Statements from central banks
Expectations and statements from influential people in the financial markets and especially from the central bank is perhaps the most important indicator of them all.
If the players on the stock and currency markets have confidence in the central bank, because they have had a good track record of assessing future inflation, then inflation will be at about the level at which the central bank has ruled.
This happens because most players will take the central bank expected inflation to actual inflation in their calculations and pricing estimates. It leads to inflation becomes more or less what the central bank has ruled.
One could say that the central bank can thus indirectly controlling and keeping inflation low and at stable levels.
