Evaluating the Solow Growth Model

Transcription

1 Evaluating the Solow Growth Model Brian C. Jenkins University of California, Irvine May 11, 2016 Brian C. Jenkins University of California, Irvine Solow 1/ 30

2 Figure 1: Transition paths: One-time permanent increase in total factor productivity A. Parameter values: α = 0.3, s = 0.15, δ = 0.06, g = 0.02, n = 0.01, and A rises from A = 1 to A = 1.25 Brian C. Jenkins University of California, Irvine Solow 2/ 30

3 Figure 2: Transition paths: One-time permanent decrease in the rate of population growth n. Parameter values: α = 0.3, s = 0.15, δ = 0.06, g = 0.02, A = 1, and n falls from n = to n = 0.01 Brian C. Jenkins University of California, Irvine Solow 3/ 30

4 Figure 3: Transition paths: One-time permanent increase in the saving rate s. Parameter values: α = 0.3, δ = 0.06, n = 0.01, g = 0.02, A = 1, and s rises from s = 0.15 to s = 0.25 Brian C. Jenkins University of California, Irvine Solow 4/ 30

5 Figure 4: Transition paths: One-time permanent increase in labor efficiency growth rate g. Parameter values: α = 0.3, δ = 0.06, n = 0.01, A = 1, s = 0.15, and g rises from g = 0.02 to g = 0.03 Brian C. Jenkins University of California, Irvine Solow 5/ 30

6 Figure 5: Theoretical growth rates implied by the Solow growth model. G( k t ) denotes the growth rate of k t. 1 Growth Rate Variable Transition to S.S. Steady State k t sa k α 1 t 1 (g + n + δ) 0 ỹ t, ỹ t, ĩ t α G( k t ) 0 k t g + G( k t ) g y t, c t, i t g + α G( k t ) g K t g + n + G( k t ) g + n Y t, C t, I t g + n + α G( k t ) g + n 1 That is, G( k t) = sa k α 1 t 1 (g + n + δ) while the economy is in transition to the steady state. Brian C. Jenkins University of California, Irvine Solow 6/ 30

7 Evaluating the Solow Model The Solow model is often evaluated based on its ability to explain: 1 The six stylized facts about economic growth in the US and UK proposed by Kaldor in Why we observe conditional convergence but not unconditional convergence. Brian C. Jenkins University of California, Irvine Solow 7/ 30

8 Kaldor (1960) Growth Facts 1 Labor productivity has grown at a sustained rate. 2 Capital per worker has also grown at a sustained rate. 3 The real interest rate, or return on capital, has been stable. 4 The ratio of capital to output has also been stable. 5 Capital and labor have captured stable shares of national income. 6 Among the fast growing countries of the world, there is an appreciable variation in the rate of growth of the order of 2-5 percent. Brian C. Jenkins University of California, Irvine Solow 8/ 30

9 Figure 6: Labor productivity Y /L has grown at a sustained rate. Real GDP per worker for the US from 1948 to 2014 in units of 2009 dollars per labor hour. Source: FRED. Brian C. Jenkins University of California, Irvine Solow 9/ 30

10 Kaldor (1960) Growth Facts Labor productivity has grown at a sustained rate. Labor productivity is measured by output per worker Y /L. According to the Solow model, in the steady state Y grows at rate n + g, while L grows at rate n so: G(Y /L) = G(Y ) G(L) (1) = n + g n (2) = g (3) So the Solow model offers an explanation for Kaldor s first fact. Brian C. Jenkins University of California, Irvine Solow 10/ 30

11 Figure 7: Capital per worker K/L has grown at a sustained rate. Physical capital per worker for the US from 1948 to 2014 in units of 2009 dollars per labor hour. Source: FRED. Brian C. Jenkins University of California, Irvine Solow 11/ 30

12 Kaldor (1960) Growth Facts Capital per worker has also grown at a sustained rate. According to the Solow model, in the steady state K grows at rate n + g, while L grows at rate n so: G(K/L) = G(K) G(L) (4) = g (5) So the Solow model offers an explanation for Kaldor s second fact. Brian C. Jenkins University of California, Irvine Solow 12/ 30

13 Figure 8: The rate of return on capital MPK δ has been stable. The average real rate of return on capital for the US from 1948 to Source: FRED. Brian C. Jenkins University of California, Irvine Solow 13/ 30

14 Kaldor (1960) Growth Facts The real interest rate, or return on capital, has been stable. The real return on capital is the marginal product of capital minus the depreciation rate: r = MPK δ (6) Since MPK = αy /K and Y and K grow at rate n + g, G(r + δ) = G(αY /K) (7) = [G(Y ) G(K)] (8) = 0 (9) So the Solow model implies that the real return to capital is approximately constant over time. Brian C. Jenkins University of California, Irvine Solow 14/ 30

15 Figure 9: The ratio of capital to output K/Y has been stable. The average ratio of capital to GDP for the US from 1948 to Source: FRED. Brian C. Jenkins University of California, Irvine Solow 15/ 30

16 Kaldor (1960) Growth Facts The ratio of capital to output has also been stable. Since Y and K grow at rate n + g, G(K/Y ) = G(K) G(Y ) (10) = n + g (n + g) (11) = 0 (12) The Solow model predicts a constant long-run ratio of capital to output. Brian C. Jenkins University of California, Irvine Solow 16/ 30

17 Figure 10: Factor shares of income are stable. The shares of US GDP paid to labor (bottom) and capital (top). Source: FRED. Brian C. Jenkins University of California, Irvine Solow 17/ 30

18 Kaldor (1960) Growth Facts Capital and labor have captured stable shares of national income. The capital share of income is: (R/P) K Y = α(y /K) K Y (13) = α (14) The labor share of income is: (W /P) L Y = (1 α)(y /L) L Y (15) = 1 α (16) The Solow model predicts constant income shares going to capital and labor. Brian C. Jenkins University of California, Irvine Solow 18/ 30

19 Kaldor (1960) Growth Facts Among the fast growing countries of the world, there is an appreciable variation in the rate of growth of the order of 2-5 percent. The Solow model predicts that Y /L grows at a rate of g. But the Solow model does not make clear from where g originates because it is given exogenously. If g reflects the growth of human capital and the influence of political institutions on growth, then it might reasonably differ across countries. But g is also determined by the growth of new technology and it is not clear why that would differ across countries. Brian C. Jenkins University of California, Irvine Solow 19/ 30

20 Kaldor (1960) Growth Facts In summary, the Solow model provides an excellent explanation for the first five of the Kaldor growth facts. The Solow model does not explain what is the source of long-run growth and it does not explain the variation in long-run growth rates across countries. Endogenous growth theory seeks to fill this gap by providing an explanation for the growth of labor efficiency. Brian C. Jenkins University of California, Irvine Solow 20/ 30

21 Convergence Unconditional convergence: countries will converge toward one another regardless of country-specific characteristics like population growth or saving rates. Conditional convergence: countries with similar characteristics will converge toward one another. Brian C. Jenkins University of California, Irvine Solow 21/ 30

22 Convergence Recall that in the steady state, the Solow model implies: Y t = E t ỹ (17) L t ( ) α = E 0 (1 + g) t sa 1 α A (18) δ + n + g Therefore, according to the model two countries will have tend towards the same quantity of output per worker as long as E 0, g, A, δ, n, s, and α are equal for both countries. Brian C. Jenkins University of California, Irvine Solow 22/ 30

23 Figure 11: Conditional Convergence. Three simulations with α = 0.3, A = 1, δ = 0.06, n = 0.01, g = 0.02, s = 0.15, s = 0.15, E 0 = 1 and L 0 = 1, but with different values for ildek 0. Brian C. Jenkins University of California, Irvine Solow 23/ 30

24 Figure 12: Conditional Convergence. Three simulations with α = 0.3, A = 1, δ = 0.06, n = 0.01, g = 0.02, s = 0.15, k 0 = 1.25, E 0 = 1 and L 0 = 1, but with different values for s. Brian C. Jenkins University of California, Irvine Solow 24/ 30

25 Convergence There is no empirical evidence for unconditional convergence. There is empirical evidence for conditional convergence. Brian C. Jenkins University of California, Irvine Solow 25/ 30

26 Figure 13: Average rate of GDP per capita growth from 1960 to 2011 against real GDP per capita in No evidence for unconditional convergence in income per capita. Source: Penn World Tables 8.1. Brian C. Jenkins University of California, Irvine Solow 26/ 30

27 Figure 14: Average rate of GDP per capita growth from 1960 to 2011 against real GDP per capita in 1960 for OECD countries. Evidence for conditional convergence in income per capita. Source: Penn World Tables 8.1. Brian C. Jenkins University of California, Irvine Solow 27/ 30

28 Figure 15: US state per capita income relative to national per capita income from 1929 to Variation across states declines. Incl. Washington, D.C. and excl. AK and HI. Source: Bureau of Economic Analysis. Brian C. Jenkins University of California, Irvine Solow 28/ 30

29 Figure 16: US state per capita income: level in 1929 versus average growth from 1929 to Lower-income states stend to grow more quickly. Incl. Washington, D.C. and excl. AK and HI. Source: Bureau of Economic Analysis. Brian C. Jenkins University of California, Irvine Solow 29/ 30

30 Causes of Economic Growth Daron Acemoglu (2009) 1 proposes four possible causes of economic growth: 1 Luck 2 Geographical differences 3 Institutional differences 4 Cultural differences And he concludes that institutional differences is the only compelling explanation on the list. 1 Introduction to Modern Economic Growth. Princeton University Press. Brian C. Jenkins University of California, Irvine Solow 30/ 30