## u* = √uv

This paper shows that under simple but realistic assumptions, the efficient unemployment rate u* is the geometric average of the unemployment and vacancy rates. In the United States, 1930–2022, u* is stable and averages 4.1%.

This paper shows that under simple but realistic assumptions, the efficient unemployment rate u* is the geometric average of the unemployment and vacancy rates. In the United States, 1930–2022, u* is stable and averages 4.1%.

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.

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

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

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.

This paper explores how the optimal replacement rate 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.

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.

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 dwarfes matching frictions.