ObstfeldRogoffChapter1A

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FOUNDATIONS OF INTERNATIONAL MACROECONOMICS Maurice Obstfeld Kenneth Rogoff 1 Intertemporal Trade and the Current Account Balance One fundamental way open and closed economies differ is that an open economy can borrow resources from the rest of the world or lend them abroad. With the aid of loans from foreigners, an economy with a temporary income shortfall can avoid a sharp contraction of consumption and investment. Similarly, a country with ample savings can lend and parti
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  FOUNDATIONS OF INTERNATIONALMACROECONOMICS MauriceObstfeld Kenneth Rogoff 1 IntertemporalTradeandtheCurrentAccountBalance Onefundamentalwayopenandclosedeconomiesdifferisthatanopeneconomycanborrowresourcesfromtherest of theworldorlendthemabroad.Withtheaid of loansfromforeigners,aneconomywithatemporaryincomeshortfallcanavoidasharpcontraction of consumptionandinvestment.Similarly,acountrywithamplesavingscanlendandparticipateinproductiveinvestmentprojectsoverseas.Resourceexchangesacrosstimearecalled intertemporaltrade. Much of themacroeconomicactioninanopeneconomyisconnectedwithitsintertemporaltrade,whichismeasuredbythecurrentaccount of thebalance of payments.Thepurpose of thischapteristoillustratethebasiceconomicprinciplesthatgovernintertemporaltradepatterns:whenarecountriesforeignborrowers,whendotheylendabroad,whatroledogovernmentpoliciesplay,andwbatarethewelfareimplications of internationalcapital-marketintegration? In theprocess,wetakea.firstlookatthekeyfactorsbehindaggregateconsumptionandinvestmentbehaviorandatthedetermination of worldinterestrates.Weassumethroughoutthatonlyonegoodexistsoneachdate,thebettertofocusattentiononaggregateinternationalresourceflowswithoutintroducingconsiderationsrelatedtochangingintratemporalprices.Alargepart of internationaleconomicsis, of course,concernedwithrelativedomesticandinternationalprices.Asseverallaterchaptersillustrate,however,themacroeconomicrolesthesepricesplayareunderstoodmosteasily if onestartsoffbyabstractingfromthecomplicationstheycreate. 1.1ASmallTwo-PeriodEndowmentEconomy You probablyarefamiliarwiththestandardtwo-periodmicroeconomicmodel of saving,duetoIrvingFisher(1930).WebeginbyadaptingFisher'smodeltothecase of asmallopeneconomythatconsumesasinglegoodandlastsfortwoperiods,labeled1and2.Althoughthemodelmayseemsimple,itisausefulbuildingblockforthemorerealisticmodelsdevelopedlater. Our maingoalinthissectionistodescribehowacountrycangainfromrearrangingthetiming of itsconsumptionthroughinternationalborrowingandlending. 1.1.1TheConsumer'sProblem Anindividual i maximizeslifetimeutility, U;, whichdepends on periodconsumptionlevels,denoted c i: 0<f3<1. (1)The MIT PressCambridge,MassachusettsLondon,England In thisequation f3 isafixedpreferenceparameter,calledthesubjectivediscountortime-preferencefactor,thatmeasurestheindividual'simpatience to consume.  2 IntertemporalTrade and theCurrent AccountBalance 3 1.1A Small1Wo-PeriodEndowmentEconomy As usual,weassumethattheperiodutilityfunction u(c i) I'S stn' tl· '. .cymcreasmgmconsumptIOnandstnctlyconcave: u' (c ') > 0 and u (c i) < 0.1 I ~ Y'. denotetheindividual'soutputand r therealinterestrateforborrowingorenb.gmthe . w 0 ~ l d capitalmarketondate 1. Thenconsumptionmustbechosensu ~ e c t tothelIfetImebudgetconstraintThisconstraintrestrictsthe p r e s ~ n t value of consumptionspendingtoequalthepresent v ~ u e 2 of output.Output IS perishableandthuscannotbestoredforlaterconsumptIOn. We assume,asweshalluntilweintroduceuncertaintyaboutfutureincomein ~ h a p t e r 2, thattheconsumerbasesdecisionson perfectforesight of thefutur Thi ~ s anextremeassumption,butanaturalonetomakewheneverthe c o m p l : ~ i t i e : ~ t r o d u c e d by u n ~ e r t a i n t y are of secondaryrelevancetotheproblembeingstudIed:PerfectforesIghtensuresthatamodel'spredictionsaredrivenbyitsintrinsic lOgIC ~ a t h e r thanbyadhocandarbitraryassumptionsabouthowpeopleformex p e c t a t I O ~ S . Unlessthefocus is ontheeconomiceffects of aparticularexpectational : s s u ~ p t i ~ n perse,thedeterministicmodels of thisbookthereforeassumeperfectloreslght. To bso.lve the p r 7 ~ l e m of maximizingeq. (1) subjecttoeq.(2),usethelattertosustitutefor c 2 mtheformer, so thattheindividual'soptimizationproblreducestoem (3) (4) 1+r f J u ' ( c ~ ) u'(ci) Theleft-handsideistheconsumer'smarginalrate of substitution of present(date 1) forfuture(date2)consumption,whiletheright-handside is theprice of futureconsumptioninterms of presentconsumption. As usual,individual i's optimalconsumptionplanisfoundbycombiningthefirst-ordercondition (3) [or(4)]withtheintertemporalbudgetconstraint(2).Animportantspecialcaseistheoneinwhich fJ = 1/(1 + r), so thatthesubjectivediscountfactorequalsthemarketdiscountfactor. In thiscasetheEulerequationbecomes u'(ci) = u ' ( c ~ ) , whichimpliesthattheconsumerdesiresafiatlifetimeconsumptionpath, ci = c ~ . Budgetconstraint(2)thenimpliesthatconsumptioninbothperiodsis c , wherewhich is calledan intertemporalEulerequation. 4 ThisEulerequation,whichwillrecurinmanyguises,hasasimpleinterpretation:atautilitymaximum,theconsumercannotgainfromfeasibleshifts of consumptionbetweenperiods.Aoneunitreductioninfirst-periodconsumption,forexample,lowers Ul by u'(ci). Theconsumptionunitthussavedcanbeconverted(bylendingit)into I + r units of second-periodconsumptionthatraise Ul by (1 + r ) f J u ' ( c ~ ) . TheEulerequation (3) thusstatesthatatanoptimumthesetwoquantitiesareequal. An alternativeandimportantinterpretation of eq. (3) thattranslatesitintolanguagemoreclosely r e s e m ~ l i n g that of staticpricetheoryissuggestedbywritingitas (2) i.i c 2 . y' c I + __ =y' + __ _ 1+r I 1+r' 4. TheSwissmathematicianLeonhardEuler (1707-1783) servedatonetime as thecourtmathematician to CatherinetheGreat of Russia.Thedynamicequationbearinghisnamearoseoriginallyintheproblemoffindingtheso-called brachistochrone, whichistheleast-timepathinaverticalplaneforanobjectpulled by gravitybetweentwospecifiedpoints. We assumethat all individualsintheeconomyareidenticalandthatpopulationsize is 1. Thisassumptionallows us todroptheindividualsuperscript i andtoidentifypercapitaquantityvariableswithnationalaggregatequantities,whichwedenotebyuppercase,nonsuperscriptedletters.Thus, if Cstandsforaggregateconsumptionand Y foraggregateoutput,theassumption of ahomogeneouspopulation of size1impliesthat c i = Cand yi = Y forallindividuals i. Ourassumeddemographicssimplifythenotationbymakingtherepresentativeindividual'sfirst-orderconditionsdescribeaggregatedynamicbehavior.TheEulerequation(3),totakeThefirst-orderconditionforthisproblemis 1. Untilfurthernotice,wealsoassumethatlim u'(c i) = 00. CI -70 !he purpose of thisassumptionis to ensurethatindividual al .. III everyperiod, so thatwedon'thavetdd ~ als w ~ y s desrreatleastalittleconsumptionmaximizationproblemsconsideredlater. 0 aormconstramtsoftheformc' ::: 0 to theutilityWheneverwerefer to thesubjectivetime-preferen .suchthat ,8 = 1/(1 + 8),thatis,8 = (1 _ ,8)/,8. ce rate III thisbook,we Will meantheparameter8 2. Atapositiverateofinterest r nobodwould.seehowthisintertemporal a l l o c ~ t i o n p r ~ b l hwant to s ~ o r e output III anycase. In section1.2wewillincapitaltobeusedinproducingfuture o u ~ ~ t ~ angeswenoutputcanbeIllvested,thatis,embodied 3. Evenundertheperfectforesight ass ti. expectation or(worse) expected V a l u e ~ J a on ~ e b : u a ~ s o ~ e l J m e s looselyrefer to anindividual'senvironment,theseexpectationsareheldwith v:a ti e.ou ~ ouldunderstandthatinanonstochastic as inlaterchaptersdsu ~ e c vecertamty.Onlywhenthereisrealuncertainty,areexpectevaluesaveragesovernondegenerateprobabilitydistributions.' c = [(1 + r)y( + y ~ ] 2+r 1.1.2EquilibriumoftheSmallOpenEconomy (5)  4IntertemporalTradeandtheCurrentAccountBalance 5 1.1 ASmallTwo-PeriodEndowmentEconomy oneinstance,willalsogovernthemotionof aggregate consumptionunderourconvention. We mustkeepinmind,however,thatournotationalshortcut,whileinnocuousinthischapter,isnotappropriateineverysetting.Inlaterchapterswereintroduceindividuallysuperscriptedlowercasequantityvariableswheneverconsumerheterogeneityandthedistinctionbetweenpercapitaandtotalquantitiesareim-portant...Sincetheonlypriceinthemodel is therealinterestrate r, andthis IS exogenouslygiventothesmalleconomybytheworldcapitalmarket,nationalaggregatequantitiesareequilibriumquantities.Thatis,thesmalleconomycancarryoutanyintertemporalexchange of consumptionitdesiresatthegivenworldinterestrate r, subjectonlytoitsbudgetconstraint.Forexample, if the s U b j e c ~ v e andmarketdiscountfactorsarethesame,eq.(5),writtenwithCinplace of c' and Y inplace of yi , describesaggregateequilibriumconsumption..Theideaofarepresentativenationalconsumer,thoughacommondevIceinmodernmacroeconomicmodeling,mayseemimplausible.Thereare,however,threegoodreasonsfortakingtherepresentative-consumercase as astartingpoint.First,severalusefulinsightsintothemacroeconomydonotdependonadetailedconsideration of householddifferences. An instanceisthepre-.dictionthatmoney-supplychangesareneutralinthelongrun.Second,thereareimportantcaseswhereonecanrigorouslyjustifyusingtherepresentative- 5 d1.. agentmodeltodescribeaggregatebehavior.Finally,manymoesm l.nter- nationalmacroeconomicsareinterestingpreciselybecausetheyassumedifferencesbetweenresidentsofdifferentcountries.Sometimesthesimplestwaytofocusonthesecross-countrydifferences is todownplaydifferenceswithincountries. We haveseen[ineq.(5)]thatwhen f3 = I/O + r), thetimepath of aggregateconsumptionisflat.Thispredictionofthemodelcapturestheideathat,otherthingsthesame,countrieswillwishto smooth theirconsumption.Whenthesubjectivetime-preferencerateandthemarketinterestratediffer,themotivationtosmoothconsumptionismodifiedbyanincentiveto tilt theconsumptionpath.Suppose,forexample,that f3 > I/O + r) butCl = Cz. Inthiscasetheworldcapitalmarketoffersthecountryarate of returnthatmorethancompensatesitforthepostponementofalittlemoreconsumption.AccordingtotheEulerequation(3), U'(Cl) shouldexceed u' (Cz) inequilibrium;thatis,individualsintheeconomymaximizeutilitybyarrangingforconsumptiontorisebetweendates1and 2. Theeffects of arisein 5. Onedoesnotneedtoassumeliterallythatallindividualsareidenticaltoconcludethat a g g r e g ~ t e consumptionwillbehaveas if chosenbyasinglemaximizingagent.Under w e l l - ~ e f i n e d butratherstrIngentpreferenceassumptions,individualbehaviorcanbeaggregatedexactly, as discussedbyDeaton ~ d Muellbauer(l980,ch.6). We deferaformal d i s c ~ s s i o n of a g ~ e g a t i ~ n untilChapter5. F.or aperspectiveonwaysinwhichtherepresentative-agentparadigmcanbeIDlsleadmg,however,seeKinnan (199Z). r oninitialconsumptionandonsavingareratherintricate. We postponediscussingthemuntillaterinthechapter. 1.1.3InternationalBorrowingandLending,theCurrentAccount,andtheGainsfromTrade Let'slookfirstathowintertemporaltradeallowstheeconomytoallocateitsconsumptionovertime. 1.1.3.1DefiningtheCurrentAccount Becauseinternationalborrowingandlendingarepossible,thereisnoreasonforanopeneconomy'sconsumptiontobecloselytiedtoitscurrentoutput.Providedallloansarerepaidwithinterest,theeconomy'sintertemporalbudgetconstraint(2)isrespec!ed.Inthespecialcase f3 = 1/(1 + r), consumptionisflatatthelevelCl = Cz = c:. ineq.(5),butoutputneednotbe. If, forexample, Yl < Yz, thecountryborrowsC- Yl fromforeignersondate 1, repaying 0 + r) (C - Yl) ondate 2. Wheneverdate2consumptionequalsoutputonthatdatelesstheinterestandprincipal On prior borrowing-that is, Cz = Yz - 0 + r)(Cl - Yl)-the economy'sintertemporalbudgetconstraintobviouslyholdstrue..Acountry's currentaccountbalance overaperiodisthechangeinthevalue of itsnetclaimsontherest of the world-the changeinitsnetforeignassets.Forexample,inourinitialsimplemodelwithoutcapitalaccumulation,acountry'sfirstperiodcurrentaccountissimplynationalsaving. (In section1.2wewillseethatingeneralacountry'scurrentaccountisnationalsavinglessdomesticinvestment.)Thecurrentaccountbalanceissaidtobeinsurplus if positive, so thattheeconomyasawholeislending,andindeficit if negative,sothattheeconomy is borrowing.Ourdefinition of acountry'scurrentaccountbalance as theincreaseinitsnetclaimsonforeignersmaypuzzleyou if youareusedtothinking of thecurrentaccount as acountry's net exports of goodsandservices(where service exportsincludetheservices of domesticcapitaloperatingabroad, as measuredbyinterestanddividendpaymentsonthoseassets).Remember,however,thatacountrywithpositivenetexportsmustbeacquiringforeignassets of equalvaluebecauseit. is sellingmoretoforeignersthanitisbuyingfromthem;andacountrywithnegativenetexportsmustbeborrowinganequalamounttofinanceitsdeficitwithforeigners.Balance-of-paymentsstatisticsrecordacountry'snetsales of assetstoforeignersunderits capitalaccountbalance. Becauseapaymentisreceivedfromforeignersforanygoodorserviceacountryexports,everypositiveitem of itsnetexportsisassociatedwithanequal-valuenegativeiteminitscapital account namely,theassociatedpaymentfromabroad,whichisaforeignassetacquired.Thus, as apurematter of accounting,thenetexportsurplusandthecapitalaccountsurplussumidenticallytozero.Hence,thecapitalaccountsurplusprecededbya  6 IntertemporalTradeand the CurrentAccountBalance 7 1.1A SmallTwo-PeriodEndowmentEconomy 1.1.3.3The Current Account and theBudgetConstraintintheTwo-PeriodModel GDPis Y tã Typicallythedifferencebetweennationalanddomesticproductisarathersmallnumber,butforsomecountries,thosewhichhaveamassedlargestocks of foreignwealthorincurredsubstantialforeigndebts,thedifferencecanbesignificant.Table 1.1 showsseveral of thesecases. Table1.1GNPversusGDPforSelectedCountries,1990(dollarspercapita)PercentDifference -1.9 -2.7-4.9 29.9 -3.2 12.41.0GNP17,0002,68020,4707,05011,16019,86021,790GDP17,3272,75321,5155,42911,53317,66921,569 Source: WorldBank, WorldDevelopmentReport1992. AustraliaBrazilCanadaSaudiArabiaSingaporeUnitedArabEmiratesUnitedStatesCountry (6) where rtBt is interestearnedonforeignassetsacquiredpreviously.(Thisconventionmakes rt theone-periodinterestratethatprevailedondate t -1.) minus sign-the net increase inforeignassetholdings-equalsthecurrentaccountbalance.Despitethisaccountingequivalence,thereisanimportantreasonforfocusingontheforeignassetaccumulationview of thecurrentaccount. It plainlyshowsthatthecurrentaccountrepresentstrade over time,whereasthenetexportsviewdrawsattentiontofactorsdetennininggrossexportsandimports within asingletimeperiod.Thosefactorsarefarmorethanunimportantdetails, as we shallseeinsubsequentchapters,buttostressthemattheoutsetwouldonlyobscurethebasicprinciples of intertemporaltrade. To clarifytheconcept of thecurrentaccount,let Bt+ 1 bethevalue of theeconomy'snetforeignassetsattheend of aperiod t. Thecurrentaccountbalanceoverperiod t is defined as CAt = Bt +1 - Bt. Ingeneral,thedate t currentaccountforacountrywithnocapitalaccumulationorgovernmentspending is 1.1.3.2GrossNationalProduct and GrossDomesticProduct Equation(6)showsthatacountry'scurrentaccount(ornetexportsurplus)isthedifferencebetweenits totalincome anditsconsumption.Thenationalincome of aneconomy is alsocalledits grossnational product (GNP)and is measured as thesum of twocomponents:thevalue of thefinaloutputproducedwithinitsborders and netinternationalfactorpayments.Here,thesefactorpaymentsconsist of interestanddividendearningsontheeconomy'snetforeignassets,whichareviewed as domesticcapitaloperatingabroad. 6 (Inlinewiththedefinition of netexportsgivenearlier,acountry'searningsonitsforeignassetsareconsideredpart of itsnationalproductdespitethefactthatthisproductisgeneratedabroad.)Interms of ourformalmodel,GNPoveranyperiod t is Yt + rtBt, as justindicated.Thefirstcomponent of nationalproduct,outputproducedwithinacountry'sgeographicalborders, is called grossdomestic product (GDP).Inthepresentmodel 6. Strictlyspeaking,nationalincomeequalsnationalproductplusnetunrequitedtransferpaymentsfromabroad(includingitemslikereparationspaymentsandworkers'remittancestofamilymembersinothercountries).Workers'remittances,whichrepresentapaymentforexportedlaborservices,arenottrulyunrequitedandarecompletelyanalogoustoassetearnings,whicharepaymentsforcapitalservices. We willtreatthemassuch in section1.5. In practice,however,nationalincomeaccountantsusuallydon'ttreatremittances as paymentsforserviceexports.Theterm gross in GNPreflectsitsfailuretoaccountfordepreciation of capital-a factorabsentfromourtheoreticalmodel.Whendepreciationoccurs, net nationalproduct(NNP)measuresnationalincomelessdepreciation.EmpiricaleconomistsprefertoworkwithGNPratherthan NNP data,especially in internationalcomparisons,becauseactualnationalaccountestimates of depreciationareaccountingmeasuresheavilyinfluencedbydomestic tax laws.Reporteddepreciationfiguresthereforearequiteunreliableandcandifferwidelyfromcountrytocountry.FortheUnitedStates,aballparkestimate of annualdepreciationwould be around10percent of GNP. . Ourformulation of budgetconstraint (2) tacitlyassumedthat B1 = 0,making CAl = Y1 - Cion theformalmodel'sdate1(butnotingeneral).Bywritingconstraint (2) as astrictequality,wehavealsoassumedthattheeconomyendsperiod 2 holdingnouncollectedclaimsonforeigners.(Thatis, B3 = O. Obviouslyforeignersdonotwishtoexpireholdinguncollectedclaimsonthehomecountryeither!)Thus,C A2 = Y2 + rB2 - C2 = Y2 + r(Yl - C1) - C2 = -(Y1 - C1) = -B2 = -CAl, wherethethirdequalityinthischainfollowsfromtheeconomy'sintertemporalbudgetconstraint,eq. (2). Overanystretch of time, as overasingleperiod,acountry'scumulativecurrentaccountbalanceisthechangeinitsnetforeignassets,butinourtwo-periodmodelwithzeroinitialandterminalassets,C A I + C A 2 = B3 - B1 =0. Figure 1.1 combinestherepresentativeindividual'sindifferencecurveswiththeintertemporalbudgetconstraint (2), graphed as Itprovidesadiagrammaticderivation of thesmalleconomy'sequilibriumandtheimpliedtrajectory of itscurrentaccount.(Thefiguremakesnospecialassumptionabouttherelationbetween fJ and1 + r.) Theeconomy'soptimalconsumptionchoiceisatpointC,wherethebudgetconstraintistangenttothehighest
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