CHAPTER 6 Unemployment MACROECONOMICS 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 CHAPTER 6 Unemployment slide 1 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. CHAPTER 6 Unemployment slide 2 Actual and natural rates of unemployment in the U.S., 1960-2007 Percent of labor force 12 Unemployment rate 10 8 6 4 2 Natural rate of unemployment 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 CHAPTER 6 Unemployment slide 3 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 CHAPTER 6 Unemployment slide 4 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 CHAPTER 6 Unemployment slide 5 The transitions between employment and unemployment s E Employed Unemployed f U CHAPTER 6 Unemployment slide 6 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 CHAPTER 6 Unemployment # of unemployed people who find jobs slide 7 Finding the “equilibrium” U rate f U = sE = s (L – U ) = s L – s U Solve for U/L: (f + s) U = s L so, U L CHAPTER 6 Unemployment s s f slide 8 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: U L CHAPTER 6 s s f 0 .0 1 0 .0 1 0 .1 9 Unemployment 0 . 0 5, o r 5 % slide 9 Policy implication A policy will reduce the natural rate of unemployment only if it lowers s or increases f. CHAPTER 6 Unemployment slide 10 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 CHAPTER 6 Unemployment slide 11 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 CHAPTER 6 Unemployment slide 12 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 CHAPTER 6 Unemployment slide 13 CASE STUDY: Structural change over the long run Agriculture Manufacturing Other industry Services 1960 2000 73.5% 57.9% 4.2% 1.6% 9.9% 28.0% CHAPTER 6 Unemployment 7.7% 17.2% slide 14 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. CHAPTER 6 Unemployment slide 15 Benefits of UI 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. CHAPTER 6 Unemployment slide 16 Why is there unemployment? The natural rate of unemployment: U L s s f Two reasons why f < 1: DONE 1. job search Next 2. wage rigidity CHAPTER 6 Unemployment slide 17 Unemployment from real wage rigidity If real wage is stuck above its eq’m level, then there aren’t enough jobs to go around. Real wage Supply Unemployment Rigid real wage Demand Labor Amount of labor hired CHAPTER 6 Unemployment Amount of labor willing to work slide 18 Unemployment from real wage rigidity If real wage is stuck above its eq’m level, then there aren’t enough jobs to go around. CHAPTER 6 Then, firms must ration the scarce jobs among workers. Structural unemployment: The unemployment resulting from real wage rigidity and job rationing. Unemployment slide 19 Reasons for wage rigidity 1. Minimum wage laws 2. Labor unions 3. Efficiency wages CHAPTER 6 Unemployment slide 20 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. CHAPTER 6 Unemployment slide 21 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. CHAPTER 6 Unemployment slide 22 Union membership and wage ratios by industry, 2005 industry Private sector (total) # employed (1000s) U % of total wage ratio 105,508 8.5% 122.3 20,381 40.5 121.7 8,053 13.8 156.9 600 9.5 113.7 Manufacturing 15,518 13.7 107.8 Retail trade 14,973 5.8 114.0 Transportation 4,379 24.4 129.2 Finance, insurance 6,304 2.1 90.7 10,951 3.1 90.6 3,312 15.4 112.7 14,045 8 115.1 Government (total) Construction Mining Professional services Education Health care wage ratio = 100(union wage)/(nonunion wage) slide 23 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. CHAPTER 6 Unemployment slide 24 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. CHAPTER 6 Unemployment slide 25 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 1-4 38% 6.1% 5-14 31% 18.8% 15 or more 31% 75.1% CHAPTER 6 Unemployment slide 26 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. CHAPTER 6 Unemployment slide 27 TREND: The natural rate rises during 1960-1984, then falls during 1985-2007 9 8 7 6 5 4 3 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 CHAPTER 6 Unemployment slide 28 EXPLAINING THE TREND: The minimum wage 9 The trend in the real minimum wage is similar to that of the natural rate of unemployment. Dollars per hour 8 7 6 5 minimum wage in 2006 dollars 4 3 minimum wage in current dollars 2 1 0 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 CHAPTER 6 Unemployment slide 29 EXPLAINING THE TREND: Union membership Union membership selected years year percent of labor force 1930 12% 1945 35% 1954 35% 1970 27% 1983 20.1% 2006 12.0% CHAPTER 6 Unemployment Since the early 1980s, the natural rate of unemployment and union membership have both fallen. But, from 1950s to about 1980, the natural rate rose while union membership fell. slide 30 EXPLAINING THE TREND: Sectoral shifts From mid 1980s to early 2000s, oil prices less volatile, so fewer sectoral shifts. $100 $80 $60 Price per barrel of oil, in 2007 dollars $40 $20 $0 1970 1975 CHAPTER 6 1980 1985 Unemployment 1990 1995 2000 2005 slide 31 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). CHAPTER 6 Unemployment slide 32 Unemployment in Europe, 1960-2006 France Percent of labor force 12 9 6 Italy 3 U.K. Germany 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 slide 33 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. CHAPTER 6 Unemployment slide 34 Percent of workers covered by collective bargaining CHAPTER 6 United States 18% United Kingdom 47 Switzerland 53 Spain 68 Sweden 83 Germany 90 France 92 Austria 98 Unemployment slide 35 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 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 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 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 CHAPTER 7 Economic Growth I: Capital Accumulation and Population Growth MACROECONOMICS 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 CHAPTER 6 Unemployment slide 41 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…. CHAPTER 6 Unemployment slide 42 Income and poverty in the world selected countries, 2000 100 Madagascar % of population living on $2 per day or less 90 India Nepal Bangladesh 80 70 60 Botswana Kenya 50 China 40 Peru 30 Mexico Thailand 20 Brazil 10 0 $0 CHAPTER 6 Chile Russian Federation $5,000 $10,000 S. Korea $15,000 Income per capita in dollars Unemployment $20,000 slide 43 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. annual growth rate of income per capita …25 years …50 years …100 years 2.0% 64.0% 169.2% 624.5% 2.5% 85.4% 243.7% 1,081.4% CHAPTER 6 percentage increase in standard of living after… Unemployment slide 44 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. CHAPTER 6 Unemployment slide 45 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 CHAPTER 6 Unemployment slide 46 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 CHAPTER 6 Unemployment slide 47 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 CHAPTER 6 Unemployment slide 48 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) CHAPTER 6 Unemployment slide 49 The production function Output per worker, y f(k) MPK = f(k +1) – f(k) 1 Note: this production function exhibits diminishing MPK. Capital per worker, k CHAPTER 6 Unemployment slide 50 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 CHAPTER 6 Unemployment slide 51 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) CHAPTER 6 Unemployment slide 52 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) CHAPTER 6 Unemployment slide 53 Output, consumption, and investment Output per worker, y f(k) c1 sf(k) y1 i1 k1 CHAPTER 6 Unemployment Capital per worker, k slide 54 Depreciation Depreciation per worker, k = the rate of depreciation = the fraction of the capital stock that wears out each period k 1 Capital per worker, k CHAPTER 6 Unemployment slide 55 Capital accumulation The basic idea: Investment increases the capital stock, depreciation reduces it. Change in capital stock k = investment – depreciation = i – k Since i = sf(k) , this becomes: k = s f(k) – k CHAPTER 6 Unemployment slide 56 The equation of motion for k k = s f(k) – 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) CHAPTER 6 Unemployment slide 57 The steady state k = s f(k) – k 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. CHAPTER 6 Unemployment slide 58 The steady state Investment and depreciation k sf(k) k* CHAPTER 6 Unemployment Capital per worker, k slide 59 Moving toward the steady state k = sf(k) k Investment and depreciation k sf(k) k investment depreciation k1 CHAPTER 6 Unemployment k* Capital per worker, k slide 60 Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k k1 k2 CHAPTER 6 Unemployment k* Capital per worker, k slide 62 Moving toward the steady state k = sf(k) k Investment and depreciation k sf(k) k investment depreciation k2 CHAPTER 6 Unemployment k* Capital per worker, k slide 63 Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) k k2 k3 k* CHAPTER 6 Unemployment Capital per worker, k slide 65 Moving toward the steady state Investment and depreciation k = sf(k) k k sf(k) Summary: As long as k < k*, investment will exceed depreciation, and k will continue to grow toward k*. k3 k* CHAPTER 6 Unemployment Capital per worker, k slide 66 A numerical example Production function (aggregate): Y F (K , L ) K L K 1/2 L 1/2 To derive the per-worker production function, divide through by L: Y L K 1/2 L 1/2 L K L 1/2 Then substitute y = Y/L and k = K/L to get y f (k ) k CHAPTER 6 Unemployment 1/2 slide 67 A numerical example, cont. Assume: s = 0.3 = 0.1 initial value of k = 4.0 CHAPTER 6 Unemployment slide 68 Approaching the steady state: A numerical example Year k y c i k 1 4.000 2.000 1.400 0.600 0.400 0.200 2 4.200 2.049 1.435 0.615 0.420 0.195 3 4.395 2.096 1.467 0.629 0.440 0.189 1.499 0.642 0.458 0.184 1.657 0.710 0.560 0.150 1.894 0.812 0.732 0.080 2.096 0.898 0.896 0.002 2.100 0.900 0.900 0.000slide 69 4 4.584 2.141 … 10 5.602 2.367 … 25 7.351 2.706 … 100 8.962 2.994 … CHAPTER9.000 3.000 6 Unemployment k 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. CHAPTER 6 Unemployment slide 70 Solution to exercise: k 0 d e f. o f s te a d y s ta te s f (k * ) k * 0 .3 k * 0 .1 k * 3 k * k * S o lv e to g e t: F in a lly, CHAPTER 6 e q 'n o f m o tio n w ith k 0 u s in g a s s u m e d v a lu e s k * k* 9 and y* k * 3 c * (1 s ) y * 0 .7 3 2 .1 Unemployment slide 71 An increase in the saving rate An increase in the saving rate raises investment… …causing k to grow toward a new steady state: Investment and depreciation k s2 f(k) s1 f(k) * CHAPTER 6 Unemployment k1 * k2 k slide 72 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. CHAPTER 6 Unemployment slide 73 International evidence on investment rates and income per person Income per 100,000 person in 2000 (log scale) 10,000 1,000 100 0 5 10 15 20 25 30 35 Investment as percentage of output (average 1960-2000) CHAPTER 6 Unemployment slide 74 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*? CHAPTER 6 Unemployment slide 75 The Golden Rule capital stock * k g o ld 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* CHAPTER 6 = y* i* = f (k*) i* = f (k*) k* Unemployment In the steady state: i* = k* because k = 0. slide 76 The Golden Rule capital stock steady state output and depreciation k* Then, graph f(k*) and k*, look for the point where the gap between them is biggest. * * y g o ld f ( k g o ld ) CHAPTER 6 Unemployment f(k*) * c g o ld * * i g o ld k g o ld * k g o ld steady-state capital per worker, k* slide 77 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: k* f(k*) * c g o ld MPK = * k g o ld CHAPTER 6 Unemployment steady-state capital per worker, k* slide 78 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? CHAPTER 6 Unemployment slide 79 Starting with too much capital If k * * k g o ld then increasing c* requires a fall in s. In the transition to the Golden Rule, consumption is higher at all points in time. y c i t0 CHAPTER 6 Unemployment time slide 80 Starting with too little capital If k * * k g o ld then increasing c* requires an increase in s. y Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption. i CHAPTER 6 c Unemployment t0 time slide 81 Population growth Assume that the population (and labor force) grow at rate n. (n is exogenous.) L n L 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. CHAPTER 6 Unemployment slide 82 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.) CHAPTER 6 Unemployment slide 83 The equation of motion for k With population growth, the equation of motion for k is k = s f(k) ( + n) k actual investment CHAPTER 6 Unemployment break-even investment slide 84 The Solow model diagram Investment, break-even investment k = s f(k) ( +n)k ( + n ) k sf(k) k* CHAPTER 6 Unemployment Capital per worker, k slide 85 The impact of population growth Investment, break-even investment ( +n2) k ( +n1) k An increase in n causes an increase in breakeven investment, leading to a lower steady-state level of k. sf(k) k 2* CHAPTER 6 Unemployment k1* Capital per worker, k slide 86 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. CHAPTER 6 Unemployment slide 87 International evidence on population growth and income per person Income 100,000 per Person in 2000 (log scale) 10,000 1,000 100 0 1 2 3 4 5 Population Growth (percent per year; average 1960-2000) CHAPTER 6 Unemployment slide 88 The Golden Rule with population growth To find the Golden Rule capital stock, express c* in terms of k*: c* = y* = f (k* ) i* ( + n) k* c* is maximized when MPK = + n or equivalently, MPK = n CHAPTER 6 Unemployment In the Golden Rule steady state, the marginal product of capital net of depreciation equals the population growth rate. slide 89 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. CHAPTER 6 Unemployment slide 90 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. CHAPTER 6 Unemployment slide 91 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 6 7 Unemployment Economic Growth I slide 92 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 6 Unemployment Economic Growth I slide 93