The difference being that you might one day see a unicorn.
A liquidity trap requires
1. Low nominal interest rates. (The nominal interest rate is the interest rate as stated.)
2. High real interest rates, due to low or negative inflation.* (The real interest rate is the nominal interest rate minus the rate of expected inflation. If the nominal interest rate is 5 percent and the expected inflation rate is 2 percent, then the real interest rate is 3 percent.)
3. No way for the monetary authority to escape from (1) and (2). Hence the term trap.
(*In this post, Paul Krugman surprises me by stating implying (as far as I can tell) that high real interest rates are a sign that we are not in a liquidity trap. That is completely the opposite of my understanding. Anyway, in the Reagan years, it is not the high real interest rates that tell us we were not in a liquidity trap. It is the fact that nominal interest rates, although they declined, were still high also.
Paul seems to be saying that currently real interest rates are low, in which case I would say that condition (2) for a liquidity trap is not satisfied. Either the low real interest rates are going to trigger an economic expansion or the interest elasticity of spending is low. Low interest elasticity of spending--meaning that consumers are not induced by low interest rates to increase their purchases of durable goods--could certainly be a problem in today's economy. But that is not the same thing as the liquidity trap. In textbook terms, a liquidity trap is a flat LM curve. A low interest elasticity of spending is a vertical IS curve.)
It is certainly possible for (1) and (2) to be satisfied. We can have a nominal interest rate of 1 percent, an inflation rate of -3 percent, and hence a real interest rate of 4 percent, which would be pretty high, certainly higher than you would want to see in a recession. However, that does not make it a liquidity trap.
Look, I can't stop you from saying that because you have seen a beast with four legs and a horn in the middle of its forehead you have seen a unicorn. Even though it was a rhinoceros. Similarly, if you want to call any period of low economic growth, low nominal interest rates, and high real interest rates a liquidity trap, I cannot stop you. (I suppose I cannot stop you from calling a period of low real interest rates a liquidity trap, either, but, again, that seems contrary to everything that used to be taught in intermediate macro courses.)
But the textbook definition of a liquidity trap is an infinite elasticity of the demand for money. The central bank can expand the money supply to an unlimited degree, without affecting interest rates, output, or prices. (As one prominent economist once put it, "no matter how much the Fed increases the monetary base, it has no effect, because it just substitutes one zero-interest asset for another.") In a liquidity trap, the monetary authority cannot cause inflation even if it wants to. If that is true, then Ben Bernanke is a unicorn.
My claim is that if you have the power to increase the amount of money in circulation, then you have the power to cause inflation. It's as simple as that.
Let us not even bother talking about the proverbial helicopter drop, in which the central bank prints currency and distributes it among the population. That might not count as pure monetary policy--I can see making a case that it is a sort of fiscal policy as well.
No, let's restrict ourselves to the central bank exchanging money for other assets. In the textbooks, the central bank buys short-term government bonds. But it could buy long-term government bonds, it could buy corporate bonds, or it could buy foreign bonds.
If these operations are done at small scale, then I can see them having no effect. In fact, I am inclined to err on the side of believing that small-scale central bank operations have no effect.
At some point, however, these operations simply must have effects on prices and/or interest rates. Think about buying foreign bonds. If the central bank purchases enough foreign bonds, the exchange rate has to depreciate. With enough depreciation, the rate of domestic inflation has to rise.
Once again, I assert that in a fiat money economy, it is never impossible for the monetary authority to debase its currency. Undesirable, usually. But impossible, never.
If the monetary authority is always in a position to cause inflation, then there can be no liquidity trap. Once inflation gets above, say, 3 percent, then as a matter of arithmetic either:
--the nominal interest must be higher than 3 percent, in which case we remove condition (1) above; or
--the real interest rate must be negative, removing condition (2) above. For example, if the nominal interest rate stayed at 1 percent and the inflation rate reached 3 percent, then the real interest rate would be negative 2 percent.
Once you admit that the central bank can cause inflation by expanding money growth, then you have admitted that there is a way out of the liquidity trap, in which case there is no trap.
I wonder if there are any prominent macroeconomists who share Krugman's view of liquidity traps.