In a recent post I proposed that Scott Sumner, the premier market monetarist, expects too much of an inflationary effect from quantitative easing because his definition of money is too narrow.
Very briefly I'll run through the QE=inflation view. If you consider inflation to be a monetary phenomenon, more or less, than increases in the supply of money should result in higher prices (all other things being equal). If you also consider QE to be adding to the supply of money because it exchanges government bonds for bank reserves, then QE appears to be inflationary.
It's the second point that deserves another look: does QE really increase the supply of money? The answer to that, of course, depends on what you consider to be money. The definition of money, however, is notoriously hard to pin down. In fact, as Milton Friedman and Anna Schwartz argued, it may be impossible to pin down on an abstract level.
What we really want is not a "definition" of money that will apply to all and any circumstances. We want one that is relevant to the question we are asking. The definition that best helps us understand the particular aspect of the world and economics that we are looking at.