Introduction

This course covers 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
  1. Organization of the labor market
  2. Unemployment rate
  3. Vacancy rate
  4. Beveridge curve
  5. Job-finding rate
  6. Vacancy-filling rate
  7. Job-separation rate
  8. Matching function
  9. Labor market tightness
Lecture notes
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

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
  1. Properties of a good model according to Kuhn
  2. Notations
  3. Labor market flows
  4. Assumption of balanced flows
  5. Computing labor supply
  6. Properties of labor supply
  7. Organization of the firm
  8. Computing the recruiter-producer ratio
  9. Properties of the recruiter-producer ratio
  10. Profits of the firm
  11. Problem of the firm
  12. Computing labor demand
  13. Properties of labor demand
  14. Review of labor supply and demand
  15. Irrelevance of unemployment dynamics
  16. Finding the wage in a competitive model
  17. Finding labor market tightness in a matching model
  18. Graphical representation of the solution
  19. Complete description of the solution
Lecture notes
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 matching model of the labor market.
  • Rogerson, Shimer, Wright (2005) – This survey reviews a range of matching models and search models.
Homework

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
  1. Unemployment over the business cycle
  2. Unemployment in the matching model
  3. Sources of business cycles
  4. Wages over the business cycle
  5. Wages in the matching model
  6. Unions
  7. Minimum wage
  8. Efficiency wages
  9. Fixed wages
  10. Rigid wages
  11. Bargained wages
  12. Surplus of the firm
  13. Surplus of the worker
  14. Surplus sharing
  15. Properties of bargained wages
Lecture notes
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. The elasticity of real wages with respect to productivity is in the 0.7–0.8 range, so strictly less than 1.
Homework

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
  1. Matching model with rigid wages
  2. Business-cycle shocks
  3. Labor supply shocks with rigid wages
  4. Labor demand shocks with rigid wages
  5. Elasticities
  6. Fluctuations in labor market tightness with rigid Wages
  7. Elasticity of labor supply
  8. Elasticity of the recruiter-producer ratio
  9. Elasticity of labor market tightness
  10. Wage rigidity required to generate realistic fluctuations
  11. Matching model with bargained wages
  12. Labor supply shocks with bargained wages
  13. Labor demand shocks with bargained wages
  14. Fluctuations in labor market tightness with bargained wages
  15. Value from unemployment
  16. Bargained wages cannot generate realistic fluctuations
Lecture notes
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

Frictional and rationing unemployment

This section turns to the sources of unemployment over the business cycle. In usual matching models, unemployment becomes vanishingly small when unemployed workers search sufficiently hard for jobs. Unemployment also becomes vanishingly small when recruiting costs are sufficiently low. In other words, usual matching models do not feature job rationing. Such lack of job rationing is difficult to reconcile with the long queues of unemployed workers at job bureaus and factory gates observed during the Great Depression.

The section then develops 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. The model features both frictional unemployment—caused by difficulties in matching workers and firms—and rationing unemployment—caused by a lack of job. The model describes well good and bad times. In bad times, labor demand is low so rationing unemployment is high. Hence total unemployment is high. But, maybe surprisingly, frictional unemployment is low. In that case, workers queue for jobs and it is easy for firms to fill vacancies. Conversely, in good times, labor demand is high so rationing unemployment is low and total unemployment is low. Frictional unemployment is higher than in bad times. In that case, it is easy for workers to find jobs but firms struggle to fill vacancies.

Technically, typical matching models do not feature job rationing because their labor demand is perfectly elastic with respect to wages and labor market tightness. Once we introduce a labor demand that is downward sloping with respect to wages and tightness into the matching model, job rationing appears and not all unemployment is frictional. The easiest way to generate a downward-sloping labor demand is by assuming that the production function has diminishing marginal returns to labor.

Lecture videos
  1. Introduction to job rationing
  2. Evolution of matching models: standard model
  3. Evolution of matching models: rigid-wage model
  4. Evolution of matching models: job-rationing model
  5. All unemployment is frictional in standard and rigid-wage models
  6. Standard model with zero recruiting cost
  7. Rigid-wage model with zero recruiting cost
  8. The case of infinite job-search effort
  9. Standard model with infinite job-search effort
  10. Rigid-wage model with infinite job-search effort
  11. Generating job rationing
  12. Unemployment with zero recruiting cost
  13. Defining rationing unemployment
  14. When is rationing unemployment positive?
  15. Unemployment with infinite job-search effort
  16. Measuring frictional and rationing unemployment
  17. Frictional and rationing unemployment over the business cycle
  18. Frictional and rationing unemployment in a calibrated model
Lecture notes
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. This is because the model is in the Diamond-Mortensen-Pissarides tradition: it only features a labor market, so there is no scope for aggregate-demand shocks.
  • Michaillat, Saez (2015) – This paper extends the model in Michaillat (2012) by introducing an aggregate demand. This is done by adding to the labor market a product market with a similar matching structure. 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

Efficient unemployment and unemployment gap

Unlike in neoclassical models, in matching models there is no guarantee of efficiency. The prevailing unemployment rate is generally inefficient: either too high or too low.

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 develops measures of the efficient labor market tightness and efficient unemployment rate. It also develops a measure of the unemployment gap to assess how far the unemployment rate is from its socially efficient level. The measure depends on three sufficient statistics: recruiting cost, social value of nonwork, and elasticity of the Beveridge curve.

The section finally shows that in the United States, the unemployment gap is generally positive, and it is sharply countercyclical. This means that the US labor market is generally inefficiently slack and especially inefficiently slack in slumps. For instance, the unemployment gap reached 6 percentage points during the Volcker Recession and the Great Recession.

Lecture videos
  1. Why do we need to know the efficient unemployment rate?
  2. Natural rate of unemployment and NAIRU
  3. Defining the efficient unemployment rate
  4. Problem of the social planner
  5. Solution to the planner’s problem
  6. Computing efficient labor market tightness
  7. Graphical representation of matching efficiency
  8. Why is the labor market generally inefficient?
  9. Description of Beveridgean models
  10. Social welfare in Beveridgean models
  11. Efficiency in Beveridgean models
  12. Graphical representation of Beveridgean efficiency
  13. Comparative statics for the efficient unemployment rate
  14. Graphical representation of the unemployment gap
  15. Sufficient-statistic formula for efficient labor market tightness
  16. Implementing the sufficient-statistic formula
  17. Unemployment gap in the United States
Lecture notes
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

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
  1. Active and passive labor market policies
  2. Modeling a minimum wage
  3. Labor supply and demand with a minimum Wage
  4. Designing an optimal policy
  5. Optimal minimum wage
  6. Evidence on the minimum wage
  7. Other possible effects of the minimum wage
  8. Modeling a payroll tax
  9. Labor supply and demand with a payroll tax
  10. Optimal payroll tax
  11. Public employment in the United States
  12. Matching process with public employment
  13. Labor supply and demand with public employment
  14. Graphical representation of public employment
  15. Computing the public-employment multiplier
  16. Slopes of the labor supply and demand curves
  17. Expression for the multiplier
  18. Multiplier is positive but less than one
  19. Multiplier is countercyclical
  20. Multiplier in slumps
  21. Multiplier in booms
  22. Optimal public employment
Lecture notes
Readings
  • Neumark, Shirley (2022) – This survey reviews US evidence on the effect of the minimum wage on employment.
  • Michaillat (2014) – This paper establishes 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. These predictions are consistent with a growing body of evidence from the United States and abroad.
  • Auerbach, Gorodnichenko (2012) – This paper finds that in the United States, government multipliers are larger when the unemployment rate is higher.
Homework

Unemployment insurance

Fluctuations in unemployment raise another policy question: how should the generosity of unemployment insurance respond to unemployment fluctuations? This question was hotly debated during the Great Recession. Some argued that unemployment insurance should be reduced because it discouraged job search and would raise unemployment further. Other countered that unemployment insurance could be increased without raising unemployment much—as there were no jobs available for jobseekers.

This section weights the two sides of the argument. It discusses the different channels through which unemployment insurance affects the labor market. It then derives a formula for optimal unemployment insurance. The formula contrasts how generous unemployment insurance should be in good times and in bad times. The formula shows that the generosity of unemployment insurance should be adjusted over the business cycle; the adjustment depends on how unemployment insurance affects labor market tightness. The effect of unemployment insurance on tightness depends on the model: increasing unemployment insurance may raise tightness by alleviating the rat race for jobs or lower tightness by increasing wages through bargaining.

In the United States, unemployment insurance is more generous in bad times than in good times. The formula, combined with evidence from the US labor market, suggests that such countercyclical generosity is desirable. The reasons are that increasing unemployment insurance appear to raise labor market tightness, and that labor market tightness is inefficiently low in slumps and inefficiently high in booms.

Lecture videos
  1. Unemployment insurance in the United States
  2. Matching process with unemployment insurance
  3. Labor demand with unemployment insurance
  4. Social welfare with unemployment insurance
  5. Effort supply with unemployment insurance
  6. Labor supply with unemployment insurance
  7. Graphical representation of unemployment insurance
  8. Unemployment insurance in the job-rationing Model
  9. Moral-hazard channel of unemployment insurance
  10. Microelasticity and macroelasticity of unemployment
  11. Rat-race channel of unemployment insurance
  12. Unemployment insurance in the rigid-wage model
  13. Unemployment insurance in the standard model
  14. Job-creation channel of unemployment insurance
  15. Optimal unemployment insurance
  16. Formula for optimal unemployment insurance
  17. Baily-Chetty term
  18. Effect of labor market tightness on welfare
  19. Effect of unemployment insurance on labor market tightness
  20. Cyclicality of optimal unemployment insurance
Lecture notes
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