The year over year change in the CPI has been roughly zero for the past 10 months, but that's purely a function of sharply lower oil prices. Ex-energy, consumer price inflation has been running about 2% per year on average for the past 13 years. What's notable is not the low level of headline inflation, it's the continued existence of 2% core inflation despite the fact that economic growth has been unusually sluggish for a number of years.
The chart above compares headline CPI inflation with "core" (ex-food and energy) inflation, with the former being much more volatile than the latter.
As the chart above attests, the difference between headline and core inflation is almost entirely due to energy prices. When you strip out energy, you find that inflation has been rising at a 2% annualized pace since the end of 2002, with the exception of the 2005-2008 period, when inflation briefly accelerated. That acceleration followed several years of aggressive Fed easing (2001-2004), and it prompted a subsequent tightening, in which raised the Fed raised its target rate from 1% to 5.25%.
Don't let the low level of headline inflation lull you into thinking that the Fed runs a great risk of triggering deflation or harming the economy if it raises short-term rates to 0.25%. I continue to believe there is a greater risk of inflation accelerating, as it did 10 years ago, if the Fed does NOT raise rates.