I have argued that inflation is a highly misleading variable, and should be dropped from macroeconomic analysis. To replace it, we would be better off looking at variables such as NGDP growth and nominal hourly wage rates. A paper by Coibion and Gorodnichenko illustrates the problems with using inflation (although they reach very different conclusions.) The paper starts off with a quote from Bob Hall:
“Prior to the recent deep worldwide recession, macroeconomists of all schools took a negative relation between slack and declining inflation as an axiom. Few seem to have awakened to the recent experience as a contradiction to the axiom.” Bob Hall 
Not my school!! In my book on the Great Depression [which my publisher seems determined shall never see the light of day] I argue that the standard model is wrong, slack does not cause disinflation. For instance, prices rose sharply after March 1933, despite the greatest level of slack in US history. Rather falling NGDP causes slack, and is often associated with falling inflation.
Here is what they discovered about inflation expectations:
Specifically, we show that an expectations-augmented Phillips curve, using household inflation expectations as measured by the Michigan Survey of Consumers, can account for the absence of strong disinflationary pressures since 2009. The primary reason for the success of a household inflation expectation-augmented Phillips curve is that household inflation expectations experienced a sharp rise starting in 2009, going from a low of 2.5% to around 4% in 2013, whereas other measures of inflation expectations such as those from financial markets or professional forecasters have hovered in the close neighbourhood of 2% over the same period.
The public’s confusion was due to the fact that they focused on price increases from the supply-side, i.e. those that reduce living standards, not the demand-side: