The Opportunistic Approach to Disinflation

(cid:3) The Opportunistic Approach to Disinflation Athanasios Orphanides and David W. Wilcox Board of Governors of the Federal Reserve System May 1996 Abstract This paper explores the theoretical foundations of a new approach to monetary policy. Proponentsofthisapproachholdthatwheninflationismoderatebutstillabovethelong-run objective, the Fed should not take deliberate anti-inflation action, but rather should wait for external circumstances|such as favorable supply shocks and unforeseen recessions|to deliver the desired reduction in inflation. While waiting for such circumstances to arise, the Fed should aggressively resist incipient increases in inflation. This strategy has come to be known as \the opportunistic approach to disinflation." We deduce policymaker preferences that rationalize the opportunistic approach as the optimal strategy for disinflationin thecontext of amodelthatis standardin other respects. Thepolicymaker whois endowed with thesepreferencestends tofocuson stabilizing output when inflation is low, but on (cid:12)ghting inflation when inflation is high. We contrast the opportunistic approach to a more conventional strategy derived from strictly quadratic preferences. Keywords: Inflation, monetary policy, interest rates, policy rules. JEL Classi(cid:12)cation System: E52 Correspondence: Orphanides: Division of Monetary A(cid:11)airs, Board of Governors of the Federal Reserve System, Washington, D.C. 20551, tel.: (202) 452-2654,email: aorphanides@frb.gov. Wilcox: Division of MonetaryA(cid:11)airs, Boardof Governorsofthe FederalReserve System, Washington, D.C. 20551,tel.: (202) 452-2441,email: dwilcox@frb.gov. (cid:3)We aregratefultonumerouscolleaguesatthe Board,especiallyDavidSmall,forhelpfulcomments on earlier drafts of this paper. The opinions expressed herein do not necessarily reflect the views of the Board of Governors of the Federal Reserve System nor of the other members of its sta(cid:11).

1 Introduction Inthelastseveralyears, anumberof currentandformermembersof theFederal OpenMarket Committee (FOMC) have developed a new view as to how the Federal Reserve should close the gap between the current rate of inflation and the long-run objective of price stability. Proponents of this new view hold that when inflation is moderate but still above the long-runobjective|as is thecase currently|theFederal Reserve shouldnottake deliberate action to reduce inflation. Instead, it should wait for external circumstances|e.g., favorable supply shocks and unforeseen recessions|to deliver the desired additional reduction in inflation. Until such disinflationary shocks occur, the Fed should move aggressively to counteract incipient increases in inflation. President Boehne of the Federal Reserve Bank of Philadelphia gave one early statement of this approach during the FOMC meeting in December 1989: Now, sooneror later, wewillhave arecession. I don’tthinkanybodyaroundthe table wants a recession or is seeking one, but sooner or later we will have one. If in that recession we took advantage of the anti-inflation [impetus] and we got inflation down from 4-1/2 percent to 3 percent, and then in the next expansion we were able to keep inflation from accelerating, sooner or later there will be another recession out there. And so, if we could bring inflation down from cycle to cycle justas we let it build upfrom cycle to cycle, that would beconsiderable progress over what we’ve done in other periods in history. [FRB, 1989, p.19] In testimony before the Senate committee that was meeting to consider his nomination to the Federal Reserve Board, former Vice Chairman Blinder summarized his views on this issue as follows: If monetary policy is used to cut our losses on the inflation front when luck runs against us, and pocket the gains when good fortune runs our way, we can continue to chip away at the already-low inflation rate. [Blinder, 1994, p.4] Thisapproachtotheconductofmonetarypolicyhascometobeknownas\theopportunistic approach to disinflation." If thePhillips curve is linear andthe policymaker’s loss function is quadratic in inflation and the deviation of output from potential, the opportunistic approach is not the optimal 1

policy. On the contrary, the policymaker should in that circumstance pursue the objective of price stability period by period, regardless of external economic circumstances, so long as inflation remains above its long-run target. If, in a conventional model, disinflation is desirable in the long run, then at least partial disinflation is desirable in the short run as well. This paper relaxes some of the assumptions that are implicit in the simplest linearquadratic model of the macroeconomy, and in so doing provides a partial rationale for the opportunistic approach. In essence, we undertake an exercise in \reverse engineering." That is, we search for a speci(cid:12)cation of the policymaker’s loss function that would lead her to pursue an opportunistic approach to disinflation. The rationale is partial in the sense that we provide only some preliminary comments on the theoretical motivation for the loss 1 function that we propose, and defer a more thorough justi(cid:12)cation to future research. Despite the anti-inflationary resolve of the opportunistic policymaker in our model, inflation can creep up, within limits, for two reasons: First, the policymaker will sometimes choose to allow inflationary shocks to feed through into higher actual inflation even when those shocks can be forecasted; this choice will sometimes be the optimal one because the sacri(cid:12)ce of output that would be required to prevent any increase in inflation would be too great. Second, the policymaker will not be able to anticipate all inflationary shocks, and the ones that are not anticipated will become embedded in actual inflation before the policymaker can do anything about them. To the best of our knowledge, none of the advocates of opportunism has addressed the issue of how the opportunistic policymaker should behave once inflation has reached a high level. The model we present in this paper predicts that the opportunistic policymaker will act deliberately to bring inflation down whenever inflation exceeds a certain threshold level. (As we show later in the paper, this threshold is a function of the policymaker’s 1Inconductingourexerciseinreverseengineering,weconstrainourselvesbymaintainingtheassumption of a linear Phillips curve. Also, we do not claim to have discovered the only loss function that might rationalize theopportunistic approach. 2

preferences.) Once inflation is back at least as low as the threshold level, the policymaker in our model will revert to the opportunistic approach, and wait for favorable shocks to deliver any further disinflation. The loss function that results from our process of reverse engineering has two key attributes: path dependence, and di(cid:11)erential valuation of deviations from the inflation and output targets. Path dependenceallows the policymaker to react di(cid:11)erently to a given level of inflation depending on the prior history of inflation itself. For example, the policymaker in our model views an inflation rate of 3 percent more favorably if inflation in the previous period was 4 percent than if inflation was 2 percent. An evolving perspective of this type is essential if the policymaker is to display determination to \hold the line" on inflation at the current level, and (cid:12)ght to prevent an earlier and higher level from recurring even though that earlier level was acceptable by previous standards. The di(cid:11)erential valuation of inflation and output deviations causes the policymaker to focus on di(cid:11)erent policy objectives under di(cid:11)erent circumstances. In particular, the opportunistic policymaker in our model concentrates on output stabilization when inflation is low and inflation reduction when inflation is high. Inthecourseof ourexercise inreverseengineering, weinvestigated whetherwemight be able to generate opportunistic behavior by assuming that the central bank is penalized for eitherhighorrisinginterestrates. Weconcludedthatwecouldnotunlesswealsointroduced somemechanism like theone wereferred toabove involving asymmetric valuation of output andinflationdeviationsfromtarget. Intheabsenceofsuchamechanism,apenaltyoneither high or rising interest rates only induces an inflationary bias in the economy and does not alter the timing of policymaker actions. In light of this (cid:12)nding, we do not pursue this alternative avenue further in this paper. The rest of this paper is organized as follows. Section II attempts to provide a more rigorous de(cid:12)nition of the opportunistic approach. Section III builds on this de(cid:12)nition, and sketches the simplest possible model that rationalizes the behavior described in Section II. 3

Section IV recti(cid:12)es a gross simpli(cid:12)cation in the model of Section III by introducing aggregate demand shocks into the analysis. Section V considers in greater detail the optimal response to supply shocks of various descriptions. In Section VI, we provide a more rigorous discussion of the implications of uncertainty for the policy prescriptions of our model. Finally, Section VII concludes with, among other things, some preliminary speculation on the critical issue of what might motivate a policymaker to adopt the loss function that generates opportunistic behavior. 2 De(cid:12)ning opportunism This section provides a more complete description of the opportunistic approach to disinflation. In drawing this more complete portrait of the strategy, we necessarily are (cid:12)lling in some of the details in the sketches provided earlier by Boehne and Blinder. While we believe the spirit of our e(cid:11)orts to be consistent with their views, we make no claim that they would subscribe to our characterization. One way to describe the behavior of an opportunistic policymaker is to contrast it with the behavior of a conventional policymaker. Theconventional policymaker we have in mind takes price stability as the long-run objective of monetary policy, and attempts to minimize a loss function that is additively separable and quadratic in inflation and the deviation 2 of output from potential. When confronted with a linear Phillips curve, this policymaker pursuesthegoalofpricestabilitygradually, butpersistently. Thepursuitisgradualbecause the policymaker su(cid:11)ers increasing marginal costs from deviations of output from potential. The pursuit is persistent because the conventional policymaker always views the bene(cid:12)t of at least a little progress on inflation as worth the cost; therefore, the policymaker pursues the long-run inflation objective every period. 2We(cid:12)nesse a numberof important issues related tothe de(cid:12)nition of price stability and simply stipulate thatpricestabilityobtainswhenthepolicymakersetstheinflationrateequaltozeroonaverage. Technically, thepricelevelthatresultsfromapolicyofthistypewilldriftovertime. Wedonotenforcethemorestringent requirementthatthepolicymakerrenderthepricelevelstationary. Wealsoignoretheissueofmeasurement error in therelevant index of inflation. 4

Like the conventional policymaker, the opportunistic policymaker we have in mind recognizes price stability as the long-run objective of monetary policy. Unlike the conventional policymaker, however, the opportunistic policymaker adopts a di(cid:11)erent mode of behavior dependingon the level of inflation. The following diagram depicts this relationship between the opportunistic policymaker’s behavior and the level of inflation. Activist Opportunistic Activist pursuit of pursuit of pursuit of inflation target inflation target inflation target (cid:27) deflation −0+ inflation In the diagram, inflation is shown on the horizontal axis. The three regions in the diagram correspond to di(cid:11)erent modes of behavior on the part of the policymaker. When prices are rising rapidly(as is the case in the right-most region) the opportunistic policymaker deliberately pursues a policy of disinflation. As we shall describe in greater detail later in the paper, the policymaker continues in this mode of deliberate disinflation until the rate of inflation has been brought down to a certain threshold, which is depicted in the diagram by the boundary between the right-most and middle regions. (As we show later, the location of this boundary is a function of the policymaker’s preferences and the slope of the Phillips curve.) Symmetrically, when prices are falling rapidly (as is the case in the left-most region), the policymaker deliberately pursues an expansionary policy, and continues doing so until the rate of inflation has been brought up to the boundary between the left-most and middle regions. Thus, in these two regions (i.e., when prices are either rising rapidly or falling rapidly), the opportunistic policymaker behaves very much like a conventional policymaker. The interesting di(cid:11)erences between the opportunistic and conventional strategies occur in the middle region|when inflation is neither too high nor too low. Consider (cid:12)rstthe case in which the rate of inflation is positive but not so high as to provoke the opportunistic policymaker into deliberate action. In this circumstance, the opportunistic policymaker 5

does not seek to open up a gap between actual and potential output for the sake of bringing inflation down, even though inflation remains above the long-run target. Instead, she adopts a more reactive stance, moving to limit the influence of shocks that would drive the inflation rate up, but accommodating shocks that drive inflation down. Importantly, the opportunisticpolicymaker allows thefullimpactoffavorable supplyshockstoshowthrough in the form of lower inflation in this middleregion, and does not attempt to reap a dividend in the form of a transitory blip in output above potential. For now, we posit symmetric policymaker behavior for rates of inflation below the longrunobjective. Thus,thereexistsamaximallynegativeinflationratewhichtheopportunistic policymaker tolerates without taking deliberate countervailing action. So long as the rate of deflation is less extreme than that maximally negative rate, the policymaker waits for inflationary supplyshocks and unforeseeneconomic expansions to bringinflation back toward the long-run objective. And while waiting for those inflationary shocks, the policymaker moves to limit the influence of deflationary shocks, which would drive the rate of inflation away from the long-run objective. As we noted in the introduction, a monetary policy conducted in the opportunistic manner has a path-dependent character when inflation is in the moderate range. That is, the policymaker’s reaction to a given rate of inflation (so long as it falls in this middle region) depends on the inherited level of inflation and thus on the prior history of shocks. For example, an opportunistic policymaker evaluates a 3 percent rate of inflation today less favorably if inflation yesterday was 2 percent than if inflation yesterday was 4 percent. In the former case, an opportunistic policymaker might well aim to drive output below potential, whereas in the latter case she would aim simply to hold output at potential. Of course, a policymaker following a conventional strategy would adopt the same policy stance regardless of the prior history of inflation. 6

3 A simple one-period model For certain parameter settings, the following model rationalizes an opportunistic approach to disinflation. We begin with a stylized Phillips curve: e (cid:25) = (cid:25) +(cid:11)y+e (1) e where (cid:25) is current inflation, (cid:25) is expected inflation, (cid:11) is a parameter (greater than zero), y is the deviation of output from potential (measured as the logarithm of actual output less the logarithm of potential output), and e is a shock. For simplicity, we assume initially that the monetary authority controls y directly and without error; in a later section of the 3 paper we relax this assumption. We also assume for now that the policymaker can observe e before choosing y. The policymaker’s loss function is given by: L A = ((cid:25)−(cid:25)~) 2 +γy 2 + jyj (2) where γ (cid:21) 0; (cid:21) 0, and (cid:25)~ is an intermediate target for inflation (zero being the longrun target). Importantly, the central bank’s loss function depends on the deviation of 4 inflation from the intermediate target, not the long-run target. The model also includes an equation describing the determination of the intermediate target as a function of the inherited inflation rate: (cid:25)~ = (cid:21)(cid:25)0: (3) where 0 (cid:20) (cid:21) < 1. Thus, the intermediate target always lies between the inherited rate and 3We realize that the resulting model is therefore incapable of addressing the circumstance highlighted by Boehne in the passage we quoted in the introduction|namely, an unforeseen recession. We make the assumptionherenonethelessinlightofthegreaterclarityita(cid:11)ords,andconsiderthecaselaterinthepaper in which the monetary authority controls theoutput gap only imperfectly. 4The device of the intermediate inflation target allows us to write the loss function in a form that more closely resembles conventionalpolicy rules. However, we show later in this section that equivalent behavior can bederivedfrom alossfunction thatpenalizes boththelevelof andchangesintherateofinflation,and that dispenses with thenotion of an intermediate target for inflation. 7

the long-run target of zero. Thelossfunctiongiveninequation(2)nestsboththeconventionalandtheopportunistic speci(cid:12)cations. If equals0(sothelossfunctionisquadraticinbothinflationandtheoutput gap) and (cid:21) equals 0 (so the intermediate target equals the long-run target), a conventional strategy for monetary policy is optimal. On the other hand, if both and (cid:21) are greater than 0, the opportunistic strategy will be optimal regardless of whether γ equals 0 or is positive. In words, the objective function can be written as: loss from loss from Loss = + inflation output gap We solve the model by calculating the derivative of the objective function with respect to the choice variable|the output gap|and setting the result equal to zero: marginal loss marginal loss marginal loss = + = 0 from inflation from output gap or, after trivial rearrangement, marginal loss marginal loss = − (4) from inflation from output gap Figure1displaysthebuildingblocksoftheopportunisticlossfunctionforthebenchmark caseinwhichγ equals 0. Theupperleftpanelshowsthelossinflictedonthepolicymaker by a deviation of output from potential, while the lower left panel shows the derivative of this componentofthelossfunctionwithrespecttooutput. Thekeyfeatureofthiselementofthe loss function is that it is linearly increasing in the output gap for positive values of the gap, and linearly decreasing in the output gap for negative values of the gap. Correspondingly, as shown in the lower left panel, the marginal loss is constant at − for negative values of the gap, and constant at for positive values of the gap. The fact that the marginal loss is everywhere bounded away from 0 implies that deviations of output from potential impose (cid:12)rst-order losses on the policymaker. It is also worth noting that the loss function 8

is nondi(cid:11)erentiable at 0, and that this nondi(cid:11)erentiability shows up in the marginal loss function as a discontinuity at 0. The upper right panel in Figure 1 shows the loss to the policymaker inflicted by deviations of inflation from the intermediate target. This portion of the loss function takes the conventional quadratic shape. Note that we plotthis element of thepolicymaker’s total loss as a function of the level of inflation rather than the deviation of inflation from the intermediate target; as a result, the quadratic function is centered around (cid:25)~ rather than 0. The lower right panel shows the derivative of this element of the loss function with respect to inflation. Of course, this schedule is linear, and cuts the horizontal axis at the intermediate target. Figure2followsthealgorithm suggestedbyequation(4), andsolves themodel(againfor the case in which γ equals 0) by superimposing the marginal loss from inflation deviations on top of minus the marginal loss from output gaps. In order to draw Figure 2, we (cid:12)rst had to rewrite the marginal loss from inflation as a function of the output gap. This we accomplished with a simple application of the chain rule: ! ! d loss from d loss from d(cid:25) = dy inflation d(cid:25) inflation dy = 2((cid:25)−(cid:25)~) (cid:11) = 2(cid:11)((cid:25) e +(cid:11)y+e−(cid:25)~) The last expression is the upward-sloping line plotted in Figure 2. If the upward-sloping line portraying the inflation schedule passes between the two branches of the output schedule without intersecting either one of them, the optimal policy action involves setting y equal to 0. On the other hand, if the inflation schedule intersects one of the two branches of the output schedule, the optimal policy action is given by the value of y at the intersection. We can summarize this condition algebraically by stating 9

that the optimal policy will involve setting output equal to potential if: (cid:21) j2(cid:11)((cid:25) e +e−(cid:25)~)j; (5) wheretheleft-hand sideof this condition gives the height of theoutputschedule in Figure 2 at y=0, and the right-hand side gives the height of the inflation schedule at the same location. Equation (5) implies that the optimal action more likely will involve setting output at potential (cid:15) themorethepolicymakercaresaboutoutputdeviationsfrompotential(i.e., thelarger is ); (cid:15) the smaller the reward to the policymaker (in terms of inflation reduction) in return for enduring an output gap of any given size (i.e., the smaller is (cid:11)); and (cid:15) the closer inflation would be to the intermediate target if the central bank set output at potential (i.e., the closer is (cid:25) e +e−(cid:25)~ to 0). e InthecaseshowninFigure2,expectedinflationplusthenewimpetustoinflation((cid:25) +e) exceeds theintermediate target ((cid:25)~) byenough tocause thepolicymaker to set outputbelow e potential. A still larger value of (cid:25) +e relative to (cid:25)~ would cause the policymaker to set output even further below potential; this would be reflected in the (cid:12)gure as a leftward shift of the upward-sloping line, and therefore a leftward-shift of the intersection between the inflation schedule and the output schedule. If no inflation is inherited from the previous period, so the intermediate target coincides with thelong-runtarget of 0, and economic agents expect noinflation inthecurrentperiod, the upward-sloping line will intersect one of the two branches of the output schedule in Figure 2 only if the inflation shock is large enough in absolute value|that is, only if jej > (6) 2(cid:11) Thus, an opportunistic central bank starting from a position of price stability will give priority to the task of output stabilization|even at the expense of some upward or downward 10

drift in the inflation rate|unless the inflation shock is large in absolute value, where large is de(cid:12)ned by equation (6). The only role of the parameter γ in the model is to determine the aggressiveness with whichthepolicymakerpursuestheinflationtargetwhenoperatingoutsidetheopportunistic middle region shown in the diagram on page 5. If γ equals 0, the policymaker concentrates exclusively on the inflation objective when she is actively combating inflation. Thus, if 2(cid:11)((cid:25) e +e−(cid:25)~)> and γ = 0, the policymaker attempts to bring inflation to the boundary of the inaction region immediately. If γ is greater than 0, on the other hand, the central bank pursues a gradual strategy for bringing inflation down to the inaction boundary. Equation(7)providesthesolutiontotheopportunisticpolicymaker’soptimization problem for the general case in which γ may be non-zero: 8 >>>>>< −2(cid:11)((cid:25) 2 e ((cid:11) + 2 e + − γ (cid:25)~ ) )− if 2(cid:11)((cid:25) e +e−(cid:25)~) > y = 0 if (cid:21) 2(cid:11)((cid:25) e +e−(cid:25)~)(cid:21) − (7) >>>>>: −2(cid:11)((cid:25)e+e−(cid:25)~)− if − > 2(cid:11)((cid:25) e +e−(cid:25)~) 2((cid:11)2+γ) Alltheelementsofthissolutionotherthantheroleof γ canbededucedfromtheinformation presented in Figure 2. e Figure 3 presents this decision rule in graphical form. We plot (cid:25) +e on the horizontal axis; this variable can be interpreted as the rate of inflation that would occur if the policymaker held output at potential. We plot y, the optimal choice of the output gap, on the vertical axis. The downward-sloping line segments in the (cid:12)gure come in pairs, the two members of which are depicted with like linetypes. (That is, one pair is shown as solid segments, another pair is shown with dotted segments, etc.) Each pair of segments pertains to a di(cid:11)erent intermediate target for inflation, and each has one member above the horizontal axis and one member below. In addition, each pair of downward-sloping segments is connnected by a third segment which is not visible in the (cid:12)gure because it runs along the horizontal axis. Together, these three segments de(cid:12)ne an \iso-intermediate-target" schedule. The optimal policy choice is determined by locating the appropriate point on the 11

relevant intermediate-target schedule. Suppose, for the sake of seeing how the diagram works, that workers and (cid:12)rms are not expecting any inflation, but that the supply shock is putting 1 percentage point’s worth of upward pressure on the inflation rate. In this case, as is shown by point A in the (cid:12)gure, the model predicts that the central bank will hold output at potential. Point A thus provides an illustration of the most notable aspect of the opportunistic strategy|namely, that the opportunistic central bank, under certain circumstances, will hold output at potential even when inflation is above its long-run target and the inflation shock is not pushing inflation downward. Indeed, as is shown by the distance between the downward-sloping segments of the schedule labelled \(cid:25)~ = 0," the policymaker operating e under an intermediate target of 0 inflation will hold output at potential whenever (cid:25) +e is between -2 percentand 2percent. As can beseen in the diagram, similar \inaction regions" obtain when the intermediate target is not equal to 0. The zone of inaction also extends to some circumstances in which the inherited rate of inflation is nonzero and the inflation shock is actually driving the level of inflation further away from the long-run objective. For example, when inflation expectations and inherited inflation are both at 2 percent, and (cid:21) equals 0.5 so the intermediate target is 1 percent, the central bankwhosebehavior isdepicted inFigure3willtolerate apositiveinflation shockof as much as 1 percentage point before taking any anti-inflationary action (see point B). It is important to note that in this case|as in most|the policy reaction function is asymmetric in the inflation shock, because the central bank would tolerate a negative inflation shock of as much as 3 percentage points before taking countervailing measures. The only case in which the policy function is symmetric is when inherited inflation is 0 percent. There are limits to even the opportunistic central bank’s tolerance of inflation. To see that this is so, assume that inflation expectations and inherited inflation are both running at 4 percent (so the intermediate target is 2 percent), and there is no inflation shock. In this case, the opportunistic policymaker will just tolerate the prevailing inflation rate and 12

refrain from taking deliberate anti-inflationary action. This situation is depicted by point C in Figure 3. However, 4 percent is the limit given this calibration, and if either inherited inflation is higher than 4 percent, or there is any upward impetus to inflation from the supply shock, the policymaker will take deliberate anti-inflationary action. As another illustration of the limits on the central bank’s tolerance of inflation, assume once again that inflation expectations and inherited inflation are both equal to 0 (and so, likewise, the intermediate target), but now assume that the supplyshock puts 3 percentage points’worthofupwardpressureontheinflationrate. Inthiscase, asisshownbypointDin the (cid:12)gure, the central bank will set output 4 percent below potential, given our calibration of the model. ThecontrastbetweenpointsB andDinFigure3highlightstheroleofinheritedinflation e in determining the behavior of the opportunistic policymaker: In both situations, (cid:25) and e sum to 3 percent. However, in the circumstance depicted by point B, inherited inflation cameinat2percent, sotheintermediate target wasestablished at1percent. Incontrast, in the circumstance depicted by point D, inherited inflation came in at 0, so the intermediate target was established at 0. In the (cid:12)rst case, the policymaker evaluated the 3 percentage points in the pipeline as (barely) acceptable, whereas in the second case she evaluated that same incipient rate of inflation as unacceptable and worth (cid:12)ghting with a recession. In other words, the policy stance of the opportunistic central bank depends on the history of inflation. The contrast between the opportunistic and conventional policies can be drawn particularly easily and sharply in the special case in which there are no inflation shocks (e = 0), e and inflation expectations are formed adaptively ((cid:25) = (cid:25)0). In this case, the opportunistic policymaker’s decision rule can be written as follows: 8 >>>>>< −(cid:11) (cid:11) (1 2 − + (cid:21) γ ) ((cid:25)0 −(cid:25) 0 ) if (cid:25)0 < (cid:25) 0 y = >>>>>: −(cid:11) 0 (cid:11) (1 2 − + (cid:21) γ ) ((cid:25)0 −(cid:25)0) i i f f (cid:25) (cid:25) 0 0 (cid:20) < (cid:25) (cid:25) 0 0 (cid:20) (cid:25)0 (8) 13

where(cid:25) 0 = − 2(cid:11)(1 −(cid:21)) and(cid:25)0 = + 2(cid:11)(1 −(cid:21)) :Thus,wheninheritedinflationexceedssomeupper threshold, the policymaker sets outputbelow potential. Likewise, when inflation falls below some lower threshold, the policymaker boosts output above potential. And when inherited inflation is between these two thresholds, the policymaker sets output at potential. Figure 4 provides a graphical description of these choices. The straight line through the origin corresponds to conventional preferences with = (cid:21) = 0. In this case, (cid:25) 0 = (cid:25)0 = 0 and the policymaker simply chooses an output gap proportional to inherited inflation (cid:11) y = − (cid:11)2+γ (cid:25)0 (9) Thedotted line represents our benchmarkexample of opportunisticpreferences with ;(cid:21) > 0 and γ = 0. Weclosethissectionbynotingthatintroducinganintermediatetargetforinflationisnot the only way to induce the type of path-dependent behavior we require of the opportunistic policymaker. Speci(cid:12)cally, we can specify that the loss depends on both the level of and change in inflation: L B = b1(cid:25) 2 +b2((cid:25)−(cid:25)0) 2 +γy 2 + jyj (10) Exactly the same behavior will result from loss function B as from loss function A provided that b1 and b2 satisfy a pair of constraints. The form of these constraints can be derived by using equation (3) to eliminate (cid:25)~ from the inflation component of equation (2)): ((cid:25)−(cid:21)(cid:25)0) 2 = (1−(cid:21))(cid:25) 2 +(cid:21)((cid:25)−(cid:25)0) 2 +((cid:21) 2−(cid:21))(cid:25) 0 2 : If b1 = (1 − (cid:21)) and b2 = (cid:21), then L A = L B up to a term in (cid:25)0 that does not a(cid:11)ect the optimal choice of the output gap, and the two problems yield identical policies. 14

4 Aggregate Demand In the basic model, we assumed that the monetary authority could control the level of output directly. Here we relax that assumption and assume instead that the central bank controls an interest rate which is only one of the factors determining aggregate demand. This alternative setup has the important bene(cid:12)t of allowing us to link the model more closely to the thoughts of Boehne and Blinder as represented by the quotes we gave in the introduction. We also assume that output follows an autoregressive process; as we shall show, this speci(cid:12)cation gives rise to Taylor’s rule as the optimal policy rule if the policymaker has a conventional loss function. Speci(cid:12)cally, we now assume that aggregate demand is given by: y =(cid:26)y0 −(cid:27)(r−r (cid:3) )+u; (11) where y0 denotes the lagged deviation of output from potential, (cid:26) is a parameter between 0 and 1 describing the persistence of output deviations, r−r (cid:3) is the deviation of the real interest rate from its \natural" long-run level, (cid:27) is a parameter greater than 0, and u is a shock. Thecentral bankcan bethought of as controlling thevariable r indirectly by setting the nominal interest rate, i, which is linked to r by the Fisher relation e i = (cid:25) +r: (12) If the central bank can observe shocks to aggregate demand contemporaneously, it will use the interest rate to fully neutralize the influence of those shocks on output. Consider, for the sake of building intuition, the case in which output in the previous period was at potential,inflationinthepreviousperiodwasatitslong-runtarget,thereisnosupplyshock, andthereisapositivedemandshock. Boththeopportunisticandconventionalpolicymakers will o(cid:11)set this shock completely if they are capable of doing so, because if they did not, they would su(cid:11)er loss directly in the current period from the excess of actual output over 15

potential, and indirectly in future periods from the resulting inflation. Because there is no penaltyineither objective functiondirectlyrelated tointerestrates, thepolicymaker su(cid:11)ers no loss if she opts for full neutralization. Thus, in this case, aggregate demand shocks are an uninteresting complication in the model, and our earlier assumption that the central 5 bank could control output directly involved no loss of generality. Even if the central bank cannot observe aggregate demand shocks contemporaneously (but the other assumptions of our model continue to hold), those shocks do not drastically altertheanalysiswepresentedearlier. Unanticipatedaggregatedemandshocksfeedthrough into inflation contemporaneously, and accordingly a(cid:11)ect the inherited rate of inflation in the following period. But once we know how to analyze theimplications of di(cid:11)erent rates of 6 inherited inflation, we also know how to analyze the implications of unanticipated shocks. For example, if the economy has been operating at potential (y0 = 0), no shocks are currently anticipated, and inherited inflation, (cid:25)0, is positive but below the upper limit of the inaction region in equation (14), (cid:25)0, the policymaker will set the nominal interest rate (cid:3) at i = (cid:25)0+r , expecting this action to result in unchanged inflation during the period and no deviation of output from potential. A negative shock to aggregate demand would drive output below potential and bring inflation down from its inherited level. In the following period,thepolicymakerwillreducethenominalinterestratesfortworeasons: (cid:12)rsttomatch the new lower level of inflation, and second to bring output back to potential more quickly than would occur if the policymaker kept the real interest rate at its natural level. This policywillconsolidatethegainintheinflationfront. Weviewthisscenarioascorresponding directly to the intuition from Boehne and Blinder that we quoted in the introduction. If neither the demand nor supply shock can be anticipated, and inflation expectations e are set adaptively ((cid:25) = (cid:25)0), the optimal rule for the conventional policymaker takes the 5Of course, this result dependsimportantly on theother assumptions maintained herethat thereare no lags in thetransmission of monetary policy to thereal economy, and that thereare no problems associated with instrument instability. 6A key aspect of our ongoing research is an e(cid:11)ort to assess the relationship between the variance of the shocks hitting theeconomy and thespeed with which theeconomy approaches price stability. 16

general form of John Taylor’s rule: (cid:26) (cid:11) (cid:3) i = (cid:25)0+r + (cid:27) y0+ (cid:27)((cid:11)2 +γ) (cid:25)0 (13) The optimal rule for the opportunistic policymaker is identical except for the form of the response to inflation: 8 >>>>>< (cid:25)0+r (cid:3) + (cid:27) (cid:26) y0+ (cid:27) (cid:11) ( ( (cid:11) 1 2 − + (cid:21) γ ) ) ((cid:25)0 −(cid:25) 0 ) if (cid:25)0 < (cid:25) 0 i= >>>>>: (cid:25) (cid:25) 0 0 + + r r (cid:3) (cid:3) + + (cid:27) (cid:27) (cid:26) (cid:26) y y 0 0+ (cid:27) (cid:11) ( ( (cid:11) 1 2 − + (cid:21) γ ) ) ((cid:25)0 −(cid:25)0) i i f f (cid:25) (cid:25) 0 0 (cid:20) < (cid:25) (cid:25) 0 0 (cid:20) (cid:25)0 (14) where, as before, (cid:25) 0 = − 2(cid:11)(1 −(cid:21)) and (cid:25)0 = + 2(cid:11)(1 −(cid:21)) : In Orphanides et al. (1996), we compare the performance of equations (13) and (14) in stochastic simulations of the U.S. economy. 5 Aggregate supply Thus far, we have interpreted e, the shock to the Phillips curve, as a \supply shock." The rationale for this interpretation is that the shock a(cid:11)ects the inflation rate through a nondemand-related channel. However, this shock di(cid:11)ers from the supply shocks studied by many other authors. In particular, it a(cid:11)ects only the rate of inflation in our model and not 7 either potential or actual output. A common view is that an adverse supply shock not only boosts the rate of inflation but also depresses the level and possibly the rate of growth of potential output; in addition, it may depress actual output. Ifthecentralbankcontrolstheoutputgapdirectly,thenthefactthatasupplyshockmay a(cid:11)ect either actual or potential output (in addition to influencing inflation) is immaterial; thepolicymaker stillsetstheoutputgapinlightofthesameconsiderations asbefore,taking 7Furthermore, it is worth noting that e a(cid:11)ects the level of the inflation rate permanently absent any o(cid:11)settingactionbythemonetaryauthoritybecauseinheritedinflationentersthePhillipsCurvewithaunit coe(cid:14)cient. 17

into account the impact of the supply shock on the inflation rate. If the central bank controls output only imperfectly (i.e., equation (11) is relevant and the central bank takes either the nominal or real interest rate as its instrument), then the exact nature of the supply shock is important for determining the stance of policy. One way to organize the analysis of the various possibilities is around the question of whether (cid:3) the supply shock a(cid:11)ects r , the natural real rate of interest. If a supply shock does not a(cid:11)ect the natural real rate (i.e., the direct e(cid:11)ect of the shock on actual output is the same as the direct e(cid:11)ect on potential), the analysis given above remains valid: An adverse supply shock has no direct e(cid:11)ect on the output gap, and the higher level of inflation is the only problem the policymaker can address. If the inherited rate of inflation was above the longrun inflation objective, the policymaker will tend to respond aggressively to the threat that inflation may be moved further from its long-run objective. If an adverse supply shock boosts the natural real rate of interest because it depresses potential output by more than it depresses actual output, the above analysis needs some modi(cid:12)cation. The optimal policy decision is most easily determined in two steps. In the (cid:12)rst step, the policymaker increases the real rate by just enough to match the increase in the natural real rate. In the second step, the policymaker adjusts the real rate from its new level according to the same analysis of inflation outlined above. If an adverse supply shock reduces the natural real rate because it a(cid:11)ects demand by more than it a(cid:11)ects supply (possibly an anomalous de(cid:12)nition of a supply shock), then the central bank is faced with a dilemma: (cid:12)ght the shortfall of activity relative even to the new lower level of potential, or (cid:12)ght inflation. If inflation was at its long-run target level, the opportunistic central bank might choose to ignore much or all of the increase in inflation and move instead to boost real activity back to potential. However, if inherited inflation was far enough above the long-run target level, then even an opportunistic central bank would tighten its policy stance in order to prevent inflation from increasing too much. 18

6 Uncertainty Thus far, we have ignored the influence of uncertainty on the optimal setting of the policy instrument. Althoughthisapproachisusefulasastartingpoint,itdoesnotyieldacomplete analysis except under very restrictive circumstances, including the one on which we have concentrated the bulk of our attention to this point in the paper|namely, a one-period model in which the policymaker can react contemporaneously to the shocks hitting the economy. This section provides an analysis of the influence of uncertainty under more 8 general assumptions. In these more general circumstances, the policymaker must be treated as minimizing the expected value of the loss function: L C = E[((cid:25)−(cid:25)~) 2 +γy 2 + jyj] (15) where the expectation is taken with respect to the probability distribution governing the inflation shocks, e, aggregate demand shocks, u, or both. As is well known, the linear-quadratic framework that gives rise to the conventional strategy has the special property that the optimal policy depends only on the expectation of the shocks and not on their variances. The loss function we use to characterize the preferences of opportunistic policymakers is not quadratic. Nonetheless, the associated decision rule does display certainty equivalence in one special circumstance|namely in a one-periodmodelinwhichthemonetaryauthoritycontrols theoutputgapperfectly. Inthis case, no modi(cid:12)cation of the earlier analysis is required even when the monetary authority cannot observe the inflation shock before it sets the level of output: The fact that the monetary authority picks the output gap e(cid:11)ectively renders that variable non-stochastic in a one-period model, and inflation enters the loss function via a quadratic function. This convenient result does not obtain when either the model is extended to more than 8To be clear, the source of the uncertainty we are concerned with in this section is the shocks in the model, not theparameters. 19

one period, or the central bank cannot control output perfectly. Speci(cid:12)cally, it does not obtain when the central bankcontrols aggregate demand imperfectly (i.e., when equation (11) comes into play, and the central bank controls the real interest rate). In that case, it is convenient to decompose the resulting output gap, y, into two components|the expected output gap corresponding to the policymaker’s choice, y(cid:22), and the unexpected additional influence from the aggregate demand shock, u. Assuming with no loss of generality that u is drawn from a zero mean distribution this yields: y = y(cid:22)+u Controlling the interest rate in this setting is equivalent to controlling the expected or intendedoutputgap,y(cid:22). Thefailureofcertaintyequivalenceintheopportunisticcaseimplies that, in general, the choice of y(cid:22) will depend on whether u is stochastic or always equal to its zero mean. Fortunately, in our model it is easy to show qualitatively the influence of uncertainty on the policymaker’s choice. Figure 5 reproduces the graphical derivation of the policymaker’s choice in the absence of uncertainty (from Figure 2), and shows how uncertainty alters the analysis. On the horizontal axis we now show the intended output gap, y(cid:22), as opposed to the actual output gap shown in Figure 2. Since in the absence of uncertainty the two are always equal, the marginal loss curves for the deterministic case are identical to those in Figure 2. (As before, we restrict attention to the benchmark case in which γ equals 0 for the (cid:12)gure). Since the marginal loss from inflation is linear in output, uncertainty does not influence its expectation. Consequently, it is identical with and without uncertainty. Uncertainty operates exclusively through the marginal loss from the output gap which is non-linear in intended output. In the case of certainty this component of marginal loss is given by: d g C (y(cid:22))(cid:17) jy(cid:22)j: dy(cid:22) 20

C As in Figure 2, we plot the negative of g (y(cid:22)) here. The intersection with the marginalloss-from-inflation schedule at point C indicates the policymaker’s intended output choice in the absence of uncertainty. When u is stochastic, themarginal expected loss from output becomes Z d +1 g U (y(cid:22)) (cid:17) jy(cid:22)+ujdF(u): dy(cid:22) −1 where F denotes the distribution of u. The intersection of −g U (y(cid:22)) with the marginal-lossfrom-inflation schedule at point U indicates the policymaker’s intended output choice with uncertainty. As is clear from the (cid:12)gure, to understand the influence of uncertainty on the poli- C cymaker’s choice, we need only compare the two marginal-loss-from-output functions, g U and g . The characteristics of the distribution function F(u) have an important role in this comparison. Some implications, however, obtain without placing unduly restrictive U assumptions on the distribution function. For instance, for any continuous distribution,g will be continuous in the intended output gap. Consequently, the policymaker’s choice of intended output gap will not exhibit the region of absolute inaction characterizing the opportunistic pursuit of the inflation target when there is no uncertainty regarding aggregate demand. If the distribution is symmetric and has positive support over the entire real line, U g (y(cid:22)) simpli(cid:12)es to: Z +y(cid:22) U g (y(cid:22)) = dF(u) −y(cid:22) ThisisthecaseweshowinFigure5. Thescheduleunderuncertaintylieseverywhere(except the origin) between the horizontal axis and the schedule under certainty. As a result, the policymaker will always pursue the inflation target more aggressively in the presence of uncertainty than in its absence. For example, as we show in Figure 5, an opportunistic policymaker facing positive inherited inflation will tilt toward a somewhat more restrictive policy in the face of aggregate demand uncertainty (point U) than she would have done in the absence of any uncertainty (point C). As a result, some progress toward price 21

stability will be achieved even when inherited inflation falls within the region characterized by inaction in the absence of uncertainty and even if no shocks actually materialize. 7 Conclusion The model we outline in this paper rationalizes the pursuit of an opportunistic approach to disinflation. When inflation is rapid, the strategy we describe calls for aggressive antiinflationary action on the part of the monetary authority. When inflation is moderate, however, the strategy involves waiting for external circumstances to deliver reductions in inflation,andinthemeantimemerelyattemptingtoholdthelineagainstupticksininflation. As we have highlighted, the key feature of the model we present is the policymaker’s objective function. By our lights, the most important unresolved issue related to opportunism concerns the economic rationale for the objective function. What considerations could motivate the policymaker to adopt an objective function with these characteristics? What evidence exists to support the view that the costs of inflation and deflation are more convex than are the costs of deviations of output from potential? In one respect, the speci(cid:12)cation of the opportunistic loss function is relatively easy to justify: As we noted earlier, the device of the intermediate target is not essential, and its function can be replicated by introducing a penalty in the change in inflation. Such a penalty has some appeal to us because our presumption is that continuity and absence of dislocation are positive attributes in the macroeconomy, and that large changes in the rate of inflation may be inconsistent with those attributes. The more challenging problem is to justify the di(cid:11)erence we posit between the penalties on inflation deviations from target and output deviations from potential. In words, this di(cid:11)erence amounts to an assertion on our part that the policymaker may be thought of as incurring a (cid:12)rst-order loss from output deviations even when output is close to potential, and yet only a second-order loss from inflation deviations when inflation is close to its target. The possible microeconomic foundations for this assertion are far from clear to us, 22

but at this stage we (perhaps imprudently) o(cid:11)er the following highly speculative remarks. The deleterious e(cid:11)ects of inflation are mainly allocative in nature: Investment decisions are distorted, borrowing, saving, and spending decisions become ine(cid:14)cient, and wealth may be transferred in possibly unpredictable ways. At least within some relatively narrow range, it 9 may bereasonable to thinkof these costs as convex in the level of inflation. In contrast, an interestingrecentstrandofliteraturetakes seriouslythefactthatformuchoftheworkforce, employment is an all-or-nothing proposition: Either you’re employed full-time, or you’re unemployed, and when the unemployment rate moves up slightly from the natural rate, it ismoreaccurate tothinkofafewindividualsbecomingcompletelyunemployed, ratherthan thinking of everyone becoming slightly underemployed. It may be that this concentration of unemployment provides the basis for treating deviations of output from potential as imposing (cid:12)rst-order costs on the policymaker. Perhapsthemoststrikingimplication of theopportunisticapproachconcernsthetiming of the attainment of price stability. Under a conventional policy (and assuming that the Phillips curve is linear), the expected time to attainment of price stability can becomputed even in the absence of information about the distribution of shocks hitting the economy. This is not the case if the monetary authority is pursuing the opportunistic approach. Indeed, this is the feature of the opportunistic approach that has led former Vice Chairman Blinder on many occasions to remark that the U.S. economy is \one recession away from price stability." In Orphanides et al. (1996), we explore the contrast between the conventional and opportunistic strategies in this dimension, using stochastic simulations of a small-scale macroeconomic model of the U.S. economy. 9It may not be reasonable to hold this view over too large a range of inflation, because there is ample anecdotal evidence that institutions and agents adapt in cost-reducing ways when inflation becomes very high. 23

References Blinder, Alan S. (1994) \Opening Statement of Alan S. Blinder at Con(cid:12)rmation Hearing Before the U.S. Senate Committee on Banking, Housing, and Urban A(cid:11)airs" (May) mimeo, Federal Reserve Board. FederalReserveBoard(1989) \TranscriptoftheFederalOpenMarketCommitteeMeeting" (December) mimeo. Orphanides, Athanasios, David H. Small, David W. Wilcox, and Volker Wieland (1996) \A Quantitative Exploration of the Opportunistic Approach to Disinflation" mimeo in process, Federal Reserve Board. 24

Figure 1 Building blocks of the opportunistic loss function Loss from output Loss from inflation 0 y (cid:25)~ (cid:25) Marginal loss from output Marginal loss from inflation 0 y (cid:25)~ (cid:25) 25

Figure 2 Graphical derivation of the opportunistic policy marginal loss from inflation 2(cid:11)((cid:25) e +e−(cid:25)~) y −1 ((cid:25) e +e−(cid:25)~) optimal choice of y (cid:11) minus the marginal loss from output Notes: This diagram presents a graphical solution to the optimization problem with the opportunistic loss function speci(cid:12)cation L = ((cid:25)−(cid:25)0=2) 2 +jyj, subject to the linear Phillips curve, (cid:25) = (cid:25)0+y=4. The horizontal axis measures the output gap,y, while the vertical axis measures marginal loss. The upward-sloping line gives the marginal loss from inflation as a functionoftheoutputgap, whilethepiecewise-linear schedulegives minusthemarginalloss from the outputgap, also as a function of theoutput gap. Theoptimal choice of the output gap is given by the horizontal location of these two schedules at their point of intersection. 26

Figure 3 The opportunistic decision rule y (cid:25)~ = 0 (cid:25)~ = 1 (cid:25)~ = 2 2 A B C −2 2 4 (cid:25) e +e −2 −4 D (cid:25)~ = 2 (cid:25)~ = 0 (cid:25)~ = 1 Notes: This diagram shows the optimal choice of output gap (measured on the vertical axis) as a function of two variables: the rate of inflation if the central bank sets output at e potential ((cid:25) +e, measured on the horizontal axis), and the intermediate inflation target, (cid:25)~. The optimal choice of output gap for the opportunistic policymaker can be determined by locating the appropriate point on the relevant intermediate-target schedule. 27

Figure 4 Conventional versus opportunistic policy: A special case y 4 2 −4 −2 2 4 (cid:25)0 −2 −4 Conventional Opportunistic Notes: This diagram compares the conventional and opportunistic policies under the assumptions that inflation expectations are formed adaptively, and neither the supply nor demand shock can be anticipated. The conventional policy rule always attempts to make some progress toward the long-run inflation objective, and so sets the output gap to some non-zero value whenever inherited inflation is non-zero. By contrast, the opportunistic policy sets output at potential whenever inherited inflation close enough to zero, even if not literally zero. 28

Figure 5 The impact of uncertainty on the opportunistic policy C U y(cid:22) Notes: Thisdiagramshowsthattheopportunisticpolicymakerwillmoreaggressivelypursue the long-run inflation target whenever there is uncertainty about aggregate demand. The logistic-shaped curve shows minus the intended value of the marginal loss from output when there is uncertainty, while the piecewise linear schedule shows minus the actual value of the marginal loss from output whenthere is no uncertainty. The curve underuncertainty lies everywhere between the horiontal axis and the curve under certainty; as a result, its intersection with the inflation schedule always occurs at a larger value of the output gap, in absolute value. 29