Bryan asks how I think that the Fed can make big changes in inflation regime but not make small changes within a regime.
Again, my thinking is based almost entirely on my reading of postwar U.S. monetary history, which went from a low-and-stable regime in the 1950's and 1960's to a high-and-variable regime in the 1970's to a long transition in the 1980's back to a low-and-stable regime where we have been since.
1. People form monetary habits. When inflation is low and stable, people do not make big attempts to economize on cash balances. When inflation is high and variable, people (and especially businesses) pay a lot of attention to how they economize on cash balances. When inflation is low and stable, workers make wage bargains without thinking much about contingencies for high inflation. Firms do not worry much about overall inflation, either. But in a high and variable inflation regime, workers and firms become keenly aware of the need to stay ahead of general price trends, so inflation becomes somewhat self-fulfilling.
2. There are fixed costs and threshold effects in getting people to change habits. So, until inflation crossed the 4 percent threshold, nobody invented money market funds or "sweep accounts" or "cash concentration accounts" or ways to game the Fed check-clearing system to earn interest on float. However, after that 4 percent threshold was crossed, people changed their habits. That raised the velocity of money. They also did more indexing of labor contracts and changed prices more frequently.
3. It took pretty much the entire decade of the 1980's, but people finally let go of their high-inflation habits. They lost interest in economizing on cash balances, and in wage and price decisions they made less use of indexing and frequent renegotiation.
Mathematically, think of a model in which both the velocity of money and the unpredictability of velocity are exponentially related to the rate of inflation. As inflation goes up, this makes inflation harder to bring down and harder to control.
When people are in the low-inflation mode of thinking, then lots of assets substitute closely for money. The Fed can keep printing and printing and, for a while at least, people say "fine, I'll take more cash and hold less of something else." Velocity tends to vary inversely with the money supply in this regime.
Eventually, however, if the Fed prints enough, you reach a point where people start to bid up the prices of goods. Once inflation gets high enough to enter people's consciousness, then money and assets are no longer close substitutes. Velocity no longer varies inversely with the supply of money. Rather, velocity tends to vary positively with the rate of money growth. In addition, because people are changing their monetary habits, velocity becomes more unpredictable.
In the late 1960's, the Fed did not react quickly enough to higher inflation. Inflation got out of control. At the end of the 1980's, inflation started to creep up again, but the Fed clamped down before we got into the high-inflation regime, and instead it sent us into the low-inflation regime.
That's my story, and I admit that it has "just so" written all over it.