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.
Beveridge curve
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.
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.