WORKING PAPER SERIES - 滋賀大学

1 WORKING PAPER SERIES ugust 2002 WORKING PAPER Government Deficit, Public Investment and Public Capital in the Transition to an Aging Japan by Ryuta Ray Kato August 2002 Faculty of Economics SHIGA UNIVERSITY 1-1-1 Banba, Hikone, SHIGA 522-8522, JAPAN ,PublicInvestmentandPublicCapitalintheTr ansitiontoanAgingJapan(AFullVersion)Augu st2002 RyutaRayKatoFacultyofEconomicsShigaUnive rsity,JapanandManagementSchoolImperialCo llege,UKForthcominginJournaloftheJapanes eandInternationalEconomies ,PublicInvestmentandpubliccapitalintheTr ansitiontoanAgingJapanAugust2002 RyutaRayKatoAbstractThispapertirestoexam inethee ,publicinvestment,publiccapitalandpublic pensionpoliciesonthetaxburden, ,thusthehighesteconomicgrowth, , , , , , ,thispaperalsopresentsnumericalresultsof thee ectsonfutureconsumptiontaxrates,taxburde ns,socialsecurityburdens, ectsofanintroductionoftechnologicalprogr essaswellasofine ,publicinvestmentandpubliccapitalontheta xburden, , ,thefuturesched-uleofpublicinvestment,or thereformofapublicpensionscheme.

2 Shouldbeevaluatedintertemporally,sinceth esepoliciesinvolveredistributionale ectsondi , , , , , ectsofgovernmentdebtpoliciesofJapanareco nsidered, ectofdebtpoliciesamongdi , ,thus, , ,ifanintergenerationalaspectoffuturegove rnmentpoliciesisexam-1 ThispaperexpandsKato(2000,2002b)byincorp oratingpubliccapitalintothemodelandre-ex aminesthee setthee ,thesethreechannels( ,publicpensionscheme,andpubliccapital) ,thee ectsofgovernmentpoliciesaredi erentamongeachfuturegeneration,aspointed outbyAuerbachandKotliko (1987). , ,sinceeco-nomicpolicieshavedi erente ectsamongfuturegenerations,theevaluation mightnotbestraightforward, ,economicpoliciesshouldultimatelybeevalu atedbasedonutilityofdi , , , , ,thus, , ,whenerationstofuturegenerations, , ,theconsumptiontaxrateisalsothehighestin thefuture, ,lifetimeincomeisnecessarilynotthehighes t,andsuchapolicyisnotpreferableifthepoli cyisevaluatedonutility, ,andSection6examinesthee ectofanintroductionoftechnologicalprogre ssaswellasofine ,publiccapitalinJapan, ectsoftheJapanesegovernmentdebtpolicyhav ebeendiscussedindi , ,sincetheirmainconcernswerewiththeevalua tionofthepastpoliciesorthesustainability oftheJapanesegovernmentdebtpolicybyusing thepastactualdata, (1979) ,Asakoetal(1993)andNakazato(2000) (1993)

3 Tested6thehypothesisbythePhillipsandPerr onunit-roottest,theCochranestatistics,an dHall s(1978) (2000)testedthehypothesisbyCampbell s(1987) ,Asakoetal(1993),FukudaandTeruyama(1994) ,Kato(1997),DoiandNakazato(1998)andDoi(2 000) , (2000)recentlypresentedseveralproposalsb ysimulatingthee (2000,2002a,2002b)examinedthee erenceofthispaperfromKato(2000,2002b)isa nincorporationofpub-liccapitaltocomprehe nsivelyexplorethee erentfromKato(2002a) ,whichwasnotavailableinKato(2002a). (1989a,1989b),therehavebeenseveralpapers toestimatethee (1990)discussedthesociallyoptimallevelof publicinvestmentinJapan,whichisbasedonAr rowandKurz(1970), (1995)alsoestimatedtheoptimallevelbyusin gthedataoflocalaswellasurbanareasandheco ncludedthatthepubliccapitalinlocal(urban )areaswouldbehigher(lower)thantheoptimal levelduetotheheterogeneityof7politicalpo werindi (1993),Asakoetal(1994),OgawaraandYamano( 1995),andYoshinoandNakano(1994,1996)esti matedthee ectofpubliccapitalontheprivatesectorprod uctionarewellsummarisedintwoexcellentboo ksbyYoshinoandNakajima(1999)andMitsuiand Ohta(1995) ,andtheestimatedparameterswillbeusedinth ispapertoexaminethee (2002a)

4 Explicitlyincorporatedpubliccapitalintot heoverlappinggenerationsmodelinordertoev aluatethee ectsofanagingpopulation,and/orthee (1983) ectoftaxpoliciesandpublicpensionpolicies ofJapanbyHommaetal(1987),andtheexistings tudieshaveexpandedAuerbach/Kotliko modeltodiscussseveralgovernmentpoliciesi nthetransitiontoanagingJapan(Iwamoto(199 0a),Iwamotoetal(1991and1993),AtodaandKat o(1993),andKato(1998)).HattaandOguchi(19 99) (2000,2002a,2002b)expandedKato(1998) , ,andthetotal3 SeealsoProfDoi / (1996), ,thee (2000,2002b)expandedKato(1998)inthefollo wingtwoaspects:Theoneaspectwasthatinthes imulationanalysisofKato(2000,2002b) (1998)wastodiscussthee ectofthetransitionofanagingpopulationinJ apanthroughtheexistingpublicpensionschem e,littleattentionwaspaidtothee (2000,2002b).

5 ,theJapanesegov-ernmentdebtpolicyhavetob eevaluatedbytakingintoaccountthee ectofpubliccapitalonfuturegenerations,if theintergenerationale , erentfromKato(2000,2002b) ,awagetaxwasalsoconsideredinKato(2000,20 02b) ,thee ,butbecauseitinvolvesmorecomplicatede ects,whichareoftendi ,thedi cultycannumericallybeovercome,andmorerea listicimplicationregardingthee ,whichconsistsofasubstitutione ectaswellasanincomee ,thesetwoe ectsfunctionoppositelytoeachother,andthu s,theoveralle ,whenlaborisassumedtobeexogenouslygiven, thee ectofthechangeofawagetaxrateisstraightfo rwardaslongasthegoodsarenormal,sincether eisnosubstitutione ,laborisassumedtobeexogenouslygiven,anda consumptiontaxisonlyconsideredinordertod eepentheanalysisbychangingseveralassumpt ionssuchasthedegreeoftechnologicalprogre ssandthedegreeofe erenceofthispaperfromKato(2002a) (2002a) ,whichwasnotavailableinKato(2002a)

6 , , , ,wheretimeisassumedtobediscreteeveryyear ,therearethreetypesofagents,households,. .rms, :Households:Eachgenerationisassumedtohav ethesameincome,mortalityrate, +1;jistheconditionalprobabilitythatahous eholdofagej+20survivestoagej+21,theproba bilityofahouseholdofage21surviving10unti ls+21canbeexpressedasSs=s 1Yj=1qj+1;j;whereqj+1; ,theexpectedutilityatages+20wouldbeU=80X s=1Ss(1+ ) (s 1)C1 1 s1 1 ;(1)whereCsrepresentsconsumptionatages+2 0; thediscountrate,and (1), +20hasthebudgetconstraintsuchthatAs+1=[1 +(1 r(t))r(t)]As+(1 y(t) p(t))w(t)es+bs+as (1+ c(t))Cs;(2)whereAsrepresentstheamountofa ssetsheldbyeachhouseholdatthebeginningof ages+20,r(t)istheinterestrateatperiodt,e sisthee ciencyunitoflaborwhichdependsonage,andwi sthewageratepere , ciencyunitoflabores,thefollowingequation hasbeenestimated:e=a0+a1A+a2A2+a3L+a4L2.

7 WhereArepresentsage,Lthelengthofemployme nt,andethewagerateperhour, ,ashaskindlybeensuggestedbyMakotoSaito, ,with yrepresentingthewageincometaxrate, rtheinterestincometaxrate, ctheconsumptiontaxrate,and ecttheactualaspectoftheexistingpublicpen sionschemeinJapan,1 ,whichisassumedsuchthatbs= H(s RP)bs=0(s<RP);H=1 IRIRXs=1w(t)es;where andHdenotethereplacementratioandtheavera geannualremuneration, +20andIR+ , , , CMIN;(3) , TheInvestigationoftheWageStructure(Ching inKozoKisoChosa)in1994, theabovevariableshavebeenestimatedasa0a1 a2a3a4 0:15370:05539 0:00075950:1045 0:001901( 0:5363)(2:865)( 4:019)(4:823)( 3:243)7 Severalpatternsofthetimingwhenbequestsar einheritedhavebeenexaminedinAtodaandKato (1993). , ,whichtheywillreceivefromtheage65,assecu rityandproduceahighlevelofconsumptionwhe ntheyareyoung,sincetheweightplacedoncons umptionatoldageisextremelyreduceduetothe iruncertaintyoftheirlifetimes, , ,aliquidityconstraintisimposedonconsumpt ionatthepresentperiodinthisway:Cs [1+(1 r(t))r(t)]As+(1 y(t) p(t))w(t)es+bs+as DYs:(4)Now,supposethateachhouseholdmaxim isesitsutilityundertheseconstraints,andt hemaximizationof(1)subjectto(2),(3),and( 4)yields(seeAppendixforthedetaileddeduct ion)Cs= ANCs C 1 1+AOBs ;(5)whereANCs=ANB(t)S1(1+ )(s 1)Ss;ANB(t)=PC(t)PC(1)Q80t=1 ARA(t);PC(t)=1+ c(t);ARA(t)=1+(1 r(t))r(t).

8 AndPC(1)expressesPC(t)ofhouseholdsatage2 1:AOBsisgivenby:AOBs=(1+ )(s 1)Ss8>>>>> <>>>>>:ANB(t)264 11 21 PC(1)P80s=2 2sDYs Qs 1t=1 ARA(t) 375+ 2s 1s9>>>>>=>>>>>;:From(5), ,andthesavingslevelcanbecalculatedfrom(2 )and(5).13 Firms:Amaindi erencefromKato(2000,2002b) ectstheprivatesectorproductionasfollows: Y(t)= (t)K(t) L(t)1 G(t) ;(6)whereK(t)representstheprivatecapital ,L(t)thelaborsupplymeasuredbythee ciencyunit,andG(t)thepubliccapitalstock, erencebetweenage,generation, ,theages,andtheperiodt,theyarerelatedtoe achothersuchthatt=I+s 1: (t)denotesthescaleparameter, (6),thetotaloutputisdistributedtothepriv atecapitalandthelabor, isgivenbythelatestestimationbyYoshinoand Nakajima(1999)inordertoexaminethescaleof thee (6), :w(t)r(t)=1 K(t)L(t)!

9 :Thepropertyofaconstant-return-to-scalep roductionfunctionwithrespecttothelaboran dtheprivatecapitalyieldsY(t)=w(t)L(t)+r( t)K(t): , :D(t+1) D(t)=GE(t)+r(t)D(t)+Pen(t) R(t);whereD(t),R(t),andGE(t)denotetheamo untofoutstandinggovernmentdebts,totaltax revenueandgeneralgovernmentexpenditureat timet, (t) :F(t+1) F(t)=r(t)F(t)+Pen(t)+P(t) B(t);whereF(t),B(t)andP(t)denotetheamoun tofthepublicpensionfund, ,andthetotalamountofthecontributiontothe publicpensionscheme, (t),P(t)andB(t)aregivenbyR(t)= y(t)w(t)L(t)+ r(t)r(t)AS(t)+ c(t)AC(t)+ h(t)BQ(t);P(t)= p(t)w(t)L(t);B(t)=80Xs=45 SsNsbs;where handNsdenotetheinheritancetaxrateandthes umofs-year-oldgenerationsattimet, (t),AC(t)andBQ(t)denotethetotalamountofs avings,consumptionandbequestsinheritedby thegenerationofage50intheeconomyattimet; respectively,andgivenbyAS(t)=80Xs=1 SsNsAs;AC(t)=80Xs=1 SsNsCs;BQ=80Xs=1(1 Ss)NsAs:MarketEquilibrium:Aequilibriumco nditioninthecapitalmarketisgivenbyAS(t)+ F(t)=K(t)+D(t).

10 15andinthegoodsmarketitisY(t)=AC(t)+K(t+ 1) K(t)+GE(t) ectsofchangesinthedemographicstructureca usedbythetransitiontoanagingpopulation,e speciallywhenapplyingthesimulatedmethod, , (thegenerationbornin1890)areassumedtohav ethesamebirthandmortalityratesasthegener ationofage100in1990, ,theactualfuturepopulationdataestimatedi n2002byNationalInstituteofPopulationandS ocialSecurityResearchhavebeenusedforthep eriodsfromyear2001to2100andtheactualpopu lationdatain PopulationCensusofJapan(Kokusei-chosa) ,whenevertheactualdatafromthePopulationC ensusofJapan(Kokusei-chosa), ,wasnotavailable,actualpopulationdatafro mthe SimpleStaticLifeTable (fromtheJapaneseMinistryofHealthandWelfa re) ,inthispaperthemediumvariantestimationin thelatestversionbytheNationalInstituteof PopulationandSocialSecurityResearchhasbe enusedinthesimulationanalysis, ,thepopulationbetweenage15and64, , , ,suchastheratiosofcertaintaxrevenuestoth etotaltaxrevenues, , , ,sincethenumberoflaborforceintermsofthef uturepopulationcannotbeobtained, , ,thefuturevalueofthepubicpensionfund-GDP ratioisassumedtobethesameinallscenarios, ,andthustheyarenotthesameastheOECD values, ,thefollowingthreecaseshavebeencon-sider edinthispaper.