LAWRENCE R. KLEIN University of Pennsylvania assisted by VIRGINIA LONG WhartonEconometric Forecasting Associates Capacity Utilization: Concept, Measuremnent, Iand Recent Estimates ON SEVERAL OCCASIONS in the past fifteen years, my colleagues and I have tried to explain disparities among alternative measures of capacity utiliza- tion and to justify our own approach to the measurementproblem.1 George Perry, in his contribution to this issue of Brookings Papers, has indicated many of the important issues, and I would like to amplify his points or restate them from another viewpoint in the interests of clarification. Briefly, the Federal Reserve index estimates that as of mid-October 1973, a fair amount of spare capacity existed in the American economy. The esti- mated operating rate was only 83.4 percent for 1973:3. By contrast, the Wharton index for manufacturing was as high as 96.7 in the same period, and was rising faster than the Federal Reserve index. The McGraw-Hill index was at an intermediate level of 86.5 percent in September. Similar divergences among the indexes had been apparent for several months. These messages are so different that they suggest the need for a close look into the whole subject. For some years the Wharton and Federal Reserve indexes of utilization followed similar paths. They began to diverge in 1965, when the Wharton index rose sharply, as if signaling the onset of the 1. LawrenceR. Klein and Robert Summers,The WhartonIndex of CapacityUtiliza- tion(University of Pennsylvania,Wharton School of Financeand Commerce,Economics ResearchUnit, 1966). 743 744 Brookings Papers on Economic Activity, 3:1973 stronginflationary pressures that accompaniedthe VietnamWar.2 Perry's Table3 bringsout sharplythis breakin the relationship.For the two sub- periods1954-65 and 1966-72the seriesall havelarge pair-wise correlations, but the Whartonindex correlatespoorly with the others for the whole period 1954-72. After 1965, the short-runmovements in the Wharton seriesare like those in the others,but its level is much higherin termsof a utilizationrate. I feel that the Whartonindex gave the correctsignals on inflationin 1965 and again at the beginningof 1973. The Concept Full capacityhas been variouslydefined as a minimumpoint on a cost function,a full input point on an aggregateproduction function, and a bottleneckpoint in a generalequilibrium system. Full capacityshould be definedas an attainablelevel of outputthat can be reachedunder normal inputconditions-without lengthening accepted working weeks, and allow- ing for usual vacationsand for normalmaintenance. Preoccupation with measuresfor individualindustries, considered separately from others at the same time, tends to overstatecapacity for the system as a whole. The standardWharton measure of trendlines throughpeaks of individualpro- ductionseries provides a systemof attainablepoints because many or most industriespeak approximatelytogether. The Whartonapproach satisfies the conditionof feasibilityunder normal conditions; it runsthe risk, how- ever,of callinga local maximumpoint one of full capacitywhen it may be only a partialrecovery point. This is the problemof the so-called"weak peak." I believethat 1959was the last time that the economypeaked out at a local maximumwith less than full recovery. Some adjustmentfor the Whartonindex around 1959 became necessary. Preston and I estimatedin- dustryproduction functions and insertedthe full employmentlabor force andcapital stockfor each industry. The valueof productioncomputed from theseinputs at full use yieldedestimates of capacityoutput that could then be used to adjustweak peaksupward.3 2. See WhartonQuarterly, Vol. 6 (Winter 1971), p. 16. 3. L. R. Klein and R. S. Preston, "Some New Results in the Measurementof Ca- pacityUtilization," American Economic Review, Vol. 57 (March 1967), pp. 34-58. Lawrence R. Klein and Virginia Long 745 By distributingthe available(full employment)labor force over indus- tries as it would be, historically,at full employmentpoints, we implicitly take accountof the feasibility,in a generalequilibrium sense, of attaining the outputlevel that we designateas full capacity.This approach is different from one relyingon a purelymacroeconomic production function or from one that estimatesoutput at full capacityin each sectorwithout taking ac- count of relationshipsto other sectors.Subsequent to 1959, the economy consistentlypeaked out at full capacitypoints. The overshootingof inter- mediate peaks like those in 1959 when the trend lines are established throughpeaks has providedus fairly reliabletrends on capacitythat we now use in the Whartonindex. As the economyapproaches a turn,however, before the maximumpoint has been fullyreached-as at the end of 1973-the capacityvalues in a few cases keep exceedingthose in the previousquarter so that the capacity trendsmust be movedslightly upward. This is a fault of our method,but I thinkthat the resultingupward bias in capacityutilization is less than2 full percentagepoints in presentcircumstances. Accordingto presentforecasts, it is likely that the economy will slow down in coming months; thereforesubsequent quarters should not push economicperformance in separateindustries on to new, higher,capacity points that would lead us to reviseupward our capacitytrend lines. The figuresin Perry'sTable 9 areinteresting to me in thatthey indicatea muchsmaller upward bias for the Whartonindex over the FederalReserve or McGraw-Hillmeasures than would be suggestedby the comparisonof the usual aggregateindexes. The FederalReserve estimates in Table 9 for major materialsindustries are more firmlybased on direct information fromengineering and tradesources. They tend to be no morethan about5 points below the correspondingWharton indexes. Generallyspeaking, I like productionfunction estimates of capacityout- put, but for quicknessof estimationand simplicityof concept,I preferto workon a largescale with our presentmethod of trendlines through peaks, usingproduction function estimates only for adjustmentand extrapolation.4 4. Interestingmeasures of productionfunctions are containedin a researchpaper by Robert M. Coen and Bert G. Hickman, "AggregateUtilization Measuresof Economic Performance,"Research Memorandum 140 (StanfordUniversity, Center for Researchin Economic Growth, February1973; processed). 746 Brookings Papers on Economic Activity, 3:1973 Yet another approachdraws on linear programmingcalculations. In studies of chemicalproduction and petroleumrefining, Malenbaum and Griffinmeasure capacity as the "bottleneck"point in expansionalong a given ray correspondingto a fixed productmix.5 When one producthits such a bottleneck,all othersdependent on it for intermediateinput are re- strictedat less thanfull capacityutilization. This provides a maximumout- put point while preservinga given productmix. The Malenbaumand Griffinestimates for petroleumand chemicalswere checkedagainst the Whartonestimates of utilizationfor the same indus- tries. In general,little agreementwas found betweenthe resultsfrom the engineering-typeestimates and the standardWharton procedures, espe- cially for short-runmovements. But in most cases, the Whartonestimates of utilizationfor petroleumrefining are higherby about 4-5 percentage pointsthan those based on the linearprogramming model. For the chemical industry,the resultsare closer,but in a few isolatedyears the discrepancy exceeds5 percentagepoints. Systematicanalysis and coverage of all major sectors by production functionestimation, input-output methods, and linearprogramming calcu- lations promisethe greatestreturn in precisionof measurement,but that combinedapproach seems to be a long way off, exceptfor intensive research in separateindustries. In this connection,I disagreewith Perry'sview that limitationson pro- ductionresulting from shortages of intermediateproducts (like today'san- ticipatedshortages of fuel)should not affectthe conceptof capacity.Capac- ity is a generalequilibrium concept, which should be alteredin the light of bottleneckswhose effectscan be tracedthrough an input-outputanalysis. That is the whole point in usingcapacity utilization measures as signalsof inflationarypressure, and accounts for my view that other measures stronglyoverstate the amount of spare capacityavailable by not taking accountof interrelationshipsamong industries.6 5. Helen Malenbaum,"Capacity Balance in the Chemical Industry,"in Lawrence R. Klein (ed.), Essays in IndustrialEconometrics, Vol. 2 (University of Pennsylvania, Economics Research Unit, 1969); James Griffin, CapacityMeasurement in Petroleum Refining:A Process Analysis Approachto the Joint Product Case (Heath, 1971). 6. A techniquefor estimatingcapacity utilizationrates in an input-outputmodel is given in L. R. Klein, "Some Theoretical Issues in the Measurementof Capacity," Econometrica,Vol. 28 (April 1960), especiallypp. 280-86. Lawrence R. Klein and Virginia Long 747 CapacityUtilization as an ExplanatoryVariable Indirectuse of capacitymeasures is importantin the constructionof econometricmodels and servesas a validationtest for the seriesactually beingconsidered. The indirectuses arein equationsfor (a) priceformation; (b) capitalformation; (c) trade.Capacity utilization is one of the most stra- tegicvariables in the Whartonmodel, and showsup in severalplaces. In the basic equationfor price formation-the manufacturingdeflator-a non- lineartransformation of capacityis one of the most significantvariables: loglg1- I CPMF' where CPMF is capacityutilization in manufacturingconstrained to