Last note I have conceptually given a state space model for an inflation control system. Each element of the inflation vector is a goods or a piece of service. They are components in inflation calculation. If we can obtain the quantitative dependencies between the inflation components, and how monetary policy such as interest rates can impact each component, then a mathematical model can be established.
Further we can find from the matrix A which part of inflation is controllable via interest rate, how effective it is, and which part is simply out of the reach of policy rates.
Inflation dynamics include an inner positive feedback loop. High inflation can push people spending early for fear that nominal prices of goods will increase, and this tends to create more demand and further push up prices, and therefore more inflation. In deflation situation, consumers will refrain spending as they expect prices will be cheaper tomorrow. This tends to reduce demand and therefore can exacerbate deflation condition.
Positive feed back is an inherent instability mechanism in a system. It is one of the most important factors why inflation control is difficult. To reduce the strength of the positive feedback, government and companies often engineer incentives to influence consumers’ behaviors, examples such as tax rebates for house upgrade.
The U. S. is facing another positive feedback mechanism in the inflation dynamics. The Fed is trying to raise interest rate to create some leeway for the future if the economy needs some stimulus from the monetary policies. The expectation of higher rate strengthens the U. S. dollar, and the strong dollar makes import cheaper for U. S. consumers, therefore push down inflation in the U. S.
Many Fed members and other economists, including Larry Summers, are calling for government fiscal policy in the course of interest rate normalization. I think they are right because within the inflation dynamics, it is hard for the Fed policy alone being able to control inflation to target of 2% while raising interest rates.