"Cash-in-advance constraints and modeling liquidity traps
It was good to see Paul Krugman's response to my previous post. We agree more than we disagree, I think. We need to move outside the Neo-Wicksellian perspective if we want to look at monetary policy where short-term interest rates are already at zero. You can't use a model which contains i and does not contain M to examine whether changes in M could have an effect even when the central bank can't change i. Sort of obvious really, once you say it like that.
And Paul Krugman had already moved outside the Neo-Wicksellian perspective (indeed he did so 10 years ago) in the paper he links to in his response. The model in that paper contains both M and i. It is not a Neo-Wicksellian model of a cashless economy. It explicitly contains money, and an explicit assumption that people need to use money to buy things. It has a "cash-in-advance constraint".
I'm not against CIA constraints as a device to get money and monetary exchange formally into a model. Sometimes a CIA constraint may be a good way to do this. But for the question at hand, whether monetary policy can still work in a liquidity trap, I don't think adding a simple CIA constraint is enough.
In other words, Paul Krugman may or may not be right that increasing the quantity of money does not work when nominal interest rates are at zero. But his model of why monetary policy does not work does not convince me that he is right. His argument that the CIA constraint is not binding in a liquidity trap, and so monetary policy cannot work, because it merely makes a non-binding constraint even less binding, does not convince be.
A CIA constraint can be written M >= P.e (the stock of money is greater than or equal to the flow of nominal expenditure on goods). When I state it like that, you can immediately see the problem with a CIA constraint, and it's a long-known problem. The left hand side of the equation is a stock, and the right hand side is a flow. The units are not the same. It only makes sense mathematically in a discrete-time model. But that means the real "bite" of the constraint is an artefact of the length of the modeler's period.
In other words, the velocity of circulation of money, which ought to be treated as an economic variable, is determined by the modeler's choice of length of period. In the limit, as the model approaches continuous time, the velocity of circulation approaches infinity, and the CIA constraint disappears.
This is not just some prissy math/technical critique (I hate those critiques). We know that velocity rises in hyperinflations. The real stock of money falls relative to real expenditure. If any economy faces a binding CIA constraint, it is an economy in hyperinflation, because that's where velocity is fastest and real money lowest. But then any economy outside of a hyperinflation, where velocity is slower, and real money is higher, would have a non-binding CIA constraint. But then monetary policy would be ineffective outside of a hyperinflation. But it isn't. The non-binding CIA constraint approach proves too much.
A CIA constraint gives you an LM curve (for a given money supply) which is L-shaped: horizontal at zero nominal interest rates and vertical elsewhere. We know it's not vertical elsewhere. There is no hard distinction between "active money" and "idle hoards". The $100 sitting in my wallet is idle right now. There is only a difference in degree: how long do I expect it to stay idle?
All models are false, of course, and that's never stopped us modeling in the past. Nor should it. But the particular place where this model is false is rather close to the place where we want it to teach us: about monetary policy.
So, I am not convinced by Paul Krugman's model. But that does not make its conclusion, or Paul Krugman's conclusion, wrong. Indeed, it would probably be possible to soften the CIA constraint to allow people to choose the frequency with which they trade money for bonds (at a cost), and generate a liquidity trap in the limit, as the rate of interest approaches zero. The puzzle would be why we have zero nominal interest rates on short-term bonds while the ratio of money to bonds is still finite.
But I don't think that's where the real action is likely to be found. There is more to monetary policy than just temporarily swapping money for short-term government bonds. The representative agent may (must) hold bonds, but not everybody does. There are more assets than just government bonds. As Paul Krugman notes at the end of his post.
But in discussing these questions, we are already well outside the Neo-Wicksellian perspective.
More to come in later post(s).
Since we're determined to buy this crap, I'm now on board with this: