1. Chapter 16 Unemployment: Search and Efficiency Wages

2. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-2 Goal Examine the behavior of the unemployment and labor participation rate in U.S. Study two models of determination of unemployment – Search model – Efficiency wage model

3. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-3 Unemployment and Labor Participation Rate E: number of working age persons who are employed. U: number of unemployed. NL: number of working age persons who are not in the labor force

4. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-4 Unemployment rate = Participation rate =

5. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-5 Figure 16.1 The U.S. Unemployment Rate, 1948–2003

6. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-6 Figure 16.2 Deviations from Trend in the Unemployment Rate and Percentage Deviations from Trend in Real GDP for 1948–2003

7. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-7 Determinants of the Unemployment Rate Aggregate economic activity: Y , u  Demographics: baby boom and baby bust. Young tend to have higher u. Government intervention: Unemployment Insurance (UI). UI , u  Sectoral shifts: from manufacturing to services, structural unemployment.

8. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-8 Stylized Facts of Participation Rate Participation rate is procyclical. After WWII, the increase in the total participation rate is accounted for solely by an dramatic increase in the participation rate of women. Women also had less children, more willing to go to college.

9. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-9 Figure 16.3 The U.S. Participation Rate, 1948–2003

10. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-10 Figure 16.5 Deviations from Trend in the Participation Rate and GDP

11. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-11 Figure 16.4 Labor Force Participation of Women and Men

12. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-12

13. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-13

14. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-14 Source: He (2005)

15. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-15

16. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-16 Table 16.1 Average Unemployment Rates in OECD Countries, 1983-1996

17. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-17 A Search Model of Unemployment In the previous chapters, we assume that consumers typically use their time for only two different purposes: working and leisure. In this chapter, we will extend this assumption. People can also use time to search for a job while they are unemployed.

18. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-18 The infinite-lived worker has preferences given by

19. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-19 We assume the workers are all in the labor force. Let U denote the fraction of workers who are unemployed. 1-U is the employment rate. is the value function of being employed at real wage w. is the value function of being unemployed. Let s denote the separation rate (firing or quitting)

20. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-20 Value of Being Employed

21. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-21 Simplify the equation, we get Hence

22. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-22 Therefore inherits the properties of U(w). It is strictly increasing and concave. We also have Separation rate   Tax on wage  

23. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-23 Figure 16.6 The Welfare of an Employed Worker

24. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-24 Value of Being Unemployed Next, we want to consider the welfare of an unemployed worker. Let b denote the constant real amount of UI, p be the frequency of receiving job offers. Assume wage offer is a random draw from the probability distribution F(w), with the probability density function f(w).

25. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-25

26. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-26 Simplify the equation

27. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-27 Unemployment benefit b   Frequency of job offers p   Tax on b  

28. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-28 The value function of a unemployed worker who receives wage offer w is

29. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-29 Reservation Wage The criteria of choice is based on if accept the offer; otherwise, turn it down w* is called the reservation wage such that

30. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-30 Figure 16.7 The Reservation Wage

31. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-31 Effects on Reservation Wage UI    w* , unemployed workers are more picky Tax on wage    w* , unemployed workers are more picky

32. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-32 Figure 16.8 An Increase in the Unemployment Insurance Benefit b

33. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-33 Figure 16.9 An Increase in the Taxes on the Wage Income of the Employed

34. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-34 The Determination of the Unemployment Rate The flow of workers from employment to unemployment is s(1-U) Let H(w) denote the fraction of unemployed workers receiving a wage offer is greater than w. H(w) is decreasing in w.

35. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-35 The flow of workers from unemployment to employment is UpH(w*).

36. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-36 Long-run Equilibrium The labor market equilibrium is determined by

37. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-37 The equilibrium unemployment rate U* is given by

38. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-38 We have

39. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-39 Figure 16.10 The Fraction of Unemployed Workers Receiving a Wage Offer Greater than w

40. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-40 Figure 16.11 The Determination of the Unemployment Rate U in the Search Model

41. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-41 Figure 16.12 The Determination of the Reservation Wage and the Unemployment Rate in the Search Model

42. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-42 Policy Experiments

43. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-43 Figure 16.13 An Increase in the Unemployment Insurance Benefit b

44. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-44 Figure 16.14 An Increase in the Job Offer Rate p

45. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-45 Figure 16.15 An Increase in Taxes on Labor Income

46. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-46 Figure 16.16 Taxes on Labor Income and Unemployment Benefits

47. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-47 Efficiency Wage Model An alternative model of unemployment Key assumption: workers’ effort depends on their wage To induce workers to work harder, a firm may be willing to pay a real wage higher than the competitive market wage This higher efficiency wage thus creates unemployment

48. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-48 Effort of the Worker A worker’s effort increases with the wage Effective labor input is working hours N multiplied by effort

49. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-49 Why e(w) increases with w? Adverse Selection: Firm does not know the productivity of workers. Higher wage will more likely attract high-ability workers More Hazard: Firm has difficulty in monitoring the on-the-job effort of its workers. Higher efficiency wage means the opportunity cost of shirking increases

50. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-50 Firm’s Optimization Problem Production function Choose N and w to maximize profits

51. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-51 FOCs FOC w.r.t. N FOC w.r.t. w

52. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-52 Determination of Efficiency Wage Combining two FOCs, we have efficiency wage is determined by

53. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-53 Figure 16.17 Effort of the Worker as a Function of His or Her Wage

54. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-54 Figure 16.18 The Demand for Labor in the Efficiency Wage Model

55. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-55 Figure 16.19 The Ratio of Effort to the Real Wage

56. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-56 Figure 16.20 Determination of the Efficiency Wage

57. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-57 Labor Market Equilibrium When efficiency wage > market wage, there is unemployment. When efficiency wage < market wage, there is labor shortage. Firms bid up to the market wage to attract workers.

58. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-58 Figure 16.21 Unemployment in the Efficiency Wage Model

59. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-59 Efficiency Wage and Business Cycle Output supply curve is vertical (Why?) Shock on demand side will not affect output, e.g., change in G Only shock on output supply curve can affect aggregate output, e.g., TFP z

60. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-60 Equilibrium effect of z  : Y , r , w* no change, N , u , C , I , Consistent with most of facts except wage

61. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-61 Figure 16.22 The Output Supply Curve in the Efficiency Wage Model

62. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-62 Figure 16.23 An Increase in G in the Efficiency Wage Model

63. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-63 Figure 16.24 An Increase in Total Factor Productivity in the Efficiency Wage Model

64. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-64 Can We Fix It? Assume z affects effort, e(w)  as z  Efficiency wage w*  Wage is countercyclical, contrast to the data!

65. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16-65 Figure 16.25 An Increase in the Effectiveness of Monitoring by the Firm