東北学院大学学術情報リポジトリ

the Rise?

著者（英）

MAEDA Shuya

journal or

publication title

Tohoku Gakuin University economic review

number

164

page range

237-261

year

2007-03-15

MeasuringPovertyTodaymJapan*

IsltontheRise？−

ShuyaMAEDA

Contents I. Introduction n. IntroductionofPovertvMeasurement Ⅱ一l Sen'sPovertVMeasurement Ⅱ−2 Takayama'sPovertyMeasurement学 Ⅱ−3 Kakwani'sPovertyMeasurement m. ComparativeExamination W.AFewFurtherlssues Ⅳ一l QuasiOrderingofPovertyMeasurement IV-2 ThelssuesConcerningtheEstablishmentofPovertyLine凶 V. SomeCalculationsandPovertyinJapan W.Conclusion I. lntroduction

Accordingtothe20040ECDREPORT,therelativepovertyratioinJapan

(thatisthenum-berofpeopleunderthepovertylme,whichisdefinedashalfofthemedianmcome) isrecorded asbeingl5.3%,rankingfifthbel血dMexico,theU.S.A,Turkeyandlreland. IncomparisonwiththeOECDaverageOfl0.7%,Japan'sratioisrelativelyhigh.Thespeedof theincreasehasalsoacceleratedrecently,risingfromll.9%inthemiddlel980's,to15.3%

today(Tachibanaki(27)).Thispaperaimstointroducethesubjectofrelativepovertymeasure-ment (Chaptern,m,N),andwiUprovideprecisecalculationsofJapanesepovertyasitexists

inpresent-dayJapan(ChapterV). Asiswen-known,sincethediscoveryofPareto'slawattheendofthenineteenthcentury,

researches on inequalitymeasurement and their applicationsI ) have interestedmany economists・Amongothers,afterAtkinson[3] showedtherelationbetweenvariousinequality

measurementsandthesocialwelfareconcept lyingbehindthemeasurements, researcheson

*ThiSpaperisapartofthestudysubsidizedbyTOHOKUGAKUINKOBETSUKENKYU2006 1 ) SeeMaeda[16]foranapplicationintobusinessconcentrationmeasurementbyLorenzcurve

inequalitymeasurementhavemadegreatprogress.2) However,thediscussiononhowtogetanobjectivegraspofpoverty,whichshouldbeequally ormoreimportantthanthediscussiononmequalitymeasurementasoneofthemajorconcerns ofeconomics,hadmdoubtedlybeenpoormtilSen[25]m1976,Takayama[30] inl979and Kakwani inl980amongothers,madeproposalsforit.Amongthewell-knownpovertyresear-chesconductedbythen,forexample,aretheworksbyB.S.Rowntree,P.TownsendinBIitain andM.OrshanskyinAmericaandmanyothers.3) Theprincipalconcernoftheseresearches,however,washowtostipulatethepoororhowto calculatetheminimumcostofliving.Inotherwords,theresearchesweretheonesaboutthe waytoestablishthepovertyline.Andthemeasurementsusedafterthefixationofpovertyline haveonlybeensuchindicesashead-countratio:H,whichrepresentstheratioofthepovertyto thetotalpopulation;andpoverty-gapratio: I,whichshowsadegreehowmuchincomeenables allthepoortogetoutofthesimation.However,aswewmseebelow,thereexistafewfatal defectsinthestandpointtotakeupeitherofthetwoapproachestouseasanobjectiveandquan-titativemeasurementofpoverty. Theaimofthispaperisasfollows;chapterlwillbrieflyoutlinethenewmeasurementsR andPIwhichweresuggestedbySenandTakayama,respectively, inordertoovercomethein- herentdefectsofthetraditionalmeasurementsmentionedabove.Inchapterlll,thetwomeas- urementswillbecomparativelyexaminedtoshowthatR,whichemployscensoredincomedis-tribution,4 ) isbetterinsomerespectsthanR.InchapterlV,Iwillconsiderafewproblems whichthenewpoveltymeasurementsstillcontain・ InchapterV,somecasesilldieswillbeconducted 2) InTerasaki [34]mostoftherecentrepresentativeresearchesaresummarized.

3) InKonuma[13] scrupuloussmdiesontheminimumcostoflivingofBritam, theUnitedStatesandJapan

areconducted.

4) "Censoredincomedistribution" isthedistributionwhichtakesallofthedegreehigherthanacertammcome

tobethepointdistributiononthetruncatedpoint． (Seesection(2) inchapterll.forthesmctdefinition.）

Bytheway,truncationorcensoringthedistributionatacertainpomtsuchasthecensoredincomedistribu-tionisunfamiliarconceptinthefieldofeconomicstatistics.Butithasavelypracticalsignificanceinthefield

ofqualitycontrolandbiomedicalstatistics Totakeafewexamples: i)Inthecaseofcheckingtheaverage

durationoflightbulbsprodIIcedinafactory, thespanofdurationofthebulbsmayextendforseveralyears, dependingoneachbulb.SDinorderncttowastetime,oneestimatestheaveragedurationofthepopulation fromthesampleswhichhavebumedoutwithmacertainperiodoftime (e.9. 1000hours). ii) Inthecaseof investigatmgtheeffectsofsomechemicalonlivingbodies,usingguineapigs,

ifthelatentperiodisempirical-lvknowntobeextremelylong, thenoneinvokessuchconcept.

Inpassing, inthefieldotherthaneconomicstatistics,adistmctionismade,withrespecttothejargcn,be-tweenthecasewherethepopulationitselfisadistributionprunedandthecasewherethesampleisapruned distribution (thereforethepopulationisacompletedistribution).Sometimestheformercaseisdubbed truncated"andthelatter "censored," tobePreCise.Thereisalsoatennlike $$intermediatelycensored

叫

distribution" fortheconcept.But,maccordancewithTakayama[33],weadopt "censoredincomedistribu. tion"hereafter.

−238−

MeasmngPOVertyTodayinJapan

aboutJapan・SimilarcalculationaboutthecasesinJapanisalsomadeinTakayama[33],but

thedatausedherearedifferentfromthoseinTakayama[33] inordertofindwhichiscalculat-edfromanovelpovertyline.

I.lntroductionofPovertyMeasurement

As ismentionedinchapterl, bothofthetraditionalmeasurements,Handr, carlyfatal defectsandeachofthemcannotbeusedasanonlypovertymeasurement:whenonlyHisused, Icannotbemadeexplicit;whenonlyrisused,Hcannot.Inaddition,asanimportantfactorof thepovertyline,dispersionofincomeamongthepoormaynotbeneglected.Letusdrawout, below,Randawhichwereaimedtoovercomethedefectsofthetraditionalmeasurements mentionedabove. Ⅱ−1 Sen'sPovertyMeasurement Assumeasocietyofnpeopleandplaceeachmember'sincome(y) intheascendingorder (1) yI三池≦． . ．≦yA≦.y"+I≦…比 Assume,further,thepovertyline(z),whichequalsYh+,in(1).

Inthiscase,whenthesetofpeo-pleearningincomelowerthanxisexpressedasS(jr),thenS(z)indicatesthepoor;andS(γ雌),all

themembersofnpeople.Todefineincomegap,&, i-thperson'sgiisarangeofhisincomesub-tractedfromz: (2) &=Z-yj Takingaccountofincomeco㎡igurationwhichisrepresentedas"-vector",5) aggregategapQ

(j:), isdefinedasweightedsumofnonnalizedgiofallthepeopleinS(x):

Q(x)=A(z,")Z"(2,")

(3)

jES(工） Here,Amdicatesconstantand"j(Z,g),non-negativeweight.TheseAandzﾉiaretobespecified bythefouraxiomsbelow.Sen'spovertymeasur･ementRisdefinedasthemaximizedQ(x)with respecttotheentirex: Ps=""Q(x) 工 (4) Becausezjjisnon-negative, Ps=Q(z) (5)

5)WewiUrepresentdismbutionofincome (vector) inboldfacebelOw

−239 q

Sen'sfouraxiomsareasfollows:

axiomE$ [relativeequity]

Concerningallthepairsi,jundervector", ifthewelfarelevel"i(")ofanmdividual,

jisal-wayslowerthanthewelfarelevel"j(9)ofanindividual/, thentheweighttobeattachedto

themmustbe"j(2")>ili(z").

Therelativelylooseconditionwithrespecttothisequityisconsequentlyincorporatedmtothe fonowingaxiomRs. axiomR, [ordinalrankwelfare]

Theweightzﾉi(z,")tobeattachedtotheincomegap&ofanindividualjisdetenninedbythe

ordinalrankbetweenthepoorpeople,namelyzﾉ!="+1-j ("representsthenumberofthe

poorpeople).

Theessentialideaofthisaxiomcanbeseenontheoccasionofvotingasintheelection: i.e. thesuccessfulcandidatesaredeterminednotbythenumberofvotesobtainedperse,butbythe positionintheranking.Thisaxiomcanalsobesaidtodealwithpovertyfromtherelativistpoint ofview.Thatistosay,whethertheamountofincomeissaidtobelargerorsmaU, itisamatter ofcomparisonandisnotanabsolutecriterion.Judgingfromthispointofview, tmsaxiomap-pearstobefairlypersuasive. Axiom"[monotonicwelfare]

Ifyj>jf, then"j (")>"j (").

Whatthisaxiommeansisthataftertheprospectoftheentireincomedistributionisgiven,the individualwelfareisdeterminedonlybyhisincomelevel: thehighertheincomelevelbecomes, thehigherthewelfarelevelbecomes;whileintheoppositecase,thewelfarelevellowers.There-fore,thisaxiomisaratherstrongpresupposition.Particlllarly, itispredictedthattherealmem-bersofthepoorincludewhatiscanedthedisabledandthesmgle-parentfamilyatamuch higherratethantheotherclassesdo. Inotherwords, thereexistmanypeoplewhosewelfareis stronglyinnuencedbythefactorsotherthanincome.Nevertheless, thisaxiomisdesignedto maketheirwelfaredependentsimplyontheincome,soitcertainlyisarelativelystrongcondi-tiontoreflectthereality. AxiomM[normativepovertyvalue]

f,I-Zgi/A"

IfaUthepoorpeopleearnthesameincome, thenR,=H･4whereH=

[Theoreml] Ifthenumberofthepo･rissufficientlylarge,thenthep･vertymeasu龍湛ntthat

satisfiestheaxioms",Rs,andJVh isunambiguouslyfixedasR=H[I-(1-I)

G"] (G"istheGinicoefficientwithinthepoor)

<proof> Becausethenumberofthepeopleabovethewelfarelevelofanindividua1, jinthe pooris"+1-i,

−24()−

Mea3uringPovertyTodayinJapan

"j(z,")=h+1-i

andifallthepoorpeopleearnthesamemcomey｡, then g｡==z-yD (6) therefore

R=A(z,")9..向("+1)/2

meanwhile, fromtheaxiom", (7)

（:)(箸）

良＝ (8) fromtheequations(7), (8) :

A(z,")=2/("+1)Mz

(9) therefore: 序 2

("+1)""Z(z-yi)("+'-i)

且＝ j＝I 1nthemeantime, theGinicoefficient,G"inthepooristransformableasfollows6) “ 的 申すＬ ｙ ｈ戸，］・Ｊ ｈ雨診］﹂１ β １ ２ 舟 ２ ’ 一 岬 Ｇ " ｈやｙ］封 Ｉ ２ ． 予 陶

=肝圭一

yi("+1-i)

("indicatesthearithmeticmean)

fromtheequationsi(jandiD, l R,= ("+1)"z

ﾄﾙ("+')+"2"(G"-"+1

)］

偽 or

"-H[1-('-II('-c"(Ffr)]

',

Making"intheequation"sufficientlylarge: Rs=H[I+(1-1)G"] 13 ForthePsdrawnoutasabove,Sensaysthatbyreplacing"withthetotalpopulation",andz 6)ThistransformationismadesignificantbySen[24] -241- 5

withtheaverageincomeofthetotalpopulation"0,thisbecomesH=1,I=0,andthereforeisthe conversionoftheinequalitymeasurementnamedGinicoefficientintothepovertymeasurement. Ⅱ−2 Takayama'sPovertyMeasurement TakayamacriticizedtheSen'sconclusiononthefollowingtwopoints: i)Strictlyspeaking, Sen'smeasurementequationiacannotbecomei3unlessthepoorpeoplearei㎡inityinnumber.

ii)TheaxiomMfornormalizationdoesnotavoidarbitrariness.SoRisunnamralforthecon-versionofGinicoefficient intothepovertymeasurement.However, thepoint ii)

isnotap-propriatewithrespecttodeductionofRs inthatthedeprivationuponwhichR,basesisdifferent fromPi.Afterall, itfollowsthatthereisadifferentviewpointbetweenSenandTakayamain capmrmgdeprivation.

Takayamaintroducedtheconcepty(z)*, "thecensoredmcomedistlibutionwhichiscutbya

povertyline"

inordertodeduceanewpovertymeasurementwhichisfreefromthetwocon-straintsmentionedabove.7)Thenwhathasbecomeclearisasfollows:

i)Takayama'smeas-urementPIissimplerthanRinitsinterpretation.ii)Onecanmanagewithlessinformation.iii)

ConversionofGini coefficient intopovertymeasurement isnaturalasfarasit isbasedon

Takayama'sdeprivation.Furthennore,anothersignificanteffectisproduced:bymeansofthe

censoredincomedistributionwhichisusedfordeductionofR,variouskindsofinequalitymeas-urementcanbemadeinterpretableaspovertymeasurement. Thatistosay,generalizationofpovertymeasurementhasbeenmade. Letusclarifyy(z)*andotherrelevantsymbols. ｊ 本 ｔ ７ ｙ ｌ Ｌ Ｊ 中 哩 弘 ｚ 染 一 一 一 一 ＊ 夕 ＊ ＊ ＃ １ 判 ｙ ｙ 舟 ｎ ｎ ｙ ｅ ｅ ＊ ゞ 出 伽 ｈ ｙ 忽 島 ｊ Ｌ く 逵 池 功 批 。 〃 〆 令 Ⅱ △ Ｆ 十 Ⅱ 坐 ＊ 凸 １ １ ・ １ 昼 Ｉ ｅ 心 ｖ 敵 一 一 Ｈ ＊ １ Ｊ 唖 ｙ “

Undersuchadistribution, theaverageincomeofthepoorpeople("z) is:

"""" F1yi*/"

jEs(y･hj

Theaverageincomeofcensoredincomedistributioncutbythepovertyline,(")is

鯛

"-Zyi*/"="""+(1-H)z

jEs(比中） Thecumulativeincomeratioofthepoorpeople,(｡)is ㈹ 7)Henceforth,unlessotherwiseindicated,weuse"｡"asamarkrelatedtocensoredincomedismbution −242 6

MeaSUringPOveltyTcdaymJapml ，＝帥盈／/’

l-'=(1-H)Z/"

⑰

(Definition)

Povertyismeasuredbymeansofthedegreeofinequalityofcensoredincomedis-tributionwhichiscutbyapovertyline. Bydefinition,PI isrepresentedasfollows:

PT=BZ"i(似一yj*)+C

⑱ JES(此酋） ”

Here,BandCareconstantsfornonnalizationand"jisaweightaddedto"anmcomeshortage

(β−yj*).Theninordertospecifythese,theaxiomswhichTakayamaemployedarethefollow-ingthreeinadditiontoSen's": AxiomJVT2 Thepovertymeasurementequalszero,whentherearenopoorpeople. AxiomRT Theweightaddedtoincomeshortageequalstotheordinalrankwelfarebe-tweenallthemembersofthesociety,thatistosayzｲﾉj="+1-j.

AxiomIVT, Whenalltheincomeofthepoorpeopleequalszero, thenpovertymeasurement equalstheratioofthenumberofthepoorpeopletothewholepopulation,thatis

tosay,ifyj*whichbelongstoS(y"*)iszero,thenPT=H,

[Theoremll]

Thepovertymeasurementwhichsatisfiestheaxioms",RT, IVT! andjVT2 is

unambiguouslydetenninedandbecomesGinicoefficientofthecensoredincome distributionwhichiscutbythepovertylme. <Proof>FromtheaxiomNT2: ⑲ C=0 Bysubstimtingi9forl3: Ｆ ＋ ｊ ＊ 伽 ノ ＊ 十Ｆ。 ｊ ｙ く く 似 ｚ 卸 〃 １ 申 申 や 全 蛎 や 省 恥 千 口 ｒ凸 巳 Ｅ Ｂ Ｂ 一 一 一 一 Ｔ Ｐ “ Here,

F=B("-2)Z"!

" jEs慨喉）

FromtheaxiomIVTI,whenalltheincomeofthepoorpeopleiszero, then"=2(邦一ﾙ)/",and

SOァ

Z""-2"｣,i"-""(";"÷1)

2 fE(Jロウ） j＝A＋l） ⑫ 243− ワ イ

From"and",

￨-"竿｡,晶州。

￨ -紬』

PT=B ⑬ Insuchcases,fromtheaxiomⅣTl， PT="/" From23and", B=2/("2) Bysubstimtinge$for":

F-('-#)('-f)

AIso,bysubstimting"forthefonnerequationin"

'’一‘≠告-蒜堯("+1-i)

...PT=GP “ 四 蝿 yj* ” Ⅱ−3 Kakwani'sPovertyMeasurement Kakwani'srelativePovertyiscalledTransfer-of-IncomeApproach(kakuwanil9).Sup-posethatincomexofapersonisarandomvariablewiththeprobabilitydistributionfunctionF

(x).Ifzisthepovertylevel(line),whichisassumedtobeknown,F(z)wiUbetheproportionof

poorpeopleinthesociety.Further,F(z),whichhasoftenbeenusedasapoveltymeasure,may becalledtheheadcountratio.If"isthemeanincomeofasociety,and"*themeanmcomeof personsbelowthepovertyline,theproposedpovertyindexstartsfromnextmeasurement,

P=F(z) -且ニー些一

鯛 幽 j wherePisinterpretedasthepercentageoftotalincomethatmustbetransferredfromthenon- poortothepoorsothattheincomeofevelyonebelowthepovertylinemayberaisedtoz.Inad-dition,zisgeneraUylessthan".If,however,z=",Pwillbeequaltotheproportionofincome thatmustbetransfeITedfromthegrouphavmganincomemorethan"tothegrouphavingan incomelessthanto/J,sothatbothgroupshavethesamemeanincome,whichisequalto".

Axioml : (Monotonisity)Otherthingsremainingthesame,areductioninincomeofaperson

belowthepovertylinemustincreasethepoveltymeasure. 8 −244−

MeasunngPovertyTodaymJapan Axiom2: (Transfer)Otherthingsremainingthesame,apuretransferofincomefromaperson belowthepovertylinetoanyonewhoisrichermustincreasethepovertymeasure. Kakwani'spovertymeasurementPksatisfyingabovetwoconditionscanbewrittenas,

ELEL[z一緯･g(G*)]

島＝ 醐 似

WhereGiniindexG*isusedasameasureoflncomeinequalityamongthepoor. (seeKakwani

⑫,Maedall)

m. ComparativeExamination

Letuscomparetheaxiomsystemssoastoshowthedifferencebetweenthetwomeasure-ments.First,Sen'sMisalsoemployedinTakayamaasit is. ItisRthatdiffers.Whilethe weightaddedtothemcomegapish+1-jinSen,itis"+1-jinTakayama・Ontopofthat, whileSen'sMisone,Takayama'saretwo,namelyIVT,andN". TakayamaexplicatedtheaxiomsystempresupposedbehindGinicoefficientinordertoshow thatRisnotanaturalconversionofGinicoefficientmtoapovertyline・Particularly, ifweputas

githedifferencebetweentheincomeofeverymemberandtheaverageincome("o),namelythe

incomegap,then: 列

gr="@-j'i, "｡=Zyi/"

“ fpl Here,thedegreeofinequality(M) isdefmedasfonows:

M="Z"' 段+E

el)

jE5(J") DandEareconstantsfornonnalizationand"f,weight.ForthisequationtobeGinicoefficient, thefonowingtwopresuppositionsarenecessaly: AxiomRG Theweightaddedtotheincomegapgiequalstheorderofeconomicwelfarebe-tweenthewholememberofthesociety,i､e. Zｲﾉj="+1-j. AxiomjVCI IftheincomeofaUthemembersisthesame,thenthedegreeofinequalityofin-comedistribution(M)iszero. However,althoughtheconstantEinGDbecomesObecauseoftheaxiomJVb],thisaxiomaloneis notsufficienttospecifyD.Soanotheraxiomisneededtospecifyit.Thus, thefollowingaxiomis

laiddownsothat"maybekeptwithintherange[0,1] :

AxiomAIG2 Whenthewholeincomeofthesocietyismonopolisticallyearnedbyoneperson andtheincomeoftheotherpeopleiszero, thenthedegreeofinequalityofin-comedistributionisl-1/". BytheaxiomJVb2,therightsideoftheequationGDbecomesD･"0"(〃−1)/2,whichequals(1 −245 9

-1/").Therefore:

D=2/("0"2)

蝿 Bysubstitutingthisforel):

;F2("+!-i)("0-"')

似,"‘Z("+'一j)(似0-y‘）

』‘＝ jEs(JI") 63

=1+-L--2

_{似iF2("'-i)y'}

〃 jEs(yﾛ） ThisleadstoM=G. NowletusseethecolTespondencebetweentheaxiomsystemofGinicoefficientandPT. First, theaxiomRTconcerningtheweightaddedtotheincomegapandtheaxiomRGconcern-ingtheweightaddedtothemcomesholtagecoITespondwitheachother.And,takmgaccountof thefactthattheaxiomsystemofPTisentirelytargetedatthecensoredincomedismbutiony*, itmaybestraightforwardtounderstandthatNb,andAKG2corTespondtojVT,andjV"respective-ly. Inthisway, itturnedoutthatPTismorenaturalthanRsastheconversionofGinicoefficient intopovertymeasurement.AIsoPTisestablishedwithouttheoperationk→｡｡,makingthe measurementsimplerinitsshape. AnotherpointonwhichPTisbetterthanPsisthatPTwassuccessful inexpressing,more

completely,therelativistpointofviewbyadopting"+1-iratherthan"+1-iasweight.Con-sequently, itbecamepossibletograsppovertyinrelationwiththewholesociety.8)Nextletus

transformPTintothefonnasini3ofPsforthepurposeofcomparingRswithPT:i.e.tofacto-rizeitintothreeelementsthatareindispensabletothepovertymeasurement. Ginicoefficientisknowntobefactorablemtointer-groupGinicoefficient,Gbandmtra-group Ginicoefficient,Gwj9) : G=Gb+Z隅．G雌ワ Here,"/mdicatestheweightwhichistheproductoftheincomeshareofthegroupj,whichis multipliedbythepopulationshare.Simmarly, Gj=Gb*+W･Gw G6* indicatestheGinicoefficientbetweenthepoorandthenonpoorinthecensoredmcomedis-tribution.G蝿＃ istheGmicoefficientwithinthepoorandWisweight.Thesearerespectively 8)Takingonlytherankingwithinthepoorasweight,Rseemstodealwithtruncateddistributionratherthan CenSOreddiStribution. 9)SeeRao[23]. −246− 10

MeasuringPGvertyTodaymJapan expressedasfollows

｝

’’

一 ■ Ｈ Ｈ ｌ ｌ ｌ − ＊ Ｑ ｗ “ Therefore “ GP="-'+H･'･GiU Bytheway, from(l7j,

(1−｡)Q=1−〃z/ji

Consequently,GPin"canbeexpressedas'0) :

PT=Gp=H[(1-')Q+.G"]

<殉 鋤

ComparethiswithRsin"WhiletheweightofRs/Hisland(1-1)thesumofwhichisnot

generallyl,theweightofPT/His (1-')and'.ThisisequaltotheweightedaverageofG"

andQandsointerpretationiseasier. Aswehaveseenabove,PTrepresentsthefonnoftherefinedRs.SoitshouldbenotedthatPT isbetterthanPsinsomerespects.'') Furthermore,ashasbeennotedinsection(2),PThas

anotherbeneficialeffect: i.e.bymeansofthecensoredincomedistribution, theconversionof thevariousinequalitymeasurementsintothepovertymeasl皿･ementhasbecomeavailable.For‐ example, ifweusetheexpectedutilitytypemeasurement,thenastheutilitarianpovertymeas-urementPofincomedistributiony,weget: 虹

PM--"Z,!M

韓 j＝l Specifyingthis"(y*)asfollows:

{!-W)I /i'-:i}

-蝿(器）

-〃(,'*）＝ E>0, E≠1 “ E=1 ヨー＝ Byputtingthisutotheoperationbelow,wecangetAtkinsonmeasurementonpoverty 1O)Bysuchresolution, itbecomesclearthatthetraditionalmeasurementanddispersionwithinthepoorarecon･ tainedinoneequation. 11)However,Sen'soriginalitytohavefirstclarifiedtheaxiomsystemlyingbehindGinicoefficientdeservesap･ preciation. 1l −247−

(AP).'2)

下

AP=1-[1-(1-6)P(y)] '/!-[ 6>0, 2≠l =1-""'[-P(y)] E=1 ㈹ Next,wespecify"(yi*)asfomows

-〃'=(帯)蝿(幕）

帥 FromthiswehaveTheilmeasurementonpoverty(乃):'3) TF=P 鋤 Also,

(張)'一‘

-"(yi*) ==

㈱

Inconsequenceofthiswecangetthesquareofthecoefficientofvariation(Cp)aspoverty

measurement. CP=PI/2 “ Lastly, letusillustrateSen'spoveltymeasurementRswithLorenzdiagram,whichisclosely relatedtoGinicoefficient.Sen[25]alsoshowsasimilardiagram.Butitisnotmmitivesoit

willbemoreunderstandabletotransformtheequationandthediagram, respectively, intothe onesbelow:'4) Rs=H[I+(1-I)Gw]

志[&Z(z-yi)/2+

H二二 ㈱ A h

ZZ

'"'-"' /4]

J ノ 12)ThisparameterErepresentsinvariableelasticityvalueofsocialsubstimtionofmdividualincomeinthecase wheresocialwelfareisrepresentedastheproductofinequalitydegreeandtheaverageincomelevel.IfE is approximatedtoO, thenthesocialwelfareeffectsoftheincometransferfromthehighincomebrackettothe lowincomebracketbecomeclosetoO,nomatterhowlargetheincomegapmaybebetweenthetwobrackets. That istosay, toincreasethevalue egraduanyfromOmeansthatrelativeimpor上anceofthelowincome bracketinsocialwelfarevaluationisgraduanyenhanced.See[1],[3],[4],[24],and[34].

13)ThismeasurementwasproposedbyH.Theilonthebasisofentropyconceptemployedininformationtheory. 14)PTmayalsobeillustratedbytheLorenzdiagrambuthereweomittedit,

−248− 12

MeasuringPove'TyTodayinJapan 蕗

K/:

"

O thepoor A F−＝言=忌引幸ｺ カ A

厩:AZ(z-｣'i)/' fi蕊謹:ZZ￨y,-Jf l /4

j画1 J ノ Fig.I:ThepovertymeasurementPSbyLorenzdiagram W.AFewFurtherlssues

Inthischapter, twoofthemost importanttopicsregardingthepovertymeasurementthat werenotconsideredinthepreviouschapterw皿bediscussed.Oneisthatthedegreeofpoverty acquiredbythetwomeasurementsdrawninchapterllbringsaboutnotthecompleteordering buttheso-calledquasiordering.'5) Theotheristheissueconcerningtheestablishmentofthe povertyline,whichispresumablythemostimportantpieceofinformationinthecaseofactually measurmgpoverty. N-1 QuasiOrderingofPovertYMeasurement

AsSen[24]andDasgupta-Sen-Starrett [7]argue,theorderingbyLorenzsuperiorityin

inequalitymeasurementbringsaboutthequasiordering'6) : i.e.whenthesocialwelfarefunction 15)Whilecompleteorderingistheorderingthatsatisfiesrenexivity,completenessamdtransitivity;quasiorder-ingistheorderingthatsatisfiesonlyreflexivityandtransitivity. 16)Foranarbitrarypairof incomedistributiondata,x,,andxB,witheachLorenzcurvedrawnonthesame plane,iftheLorenzcurveofxAnevercomeslowerthanthatofxB,thenitisrepresentedasxBpFSEW,which reads,"DistributionxBisLorenz-exceededbydistributionx｣4,"or,"DistributionxALorenz-exceedsdistri-butionxB. (DistributionxAisLorenz-superiortodistrireads,"DistributionxBisLorenz-exceededbydistributionx｣4,"or,"DistributionxALorenz-exceedsdistri-butionxB.)" IfxBp謁閑andnotxAp巧轟. thenit is representedasxB<A,whichreads"Distributionx,istronglyLorenz-exceedsdistributionxB. (Dismbution x｣isstronglyLorenz-superiortodistributionxB.)"

definedwithrespecttoanarbitralyincomedistributionvectorissymmetric'7) andisthequasi-concave'8' increasingfunction,thenanysocialweMarefunctionmayequallybeorderedwiththe Lorenzsuperiority.Therefore,inthecasewheretwoarbitraryLorenzcurvesintersectwithone another, there isapossibilityofdifferentorderingsthroughvariouskindsofmeasurements

whichsatisfvtheabovetwoconditions.響 Asismentionedinthepreviouschapter,wehavesucceededinobtainingnumerouspoverty measurementsbytheapplicationofthecensoredincomedistributiontoeachinequalitymeas- urement.Now,letusapplythepropertyofquasi-orderingoftheLorenzmeasurementasthein-equalitymeasurementtothecensoredincomedistributionwhichiscutbythepovertyline.

Assumethatundertheincomevector",thesocialwelfarefunction,F(y,,....y")issymmetric

andisthestrictlyquasi-concaveincreasingfunction.Giventhepovertylinehere,thequasi-or-deringofpoverty,RQisdefinedasfollows:

(Definition) ForallF, ifF(x*)≦F("*),then"*RQr*.Thisbinominalrelation,"*RQx*

meanseitherg*isLorenz-superiortoJr*orJr*and"*aretheequaldistribution.Additionamy, it

hasbeenmadeclearbySen[24] thatRQsatisfiesreflexivityandtransitivity. NextwewillshowthateveninthecasewheretwoLorenzcurvesbythecensoredincomedis-tributionintersect, theLorenzsuperiorityholdsinonecaseanddoesnotinanother,depending

onwhetherthepointofintersectionofthecurvesislocatedbeforeorafterz.Thatis,in(A)of

Fig.II,ifoneistoindicatetheLorenzsuperioritybycensoredincomedistribution,thenitis

shownbythecurveb,whichisdrawnwithintheareaofthecurvea.Moreover,evenifthe

curvesintersectatthepointonthepovertyline, i.e.atthepointonJEorhigher, thisdoesnot

havemnuenceontheorderingofpoverty.Ontheotherhand,inthecasewherethecurvesinter-sectatthepointonthepovertylineorlower,asin(B)ofFig.1,Lorenzsuperioritydoesnot

holdtrue.

17)Symmetryisstatedasfollows;Assumingthatallelementsofaset A" (xI ,…xn) isreorderedmtoえ閲(xp' ,". xpn), if JI" (xI．…xn)=スn (xP',….Xpn),thenitissymmemc.

18)ForwelfarefunctionFtobequasi-concave, thesmallervalue,whichisobtainedfromthewelfarelevels whichrespectivelycoITespondtothedismbutionsxAandxB, isnecessarytobesmallerthanorequaltothe socialwelfarelevelwhichcorrespondstcmeweightedaverageofthetwodistributions:i,e.foranarbitralyr (0<j<l) , itmustbeMin[F(xA),F(xB)]三F(txA+(1-t)xB).Ifonewantsittobestronglyquasi-con-cave,thentheequalsignistakenaway. -250-14

MeasuringPovertyTodayinJapan 巳 B

］

(B) (A) 」 』

諺

諺

･−−−a ･−−−a O E AO E A Fig．ⅡLorenzsuperiorityofcensoredincomedistributionrepresentedbyLorenzdiagram Ⅳ−2 ThelssuesConcerningtheEstablishmentofthePovertyLine Sofar,wehavetakenthepovertylineforgranted.However,determiningthepovertylineis themost importantfactorinregardtomeasuringthedegreeofpoverty・Sointhissectionwe willfocusontheissueofdetenniningthepovertyline. Takayamadefinesthepovertylineas "theincomelevelonwhichpeoplewithalargermcome reservejudgmentofpeoplewithrespecttothefluctuationofincome,asfarastherankingof

povertyisconcerned."'9)Heholdstheviewthatconsciousnessofpovertyisultimatelydominat-edbyrelativedeprivationatleastinthedevelopedcountries. Incidentany, inpastpovertyresearches,thereseemtohavebeentwomajordirectionsines-tablishingaproperpovertyline: i､e・

thedirectionoftheabsolutemeasurementandoftherela-tivemeasurement.Wewillconsiderthembelowonebvone.ご Theabsolutemeasurement isacquiredbycalculatingthestandardoflivingrationanyonthe basisoftheknowledgeofdomesticsciencelikedietetics,convertingitintoprices,andpilingup allofthem.Here,thestandardoflivingissomethingnecessaryforretainingmindandbodyand islowerthanacertainobjectivelytargetedbasicstandardofliving.Thisprocessisalsocalled themethodofthecostoflivingonthetheoreticalbasis.Themarketbasketmethodisthemost typicalcalculationamongthesimilarmethods.Themethodistoshowthenecessalygoodsand serviceforleadingsomefixedstandardoflivmgbyputtingthemintothebasketasanamountof materials.ThetermissaidtohavebeenadvocatedbytheLabourPartyintheUnitedKingdom inl923. 19)CitationfromTakayama[32] 251- 15

However,thereseemtobesomemajorproblemsinthismethod.Thefirstis "thetargeted

万

fixedstandardofliving.

Asforfoodexpenses, thetargetamountandmoneyaretheoreticallycalculablefromphysio-logicalnecessity.Butthereisnobasistobefoundonother items.Clothing, shelterandother aspectsof lifearelargelydependentontheculturalandsocialbackgroundsophysiological necessitycannotsimplydetenninetheamOuntofmaterialsandmoneyinthatitwouldbeunsuit-abletodosoforacmallife.

Asecondproblemisthatifthestandarddetenninedbyscienceisinfeasibleandisolatedfrom theacmal life, thentheresultofnaturalsciencewiUpracticallycometonothing.

Athirdproblemistheoneconcerningtheratiobetweenitemsofexpensewithrespecttothe standardamountofmoneythathasbeenaddedup.Thiscalculatingmethodisrationalwithin eachitemofexpense,buttheamountofmoneyistheadditionofitemsofexpensewhereeach itemiscalculatedindependentofotheritems.Thereforethereisapossibilitythattheratioofi-temsofexpensecalculatedbythemethodisincompatiblewiththerealratio. Therelativemeasurementiscalledthemethodofcostoflivingonthepracticalbasis.Onthe occasionofpresentingacertainstandardofliving,oneanalyzesthefamilybudgetputundercer-tainconditions,e.9.occupation,thenumberofpeoplemahousehold,andtheirage,onthebasis ofactualdataofrevenueandexpenditure,withtakingahouseholdasaunit.Ontheotherhand, oneidealizesthestandardofliving, findsoutthefamilybudgetwhichisconsistentwiththis idealizedstandardoflivingfromthefindingsofthefamilybudgetsurvey,andpresentsitinthe formofthehouseholdexpenditure.Thismeasurementiscalledthemethodofcostoflivingon thepracticalbasisbecauseitisthesociallyfixedstandardoflivingthatisdecidedfromtheac- malhouseholdphenomena.ThewelfarestandardusedinchapterVisthislnethodofcostofliv-ingonthepracticalbasis. Thereisacompromisebetweenthecostoflivmgonthetheoreticalbasisandtheoneonthe practicalbasis:Engel'smethod.First, thismethodcalculatesthefoodexpendimrebasedonthe resultofdieteticsintheprocessofcalculatingacertainstandardofliving.Sofaritisthemethod ofthecostoflivingonthetheoreticalbasisbecausethefoodexpenditureisaddedupaccording tothenecessaryintakeoffoodindietetics.ThenthefoodexpenditureisdividedbytheEngel's coefficientobtainedbyafact-findingsurvey,resultinginthetotalcostofliving. Inthenextchapterwewillcalculatethelevelingcoefficientofredistributioneffectbythe povertymeasurementinordertogiveanoverviewofredistributionpolicyforthepoorconduct-edbythepoliticalauthoritiesinthepast.Wewillemploythesamestandardamountofmoney forwelfareasTakayama[33]used: theonedesignatedbytheLivelihoodProtectionLawof theMinistryofHealthandWelfare･AsTakayamanotes, thisisbecausethereis,atleastinthe 16 −252

Mea5uringPGvertyTodayinJapan developedcountries,anunderstandingofdeprivationthatitissomethingrelative,andisalsobe-cause, inspiteofthedifferenceontherelativedeprivation,therelativisticideasarerenectedon theaxiomsbehindthepovertymeasurementsofSenandTakayama.

V･ SomeCalculationsandPovertyinJapan

Asacommonmethodofsearchingforhowmuchredistributivefunctionofincomethetaxsys-temhas, thereisamethodinwhichonecomparesthedegreeofmequalitybeforeandafterthe taxationandcalculatestherelativerateofchange・ItisusuallVcalledtheredistributionratio.20) IfoneusesGinicoefficienttomeasurethedegreeofinequalitymincomedistribution,then,put- tingtheGmicoefficientbeforeandafterthetaxationasGbandGa,respectively,theredistribu-tionratiO2o'is:

,＝旦血二旦吐

Gb Thelarger｡becomes,thehighertheredistributioneffectoftaxationbecomes.Therefore,by calculating.duringacertainperiodoftimeandexaminingthechangesinthesimation,one mayobservetheeffectoftheincomeredistributionpolicy. Inthischapter,wewillobservetheeffectsoftheincomeredistributionforthepoorconducted bythepoliticalauthoritythroughtheapplicationof,tothepovertymeasurementRs,before andaftertheredistribution. Bytheway,therehaveonlyexistedtwocasestudiessofar,whereRsandPTareemployed, whicharetheonesaboutMalaysiabyAnand[2]andaboutJapanbyTakayama=Hamada [32].Thefonnerwasbasedonthedataconductedonlvinl970.Thelatterbasesitsdataon “

protege(e)nationwidegeneralsurvey,"whichistoodistincttoobtaindistributionalstatistics

ofbeforeandaftertheredistribution. Infact, somepointoutthatdistributionalstatisticsof Japanareconsiderablylaggingbehindthoseofotherdeveiopedcountries.2' ' Especially, those

ofthelowincomebracketarerougheveniftheyareobtainedatall.Weconjecturethattherea-sonwhyTakayama=Hamadaemployed"protege(e)nationwidegeneralsurvey" isbecausea

finedistributionalstatisticsofthelowincomebracketwerenecessary.Butitshouldbenoted that, forthedistributionalstatisticsofthelowincomebracket,dependingonlyonthediStribu-tionoftheprotege(e) isalittleproblematic・Becausetheprotectedfamiliesareexpectedtoin-cludealargenumberofthedisabledfamilies, thesingle-parentfamilies, andtheagedfamilies, andthiswouldresult inastrongbiasinthedistribution. Inaddition, impOrtantpiecesofinfOr-mationliketheredistributionratio,whichistobefoundinthischapter,wouldbeunavailable.

20) Somesimplysay・changeratio" [18], [19]

21) Seelshizaki [l 1].

Inthispaper, concedingsomerougmess,webasethedistributionalstatisticson"Income

RedistributionSurveyReport (S加如陶"-勤め""""-C加蟠α)"oftheMinistryofHealth,Labour

andWelfare. This"IncomeRedistributionSurveyReport"wasstartedinl96222' andhasbeenconducted andreportedfivetimessincethen: 1962,1967,1972,1975,1978,1981,1984,1987,1990,1993, 1996, 1999,2002,2005.Thereportaimsatclarifyingthesocialsecuritysystemandthestateof theaffairsofincomeredistributioneffectthroughtaxwithineachincomebracket・ Italsoaims atcapillringthestateoftheaffairsofincomeredistributioneffectthroughsocialsecuritysys-tem.Thereport isthereforesuitableforfmdingtheredistributionratio,butwiththepovel-W linegiven,divisionoflowincomebracketintostrataisundoubtedlylimitedfrom3to6classes. SointhecaseoffindingGinicoefficientofthelowincomebracket,wedecidedtoacmallydraw theLorenzdiagraminterpolativelyfortheinsufficientpart.23) Concerningtheissuesonfixingthepovertyme,becausePs,PTpresupposerelativepoverty,

asmentionedinthepreviouschapter,weuse"welfarecritelion"

inaccordancewiththeLiveli-hoodprotectionLawofMinistlyofHealthandWelfareforthepurposeofemployingthemost availabledatawhicharenearesttotheconcept.Thedataarealsoemployedinthecasestudies

inTakayama=Hamada.The"IncomeRedistributionSurvey" iswrittenintheannualamount

ofmoneysothepovertylineisdetenninedbymultiplyingthecriteriamoneybytwelve. ThewelfarecriterionoftheLivelihoodProtectionLawwasestablishedintheoutlmeofthe

urgentsupportivemeasuresforthepoor"inNovember,1945,andwasdependentonthesubjec-tivejudgmentoflocalwelfarecommissionersfromthefirstoutlinethroughtheseventh.From

theeighth(August,(1948)) throughthesixteenth,(1980),themethodofthecostoflivingon

thetheoreticalbasis (themarketbasketmethod)wasadopted.Thedefectsinherentmthe methodofthecostoflivingonthetheoreticalbasismentionedabove,however,becamenecessa-rytobesolved;andsothecalculationswereconductedbyEngel'smethodfromtheseventeenth outline(April,1961)andhavebeenconducted,ml965andthereafter,withthewelfarecliterion keepingupwiththeimprovementoflifeofthecommonhouseholdofworkers,towardreducing

thegapbetweenthelifeofthepoorandtheworkers (infonnallythough, therateisabout60%

oftheaverageamountofexpenditureofthecommonhouseholdofworkers) . n Thetitleofthereportofl962is"socialsecuritylevelbasicsurvey. Afterinterpolatingfreehand,weobtainedthearea,byusingaplanimeter 22） 23） 254 18

MeasuringPoveITyTodayinJapan Tabiel ExamplesofPovertyLine Year Criteria amountof

money(yen)

Theratio ofincrease fromthe prevlousyear Criteria amOuntof money(yen) Theratio ofincrease fromthe 由 prevlousyear Year ｎ Ⅱ Ｕ ﹃ ｌ Ｌ ｎ 〃 白 心 ﹁ Ｊ ４ ４ Ｌ Ｐ Ｒ Ｊ ハ ｈ ﹀ 再 ｊ ｊ ︵ Ｈ Ｕ ｎ ｕ Ｊ ︿ Ⅱ Ｕ 勺 Ｉ 上 ハ ノ 白 小 歪 Ｕ ４ ４ ４ 一 晩 Ｊ 行 ｈ ﹀ 再 Ｊ Ｉ ｎ ｘ ｕ ｎ Ⅶ Ｊ ｎ Ⅱ ︺ Ｇ Ｉ 且 戸 栖 ︺ か ｈ ﹀ か 仇 Ｕ か れ Ｕ ︿ 恥 Ｕ ハ ｈ ︺ ハ 恥 Ｕ ︿ ｈ Ｕ ハ 院 Ｕ 戸 院 Ｕ 弓 Ｊ Ｊ 再 ｆ Ｊ 茸 Ｊ １ 毎 Ｊ １ 句 ｆ １ 月 Ｊ Ｊ 再 ｆ ｌ 弓 ｆ ｌ 可 ｊ ｊ 房 ｊ ｊ ︹ ｘ Ｕ ｎ ｘ Ｕ ︿ ｕ ゾ タ ７ ？ ７ 夕 ７ 夕 ７ ７ ７ Ｆ ７ Ｉ ７ 夕 ９ ？ ？ ？ ？ ？ １ 8，914 10,344 12,213 14,289 16,147 18,084 20，662 23,451 26,500 29，945 34,137 38,916 44，364 50,575 60,690 74，952 84,321 95,114 105,577 114,340 124,173 134,976 1982 ’83 ，84 ，85 ’86 ，87 ，88 ，89 '90 '91 ，92 ，93 ’94 ，95 ，96 ，97 ，98 ’99 '00 '01 ，02 ，03 143，345 148,649 152,960 152,960(124,487) 126,977 129,136 130,944 136,444 140,674 145,457 149,966 153,265 155,717 157，274 158,375 161,859 163,316 163,806 163,970 163,970 163,970 162,490 ２ ７ ９ ９ ０ ７ ４ ２ １ ４ １ ２ ６ ０ ７ ２ ９ ３ １ ０ ０ ９

句■■甲○甲凸。■凸廿山口■？■■■。■。■

６ ３ ２ ２ ２ １ １ ４ ３ ３ ３ ２ １ １ ０ ２ ０ ０ ０ ０ ０ ０ 16.0 18.0 17.0 13.0 12.0 13.5 13.5 13.0 14.0 14.0 14.0 14.0 14.0 20．0 23．5 12.5 12.8 11.0 8．3 8．6 8．7 Data:ComposedofdatafromP"ffgf(2)Mz"0fzz""eG2fzE池ノS"γ〃妙(HI-HOGOSHZI-ZEA【KOKびおSEI CHCUSA). Tabien

CalculationExamplesofPsandPT. (ExamplesofJapanandMalaysia)

Year H(%) I(%) F(%) Gw PT Gb*/GD(%) Ps 1960 ，67 '71 ，75 １ １ 弓 ﹄ ワ ﹄ ワ ｊ ｌ 88 08 23 55 0.311 0.524. 0.535‘ 0.789' 0642 0484 0530 0551 96．8 98．2 98．8 98．3 ４ ８ ７ ７ ■○○○ ５ ８ ３ ３ ５ ６ ７ ７ l l O l 32 19 80 24 ０ ０ ０ ０ ０ ０ ０ ０ 082 060 064 071 1970* 40．2 14.5 8.3 0.213 0.200 Notes:1970*isanexampleofMalaysiabyAnand. Gb*=H(1-')I,Ginicoefficientbetweenthepoorhouseholdandthenon-poorhousehold indistributionv*苧 F:Theratioofthecostwhichisnecessalytogetridofpovertytotheincomewhichis earnedbythenon-poorpeople. Source:NoriyukiTakayama,EcD720""cA"α〃scsQf"""α"砂fromToyoKeizaiShinbunsha[33] −255− 19

CalcuIated by author usingl

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Sur

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'

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R

e

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(Ministry

of

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,

Labour and WeIfare)

Notes:Superiorletters

B,A

indicate

beforc、and

after redistribution

,

respectively

.

:Redistributionincome =Initialincome-

(

taxes+socialsecuritypremiums

)

+socia1

sccurity benefits.

:For

socialsecurity benefits

, t h e

state of

thc、

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the

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in

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,

is noted.For

in-kind

m

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m

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in

-vestigated.And

the

amount

of

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is estimated on the basis of thcsc figures

.

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RelativePovertyinJapan (CalculatedbyAuthor)

("･ F 0.3 野 ） (theredistributionratio｡) 80% 70% 1 60%

／／

_／

ノ ノ 50% 一 一一 字︷角野晩こ﹃ヨ輻畠︺ロぞ、凡。︾﹃﹃︵呈画ぞ、言濤邑印昌 O~15 40% 30%

，／

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’ '62 ’ '62 ｜ ,67 ｜ ,67 ｜ ､72 ｜ ､72 ’ '75 ’ '75 ’ '78 ’ '78 棚81棚81 ’ '84 ’ ’84 Ⅲ87Ⅲ87 ’ '90 ’ '90 '93'93 ､96､96 ’ '99 ’ '99 ’ 2002 ’ 2002 0．0 0 -10% ｆ ｒ ﹄ ｒ Ｊ − Ｉ ’

’

一一曙−−Fぜ−

一一啓一F¥ −−−

噸卜

の -20% -30%

l ) ｡ isrel)resentedbytherightscale;RAPEFarcrepresentedbytheleftscale

2 )ThedataOnl952iSinCOmplete,andtherefOrecanbemiSleading. 陸 一

Theyearlytransitionsofthecriteriaamountofmoneyofastandardhousehold(consistingof 35-year-oldmale,30-year-oldfemale,9-year-oldmale,4-year-oldfemale,withthefirst-rate pieceofland)areshowninTablel・Thesummaryofouranalysisisasfonows: 1 . ContrastingtablenandTablem,althoughbeingalittledifferent, theyearscompared arepracticallythesameexceptforthecaseofl978inTablem.Comparethentheratioofthe

poorhouseholdstoallthehouseholds,head-countratioH,andwehavel2.2%inl962inTable

m,whichisclosetoll､88%inl960inTableⅡ.ButafterthatthevaluesinTablemvaryfrom 4tolOpomtsincomparisonwiththosemTableⅡ、 2.Letusseenextthevaluesofpovertygapl・WhilethevaluesmTablemmcreaserapidly from55.4%to73.3%,thoseinTablemaremosdyat30%levelexceptfor56.4%inl962.The differencebetweenthevaluesseemstohaveresultedfromthenatureofthedatabecauseitis

theprotege(e)householdsthatrepresentthepoormTablen.Ifweseethecompositionofthe

prote96(e)households, thenwefmdthatthedisabledandthesickoccupyapproximatelyhalfof

theprotege(e)householdsinl975・Takingtheelderlyandthesingle-parenthouseholdsintoac-count, thevaluebecomesover30%.24)Thereforetheratioof

"thehouseholdswithoutabread-winner" totheprotege(e)householdsthatcontamthemisabout80%in1975.Asaresult, the

valueslinTablenseemtobeoverestimated.

3 ．Accordingly,thevaluesofG"inTablenarequitehigh: theyrapidlyriseupfromO.31to

0.79.Thisisalsotheconsequenceoftheshalpriseoftheratioof "thehouseholdswithouta

breadwinner" totheprot6ge(e)householdsthatcontainthem.

4.ThepovertyindexRsmTablembeginswithhighvaluesinl962andshowsratherhigh valuesml975again.AsforthesharpriseoftheRsvalueofl975, itisclearthattheheightenmg ofthewelfarecriterionisreflectedinthevalue, fortherateofincreaseofthevaluesfor 1974andl975inTableIarehigher--i.e.20.0%and23.5%,respectively--thanthosefor otheryears.Ajumpintheconsumerpricesaftertheoilcrisisintheautumnofl973exerted

stronginnuenceonthelowincomebracket,especiailyonthelifeoftheprotege(e)households,

andsothewelfarecriterionwasrevisedseveraltimesmeachofl973andl974.Inanycase,it seemstobeveryimpoltanttoconsidertheinfluencewhichtheeconomicconditionsatthetime hadonthepovertyindex.

5.Lastly,letusexaminetheredistributionratio.Thevaluehitsbottomwithl6.7%in

1962andrisesrapidlyinl967.Afterthat,thoughitsamplitudeiswide,itshiftsupanddown around20%.LetuscomparethiswiththelevelingcoefficientforaUthehouseholds.Each coefficientfroml962isll.8%,12.6%,11.4%,6.5%and5.7%.25)Theincomeredistribution 24)SeeTakayama[33]. 25)Theyareeachobtainedfrom"""zER"fsか釣卿蜘ﾅzS脚翻り −258− 22

MeasuringPOvertyTodayinJapan effectonthepoorismorethanthatonanthehouseholds.Amorespecificeconomicpolicythat wnlbringaboutsuchaneffectstinneedseconomicconsiderations. m｡ Conclusion Inthischapter, Iwillstatesomefindingsthatresultedfromthediscussioninthispaperasa whole,andmakesomecommentsabouttheissueofpovertymeasurementsurveys. Inchapterm,thenewmeasurementsproposedbySen,TakayamaandKakwaniwerecom-paredandexamined.Asaresult,althoughSen'soriginalityinclarifyingtheaxiomsystemOf Ginicoefficientandcreatinganovelmeasurementtoovercomethedefectsinherentintradition- almeasurementdeservespraiseitturnedoutthatPTissuperiortoRsinsomerespectsbyin-troducingthecensoredincomedistributionwhichiscutbyapovertyline.Thatis,PTisbetter

thanRsintermsofthefollowingthreepoints:

i)PTneedslessinformation.ii)Bypresuppos-ingadifferentaxiomsystemfromRs, amorenaturalconversionofGinicoefficient intothe

povertymeasurementbecameavailable・ iii)Bymtroducmgthecensoredincomedistribution, copiousinequalitymeasurementcametobeusedasthepovertymeasurement.Additionally,a morestraightforwarddiagramofRswaspresentedattheendofchapterm.

InchapterV,weshowedsomecalculations,usmgdifferentdatafromTakayama[33].Asa

result,thefollowmgpointsbecameclear i)Itisproblematictoletonlytheprotege(e)

representthepoor.ii) Inconsequenceofusingthedataof"IncomeRedistributionSurvey

Report," thefollowingresulted:i.e・amongthemeasurementsHJ,G,whichareresolutionofR

especiallyGandrturnedouttobemuchdifferenthomtheanalysisofTakayama[33],and

becamerelativelyclosertotheanalysisofthedevelopingCountries[Anand].iii)PSitselfisnot

muchdifferent. iv)Althoughtheamplitudeiswide, theredistributionratioisalwayshigher thanthecoefficientofallthehouseholdsandthesubsequentredistributioneffectonthepoor wasfoundtobelarge.

NowletusanalyzeTablem,titled :RelativePovertymJapan'.PsBwhichstandsforSen's

measurementofinitialincomedistributionhasincreasedbyoverO.lOinl975,sincel980ithas beenoverO.10.Themainreasonmightbethedefinitionofinitialincomeusedinthissurvey,as itdiffersfromtheothersurveyssuchastheU.Smcomesurvey.Forexample,Theinitialincome ofUSincomesurveyincludespensions,however,theincomeredistributionsurveyinJapandoes nOt. Onetheotherhand,altoughinl975andl984,Pg'irregularlyshowedhigherfigures,ithas beenstablebetweenO.05and0.06.ThedifferenceofthevaluesofPsBandPgkappearsinthe formoftheredistributionratio.inrightcolumnoftablem.Sincethelatterhalfofl980s,the redistributionratioincreasedbyapproximately60%,andithasbeenstableupuntntoday. In 23 −259−

anycase, thedegreeofrelativepovertyinJapandoesnotseemtoberisingifwenmitourcon-siderationtoredistributionincome. Finally,summarizingtheremainingissuesaboutpovertymeasurement,wehavethefollowing findings: i)Althoughweencounterdifficultyaboutestablishmentofpovertylineandavailabil-ityfordistributionstatistics, internationalcomparisonusingthenewpovertymeasurementwill beexpectedtoproducesignificantresults.ii)Withthe"""eRedis""蜘〃S況荊ﾉ鋤}R"0", the redistributioneffectofthepovertymeasurementofvarioussocialsecuritybenefitswmbecal-culable. iii)Usingotherinequalitymeasurementsbycensoredincomedistributionwillenable ustoconductpositiveresearchesmabroaderarea:e.g.iftheLorenzcurvecrossedbelowthe poveItyline,thenwewouldbeabletoemployAtkinsonmeasurementaspovertymeasurement. References [l]Aoki,M. 1979.D酎鰄”蜘祁TIJEoFy.Tokyo;Chikuma-Shobou(inJapanese). [2)Anand,S., 1977.AspectofPoverty.MM""sAz,R"j"ﾉqf"cOjwe""W""",23(1). [3]Atkinson,A.B.1970,OntheMeasurementoflnequality.""wizIQfEcり抑0"ziCTjZ"jfy, 2(3).

[4]Atkinson,A.B. 1975,TheECowo"ziCs"""""秒 Oxford;OxfordUnivPress

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