Gary confuses liquidity preference theory and liquidity traps in the comment section of this post. I want to clear up exactly what we're talking about here, and why liquidity preference is very important (whereas liquidity traps are just an interesting curiosity).
Gary writes: "Daniel, While liquidity preference theory is not controversial amongst a subset of financial economists, how often it happens is. This was Milton Friedman's point; yeah, it is possible to get into a liquidity trap (though it is not very likely to ever occur), but to build your entire notion of economics around it (as Keynesians of all stripes do) is silly."
Liquidity preference theory says that one determinant of interest rates is the tradeoff that people make between holding and parting with liquidity. Keynes thought this was the determinant of interest rates. Most people since Keynes (myself included) think it is a determinant of interest rates, but not the only one. If liquidity preference is the only determinant of interest rate, there's no guarantee that the loanable funds market will clear or be consistent with full employment. If interest rates are determined jointly with the market for loanable funds, then the loanable funds market will clear but there's still no guarantee that it will be consistent with full employment.
That's the liquidity preference theory of the interest rate, but that has nothing at all to do with liquidity traps. You could firmly believe liquidity traps are impossible and still have a liquidity preference theory of the interest rate and a Keynesian perspective on the macroeconomy.
So then what's a liquidity trap? A liquidity trap is a situation where the demand for liquidity or money is virtually unlimited - where the money demand curve is highly elastic. Liquidity is in such high demand that no matter how much liquidity is pumped into the market, interest rates don't lower. The demand curve is not downward sloping, it is horizontal. People can't be satiated.
This is the traditional liquidity trap, at least. This is the version that Keynes speculated on briefly. Today, though, the liquidity trap has become associated with the "zero lower bound" thanks to Paul Krugman. In the 1990s, Krugman pointed out that in Japan a nominal interest rate floor acted like a horizontal money demand curve. You can think of the zero lower bound as a price floor in the market for liquidity. Money demand may not be horizontal at all, but the zero lower bound makes it look like we're in a region where it is. I've outline both of these situations (the traditional case and the Krugman case) below in red:
Most Keynesians are pretty skeptical of liquidity traps. We only think two have happened in U.S. history, with a few other cases in other countries. Here's the thing, though: all of these cases have been of the Krugman/ZIRP/faux-liquidity-trap variety. Keynes's original skepticism about a horizontal money demand curve seems to have held up pretty well. We're at the point now where the Krugman version is essentially taken to be synonymous with "liquidity trap" because it's the only version we ever see!
Liquidity traps are very bad news. I'm not of the opinion that they make monetary policy impossible. You can always create inflation with monetary policy, which lowers real interest rates even if nominal interest rates are stuck at zero. You can also do unconventional stuff like charge negative interest rates on reserves held at the Fed. However, it does make a much stronger case for fiscal policy. Creating inflation is hard in the current depressionary environment, so while in theory it's plausible to lower real interest rates that way it's a dicey proposition. Why mess with this horizontal money demand curve when we can increase public investments easily and when there are lots of worthwhile public investments to make? Why mess with a stubborn LM curve when the IS curve is easy enough to shift? So the liquidity trap/ZIRP situation is relevant to Keynesians insofar as it tips the scales in favor of fiscal policy. It has nothing to do with the broader Keynesian point about liquidity preference theory and the cause of the recessions.
A good source on this is Boinavosky (2004).
It's interesting - Krugman has been celebrated for his trade theory, but in the end he will probably be most remembered for permanently switching us from the old view of liquidity traps to the ZIRP view - first as it applied to Japan, and now as it applies to the U.S..