What is the link between inflation and the unemployment rate?

We estimate a Phillips curve, i.e. the relationship between the unemployment rate and inflation, in the United States and the euro zone. We seek to determine what rise in the unemployment rate would be needed to bring headline and core inflation down to 2%. We see that the disinflation that is being observed today cannot be caused by rising unemployment. It therefore has other causes: In the United States, falling energy and food prices, and productivity gains; In the euro zone, the fall in inflation is linked to the fall in energy and unprocessed food prices and the decline in corporate profit margins from the third quarter of 2023 . The fall in import prices explains a 0.6 percentage point fall in year-on-year inflation in the third quarter 2023 in the United States and a 1.9 percentage point fall in year-on-year inflation in the third quarter 2023 in the euro zone.