外文翻译再议生产效率的测度Word格式文档下载.docx
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RAYMONDJ.Kopp
Nationality:
USA
Source:
TheQuarterlyJournalofEconomics,Vol.96,No.3(Aug.,1981),pp.477-503
Abstract
ThepurposeofthispaperistogeneralizetheFarrellindexesofproductiveefficiencytononhomotheticproductiontechnologies,andatthesametimemaintainthecostinterpretationoftheFarrellmeasures.Sincethegeneralizedindexesrelyheavilyonrecentdevelopmentsintheestimationoffrontiercostandproductionfunctions,severalfrontiermodelsarereviewed.Inadditiontogeneralizedindexesoftechnical,allocative,andoverallproductiveefficiency,avarietyofsingle-factorefficiencymeasuresarediscussed.Theapplicabilityoftheproposedefficiencymeasuresisillustratedwithanumericalexampleofelectricpowergeneration.
Introduction
ThepioneeringworkofMichaelFarrell[1957]focusedattentionontheconceptofproductiveefficiencyandtheconsequencesofitsrecognitionforthemodelingofproductionprocesses.ThispaperreviewstheelementsoftheoriginalFarrellapproachtoefficiencymeasurementandcontemporaryeffortsutilizingfrontierfunctions.ItprovidesthefoundationforasynthesisofFarrellefficiencymeasuresandfrontierefficiencystandards.TheresultantapproachtoefficiencymeasurementamelioratesmanyoftheweaknessesassociatedwithboththeFarrellandfrontiermethodswhilecapitalizingontheircombinedstrengths.
Tobeclearattheoutset,productiveefficiencyisdefinedastheabilityofaproductionorganizationtoproduceawell-specifiedoutputatminimumcost.Tobemoreprecise,theoutputandfactorinputsmustbeclearlyspecifiedbyvectorsofmeasurableattributesthatunambiguouslydefinetheircharacteristics.Further,forthesakeofexposition,itisassumedthattheproductionorganizationhasadoptedaspecifictechnology;
i.e.,theexanteproductiondecisionshavebeenmade,andwhatweobserveistheoperationoftheexposttechnology.
Thebodyofthispaperisinfoursections.ThefirstsectionreviewstheoriginalcontributionbyFarrell,focusingonthechoiceofanefficiencystandard.Contemporaryefficiencystandardsderivedfromfrontierfunctionsarediscussedinthesecondsection.ThethirdsectionproposesaseriesofFarrell-typeefficiencymeasuresutilizingfrontierfunctions,andthefourthsectionillustratestheempiricalapplicationofthemeasureswithanumericalexampleofelectricpowergeneration.
I.THEFARRELLAPPROACH
InapaperreadbeforetheRoyalStatisticalSociety,Farrellpresentedaningeniousmethodformeasuringtwoformsofproductiveefficiency.Hehypothesizedthatefficiencycouldbedichotomizedintotwosubcomponentsreflectingthephysicalefficiencyoftheinput-outputproductiontransformation(thetechnicalcomponent)andtheeconomicefficiencyofoptimalfactorallocation(priceefficiency).Itcanbearguedthatthedecisionsofeconomicagentsinvolvedinproductionarejoint;
thatis,decisionsthataffectallocative(technical)efficiencymightalsohavetechnical(allocative)ramifications.ThisclearlyisapossibilitythatFarrelldidnotreject.Whathedidassumeistheabilitytodisaggregatetheeffectofthesejointdecisionsintotwosubcomponents,andtomeasureempiricallytheirindividualeffects.
TofollowFarrell'
sexposition,consideralinearhomogeneousproductionprocessemployingtwofactors,capital(
)andfuel(
)toproduceasingleoutput,electricity(
).Summarizingthetechnologybyaunitisoquantallowsonetomeasureproductiveefficiencyrelativetothestandardsetbytheisoquant.Figure1depictsaunitisoquantdenoted
.Pointstothesouthwestof
areinfeasible,whilethosetothenortheastareinefficient.GivenaninputcombinationsuchasR,FarrelldefinedthedegreeofR’stechnicalefficiency(
)astheratio
.Thetechnicalefficiencyindex(boundedbetweenzeroandone)isaninput-basedmeasurethatistheratioofbestpracticeinputusagetoactualusage,outputheldconstant.
Figure1
Farrelldefinedandprovidedameasurefortheallocativeefficiency(
)ofaproductionorganization,whichisindependentoftechnicalefficiency.Allocativeefficiencyinvolvestheselectionofaninputmixthatallocatesfactorstotheirhighestvaluedusesandthusintroducestheopportunitycostoffactorinputstothemeasurementofproductiveefficiency.ReturningtothemodeldepictedinFigure1andassumingcompetitivemarketsforthepurchaseoffactorinputs,weseethattherelativefactorpricescanbeembodiedintheisocostline
.Theinputsetcorrespondingtopoint
minimizesthecostofproducingtheunitoutput.MeasuringtheextentofR'
sallocativeinefficiencyindependentofitstechnicalinefficiency,weutilizeR'
stechnicallyefficientprojectionpoint
andevaluatetheratio
.
Farrellcombinedphysical(
)andeconomic(
)efficiencyintoasingleindextermedoverallproductiveefficiency(
).Overallproductiveefficiencyismeasuredbyevaluatingtheratio
whichistheproductofthe
and
indexesandthusisacompositeofthetwo.AlloftheFarrellmeasuresaremadealongarayfromtheoriginthroughtheinefficientinputset,thuspreservingtheinefficientfactorproportions.Undertheassumptionofcontinuityandstrictmonotonicity,measurementalongtherayensuresthedistinctionbetweentechnicalandallocativeefficiency,andenablestheindexestobeinterpretedintermsoftotalfactorcost.
Aunitisoquantspecifyingthelocusofminimumunit-output-inputrequirementswaschosenbyFarrellashisefficiencystandard.Therearethreefeaturesofthisstandardthatdeservediscussion.First,theisoquantisderivedfromtheprimalproductionfunctionrelatingphysicalunitsofinputtophysicaloutput.Thechoiceoftheprimalfunctionratherthanitsdual,thecostfunction,isnecessaryifthedistinctionbetweentechnicalandallocativeefficiencyistobemaintained.Acostfunctionwouldsupplyinformationon
butnotonitsconstituentelements.Thesecondfeaturedealswiththerelativenatureofthestandard.Discussinghischoice,Farrellstates:
Althoughtherearemanypossibilities,twoatoncesuggestthemselves-atheoreticalfunctionspecifiedbyengineersandanempiricalfunctionbasedonthebestresultsobservedinpractice.Theformerwouldbeaverynaturalconcepttochoose-afterall,shouldnotapostulatedstandardofperfectefficiencyrepresentthebestthatistheoreticallyobtainable?
Certainlyitisaconceptusedbyengineersthemselveswhentheydiscusstheefficiencyofamachineorprocess.However,althoughitisareasonableandperhapsthebestconceptfortheefficiencyofasingleproductionprocess,thereareconsiderableobjectionstoitsapplicationtoanythingsocomplexasatypicalmanufacturingfirm,letaloneanindustry.
Thus,althoughthetheoreticalstandardisperfectlyvalidandhasitsownuses,thispaperwillbeconcernedwiththeobservedstandard[1957,p.255].
Theobservedstandardisdeterminedbythoseproductionorganizationssharingacommontechnologythatproducethegreatestoutputfromagiveninputset.Efficiencymeasuresbasedontheobservedstandardarerelativeinthesensethatindividualproductionorganizationsarecomparedwiththeperformanceoftheirpeergroups.Astheperformanceofthepeergroupchanges,sowillmeasuredefficiency.Finally,theadoptionofaunitisoquantnecessarilyimpliesthatthetechnologyemployedbytheproductionorganizationsislinearhomogeneous.ItisthisassumptionofconstantreturnstoscalethatisrelaxedinSectionIII.
II.FRONTIERFUNCTIONSASEFFICIENCYSTANDARDS
Farrell'
sefficientunitisoquantwastheprecursorofthefrontierproductionfunctionsoftoday.WhileFarrell'
ssoleintentwastoevaluatetheperformanceofproductionorganizations,frontierproductionandcostfunctionscanserveasefficiencystandardsandprovideinformationonthefeaturesofthebestpracticetechnologyaswell.Motivatedbythetheoreticaldefinitionsofproductionandcostfunctions,empiricalfrontierfunctionsspecifymaximaloutputfromgiveninputsorminimumcostforgivenoutputandfactorprices.Deviationsinoutputorcostfromthesefrontierscanbeusedasmeasuresofproductiveefficiency.However,thesemeasuresaredifferentfromthoseofFarrell,wherehisindexesholdoutputconstantandfocusondifferencesininputlevels.Frontierestimatorsofthemostrecentvintage(originatingwithAfriat[1972])explicitlyparameterizemeasuresofproductiveefficiencywithintheestimator.Thesefrontiermodelstreatthetechnicalparametersoftheproductionfunctionandtheefficiencyparameterssimultaneously.Ingeneral,theseefficiencyparametersarerelatedtotheassumedcausesofinefficiencyandaremodeledbyvariousstochasticdisturbancestructures.
Considertheprimalproductionrelationgiveninequation
(1):
(1)
where
isavectorofobservationsonoutput,
isamatrixofobservationsonproductivefactors,
isavectorofunknownproductionparameters,and
isavectorofrandomdisturbances.Traditionalaverageproductionfunctionestimationwouldspecify
tobedistributedindependentlyandidentically
andwouldapplyOLStoestimatetheparametervector
.Thefrontierestimators,ontheotherhand,generallyspecify
tohaveanonzeroexpectationreflectingthepresenceoftechnicalinefficiencyinproduction.
Table1summarizeseightofthemostrecentfrontierfunctionestimatorsbydetailingthetypeoffunctionestimated,theassumptionsmadeconcerningthestochasticdisturbance,theconstraintsontheerror,theestimationmethodemployed,andthecorr
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