u* = vuv

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• Department of Economics

This paper aims to compute the unemployment rate u* consistent with "full employment". First, we must translate this legal notion in economic terms. We propose that the most appropriate marker of full employment is the efficient unemployment rate, which minimises the non-productive use of labour—both unemployment and recruiting. The non-productive use of labour 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 = constant. With such symmetry, the labour market is efficient when there are as many jobseekers as vacancies (u = v), too tight when there are more vacancies than jobseekers (v > u), and too slack when there are more jobseekers than vacancies (u > v). Moreover, the efficient unemployment rate is the geometric average of the unemployment and vacancy rates: u* =vuv. In the United States, we find that u* averages 4.1% over 1930–2022, and is very stable. Accordingly, the US labour market is generally inefficiently slack, and especially slack in recessions. The US labour market sometimes becomes inefficiently tight in wars: World War 2, Korean War, Vietnam War. And the US labour market has also been inefficiently tight in the aftermath of the coronavirus pandemic, from the middle of 2021 to today. Such excessive tightness might explain the flare-up in inflation in 2021–2023. In fact, recent evidence shows that inflation is stable whenever the labour market is efficient, so the Fed's full-employment and price-stability mandates might just coincide.