Inflation is already here, it's just that the wealth hasn't "trickled down" into the middle/lower class so consumer goods haven't spiked yet. It will seep out eventually, but right now it's mostly still sitting in financial markets and corporate accounts. The trillions (yes, trillions) of dollars that have been pumped into the economy via QE and other fed programs don't just go away.
Where's the inflation in the Eurozone? They're way ahead of the US. Or even better, Japan, "printing" like a madman since the 90s, uhm where is that inflation you mentioned?
But yes, they don't go away, such things actually cause deflation because they prevent recession-cleansing of inefficient organizations, keep property prices high, cripple people and organizations with debt, ...
