Macroeconomics BGSE/UPF

1. MacroeconomicsBGSE/UPF LECTURE SLIDES SET 5 Professor Antonio Ciccone

2. III. Economic Growth with Human Capital and Externalities

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

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

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

6. COBB-DOUGLAS PRODUCTION FUNCTION

7. STRONG AND WEAK DECREASING RETURNS TO CAPITAL WEAK DECREASING RETURNS STRONG DECREASING RETURNS TO CAPITAL

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

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

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

12. CONVERGENCE UNDER STRONG DECREASING RETURNS TO CAPITAL

13. CONVERGENCE AND WEAK DECREASING RETURNS TO CAPITAL

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

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

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

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

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

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

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

21. PERPETUAL CAPITAL ACCUMULATION WITHOUT TECHNOLOGICAL CHANGE

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

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

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

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 !!

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

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!

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

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

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

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

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

33. Rivalry and excludability

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

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

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)

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

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

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

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)

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

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

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)

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

45. Empirical work on link between human capital and growth

46. The human capital “level” effect

50. 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: