Thursday, August 11, 2011

Kocherlakota vs. Selgin (amv)

I am currently engaged in a discussion with George Selgin and Nick Rowe on two only partly related subjects (check the comment section of Sumner's post):

The discussion emerged in reaction to Kocherlakota's (K in the following) controversial statement exactly a year ago. There he states the following: 

It is conventional for central banks to attribute deflationary outcomes to temporary shortfalls in aggregate demand. Given that interpretation, central banks then respond to deflation by easing monetary policy in order to generate extra demand. Unfortunately, this conventional response leads to problems if followed for too long. The fed funds rate is roughly the sum of two components: the real, net-of-inflation, return on safe short-term investments and anticipated inflation. Monetary policy does affect the real return on safe investments over short periods of time. But over the long run, money is, as we economists like to say,neutral. This means that no matter what the inflation rate is and no matter what the FOMC does, the real return on safe short-term investments averages about 1-2 percent over the long run.
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.
My position is that, if you accept K's premises, then his statement is fundamentally correct (no inconsistencies). I argue further that if you accept modern modelling practices, then K's premises are quite conventional. The reason for the outlandish flavor of his prediction may follow from a discrepancy between the representative economist's believe of how the real world behaves and the world described by their own models.

I entered the debate  not to defend K. I entered it to debate Selgin's use of Wicksell's concept of interest spead. In concrete, Selgin argues that - given the FOMC's promise to hold FFR close to zero up to mid-2013 - if for whatever reason Wicksell's natural or equilibrium rate turns positive before mid-2013, then (1) either will the Fed engage in open market operations to keep FFR at the promised level and, thus, will act inflationary, (2) or the Fed will tighten policy to depress the natural rate to the zero level to keep its promise without allowing for inflation, (3) or the Fed has to break its promise (see also the comment section here).

(1) Let me begin with Wicksell. I entered the comment section by arguing that - given Wicksell's own premise of perfectly flexible prices - his framework is not robust for alternative assumptions of how agents form expectations. In contrast to NK models, Wicksell induces persistency no by price rigidities, but by assuming adaptive expectations. If you substitute rational for adaptive expectations, you get rid of all persistency. You have an essentially frictionsless model. Then, of course, the entire notion of Wicksell's interest rate spread breaks down.

Why is this? In Wicksell's pure credit economy (or cashless economy, if you wish) - given passive monetary policy - a shock to the natural real rate of interest is accommodated by an increase of the consolidated balance sheet of the banking system such that the inflation-adjusted monetary rate remains constant. Thus, we have an interest spread indicating an increase in AD. Since Wicksell assumes neutrality, the real output level remains constant in his deterministic, stationary model. Thus, a positive shock to the natural rate suggests a positive aggregate excess demand and, thus, a rising price level (vice versa for negative shocks to the natural rate). Evidently, Wicksell's cumulative process is disequilibrium analysis, because - in contrast to modern theorists - he is endowed with a static long-run notion of equilibrium only. He recommends monetary policy to increase the inflation-adjusted rate of interest as soon as the central bank observes inflation. Optimal policy sets the policy rate equal to the natural rate (implicit target: zero inflation).

What happens in case of RE in Wicksell's otherwise frictionless economy? RE suggests that agents know the true model; they understand that inflation is a function of aggregate excess demand. Further, actual inflation equals expected inflation. It follows that the inflation-adjusted monetary rate always and by necessity equals the natural rate (a real rate, of course). Further, monetary policy cannot influence the inflation-adjusted money rate of interest; money is neutral even in the short-run. Thus, Wicksell's concept of the spread between the real money rate and the natural rate breaks down if you substitute rational for adaptive expectations. 

Note that Selgin applies Wicksell's aggregate excess demand concept to the case of frictionless RE models (see item (5) in his last comment here). As argued above, this is illegitimate. 

(2) Now that I have clarified my position, let us turn to Kocherlakota. Before, however, I bring in some theory. In contrast to K, let me maintain the assumption that our reference model is frictionless and that it predicts REE. I will relax the former assumption later. In concrete, I assume a RBC model that implements Arrow-Debreu allocations and, thus, predicts optimal sequences. Of course, there is no medium of exchange in our model; but this is also true for NK-variations (see Woodford's cashless economy). Thus, Selgin's OMO-based story does not apply. In fact, we are faced with Say's Identity, that is, aggregate purchasing power is determined by aggregate supply, always and by necessity. RBC does not house Wicksellian processes; monetary disequilibria are ruled out. 

There is, however, a role for money as a unit of account! Choose a commodity as numeraire. The role of the central bank is not to control AD, but to fix nominal values by determining the relative price of the unit of account over time. One way to do so is by making use of the Fisher relation. Since the inflation-adjusted interest rate is an intertemporal price relation determined by primitives, the central bank determines the expected time path of the relative price of the numeraire-commodity by communicating its preferred nominal yield curve. This, essentially, is K's logic.

(3) Finally, I have to show how the unit-of-account model relates to NK models: RBC is at the core of the NK model that allows us to measure the deviation from optimal time-series due to sticky prices (or information). Such persistency is implemented by adjustung a forward-looking Phillips-curve. Some Taylor-rule accounts for the central banks ability to alter the representative household's intertemporal consumption plan such that welfare-losses are minimized.

K effectively argues (see the bold emphasis above)  that - in contrast to standard Calvo-pricing - persistency fades out in the long-run. If, for instance, persistency is due to the average length of contracts, a promise of the central bank at an initial date to hold nominal rates at zero for a period extending the average length of contracts, markets rationally apply the unit-of-account model to predict inflation rates beyond that average length. For earlier periods, markets apply the NK model. It is this deviation from standard theory that accounts for so much confusion with K's statement.

I'm still surprised by Sumner who sides with Selgin and Rowe. After all, he often refers to Friedman's correct observation:
After the U.S. experience during the Great Depression, and after inflation and rising interest rates in the 1970s and disinflation and falling interest rates in the 1980s, I thought the fallacy of identifying tight money with high interest rates and easy money with low interest rates was dead. Apparently, old fallacies never die.
Certainly, the high interest rates in the 70s were not due to high natural rates of interest (due to positive growth prospects), but due to high inflation expectations. Likewise, falling nominal yields in the 80s cannot be explained by falling growth expectations only, but by expected disinflation.

Disclaimer: All this does not mean that I prefer interest-based monetary policy. I prefer some kind of level-targeting making use of whatever instruments necessary to control expectations.