The underlying trend in inflation is driven by the laws of supply and demand, which are as applicable today as they ever were. Excess demand pushes inflation up; excess supply pushes inflation down. Central banks exploit this relationship, working to create excess demand or excess supply in the economy, to target the inflation rate.
A central role in this relationship between the economy and inflation is played by inflation expectations. The more anchored those expectations are, the more quickly the economy will find its way back to normal after an economic shock. This is known as the credibility dividend: a credible central bank will see inflation expectations well anchored at the target level and will have a relatively easy time restoring normality after a shock. What this means is that the underlying trend in inflation may become more stable as expectations become more anchored. In short, the more successful the inflation target is, the less obvious the relationship between economic shocks and inflation will become.
Currently, US expectations are very well-anchored:
The top chart shows the 5-year breakeven inflation rate while the bottom chart has the 10-year breakeven rate. Both are actually a bit lower now than at the beginning of the expansion.
As a result, we've seen very stable inflation:
The top chart shows the PCE implicit price deflator -- the Fed's preferred inflation gauge. The bottom chart shows the Dallas Fed's trimmed mean PCE inflation gauge, which removes extreme movements from the index, reasoning that these are short-term deviations from a longer-term norm. Both measures have flummoxed the Fed as they have failed to hit their 2% target.
But the recent weakness in inflation expectations is probably contributing to this lower level of price pressure.