Sad News

Robert Clower has passed away.

Liquidity Traps

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).

Rognlie continues:

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.

What Monetarism Really Wasn’t

Arnold Kling recently had a post entitled, “Monetarism Debated” in which he links to a post by Matt Rognlie entitled, “Is MV = PY Useful?”

Hopefully neither Arnold nor Matt think that this is what monetarism really was, but based upon the context, it seems that they do. As a result, I would like to discuss the use of MV = PY as well as monetarism to clear the air about what the equation of exchange really means and what monetarism was really all about.

First, let’s begin with the equation of exchange. Rognlie suggests that the equation of exchange isn’t useful:

First, we have to understand what the equation of exchange is: without additional assumptions, it’s a tautology. Velocity, “V”, is defined as the number such that MV = PY will hold. Unless V happens to be relatively stable, or obey some kind of predictable pattern in response to other variables (e.g. the nominal interest rate), the equation tells us nothing.

There are essentially two claims here: (1) the equation of exchange is just an identity, and (2) the only way the equation is useful is if velocity is a stable function of other variables. On point (1), I would mention that the New Keynesian Phillips curve and IS equation face the same identification problems as each of these is simply an equilibrium relation and tells us nothing about the direction of causality.

Now on to point (2). In Allan Meltzer’s paper entitled, “Learning About Policy From Federal Reserve History“, he plots (Chart 1 here) the velocity of the monetary base and the nominal interest rate (as measured by the AAA corporate bond rate) from 1919 to 1997. If you follow the link, you will find that this looks like a pretty stable relationship.

Rognlie continues:

As James Hamilton observes (and as economists since the 1980s have understood), “V” isn’t stable: instead, it moves around almost exactly opposite to “M”, as nominal GDP (“PY”) does its own thing. Of course, this isn’t entirely fair. Financial innovation has made “V” meaningless today, but decades ago, the old-school monetarists had reason to think that it was stable.

Has financial innovation made V meaningless? Not really. What has been observed by a number of individuals is that there appears to be “shifts” in velocity in the early 1980s for most monetary aggregates. This has typically been attributed to financial innovation. However, the problem with this type of analysis is that it ignores the way in which monetary aggregates are calculated. Monetary aggregates are typically just simple sums of the collection of assets included in the particular aggregate. This is not a correct form of aggregation. Why does this matter? It matters because in the early 1980s there were a number of assets that got added to the monetary aggregates. Since these aggregates are simple sums, this meant that there were temporary spikes in the growth rates of money that had nothing to do with the money supply itself, but rather how money is calculated. As such, when M significantly rises for reasons that have nothing to do with actual changes in the money supply and therefore be definition does not affect PY, it must be true that V falls significantly. If you are relying on simple sum measures of money to calculate velocity, you will be led to believe that it has become unstable when, in fact, this is a flaw of simple sum aggregation.

Rognlie makes the claim that the nominal interest rate is the only thing we need to know about monetary policy:

Scott Sumner is fond of citing the following remark from Milton Friedman:

“Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy.”

This is very true, and very wise. But this is precisely the kind of observation that MV=PY cannot rationalize: given the economic model implicit in the equation of exchange, nominal interest rates are sufficient to summarize the stance of monetary policy. And that’s why the basic monetarist model is such a poor tool for analyzing the effect of money.

The Friedman quote is great, except that it is not uniformly correct. The point that Friedman was making was a response to the same type of criticism he had received since the publication with Anna Schwartz of A Monetary History of the United States. A number of critics of their interpretation of the Great Contraction as well as critics of Friedman’s views on Japan would often cite low interest rates as evidence that monetary policy could not have been tight. Friedman would then point out that while nominal interest rates were low, real interest rates were higher. Of course, this statement is not uniformly true. Interest rates were high when monetary policy was tight during the Volcker disinflation. Interest rates were low when monetary policy was loose during the early part of the 2000s. Thus, it appears that nominal interest rates are not sufficient for understanding the stance of monetary policy.

Finally, Rognlie writes:

Since I don’t want to perpetuate any popular misconceptions, I should mention that no credible monetary economist is a “monetarist” anymore, at least in the old sense of the term. The profession moved on long, long ago. But since I still see MV=PY popping up quite frequently on the internet, I think it’s important to emphasize what a poor model it really is.

What does this mean “no credible monetary economist is a ‘monetarist’ anymore”? Does it mean that nobody buys the quantity theory of money? Does it mean that nobody thinks that money matters? Does it believe that nobody believes in MV=PY? Rognlie isn’t clear. As a result, it is important to talk about what the quantity theory and monetarism are really about while also pointing out that every credible monetary economist today is a monetarist in the sense that they recognize that money growth causes inflation.

Let’s begin to answer these questions with a discussion of the quantity theory of money. Consider a simple static representation of the economy. Since we are concerned with the determination of the price level, we can limit our attention to the asset market. There are three assets, capital, bonds, and money. In equilibrium, the real stock of each asset is equal to the demand. These equilibrium relations are shown respectively:

K = K(Y, r, i)

B/ip = D(Y, r, i)

M/p = L(Y, r, i)

where M is money, K is capital, B is the supply of bonds, i is the interest rate, r is the yield on capital goods, and Y is income.  Now suppose (as is the case in the New Keynesian model) that the capital stock is fixed.  Consider the effects of an increase in the money supply. To do this we can ignore the capital equation and assume that r is constant. As such, we can differentiate the bond market equation and the money market equation to determine the effect of an increase in the money supply. In doing so we get the following result:

dp/dM = 1/∆p (D_i + B/i²p) > 0

where

∆ = (D_i + B/i²p)(M/p²) – L_i(B/ip²) > 0

In other words, an increase in the money supply leads to an increase in the price level. However, the increase in the money supply does not necessarily lead to an equiproportionate increase in the price level. In fact, it must be true that the bond supply is equal to zero for the money supply to have such an effect (if you don’t believe me, set B = 0 in the equations above). As such, we should expect velocity to change in response to changes in the money supply so long as the bond supply is positive.

So does this mean that the quantity theory is not valid? Of course not. Jurg Niehans explains in The Theory of Money (p. 219):

It may be worth repeating that the quantity theory does not maintain that all changes in the price level are caused by changes in the money supply. In terms of the present model, any number of shifts in the underlying functions may result in price changes. The historical observation, therefore, that movement in the price level do not always parallel the movements in the money supply does not invalidate the quantity theory for at least two reasons, namely, (1) because other exogenous assets like bonds would also have to be considered, and (2) because the quantity of financial assets is only one of the forces determining the price level. The quantity theory dos not ask us to adopt a monetarist view of economic history. It does claim, however, that the historical course of prices would have been different if the suplies of financial assets by the government had been different, all in roughly the same proportion. In this sense, which seems to be the correct one, it is neither false nor trivial, but one of the important, if elementary, insights of economic science.

Even if one disputes the admittedly simple example given above, the same insight is true even of the New Keynesian model. For all the talk about the interest rate being all that is necessary for the conduct of monetary policy, Ed Nelson has shown that even in the New Keynesian model money growth determines the steady state rate of inflation. (Bear in mind that the NK model implies that B = 0 because it assumes the government is following a Ricardian policy. Thus, money growth does affect inflation equi-proportionately.)

In other words, the quantity theory is relevant even in the context of the New Keynesian model in which money is perceived to be unimportant.

(Empirically, it might be hard to disentangle all of these different effects to determine to what extent money growth causes inflation. One method would be to look at Granger causality tests to determine whether money is useful in predicting inflation — or, for that matter, nominal income. It turns out that money is, in fact, useful in this respect. I can provide empirical evidence if anyone is both still reading this post and interested.)

This would then bring us to the point at which we question what monetarism was really about. The perspective that we seem to get from the Rognlie is that MV = PY is all that matters or that the quantity theory is valid. (Of course, the vast majority of monetary economist accept these propositions either explicitly or implicitly in the steady state of their models.) However, monetarism was about much more than the quantity theory. Monetarism was indeed about understanding the importance of money in economic fluctuations and inflation, but it was also about understanding the monetary transmission mechanism, the interaction between monetary and fiscal policy, and the behavior of money demand. Brunner and Meltzer’s work, in particular, on the monetary transmission mechanism was particularly important as it stressed the fact that “the” nominal interest rate was an imperfect measure of the transmission of monetary policy.

This post is already pushing 2000 words and few have likely made it this far, but if anyone is interested in what monetarism was really about I would urge you to read the work of Karl Brunner and Allan Meltzer and David Laidler in addition to the usual Friedman stuff. Anyone who reads Brunner and Meltzer cannot claim that monetarism was simply about MV = PY and still be taken seriously.

UPDATE: See also, Nick Rowe, David Beckworth, and Scott Sumner.

Self-Recommending

Nick Rowe on Walras’ Law and money.

Who Needs the History of Thought?, Part 2

In 1982, Thomas Sargent and Neil Wallace published a paper entitled, “The Real Bills Doctrine Versus the Quantity Theory: A Reconsideration.” Within the paper, the authors outlined what they called a “real-bills regime.” Sargent and Wallace showed that within the regime the price level could be indeterminate and yet still produce a Pareto-optimal allocation of resources. This conclusion is viewed as calling into question the desirability of price stability.

However, as David Laidler explained:

Sargent and Wallace’s attempted rehabilitation of the real-bills doctrine suffers from the following deficiencies: (1) the conclusions on whose basis they seek to rehabilitate the real-bills doctrine would have been anathema to its proponents; (2) what they refer to as the real-bills doctrine is not the real-bills doctrine; and (3) their interpretation of Adam Smith’s analysis of the social productivity of banking is quite misconceived.

This, of course, does not denigrate the findings of the paper. The implications of the paper can be judged based on the contents without reference to the history of thought. However, the explicit reference to the real bills doctrine remains problematic as David Laidler subsequently explains (p. 155):

If economics is to make progress, it clear needs analytic results, and Sargent and Wallace have certainly provided these. However, new results are only a necessary condition for progress, which also requires that, in the process of working out new ideas, we do not lose sight of or distort old ones. I hope that this note has done something to help ensure that, in the process of absorbing Sargent and Wallace’s new and provocative analysis, readers of the Journal of Political Economy do not lose sight of what was at stake in earlier monetary debates.

Who Needs the History of Thought?

Brad DeLong urges change:

We need fewer equilibrium business-cycle theorists and more old-fashioned Keynesians and monetarists. We need more monetary historians and historians of economic thought and fewer model-builders.

Stephen Williamson responds:

Seriously, DeLong and Summers need to use some basic economics to organize their thinking before attempting to instruct the world in what should be taught to Economics PhD students. Successful departments teach what the marketplace wants. It seems to me that the markets in Old Keynesians, Old Monetarists, monetary historians and, particularly, historians of economic thought, are pretty thin these days. A department filled with people like that would ultimately be unsuccessful, and be shut down like the old Economics Department at Notre Dame.

Of course, Brad DeLong didn’t say that we need departments full of people doing nothing but the history of thought. Nonetheless, I am puzzled at the ridicule that Williamson places on the history of thought and monetary history. For example, it could easily be argued that monetary economics benefited greatly from the contribution of Friedman and Schwartz. In addition, David Laidler has an excellent paper that documents the usefulness of the history of thought (and its absence from modern macro).