$u^* = \sqrt{uv}$

TL;DR

This paper derives a new measure of the full-employment unemployment rate in the US, based on economic efficiency principles and the Beveridge curve, showing it averages around 4.1% over nearly a century.

Contribution

It introduces the geometric average formula for the full-employment unemployment rate, linking social efficiency to labor market equilibrium.

Findings

The FERU averages 4.1% from 1930 to 2023.

The FERU remains between 2.5% and 6.6%.

The geometric mean captures the efficiency-based unemployment rate.

Abstract

This paper aims to compute the unemployment rate $u^*$ that is consistent with full employment in the United States. First, it argues that the most appropriate economic translation of the legal notion of full employment is social efficiency. Here efficiency requires to minimize the nonproductive use of labor -- both unemployment and recruiting. The nonproductive use of labor is measured by the number of jobseekers and vacancies, $u + v$. Through the Beveridge curve, the numbers of vacancies and jobseekers are inversely related, $uv = \text{constant}$. With such symmetry the labor market is efficient when there are as many jobseekers as vacancies ($u = v$), inefficiently tight when there are more vacancies than jobseekers ($v > u$), and inefficiently slack when there are more jobseekers than vacancies ($u > v$). Accordingly, the full-employment rate of unemployment (FERU) is the geometric average of the unemployment and vacancy rates: $u^* = \sqrt{uv}$. Between 1930 and 2023, the FERU averages $4.1\%$ and is quite stable -- it always remains between $2.5\%$ and $6.6\%$.