10/23/10 5:40 PMExtremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of …eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands

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Grasping Reality with Both HandsThe Semi-Daily Journal of Economist J. Bradford DeLong: Fair, Balanced, Reality-Based, and Even-HandedDepartment of Economics, U.C. Berkeley #3880, Berkeley, CA 94720-3880; 925 7080467; delong@econ.berkeley.edu.

Economics 210aWeblog ArchivesDeLong Hot on GoogleDeLong Hot on Google BlogsearchAugust 04, 2010

Extremely Rough: A Note on Bullard's Interpretation in his

"Seven Faces of 'The Peril'" Paper of Benhabib et al. (2001).

Extremely rough: A note on James Bullard (2010), "Seven Faces of 'The Peril'"http://research.stlouisfed.org/econ/bullard/pdf/SevenFacesFinalJul28.pdf...

Here is the graph:

Dashboard Blog Stats Edit Post

10/23/10 5:40 PMExtremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of …eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands

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Bullard:

In this paper I discuss the possibility that the U.S. economy may becomeenmeshed in a Japanese-style, deflationary outcome within the next several years.To frame the discussion, I rely on an analysis that emphasizes two possible long-run outcomes (steady states) for the economy, one which is consistent withmonetary policy as it has typically been implemented in the U.S. in recent years,and one which is consistent with the low nominal interest rate, deáationary regimeobserved in Japan during the same period.... When the line describing the Taylor-type policy rule crosses the Fisher relation [i.e., Wicksellian Balance], we say thereis a steady state at which the policymaker no longer wishes to raise or lower thepolicy rate, and, simultaneously, the private sector expects the current rate ofináation to prevail in the future.... In the right-hand side of the Figure, short-termnominal interest rates are adjusted up and down in order to keep inflation low andstable. [Point A]... [A]s we move to the left... the two lines cross again, creating asecond steady state [at Point B].... The policy rate cannot be lowered below zero,and there is no reason to increase the policy rate since well, inflation is already"too low." This logic seems to have kept Japan locked into the low nominalinterest rate steady state. Benhabib, et al., sometimes call this the "unintended"steady state...

As I understand this model, the "Policy Rule" line shows what the Federal Reservewishes it had set its policy nominal interest rate i--the Federal Runds rate--given therate of inflation π. When i lies above the policy rule line, monetary policy is "too tight"and the Federal Reserve will reduce i. When i lies below the policy rule line, monetarypolicy is "too loose" and the Federal Reserve will raise i. As the vertical arrows in theversion below show, i is falling everywhere above the policy rule line and risingeverywhere below it.

The "Wicksellian Balance" line is what Bullard (and Benhabib et al.) call the "FisherRelationship." I prefer to think of it in Hicksian IS or Wicksellian terms: for aggregatedemand Y to be equal to potential output Y*, the market real interest rate r must beequal to the natural real interest rate re. When the market real rate r exceeds thenatural real rate re, investment spending is too low for aggregate demand to matchpotential output and there is downward pressure on the rate of change of prices. If themarket rate r is less than the natural real rate re, investment spending is too high foraggregate demand to match potential output and there is upward pressure on the rateof change of prices. Above the Wicksellian Balance line, there is downward pressureand so inflation is falling. Below the line, there is upward pressure and so inflation isrising.

Complicating the dynamics further is the zero-bound requirement: i cannot fall belowzero.

Complicating the dynamics still further is downward price stickiness: π cannot becomelarge and negative (although we see hyperinflation in the real world, we have neverseen hyperdeflation with governments adding zeroes to the denomination of theircurrency). Just as i cannot fall below zero, π cannot fall below the vertical line startingat point C.

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The natural dynamics of this model separates the graph into two regions. The firstregion consists of a subset of those points above the Wicksellian Balance line and tothe right of the Policy Rule line for which the economy's dynamics lead it to eventuallyhit the X-axis to the left of point B, and then converge to point C. The economy startsout with monetary policy "too tight" and with aggregate demand below potentialoutput, hence both inflation π and the policy interest rate i fall until the economy hitsthe x-axis. Then i stops falling--it can't fall any further--and inflation π continues tofall until the economy reaches its sticky-price deflationary speed limit at Point C. Therethe economy sits.

The second region consists of all those points that generate paths that at some pointfall below the Wicksellian Balance line--that at some point produce situations in whichaggregate demand is higher than potential output. Those paths then spiral into thestable equilibrium at point A. There the economy sits.

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Note, under these dynamics, that point B is not of especial interest as an equilibrium

of any kind, but rather because it marks the bottom of the curve that is the boundarybetween the two regions: the region of states that ultimately converges to the goodequilibrium A and the region of states that converge to the absorbing deflationary-Japan equilibrium C. If the economy is sitting at point B, we do not expect it to staythere. A small downward shock to aggregate demand or a small upward shock to thepolicy interest rate would throw the economy into the zone that converges to C. Asmall upward shock to aggregate demand would throw the economy into the converge-to-point A zone.

Bullard suggests two possible policies to deal with the danger of convergence to Japan-style chronic deflation a la point C.

His first policy suggestion is to engage in a policy of quantitative easing if deflationthreatend: have the Federal Reserve expand its balance sheet even after pushing itspolicy interest rate i to the floor and take duration, systemic, and possibly default riskonto its own books. In this model, such a policy of quantitative easing can beinterpreted as changing the position of the "Wicksellian Balance" line when inflation isvery low. With more risk of various kinds taken onto the government's books inresponse to threatening deflation, firms are more willing to invest at higher realinterest rates. Thus the "natural" real interest rate falls, and falls discontinuously if thequantitative easing program is switched on discontinuously when, say, inflation fallsbelow zero. The effect is to change the model to:

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When inflation hits zero and the quantitative easing program begins, the policy interestrate i consistent with Wicksellian balance rises--points lying below the now-discontinuous blue line produce upward pressure on inflation. The effect on thedynamics is to eliminate the zone that converged to point C, and thus to eliminate thedanger of a Japan-style chronic deflation.

A second policy suggestion is for the Federal Reserve to contract rather than expand itsassets when deflation begins: to engage not in quantitative easing but rather incontractionary open-market operations to raise the policy interest rate i away fromzero to some higher level, like so:

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Bullard's thought is that this would eliminate the danger of an adverse outcome byeliminating the point B where the red and the blue curves cross. If point A is the goodstable equilibrium and point B is thought of as a bad alternative equilibrium, adoptinga monetary policy that keeps the curves from crossing at point B and so eliminatespoint B entirely might help the sitaution.

A little investigation, however, shows that under these dynamics the correct conclusionis otherwise. The problem is not the existence of point B. Rather, the problem is theexistence of a zone within which the dynamics of the system drive it to the absorbingpoint C. This second policy suggestion increases the size of that unfortunate region.

The dynamics of our new system are given by:

Tracing paths through these dynamics, we see that the boundary between those statesthat converge to C and those that converge back to normal affairs at A has shifted fromthe green curve to the orange curve. Basically, almost every path that ends in anydeflation at all now converges to point C--only those where the pace of deflation istrivial and is accompanied by aggregate demand well above potential output escape theblack hole at point C:

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Even though the point B at which the curves crossed is indeed eliminated, raisinginterest rates if the economy actually goes into deflation does not diminish but ratherincreases the peril of a bad outcome. This should not be surprising: if expanding themoney stock via quantitative easing helps, how can contracting the money stock--which is what raising the policy interest rate is--fail to hurt?

To recap: I think Bullard has been led astray in part of his analysis. I think the flaw isin his conceptualization of point B--where the curves cross--as an equilibrium atwhich the economy might sit. The actual equilibria in his model are, I think, point A--where active monetary policy keeps inflation near its target and aggregate demand nearpotential output--and point C--where the policy rate i is at its zero bound and wherethe deflation rate π is at its lower bound as determined by the economy's resistance tonominal wage declines.

Thus Bullard thinks in terms of eliminating point B where the curves cross, when heought to be thinking of how to eliminate the zone of initial conditions that converge topoint C. He--correctly--concludes that policies of quantitative easing can helpeliminate 'The Peril." But he also, I think incorrectly, concludes that policies thatreduce the set of states in which very low interest rates are pursued (or that shortenthe duration of very low interest rates) can help. However, if my analysis is correct,such contractionary policies would oly hurt. True, they eliminate the point B where thecurves cross. But we are interested in where the curves cross only when those pointsare where dynamic trajectories end. And that is not the case here: here eliminatingpoint B via raising policy interest rates in deflation states increases rather thandecreases the zone that converges to the bad equilibrium C.

Jess Benhabib et al. (2001), "The Perils of Taylor Rules," Journal of Economic Theory

http://www.columbia.edu/~mu2166/perils.pdf

James Bullard (2010), "Seven Faces of 'The Peril'"http://research.stlouisfed.org/econ/bullard/pdf/SevenFacesFinalJul28.pdf

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Brad DeLong on August 04, 2010 at 08:50 PM in Economics, Economics: FederalReserve, Economics: Finance, Economics: Macro | Permalink

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Comments

himaginary said..."I think the flaw is in his conceptualization of point B--where the curves cross--as anequilibrium at which the economy might sit."

That is not Bullard's conceptualization. That idea is in original Jess Benhabib et al.paper (See Figure 2).

They used the natural interest rate as discounting rate of consumers. So, theconsumer's choice between current and future consumption is not affected by themonetary policy. The monetary policy only affects return from financial assets. So, ifthe central bank hikes interest rate, the consumer's interest income goes up, but theconsumer's discount factor remains unchanged. That leaves inflation rate as the onlyadjusting factor. Now, how realistic does it sound?

Reply August 05, 2010 at 04:08 AMNylund said in reply to tomp...Maybe he added it after your comment, but the axes are labeled. There is a little black"i" (nominal interest rate) above the y axis and the little blue "pi" (inflation) that lookslike an "n" by the x axis.

Although, honestly, I wouldn't fault you for overlooking them.

Reply August 05, 2010 at 06:39 AMMarc said...Yes, adding "inflation" and "nominal interest rate" labels would help people outside thefield. Or saying "plot of inflation vs. nominal interest rate".

It would also help a broader readership if you could explain the logic of the lines andwhat sets the relative slopes.

Reply August 05, 2010 at 08:15 AMLord said...Why is C to the left of B?

Reply August 05, 2010 at 09:28 AMLord said...

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What if the natural rate is negative at zero inflation?

Reply August 05, 2010 at 09:47 AMOmega Centauri said...This seems to be the usual stuff economists throw out. A couple of single characterlabels and a few lines. And the non initiates are supposed to instantly understand whatthey are talking about. Even if redundant for some folks, defining your variables, andmaybe writing a few equations, and perhaps explaining that the graph is a way tovisualize the solution of wht (presumably two equations in two unknowns, or somesuch). But as thrown out they are just meaningless diagrams to some folks.

And an unstable equilibrium, in a system with feedback controls can in some cases bestabilized (ask any tightrope walker). So if the possibility of feedbacks exist you can'tjust evoke instability, but must show that the potential feedback loops are incapable ofstabilizing the system.

Reply August 05, 2010 at 12:30 PMBob Athay said...Wow, wading through that took some doing and I *thought* I was reasonably adept atthis sort of reasoning. One thing that confused me:

"... When i lies above the policy rule line, monetary policy is "too tight" and the FederalReserve will reduce i. When i lies below the policy rule line, monetary policy is "tooloose" and the Federal Reserve will raise i."

This makes sense, but then you said:

"The first region consists of a subset of those points above the Wicksellian Balance lineand to the right of the Policy Rule line... The economy starts out with monetary policy"too tight" and with aggregate demand below potential output..."

The way you drew it, i > i(policy rule) is to the *left* of the policy rule line. So either Igot completely lost somewhere or you left a small mistake. If I got lost, please help meout!

If I didn't get lost and the dynamic model you described is qualitatively correct withrespect to historical data:

** It seems intuitive to me that B would have no particular significance; it's just the X-intercept of a curve that divides trajectories leading to C from trajectories that convergearound A. So far, so good.

** I'd like to believe that there's a stable region in the neighborhood of A wheremonetary policy can keep aggregate demand close to the potential output. Whatdefines the boundaries of such a region?

** Why would we think that C is an absorbing state?

Anyway, thank you for posting this. I needed some intellectual exercise today!

For Omega Centauri: As I read it, feedback is implicit in this model since the policyinterest rate is a control parameter that can be adjusted based on the observedinflation and estimates of what the natural interest rate *should* be. What isn't clear tome is that the system responds to the control in a sufficiently predictable manner...

Reply August 05, 2010 at 12:51 PMwalt said...Interesting how many feel free to comment without even looking at Bullard's paper.

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Reply August 05, 2010 at 12:57 PMHarold R. Chorney said...Another way of thinking about this issue still well within the Wicksellian traditionwhich by the way Milton Friedman drew on when he came up with his notion of thenatural rate of unemployment is to explore the natural rate of inflation. The naturalrate of inflation is that rate of inflation below which there is an accelerating rate ofunemployment.The monetarist logic of raising interest rates in response to a perceivedthreat of inflation if overdone will have this impact. The rate will pass the pointcompatible with stable non inflationary unemployment and throw the tendency intoreverse. The current slump occurred after the panic that accompanied the crash andthe bursting of the bubble. The Fed had reversed its policy of low rates and wasattempting to raise them when everything unravelled. We are now in the zone that liesbelow the natural rate of inflation which translates into accelerating unemploymentand possible deflation. I discussed this approach in detail in a paper I presented atAdelphi university at the conference Social Policy as if People Matter on nov. 12,2004.The paper is entitled Restoring full Employment:The Natural rate of Inflation versusthe Natural Rate of Unemployment. it available atwww.adelphi.edu/peoplematter/pdfs/Chorney.pdf. Quantitative easing which Iproposed in a series of papers and monographs in the 1980s and early 1990s isintended to prevent crowding out from occurring. It may result in rising prices, but itmay not ,depending upon the circumstances. I found an extremely small R squaredand therefore no necessary correlation over a forty year time series for Canadian dataon monetized debt in relation to the broadly defined money stock and the rate ofinflation.

Reply August 05, 2010 at 01:48 PMOmega Centauri said in reply to Bob Athay..."What isn't clear to me is that the system responds to the control in a sufficientlypredictable manner... "But, once we give the feedback "actor" some intelligence, rather than just kneejerkfashion following the simplistic rules which lead the trajectory to the "bad attractor" C,wouldn't some drastic action designed to knock the trajectory into A's realm ofattraction be tried?

Reply August 05, 2010 at 02:34 PMcsissoko said...I think you've missed Bullard's point entirely. He is distinguishing between "active" and"passive" interest rate policy. Near the good equilibrium, "active" Fed policy prettymuch determines the inflation rate, because changes can be large enough to makeinflation (see Volcker). Near B, the dynamics that you describe break down preciselybecause the policy tool is no longer a tool -- it has become passive. (Bullard isundoubtedly aware that the effective Federal Funds rate has increased over the pastfew months, but the strong inflation response to this tightening that is predicted by themodel has not taken place.) In Bullard's model, forces other than Fed policy aredetermining the inflation rate and the Fed is passively responding to this with extendedZIRP. That is, his paper explicitly rejects your vision of the model's dynamics. (I noticethat himaginary above gives a hint of the full explanation underlying Bullard'sanalysis.)

Your model indicates that in order to have the unresponsiveness to the Federal Fundsrate that has been observed over the past few months, we must be on the other side ofthe B equilibrium and converging to C. Thus, "Even though the point B at which the

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Me: Economists:Juicebox Moral

curves crossed is indeed eliminated, raising interest rates if the economy actually goesinto deflation does not diminish but rather increases the peril of a bad outcome" doesnot make sense given the data we already have. Since we have reason to believe we arealready on a path to C, it isn't clear that it matters if we increase C's basin of attraction.

And there are other models -- of moral hazard in the financial industry -- that make usthink that avoiding negative real interest rates may be a valuable objective in itself.

Reply August 05, 2010 at 05:49 PMBob Athay said in reply to Omega Centauri...I would certainly hope so, but these days it seems that the collective intelligence of thefeedback actors is more than a little questionable! In particular, the aptly-named PainCaucus seems to think that C, rather than A, is the point to be aiming for.

But even if the feedback actor is highly intelligent, there's still the problem of beingable to predict the response of the system well enough to know whether or not a givenpolicy is likely to produce the desired result. It get back to what Brad said earlier aboutthe lack of a robust, underlying theory.

Reply August 05, 2010 at 07:45 PMcharley said...You can accomplish Bullard's goal by devaluing the dollar against gold

Reply August 07, 2010 at 07:22 AMcharley said in reply to charley...Of course, this would plunge working families into poverty...but I don't think Bullard isall that concerned about working families when the dollar is at stake.

Reply August 07, 2010 at 07:24 AMcharley said in reply to charley...devaluing the dollar against gold would be a simple matter of pegging it some pricehigher than the current market price for gold.

Reply August 07, 2010 at 07:26 AMComments on this post are closed.

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