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Endogenous Growth. Endogenous Growth. Beginning with the 1970’s, US and other developed economies went through a 20 year period of relatively low productivity growth. Economists began looking for models which could explain productivity growth as function of fundamentals. AK Models.

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Endogenous Growth

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Endogenous Growth

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Endogenous Growth

  • Beginning with the 1970’s, US and other developed economies went through a 20 year period of relatively low productivity growth.

  • Economists began looking for models which could explain productivity growth as function of fundamentals.

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AK Models

  • A simple way to develop endogenous growth is to assume that capital intensity equals 1 and technology is constant. (i.e. α=1)

  • Assume constant savings rate, then growth rate of capital is equal to the growth rate of output

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Growth in AK Models

  • Q: Why do we have constant growth as a function of investment levels, when that is not the case in the neo-classical model?

  • A: Marginal productivity of capital, A, is constant. Because the effect of capital on output does not diminish, capital accumulation can persistently cause output to increase.

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Endogenous Growth

  • A large body of work has explored channels to explain why labor productivity continues to grow and why productivity differs across countries.

  • Theories that explain long-term growth as an outcome of the decisions of economic agents are called endogenous growth theories.

  • Capital accumulation cannot be the source of long-term growth because capital has diminishing returns.

  • We must find an engine of growth which does not have diminishing returns.

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Two Strands: Brains vs. Ideas

  • Brains: Human capital is the source of long-term growth. Human capital can be used to produce future human capital without diminishing returns.

  • Ideas: Research and development explains long term growth. If you invent a new idea, other inventors can use your ideas to invent even newer ideas.

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Example: Human Capital Accumulation

  • Total labor input is a function of total hours worked and worker quality.

  • Assume that hours worked and technology remain constant, A = 1.

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  • Let 1-u be the fraction of human capital which is used to teach new workers.

  • Let u be the fraction of human capital used to produce goods.

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Human Capital Accumulation

  • Human capital accumulation is done with human capital.

  • If ut is converges to a steady-state level that is above zero, human capital will grow at a constant rate. {Economics of selection of u is beyond the scope of this clas.}

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  • Along the balanced growth path, if human capital grows at a constant rate, then output per hour and capital per hour will also converge to the same growth rate.

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Technological Advance

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Sources of Growth

  • Techniques for producing goods can be deliberately increased through research and development.

  • Ideas developed through R&D have a property unlike physical or human capital.

  • A rival good, if used by one user, cannot be used by others.

  • Ideas are non-rival. Once the ideas are produced they can be used by multiple producers at the same time.

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Fixed Costs of Research and Development

  • Production of Ideas: Each unit of technology requires units of labor to produce. Thereafter ideas can be used for free.

  • Accumulation of ideas is through research work.

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Technology Growth

  • Assume that a constant share of labor is devoted to goods production and R & D.

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Balanced Growth Path

  • Along the balanced growth path, labor productivity, capital-labor ratio and technology all grow at the same rate.

  • If technology is constant, the numerator must grow at the same rate at the denominator.

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People are the source of new ideas.

  • Ideas have diminishing returns. If the stock of ideas gets to be high relative to the number of researchers, the growth rate of innovation will start to slow down.

  • As the population grows, the number of researchers will grow generating growth in ideas.

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People per Idea and Growth of Technology



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Research & Development

  • Increasing the share of workers in R&D will not affect productivity growth in the long-run.

    • More researchers will generate more new ideas each period. But in % terms these extra new ideas will shrink relative to the growing technology level.

    • This will be mitigated by the knowledge spillovers generated by the new ideas. But new ideas have decreasing returns in creating new knowledge. As these new ideas accumulate, the marginal impact of extra research will diminish.

  • However, R&D shares will affect the level of technology along the BGP!

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Increase in sRD



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Increase in sRD



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Increase in sRD



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Standing on the shoulders of giants

  • Technology is non-rival in two ways.

  • It can be used freely in producing goods

  • but also makes it even easier to produce goods in the future.

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Endogenous Growth

  • In the long run, research and development has an effect of long-run growth rates only in one case: γ = 1

  • When technology spillovers have no diminishing returns, then sRD will directly impact long term growth rate.

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Scale Problem

  • Long run growth is a function of the scale of the economy.

  • As the economy increases in size (i.e. population) the number of researchers will increase.

  • The growth rate of technology should accelerate.

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  • Production of ideas is done with increasing returns to scale. Once idea is developed it can be used over and over again at zero marginal cost.

  • Average cost of production is greater than marginal cost.

  • If the good were sold under perfect competitive conditions (i.e. with price below marginal cost), any firm that invested in R&D would make loss.

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Production Function

  • Output is produced with labor and At different types of capital goods:

  • Constant returns to scale, but diminishing returns to each type of capital good.

  • Each type of capital good is rented to the production firm by its inventor.

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Rent capital

  • If the rental price of each capital good is the same, the production firms will rent the same number of each type of intermediate good.

    • Due to diminishing returns, get high marginal product from using more of an underused type of capital.

  • Aggregate capital stock is divided evenly among each good.

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Returns to Variety

  • Examine production function

  • Number of types of goods is analogous to technology level. Economy benefits by having more types of goods in which to allocate their capital – Diminishing returns.

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Investment in R & D

  • Inventors have a monopoly on producing the good of their type. They rent their capital at a rate higher than their marginal cost - earning profits.

  • Inventors invest in research up to that point that the present value of future profits equals the fixed costs of R&D investment.

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Demand for Invention

  • The producers decide how much of invention i, they want to rent in any time period.

  • Profit maximizing level of xi sets marginal product equal to the real cost. Assume that the producer rents the invention from inventor for ROYt

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Demand Curve for Inventions

  • Profit Maximization

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  • The inventor rents capital at rate R and uses the blueprint to transform it into at a 1-for-1 transformation.

  • Profits: Roy*x- R*x

  • Inventor is a monopolist. The amount of x they produce determines ROY

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Policy Issues

  • Markets fail in a number of ways

    • Inventors don’t take knowledge spillovers into account

    • Monopolists produce an inefficiently low level of the capital good.

    • Inventors will diminish the effect of previous inventions.

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Estimating Cross-country Technology Differences

  • It is easy to think of a number of factors which might cause the efficient allocation of resources to be different across countries.

  • These are sometimes estimated through multivariate regression analysis.

    Estimate TFP level:

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Examples of X

  • Variables which might affect technology growth include inflation, openness to trade, capital controls, tariffs, marginal tax rates, education levels, income distribution, political instability, weather, colonial history, type of government etc.

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Discussion of

The Myth of the Asian Miracle

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Reference Points

  • Growth Accounting

    • We can calculate the share of output growth attributed to a variety of sources

  • Neo-classical growth model

    • Capital accumulation cannot be the long-term engine of growth because it has diminishing returns.

    • Advances in technology & TFP can be a source of permanent growth.

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Analogy between East Asia and Soviet Union

  • Krugman compares East Asian Tigers with Soviet Union

  • In 1994, East Asian tigers were thought of as “Miracle” economies. USSR was thought of as the miracle economy of the 1950’s with very high GDP growth.

  • In both cases, high GDP growth was due to rapid accumulation of resources.

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  • Output growth in East Asia was substantially higher than the USA.

  • Labor productivity growth was also higher, but difference not as stark. Large growth in E.A. workforce during this time period.

  • Capital Productivity Fell Dramatically as Capital Stock increased much faster than output levels.

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Data from

  • Allwyn Young, 1995, “The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience,” Quarterly Journal of Economics 110, 641-680.

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Growth in East Asia

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Capital Growth

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Labor Productivity

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Capital Productivity

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  • Combination of high but less fantastic than originally though labor productivity growth and diminishing capital productivity implies slow or mild TFP growth.

  • This has been especially pronounced in Singapore which has had very strong capital growth.

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TFP Growth

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  • Why has TFP growth been much higher in HK than in Singapore?

  • What is your prediction for further growth? Does Asia have existing opportunities to push

    • Young’s answer: Singapore tried to push its way up the manufacturing chain to fast.

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  • Implications: Less than 30% of outstanding output growth in East Asia is due to TFP growth.

  • Since capital accumulation has diminishing returns and labor forces reach saturation, East Asia is likely to slow in growth.

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Complaints about Young’s methodology

  • Young calculates TFP growth using labor shares of income to estimate labor and capital intensity.

  • But Young’s estimates generally attribute 50% of income to labor. But EA national accounts may not do a good job of calculating labor income, especially of the self-employed.

  • How does TFP growth look if we use numbers for α = 1/3 as in developed world.

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Bosworth and Collins

  • Measure labor quality increase

    • φ = .07

      Capital income shares

    • α = .35

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Increase in Labor Participation

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Education per Worker

East Asian expansion in Education came from broadening primary and secondary education.

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Spectacular East Asian growth performance due mostly to increase in k

  • East Asian TFP growth strong relative to USA and developing world.

  • Average relative to most industrial countries.

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Productivity Differences

  • McKinsey Global Institute conducts a number of studies of labor and capital productivity at aggregate level in a number of countries.

  • Results in “The Power of Productivity: Wealth, Poverty, and the Threat to Global Stability” U. of Chicago Press 2004.

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Some Conclusions

  • “An evaluation of economic performance requires an analysis at the level of individual industries, such as automotive, steel, banking, and retailing.”

  • An economy’s productivity is determined by “the way it organizes and deploys both its labor and its capital”

  • Policies governing competition in product markets are as important as macroeconomic policies. …One factor that was profoundly underestimated was the importance of a level playing field..””

  • “Direct investments by the more productive companies from the rich countries would raise the poor countries’ productivity and growth…”

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  • Korea’s TFP and GDP per Capita are about 50% of the U.S. level, but capital productivity and capital returns are lower than U.S. levels.

  • Korean education levels are similar (slightly less) than U.S. levels.

  • Korea has many advanced technological industries (Samsung, Hynix)

    Korea digital connectivity much better than USA.

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Sectoral Approach

  • Manufacturing

    • Pohang Steel, Worlds most productive integrated steel producer, exceptional success story.

    • Most manufacturing (automotive, semi-conductor) are dominated by uncompetitive conglomerates chaebols protected from international competition and have not adopted best practice manufacturing techniques.

    • Semiconductors have lagged technological leaders and sell commodity chips and low prices.

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  • Retailing

    • Until recently, government regulations prevented large stores and shopping centers from developing. Labor productivity in retailing sector is 1/3 of US..

  • Construction

    • Reasonably strong productivity in apartment construction, but needs rezoning of outlying areas to develop new single family dwellings.

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