developed countries may grow faster or slower than more developed ones. 23 Time Neoclassical revival: the Mankiw-Romer-Weil (augmented Solow) model Mankiw, Romer, Weil (1992) The MRW model includes human capital. The production function: Y K H AL where > 0, > 0, + < 1. The production function shares all the neoclassical properties: the diminishing marginal product of each input and constant returns to scale. Output may be devoted to consumption, accumulation of physical capital, or accumulation of human capital. The time paths for physical capital and human capital are: K sK Y K H sH Y H 24 Time The Mankiw-Romer-Weil (augmented Solow) model (cont.) Capital and output per unit of effective labour: K k AL H h AL y Y AL K H AL AL k h Equations describing the dynamics of the economy: k sK y n a k s K k h n a k h sH y n a h s H k h n a h In the steady-state, the capital per unit of effective labour is constant. Setting the above equations to zero, we get the stock of physical and human capital in the long-run equilibrium: 1 K H s s k* n a 1 1 1 s s h* K H n a 1 1 25 Time The Mankiw-Romer-Weil (augmented Solow) model (cont.) k B h0 C k 0 k* E D A h* h Figure 2 The transition period and the steady-state in the augmented Solow model The steady-state is at the point of intersection between dk/dt = 0 and dh/dt = 0 functions (point E). The long-run equilibrium is stable: from any starting point the economy is moving towards the steady-state. 26 Time The Mankiw-Romer-Weil (augmented Solow) model (cont.) In the steady-state, physical capital, human capital, consumption, and output per unit of effective labour are all constant. In the steady-state (long-run equilibrium): the growth rate of GDP equals technological progress plus population growth, the growth rate of per capita GDP equals technological progress. The Mankiw-Romer-Weil model, like other neoclassical models, confirms the existence of conditional convergence. 27 Time Growth empirics: Growth determinants We use correlation and regression analysis. Correlation coefficient shows the relationship between the GDP growth rate and a variable tested as an economic growth determinant. In the regression equation, it is possible to test simultaneously many variables that are economic growth determinants: ggdpt 0 1 x1t 2 x2t n xnt 1initialgdpt 2 dummyt t The explained variable (ggdpt) is the GDP growth rate. The explanatory variables (x1t, x2t, …, xnt) are economic growth determinants. The regression equation may include the GDP per capita from the previous period (initialgdpt) to control the influence of initial conditions; and/or dummy variables (dummyt) to assess the impact of a single shock on economic growth. 28 Time Growth empirics: Growth determinants (cont.) Table 1. Empirical models of economic growth for the CEE-10 countries, 1993-2009 Variable MODEL 1 Gross capital formation (% of GDP) General government balance (% of GDP) Lending interest rate (%) Private sector share in GDP (%) GDP per capita at PPP (constant 2005 US$) from the previous period Dummy (=1 for the 2008-2009 period; =0 otherwise) Constant n = 54 R2 = 0.6347 R2 adjusted = 0.5881 MODEL 2 Gross capital formation (% of GDP) Market capitalization of listed companies (% of GDP) General government balance (% of GDP) CPI inflation (%) GDP per capita at PPP (constant 2005 US$) from the previous period Dummy (=1 for the 2008-2009 period; =0 otherwise) Constant n = 55 R2 = 0.6246 R2 adjusted = 0.5777 MODEL 3 Gross capital formation (% of GDP) General government balance (% of GDP) CPI inflation (%) Private sector share in GDP (%) GDP per capita at PPP (constant 2005 US$) from the previous period Dummy (=1 for the 2008-2009 period; =0 otherwise) Constant n = 56 R2 = 0.6033 R2 adjusted = 0.5547 Coefficient t-statistics p-value 0.1572 1.81 0.2427 2.05 –0.0569 –3.16 0.0696 1.65 –0.0002 –2.02 –7.1788 –5.21 –0.1681 –0.05 F = 13.61 (p-value for F = 0.000) 0.076 0.046 0.003 0.105 0.049 0.000 0.962 0.1985 2.47 0.0620 1.63 0.2688 2.28 –0.0241 –3.66 –0.0002 –1.89 –4.6624 –3.92 2.0208 0.93 F = 13.31 (p-value for F = 0.000) 0.017 0.111 0.027 0.001 0.064 0.000 0.355 0.1510 1.78 0.2732 2.26 –0.0234 –3.37 0.0971 2.40 –0.0002 –1.56 –5.5737 –4.64 –3.0093 –1.03 F = 12.42 (p-value for F = 0.000) 0.082 0.029 0.001 0.020 0.126 0.000 0.308 29 Time Growth empirics: Convergence In empirical analyses, two most popular concepts of income-level convergence usually are tested: absolute -convergence, -convergence. Absolute -convergence exists when less developed economies grow faster than more developed ones. -convergence appears when income differentiation between economies decreases over time. 30 Time Growth empirics: Convergence (cont.) To verify the absolute -convergence hypothesis, we estimate: 1 yT ln 0 1 ln y0 T y0 The explained variable is the average growth rate of real GDP per capita between period T and 0. The explanatory variable is the log GDP per capita in the initial period. If 1 is negative and significant, -convergence exists. To verify the -convergence hypothesis, we estimate the trend line of dispersion in income levels: sd ln yt 0 1t The explained variable usually is the standard deviation of log GDP per capita levels between countries. The explanatory variable is the time variable. If 1 is negative and significant, -convergence exists. 31 Time Growth empirics: Convergence (cont.) Annual growth rate of real GDP per capita, 1993-2009 0,05 EST LAT POL SLK IRE LIT 0,04 SLV EU10 ROM 0,03 CZE HUN GRE 0,00 8,65 R = 0.5485 SWE SPA EU10 (average) & EU15 (average) EU10 EU15 Trend line: EU10 and EU15 Trend line: EU10 (average) & EU15 (average) 8,85 LUX 2 0,02 0,01 g y = -0.0164y 0 + 0.1850 FIN BGR 9,05 9,25 POR UK EU15 BEL NET AUS DEN FRA GER ITA g y = -0.0226y 0 + 0.2424; 9,45 9,65 9,85 10,05 Log of real 1993 GDP per capita 10,25 2 R =1 10,45 10,65 10,85 Figure 3 GDP per capita growth rate over the period 1993-2009 and the initial GDP per capital level 32 Time Growth empirics: Convergence (cont.) Standard deviation of log of real GDP. per capita 0,60 0,56 sd(y ) = -0.0100t + 0.6031 2 R = 0.8693 0,52 0,48 0,44 0,40 25 countries 2 regions 0,36 Trend line: country differentiation Trend line: regional differentiation sd(y ) = -0.0118t + 0.5441 2 R = 0.9251 0,32 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Year Figure 4 Standard deviation of GDP per capita, 1993-2009 33 Time Growth empirics: Growth accounting – total factor productivity (TFP) We differentiate the production function: F A, L, K F A, L, K F A, L, K A L K Y A L K A L K Y Y A Y L Y K We further assume: Hicks-neutral technological progress: F(A,L,K) = Af(L,K). The technological share in income (∂F/∂A)A/Y is simply 1. All markets are perfectly competitive and there are no externalities. The marginal social product of capital ∂F/∂K equals the price of capital r; similarly for labour: ∂F/∂L = w. Let sK be the capital share in income (rK/Y), and sL – the labour share in income (wL/Y). Total income is obtained from labour and capital (Y = wL + rK). sK + sL = 1. 34 Time Growth empirics: Growth accounting – TFP (cont.) Y A K L sK 1 sK Y A K L The above equation is the basic equation in standard growth accounting. From this equation, we can calculate the TFP growth rate as the difference between the GDP growth rate and the weighted average growth rate of labour and physical capital: A Y K L TFP growth rate sK 1 sK A Y K L 35 Time Growth empirics: Growth accounting – TFP (cont.) Table 2 Labour (L), physical capital (K), and TFP contribution to economic growth in Poland, 2000-2008 2000 2001 2002 2003 2004 2005 2006 2007 2008 contr. contr. contr. contr. contr. contr. contr. contr. contr. growth contr. growth contr. growth contr. growth contr. growth contr. growth contr. growth contr. growth contr. growth contr. (% (% (% (% (% (% (% (% (% (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) points) points) points) points) points) points) points) points) points) L K TFP GDP –1.6 –0.8 –19.1 –2.2 –1.1 –99.1 –3.0 –1.2 –0.6 –15.7 1.2 0.6 11.3 2.2 1.1 31.2 3.2 1.6 25.8 4.4 2.2 32.4 3.8 1.9 38.0 4.6 2.3 55.3 4.3 2.2 195.5 2.9 –1.5 –107.1 1.4 103.4 2.0 1.0 26.8 2.0 1.0 18.7 2.2 1.1 30.5 2.3 1.1 18.4 3.2 1.6 23.5 4.3 2.1 43.0 2.7 2.7 63.8 0.0 0.0 3.5 1.5 1.5 103.7 3.4 3.4 88.9 3.7 3.7 70.0 1.3 1.3 38.3 3.5 3.5 55.8 3.0 3.0 44.2 1.0 1.0 19.0 4.2 4.2 100.0 1.1 1.1 100.0 1.4 1.4 100.0 3.8 3.8 100.0 5.3 5.3 100.0 3.5 3.5 100.0 6.2 6.2 100.0 6.8 6.8 100.0 5.0 5.0 100.0 contr. = contribution. 36 Time Summary 1. The models of economic growth can be divided into two groups: neoclassical and endogenous models. The first ones are characterized by a neoclassical production function which exhibits diminishing returns to accumulable inputs and constant returns to scale. The endogenous models assume at least constant returns to accumulable inputs. The most important neoclassical approaches include the Solow, Ramsey, and Diamond models. The basic endogenous theories are the Romer learning-by-doing model, the Lucas model, and models with an expanding variety or an improving quality of products. The new growth theory also includes the Mankiw-Romer-Weil (augmented Solow) model. 2. Neoclassical growth theory does not explain well the determinants of long-run economic growth. According to these models, long-run economic growth depends on technological progress which is exogenously given. 3. The conditional -convergence is confirmed by all neoclassical models. Endogenous growth models, however, do not confirm the existence of convergence. Some of them even indicate that economic growth increases with income suggesting rather divergence trends. 37 Time References • Barro R. and X. Sala-i-Martin (2003), Economic Growth, Cambridge – London: The MIT Press. • Mankiw N.G., D. Romer, and D.N. Weil (1992), A Contribution to the Empirics of Economic Growth, “Quarterly Journal of Economics”, 107, pp. 407-437. • Romer D. (2006), Advanced Macroeconomics, New York: McGraw-Hill. Polish translation: Romer D. (2000), Makroekonomia dla zaawansowanych, Warszawa: Wydawnictwo Naukowe PWN. 38 Time Additional references • Aghion P. and P. Howitt (1992), A Model of Growth through Creative Destruction, “Econometrica”, 60, pp. 323-351. • Arrow K. (1962), The Economic Implications of Learning by Doing, “Review of Economic Studies”, 29, pp. 155-173. • Barro R. and X. Sala-i-Martin (1995), Economic Growth, New York – St. Louis – San Francisco: McGraw-Hill. • Cass D. (1965), Optimum Growth in an Aggregative Model of Capital Accumulation, “Review of Economic Studies”, 32, pp. 233-240. • Diamond P.A. (1965), National Debt in a Neoclassical Growth Model, “American Economic Review”, 55, pp. 1126-1150. • Domar E.D. (1946), Capital Expansion, Rate of Growth, and Employment, “Econometrica”, 14, pp. 137-147. • Grossman G.M. and E. Helpman (1991), Quality Ladders in the Theory of Growth, “Review of Economic Studies”, 58, pp. 43-61. • Harrod R. (1939), An Essay in Dynamic Theory, “Economic Journal”, 49, pp. 14-33. • Inada K.-I. (1963), On a Two-Sector Model of Economic Growth: Comments and a Generalization, “Review of Economic Studies”, 30, pp. 119-127. • Kaldor N. and J.A. Mirrlees (1962), A New Model of Economic Growth, “Review of Economic Studies”, 29, pp. 174-192. • Koopmans T.C. (1965), On the Concept of Optimal Economic Growth, in: The Econometric Approach to Development Planning, Amsterdam: North Holland. • Lucas R.E. (1988), On the Mechanics of Economic Development, “Journal of Monetary Economics”, 22, pp. 3-42. • Matkowski Z. and M. Próchniak (2010), Real Convergence or Divergence in GDP Per Capita, in: Poland. Competitiveness Report 2010. Focus on Clusters (ed. M.A. Weresa), Warsaw: World Economy Research Institute, Warsaw School of Economics, pp. 42-56. • Próchniak M. (2010a), Economic Growth Determinants in the 10 Central and Eastern European Countries, 1993-2009. Paper presented at the EuroConference 2010 „Challenges and Opportunities in Emerging Markets”, organised by the Society for the Study of Emerging Markets, Milas (Turkey), 16-18 July. • Próchniak M. (2010b), Total Factor Productivity, in: Poland. Competitiveness Report 2010. Focus on Clusters (ed. M.A. Weresa), Warsaw: World Economy Research Institute, Warsaw School of Economics, pp. 171-179. 39 Time Additional references (cont.) • Ramsey F. (1928), A Mathematical Theory of Saving, “Economic Journal”, 38, pp. 543-559. • Rapacki R. and M. Próchniak (2006), Charakterystyka wzrostu gospodarczego w krajach postsocjalistycznych w latach 1990-2003 [The Characteristics of Economic Growth in Post-Socialist Countries, 1990-2003], “Ekonomista”, 6, pp. 715-744. • Rapacki R. and M. Próchniak (2010), Wpływ rozszerzenia Unii Europejskiej na wzrost gospodarczy i realną konwergencję krajów Europy Środkowo-Wschodniej [The Impact of EU Enlargement on Economic Growth and Real Convergence of the CEE Countries], “Ekonomista”, 4, pp. 523-546. • Rebelo S. (1991), Long-Run Policy Analysis and Long-Run Growth, “Journal of Political Economy”, 99, pp. 500-521. • Romer P.M. (1986), Increasing Returns and Long-Run Growth, “Journal of Political Economy”, 94, pp. 1002-1037. • Romer P.M. (1990), Endogenous Technological Change, “Journal of Political Economy”, 98, pp. S71-S102. • Shell K. (1966), Toward a Theory of Inventive Activity and Capital Accumulation, “American Economic Review”, 56, pp. 62-68. • Sheshinski E. (1967), Optimal Accumulation with Learning by Doing, in: Essays on the Theory of Optimal Economic Growth (ed. K. Shell), Cambridge, MA: The MIT Press, pp. 31-52. • Solow R.M. (1956), A Contribution to the Theory of Economic Growth, “Quarterly Journal of Economics”, 70, pp. 65-94. • Solow R.M. (1957), Technical Change and the Aggregate Production Function, “Review of Economics and Statistics”, 39, pp. 312-320. • Swan T.W. (1956), Economic Growth and Capital Accumulation, “Economic Record”, 32, pp. 334-361. • Uzawa H. (1964), Optimal Growth in a Two-Sector Model of Capital Accumulation, “Review of Economic Studies”, 31, pp. 1-24. • Uzawa H. (1965), Optimal Technical Change in an Aggregative Model of Economic Growth, “International Economic Review”, 6, pp. 18-31. 40 Time Thank you very much for the attention!!! 41 Time