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 1.THE IMPORTANCE OF THE ROLE PLAYED BY CAPITAL IN PRODUCTION 2.A SIMPLE MODEL OF ENDOGENOUS GROWTH 3.EXTERNALITIES AND GROWTH 4.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 DECREASING RETURNS TO CAPITAL WEAK DECREASING RETURNS STRONG AND WEAK 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> , 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) To growth rate of capital From equilibrium accumulation equation Macroeconomics Set 5

23 To growth rate of output Hence in this ENDOGENOUS GROWTH MODEL 1)long run growth in absence of technological progress 2)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,  ), 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  > 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

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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: Macroeconomics Set 5

51 Something that is easier to interpret intuitively would be: 1 YEAR increase in average years of schooling  income per capita growth(?) Macroeconomics Set 5

52 ElasticityAggr. Return % % % 0.45% % % 112% 1.215% Macroeconomics Set 5

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56 HUMAN CAPITAL QUALITY Macroeconomics Set 5

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62 Human capital externalities Moretti, AER 2004 Macroeconomics Set 5

63 Estimating externalities: PLANT INDUSTRY CITY -- does output IN THE PLANT (controlling for inputs in plant and industry) INCREASE with THE SHARE OF COLLEGE WORKERS outside of INDUSTRY but inside CITY? Macroeconomics Set 5

64 Estimating equation: Macroeconomics Set 5

65 Data: Macroeconomics Set 5

66 Benchmark results: Macroeconomics Set 5

67 Macroeconomics Set 5

68 Physical capital externalities? Macroeconomics Set 5

69 Macroeconomics Set 5