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Macroeconomics

Macroeconomics. LECTURE SLIDES SET 5 Professor Antonio Ciccone. III. Economic Growth with Human Capital and Externalities. Outline. THE IMPORTANCE OF THE ROLE PLAYED BY CAPITAL IN PRODUCTION A SIMPLE MODEL OF ENDOGENOUS GROWTH EXTERNALITIES AND GROWTH HUMAN CAPITAL AND GROWTH.

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Macroeconomics

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  1. Macroeconomics LECTURE SLIDES SET 5 Professor Antonio Ciccone Macroeconomics Set 5

  2. III. Economic Growth with Human Capital and Externalities Macroeconomics Set 5

  3. Outline • THE IMPORTANCE OF THE ROLE PLAYED BY CAPITAL IN PRODUCTION • A SIMPLE MODEL OF ENDOGENOUS GROWTH • EXTERNALITIES AND GROWTH • HUMAN CAPITAL AND GROWTH Macroeconomics Set 5

  4. 1. THE IMPORTANCE OF THE ROLE PLAYED BY CAPITAL IN PRODUCTION Let us return to the Solow model • Savings a constant fraction s of income • Depreciation rate of capital is  • Population growth n • Rate of echnological progress a Macroeconomics Set 5

  5. PRODUCTION FUNCTION with DECREASING RETURNS TO CAPITAL  DECREASING RETURNS TO CAPITAL CLOSE TO ZERO: STRONG DECREASING RETURNS CLOSE TO UNITY: WEAK DECREASING RETURNS Macroeconomics Set 5

  6. COBB-DOUGLAS PRODUCTION FUNCTION Macroeconomics Set 5

  7. STRONG AND WEAK DECREASING RETURNS TO CAPITAL WEAK DECREASING RETURNS STRONG DECREASING RETURNS TO CAPITAL Macroeconomics Set 5

  8. Effect of savings rate on BGP income/capital under STRONG and WEAK decreasing returns to capital • STRONG DECREASING RETURNS TO CAPITAL • Small BGP effects of savings rate • WEAK DECREASING RETURNS TO CAPITAL •  Large BGP effects of savings rate

  9. STRONG DECREASING RETURNS TO CAPITAL • Small BGP effects of savings rate • WEAK DECREASING RETURNS TO CAPITAL •  Large BGP effects of savings rate Macroeconomics Set 5

  10. How much of international income differences explained by “propensity of countries to accumulate”? Depends on strength of decreasing returns to capital Macroeconomics Set 5

  11. Convergence to the BGP under WEAK and STRONG decreasing returns to capital EQUILIBRIUM CAPITAL ACCUMULATION EQUATION Macroeconomics Set 5

  12. CONVERGENCE UNDER STRONG DECREASING RETURNS TO CAPITAL Macroeconomics Set 5

  13. CONVERGENCE AND WEAK DECREASING RETURNS TO CAPITAL Macroeconomics Set 5

  14. INCOME CONVERGENCE EQUATION (CLOSE to balanced growth path) Macroeconomics Set 5

  15. Speed of convergence • STRONG decreasing returns to capitalFAST convergence to BGP • WEAK decreasing returns to capitalSLOW convergence to BGP EMPIRICALLY, using cross-country data Macroeconomics Set 5

  16. REMEMBER THAT IN THE SOLOW MODEL Elasticity of output with respect to capital = Capital income share = 1/3 (empirically) =STRONG DECREASING RETURNS: • Fast convergence to BGP • Small BGP level effects of savings rate Macroeconomics Set 5

  17. 2. A SIMPLE MODEL OF ENDOGENOUS GROWTH Return to the Solow model • Savings a constant fraction s of income • Depreciation rate of capital is  • No population growth • No technological change Macroeconomics Set 5

  18. BUT BUT BUT NO DECREASING RETURNS TO CAPITAL(!) where A is a CONSTANT which implies Macroeconomics Set 5

  19. THIS PRODUCTION FUNCTION ALSO IMPLIES THAT Elasticity of output with respect to capital = Capital income share • which is evidently in CONTRADICTION with empirical observation • but let’s see where it leads us Macroeconomics Set 5

  20. EQUILIBRIUM CAPITAL ACCUMULATION EQUATION -- if sA>d, CAPITAL per WORKER and therefore OUTPUT per WORKER grow forever, even if there is NO TECHNOLOGICAL PROGRESS Macroeconomics Set 5

  21. PERPETUAL CAPITAL ACCUMULATION WITHOUT TECHNOLOGICAL CHANGE Macroeconomics Set 5

  22. Is there a BALANCED GROWTH PATH? (path where all variables grow at constant rate) From equilibrium accumulation equation To growth rate of capital Macroeconomics Set 5

  23. To growth rate of output Hence in this ENDOGENOUS GROWTH MODEL • long run growth in absence of technological progress • a higher savings rate means FASTER GROWTH IN the SHORT, MEDIUM, and LONG run Y=AK Macroeconomics Set 5

  24. Moreover, - Implies that the growth rate of capital does NOT fall as economies accumulate capital Macroeconomics Set 5

  25. GROWTH RATE OF CAPITAL (AND OUTPUT) STAYS CONSTANT IN TIME  same macro fundamentals (s,A,d), same growth rate, no matter what initial conditions !! Macroeconomics Set 5

  26. MAIN RESULTS: • perpetual accumulation-driven growth: capital accumulation alone can be the “engine of economic growth” • savings rate has long-run growth effects: an increase in the savings rate increases the growth rate of capital and output forever Macroeconomics Set 5

  27. Endogenous growth and convergence The AK model has two interesting features: (A) a poor economy will NOT achieve the income per capita of a rich economy even if has the same macro fundamentals (B) holding deep parameters or macro fundamentals constant as economies become richer, growth does not slow down  are these two linked? NO! Macroeconomics Set 5

  28. Endogenous growth model where GROWTH RATE OF CAPITAL FALLS IN TIME Macroeconomics Set 5

  29. Endogenous growth and convergence (A) a poor economy will NOT achieve the income per capita of a rich economy even if has the same macro fundamentals (B) holding deep parameters or macro fundamentals constant as economies become richer, growth MAY STILL slow down Macroeconomics Set 5

  30. The problem with the AK model? • Capital share too large • Back to the Solow model? -- externalities -- human capital Macroeconomics Set 5

  31. 3. EXTERNALITIES AND ENDOGENOUS GROWTH In the Solow model we have • perfect competition • no externalities As a result which we said was around Macroeconomics Set 5

  32. Why ? Because the RESULTS of INVESTMENT are assumed to be • EXCLUDABLE (only the INVESTOR benefits directly) But sometimes investments by one particular firm yields results that are • NON-EXCLUDABLE • NON-RIVAL Macroeconomics Set 5

  33. Rivalry and excludability Macroeconomics Set 5

  34. What if investment has a non-rival, non excludable element? Externalities:  real world has SLOWER convergence than Solow model, but not as slow as in endogenous growth model Macroeconomics Set 5

  35. Non-excludability, non-rivalry in the Solow model? • Technological progress! • But fell from heaven; or to put it differently COMES WITH THE PASSAGE OF TIME, not with investment Macroeconomics Set 5

  36. The Solow model with externalities • Capital income share reflects the internal return to capital • Elasticity of aggregate output wrt to capital reflects the social return to capital (private plus external return) Macroeconomics Set 5

  37. Solow model with externalities where f is an index for firms: f=1,…,N where A grows at rate a; and there are positive externalities to aggregate capital accumulation if and only if g > 0 Macroeconomics Set 5

  38. Solve: • Optimal behavior of each firm (rental of capital and labor) • Aggregate production as a function of aggregate inputs (capital and labor) • Solow and non-Solow dynamics Macroeconomics Set 5

  39. 4. HUMAN CAPITAL AND ENDOGENOUS GROWTH In the Solow model we have • perfect competition • no externalities • only ONE TYPE OF CAPITAL: PHYSICAL CAPITAL As a result Macroeconomics Set 5

  40. But what about HUMAN CAPITAL? What is human capital? • knowledge in people that makes them more productive In many ways similar to physical capital • first INVEST (go to school; get some training) • then GET A RETURN (higher wage) Macroeconomics Set 5

  41. Human capital (like capital externalities): • real world has SLOWER convergence than Solow model, but not as slow as in endogenous growth model • capital and savings explains more of international differences in income than in the Solow model Macroeconomics Set 5

  42. Level and growth effects of HC • Level effect of HC: more HC raises output (“neoclassical view of HC”) • Growth effect: human capital may determine the rate of technological progress:  may affect growth rate in BGP  or have transitional growth effects only Macroeconomics Set 5

  43. Growth effects of HC (A) • Lucas, JME, 1988: human capital can produce output or “technology”: • increasing HC allocated to learning may therefore increase the BGP growth rate (the downside is that output is reduced in the short and medium run) Macroeconomics Set 5

  44. “Growth” effects of HC (B) Nelson and Phelps, AER, 1966 BGP:  Macroeconomics Set 5

  45. Empirical work on link between human capital and growth Macroeconomics Set 5

  46. The human capital “level” effect Macroeconomics Set 5

  47. Macroeconomics Set 5

  48. Macroeconomics Set 5

  49. FROM ELASTICITIES to AGGREGATE RATES OF RETURN TO SCHOOLING Much of the aggregate work estimates: 1% increase in average years of schooling income per capita growth(?) Formally: Macroeconomics Set 5

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