AbstractDuring the 1990s, many OECD countries had declining rates of inflation while their unemployment rates were also falling, something that on the surface seemed at odds with the Phillips curve relationship between inflation and unemployment. For the USA, these seemingly contradictory developments have been reconciled in terms of two factors: (1) an acceleration in productivity and (2) structural changes in labour markets that lowered the natural unemployment rate (NAIRU). Here we ask whether comparable forces were at work in 19 other industrial countries. We find that productivity advancements were the main structural factor reducing inflation only in the USA. In other industrial countries, persistent labour‐market slack was the main factor exerting downward pressure on inflation. This persistence stemmed, in part, from structural reforms that lowered the NAIRU while the unemployment rate was declining. Ireland, New Zealand and Norway were three countries where labour‐market reforms helped to push inflation down dramatically.