New Growth Theory

1. Chapter 3 New Growth Theory

2. Part A: Research and Development Assumptions UNO, ECON 6204, Summer 2008, Dr. Tufte 2 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

3. 3.1 Framework and assumptions UNO, ECON 6204, Summer 2008, Dr. Tufte 3 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

4. Overview We�ll model technology as the output of a research and development industry So the economy produces two things: consumption goods and ideas Major simplification We�re going to go back to the idea that the saving rate is constant, and not optimally determined Continuous time UNO, ECON 6204, Summer 2008, Dr. Tufte 4 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

5. Specifics Same four endogenous variables: K, L, A and Y For simplicity, there is no depreciation Two sectors Goods Ideas Labor and capital are split between the two sectors You can only work in one sector Technology is not split Ideas can be used anywhere UNO, ECON 6204, Summer 2008, Dr. Tufte 5 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

6. Specifics Goods production function Y(t)=[(1-aK)K(t)]?[(1-aL)A(t)L(t)](1-?) The shares of labor and capital devoted to goods production, aK and aL, are exogenous. Ideas production function dA/dt=B[aKK(t)]�[aLL(t)]?A(t)? Note that this is production of new ideas (old ideas do not have to be replaced) This function allows for decreasing, constant or increasing returns to scale UNO, ECON 6204, Summer 2008, Dr. Tufte 6 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

7. Specifics Returns-to-scale restrictions are made to capture scalability of production processes Constant-returns-to-scale makes sense for most physical processes It isn�t clear what makes sense for the production of ideas, so �+?+? isn�t restricted to equal 1 UNO, ECON 6204, Summer 2008, Dr. Tufte 7 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

8. Specifics The key to understanding the model is the similarities and differences between output, capital and technology New output is produced every period, but it is all used in that period (its �depreciation� = 100%) New technology is produced every period, but it never depreciates, so it accumulates like capital Capital is output diverted from consumption Technology is produced instead of consumption UNO, ECON 6204, Summer 2008, Dr. Tufte 8 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

9. 3.2 The model without capital UNO, ECON 6204, Summer 2008, Dr. Tufte 9 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

10. The Dynamics of Knowledge Accumulation For simplicity, assume ?=�=0 The production functions are then Y(t)=(1-aL)A(t)L(t) dA/dt=B[aLL(t)]?A(t)? The growth rate of technology is then: gA(t)=(dA/dt)/A=B[aLL(t)]?A(t)?-1 UNO, ECON 6204, Summer 2008, Dr. Tufte 10 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

11. The Dynamics of Knowledge Accumulation What we want is the growth rate of the growth rate of technology, (dgA/dt)/gA Substitute in for L(t) and A(t) to get: gA(t)=B[aLL(0)ent]?[A(0)egt]?-1 Take logs to get: lngA(t)=lnB+?ln[aLL(0)]+nt?+(?-1)lnA(0)+gAt(?-1) Note the switch from g to gA in this chapter Take the time derivative to get: (dgA/dt)/gA=n?+gA(?-1) UNO, ECON 6204, Summer 2008, Dr. Tufte 11 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

12. The Dynamics of Knowledge Accumulation Multiply through by gA to get: (dgA/dt) =n?gA+(gA)2(?-1) The behavior of this quadratic will depend on the size of ? The growth of technology is endogenous, so new growth models are sometimes called endogenous growth models UNO, ECON 6204, Summer 2008, Dr. Tufte 12 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

13. Case 1: ?<1 This is not the same ? as in the CRRA function Here, it is the effect of existing technology on the creation of new ideas The steady state is where: (dgA/dt) =n?gA+(gA)2(?-1)=0, Or gA* = ?n/(1-?) So the rate of growth of technology converges to a positive value UNO, ECON 6204, Summer 2008, Dr. Tufte 13 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

14. Case 1: ?<1 This is a model of endogenous growth Output growth occurs because of technological growth Technology grows because new ideas are created and old ideas don�t depreciate It�s kind of odd that the growth of technology depends on population growth This seems truer at larger scales, but not at smaller ones Technological growth does not depend on the proportion of people working in research and development UNO, ECON 6204, Summer 2008, Dr. Tufte 14 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

15. Case 2: ?>1 In this case, there is no steady-state growth rate of technology The growth rate accelerates This implies that the overall economy never reaches a steady-state either This is implausible, but shouldn�t be completely dismissed. Growth rates of developed countries have been inching up over the decades. UNO, ECON 6204, Summer 2008, Dr. Tufte 15 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

16. Case 3: ?=1 The model simplifies to: gA(t)=B[aLL(0)ent]? Growth of ideas depends on population Growth of ideas depends on the proportion of the population working in research and development (dgA/dt) =n?gA Growth of ideas is accelerating when population growth is positive Growth of ideas stops when population growth stops These models are simple and plausible UNO, ECON 6204, Summer 2008, Dr. Tufte 16 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

17. The Importance of Returns to Scale to Produced Factors UNO, ECON 6204, Summer 2008, Dr. Tufte 17 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

18. 3.3 The general case UNO, ECON 6204, Summer 2008, Dr. Tufte 18 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

19. The Dynamics of Knowledge and Capital The instantaneous growth rate of capital is: dK/dt = sY(t) Substitute in the production function to get: dK/dt = s[(1-aK)K(t)]?[(1-aL)A(t)L(t)](1-?) Gather constants so that: cK=s(1-aK)?(1-aL)(1-?) dK/dt = cK[K(t)]?[A(t)L(t)](1-?) gK(t)=(dK/dt)/K = cK[K(t)]?-1[A(t)L(t)](1-?) UNO, ECON 6204, Summer 2008, Dr. Tufte 19 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

20. The Dynamics of Knowledge and Capital Take logs of both sides to get: lngK(t)=lncK+(1-?)ln[A(t)L(t)/K(t)] Now take the derivative with respect to time to get: dgK(t)/dgK(t)=(1-?)[gA(t)+n-gK(t)] UNO, ECON 6204, Summer 2008, Dr. Tufte 20 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

21. The Dynamics of Knowledge and Capital In gA-gK space, the locus where this equals zero is: dgK(t)/dgK(t)=0=(1-?)[gA(t)+n-gK(t)] This must slope upward, and Intercept the gK axis at n. The implied dynamics are that when we are above the line gK(t) is relatively large and must be declining UNO, ECON 6204, Summer 2008, Dr. Tufte 21 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

22. The Dynamics of Knowledge and Capital Recall that the growth rate of technology is: gA(t)=B[aKK(t)]�[aLL(t)]?A(t)?-1 Factor out constants to get: gA(t)=B[aK]�[aL]?[K(t)]�[L(t)]?A(t)?-1 Take logs to get: lngA(t)=ln{B[aK]�[aL]?}+�lnK(t)+?lnL(t)+(?-1)lnA(t) Now take the derivative with respect to time: [dgA(t)/dt]/gA(t)= �gK(t) + ?n + (?-1)gA(t) UNO, ECON 6204, Summer 2008, Dr. Tufte 22 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

23. The Dynamics of Knowledge and Capital In gA-gK space, the locus where this equals zero is: [dgA(t)/dt]/gA(t) = 0 = �gK(t) + ?n + (?-1)gA(t) The intercept on the gK axis is at -?n/� <0 The slope, (1-?)/�, is indeterminate There are several cases, most of them implausible The direction of movement is to the right, dgA> 0, when above the line Since this is where gK is relatively large UNO, ECON 6204, Summer 2008, Dr. Tufte 23 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

24. Case 1: � + ? < 1 In this case the slope of the dgA/dt locus is steeper than the dgK/dt locus The direction of the arrows indicates a sink at the steady-state This means that sunspots can lead to one country being on one path and another being on a different path without it really making much difference to the long-run outcome UNO, ECON 6204, Summer 2008, Dr. Tufte 24 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

25. Case 1: � + ? < 1 At the steady state: dgK(t)/dgK(t)=0=(1-?)[gA(t)+n-gK(t)] gA(t)+n = gK(t) [dgA(t)/dt]/gA(t) = 0 = �gK(t) + ?n - (?-1)gA(t) �[gA(t)+n] + ?n - (?-1)gA(t) = 0 gA(t)[� + (?-1)] = -?n � �n gA(t) = (? + �)n/[1 � � - ?] So, technological and capital growth depend positively on ?, �, n, and ? They do not depend on the labor and capital shares devoted to research and development, or the saving rate UNO, ECON 6204, Summer 2008, Dr. Tufte 25 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

26. Case 2: � + ? = 1, and n=0 In this case the two loci coincide All points on the intersection are steady states All of them are sinks Now sunspots make a big difference, because they can take you to a steady-state where growth is higher or lower than in other countries UNO, ECON 6204, Summer 2008, Dr. Tufte 26 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

27. Scale Effects and Growth There is a distinction that needs to be made between two mathematical possibilities. � + ? < 1 This leads to a sink in which rates of growth converge upward to the steady-state, so that growth rates accelerate � � ? + ? > 1 Increasing-returns-to-scale in idea production Note that in this model you do not need to have increasing-returns-to-scale in order to have high and accelerating growth rates UNO, ECON 6204, Summer 2008, Dr. Tufte Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics" 27

28. Scale Effects and Growth Jones �95 argues that it is unlikely that there are increasing returns to scale in research and development We�ve spend so much more on these over the last 50 years that growth rates would�ve gone way up if this case were true Jones suggests that returns to research and development are decreasing That ? + � + ? < 1 UNO, ECON 6204, Summer 2008, Dr. Tufte 28 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

29. Scale Effects and Growth Others argue that the number of sectors in which R&D is performed increases with the size of the economy Each sector still has increasing-returns-to-scale, but doesn�t get the resources for that to make much difference These models require implausible parameter restrictions UNO, ECON 6204, Summer 2008, Dr. Tufte 29 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

30. Scale Effects and Growth With decreasing returns to scale, increases in R&D share or the saving rate do improve growth rates, but the effect is transitory Remember that this doesn�t necessarily mean it will be short This is a transitory effect on growth rates. There will still be a permanent effect on the levels of output. UNO, ECON 6204, Summer 2008, Dr. Tufte 30 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

31. 3.4 the nature of knowledge and the determinants of the allocation of resources to r&d UNO, ECON 6204, Summer 2008, Dr. Tufte 31 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

32. Overview Goods are rival If you are using it, other people can�t use it Knowledge is non-rival If you are using it, other people still can use it Non-rivalry implies marginal costs that are zero in most situations. Thus either: Knowledge production can�t be profitable, or The price of knowledge is marked up in imperfect markets UNO, ECON 6204, Summer 2008, Dr. Tufte 32 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

33. Overview Goods tend to be excludable You can prevent someone else from using your (private) good Non-excludability is why we learn about public goods Knowledge can be excludable or non-excludable Excludability can be due to Complexity Legal and social restrictions Excludability helps make knowledge production profitable UNO, ECON 6204, Summer 2008, Dr. Tufte 33 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

34. Support for Basic Scientific Research If you support basic research with a subsidy, you can get around the non-rivalry and non-excludability problems It makes sense to do this because there is a positive externality to research UNO, ECON 6204, Summer 2008, Dr. Tufte 34 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

35. Private Incentives for R&D and Innovation Models exist in which innovators can earn monopoly profits (or at least positive but sub-optimal economic profits) from their new ideas Outcomes are not Pareto-optimal due to imperfect markets Positive externalities lead to too little R&D Negative externalities lead to too much R&D UNO, ECON 6204, Summer 2008, Dr. Tufte 35 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

36. Private Incentives for R&D and Innovation Consumer Surplus Effects The positive externality associated with knowledge spillovers Business-Stealing Effects The negative externality from new technology displacing old technology R&D Effects The positive externality from innovators profiting from making new goods, but not from others expanding on their ideas UNO, ECON 6204, Summer 2008, Dr. Tufte 36 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

37. Alternative Opportunities for Talented Individuals Rent seeking can include lots of activities that are not beneficial for growth We should see more rent seeking in: Small (and/or artificially closed) market Innovators profit more in bigger markets Markets in which severely diminishing returns are protected Why innovate if you can still profit in a field that isn�t scalable? Regions in which property rights are poorly defined Why innovate when you might not get to keep the money? UNO, ECON 6204, Summer 2008, Dr. Tufte 37 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

38. Learning-by-Doing (AK Models) The Solow production function is used But, the aggregate stock of technology is now driven by the aggregate stock of capital: A(t)=BK(t)f, f > 0 The more capital in existence, the more ideas there are about how to use capital So, dK/dt=sK(t)aB(1- a)K(t)f(1- a)L(t)(1- a) The behavior of this equation is similar to the model with no capital; f here and ? there work similarly When f<1, output growth depends on population growth UNO, ECON 6204, Summer 2008, Dr. Tufte 38 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

39. 3.5 endogenous saving in models of knowledge accumulation: an example UNO, ECON 6204, Summer 2008, Dr. Tufte 39 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

40. Endogenous Saving In Models of Knowledge Accumulation This works with any sort of model, but we continue with the learning-by-doing model, and assume for simplicity that: f=1 (there are still increasing-returns-to-scale) n=1, so L(t)=L d=0 Now, consider the production function of a single firm It depends on the capital and labor that it uses, and the aggregate stock of knowledge Yi(t)=Ki(t)a[A(t)Li](1-a)=Ki(t)a[BK(t)Li](1-a) UNO, ECON 6204, Summer 2008, Dr. Tufte 40 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

41. Endogenous Saving In Models of Knowledge Accumulation Given the production function for the individual firm, then ri(t)=aKi(t)(a-1)[BK(t)Li](1-a) Or ri(t)=a[BK(t)(1-a)][Ki(t)/Li]-(1-a) The a is critical: it reflects that a firm gets less than 100% of the marginal product that society gets from the firm�s new capital With identical firms the K�s cancel out: r(t)=aB(1-a)L(1-a), which is constant Let b=B(1-a)L(1-a), so r=ab UNO, ECON 6204, Summer 2008, Dr. Tufte 41 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

42. Endogenous Saving In Models of Knowledge Accumulation The wage rate for an individual firm is then: wi(t)=(1-a)Ki(t)a[BK(t)](1-a)Li-a Since firms are identical, we can now aggregate the K�s to get: w(t)=(1-a)B(1-a)K(t)Li-a Substitute b=B(1-a)L(1-a) w=(1-a)bK(t)/L This is increasing in aggregate capital UNO, ECON 6204, Summer 2008, Dr. Tufte 42 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

43. Endogenous Saving In Models of Knowledge Accumulation Adopt the CRRA utility from Chapter 2 Change Chapter 2�s ? to s The critical part is the Euler equation (dC/dt)/C(t)=[r(t)-?]/s=[r-?]/s, a constant Recall that at a steady state, this is also the growth rate of the economy In this simplified framework, there are no diminishing returns to capital, so there are no interesting dynamics produced from K and Y changing at different rates UNO, ECON 6204, Summer 2008, Dr. Tufte 43 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

44. Endogenous Saving In Models of Knowledge Accumulation Now go back to the aggregate production function Y(t)=K(t)[BL](1-a)=bK(t) At a steady state, this implies that the economy should grow at a rate that is b times the rate of growth of capital, since dY/dt = b(dK/dt), or alternatively, that the saving rate is 1/b times the economy�s growth rate, since K=Y/b, then dK/dt = (1/b)(dY/dt). UNO, ECON 6204, Summer 2008, Dr. Tufte 44 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

45. Endogenous Saving In Models of Knowledge Accumulation It should now be easy to see why the economy is not Pareto optimal It grows at [ab-?]/s From a saving rate of [ab-?]/bs These rates increase with a Yet a is capturing the positive externality: since firms don�t capture all the benefit of their individual increase in capital, they make smaller investments and the economy as a whole suffers The smaller the a, the more sub-optimal the outcome UNO, ECON 6204, Summer 2008, Dr. Tufte 45 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

46. 3.6 models of knowledge accumulation and the central questions of growth theory UNO, ECON 6204, Summer 2008, Dr. Tufte 46 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

47. Models of Knowledge Accumulation and the Central Questions of Growth Theory Growth Good: the Solow residual is very large, so endogenizing technology growth is a good thing Cross-Country Income Differences Bad: the huge differences in income would need to be explained by huge differences in technology Bad: technology is non-rival, so why can�t capitalists just take it overseas for higher returns? UNO, ECON 6204, Summer 2008, Dr. Tufte 47 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

48. 3.7 empirical application: population growth and technological change since 1 million b.C. UNO, ECON 6204, Summer 2008, Dr. Tufte 48 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

49. Population Growth and Technological Change Since 1 Million B.C. Really only to the onset of per capita income growth In a subsistence society, endogenous growth (pushed by population growth) makes two predictions Population growth rates rise with population Population density, in isolated regions, is proportional to the land available to support the population Alternatively, more advances are made in more populous regions, but measuring this would require evaluating which advances were actually important UNO, ECON 6204, Summer 2008, Dr. Tufte 49 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

50. A Simple Model (with ?=1) Cobb-Douglas production with fixed land, T: Y(t)=Ta[A(t)L(t)](1-a) Technological growth is population driven: dA/dt=BL(t)A(t) Per capita incomes are constant at a subsistence level, y Then: y=Ta[A(t)L(t)](1-a)/L(t) Or: L(t) is proportional to A(t)(1-a)/aT So: (dL/dt)/L=[(1-a)/a]{(dA/dt)/A}=[(1-a)/a]BL(t) UNO, ECON 6204, Summer 2008, Dr. Tufte 50 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

51. Results Regression results show a good linear fit between growth rates and levels of population prior to 1700 Regression results also indicate population density is highest in larger regions UNO, ECON 6204, Summer 2008, Dr. Tufte 51 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

52. Discussion This offers a new �solution� to a set of outstanding anthropological problems: Why were dense areas important? Why were �the hills� filled with backward people all over the globe How could China make so many advances without becoming rich? Why did the Islamic world decline? There were always barbarians, but why did barbarian hordes always seem to arrive equipped with better technology? UNO, ECON 6204, Summer 2008, Dr. Tufte 52 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

53. Population Growth vs. Growth In Income Per Person over the Very Long-Run Why did incomes explode after 1700 then? Because population growth rates can�t change as quickly as technological growth rates, and eventually the latter swamped the former Why won�t this persist? People prefer to be less fertile when richer UNO, ECON 6204, Summer 2008, Dr. Tufte 53 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

54. Part b: cross-country income differences UNO, ECON 6204, Summer 2008, Dr. Tufte 54 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

55. 3.8 extending the solow model to include human capital UNO, ECON 6204, Summer 2008, Dr. Tufte 55 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

56. Assumptions Continuous time Exogenous saving rate Solow-style capital accumulation Solow-style technology growth Production function Y(t)=K(t)a[A(t)H(t)](1-a) H includes both time and human capital H(t)=L(t)G(E), where E is the exogenous education level UNO, ECON 6204, Summer 2008, Dr. Tufte 56 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

57. Analyzing the Model If we define k(t)=K(t)/A(t)G(E)L(t), with E exogenous, then the model behaves exactly like a Solow model dk/dt does not depend on E Recall that in a Solow model is depends only on s, n, g, and d Per capita output is now Y/L=AG(E)y Instead of Y/L = Ay in the Solow model There isn�t much going on here � simply adding education doesn�t change the Solow model. UNO, ECON 6204, Summer 2008, Dr. Tufte 57 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

58. Students and Workers The mechanics of education do, however, change how the model works, if School and work are rivalrous We go to school when young and work when old Students are those born between 0 and E periods ago Workers are those born between E and T periods ago UNO, ECON 6204, Summer 2008, Dr. Tufte 58 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

59. Students and Workers Assume that the net instantaneous population increase is B(t) We don�t need to be more specific Assume that it grows at rate n, so that looking back s periods we have B(t)=B(s)e-ns, for any t or s What we want is an expression for population as a multiple of births. This multiple will be: Decreasing in birth rates Increasing in life expectancy UNO, ECON 6204, Summer 2008, Dr. Tufte 59 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

60. Students and Workers If people live for T periods, the population is the integral from 0 to T of B(t)e-nt, for any B(t) Thus N(t)={[1-e-nT]/n}B(t) If workers are those people born from E to T periods ago, then the labor force is the integral from E to T of B(t)e-nt, for any B(t) Thus L(t)={[e-nE-e-nT]/n}B(t) Labor force participation is then: [e-nE-e-nT]/[1-e-nT] UNO, ECON 6204, Summer 2008, Dr. Tufte 60 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

61. Students and Workers Per capita income now equals yAG(E) times the labor force participation rate The labor force participation rate is Decreasing in the population growth rate Increasing in life expectancy This suggests that poorer countries will have higher population growth rates and less healthy populations UNO, ECON 6204, Summer 2008, Dr. Tufte 61 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

62. Students and Workers The model of human capital also suggests very long adjustment times Suppose we want to increase education by one year for all workers It will take T-E years to get the full effect of this Capital adjustments will slow this even further UNO, ECON 6204, Summer 2008, Dr. Tufte 62 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

63. 3.9 empirical application: accounting for cross-country income differences UNO, ECON 6204, Summer 2008, Dr. Tufte 63 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

64. Procedure Growth accounting Start with Y=Ka[AH](1-a) Divide by L: Y/L=(K/L)aA(1-a)(H/L)(1-a) Take logs: ln(Y/L)=?ln(K/L)+ (1-?)lnA+ (1-?)ln(H/L) Subtract ?ln(Y/L) from each side to get Note that ?ln(K/L)-?ln(Y/L)= ?ln(K/Y), so: (1-?)ln(Y/L)=?ln(K/Y)+ (1-?)lnA+ (1-?)ln(H/L) ln(Y/L)=[?/(1-?)]ln(K/Y)+ lnA+ ln(H/L) lnA is a Solow residual that is mostly things other than human capital UNO, ECON 6204, Summer 2008, Dr. Tufte 64 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

65. Data and Basic Results Per capita output and capital per unit of output are readily available Labor services per capita are harder to estimate Estimates suggest weak diminishing returns to extra years of school UNO, ECON 6204, Summer 2008, Dr. Tufte 65 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

66. Data and Basic Results The thirty to one difference in income between the richest countries and the poorest ones for which we have good data can be decomposed as: 1/6 from more capital 1/4 from more human capital The rest is still a residual � it isn�t physical or human capital, saving rate, or endogenous technological change Parente and Prescott assert that it is (upstream) monopoly power restraining (downstream) total factor productivity UNO, ECON 6204, Summer 2008, Dr. Tufte 66 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

67. Extensions Improvements have been made in the measurement of human capital, none to much effect More complex returns to education Differences in quality of education Mismatch of high and low quality human capital in poorer countries UNO, ECON 6204, Summer 2008, Dr. Tufte 67 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

68. Extensions Balassa-Samuelson Effect Non-tradable goods tend to be much cheaper in poor countries Lower prices for non-traded goods mean less income available to be saved for investment in physical or human capital This seems to explain some of the strength of the effect of human capital on growth, making the true effect weaker than it appears at first glance UNO, ECON 6204, Summer 2008, Dr. Tufte 68 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

69. Factor Returns and Factor Flows There has been a big improvement in the ability of the model to explain marginal returns to physical capital by introducing human capital The difference in returns between rich and poor countries needed to be 1000 to 1 in the Solow model 3 to 1 in this model. This seems possible. UNO, ECON 6204, Summer 2008, Dr. Tufte 69 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

70. Factor Returns and Factor Flows Since production is Cobb-Douglas, the marginal product of labor services is (1-?)Y/H The growth accounting result can be modified: ln(Y/L)=[?/(1-?)]ln(K/Y)+ lnA+ ln(H/L) Reverse the logs: Y/L=(K/Y)[?/(1-?)]A(H/L) Multiply through: Y=(K/Y)[?/(1-?)]AH Then: (1-?)Y/H=(1-?)(K/Y)[?/(1-?)]A So a worker can improve their lot just by moving to a place with higher K/Y or Aq UNO, ECON 6204, Summer 2008, Dr. Tufte 70 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

71. 3.10 social infrastructure UNO, ECON 6204, Summer 2008, Dr. Tufte 71 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

72. Overview An individual faces this choice: Produce Where private returns are less than those to society Rent-seek Where societal returns are zero by definition, but private returns can be higher UNO, ECON 6204, Summer 2008, Dr. Tufte 72 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

73. Overview Social infrastructure are institutions and policies that try to improve the alignment of private and social returns Three types of social infrastructure Tax policy Rule of, and predictability of, law Limits on rent-seeking by the government or its agents UNO, ECON 6204, Summer 2008, Dr. Tufte 73 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

74. Evidence Measurements of social infrastructure are difficult, and not yet widely accepted But, there are natural experiments How did W. Germany more than double the per capita output of E. Germany in 40 years? How did Taiwan produce 5-10 times the per capita output of China in 40 years? UNO, ECON 6204, Summer 2008, Dr. Tufte 74 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

75. The Determinants of Social Infrastructure Vested interests may have little interest in changing infrastructure that works towards their advantage See Parente and Prescott �99 Some cultures may lead to better economic results Historically, laissez-faire has not been a system which people �trusted� Folk economics UNO, ECON 6204, Summer 2008, Dr. Tufte 75 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

76. Empirical Application: Geography, Colonialism, and Economic Development Poverty seems to be related to latitude Social infrastructure is worse in many poor countries today than it was in Europe 100 years ago, even though real incomes are comparable (much of Europe was at a subsistence level in 1900), while technology is better in poor countries today, and capital is often comparable UNO, ECON 6204, Summer 2008, Dr. Tufte 76 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

77. Geography, Colonialism and Economic Development Weak social infrastructure was caused by: The type of colonialism Extractive in hostile tropical environments The degree of pre-colonial advancement More advanced societies were co-opted for extraction Slavery Tropical agriculture was more conducive to slavery UNO, ECON 6204, Summer 2008, Dr. Tufte 77 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

78. Limitations and Extensions How do we figure out what social infrastructure is important? UNO, ECON 6204, Summer 2008, Dr. Tufte 78 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

79. Limitations and Extensions If positive externalities from capital are more important than we think, growth accounting will understate the importance of capital If this is the case, then social infrastructure that influences capital accumulation is what counts UNO, ECON 6204, Summer 2008, Dr. Tufte 79 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

80. Limitations and Extensions Three criticisms What are these externalities? Technology isn�t regressing, but investment in education continues to rise; this doesn�t leave much growth to be explained by externalities Many countries have successfully accumulated physical and human capital � if externalities are a big part of the story, they should be rich. Often, they�re poorer. UNO, ECON 6204, Summer 2008, Dr. Tufte 80 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

81. 3.11 a model of production, protection and predation UNO, ECON 6204, Summer 2008, Dr. Tufte 81 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

82. Assumptions Agents have 1 unit of time They either produce, protect, or predate Production is linear The fraction f is used for protection The fraction predated, L, depends on f, and the proportion of rent-seekers, R So, L=L(f,R) UNO, ECON 6204, Summer 2008, Dr. Tufte 82 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

83. Analyzing the Model The agent chooses f to maximize (1-L)(1-f) The FOC is: -(1-L)-Lf(1-f)=0 Total differentiation of this can tell us how f responds to changes in R � not surprisingly this is positive The income of both producers and predators is higher when there are fewer predators Equilibrium requires that their incomes be equal, and there is no reason this must occur at one level of R UNO, ECON 6204, Summer 2008, Dr. Tufte 83 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

84. Discussion Increasing penalties for rent-seeking increases the income of both producers and predators This increases the incentive for predation It reduces the incentive for protection This is self-reinforcing Predation will never go away completely UNO, ECON 6204, Summer 2008, Dr. Tufte 84 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

85. Capital Predation affects growth by changing rates of return. In a Cobb-Douglas, the capital share follows: rK = ?Y So: K/Y = ?/r Giving up some of your output to predation changes this to K/Y = (1-L)?/r, so capital will fall It gets worse if some of your capital is predated in addition to your output UNO, ECON 6204, Summer 2008, Dr. Tufte 85 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

86. 3.12 differences in growth rates UNO, ECON 6204, Summer 2008, Dr. Tufte 86 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

87. Convergence to Balanced Growth Paths Growth rates increase with distance from the steady-state Convergence means towards the same steady-state The poor grow faster Conditional convergence means towards different steady-states The poor may not grow faster if they are closer to their lousy steady-state UNO, ECON 6204, Summer 2008, Dr. Tufte 87 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

88. Changes In Fundamentals We want to figure out what will happen to growth rates when the steady-state moves Consider 2 periods in the discrete case Growth depends on distance from the steady-state: ?kt+1=?(kt*-kt) Then: ?kt+1 +?kt+2= ?(kt+1*-kt+1)+?(kt*-kt) Or: ?kt+1 +?kt+2= ?(kt*+ ?kt+1*-kt- ?kt+1)+?(kt*-kt) Or: ?kt+1 +?kt+2= [?+ ?(1-?)](kt*-kt)+ ??kt+1* UNO, ECON 6204, Summer 2008, Dr. Tufte 88 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

89. Changes In Fundamentals The first term says that growth depends on distance from the steady-state This is conditional, since your steady-state may differ from others The second term says that growth depends on how much your steady-state changed Due to policies that change your economies fundamentals This term has a permanent effect, so for levels, the further back in time the better UNO, ECON 6204, Summer 2008, Dr. Tufte 89 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

90. Changes In Fundamentals The fact is that growth rates seem unrelated to levels of income results from two possibilities: Poorer countries weren�t actually that far from their steady-states in the first place They were destined to be poor Many countries changed their steady-state in the wrong direction UNO, ECON 6204, Summer 2008, Dr. Tufte 90 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"

91. Growth Miracles and Disasters Movements down and away from a fixed steady-state require the destruction of large amounts of capital on a national level This can cause a growth miracle, but it is rare This suggests that growth miracles and disasters are about intentional policies that changes the steady state Folk economics is a big problem for getting this choice right. UNO, ECON 6204, Summer 2008, Dr. Tufte 91 Notes drawn from Chapter 3 of Romer's "Advanced Macroeconomics"