Monetary policy withuncertain estimates ofpotential output

Kenneth Kuttner

After years of neglect, poten-tial output has drawn renewedattention as an input to mone-tary policy, appearing in abroad range of recent Federal

Reserve system and academic research) Atone level, it is the raison d' etre of an activistmonetary policy. If potential output measuresthe economy's capacity to produce goods andservices without adding to inflationary pres-sures, the goal of a stabilization policy shouldbe to keep the economy operating as close topotential as possible.

While its significance is widely acknowl-edged, there is little agreement on the bestmeasure of potential output. Until it was dis-continued ten years ago, the series maintainedby the Council of Economic Advisors (CEA)and published in the Economic Report of thePresident was probably the most prominent;since then, a number of competing measureshave appeared. The first section of this articlediscusses in greater detail what it is that poten-tial output is supposed to measure, and reviewssome of the estimates in current use.

The next section discusses a new techniquefor estimating potential output. This methoddiffers from existing measures by explicitlymodelling potential real GNP as an unobserv-able variable, using data on output growth andinflation to infer its level. It also offers twosignificant advantages over existing measures.First, because it is defined in terms of inflation,it is not vulnerable to the structural changes inthe labor market that have distorted measures

based on the unemployment rate. Second, itprovides a way to calculate the uncertaintyassociated with the estimate, which is particu-larly important to policymakers charged withkeeping output at or near potential. The finalsection of the article highlights the practicalimplications of this uncertainty and examinesits role during the rapid expansion of 1988-89.

What is potential output?

In broadest terms, potential output is ameasure of the economy's overall productivecapacity, or its equilibrium level of output. Inother words, potential output is supposed tosummarize the state of the supply side of theeconomy, whose main determinants are labor,capital, and productivity. Fluctuations in theseand other supply side factors—oil prices, forexample—all contribute to variation in thegrowth of potential output through time.

In contrast to supply shocks, which affectpotential as well as actual output, demandshocks alter the economy's status relative topotential. Examples include monetary andfiscal policy, as well as exogenous changes inconsumption, investment, or demand for U.S.exports. Insufficient aggregate demand mayresult in a level of output at which factors ofproduction are less than fully employed; simi-larly, excess aggregate demand may temporari-ly lift the economy above its equilibrium level

Kenneth Kuttner is a senior economist at the Feder-al Reserve Bank of Chicago. The author thanksSteve Strongin and Mark Watson for their com-ments.

2 F::( 1I; PERSPECTIVES

of output. This taxonomy of shocks in terms ofsupply or demand suggests defining potentialoutput as full-employment production, corre-sponding to the real GNP the economy wouldproduce in the absence of demand shocks. Inother words, with the economy operating nearpotential, labor and capital will be utilizedas fully as possible, given any supply sideconstraints.'

An alternative but complementary defini-tion of potential output exploits the link be-tween output and inflation embodied in theaggregate supply curve. The aggregate supplyfunction describes a positive relationship be-tween levels of real output and the inflationrate, much as the well known Phillips Curvedescribes the negative correlation between theunemployment rate and inflation. However, ithas long been recognized that this output-infla-tion tradeoff works only in the short run; that is,in the long run, the aggregate supply curve isvertical. Therefore, a stable inflation rate—onethat is neither increasing nor decreasing—ispossible only with output equal to potential.

This connection between potential outputand a stable inflation rate inspired ArthurOkun's (1970) definition, in which potentialoutput is the "maximum production withoutinflationary pressure, ... or more precisely ... thepoint of balance between more output andgreater stability."' So long as there is a stablerelationship between employment (or capacityutilization) and inflation, this noninflationarycharacterization of potential output is compati-ble with its definition as full-employment out-put. Conceptually, defining potential output interms of stable inflation simply shifts the focusfrom its underlying determinants to its infla-tionary implications. At a practical level, thelink between potential output and stable infla-tion provides the foundation for the potentialoutput measure discussed in this article.

Although potential output is sometimesassociated with a simple trend line fitted to realGNP, nothing in either of these alternativedefinitions implies that the growth rate of po-tential output remains constant over time. Thesource of this perception is that throughoutmuch of the 1960s, a log-linear trend was wide-ly used as a proxy for potential output. Asdescribed below, events of the 1970s demon-strated that the straight-line method was satis-factory only in the absence of any significant

supply shocks. Since then, much of the re-search on potential output has focused on cap-turing the time-variation induced by aggregatesupply shifts.

An aside on classical versus traditionalperspectives on potential output

Not all economists agree that it makessense to describe business cycles in terms ofdepartures from potential output, a disagree-ment that surfaces in well known recent inter-mediate level macroeconomics textbooks. Adiscussion of potential GNP appears prominent-ly in the introduction to Dornbusch and Fisch-er's (1990) book, whose view is consistent withthe description of potential output sketchedabove. By contrast, the subject receives nomention at all in Barro's (1990) text.

Barro's omission of any discussion ofpotential GNP reflects the New Classical ap-proach to business cycles, as embodied in theReal Business Cycle (RBC) theory pioneeredby Kydland and Prescott (1982). 4 RBC theoryasserts that economic fluctuations are the out-come of competitive equilibria in which wagesand prices adjust rapidly to clear all markets.According to this view, supply shocks (usuallylabelled technology shocks) are the sole sourceof fluctuations in real economic variables, suchas output and employment. Demand shockstypically affect only nominal variables—theaggregate price level, for instance—withoutaffecting relative prices, real output, or employ-ment.' According to the RBC view, therefore,it makes no sense to distinguish between actualand full-employment output. With output de-termined entirely by the supply side of theeconomy, potential output is simply equal toactual output.

The policy implications of RBC theory arefar reaching. In these models, discretionarymonetary policy can play no useful role instabilizing the economy, as the only effect ofmonetary policy is on the price level. Further-more, because the economy's fluctuations re-sult from competitive equilibria, they are eco-nomically efficient.° Therefore, even in thosemodels in which monetary policy can affectreal variables, doing so will typically reduceoverall welfare.

Clearly, a pure RBC framework has noplace either for estimating potential output, orfor using it as a guide to macroeconomic poli-cy. Instead, viewing business cycles as depar-

FEDERAL RESERVE RANK OF CHICAGO

tures from potential output is much more con-sistent with the so-called traditional approach tomacroeconomic fluctuations sketched earlier.'Although the methodological differences be-tween the traditional and the classical views aredeep, RBC models have had a major impact onresearch that follows the traditional approachprimarily by demonstrating the importance ofsupply shocks as a source of business cyclefluctuations. The new measure of potentialoutput discussed in this article takes this propo-sition seriously, and seeks to quantify the rela-tive importance of supply and demand factors.

Existing measures of potential output

Most existing measures of potential GNPhave relied on one or more of the followingtechniques: segmented trends, supply-side

analysis, or Okun's law. Of the three, the seg-mented trend technique is perhaps the simplest.Typically, this involves drawing straight linesegments through a plot of (log) real GNP.Giving each line segment its own slope is asimple way to capture local variations in thetrend growth rate.

A key distinction among segmented trendmeasures lies in the choice of the segments'endpoints. One well known example is themid-expansion GNP series published by theBureau of Economic Analysis (BEA), 8 plottedin the top panel of Figure 1. (The series isplotted on a logarithmic scale.) As the nameimplies, the segments' endpoints are the mid-points of business cycle expansions, whosedates are determined ex post by the NationalBureau of Economic Research. The lower

FIGURE 1

Mid-expansion GNPlogarithms of 1982 dollars8.4 —

Trend

8.0

7.6

7.2 I I I I I I I I I I I

1961 '64

percent, annual rates

'67 '70 '73 '76 '79 '82 '85 '88 '91

4.0 —

Growth rate

3.6

3.2

2.8

2.4

2.0 I I I I I I i I I i I I I I I I I i i i i i i

1961 '64 '67 '70 '73 '76 '79 '82 '85 '88 '91SOURCE: Bureau of Economic Analysis, Survey of Current Business.

4

ECONOMIC PERSPECTIVES

panel of Figure 1 plots the annualized growthrate of mid-expansion GNP, whose stairstepappearance is due to the segmented trend con-struction of the series.

The supply-side analysis that was the basisfor the discontinued CEA estimate is conceptu-ally much more sophisticated than the mid-expansion series. 9 This method gauges poten-tial output by way of an aggregate productionfunction relating factor inputs—labor and capi-tal—to real output. Potential output is thendetermined by substituting the full-employmentvalues of labor and capital into the productionfunction. The main drawback to this techniqueis its formidable data requirements. Becausequarterly capital stock figures are so unreliable,implementations of this method usually focuson labor inputs. Even so, it requires data oncyclically adjusted employment, hours, laborforce participation rates, and productivity toconstruct its estimate of full-employment out-put. The Boschen and Mills (1990) series is arelated measure which attempts to capture thesupply-side effects of oil price shocks andchanges in individuals' marginal tax rates.

The third commonly used technique isbased on Okun's celebrated law, which uses theunemployment rate as a proxy for the gap be-tween potential and actual output. With Udenoting the unemployment rate, and lettingGNP* and U* represent potential real GNP andthe natural rate of unemployment respectively,Okun's law,

(1) GNP* = GNP • [1 + 0.03 (U – U*)],

states that the percentage deviation of GNPfrom potential is proportional to the gap be-tween unemployment and the natural rate. Thecoefficient of 0.03 means that a 1 percent un-employment gap corresponds to a 3 percent gapbetween real GNP and potential. If the naturalrate is known (Okun assumed it was 4 percent)this equation easily delivers an estimate ofpotential GNP. During the economically quies-cent 1950s and 1960s, a log-linear trend pro-duced estimates of potential output nearly iden-tical to those generated by Okun's law with U*equal to a constant 4 percent. In fact, becauseit produced a smoother series, Okun recom-mended using the trend method as an alterna-tive to the above equation.

The events of the 1970s—the oil shock, the1974-75 recession, and the productivity slow-

down—contributed to the breakdown of a vari-ety of potential output measures. The disinte-gration of measures based on Okun's law with afixed natural rate of unemployment was espe-cially conspicuous. With unemployment rateswell above 4 percent, these measures indicatedthat output was far below potential, yet inflationcontinued to rise. The usual measures of poten-tial output no longer seemed to correspond tostable inflation leading some, notably Gordon(1975), to use alternative time-varying measuresto explain the behavior of inflation.

The deterioration of Okun's law can betraced to growth in the ranks of the structurallyunemployed: workers who, because of structur-al change in the economy, had to retrain orrelocate in order to find new employment. Inresponse to the rise in structural unemployment,economists revised their conception of full em-ployment, and the language used to describe it.The awkward phrase "nonaccelerating inflationrate of unemployment" replaced "natural rate,"avoiding the implication that stable inflationwas necessarily associated with a low unem-ployment rate. Likewise, the BEA switched towhat it called a "high-employment benchmark"rate of unemployment, equal to 6 percent.

This experience exposed the Achilles' heelof Okun's law as a foundation for potentialoutput: the unobservability of the time-varyingnatural rate of unemployment. If U* is neitherfixed nor observable, Okun's law merely de-scribes a relationship between two unobserv-ables, and cannot be used by itself to computepotential GNP; only in conjunction with someindependent measure of the natural rate ofunemployment will it yield an estimate of po-tential output.

The potential GNP series proposed by Clark(1983) and Braun (1990) are two recent exam-ples of measures based on independent estimatesof the natural rate of unemployment. Braun'sseries is actually a hybrid measure, combiningan Okun's law equation with a segmented trendspecification for potential output. Like othersegmented trend measures, it also relies on someprior determination of the appropriate dates fortrend breakpoints.'"

Two-sided versus one-sided estimates

One essential distinction between thesealternative techniques is the degree to whichthey rely on ex post information, that is, whetherthey are constructed contemporaneously or

FEDERAL RESERVE RANK OF CHICAGO 5

retrospectively. An estimate of a given quar-ter's level of potential GNP is one-sided if itutilizes only data available in that quarter. Atwo-sided estimate, on the other hand, incorpo-rates data that become available later. Forinstance, an estimate of 1990:4 potential thatused 1991:1 inflation would be two-sided; onethat relied only on data through 1990:4 wouldbe one-sided. In other words, one-sided esti-

mates use only current and lagged data, whiletwo-sided estimates use both lags and leads.

The BEA's mid-expansion trend GNP is agood example of an explicitly two-sided mea-sure. Because business cycle peaks are datedwell after the fact, the expansion's midpointcan be determined only retrospectively—obvi-ously too late to be of any use for a policydesigned to avert a recession. To produce a

An econometric model of potential output

The potential output measure proposed in Kuttner(1991) builds on a statistical technique known as adynamic factor or multiple-indicator model. The basicidea behind these models is to describe the behavior ofthe observable data in terms of some underlying, unob-served variable. In this application, potential output isthe key latent variable; inflation and real growth dataare used as indicators of the unobserved level of poten-tial output.

Let x, represent the natural logarithm of real GNPat time t, and let e,a denote a period t shock to real GNPthat does not affect potential output, denoted by x*,.The Greek letter A is the first-difference operator, sothat Ax, = x, — x The first component of the multiple-indicator model is the error-correction equation forreal output,

(1) Ax,= a0 + a i (x,* — x,) + a2 x,_ i + a 3 x,_ 2 + + a4e,a

where ao through a 4 are coefficients to be estimated. Ifa i is positive, x,* in excess of x, implies higher thanaverage future real growth rates (subject to the distribut-ed lag captured by the a 2Ax,_, and a 3Ax,_2 terms, and thecurrent and lagged shocks e,̀'+ a4e,d i ). In this way, outputtends towards potential over time, unless perturbed bye4 shocks.

The model's second building block is the inflationequation, based on a simple dynamic aggregate supplyrelationship reflecting the link between potential outputand stable inflation. The change in the inflation rate isproportional to the gap between actual and potentialoutput; GNP in excess of potential implies rising infla-tion, while falling inflation is a symptom of GNP belowpotential. The growth rate of M2 is allowed to exert anindependent effect on the inflation rate. Using it, torepresent the current inflation rate, and letting m,_, and

represent the lagged logarithms of M2 and the pricelevel, the following equation embodies this output-inflation relationship:

(2) Aic, = b i (x.„ — x,'1 1 ) + b2(x,_2 — +b 3A(m,_,— — p,_,)+

which includes a moving-average error term, e,"+ 134e,' 1 .The — x,_, — p, I term, recognizable as the laggedlogarithm of the inverse of M2 velocity, captures thedirect effect of money stock changes on the price level.

Having described the link between the unobservedlevel of potential output and observed realizations ofreal output growth and inflation, it remains only tospecify how potential output, x; evolves over time. Themultiple indicator model replaces the traditional seg-mented trend with a more flexible stochastic trendspecification discussed in Stock and Watson (1988).This specification says that over the long run, outputwill grow at some average rate, labelled g. However,shocks to potential output, can cause potential outputgrowth to deviate from its mean. Moreover, theseshocks are persistent with respect to the level of poten-tial output: once perturbed by an e,' shock, x*will showno tendency to return to its trendline. Plotting it along-side a deterministic trend with slope equal to g, thestochastic trend will appear to wander.

The mathematical expression of the stochastictrend specificaion is a random walk with drift:

(3) x,*= g + ery.

The intercept g is the "drift" term in the random walk,corresponding to the long run growth rate of output.The unit coefficient on lagged .x,* makes (log) potentialoutput a random walk. By constraining the coefficientc/o in Equation 1 to equal g(1 — a 2 — a 3 ), real output isforced to grow at the same rate as potential on average.

The practical advantage of the stochastic trendassumption is to allow smooth variations in the growthrate of potential output unlike the segmented trend withits discrete kinks. While some research has endowed therandom walk specification with a deeper economicinterpretation, it was chosen for this application as aconvenient way to pick up low-frequency time variationin the underlying trend.

One attractive interpretation of the overall modelis in terms of supply and demand shocks, along the linessketched earlier. The notation used here is consistentwith this interpretation: the e,' in Equation 3 representsupply shocks, affecting the economy's underlyingcapacity to produce goods and services without addi-tional inflationary pressure. Similarly, the shocks inEquation 1 are disturbances to aggregate demand,which can deflect the economy's convergence to poten-tial output.

Two specific features of this interpretation deservespecial note. First, the supply shocks are assumed to

6 ECONOMIC PERSPECTINES

TABLE 1

Estimates of the parameters of thepotential output model

Output growth equation (1) Standard deviation of e°= 0.943

Axt = 0.36 + xt) + 0.45 x, i + 0.20 xr_2 + - 0.17(0.05) (0.30) (0.15) (0.31)

Inflation equation (2) Standard deviation of ex = 0.254

An t = 0.12 (x;_ 1 — xt_ 1 )— 0.10 (x; 2 - Xt2 ) 0.06A(In t_ i - - pt_ i ) + — 0.70e; 1

(0.03) (0.03) (0.03) (0.23)

Potential output equation (3) Standard deviation of es = 0.702

= 0.75 + + est

(0.07)

NOTES: The sample is 1960:1 through 1991:3.

The data are expressed as quarterly percent growth rates.

The numbers in parentheses are estimated standard errors.

contemporaneous estimate would involve depart-ing from the mid-expansion definition in someway, such as extrapolating the local trend fromthe previous reference cycle. Most segmentedtrend estimates share this two-sided property, asit usually takes several years of data to discern achange in the economy's underlying growth rate.

Other techniques can yield either one- ortwo-sided estimates. As described above, the

simple procedure using Okun's law with aconstant natural rate of unemployment is one-sided. By contrast, the technique described inClark (1983) is two-sided, utilizing leads aswell as lags of the gap between unemploymentand a time-varying natural rate.

Frequently, the benchmark natural unem-ployment rate used as an input to Okun's law isitself two-sided. Estimates of potential output

have permanent effects on theeconomy's productive capac-ity, while the demand shocks'impact is purely transitory.This distinction reflects theimplications of the naturalrate hypothesis introducedearlier, in which changes inaggregate demand have nolasting effects on real vari-ables. Second, the combina-tion of the stochastic trendand error-correction specifi-cations of Equations 1 and 3allows supply shocks togenerate business cyclebehavior. In other words,demand shocks are not thesole cause of output gaps;some fluctuations of outputaround potential are attribut-able to the dynamics ofadjusting to a new equilibri-um level of output.

Estimating the model

If data on x:existed, one could easily estimateEquations 1 and 2 with the familiar linear regressiontechnique. What complicates matters here is the factthat the key right-hand-side variable, (x:— x,), is unob-servable. One technique that makes it possible toestimate models with unobserved independent variablesis the recursive Kalman filter algorithm.' Essentially,this algorithm uses the law of motion for potentialoutput in Equation 3 to compute its optimal guess of theunobserved In the next step, it uses that guess inEquations 1 and 2 to generate one-quarter-ahead pre-dictions for Art and Ax. The equations' fit is gauged bycomparing these predictions to the actual data. Amaximum-likelihood routine is then used to determinethe coefficients that yield the best predictions. A by-product of this process is an estimate of the unobservedx* series, based on the observable output growth andinflation data and the best-fit coefficients from Equa-tions 1 - 3.

Table 1 displays estimates of Equations 1-3, fittedto quarterly data from 1960:1 through 1991:3. In

Equation 1, the coefficient of 0.11 on (x:— x,) meansthat in the absence of any shocks, output will graduallyconverge to potential at a rate of 11 percent per quarter.However, this adjustment is interrupted by demandshocks with a standard deviation of 0.95 percent perquarter, or almost four percent in annualized terms. InEquation 2, the statistically significant coefficients onthe two lags of the output gap are consistent with astrong relationship between aggregate demand andinflation. Similarly, M2 growth (less nominal outputgrowth), appears as a significant additional determinantof inflation. The intercept in Equation 3, which repre-sents the mean quarterly growth rate of potential out-put, is consistent with an average annual growth rate ofroughly 3 percent. The magnitude of the persistentshock to potential output, as measured by its standarddeviation, is similar, endowing the potential outputseries with a relatively large amount of time variation.

'The Kalman filter technique is discussed in many time-serieseconometrics texts, including Harvey (1981).

FEDERAL RESERVE BANK OF CHICAGO 7

based on such measures should therefore beclassified as two-sided, even when they useonly current and lagged values of the unem-ployment gap. Rissman's (1986) time-varyingestimate of structural unemployment is a goodexample, as it uses leads and lags of employ-ment growth dispersion. Similarly, the com-mon supply-side measures could fall into eitherof these two categories, depending on whetherthey used one- or two-sided methods to cycli-cally adjust the factor input data.

One area where the two- versus one-sideddistinction is key is in the formulation of apolicy feedback rule. Some economists, Taylor(1985) for example, have proposed versions ofmonetary policy rules in which the FederalReserve would target the gap between real GNPand trend, or potential GNP. To achieve anappropriate balance between inflation andoutput goals, the output gap target would besubject to feedback: adjusted downwards whenthe rate of inflation exceeded its target, andvice versa.

Any systematic implementation of such arule would have to operate in real time; that is,the target would have to be adjusted on thebasis of currently available information, with-out the benefit of subsequently available data.In other words, feedback rules could rely onlyon one-sided estimates of potential output,precluding the use of some of the measuresdiscussed above. This consideration is espe-cially relevant to segmented trend measureslike mid-expansion GNP. As noted earlier,extrapolating these series to provide currentperiod estimates would usually fail to trackcontemporaneously changes in the growth ofpotential output.

A new, inflation-based measure ofpotential output

The alternative measure of potential realGNP described in Kuttner (1991) (see Box)uses a technique that differs significantly fromthose described above, relating potential outputdirectly to the observed behavior of inflation.This method uses real GNP growth and infla-tion as gauges of the level of potential output,which itself is unobserved. Unlike existingmeasures, this technique explicitly recognizesthe uncertainty involved in extracting a mea-sure of potential output from the available data.An additional advantage of this technique is itsability to produce either one- or two-sided

estimates; comparing them brings the distinc-tion into sharp focus. An examination of theexpansionary 1988-89 period illustrates thepractical importance of this distinction.

This measure defines potential output interms of two key attributes. First, it corre-sponds to a sustainable level of production; thatis, a level consistent with stable future realgrowth rates. One way to capture this propertyis through an error correction equation for realand potential GNP. This equation describes theeconomy's real growth rate as a function of thediscrepancy (the "error") between actual andpotential GNP, and demand shocks. If outputequals potential, the economy will grow at thesame rate as potential, in the absence of de-mand shocks. When output exceeds potential,the economy tends to grow more slowly thanpotential, restoring equilibrium over time.Similarly, when the economy's real GNP isbelow potential, output tends to grow morerapidly. In this equation, demand shocks repre-sent those factors that perturb the economy'sadjustment process.

The second main feature of this measure isits connection to the inflation rate. As in theusual aggregate supply relation described earli-er, potential output is defined as that level ofoutput at which inflation shows no tendency toincrease or decrease, holding other factors(money growth, for example) constant. Whenoutput exceeds potential, the inflation rate tendsto rise, reflecting the upward slope of the aggre-gate supply curve. Because they both dependon the gap between actual output and unob-served potential output, real growth and infla-tion data can be used to estimate the size of thegap between the two.

Figure 2 plots the logarithm of potentialGNP estimated using this technique, along witha linear trend and the logarithm of observedreal GNP. Comparing potential output with thetrend highlights the considerable time variationin potential output growth. From a relativelyrapid growth rate in the early 1960s, potentialoutput slows late in the decade and into the1970s, reflecting the well known productivityslowdown of that period. Potential outputgrowth increased once again in the early 1980sas oil prices stabilized, and the economy recov-ered from the 1981-82 recession.

While this method offers a convenient andappealing way to estimate potential output, it,like the traditional measures discussed earlier,

8

ECONOMIC PERSPECTIVES

FIGURE 2

Actual GNP, potential GNP, and linear trend

logarithms of 1982 dollars8.4 —

8.0

7.6

7.2

is an estimate of a somewhat imprecise entity.As such, it is important to emphasize that Fig-ure 2 plots only the point estimate of potentialoutput. Unlike the traditional measures, how-ever, this new method models the error associ-ated with estimating potential output, and pro-vides an estimate of the magnitude of that error.The following section explores the consequen-ces of this uncertainty for policy based on anuncertain estimate of potential output.

Uncertainty and macroeconomic policy

One of the most important practical prob-lems facing policymakers is the uncertaintyassociated with contemporaneous measures ofmacroeconomic performance. Data revisionsare evidence of the uncertainty that pervadeseven the most basic macroeconomic data. Theadvance estimate of GNP, for example, usuallydiffers significantly from the preliminary andfinal estimates, released one and two monthslater. Even the final estimates are revised annu-ally, as well as every five years during thebenchmark revision process. Money stockstatistics undergo similar revisions."

How should policy respond when econom-ic signals are uncertain? To illustrate this prob-lem with a specific example, consider the ef-fects of data uncertainty. Suppose the FederalReserve wishes to maintain nominal GNPgrowth at an annual rate of 7 percent. Supposealso that the advance national income dataindicate nominal GNP growth of 8 percent. In

light of the likelihood of a subsequent down-ward revision to the data, should policy actnow to reduce the growth rate of nominalGNP? Clearly, the proper reaction dependssignificantly on the amount of uncertainty: theless certain the estimate, the smaller the appro-priate policy response.

In this example, the Federal Reserve'starget is known with certainty, but the true stateof the economy is not. The problem is com-pounded when the policy target itself is uncer-tain, as in the case of a potential output target.

One- versus two-sided uncertainty inpotential output

One useful feature of the multiple-indica-tor model is that it can yield either one- or two-sided estimates of unobserved potential output.As described in the accompanying Box, theKalman filter technique delivers the optimalestimate of potential output given the dataavailable at the time. A complimentary algo-rithm—the Kalman smoother—uses datathrough the end of the sample to extract anestimate of potential output given both past andfuture data. At the same time, both the filterand the smoother also produce estimates of thestatistical uncertainty associated with the esti-mate, referred to as filter uncertainty. An addi-tional source of variance, the parameter uncer-tainty, comes from the estimation of the mod-el's parameters.

FEDERAL RESERVE BANK OF CHICAGO 9

Filter variance 0.89 1.84

Parameter variance 0.99 0.81

Overall standard error 1.36% 1.62%

Figure 3 displays the size of this uncertaintyby plotting the two-sided estimate of potentialoutput along with the 5th and 95th percentiles ofits distribution, which represent the 90 percentconfidence bounds, calculated using the tech-nique proposed by Hamilton (1986). As report-ed on the last line of Table 1, the average two-sided standard error is approximately 1.4 percent(relative to the level of potential output), corre-sponding to a 90 percent confidence bound ofover 2 percent. The contributions of the filterand parameter variance to the two-sided standarderror, shown on the first two lines of the Table,show how the process of signal extraction andthe imprecision of the parameter estimates con-tribute comparably to the uncertainty of thepotential output estimate.

However, because the two-sided estimatesrely on data unavailable to policymakers in realtime, they understate the amount of uncertaintypresent in those estimates. A better measure ofthis uncertainty is that associated with the one-sided estimates. Comparing the two columns ofTable 1 shows that with an average standarderror of 1.62 percent, the one-sided estimates areless precise than the analogous two-sided series.While the two-sided estimates are more preciseon average than the one-sided estimates, this isnot true for the last quarter of the sample. Here,in the absence of data on future output growthand inflation, the two- and one-sided estimates,and their standard errors, are identical.

Why hindsight reduces uncertainty

Subsequent data improves the estimates'precision for two reasons. First, there is thephysical lag. Certain indicators—notably infla-tion—react to GNP changes with a lag. Theinflation equation of the potential output modelincorporates this delay by relating the currentchange in the inflation rate to lagged values ofthe gap between output and potential. Thus, awidening of the output gap this quarter does notappear as a change in the inflation rate until thefollowing quarter.

A second, more subtle reason for a lagcomes from the process of signal extractionitself, in this case, the process of extracting an,estimate of the unobserved level of potentialoutput. This lag comes from the fact that theinflation and output data are noisy indicators ofthe output gap, subject to random movementswhich may not reflect a change in the level ofpotential GNP.

FIGURE 3

Actual and two-sided potential GNP

logarithms of 1982 dollars8.4

8.0

7.6

7.2

10 FA1)1()1111' IN

8.0

7.6

7.2

For instance, suppose we were to see anincrease in the inflation rate from 5 percent to 6percent over the span of one quarter. Thisadditional inflation could be the sign of anoverheating economy, as the added demandpressure led firms and workers to demand wageand price increases. On the other hand, the risecould be a fluke, the result of a statistical aber-ration, or special factors. If this were the case,interpreting the inflation as a symptom of awidening output gap would be a mistake.

There are two ways to distinguish mereblips from real demand pressure. First, onemight look at the co-movement between infla-tion and output. If the inflation accompaniedslackening output growth, the two indicatorstogether would point to excess demand. Like-wise, if the inflation continued over the courseof several quarters, it would provide strongerevidence of an output gap. However, waitingaround for more data to arrive takes time. Andthe less reliable the indicator—in time-seriesparlance, the larger the ratio of noise to sig-nal—the stronger the inclination to wait forcorroborating evidence to appear before takingaction. In other words, signal extraction uncer-tainty can be characterized as another source ofwhat Milton Friedman called the recognitionlag, referring to the length of time it takes torecognize the appearance of a situation requir-ing a policy action.

Discerning output gaps in real time

Except for the fact that the parameters ofthe model are estimated using data from theentire sample, the one-sided estimates roughlycorrespond to the estimates of potential outputthat would have been available to policymakersat the time. This raises the question of whetherthere are instances where the contemporaneousuncertainty surrounding the potential outputgoal is so large that appropriate policy correc-tions can be discerned only in retrospect.

The 1965-69, 1973-74, and 1978-79 expan-sions and the 1981-82 recession all representstatistically significant deviations of outputfrom potential, as measured by the 90 percentbounds. However, the 1974-75 recession andthe 1988-89 portion of the most recent expan-sion are ambiguous. Relative to the two-sidedestimates in Figure 3, these two episodes aresignificant deviations from potential output.However, neither of these deviations is signifi-cant with respect to the one-sided 90 percentbounds in Figure 4, suggesting that at the time,distinguishing the appropriate course of mone-tary policy might have been difficult. Themore recent episode is examined in greaterdetail below.

A closer look at the 1988-89 boom

One especially good illustration of theuncertainty problem is the small boom of 1988-89. After several years during which output fell

FIGURE 4

Actual and estimated one-sided GNP

logarithms of 1982 dollars8.4 —

90% error bounds

PotentialGNP

1111111111111111111111111111111i

1961 '64 '67 '70 '73 '76 '79 '82 '85 '88 '91

FEDERAL, RESERVE BANK OF CHICAGO

11

FIGURE 5

Two-sided estimates as of 1991 Q3

percent3 —

2

I •0

1111111111111111

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 01 Q2 Q3 Q4 Q1 Q2 Q3 Q41987 1988 1989 1990

FIGURE 6

One-sided estimates as of 1991 Q3

v.00111.1.

I I II I I

2 1 1 I I I I I 1 1 111111

Q1 Q2 03 Q4 01 02 Q3 Q4 CH 02 03 04 01 Q2 Q3 Q4

1987 1988 1989 1990

percent3

2

0

short of potential, the economygrew rapidly in 1987 and early1988, achieving annualized realgrowth as high as 4.5 percent. Re-acting to the economy's unforseenstrength, Federal Reserve policygradually tightened throughout1988, resulting in a rising federalfunds rate. Using the term spread(the difference between the ten yearTreasury bond yield and the federalfunds rate) as a rough measure ofmonetary policy as suggested byLaurent (1988) and Bernanke andBlinder (1989), this change in poli-cy corresponded to a decline in theterm spread from +200 basis pointsin 1988:1 to —100 basis points in1989:2. This section examines thequestion of whether policymakers could havediscerned this boom sooner and acted to offsetit, given the data available at the time.

This question is explored in Figures 5-7.The bars in each graph represent the outputgap—measured real GNP less estimated poten-tial GNP—expressed in percentage terms. Apositive output gap describes an overheatedeconomy with increasing inflation pressure.Similarly, a negative output gap corresponds tosubsiding inflation pressure. However, becausethey refer to the level of output relative to po-tential, negative output gaps do not necessarilycorrespond to recessions, which are typicallydefined in terms of the growth rate of real out-put. The solid line in each graphrepresents the upper 90 percentconfidence bound discussed earlier.An output gap in excess of thisbound says that the observed be-havior of output and inflation isstatistically quite unlikely to havecome from an economy in whichthe output gap is zero.

Figure 5 shows the two-sidedestimate of the output gap and itsupper error bound. From the van-tage point of 1991, it is apparentthat the very rapid output growth of1987-88 led real GNP to exceedpotential by the first quarter of1988, where the gap reaches 2.3percent. Output continues to ex-ceed the 90 percent confidencebound throughout the rest of 1988

and through the first quarter of 1989, at whichpoint the gap gradually begins to fall. Mean-while, although monetary policy was slowlytightening over this period, the term spread didnot become negative—usually a sign of mone-tary restriction—until the first quarter of 1990.In retrospect, then, it appears that monetarypolicy should have tightened more rapidly inearly 1988. Did the available data support suchan action?

Figure 6 displays the analogous one-sidedestimates of the output gap and the upper 90percent confidence bound. As one-sided esti-mates, they are similar to those which wouldhave been available at the time. However,

12 ECON01111. PERSPECTIVES

FIGURE 7

One-sided estimates as of 1989 Q3

percent3

I I1 1 1 1 1 1 1 1

I I I I

111111111

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q41987 1988 1989 1990

2

-1

2

there is an important difference: while they donot explicitly use any post-dated data, the esti-mates are based on the revised GNP and M2series available as of late 1991. Using thesefigures, the output gap never exceeds the uppererror bound. The estimated output gap changeslittle between Figure 5 and 6. The main differ-ence between the two is the size of the errorbound: the two-sided bound is less than 2 per-cent, while the one-sided bound is nearly 3percent. This discrepancy directly reflects thereduction in signal-extraction uncertainty thatresults from additional data. The policy impli-cation of this comparison is striking: judged bythe 90 percent error bounds, the case for fastermonetary policy tightening was much less clearin 1988 than it is with hindsight.

Using the unrevised GNP data—those dataactually available at the time—the evidence forquicker policy action becomes even weaker.Figure 7 shows the output gap based on one-sided estimates using the data available in thefourth quarter of 1989, which include the pre-liminary estimate of third quarter GNP. Moreimportantly, these data also predate the 1990annual revisions. Using these data, the one-sided error bounds are comparable to those inFigure 6. However, the output gap over theperiod is somewhat smaller, reaching a peak ofonly 1.9 percent, compared with 2.3 percentusing the 1991 estimates. Behind this discrep-ancy is the fact that the initial figures from1989 showed considerably stronger growth thanthe revised estimates. Because rapid output

growth is normally associated with output beingbelow potential, the model interprets faster-than-normal growth as one sign of a negativeoutput gap. Thus the two sources of uncertain-ty—that associated with potential output andthe error in estimating GNP itself—combinedto distort the true state of the economy, compli-cating the policy decision.

Conclusions

To the extent that the Federal Reservetakes responsibility for dampening demand-induced fluctuations in the economy, it will either explicitly or implicitly—base its policyon some appraisal of the economy's level ofpotential output. This article has proposed anew technique for rigorously constructing sucha measure, using inflation and real growth datato determine the level of GNP consistent withstable growth and constant inflation. This newpotential output series successfully capturesgradual changes in the economy's underlyinggrowth rate, without introducing the abruptkinks that characterize series based on segment-ed trends. Furthermore, this new series isunique in the way it delivers a measure of thestatistical uncertainty involved in constructingthe series. As argued above, a measure of thisuncertainty is essential for calibrating the re-sponse of monetary policy.

The explicit recognition of this uncertaintyalso highlights its consequences for real-timepolicymaking. Because the signal-extractionerror associated with a given quarter's estimate

of potential output falls as moredata become available, situationsrequiring policy action may notbe recognizable until later on.This phenomenon limits thescope of monetary stabilization.Frequently, the best response touncertainty is to adopt a wait andsee attitude until more informa-tion becomes available. As dem-onstrated by the 1988-89 exam-ple, by that time it may be toolate to respond effectively.

This conclusion is not limit-ed to the case of potential output.So long as there is any uncertain-ty in policymakers' assessmentof economic conditions, mone-tary policy will never be able to

FEDERAL RESERVE RANK OF CHICAGO 13

offset the undesirable effects of demand shocks.A less pessimistic restatement of the sameconclusion is that reducing the error associatedwith measures of macroeconomic performancecan improve the performance of policy, as moreprecise estimates enable policy to respond morequickly to changing economic conditions.

One way to improve the measurement ofpotential output is to incorporate other indica-tors of the gap between output and potential,such as the unemployment rate, or the rate ofcapacity utilization. Another way is to augmentthe model with measures of factor inputs: laborforce and the capital stock. Both of these arepromising directions for future research.

FOOTNOTES

'For example, see Boschen and Mills (1990), Braun (1990),and Hallman, Porter, and Small (1989). Prominent in theacademic literature is Blanchard and Quah (1989), whodecompose output fluctuations into the distinct effects ofsupply and demand shocks. See also the references inBoschen and Mills (1990).

2The use of the term "full employment" in this context issomewhat misleading. Because supply shocks also createshort term economic dislocation, full-employment potentialneed not correspond to a situation in which no resources gounused. One definition of potential output that takes thefull-employment idea to an extreme is the Delong andSummers (1988) measure. They argue that potential outputshould represent the maximum feasible level of outputattainable during peacetime.

3 Okun (1970), pp. 132-133.

4Eichenbaum (1991) provides a useful appraisal of thecurrent state of RBC research. Further discussion of theimplications for RBC theory for the measurement of poten-tial output appears in Boschen and Mills (1990).

5Some recent RBC models do allow demand shocks toaffect real variables: Cooley and Hansen (1989) and Chris-tiano and Eichenbaum (1990) are examples.

6To be precise, competitive equilibria are Pareto efficient,meaning no individual in the economy could be madebetter off without making someone else worse off. This isa statement of the well known First Welfare Theorem ofgeneral equilibrium economics.

7A recent exposition of the traditional approach to macro-economic fluctuations appears in Blanchard (1989).

8DeLeeuw and Holloway (1983) describe the constructionand use of the BEA's mid-expansion and high-employmentmeasures.

9Papers discussing the CEA's methodology include Perry(1977) and Clark (1979).

"This series gained prominence as the potential GNP seriesused in Hallman, Porter, and Small's (1989) definition ofP*. Aside from the choice of breakpoints, a priori judge-ment is also implicit in the choice of the four 14 ,, distributedlag weights in Braun's Equation Cl..

"See Strongin (1986).

REFERENCES

Barro, Robert, Macroeconomics, 3rd edition,John Wiley & Sons, 1990.

Bernanke, Benjamin, and Alan Blinder, "Thefederal funds rate and the channels of monetarytransmission," Manuscript, Princeton Universi-ty, 1989.

Blanchard, Olivier, "A traditional interpreta-tion of macroeconomic fluctuations," AmericanEconomic Review 79, December 1989, pp.1146-1164.

Blanchard, Olivier, and Danny Quah, "Thedynamic effects of aggregate demand and sup-ply disturbances," American Economic Review79, September 1989, pp. 655-675.

Boschen, John, and Leonard Mills, "Mone-tary policy with a new view of potential GNP,"Federal Reserve Bank of Philadelphia, BusinessReview, July/August 1990, pp. 3-10.

Braun, Steven, "Estimation of current-quartergross national product by pooling preliminarylabor-market data," Journal of Business andEconomic Statistics 8, July 1990, pp. 293-304.

Christiano, Lawrence, and Martin Eichen-baum, "Current real business cycle theoriesand aggregate labor market fluctuations," Insti-tute for Empirical Macroeconomics, DiscussionPaper #24, 1990.

14 ECONOMIC PERSPECTIN EI■

Clark, Peter, "Potential GNP in the UnitedStates, 1948-80," Review of Income and Wealth25, June 1979, pp. 141-166.

Clark, Peter, "Okun's law and potential GNP,"Manuscript, Federal Reserve Board of Gover-nors, 1983.

Cooley, Thomas, and Gary Hansen, "Theinflation tax in a real business cycle model,"American Economic Review 79, September1989, pp. 733-748.

DeLeeuw, Frank, and Thomas M. Holloway,"Cyclical adjustment of the federal budget andfederal debt," Survey of Current Business 63,December 1983, pp. 25-40.

Delong, James Bradford, and Lawrence Sum-mers, "How does macroeconomic policy affectoutput?," Brookings Papers on Economic Ac-tivity 1, 1988, pp. 433-480.

Dornbusch, Rudiger, and Stanley Fischer,Macroeconomics, 5th edition, McGraw-Hill,1990.

Eichenbaum, Martin, "Technology shocks andthe business cycle," Federal Reserve Bank ofChicago, Economic Perspectives 15, March/April 1991, pp. 14-31.

Gordon, Robert, "The impact of aggregatedemand on prices," Brookings Papers on Eco-nomic Activity 1, 1975, pp. 433-480.

Hallman, Jeffrey, Richard Porter, and DavidSmall, "M2 per unit of GNP as an anchor forthe price level," Board of Governors of theFederal Reserve System Staff Study #157, 1989.

Hamilton, James, "A standard error for theestimated state vector of a state-space model,"Journal of Econometrics 33, December 1986,pp. 387-398.

Harvey, Andrew, Time Series Models, JohnWiley & Sons, 1981.

Kuttner, Kenneth, "Using noisy indicators tomeasure potential output," Federal ReserveBank of Chicago, Working Paper #1991-14,1991.

Kydland, Finn, and Edward C. Prescott,"Time to build and aggregate fluctuations,"Econometrica 50, 1982, pp. 1345-1370.

Laurent, Robert, "An interest rate-based indi-cator of monetary policy," Federal ReserveBank of Chicago, Economic Perspectives 12,January/February 1988, pp. 3-14.

Okun, Arthur, The Political Economy of Pros-perity, The Brookings Institution, 1970.

Perry, G., "Potential output: Recent issues andpresent trends," in U.S. Productive Capacity:Estimating the Utilization Gap, Center for theStudy of American Business, Working Paper#23, Washington University, 1977.

Rissman, Ellen, "What is the natural rate ofunemployment?," Federal Reserve Bank ofChicago, Economic Perspectives 10, Septem-ber/October 1986, pp. 3-17.

Stock, James, and Mark Watson, "Variabletrends in economic time series," Journal ofEconomic Perspectives 2, 1988, pp. 147-174.

Strongin, Steven H., "Ml: The ever-changingpast," Federal Reserve Bank of Chicago,Econonomic Perspectives 10, March/April1986, pp. 3-12.

Taylor, John, "What would nominal GNPtargeting do to the business cycle?," Carnegie-Rochester Conference Series on Public Policy22, Spring 1985, pp. 61-84.

FEDERAL RESERVE BANK OF CHICAGO 15