Arguably, the outcome could have been quite different if, for instance, interest rates declined on the back of ebbing inflation but there was no accommodation in monetary policy and therefore no excess liquidity.
There is also a persuasive opposite view, as best articulated by Alan Greenspan, that the great moderation in inflation could be attributed to real economy phenomena: the long run of productivity growth in the US; and the impact of new workers in China and India in dampening wage growth worldwide and hence inflation.