Labour market flows, unemployment and the Phillips curve

We present empirical evidence from the United States demonstrating that labour market flows provide valuable insights into subsequent wage and price inflation. Specifically, we introduce a novel measure of the unemployment gap, defined as the difference between the unemployment rate implied by current labour market transitions -referred to as "flow-based unemployment"- and the observed, or stock-based unemployment, rate. Our findings reveal that inflationary pressures tend to subside when the unemployment gap becomes positive, i.e., when flow-based unemployment exceeds stock-based unemployment. To further investigate this relationship, we develop a search-and-matching model incorporating nominal wage rigidities and persistent (non-i.i.d.) shocks. In this framework, while firms face wage rigidities, they retain the ability to negotiate wages with new hires, making firms' bargaining power endogenous and dependent on both stock- and flow-based unemployment. Consistent with our empirical results, the model demonstrates that a larger unemployment gap-whether driven by higher flow-based unemployment or lower stock-based unemployment-typically leads to lower wages, provided that shocks to transition probabilities exhibit sufficient persistence.