Economics 302 Growth 2 Getting a Sense of Magnitudes Some Questions: 1.How large is the effect of a change in the saving rate on output in the long run? 2.For how long and by how much does an increase in the saving rate affect growth? 3.How far is the U.S. from the Golden Rule of Level of Capital?

Economics 302 Growth 2 Calculating the Answers Assume: (Constant return to scale and decreasing returns to either capital or labor) Getting a Sense of Magnitudes

Economics 302 Growth 2 Replace with Recall: Getting a Sense of Magnitudes

Economics 302 Growth 2 The Effects of the Saving Rate on Steady-State Output In steady-state is constant and the left side = 0 and: Getting a Sense of Magnitudes

Economics 302 Growth 2 Implications of Alternative Saving Rates The Effects of the Saving Rate on Steady-State Output : square both sides : Divide by and reorganize

Economics 302 Growth 2 The Effects of the Saving Rate on Steady-State Output Steady-State Output/Worker: Observation Higher saving rate and lower depreciation both lead to higher and in the long run. Getting a Sense of Magnitudes

Economics 302 Growth 2 The Effects of the Saving Rate on Steady-State Output Assume: Getting a Sense of Magnitudes

Economics 302 Growth 2 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule What saving rate that would maximize steady-state consumption? In Steady-State:

Economics 302 Growth 2 Getting a Sense of Magnitudes The Saving Rate and the Steady-State Levels of Capital, Output, and Consumption per Worker CapitalOutputConsumption Saving Rate,per Worker,per Worker,per Worker, sK/NY/NC/N

Economics 302 Growth 2 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule Observation If s <.50: increasing s will increase long-run consumption In the U.S., s < 20%

Economics 302 Growth 2 Physical Versus Human Capital Human Capital: The set of skills of the workers in the economy.

Economics 302 Growth 2 Physical Versus Human Capital Observations OECD Countries: 100% of children get a primary education 90% of children get a secondary education 38% of children get a higher education Literacy rate above 95%

Economics 302 Growth 2 Physical Versus Human Capital Extending the Production Function Measuring the Impact of Human Capital:

Economics 302 Growth 2 Physical Versus Human Capital Human Capital, Physical Capital, and Output How does including human capital impact our analysis? Investment now includes physical and human capital In the U.S.: Education spending =6.5% of GDP Investment =16.0% of GDP

Economics 302 Growth 2 Physical Versus Human Capital Human Capital, Physical Capital, and Output Some Complications: Education is partly consumption Education cost should include the opportunity cost On-the-job training is not included Should compare investment rates net of depreciation

Economics 302 Growth 2 Technological Progress and Growth Larger output from given quantities of capital and labor Better products New products A larger variety of products Technological Progress and the Production Function The Dimensions of Technological Progress

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function Technology Defined: How much output can be produced from capital and labor at any time.

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function The production function with technology (A) Given K & N an improvement in technology (A) leads to an increase in output (Y).

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function Interpreting Given K: Technological progress reduces the number of workers needed to achieve a given amount of output (Y) Given K: Technological progress increases AN, the amount of effective labor

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function Assuming: Constant returns to scale Given state of technology 2Y = F(2K,2AN) Or: xY = F(xK,xAN)

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function Assume: Decreasing Return to K & AN x=1/AN Output/Effective Worker Capital/Effective Worker  

Economics 302 Growth 2 Technological Progress and Growth Technological Progress and the Production Function Output/Effective Worker,, increases if and only if Capital/Effective/Worker, , increases

Economics 302 Growth 2 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

Economics 302 Growth 2 Technological Progress and Growth Interactions between Output and Capital Capital/Worker & Output/Worker increase when: Recall: Investment/Worker > Depreciation/Worker

Economics 302 Growth 2 Technological Progress and Growth Interactions between Output and Capital Focusing on: Output, Capital, and Investment per Effective Worker Assuming: I = S = sY Divide both sides by AN: Substituting  

Economics 302 Growth 2 Investment sf(K/AN) Technological Progress and Growth Investment, Capital, & Output per Effective Worker Production f(K/AN) Output per effective worker, Y/AN Capital per effective worker, K/AN

Economics 302 Growth 2 Technological Progress and Growth Determining the needed to maintain a given Assume: Then: A population growth rate/yr (g N ) N grows at same rate as g N Rate of technological progress g A Growth rate of effective labor (AN) = g A + g N If: g A = 2% & g N = 1%, then AN growth = 3%

Economics 302 Growth 2 Technological Progress and Growth Determining the needed to maintain a given The level of investment needed to maintain :

Economics 302 Growth 2 Technological Progress and Growth Determining the needed to maintain a given For Example: And: (g A + g N )K is needed to ensure K increases at the same rate as AN If:, then investment = 10% of K to maintain K

Economics 302 Growth 2 Technological Progress and Growth Determining the needed to maintain a given Required investment = An Example: Assume: Then: Growth of AN = 3% Required investment = 13%

Economics 302 Growth 2 Technological Progress and Growth Determining the needed to maintain a given Amount of Investment Needed/Effective Worker to maintain a constant

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output Investment sf(K/AN) Production f(K/AN) Required investment ( + g A + g N )K/AN Output per effective worker, Y/AN Capital per effective worker, K/AN A B (K/AN) o C D Observe (K/AN) 0 : AC > AD (K/AN)* *

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output The Steady State: are constant & equal to (K/AN)* & (Y/AN)*respectively InvestmentRequired Investment

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output Observations about the Steady State: Growth rate of Y = growth rate of AN AN growth rate = (g A + g N ) Y growth rate = (g A + g N ) K growth rate = (g A + g N )

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output The Steady State: If the growth rate of Y = (g A +g N ) Then the growth rate is independent of the savings rate

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output Determining the Output/Worker In steady-state output/worker grows at the rate of technological progress Conclusion: Y growth rate = (g A + g N ) Growth rate of workers = g N Y per worker growth rate = g A

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output The Characteristics of Balanced Growth Growth: rate of Capital per effective worker0 Output per effective worker0 Capital per workerg A Output per workerg A Laborg N Capitalg A +g N Output g A +g N

Economics 302 Growth 2 Technological Progress and Growth Dynamics of Capital & Output The Balanced Growth Path are constant growth rate = g A Labor growth rate = g N K & Y growth rate = (g A + g N )

Economics 302 Growth 2 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 0 ( + g A + g N )K/AN s 0 f(K/AN) Savings = s 0 Steady-state = & 0 0 s 1 f(K/AN) (K/AN) 1 B Savings increase to s 1 S 1 f(K/AN) Steady-state = & 1 1 1

Economics 302 Growth 2 Technological Progress and Growth The Effects of an Increase in the Savings Rate Output, Y (log scale) Time t Associated with s 0 Associated with s 1 > s 0 B slope (g A + g N ) B A A Capital, K (log scale) Time t Associated with s 0 Associated with s 1 > s 0 B slope (g N + g A ) B A A

Economics 302 Growth 2 Technological Progress and Growth The Determination of Technological Progress Research and Development (R&D) U.S., France, Germany, Japan, & U.K % of GDP 75% of U.S. researchers & scientists employed by firms U.S. firms spend 20% of gross investment and 60% of net investment on R&D R&D spending depends on the fertility of research and the appropriability of research results

Economics 302 Growth 2 Technological Progress and Growth The Fertility of the Research Progress Fertility: How R&D translates into new ideas and products Determinants of Fertility of Research: The interaction between basic and applied research The culture of basic research versus the culture of entrepreneurship The time lag of implementation of R&D

Economics 302 Growth 2 Technological Progress and Growth The Appropriability of Research Results Appropriability: The extent to which firms benefit from their R&D Determinants of Appropriability The nature of the research process The degree of legal protection from competition (patents)

Economics 302 Growth 2 Technological Progress and Growth The Facts of Growth Revisited Understanding These Trends Determinants of Fast Growth: Higher rate of technological progress (g A ) Higher level of capital/effective worker (K/AN) Capital Accumulation vs. Technological Progress

Economics 302 Growth 2 Technological Progress and Growth The Facts of Growth Revisited Understanding These Trends Identifying the Cause of Fast Growth: If g A is increasing: Output/Worker will grow at the same rate as technological progress If K/AN is increasing: growth of Output/Worker is greater than the rate of technological progress Capital Accumulation vs. Technological Progress

Economics 302 Growth 2 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 Change Change (1)(2)(3)(4)(5)(6) France Germany Japan United Kingdom United States Average

Economics 302 Growth 2 Technological Progress and Growth The Findings 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 Capital Accumulation vs. Technological Progress

Economics 302 Growth 2 Technological Progress and Growth The Rise of the Service Sector Limited technological progress in the service sector Why has technological progress slowed since the mid 1970s? The Evidence

Economics 302 Growth 2 Technological Progress and Growth Why has technological progress slowed since the mid 1970s? Decreased R&D Spending: The Evidence France Germany Japan United Kingdom United States Source: Kumiharu Shigehara, “Causes of Declining Growth in Industrialized Countries.” Spending on R&D as a Percentage of GDP

Economics 302 Growth 2 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

Economics 302 Growth 2 Technological Progress and Growth The Secrets of Growth: Some Unanswered Questions How do we increase growth? Are governments spending the right amount on basic research? Should patent laws be modified? Is there a case for an industrial policy? How does education impact growth?

Economics 302 Growth 2 Technological Progress and Growth The Secrets of Growth: Comparing Rich (USA) to Poor (China) Countries USA: Y/N is 16 times greater than China If the difference is explained by differences in human and physical capital per worker--adjusting the difference should yield the same value of A - technology would be equal in both countries Existing estimates imply A is 10 times higher in the U.S.

Economics 302 Growth 2 Technological Progress and Growth The Secrets of Growth Comparing Rich (USA) to Poor (China) Countries If physical and human capital in China was equal to the U.S., Y/N in China would still be a fraction of the U.S. Conclusion:

Economics 302 Growth 2 Technological Progress and Growth Epilogue: The Secrets of Growth Barriers to Closing the Technology Gap Property rights Political instability Entrepreneurship Financial markets

Economics 302 Growth 2 Case Study: East Asian Tigers From 1966 to 1990 real income per person grew at 2% in US; grew more than 7% per year in East Asian Tigers Real income per person increased 5- fold in a course of a generation

Economics 302 Growth 2 East Asian Tigers – A Puzzle Some suggested that this evidence is hard to reconcile with basic Solow model where technological progress grows at a constant exogenous rate Hypothesis: Rapid growth is due to fast imitation of foreign technologies. In the data should see it in unusually high growth in TFP

Economics 302 Growth 2 East Asian Tigers

Economics 302 Growth 2 East Asian Tigers – Education

Economics 302 Growth 2 East Asian Tigers – TFP

Economics 302 Growth 2 Other Countries – TFP

Economics 302 Growth 2 East Asian Tigers - Conclusion Growth is due to large increases in measured factor inputs  Labor force participation  Capital stock  Educational attainment E.g. in South Korea Investment/GDP rose from 5% in 1950 to 30% in 1980; high school degree from 26% in 1966 to 75% in 1991

Economics 302 Growth 2 East Asian Tigers - Conclusion Having accounted for growth in N, K and H, little growth is left to explain. No rapid growth in TFP!!! Consistent with Solow Model and less impressive…