DynamicandstaticproductivitymeasurementsofJapanese airlines:cantheyreallycompetethroughtheliberalization inAsianaviationindustry?

! "

Dyna mi ca nds t a t i cpr oduc t i vi t yme a s ur e me n t so fJ a pa ne s e a i r l i ne s :c a nt he yr e a l l yc o mpe t et hr o ug ht hel i be r a l i z a t i o n

i nAs i a na vi a t i o ni ndus t r y? *

YuichiroYoshidaI KatsuhiroYamaguchiⅠ M asashiYamamoto§

Abstract

Objectiveofthispaperistwofold.FirstistoprovideamethodologiCalframework calleddynamicTFP.Inthisparametricmethod,theoptimalchoiceofthelevels ofquasi‑fixedinputsinadynamicoptimizationproblem conformsthebenchmark, relativetowhichdynamicefBciencyismeasured.Asitssecondobjective,thepaper appliesthedynamicTFPmethodtotheefBciencymeasurementofJapaneseairlines.

Theresultsshow thattheoverallanddynamicefBciencyisthehighestforJAL,

followedbyANA thenbyJAS.Thepaperalsodiscussesabouttheimplicationsof theresultsonJapaneseaviationindustryanditspolicy.

Keywords:Japaneseairlines,dynamicefBciency,totalfactorproductivity

1 1 nt r oduct i on

Airlineindustryisoneofthoseindustriesthatareparticularlydynamicandever‑changlng.

Inthelastfew decadesitwentthroughdrasticchangesinregulationreglmeSWhilebeing washedinaseriesofmacroeconomicshocksandpoliticalinstabilities.Japaneseaviation industrylSnotanexception.Thesun usedtobeshininghigh isnow quicklysetting;

Japan Airlines(JAL),theJapaneseaagcarrierwhich usedtobeleadingtheindustry

*ResearchenvironmentandBnancialsupportfrom InternationalTransportPolicyResearchUnit (ITPU),GraduateSchoolofPublicPolicy,TheUniversityofTokyoarehighlyappreciated.

tcorrespondingauthor･AssociateProfessor,NationalGraduateInstituteforPolicyStudies,712211 Roppongi,Minato‑ku,Tokyo,Japan106‑8677,E‑mail:[email protected],Tel:+81‑3‑6439‑6147, Fax:+81‑3‑6439‑6010.

辛visitingProfessor,GraduateSchoolofPublicPolicy,TheUniversityofToky0,7‑3‑1Hongo,Bunkyo‑ ku,Tokyo,Japan113‑0033,E‑mail:[email protected]‑tokyo.ac.jp.

§ AssociateProfessor,CenterforFarEasternStudies,UniversityofTbyama,3190Gofuku,Tbyama, Japan,E‑mail:mya[email protected]‑tOyama.aC.jp

inthedawnofderegulationinthelate80'sisnow facingthedeepbottom. Oneof manyreasonsbehindthisisthemergerofJapanAirSystem (JAS)intoJALin2002.

Intur n,AllNipponAirways(ANA)thatnowseemstohavegaineditssolidpositionin themarketwasclearlythefollowerinthelate80'S.Thispaperintroducesadynamic productivitymeasurementmethodologyandadoptsittoinvestigatethedynamicchange oftheproductiveefncienciesofthesethreeairlinecompaniesinJapanduringthisperiod ofchange,uptothepointwhenJAShasbeenmergedintoJALin2002.

ThelasttwodecadeswereindeedtempestuousfortheJapaneseairlines.According toOum andYu[5]andOum andYu[6],intheearly1990'sJapaneseairlines'produc‑ tivitywasconsiderablylowerthanothermajorairlinesintheworld.Buthow welldid theymanagesincethen? Therewerethreemajorforcesofdynamism inJapaneseair transportmarketduringthepasttwodecades,namely,domesticcompetition,interna‑ tionalcompetition,andmacro‑economicfactors.Regardingdomesticcompetition,before mid‑1980'StherewasareglmeunderwhichmarketsweredividedintotrunkandreglOnal routes.JALwouldoperateontrunkroutes,ANA ontrunkandreglOnalroutes,and JASonreglOnalroutes.Inthosedaysroutestructureandentryofairlineswerecarefully coordinatedbytheaeronauticalauthorities.In1986,thegovernmentdecidedtorescind theoldreglmeSOthatmultipleairlinescouldenterandoperate.Inthedomesticmarket

,

thresholdinpassengervolumewasinitiallysetformultipleoperationstobeapplicable.

Thethresholdwassubsequentlyreducedandabolishedby1998.In2000theremainlng routelicenseandairfareregulationswererevisedfrom approval‑basedtoreport‑based.

Astotheinternationalcompetition,before1986JALwasthesoleJapaneseairline thatprovidedinternationalscheduledservice.Since1986,multipledesignationsinin‑

ternationalrouteshavebeenadopted.Tbdaythereare28internationalroutesonwhich multipleJapaneseairlinesoperate.

Macro‑economicfactorsplayedanimportantroleonJapaneseaviationindustry.After aperiodofeconomicboom inlate1980'S,theJapaneseeconomyenteredintoaprolonged stagnation.AlsoaffectingtheeconomywastheappreciationofJapanesecurrency.Strong YeninducedoverseastravelbyJapaneseresidents:atailwindfortheJapaneseairline industry.Soon,however,theywereencounteredbypriceunder‑cutbyforelgnCarriers.

Coupledwithdeaation,averageyieldplunged.

HavetheyImprovedtheproductivitydrastically? Aretheyreadyforfurthersteps ofliberalization,particularlyinthegrowlngmarketofEastAsia? Thispapertriesto provideastepplngStonetOanswertOthesequestionsbyanalyzlngrecenttrendsin theproductivityofJapaneseairlinestakingintoaccountthedynamicefnciencyoftheir decisionmaking.

Inpursulngtheultimategoalasmentionedasabove,thispaperachievestwoobjec‑ tives.Thefirstistoprovideaparametricmethodofmeasurlngproductiveefnciency whichtakesintoaccountthedynamicnatureoffirms'decision.Thepaperconsidersa situationwhereadecisionmakingunitsuchasafirm employsquasi‑fixedinputsaspart ofitsproductionfactors.Thefirm usesstockofquasi‑fixedinputsfrom theprevious periodaswellasothervariableinputsinthecurrentperiodtoproduceoutputsjointly withthenew levelsofquasi‑fixedinputs.Thechoiceofthelevelsofquasi‑fixedinputs

overtimethusbecomestheproblem ofdynamicoptimization.Solutiontothisoptimiza‑ tionproblemglVentheproductiontechnologyandfactorpricesconformsthebenchmark^, relativetowhichdynamicproductiveefnciencyofeachfirm ismeasured.

Theideaofdynamicefnciencydescribedaboveisfirstintroducedintheframework ofdataenvelopmentanalysis(DEAinshorthereafter.)OriginallySengupta[7]andFare andGrosskopf[2],andrecentlyNemotoandGoto[3]introduceddynamicelementsof productionandobtaineditsfrontierthrough theDEAefnciencymeasurement.Fareand Grosskopf[2]includedcapitalstocksofcurrentandsucceedingperiodsasinputsand outputsrespectively,aswellasvariableinputsandoutputsintheirDEAmodel.Nemoto andGoto[3]elaboratesonSengupta[7]inincorporatingcost一minimizationbehaviorof thefirmsintheframeworkpresentedbyFareandGrosskopf.

TheuseofDEAasameasurementmethodoftheproductionfrontier,however,implies themultiplicityofbestperformersandthesensitivitytooutliers.Thenaturalalternative istomeasuretheproductionfrontierthrough aparametricapproach,whichwecallthe dynamictotal‑factorproductivityapproach,(ordynamicTFP inshort.) Thepaper suggeststoestimatetheproductiontransformationfunctionafterspecifyingitasan appropriatefunctionalform.Thentheestimatedproductiontransformationfunctionis

Correctedbyshiftingaboveasmuchasthelargestpositivedeviationinthesampleto producetheproductionpossibilityfrontier

･

1Usingthisproductionpossibilityfrontier,

optimal(cost‑minimizing)pathsofquasi‑fixedinputsandthecorrespondingminimum totalcostoffulfillingtheactualdemandovertheobservationperiodareobtained.Finally^, dynamicefnciencylSmeasuredbytakingaratiobetweentheactualandtheminimum possiblecostsmeasuredasabove.

Asitssecondobjective,thepaperappliestheabove一mentionedmethodtothedynamic productiveefnciencymeasurementofJapaneseairlines.DynamicTFPisthencomputed forthreeJapaneseairlinesovertheperiodof1986‑2002,toevaluatetheefnciency intheirinvestmentandproductionbehavior.Theresultsshow thatJAL'Soveralland dynamicefnciencyisthehighest,followedbyANA thenbyJAS.Inthebackgroundof lowerefnciencyforANA andJASthereseemstobeover‑investmentinaircraftstock,

andforthecaseofJAS,thereisexcessiveuseoflaboraswell.

Thepaperalsospendsanindependentsectioninanalyzlngandinterpretingtheob‑

tainedresultsinthebackgroundofJapaneseaviationindustryandpolicy.Itarguesthat JAL'shigherproductivityisattributabletothefactthatithasbeenfacinginternational competitionandtighteningmacroeconomicenvironmentbothinJapanandintheworld.

ANA wasinabettersituationowlngtOitsfavorablepositioninthedomesticmarket

,

whichinturncouldhavelowereditsproductivityandefnciencyrelativetoJAL.How‑

ever,notonlyinternationalbutdomesticmarketisalsogettingmorecompetitivesince themidtolate90'S,whichinducedANA tostriveforenhanclngOperationefnciency.

JAShowever,didnothavesuchadvantagethatANA usedtohaveindomesticmarket. Besides,JAShasbeenstrugglingwiththeover‑investmentandexcessiveuseoflabor inputthroughoutourobservationperiod.

Thepaperiscomposedasfollows.ThefouowlngSectiondiscussesthemethodology ofdynamicproductivitymeasurementthroughthedynamicTFP.Sectionthreeadopts thedynamicTFPmethodtothecaseofJapaneseairlines.Sectionfourinterpretsthe obtainedresultsinthebackgroundofJapaneseaviationindustryanditspolicy.Finally,

sectionfiveconcludes.

1TheideaissimilartothecorrectedordinaryleastsquaresbyCoelliandPerelman[1]

2 Dynami cTFP

2.1 BasicStructure

ProposedmethodofthispapersharesthebasicstructurewiththatofNemotoandGoto l4].Thissectionbrieflyreviewstheirsetupwithslightmodificationsinassumptionsand notations.Definextasalx1vectorofvariableinputsandktasanm x1vectorof quasi‑fixedinputssuchascapitalstockinperiodi.A firm usesvariableinputsこrtand capitalstockintheendofthelastperiodkt̲1tOproduceanx1vectorofoutputsytand thecapitalstockintheendofcurrentperiod,kt.Naturally,aninputvector(xt,kl̲1)lies inl+m dimensionalspaceofnon‑negativerealnumbersIRE++m andsimilarly'anoutput vector(yt,kt)liesinRn++m･Let◎tdenotetheproductionpossibilitysetinperiodiwhich satisfiesthestandardpropertiessuchasdisposabilityandmonotonicity･2Thatis

･t‑((xt,kill,

y

t,kt)∈RlrmxRnrmI(xt,kill)Canproduce(yt,kt)), (1) where

l･if

(

^縞

1

1,

y

t,kt)∈◎tand

(

^{捕 ll)≦(xt,kill),then(xt,kt‑1,}

y

t,kt)∈◎t;and 2

･ i f

^{(xt,kill,縞 )∈◎tand(縞 )≧(yt,kt),then(xt,kill,}

^y

^{t,kt)∈◎t･}

Thedynamicallyefncientpathsofvariableandquasi‑fixedinputsaredefinedasthe solutionofthefollowlngminimizationproblem,glVendemandforoutputsasyTtandfactor prlCeS:

c( k o

, ‑ {xtTtiFT=

1

(套TL(wixl

･

恥 1

,I

(xl,kill,y‑i,kl)T‑1∈ ×T‑1◎t,ko

‑k o

) (2, where71Saconstantdiscountfacto r,Wtisalx1pricevectorforvariableinputsin periodi ,vtisanm x1pricevectorforquasi‑fixedinputsinperiodi,andabar(‑) indicatestheactualvalue.InitialamountofcapitalstockisexogenouslyglVenaSko. TheterminaltimeTisglVenbutkTCanbeeitherfreeorglVenaStheactualvaluekT.

Overallefnciency(denotedbyOE)isthendefinedastheratiobetweentheminimum 2sinceweallowthepossibilityofincreasingreturn,unlikeNemotoandGoto[4],wedonotassume◎t tobeconvex.

cost

c( k o )

andtheactualcost

a:

(3) NextwedecomposetheoverallefnciencyOE intostaticefnciencySE anddynamic efnciencyDE.DefinethestaticefnciencySE asthefollowlng:

sE‑筈 (4)

where

CSE

‑

{x

T

}

i

T

n

‑

1 (套 7 1 t w i x t ･ v i k l 1 1 ) ｡

.

x

t.,kill,

y ‑ i

,

k l ' T ‑ 1 ∈× T ‑ 1 O

l,ko

‑k o )･

(5, TheaboveequationsaysthatCSEisthemlnlmum costafirm canachievebyadjusting thelevelsofvariableinputsonly,whilethelevelsofquasi‑fixedinputsarefixedatactual values.Thenbydefinition,dynamicefnciencyDE iscomputedastheresidualofoverall efnciencyOE aftertakingoutthestaticefnciencySE:

DE‑諾 ･ (6)

StaticefnciencySE canbefurtherdecomposedintotechnicalefnciencyTE andthe allocativeefnciencyAE.TechnicalefnciencyTE isdefinedas

TE =∈ 竺

e (7)

where

C

TE

‑

{OT}

i

T

n

=1

(套 T L ( ‑ + v i k l l l , ･( 蛎 k t 1 1 , y ‑ i , k t , T ‑ 1

∈ ×

T ‑ 1 ◎ t , k o ‑k o )

(8) forsomepositivesealer￠l∈[0,1]for

i

‑ 1

, ‑

T .Thescaler￠t"shrinks"thevariable inputvector動 sothat￠t動 liesexactlyontheproductionpossibilityfrontier,orequiv‑

alently,attheboundaryoftheproductionpossibilitysetattimei.Thentheallocative efnciencyAE isdefinedastheresidualafterextractingTE outofstaticefnciencySE:

AE = 些 TE Notethatcombiningabovewehavethefollowlng:

OE = DE･SE

= DE･TE･AE

(9)

2.2 ParametricApproach ofM easuringDynamicE用.Ciency

Onecantakeeitherparametricornon‑parametricapproachinestimatingtheproduction possibilityset◎t.NemotoandGoto[3]andNemotoandGoto[4]tookthelatterbyusing DEA,whichtheycalleddynamicDEA.DynamicDEAtransformsthecost‑minimization problem describedin(2)intoalinearprogrammingproblem,andbysolvingitthey obtainedtheproductionpossibilitysetandtheminimum costatthesametime.Useof DEA,however,impliesthatobtainedresultsaremoresensitivetooutliers,andthereare multiplebestperformers･3Hereinstead,wetaketheparametricapproachinestimating theproductionpossibilityset,whichwecalldynamicTFPincontrasttodynamicDEA.

Insteadofsolvingfortheproductionpossibilitysetandtheminimum costinthesame onestep asinthedynamicDEA,dynamicTFP dividestheentireprocessintotwo stages.Inthefirststage,itspecifiesandestimatesaproductionpossibilityset.Inthe second,cost‑minimizationproblemsaresolved.DynamicTFP transformstheoverall cost一minimizationproblem inthesecondstageintoanoptimalcontrolproblem･4

Letusnowdiscussthefirststage.Productionpossibilitysetisobtainedbyspecifying theproductionpossibilityfrontierasanappropriatefunctionalform andestimatingit from thedata.Thereforeinourcase,theproductionpossibilitysetisexpressedas

壷t‑((xt,kill,

y

t

,

kt)∈R^lrmxRnr m)

suchthat,forsomeproductionpossibilityfrontier

i(

xt,kt̲1,yt,k

t , i )

‑0,

(12)

･･i

f

f

( i t , k i l l , y

t,帰)^{‑ 0and}

(

縞 11)≦(xt,kill),then(xt,kill,

y

t,kt)∈◎t; and

2･i

f

f(xl,kill,

捕

,i)^‑oand(

捕

)≧(yl,kt),then(xt,kill,

y

t,kt)∈◎t･ 3NemotoandGotol4]Showedthat,withvariable‑returnassumption,sevenoutofni.neJapanese electricutilitycompaniesareassignedunityfortheirstaticefnciency,1.e.,SevenOutOfnlnehavefull efnciencyscoreforbothtechnicalandallocativeefnciencies.Amongthosesevencompanies,twohavethe fullefnciencyscoreforoverallanddynamicefncienciesaswell.

4Thisdichotomybetweenthefirststageofproductiontechnologyestimationandthesecondstageof computationofminimumcostandefnciencyenhancestheapplicabilityofthedynamicTFP.Dynamic TFPcanbeappliedintocaseswheretheavailabilityofcostdataislimitedtoasubsetofthearms. Computationoftheefnciencylnthesecondstagedependsonlyoneachfirm'scostdataavailability^, andestimationoftheproductionpossibilitysetinthefirststageonlyrequiresthephysicaldata.Ifthe costdataisavailableforall伝rms,thenonecanalternativelyestimatedynamiccostfunctionsorEuler equationsasderivedfactordemandfunctionsthroughgeneralizedmethodofmoments.

Wenow turntothesecondstage.Usingtheestimatedproductionpossibilityset◎t obtainedaboveinthecost‑minimizationproblem in (2)yieldsthefollowing(discrete‑ time)optimal‑controlproblem.Letutbeanm x1vectorofinvestmentinperiodisuch thatkt‑kt̲1

+

^ut,thentheproblem canbeexpressedas:

T

a( k o ) ‑

{xt誓t

l

YT=

1 呂 T L( 擁 +

vikt

l l )

S.i.kt‑kt̲1

+

ut

, f

(xt,kt̲1,kt,

y

Tt,i)‑0

foralli∈(1,‑

, T

)WithkobeinggivenaskoandkTbeingfreeorgivenaskT.Then theLagranglantOthisminimizationproblem is

T

L‑

∑ [ T L( 壷 t+ 鵜 1 1 )

+刃 (kt‑kill+

u t )+ pt

f(xt,kt‑1,ut,

y ‑ i , i ) ]

(16)

l

=

1

where入tisam x1vectorofcostatevariables.Thecorrespondingfirst‑orderconditions are

旦砺旦恥旦弼

二

二

･tw

l ,･p

署 ^{‑0, vj‑(1 ,‑ ,l) (17)}

･

ー

〟 + (.〟

･ー1∧

し 工

上土

∂utJ

‑0, Vj‑ (1,･･

･

,m) (18)

7^{叫 ‑} ,

,

･右∫一入‑

,

^{I‑ 篭 ㌘} ‑0,vj‑(^{1 ,‑} 両 (19) for

i

‑ (1,‑ ,T),wherei(i)

‑i(

x t,kt̲1,

u

t,y‑i,i)andthesubscriptidenotesthejth elementofeachvector.Solvingtheabovefirstl0rderconditionstogetherwithconstraints

intheproblem yieldstheoptimalpathsforthevariableinputsandinvestment

x

言and ul*･ThisthenglVeSthecorrespondingoptimalpathofcapitalstockkl*andtheresulting optimalvaluefunction

a( k o ) ･

Infinding

a( k o )

above,itisusefulandillustrativetoconverttheaboveoptimal controlproblem intoadynamicprogrammlngproblem. Theproblem attimeithen

becomes

x

T, i u B T t( 擁 +

価 ll)

+

J(帰 ) S.i.i(xl,kill,kt,

y

Tt,i)‑ 0

kt‑g(xt,kt

̲

1,ul,

y

Tl,i)

g

‑ kt̲1

+

ut

whereJistheBelmanvaluefunctionandJ(kT,T)‑0.TheLagrangianis Lt

‑T L(

wixt

+

viktll)

+

J(k

t , i ) + p t

f(xt,kill

, k t

,y

T t , i )

^,

andthecorrespondingfirst‑orderconditionsare aL

こ)LI･1.,

ーー‑ー‑ー‑ー01232222Jrl■lLUJrl■lLUJrl■lLUJrl■lLU

(24)

‑

梅

+

p濃 ‑ 0, vj‑(1,‑ ,l) (25)

aau三 富 +p濃 ‑ 0, ∀j‑(

1 , ‑

,l) (26) foralli∈ 〈1,‑

, T

)wherethesubscriptidenotesthejthelementofeachvecto r,

andthesecondlineusesthefactthatagJ/aut

J

‑ 1･Theimplicationofthefirst‑order conditionsare

fxt, wtJ

古 √〜 LLTIt Vi,jE(^{1 ,･･}

･

,l) wherefxt,≡af/∂xt,;and

芸

‑, I

wt

,

^告

,

vj∈(^{1 ,‑} ,l)

(27)

(28)

wherejut, ≡∂f/∂ut,･Solvingbackwardfrom

i

‑ T

, a( k o )

isobtainedasJ(ko,0)･ Noteherethat

∂ J /

autJcoincideswith入tJintheoptimalcontrolproblem･

Asmentionedearlier,overallefnciencyOEiscomputedastheratiobetween

a( k o )

andtheactualcoste.Intu

r n

,Staticandtechnicalefncienciesareobtainedbysolving thefollowlngtwoStaticminimizationproblems.Astostaticefnciency,theminimization problem is

T

e sE ‑ {xT}iT

n

=

1 呂 T t( 擁 + 恥 1 )

S･t･ i (xt,

k

il l,転

y

Tt,i)‑ 0,

andfortechnicalefnciency,itis

T

eT E ‑

{OT}

i

T

n

=1

呂 T L ( 赫 l + 恥 1 )

S･t

･

i(￠

動

転11,転

y

Tt,i)‑0･

Thuswecancomputeefnciencymeasuresas

oE ‑ e( k o )/ e sE ‑ ^{eS E/ a}

DE ‑ OE/ SE TE ‑ ^{eT E/ a}

AE ‑ SE/ TE.

ーー‑ー1233Jrl■lLUJrl■lLU )))))3456733333(((((

3 Dynami cE用. Ci enc yM eas ur ementofJapanes eAi rl i nes

3.1 TheData

Ourdatasetincludestwovariableinputs,onequasi‑fixedinput,andtwooutputsfor threeJapaneseairlines,namely,JapanAirlines(JAL),AllNipponAirways(ANA),and JapanAirSystem (JAS),fortheyearsfrom 1986to2002(forquasi‑fixedinput,data startfrom 1985.)Twovariableinputsarematerialsandlab

o r

,whichwelabelasxland

∬2respectively.Materialsincludesallthevariableinputsexceptlabor,fuel,andaircraft maintenance.Laboristhenumberofemployees,includingforelgnandcontract‑based f

lightcrews.Oneofthetwooutputsisprimary(or"air‑side")Outputwhichwedenote asylandisthegeometricmeanofthepaidpassengerandcargovolumes,whileanother issecondary(or"land‑side")Outputwhichisincidentalsanddenotedbyy2.Stockof aircraftmeasuredbythenumberofseatsavailableistreatedasaquasi‑fixedinputand denotedbyk.AllthedataarenormalizedsuchthatvaluesforJALin1986isone.

CostdataforeachofthesevariablesarealsoincludedaswellasGDPdeflat,or.Ma‑ terialinputindexandincidentaloutputindexareobtainedthroughdividingmaterial costsandincidentalrevenuebyGDPdeflatorin eachyear,respectively.Totalcostand expenditureoneachinputincludingaircraftstockisnormalizedbyGDPdeflatorand

hencethesearemeasuredinrealterms.Thisimpliesthatthematerialinputservesasa numeraireinourfollowlnganalystsOfefnciencymeasurements.

3.2 DynamicTFP M easurements

3.2.1 EstimationorProductionPossibilitySet

Toidentifytheproductionpossibilityset,wefirstspecifyandthenestimateaproduction transformationfunction.Second,weshiftitupwardasmuchasthemaximum positive errortomakeittheproductionpossibilityfrontier.Thisideaofshiftingtheestimated productiontransformationfunctiontoyieldtheproductionpossibilityfrontierisanalo‑

goustothatofthecorrectedordinary‑least‑square(orCOLS)methodpresentedbyCoelli andPerelman[1].5

Inestimatingtheproductiontransformationfunction,weemploythefollowlngnOn‑

autonomousspecification,whichisessentiallynestedCESfunctions･6 oi

l

‑eβ+Atzfl

ou ‑ [α11YJ p ll+(1‑α

l

l)kt7 p l

l ]

^{11/p l l}

･u ‑ [α21Xt^Ip21+(1‑α21)

k t T

^t

p

^̲

2 i ] 1

¹

/

^{p 2 1}

yu ‑ [α12y1‑%f12+(1‑ α12)y21%f 1

2 ]

11 /p12

xu ‑ [α22堤 22+(1‑α22)x21%⁷2

2 ]

^11/p22

where

and

(38)

Intheabovespecification,OilandIilareconsideredtobeoutputandinputindices respectively,andYitandXilareVariable‑inputandvariable‑outputindices.Parameter AcapturesthetechnologlCaladvancewhile♂isthereturn‑to‑scaleparameter.Subscript

5Bydoingthis,absolutelevelsofefnciencymeasuresisnotefncient,however,relativerelationships amongthemeasuredefncienciesarestillefncientunlikeDEA,asitutilizesallavailableinformationin estimatingtheshapeoftheproductionpossibilityfrontier.

6Themostconventionalapproachtospecifytheproductiontransformationfunctionwouldbetouse thetranslogfunctions.However,itinvolvesalargenumberofparameterswhilewedonothaveenough datapointstoretainsufncientdegreesoffreedom.Alsoitishardtointerpretetheestimatedparameters withtranslogfunctionsasitisasecond‑orderapproximationofananonymousfunctionaroundunity.

istandsforcompanyiandthusiE(JAL,ANA,JAS).Thatis,weestimateacommon butnon‑autonomousproductiontransformationfunctionforthreeairlinecompanies.

Wetakethelogofbothsidesof(38)andassumethattheirdi庁erencefollowsa symmetricerrordistribution･7ThusweestimatetheparametersbyminimlZlngthesum ofsquarederrors:

α ′ S , p T 6 i , B , S , A ∑∑E ti t 2 t

⁽⁴³⁾

where

Eit‑1nOit‑

β‑

At‑61nZit. (44) Afterestimatingtheparameters,wefindthemaximumpositiveerrorEma

X

‑max(fit), and"shift‑up"theproductiontransformationfunctionasmuchasEmaX,a‑1aCoelliand Perelman.Finallyweobtaintheproductionpossibilityfrontier

i(

^{x t},kt̲1,^kt,yt,i)as

oi

l

‑ eβ+AL+EmaXzft (45) whereOilandIitaredefinedasabove.

Parametersareestimatedasfollows(valuesinparenthesesarestandarderrors): α1

1

‑0.4043 (0.1119)

α12‑0.7719 (0.1725) α21‑0.1311 (0.1314) α22‑0.4139 (0.4093)

β

‑0.0690 (0.0221)

∂

‑0.8965 (0.0591) pl

1

‑ 14.3871 (3.7112) p12‑ 10.6304 (1.7424) p21‑6.6818 (4.7947) β22‑ ‑0.3144 (2.7816) A‑0.0124. (0.0041).

Theresultindicatesthatproductionpossibilityfrontierisconcaveinvariableoutput indexYtandstockofaircraftktwithpllbeing‑4.3871. Also,thefactthatp21is 6.6818indicateslowelasticityofsubstitutionbetweenthevariableinputsXtandaircraft stockkill.Return‑toISCaleparameter6isslightlysmallerthanone,thusindicatinga weakdecreaslngreturntOscale.EstimateforAbeing0.0124impliesthatthereisa technologicaladvanceabout

1 . 2 %

peryearthroughtheobservedperiod.

7Analternativeofestimatingtheproductiontransformationfunctionistoassumeanerrordistribution consistedofwhitenoiseandinefnciencyasinthestochasticfrontierapproach,andthentousemaximum‑

1ikelihoodmethod.

3.2.2 M easurementResultsofStaticandDynamicE用.ciencies

Next,Wecomputetheoverallandstaticefncienciesandobtaindynamicefnciency,by solvingtwocost‑minimizationproblemsin(2)and(5)respectively.Staticefnciencyis decomposedintotechnicalandallocativeefncienciesbysolvinganothercost‑minimization problem asdescribedin(8).Inthecost‑minimizationproblem findingtheoverallefn‑

ciencyin(2),kTCanbeeitherfreeorgivenastheactualvaluekTaSmentionedearlier. Inourcomputation,WetakethelatteroptionbysettingkT ‑ kTtOavoidkTbeing extremelysmallintheoptimalpath,whichcanresultfrom thefirm'sincentivetosave variableinputsintimeT.8Discountrateof4% isusedforthevalueof7.

DynamicE用.ciencyand Over‑investmentinAircraftStock Table1.presents thecomputationresultsofefnciencymeasures.Theresultsshowthatoverallefnciency isthehighestforJAL andlowestforJAS,whileANA beinginthemiddle.Atthe sametime,allthreeairlinesachievedsimilarscoresforstaticefnciencies,resultingln starkdifferencesindynamicefnciencies.DynamicefnciencyforJALisashigh as0.9681 whilethatforJASisaslow as0.6406,andANA beingagalninthemiddleat0.8241.

TheseresultssuggestJAUscompetitiveadvantageoverothertwoairlines,andforANA andJAS(especiallyforJAS)over‑investmentforaircraftstockissuspected.Indeed,as Figure1andFigure2show,thedeviationoftheactualaircraftstockkfrom theoptimal valuek*isthelargestforJASandthenforANA.

AdjustmentCostsandLumpyInvestment Figure3presentstheactualandop‑

timalinvestmentinaircraftstockforthreeairlines.Optimalpathsareingeneralmuch smootherthantheactualpath,indicatingtheexistenceofadjustmentcostsinreality

,

whichisnotincorporatedinourmodelthistime^･9 Thisappliesmoretothecaseof JAL,followedbyANA,andlesstothecaseofJAS.ThisispartlyduetothatJALflies internationallyandthususeslargeraircraftscomparedtoothertwoairlines,andthat airlinestypicallyorderaircraftincertainbulk.

8Alternatively,onecanaddasalvage(residual)Valueterm totheobjectivefunctiontoavoidsuch behaviorofkTifthemarketvalueofthecapitalstockattimeTisknown.

9NemotoandGoto[3]discussedabouttheadjustmentcostsinthecontextofdynamicDEA.

AllocationbetweenMaterialsandLabor Figures4and5givethecomparisonof actualandoptimalpathsofbothvariableinputs,namelymaterialsandlabor.Relative totheshapeofestimatedisoquantcurvesandtherelativepricesoftheseinputs,all threecompaniesareemploylngtoomuchmaterialsandtoolittlelabor.Asmaterials includeoutsourclngOflab^{o r},thisresultseemstocontradictwiththecommonbelief ofefnciencygalnSthrough outsourclng.Figure6showstheratiobetweenactualand optimalproportionsofmaterialandlaborinputsforthreeairlines.Itindicatesthatfor JALactualratioistheclosesttotheoptimum,whileANAisthefarthest,andJASbeing inthemiddle.ThisrankinglSCOmpatiblewithourallocationefnciencymeasures.Given thatstaticefncienciesarealmostthesameforthesethreeairlines,rankingfortechnical efnciencylSjustthereverseofthatforallocativeefnciency,1.e.,itisthehighestforANA.

ExcessiveLaborInputfわrJAS Figure7presentsthecomparisonofoptimaland actualpathsforvariableinputindices,andFigure8takestheratioofthem.Itshows thatdeviationfrom optimalpathisdiscretelylargeforJAS,relativetoJALandANA forwhom extentofdeviationissimilar.ThislowersJAS'soverallefnciencyevenmore thanthatofANAwhosharestheover‑investmentinefnciencymentionedearlier.Figures 9and10decomposessuchdeviationintomaterialsandlabor.ItisevidentthatJAS isuslngCOnSistentlymorelaborthanothertwoairlinesthroughtheobservationperiod.

Astothedeviationinmaterials,JASisthehighestthroughouttheperiod,whileANA seemstobesuccessfullylowerlngSuchdeviation,andgettingclosertothelevelofJAL towardtheendoftheperiod.

T

r ansitionofOverallE用.Ciencies Figurellcontraststhetransitionofthreeairlines^' overallefncienciesovertime.Inearly90'sbothJALandANA loweredtheirefnciencies whileJASdidtoamuchlesserextent.ThisisclearlytheimpactofGulfwar,asJASwas mostlyflyingdomesticroutes.After'93,however,JALandANA successfullyreverses thedownwardtrendtoupwardrathersharply,whileagainJAScouldnotquitefollow thesetwo.Also,itisinacontrastth^叫 towardthelate90'sANA managedtoimprove

itsefnciency,whileJAS'sefnciencyremainedlow･10

StageLength Lastly,itisworthnotingthatthedatausedforoutputarethepassenger andcargovolumeswhichdonottakeintoaccountthedistanceflown.AsJALmainly f

liesinternationallywhileANA andJASflydomestically,theobtainedresultswouldbe evenmoredistinctandunambiguous,oncewetakeintoaccountthesedifferencesinthe stagelengths.

4 Japanes eAvi ati onPol i cyandI mpl i cat i onsofRes ul t s

4.1

J

apaneseAviation PolicyanditsBackground 4.1.1 AirTransportIndustryinitsPrimaryStage

In1951,Japan'saviationindustrywasallowedtoresumeitsserviceandin1953,Japan AirLines(JAL)wassetupthroughgovernmentfun°ingandspeciallegalstatus.JAL wasdesignatedtooperateinternationalanddomestictrunkroutes,whileanumberof otherairlineswereallowedtooperateonlyondomesticlocalroutes.Asthedemandfor airtransportincreased,competitioninthedomesticmarketbecamesevere.Thiscalled forestablishmentofaframeworkunderwhichfairandmoderatecompetitioncouldbe achieved.Recommendationof1970bytheTransportPolicyCouncilundertheMinistryof T

ransportllandtheMinisterialOrderof1972stipulatedareaofoperationforthethree majorCarriers:JALoninternationalanddomestictrunkroutes,AllNipponAirways (ANA)ondomestictrunkandlocalroutes,andJapanAirSystems(JAS,ex‑IbaDomes‑ ticAirlines(TDA))ondomesticlocalroutes.Thisconsistedapartofso‑called45/47 reglme,WhichhadstronglyregulatedJapaneseaviationindustryuntilmid‑1980'S･12

4.1.2 Pro‑CompetitiveAirTransportPolicysinceM id‑1980's

PromotionorM ultipleAirlineOperationinDomesticAirTransportMarket In1985,afterthe45/47regimehadbeenineHectformorethan10years,Transport

10WeshouldnotethatvaluesforANA in2002andJASbetween2000and2002isoverestimateddue totheboundaryconditionthattheoptimalvalueofkTmustcomebacktoitsactualvaluekT.

llAsofJanuary2001,MinistryofTransportwasintegratedwithMinistryofConstructionetc･,into MinistryofLand,InfrastructureandTr ansport(MLIT).

1245/47standsfor1970and 1972inJapan'sShowaera.Thisregimeisoftenreferredtoas"aviation constitution"intheliteratureincludingYamauchiandlto[8]･

PolicyCouncilreviewedthisframeworkandwassubsequentlyabolishedbytheCabinet. Newpolicywasintroducedtopromotemultiplenumbersofairlinesoperatinglnroutes withlargevolume.MinistryofTransportsetthelevelofpassengersforarouteinwhich twoairlines(doubletracking)orthreeairlines(tripletracking)couldoperate.Initially,

thresholdwassetat700thousandandonemillionannualpassengersrespectively,I.e.

,

inrouteswithannualpassengersofmorethan700thousand,twoairlineswereallowed tooperate;andinrouteswithmorethanonemillion,threeairlineswereallowed.The thresholdwasreducedtwice,oncein1992andagalnin1996topromotecompetition.In 1998,theruleitselfwasabolishedsothatairlinescouldenterintoanyrouteundertheir initiative.Asaconsequence,theratioofavailableseatsinrouteswithmultipleairlines againsttotalavailableseatsinthedomesticaviationmarketrosefrom 53% in1985to 80% in1999.

Inadditiontopro‑competitivereform inthedomesticmarket,multipledesignations ininternationalairtransportmarketwasintroduced.AlsoJALwascompletelyprivatized in1987.

RegulatoryReform ofDomesticAirfare DomesticairfareregulationinJapanwas designedtocheckandcontrolfareraise.Whentheairlinesappliedforapermissionto increasetheirairfaresduetoinflationorupsprlnginfuelprice,aggregatecostofairline wasreviewedbytheCivilAviationBureau.Airfarewasonlyallowedtoincreaseupto theleveljustifiablebythecostunderefncientoperation.Thiswastheruleinmostpublic utilitiesbackthen.

Inthemidl1990'S,regulatoryreformofpublicutilitiesbecameakeenpoliticalagenda.

Indomesticairfare,"zone"fornormalfarewassetallowlngairlinestosetairfaresfreely betweenthecapand25% belowit.Thecapwassetfrom thecostofcompetitiveroutes,

i.e.,double‑ortriple‑trackingroutes.Incumbentairlines,however,tookadvantageofthis reform andwhileintroducingvariousdiscountfaressuchasadvancebookingdiscounts andimprovedfrequentflyerprograms(FFPs),theyincreasedthenormalfaresintrunk routessuchasTokyoIFukuokaandTokyo‑Sapporo.Pricehikesinrouteswithtwoof theworld'SheaviesttrafncsuchasTokyoIFukuokaandTokyoISapporotriggeredsevere criticism from FukuokaandSappororeg10nS.

EntryofNew Airlines Meanwhile,airportcapacityexpansionofhighlycongested HanedaAirport13‑ thedomestichubairportlocatedinTbkyo‑ wasproceedingln duecourse.InMarch1997,anewrunwaywasopenedwhichmadeitpossibletoincrease landingslotsforadditional40flightsperday.Theseslotswereallocatedtoairlinesintwo stages:July1997andApril1998.Atthattime,thereweresixprojectslaunchedtoraise new airlinesandthefirsttwotobeinthemarketwasSkymarkAirlinesinSeptember 1998onTokyo‑Fukuoka,andHokkaidoInternationalAirlines(AIR DO)inDecember 1998onTbkyo‑Sapporo;new entrysince35yearsago.Incumbentcarriersmatchedto thelowairfaresofthesenewentrants,andasaresultpassengersincreasedby16.3% on Tokyo‑Fukuokaroute,and9.4% onTokyo‑Sappororoute14.

1nordertoacceleratederegulationinvarioustransportationsectors,inDecember 1996MinistryofTransportdecidedtoabolishsupply/demandtestinthetransportsector bytheendofthecentury･15AsforairtransportCivilAeronauticsLaw wasamended andputintoeffectonFebruary2000andthesupply/demandregulationpolicywas abolished.Sincethen,pro‑competitiveslotallocationpolicyatcongestedairportshas beenintroduced.Allocatedlandingslotsarereviewedeveryfiveyears.Also,airfare changeisonlysubjecttonotificationbyairlinestotheMinistrylnadvance.

MarketPerfわrmance Between1980and2000,thenumberofpassengersindomestic markethasmorethandoubledandaverageairfaredecreasedbyonethird.International marketgrewfaster,andthenumberofpassengersgrewbyfour‑fold.Initsbackground,

JapaneseYenappreciatedagainstUSSasmuchas2.5timebetween1985and1995,which gaverisetoarapidincreaseininternationalairtransportdemandforJapanesetravellers. However,theappreciationofyenresultedinhigh‑coststructureofJapaneseaircarriers,

whiletheyfacedseverecompetitionagainstforelgnCarriersintheinternationalaviation market.Asaresult,forelgnairlinesoutgrew Japaneseairlines,andmarketshareof Japaneseairlinesdroppedfrom 40% to37%.Also,theaverageyieldperpassengerhas beenpulleddownward,asitstransitionalmostcompletelycoincideswiththatofforelgn

13TbkyoInternationalAirport(Haneda)hasbasicallyservedasadomesticairportafterNaritaInter‑ nationalAirportopenedin1978.

14Thenumbersareaverageratesduringtheperiod･

15Thisregulationrequiredsufncientlevelofdemandtobeexpectedoneachrouteinordertoenterthe market.

exchangerateduetointernationalcompetition.AverageairfareofJapaneseinternational servicesdecreasedtolessthanhalfofwhatitwastwentyyearsago.

4.2 1mterpretingDynamicTFPofJapaneseAirCarriers

Since1986,whenregulatoryreglmeWasreplacedbypro‑competitivepolicy,Japanese airlineswentthrough aprocessofreform.ThestrongestimpetusthatforcedJapanese airlinestoimprovetheirproductiveefnciencycamefrom theinternationalmarket.As mentionedearlier,JapaneseYenappreciatedduringthisperiod,andthiswasasource ofrelativelyhigh costsforJapaneseairlinesaswellasforJapaneseindustrylngeneral. Macroeconomicdepressionalsoservedasaseveredeflationaryforce.Coupledwithcom‑

petitionfrom otherdomesticairlines,JALwasconfrontedwithunprecedenteddifnculty intheinternationalmarket.JAL'srevenuesharefrom theinternationalmarketwas70%

ofthetotaLIn1991JALplungedintotheredwith97millionUSSoperatingloss.Until thenJALhadenjoyedtenyearsofmoderategalnS.Operatinglossexpandedto388and 273millionUSSin1992and1993,respectively.Facedwiththiscrisis,JALestablished aCorporateRestructuringCommitteein1992andputtogethertheso‑called"Survival Plan"inwhichinvestmentinflectswasslashedandcost‑cutsundertakentorestorepro‑

ductivity.By1995JAL'sbalancereturnedtoblack.Hence,JAL'Shigherproductivityis attributabletothefactthatithasbeenfacinginternationalcompetitionandtightening macroeconomicenvironmentbothinJapanandintheworld.

ANA'sposition,ontheotherhand,wasrelativelysecuredduetoitsadvantageous positioninthedomesticmarketwithitsmarketsharebeingaround50%.Leveraged bythisadvantageindomesticmarket,ANAgraduallypenetratedintotheinternational market.Itwasnotuntil1998whentwonew airlinesenteredthemostlucrativeroutes inJapansuchasTokyoIFukuokaandTokyo‑Sappo

r

o,thatANA postedoperatingloss of102millionUSS.ThefactthatANAwasinabettersituationowingtoitsfavorable positioninthedomesticmarket,inturncouldhaveweakeneditsincentivetoimprove productivityandefnciencyrelativetoJAL.However,concordin1998Japan‑USaviation talksexpandingopportunitiesacrossthePaciacallowlngANA tooperateinthesame liberalstatusastheincumbentsalsoputpressureonthecompany.Itisnotonlyin‑

ternationalbutalsodomesticmarketthatisgettingmorecompetitivesincethemidto

late90'

S

,whichinducedANAtostriveforenhanclngOperationefnciencyduringthelast decade.

JAShowever,didnothaveanyparticularcompetitiveedgeineitherinternational ordomesticmarket.JASdidnothavesuchadvantagethatANA usedtohaveinthe domesticmarket,nordidithaveanyopportunitytooperateininternationalmarket unlikeJAL Besides,JAShasbeenstrugglingwithover‑investmentandexcessiveuseof laborinputthroughitshistory.Thisvulnerablecompanystruggledtocompetewiththe twomega‑carrierswithoutmuchsuccess.ItmayhavebeenadestinyforJAStomerge withJALin2002.

ThequestionnowiswhethernewJALcouldovercometheheritageofover‑investment andlow laborproductivityfrom JAS,aswellastorevivefrom devastatingdamage from 9.llandIraq/SARSthatshooktheairlineindustryatthewakeof21stCentury.

WeshouldnoteherethatJAListhemostefBcientamongthreeJapaneseairlinesonly historically,andthathavingdonewellinthelast20yearsdoesnotautomaticallymean thattheywilldothesameinthenext20years.Infact,ifwelookonlyatthecurrent picturewithoutthepast20yearsinourscope,therankingmaywellbealreadyreversed forJALandANA.

WhatisimportantforJapaneseairlinesistolookatthenext20yearsanddoit right,andindeedopportunitiesarethereforthem.By2009anew runwaywillopen atHanedaAirport,adding50% moreslotsfordomesticandshortinternationalroutes inEastAsia･16 Narita'ssecondrunwaywillbeextendedto2,500metersby2010,and themaximum numberofaircraftlandingswinincreaseby30,000.Expansionofthese capacity‑constrainedairportsinTokyowillopenawindow ofopportunityforJapanese airlines.TimeisrunnlngOut,however.Theyneedtogothough thesecondphaseof productivityimprovementquiteswiftlytobepreparedforanewcompetitiveenvironment inandaroundeastAsia.

161tisplannedtoincreasefrom about260,000to400,000landingsperyear

5 Con c l us i ons

Themaincontributionofthispaperistwofold.FirstithasprovidedamethodologlCal frameworkcalleddynamicTFP whichisaparametricmethodofmeasurlngdynamic productiveefnciency.Thepaperhasconsideredasituationwhereadecisionmakingunit employsquasi‑fixedinputsaspartofitsproductionfactorsandproducesnew levelsof quasi‑fixedinputsjointlywithotheroutputs.Thechoiceofthelevelsofquasi‑fixedinputs

overtimethusbecomestheproblem ofdynamicoptimizationinthecost一minimization problem.Solutiontothisoptimizationproblem glVentheproductiontechnologyand factorpricesconformsthebenchmark,relativetowhichdynamicproductiveefnciencyof eachfirm ismeasured.Theideaofdynamicefnciencydescribedaboveisfirstintroduced intheframeworkofDEA,however,theuseofDEA,impliesthesensitivitytooutliers andmultiplicityofbestperformers.Asanaturalalternative,thepaperhassuggested toestimatetheproductiontransformationfunctionafterspecifyingitasanappropriate functionalform,thentocorrectitbyshiftingaboveasmuchasthelargestpositiveerror toyieldtheproductionpossibilityfrontier.Usingthisproductionpossibilityfrontier

,

dynamicefnciencylSmeasuredasaratiobetweentheactualandtheminimum possible costsglVentheoutputlevelsandprices.

Asitssecondobjective,thepaperhasappliedtheabove一mentionedmethodtothe dynamicproductiveefnciencymeasurementofJapaneseairlines.Theresultshaveshown thattheoverallanddynamicefnciencyisthehighestforJAL,followedbyANAthenby JAS.LowerdynamicefnciencyforANA andJASisattributabletoover‑investmentin aircraftstock.OverallefnciencyisthelowestforJASduetoexcessiveuseofvariable inputs,especiallylabor,relativetoothertwoairlines.Thepaperalsodiscussedindetail abouttheinterpretationoftheresultsanditsimplicationsonJapaneseaviationindustry anditspolicy.Ithasarguedthatheightenedinternationalcompetitionhastriggeredthe efnciencylmprOVementOfJapaneseairlines,especiallyforJAL,followedbyANA,who arenowfacingrapidderegulationinthedomesticmarketaswell.

Oneimmediateextensionofthepaperwouldbetoincorporateadjustmentcosts ofquasi‑fixedinputs,assuggestedbythedata.Anotherwillbetheinclusionofforelgn airlinesinthedatasetwithlongerobservationperiod,toanswertotheultimatequestions

mentionedinthebeginning:aretheJapaneseairlinesreadyforfurtherstepsofgloba1 liberalization,particularlyinthegrowlngmarketofEastAsia?

Ref er ences

l1]Coelli,T.andS.Perelman(2000),"TechnicalefnciencyofEuropeanrailways:a distancefunctionapproach,"AppliedEconomics32,pp.1967176.

[2]Fare,R.andS.Grosskopf,(1996),IntertemporalProduction介ontiers:WithDynamic DE⁴ Boston,MA,KluwerAcademicPublishers.

[3]Nemoto,∫.andM.Goto,(1999),"Dynamicdataenvelopmentanalysis:modelingin‑

tertemporalbehaviorofafirm inthepresenceofproductiveinefnciencies^," Economic Letters64,pp.51‑6.

[4]Nemoto,∫.andM.Goto,(2003),"Measurementofdynamicefnciencyinproduction:

anapplicationofdataenvelopmentanalysistoJapaneseelectricutilities

, "

Journalof ProductivityAnalysis19,pp.1911210.

[5]Oum,T.H.andC.Yu,(1995), "A productivitycomparisonofthewor^ld'smajor Airlines^," JournalofAir升ansportManagement2(3/4),pp.181‑95.

[6]Oum,T.H.andC.Yu,(1998),"Costcompetitivenessofmajorairlines:aninterna‑ tionalcomparison," 升ansportationResearchPartA:PolicyandPractice32(6),pp.

407‑22.

[7]Sengputa,∫.

K

.,(1995),DynamicsofDataEnvelopmentAnalysis,Netherlands

,

KluwerAcademicPublishers.

[8]Yamauchi,H.andT.Ito,(1995),"AirTransportPolicyinJapan," WorkingPaper Series,CenteronJapaneseEconomyandBusiness,ColumbiaUniversity.

Table1.Overallefficiencyanditsdecompositions JAL ANA JAS

川川?〃〟

0.6909 0.5946 0.4701 0.9681 0.8241 0.6406 0.7137 0.7215 0.7339 0.8369 0.9176 0.9154 0.8528 0.7863 0.8017

Note:

OE:overallefficiency

DE:dynamicefficiency(computedasOE/SE) SE:staticefficiency

TE:teclmicalefficiency

AE:allocativeefficiency(computedasSEqE)

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z (a)

ANA

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z (C)

Figure1.Optimalandactualpathsofaircraftstockmeasuredinthenumberofseatsavailablefor(a)JAL,(b)ANA,

and(C)JAS.

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z (C)

Figure2.RatiosofactualandoptlmalpathsofaircraftstocksforJAL,ANA,andJAS.

0.3

0.〜

0.1

0.0

‑0.1

‑0.2 86 87 88 89 90 91 92 93 94 95 96 9798 99 ()0 01 0Z

(C)

Figure3.OptimalandactualpathsofinvestmentinaircraRstockmeasuredinthenumberofseatsavailablefor(a) JAL,(b)ANA,and(C)JAS.

0.6 0.5 0.4 0.3 0.2 0

. 1

0.0

86 87 88 89 90 919Z 93 94 95 96 97 98 99 00 01 0Z (C)

Figure4.Optimalandactualpathsofmaterialsfor(a)JAL,(b)ANA,and(C)JAS.

86 87 88 89 90 919Z 93 94 95 96 97 98 99 00 01 0Z (a)

ANA

86 87 88 89 90 919Z 93 94 95 96 97 98 99 00 01 0Z (C)

Figure5.Optimalandactualpathsoflaborinputfor(a)JAL,(b)ANA,and(C)JAS.

■ xz*

■ xz

(xl/x2)/(xl*/xZ*)

86 87 88 89 90 91 92 93 94 95 96 97 98 99 ()0 01 ()Z (C)

Figure6.RatiosofactualandoptlmalproportionsofmaterialsandlaborlnPutSforJAL,ANA,andJAS.

86 87 88 89 90 91 9Z 93 94 95 96 97 98 99 00 01 0Z (C)

Figure7.Optimalandactualpathsofvariable‑inputindicesfor(a)JAL,(b)ANA,and(C)JAS.

∨Ⅰ/VI*

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z (C)

Figure8.Ratiosofactualandoptlmalpathsofvariable‑1nPutindicesforJAL,ANA,andJAS.

Xl/Xl* 7.0

6.0

5.0

4.0

3.0

Z.0

1.0

0.0

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z

(C)

Figure9.RatiosofactualandoptlmalpathsofmaterialsforJAL,ANA,andJAS.

XZ/XZ*

86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 0Z (C)

Figure10.RatiosofactualandoptlmalpathsoflaborlnPutSforJAL,ANA,andJAS.

OverallEfflClenCybyyear

■86 ■87 ■88 ■89 '90 ■91 ■92 ■93 ■94 ■95 ■96 ■97 ■98 ■99 ■00 '01 '02

Figurell.TransitionofoverallefficienciesovertimeforJAL,ANA,andJAS.