The first thing to note is that inflation is not a price phenomenon (don´t reason from a price change is relevant here), but a monetary phenomenon.
For example, changes in relative prices (due to an oil price shock, for example) will only turn into inflation (a continued increase in all prices), if monetary policy allows it to happen (as we´ll see contrasting the 70s with the last 30 years.
Another point I´ll make is that the price index the Fed should target is the PCE Core index. Why? Because the headline index is much more volatile and, like in 2008, will lead the Fed astray.
The first chart shows that over a long period (60 years in this case) both the Core & Headline index show the same thing.
If you break the 1960 – 2020 period by decades, you´ll note that the core index functions as an “upper bound” to the headline index. The next chart shows two examples. The first from the high inflation 1970s and the second from the low inflation 1990s.
The next charts show the two in the form of year over year rate of change – inflation – and the corresponding behavior of nominal spending (NGDP) growth. Note that rising inflation (both for the headline & core indices) only happens when monetary policy, as gauged by NGDP growth, is on a rising trend. Relative prices do change but only with overall prices going up.
During the low and stable core PCE inflation period, the headline PCE inflation wonders up and down, buffeted by the price shocks (mostly oil). For this low inflation period, the average headline PCE inflation is 1.8, with a standard deviation (volatility) of 0.86. The average for core PCE inflation is the same 1.8, but with a standard deviation less than half that (0.41). So it´s much better to target the low volatility index.
What does the Fed face at present? The next chart shows that the core PCE index has hugged closely to a 1.8% trend path since 1993. This trend path was established from the data to 2006, before the upheavals of the Great Recession. Fourteen years later, even after the effects of the Covid19 shock, the index hasn´t deviated from the path.
If the Fed manages to keep the core PCE index following this path going forward, in ten years’ time, the index will reach Scott Sumner´s “magic number” of 135 (Ok, he means the headline index, but I´ve argued that´s a bad index to target and anyway, the core index is an upper bound on the headline index).
How to do that? Basically, don´t invent new benchmarks. Take what you have and do the best with it. Moreover, the best the Fed can do is what has been proven adequate for a long time, to wit, keep NGDP growth stable. The Fed can improve on that by not making the mistakes it made in 2001 and particularly in 2008, as the charts below indicate.
Now, NGDP is still far below the trend path it followed from the end of the Great Recession. The Fed´s first order of business is to make monetary policy expansionary enough to take NGDP back to that trend path. Once (if?) that´s done, the Fed should pursue a monetary policy that allows NGDP to grow close to the 4% rate it averaged from 2010 to 2019.
With that, the core price level will be close to 135 in 10 years’ time.