The only meaningful definition of a liquidity trap is given by the situation in which individuals are satiated with money balances. Under this scenario, individuals are willing to hold any amount of money balances above some specific level. It necessarily follows that monetary policy is impotent.
Suppose, for example, that the central bank targets the federal funds rate and it reaches the zero lower bound. At that point, the central bank can no longer lower short-term interest rates. However, in theory, they could lower the real rate of interest by generating inflation. Basic quantity theoretic analysis would suggest that the central bank could increase the money supply, which in turn would increase inflation, lower the real interest rate, and increase aggregate demand.
Paul Krugman (1998) and Lars Svensson (1999) present models in which individuals are satiated with money balances at the zero lower bound. In other words, once the interest rate reaches the zero lower bound, individuals are content to hoard any additional money balances. As a result, the central bank loses control of the price level. Monetary policy is impotent. (Admittedly, Krugman suggests that policy could be successful if the central bank increases inflation expectations, but we will put that aside for the moment.) So if we are really concerned with liquidity traps, it is necessary to consider the circumstances under which they arise.
The reason that liquidity traps exist in the models presented by Krugman and Svensson is because money is not net wealth. Since money is not part of private sector net wealth in these models, there is no real balance effect from an increase in the money supply and agents are therefore willing to hoard any additional money balances.
Peter Ireland (2005), however, has shown that if one extends Krugman’s model that produces a liquidity trap to include population growth, the real balance effect emerges and the liquidity trap disappears. In other words, population growth introduces a distributional effect that transforms money into net wealth. As a result, an increase in the money supply increases net wealth and thereby eliminating the liquidity trap.
The implications of each of these models is important for understanding the role of monetary policy at the zero lower bound. As a result, it was encouraging to see David Beckworth’s recent post in which he points out that one cannot simultaneously claim the existence of a liquidity trap and the potential for monetary policy to generate portfolio balance effects. Indeed, David is correct on this point. If a liquidity trap exists, individuals must be satiated with money balances. As a result, open market operations are irrelevant because as the Fed exchanges money for bonds, the increased money balances are simply held — regardless of what type of bonds the Fed is buying. In effect, money becomes a perfect substitute for all other assets (a point made, by the way, by Brunner and Meltzer in 1968 — another reason why the history of thought is important).
It is puzzling, however, to read Matt Rognlie’s comments in response to David’s post. For example, Rognlie begins his comment by claiming that:
I want to emphasize that I’m not interested in defending a phrase; if you take the term “liquidity trap” to mean that the Fed has absolutely no tools at its disposal that could conceivably affect interest rates, then I don’t believe in a liquidity trap either. For the sake of avoiding a purely semantic argument, let’s take my claim to instead be the following: monetary stimulus becomes much, much harder at the zero lower bound, and fundamentally different in character from monetary policy above the zero lower bonud. [sic]
This seems to get causation backwards. We are not “defining” a liquidity trap to mean that monetary policy is impotent. The impotence of monetary policy follows from the definition of a liquidity trap. I have defined the liquidity trap above. If you don’t agree with the definition, then you don’t believe in liquidity traps. Saying that monetary policy is different at the zero lower bound is different is not synonymous with a liquidity trap and therefore should not be referred to as such (this was one of David’s main points).
Unfortunately, it is not obvious that the portfolio balance effects from QE are of macroeconomically relevant magnitude. Eggertsson and Woodford (2003) even proved an irrelevance result stating that, under certain conditions, portfolio balance effects do not exist at all.
This is correct so far as it goes. However, it is important to bear in mind that the Eggertson and Woodford paper is somewhat of an extension of Krugman’s framework. There is no population growth and no distributional effects. As such, money is not net wealth in the model and therefore real balance effects are absent — by assumption. Rognlie implicitly recognizes this point as he notes:
(It’s essentially a variation on Ricardian equivalence: since consumers are ultimately liable for the risk on the government’s balance sheet as well, shifting the ownership of securities from the private sector to the government does nothing.)
This is similar to the analogy made by Weil (1991). However, Weil notes that this result is derived from the fact that money is not net wealth because of the absence of distributional effects — effects that are assumed out of the Eggertson and Woodford model.
In short, there seems to be a misunderstanding about liquidity traps and what the models in the literature really tell us about such conditions. It has become common in discussions to associate the zero lower bound with a liquidity trap, but this is not necessarily the case. It is important to be mindful of such differences (or at the very least more careful about our wording) when discussing monetary policy.