The current state of the US labor market
In this paper, Domash et al. evaluate the labor market tightness by exploring the relationship between four different slack indicators from the household survey and measures of wage inflation. Their slack indicators are: a) the U-3 unemployment rate (the most commonly reported rate of unemployment in the United States and represents the number of people actively seeking a job), b) the prime age employment ratio, c) the vacancy rate, and d) the quits rate. For the firm-side indicators, they estimate an equivalent unemployment rate by examining what unemployment rate is consistent with the current measures of the job vacancy rate and the quits rate. In December 2021, the predicted firm side unemployment rate was between 1.2 to 1.7 percent, compared to the actual unemployment rate of 3.9 percent. They then evaluate the relative efficacy of these two unemployment rates in predicting past wage inflation using pre-pandemic data, and find that their results indicate that the firm-side equivalent unemployment rate is likely the best predictor of wage inflation. This indicator currently suggests that the labor market is very tight.
Some economists believe that labor market tightness will be alleviated over the coming year by increases in labor supply. We present a cursory analysis of the employment shortfall, and conclude that even under optimistic Covid-19 outcomes, the majority of the employment shortfall will likely persist moving forward. Moreover, if employment were to increase due to an increase in labor force participation, it would be accompanied by increases in incomes, and therefore an increase in demand. We therefore conclude that any benefits from the supply-side over the next year are unlikely to substantially mitigate inflation pressures from the labor market.

How Tight are U.S. Labor Markets?
Authors: Alex Domash, Larry Summers
From: Harvard University
The US Phillips curve and inflation forecasts
In this paper, Crump et al. estimate the natural rate of unemployment, u∗ over the period 1960 to 2021 using data on labor market flows, short-term and long-term inflation expectations and a forward looking New-Keynesian Phillips curve. Their Phillips curve captures the joint behavior of unemployment, wage and price inflation, and inflation expectations very well with a time-invariant slope—estimated to be quite flat. They find that u∗ was at around 4.5% before the onset of the pandemic and increased to 5.9% by the end of 2021, an increase, they argue, which reflects a strong wage growth rather than changes in inflation expectations. The authors further investigate the current and prospective path of wages using a variety of cross-sectional data sources:
Our analysis has two important implications for the reconciliation of the unemployment-inflation trade-off in the medium-run. First, our model projects underlying inflation to remain 0.5 percentage point above its long-run trend even by the end of 2023 even if wage growth slows down to levels similar to its pre-pandemic levels and long-run inflation expectations remain well anchored. Second, the flat Phillips curve we estimate does not necessarily imply high unemployment costs of reducing inflation but rather underscores the importance of anchored inflation expectations and credible monetary policy.
The Unemployment-Inflation Trade-Off Revisited: The Phillips Curve in COVID Times
Authors: Richard K. Crump, Stefano Eusepi, Marc P. Giannoni, Aysegul Sahin
From: Federal Reserve Bank of New York, University of Rome Tor Vergata, Federal Reserve Bank of Dallas, University of Texas at Austin