Does QE cause inflation?
I actually think that's a very interesting question. I think there are some things that are definitely NOT true about QE: There's no fixed money multiplier such that if MB increases then M1 or M2 etc will definitely increase by some fixed multiplier. QE is not the same as the government sending everyone a check, which would definitely be inflationary. It's not the same as legalizing counterfeiting, which also would definitely be inflationary. QE is also not the Fed overpaying people for worthless assets ... "bags of dirt" as Cullen likes to say, although QE1 did involve some overpaying. So it's not as simple as "more money = higher prices" as far as QE goes.
The monetization issue is an interesting one for me. Cullen is pretty clear that he doesn't think that QE is monetization. His main argument here is that the Fed is not making a market for Tsy debt: that market exists outside of the Fed's purchases. If the Fed were to stop purchasing Tsy debt the market for it would not collapse.
Assuming Cullen is correct, could we get to a place accidentally where the Fed **is** making the market for Tsy debt, such that if the Fed stopped making purchases the Tsy bond market would collapse? I don't think so, but people like this (Vincent Cate):
http://howfiatdies.blogspot.com/
have worked out a bunch of scenarios wherein this kind of thing does sneak up on us... but rather than the Fed stopping its purchases, the bond buying/owning public starts to panic, which forces the Fed to pick up the Tsy bond purchasing slack, etc, in a positive feedback loop. Some of Vincent's thinking on this is kind of fun to read, and he's convinced that historically we are in dangerous waters. I'm not convinced by his arguments, but I don't write him off as insane either.

(BTW, Vincent has a contest up for finding a counter example: he'll pay $100 if you can find one, and he's a man of his word too: I split the $100 prize money with JP Koning and Mark Sadowski on a previous contest).
New Keynesians (NKs) and post-Keynsians (PKs) are in a similar place regarding QE I think: they both take the position that it's not inflationary in our current circumstances but also it doesn't do as much good as QE promoters say it will. NKers and PKers differ as to why. NKers say it's because of the "liquidity trap" we're experiencing at the zero lower bound (ZLB).
The Market Monetarists (MMs) think QE is better than nothing (they're similar to NKs on this point actually), but they argue that without clear communication from the central bank (CB), its effects are pretty much undone. If the CB acted like Chuck Norris, then the hot potato effect (HPE) would be much more powerful and QE's effectiveness would be multiplied such that only a small QE program could be very effective. Essentially if the market perceives that QE has not **permanently** increased MB, then it becomes a very weak mechanism. Here's my favorite Scott Sumner piece on this:
http://www.themoneyillusion.com/?p=23314
That article is very much worth reading! Some people would argue that we're essentially in his case 5b right now. Scott disagrees, stating that we're closer to case 5c, although he admits in the comments to "Jared" that we may be somewhere in between 5b and 5c due to uncertainty about when interest rates might eventually increase.
Now check out his case 7: the case of the cashless society. I think that case in particular is very interesting. Especially his remark about the zero bound, which effectively gives us cases 7b and 7c to match cases 5b and 5c.
Even though Scott explicitly tells people he's not interested in accounting or banking, that doesn't mean that he's not aware of how the system works. A lot of PK types annoy Sumner and other MMs by making the mistake of thinking MMs are ignorant about those issues, when in reality, they pretty much do understand how the system operates, but philosophically, it still doesn't matter much to them. The reason for this can be inferred from Scott's story and his seven cases in the above article. Nick Rowe is more inclined to think that banks can be important, at least in the near to mid term. This maybe isn't his best article on the subject, but it's pretty good:
http://worthwhile.typepad.com/worthwhil ... ecial.html
Cullen fundamentally disagrees with Scott and other Market Monetarists because he thinks of bank deposits as equivalent to base money (what Scott calls "medium of account" (MOA)). I think Cullen has an excellent argument for that, but Nick Rowe (another MMist) has some good arguments against this as well. Scott and Nick don't fully agree on these concepts either. Here's one of many good Nick Rowe articles on the subject:
http://worthwhile.typepad.com/worthwhil ... hange.html
So to me the question is not very clear cut at all. I think people like Peter Schiff tend to make an oversimplified case for high inflation or hyperinflation. Someone like Vincent Cate actually makes some better arguments I think, even though he's an amateur (like me!).
Other Austrians, like Mish Shedlock, think Schiff is completely wrong about hyperinflation. Mish has an attitude towards bank deposits more in line with PK types (like Cullen). Shedlock basically argues that since credit money can shrink due to deleveraging at the same time the CB is pumping up base money, the overall effect can be a wash or even deflation. Where I differ with Shedlock is in his interpretation of "fractional reserve banking" and how that works. He seems to think that a 100% reserve requirement would fix a lot of problems, but I don't see it. Perhaps increasing the required capital ratios would have more of an effect. MMer Nick Rowe tackles that question here:
http://worthwhile.typepad.com/worthwhil ... atios.html
Sorry for the long rambling piece, but I just wanted to point out some arguments that make the whole question of QE and inflation a lot less straightforward than some people make it out to be. As Vincent Cate points out, we are in some uncharted waters here (in the US) and in Japan and the UK. It'll be very interesting to see what happens. But I doubt very much we'll have a case like Zimbabwe or Argentina wherein the "independence" of the CB is completely eliminated, and the CB becomes simply a mechanism whose sole purpose is to enable unlimited gov deficit spending.
Also, I highly recommend reading the blogs of JP Koning and David Glasner on any of these issues. JP is especially strong on defining exactly what the medium of account (MOA), unit of account (UOA), and the medium of exchange (MOE) are. He comes up with some really interesting historical examples to illustrate his points. He also explores a concept he calls the "convenience yield" which goes a long way to describing the effects of QE in an understandable way. Also, the monetaryrealism.com blog is very good: especially articles by JKH. Nick Edmonds and Ramanan also maintain related blogs worth reading. You can find them in the comments section to many Nick Rowe and JKH articles.
http://jpkoning.blogspot.com/
http://www.monetaryrealism.com