10/21/10 7:56 PMA Question I Can Answer: Why Is the Speed Limit on Deflation so Low? - 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 BlogsearchSeptember 04, 2010

A Question I Can Answer: Why Is the Speed Limit on

Deflation so Low?

Nick Rowe asks:

Worthwhile Canadian Initiative: Re-learning the New Keynesian IS curve: [A]nempirical puzzle for New Keynesian macroeconomists. If macroeconomic blackholes of deflationary spirals exist, and if bad monetary policy can cause economiesto fall into one, why haven't we ever observed this happening? Does somebody upthere like us? (At least, until now). Or is something wrong with the model?

The Akerlof-Yellen answer--which I think is correct--is that the expectational PhillipsCurve model of pricing is wrong. Cutting nominal wages substantially has suchdevastating effects on worker morale that employers simply do not do it in largenumbers--even with enormous amounts of slack in the labor market.

Thus the dynamic system has two basins that converge to two attractors: a basin thatconverges to "normal" with employment near full, the nominal interest rate equal toinflation plus the warranted natural real rate of interest, and inflation near the centralbank's target; and a basin that converges to "Japan" with nominal interest rates attheir floor and deflation proceeding at its (slow) speed limit.

That, at least, is what you have to think the right model is, if you think Japan'sexperience over the past two decades has something to tell us about how the otherNorth Atlantic economies work...

And let me, to please Rajiv, reprint my draft comment on Bullard...

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

Dashboard Blog Stats Edit Post

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Here is the graph:

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...

Let's graph this, with the nominal interest rate on the vertical axis and the inflationrate on the horizontal axis...

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 rising

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everywhere 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.

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.

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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.

Note, under these dynamics, that point B is not of especial interest. It is not anattractor of any kind for any basin. Rather, it merely marks the bottom of the curvethat is the boundary between the two regions: the region of states that ultimatelyconverges to the good equilibrium A and the region of states that converge to theabsorbing deflationary-Japan equilibrium C. If the economy is sitting at point B, we donot expect it to stay there. A small downward shock to aggregate demand or a smallupward shock to the policy interest rate would throw the economy into the zone thatconverges to C. A small upward shock to aggregate demand would throw the economyinto 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.

(1) 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.

(2) A second policy suggestion is for the Federal Reserve to contract rather thanexpand its assets when deflation begins: to engage not in quantitative easing but ratherin contractionary 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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Comments

chrismealy said...Bonus points for using skitch.

Reply September 04, 2010 at 11:29 AMAlex said...Presumably, hyperdeflation would correspond to an environment where everyoneexpected a massive downward price shock, and anticipated it by hugely increasing theirnet financial balances (interestingly, for a lot of possibilities, the asset they mightchoose to hold would be cash - like a surge in liquidity-preference, driven by theprecautionary demand for money). I'm thinking of an immediate pre-war panic -anything I could buy might be destroyed at any moment.

Perhaps the typical conditions that might give rise to hyperdeflation are so closelyassociated with the typical conditions that give rise to hyperinflation that it neverarises?

Reply September 04, 2010 at 12:18 PMDeamiter said...Great explanation!

If I may be allowed to nit pick, in hyper-deflation, wouldn't governments beREMOVING zeros from their currency?

Reply September 04, 2010 at 01:06 PMRichard Careaga said...Employers may hesitate to reduce __nominal__ wages, but they have no hesitation atall in reducing __effective__ wages through overloading. While this is limited by wageand hour laws and union contract, exempt employees are fair game. Since the speed atwhich it is possible to attend meetings is a constant, and the speed at which it ispossible to answer email and prepare reports declines as a function of contextswitching, the inevitable result is longer hours for the same wage.

Reply September 04, 2010 at 05:19 PMThomas T, Schweitzer said...

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Deamiter, to pick your nit, in hyper-inflation governments add zeros to the left of thedecimal point of their currency; in hyper-inflation they would add zeros to the right ofthe decimal point.

Reply September 04, 2010 at 05:37 PMRobert Waldmann said...I think that for some Taylor rules there is a third basin with hyperinflation.

Also didn't the economy fall into the deflationary black hole in the great depression ?

Reply September 04, 2010 at 07:08 PMNick Rowe said...I wasn't sure how to interpret Bullard. He seemed to be saying what you interpret himto be saying. But at the same time he seemed familiar with stuff like George Evans'analysis. If you are right in your interpretation of what he was saying, then yourcriticism is right. God help us!

I think you are half right in your response to my question (and thanks for theresponse).

There are two potentially destabilising positive feedback loops:

1. Low demand leads to falling inflation leads to falling expected inflation leads torising real interest rates leads to falling demand.

2. Low demand leads to low income leads to low expected future income leads to lowdemand. (This was the feedback loop I was exploring in my blog post).

Your argument, if correct (it may be) puts a stop on 1. But it still leaves 2 wide open todo some very nasty stuff. As far as I can see, it is quite possible, if the real rate is stuckpermanently above the natural rate, even if the gap between the two rates is constant,for output to fall *without limit*. In fact, if you have homothetic preferences, and ifconsumption is the only type of demand (investment is too hard for me to thinkabout), then I think (I'm not 100% sure) that this *must* happen. Intuitively, becauseof homothetic preferences, everything is proportionate to permanent income. A 1%drop in permanent income leads to a 1% drop in consumption, which leads to a 1%drop in output, which leads, via learning, to a 1% drop in permanent income. Likehaving an mpc=1. The long-run multiplier is infinite. The economy spirals to zero, evenif you stop deflation.

Reply September 04, 2010 at 07:10 PMNick Rowe said...Output wouldn't spiral down to zero in an Old Keynesian model, because the OldKeynesian IS curve has a finite slope. Stop the real rate from rising, by stoppingdeflation, and output stops falling. It's just low, like in Japan, or the 1930's US. But theNew Keynesian IS curve is different. The gap between current planned consumptiondemand and permanent income is (under homothetic preferences) proportional to thegap between the real rate and the natural rate. There's zero autonomous expenditure,to put it in Old Keynesian terms, in the long run. So output spirals to zero, at the samespeed that agents learn to revise their beliefs about permanent income.

Now, you would probably argue that Government expenditure plays the role ofautonomous expenditure. And that is what has stopped Japan spiralling to zero. Butcan G play this role indefinitely? That implies an indefinitely growing stock ofmoney+bonds. Is that possible? Well, the trouble is that money and bonds do notappear explicitly in the NK model. So it cannot even address this question.

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Back to some sort of variant on monetarism? We can't ignore what is happening to thestock of money, and promises to pay money.

Reply September 04, 2010 at 07:27 PMOther Peter T said...

Isn't there a stop to the downside of the deflationary spiral set by the real economy?You can add any amount of zeros to left of the zero - the limit is set by the size of thepiece of paper. But the real economy -that is, people actually living in houses, cookingfood, making things - has some lower bound of activity (while there are people alive).In short, money can become worthless, but it can't be of infinite worth.

Reply September 05, 2010 at 03:16 AMbakho said...Bankruptcy protection from creditors is also an important backstop to deflation.

Competition of workers and information are important in addition to morale issues.Organizations invest a lot of money in workforce training. Untrained workers are notperfect substitutes for trained workers. Poaching workers trained by anotherorganization eliminates training costs AND can provide the winning bidder with insideinformation on the competitor. Institutional memory is important. Imagine the impactif your entire secretarial support staff was gone tomorrow and replaced by temps??Would anything get done? Workplace dynamics and institutional memory (sunktraining costs) are more important than morale.w

Reply September 05, 2010 at 07:02 AMIndigenous Centurion said in reply to Thomas T, Schweitzer...

"hyper-inflation governments add zeros to the left of the decimal point of theircurrency; in hyper-inflation"~~ Thomas T, Schweitzer~

Hyper-Inflation Vs. Hyper-Inflation

Ask not where you could do zero for Your Country, but ask where is Your Country'sDecimal Point with respect to your significant figures. And watch your figures, FatsoPeople!

2200000000.0000000 Zimbav Dollars

0.0000000002200000 Zimbav Dollars

^||^Add zeros here, Zoro!

Grazia!

But where is the Robert's Radius of deflationary unity point on the event horizon?Additionally, what is the critical neutron mass for super-nova hyper-inflationary bangfor our Zim Buck, Tutu?

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Me: Economists:Juicebox Moral

But if the psychological devastation of pay cut has all the zeros drained from itsmagnitude when the employee is paid in gold bullion, the worker will see his goldappreciate in spite of inflation as it has doubled in value twice since it was recentlyworth only a quarter length shadow of its new self.

This then begs the question of extant deflation when gold price is doubling so rapidly.Have wages lost strength merely because of recent distortions in their previous truevalue, distortions rooted in Capitol Hill? Will you find a reasonable answer by writingyour Congressional Nancy?

Got a pencil?

Reply September 05, 2010 at 11:13 AMIndigent Centurion said in reply to Indigenous Centurion...2200000000.0000000 Zimbav Dollars

0.0000000002200000 Zimbav Dollars

~~~~^~~~~|~~~~|~~~~^Add zeros here, Zoro!

My hex20 spaces hit the bit-bucket.Not enough security cameras.

Reply September 05, 2010 at 11:47 AMComments on this post are closed.

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