The first of Noah Smith's points in his post on Abenomics is that "QE does not cause deflation" (emphasis in the original). I will second that with regards to QE, but not go as far as to rule out deflationary monetary expansion completely. I've thought of Japan as a stressing case for any monetary economic theory. Here I've applied a model that has deflationary monetary expansion in it to the price level in Japan using both the full monetary base including reserves (MB) and just the currency component (M0). The result pretty much rules out MB as a good model (as I mentioned earlier this week), hence the "??!" annotation:
But this doesn't rule out deflationary monetary expansion via the currency component. Now this may seem insane -- the central bank is printing fiat, yet physical, notes and coins and putting them in circulation: how can this not produce inflation? Well, the information transfer model strongly depends on whether the government is buying goods and services with those bills or adjusting to market indicators like NGDP, interest rates or inflation. In the former case you get hyperinflation (the central bank effectively ignores the information transferred from AD) while the second allows for deflationary monetary expansion (a diminishing marginal utility of monetary expansion).
I mentioned earlier that the apparent (tiny) expansion in the currency component of the base beginning in 2011 pre-dates Abe; see the two black dotted paths on the M0 component (red) in this graph from the previous post:
According to the information transfer model, this expansion of M0 has been ever so slightly deflationary (expansion case is dark brown while the counterfactual no expansion case is light brown):
The effect on the inflation rate has been microscopic:
The cumulative effect has been large enough to be significant, but it's still obscured by empirical and model error. So I agree with Noah Smith about the QE component (MB) fairly definitively not causing deflation, but it's not so cut and dried with the currency component (M0).
Addendum: Model parameters (see e.g. here for the equation)
MB model:MB0 = 33.2 T¥
α = 0.56
γ = 0.0016
M0 model:MB0 = 24.0 T¥
α = 0.50
γ = 0.0016