1. BGSE/UPF Macroeconomics Slide SET 2Slide 1 MACROECONOMICS BGSE/UPF LECTURE SLIDES SET 2 Professor Antonio Ciccone

2. BGSE/UPF Macroeconomics Slide SET 2Slide 2 5.SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM— OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE 1.Investment and savings meet in the credit (also loan) market Households may have a PREFERENCE to save for consumption tomorrow. This is captured by the following extremely simple SAVINGS FUNCTION: (E19) Households simply save a constant fraction s of their total income Y (this includes labor and capital income). Savings are deposited in banks that use them to make loans to firms. Firms use credit to buy NEW machines. INVESTMENT refers to the total purchases of NEW MACHINES and ALSO TO THE VOLUME OF LOANS IN THE ECONOMY. Firms can therefore buy machines or instead rent them. This will give rise to the rent-or-buy decision which determines the real interest rate.

3. BGSE/UPF Macroeconomics Slide SET 2Slide 3 HOUSEHOLDS (aggregate labor endowment L(t) plus property rights in firms; preferences for consumption today and savings) FIRMS (technology of production; capital owned at the beginning of the period K(t))). GOODS MARKET (consumption and investment goods) LABOR MARKET RENTAL MARKET FOR CAPITAL GOODS CREDIT/LOAN MARKET (credit/loans for interest) FIGURE 7

4. BGSE/UPF Macroeconomics Slide SET 2Slide 4 How firms finance purchase of new machinery (1)Loans: firms ask banks for loans and banks make these loans with the savings of households (2)Retained earnings: firms ask their owners whether they can retain some of their earnings in order to fund purchases of new machinery (3)Issues of new shares: they purchases new machines and issue property titles to the machines (shares) directly to households  In the Solow environment these ways of financing machinery are all EQUIVALENT. We can therefore just think of firms financing the purchase of new machinery by asking banks for loans.

5. BGSE/UPF Macroeconomics Slide SET 2Slide 5 2. The rent or buy decision 1.The user cost of capital definition in discrete time Firm can demand credit/loans to purchase capital goods: - in principle, this gives them an alternative to the rental market for capital - instead of renting the capital good next year, for example, you could buy it on credit today, use it for one year and then sell it off. The cost of doing so is the USER COST OF CAPITAL -higher real interest rate and depreciation rate increase user cost -high future price for capital goods relative to current price reduces user cost

6. BGSE/UPF Macroeconomics Slide SET 2Slide 6 2. The user cost in one-sector growth models (which includes, among many, the Solow model) Assume that consumption goods and investment goods can be produced with identical technologies. In this case, the price of the investment goods relative to the capital good is always unity. If investment goods were more expensive only investment goods would be produced by profit maximizing firms. And vice versa. (E21)

7. BGSE/UPF Macroeconomics Slide SET 2Slide 7 3. The credit/loan market equilibrium The CREDIT/LOAN MARKET is in equilibrium at time t when: SAVINGS(t)=INVESTMENT(t) S(t)=I(t) As we will see, the CREDIT/LOAN market is brought into equilibrium by adjustments of the REAL INTEREST RATE. The rent or buy decision and the credit/loan market equilibrium: - firms can either buy capital goods today (invest) for future use, or go to the rental market for capital in the next period. - the cost of renting next period is the cost of buying the investment goods use it and resell what is left is

8. BGSE/UPF Macroeconomics Slide SET 2Slide 8 We will now show that in a CREDIT MARKET EQUILIBRIUM where INVESTMENT=SAVINGS>0: PART 1 OF THE ARGUMENT: Can it be that and that, at the same time the credit market is in equilibrium? No: in this case no firm wants to invest and I<S. Given the expected rental cost of capital, firms find it cheaper to rent some of this existing capital rather than invest in new one. Hence, the savings of HH are greater than the investment (which is 0). This situation will be eliminated by a fall in the real interest rate. (E22)

9. BGSE/UPF Macroeconomics Slide SET 2Slide 9 PART 2 OF THE ARGUMENT: Can it be that and that, at the same time the credit market is in equilibrium? No: in this case firms want infinite investment because they can earn a profit by buying capital today and rent it out tomorrow. Hence, the desired investment by firms will be greater than the desired savings by firms, I>S. Hence, for the credit market to be in equilibrium firms must be indifferent by buying today and expecting to rent next period

10. BGSE/UPF Macroeconomics Slide SET 2Slide 10 Because the expected rental price of capital next period is equal to the expected equilibrium MPK, see the static equilibrium condition, we obtain: -in equilibrium firms invest to the point where the MPK is equal to the real interest rate plus depreciation - the equilibrium real interest rate is equal to the net MPK of the capital a society has accumulate up to time t (E23)

11. BGSE/UPF Macroeconomics Slide SET 2Slide 11 3. Summarizing the credit market equilibrium (E25) (E24) The STATIC EQUILIBRIUM CONDITIONS, -in the LABOR MARKET and the RENTAL CAPITAL MARKET and -the CREDIT MARKET EQUILIBRIUM CONDITIONS  DYNAMIC GENERAL EQUILIBRIUM

12. BGSE/UPF Macroeconomics Slide SET 2Slide 12 4. The credit market equilibrium and the link between present and future (or the capital accumulation equation in equilibrium) As far as the economics of the Solow model are concerned we are done! -We know how to determine output at a given moment in time given L and K; we also how to obtain factor prices and the real interest rate. - Now we know how to determine tomorrow’s capital stock given today’s capital stock and employment: (E26) Net InvestmentGross Investment Depreciation

13. BGSE/UPF Macroeconomics Slide SET 2Slide 13 Making use of HH SAVINGS behavior in (E19) S(t)=sY(t) (E27) Making use of the fact that aggregate income=aggregate output: (E28) this is the EQUILIBRIUM CAPITAL ACCUMULATION EQUATION

14. BGSE/UPF Macroeconomics Slide SET 2Slide 14 6. THE DYNAMICS OF THE SOLOW MODEL 1. The dynamics of capital accumulation To solve the Solow model completely, we need to specify the evolution over time of some EXOGENOUS factors like EFFICIENCY A and LABOR SUPPLY L We will assume that labor supply grows at (exogenous) rate n : (E30) (E29) (E31)

15. BGSE/UPF Macroeconomics Slide SET 2Slide 15 Similarly, we will assume that exogenous efficiency A we will assume growth at (exogenous) rate a : (E33) (E34) (E32)

16. BGSE/UPF Macroeconomics Slide SET 2Slide 16 SUMMARIZING THE DYNAMIC EQUATIONS OF THE SOLOW MODEL (E36) (E37) Following all 3 (so-called state) variables separately over time is somewhat cumbersome and inconvenient. And WE DO NOT HAVE TO, because as we have seen many things depend on capital per efficiency worker, NOT separately on K, L, and A. (E35)

17. BGSE/UPF Macroeconomics Slide SET 2Slide 17 More convenient to focus on the change over time of CAPITAL PER EFFICIENCY WORKER - determines output per efficiency worker through the production function in efficiency form - getting to the quantities we are interested in is simple (E39) (E40) (E38) WHY?

18. BGSE/UPF Macroeconomics Slide SET 2Slide 18 From TIME CHANGES OF K,L,A to TIME CHANGES in capital per efficiency worker (E41)

19. BGSE/UPF Macroeconomics Slide SET 2Slide 19 (E42) (E43) (E44) Using the equilibrium capital accumulation equation (E28):

20. BGSE/UPF Macroeconomics Slide SET 2Slide 20 This equation gives us the change in as a function of the present Therefore, given a starting point, it allows to study the whole time path of SO NOW WE ARE DONE WITH THE “MECHANICAL” DYNAMIC ASPECTS OF THE SOLOW MODEL TOO. Now is the time to remember: What is it we want to know about?

21. BGSE/UPF Macroeconomics Slide SET 2Slide 21 What we want to know: “INTERMEDIATE” QUESTIONS - Will capital per efficiency worker INCREASE or FALL over time? - Will capital per efficiency worker GROW FOREVER? - Will the GROWTH RATE of capital per efficiency worker INCREASE or DECREASE in time? “FINAL” QUESTIONS - What does this imply for INCOME, WAGES, and INTEREST RATES. The questions are most easily approached graphically.

22. BGSE/UPF Macroeconomics Slide SET 2Slide 22 FIGURE 8a Following capital per efficiency worker in time: THE PRODUCTION FUNCTION 0

23. BGSE/UPF Macroeconomics Slide SET 2Slide 23 FIGURE 8b Following capital per efficiency worker in time: SAVINGS AND THEREFORE INVESTMENT 0

24. BGSE/UPF Macroeconomics Slide SET 2Slide 24 FIGURE 8c Following capital per efficiency worker in time: THE EFFECTIVE DEPRECIATION LINE 0

25. BGSE/UPF Macroeconomics Slide SET 2Slide 25 FIGURE 8d Following capital per efficiency worker in time: CAPITAL GROWTH 0

26. BGSE/UPF Macroeconomics Slide SET 2Slide 26 FIGURE 8e Following capital per efficiency worker in time: THE CAPITAL GROWTH ZONE 0

27. BGSE/UPF Macroeconomics Slide SET 2Slide 27 FIGURE 8f Following capital per efficiency worker in time: FALLING CAPITAL ZONE 0

28. BGSE/UPF Macroeconomics Slide SET 2Slide 28 FIGURE 8g Following capital per efficiency worker in time 0

29. BGSE/UPF Macroeconomics Slide SET 2Slide 29 Some important terminology - BALANCED GROWTH PATH (also called STEADY STATE sometimes) An equilibrium where all variables grow at constant rates (this growth rate can be 0) - GLOBALLY STABLE BGP A BGP is globally stable if the economy ends up in the BGP in the long run NO MATTER WHERE THE ECONOMY STARTS. - CONVERGENCE A somewhat fuzzy concept. Many people seem to say that there is convergence if the growth rate of income per capital decreases as the country grows richer.

30. BGSE/UPF Macroeconomics Slide SET 2Slide 30 The growth rate of capital per efficiency worker over time (E46) (E45)

31. BGSE/UPF Macroeconomics Slide SET 2Slide 31 MPK 0

32. BGSE/UPF Macroeconomics Slide SET 2Slide 32 0

33. BGSE/UPF Macroeconomics Slide SET 2Slide 33 APK= AVERAGE PRODUCT OF CAPITAL 0

34. BGSE/UPF Macroeconomics Slide SET 2Slide 34 APK 0

35. BGSE/UPF Macroeconomics Slide SET 2Slide 35 The growth rate of capital per efficiency worker over time (E46)

36. BGSE/UPF Macroeconomics Slide SET 2Slide 36 0

37. BGSE/UPF Macroeconomics Slide SET 2Slide 37 0

38. BGSE/UPF Macroeconomics Slide SET 2Slide 38 0

39. BGSE/UPF Macroeconomics Slide SET 2Slide 39 0

40. BGSE/UPF Macroeconomics Slide SET 2Slide 40 0

41. BGSE/UPF Macroeconomics Slide SET 2Slide 41 - Result 1: Over time capital per efficiency worker tends to its balanced growth path value, which we have denoted by (as long as the initial capital stock is strictly positive) - hence, the economy will end up at the same level of capital per efficiency worker, no matter what the initial values for A,K,L - Result 2: The closer capital per efficiency worker to its BGP value, the lower its growth rate - in the absence of SHOCKS to preferences or technology, the GROWTH RATE of capital per efficiency workers is therefore falling over time Result 3: In the balanced growth path, growth of capital per efficiency worker is ZERO We have therefore shown the three following results:

42. BGSE/UPF Macroeconomics Slide SET 2Slide 42 Time t FIGURE 11 RESULT 1: over time capital per efficiency worker tends to its balanced growth path value 0

43. BGSE/UPF Macroeconomics Slide SET 2Slide 43 Time t FIGURE 12 RESULT 2 and 3: the closer capital per efficiency worker to its BGP value, the lower its growth rate; in the long-run the growth rate is ZERO 0

44. BGSE/UPF Macroeconomics Slide SET 2Slide 44 2. From capital accumulation to growth of output per worker The easiest way to make the link is to assume the production function takes the so-called Cobb-Douglas form (E47) where is the elasticity of output with respect to capital: or (E48)

45. BGSE/UPF Macroeconomics Slide SET 2Slide 45 The Cobb-Douglas production function in efficiency unit form is (E49) or (E50) hence is also the elasticity of output per efficiency worker with respect to capital per efficiency worker.

46. BGSE/UPF Macroeconomics Slide SET 2Slide 46 Growth in output per worker - ouput per worker is output per efficiency worker times efficiency (E51) - differentiating therefore yields (E51)

47. BGSE/UPF Macroeconomics Slide SET 2Slide 47 Time t FIGURE 13 Evolution of output per worker (on LN scale) 0

48. BGSE/UPF Macroeconomics Slide SET 2Slide 48 Time t a FIGURE 14: growth of output per worker 0

49. BGSE/UPF Macroeconomics Slide SET 2Slide 49 3. Real wage growth and changes in the real interest rate Again, the easiest case is to assume the production function takes the so-called Cobb-Douglas form - the real wage is (E53) (E54)  the real wage is simply A CONSTANT FRACTION of income per capita and real wage growth is EQUAL TO output per worker growth

50. BGSE/UPF Macroeconomics Slide SET 2Slide 50 Time t FIGURE 15a Evolution of REAL WAGE (on LN scale) 0

51. BGSE/UPF Macroeconomics Slide SET 2Slide 51 - the real interest rate is the net marginal product of capital (E55) hence (E56) the real interest rate FALLS as capital per efficiency worker increases NEGATIVE NUMBER!

52. BGSE/UPF Macroeconomics Slide SET 2Slide 52 Time t FIGURE 15b real interest rate over time 0

53. BGSE/UPF Macroeconomics Slide SET 2Slide 53 7. THE EFFECTS OF AN INCREASE IN SAVINGS ON INCOME 1. Growth in the long run (in the balanced growth path) After having analyzed the DYNAMICS of growth for all moments in time we will now focus on the long-run, i.e. the balanced growth path - we already have shown that (E57) and therefore (E58)

54. BGSE/UPF Macroeconomics Slide SET 2Slide 54 Result: The long-run growth rate output per worker of a country is determined by the GROWTH RATE OF LABOR EFFICIENCY ONLY. - In particular, the long-run growth rate of output per worker does NOT depend on the SAVINGS RATE at all. - This is because of DECREASING RETURNS TO CAPITAL IN PRODUCTION. Recall that (E59) Because of decreasing returns to capital, SAVINGS per efficiency worker rises less than proportionally with capital. But BREAK-EVEN INVESTMENT rises proportionally. So they will be eventually equal NO MATTER what the SAVINGS RATE may be. At that point growth in income per capita is equal to growth in labor-efficiency.

55. BGSE/UPF Macroeconomics Slide SET 2Slide 55 2. Output per worker in the long run (in the balanced growth path) The savings rate does, however, affect the LEVEL OF OUTPUT PER WORKER - having a simple expression for output per worker in the BGP is easiest with a Cobb-Douglas production function - note that in the BGP: (E60) (E61)

56. BGSE/UPF Macroeconomics Slide SET 2Slide 56 - the Cobb-Douglas production function in intensive forms is which yields: (E62) solving for the BGP amount of capital per efficiency worker: (E63) the amount of capital per worker can be obtained by multiplying by efficiency A (E64)

57. BGSE/UPF Macroeconomics Slide SET 2Slide 57 - substituting in the production function yields output per efficiency worker and output per worker (E65) (E66)

58. BGSE/UPF Macroeconomics Slide SET 2Slide 58 Hence, if efficiency growth is constant in time, as assumed, we get that income per capita growth in the BGP is constant in time. We also get that the CAPITAL-OUTPUT (k/y) ratio is constant in time. A constant capital-output ratio and steady growth of income per capita is often seen to describe the U.S. well, especially for a longer time period. (Solow developed his model thinking of the U.S. economy.)

59. BGSE/UPF Macroeconomics Slide SET 2Slide 59 JONES Slide1: US IN BGP?

60. BGSE/UPF Macroeconomics Slide SET 2Slide 60 LOW SAVINGSHIGH SAVINGS FIGURE 16 Effect of SAVINGS RATE on capital per efficiency worker 0

61. BGSE/UPF Macroeconomics Slide SET 2Slide 61 Time t a INCREASE IN SAVINGS RATE FIGURE 17 Effect of SAVINGS RATE INCREASE on growth (starting from BGP) 0

62. BGSE/UPF Macroeconomics Slide SET 2Slide 62 Time t a INCREASE IN SAVINGS RATE 0

63. BGSE/UPF Macroeconomics Slide SET 2Slide 63 8. QUANTITATIVE IMPLICATIONS OF THE SOLOW MODEL 1. Effect of savings on long run income We have seen that the effect of the savings rate on long run output per worker can be obtained very easily when the production function is Cobb-Douglas (E67) -- the PERCENTAGE INCREASE in long-run income that comes from a ONE- PERCENT INCREASE in the savings rate is the (E68)

64. BGSE/UPF Macroeconomics Slide SET 2Slide 64 - the greater the elasticity of output with respect to capital, the greater the effect of savings on long run income -- HOW LARGE IS THIS ELASTICITY? It turns out that under the assumption of the Solow model there is a simple way to estimate - the definition of is: - equilibrium in the capital market implies that - hence - constant returns to scale implies that all income is paid to capital or labor; therefore (E69)

65. BGSE/UPF Macroeconomics Slide SET 2Slide 65 - the LABOR INCOME SHARE in industrialized countries is around 1/3: (E70) -- hence, increasing the savings rate by 1% raises long-run income per capita by only 0.5% under the assumptions of the Solow model -- HOW MUCH CAN DIFFERENCES IN SAVINGS RATE OF CAPITAL EXPLAIN? (E71)

66. BGSE/UPF Macroeconomics Slide SET 2Slide 66 - take two countries that are identical in everything but SAVINGS/INVESTMENT rates -denote their savings rates by s1 and s2 respectively; what is then the difference in long-run incomes between the two countries? (E72) (E73) - rather small given the enormous differences in savings rates  differences in savings rates alone cannot explain enormous differences in income between rich and poor countries

67. BGSE/UPF Macroeconomics Slide SET 2Slide 67 2. Income per capita versus output per worker The Solow model is about OUTPUT PER WORKER; how do we get from there to OUTPUT PER CAPITA? As L=NUMBER OF WORKER, we get (E74) this can be written further as ((E75))

68. BGSE/UPF Macroeconomics Slide SET 2Slide 68 hence (E76) INCOME or OUTPUT per CAPITA = DEMOGRAPHIC FACTOR X LABOR FORCE PARTICIPATION RATE X (1-UNEMPLOYMENT RATE) X OUTPUT PER WORKER Income or output per capita may therefore be low because of - LOW output per worker - HIGH unemployment among those who do participate - LOW participation of the population in the labor market - HIGH share of children and retired persons

69. BGSE/UPF Macroeconomics Slide SET 2Slide 69 With information on OUTPUT PER HOUR WORKED, we can do even better and decompose output per worker into: (E80) where Hours= total hours worked in the economy Hours/Workers= hours worked per employed person

70. BGSE/UPF Macroeconomics Slide SET 2Slide 70 The next table, from “International comparisons of labor productivity and per capita income” by van Ark and McGuckin, Monthly Labor Review, July 1999 illustrates the effect of the different components for the US, Japan, and the EU (all relative to the OECD average)

71. BGSE/UPF Macroeconomics Slide SET 2Slide 71 USEUJAPAN OUTPUT PER HOUR 12010382 OUTPUT PER WORKER 1189892 OUTPUT PER PERSON IN LABOR FORCE 1219496 OUTPUT PER WORKING-AGE PERSON (age 15-64) 13090102 OUTPUT PER PERSON 12890106 TABLE 1 FIGURES ARE RELATIVE TO OECD AVERAGE, data refer to 1997 Hence factors other than output per hour play an important role in explaining differences in income per capita between these rich countries/regions.

72. BGSE/UPF Macroeconomics Slide SET 2Slide 72 FIGURE 18 But the main explanation for differences in INCOME PER CAPITA are differences in OUTPUT PER WORKER (country or region relative to US)

73. BGSE/UPF Macroeconomics Slide SET 2Slide 73 9. EMPIRICAL APPLICATIONS 1. Growth accounting The aggregate production function makes clear that GROWTH in OUTPUT can be written in terms of GROWTH in INPUTS plus GROWTH OF EFFICIENCY (E81) The EFFICIENCY FACTOR multiplying all inputs is called TOTAL FACTOR PRODUCTIVITY (TFP) (E82)

74. BGSE/UPF Macroeconomics Slide SET 2Slide 74 (E83) Re-arranging allows us to see how TFP growth can be estimated: (E84) - OUTPUT (Y), CAPITAL (K), and EMPLOYMENT (L) are easy to estimate for many countries

75. BGSE/UPF Macroeconomics Slide SET 2Slide 75 - but to calculate TFP growth we ALSO need to know the ELASTICITY OF OUTPUT TO CAPITAL AND TO LABOR - we know that, in equilibrium, the MARGINAL PRODUCT of a factor is equal to the PRICE OF THAT FACTOR and therefore (E85) (E86) - data on these INCOME SHARE is available for many countries

76. BGSE/UPF Macroeconomics Slide SET 2Slide 76 TFP growth and the SOLOW RESIDUAL We can therefore estimate TFP growth as (E87) under CONSTANT RETURNS TO SCALE, K_SHARE+L_SHARE=1 and (E88)

77. BGSE/UPF Macroeconomics Slide SET 2Slide 77 AVERAGE ANNUAL GROWTH (OVER 1960- 1990 PERIOD) GDPCAPITAL STOCK EMPLOYMENTSHARE OF LABOR IN INCOME TECHNOLISTAN8%10%4%0.5 SAVISTAN8%12%4%0.5 TABLE 2 macroeconomic growth data for 2 countries - note that in both countries output per worker was growing at 8%-4%=4% Suppose that based on this figures you are asked to make best possible forecast of LONG-RUN INCOME PER WORKER GROWTH in SAVISTAN relative to TECHNOLISTAN

78. BGSE/UPF Macroeconomics Slide SET 2Slide 78 TABLE 3 ANNUAL CONTRIBUTION OF ANNUAL GDP GROWTH CAPITAL STOCK EMPLOYMENTTFP TECHNOLISTAN8%5%2%1% SAVISTAN8%6%2%0% What implications for long-run growth does this TFP growth difference have according to the SOLOW MODEL? (E89)

79. BGSE/UPF Macroeconomics Slide SET 2Slide 79 (E90) (E91) (E92)

80. BGSE/UPF Macroeconomics Slide SET 2Slide 80 TABLE 4 LONG-RUN OUTPUT PER WORKER FORECAST ANNUAL CONTRIBUTION OF ANNUAL TFP GROWTH SHARE OF LABOR IN INCOME LONG-RUN OUTPUT PER WORKER FORECAST TECHNOLISTA N 1%0.52% SAVISTAN0%0.50% - one would expect TECHNOLISTAN to grow faster because it has proven capable to improve efficiency (adopt or invent better technologies) - SAVISTAN has been growing by brute force--they were savings a lot and therefore accumulating capital rapidly; the SOLOW model says that this cannot lead to growth in the long run because of decreasing returns to capital

81. BGSE/UPF Macroeconomics Slide SET 2Slide 81 1. Output and TFP growth of the Asian “Tigers” The Asian “Tigers”, South Korea, Taiwan, Hong Kong, and Singapore have had very rapid growth of OUTPUT and OUTPUT PER CAPITA What are the PROXIMATE CAUSES of that?: - increases in labor force participation - capital accumulation - TFP IMPORTANT TO KNOW because increases in participation and capital intensity CANNOT FUEL GROWTH FOREVER. Alwyn Young has analyzed this issue in “The Tyranny of Numbers: Confronting the Statistical Realities of the East-Asian Growth Experience” Quarterly Journal of Economics, 1995

82. BGSE/UPF Macroeconomics Slide SET 2Slide 82 Young estimates:  GROWTH ON INPUTS, OFTEN WEIGHTED BY “QUALITY”  TFP GROWTH

83. BGSE/UPF Macroeconomics Slide SET 2Slide 83 YOUNG SLIDE 1: growth of income and output all 4 countries

84. BGSE/UPF Macroeconomics Slide SET 2Slide 84 YOUNG SLIDE 2: TFP growth HK

85. BGSE/UPF Macroeconomics Slide SET 2Slide 85 YOUNG SLIDE 3: TFP growth SINGAPORE

86. BGSE/UPF Macroeconomics Slide SET 2Slide 86 YOUNG SLIDE 4: TFP growth in other countries

87. BGSE/UPF Macroeconomics Slide SET 2Slide 87 2. US versus EU growth: when did the EU stop to catch up (and why)? The US has higher levels of output per worker than the EU, but the EU has been CATCHING UP for most over the post World-War II period. This process of CATCHING-UP has stopped in the late 1990s Has the EU stopped catching up because of: - TFP growth? - CAPITAL ACCUMULATION? Robert Gordon from Northwestern University and co-authors have researched this in much detail; they argue that the process stopped because of both TFP and capital growth and that new INFORMATION and COMMUNICATION TECHNOLOGIES (ICT) played a role

88. BGSE/UPF Macroeconomics Slide SET 2Slide 88 GORDON SLIDE 1 catch up of GDP per worker stops in 1998

89. BGSE/UPF Macroeconomics Slide SET 2Slide 89 GORDON SLIDE 2 catch up TFP also stops in 1998

90. BGSE/UPF Macroeconomics Slide SET 2Slide 90 GORDON SLIDE 3 catch up capital intensity also stops in 1998

91. BGSE/UPF Macroeconomics Slide SET 2Slide 91 2. Productivity level accounting It is also interesting to ask how much of the difference in the LEVEL of OUTPUT PER WORKER (AVERAGE LABOR PRODUCTIVITY) are driven by: - CAPITAL (physical and human) - TFP This can be done working with the Cobb-Douglas production function or implies that we can estimate the level of TFP as

92. BGSE/UPF Macroeconomics Slide SET 2Slide 92 Labour Productivity gaps (Output per hour, Market economy 2001) USUKGERFR

93. BGSE/UPF Macroeconomics Slide SET 2Slide 93 Explanations for labour productivity gaps Capital per hour, market economy US UK GER FR

94. BGSE/UPF Macroeconomics Slide SET 2Slide 94 Table 5 For US, UK, FRANCE, and GERMANY we get OUTPUT per HOUR CAPITAL per HOUR USBENCHMARK FRANCE& GERMANY Minus 20% approximately Similar to US UKMinus 30-35% approximately Minus 30% approximately

95. BGSE/UPF Macroeconomics Slide SET 2Slide 95 Hence: US versus France & Germany - the productivity gap between US on one hand and France and Germany on the other CANNOT be explained by PHYSICAL CAPITAL - biggest part of the gap is due to TFP UK - appears to be behind in TFP and PHYSICAL CAPITAL relative to both US and France and Germany

96. BGSE/UPF Macroeconomics Slide SET 2Slide 96 3. Convergence 1. Definition and mechanisms Convergence: - When poorer countries grow faster than rich countries. Mechanisms: - Higher average and marginal productivity of capital in poor countries (the flip side of decreasing returns to capital) - Technological convergence

97. BGSE/UPF Macroeconomics Slide SET 2Slide 97 2. Was there convergence among today’s rich countries? Many of today’s rich countries have data on output per person going back to the 19th century. This allows us to ask: Did those that started poorer grow faster since the 19th century? For the period 1870-1980, this is the question asked by Baumol “Productivity, Convergence, and Welfare” American Economic Review, 1986

98. BGSE/UPF Macroeconomics Slide SET 2Slide 98 Baumol Slide1: Convergence among ex-post rich

99. BGSE/UPF Macroeconomics Slide SET 2Slide 99 The figure suggests a clear pattern of convergence among today’s rich countries. BUT there are problems with this approach: Problem 1: The sample we have are only countries that eventually became rich. Maybe there were some countries that were as rich as, say, Finland, in the 19th century, but then did poorly. These countries would then BREAK the pattern of convergence of the figure. What countries would that be? -Chile -Argentina -Portugal -… DeLong considers a sample consisting of the richest countries in the 19th century (not today) and follows them over the same time period. DeLong “Have Productivity Levels Convergence?” American Economic Review, 1988.

100. BGSE/UPF Macroeconomics Slide SET 2Slide 100

101. BGSE/UPF Macroeconomics Slide SET 2Slide 101 Problem 2: Related to data quality. If the data for the 19th century is worse than that of today, we may conclude based on this data that there is convergence when in reality there is none. Imagine: - In 1870: all countries really have income the same income, equal to y(1870) - In 1980: all countries have STILL the same income Now imagine that the data we have is wrong and underestimates 1870 income for some countries and overestimates it for others. I.e. there is measurement error. Then we get the following figure.

102. BGSE/UPF Macroeconomics Slide SET 2Slide 102 Time t y* 1870 1980 Figure 19: Measurement error and (fictitious) convergence

103. BGSE/UPF Macroeconomics Slide SET 2Slide 103 DeLong argues that if this measurement problem is taken into account than the pattern of growth 1870-1980 actually indicates DIVERGENCE among rich countries in the 19th century. Probably not too surprising because: - the forces of convergence are most likely stronger in market economies, i.e. economies with economic freedom and protected property rights - many economies did not conform to this pattern over long periods of time because of communisms, expropriatory dictatorships etc.

104. BGSE/UPF Macroeconomics Slide SET 2Slide 104 3. Convergence among regions We can also look at the pattern of convergence across regions of one country. The following two figures are about long-term income convergence and output convergence across the STATES of the UNITED STATES. This question is analyzed in Barro and Sala-i-Martin “Convergence” Journal of Political Economy, 1990.

105. BGSE/UPF Macroeconomics Slide SET 2Slide 105

106. BGSE/UPF Macroeconomics Slide SET 2Slide 106

107. BGSE/UPF Macroeconomics Slide SET 2Slide 107 Advantages and disadvantages of looking for convergence across regions Advantages: Regions in the same country tend to share the same political framework. Differences in income are therefore more likely to be driven by economics. Disadvantages: Income of a region is closely related to what the region specializes in (agriculture?, gold mining?, car manufacturing?, financial services?) and to the process of migration of city-formation (urbanization). Growth theory has little to say about all that.

108. BGSE/UPF Macroeconomics Slide SET 2Slide 108 4. Convergence world-wide after World War II What if we look at the relation between output growth and initial output per worker for as broad a sample as possible in the post WWII period? As has been documented by many economists, we get no indication of convergence. Rich countries may on average even have been growing faster than poor countries.

109. BGSE/UPF Macroeconomics Slide SET 2Slide 109

110. BGSE/UPF Macroeconomics Slide SET 2Slide 110 Or for the 1965-1985 period:

111. BGSE/UPF Macroeconomics Slide SET 2Slide 111 It looks like poor countries have been falling behind in output per worker But does this prove the absence of the two convergence mechanisms: - decreasing returns to capital? - technological convergence? Not necessarily, because BAD ECONOMIC POLICIES in many poor countries have hindered growth. For example: not protecting even most basic human and economic rights not investing in critical factors like infrastructure (roads, electricity etc.) and human capital (primary and secondary education)

112. BGSE/UPF Macroeconomics Slide SET 2Slide 112 1. Cross-country convergence in the Solow model CASE 1: -- poor country: poor only because SCARCE CAPITAL: LOW K(0)/L(0) -- rich country: rich only because ABUNDANT CAPITAL: HIGH K(0)/L(0) in all other dimensions the two countries are identical (s, ,n,a,A(t))

113. BGSE/UPF Macroeconomics Slide SET 2Slide 113 rich kpoor k

114. BGSE/UPF Macroeconomics Slide SET 2Slide 114 CASE 2: -- poor country: poor because SCARCE CAPITAL and LOW SAVINGS RATE -- rich country: rich because ABUNDANT CAPITAL and high SAVINGS RATE

115. BGSE/UPF Macroeconomics Slide SET 2Slide 115 poor k(0) rich k(0)

116. BGSE/UPF Macroeconomics Slide SET 2Slide 116 2. Conditional convergence The basic idea is that there is CONDITIONAL CONVERGENCE if  poorer countries would have grown faster than richer countries had they adopted the same “ECONOMIC POLICIES”.

117. BGSE/UPF Macroeconomics Slide SET 2Slide 117 How could we check in practice? By running a regression. For example, estimate the parameters a, b, c below GROWTH “EXPLAINED” BY “POLICIES” GROWTH “EXPLAINED” BY “CONDITIONAL CONVERGENCE” This is done in Barro “Economic Growth in a Cross-Section of Countries”, Quarterly Journal of Economics 1989.

118. BGSE/UPF Macroeconomics Slide SET 2Slide 118 Growth 1960-1985 assuming same schooling and political stability in all countries Income in 1960

119. BGSE/UPF Macroeconomics Slide SET 2Slide 119 Approach makes sense but also has problems. Because ECONOMIC POLICIES are not exogenous and maybe at least in part due to low initial incomes. For example: - The approach says that low growth in poor countries may be due to low investment in schooling. But maybe low investment in schooling is a consequence (not cause) of the poverty of countries. - The approach says that low growth in poor countries may be due to political instability. But maybe political instability is a consequence (not cause) of the poverty of countries. - Etc.

120. BGSE/UPF Macroeconomics Slide SET 2Slide 120 5. Forecasting growth of the BRICS 1. The who? - Brazil, Russia, India, and China - Large countries that are still quite poor but have shown periods of rapid growth in recent times - Could soon represent a huge part of world GDP, leading to important changes in international politics and economics (which is why Goldman Sachs is interested in forecasting their future growth)

121. BGSE/UPF Macroeconomics Slide SET 2Slide 121 2. Forecasts Let us consider the Goldman-Sachs forecast of when total GDP in these countries will overtake the GDP of Germany.

122. BGSE/UPF Macroeconomics Slide SET 2Slide 122

123. BGSE/UPF Macroeconomics Slide SET 2Slide 123

124. BGSE/UPF Macroeconomics Slide SET 2Slide 124 As you know there are many things that must analyzed to get a forecast of total GDP. Among them: - working-age population and labor-force participation - output per worker ….

125. BGSE/UPF Macroeconomics Slide SET 2Slide 125

126. BGSE/UPF Macroeconomics Slide SET 2Slide 126

127. BGSE/UPF Macroeconomics Slide SET 2Slide 127 Avoid that by building in a process of convergence (or growth slowdown): This can be done by building the forecasts of growth in these countries around the Solow model.

128. BGSE/UPF Macroeconomics Slide SET 2Slide 128

129. BGSE/UPF Macroeconomics Slide SET 2Slide 129 Can one check the reliability of these forecasts? One approach is to do WITHIN SAMPLE FORECASTING. - Pretend it is 1960. - Use the approach used to forecast GDP of the BRICs to predict growth of countries 1960-2000. - Compare to the realized 1960-2000 growth rates.

130. BGSE/UPF Macroeconomics Slide SET 2Slide 130