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Neo-Classical Growth Model

Neo-Classical Growth Model. Large Variations in Labor per Person (www.ggdc.net). Variation in Labor Force Participaton. Main Differences in Countries are Due to Variation in Labor Productivity. Plan. Come up with separate theories governing both labor productivity and hours worked.

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Neo-Classical Growth Model

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  1. Neo-Classical Growth Model

  2. Large Variations in Labor per Person (www.ggdc.net)

  3. Variation in Labor Force Participaton

  4. Main Differences in Countries are Due to Variation in Labor Productivity

  5. Plan • Come up with separate theories governing both labor productivity and hours worked. • First, labor productivity.

  6. Rule of Thumb • Growth Rate Rule of Thumb • Productivity growth is output growth minus labor growth.

  7. Agricultural Era • Prior to about 1775 or so, GDP per capita remained stagnant in virtually every country in the world. • There were many technological advances during this period. • Greater, productivity per unit of land tended to go into increasing the population level.

  8. GDP per capita through history YearPopulation GDP per Capita -5000 5130 -1000 50160 1 170135 1000 265165 1500 425 175 1800 900250 Macroeconomics by J. Bradford DeLong, Chap. 5

  9. Pre-Industrial RevolutionSource: Angus Madisson, Measuring the Chinese Economy

  10. Industrial Revolution Spreads to NA, W, Europe and East Asia

  11. Capital Productivity

  12. Productivity Catch Up: EuropeSource: Groningen Growth & Development Center 1990 US$, Average Output per Hour (Y/L)

  13. Productivity Catch Up: Latin AmericaSource: Groningen Growth & Development Center

  14. Productivity Catch Up: East AsiaSource: Groningen Growth & Development Center

  15. Growth by Region The World Economy, A Millienial Perspective by Angus Madisson

  16. USA in Industrial Era • Average Productivity of Capital, shows no trend upward or downward. • The shares of income devoted to capital and labor show no trend. • The average growth rate of output per person has been positive and relatively constant over time.

  17. USA Factor Productivity 1980-2003

  18. Productivity Growth in Korea and the USA • Compare the post-war growth of labor productivity of Korea and the US. The US started out with much higher labor productivity than the Korea. Both countries have seen positive productivity growth, Korea’s has been much faster.

  19. Korean Labor Productivity goes from less than 10% of USA to more than 40%.

  20. Capital Productivity:How do you measure capital • Option: Count it. Take surveys of industries, firms and households to find out the value of the capital that they own. • Problem: Expensive • Use the perpetual inventory method, to calculate the capital stock.

  21. Capital Accumulation • Capital is accumulated through investment and is lost through depreciation. • Depreciation is not measured either. We might assume a constant rate of depreciation, δ.

  22. Perpetual Inventory Method • Steps • Estimate capital depreciation rate (usually δ≈.08 for annual). • Guess initial capital stock (e.g. K1950 = I1950/ δ). • Solve recursively forward.

  23. Relatively Stable Capital Productivity in USA, decline in South Korea

  24. Data • Labor productivity is from All series derived from this database need to be referred to as:“Groningen Growth and Development Centre and The Conference Board, Total Economy Database, August 2004, http://www.ggdc.net" • Capital productivity data can be downloaded at Center for International Comparisons at University of Pennsylvania. • URL Address: http://pwt.econ.upenn.edu/

  25. Labor Force Growth • Typically, we expect to see growth in the labor force due to population growth. • This has been true in the US and Korea. • Note that the labor force growth rate has been roughly constant over time in each country (though faster in Korea).

  26. Labor Force Growth • World Bank Global Development Database.

  27. Objective • Construct an economic theory that is consistent with these growth facts: • In mature economies (like the USA) • Labor productivity grows at a roughly constant rate. • Capital productivity stays roughly constant. • In developing economies (like Korea) • Labor productivity grows faster than mature economies. • Capital productivity shrinks over time.

  28. Neo-classical Productivity Function(see Branson, p.576) • We assume constant returns to scale production function • Because of constant returns we can write this as a productivity function • Define and then,

  29. Example: Cobb-Douglas • Divide both sides by L • The labor productivity function is in capital per labor unit and technology.

  30. Marginal Product • It is true (because of CRTS) that the marginal effect of capital on output is equal to marginal product of capital per labor unit on labor productivity. • Example: Cobb-Douglas

  31. Labor Productivity Function(Constant A) y f(k,A) Slope = MPK= k

  32. Diminishing Returns • The production function has diminishing returns to capital and so does the productivity function have diminishing returns to capital per labor unit.

  33. Cobb-Douglas Capital Productivity Function • We can also write the capital productivity function as a function of the capital labor ratio. • In the Cobb-Douglas case, average productivity of capital

  34. Capital Productivity • Capital productivity is a decreasing function of the capital/labor ratio. • Intuition: If you give more and more capital to the same amount of workers, the output that each machine will produce will go down.

  35. Capital Productivity Function(Constant A) k

  36. Reading Supplement • The best intermediate macroeconomics text on growth theory is Delong, Chapter 4. • The main difference between these notes and Delong is that • what we call technology, At, Delong calls Et. • Delong emphasizes the importance of the capital output ratio. We emphasize capital productivity which is the inverse of the capital-output ratio.

  37. Capital Accumulation • The increase in the capital stock that occurs in every period is gross investment, It, net of depreciation, δKt.

  38. Growth Rates vs. Continuous Growth Rates • The growth rate over a period of time is written as the difference in the variable over the period over its initial start value. • When the change in the variable is not too large or the length of the time period is not too long, the growth rate is close to the continuous growth rate.

  39. Investment Rate(see Branson, p. 579) • Define the Investment rate, • The growth rate of capital is a function of the investment rate, capital productivity and the depreciation rate.

  40. Growth Rate of Capital Per Labor Unit • The growth rate of capital per labor unit is equal to capital growth rate minus labor growth rate

  41. Investment per Labor Unit • We can define investment per labor unit as • Assume a constant investment rate

  42. Investment per Worker Function(Constant A) y sF(k,A) k

  43. Replacement Investment per Worker • Assume you had a constant growth rate of labor • If you invest just enough per worker to keep the capital-labor ratio constant, you need to replace depreciated capital and equip new workers. The greater is k, the more replacement investment you need to do.

  44. Replacement Investment per Worker Function (Constant s,n) y,rep sF(k,A) (δ+n)k k

  45. Capital per Worker as an Engine of Labor Productivity Growth. • As long as investment per worker is greater than replacement investment per worker, the capital stock per worker will be growing. • Holding A constant, this implies output per worker will be growing.

  46. Steady State Capital Stock • Investment per worker is an increasing function the capital per worker since it is proportional to output per worker. • However, both output per worker and investment per worker are diminishing functions of k. • Investment per worker increases with k at a non-diminishing rate. • Implication:There is a steady state capital stock where investment per worker is exactly equal to replacement investment per worker.

  47. Replacement Investment per Worker Function (Constant s,n) y,rep sF(k,A) (δ+n)k k k*

  48. Steady State Capital per Worker • Define steady-state k* will solve the function • Cobb-Douglas Example

  49. Determinants of Long-term Capital Productivity • Investment Rates: When economies invest a high percentage of their output, they can “support” a high level of capital per worker. • To maintain a steady level of capital per worker, investment must be done in every period to replace depreciated equipment and equip new workers. • If investment levels are high, a high level of depreciated capital can be replaced. • A high ratio of capital to labor implies a low level capital productivity and a relatively high level of labor productivity.

  50. Steady State Capital in Two Countries, B and D , sB > sD (Constant A,n) sB F(k,A) sD F(k,A) (δ+n)k k kD* kB*

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