Technological Progress and Growth

1. xY = F(xK,xAN) • Y/AN = f(K/AN) Technological Progress and Growth Technological Progress and the Production Function AN = Effective Labor. Assuming: • Constant returns to scale • Given state of technology • 2Y = F(2K,2AN)

2. f(K/AN) Output per effective worker, Y/AN Capital per effective worker, K/AN Technological Progress and Growth Technological Progress and the Production Function

3. Production f(K/AN) Investment sf(K/AN) Technological Progress and Growth Investment, Capital, & Output per Effective Worker Output per effective worker, Y/AN Capital per effective worker, K/AN

4. Determining the needed to maintain a given Technological Progress and Growth Assume: • A population growth rate/yr (gN) • N grows at same rate as gN • Rate of technological progress gA Then: Growth rate of effective labor (AN) = gA + gN If: gA = 2% & gN = 1%, then AN growth = 3%

5. Determining the needed to maintain a given The level of investment needed to maintain : Or: is needed to keep K constant Therefore: Technological Progress and Growth

6. Determining the needed to maintain a given If: , then investment = 10% of K to maintain K Technological Progress and Growth For Example: And: (gA + gN)K is needed to ensure K increases at the same rate as AN Required Investment to maintain K/AN = (d + gA + gN)K

7. Determining the needed to maintain a given Amount of Investment Needed/Effective Worker tomaintain a constant Technological Progress and Growth

8. Required investment ( + gA + gN)K/AN Production f(K/AN) * B Investment sf(K/AN) C Observe (K/AN)0: AC > AD D A (K/AN)o (K/AN)* Technological Progress and Growth Dynamics of Capital & Output Output per effective worker, Y/AN Capital per effective worker, K/AN

9. Technological Progress and Growth Dynamics of Capital & Output Observations about the Steady State: • Growth rate of Y = growth rate of AN • AN growth rate = (gA + gN) • Y growth rate = (gA + gN) independent of s • K growth rate = (gA + gN) • Y/N growth rate = gA

10. Growth: rate of 1. 2. 3. 4. 5. 6. 7. Capital per effective worker 0 Output per effective worker 0 Capital per worker gA Output per worker gA Labor gN Capital gA+gN Output gA+gN Technological Progress and Growth Dynamics of Capital & Output The Characteristics of Balanced Growth

11. f(K/AN) B ( + gA + gN)K/AN 0 A Savings = s0 s1f(K/AN) Output per effective worker, Y/AN s0f(K/AN) 1 0 1 Savings increase to s1 S1f(K/AN) Steady-state = & Steady-state = & (K/AN)0 (K/AN)1 1 0 Capital per effective worker, K/AN Technological Progress and Growth The Effects of the Savings Rate

12. Associated with s1 > s0 Associated with s1 > s0 B B Output, Y (log scale) Capital, K (log scale) B B A A Associated with s0 slope (gA + gN) slope (gN + gA) Associated with s0 A A t t Time Time Technological Progress and Growth The Effects of an Increase in the Savings Rate

13. Technological Progress and Growth The Facts of Growth Revisited A Review • Observations on growth in developed countries since 1950: • Sustained growth 1950-mid 1970s • Slowdown in growth since the mid 1970s • Convergence: countries that were further behind have been growing faster

14. Technological Progress and Growth The Facts of Growth Revisited Understanding These Trends Capital Accumulation vs. Technological Progress • Determinants of Fast Growth: • Higher rate of technological progress (gA) • Higher level of capital/effective worker (K/AN)

15. Growth of Output per Capita Rate of Technological Progress 1950-73 1973-87 Change 1950-73 1973-87 Change (1) (2) (3) (4) (5) (6) France 4.0 1.8 -2.2 4.9 2.3 -2.6 Germany 4.9 2.1 -2.8 5.6 1.9 -3.7 Japan 8.0 3.1 -4.9 6.4 1.7 -4.7 United Kingdom 2.5 1.8 -0.7 2.3 1.7 -0.6 United States 2.2 1.6 -0.6 2.6 0.6 -2.0 Average 4.3 2.1 -2.2 4.4 1.6 -2.8 Average is a simple average of the growth rates in each column. Germany refers to West Germany only. Technological Progress and Growth Capital Accumulation vs. Technological Progress

16. Technological Progress and Growth Capital Accumulation vs. Technological Progress The Findings • 1950-1973 high growth of output per capita due to technological progress • Since 1973 slowdown in growth of output per capita due to a decrease in the rate of technological progress • Convergence is the result of technological progress

17. Technological Progress and Growth Why has technological progress slowed since themid 1970s? Measurement Error • Measuring productivity • Quality changes and inflation What do you think… Has the measurement error increased?

18. Technological Progress and Growth Why has technological progress slowed since themid 1970s? The Rise of the Service Sector • Limited technological progress in the service sector The Evidence

19. Spending on R&D as a Percentage of GDP 1963 1975 1989 France 1.6 1.8 2.3 Germany 1.4 2.2 2.9 Japan 1.5 2.0 3.0 United Kingdom 2.3 2.0 2.3 United States 2.7 2.3 2.8 Source: Kumiharu Shigehara, “Causes of Declining Growth in Industrialized Countries.” Technological Progress and Growth Why has technological progress slowed since themid 1970s? Decreased R&D Spending: The Evidence

20. Technological Progress and Growth Why has technological progress slowed since themid 1970s? The Findings: The proximate reason for the decline in the rate oftechnological progress is a decline in fertility ofR&D What do you think… Why has the fertility of R&D declined?