Unemployment

Introduction

This course covers research topics related to unemployment. It discusses models used to describe unemployment, and policies used to tackle unemployment. It tries to answer several questions:

• Why does unemployment exist?
• Why does unemployment vary over the business cycle?
• What is the socially optimal level of unemployment?
• How should labor market policies respond to fluctuations in unemployment?

Introductory videos

1. Why do we care about unemployment?
2. Absence of unemployment in the competitive model

Introductory readings

• Darity, Goldsmith (1996) – This survey reviews the social-psychological consequences of unemployment. It finds that exposure to unemployment severely damages psychological health.
• Di Tella, MacCulloch, Oswald (2003) – This paper finds in well-being surveys that unemployment make people unhappy. Being unemployed makes you unhappy, and having unemployment in your country makes you unhappy. In fact, they find after controlling for income and other personal characteristics that becoming unemployed is as painful as divorcing.

Labor market facts and matching function

This section reviews basic facts about the labor market and unemployment in the United States. We then introduce the matching function—the main tool that we will use to model the labor market and unemployment. The matching function summarizes the complex process through which workers searching for jobs and firms searching for employees meet each other.

Lecture videos

3. Organization of the labor market
4. Unemployment rate
5. Vacancy rate
6. Beveridge curve
7. Job-finding rate
8. Vacancy-filling rate
9. Job-separation rate
10. Matching function
11. Labor market tightness

Readings

• Elsby, Michaels, Ratner (2015) – This survey reviews the empirical properties of the Beveridge curve and possible microfoundations for it.
• Shimer (2012) – This paper shows that in the United States, unemployment fluctuations are caused by fluctuations in the job-finding rate and not fluctuations in the job-separation rate.
• Petrongolo, Pissarides (2001) – This survey reviews the microfoundations of the matching function, its empirical properties, and its applications.

Homework

• Quiz on labor market facts
• Quiz on matching function
• Problem set on matching function

Matching model of the labor market

This section introduces the matching model of the labor market. This is the model that we will use to study unemployment and labor market policies in this course. The model was developed by Peter Diamond, Dale Mortensen, and Christopher Pissarides in the 1980s—for this they received a Nobel Prize in 2010. In the matching model, unlike in the neoclassical model, all trades are mediated by a matching function. Nevertheless, we can construct labor supply and labor demand curves, and use them to solve the matching model.

Lecture videos

12. Properties of a good model according to Kuhn
13. Notations
14. Labor market flows
15. Assumption of balanced flows
16. Computing labor supply
17. Properties of labor supply
18. Organization of the firm
19. Computing the recruiter-producer ratio
20. Properties of the recruiter-producer ratio
21. Profits of the firm
22. Problem of the firm
23. Computing labor demand
24. Properties of labor demand
25. Review of labor supply and demand
26. Irrelevance of unemployment dynamics
27. Finding the wage in a competitive model
28. Finding labor market tightness in a matching model
29. Graphical representation of the solution
30. Complete description of the solution

Readings

• Kuhn (1992) – This book studies the Copernican Revolution in astronomy and in the process isolates the three properties of a good model: economy, accuracy, and fruitfulness.
• Pissarides (2001, chapter 1) – This chapter introduces the standard version of the labor-market matching model.
• Rogerson, Shimer, Wright (2005) – This survey reviews a range of matching models and search models.

Homework

• Quiz on matching model of the labor market

Wage functions

This section discuss the labor market institutions that determine wages—such as unions, the minimum wage, and corporate policies. It then discusses various wage functions that can be used in the matching model to describe wages in worker-firm relationships—such as fixed wages, rigid wages, and bargained wages.

Lecture videos

31. Unemployment over the business cycle
32. Unemployment in the matching model
33. Sources of business cycles
34. Wages over the business cycle
35. Wages in the matching model
36. Unions
37. Minimum wage
38. Efficiency wages
39. Fixed wages
40. Rigid wages
41. Bargained wages
42. Surplus of the firm
43. Surplus of the worker
44. Surplus sharing
45. Properties of bargained wages

Readings

• Bewley (1999) – This book reports results from a survey of 300 business managers and labor leaders as well as professional recruiters in the United States. It explains how wages are set, why wages are rigid, and in particular why wages do not fall more in recessions.
• Akerlof (1984) – This survey reviews various theories of efficiency wages. These theories try to explain how firms set wages in practice. They consider the effect of wages on productivity, attachment to the firm, retention, hiring, and so on.
• Haefke, Sonntag, Van Rens (2013) – This paper estimates that real wages for new hires are somewhat rigid: their elasticity with respect to productivity is strictly less than 1.

Homework

• Quiz on wage functions

Unemployment fluctuations

This section discusses unemployment fluctuations in the matching model. We first show that the model with rigid wages generates realistic fluctuations in unemployment. We then show that the model with bargained wages is unable to generate such fluctuations. The reason is that bargained wages are too flexible.

Lecture videos

46. Matching model with rigid wages
47. Business-cycle shocks
48. Labor supply shocks with rigid wages
49. Labor demand shocks with rigid wages
50. Elasticities
51. Fluctuations in labor market tightness with rigid Wages
52. Elasticity of labor supply
53. Elasticity of the recruiter-producer ratio
54. Elasticity of labor market tightness
55. Wage rigidity required to generate realistic fluctuations
56. Matching model with bargained wages
57. Labor supply shocks with bargained wages
58. Labor demand shocks with bargained wages
59. Fluctuations in labor market tightness with bargained wages
60. Value from unemployment
61. Bargained wages cannot generate realistic fluctuations

Readings

• Shimer (2005) – This paper shows that the textbook matching model of the labor market cannot generate realistic fluctuations in unemployment and vacancies because bargained wages are too flexible.
• Hall (2005) – This paper shows that a matching model with fixed wages can generate large fluctuations in unemployment and vacancies— larger in fact that the fluctuations observed in the United States.
• Hall, Milgrom (2008)) – This paper proposes a form of wage bargaining that produces somewhat-rigid wages. With such bargaining protocol, the matching model generates realistic fluctuations in unemployment and vacancies.

Homework

• Quiz on unemployment fluctuations
• Problem set on matching model, wages, and fluctuations

Frictional and rationing unemployment

This section turns to the sources of unemployment over the business cycle. We first establish that usual matching models do not have job rationing. That is, all unemployment would disappear in these models if workers searched sufficiently hard. We then develop a matching model with job rationing. In this model, in recession, jobs are lacking, so some unemployment remains even if workers are desperate to find a job. As a result, unemployment can be divided into rationing and frictional components. The frictional component is larger in good times but smaller in bad times.

Lecture videos

62. Introduction to job rationing
63. Evolution of matching models: standard model
64. Evolution of matching models: rigid-wage model
65. Evolution of matching models: job-rationing model
66. All unemployment is frictional in standard and rigid-wage models
67. Standard model with zero recruiting cost
68. Rigid-wage model with zero recruiting cost
69. The case of infinite job-search effort
70. Standard model with infinite job-search effort
71. Rigid-wage model with infinite job-search effort
72. Generating job rationing
73. Unemployment with zero recruiting cost
74. Defining rationing unemployment
75. When is rationing unemployment positive?
76. Unemployment with infinite job-search effort
77. Measuring frictional and rationing unemployment
78. Frictional and rationing unemployment over the business cycle
79. Frictional and rationing unemployment in a calibrated model

Readings

• Michaillat (2012) – This paper establishes that usual matching models do not have job rationing and develops a matching model with job rationing. In this model all fluctuations are caused by shocks to labor productivity.
• Michaillat, Saez (2015) – This paper extends the model in Michaillat (2012) by introducing an aggregate demand. Aggregate demand shocks generate fluctuations in unemployment and vacancies along the Beveridge curve.
• Michaillat, Saez (2022) – This paper builds a dynamic version of the model in Michaillat, Saez (2015), which is static. In this model the central bank can influence aggregate demand and unemployment through interest rates.

Homework

• Quiz on frictional and rationing unemployment

Efficient unemployment and unemployment gap

This section defines and computes the socially efficient rate of unemployment in the matching model. It then extends the analysis to all models with a Beveridge curve—not only the matching model. It finally argues that in the United States unemployment is generally inefficient, and the unemployment gap is countercyclical.

Lecture videos

80. Why do we need to know the efficient unemployment rate?
81. Natural rate of unemployment and NAIRU
82. Defining the efficient unemployment rate
83. Problem of the social planner
84. Solution to the planner’s problem
85. Computing efficient labor market tightness
86. Graphical representation of matching efficiency
87. Why is the labor market generally inefficient?
88. Description of Beveridgean models
89. Social welfare in Beveridgean models
90. Efficiency in Beveridgean models
91. Graphical representation of Beveridgean efficiency
92. Comparative statics for the efficient unemployment rate
93. Graphical representation of the unemployment gap
94. Sufficient-statistic formula for efficient labor market tightness
95. Implementing the sufficient-statistic formula
96. Unemployment gap in the united states

Readings

• Michaillat, Saez (2021) – This paper derives sufficient-statistic formulas for efficient labor market tightness and efficient unemployment rate. It also applies the formulas to the United States.
• Michaillat, Saez (2022) – This paper shows that under simple but realistic assumptions, the sufficient-statistic formula for the efficient unemployment rate reduces to $u^\ast = \sqrt{uv}$.
• Hosios (1990) – This paper shows that in a textbook matching model, unemployment is efficient when workers’ bargaining power equals the elasticity of the matching function with respect to unemployment.

Homework

• Quiz on efficient unemployment and unemployment gap
• Problem set on frictional, rationing, and efficient unemployment

Labor-demand policies

Over the business cycle, fluctuations in labor demand generate fluctuations in unemployment that are inefficient. Labor market policies that can influence labor demand should therefore counterbalance these fluctuations and bring the unemployment rate closer to its efficient level. This section discusses how minimum wage, payroll tax, and public employment—all policies that directly influence labor demand—should respond to unemployment fluctuations over the business cycle.

Lecture videos

97. Active and passive labor market policies
98. Modeling a minimum wage
99. Labor supply and demand with a minimum Wage
100. Designing an optimal policy
101. Optimal minimum wage
102. Evidence on the minimum wage
103. Other possible effects of the minimum wage
104. Modeling a payroll tax
105. Labor supply and demand with a payroll tax
106. Optimal payroll tax
107. Public employment in the United States
108. Matching process with public employment
109. Labor supply and demand with public employment
110. Graphical representation of public employment
111. Computing the public-employment multiplier
112. Slopes of the labor supply and demand Curves
113. Expression for the multiplier
114. Multiplier is positive but less than one
115. Multiplier is countercyclical
116. Multiplier in slumps
117. Multiplier in booms
118. Optimal public employment

Readings

• Neumark, Shirley (2022) – This survey reviews US evidence on the effect of the minimum wage on employment.
• Michaillat (2014) – This paper obtains the results that in a matching model with job rationing, the public-employment multiplier is positive but less than one, and the multiplier is larger when the unemployment rate is higher.
• Auerbach, Gorodnichenko (2012) – This paper finds that in the United States, government multipliers are larger when the unemployment rate is higher.

Homework

• Quiz on labor-demand policies

Unemployment insurance

In the United States, unemployment is more generous in bad times than in good times. This section studies optimal unemployment insurance in a matching model to assess whether such countercyclical generosity is desirable. We discuss the different channels through which unemployment insurance affects the labor market. We then derive a formula for optimal unemployment insurance. We conclude that indeed optimal unemployment insurance is countercyclical.

Lecture videos

119. Unemployment insurance in the United States
120. Matching process with unemployment insurance
121. Labor demand with unemployment insurance
122. Social welfare with unemployment insurance
123. Effort supply with unemployment insurance
124. Labor supply with unemployment insurance
125. Graphical representation of unemployment insurance
126. Unemployment insurance in the job-rationing Model
127. Moral-hazard channel of unemployment insurance
128. Microelasticity and macroelasticity of unemployment
129. Rat-race channel of unemployment insurance
130. Unemployment insurance in the rigid-wage model
131. Unemployment insurance in the standard model
132. Job-creation channel of unemployment insurance
133. Optimal unemployment insurance
134. Formula for optimal unemployment insurance
135. Baily-Chetty term
136. Effect of labor market tightness on welfare
137. Effect of unemployment insurance on labor market tightness
138. Cyclicality of optimal unemployment insurance

Readings

• Chetty (2006) – This paper studies optimal unemployment insurance in a model with fixed tightness and obtains the Baily-Chetty formula.
• Landais, Michaillat, Saez (2018) – This paper studies optimal unemployment insurance in a matching model and obtains a sufficient-statistic formula for optimal unemployment insurance.
• Landais, Michaillat, Saez (2018) – This paper applies the sufficient-statistic formula to the United States and finds that optimal unemployment insurance is countercyclical—more generous in bad times than in good times.

Homework

• Quiz on unemployment insurance