Nick Rowe does a great job with mechanical analogies for monetary policy.
Scott Sumner mentions Rowe and New Keynesian and Neo-Fisherism and then links to a video about someone who put tremendous energy into learning to ride a bike with reversed steering. Scott found it linked by Tyler Cowen here. Here is link to the video.
I can't begin to link all the relevant posts by Rowe. The video really relates to many posts about how the conventional wisdom today for central banks is that they need to lower nominal interest rates to raise inflation and raise nominal interest rates to raise inflation. Monetary policy in new Keynesian models has traditionally followed that conventional wisdom exclusively.
With neo-Fisherism, a higher nominal interest rate is associated with higher inflation and a lower nominal interest rate is associated with lower inflation. Therefore, couldn't it be that when central banks raise their interest rate target, they cause higher inflation? Could it be that the low interest rate targets set by the Fed for the last 7 years is why inflation continues to run below the Fed's target of 2%?
The video is about a bicycle constructed to go left when the ride turns right and right when the rider turns left. It is about how difficult it was for him to learn to ride the new bike.
Rowe has argued that the conventional view that the way to raise inflation is to first lower the nominal interest rate seems convoluted. This is especially true when the higher inflation will later require the central bank to raise its target for the nominal interest rate.
Those, like Rowe (and I) who have never accepted the new Keynesian approach would point out that a more rapid growth rate of the quantity of money may well result in a lower nominal interest rate in the short run, but that the long run effect is a higher inflation rate and a higher nominal interest rate. If the short run "liqudity effect" on the interest rate were to not materialize, say because of anticipation of inflation or rapid growth in real output, it would not be of central importance. A possible, transitional effect does not appear. So what? Josh Henderson has a good post along those lines. The "problem" with neo-Fisherist results in a new Keynesian model is a reason to believe that the new Keynesian approach to modeling is problematic. If the Fed expands money growth, even if this does lead to a temporary decrease nominal interest rates, it won't result in lower inflation. And if the more rapid money grown results in immediately higher nominal interest rates, that won't result in lower inflation either.
But perhaps most relevant is Rowe's post about how it is all about communication. If the Fed raises interest rates and everyone thinks this means the Fed is trying to stop inflation, then inflation will fall. But if the Fed raises interest rates and everyone thinks this is due to a new inflationary policy, inflation will rise.
And even more relevant to the bicycle experiment is David Glasner's post about central bankers having a couple of centuries of gold standard experience to narrow their perspective--that is, they learned to ride a "normal" bike. In that world, they were trying to keep their own liabilities redeemable in gold. Raise interest rates to attract more gold. Lower interest rates (if you want) because you would rather hold earning assets rather than gold. The price level and inflation rate depended on the world supply and demand for gold.
And after the gold standard disappeared, we are now suffering through the efforts of our central bankers to ride a new type of bicycle--one that determines the value of money.
My solution is to constrain central banks so that they are no longer responsible for determining the value of money. A nominal GDP level target determines the price level. A central bank (or a free banking system) subject to an nominal GDP level rule would no more be in a position to use the neo-Fisherist approach than a central bank (or free banking system) subject to gold redeemability. The inflation rate necessary to return to target is tied down, so if the rule is credible, so is the expected inflation rate.