Divine Coincidence and the Fed's Dual Mandate

John Taylor says the Fed should adopt a single mandate. In his view, which seems to be fairly common on the political right, the Fed should abandon targeting the output gap and restrict its attention it keeping the inflation rate stable:

Former U.S. Treasury Department undersecretary John Taylor on Wednesday called for overhauling the Federal Reserve’s dual mandate of ensuring stable prices and maximum employment, saying that the central bank should focus on prices.

“It would be better for economic growth and job creation if the Fed focused on the goal of “long run price stability within a clear framework of economic stability,’” Taylor told the House Financial Services Committee. ...

Taylor said that “too many goals blur responsibility and accountability.” ...

Robert Barbera, a fellow at John Hopkins, sends an email making the case that a single mandate is a bad idea, particularly near the zero bound. It is based upon an IMF paper showing that deflation does not generally occur when there are large output gaps. Instead, downward price and wage rigidities cause inflation to stabilize at low rates, and this is part of the reason for a suboptimal response under a single mandate.

Note that the term "divine coincidence" used in the email refers to a situation where stabilizing inflation is the same as stabilizing output. When particular assumptions are imposed on theoretical NK DSGE models, there is no difference in terms of household welfare between a single and a dual mandate. Unfortunately, the assumptions that are required for the existence of divine coincidence are relatively strict and we shouldn't expect it to hold generally. (The wide adoption of a single mandate in Europe is due, in large part, to the difficulties of targeting output gaps when multiple countries are involved. Thus, it's based more on politics than on economics. Suppose, for example, that Germany is doing well and does not favor expansionary policy, but Ireland is struggling and wants help. Whose interests should prevail?).

Here's Robert's email:

IMF did a bang up working paper on Persistent Large Output Gaps, looking at 20 or so nations over 30 years. A super short version of their conclusions? PLOGS weigh on price pressures for years, even amid strong recoveries--a standard Keynesian conclusion. Two, PLOGS lose much of their deflationary power, the closer inflation gets to zero--a not so common conclusion. It seems slowing pay and price increases is much easier than actually cutting wages and prices...

Now imagine a two nation world near zero inflation amid PLOG circumstances. Imagine further that one nation has a dual mandate and the other is an inflation targeter. What happens?

The dual mandate CB sees high joblessness keeps pedal to the metal till strong growth arrives. The other CB fails to see deflation appear and therefore is less stimulative. As the big ease in nation #1 succeeds, stronger growth lifts it's currency. A touch of adverse terms of trade lifts price pressures in nation #2 just enough to confirm, in the CB inflation nutter one track minds, that they are doing "the right thing". They stick to their guns, and over time cyclical joblessness becomes structural. In other words, they are unwitting agents of hysteresis.

Thus the divine coincidence categorically fails amid near zero inflation. More to the point, single focused CBs are quite likely to pursue suboptimal policy.

The argument is not that the Fed will remain passive under a single mandate. When inflation is below target -- as it would be near the zero bound -- there is still a response from the Fed. The Fed will still try to hit its inflation target and hence should ease up. However, because the Fed pursues a single rather than a dual target, and because of the effects on the terms of trade, the response will be smaller than it would be under a dual mandate, and hence suboptimal (there is a result in the background showing that the variance of output is lower under the dual mandate unless, again, restrictive assumptions are made).

Note: A good description of the special conditions that are needed for divine coincidence comes from this paper by Jordi Gali and Olivier Blanchard:

...In this paper, we show that this divine coincidence is tightly linked to a specific property of the standard NK model, namely the fact that the gap between the natural level of output and the efficient (first-best) level of output is constant and invariant to shocks. This feature implies that stabilizing the output gap the gap between actual and natural output is equivalent to stabilizing the welfare-relevant output gap the gap between actual and efficient output. This equivalence is the source of the divine coincidence: The NKPC implies that stabilization of inflation is consistent with stabilization of the output gap. The constancy of the gap between natural and efficient output implies in turn that stabilization of the output gap is equivalent to stabilization of the welfare-relevant output gap.

The property just described can in turn be traced to the absence of non trivial real imperfections in the standard NK model. This leads us to introduce one such real imperfection, namely real wage rigidities. The existence of real wage rigidities has been pointed to by many authors as a feature needed to account for a number of labor market facts (see, for example, Hall [2005]).We show that, once the NK model is extended in this way, the divine coincidence disappears.

The reason is that the gap between natural and efficient output is no longer constant, and is now affected by shocks. Stabilizing inflation is still equivalent to stabilizing the output gap, but no longer equivalent to stabilizing the welfare-relevant output gap. Thus, it is no longer desirable from a welfare point of view. ...

Suppose, for example, that firms have market power. Then the natural rate of output will be lower than the welfare maximizing level (because market power leads to lower output and higher prices than is socially optimal). So long as the gap between the two stays constant, then divine coincidence will exist. However, it is very easy to make this gap variable and, in fact, realism within our models demands it (divine coincidence can fail for reasons besides a variable gap due to wage rigidities, so this does not exhaust the resons why divine coincidence can fail).

Thus, theory tells us that a single mandate is a bad idea except under conditions that are unlikely to exist. Since the conditions are special, and since inappropriately adopting a single mandate leads to too much unemployment and potential hysteresis, the burden of proof that the special conditions required for a single mandate are present, at least approximately, is on the proponents of the single mandate -- and they simply have not made the case.

Update: I forgot that Paul Krugman wrote about "PLOGS" in August:

The Price Stability Trap, by Paul Krugman: There’s an important new paper from the IMF about inflation in the face of Prolonged Large Output Gaps — yes, PLOGs. You can think of it as a careful, multi-country version of the quick-and-dirty analysis of US experience I did recently, with an assist from Tim Duy. What the analysis shows is that prolonged periods of economic weakness are, with almost no exceptions, associated with falling inflation rates.

The analysis also suggests something else, however: as the inflation rate goes toward zero, it seems to become “sticky”: in the modern world, rapid deflation doesn’t happen, and in fact slight positive inflation often persists in the face of an obviously depressed economy:

IMF

The authors discuss several possible explanations, but it does seem as if downward nominal rigidity is playing a role.

And this raises the specter what I think of as the price stability trap: suppose that it’s early 2012, the US unemployment rate is around 10 percent, and core inflation is running at 0.3 percent. The Fed should be moving heaven and earth to do something about the economy — but what you see instead is many people at the Fed, especially at the regional banks, saying “Look, we don’t have actual deflation, or anyway not much, so we’re achieving price stability. What’s the problem?”

And the slump will just go on.