Friday, May 13, 2011

Fixing What’s Wrong with the Taylor Rule

I see four problems with the original Taylor rule:

  1. It’s not really a rule at all. The Taylor rule depends on an estimate of potential output. In practice, most of the discretion that goes into central banking is in the estimate of potential output. Even “discretionary” central bank policy is effectively constrained by the consensus of what would be considered reasonable policy actions, and any of those actions can be rationalized by changing your assumption about potential output. Usually, a central bank that has committed to following a “strict” Taylor rule has roughly the same set of options available as one that is ostensibly operating entirely on its own discretion.

  2. It doesn’t self-correct for missed inflation rates. Since the inflation rate in the Taylor rule is over the previous four quarters, the rule “forgets” any inflation that happened more than four quarters ago. This is a problem for four reasons:

    • It leaves the price level indeterminate in the long run, thus interfering with long-term nominal contracting and decisions that involve prices in the distant future.

    • It leaves the central bank without an effective tool to reverse deflation when the expected deflation rate exceeds the natural interest rate.

    • It reduces the credibility of central bank attempts to bring down high inflation rates, because the bank always promises to forgive itself when it fails.

    • It aggravates the “convexity” problem described below, because the central bank effectively ignores small deviations from its inflation target, even when they accumulate.

  3. It doesn’t allow for convexity in the short-run Philips curve. If the estimate of potential output is too low, for example, and the coefficient on output is sufficiently low, then, if the short-run Philips curve is convex, the central bank will allow output to persist below potential output for a long time before “realizing” that it has made an error. In the extreme case, where the short-run Phillips curve is L-shaped, the central bank may allow actual output to be permanently lower than potential output. More generally, the convexity problem can be aggravated by hysteresis effects, in which lower actual output leads to lower potential output, so that the central bank’s wrong estimate of potential output becomes a (permanently) self-fulfilling prophecy.

  4. It can prescribe a negative interest rate target, which is impossible to implement. This appears to have been the case for at least part of 2009 and 2010, although there is disagreement about the details.

So how do we fix these problems? I suggest the following solutions:

  1. Adopt a fixed method for estimating potential output. (One might allow future changes to the method, but they should be implemented only with a long lag: otherwise, they’ll interfere with the central bank’s credibility, since they can be used to rationalize discretionary policy changes.) Since I like simplicity, I suggest the following method: take the level of actual output in the 4th quarter of 2007 (when most estimates have the US near its potential) and increase it at an annual rate of 3% (the approximate historical growth rate of output) in perpetuity.

  2. Replace the target inflation term with a target price level term. In other words, express it as a deviation from a target price level that rises over time by the target inflation rate. To be clear what I mean by the “target inflation term,” take Taylor’s original equation
    r = p + .5y + .5(p - 2) + 2 (where p refers to the inflation rate)
    and note that I am referring to the “p – 2” term but not to the initial “p” term, which is not really a target but part of the definition of the instrument (an approximation of the real interest rate). In my new formulation, “p – 2” becomes “P – P*,” where “P is (100 times the log of) the actual price level and P* is (100 times the log of) the target price level (i.e., what the price level would be if the inflation rate had always been on target since the base period).

  3. Increase the coefficient on output. If you wish, in order to avoid a loss in credibility, you can also increase the coefficient on the price term by the same amount. What we have then is a more aggressive Taylor rule. It doesn’t solve the convexity problem completely, but it does assure that, when output is far from target, the central bank will take aggressive action to bring it back (unless the price level is far from target in the other direction). That way at least you don’t end up with a long, unnecessary period of severe economic weakness. (John Taylor claims that, according to David Papell’s research, there is “no reason to use a higher coefficient, and…the lower coefficient works better.” But that research only looks at changing the coefficient on the output term without either changing the coefficient on the inflation term or replacing it with a price term, as I suggest above. Having a too-small coefficient on the output term, as in the original rule, is only a second-best way of achieving the results that those other changes would achieve.)

  4. “Borrow” basis points from the future when there are no more basis points available today. In other words, if the prescribed interest rate is below zero, the central bank promises to undershoot the prescribed interest rate once it rises above zero again, such that the number of basis-point-years of undershoot exactly cancel the number of basis-point-years of (unavoidable) overshoot. This method will only work, of course, if the market knows what rule the central bank is following, hence (among other reasons) the need for a rule that really is a rule. If the rule is well-defined, the overshoot will be well-defined, the market will expect the central bank to “pay back” the “borrowed” basis points, and the central bank will be obliged to do so in order to maintain its subsequent credibility.

OK, let’s look at the big picture. What have I proposed? I have proposed nominal GDP targeting (along with a specific method for how to implement it). When the price level term and the output term have the same coefficient and both are specified as a deviation from target, the Taylor rule can be simplified by combining the price level target with the output target. Combining Taylor’s original 2% inflation target (re-expressed as a price level path target as per my suggestion) with my suggested method for estimating potential output, we arrive at a 5% nominal output growth path as the target.

If you wish, you can go further by making the rule forward-looking (using a forecast of nominal GDP instead of a lagged observation) and increasing the coefficient to a very high number. And you can enforce the credibility of the forecast by requiring the central bank to use the forecast implicit in a publicly traded nominal GDP futures contract, so that the market is putting its money where the central bank’s mouth is. You end up with the proposal that Scott Sumner has already made. People seem to think that Scott Sumner’s ideas about monetary policy are far out of the mainstream. But I’m not proposing anything radical here, just trying to fix some problems with the very orthodox Taylor rule.




DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product.

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