Interpret at will. Today, domestic oil consumption represents about 4% of the US GDP, so while a key input to the overall economy, not a great proxy for overall inflation. Instead, I think this metric (or perhaps its first derivative) is more plausibly characterized as economic ‘head winds’ or ‘tail winds’. This is why we frack.
Still, the ‘bubble’ from 1984 to 2007 coincides pretty well with ‘The Great Moderation’. Those days seem long gone.