Can we measure whether the Fed is "behind the curve"

The Fed is behind the curve with respect to fighting inflation.  I believe it and so do many others, but can some number be put to this belief. Of course, we can look at the difference between some inflation measure and Fed funds. Whether CPI, PCE, core, or trimmed, inflation is high versus short rates and real rates are at extreme negative values, yet we can be more precise about being behind the curve. 

St Louis Fed president Bullard has done a good presentation last month on this issue that is short, clear, and easy to read. It was updated and presented at the Hoover Institute this week, see "Is the Fed behind the curve? Two Interpretations". It takes a conservative approach and shows that by using a simple Taylor Rule, the Fed is behind and has a lot of wood to chop. 

If you account for the market moves out the curve as a response to forward guidance, the Fed is still behind the curve. The gap has closed slightly since March given the fixed income sell-off, but there is still more rate increases necessary. 

The question is not whether the Fed is behind the curve, it is, but what is the cost of closing the gap and how fast should it be done. It can be done quickly or slowly but the path does matter. Right now, the Fed has provided guidance on the path. A fast path may work but at the expense of financial markets. A slow path may cause inflation expectations to be driven higher.