As Bryan offers data for study, let me suggest that in the United States the regime changes somewhere between 5.0 and 6.0 percent for the annualized "core" inflation rate (the CPI excluding food and energy).
1. Take the moving six-month average inflation rate, as measured in the U.S. by the CPI excluding food and energy. Express this as an annualized rate.
From July of 1957 through August of 1966 this moving average inflation rate stayed within a range of 0 to 3.66. (Actually, the raw index itself never went up or down by more than one tenth of one point during any month in this period. Things were very dull on the inflation front.) It did not cross the 5.5 percent barrier until October of 1968. By that point, we were in the high and variable range, but this was briefly suppressed by a recession and, more importantly, wage-price controls.
The next time the 5.5 percent barrier was crossed, in December of 1973, from that point until November of 1982 the 6-month average of inflation only dipped below 5.5 percent in two months. Otherwise, it got as high as 15.42 percent, and was over 10 percent in three episodes totaling 32 months. This was the period of high and variable inflation.
From June of 1983 through February of 1990, the six-month moving average stayed between 3.5 and 5.5 percent. If you call this a low rate of inflation, then it fits with the two-regime theory. However, if you call it a moderate rate of inflation (which seems like a quite reasonable point of view), then it contradicts the theory.
The 5.5 percent barrier was crossed in 1990, with the six-month moving average peaking at 5.96 percent in August of 1990, but inflation turned down from there, falling below 5.5 percent in February of 1991 Until the 1990 recession, we might have been flirting with the high-inflation regime.
Between February of 1992 and the end of 2009, the six-month average of core inflation never went above 3.68 percent or below 0.94 percent. Low and stable.