I struggle and struggle to understand the fear of near-term, rapid inflation that is being stoked by the likes of commentators noted here and here. This struggle becomes even more profound when I examine actual data.
Below I plot the series that are purportedly of most concern, namely measures of the money stock: the standard M1 and M2 series, plus the M3 series that the Fed discontinued, all divided by real GDP.
Figure 1: M1 (green), M2 (red) and M3 (blue), seasonally adjusted, divided by GDP in Ch.2005$. NBER defined recession dates shaded gray. Source: BEA, 2010Q3 GDP second release, and for M1 and M2, and M3 up to 2005Q4 from Federal Reserve Board via FRED, and for M3 from 2006Q1, from A World of Possible Futures, and NBER.
From Tautology to Theory
The logic that some individuals seem to be using is that greater money creation must induce greater price increases. Even by this model (so to speak), it hardly seems like high inflation is around the bend.
To formalize the argument I think various commentators are using, start with the tautology:
(1) MV ≡ PY
The Quantity Theory requires that V = PY/M be stable. Then:
(2) P = μ(M/Y)
Where μ is V held constant. (M/Y) is the variable plotted in Figure 1. Take logs:
(3) p = m + log(μ) – y
Take the time differential:
(4) π = Δm + Δ log(μ) – Δ y
π is inflation. If μ is constant, then Δ log(ν) drops out. Note that the monetarist logic that greater money supply necessarily leads one-for-one to higher prices also requires that Y be also constant, which would be true in a Classical model. Suppose for the sake of argument that Y (real GDP) grows at an exogenous rate. Then inflation is the money growth rate minus trend real GDP growth. By this measure, high inflation hardly seems likely.
Now let’s examine the underlying assumptions. First, is velocity constant? I’ll let the reader decide:
Figure 2: M1 (green), M2 (red) divided by nominal GDP. NBER defined recession dates shaded gray. Source: BEA, 2010Q3 GDP second release, and for M1 and M2, and M3 up to 2005Q4 from Federal Reserve Board via FRED, and for M3 from 2006Q1, from A World of Possible Futures, and NBER.
Figure 2 clearly demonstrates that velocity is not constant; nor does it even trend in a stable fashion. Hence, a critical piece of the monetarist worldview is missing. (Actually, it’s much worse than mere instability; all three velocity series fail to reject the unit root null using the UMPI DF-GLS test of Elliott, Rothenberg and Stock. At the same time they all reject the trend stationary null of the Kwiatkowski, Phillips, Schmidt and Shin test. Of course, anybody with a shred of acquaintance with statistical techniques would not be surprised by this finding.)
Now, none of the foregoing is controversial, or even new. In fact, the instability of velocity is one of the basic tenets of monetary analysis I teach in intermediate macroeconomics. So why does this worldview hold such sway? One interpretation is sheer innumeracy. An alternative is sheer demagoguery. I do not have sufficient information (nor inclination) to make a judgment for each particular commentator.
A second point is that we have a suspicion that GDP is not exogenous with respect to money, at least at the short to medium run. One might argue that (4) holds in the long run; but that I think is not what critics of QE2 are propounding.
Is there even a correlation in growth rates? Consider four quarter inflation and four quarter changes in the log M2 to GDP ratio.
Figure 3: 4 quarter change in log GDP deflator against 4 quarter change in log M2 to real GDP ratio, 1986Q1-2010Q3. Source: BEA, 2010Q3 GDP second release, Federal Reserve Board via FRED, and author’s calculations. [Corrected/updated 8am Pacific – mdc]
The slope is 0.015 -0.026, and not statistically significant at anywhere near the conventional levels.
Does a Credit View Give More Cause for Inflation Anxiety?
Some observers (including some adherents to M3) argue that broader measures of monetary aggregates, or ones that are more credit-like, are better linked to inflation. Figure 1 suggests that inflationary pressures are then, if anything, decreasing, as M3 to real GDP has been decreasing since the end of the recession. As of September, M3 growth has been -5.1% over the previous 12 months.
So the quantity theory (which, just to remind readers, refers to money and not money base) suggests little prospect of rapid inflation, given the recent evolution of money aggregates. With the 2010 output gap between 3.4 to over 6 percentage points of GDP , a Phillips curve analysis seems to point to muted inflation if not disinflation.
One plausible inflation scenario is the one wherein the Fed is not able, politically, to prevent reserves from leaking into expanded money supply in the future (or course, if one wanted to politically insulate the Fed, one wouldn’t be signing letters like this, as Brad Delong observed. Perhaps those individuals are thinking of the aphorism, “in order to save the village, we had to destroy it.”) But if there are fears of increase money base feeding into money supply, they haven’t shown up in market based measures of expected inflation. 
By the way, Econbrowser reader W.C. Varones asks:
Does anyone have an example of a central bank actually shrinking its balance sheet significantly ever in history?
And the answer is, “yes”. For edification, all he has to do is read this article.