What is the likely level of the structural unemployment rate in the United States and the euro zone?

For headline inflation to fall, the unemployment rate must become higher than the structural unemployment rate, by including the trend in relative import prices (terms of trade) in the calculation of the structural unemployment rate. For core inflation to fall, the unemployment rate must become higher than the structural unemployment rate, calculated with a constant relative price of imports (of commodities). It is therefore important to know how high the structural unemployment rate is: Overall, including the effect of changes in the terms of trade; With constant terms of trade. We want to estimate it by comparing the unemployment rate with: Changes in headline and core inflation; Indirect indicators of the position of the unemployment rate in relation to the structural unemployment rate, such as companies' hiring difficulties. We conclude that the unemployment rate is between 4.5% and 5% in the United States (compared to 3.5% for the observed unemployment rate), and around 8% in the euro zone (compared to 6.6% for the observed unemployment rate). In both cases, slowing inflation, without using the terms of trade improvement, requires a nearly 1.5 percentage point increase in the unemployment rate.