EXTENSION OF THE SOLOW MODEL

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1 Macroeconomics II Class 2 EXTENSION OF THE SOLOW MODEL A Road Map EXTENSION OF THE SOLOW MODEL the Solow Growth Model 1.1 Convergence 1.2 Technological Progress Human Capital 1

2 Motivation Decomposition of average annual growth rate in output, DK FR DE NL ES SE UK Average annual growth in output (%) Of which: (p.p.) contribution of y 1,8 2,2 1,8 2,5 3,7 3,2 2,8 1,1 1,7 1,8 1,4 0,1 2,3 2,2 Of which (p.p.) contribution of: k 0,2 0,8 0,6 0,4 0,4 0,3 0,7 TFP 0,6 0,6 1,1 0,8 0,7 1,6 1,1 skills accumulation 0,3 0,3 0,1 0,2 0,3 0,4 0,4 1.1 Convergence 1/7 Absolute convergence: Consider a group of countries, all of which have access to the same technology, the same population growth rate and the same savings propensity, and only differ in terms of their initial capital-labor ratio. Then, we should expect all countries to converge to the same steady-state output per capita and the same growth rate. 2

3 1.1 Convergence 2/7 Income Growth (average) Across the OECD Countries Convergence 3/7 Absolute divergence across the world economy (113 countries) in period 3

4 1.1 Convergence 4/7 Absence of absolute convergence across 89 developing countries in period 1.1 Convergence 5/7 Convergence in emerging Europe and in the rest of the world,

5 1.1 Convergence 6/7 Growth trends in developing and developed countries (Rodrik 2011) 1.1 Convergence 7/7 Developing country growth trend by region (Rodrik 2011) 5

6 1.2 Technological Progress 1/4 The Solow growth model suggests that poor countries are poor because they have not sacrificed and saved as much as rich countries. However, there are many examples of countries around the world that have stagnated while investing heavily in physical capital. For example, the Soviet Union invested a tremendous amount in physical capital. When the Soviet Union broke apart, most of the countries comprising the union had income levels comparable to those of developing countries 1.2 Technological Progress 2/4 Productivity ratios to U.S. Values (for 1988) Country Y/L K/Y A U.S France Japan China Greece U.S.S.R Hungary Poland

1.2 Technological Progress 3/4 Productivity is the key factor that explains income differentials Technology is a residual in the Solow growth model.

7 1.2 Technological Progress 3/4 Productivity is the key factor that explains income differentials Technology is a residual in the Solow growth model. TFP measures the contribution of technological progress to growth after measurable factors are accounted for. Estimates of the growth accounting formula suggest that technological progress accounts for a large portion of growth, but technology is not explained in the Solow growth model, leaving a large portion of growth unexplained. 1.2 Technological Progress 4/4 Example: Growth accounting in emerging Europe (averages) 7

8 Human Capital 1/8 Capital can also have a non-material dimension knowledge, experience, skills. Since all these elements are implanted in labor, they are collected under the term human capital. If we make an adjustment for the quality of labor, the Solow growth model s predictions change. Capital per quality-adjusted worker may be smaller in the developed country and it would be growing more quickly. Human Capital 2/8 With large differences in the quality of labor, using total employment to represent the labor force in the Solow growth model might not meaningfully capture differences in the labor input. Output is then produced according to Where K = stock of physical capital H = amount of human capital-augmented labor A = labor-augmenting measure of productivity Y F K, AH 8

9 Human Capital 3/8 Level of education is a commonly used measure of human capital Each unit of labor N has been trained with E years of schooling (education). Human capital-augmented labor is given by: H E N where reflects the efficiency of a unit of labor with E years of schooling relative to one with no schooling Human Capital 4/8 Suppose that the rate of growth of human capital is equal to (n+) where The inclusion of human capital does not change the basic philosophy of the Solow growth model. To keep capital per human-capital-augmented efficiency unit constant investment must not only replace capital lost due to depreciation. But also accommodate population, efficiency and human capital growth. E E 9

10 Human Capital 5/8 Steady-state and transition paths in the modified Solow growth model Output per human-capital augmented effective worker, Y/AH Y AH (K/AH) 0 Required investment (d+n++g)(k/ah) (K/AH) * Production f(k/ah) Investment sf(k/ah) Capital per human-capital augmented effective worker, K/AH Human Capital 6/8 Suppose that the rate of growth of human capital rises from (n+ 1 ) to (n+ 2 ). The required investment line becomes steeper The new steady state features less capital and lower output per human-capital augmented efficiency units of labor However, there is more capital and higher output per worker yˆ Y AH A Y E N Y N ya ˆ E 10

Human Capital 7/8 The average annual rate of GDP per capita growth over 1960-2000 period against

Human Capital 8/8 Quality of education matters.

11 Human Capital 7/8 The average annual rate of GDP per capita growth over period against years of schooling at the beginning of the period for a sample of 92 countries. Human Capital 8/8 Quality of education matters... The effect on the growth in real GDP per capita in of test-score (after controlling for the initial level of GDP per capita and for years of schooling). 11

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

Economic Growth. (c) Copyright 1999 by Douglas H. Joines 1 Economic Growth (c) Copyright 1999 by Douglas H. Joines 1 Module Objectives Know what determines the growth rates of aggregate and per capita GDP Distinguish factors that affect the economy s growth rate