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## Matching model of the labor market
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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. This 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 model.
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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. Early work on this model was conducted by Peter Diamond, Dale Mortensen, and Christopher Pissarides in the 1970s and 1980s, so the canonical version of the model is often called the Diamond-Mortensen-Pissarides model, or DMP model. For their work, Diamond, Mortensen, and Pissarides received the Economics 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 model.
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##### Lecture videos
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##### Main readings
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+[Kuhn (1957, chapters 1 and 5)](https://www.hup.harvard.edu/catalog.php?isbn=9780674171039) – This book studies the Copernican Revolution in astronomy and in the process isolates the three properties of a good model: economy, accuracy, and fruitfulness.
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+[Pissarides (2001, chapter 1)](https://mitpress.mit.edu/9780262533980/equilibrium-unemployment-theory/) – This chapter introduces the standard version of the matching model of the labor market.
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+[Pissarides (2001, chapter 1)](https://mitpress.mit.edu/9780262533980/equilibrium-unemployment-theory/) – This chapter introduces the canonical version of the matching model of the labor market (the DMP model).
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##### Additional readings
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+[Rogerson, Shimer, and Wright (2005)](https://doi.org/10.1257/002205105775362014) – This survey reviews a range of matching models and search models.
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+[Pissarides (2011)](https://doi.org/10.1257/aer.101.4.1092) – In this Nobel lecture, Christopher Pissarides presents the history of the matching model of the labor market. He also discusses several applications of the model.
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+[Mortensen (2011)](https://doi.org/10.1257/aer.101.4.1073) – In this Nobel lecture, Dale Mortensen presents a brief history of the matching model and a basic version of the model. He then discusses how the model can help understand the Great Recession of 2008–2009.
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+[Rogerson, Shimer, and Wright (2005)](https://doi.org/10.1257/002205105775362014) – This survey reviews a range of search and matching models.
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+[Pissarides (2011)](https://doi.org/10.1257/aer.101.4.1092) – In this Nobel lecture, Christopher Pissarides presents the history of the DMP model. He also discusses several applications of the model.
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+[Mortensen (2011)](https://doi.org/10.1257/aer.101.4.1073) – In this Nobel lecture, Dale Mortensen presents a brief history of the DMP model and a basic version of the model. He then discusses how the model can help understand the Great Recession of 2008–2009.
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+[Michaillat (2024)](/14.pdf) – This paper develops a basic matching model of the labor market and uses it to study the impact of immigration on local workers. The model and its presentation are similar to those in the course. The paper highlights how different assumptions alter the effects of immigration in the model. The paper shows that despite its simplicity, the model developed in the course is helpful to understand contemporary economic and political issues.
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##### Practice material
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+[Akerlof (1984)](https://www.jstor.org/stable/1816334) – 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.
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+[Jacoby (1984)](https://mitpress.mit.edu/9780262651059/internal-labor-markets/) – This chapter analyzes the development of internal labor markets in American manufacturing firms. It explains how internal labor markets replaced spot labor markets, and how such replacement provided workers with an employment system that was more bureaucratic, more
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rule-bound, and more secure. In particular, wages paid to workers were much more rigid in internal labor markets.
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+[Raff and Summers (1987)](https://doi.org/10.1086/298165) – This paper examines Henry Ford's introduction of the five-dollar day in 1914. It finds that Ford's decision to increase wages dramatically is most plausibly the consequence of labor problems of the kind efficiency-wage theories stress. Moreover, the introduction of the five-dollar day resulted in substantial queues for Ford jobs, significant increases in productivity, and significant increases in profits.
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+[Mas (2006)](https://doi.org/10.1162/qjec.121.3.783) – This paper finds evidence in favor of efficiency-wage theories: when police officiers receive a wage below what they consider a fair wage, they are disappointed, and their performance on the job drops. This finding confirms that fairness might be an important source of wage rigidity.
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+[Raff and Summers (1987)](https://doi.org/10.1086/298165) – This paper examines Henry Ford's introduction of the five-dollar day in 1914 in his automobile factory. It argues that Ford's decision to increase wages dramatically is the consequence of labor problems of the kind featured in efficiency-wage theories. Moreover, it finds that the five-dollar day resulted in substantial queues for Ford jobs, significant increases in productivity, and maybe surprisingly, significant increases in profits.
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+[Mas (2006)](https://doi.org/10.1162/qjec.121.3.783) – This paper finds evidence in favor of efficiency-wage theories: when police officers receive a wage below what they consider a fair wage, they are disappointed, and their performance on the job drops. This finding confirms that fairness might be an important source of wage rigidity.
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##### Practice material
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##### Main readings
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+[Shimer (2005)](https://doi.org/10.1257/0002828053828572) – 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.
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+[Hall (2005)](https://doi.org/10.1257/0002828053828482) – 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.
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+[Shimer (2005)](https://doi.org/10.1257/0002828053828572) – This paper shows that the canonical matching model of the labor market (the DMP model) cannot generate realistic fluctuations in unemployment and vacancies. This anomaly of the DMP model is known as the Shimer puzzle. The reason behind the Shimer puzzle is that the wage bargaining protocol assumed in the DMP model (period-by-period Nash bargaining) produces wages that are too flexible.
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+[Hall (2005)](https://doi.org/10.1257/0002828053828482) – This paper shows that a matching model with fixed real wages generates large fluctuations in unemployment and vacancies—larger in fact that the fluctuations observed in the United States. Hence fixed real wages solve the Shimer puzzle.
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##### Additional readings
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+[Hall and Milgrom (2008)](https://doi.org/10.1257/aer.98.4.1653) – 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.
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+[Hagedorn and Manovskii (2008)](https://doi.org/10.1257/aer.98.4.1692) – This paper shows that if workers are almost indifferent between working and not working, then a matching model with wage bargaining generates realistic fluctuations in unemployment and vacancies. A downside of this assumption, however, is that it is completely inconsistent with the large psychosocial cost of unemployment documented at the beginning of the course. Another downside is that it implies that the socially efficient rate of unemployment is above 20%.
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+[Hagedorn and Manovskii (2008)](https://doi.org/10.1257/aer.98.4.1692) – This paper shows that if workers are almost indifferent between working and not working, then a matching model with wage bargaining can generate realistic fluctuations in unemployment and vacancies. A downside of this assumption, however, is that it is completely inconsistent with the large psychosocial cost of unemployment documented at the beginning of the course. Another downside is that it implies that the socially efficient rate of unemployment is above 20%.
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+[Gertler and Trigari (2009)](https://doi.org/10.1086/597302) – This paper shows that the matching model generates realistic fluctuations in unemployment and vacancies when period-by-period wage bargaining is replaced by multiperiod wage bargaining. Under multiperiod bargaining, firm and worker agree on a fixed wage that remains in place for several periods.
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+[Blanchard and Gali (2010)](https://doi.org/10.1257/mac.2.2.1) – This paper
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+[Blanchard and Gali (2010)](https://doi.org/10.1257/mac.2.2.1) – This paper blends the matching model of the labor market with a New Keynesian model of the product market. It then shows that under wage bargaining (in particular when the wage is efficient), unemployment and vacancies do not fluctuate at all in the model. This is a strong form of the Shimer puzzle. By contrast, when the real wage is a subproportional function of labor productivity, the model generates realistic fluctuations in unemployment and vacancies.
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##### Practice material
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## Frictional and rationing unemployment
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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. This 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.
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This section turns to the sources of unemployment over the business cycle. In the DMP model, 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, the DMP model does not feature job rationing. This 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.
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The section then develops a matching model with job rationing. In the 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 job vacancies.
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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, 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.
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Technically, the DMP model does not feature job rationing because its 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, 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 returns to labor.
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##### Lecture videos
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62.[Introduction to job rationing](https://youtu.be/rgcpMgKfCk8)
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63.[Evolution of matching models: standard model](https://youtu.be/P8mHdabkF0Q)
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63.[Evolution of matching models: standard model (DMP model)](https://youtu.be/P8mHdabkF0Q)
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64.[Evolution of matching models: rigid-wage model](https://youtu.be/GBSNJw9KuUM)
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65.[Evolution of matching models: job-rationing model](https://youtu.be/i_EHrRFMXgc)
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66.[All unemployment is frictional in standard and rigid-wage models](https://youtu.be/NwViMyIBu_8)
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##### Main readings
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+[Michaillat (2012)](/1.pdf) – This paper first establishes that usual matching models do not have job rationing and then develops a matching model with job rationing. In that model unemployment can be decomposed into rationing and frictional components. In recessions, the rationing component is large while the frictional component is small.
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+[Michaillat (2012)](/1.pdf) – This paper first establishes that the DMP model does not have job rationing and then develops a matching model with job rationing. The job-rationing model departs from the DMP model by assuming that the production has diminishing returns to labor instead of constant returns to labor, and that the real wage is given by a rigid wage norm instead of Nash bargaining. In that model unemployment can be decomposed into rationing and frictional components. In recessions, the rationing component is large while the frictional component is small.
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+[Michaillat and Saez (2015)](/3.pdf) – This paper adds aggregate demand to the model in Michaillat (2012). This is done by adding a product market to the labor market with a similar matching structure. Aggregate demand shocks generate fluctuations in unemployment and vacancies along the Beveridge curve. In that model, unemployment can be decomposed into three components: Keynesian unemployment (due to insufficient aggregate demand), classical unemployment (due to high real wages), and frictional unemployment (due to matching frictions).
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##### Additional readings
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+[Crepon, Duflo, Gurgand, Rathelot, and Zamora (2013)](https://doi.org/10.1093/qje/qjt001) – This paper reports the results from a randomized experiment designed to evaluate the direct and indirect effects of job-placement assistance on the labor market outcomes of young educated jobseekers in France. It finds that jobseekers who are given job-placement assistance find jobs more rapidly, while jobseekers in the same labor market who are not assisted take longer to find a job. This finding suggests that jobs are somewhat rationed, and that assisted jobseekers move ahead of nonassisted jobseekers in job queues.
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+[Crepon, Duflo, Gurgand, Rathelot, and Zamora (2013)](https://doi.org/10.1093/qje/qjt001) – This paper reports the results from a randomized experiment designed to evaluate the direct and indirect effects of job-placement assistance on the labor market outcomes of young educated jobseekers in France. It finds that jobseekers who are given job-placement assistance find jobs more rapidly, while jobseekers in the same labor market who are not assisted take longer to find a job. This finding suggests that jobs are somewhat rationed, and that assisted jobseekers move ahead of non-assisted jobseekers in job queues.
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+[Akerlof, Rose, and Yellen (1988)](https://www.jstor.org/stable/2534536) – This paper develops an early matching model of the labor market with job
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rationing. The model reproduces a number of stylized facts of the US labor market regarding quits and vacancy chains. While the model in not in the DMP tradition, it does feature a Beveridge curve.
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+[Michaillat and Saez (2022)](/7.pdf) – This paper builds a dynamic version of the model in Michaillat and Saez (2015), which is static. In this model the central bank can influence aggregate demand and unemployment through interest rates.
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+[Michaillat and Saez (2024)](/15.pdf) – This paper uses the dynamic model in Michaillat and Saez (2022) and generates a Phillips curve by introducing price competition through directed search. To ensure that unemployment fluctuates, the model assumes price rigidity through quadratic price-adjustment costs. The Phillips curve produced by the model guarantees divine coincidence: inflation is on target when unemployment is efficient.
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##### Main readings
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+[Michaillat and Saez (2021)](/9.pdf) – This paper derives sufficient-statistic formulas for efficient labor market tightness and efficient unemployment rate. It also applies the formulas to the United States.
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+[Michaillat and Saez (2024)](/13.pdf) – This paper shows that under simple but realistic assumptions, the sufficient-statistic formula for the efficient unemployment rate from Michaillat and Saez (2021) reduces to $u^\ast = \sqrt{uv}$. This unemployment rate marks not only social efficiency but also full employment.
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+[Michaillat and Saez (2021)](/9.pdf) – This paper derives sufficient-statistic formulas for efficient labor market tightness and efficient unemployment rate. It applies the formulas to the United States and finds that the US labor market is generally inefficiently slack, and especially inefficiently slack in slumps.
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+[Michaillat and Saez (2024)](/13.pdf) – This paper shows that under simple but realistic assumptions, the sufficient-statistic formula for the efficient unemployment rate from Michaillat and Saez (2021) reduces to $u^\ast = \sqrt{uv}$. This unemployment rate marks not only social efficiency but also full employment. In the United States, 1930–2024, the efficient unemployment rate $u^\ast$ averages 4.1%.
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##### Additional readings
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+[Chetty (2009)](https://doi.org/10.1146/annurev.economics.050708.142910) – This survey describes the sufficient-statistic method for welfare and policy analysis.
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+[Hosios (1990)](https://doi.org/10.2307/2297382) – 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.
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+[Hosios (1990)](https://doi.org/10.2307/2297382) – This paper shows that in a DMP model, unemployment is efficient when workers' bargaining power equals the elasticity of the matching function with respect to unemployment.
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