Did monetary policy cause inflation?

Scott Sumner asks the question:

Low rates caused by expansionary monetary policies are inflationary, and low rates caused by contractionary monetary policies are deflationary.

Well, first of all, monetary policy is not low rates as the Fed has not executed any market move that would lower rates and the two rates it has effected, interest on reserves, is above market levels, and QE effects on long term bond rates is up. So we have no evidence on low rates since 2007.

So, has the Fed's effect in raising rates caused inflation or not? What inflation would that be?  The stock market has risen like a rocket. So that would be high rates caused by  expansionary policy? QE had clearly caused a one point rise in consumer prices right in 2010 that lasted a year.

How about Canada?

 See any causality? How does Nick Rowe differentiate between the bank and inflation responding to a third variable? 

The issue is something called the neo-Fisher view that the central bank pushing rates beyond equilibrium causes the opposite effect.  Pushing rate too high can cause inflation, too low can cause deflation.  When that happens central banks do a noticeable rate cycle, they end up out of phase with price changes and are always responding too late.  Canada certainly has a rate cycle, prices clearly drive the bank, not the other way around.

A little research on the web in fact tells me that the provinces in Canada are often at variance with the average inflation. In the USA also we can see inflation vary from 3 to 0 percent from Texas to New York, the USA being the worse monetary zone. So in Texas the fed will drive real rates down while waiting for New York to catch up.

What's the point here?

The USA is not an optimum monetary zone and the Fed will never get rates settled one way or the other.