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) xY = F(xK,xAN) Y/AN = f(K/AN)

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

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

Technological Progress and Growth Determining the needed to maintain a given 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%

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

Technological Progress and Growth Determining the needed to maintain a given For Example: If: , then investment = 10% of K to maintain K 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

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

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

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

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

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

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

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)

Technological Progress and Growth Capital Accumulation vs. Technological Progress Average is a simple average of the growth rates in each column. Germany refers to West Germany only. 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

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

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

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

Technological Progress and Growth Why has technological progress slowed since the mid 1970s? Decreased R&D Spending: The Evidence 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.” Spending on R&D as a Percentage of GDP

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