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Saturday, August 28, 2010

The Correspondence Principle

Rajiv Sethi, who I've come to trust to get things right, has a nice summary of the recent controversy over the relationship between interests rate and inflation:

Lessons from the Kocherlakota Controversy, by Rajiv Sethi: In a speech last week the President of the Minneapolis Fed, Narayana Kocherlakota, made the following rather startling claim:

Long-run monetary neutrality is an uncontroversial, simple, but nonetheless profound proposition. In particular, it implies that if the FOMC maintains the fed funds rate at its current level of 0-25 basis points for too long, both anticipated and actual inflation have to become negative. Why? It’s simple arithmetic. Let’s say that the real rate of return on safe investments is 1 percent and we need to add an amount of anticipated inflation that will result in a fed funds rate of 0.25 percent. The only way to get that is to add a negative number—in this case, –0.75 percent.

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation.

The proposition that a commitment by the Fed to maintain a low nominal interest rate indefinitely must lead to deflation (rather than accelerating inflation) defies common sense, economic intuition, and the monetarist models of an earlier generation. This was was pointed out forcefully and in short order by Andy Harless, Nick Rowe, Robert Waldmann, Scott Sumner, Mark Thoma, Ryan Avent, Brad DeLongKarl Smith, Paul Krugman and many other notables.

But Kocherlakota was not without his defenders. Stephen Williamson and Jesus Fernandez-Villaverde both argued that his claim was innocuous and completely consistent with modern monetary economics. And indeed it is, in the following sense: the modern theory is based on equilibrium analysis, and the only equilibrium consistent with a persistently low nominal interest rate is one in which there is a stable and low level of deflation. If one accepts the equilibrium methodology as being descriptively valid in this context, one is led quite naturally to Kocherlakota's corner.

But while Williamson and Fernandez-Villaverde interpret the consistency of Kocherlakota's claim with the modern theory as a vindication of the claim, others might be tempted to view it as an indictment of the theory. Specifically, one could argue that equilibrium analysis unsupported by a serious exploration of disequilibrium dynamics could lead to some very peculiar and misleading conclusions. I have made this point in a couple of earlier posts, but the argument is by no means original. In fact, as David Andolfatto helpfully pointed out in a comment on Williamson's blog, the same point was made very elegantly and persuasively in a 1992 paper by Peter Howitt.

Howitt's paper is concerned with the the inflationary consequences of a pegged nominal interest rate, which is precisely the subject of Kocherlakota's thought experiment. He begins with an old-fashioned monetarist model in which output depends positively on expected inflation (via the expected real rate of interest), realized inflation depends on deviations of output from some "natural" level, and expectations adjust adaptively. In this setting it is immediately clear that there is a "rational expectations equilibrium with a constant, finite rate of inflation that depends positively on the nominal rate of interest" chosen by the central bank. This is the equilibrium relationship that Kocherlakota has in mind: lower interest rates correspond to lower inflation rates and a sufficiently low value for the former is associated with steady deflation. 

The problem arises when one examines the stability of this equilibrium. Any attempt by the bank to shift to a lower nominal interest rate leads not to a new equilibrium with lower inflation, but to accelerating inflation instead. The remainder of Howitt's paper is dedicated to showing that this instability, which is easily seen in the simple old-fashioned model with adaptive expectations, is in fact a robust insight and holds even if one moves to a "microfounded" model with intertemporal optimization and flexible prices, and even if one allows for a broad range of learning dynamics. The only circumstance in which a lower nominal rate results in lower inflation is if individuals are assumed to be "capable of forming rational expectations ab ovo".

Howitt places this finding in historical context as follows (emphasis added):

In his 1968 presidential address to the American Economic Association, Milton Friedman argued, among other things, that controlling interest rates tightly was not a feasible monetary policy. His argument was a variation on Knut Wicksell's cumulative process. Start in full employment with no actual or expected inflation. Let the monetary authority peg the nominal interest rate below the natural rate. This will require monetary expansion, which will eventually cause inflation. When expected inflation rises in response to actual inflation, the Fisher effect will put upward pressure on the interest rate. More monetary expansion will be required to maintain the peg. This will make inflation accelerate until the policy is abandoned. Likewise, if the interest rate is pegged above the natural rate, deflation will accelerate until the policy is abandoned. Since no one knows the natural rate, the policy is doomed one way or another.

This argument, which was once quite uncontroversial, at least among monetarists, has lost its currency. One reason is that the argument invokes adaptive expectations, and there appears to be no way of reformulating it under rational expectations... in conventional rational expectations models, monetary policy can peg the nominal rate... without producing runaway inflation or deflation... Furthermore... pegging the nominal rate at a lower value will produce a lower average rate of inflation, not the ever-higher inflation predicted by Friedman...

Thus the rational expectations revolution has almost driven the cumulative process from the literature. Modern textbooks treat it as a relic of pre-rational expectations thought... contrary to these rational expectations arguments, the cumulative process is not only possible but inevitable, not just in a conventional Keynesian macro model but also in a flexible-price, micro-based, finance constraint model, whenever the interest rate is pegged... the essence of the cumulative process lies not in an economy's rational expectations equilibria but in the disequilibrium adjustment process by which people try to acquire rational expectations... under a wide set of assumptions, the process cannot converge if the monetary authority keeps interest rates pegged and that the cumulative process is a manifestation of this nonconvergence. 

Thus the cumulative process should be regarded not as a relic but as an implication of real-time belief formation of the sort studied in the literature on convergence (or nonconvergence) to rational expectations equilibrium... Perhaps the most important lesson of the analysis is that the assumption of rational expectations can be misleading, even when used to analyze the consequences of a fixed monetary regime. If the regime is not conducive to expectational stability, then the consequences can be quite different from those predicted under rational expectations... in general, any rational expectations analysis of monetary policy should be supplemented with a stability analysis... to determine whether or not the rational expectations equilibrium could ever be observed. 

To this I would add only that a stability analysis is a necessary supplement to equilibrium reasoning not just in the case of monetary policy debates, but in all areas of economics. For as Richard Goodwin said a long time ago, an "equilibrium state that is unstable is of purely theoretical interest, since it is the one place the system will never remain."

[The title of the post refers to Samuelson's Correspondence Principle, and I want to make clear that I understand its limitations in the DSGE context. See, for example, the introduction to this paper for a discussion of its applicability to DSGE models with learning.]

    Posted by on Saturday, August 28, 2010 at 09:49 AM in Economics, Macroeconomics, Methodology | Permalink  Comments (18)


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