Just going to throw this one out there as it's something we've been discussing a lot on the trading floors, and it's not quite as black and white as the theoretical arguments posted above. And apologies in advance to anyone who hates Krugman.
When the Fed buys up any asset under the sun, it goes to an investment bank and credits its reserve account with cash in exchange for the assets. Because of the massive size of the Fed purchases, it drives up the prices of these fixed income products and thereby decreases interest rates. That much is obvious. The conventional economic argument then argues that this excess supply of money should cause inflation, and the economy should be jumpstarted by consumers' access to cheap money via low interest rates for borrowers to finance whatever they want to buy (e.g. housing, cars). That's all well and good, and logical, but it's just not what has happened. Inflation hasn't been soaring due to extremely low interest rates and the system being flush with cash. The reason is explained by those bank reserve accounts from the first sentence of this paragraph. Since the beginning of QE, these reserve accounts have just been stockpiling that electronically credited cash. Banks traditionally make money by paying low front end interest rates on deposits and lending out at high back end rates - but if you were a bank and could see that long dated interest rates were artificially low, you might hold off on making a ton of loans until the Fed tapers QE and rates return to normal levels. And that is what we have been seeing. The supply of money accessible to you and me hasn't gone up because the cash has never left the reserve account vault, and therefore this low interest rate environment has not spurred on inflation. Perversely, when the Fed begins to taper its asset purchases and back end rates correct, banks could then start making all those loans, release the ocean of cash into the economy, and then we might have some inflationary issues on our hands. Now all of this isn't meant to say that traditional macroeconomic theory is wrong, it's just to say that because of the way our system works and because we're in a near-zero rate environment, the normal relationship between interest rates and inflation just doesn't hold.