u* = √uv

This paper argues that in the United States the full-employment rate of unemployment (FERU) is the geometric average of the unemployment and vacancy rates. Between 1930 and 2023, the FERU averages 4.1% and is very stable.

June 2024 · Pascal Michaillat, Emmanuel Saez


This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance.

March 2024 · Pascal Michaillat

Moen Meets Rotemberg: An Earthly Model of the Divine Coincidence

This paper develops a simple business-cycle model with divine coincidence: inflation is on target when unemployment is efficient. The divine coincidence arises from directed search under a quadratic price-adjustment cost.

January 2024 · Pascal Michaillat, Emmanuel Saez

Economic Slack

This graduate course presents various matching models of economic slack. It uses them to study business-cycle fluctuations; Keynesian, classical, and frictional unemployment; optimal monetary policy and the zero lower bound; and optimal government spending.

January 2024 · Pascal Michaillat

Business Cycles and How to Tame Them

This minicourse presents basic facts about business cycles. It then develops a matching model to explain these business-cycle facts. Finally, it explains how monetary policy and government spending should be designed to tame business cycles.

December 2023 · Pascal Michaillat

Modeling the Displacement of Native Workers by Immigrants

This paper explains why a wave of immigration reduces the employment rate of native workers, and why this reduction is larger in bad times. Yet, immigration improves native welfare when the labor market is inefficiently tight, because it helps firms to recruit.

November 2023 · Pascal Michaillat

An Economical Business-Cycle Model

This paper develops a policy-oriented business-cycle model with fluctuating unemployment and long zero-lower-bound episodes. The innovations are that producers and consumers meet through a matching function, and wealth enters the utility function.

April 2022 · Pascal Michaillat, Emmanuel Saez

Beveridgean Unemployment Gap

This paper develops a sufficient-statistic formula for the unemployment gap. The formula depends on the elasticity of the Beveridge curve, cost of unemployment, and recruiting cost. In the United States the unemployment gap is countercyclical and often positive.

December 2021 · Pascal Michaillat, Emmanuel Saez

Pricing under Fairness Concerns

This paper develops a model of pricing in which buyers care about the fairness of markups but misinfer them from prices. The model yields price rigidity, generates realistic Phillips curves, and explains why people dislike inflation so much.

June 2021 · Erik Eyster, Kristof Madarasz, Pascal Michaillat

Resolving New Keynesian Anomalies with Wealth in the Utility Function

This paper resolves the anomalies of the New Keynesian model at the zero lower bound—explosive recession, forward-guidance puzzle, multiplier puzzle—by introducing wealth into the utility function.

May 2021 · Pascal Michaillat, Emmanuel Saez

Optimal Public Expenditure with Inefficient Unemployment

This paper shows that when unemployment is inefficient, optimal public expenditure deviates from the Samuelson rule to reduce the unemployment gap. Optimal stimulus spending depends on the unemployment gap, unemployment multiplier, and an elasticity of substitution.

May 2019 · Pascal Michaillat, Emmanuel Saez

Intermediate Macroeconomics

This undergraduate course introduces macroeconomic concepts—such as GDP and inflation—and covers the IS-LM model of business cycles, matching model of unemployment, Phillips curve, Malthusian model of growth, and Solowian model of growth.

December 2018 · Pascal Michaillat

A Macroeconomic Approach to Optimal Unemployment Insurance: Applications

This paper explores how the optimal generosity of unemployment insurance varies over the business cycle in the United States. It finds that the optimal replacement rate is countercyclical, just like the actual replacement rate.

May 2018 · Camille Landais, Pascal Michaillat, Emmanuel Saez

A Macroeconomic Approach to Optimal Unemployment Insurance: Theory

This paper develops a theory of optimal unemployment insurance in matching models. It derives a sufficient-statistic formula for optimal unemployment insurance, which is useful to determine the optimal cyclicality of unemployment insurance.

May 2018 · Camille Landais, Pascal Michaillat, Emmanuel Saez

Aggregate Demand, Idle Time, and Unemployment

This paper develops a model of unemployment fluctuations. The innovation is to represent the labor and product markets with a matching structure. The model simultaneously features Keynesian unemployment, classical unemployment, and frictional unemployment.

May 2015 · Pascal Michaillat, Emmanuel Saez

A Theory of Countercyclical Government Multiplier

This paper develops a New Keynesian model in which the government multiplier doubles when the unemployment rate rises from 5% to 8%. The multiplier is so countercyclical because in bad times, on the labor market, job rationing dwarfs matching frictions.

January 2014 · Pascal Michaillat

Do Matching Frictions Explain Unemployment? Not in Bad Times

This paper proposes a matching model of the labor market with job rationing: unemployment does not disappear in the absence of matching frictions. In recessions, job rationing drives the rise of unemployment, whereas matching frictions contribute little to it.

June 2012 · Pascal Michaillat