# Economic Growth. (c) Copyright 1999 by Douglas H. Joines 1

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1 Economic Growth (c) Copyright 1999 by Douglas H. Joines 1

2 Module Objectives Know 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 (c) Copyright 1999 by Douglas H. Joines 2

3 If South Korea 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 Focus on growth rates of: aggregate output (the best indicator of the size of a market) per capita output per capita consumption real wages (the last three are indicators of the standard of living) (c) Copyright 1999 by Douglas H. Joines 3

4 U.S. Real GDP U.S. Real GDP (billions of 1987 dollars) Log of U.S. Real GDP Year Year Time-series data are most commonly displayed on a line graph, also known as a time-series plot. What are the time-series characteristics of U.S. real GDP? (c) Copyright 1999 by Douglas H. Joines 4

5 International GDP Comparison USA GDP, Japan China India W.Ger. Brazil Mexico Belg. Zimb Billions of 1985 U.S. dollars GDP is the single factor that most influences the size of a market. Why is there so much variation in GDP across countries? If we can t explain these large variations, we can t hope to explain the much smaller variations due to business cycles. (c) Copyright 1999 by Douglas H. Joines 5

6 Production Function Y = f(k, L, F Technology) K L F Production Process Y The box represents production technology. K = capital, L = labor, F = fixed factors (e.g., land). F can vary across countries. K and L can vary across countries and over time within a country. (c) Copyright 1999 by Douglas H. Joines 6

7 U.S. GDP and Capital Stock Capital 2000 GDP Year Billions of 1987 dollars (log scale) (c) Copyright 1999 by Douglas H. Joines 7

8 U.S. GDP and Labor Input Labor GDP 1000 GDP 0.10 Labor Year GDP: Billions of 1987 dollars per year (log scale) Labor: Trillions of hours per year (log scale) Making quantitative statements about the importance of capital and labor inputs requires a specific form for the production function. (c) Copyright 1999 by Douglas H. Joines 8

9 Cobb-Douglas Production Function Y t = A t K t α L t 1-α A is called total factor productivity (TFP) How can we measure A? A t = Y t /(K t α L t 1-α ) The time subscript indicates variables that can change over time. Technology (TFP) can vary over time. (c) Copyright 1999 by Douglas H. Joines 9

10 Growth Accounting d ln Y = d ln A + αd ln K + ( 1 α) d ln L GDP Capital Labor TFP Ratio (1992/1896) d ln ( ) Growth share How much of U.S. real GDP growth is attributable to K, L, and A? d ln denotes change in natural log of a variable between 1896 and 1992 The figures in this slide are calculated using α = 0.33 and 1 α = 0.67 rather than the values of 0.3 and 0.7 used in class. The table indicates that ln(gdp) = From the formula, we have ln(gdp) = ln(tfp) + α ln(k) + (1 α) ln(l), or = * *1.387 = Dividing through by gives the fraction of the total increase in output attributable to each of the three causes 1.0 (i.e., 100%) = (c) Copyright 1999 by Douglas H. Joines 10

11 Labor Productivity Y/L = A(K/L) α What causes variations in labor productivity? * Variations in A * Variations in K/L How does output per worker (or per worker hour) in the U.S. compare with that in other countries? What accounts for these differences? What can lead to international differences in A? (c) Copyright 1999 by Douglas H. Joines 11

12 U.S. Labor Productivity and Total Factor Productivity Y/L A 300 A Y/L Year (c) Copyright 1999 by Douglas H. Joines 12

13 Level vs. Growth Rate ln Y ln Y time Increase in Level time Increase in Growth Rate Distinguish increase in slope of growth path from parallel upward shift in growth path. Faster growing variable will eventually become larger, no matter what the initial levels. Implies that, within an economy, nothing can grow faster than GDP forever. Can economies grow forever at different rates? How long does it take for the level of a variable to double? Rule of 72: no. of periods = 72/g Example: 12% annual growth 6 periods to double 2% annual growth 36 periods to double (c) Copyright 1999 by Douglas H. Joines 13

14 Y Malthusian Model Add more L to fixed K and land f ( L ) L Will L grow forever under these circumstances? -- population growth stops at subsistence level of output (c) Copyright 1999 by Douglas H. Joines 14

15 Adjustment to Equilibrium Y/L population adjusts to equilibrium level no long-run growth _ y Subsistence Output f(l)/l L 0 L Birth and death rates depend on Y/L Subsistence level of output is output at which birth rate and death rate are equal, giving stable population. -- growth rate is zero in Malthusian model, i.e., growth path is flat Subsistence output is affected by factors that affect birth and death rates. What would be the effect of programs to improve public health, e.g., immunization? would lower death rate at the old subsistence y population would increase implies lower subsistence (and thus actual) y parallel downward shift in growth path (c) Copyright 1999 by Douglas H. Joines 15

16 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 Malthusian model emphasizes fixed factors of production. Increasing Y/L over time requires increasing K and/or T fast enough to offset the increase in L, if L increases at all -- for now, hold L fixed to see how K and T affect living standards (c) Copyright 1999 by Douglas H. Joines 16

17 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 (c) Copyright 1999 by Douglas H. Joines 17

18 Y Production Function f ( K ) K Question: Can capital accumulation alone sustain growth? (c) Copyright 1999 by Douglas H. Joines 18

19 Depreciation Capital depreciates at a constant rate. Y δk K K t+1 = K t + I t - δk t (c) Copyright 1999 by Douglas H. Joines 19

20 Definition of Equilibrium Long-run equilibrium is called a steady state Capital remains constant over time This requires that investment equal depreciation C = Y I K t+1 = K t implies I t - δk t (c) Copyright 1999 by Douglas H. Joines 20

21 Y Output, Consumption, and Investment I = δk Y = f ( K ) K Implies maximum sustainable capital stock of K max -- at K max, consumption is zero (c) Copyright 1999 by Douglas H. Joines 21

22 Result 1 Capital accumulation alone cannot sustain growth (c) Copyright 1999 by Douglas H. Joines 22

23 Maximum Consumption (Golden Rule) Y δk f ( K ) K* K Implies MPK = δ, or MPK = δ What determines actual steady-state capital? (c) Copyright 1999 by Douglas H. Joines 23

24 Aggregate Saving Assume consumption is given by C = βy Thus, saving is In equilibrium, S = (1 β)y S = I (c) Copyright 1999 by Douglas H. Joines 24

25 Steady-State Equilibrium Y δk Y (1-β)Y K 0 K In equilibrium, actual saving (investment) equals investment required to replace worn-out capital. Steady-state equilibrium is stable. Growth rate is zero in this simple version of Solow model: growth path is flat aggregate quantities constant over time per capita quantities also constant real wage rate (MPL) constant net MPK constant Question: What would happen if the saving rate increased? economy would move to higher steady-state capital stock parallel upward shift in growth path long-run growth rate remains zero (c) Copyright 1999 by Douglas H. Joines 25

26 Result 2 - Convergence Countries with the same technology and saving rate will converge to the same capital stock and output level What would happen to 2 countries with fixed A and L, where A is the same in the 2 countries, but where Y/L differs across countries? why might Y/L initially differ across countries? because of differences in K/L countries converge to same K/L if they have the same saving rate Convergence occurs because of adjustment of capital stock. This takes a long time. Evidence supports convergence for developed countries. Barro evidence on speed of convergence, with applications to East Germany, China, Japan. What might generate growth? Try population growth. (c) Copyright 1999 by Douglas H. Joines 26

27 Population Growth y (δ+n)k f ( k ) (1-β)y k 0 k Suppose population grows at a constant rate n. The same model as before can be used, with 2 changes: the relevant variables are now per capita quantities y=y/l, k=k/l, etc. more investment is required to keep K/L constant must equip new workers as well as replace worn-out capital In a steady state: all per capita quantities are constant over time (flat growth path) all aggregate quantities grow at rate n (upward-sloping growth path) the real wage is constant the net marginal product of capital is constant Golden Rule now requires MPK - δ = n (c) Copyright 1999 by Douglas H. Joines 27

28 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 I.e., it changes the slope of the growth path of aggregate output, but causes only a parallel shift of the growth path of per capita output. Evidence seems to support this prediction. See the scatter plot of Y/L vs. n in Mankiw s text. We still do not have growth of per capita output. What can cause such growth? Technical progress is the only remaining explanation. (c) Copyright 1999 by Douglas H. Joines 28

29 Y Technical Improvement Raises the Steady-State Capital Stock f ( K ) 1 δk (1-β)f 1(K) f ( K ) 0 (1-β)f (K) 0 K K 1 0 K Examine a one-time improvement in technology. This raises the production function. This raises the steady-state levels of capital, income, etc. I.e., it causes a parallel upward shift in the economy s growth path. The one-time technical improvement illustrates an important point: Technical progress stimulates capital accumulation, which reinforces the beneficial effects of the technical progress. (c) Copyright 1999 by Douglas H. Joines 29

30 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 Now consider ongoing technical progress. Assume that total factor productivity grows at the rate γ. Because technical progress stimulates capital accumulation, per capita output grows at an even faster rate of g = γ/(1-α). In the steady state: all per capita quantities grow at rate g all aggregate quantities grow at rate n + g real wage grows at rate g net MPK is constant over time Golden Rule now requires MPK - δ = n + g (c) Copyright 1999 by Douglas H. Joines 30

31 Productivity Slowdown AVERAGE ANNUAL GROWTH RATES GDP Capital Labor TFP (c) Copyright 1999 by Douglas H. Joines 31

32 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 (c) Copyright 1999 by Douglas H. Joines 32

33 Taxation, Saving, and Investment r S r Revenue r(1 τ k ) I I 1 I 0 S, I The before-tax rate of return is r. The after-tax rate of return is r(1 τ k ). The higher the tax rate, the wider the gap between these two rates of return and the smaller the level of saving and investment. (c) Copyright 1999 by Douglas H. Joines 33

34 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 34

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