RatiosVaryAcrossCountries
BhagwanChowdhry
and
SheridanTitmanRevised:January1999
TheauthorsarecurrentlyatUCLAandUniversityofTexas.Thisresearchstartedin1993whenbothauthorswereattheHongKongUniversityofScienceandTechnology(HKUST).Ad-dressallcorrespondencetoBhagwanChowdhry,TheAndersonSchoolatUCLA,110WestwoodPlaza,LosAngeles,CA90095-1481,Phone:(310)-825-5883,Fax:(310)-206-5455,Email:bhag-wan@anderson.ucla.edu.Wethanktheseminarparticipantsatthe1999AFAconferenceinNewYork,ColumbiaUniversity,DukeUniversity,HebrewUniversity,HongKongUniversityofScienceandTechnologyIMF,LondonBusinessSchool,NYU,UBC,UCLAandUniversityofMarylandformanyusefulcomments.
1
Abstract
Thispaperexamineshowproductivitychangesa®ectrealratesofreturnandprice/earningsratiosinasmallopeneconomy.Themodelprovidesconditionsunderwhichincreasedproductivityinacountry'stradedgoodssectorcausespricesofnon-tradedgoodstoincreaserelativetothepriceoftradedgoods.Undertheseconditions,realratesofinterestdeclineandtheproductionofcertainnon-tradeddurablegoods(suchascapitalequipmentandhousing)immediatelyincrease.This`overconstruction'hastwoe®ects.First,theincreaseincapitalrelativetolaborinthesesectorsincreasesthemarginalproductoflaborandhenceimmediatelycausesanincreaseinwagesandthepricesofnon-tradedgoods.Second,an`oversupply'ofcapitalgoodsandhousingdepressestheirrentalratesinthecurrentperiodtherebyincreasingtheirpricetorentalratiosorequivalently,theirprice/earningsratios.
1Introduction
Anumberofstudiesdocumentsigni¯cantdi®erencesinrealratesofinterestacrosscoun-tries,(e.g.,Mishkin(1984)).AttractingparticularattentionwasthelowerrealratesofinterestinJapan,relativetotheU.S.,duringthe1980s.Thisobserveddi®erenceledsev-eralgovernmento±cials,journalistsaswellassomeeconomiststoconcludethatJapan,asaresult,hadalowercostofcapitalduringthatperiodandthus,acompetitiveadvantageovertheU.S..1Arelatedissuethatalsoreceivedconsiderableattentionwastheextremelyhighprice/earningsratiosobservedinJapan.2Whiletheconnectionbetweenprice/earningsra-tiosandrealinterestratesacrosscountrieshasbeeninformallydiscussed,3wearenotawareofanypastattemptstoformallyconsidertheunderlyingcausesofdi®erencesinrealratesandhowthesecausesrelatetoobserveddi®erencesinprice/earningsratiosacrosscountries.It'sclear,thatceterisparibus,adecreaseinrealinterestratescausesprice/earningsratiostoincreasesincefutureearningsarediscountedatlowerrates.However,onemightexpectthatthefactorswhichcauserealinterestratestodi®eracrosscountrieswouldcauseearn-ingsgrowthratestoalsodi®er,sotherelationbetweenrealinterestratesandprice/earningsratiosmaynotbesostraightforward.
Anumberofauthorshaveattributeddi®erencesinrealratestodi®erencesinriskpre-miums.Forexample,Darby(1986)argues:
`Theincompletelinkageofrealinterestratesinternationallyappearstore°ectriskpremiums...'
Othershaveattributeddi®erencesinrealratestobarrierstocapital°ows.Koraczyk(1985)states:
`Therearetwomajorreasonswhyexpectedrealinterestmayfailtobeequalacrosscountries...Inaworldwithriskaverseinvestors,di®erencesinriskwillleadtodi®erencesinexpectedreturns...Adi®erentialinexpectedrealreturnsacrosscountriesmayalsobeduetomarketsegmentationorbarrierstocapitalmovementsacrosscurrencies.'
See,forinstance,Hatsopoulos(1983)andreferencescitedinFrankel(1991),Lippens(1991)andMeer-schwam(1991).2
SeeFrenchandPoterba(1991).3
See,forinstance,Frankel(1991).
1
1
Theseclosedeconomyexplanationsfordi®erencesinrealratescouldsuggestapositiveaswellasanegativerelationbetweenrealinterestratesandprice/earningsratios.Forexample,acountryexpectinggreatlyincreasedproductivityinthefuturemightexperienceaninvestmentboomdrivinguprealinterestrates.However,theanticipationofincreasedearningscouldmorethano®settheincreaseddiscountratesimplyingincreasedratherthandecreasedprice/earningsratios.Thefactthatcross-countrydi®erencesinrealrateshavepersisteddespitedramaticincreasesincapitalmobilitysuggeststhatmarketsegmentationmaynotbethedominantcauseofthesedi®erences.TherecentexperienceinHongKongprovidesperhapsthebestexampleofhowrealratescandi®ersigni¯cantlyintheabsenceofbarrierstocapital°ows.TheHongKongdollarisdirectlylinkedtotheU.S.dollar,andhence,becausetherearenorestrictionsonthemovementofcapitalinandoutofHongKong,internationalarbitrageensuresthatthenominalinterestratesinthetwocurrenciesareessentiallyequal.However,sincetherateofin°ationhasbeenconsistentlyhigherinHongKongthanintheU.S.,therealinterestratemustnecessarilybelowerinHongKongthanintheU.S..Obviously,sincethecurrenciesareessentiallythesame,thedi®erencesinrealratescannotbeduetocurrencyrisk(majordevaluationrisks,iftheyexisted,wouldbere°ectedinthenominalrates).4
Tounderstandthedi®erencebetweentheHongKongandU.S.realrates,wemustunderstandhowtwocountrieswithlinkedmonetarypolicieshavesuchdi®erentin°ationrates.Thecurrentin°ationinHongKongismainlyduetopriceincreasesofgoodsandservices,suchashousingandrestaurantmeals,thatcannotbetradedinternationally(seeWong,LiuandSiu(1991)).Inthissense,theHongKongexperienceappearstobeconsistentwithanobservation(inFrankel(1991))thathasbeenattributedtoBalassa(1964)andSamuelson(1964):
`arapidlygrowingcountrytends(i)toexperienceanincreaseinthepriceofitsnontradedgoodsrelativetoitsinternationallytradedgoods(becauseofhigherproductivitygrowthinthetraded-goodssector,orelsebecausenontradedgoodsaresuperiorgoodsinconsumption),andtherefore(ii)toexhibitanapparentrealappreciationofitscurrencywhenthede°ationisdoneusingCPIswhich
Attheendof1997HongKongnominalratesdidincreaserelativetoU.S.ratesre°ectingconcernsaboutapossibledevaluationoftheHongKongdollar.WhenthesefearssubsidedtheHongKongnominalratesfelltoalevelclosetothelevelintheUnitedStates.
4
2
includealargeshareofnontradablegoodswithinthem.'
Itisstraightforwardtoshowthatananticipatedincreaseintherealvalueofacountry'scurrency,asdescribedbyBalassaandSamuelson,impliesadecreaseinthecountry'sexanterealrateofinterestifnominalinterestratesandexchangeratesaredeterminedinfrictionlesscapitalmarkets.Thisdecreaseinrealratesexperiencedinasmallopeneconomyshouldbecontrastedtothelikelyresponsetoaproductivityincreaseinaclosedeconomy.Intheabsenceofinternationalcapital°ows,ananticipatedincreaseinfutureproductivityislikelytoleadtoanincreaseintherealrateofinterestasindividualsattempttoborrowmoretoshiftconsumptionfromthefuture,whentheywillbewealthier,tothepresent,whenthemarginalutilityofconsumptionishigher.
Toexploretherelationbetweendi®erencesinrealratesanddi®erencesinprice/earningsratiosacrosscountrieswedevelopasimplemodelthatisconsistentwiththeobservationsofBalassa(1964)andSamuelson(1964).5Thetwocountrymodelexaminesasmallopeneconomy,suchasHongKong,andalargeeconomythatcanbethoughtofaseithertherestoftheworldortheUnitedStates.Themodelconsidersdurableandnon-durablegoodsandservicesthateitherareorarenotinternationallytraded.Themodelalsoconsidersnon-tradedcapitalgoods,suchaso±cebuildings,steelmillsandcarfactoriesaswellastradedcapitalgoodssuchashammersandtractors.Althoughfrictionscancausethepricesofthenon-tradedgoodsaswellaslabortodi®eracrosscountries,weassumethattherearenofrictionsintheinternationalmarketsfor¯nancialclaims.Ouranalysisindicatesthatifproductivityinanopeneconomy'stradedgoodssectorincreases,wageratesintheeconomymustalsoincrease.Undercertainfairlyplausibleconditions,thisproductivityshockleadstoanincreaseinthepricesofnon-tradedgoods,suchashaircuts,housingandfactories.Thisinturnimpliesastrengtheningofthecountry'scurrencyinrealtermsandacorrespondingreductioninitsexpostrealrateofinterest.
Sinceashiftinproductivitygenerallyevolvesonlyslowlyovertime,thefuturepro-ductivitypathcanbesomewhatanticipatedbyinvestorswhoimmediatelyincorporatethisinformationintothepricesofcapitalassets.Inourmodel,inanticipationoffutureproduc-tivityimprovements,resourcesareimmediatelyshiftedintoproducingnon-tradeddurablegoods,suchashousingandfactories,totakeadvantageofanticipatedpriceincreasesin
5
Also,seeMarston(1987).
3
thefuture.Theincreasedinvestmentinthesedurablegoodshastwoe®ects.First,theincreasedcapitalrelativetolaborinthecurrentperiodincreasesthemarginalproductoflaborimplyingthatwagesandthepricesofnon-tradedgoodsincreasepriortotheproduc-tivityincrease.Second,an`oversupply'ofcapitalgoodsandhousingdepressestheirrentalratesinthecurrentperiodtherebyincreasingtheirpricetorentalratiosorequivalently,theirprice/earningsratios.Weshowthatundercertainfairlyplausibleconditionsthisalsoimpliesthattheexanterealrateofinterestalsodecreasesinthesmallopeneconomy.
Ouranalysisofprice/earningsratiosisthusconsistentwiththeintuitionmentionedattheoutset,(seealsoFrankel(1991)),whichattributesthehigherP/EratiosincountriessuchasJapantothelowerratesusedtodiscounttheirfutureearnings.However,asweshow,thisintuitionissomewhatoversimpli¯ed.OuranalysisindicatesthatP/Eratiosarehighwhenthecostsofproducingcapitalgoods,andhencethepriceofcapitalgoods,isexpectedtoincreaseinthefuture.If,however,thecapitalgoodssectorisexpectedtoexperienceastrongincreaseinproductivityinthefuture,thefuturecostofproducingthecapitalgoodswouldbeexpectedtodecrease,andourresultswouldbereversed.Investorswilltendtoinvestlessincapitalofthistypetoday,preferringtowaituntilitspriceischeaper.Asaresult,therentalrateforthistypeofcapitalwillbehigh,andthepricetorental(orP/E)ratiowillbelow,evenwhenrealinterestratesarelow.
Inthenextsection,wepresentamodelthatformalizesourintuitionandderiveitsimplications.InSection3,wecalibrateamulti-periodextensionofthemodeltoexamineifobservedhighprice/rentalratiosobservedinmanycountriescanarisefromempiricallyreasonableassumptionsaboutparametervalues.WediscusssomeextensionsandtheirimplicationsinSection4.Concludingremarksarepresentedinthelastsection.
2TheModel
Weconsideratwo-period,perfectcertaintymodelwithtwocountries;asmallcountrysuchasHongKong{andtherestoftheworld(oralargecountry{suchastheUnitedStates).Ouranalysisfocusesonthesmallcountry,whichbothproducesandconsumeswhatwecalltradedgoodsandnon-tradedgoods.Thetradedgoodsarecharacterizedasproductswhichcanbefreelytradedacrosscountries,withouttransactioncosts,atpricesdeterminedontheworldmarket.Fromtheperspectiveofthesmallcountry,theseprices
4
areexogenouslydetermined.Incontrast,thenon-tradedgoodscannotbeimportedorexportedsotheirpricesmustbedeterminedwithinthesmallcountry.Inadditiontomakingadistinctionbetweentradedandnon-tradedgoods,wewillbeseparatelyanalyzingdurablesandnon-durablesaswellasconsumptionandcapitalgoods(whichareusedintheproductionofconsumptionandothercapitalgoods).Insummary,themodelassumesthattheindividualsintheseeconomiesconsumeandproducegoodsandservicesthatarecharacterizedasfollows:
²Non-tradedgoodsandservices,denotedN.Thesearefurtherclassi¯edasfollows:
{Non-durables,denotedB(barbers'services).Thesearegoodssuchashair-cuts,householdhelp,restaurants,freshvegetablesetc.thatcannotbestoredovertime.
{Durableconsumptiongoods,suchashouses,denotedH.
{Durablecapitalgoods,calledfactoriesanddenotedF.Examplesareasteelmill,acarfactoryoracommercialbuilding.
²TradedconsumptionandcapitalgoodsdenotedT.Examplesofthesearecars,steel,investmentbankingservicesetc.Forsimplicity,andwithoutanylossofgeneralityinourresults,weassumethatthetradedgoodsarenon-durableandlastonlyoneperiod.
Itshouldbenotedthatbyrulingoutuncertainty,wehaveruledoutthepossibilitythatacountry'smonetarypolicya®ectsitsrealrateofinterestanditsrealexchangerate.Barrierstocapital°owscreatedbyuncertaintyaboutchangingcurrencyvaluesaswellasdi®erentrealratescausedbydi®erencesinriskpremiaarealsoruledoutbythisassumption.Ourresultsarenotlikelytoholdifacountry'smonetarypolicyrespondstoproductivityshocksinawaythata®ectsboththerealexchangerateandtherealrateofinterest.However,ifweassumethatmonetarypolicyhasnoe®ectonrealexchangeratesandinterestrates,thenourresultsshouldholdinamoregeneralmodelthatallowsforuncertainexchangerates.
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2.1PurchasingPowerParityandRealInterestRates:AReview
LetusdenotethehomecurrencyasH$andtheforeigncurrencyasFX.LetStdenotethespotpriceinperiodtoftheforeigncurrencyFXintermsofthehomecurrencyH$.Wewillusethesuperscript
¤
todenoteallFXpricesandnosuperscripttodenoteH$prices.We
¤PtStPt
de¯netherealexchangerate,Et´Onecanthuswrite
wherePandP¤denotethegeneralpricelevels.
(1)
S1¦¤E1=E0S0¦where¦and¦¤denoteoneplustheoverallratesofin°ation.IfPurchasingPowerParity(PPP)holdsinlevels,then,byde¯nition,therealexchangerateequalsone.IfPPPholdsintherateofchangeformthen,byde¯nition,therealexchangeratedoesnotchangefromoneperiodtothenext.
TheFXpricesoftradedgoodsaredeterminedintheworldmarketsandarespeci¯ed
¤denotethepricesofthetradedgoodinperiodt.exogenously.LetPTtandPT
t
Assumption1Thelawofonepriceholdsforthetradedgoods.
¤foreachperiodt.ThisimpliesthatThereforePTt=S1PTt
S1¦T
=¤S0¦T
(2)
where¦Tand¦¤Tdenoteoneplustheratesofin°ationinthepricesoftradedgoods.Substituting(2)in(1),weget
E1¦T¦¤=¤:E0¦T¦
(3)
IfweletidenotethenominalH$interestrate,therealdomesticinterestratercanbede¯nedas
1+r´
1+i
:¦(4)
Similarly,ifweleti¤denotethenominalFXinterestrate,therealworldinterestrater¤canbede¯nedas
1+i¤
1+r´:
¦¤¤
(5)
Assumption2Thereisperfectcapitalmobility.
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Noarbitrageopportunitiesandperfectcertaintyimpliesthatthefollowinginterestrateparityconditionholds:
1+iS1
=:1+i¤S0
Substitutingfrom(2)andrearranging,theinterestrateparityconditionimplies
1+i¤1+i
=:¦T¦¤T
(6)
Theaboveequationimpliesthatthenominalratesde°atedbychangesintradedgoodspricesshouldbeequal.However,asweshallsee,therealinterestrates,calculatedbyde°atingnominalratesbytheoverallpriceindex,neednotbeequatedacrosscountries.
Dividing(4)by(5),substitutingfrom(6)andrearranging,weget
1+r¦T¦¤
=:
1+r¤¦¦¤T
>From(3)and(7),wegetthefollowing,
E11+r¦T¦¤==:E01+r¤¦¦¤T
(8)(7)
TheaboveequationsprovideagoodillustrationoftherelationbetweenPPPandtheequiv-alenceofrealinterestratesacrosscountries:non-tradedgoodsandservicesthatcreateviolationsofPPPalsogeneratedi®erencesinrealrates.WethusobtainthefollowingpropositionwhichcanalsobefoundinvariousformsinAdlerandDumas(1983),AdlerandLehman(1983),Dumas(1992),Dornbusch(1983,1988),Hsieh(1982),Mussa(1982),O±cer(1976),Roll(1979)andStulz(1987)amongothers.Proposition1Thefollowingstatementsareequivalent:
1.PurchasingPowerParityholdsintherateofchangeform(i.e.,therealexchangeratestaysconstantfromoneperiodtothenext).
2.Thedomesticrealinterestrateisequaltotheworldrealinterestrate(r=r¤).3.Theratiooftherateofin°ationinthepricesoftradedgoodstotheoverallrateofin°ationisthesamedomesticallyasitisintherestoftheworld
³
¦T¦=
¦¤T¦¤´
.
Astheabovepropositionindicates,whenpricechangesarecertain,di®erencesinrealratesofinterestacrosscountriesmustbedrivenbydi®erencesintheratesofappreciation
7
oftradedandnon-tradedgoodsinthetwoeconomies.Sinceourprimaryinterestisinstudyingthesmallereconomy,wecansimplifyouranalysis,withoutlossofgenerality,bymakingthefollowingassumption:
Assumption3Theworldrateofin°ationinthepricesoftradedgoodsisequaltothe
¤overallworldrateofin°ation,i.e.,¦¤T=¦.
Thisassumptionimpliesthat
1+i
=1+r¤:¦T
(9)
2.2ProductionTechnology
Theproductionofallconsumptionandcapitalgoodsrequirestwofactorsofproduction,labor(L)andcapital(K).Althoughlaborisassumedtobehomogeneous,capitalcomesintwoforms,tradedandnon-traded.Ourde¯nitionofnon-tradedcapitaliscapitalthatrequireslocallaborforitsproduction.Afactorywouldbeanexampleofthis.Although¯nancialclaimsforafactorycanbetradedinternationally,theactualphysicalassetsarenotmobile.Onecouldalsothinkofacorporation'sorganization(orthetrainingcostsofitsemployees)asnon-tradedcapital.Thetradedcapitalcanbethoughtofasairplanes,tractors,hammers,screwdriversandothertools.
Tokeepthemodeltractableweassumethatproducersarecompetitiveandtheirpro-ductionfunctionsrequireonlyoneformofcapitalandexhibitconstantreturnstoscale.Weassumethattheproductionoftradedgoodsrequiresafactory(non-tradedcapital)butdoesnotrequiretradedcapital.Thisparticularassumptiondoesnota®ectourmainresults.Inaddition,weassumethattheproductionofnon-tradedgoodsrequiresvarioustools(i.e.,tradedcapitalgoods)butdoesnotrequireafactory(i.e.,non-tradedcapitalgoods).
Insummary,thefollowingassumptiondescribestheproductionfunctionsconsideredinourmodel:
Assumption4Theperiod0productionfunctionforallofthecapitalandconsumptiongoodsaredescribedbythefollowingCobb-Douglasspeci¯cation:
®G1¡®GKGLG0
0
G2fN;Tg
8
whereKG0,isthecapitalgood,eitheranon-tradedfactory(KT=F)oratradedgood(KN=T),LG0istheperiod0inputoflaborandtheparameter®G2(0;1)measuresthecapitalintensityoftheproductionofgoodG.Thelaborinthetwocountriesshouldbethoughtofasanon-tradedgood,i.e.,thewageratesneednotbethesameinthetwocountries.
Ourmodelexaminesthee®ectofaproductivityshockthata®ectsthesmallcountry'sproductionfunctionsinperiod1,leavingproductivityinthelargecountryunchanged.Perhaps,thesmallercountryinitiallyhasaccesstolesssophisticatedtechnologythanthelargercountry,butthroughinformation°ows,thetechnologicaldi®erencesnarrowovertimeraisingproductivityinthesmallercountry.Theseproductivityshocksareassumedtobeperfectlyanticipatedatdate0,generatinganimmediatee®ectonthedomesticeconomy.Tosimplifyouranalysiswewillassumethattheproductivityshocklastsonlyoneperiod.Afterperiod1,productivitygrowthratesinthetwocountriesareassumedtobeidentical(andequaltozero.)Speci¯cally,weassumethefollowing:6
Assumption5Theproductionfunctioninperiod1onwardsisofthefollowingform:
®G1¡®G
ªGKGLG1
1
G2fN;Tg
whereKG1andLG1denotetheinputsinperiod1ofcapitalandlaborrespectively,andªGmeasurestheincreaseinproductivityofgoodG'sproduction.
Thetechnology°owsa®ecttheproductivityofdi®erentgoodsdi®erently.Forexample,thenon-tradednon-durablegoodsandservices(B),suchashaircuts,maynotbene¯tfromthetechnologyimprovementsandhence,shownogaininproductivity(ªB=1).Incontrast,productivityinthenon-tradeddurablegoods(housing),thenon-tradedcapitalgoods(factories)andthetradedgoodssectorsarelikelytobene¯tfromthetechnologyshock(ªH;ªF;ªT>1),butpossiblybydi®erentamounts.
Finally,wemustmakethefollowingassumptiontoguaranteetheexistenceofanequi-librium:
Onemightalternativelyconsiderthepossibilityofthesmallcountrybene¯tingfromanincreaseinthedemandforatradedgoodthatitproduces.Forexample,HongKonginvestmentbankershaverecentlyexperiencedanincreaseinthedemandfortheirservicesinChina.Directlymodelinganincreaseddemandofthistypewouldaddtothecomplexityofourmodel.However,wethinkthataproductivityincreaseisconceptuallyverysimilartoanincreaseindemand(theinvestmentbanker'smarginalproductishigherasaresultofthegreaterdemand)andthattheintuitiondevelopedinourmodelthusappliesmorebroadly.
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9
Assumption6Laborisnotsuppliedwithperfectelasticity.
Whatwearerulingoutwiththisassumptionisthepossibilitythatthesmallcountryimportsanin¯niteamountoflaborata¯xedpriceinresponsetoaproductivityincrease.Weassumethatthepriceoflaborincreasesasthedemandforlaborincreases,however,apartfromthat,wearemakingnoassumptionsabouttheelasticityofthesupplyoflabor.
2.3Rents,WageRatesandPricesofNon-tradedGoods
Mostofourresultsfollowdirectlyfromthe¯rstorderconditionsforpro¯tmaximization.These¯rstorderconditionsallowustosolveforthecompetitivewageratesinperiods0and1,asfunctionsofthemarginalproductoflaborinthevarioussectorstimesthepriceofthegoods.Sincewagesareequalinallsectors,wehavethefollowingequalities:
F0
W0=PT0(1¡®T)
LT0
F1
W1=PT1ªT(1¡®T)
LT1
µµ
¶®T
µ
¶®N
KN0
=PN0(1¡®N)
LN0
µ
8N2fB;Hg;8N2fB;Hg;
(10)(11)
¶®T
KN1
=PN1ªN(1¡®N)
LN1
¶®N
whereW0andW1denotethewageratesinperiod0and1respectively.
Similarly,themarginalproductofthetradedcapital,whichisusedintheproductionofnon-tradedgoods,mustbeidenticalineachofthenon-tradedgoodssectorsandequaltothepriceofthetradedcapital(whichlastsonlyoneperiod).Therefore,
PT0=PN0®N
µ
¶1¡®N¶1¡®N
LN0KN0
µ
8N2fB;Hg;8N2fB;Hg:
(12)(13)
PT1=PN1ªN®N
LN1KN1
Inadditiontoexaminingrealexchangeratesandrealratesofinterest,wewillbeex-amininghowproductivityshocksa®ectprice/earningsratios,orequivalently,theratiooftherentalratesonfactoriestotheirsellingprices.Sincefactoriesareusedtoproducethetradedgood,thecompetitiverentonfactoryunitsequalsthemarginalproductoffactoryunitstimesthepriceofthetradedgood.Thus,
RF0=PT0®T
µ
¶1¡®T
LT0F0
µ
;;
(14)(15)
RF1=PT1ªT®T
10
LT1F1
¶1¡®T
whereRF0andRF1denotetherentsonfactoriesinperiod0and1respectively.
Wenowexpressthedate0valueofthefactories(aswellashouses)asthediscountedvalueoftheirfuturerents:
PN0=RN0+
1¡±N
PN1
1+i8N2fH;Fg;
(16)
where±N2[0;1]denotestherateatwhichthefactoriesandhousesdepreciateperperiodandRN0istheperperiodrentalincome.Noticethattoavoidconfusionaboutrealratesofinterestandrealpriceswearediscountingnominalpricesintheaboveequationsatthenominalrateofinterest.Alsonoticethatsince,inthemodel,thereisnouncertainty,thenominalrateofreturnonallassetsequalstherisk-freenominalratei(andthereforetherealrateofreturnonallassetsisalsoidentical).
Finally,weassumethat,afterperiod1,productivitygrowthratesinthetwocountriesareidenticalandequaltozero.Therefore,itmustbethecasethat
RFt+1
=¦T8t¸1:RFt
Thepriceoffactories,inperiod1,isthediscountedsumofallrentalincome.Thus,
PF1=RF1
whichsimpli¯esto
PF1
¦2¦T2T+(1¡±F)RF1+(1¡±F)RF+:::
(1+i)(1+i)21
(1+r¤)=RF1¤:
(r+±F)
(17)
Theequilibriumischaracterizedbyequations10-17.Tosolvefortheequilibriumwemust¯rstdeterminethepricesinperiod1,andthenworkbackwardstosolveforthepricesinperiod0.Theperiod1equilibriumrequiresasolutionforthewagerateandthepricesofthethreenon-tradedgoods(factoryunits,housesandbarbers).Thesepricesaredeterminedasfunctionsoftheparametersintheproductionfunctionsandthepriceofthetradedgoodwhichisdeterminedexogenously.Thesolutionsforthesepricesassumethatthe¯rmsselectthecostminimizingproductionfunctionsandareperfectlycompetitiveandthusearnzeropro¯ts.
Itshouldbenotedthatthisframeworkallowsustosolveforpriceswithouthavingtoexplicitlysolvetheconsumer'smaximizationproblem.Thefactthatthetradedgoods'priceaswellasinterestratesareexogenousimpliesthatthesmallcountry'sconsumers'
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consumption/savingsdecisionsdonota®ectprices.Ourmodelisthusconsistentwiththesmallcountryexperiencingeithertradesurplusesorde¯cits,whichwouldbea®ectedbytheirsavingsrate.Tomodeltwolargecountries,suchastheU.S.andJapan,onewouldneedtosolvetheconsumer'sproblemexplicitly,sincetradedgoodpricesandinterestrateswouldbea®ectedbyproductivityshocksinthesecountries.Modelingtheconsumer'sproblemconsiderablycomplicatesthemodelandisnotlikelytoa®ectthecentralresultsinthepaper.
Anadditionalnotablefeatureofthispartialequilibriummodelisthattheequilibriumwagerateisdeterminedwithoutanyassumptionsaboutthesupplyoflabor,(exceptthatthesupplycurvecannotbeperfectlyelastic).Becauseofourconstantreturnstoscaleproductionfunctions,thezeropro¯tconditionandtheinelasticdemandforthetradedgood,thedemandforlaborfromthetradedgoodssectorisalsoperfectlyelastic.Iflaborcostsareslightlyless,thenpro¯tscanbeearnedinthissectorandanin¯niteamountoflaborwillbedemanded.Conversely,ifwageratesareonlyslightlyhigher,pro¯tsinthissectorwillbenegativesothattherewillbenolabordemanded.Hence,thepriceoftradedgoodsdeterminesthewagerate,regardlessofthesupplyoflabor.7
2.4Implications
Thefollowingtwopropositionsprovidethepaper'scentralresults.Inparticular,thepropo-sitionsspecifyhowproductivityshocksa®ectrealratesofinterest,theprice/earningsratiosofmanufacturing¯rmsandthepricetorentalratioofhousing.
Proposition2Iftheproductionoffactoriesisatleastaslaborintensiveastheproductionoftradedgoods(®F·®T)andiftheproductivityincreasenextperiodinthetradedgoodssectorislargerthantheproductivityincreasenextperiodintheproductionoffactories(ªT>ªF)thenthefollowingpropositionshold:
1.Theshocktoperiod1productivitycausesthepriceoffactoriesinperiod0,PF0,andthewagesinperiod0,toriseimmediatelyinperiod0andtherentalratesonfactories,RF0,tofallinperiod0.Themagnitudeoftherise(orthefall)islarger:
Inreality,wewouldexpectthatthepriceofthetradedgoodwoulddeclineasthesupplyofthegoodfromthesmallcountryincreased.Ifthatwerethecase,thentheproductivityshockwouldhavelessofane®ectonthewagerate,withthemagnitudeofthee®ectbeingrelatedtotheelasticityofthelaborsupplycurve.
7
12
(a)thelargeristheincreaseinproductivityinthetradedgoodssector,ªT,and(b)thesmalleristheincreaseinproductivityintheproductionoffactories,ªF.2.Thepricetorentalratioforfactoriesislargerinperiod0thaninperiod1.(
³P
RF1
F1´
).
³P
´
³P
RF0
F0´
>
3.Therateofincreaseinpricesoffactoriesbetweenperiod0and1exceedstherateofin°ationintradedgoods'prices.(
F1PF0
>¦T).
³P
³P´RF0
F04.Thepricetorentalratioforfactoriesinperiod0,thepricesoffactoriesbetweenperiod0and1,
PF0
F1,arelarger:
´
andtherateofincreasein
(a)thelargeristheincreaseinproductivityinthetradedgoodssector,ªT,(b)thesmalleristheincreaseinproductivityintheproductionoffactories,ªF,and(c)thelargeristhelaborintensityofproducingfactories,(1¡®F).(d)thelargeristhelaborintensityofproducingtradedgoods,(1¡®T).Proof:SeetheAppendix.Theprecedingpropositionstatesthatwhenfactorycostsareexpectedtoincreaseinperiod1,theproductionoffactoryunitswillincreaseinperiod0,whichhastheimmedi-atee®ectofincreasingcapitaltolaborratiosdrivingupwages,drivingdownrents,andincreasingprice/rentratios.Changesthattendtoincreaseperiod1factorypriceswilltendtomagnifythise®ectonwagesandrents.Asweshowinthenextproposition,similarconditionsontheproductionfunctionsinthenon-tradedconsumptiongoodssectorim-pliesthatrealratesofinterestwillalsobenegativelya®ectedbyananticipatedincreaseinproductivity.
Proposition3Iftheproductionofanon-tradedconsumptiongood(housesandothernon-durablegoodssuchashaircuts)isatleastaslaborintensiveastheproductionoffactories,whichinturnisatleastaslaborintensiveastheproductionoftradedgoods(®N·®F·®T),andiftheproductivityincreasenextperiodinthenon-tradedconsumptiongoodssectorisnolargerthantheproductivityincreasenextperiodintheproductionoffactories,whichinturnissmallerthantheproductivityincreasenextperiodintheproductionoftradedgoods(ªN·ªF<ªT),thenthefollowingpropositionshold:
13
1.Thepricetorentalratioforhousesislargerinperiod0thaninperiod1.(
³P
RH1
H1´
).
³P
H0RH0
´
>
2.Therateofincreaseinpricesofthenon-tradedgoodbetweenperiod0and1isatleastaslargeastherateofincreaseinthepricesoffactorieswhichexceedsthein°ationintradedgoods'prices.(
³P
N1PN0
´
¸
³P
PF0
F1´
>¦T).
³P
RH0
H03.Thepricetorentalratioforhousesinperiod0,
pricesofthenon-tradedgoodbetweenperiod0and1,
´
³P
andtherateofincreaseinthe
N1PN0
´
,arelarger:
(a)thelargeristheincreaseinproductivityinthetradedgoodssector,ªT,(b)thesmalleristheincreaseinproductivityintheproductionofthenon-traded
good,ªN,and
(c)thelargeristhelaborintensityofproducingthenon-tradedgood,(1¡®N).4.(a)Thedomesticoverallrateofin°ationexceedsthedomesticrateofin°ationin
thepricesoftradedgoods.(¦>¦T).
(b)Thedomesticrealrateofinterestissmallerthantheworldrealrateofinterest.
(r Thein°ationrateinthenon-tradedcapitalgoodsandconsumergoodssectorsneednotbethesame.Conditionscanexistwhereconsumerpricesdonotincrease,(e.g.,whenpro-ductivityincreasessu±cientlyinthenon-tradedconsumergoodssector),butcapitalgoodspricesdoincreaseasaresultoftheproductivityshock.Insuchacase,realrates,astradi-tionallymeasured,willnotdecreasebutprice/earningsratioswillincrease.Alternatively, 14 conditionsexistwhererealratesdofallbutprice/earningsratiosdecrease.Hence,there-sultsprovidedinthepreviouspropositionsareparameterspeci¯c.Toillustratethispoint,thefollowingpropositionispresentedwhichprovidesconditionsunderwhichapositiveproductivityshockcausesprice/earningsratiostodecrease. Proposition4Iftheproductionoffactoriesisaslaborintensiveastheproductionoftradedgoods(®F=®T)andiftheproductivityincreasenextperiodintheproductionoffactoriesislargerthantheproductivityincreaseinthetradedgoodssectornextperiod(ªF>ªT)thenthefollowingpropositionshold: 1.Theshocktoperiod1productivitycausesthepriceoffactoriesinperiod0,PF0,andthewagesinperiod0,tofallinperiod0andtherentalratesonfactories,RF0,toriseinperiod0. 2.Thepricetorentalratioforfactoriesissmallerinperiod0thaninperiod1.( ³P RF1 F1´ ). ³P ´ ³P RF0 F0´ < 3.Therateofincreaseinpricesoffactoriesbetweenperiod0and1issmallerthantherateofin°ationintradedgoods'prices.(Proof:SeetheAppendix.PF0 F1<¦T). 3 CalibratingtheModel:CantheHighJapanesePrice/EarningsRatiosBeJusti¯ed? Intheprevioussectionweestablishedthattheprice/rentalratiosinaneconomywouldincreaseifproductivitywasexpectedtogrowfasterinthetradedgoodssectorthaninthenon-tradedgoodssector.Inadditiontodi®erencesinproductivitygrowthrates,price/rentalratioswereshowntodepend,amongotherthings,onthelaborintensitiesoftheproductionoftradedandnon-tradedgoodsaswellasonthelaborintensitiesoftheproductionofthenon-tradedfactories.Inthissectionwepresentacalibrationexercisethatillustratestheimportanceoftheselaborintensitiesinthedeterminationofprice/rentalratios.Thisexercisealsodemonstratesthatthefairlylargedi®erencesbetweentheprice/rentalratiosinJapanandtheUnitedStatescanarisefromplausibleassumptionsaboutthelevelandthedurationofproductivityshocksinthetradedgoodssector. 15 Forthiscalibrationexercise,weconsideramulti-periodextensionofourmodel.Sup-posetheproductivityshocklastsforNperiods.Wecalculatetheprice/rentalratiosbysolvingthedynamicprogrammingproblemrecursivelybackwards,i.e.,we¯rstsolvetheprice/rentalratioinperiodN¡1.Theequilibriumischaracterizedbyequations10-17whichrepresentasystemofeightsimultaneousequationswitheightunknownvariables,PF0;PF1;RF0;RF1;F0=LT0;F1=LT1;KF0=LF0;KF1=LF1.WethensolvetheperiodN¡2problemusingPF0asaninputforPF1inthecurrentperiod.Wenowhaveequations10,12,14and16andfourunknownvariablesPF0;RF0;F0=LT0;KF0=LF0:WeproceedanalogouslyforperiodsN¡3,N¡4etc.untilweobtaintheprice/rentalratioforthecurrentperiod. Withoutlossofgenerality,weassumezeroin°ationfortradedgoods: ¦T=1 sothat 1+i=1+r¤: Wenormalizethetradedgoodsprices PT0=PT1=1; andforsimplicity,wefurtherassumezerodepreciationandnoproductivityimprovementsintheproductionoffactoriesandnon-tradedgoods. ±F=0;ªF=ªN=1: OurcalibrationexerciseusesasitsbasisempiricalestimatesdocumentedinMarston(1987)andcalculatesprice/rentalratiosasafunctionofthenumberofyearstheproduc-tivitygrowthdi®erentialsareexpectedtopersist.Marston(1987)documentsthattheproductivitygrowthrateinthetradedsectorexceededtheproductivitygrowthrateinnon-tradedsectorbymuchmoreinJapanthanintheUnitedStateswhichatleastpartiallyexplainsthelowerrealrateofinterestinJapan.Speci¯cally,Marston,usingtheOECDInternationalSectoralDataBase,documentedthatoverthe1973-83period,Japanese\\pro-ductivitygrowthinthetradedsectorwas73.2percentgreaterthaninthenontradedsector,\"whereas\\[p]roductivityintheU.S.tradedgoodssectorgrewby13.2percentfasterthanintheU.S.nontradedsector.\"8ThisimpliesthatinJapantheproductivitygrowthdi®erential MarstonusedOECDdataontotalvalueaddedandcorrespondingemployment¯gurestogenerateproductivityseriesforeachof10sectorsoftheJapaneseandtheU.S.economies.Ofthetensectors,twowereclassi¯edastradedandsixasnontraded(oneenergy-intensivesectorwasdeleted). 8 16 betweenthetradedandnon-tradedsectorsexceededthisdi®erentialintheU.S.byroughly5percentperyearoverthis10yearperiod.Ourcalculations,madefromtheperspectiveofinvestorslookingforwardafter1983,assumethattheseproductivitygrowthratedi®erenceswilllastforanother1to15years.Thecalculationsalsoassumethatthenominal(andreal)interestrateintheUnitedStatesis5percent,whichcorrespondstoabenchmarkprice/rentalratioof21intheUnitedStates.9 Figure1plotstheprice/rentalratioofJapanesenon-tradedcapital(factories)asafunctionofthenumberoffutureyearsthatJapanwillexperienceextraordinary(relativetotheUnitedStates)growthinitstradedgoodsector(relativetothenon-tradedgoodssector).The¯gureprovidesseparateplotsthatassumedi®erentcapitalintensitiesoftheproductionofthefactories(the®TparameterintheCobb-Douglassproductionfunction)andtheproductionofthetradedgoods(the®FparameterintheCobb-Douglassproductionfunction).Thesecapitalintensitiesareassumedtorangefrom.10to.50. TheplotsshowninFigure1illustratethedegreetowhichprice/rentalratesaresensitivetothenumberofyearsthattheproductivitygrowthdi®erentialisexpectedtoincrease.Asonewouldexpect,theprice/rentalratioishigherwhenthedi®erentialisexpectedtopersistlonger.Theplotsalsoillustratehowlaborintensitiesa®ectprice/rentalratios.Whentheproductionofnon-tradedcapitalismorelaborintensive,thecapitalmoree±cientlystoreslaborthatwillbemorevaluableinthefuture.Hence,investorswilloverbuildthemorelaborintensivecapitalinthesesituationsdrivinguptheirpricesanddrivingdowntheirrentalrates.Thelaborintensityofthetradedgooda®ectsprice/rentalratiosthroughitsa®ectonfuturewagerates.Iftheproductionofthetradedgoodismorelaborintensive,thenwagesincreasemoreforanygivenincreaseinproductivity.Hence,theincentivetostorelaborishigherwhich,inturn,causesprice/rentalratiostoincrease. Theprice/rentalratiosplottedinFigure1demonstratethatthehighprice/earningsandprice/rentalratiosobservedinJapanduringthemidtolate1980scouldhavebeenjusti¯edbyextrapolatingthegrowthratesfromtheprevious10yearperiod.Becauseofvariousaccountingdi®erencesitisdi±culttodirectlycompareU.S.andJapaneseprice/earnings A5%realrateofinterestmayappeartobehighcomparedtohistoricalestimates.However,becausethereisnouncertaintyinourmodel,choosingamorereasonablerealrate,say2to3%,wouldimplyaprice/rentalratioof34-51whichishighcomparedtoempiricalestimatesfortheUnitedStates.Assumingahigherrealrateof5%impliesabenchmarkprice/rentalratioof21whichisempiricallymoreplausible.Intuitively,choosingahigherrealrateamountstoaccountingforuncertaintyinearningsandrentalrates. 9 17 ratios,(FrenchandPoterba(1991)discusstheseproblemsandprovideestimatesofadjustedprice/earningsratiosthatcanbeusedforcomparisonpurposes),however,price/rentalratiosobservedforcommercialrealestatedonothavetheseaccountingproblems.Jones,LangandWootten,acommercialrealestatebrokerage¯rm,reportedthatJapaneseprice/rentalratiosrangedfromabout35to60inthe1985to1987timeperiodwhichisconsistentwiththenumbersgiveninFigure1. Ofcourse,withthebene¯tofhindsightwenowknowthattheassumedproductivitygrowthrateswereoverlyoptimisticandthatJapanesestockandrealestatepricesweretoohigh(givenwhatwenowknow).Asweknow,Japanesestockandrealestatepricesfellconsiderablywhentheseassumedproductivitygrowthrateswerenotrealized. 4 4.1 ExtentionsandImplications HomeBiasandDynamicPortfolioChoices Althoughanunexpectedboostinproductivitywillmakemostindividualsinaneconomybettero®,ouranalysissuggeststhattherecanalsobesomeunfortunatedistributionalimplications.Forexample,aretiredindividuallivingo®pastsavingswouldbemadeworseo®fromaproductivityincreaseifitreducedtherealrateofreturnonhissavings. Onecouldanalyzetheportfolioimplicationsofuncertainfutureproductivityshocksinthisframeworkbyaddinganinitialdatewhereindividualsformportfoliostakingintoaccounthowuncertainproductivityshocksa®ectbothassetpricesanddiscountrates.TheinsightsprovidedbyMerton(1971)andothersabouttheneedtohedgeagainstshiftsintheinvestmentopportunitysetwouldbeespeciallyrelevantinthissetting.Althoughwehavenotsolvedsuchamodel,wewouldconjecturethatolderindividualssavingfortheirretirementwouldliketotilttheirportfoliostowardsassetswhosevaluesincreaseintheeventofanunanticipatedproductivityshocksincesuchashockwouldlowertherealrateofreturnthattheywouldreceiveontheirsavings. Thislineofreasoninghasimplicationsforwhathascometobeknownintheinter-nationalinvestmentsliteratureasthehomecountrybias.Oneobservationthathasbeenmadebyanumberofauthorsisthatevenwhencapitalmarketsareopen,investorsprefer 18 toinvestintheirhomemarkets.10Whilethismaynotseemrationalwhenviewedfromtheperspectiveofastaticmodel,ahomecountrybiaswillarise,aswehavedescribedabove,ifinvestorsareconcernedabouthedgingagainstchangesintherealrateofreturnintheircountries.11Incontrasttoearlierworkonthishomebias,ouranalysissuggeststhatthehomecountrymarketportfoliomaynotprovidethemoste®ectivehedgeagainstchangesintheopportunityset,anddependingontheirpointinthelifecycle,di®erentinvestorswillhavedi®erenttendenciestoinvestinthelocalmarket.Olderinvestors,whoarelikelytobeconcernedabouthedgingagainstchangesintherealrateofinterest,shouldinvestinstocksthatrepresentclaimsonnon-tradeddurablegoodsthatcontainsalargeamountofembeddedlabor.Intuitively,investorscanhedgeagainstincreasedpricesresultingfromincreasedlocallaborcostsbybuyingassetswhichembedlocallabor.However,youngerinvestors,whoareexpectedtobenetsellersoflocallaborinthefuture,maybeexpectedtoholdverydi®erentportfolios.Wewouldexpectthattheseinvestorswouldbemoreinter-nationallydiversi¯edtoreducetheirexposuretorisksthatarehighlycorrelatedwiththeirownhumancapital. 4.2ImplicationsRelatingtoJapan Aswementionedintheintroduction,barrierstocapitalmovements,resultingperhapsfromcurrencyrisks,havebeenthemostpopularexplanationsforthelowrealratesandhighprice/earningsmultiplesobservedinJapanduringthe1980s.However,webelievethattheargumentspresentedinthispaperprovideamoreconvincingexplanationforthesephenomena.OnepopularargumentwasthattheJapaneseinterestrateswerekeptarti¯ciallylowbecauseofacombinationofhighsavingsratesinJapan,largede¯citsandlowsavingsratesintheU.S.,andcurrencyrisksthatactedasabarriertocapital°owsfromJapantotheU.S..Althoughthisargumentsoundsplausibleintheory,expostevidenceindicatesthatJapaneseinterestrateswereinfactarti¯ciallyhighduringthisperiod(oratleasthigherthantheywouldhavebeenifpeoplehadperfectforesight).Theexpost Forexample,CooperandKaplanis(1991)documentsthatdomesticequitiesaccountedfor98%ofU.S.investors'portfoliosin1990.Similarly,Japanese(87%),U.K.(79%)andWestGerman(75%)investorsstronglyfavordomesticassetsintheirportfolios.InHongKong,whichisverysmall,veryopen,andisnotaverydiversi¯edeconomy,investorsstillinvestclosetohalfoftheirstockportfolioinHongKongstocks.11 Solnik(1974),Stulz(1981),AdlerandDumas(1983),StockmanandDellas(1989),Stulz(1992),Uppal(1993)andGlassmanandRiddick(1993),amongothers,describemodelsthatderiveahomebiasininvestor'sportfoliosarisingfromdi®erencesininvestors'consumptionbasketsacrosscountriesorfromthepresenceofnon-tradedgoods. 10 19 rateofreturnondefault-freeYendenominatedbondsturnedouttobesubstantiallyhigherthantherateofreturnondefault-freedollardenominatedbonds.IfinvestorshadperfectforesightandhadanticipatedtheproductivityimprovementsrealizedinJapanduringthe1980s,internationalarbitragewouldhaveforcedJapanesenominalratesdowntoalevelwhereJapaneserealratesofinterestwouldhavebeenmuchlowerthantheyactuallywereandquitepossiblynegative.Itislikelythatbarrierstocapital°owsincreasedratherthandecreasedJapan'srealinterestrate. Itshouldbestressedthatitisdi®erencesinthechangesinproductivity,bothacrosscountriesandacrosssectorswithinthecountries,thata®ectrealratesofinterest,P/Eratiosandinvestmentexpenditures.Realratesofinterestwillbelowinacountrywhenitsproductivityisgrowingmuchfasterinitstradedgoodssector(relativetoitstradingpartners)thaninitsnon-tradedgoodssector.Uniformincreasesintheproductivityofaneconomymayhavenoe®ectonthesevariables. Thesedi®erencesinproductivitygrowthrates,whichdriveourresults,arelikelytooccurindevelopingeconomiessincetechnologytransfersfromdevelopedtolessdevelopedcountriestendtobefocusedonthetradedgoodssector.Itshouldalsobenotedthatsinceitisthedi®erencebetweentheproductivitygrowthratesinthetradedandnon-tradedgoodssectorthatdriveourresults,thatverysluggishproductivityimprovementsinthenon-tradedsectorscanhavethesamee®ectonrealexchangeratesasrapidproductivityimprovementsinthetradedgoodssector.Forexample,thelargeproductivitygainsinretailinggeneratedby¯rmssuchasWal-MartintheU.S.wouldhavethee®ectofincreasingrealratesofinterestintheU.S.relativetoJapan.Perhaps,theinferiorproductivitygainsinJapan'snon-tradedsectorhadaslargeane®ectonitsappreciatingcurrencyasitssuperiorproductivitygainsinitstradedgoodssector. OuranalysismayalsoprovideinsightsrelatingtotheallegedwillingnessofJapanese¯rmstosell(dump)theirproductsonworldmarketsatverylow,andinsomecases,negativepro¯tmargins.Weshowthat¯rmswillindeedselltheiroutputatlowerpro¯tmarginsifananticipatedincreaseinthepriceofcapitalgoodsleadsthemtotemporarily`overinvest'incapitalequipment.Ananticipatedincreaseinthecostofproducingcapitalgoodswilloccurwhenthetradedgoodssectorsareexpectedtoexperiencegreaterproductivitygainsthanthesectorthatproducescapitalgoods.Forexample,ananticipatedproductivity 20 increaseintheJapaneseautomobilesectorthatisnotmatchedbyacomparableproductivitygaininthesectorthatproducescapitalgoodswillresultinanincreaseinthepriceofcapitalequipment(duetoincreasedlaborcosts).Anticipatingthisincreaseincapitalgoodsprices,theJapaneseauto¯rmswillhaveatendencyto`overinvest'today,inordertoavoidthehighercapitalgoodspricesinthefuture.Inequilibrium,theyarewillingtoachievelowerinitialpro¯tsfromtheircapitalinvestmentsbecausetheyanticipatethattheircapitalequipmentwillappreciateinpriceovertime. Dotheseincentivesto`overinvest'putU.S.¯rmsatacompetitivedisadvantage?Ourmodelassumesthatthecountryexperiencingtheproductivityshockisverysmall,sothat¯rmsinthelargecountryareuna®ectedbytheincreaseinthesmallcountry'sinvestmentincapitalgoods.However,wewouldexpectthatinageneralequilibriumsettingwithtwolargecountriessuchasJapanandtheU.S.,anincreaseincapitalgoodsinvestmentinJapancouldresultinano®settingdecreaseincapitalinvestmentintheU.S..InsomesensewemightsaythattheU.S.¯rmsareatacompetitivedisadvantagesinceinsuchageneralequilibriumeconomicforcesgivetheU.S.¯rmsanincentivetoatleasttemporarilygiveupmarketsharetotheirJapanesecounterpartswithexcesscapacity. 5Conclusion Themodelpresentedinthispaperanalyzeshowproductivityshockscana®ectrealinter-estrates,realexchangeratesandprice/earningsmultiples.Ouranalysisillustrateshowintuitiondevelopedfromstudyinglargedomesticeconomiesmaynotbeapplicabletosmallopeneconomiesinaninternationalsetting.Intheabsenceofinternationalcapital°ows,ananticipatedincreaseinfutureproductivityislikelytoleadtoanincreaseintherealrateofinterestasindividualsattempttoborrowmoretoshiftconsumptionfromthefuture,whentheywillbewealthier,tothepresent,whenthemarginalutilityofconsumptionishigher. Inasmallopeneconomy,individualswillalsohaveanincentivetoshiftincome.How-ever,sincetheyaresmallrelativetotheworldcapitalmarkets,theyhavenoe®ectonworldinterestratesandtheirproductivityincreasewillnota®ectthepriceofgoodsthatarefreelytradeableinternationally.Incontrast,aproductivityshockwilla®ectthepricesofthenon-tradedgoodsintheeconomy.Underfairlyplausibleconditions,aproductivity 21 shockwillincreasethepriceofnon-tradedgoods,implyinganincreasedrateofin°ationandadecreasedrealrateofinterest. Ouranalysisindicatesthatthisdeclineinrealratesisgenerallyassociatedwithanincreaseinprice/earningsratios.Intuitively,investorsanticipatetheincreasedcostofpro-ducingcapitalgoodsinthefuture,andthusoverproducecapitalgoodsinthepresentperiod.Thisleadstobothhighercostsofproducingthecapitalgoodaswellaslowerequilibriumrentalratesonthecapital.Ournumericalresultssuggestthatthesee®ectscanexplaintheveryhighprice/earningsratiosobservedinJapanduringthemid-1980s. Thesenumericalresultsalsoillustratehowproductivityshockscandi®erentiallya®ectprice/earningsratiosindi®erentindustries.Forexample,industrieswhosecapitalgoodsareproducedwithmorelabor-intensiveproductionprocesseswillhavehigherprice/earningsratiosthanindustrieswithcapitalgoodsthatareproducedmainlyfromexistingcapital. OurmodelisdirectlyapplicabletotheanalysisofthesituationinHongKongduringtheearlytomid1990s,whererealinterestrateswerenegativeandalsoprovidesinsights,discussedabove,aboutthedi®erencesinrealratesintheU.S.andJapanduringthe1980s.Thepopular`segmentedmarkets'explanationforthesedi®erencessuggeststhatrealrateswere`toolow'inJapan(becauseoftheirhighersavingsrate)and`toohigh'intheU.S.(becauseofhighgovernmentde¯cits).Ithasbeenarguedthatthis,inturn,leadstoacompetitiveadvantageforJapanese¯rmsovertheirU.S.counterparts,therebycausinglessthanthee±cientlevelofinvestmentintheU.S.comparedtoJapan.Incontrast,thedi®erentlevelsofinvestmentsinthetwocountriesariseinourmodelbecauseofane±cientreallocationofresourcescausedbyaproductivityshock.Theallocationofinvestmentcapitalinthismodelfollowsasaresultofunimpededcapital°owsacrosscountriesratherthanasaresultofsegmentedmarkets.Ouranalysis,thus,suggestsverydi®erentpolicyimplicationsthanthosesuggestedbythesegmentedmarketsview. Beforeclosing,wemustnotethatalthoughouranalysisisdirectlyapplicabletotheHongKongandJapanesesituationsdescribedabove,oneshouldbecautiousaboutdirectlyapplyingtheanalysistocountrieslikeChinaandIndiawhichhaveexperiencedsubstantialproductivityimprovementsintheiragriculturalsectors.Inourmodel,theproductivityimprovementsinthetradedgoodssectorleadstoanincreaseintheproductionofthetradedgoodswhichinturngeneratesincreaseddemandforlaborandhigherwages.In 22 contrast,productivityimprovementsinagricultureoftenresultinadecreaseinthedemandforlabor.12Theselabor-savingproductivityincreasescouldincreasethesupplyofnon-farmlabor,whichwouldinturnlowerwagesandreducethepriceofnon-tradedgoods.Thenegativee®ectonwagescomingfromtheproductivityimprovementsintheagriculturalsectorcouldo®setthepositivee®ectonwagescomingfromtheproductivityincreasesinthetradedgoodssectorwhichcouldo®setthereductioninrealratesandtheincreaseinprice/earningsratiosdescribedinthispaper.Perhaps,thisexplainswhywedon'ttendtoobserveverylowrealratesandveryhighprice/earningsratiosinmanydevelopingcountries. Onecouldshowthiswithinthecontextofourmodelbyassumingthatthecapitalcomponentoftheproductionofthetraded(agriculturalgood),inthiscaseland,isin¯xedsupply. 12 23 Appendix BeforeprovingPropositions2-4,wemust¯rstprovethefollowingfourlemmas:Lemma1IfªT=ªF=1orif®F=®TandªF=ªT,thenProof:From(11)and(13),weget F1 ªT(1¡®T) LT1 µ ¶®T PF0RF0 = PF1RF1 and PF1PF0 =¦T. = (1¡®N)KN1 ®NLN1 8N2fB;Hg:(18) Substitutingin(17)forPF1from(13)and(18)andforRF1from(15)andsimplifying,weget, µ F1 LT1 ¶1¡®T®F = µ 1+r¤®F ªTªFA¤r+±F1¡®F1¡®T ¶1¡®F ;(19) where F A´®T®®F : From(10)and(12),weget, F0 (1¡®T) LT0 µ ¶®T = (1¡®N)KN0 ®NLN0 8N2fB;Hg:(20) Now,from(16)and(17),wehave PF0=RF0 1¡±F1+r¤+RF1:1+ir¤+±F · ¸ (21) SubstitutingforPF0from(12)and(20)andforRF0from(14)andsimplifying,weget, µ F0LT0 ¶1¡®T®F 1¡±F =A1+¤¼R; r+±FF RF1=RF0 :¦T (22) where, ¼RF´ (23) Substitutingin(22)from(19),(23),(14)and(15)andsimplifying,weget, îT!1¡®F1¡®T ¼RFªT ªF= · 1¼RF1¡±F+¤r+±F ¸¤ r+±F 1+r¤:(24) ForN=F,dividing(16)byRF0andsimplifying,weget PF01¡±F =1+¤¼R:RF0r+±FF (25) 24 IfªT=ªF=1orif®F=®TandªF=ªT,thenfrom(24),¼RF=1.Substituting¼RF=1intheaboveequationimpliesthat PF01+r¤PF1 =¤=:RF0r+±FRF1 ForN=F,dividing(16)byPF0,weget, 1= 1¡±FPF1RF0 +:PF01+iPF0 PF1PF0 (26) (27) Substitutingfrom(26)andsimplifyingweget=¦T.Lemma2¼RFisincreasinginªTanddecreasinginªF,®Fand®T.Proof:Followsfromimplicitlydi®erentiating(24)andsimplifying.Lemma3Thepricetorentalratioinperiod1forfactories,inthepriceoffactoriesfromperiod0to1,and®F. Proof:Followsdirectlyfrom(25),(27)andLemma2.Lemma4Thepriceoffactoriesinperiod0,PF0,andwagesinperiod0,W0,areincreasinginªTanddecreasinginªF.Therentalrateonfactoriesinperiod0,RF0isdecreasinginªTandincreasinginªF. Proof:ResultsforW0andRF0followdirectlyfrom(10),(14),(22)andLemma2.ToseetheresultforPF0,wesubstituteforRF0from(14)in(25)andsimplifytoobtain: PF0=PT0®TA 1¡®¡1¡®TT®F PF1PF0 PF0RF0 andtherateofincrease areincreasinginªTanddecreasinginªF · 1¼RF1¡±F+¤r+±F ¸®T(1¡®F) 1¡®T®F :(28) theresultthenfollowsfromLemma2.ProofofProposition2FollowsfromLemmas1-4.25 ProofofProposition3From(18)and(20),wehave µ KN1=LN1KN0=LN0 ¶ =ªT µ F1=LT1F0=LT0 ¶®T 8N2fB;H;Fg:(29) Substitutingfrom(23),(14)and(15)andrearranging,weget ªT From(10)and(11),weget PN1PF1ªF =PN0PF0ªN µµ F1=LT1 F0=LT0 ¶®T = îT!¡1 1¡®T ¼RFªT :(30) KN1=LN1KN0=LN0 ¶®F¡®N 8N2fB;Hg: Substitutingfrom(29)and(30)andrearranging,weget PN1PF1ªF6 =4³PN0PF0ªN 2 ªF ¼RF1+ 1¡±Fr¤+±F ´r¤+±F1+r¤3®F¡®N75 1¡®F 8N2fB;Hg:(31) Sincethattheterminthesquarebracketsin(31)isstrictlygreaterthanone(because¼RF>1andªF¸1),theresultsabout 1= theresultsfor PN0RN0 PN1PN0 followimmediatelybyinspection.Also,since RN01¡±NPN1 +;PN01+iPN0 follow.ProofofProposition4FollowsfromLemmas1-4.26 References Adler,MichaelandBernardDumas.1983.InternationalPortfolioChoiceandCorporationFinance:ASynthesis.JournalofFinance38.925-984. 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Wong,RichardY.C.,Pak-WaiLiuandAlanK.F.Siu.1991.In°ationinHongKong:Patterns,CausesandPolicies.ResearchReport,BusinessandProfessionalsFederationofHongKong.October. 29 Figure 1 Price/Rental Ratios as a function of the Years of Productivity Shock 140 120 αT =.10, αF =.10100 Price/Rental Ratios80 αT =.10, αF =.2560 αT =.25, αF =.2540 αF =.25αT =.50,20 00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Years of Productivity Shock 因篇幅问题不能全部显示，请点此查看更多更全内容