If oil prices rise (like in 2007-08) there´s a risk of permanently lifting inflation; but if oil prices fall, the effect on (dis)inflation is only temporary!
From Fed Watcher Tim Duy:
As I anticipated, the Fed dismissed the decline in market-based inflation expectations. They clearly believe financial markets over-reacted to the decline in oil prices, and that that decline would ultimately prove to be a one-time price shock rather than the beginning of a sustained disinflationary process.
This is why we watch core-inflation.[One would wish!]
If only symmetry held, the “Great Recession” would have been only “Recession”! And as a bonus we would not have been listening, insufferably, to “Great Stagnation” talk.