Let's start with the very basics.
In the latest version of QE, the Fed is buying both longer-term Treasuries and agency mortgage-backed securities. It buys these from its primary dealers, who in turn buy them from private investors in anticipation of selling them to the Fed.
The buying process involves the banks crediting the deposit accounts of investors with dollars and the Fed crediting banks with additional reserves equal to the price it pays for the securities.
Why would a private investor accept dollars in exchange for a long-term Treasury or a mortgage-backed security? All other things being equal, they wouldn't. They've already expressed a preference for a long-term bond over a bank deposit.
But, of course, all other things aren't equal.
Many investors require a premium to hold long-term assets, something usually called a "term premium." They want to be paid more to tie their money up for the long-term.
This applies even to highly liquid assets like Treasurys. When the Fed buys securities, it raises the prices of the securities and lowers their yields. Exactly why this is so is subject to quite a bit of controversy but whatever the reason, that's what seems to happen.
(Read also: You may have already missed the taper's start.)
One effect of lower yields and higher prices is that the term premium—the added return of holding long-term bonds over cash—shrinks. If it shrinks below the premium an investor demands, he'll gladly trade you the security for cash. In his mind, the trouble of tying up money in a long-term bond just isn't worth it. Alternatively, he'll take the cash from the Fed and go invest it in some other bond with a premium that meets his requirement.
In other words, you don't need deflation to get people to accept cash for securities. You just need falling term premiums. And that appears to be what happens with QE, according to a study by a pair of Fed economists published earlier this year. (Here's a 2010 paper from a crew at the New York Fed showing the same thing in a different way.)
But just because Williamson is wrong, that doesn't mean his critics are right.
Sumner, for example, insists on treating quantitative easing as an increase in the monetary base and thinks that must be inflationary. But this is flat-out wrong because it is only looking at one side of the QE ledger—the growth of reserves—while ignoring the other—the shrinking supply of Treasurys.
(Read more: QE is a sugar pill.)
Again, let's return to our QE'd investor.
He used to hold a claim on a bunch of securities held by his bank, now he holds a large bank deposit. Sumner and other monetarists insist that he's more likely to spend this bank deposit, triggering inflation.
But why would he do this? He's already demonstrated that he doesn't want to spend the money, that's why he held the bond to begin with. He wants to preserve his capital for future uses—retirement, bequests to heirs, whatever. The shift from holding a claim on a Treasury to holding a claim on a bank deposit doesn't change this.
QE makes a lot more sense when it is viewed as a swap that reduces the supply of long duration assets (Treasurys and MBS) and increased the supply of zero duration assets (reserves).
In order to work—that is, in order to get people to sell the long duration assets—it doesn't require inflation or deflation—just a change in the relative return on the assets—lowering the term premium, or raising the return on zero duration assets (by paying interest on excess reserves).
Or both (which is what the Fed is actually doing now.)