The creation/destruction matrix tells us about employment. What about inflation?
In my view, there is no reliable Phillips Curve. Also, the behavior of velocity means that the monetary authority cannot precisely control inflation (or nominal GDP). Instead, there are three regimes for inflation.
1. Anchored expectations. People expect inflation to be low. When the central bank alters the money supply, velocity tends to move in an equal and opposite direction.
2. Hyperinflation. The fiscal deficit is out of control. Government spending far exceeds what the government is able to take in through taxes and borrowing. Money is printed at an ever-accelerating rate, and its velocity rises as households and businesses try to minimize their losses from holding money. The private sector becomes reluctant to use money at all, and its use becomes increasingly confined to transactions with the government.
3. Inflation fever. As in the U.S. in 1970-1985, inflation reaches a level where it becomes a major factor in the financial planning of households and businesses. They put cost-of-living escalators into contracts. They adopt financial innovations that allow them to minimize holdings of non-interest-bearing money, creating upward lurches in the velocity of money. This behavior in turn reinforces inflation, producing a vicious cycle of high and variable inflation.
In terms of the monetarist equation, MV = PY, I view velocity has highly unstable. When inflation expectations are anchored, monetary policy is ineffective because of offsetting movements in velocity. Under hyperinflation, there is no independent monetary policy–money is printed to fund the government debt. When there is inflation fever, velocity is high and variable, and the monetary authorities can do little about this. In the early 1980s, perhaps Paul Volcker was able to turn things around. Or perhaps the bond market vigilantes, by raising long term real interest rates, boosted the value of the dollar and brought down oil prices, thereby breaking the inflation fever.