Extremely 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 Hands The Semi-Daily Journal of Economist J. Bradford DeLong: Fair, Balanced, RealityBased, and Even-Handed Department of Economics, U.C. Berkeley #3880, Berkeley, CA 94720-3880; 925 708 0467; delong@econ.berkeley.edu.
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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:
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of …eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
Bullard: In this paper I discuss the possibility that the U.S. economy may become enmeshed in a Japanese-style, deflationary outcome within the next several years. To frame the discussion, I rely on an analysis that emphasizes two possible longrun outcomes (steady states) for the economy, one which is consistent with monetary 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 regime observed in Japan during the same period.... When the line describing the Taylortype policy rule crosses the Fisher relation [i.e., Wicksellian Balance], we say there is a steady state at which the policymaker no longer wishes to raise or lower the policy rate, and, simultaneously, the private sector expects the current rate of ináation to prevail in the future.... In the right-hand side of the Figure, short-term nominal interest rates are adjusted up and down in order to keep inflation low and stable. [Point A]... [A]s we move to the left... the two lines cross again, creating a second 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 nominal interest 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 Reserve wishes it had set its policy nominal interest rate i--the Federal Runds rate--given the rate 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, monetary policy is "too loose" and the Federal Reserve will raise i. As the vertical arrows in the version below show, i is falling everywhere above the policy rule line and rising everywhere below it. The "Wicksellian Balance" line is what Bullard (and Benhabib et al.) call the "Fisher Relationship." I prefer to think of it in Hicksian IS or Wicksellian terms: for aggregate demand Y to be equal to potential output Y*, the market real interest rate r must be equal to the natural real interest rate re. When the market real rate r exceeds the natural real rate re, investment spending is too low for aggregate demand to match potential output and there is downward pressure on the rate of change of prices. If the market rate r is less than the natural real rate re, investment spending is too high for aggregate demand to match potential output and there is upward pressure on the rate of change of prices. Above the Wicksellian Balance line, there is downward pressure and so inflation is falling. Below the line, there is upward pressure and so inflation is rising. Complicating the dynamics further is the zero-bound requirement: i cannot fall below zero. Complicating the dynamics still further is downward price stickiness: π cannot become large and negative (although we see hyperinflation in the real world, we have never seen hyperdeflation with governments adding zeroes to the denomination of their currency). Just as i cannot fall below zero, π cannot fall below the vertical line starting at point C.
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar…pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of …eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
The natural dynamics of this model separates the graph into two regions. The first region consists of a subset of those points above the Wicksellian Balance line and to the right of the Policy Rule line for which the economy's dynamics lead it to eventually hit the X-axis to the left of point B, and then converge to point C. The economy starts out with monetary policy "too tight" and with aggregate demand below potential output, hence both inflation π and the policy interest rate i fall until the economy hits the x-axis. Then i stops falling--it can't fall any further--and inflation π continues to fall until the economy reaches its sticky-price deflationary speed limit at Point C. There the economy sits. The second region consists of all those points that generate paths that at some point fall below the Wicksellian Balance line--that at some point produce situations in which aggregate demand is higher than potential output. Those paths then spiral into the stable equilibrium at point A. There the economy sits.
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar…pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of ‌eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
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 boundary between the two regions: the region of states that ultimately converges to the good equilibrium A and the region of states that converge to the absorbing deflationaryJapan equilibrium C. If the economy is sitting at point B, we do not expect it to stay there. A small downward shock to aggregate demand or a small upward shock to the policy interest rate would throw the economy into the zone that converges to C. A small upward shock to aggregate demand would throw the economy into the convergeto-point A zone. Bullard suggests two possible policies to deal with the danger of convergence to Japanstyle chronic deflation a la point C. His first policy suggestion is to engage in a policy of quantitative easing if deflation threatend: have the Federal Reserve expand its balance sheet even after pushing its policy interest rate i to the floor and take duration, systemic, and possibly default risk onto its own books. In this model, such a policy of quantitative easing can be interpreted as changing the position of the "Wicksellian Balance" line when inflation is very low. With more risk of various kinds taken onto the government's books in response to threatening deflation, firms are more willing to invest at higher real interest rates. Thus the "natural" real interest rate falls, and falls discontinuously if the quantitative easing program is switched on discontinuously when, say, inflation falls below zero. The effect is to change the model to:
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of ‌eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
When inflation hits zero and the quantitative easing program begins, the policy interest rate i consistent with Wicksellian balance rises--points lying below the nowdiscontinuous blue line produce upward pressure on inflation. The effect on the dynamics is to eliminate the zone that converged to point C, and thus to eliminate the danger of a Japan-style chronic deflation. A second policy suggestion is for the Federal Reserve to contract rather than expand its assets when deflation begins: to engage not in quantitative easing but rather in contractionary open-market operations to raise the policy interest rate i away from zero to some higher level, like so:
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of ‌eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
Bullard's thought is that this would eliminate the danger of an adverse outcome by eliminating the point B where the red and the blue curves cross. If point A is the good stable equilibrium and point B is thought of as a bad alternative equilibrium, adopting a monetary policy that keeps the curves from crossing at point B and so eliminates point B entirely might help the sitaution. A little investigation, however, shows that under these dynamics the correct conclusion is otherwise. The problem is not the existence of point B. Rather, the problem is the existence of a zone within which the dynamics of the system drive it to the absorbing point 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 states that converge to C and those that converge back to normal affairs at A has shifted from the green curve to the orange curve. Basically, almost every path that ends in any deflation at all now converges to point C--only those where the pace of deflation is trivial and is accompanied by aggregate demand well above potential output escape the black hole at point C:
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of ‌eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
Even though the point B at which the curves crossed is indeed eliminated, raising interest rates if the economy actually goes into deflation does not diminish but rather increases the peril of a bad outcome. This should not be surprising: if expanding the money 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 is in his conceptualization of point B--where the curves cross--as an equilibrium at which 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 near potential output--and point C--where the policy rate i is at its zero bound and where the deflation rate π is at its lower bound as determined by the economy's resistance to nominal wage declines. Thus Bullard thinks in terms of eliminating point B where the curves cross, when he ought to be thinking of how to eliminate the zone of initial conditions that converge to point C. He--correctly--concludes that policies of quantitative easing can help eliminate 'The Peril." But he also, I think incorrectly, concludes that policies that reduce the set of states in which very low interest rates are pursued (or that shorten the 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 the curves cross. But we are interested in where the curves cross only when those points are where dynamic trajectories end. And that is not the case here: here eliminating point B via raising policy interest rates in deflation states increases rather than decreases 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
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of ‌eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
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Comments himaginary said... "I think the flaw is in his conceptualization of point B--where the curves cross--as an equilibrium 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, the consumer's choice between current and future consumption is not affected by the monetary policy. The monetary policy only affects return from financial assets. So, if the central bank hikes interest rate, the consumer's interest income goes up, but the consumer's discount factor remains unchanged. That leaves inflation rate as the only adjusting factor. Now, how realistic does it sound? Reply August 05, 2010 at 04:08 AM Nylund 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 looks like an "n" by the x axis. Although, honestly, I wouldn't fault you for overlooking them. Reply August 05, 2010 at 06:39 AM Marc said... Yes, adding "inflation" and "nominal interest rate" labels would help people outside the field. 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 and what sets the relative slopes. Reply August 05, 2010 at 08:15 AM Lord said... Why is C to the left of B? Reply August 05, 2010 at 09:28 AM Lord said... http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely 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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What if the natural rate is negative at zero inflation? Reply August 05, 2010 at 09:47 AM Omega Centauri said... This seems to be the usual stuff economists throw out. A couple of single character labels and a few lines. And the non initiates are supposed to instantly understand what they are talking about. Even if redundant for some folks, defining your variables, and maybe writing a few equations, and perhaps explaining that the graph is a way to visualize the solution of wht (presumably two equations in two unknowns, or some such). 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 be stabilized (ask any tightrope walker). So if the possibility of feedbacks exist you can't just evoke instability, but must show that the potential feedback loops are incapable of stabilizing the system. Reply August 05, 2010 at 12:30 PM Bob Athay said... Wow, wading through that took some doing and I *thought* I was reasonably adept at this sort of reasoning. One thing that confused me: "... 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, monetary policy is "too loose" 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 line and 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 I got completely lost somewhere or you left a small mistake. If I got lost, please help me out! If I didn't get lost and the dynamic model you described is qualitatively correct with respect to historical data: ** It seems intuitive to me that B would have no particular significance; it's just the Xintercept of a curve that divides trajectories leading to C from trajectories that converge around A. So far, so good. ** I'd like to believe that there's a stable region in the neighborhood of A where monetary policy can keep aggregate demand close to the potential output. What defines 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 policy interest rate is a control parameter that can be adjusted based on the observed inflation and estimates of what the natural interest rate *should* be. What isn't clear to me is that the system responds to the control in a sufficiently predictable manner... Reply August 05, 2010 at 12:51 PM walt said... Interesting how many feel free to comment without even looking at Bullard's paper.
http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌pretation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely 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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Reply August 05, 2010 at 12:57 PM Harold R. Chorney said... Another way of thinking about this issue still well within the Wicksellian tradition which by the way Milton Friedman drew on when he came up with his notion of the natural rate of unemployment is to explore the natural rate of inflation. The natural rate of inflation is that rate of inflation below which there is an accelerating rate of unemployment.The monetarist logic of raising interest rates in response to a perceived threat of inflation if overdone will have this impact. The rate will pass the point compatible with stable non inflationary unemployment and throw the tendency into reverse. The current slump occurred after the panic that accompanied the crash and the bursting of the bubble. The Fed had reversed its policy of low rates and was attempting to raise them when everything unravelled. We are now in the zone that lies below the natural rate of inflation which translates into accelerating unemployment and possible deflation. I discussed this approach in detail in a paper I presented at Adelphi 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 versus the Natural Rate of Unemployment. it available at www.adelphi.edu/peoplematter/pdfs/Chorney.pdf. Quantitative easing which I proposed in a series of papers and monographs in the 1980s and early 1990s is intended to prevent crowding out from occurring. It may result in rising prices, but it may not ,depending upon the circumstances. I found an extremely small R squared and therefore no necessary correlation over a forty year time series for Canadian data on monetized debt in relation to the broadly defined money stock and the rate of inflation. Reply August 05, 2010 at 01:48 PM Omega Centauri said in reply to Bob Athay... "What isn't clear to me is that the system responds to the control in a sufficiently predictable manner... " But, once we give the feedback "actor" some intelligence, rather than just kneejerk fashion 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 of attraction be tried? Reply August 05, 2010 at 02:34 PM csissoko 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 pretty much determines the inflation rate, because changes can be large enough to make inflation (see Volcker). Near B, the dynamics that you describe break down precisely because the policy tool is no longer a tool -- it has become passive. (Bullard is undoubtedly aware that the effective Federal Funds rate has increased over the past few months, but the strong inflation response to this tightening that is predicted by the model has not taken place.) In Bullard's model, forces other than Fed policy are determining the inflation rate and the Fed is passively responding to this with extended ZIRP. That is, his paper explicitly rejects your vision of the model's dynamics. (I notice that himaginary above gives a hint of the full explanation underlying Bullard's analysis.) Your model indicates that in order to have the unresponsiveness to the Federal Funds rate that has been observed over the past few months, we must be on the other side of the B equilibrium and converging to C. Thus, "Even though the point B at which the http://delong.typepad.com/sdj/2010/08/extremely-rough-a-note-on-bullar‌retation-in-his-seven-faces-of-the-peril-paper-of-benhabib-et-al.html
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Extremely Rough: A Note on Bullard's Interpretation in his "Seven Faces of …eril'" Paper of Benhabib et al. (2001). - Grasping Reality with Both Hands
10/23/10 5:40 PM
curves crossed is indeed eliminated, raising interest rates if the economy actually goes into deflation does not diminish but rather increases the peril of a bad outcome" does not make sense given the data we already have. Since we have reason to believe we are already 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 us think that avoiding negative real interest rates may be a valuable objective in itself. Reply August 05, 2010 at 05:49 PM Bob Athay said in reply to Omega Centauri... I would certainly hope so, but these days it seems that the collective intelligence of the feedback actors is more than a little questionable! In particular, the aptly-named Pain Caucus 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 being able to predict the response of the system well enough to know whether or not a given policy is likely to produce the desired result. It get back to what Brad said earlier about the lack of a robust, underlying theory. Reply August 05, 2010 at 07:45 PM charley said... You can accomplish Bullard's goal by devaluing the dollar against gold Reply August 07, 2010 at 07:22 AM charley said in reply to charley... Of course, this would plunge working families into poverty...but I don't think Bullard is all that concerned about working families when the dollar is at stake. Reply August 07, 2010 at 07:24 AM charley said in reply to charley... devaluing the dollar against gold would be a simple matter of pegging it some price higher than the current market price for gold. Reply August 07, 2010 at 07:26 AM Comments on this post are closed.
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Extremely 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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Extremely 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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