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Monetary Policy Rules and Macroeconomic Stability: Evidence and Some TheoryAuthor(s): Richard Clarida, Jordi Gali and Mark GertlerSource: The Quarterly Journal of Economics, Vol. 115, No. 1 (Feb., 2000), pp. 147-180Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2586937 .

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MONETARY POLICY RULES AND MACROECONOMICSTABILITY: EVIDENCE AND SOME THEORY*

RICHARD CLARIDAJORDIGALf

MARKGERTLER

We estimate a forward-looking monetary policy reaction function for thepostwar United States economy, before and after Volcker's appointment as FedChairman in 1979. Our results point to substantial differences n the estimatedrule across periods. In particular, nterest rate policy n the Volcker-Greenspanperiod appears to have been much more sensitive to changes in expected inflationthan in the pre-Volcker eriod. We then compare some of the implications of the

estimated rules for the equilibrium properties of inflation and output, using asimple macroeconomic model, and show that the Volcker-Greenspan rule isstabilizing.

I. INTRODUCTIONFrom the late 1960s through the early 1980s, the United

States economy xperienced high and volatile inflation long withseveral severe recessions. Since the early 1980s, however, nfla-tion has remained steadily low, while output growth has beenrelatively stable. Many economists cite supply shocks-and oilprice shocks, in particular-as the main force underlying theinstability f the earlier period. t is unlikely, owever, hat supplyshocks alone could account for the observed differences etweenthe two eras. For example, while umps in the price of oil mighthelp explain transitory periods of sharp increases in the generalprice level, it is not clear how they alone could explain persistenthigh inflation in the absence of an accommodating monetarypolicy.' Furthermore, as De Long [1997] argues, the onset ofsustained high nflation ccurred prior to the oil crisis episodes.

* We thank seminar participants at Universitat Pompeu Fabra, New YorkUniversity, he Board of Governors of the Federal Reserve System, University ofMaryland, NBER Summer Institute, Universit6 de Toulouse, Bank of Spain,Harvard University, Bank of Mexico, Universitat de Girona, and the FederalReserve Banks of Atlanta, New York, Richmond, Dallas, and Philadelphia, as wellas two anonymous referees and two editors for useful comments. We thank JeanBoivin and Mark Watson for pointing out an error in a previous version of themanuscript. Tommaso Monacelli provided valuable research assistance. Thesecond and third authors are gratlefl to the C. V. Starr Center (Gali and Gertler)and CREI (Gali) for financial upport.

1. In subsection III.D, we provide more detail on the role of oil shocks versusmonetary policy and also on how the monetary policy rule influences the effectsthat oil shocks have on the economy.

e 2000by hePresident nd Fellows fHarvard ollege nd the Massachusetts nstitute f

Technology.TheQuarterly ournal f conomics, ebruary000

147

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148 QUARTERLYJOURNALOF ECONOMICS

In this paper we explore the role of monetary policy. We firstdemonstrate that there is a significant difference n the waymonetary policy was conducted pre- and post-1979, the year PaulVolcker was appointed Chairman of the Board of Governors of theFederal Reserve System. We then go on to argue that thisdifference ould be an important ource of the shift n macroeco-nomic behavior. n some ways, our story hould not be surprising.Many economists agree that monetary policy n the United Stateshas been relatively well managed from he time Paul Volcker ookover the helm, through he current egime ofAlan Greenspan. It is

also generally agreed that monetary policy was not so wellmanaged in the fifteen r so years prior to Volcker.2 he contribu-tion of our paper is to add precision to this conventional wisdom.

We identify how monetary policy differed efore and afterVolcker came to office by estimating policy rules for each era.Specifically, we estimate a general type of rule that treats theFederal Funds rate as the instrument f monetary policy.The rulecalls for adjustment of the Funds rate to the gaps between

expected nflation nd output and their respective target evels. Itis a version of the kind of policy rule that emerges n both positiveand normative analyses of central bank behavior that haveappeared in recent iterature.3 A distinctive feature of our specifi-cation is that it assumes forward-looking ehavior on the part ofthe central bank.

The key difference n the estimated policy rules across timeinvolves the response to expected inflation. We find not surpris-

ingly) that the Federal Reserve was highly "accommodative" nthe pre-Volcker years: on average, it let real short-term nterestrates decline as anticipated nflation ose. While it raised nominalrates, it typically did so by less than the increase in expectedinflation. On the other hand, during the Volcker-Greenspan rathe Federal Reserve adopted a proactive tance toward controllinginflation: t systematically raised real as well as nominal short-term nterest rates in response to higher expected inflation. Our

results thus lend quantitative support to the popular view thatnot until Volcker took office id controlling nflation become theorganizing focus ofmonetary policy.

The second part of the paper presents a theoretical model

2. See, e.g., the recent discussions n Friedman nd Kuttner 19961 ndGertler 19961.

3. See Clarida,Gali, nd Gertler 19991 or review f he recent iterature nmonetary olicy.

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MONETARY POLICY RULES 149

designed to flesh out how the observed changes in the policy rulecould account for the change in macroeconomic performance. We

embed policy rules of the type we estimate within a fairlystandard business cycle model and then analyze the dynamics ofinflation nd output in the resulting equilibrium. We show thatthe estimated rule for the pre-Volcker period permits greatermacroeconomic nstability han does the Volcker-Greenspan ule.It does so in two distinct respects.

First, the pre-Volcker rule leaves open the possibility ofbursts of inflation and output that result from self-fulfilling

changes in expectations. These sunspot fluctuations may ariseunder this rule because individuals (correctly) nticipate that theFederal Reserve will accommodate a rise in expected inflation byletting short-term real interest rates decline (which in turnstimulates the rise in aggregate demand and inflation).4 On theother hand, self-fulfilling luctuations cannot occur under theestimated rule for the Volcker-Greenspan ra since, within thisregime, the Federal Reserve adjusts interest rates sufficiently o

stabilize any changes in expected inflation. Second, the pre-Volcker rule is less effective han the Volcker-Greenspan rule atmitigating he impact of fundamental hocks to the economy. hatis, holding constant the volatility of exogenous fundamentalshocks, the economy exhibits greater stability under the post-1979 rule than under a rule that closely approximates monetarypolicypre-1979.

The plan of the paper is as follows. Section II presents our

policyrule specification, nd discusses the econometric procedureused to estimate it. Section III reports estimates of this rule fordifferent ample periods, conducts a number of robustness checks,and identifies the main differences n the coefficient stimatesacross periods. Section IV presents the theoretical model: a (now)conventional New Keynesian framework with money, monopolis-tic competition, nd sticky prices. We then present both a qualita-tive and quantitative analysis of the model under the pre- and

post-1979 policy rules. Section V offers oncluding remarks. Herewe discuss an important ssue that the paper raises but does notresolve: why in the pre-Volcker period the Federal Reserve

4. Chari, Christiano, nd Eichenbaum [19971 lso suggest that the nflation fthe 1970s may have been due mainly to self-fulfilling ehavior. Their argumentexploits the idea that there may be a multiplicity f equilibria in reputationalmodels of monetary policy.Our analysis is based simply on the implications of theestimated historical policy reaction function.


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appeared o pursue systematic olicy ule that not only ccom-modated nflation, ut did so in a way that was entirely redict-

ableby he private ector at least with he benefit f hindsight).

II. THE FEDERALRESERVE'S OLICYREACTION UNCTION:A FORWARD-LoOKINGODEL

A. A Simple Forward-Looking RuleWe begin with baseline specification f the policy eaction

function. We take as the instrument f monetary olicy theFederalFunds rate. Except possibly or brief eriod f reservestargeting t the start of he Volcker ra, this seemsa reasonablechoice see, e.g., Bernanke and Mihov [1998]).Further, Good-friend 1991]argues that even under the period of official eservestargeting, he Federal Reservehad in mind n implicit arget orthe Funds rate.

The baseline policy rule we consider takes a simple form. etr* denote the target rate for the nominal Federal Funds rate inperiod t. The target rate each period is a function of the gapsbetween expected nflation nd output and their respective targetlevels. Specifically, we postulate the linear equation:

( 1) rht r* +3 (E[rtk I t] - X*) + y [Xt, qft],where 1rt,k denotes the percent change in the price level betweenperiods t and t + k (expressed in annual rates). ar* s the target for

inflation. xtq is a measure of the average output gap betweenperiod t and t + q, with the output gap being defined as thepercent deviation between actual GDP and the correspondingtarget.5 is the expectation operator, nd ft is the information etat the time the interest rate is set. r* is, by construction, hedesired nominal rate when both nflation nd output are at theirtarget evels.

The policy rule given by (1) has some appeal on both

theoretical and empirical grounds. Approximate (and in somecases exact) forms f this rule are optimal for central bank that

5. The flow nature of GDP forces us to be more precise here: xt includes GDPgenerated between the beginning of period t and the beginning of period t + q (i.e.,it includes periods-e.g., quarters-t, t + 1,... and t + q - 1). In our empiricalwork we account for the fact that period t GDP is not known as of the time theinterest rate is set in that period; i.e., xt X fQt. his is not true in our theoreticalmodel of Section IV, where all variables dated in period t are determinedsimultaneously.


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MONETARYPOLICY RULES 151

has a quadratic loss function n deviations of nflation nd outputfrom their respective targets, given a generic macroeconomic

model with nominal price nertia.6On the empirical side a number of authors have emphasizedthat policy rules like (1) provide reasonably good descriptions ofthe way major central banks around the world behave, at least inrecent years. It is true that the most notable of these papers,Taylor [1993], proposes a rule where the Funds rate responds tolagged inflation and output rather than their expected futurevalues. However, our forward-looking ule nests the Taylor rule asa special case: if either agged inflation r a linear combination oflagged inflation and the output gap is a sufficient tatistic forforecasting future inflation, then equation (1) collapses to theTaylor rule.7 On the other hand, our forward-looking pecificationallows the central bank to consider a broad array of nformation(beyond lagged inflation and output) to form beliefs about thefuture condition of the economy, feature that we find highlyrealistic.

B. Implied Real Rate RuleThe implications of a policy rule like (1) for the cyclical

behavior of the economy will of course depend on the sign andmagnitude of the slope coefficients, and -y. To gain the basicintuition, consider the implied rule for the (ex ante) real rate

target, rrt*:(2) rr* rr* + (3 -1) (E17rtkIQt] - a*) + -yE[xtqI t],where rr rt - E rtk I Qt and where rr*=r* - *is the long-runequilibrium real rate.8 We assume that the real rate is stationaryand is determined by nonmonetary factors in the long run,

6. See, e.g., Svensson [19961, nd Clarida, Gali, and Gertler 1999].7. In this case, however, he estimated coefficients f the Taylor rule may bemisleading as indicators of the Fed's intended response to inflation nd outputchanges since, n addition to the size of the policyresponse, they apture the abilityof ach variable to forecast he state of the economy.

8. Note that rr* s an "approximate" real rate since the forecast horizon forinflation will generally differ rom he maturity of the short-term nominal rateused as a monetary policy nstrument. n practice, this is of ittle relevance, giventhe high correlation among short-term rates at maturities associated withplausible target horizons. Hence, e.g., the correlation between the federal fundsrate and the three-months reasury Bill rate (our baseline horizon) s 0.982 in oursample.


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consistent with conventional wisdom.9Accordingly, r* s a con-stant and is independent ofmonetary policy. 0

As equation (2) makes clear, the sign of the response of thereal rate target to changes in expected inflation nd the outputgap depends on whether is greater or less than one and on thesign of -y, espectively. Roughly speaking, to the extent that lowerreal rates stimulate economicactivity nd inflation as implied bystandard macroeconomic models and as perceived by policy-makers and market participants alike), interest rate rules charac-terized by 1 > 1 will tend to be stabilizing, while those with 1 < 1

are likelyto be destabilizing or, at best, accommodative of shocks

to the economy.11 similar logic applies to the sign of -y i.e.,stabilizing if -y 0; destabilizing if -y 0). We thus have bench-marks (1 = 1, -y 0) to evaluate differences n the estimatedpolicyrules across time.

C.Interest ate Smoothing nd Exogenous hocksAbsent any further modification, he policy reaction function

given by equation (1) is too restrictive o describe actual changesin the Funds rate. There are at least three reasons why. First, thespecification assumes an immediate adjustment of the actualFunds rate to its target level, and thus ignores the FederalReserve's tendency o smooth changes in interest rates. 2Second,it treats all changes in interest rates over time as reflecting heFederal Reserve's systematic response to economic conditions.Specifically, t does not allow for ny randomness n policy ctions,

9. In our empirical work, however, we allow for he possibility hat there havebeen shifts over time in the long-run quilibrium real rate, since we assume onlythat rr is constant within the subperiod over which we estimate.

10. In our empirical work we allow for hanges in the equilibrium real rateacross subperiods.

11. Another way to model accommodation of inflation would be to allow forendogenous adjustment of the target nflation ate, irT.We view this approach as asympathetic alternative to the one we take of focusing on whether the slopecoefficient is less than unity. We opt to treat nr' s a constant and instead let ,characterize the degree of ccommodation for woreasons. First, this approach hasthe advantage of parsimony-there is no need to model the adjustment of nr'.Second, as a matter of ogic, t is a priori reasonable to treat nT'as constant since itis meant to reflect an optimum for inflation that is independent of currenteconomic onditions. n our robustness exercises, however, we do let nT'vary withineach subsample. To foreshadow, we find that the magnitude of p seems to do abetter ob of apturing the degree of accommodation han any time variation n nr',consistent with the approach we take.

12. See also Rudebusch [19951forevidence n the serial correlation f nterestrate changes. Why this smoothing occurs is beyond the scope of this paper,although a number of explanations are found n the literature, ncluding fear ofdisruption f financial markets Goodfriend 9911,or uncertainty bout the effects

of nterest rate changes [Sack 19971.


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MONETARYPOLICYRULES 153

other than that associated with misforecasts of the economy.Third, it assumes that the Federal Reserve has perfect control

over nterest rates; i.e., it succeeds in keeping them at the desiredlevel (e.g., through necessary open market operations).We relax the first ssumption by extending the model in a

straightforward way. In particular, we specify the followingrelationship for he actual Funds rate, rt:

(3) rt = p(L) rt l + (1 - p)rwhere p(L) = pi + p2L+ . . . + pLn-1, and where p =p(l). vt is azero mean exogenous interest rate shock, and the Funds ratetarget r* s given by (1). Equation (3) postulates partial adjust-ment of the Funds rate to the target r*. Specifically, ach periodthe Federal Reserve adjusts the Funds rate to eliminate a fraction(1 - p) of the gap between ts current arget evel and some linearcombination of ts past values. We interpret p as an indicator ofthe degree of moothing f nterest rate changes.

Combining the partial adjustment equation (3) with thetarget model 1) yields the policyreaction function,(4) rt = (1 - p) [rr* (I - lfr* + Wgtk + YXtq]+ p(L) rti- + Et,where t -(1 - p) IP(3Tt,k Ebrt,kfQt]) + Y(Xtq- E[Xt,qKIt])l No-tice that the term in curly brackets is a linear combination offorecast errors and is thus orthogonal to any variable in theinformation et Qt

Let zt denote a vector of instruments known when rt s set(i.e., Zt E ft). Equation (4) then implies the set of orthogonalityconditions,

(5) Ej[rt - (1 - p) rr* (f3 1)7T* + WTt,k + 'YXtq)+ p(L) rt-1] ztl = 0,

which provide the basis for he estimation of the parameter vector(0xt,,-y,p), sing the Generalized Method of Moments [Hansen1982], with an optimal weighting matrix that accounts for pos-sible erial correlation n kEtl.3 o the extent hat he dimension fvector zt exceeds four-the number of parameters being esti-mated-(5) implies some overidentifying estrictions hat we can

13. Note that, by construction, he first omponent of JEti follows an MA(a)process, with a = max [k,q] - 1, and will thus be serially correlated (un-less k = q = 1).


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test in order to assess the validity of our specification s well asthe set of nstruments used.

In the absence of further ssumptions our approach identifiesonly the term rr* - (I - 1),r*,but not rr* or ar* eparately. Sincetarget inflation ar* s of some interest in our characterization ofmonetary policy,we impose an additional restriction hat permitsus to identify nd estimate this parameter. Specifically, we takethe observed sample average as a measure of the equilibrium realrate rr*, an assumption that we view as providing a reasonablefirst pproximation, given our sample size. Imposing this restric-

tion directly n equation (5) allows us to estimate ar*ointly withthe parameter vector axA-yp).Before proceeding, we briefly ddress several econometric

issues. First, our empirical analysis maintains the assumptionthat both inflation nd the nominal interest rate are stationary.We view this assumption as reasonable for the postwar UnitedStates, even though the null of a unit root in either variable isoften hard to reject at conventional significance evels, given the

persistence of both series and the well-known ow power of unitroot tests. In addition to its empirical plausibility, tationarity ofboth inflation nd the nominal interest rate is also a property fmany of he theoretical models that rationalize the use of he kindof policy rule considered here.14 In our robustness analysis,however, we do allow for he possibility f drift n the trend rate ofinflation by letting the target inflation rate vary across theregimes ofdifferent ederal Reserve chairmen.

Second, the sample period must contain sufficient ariation ninflation and output and must be sufficiently ong in order toidentify he slope coefficients n the policy reaction function, swell as the target inflation rate 7r*. n particular, estimating therule over a short sample with little variability in inflation canyield highly misleading results. Suppose, for example, that theFederal Reserve responds aggressively to large deviations ofinflation rom arget but not to small deviations. Then by estimat-

ing over a period where inflation does not vary much from tstarget, one might mistakenly conclude that the Fed is notaggressive in fighting nflation i.e., one might mistakenly obtaintoo low an estimate of 1). Alternatively, uppose that a centralbank confronting igh nflation s in the process ofraising rates toengineer a disinflation. By estimating the rule only over the

14. See,e.g.,Clarida,Gali, nd Gertler 19991.


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current period of high inflation, ne might mistakenly concludethat the central bank has a high target inflation rate (i.e., one

might mistakenly obtain too high an estimate of frr* nd, as aresult, too low an estimate of 1).15 The subsamples we consider,however, appear to contain sufficient ariation in inflation rela-tive to the sample mean and are sufficiently ong to permit us tocorrectly dentify oth the slope coefficient n inflation, , and thetarget nflation ate 1r*.16

III. THE FEDERALRESERVE'SOLICYREACTION UNCTION:THE EVIDENCE

In this section we report estimates of the policy reactionfunction efined by equations (1) and (3).We accomplish two mainobjectives. First, we demonstrate the existence of a systematicrelationship between the Funds rate and forecasts of futureinflation and output along the lines suggested by our model.Second, we identify ifferences n the conduct of monetary policy

pre- and post-1979. We do so by estimating monetary policy rulesfor each era and performing ests of structural stability acrossperiods.

The data are quarterly time series spanning the period1960:1-1996:4. With one exception, we obtain the data fromCITIBASE (mnemonics follow in parentheses). We use as theinterest rate the average Federal Funds rate (FYFF) in thefirst-month f each quarter, expressed in annual rates. The

baseline inflation measure is the (annualized) rate of change ofthe GDP deflator GDPP) between two subsequent quarters. Butwe also report results using CPI (PUNEW) inflation. he baseline"output gap" measure is the series constructed by the Congres-sional Budget Office CBO). We also use two alternative measures(described below) based on the detrended series for GDP (GDPQ)and the unemployment ate (LHUR).The instrument et includeslags of he Funds rate, nflation, nd the output gap, as well as the

15. The estimate of -r* will depend heavily on the sample mean of nflation.Thus, estimating over a short period of bove target nflation an generate too highan estimate of wr*.The overestimate of w* will be accompanied by an under-estimate of A,since the former will account for the high nominal rates over theshort period. By lengthening he sample to nclude the full disinflation nd beyond,one will obtain an estimate of wr* hat is closer to the true target, and as aconsequence a (higher) estimate of 1that is closer to its true value.

16. When we consider subsample stability of our estimates in Section III,we address the short ample problem by restricting ome coefficients obe constantacross the sample (in the cases where we cannot reject that coefficient s stable).


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TABLE IAGGREGATEOLATILITYNDICATORS

Standard Deviation of:Inflation Output

Level hp Gap hp

Pre-Volcker 2.77 1.48 2.71 1.83Volcker-Greenspan 2.18 0.96 2.36 1.49post-82 1.00 0.79 2.06 1.34

same number of ags of commodity rice nflation PSCCOM), M2growth FM2), and the "spread" between the long-term ond rate(FYGL) and the three-month reasury Bill rate (FYGM3).17

We divide the sample into two main subperiods. The first(60:1-79:2), encompasses the tenures of William M. Martin,Arthur Burns, and G. William Miller as Federal Reserve chair-

men. The second (79:3-96:4) corresponds to the terms of PaulVolcker nd Alan Greenspan. As we discussed in the Introduction,these subperiods roughly correspond to the unstable and stableeras ofrecent macroeconomichistory. his characterization, whilesimplistic, is clearly reflected n the data. Table I reports thestandard deviation of inflation levels and HP-detrended) andoutput CBO gap and HP-detrended), for he two subperiods. Thereduction n volatility ppears substantial for each variable. Notsurprisingly, he decline is more dramatic when we begin thesecond subperiod n 82:4, after Volcker disinflation, s the bottomrow of he table indicates.

A. Baseline EstimatesTable II reports GMM estimates of the interest rate rule

parameters 7r*, A,y, and p for ach sample period, using the CBOoutput gap and GDP deflator nflation our baseline variables).The target horizon s assumed to be one-quarter for both nflationand the output gap (i.e., k = q = 1). Standard errors are reportedin parentheses. The right-most olumn reports he p-value associ-ated with a test of the model's overidentifying estrictions Han-

17. In closely related work Orphanides [19971estimates a reaction functionusing more direct measures of the Fed's perception of both the output gap andinflation, ased on real time data. His results, by and large, confirm he results weobtain.


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TABLE IIBASELINEESTIMATES

rr* P p

Pre-Volcker 4.24 0.83 0.27 0.68 0.834(1.09) (0.07) (0.08) (0.05)

Volcker-Greenspan 3.58 2.15 0.93 0.79 0.316(0.50) (0.40) (0.42) (0.04)

Standard errors re reported n parentheses. The set of nstruments ncludes four ags of nflation: utputgap, the federal funds rate, the short-long pread, and commodity rice nflation.

sen's J-test). The estimates are based on a specification of theinterest rate rule with two lags of the interest rate (n = 2), whichseemed to be sufficient o eliminate any serial correlation n theerror erm. Four lags ofthe instruments were used.

A number of nteresting esults stand out. Note first hat themodel is not rejected at conventional significance evels for ny ofthe specifications or sample periods. The estimates of 1 and y,further, enerally have the expected sign and are significant nmost cases. These estimates also point to substantial differencesin the policy reaction function cross periods. Most importantly,the estimate of 1, the coefficient ssociated with expected infla-tion, s significantly elow unity for the pre-Volcker eriod 0.83,with s.e. = 0.07), and far greater than one for the Volcker-Greenspan period 2.15, with s.e. = 0.40). On the other hand, theestimates of y-the coefficient measuring the sensitivity to thecyclical variable-are also significant n both periods, but onlymarginally o for he Volcker-Greenspan ra. 18

The estimates of the inflation arget, 7r*, eem quite plausiblein all cases: roughly four and a quarter percent pre-Volcker ndthree nd half percent ost-Volcker. hile he point stimates evealaslight downward trend over time, the difference s not significant.Based on this result nd the estimates f t and 1 cross subsamples, tdoes not seem to be the case that differences n monetary olicy pre-and post-1979 simply reflect differences n the target inflationrate. We shortly present some more evidence that bears on thisissue that stems from n analysis of within) subsample stability.

Finally, the estimate of the smoothing parameter p is high inall cases, suggesting considerable interest rate inertia: onlybetween 10 and 30 percent of a change in the interest rate target

18. See below for urther iscussion.


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20.0 -

17.5

15.0

12.5

10.0 )

7.5 -

0.0 L--- -rNV FF 1_f1, TT ,- ,' t--, *T-' -r-fT'Th-,-61 63 65 67 69 71 73 75 77 79

7 Actual --- Target]FIGURE I

Actual versus Target Rates:Pre-Volcker ra

is reflected n the Funds rate within the quarter of the change.Thus, our estimates confirm he conventional wisdom that theFederal Reserve smooths adjustments n the interest rate.

To illustrate how well the model characterizes the behavior ofthe Funds rate, Figures I and II present the target rate estimatesfor ach subperiod relative to the actual values of the Funds rate,using our baseline estimates. In each subperiod, the target ratecaptures the broad swings in the actual rate reasonably well.Interestingly, uring the 1987-1992 period that Taylor [1993]analyzes, our target rate tracks the actual rate about as well asdoes the simple Taylor rule.19

B. Robustness AnalysisWe next explore the robustness of our results along a number

of dimensions. We consider (1) alternative measures of inflation

19. We stress that we are comparing the actual rate with the implied targetrate, as opposed to the fitted model, which allows for artial adjustment. The fittedmodel, of ourse, would track the actual rate even more closely than does the targetrate.


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20.0

17.5-

15.0

12.5-

10.0-

7.5

5.0

0.0 - I- T T ||U*r - 7F ,XrWIWo Ur T- 7w-i79 81 83 85 87 89 91 93 95

L_-___ ctual Target 1FIGUREII

Actual versus Target Rates: Volcker-Greenspan ra

and the output gap, 2) alternative arget horizons or ach variable,(3) parameter tability ithin ubsamples, nd (4)a backward-lookingvariation of our policy reaction function. We demonstrate that ineach instance, the insights from he baseline case remain intact.

1. Alternative Measures. We first reestimate the reactionfunction sing different measures of the output gap and inflation.We consider two alternative measures of the output gap: (a) thedeviation of log)GDP from fitted uadratic function f ime; and(b) the deviation of the unemployment ate from similar timetrend, with the sign of the resulting series switched.20 inally, weconsider one alternative measure of nflation: he rate of change of

the consumer price ndex (CPI).Table III reports the estimates for the two main subperiods.The key results from he baseline case are robust to the use ofalternative output gap and inflation measures. In fact, both thesigns and magnitudes of he estimated parameters remain largelyunchanged. There is, however, one minor difference: he esti-

20. We switch the sign of the series in order to preserve the sign interpreta-tion for parameter y.


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160 QUARTERLY JOURNAL OF ECONOMICS

TABLE IIIALTERNATIVE VARIABLES

'Tr*'Y P P

Detrended outputPre-Volcker 4.17 0.75 0.29 0.67 0.801

(0.68) (0.07) (0.08) (0.05)Volcker-Greenspan 4.52 1.97 0.55 0.76 0.289

(0.58) (0.32) (0.30) (0.05)Unemployment ate

Pre-Volcker 3.80 0.84 0.60 0.63 0.635(0.87) (0.05) (0.11) (0.04)

Volcker-Greenspan 4.42 2.01 0.56 0.73 0.308(0.44) (0.28) (0.41) (0.05)CPI

Pre-Volcker 4.56 0.68 0.28 0.65 0.431(0.53) (0.06) (0.08) (0.05)


Standard errors re reported n parentheses. The set of nstruments ncludes four ags of nflation, utputgap, the federal funds rate, the short-long pread, and commodity rice nflation.

mated output gap coefficient or the Volcker-Greenspan subpe-riod, although positive, is now insignificant under the threespecifications. At the same time, there remains a striking differ-ence in the estimated slope coefficient or nflation cross subperi-ods: less than one before Volcker, reater than one under Volcker-

Greenspan, with point estimates very close to those obtained inthe baseline case.2. Alternative Horizons. In the baseline case we assume that

the Federal Reserve looks ahead one quarter for both nflation ndthe output gap. We now consider allowing for lternative-and, inour opinion, more realistic-target horizons for the same vari-ables. Table IV reports results for k = 4, q = 1)as well as (k = 4,q = 2); i.e., the Fed is assumed to have a target horizon ofone yearfor ts inflation arget and of one (or two) quarters for he output.One formal rationale is that these horizons are roughly n linewith the conventional wisdom regarding the lag with whichmonetary policy ffects ither variable (e.g., Bernanke and Mihov[1998]). In addition, these values are roughly consistent withinformal iscussions of policy tactics by Federal Reserve officials.In either case, the results are qualitatively very similar to those

reported n Table II.


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MONETARY POLICY RULES 161

TABLE IVALTERNATIVE HoRIZONS

IT* (Y P

k = 4,q = 1Pre-Volcker 3.58 0.86 0.34 0.73 0.835


(0.23) (0.31) (0.28) (0.03)k = 4,q = 2

Pre-Volcker 3.32 0.88 0.34 0.73 0.833(1.80) (0.06) (0.09) (0.04)


Standard errors re reported n parentheses. The set of nstruments ncludes four ags of nflation, utputgap, the federal funds rate, the short-long pread, and commodity rice nflation.

3. Subsample Stability. We next explore the stability of

parameters within each subsample. Among other things, thisexercise permits us to relax the assumption that the inflationtarget T* is constant within the estimation period. It is conceiv-able, for example, that there was an upward shift n the targetduring the period of rising nflation n the 1970s.

A simple and natural way to proceed is to assume that thepolicy reaction function s stable during the tenure of the FederalReserve chairman in charge at the time, but may vary acrossChairmen. If we tack the brief period of Miller (78:1-79:3) on toBurns (70:1-78:1), then each subperiod may be divided into tworegimes of roughly qual length. For the pre-1979 sample we thushave Martin 60:1-69:4) and Burns and Miller 70:1-79:2); for hepost-1979 sample Volcker 79:3-87.2) and Greenspan (87.3-96:4).

As discussed earlier, estimating the policy rule over shortsamples can generate imprecise estimates, given the limitednumber of observations. Accordingly, we adopt the followingprocedure: we first stimate the reaction function for each base-line period pre-Volcker r Volcker nd Greenspan), but allow forshift across Chairmen in each of the coefficients by means ofappropriate dummies). Second, we reestimate the rule afterconstraining ll the parameters for which the shift was found tobe insignificant n the first tage to be constant across Chairmen,while allowing for changes in the remaining parameters. The

resulting estimates are reported n Table V. We present estimates


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TABLE VSUBSAMPLE TABILITY

TY PMartin

(1,1) 5.16 0.86 0.14 0.77 0.524(1.72) (0.08) (0.16) (0.06)

(4,1) 7.15 0.92 0.06 0.72 0.719(5.55) (0.08) (0.07) (0.05)

Burns-Miller(1,1) 5.16 0.86 0.78 0.69 0.524

(1.72) (0.08) (0.18) (0.04)(4,1) 7.15 0.92 1.24 0.80 0.719

(5.55) (0.08) (0.39) (0.05)Volcker

(1,1) 3.75 2.02 -0.02 0.63 0.612(0.28) (0.23) (0.15) (0.04)

(4,1) 2.45 2.38 0.68 0.74 0.804(0.47) (0.35) (0.30) (0.04)

Greenspan(1,1) 3.75 2.02 0.99 0.63 0.612

(0.28) (0.23) (0.18) (0.04)(4,1) 2.45 2.38 0.68 0.91 0.804(0.47) (0.35) (0.30) (0.02)

Post-82(1,1) 3.43 1.58 0.14 0.91 0.416

(1.24) (0.72) (0.42) (0.03)(4,1) 3.16 3.13 0.09 0.82 0.894

(0.10) (0.33) (0.15) (0.02)

Standard errors re reported n parentheses. The set of nstruments ncludes two ags of nflation, utput

gap, the federal funds rate, the short-long pread, and commodity rice nflation, s well as the same variableswith a multiplicative ubperiod dummy.

for wo different arget horizons for nflation nd the output gap:(1,1) and (4,1).21

Consider first he pre-Volcker eriod. nterestingly, osignifi-cant difference rises across Chairmen in either the value of theinflation target ar*, r in the inflation coefficient . The pointestimates for the inflation arget (in the 5-7 percent range) aresomewhat above the baseline estimates for the full pre-Volckersample, although not significantly ince the standard errors arenow rather arge. The estimated value for he inflation oefficientis below unity nd is in line with the baseline estimates. The only

21. Since we also dummy all the instruments, we only use only two instru-ment lags in our subsample stability analysis, thus keeping the total number ofinstruments and the degrees of freedom) omparable to the other pecifications.


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notable departure from he baseline case is that the output gapcoefficient s insignificant nder Martin's tenure, but positive and

significant nder Burns and Miller.Our procedure detects few robust differences across theVolcker and Greenspan eras. As in the pre-Volcker era, theestimates ar* nd IB re stable across chairmen. Estimates for achparameter, further, re close to those obtained in the baselinecase. With a one-period horizon for both nflation nd the outputgap, the coefficient n the latter s close to zero (and insignificant)under Volcker, but is positive and significant under Greenspan.

On the other hand, when the target horizon for nflation s fourquarters, this difference anishes. The estimated common value ispositive and significant. n addition, the estimates under the 4,1)horizon point to a significant ncrease in the degree of smoothingof interest rate changes under Greenspan, as reflected n thesignificantly igher estimate of the parameter p.

As a final check on subsample stability, we explore the effectsof removing he first hree years of the Volcker ra from he entire

Volcker-Greenspan sample. There are at least two reasons fordoing this. First, this period was characterized by a sharp,one-shot disinflation pisode, which brought nflation down fromroughly 10 percent in 1980 to 4 percent in 1983, a level aroundwhich it stabilized. Second, over the period 1979:4-1982:4, theoperating procedures of the Federal Reserve involved targetingnonborrowed eserves as opposed to the Federal Funds rate.22 norder to make sure that neither of those features are overinfluenc-

ing our estimates for the Volcker-Greenspan period, we reesti-mate the reaction function or he period 82:4-96:4, thus exclud-ing the period of nonborrowed reserves targeting. Thecorresponding esults, for wo alternative horizons, are shown inthe bottom panel ofTable V.

Once again, the estimates of 13-the coefficient ssociatedwith expected inflation-are above unity and not statistically

22. As we noted arlier, oodfriend 1991] rgues forcefully hat he FederalReservedid indeed choose targets for nonborrowed eserves ver this periodultimately ith n objective or hepath f he nterest ate n mind. Nevertheless,Bernanke nd Mihov 1998]present vidence hat over he 1979:10-1982 eriodnonborrowed eserveswas the operating nstrument f monetary olicy, hichaccordswith onventional isdom. or the rest of the time hey howthat t isreasonable o treat heFederalFundsrate s the nstrument fmonetary olicy.na companion aper Clarida,Gali, and Gertler 9971we show that our baselinespecifications robust o allowing or he possibility hat he Fed may respond omoney rowth ndependently f ts predictive ower or nflation. hat s, we rejectthe hypothesis hat the Fed was targeting money rowth. ur results re thusconsistent ith riedman nd Kuttner 19961.


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TABLE VIBACKWARD-LOOKINGSTIMATES

IT* Y PPre-Volcker 5.95 0.86 0.39 0.68 0.590


(0.56) (0.28) (0.19) (0.05)Post-82 2.96 2.55 -0.15 0.89 0.486

(0.27) (0.56) (0.28) (0.03)

Standard errors re reported n parentheses. The set of nstruments ncludes four ags of nflation, utput

gap, the federal funds rate, the short-long pread, and commodity rice nflation.

different rom hebaseline ase (although heestimate or he 1,1)horizon s noisy).23 n the other hand, the estimates f y-thecoefficient easuring he sensitivity o the cyclical ariable-allbecome ery mall and insignificant henweuse post-82 ata (incontrast with our results for he full Volcker-Greenspan eriod).Thus, here we cannot reject the hypothesis hat the Fed haseffectively ursued "pure nflation argeting" olicy.

In sum, the key nsights btained n the baseline case arerobust o allowing for tructural hanges across Chairmen. nparticular, hestriking ifference n the reaction unction crosstime s the rise n the slope oefficient n nflation rom lightly essthan nity re-Volcker o round wo n theVolcker-Greenspanra.

4. Backward-looking estimates. We complete our robustness

analysis by reporting he estimates ordifferent ubperiods f abackward-lookinguleof he ort onsidered yTaylor 1993]. Ourversion f that rule corresponds o specification 4) with both kandq set to -1. Table VIreports he orresponding esults.Allthequalitative eatures f our baselinespecification stimates eemto hold here as well, uggesting hat they re not nherent otheforward-looking pecification f the interest ate rule. In sum,whileweview heforward-lookingpecification s more lausiblea priori, ur key nsights lso obtain from he backward-lookingspecification.C. Discussion of the Empirical Results

Overall, our estimates point to the existence f importantdifferences cross periods n the sensitivity f monetary olicy.

23. Notice that the null hypothesis of a unit inflation coefficient annot berejected n this case.


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This result, urther, ppears to be a robust feature f the data.Specifically, uring he pre-Volcker eriod, n response o fore-

castable nflationary ressures, heFederalReserve ended o etreal nterest ates decline r, t best, did not ry o raise them. notherwords,while he central ankdid raise nominal ates, t didnot do so sufficiently o raise real rates.24 his kind of responseclearly oes not tabilize nflation nder ny plausibleviewof helinkages between real rates, aggregate demand, output, andinflation.25 hus, according o our results, the persistent ndvolatilebehavior f nflation n the pre-Volcker ra may be partly

due to the monetary ule n place, ndependently f he nature fthe fundamental hocks hat mayhave mpinged n the economyduring hat period.

By way of ontrast, nder heVolcker-Greenspan egime, heFederal Reserve has substantially aised target eal rates n thewake of an anticipated ncrease n inflation on a two-for-onebasis, ccording o a rough verageof ur point stimates). otheextent hat rise n the real rate lows down he evel of conomic

activity nd relieves nflationary ressures, he interest ratepolicy n the Volcker-Greenspan ra provides natural explana-tion for he tability f nflation xperienced y heU. S. economyin recent ears.

D. Oil Shocks versus Monetary PolicyOur analysis has emphasizedhow differences n monetary

policymight ccount for differences n macroeconomic ehavior

pre- and post-1979. An alternative although not incompatible)hypothesis oints to the role of the two major oil shocks thatoccurred n 1973and n 1979. ndeed,Hamilton 1983]has arguedforcefully hat oil shocks re a central driving orce n businesscycles.This raises the question of whether he pattern of oilshocks lone could ccount or he hift nmacroeconomicolatility.

24. Our finding f a less than one-for-one djustment of the nominal rate tochanges in expected inflation s closely related to the finding f a strong negativecorrelation between the estimated expected inflation rate and the estimated realrate by Mishkin [1981] and others in the context of an exploration of the Fisherhypothesis. nterestingly, he sample period in Mishkin's paper ends in 1979:4,just one quarter after Volcker began his tenure as Fed chairman Furthermore, nsubsequent work Huizinga and Mishkin [1986] show formally hat there s a shiftin interest rate behavior before nd after October 1979.

25. As we noted at the end of Section II, if the Fed responds aggressively onlyto large deviations of nflation rom arget but not to small deviations, then t maybe possible to obtain an estimate of Rthat s less than unity, ven though the policyregime is geared toward stabilizing inflation. However, for this scenario to beplausible, we should also observe ittle variation of nflation bout target. This wasclearly not the case in the Martin-Burns-Miller ample.


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For two distinct easons, however, e believe hat differencesin monetary olicy emain ritical o the story. irst, ecent work

byDeLong 1997];Bernanke,Gertler, nd Watson 1997] BGW);Barsky nd Killian [1998] BK); and others uestions he degreeto which oil shocks can account for the events of the 1970s.Second, nd perhaps more mportant, ven f ne accepts he viewthat the oil shocks were critical o the two major recessions, twould be difficult or these shocks to generate the kind ofpersistent nflation hat arose in this era in the absence of anaccommodatingmonetary olicy. We briefly laborate on each

point.At a minimum, he notion hat the oil shocks can largelyaccount or hevolatile ehavior noutput uring he1970speriodis open to debate. While a major shock to the real price of oilpreceded oth he 1974-1975 nd 1980-1982 recessions, t s alsotrue hat ignificant ightening fmonetary olicy receded achof hese downturns see, e.g., BGW).Thebottom ine s that t s anontrivial xercise o sort out the relative mportance f the oil

shocks versus monetary olicy over this period. The originalHamilton 19831 vidence,which s based on a bivariate nalysisof oil prices and output, does not confront his identificationproblem.Multivariate nalyses, which mong ther hings llowsfor n indicator f monetary olicy, oint o a significantly eakerrole for il shocks n output dynamics see, e.g., BGWand thereferences herein). BGW, further, resent vidence o suggestthat the endogenous ightening fmonetary olicy n response o

the oil price increases accounts for much of the subsequentdownturn n output, s opposedto the direct mpact of the oilshocks hemselves.26

While here s room o debate he mportance f he oilshocksfor ealactivity ver hisperiod, hecase that these hocks loneaccountfor he sustained high nflation s completely npersua-sive. Note first hat the Hamilton vidence s silent on the linkbetween he oil shocks nd inflation. n the other hand, as De

Long [1997] emphasizes, timing considerations make the oil26. Along hese ines, oth GW nd BK present vidence o uggest hat he

tightening f monetary olicy n response o the nonoil ommodity rice hocksthat preceded he oil shocks had a much greater ole n the 1974-1975 ecessionthan did the oil shocks.BKargue further hat asy monetary olicy uring 972induced he run-up ncommodity rices. inally, he ong ag between he 1979oilshock nd the 1981-1982 recessionmakesquestionablewhether heformer ascentral o the atter, specially iven he ustained ightening fmonetary olicyover hisperiod. urther, heCarter redit ontrols ppeared o havebeen t workduring hebrief ownturn n 1980.


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12 - 0.60Inflation_OilPrIce

100.30

8

-0.00

6

-0.30

4erod Fiur II lutae hspit h iguesostr

-0.602

0qFFaTFFe-r-I entered moin Fa of tr-T-1-r

"I TIag s0.901961 1965 1969 1973 11977 1981 1985.D989 1993 1997

FIGUREIIIReal Oil Price and Inflation

shocks suspect as the leading explanation for nflation over thisperiod. Figure III illustrates this point. The figure hows three-quarter centered moving averages of the real oil price againstinflation ver the period 1960:1-1997:1. As De Long argues, theinitial build-up of inflation n the late 1960s and early 1970soccurs prior o the first il shock. Indeed, until the time of the firstoil shock in 1974, the real oil price is steadily declining, whileinflation is steadily rising. The real oil price then remainsconstant until late 1979, the period of the second major oil shock.Note again that there s a steady rise in inflation ver a three-yearperiod prior to this shock. In turn, the decline in inflation n theearly 1980s appears to ead the decline n the real oil price. Formalevidence in BGW and BK supports this descriptive evidence. Thesame multivariate analysis that suggests a modest effect f oilprices on output ndicates an even weaker effect n inflation.7

27. In a multivariate system that includes real GDP, the GDP deflator, onoilcommodity rices, the Federal Funds rate, and Hamilton's preferred ndex of oilshocks the minimum of zero and the current il price minus the largest price overthe previous four uarters), the oil shock measure accounts for t best roughly 10


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12 --Inflation

T R IteReal Rate

10

8-

6-

4-

2-J

-2 - 1 -FTr hF-rTir 1 1 TTTTFFF -i i r - --i-I rT1

1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997FIGUREV

The Real Interest Rate and Inflation

Even assuming that the oil shocks played a critical role, theultimate impact of these disturbances on output and inflationdepends very much on the feedback monetary policyrule that s inplace. It is hard to imagine, for xample, that the 1973 oil shockalone could have generated high inflation up to the time of thesecond shock in 1979, in the absence of an accommodatingmonetary policy. We demonstrate this point explicitly n the nextsection. In particular, we show in the context of a small macromodel that a supply shock can indeed induce persistent nflationunder the estimated pre-Volcker ule, but not under the estimatedVolcker-Greenspan ule. In this respect, the nature of the mone-tary policy rule must undoubtedly be a critical factor n the 1970speriod of tagflation.

Finally, Figure IV plots the behavior of the ex post realinterest rate versus inflation again using three-quarter enteredmoving averages). Note that pre-1979 the real rate steadily

percent of the variation in the GDP deflator over the period 1960:1 to 1984:4.Extending the sample to 1997:4points to an even weaker effect f the oil shock.


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declines as inflation ises. Conversely, he real rate rises sharplyin late 1979, leading the subsequent decline in inflation. Thispicture is thus consistent with our story, which emphasizes theswitch in monetary policy from accommodating to combatinginflation.28 n the next section we flesh out the implications of thedifferences n monetary policy pre- and post-Volcker, using asimple macroeconomic ramework.

IV. INTEREST RATE RULES AND ECONOMICFLUCTUATIONS

In this section we analyze some of he macroeconomic mplica-tions of the estimated monetary policy reaction functions. We doso in the context of a monetary business cycle model with stickyprices. We first present the model's equilibrium conditions, andthen analyze how the properties depend on the monetary policyrule in place. A comprehensive analysis of the quantitativeproperties of the model is beyond the scope of the present paper.Instead, we choose to focus our attention on a specific, ut (in our

opinion) ather mportant nd fascinating ssue, namely, he extent owhich the change in the systematic omponent f monetary olicyacross the pre-Volcker nd the Volcker-Greenspan ras may explainsome of he differences n the degree ofmacroeconomic nstability,as reflected n the volatility measures reported n Table I.

A. A BaselineModelOur baseline model is a version of the sticky price models

found in King and Wolman [19961,Woodford 1996, 1998], andYun [1996], among others. After og-linearization around a zeroinflation steady state, the model's equilibrium conditions aresummarized by the following quations (ignoring uninterestingconstants):(6) trr 8E1-rrt+jlftb X Yt - zt)(7) yt = E[yt+ljj1t1 - (1/U) rt - E[krt+jljftl) gt

(8) r*= ,3E-t+jIjft] yxt(9) rt = prti1 + (1 - p) rt.

28. Note that the monetary olicy ightening rior o the 1974-1975 recessionis quickly reversed, n contrast o the tightening rior o the 1980-1982 downturn.Thus, although policy tightening may have played a role in the 1974-1975recession, the overall pattern pre-1979 is consistent with accommodation ofinflation, s our formal vidence suggests.


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170 QUARTERLYJOURNALOFECONOMICS

Equation (6) describes the change in the aggregate price evelas a function f expected future nflation nd the deviation of log)

output from ts natural rate zt, where the latter s defined s thelevel of output that would obtain under fully flexible prices.29 tcan be derived from the aggregation of optimal price-settingdecisions by monopolistically competitive firms, n an environ-ment in which each firm adjusts its price with a constantprobability n any given period.30 quation (7) combines a stan-dard Euler equation for consumption with a market clearingcondition.3l t is often nterpreted s an IS schedule, determining

the current output gap as a function f the ex ante real rate andexpected future utput. n this context t can be interpreted s anexogenous demand factor. We assume that both zt and gt followstationary AR(1)process. Equations (8) and (9) specify he policyrule. They are the theoretical model's counterpart to (1) and (3).For simplicity, we restrict ourselves to the case of a one-periodhorizon (k = q = 1), and assume that all variables dated t orearlier belong to information et S1t.

Our objective here is to simulate the model under alternativepolicyrules. We use standard methods to solve for he equilibriumdynamics see, e.g., Blanchard and Kahn [19801).We then choosethe nonpolicy parameters as follows. We set the quarterly dis-count factor qual to 0.99, implying n annual risk-free ate of 4percent. We set (u,the coefficient f relative risk aversion, to beequal to 1, and X,the output elasticity of nflation, qual to 0.3,32and the autoregressive coefficient f the Zt and gt processes equalto 0.9. We choose the policy parameters, 3, y, and p, to correspondto our estimated policy-reaction functions, depending on theregime we wish to analyze.

We first xplore how the estimated rule for the pre-Volckerera opens up the possibility of self-fulfilling luctuations. We then

29. Gali and Gertler [19991 and Sbordone [1998] present some evidencesuggesting that 6) provides a good first pproximation o the dynamics of nflationin the United States.

30. Such a price-setting tructure was first ntroduced n Calvo [19831,andhas been frequently dopted in macroeconomic pplications as a simple, flexibleway of introducing price stickiness. A similar forward-looking hillips curvearises, however, under alternative price-setting assumptions (e.g., quadraticadjustment costs or deterministic ime-dependent ules with staggered pricing).

31. It assumes a CRRA period-utility ith relative risk aversion parameter ox32. There is no widespread consensus on the value of X. Values found n the

literature range from 0.05 [Taylor 19801to 1.22 [Chari, Kehoe, and McGrattan19961.Following Woodford 19961,we choose the intermediate value 0.30, which sconsistent with the empirical findings n Roberts 1995].


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compare how the estimated pre-Volcker nd Volcker-Greenspanrules affect he economy's response to fundamental disturbances.

B. Interest Rate Rules and Endogenous FluctuationsAs emphasized by Kerr and King [19961; Bernanke and

Woodford 1997]; and Clarida, Gali, and Gertler 19971, he policyfeedback rule itself may be a source of nstability f the coefficienton the inflation gap, 3, is below unity. Values of 13 n this rangelead to indeterminacy f the equilibrium, and raise the possibilityof fluctuations n output and inflation round their steady state

values that result from elf-fulfilling evisions in expectations.33The intuition is straightforward: with (3 elow unity, a rise inanticipated inflation eads to a decline in the real interest rate.The decline in the real rate then stimulates aggregate demandwhich, in turn, induces a rise in inflation. The initial rise inexpected nflation hus becomes self-confirmed.

Since the estimate of (3s consistently ess than unity for hepre-Volcker rule, self-fulfilling luctuations are possible in this

regime. What do these fluctuations ook like? Figure V displayssimulated time series of he response of he economy o a sequenceof self-fulfilling evisions in inflationary xpectations ("sunspotshocks"). We use the baseline estimates of the pre-Volcker egimeto fix the parameters of the policy rule (first row of Table II). Wedraw the "sunspot shocks"to expectations from standard normaldistribution. Our 1997 working paper provides the details.

The figure reports the cyclical behavior of output, inflation,

and the nominal interest rate. Note that persistent fluctuations noutput and inflation rise, despite the absence of ny fundamentalshocks.34 In order to get some intuition for the mechanismsunderlying these self-fulfilling luctuations, Figure VI displaysthe impulse responses of everal variables to a sunspot shock. The

33. In Clarida, Galh, and Gertler [19971it is shown that the unit thresholdvalue for P obtains exactly only when y = 0; i.e., when there is no systematicresponse to output variations. As we increase y, the lower bound for 13oes down,although the deviation from nity s quantitatively very mall (almost negligible),and independent of p. In addition, the range of 13alues for which the equilibriumis unique also has an upper bound. In other words, an "excessive" response tochanges in expected inflation may also lead to indeterminacy. This is the caseemphasized by Bernanke and Woodford 19971.

34. Generally speaking, the sunspot shocks give rise to positive comovementbetween output and inflation. To account for the negative comovement thatoccurred n the 1970s, it appears necessary also to mix in adverse supply shocks.As we make clear in the next subsection, however, supply shocks alone cannotaccount for he persistent nflation ver this era: for hem to do so, it is critical alsoto have an accommodating monetary policy.


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172 QUARTERLYJOURNALOFECONOMICS

10

8-1

2 -t /\

0 10 20 30 40 50 60 70 80 90 100inflation

4

-2

10

0 10 20 30 40 50 60 70 80 90 100nominal ate

FIGUREVSimulated Sunspot Fluctuations under Pre-Volcker Rule

sunspot realization generates, on impact, an increase in expectedinflation as well as the anticipation ofa slow return o its originallevel). Given the assumed policy rule, that forecast revision eads

to a rise in the nominal rate, but the latter falls short of the


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-0.2

-0.4 -

-0.6 -a

-0.8 -

0 2 4 6 8 10 12inflation

-0.2 -

-0.4 -

-0.6 - /

-0.8 -

-1 l0 2 4 6 8 10 12

output gap

-0.2 l l

-0.25 -

-0.3 -

-0.35 -

-0.40 2 4 6 8 10 12

nominal rate

0.5

0.4 -

0.3 -

0.2 -

0.1 -

C.0 2 4 6 8 10 12

real rate

FIGUREVIImpulseResponses oa Sunspot hock

increase in expected inflation hroughout he entire adjustmentprocess. As a result, the real rate shows a persistent decline,fueling an expansion in output and a rise in inflation, thus

validating the initial increase inexpected inflation. Over time,


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output gradually returns to trend, nd so do the nominal rate andinflation, s well as the real rate.

By way of contrast, self-fulfilling luctuations cannot ariseunder the estimated interest rate rule for he Volcker-Greenspanperiod. Because ,B s well above unity n this regime, short-termreal rates cannot adjust to accommodate unspot shifts n inflation-ary expectations, as they instead do under the estimated pre-Volcker policy. Under this type of regime, accordingly, macroeco-nomic fluctuations arise only in the presence of shocks tofundamentals. n other words, the monetary policyrule in place is

not, n itself, source of macroeconomic nstability. On the otherhand, the policy rule does affect how the economy responds tofundamental hocks. We explore this issue in the next section.

C. Near-Indeterminacy nd Fundamental ShocksAs we have ust seen, the point estimates for he inflation nd

output gap coefficients uring the pre-Volcker ra fall within theindeterminacy region of the canonical model presented above.

This is true for all specifications considered. In some cases,however, he standard errors for he estimate of B re too large torule out the possibility that the true value is unity or slightlyabove.35 n this borderline nstance the economy s ust outside theregion of ndeterminacy.

Even though sunspot fluctuations are not feasible in thiscase, however, he economy s still likely to be relatively unstableunder this kind policy regime. We illustrate this issue in the

context of our calibrated model. In particular, we compute theimplied standard deviation of nflation nd output, under alterna-tive values of B, he inflation oefficient nd conditional on a givensource of fluctuations supply Zt or demand gt .36Throughout thisexercise, we keep both My nd p constant and equal to theirestimated values for the pre-Volcker period under the baselinespecification i.e., 0.27 and 0.68, respectively).

Table VII reports the results. It shows how the standard

deviations of output, inflation, and the output gap vary in

35. In fact, t is possible to find ombinations f rule specifications ndsubperiods ithin he pre-Volcker ra for which he point stimate or 3s slightlyabove ne although ot ignificantly o). Wethank n anonymous eferee or hatobservation, hich ncouraged s to conduct he robustness nalysis ound bove.

36. A general analysis of the effectiveness nd desirability f alternativeinterest ate rules n a model losely elated o ours an be found n Rotemberg ndWoodford 1997], mong thers. We differ y focusing n the mplications f thefeedback arameter n expected nflation.


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TABLE VIIFUNDAMENTALHOCKS

Supply shocks Demand shocksa(s) U(x) a(y) a(s) a(y)

2.0 1.00 1.00 1.00 1.00 1.001.5 1.48 1.36 1.29 1.61 1.671.1 2.57 2.16 2.26 3.04 1.961.0 3.20 2.61 2.88 3.88 4.25

response to shifts n the feedback parameter P3.The first threecolumns display the results conditional on the supply shock z,being the fundamental driving force. The last three columnsrepeat the exercise, this time with the demand shock. For ease ofexposition, we normalize to unity the standard deviations corre-sponding to the calibration with P3 2.0.

The results make it clear that the cyclical response of theeconomy ofundamental shocks is quite sensitive to P3, speciallyover the estimated range of values across the pre-Volcker ndVolcker-Greenspan periods. As [P rises from one to two, thevolatility of both output and inflation declines by more than half.This occurs for both the supply shock and the demand shock. Thereduction n volatility hat the Volcker-Greenspan ule achieves isthus quite substantial.

The intuition s straightforward: value of [P qual to or ustabove unity suggests that the central bank comes close to fullyaccommodating nflationary ressures, by raising nominal ratesto keep real rates roughly constant. The absence of a strongstabilizing adjustment of the real rate suggests, in turn, thatfundamental hocks may generate considerable volatility n infla-tion and the output gap, at least relative to the Volcker-Greenspantype policy,where the central bank adjusts real rates in a stronglycountercyclical manner.

We next illustrate explicitly how the ability of supply shocksto generate stagflation and hence account for he 1970s) dependson the nature of the monetary policy rule. Figure VII reports theresponse of inflation and output to a negative supply shock(negative shock to zt) for everal values of the feedback coefficienton expected inflation, 3, hat range from 1.01 to 2.00. The keypoint is that the supply shock produces a persistent effect ninflation only for values of [3 ear unity. As [3 ises to 2.00, the


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In f a t o n

Co

0 -_ beta=1 .01\ - - beta = 1.5

o~~~~~~~~~~... beta. 2. .= =CD

CD

0 0 5 10 15 20 25 30 35 40 45 50quarters after the shock

Output

CD

CD

0I A_/ beto=2.2CD

CD? 5 10 15 20 25 30 35 40 45 50quarters after the shock

FIGUREVIIImpulseResponses oa Supply hock


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supply shock has only a small transitory mpact on inflation. nsum, how large and persistent s the response of nflation o the

supply shocks

quite sensitive to the feedback rule. The accommo-dating pre-Volcker olicy, t appears, can account for persistentresponse of nflation. The same does not appear to be true for heVolcker-Greenspan olicy, s is consistent with our hypothesis.

Finally, we note that the results we obtain in the context ofour simple New Keynesian model are largely robust to using amuch broader set of macroeconomic models. Two model featuresare critical, but they are features that are commonplace in most

conventional macroeconomic rameworks. irst, there must be aninverse relationship between output and the ex ante real rate (i.e.,an IS-type relationship). Second, there must be a positive short-run link between output and inflation i.e., a Phillips curve).Given these features, a monetary policy rule that accommodatesinflationary pressures is, in general, more likely to bring abouthigher unconditional volatility of inflation and the output gapthan otherwise.37

V. SUMMARYANDCONCLUDING REMARKS

In this paper we have provided an empirical characterizationof the systematic component of United States monetary policy nthe postwar era. In order to do so, we have estimated a simpleforward-looking olicy reaction function.

Our estimates point to a significant difference n the way

monetary policy was conducted pre- and post-late 1979. In thepre-Volcker ears the Fed typically raised nominal rates by lessthan any increase in expected inflation, hus letting real short-term rates decline as anticipated inflation rose. On the otherhand, during the Volcker-Greenspan ra the Fed raised real aswell as nominal short-term nterest rates in response to higherexpected nflation. Thus, our results lend quantitative support tothe view that the anti-inflationary tance of the Fed has been

stronger n the past two decades.Finally, we have argued that the pre-Volcker ule may havecontained the seeds of macroeconomic nstability that seemed to

37. One difference hat arises between the New Keynesian model and asimple backward-looking Keynesian model (see, e.g., Svensson [19961) s that, inthe latter, elf-fulfilling luctuations re not possible since beliefs about the futuredo not affect ehavior. n this instance, a feedback rule with ,B 1 simply eads toexplosive behavior, ultimately necessitating a shift n the policy rule.


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characterize the late sixties and seventies. In particular, n thecontext f calibrated ticky rice model, he pre-Volcker ule eavesopen the possibility fbursts of nflation nd output hat result fromself-fulfilling hanges in expectations. At best, the pre-Volckerrule does a considerably worse job than the Volcker-Greenspanpolicyof nsulating the economy from undamental hocks.

One important uestion our paper raises but does not answeris the following: why is it that during the pre-1979 period theFederal Reserve followed rule that was clearly nferior? notherway to look at the issue is to ask why t is that the Fed maintained

persistently ow short-term eal rates in the face of high or risinginflation. One possibility, mphasized by De Long [1997], is thatthe Fed thought the natural rate of unemployment t this timewas much lower than it really was (or equivalently, that theoutput gap was much smaller). There is considerable anecdotalevidence to support this interpretation, lthough it is not clearwhy the Fed should have held this view over such a long period oftime. Orphanides [1997] emphasizes that preliminary stimates

of potential output are often quite different han revised esti-mates. One possibility, hus, is that during the 1970s the FederalReserve had consistently verly optimistic preliminary stimatesofpotential output. Again, one has to explain why the misforecastwere so persistently ne-sided.

Another somewhat related possibility s that, at that time,neither he Fed nor heeconomics rofession nderstood he dynamicsof nflation ery well.8 Indeed, t was not until the mid-to-late 970s

that intermediate extbooks began emphasizing the absence of along-run rade-off etween inflation nd output. The ideas thatexpectationsmay matter n generating nflation nd that credibility simportant n policy-making ere simply not well established duringthat era. What all this suggests s that in understanding istoricaleconomicbehavior, t is important o take into account the state ofpolicy-maker's nowledge of the economy and how it may haveevolved over time. Analyzing policy-making rom his perspective,

we think, would be a highly useful undertaking.39COLUMBIAUNIVERSITYNEWYORK UNIVERSITYANDUNIVERSITATPOMPEUFABRANEWYORK UNIVERSITY

38. See, e.g., Croushore [19961for evidence of systematic bias in inflationforecasts during that period.

39. Recent work n this direction an be found n Sargent [19981.


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