I pondered the wording of the question in this post’s title for a while because while it may seem that the clear cut answer is yes, my guess is that the real answer is: It depends.
From the equation of exchange, M*V = P*Y, one cannot really tell whether growth in M will result in more P or more Y. From discussions about what actually happens with growth in M around the macro blogosphere, it appears that the general rule of thumb is to assume a split between the two, and I haven’t found any literature on anything more precise.
So when I hear discussions about the Fed being behind the curve, such as the piece from AEI I critiqued last week, and talk of being well below the natural rate with inflation about to come roaring back at any moment, a big bright question mark appears above my head with the word “Huh?” in bold, and my eyes sort of glaze over because what the CB actually looks at is M*V = NGDP. If the central bank goes out to assassinate a modest rise in P by lopping M, it is likely to also assassinate Y because it just downshifts NGDP that splits between the two depending on conditions.
The way I understand inflation targeting is that NGDP is soft-capped so that Y is never optimized and that prevents P from moving around too much. So if one reasons that NGDP is maintained so that Y is never optimized to prevent P from moving around, then Y is never optimized under the current regime. It is impossible then, barring masked supply shocks, for the economy to be at the natural rate under the current regime – unless, of course, one can imagine the natural rate to be achievable along with every other possibility for Y to occur under the soft NGDP cap where P is not allowed to rise faster than a rate of under 2%. At least, my guess is that the natural rate antagonists probably don’t have much of an argument because the odds of having one’s cake and eating it too are probably very occasional and slim.
I could go on about how the current IT regime at the Fed isn’t consistent with its mandates of full employment and balanced growth and the human tragedy baked into it – Y never being optimized to control P. But most people are smart enough to figure out what it means on an up close and personal basis.