What measure of unemployment is used by central banks to find out whether the rate of unemployment is below the natural rate of unemployment?
The phrase “natural rate of unemployment” has been largely replaced by NAIRU or similar concepts. Each country has its own definition of the unemployment rate, the U.S. “headline” measure is U-3.
Nobody has created an estimate for NAIRU that is based on a function of other variables, instead it is estimated based on the behaviour of the economy and the chosen unemployment rate measure. This implies that a NAIRU estimate is defined relative to the unemployment rate used in the estimation procedure. In the United States, most researchers would run their estimation versus U-3, but one might need to validate this.