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.



paine said...

bang away dear boy
the thing as is is a looped holed farce
designed to hocus pocus
what is really really
all about
domestic nominal
wage change control

taylor and his holey of holey rules
needs a pranging big time

nothing makes me happier then
a wallyworlder like yourself
administering the paddle ho

Mark A. Sadowski said...

Excellent post.


And, ultimately, making several adjustments to the Taylor Rule is a little akin to trying to save the horse and buggy by adding pneumatic tires, GPS, satellite radio, and feeding the poor beast genetically modified alfalfa.

In my opinion nominal GDP level targeting with a NGDP futures market would be more to the point, and would get us beyond our current obsession with interest rates, which in turn causes us to believe in zombie myths like the liquidity trap.

Matt Rognlie said...

Excellent post---I agree with (almost) all of it.

I'm curious, though, about the discussion of a highly convex short-run Phillips curve. Is there much evidence for this being the case? The New Keynesian Phillips curve is usually presented in log-linearized form (and thus it literally can't be convex), but it's not clear to me that a second-order approximation would reveal some kind of substantial convexity.

The results that an optimal Taylor rule can be achieved with no weight on the output gap rely on what Blanchard and Gali memorably called divine coincidence: the absence of any nontrivial real imperfections in the New Keynesian model other than monopolistic competition and sticky prices. But to think about how the output gap should figure into the Taylor rule, we need to make a stab at what those real imperfections are, and how they interact with monetary policy.

In fact, it seems possible to me that the Taylor rule should include estimates of the impact of these imperfections (e.g. "binding credit constraints") rather than the output gap itself, which might be a very flawed proxy.

Andy Harless said...


The traditional Phillips curve, in inflation-unemployment space, must be convex, because otherwise it would pass through the y-axis and imply the possibility of negative unemployment rates. And from what I recall, if you plot Phillips curves from the 50’s and 60’s (when inflation expectations were presumably close to constant), they certainly look convex, even away from very low unemployment rates.

For practical purposes, the issue may not really be whether the SRPC is convex but whether the LRPC is convex. Although it’s vertical (and therefore linear) in standard models, the empirical LRPC probably becomes quite convex in the neighborhood of the x-axis, as suggested by the recent IMF study of persistent, large output gaps. The likely explanation is downward nominal wage rigidity. If one were willing to target a sufficiently high inflation rate, the shape of the LRPC in the neighborhood of the x-axis would be academic, but given the seemingly unshakable consensus is that the inflation rate should be near 2%, the shape of the SRPC in practice may be determined to an important degree by the shape of the LRPC.

If you look at the US today (or Japan over most of the past 20 years), you see an output gap that would be consistent with inflation realizations far below expectations if the SRPC were linear, but you see actual inflation realizations only slightly below expectations. It’s hard to continue believing in the Phillips curve at all unless you believe it has significant convexity (or if you believe that our output gap estimates are totally wrong, but in that case, the Phillips curve concept isn’t of much practical value).

Scott Sumner said...

You can defend my NGDP targeting proposal more effectively than I can--excellent post.

I agree that PCs are fairly convex, although oddly they plunged right through the x-axis back in the gold standard days. Obviously the shape of the PC is very dependent on all sorts of structural factors, as well as the nature of the monetary regime (a good example of the Lucas Critique.)

Anonymous said...

why assume GDP growth of 3% in perpetuity? clearly this changes over time - and indeed the estimates i've seen of US potential GDP growth range from about 2.2% to 2.85% (OECD, robert gordon, etc.)

Benjamin said...

I like this--but at zero bound do we go to QE?

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Flow5 said...

The Taylor rule doesn't measure anything. The formula uses yesterday's variables which have no future nexus. It’s useless.

Donald Pretari said...

"As it was, the collapse of nominal GDP drove the “fiscal multiplier” to zero, leaving us with more debt and nothing to show for it."

I'm a bit confused here. If the Debt were the problem, shouldn't our interest rates be going up as investors would want more return for their risk?

Andy Harless said...


Today's federal debt isn't a problem today (especially since the Fed can just buy it without causing any ill effects), but it could theoretically become a problem once the recovery takes place (assuming it ever does). If it weren't for political problems and the distortionary impact of taxation, this shouldn't matter: we would just raise taxes after the recovery, just in time to prevent the economy from overheating. As it is, the federal debt is a little bit worrisome (though not very much so in my own opinion). At some point in the future, the Fed may have to sell it back into the market (or else raise the interest rate on reserves, which amounts to the same thing, since reserves are essentially government debt issued by the Fed instead of the Treasury), and that could end up crowding out private capital formation and/or costing the government a lot for debt service.

I think that was David Levey's concern about "more debt," though I don't understand what he means when he says that "the collapse of nominal GDP drove the 'fiscal multiplier' to zero." You can believe that the fiscal multiplier is zero if you think the Fed fully offsets fiscal policy, but the collapse of nominal GDP seems to indicate just the opposite. If the Fed wouldn't offset the increased private sector demand for money that caused nominal GDP to collapse, then why would one expect it to offset fiscal policy?

Donald Pretari said...


Thanks for the explanation.


Patrick said...


1. Theoretically: it could be anything, including concave, truncated at the value u=0.

2. Empirically: it's a mess, at times convex, at times concave, because it's just not a structural relationship.

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