1. M ACROECONOMICS C H A P T E R Unemployment 6

2. slide 1 CHAPTER 6 Unemployment In this chapter, you will learn… …about the natural rate of unemployment:  what it means  what causes it  understanding its behavior in the real world

3. slide 2 CHAPTER 6 Unemployment Natural rate of unemployment  Natural rate of unemployment: The average rate of unemployment around which the economy fluctuates.  In a recession, the actual unemployment rate rises above the natural rate.  In a boom, the actual unemployment rate falls below the natural rate.

4. slide 3 CHAPTER 6 Unemployment Actual and natural rates of unemployment in the U.S., 1960-2007 Percent of labor force Unemployment rate Natural rate of unemployment 0 2 4 6 8 10 12 1960196519701975198019851990199520002005

5. slide 4 CHAPTER 6 Unemployment A first model of the natural rate REMEMBER? L = # of workers in labor force E = # of employed workers U = # of unemployed U/L = unemployment rate

6. slide 5 CHAPTER 6 Unemployment Assumptions: 1.L is exogenously fixed. 2.During any given month, s = fraction of employed workers that become separated from their jobs s is called the rate of job separations f = fraction of unemployed workers that find jobs f is called the rate of job finding s and f are exogenous

7. slide 6 CHAPTER 6 Unemployment The transitions between employment and unemployment Employed Unemployed s  E f  U

8. slide 7 CHAPTER 6 Unemployment The steady state condition  Definition: the labor market is in steady state, or long-run equilibrium, if the unemployment rate is constant.  The steady-state condition is: s  E = f  U # of employed people who lose or leave their jobs # of unemployed people who find jobs

9. slide 8 CHAPTER 6 Unemployment Finding the “equilibrium” U rate f  U = s  E = s  (L – U ) = s  L – s  U Solve for U/L: (f + s)  U = s  L so,

10. slide 9 CHAPTER 6 Unemployment Example:  Each month,  1% of employed workers lose their jobs (s = 0.01)  19% of unemployed workers find jobs (f = 0.19)  Find the natural rate of unemployment:

11. slide 10 CHAPTER 6 Unemployment Policy implication  A policy will reduce the natural rate of unemployment only if it lowers s or increases f.

12. slide 11 CHAPTER 6 Unemployment Why is there unemployment?  If job finding were instantaneous (f = 1), then all spells of unemployment would be brief, and the natural rate would be near zero.  There are two reasons why f < 1: 1. job search 2. wage rigidity

13. slide 12 CHAPTER 6 Unemployment Job search & frictional unemployment  frictional unemployment: caused by the time it takes workers to search for a job  occurs even when wages are flexible and there are enough jobs to go around  occurs because  workers have different abilities, preferences  jobs have different skill requirements  geographic mobility of workers not instantaneous  flow of information about vacancies and job candidates is imperfect

14. slide 13 CHAPTER 6 Unemployment Sectoral shifts  def: Changes in the composition of demand among industries or regions.  example: Technological change more jobs repairing computers, fewer jobs repairing typewriters  example: A new international trade agreement labor demand increases in export sectors, decreases in import-competing sectors  Result: frictional unemployment

15. slide 14 CHAPTER 6 Unemployment CASE STUDY: Structural change over the long run

16. slide 15 CHAPTER 6 Unemployment Unemployment insurance (UI)  UI pays part of a worker’s former wages for a limited time after losing his/her job.  UI increases search unemployment, because it reduces  the opportunity cost of being unemployed  the urgency of finding work  f (job finding rate)  Studies: The longer a worker is eligible for UI, the longer the duration of the average spell of unemployment.

17. slide 16 CHAPTER 6 Unemployment  By allowing workers more time to search, UI may lead to better matches between jobs and workers, which would lead to greater productivity and higher incomes. Benefits of UI

18. slide 17 CHAPTER 6 Unemployment Why is there unemployment?  Two reasons why f < 1: 1. job search 2. wage rigidity DONE Next  The natural rate of unemployment:

19. slide 18 CHAPTER 6 Unemployment Unemployment from real wage rigidity Labor Real wage Supply Demand Unemployment Rigid real wage Amount of labor willing to work Amount of labor hired If real wage is stuck above its eq’m level, then there aren’t enough jobs to go around.

20. slide 19 CHAPTER 6 Unemployment Unemployment from real wage rigidity Then, firms must ration the scarce jobs among workers. Structural unemployment: The unemployment resulting from real wage rigidity and job rationing. If real wage is stuck above its eq’m level, then there aren’t enough jobs to go around.

21. slide 20 CHAPTER 6 Unemployment Reasons for wage rigidity 1. Minimum wage laws 2. Labor unions 3. Efficiency wages

22. slide 21 CHAPTER 6 Unemployment 1. The minimum wage  The min. wage may exceed the eq’m wage of unskilled workers, especially teenagers.  Studies: a 10% increase in min. wage reduces teen unemployment by 1-3%  But, the min. wage cannot explain the majority of the natural rate of unemployment, as most workers’ wages are well above the min. wage.

23. slide 22 CHAPTER 6 Unemployment 2. Labor unions  Unions exercise monopoly power to secure higher wages for their members.  When the union wage exceeds the eq’m wage, unemployment results.  Insiders: Employed union workers whose interest is to keep wages high.  Outsiders: Unemployed non-union workers who prefer eq’m wages, so there would be enough jobs for them.

24. 105,508Private sector (total) 20,381Government (total) 14,045Health care 3,312Education 10,951Professional services 6,304Finance, insurance 4,379Transportation 14,973Retail trade 15,518Manufacturing 600Mining 122.3 121.7 115.1 112.7 90.6 90.7 129.2 114.0 107.8 113.7 156.9 8.5% 40.5 8 15.4 3.1 2.1 24.4 5.8 13.7 9.5 13.8 8,053Construction wage ratio U % of total # employed (1000s) industry wage ratio = 100  (union wage)/(nonunion wage) slide 23 Union membership and wage ratios by industry, 2005

25. slide 24 CHAPTER 6 Unemployment 3. Efficiency wage theory  Theories in which higher wages increase worker productivity by:  attracting higher quality job applicants  increasing worker effort, reducing “shirking”  reducing turnover, which is costly to firms  improving health of workers (in developing countries)  Firms willingly pay above-equilibrium wages to raise productivity.  Result: structural unemployment.

26. slide 25 CHAPTER 6 Unemployment Question for discussion: Use the material we’ve just covered to come up with a policy or policies to try to reduce the natural rate of unemployment. Note whether your policy targets frictional or structural unemployment.

27. slide 26 CHAPTER 6 Unemployment The duration of U.S. unemployment, average over 1/1990-6/2007 # of weeks unemployed # of unemployed persons as % of total # of unemployed amount of time these workers spent unemployed as % of total time all workers spent unemployed 1-438%6.1% 5-1431%18.8% 15 or more31%75.1%

28. slide 27 CHAPTER 6 Unemployment The duration of unemployment  The data:  More spells of unemployment are short-term than medium-term or long-term.  Yet, most of the total time spent unemployed is attributable to the long-term unemployed.  This long-term unemployment is probably structural and/or due to sectoral shifts among vastly different industries.  Knowing this is important because it can help us craft policies that are more likely to work.

29. slide 28 CHAPTER 6 Unemployment TREND: The natural rate rises during 1960-1984, then falls during 1985-2007

30. slide 29 CHAPTER 6 Unemployment EXPLAINING THE TREND: The minimum wage 0 1 2 3 4 5 6 7 8 9 195019551960196519701975198019851990199520002005 Dollars per hour minimum wage in current dollars minimum wage in 2006 dollars The trend in the real minimum wage is similar to that of the natural rate of unemployment.

31. slide 30 CHAPTER 6 Unemployment EXPLAINING THE TREND: Union membership Since the early 1980s, the natural rate of unemploy- ment and union membership have both fallen. But, from 1950s to about 1980, the natural rate rose while union membership fell. Since the early 1980s, the natural rate of unemploy- ment and union membership have both fallen. But, from 1950s to about 1980, the natural rate rose while union membership fell. Union membership selected years yearpercent of labor force 193012% 194535% 195435% 197027% 198320.1% 200612.0%

32. slide 31 CHAPTER 6 Unemployment EXPLAINING THE TREND: Sectoral shifts Price per barrel of oil, in 2007 dollars From mid 1980s to early 2000s, oil prices less volatile, so fewer sectoral shifts.

33. slide 32 CHAPTER 6 Unemployment EXPLAINING THE TREND: Demographics  1970s: The Baby Boomers were young. Young workers change jobs more frequently (high value of s).  Late 1980s through today: Baby Boomers aged. Middle-aged workers change jobs less often (low s).

34. Unemployment in Europe, 1960-2006 slide 33 Percent of labor force Italy Germany France U.K. 0 3 6 9 12 1960196519701975198019851990199520002005

35. slide 34 CHAPTER 6 Unemployment The rise in European unemployment  Shock Technological progress has shifted labor demand from unskilled to skilled workers in recent decades.  Effect in United States An increase in the “skill premium” – the wage gap between skilled and unskilled workers.  Effect in Europe Higher unemployment, due to generous govt benefits for unemployed workers and strong union presence.

36. slide 35 CHAPTER 6 Unemployment Percent of workers covered by collective bargaining United States18% United Kingdom47 Switzerland53 Spain68 Sweden83 Germany90 France92 Austria98

37. Chapter Summary 1. The natural rate of unemployment  the long-run average or “steady state” rate of unemployment  depends on the rates of job separation and job finding 2. Frictional unemployment  due to the time it takes to match workers with jobs  may be increased by unemployment insurance CHAPTER 6 Unemployment slide 36

38. Chapter Summary 3. Structural unemployment  results from wage rigidity: the real wage remains above the equilibrium level  caused by: minimum wage, unions, efficiency wages 4. Duration of unemployment  most spells are short term  but most weeks of unemployment are attributable to a small number of long-term unemployed persons CHAPTER 6 Unemployment slide 37

39. Chapter Summary 5. Behavior of the natural rate in the U.S.  rose from 1960 to early 1980s, then fell  possible explanations: trends in real minimum wage, union membership, prevalence of sectoral shifts, and aging of the Baby Boomers CHAPTER 6 Unemployment slide 38

40. Chapter Summary 6. European unemployment  has risen sharply since 1970  probably due to generous unemployment benefits, strong union presence, and a technology-driven shift in demand away from unskilled workers CHAPTER 6 Unemployment slide 39

41. M ACROECONOMICS C H A P T E R Economic Growth I: Capital Accumulation and Population Growth 7

42. slide 41 CHAPTER 6 Unemployment In this chapter, you will learn…  the closed economy Solow model  how a country’s standard of living depends on its saving and population growth rates  how to use the “Golden Rule” to find the optimal saving rate and capital stock

43. slide 42 CHAPTER 6 Unemployment Why growth matters  Data on infant mortality rates:  20% in the poorest 1/5 of all countries  0.4% in the richest 1/5  In Pakistan, 85% of people live on less than $2/day.  One-fourth of the poorest countries have had famines during the past 3 decades.  Poverty is associated with oppression of women and minorities. Economic growth raises living standards and reduces poverty….

44. slide 43 CHAPTER 6 Unemployment Income and poverty in the world selected countries, 2000

45. slide 44 CHAPTER 6 Unemployment Why growth matters  Anything that effects the long-run rate of economic growth – even by a tiny amount – will have huge effects on living standards in the long run. 1,081.4%243.7%85.4% 624.5% 169.2% 64.0% 2.5% 2.0% …100 years …50 years …25 years percentage increase in standard of living after… annual growth rate of income per capita

46. slide 45 CHAPTER 6 Unemployment Why growth matters  If the annual growth rate of U.S. real GDP per capita had been just one-tenth of one percent higher during the 1990s, the U.S. would have generated an additional $496 billion of income during that decade.

47. slide 46 CHAPTER 6 Unemployment The Solow model  due to Robert Solow, won Nobel Prize for contributions to the study of economic growth  a major paradigm:  widely used in policy making  benchmark against which most recent growth theories are compared  looks at the determinants of economic growth and the standard of living in the long run

48. slide 47 CHAPTER 6 Unemployment How Solow model is different from Chapter 3’s model 1. K is no longer fixed: investment causes it to grow, depreciation causes it to shrink 2. L is no longer fixed: population growth causes it to grow 3. the consumption function is simpler

49. slide 48 CHAPTER 6 Unemployment How Solow model is different from Chapter 3’s model 4. no G or T (only to simplify presentation; we can still do fiscal policy experiments) 5. cosmetic differences

50. slide 49 CHAPTER 6 Unemployment The production function  In aggregate terms: Y = F (K, L)  Define: y = Y/L = output per worker k = K/L = capital per worker  Assume constant returns to scale: zY = F (zK, zL ) for any z > 0  Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y = f(k)where f(k) = F(k, 1) (think of this as a per worker production function)

51. slide 50 CHAPTER 6 Unemployment The production function Output per worker, y Capital per worker, k f(k) Note: this production function exhibits diminishing MPK. 1 MPK = f(k +1) – f(k)

52. slide 51 CHAPTER 6 Unemployment The national income identity  Y = C + I (remember, no G )  In “per worker” terms: y = c + i where c = C/L and i = I /L

53. slide 52 CHAPTER 6 Unemployment The consumption function  s = the saving rate, the fraction of income that is saved (s is an exogenous parameter) Note: s is the only lowercase variable that is not equal to its uppercase version divided by L  Consumption function: c = (1–s)y (per worker)

54. slide 53 CHAPTER 6 Unemployment Saving and investment  saving (per worker) = y – c = y – (1–s)y = sy  National income identity is y = c + i Rearrange to get: i = y – c = sy (investment = saving, like in chap. 3!)  Using the results above, i = sy = sf(k)

55. slide 54 CHAPTER 6 Unemployment Output, consumption, and investment Output per worker, y Capital per worker, k f(k) sf(k) k1k1 y1y1 i1i1 c1c1

56. slide 55 CHAPTER 6 Unemployment Depreciation Depreciation per worker,  k Capital per worker, k kk  = the rate of depreciation = the fraction of the capital stock that wears out each period  = the rate of depreciation = the fraction of the capital stock that wears out each period 1 

57. slide 56 CHAPTER 6 Unemployment Capital accumulation Change in capital stock= investment – depreciation  k = i –  k Since i = sf(k), this becomes:  k = s f(k) –  k The basic idea: Investment increases the capital stock, depreciation reduces it.

58. slide 57 CHAPTER 6 Unemployment The equation of motion for k  The Solow model’s central equation  Determines behavior of capital over time…  …which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g., income per person: y = f(k) consumption per person: c = (1–s) f(k)  k = s f(k) –  k

59. slide 58 CHAPTER 6 Unemployment The steady state If investment is just enough to cover depreciation [sf(k) =  k ], then capital per worker will remain constant:  k = 0. This occurs at one value of k, denoted k *, called the steady state capital stock.  k = s f(k) –  k

60. slide 59 CHAPTER 6 Unemployment The steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*

61. slide 60 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*  k = sf(k)   k depreciation kk k1k1 investment

62. slide 61 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k* k1k1  k = sf(k)   k kk

63. slide 62 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k* k1k1  k = sf(k)   k kk k2k2

64. slide 63 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*  k = sf(k)   k k2k2 investment depreciation kk

65. slide 64 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*  k = sf(k)   k kk k2k2

66. slide 65 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*  k = sf(k)   k k2k2 kk k3k3

67. slide 66 CHAPTER 6 Unemployment Moving toward the steady state Investment and depreciation Capital per worker, k sf(k) kk k*k*  k = sf(k)   k k3k3 Summary: As long as k < k *, investment will exceed depreciation, and k will continue to grow toward k *.

68. slide 67 CHAPTER 6 Unemployment A numerical example Production function (aggregate): To derive the per-worker production function, divide through by L: Then substitute y = Y/L and k = K/L to get

69. slide 68 CHAPTER 6 Unemployment A numerical example, cont. Assume:  s = 0.3   = 0.1  initial value of k = 4.0

70. slide 69 CHAPTER 6 Unemployment Approaching the steady state: A numerical example Year k y c i  k  k 14.0002.0001.4000.6000.4000.200 24.2002.0491.4350.6150.4200.195 34.3952.0961.4670.6290.4400.189 Year k y c i  k  k 14.0002.0001.4000.6000.4000.200 24.2002.0491.4350.6150.4200.195 34.3952.0961.4670.6290.4400.189 44.5842.1411.4990.6420.4580.184 … 105.6022.3671.6570.7100.5600.150 … 257.3512.7061.8940.8120.7320.080 … 1008.9622.9942.0960.8980.8960.002 …  9.0003.0002.1000.9000.9000.000

71. slide 70 CHAPTER 6 Unemployment Exercise: Solve for the steady state Continue to assume s = 0.3,  = 0.1, and y = k 1/2 Use the equation of motion  k = s f(k)   k to solve for the steady-state values of k, y, and c.

72. slide 71 CHAPTER 6 Unemployment Solution to exercise:

73. slide 72 CHAPTER 6 Unemployment An increase in the saving rate Investment and depreciation k kk s 1 f(k) An increase in the saving rate raises investment… …causing k to grow toward a new steady state: s 2 f(k)

74. slide 73 CHAPTER 6 Unemployment Prediction:  Higher s  higher k *.  And since y = f(k), higher k *  higher y *.  Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run.

75. slide 74 CHAPTER 6 Unemployment International evidence on investment rates and income per person 100 1,000 10,000 100,000 05101520253035 Investment as percentage of output (average 1960-2000) Income per person in 2000 (log scale)

76. slide 75 CHAPTER 6 Unemployment The Golden Rule: Introduction  Different values of s lead to different steady states. How do we know which is the “best” steady state?  The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*).  An increase in s  leads to higher k* and y*, which raises c*  reduces consumption’s share of income (1–s), which lowers c*.  So, how do we find the s and k* that maximize c*?

77. slide 76 CHAPTER 6 Unemployment The Golden Rule capital stock the Golden Rule level of capital, the steady state value of k that maximizes consumption. To find it, first express c * in terms of k * : c * = y *  i * = f (k * )  i * = f (k * )   k * In the steady state: i * =  k * because  k = 0.

78. slide 77 CHAPTER 6 Unemployment Then, graph f(k * ) and  k *, look for the point where the gap between them is biggest. The Golden Rule capital stock steady state output and depreciation steady-state capital per worker, k * f(k * )  k* k*

79. slide 78 CHAPTER 6 Unemployment The Golden Rule capital stock c * = f(k * )   k * is biggest where the slope of the production function equals the slope of the depreciation line: steady-state capital per worker, k * f(k * )  k* k* MPK = 

80. slide 79 CHAPTER 6 Unemployment The transition to the Golden Rule steady state  The economy does NOT have a tendency to move toward the Golden Rule steady state.  Achieving the Golden Rule requires that policymakers adjust s.  This adjustment leads to a new steady state with higher consumption.  But what happens to consumption during the transition to the Golden Rule?

81. slide 80 CHAPTER 6 Unemployment Starting with too much capital then increasing c * requires a fall in s. In the transition to the Golden Rule, consumption is higher at all points in time. then increasing c * requires a fall in s. In the transition to the Golden Rule, consumption is higher at all points in time. time t0t0 c i y

82. slide 81 CHAPTER 6 Unemployment Starting with too little capital then increasing c * requires an increase in s. Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption. then increasing c * requires an increase in s. Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption. time t0t0 c i y

83. slide 82 CHAPTER 6 Unemployment Population growth  Assume that the population (and labor force) grow at rate n. (n is exogenous.)  EX: Suppose L = 1,000 in year 1 and the population is growing at 2% per year (n = 0.02).  Then  L = n L = 0.02  1,000 = 20, so L = 1,020 in year 2.

84. slide 83 CHAPTER 6 Unemployment Break-even investment  (  + n)k = break-even investment, the amount of investment necessary to keep k constant.  Break-even investment includes:   k to replace capital as it wears out  n k to equip new workers with capital (Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers.)

85. slide 84 CHAPTER 6 Unemployment The equation of motion for k  With population growth, the equation of motion for k is break-even investment actual investment  k = s f(k)  (  + n) k

86. slide 85 CHAPTER 6 Unemployment The Solow model diagram Investment, break-even investment Capital per worker, k sf(k) ( + n ) k( + n ) k k*k*  k = s f(k)  (  +n)k

87. slide 86 CHAPTER 6 Unemployment The impact of population growth Investment, break-even investment Capital per worker, k sf(k) ( +n1) k( +n1) k k1*k1* ( +n2) k( +n2) k k2*k2* An increase in n causes an increase in break- even investment, leading to a lower steady-state level of k.

88. slide 87 CHAPTER 6 Unemployment Prediction:  Higher n  lower k*.  And since y = f(k), lower k*  lower y*.  Thus, the Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run.

89. slide 88 CHAPTER 6 Unemployment International evidence on population growth and income per person 100 1,000 10,000 100,000 012345 Population Growth (percent per year; average 1960-2000) Income per Person in 2000 (log scale)

90. slide 89 CHAPTER 6 Unemployment The Golden Rule with population growth To find the Golden Rule capital stock, express c * in terms of k * : c * = y *  i * = f (k * )  (  + n) k * c * is maximized when MPK =  + n or equivalently, MPK   = n In the Golden Rule steady state, the marginal product of capital net of depreciation equals the population growth rate.

91. slide 90 CHAPTER 6 Unemployment Alternative perspectives on population growth The Malthusian Model (1798)  Predicts population growth will outstrip the Earth’s ability to produce food, leading to the impoverishment of humanity.  Since Malthus, world population has increased sixfold, yet living standards are higher than ever.  Malthus omitted the effects of technological progress.

92. slide 91 CHAPTER 6 Unemployment Alternative perspectives on population growth The Kremerian Model (1993)  Posits that population growth contributes to economic growth.  More people = more geniuses, scientists & engineers, so faster technological progress.  Evidence, from very long historical periods:  As world pop. growth rate increased, so did rate of growth in living standards  Historically, regions with larger populations have enjoyed faster growth.

93. slide 92 CHAPTER 6 Unemployment Chapter Summary 1. The Solow growth model shows that, in the long run, a country’s standard of living depends  positively on its saving rate  negatively on its population growth rate 2. An increase in the saving rate leads to  higher output in the long run  faster growth temporarily  but not faster steady state growth. CHAPTER 7 Economic Growth I slide 92

94. slide 93 CHAPTER 6 Unemployment Chapter Summary 3. If the economy has more capital than the Golden Rule level, then reducing saving will increase consumption at all points in time, making all generations better off. If the economy has less capital than the Golden Rule level, then increasing saving will increase consumption for future generations, but reduce consumption for the present generation. CHAPTER 7 Economic Growth I slide 93