Economic Growth Module Objectives now what determines the growth rates of aggregate and per capita GDP Distinguish factors that affect the economy s growth rate from those that merely shift the level of GDP Explain the concept of convergence If South orea and Taiwan continue to grow as fast as they have over the past decade, then they could overtake America s income-per-head within the next quartercentury or so. - The Economist, October 16, 1993 (c) Copyright 1999 by Douglas H. Joines 1
U.S. Real GDP 5000 9.0 4000 U.S. Real GDP (billions of 1987 dollars) 8.5 Log of U.S. Real GDP 8.0 3000 7.5 2000 7.0 6.5 1000 6.0 0 00 10 20 30 40 50 60 70 80 90 ear 5.5 00 10 20 30 40 50 60 70 80 90 ear International GDP Comparison 5000 4000 USA GDP, 1992 3000 2000 Japan China 1000 0 India W.Ger. Brazil Mexico Belg. Zimb. 1 2 3 4 5 6 7 8 9 Billions of 1985 U.S. dollars Production Function = f(, L, F Technology) L Production Process F (c) Copyright 1999 by Douglas H. Joines 2
14000 12000 10000 8000 6000 4000 U.S. GDP and Capital Stock Capital 2000 GDP 00 10 20 30 40 50 60 70 80 90 ear Billions of 1987 dollars (log scale) 5000 4000 3000 2000 U.S. GDP and Labor Input 0.25 0.20 0.15 Labor GDP 1000 GDP 0.10 Labor 0.05 00 10 20 30 40 50 60 70 80 90 ear GDP: Billions of 1987 dollars per year (log scale) Labor: Trillions of hours per year (log scale) Cobb-Douglas Production Function t = A t t α L t 1-α A is called total factor productivity (TFP) How can we measure A? A t = t /( t α L t 1-α ) (c) Copyright 1999 by Douglas H. Joines 3
Growth Accounting d ln = d ln A + αd ln + ( 1 α) d ln L GDP Capital Labor TFP 1992 4919.9 12020.3.24391 570.34 1896 264.4 851.7.06093 185.96 Ratio (1992/1896) 18.61 14.11 4.00 3.07 d ln (1992 1896) 2.924 2.647 1.387 1.121 Growth share 1.000.299.318.383 Labor Productivity /L = A(/L) α What causes variations in labor productivity? * Variations in A * Variations in /L U.S. Labor Productivity and Total Factor Productivity 600 /L 25000 20000 15000 10000 A 500 400 A 300 /L 200 5000 00 10 20 30 40 50 60 70 80 90 ear (c) Copyright 1999 by Douglas H. Joines 4
Level vs. Growth Rate ln ln time Increase in Level time Increase in Growth Rate Malthusian Model Add more L to fixed and land f ( L ) L Adjustment to Equilibrium /L population adjusts to equilibrium level no long-run growth _ y Subsistence Output f(l)/l L 0 L (c) Copyright 1999 by Douglas H. Joines 5
Predictions of Malthusian Model The model s predictions are generally contradicted by evidence Time series: per capita output Cross section: per capita output vs. population density Time series: fertility rates Neoclassical (Solow) Model Emphasizes reproducible capital and technical progress Population grows at rate n TFP increases at a constant rate γ (for now, assume n = γ = 0) Closed economy, no government Production Function f ( ) (c) Copyright 1999 by Douglas H. Joines 6
Depreciation Capital depreciates at a constant rate. δ Definition of Equilibrium Long-run equilibrium is called a steady state Capital remains constant over time This requires that investment equal depreciation C = I Output, Consumption, and Investment I = δ = f ( ) (c) Copyright 1999 by Douglas H. Joines 7
Result 1 Capital accumulation alone cannot sustain growth Maximum Consumption (Golden Rule) δ f ( ) * Aggregate Saving Assume consumption is given by C = β Thus, saving is In equilibrium, S = (1 β) S = I (c) Copyright 1999 by Douglas H. Joines 8
Steady-State Equilibrium δ (1-β) 0 Result 2 - Convergence Countries with the same technology and saving rate will converge to the same capital stock and output level Population Growth y (δ+n)k f ( k ) (1-β)y k 0 k (c) Copyright 1999 by Douglas H. Joines 9
Result 3 Other things equal, higher population growth: raises the growth rate of aggregate output has no effect on the growth rate of per capita output results in a lower level of per capita output Technical Improvement Raises the Steady-State Capital Stock f 1 ( ) δ (1-β)f 1() f ( ) 0 (1-β)f 0() 0 1 Result 4 A higher rate of technical improvement results in: a higher rate of growth of the capital stock a higher rate of growth of aggregate output a higher rate of growth of per capita output (c) Copyright 1999 by Douglas H. Joines 10
Productivity Slowdown AVERAGE ANNUAL GROWTH RATES GDP Capital Labor TFP 1896-1923 3.59 3.14 2.09 1.15 1923-53 2.95 2.07 0.87 1.68 1953-73 3.31 3.67 1.23 1.29 1973-90 2.35 2.45 1.90 0.27 1896-1990 3.10 2.79 1.49 1.19 Tax on Income from Capital Forms of tax on income from capital Personal income tax capital gains tax Corporate profits tax Property tax In general, taxation exerts substitution effects that reduce the amount of the taxed activity Taxation, Saving, and Investment r S r Revenue r(1 τ k ) I I 1 I 0 S, I (c) Copyright 1999 by Douglas H. Joines 11
Taxation and Growth A capital income tax reduces saving and investment A lower saving rate implies a smaller steady-state capital stock and lower income If taxation reduces the rate of technical progress, then the long-run growth rate is also reduced (c) Copyright 1999 by Douglas H. Joines 12