1 IntertemporalTradeandthe CurrentAccountBalance FOUNDATIONS OFINTERNATIONALMACROECONOMICS Onefundamental way openandclosedeconomiesdifferisthat an openeconomy MauriceObstfeld can borrow resources from the rest ofthe world or lend them abroad. With the aid ofloans from foreigners, an economy witha temporary income shortfall can KennethRogoff avoidasharpcontractionofconsumptionandinvestment.Similarly,acountrywith amplesavingscanlendandparticipateinproductiveinvestmentprojectsoverseas. Resourceexchangesacrosstimearecalledintertemporaltrade. Much ofthe macroeconomic action in an open economy is connected with its intertemporal trade, which is measured by the current account ofthe balance of payments. The purpose of this chapter is to illustrate the basic economic prin ciples that govern intertemporal trade patterns: when are countries foreign bor rowers, when do they lend abroad, what role do government policies play, and wbatarethewelfareimplicationsofinternationalcapital-marketintegration?Inthe process, wetake a.firstlookatthekey factors behindaggregateconsumption and investment behavior and atthe determination ofworld interest rates. We assume throughout that only one good exists on each date, the betterto focus attention on aggregate international resource flows without introducing considerations re latedtochangingintratemporalprices. Alargepartofinternationaleconomicsis, ofcourse, concerned with relative domestic and international prices. As several later chapters illustrate, however, the macroeconomic roles these prices play are understoodmosteasilyifonestartsoffbyabstractingfromthecomplicationsthey create. 1.1 ASmallTwo-PeriodEndowmentEconomy You probably arefamiliar withthestandardtwo-periodmicroeconomic modelof saving, due to Irving Fisher (1930). We begin by adaptingFisher's model to the case of a small open economy that consumes a single good and lasts for two periods, labeled 1 and 2. Although the model may seem simple, it is a useful buildingblockforthemorerealisticmodelsdevelopedlater.Ourmaingoalinthis section is to describe how a country can gain from rearranging the timing ofits consumptionthroughinternationalborrowingandlending. 1.1.1 TheConsumer'sProblem U;, Anindividuali maximizeslifetimeutility, whichdependsonperiodconsump tionlevels,denotedci: 0<f3<1. (1) In this equation f3 is a fixed preference parameter, called the subjective discount or time-preferencefactor, that measures the individual's impatience to consume. TheMITPress Cambridge,Massachusetts London,England 2 IntertemporalTradeandtheCurrentAccountBalance 3 1.1 ASmall1Wo-PeriodEndowmentEconomy As usual,'wea.ssumethatthe periodut.ilityfunction u(ci) I'S stn'ctly·mcreasm"gm (3) consumptIOnandstnctlyconcave:u'(c')> 0andu"(ci) < 0.1 I ~Y'.denotetheindividual'soutputandr therealinterestrateforborrowingor whichis calledanintertemporalEulerequation.4ThisEulerequation,whichwill en. gmthe.w0~ldcapitalmarketondate 1.Thenconsumptionmustbechosen recurin many guises, has asimpleinterpretation: at autility maximum, the con sub~ecttothelIfetImebudgetconstraint sumer cannot gain from feasible shifts ofconsumption between periods. A one i . unitreductioninfirst-period consumption, for example, lowers Ul byu'(ci). The ci +_c2_ =y'.+_y_2'_ consumptionunit thus saved can beconverted (by lending it) into I +r units of I 1+r I 1+r' (2) second-period consumption that raise Ul by (1 +r)fJu'(c~). The Euler equation This constraint restricts the pres~nt value ofconsumption spending to equal the (3)thusstatesthatatanoptimumthesetwoquantitiesareequal. present v~ue2ofoutput. Output IS perishable and thus cannot be stored forlater An alternative andimportantinterpretationofeq. (3) thattranslates itinto lan consumptIOn. guage moreclosely resem~lingthat ofstaticprice theory is suggestedby writing We assume, as we shall until we introduce uncertainty aboutfuture incomein itas ~hapter 2,thattheconsumerbasesdecisionsonperfectforesightofthefutur Thi fJu'(c~) I ~s compl:~itie: (4) an extreme assumption, but a natural one to make whenever the u'(ci) 1+r ~troduced un~ertainty by are ofsecondaryrelevance to the problembeing stud Ied:PerfectforesIght ensuresthatamodel's predictions aredrivenbyitsintrinsic Theleft-handsideis the consumer'smarginalrate ofsubstitutionofpresent(date ~ather lOgIC than byadhoc andarbitraryassumptions abouthowpeopleform ex 1)forfuture (date2)consumption, whiletheright-handsideis thepriceoffuture pectatIO~S. Unlessthefocusisontheeconomiceffectsofaparticularexpectational consumptioninterms ofpresentconsumption. :ssu~pti~nperse, the deterministicmodelsofthis bookthereforeassumeperfect As usual, individual i's optimal consumption plan is found by combining the loreslght. first-order condition (3) [or (4)] with the intertemporalbudget constraint (2). An Tobso.lve the pr7~lem of maximizing eq. (1) subject to eq. (2), use the latter important special case is the one in which fJ = 1/(1 +r), so that the subjective to su stitute for c2 m the former, so that the individual's optimization probl discountfactor equals the market discountfactor. Inthis casethe Eulerequation reducesto em becomes u'(ci) =u'(c~), which implies that the consumer desires a fiat lifetime consumptionpath,ci =c~.Budgetconstraint(2)thenimpliesthatconsumptionin bothperiodsisci,where c = + +y~] Thefirst-orderconditionforthisproblemis i [(1 r)y( (5) 2+r 1. Untilfurthernotice,wealsoassumethat 1.1.2 EquilibriumoftheSmallOpenEconomy lim u'(ci)= 00. Weassumethatallindividualsintheeconomyareidenticalandthatpopulationsize CI-70 is 1.This assumptionallowsustodroptheindividualsuperscripti andtoidentify !hepurposeofthisassumptionistoensurethatindividual al . . III every period, so that we don'thave t dd ~ al s w~ysdesrreatleastalittleconsumption percapitaquantity variables with nationalaggregatequantities, whichwe denote maximizationproblemsconsideredlater. 0 a orm constramts ofthe form c':::0 to the utility byuppercase, nonsuperscriptedletters. Thus, ifC stands for aggregateconsump Wheneverwerefertothesubjectivetime-preferen " . suchthat,8=1/(1+8),thatis,8=(1_ ,8)/,8. cerateIIIthisbook,weWillmeantheparameter8 tion and Y for aggregate output, the assumption ofahomogeneous population of is2ne.ecAahptoiwatapltohtosisitbiivenetuersraettedemionpfopirnraotledrauelcslitoncrg~tfniuootnbuorpedr~obuwl~o~utl~dhwanagnetstows~eorneoouuttppuuttcI.IaInanbyecIlalvsee.stIend,sethctaitonis,1e.2mwboedwieildl sgirzaeph1icismspilmiepslitfhyatthcein=otaCtioanndbyyim=akYingfotrhealrleipnrdeisveindtuaatilvsei.inOdiuvridausaslu'smfeidrstd-oemrdoer conditions describe aggregate dynamic behavior. The Euler equation (3), to take 3. Even undertheperfectforesighVtaalssue~Jtion ~eb:ua~so~elJ.mes "expectation"or(worse)"expected a loosely refer to anindividual's environment,theseexpectationsareheldwith v:atie. ou~ ouldunderstandthatinanonstochastic asinlaterchapters d su ~ec vecertamty.Onlywhenthereisrealuncertainty 4. TheSwissmathematicianLeonhardEuler(1707-1783)servedatonetimeasthecourtmathemati ,areexpecte valuesaveragesovernondegenerateprobabilitydistributions. ' ciantoCatherinetheGreatofRussia.Thedynamicequationbearinghisnamearoseoriginallyinthe problemoffindingtheso-calledbrachistochrone,whichistheleast-timepathinaverticalplaneforan objectpulledbygravitybetweentwospecifiedpoints. 4 IntertemporalTradeandtheCurrentAccountBalance 5 1.1 ASmallTwo-PeriodEndowmentEconomy oneinstance,willalsogovernthemotionofaggregateconsumptionunderourcon r oninitialconsumptionandonsavingareratherintricate.Wepostponediscussing vention. themuntillaterinthechapter. Wemustkeep in mind, however, that ournotationalshortcut, whileinnocuous in this chapter, is not appropriate in every setting. In later chapters we reintro 1.1.3 InternationalBorrowingandLending,theCurrentAccount,andtheGains fromTrade duce individually superscripted lowercase quantity variables wheneverconsumer heterogeneity and the distinction between per capita and total quantities are im- Let'slookfirst athowintertemporaltradeallows theeconomyto allocateits con portant. . . sumptionovertime. Since the only pricein the model is the real interestrate r, and this IS exoge nouslygiventothesmalleconomybytheworldcapitalmarket,nationalaggregate 1.1.3.1 DefiningtheCurrentAccount quantitiesareequilibriumquantities.Thatis,thesmalleconomycancarryoutany Because internationalborrowing and lending are possible, there is no reason for intertemporal exchange ofconsumption itdesires at the given world interestrate an openeconomy'sconsumptiontobecloselytiedto its currentoutput. Provided r, subjectonly to its budgetconstraint. Forexample, ifthe sUbjec~ve and market all loans are repaid with interest, the economy's intertemporal budget constraint discountfactors arethesame, eq. (5), writtenwith Cinplaceofc' and Yinplace (2)isrespec!ed. Inthespecialcasef3 = 1/(1+r), consumptionisflatatthelevel ofyi,describes aggregateequilibriumconsumption. . Cl = Cz= c:.ineq. (5),butoutputneednotbe.If,forexample,Yl < Yz, thecoun The idea of a representative national consumer, though a common devIce tryborrows C- Yl fromforeignersondate1,repaying0 +r)(C- Yl) ondate2. in modern macroeconomic modeling, may seem implausible. There are, how Wheneverdate2consumptionequalsoutputonthatdatelesstheinterestandprin ever, three good reasons for taking the representative-consumer case as a start cipal On prior borrowing-that is, Cz= Yz - 0 +r)(Cl - Yl)-the economy's ing point. First, several useful insights into the macroeconomy do not depend intertemporalbudgetconstraintobviouslyholds true. . on a detailed consideration of household differences. An instance is the pre- A country's currentaccount balance over a period is the change in the value .diction that money-supply changes are neutral in the long run. Second, there ofits netclaims ontherestoftheworld-thechangeinitsnetforeign assets. For are important cases where one can rigorously justify using the representative- example,inourinitialsimplemodelwithoutcapitalaccumulation,acountry'sfirst agent model to describe aggregate behavior.5 Finally, many mode1s m. l..nter- periodcurrentaccountissimplynationalsaving. (Insection1.2wewillseethatin national macroeconomics are interesting precisely because they assume differ general a country's current accountis national saving less domestic investment.) ences between residents of different countries. Sometimes the simplest way to Thecurrentaccountbalanceissaidtobeinsurplusifpositive,sothattheeconomy focus on these cross-country differences is to downplay differences within coun as a whole is lending, and in deficitifnegative, so that the economy is borrow tries. ing. Wehave seen [ineq. (5)] that when f3 = I/O +r), the time pathofaggregate Ourdefinition ofacountry's currentaccountbalance as the increaseinits net consumptionisflat.Thispredictionofthemodelcapturestheideathat,otherthings claims on foreigners may puzzle you ifyou are used to thinking ofthe current the same, countries will wish to smooth their consumption. When the subjective accountas acountry'snetexportsofgoods and services (where"service"exports time-preference rate andthe market interestrate differ, the motivation to smooth includetheservices ofdomesticcapitaloperatingabroad, as measuredbyinterest consumptionismodifiedbyanincentivetotilttheconsumptionpath. Suppose,for and dividendpayments onthose assets). Remember, however, thatacountry with example,thatf3 > I/O +r)butCl = Cz.Inthiscasetheworldcapitalmarketof positive net exports must be acquiring foreign assets of equal value because it fersthecountryarateofreturnthatmorethancompensatesitforthepostponement .is selling more to foreigners than it is buying from them; and a country with ofalittle more consumption. Accordingto the Eulerequation (3), U'(Cl) should negativenetexportsmustbeborrowinganequalamounttofinanceitsdeficitwith exceedu'(Cz) inequilibrium; thatis,individualsintheeconomymaximizeutility foreigners. Balance-of-payments statisticsrecord acountry's netsales ofassetsto byarrangingforconsumptiontorisebetweendates 1and2.Theeffectsofarisein foreigners underits capitalaccountbalance. Becauseapaymentisreceivedfrom foreigners foranygoodorserviceacountryexports,everypositiveitemofits net 5. Onedoesnotneedtoassumeliterallythatallindividuals areidenticaltoconcludethataggreg~te exports is associated with an equal-value negative item in its capital account consumptionwillbehaveasifchosenbyasinglemaximizingagent.Underwell-~efinedbutratherstrIn namely, the associated payment from abroad, which is a foreign asset acquired. gentpreferenceassumptions,individualbehaviorcanbeaggregatedexactly,asdiscussedbyDeaton~d Muellbauer(l980,ch.6).Wedeferaformaldisc~ssionofag~egati~nuntilChapter5.F.oraperspective Thus,asapurematterofaccounting,thenetexportsurplusandthecapitalaccount onwaysinwhichtherepresentative-agentparadigmcanbeIDlsleadmg,however,seeKinnan(199Z). surplus sumidenticallyto zero. Hence, thecapitalaccountsurplus precededby a 6 IntertemporalTradeandtheCurrentAccountBalance 7 1.1 ASmallTwo-PeriodEndowmentEconomy minussign-thenetincreaseinforeignassetholdings-equalsthecurrentaccount Table1.1 balance. GNPversusGDPforSelectedCountries,1990(dollarspercapita) Despite this accounting equivalence, there is an importantreason for focusing Country GDP GNP PercentDifference on the foreign asset accumulation view of the current account. It plainly shows that the currentaccountrepresents trade over time, whereas the netexports view Australia 17,327 17,000 -1.9 draws attention to factors detennining gross exports and imports within a single Brazil 2,753 2,680 -2.7 Canada 21,515 20,470 -4.9 timeperiod.Thosefactors arefarmorethanunimportantdetails,asweshallseein SaudiArabia 5,429 7,050 29.9 subsequentchapters,butto stressthemattheoutsetwouldonlyobscurethebasic Singapore 11,533 11,160 -3.2 principlesofintertemporaltrade. UnitedArabEmirates 17,669 19,860 12.4 UnitedStates 21,569 21,790 1.0 Toclarifytheconceptofthecurrentaccount,let Bt+1bethevalueofthe econ omy'snetforeign assets attheendofaperiodt. Thecurrentaccountbalanceover Source:WorldBank,WorldDevelopmentReport1992. periodt isdefinedasCAt=Bt+1 - Bt.Ingeneral,thedate tcurrentaccountfora countrywithnocapitalaccumulationorgovernmentspendingis GDP is Yt•Typically the difference between national and domestic product is a rather small number, but for some countries, those which have amassed large (6) stocks offoreign wealth orincurred substantial foreign debts, the difference can where rtBt isinterestearnedon foreign assets acquiredpreviously. (Thisconven besignificant.Table 1.1 showsseveralofthesecases. tionmakesrt theone-periodinterestratethatprevailedondatet - 1.) 1.1.3.3 TheCurrentAccountandtheBudgetConstraintinthe 1.1.3.2 GrossNationalProductandGrossDomesticProduct Two-PeriodModel Equation (6) shows that acountry's current account (ornetexportsurplus) is the Our formulation of budget constraint (2) tacitly assumed that B1 =0, making difference between its total income and its consumption. The nationalincome of CAl = Y1 - Ciontheformalmodel'sdate 1(butnotingeneral).Bywritingcon an economy is also called its gross national product (GNP) and is measured as straint(2)asastrictequality,wehavealsoassumedthattheeconomyendsperiod2 the sum of two components: the value of the final output produced within its holdingnouncollectedclaimsonforeigners. (Thatis, B3=O. Obviouslyforeign bordersandnetinternationalfactorpayments.Here, thesefactorpaymentsconsist ersdonotwishtoexpireholdinguncollectedclaimsonthehomecountryeither!) ofinterestand dividend earnings on the economy's net foreign assets, which are Thus, viewed as domestic capital operating abroad.6 (In line with the definition ofnet + + CA2= Y2 rB2- C2= Y2 r(Yl - C1) - C2 exports givenearlier,acountry'searnings onitsforeign assetsareconsideredpart = -(Y1 - C1) = -B2= -CAl, ofits national product despite the fact that this product is generated abroad.) In + termsofourformal model,GNPoveranyperiodtis Yt rtBt, asjustindicated. where the third equalityin this chain follows from the economy's intertemporal Thefirstcomponentofnationalproduct,outputproducedwithinacountry'sge budget constraint, eq. (2). Over any stretch of time, as over a single period, a ographicalborders, is calledgrossdomesticproduct (GDP). Inthepresentmodel country'scumulativecurrentaccountbalanceisthechangeinitsnetforeignassets, + butinourtwo-period model with zeroinitial and terminal assets, CAI CA2= B3 - B1=0. 6. Strictly speaking, nationalincomeequals nationalproductplus netunrequitedtransferpayments fromabroad(includingitemslikereparationspaymentsandworkers' remittancestofamilymembers Figure 1.1combinestherepresentativeindividual'sindifferencecurves withthe inothercountries). Workers' remittances, whichrepresentapaymentforexportedlaborservices,are intertemporalbudgetconstraint(2),graphedas nottrulyunrequitedandarecompletelyanalogousto assetearnings, whicharepaymentsforcapital services.Wewilltreatthemassuchinsection1.5.Inpractice,however,nationalincomeaccountants usually don't treat remittances as payments for service exports. The term "gross" in GNP reflects itsfailure to accountfor depreciation ofcapital-afactor absentfrom our theoretical model.When depreciationoccurs,netnationalproduct(NNP)measuresnationalincomelessdepreciation.Empirical Itprovidesadiagrammaticderivationofthesmalleconomy's equilibriumandthe economistspreferto workwithGNPratherthanNNPdata, especiallyininternationalcomparisons, implied trajectory ofits current account. (The figure makes no special assump becauseactualnationalaccountestimatesofdepreciationareaccountingmeasuresheavilyinfluenced bydomestictaxlaws.Reporteddepreciationfiguresthereforearequiteunreliableandcandifferwidely tion about the relation between fJ and 1+r.) The economy's optimal consump from countrytocountry. FortheUnitedStates, aballparkestimateofannualdepreciationwouldbe tion choice is at point C, where the budget constraint is tangent to the highest around10percentofGNP. . 8 IntertemporalTradeandtheCurrentAccountBalance 9 1.1 ASmallTwo-PeriodEndowmentEconomy Period2consumption, C 2 lean,starvingcattle.Inthesecond,sevenfullearsofcornwereeatenbyseventhin ears.Mterhearingthesedreams,JosephprophesiedthatEgyptwouldenjoyseven yearsofprosperity,followedbysevenoffamine.Herecommendedaconsumption smoothingstrategytoprovidefortheyearsoffamine,underwhichPharaohwould appropriateandstoreafifthofthegrainproducedduringtheyearsofplenty(Gen esis41:33-36). AccordingtotheBible,Pharaohembracedthisplan, madeJoseph hisprimeminister,andtherebyenabledJosephtosaveEgyptfromstarvation. Why didJoseph recommend storingthe grain (aform ofdomestic investment yieldingarateofreturnofzerobeforedepreciation)ratherthanlendingitabroadat C ~----- C apositiverateofinterest?Cuneiformrecordsoftheperiodplacetheinterestrateon 2 , , loansofgraininBabyloniainarangeof20to33percentperyearandshowclear , evidenceofinternationalcredittransactionswithinAsiaMinor(Heichelheim1958, pp. 134-135). At such high interest rates Egypt could have earned a handsome returnonitssavings.Itseemslikely,however,that,underthemilitaryandpolitical conditions ofthe secondmillennium B.C., Egypt wouldhave found itdifficult to Period1 consumption,C compel foreign countries to repay a large loan, particularly during a domestic 1 .famine. Thusstoringthegrainathomewasamuchsafercourse.Themodelinthis chapterassumes, ofcourse,thatinternationalloancontracts are alwaysrespected, Figure1.1 butwehavenotyetexaminedmechanismsthatensurecompliancewiththeirterms. Consumptionovertimeand.thecurrentaccount WewillstudythequestioninChapter6. • attainableindifferencecurve.Thefirst-period currentaccountbalance(adeficitin Figure 1.1)is simply the horizontal distance betweenthe date 1output and con 1.1.4 AutarkyInterestRatesandtheIntertemporalTradePattern sumption points. As an exercise, the reader should show how to read from the figure's verticalaxisthesecond-periodcurrent-accountbalance. DiagramslikeFigure1.1canilluminatethemainfactors causingsomecountriesto Economic policymakers often express concern about national current account runinitialcurrentaccountdeficits whileothersrun surpluses.Thekeyconceptwe deficitsorsurpluses. Oursimplemodelmakestheveryimportantpointthatanun needforthis analysis istheautarky realinterestrate, thatis, theinterestratethat balancedcurrentaccountisnotnecessarilyabadthing.InFigure1.1,forexample, wouldprevailinaneconomybarredfrominternationalborrowingandlending. the countryclearlydoesbetterrunning anunbalancedcurrentaccountinbothpe WeretheeconomyrestrictedtoconsumeattheautarkypointAinFigure1.1,the riods than it would ifforced to set Cl = Yl and C2= Y2 (the autarky point A). onlyrealinterestrateconsistentwiththeEulereq.(3)wouldbetheautarkyinterest Intertemporaltrademakespossiblealessjaggedtimeprofileofconsumption.The raterA,definedbyeq. (4)withoutputsreplacingconsumptions: utility gain betweenpointsA and Cillustratesthegeneralandclassicinsightthat f3ul(Y2) countriesgainfromtrade. + (7) UI(Yl) 1 rA Thisequationalsogivestheautarkypriceoffutureconsumptionintermsofpresent Application:ConsumptionSmoothingintheSecondMillenniumB.C. consumption. Figure 1.1 shows that when the latter autarky price is below the world rela An early anecdote concerning the consumption-smoothing behavior underlying tivepriceoffutureconsumption-whichisequivalenttorA beingabover-future thischapter'smodelcomesfromthestoryofJosephintheBookofGenesis.Schol consumption is relatively cheap in the home economy and present consumption arsofthebiblicalperiodplacetheepisodesomewherearound1800B.C. relativelyexpensive. Thus thehomeeconomy will "import"present consumption ThePharaohofEgyptsummonedJoseph, thenanimprisonedslave,tointerpret from abroadin thefirstperiod(byrunning acurrentaccountdeficit) and"export" two dreams. Inthefirst, sevenplumpcattlewerefollowedanddevouredbyseven future consumption later (by repaying its foreign aebt). This result is in accord 10 IntertemporalTradeandtheCurrentAccountBalance 11 1.1 ASmallTwo-PeriodEndowmentEconomy withtheprincipleofcomparativeadvantagefrominternationaltradetheory,which Imagine an economy that initially expects its outputto be constant over time. states that countries tend to import those commodities whose autarky prices are The economy will plan on a balanced current account. But suppose Yl rises. If highcomparedwithworldprices andexportthosewhose autarkyprices arecom Yz does notchange, theeconomy's autarky interestratewillfall belowthe world paratively low? It is the opportunity to exploit these pretrade internationalprice interest rate: a date 1current account surplus will result as people smooth their differentialsthatexplainsthegainsfromtradeshowninFigure1.1. consumption by lending some oftheir temporarily high output to foreigners. If Ariseinpresentoutputorafallinfuture outputlowerstheautarkyrealinterest Yz rises by the same amount as Yl, however, the autarky interest rate does not rate: eitherevent wouldraise desired saving at the previous autarky interestrate, change, and there is no current account imbalance. Alternatively, consumption butsince the residents ofaclosedendowmenteconomycannot save more in the automaticallyremainsconstantthroughtimeifpeoplesimplyconsumetheirhigher aggregatewithoutlendingabroad,rAmustfalluntilpeoplearecontenttoconsume outputinbothperiods. theirnewendowment.Similarly,greaterpatience(ariseinf3)lowersrA•Bymodi Onewaytointerprettheseresultsisasfollows:permanentchangesinoutputdo fyingFigure1.1,youcancheckthatwhenrAisbelowtheworldinterestrater,the notaffectthecurrentaccountwhenf3 =1/(1+r),whereastemporarychangesdo, country runs a first-period currentaccountsurplus followed by adeficit, but still temporaryincreases causingsurpluses andtemporary declinesproducingdeficits. gainsfromtrade. Likewise,achangeinfutureexpectedoutputaffectsthesignofthecurrentaccount Itmay come as a surprisethat the existence ofgains from intertemporal trade inthesamequalitativemannerasanoppositemovementincurrentoutput.Wewill does not depend on the signofthe country's initialcurrentaccountbalance. The generalizethisreasoningtoamany-periodsettinginthenextchapter. reasonissimple,however.Whatproducesgainsisthechancetotradewithsome 1.1.6 AddingGovernmentConsumption one different from oneself. Indeed, the greater is the difference, the greater the gain.Theonlycaseofno gainis the oneinwhich,coincidentally,ithappens that Sofar wehave notdiscussedtherole ofagovernment.Governmentconsumption rA=r. is,however,easytointroduce. Thisreasoning also explains how changesinworld interestrates affectacoun Supposegovernmentconsumptionpercapita, G, enterstheutilityfunction ad + try's welfare. In Figure 1.1 the economy reaps trade gains by borrowinginitially ditively, giving period utility the form u(C) v(G). This case is, admittedly, a becauseits autarky interestrate is above the worldrate, r. Notice, however, that, simpleone, butitsufficesfor theissues onwhich wefocus. Fornow, itiseasiest were the world interestrate evenlower, the economy's welfare aftertrade would to supposethat the government simply appropriates Gt in taxes from the private behigherthaninFigure 1.1.Thebasicreasonforthiswelfaregainisthatafallin sectorfort =1,2. Thispolicyimpliesabalancedgovernmentbudgeteachperiod theworldinterestrateaccentuatesthedifferencebetweenthehomecountryandthe (wewilllookatgovernmentdeficitsinChapter3).Therepresentativeprivateindi restoftheworld, increasingthe gains from trade. Asmallriseintheworldinter vidual'slifetimebudgetconstraintisthus estrate(onethatdoesn'treversetheintertemporaltradepattern)thereforeharinsa Cz Yz - Gz first-periodborrowerbutbenefitsafirst-periodlender. Cl +-1- = Yl - Gl+--- (8) +r l+r 1.1.5 TemporaryversusPermanentOutputChanges Government spending also enters the date t current account identity, which is Asuggestiveinterpretationoftheprecedingideasleadstoasuccinctdescriptionof now howalternativepathsforoutputaffectthecurrentaccount. Thenaturalbenchmarkforconsideringtheeffectsofchangingoutputisthecase f3 =1/(1+r). Thereasonisthat,inthiscase,eq. (7)becomes The new feature here is that both government and private consumption are sub tracted from national income to compute the current account. (Plainly we must l+r accountfor all domestic expenditure-public as well as private-to reckon how 1+rA' muchacountryas awholeissaving.) whichimpliesthatthesolefactorresponsibleforanydifferencebetweentheworld Since G is beyond the private sector's control we can follow the same steps andautarkyinterestratesisachangingoutputlevel. as in section 1.1.1 to conclude that the Euler equation (3) remains valid. In deed, introducing government consumption as we have done here is equivalent 7. Foradetaileddiscussion,seeDixitandNorman(1980). 13 1.1 ASmallTwo-PeriodEndowmentEconomy d dtheCuuentAccountBalance IntertemporalTra ean l2 strictive (provided T > 2, of course). It rules out certain kinds of intertemporal f rumentcon- , endowment Y as output net0 gove consumption dependencies, such as complementarity between total consumption to relabe1m· gtheprivate sectors t? Anat- levelsin differentperiods. Suchdependencies areattheheartofrecentmodels of un . n y _ G. .' affect the current acco . habitpersistenceinaggregateconsumption.8 sumptiO , t consumptiondeCISIOnS ) andoutputiscon- H do govemmen hi h f3 - 1/(1+r , AlthoughwewilldiscusspartiCUlaralternativeassumptions ontastes at several oW onceagainisthecaseinw c --:- rivateconsumptionwould uralbenchmark_ y Absentgovernmentconsump1:lon,P t balanced. suppose, pointsinthebook, theassumptionofintertemporallyadditivepreferenceswithan stantatYl==Yz-.' at C== Y, with the current accoun . wantto borrow unvarying period utility function will form the backbone ofourformal analysis. be constant in this case. G _ 0 Now the private sectorw~l1 art fthebur- Thereareseveralreasonsforthischoice: th t G > 0 while z- . . me to shift P 0 however, a .1 1 hi h second-period after-tax mco f illrunadeficitin 1. Itis true that sometypes ofgoods, such as refrigerators and automobiles, are ainst its re1atlVeY g fu ThecountrYthere orew ag t estothe tare. durable goods typically consumed over many periods rather thanjust one. This denofthetemporary ~ . . Ie . d I andasurplusmpenod2. . r thatintheprecedingexamp typeofconsumptionlinkage, however, is fundamentally technological. By defin penO . Y ·thY _ Gineq. (5)Imples ing utility over the flow of services from durables, and by imputing their rental Replaclllg WI cost,onecaneasilyincorporatesuchgoods withintheumbrellaofintertemporally - (l+r)Gl _ 1(1+r)(Y - Gl) +Y] ==Y- ~. additivepreferences. rNeshowthisinChapter2.) c- - + . - 2 r 'vate consumptlon, but by an 2. Forsometypes ofgoods, consumption atonepointintimeclearly does influ . . d I lowers pn . .stem- ment consumption ill peno verumentconsumptlon1 enceone's utility from consuminginclosely neighboring periods. After eatinga Govem G1: The.reasonisthatthe go t quation presented largemeal,oneis lessinclinedtowantanotheranhourlater.Thetimeintervalsof amountsmaller than d2 Thus the current accoun e porary: it drops to ze~o mpe~othat'Bl ==0here) impliesthat aggregationwelookatinmacroeconomicdata,however,typicallyaremeasuredin earlierinthissubsectlon(rec months,quarters,oryears,periodsoverwhichmanytypesofintertemporaldepen denciesfade. ..0- - G <0. A _y_C- 1==-2+r - 3. Admittedly, even over long periods, habit persistence can beimportant. Drug C 1- _ nsumption is constantat C == addiction is an extremeexample; watching television is a closely related one. In ose that Gl ==Gz==G.Then.co cedalways. Government ~ontrast, p macroeconomics,however, oneshouldthinkofpreferencesasbeingdefinedover In sup . d andthe current accountISbalan tthatittiltsthepath Y_G inbothpeno s, thereonlytotheexten consumption variablesthatreallyrepresentaggregate spendingonawidearrayof . affectsthecurrentaccoun different goods. While wemay have some intuition about thepersistenceeffects consumption ofprivatenetincome. ofconsuming certainitems, itis harderto see obvious andquantitatively signifi oralPreferences cantchannelsthroughwhichthetotalityofconsumptionhaslong-livedpersistence * 1.1.7 ADigressiononIntertelllp .., . ual's referencesarecapturedby a effects. ~ . assumestherepresenta1:lvemdiVld unrestricted function VI == EquatIon(1) . tift function rather than dditively' more- 4. One can think ofsome types of goods that most individuals would prefer to art' ularlifetimeu 1Y d'ff entdatesentera ' consumeonly once, such as marriage services. But even though consumption of very P lC (1) nsumptionlevelsfor I er . With consumption V(C Cz) Ineq. co ). onstant over time. 'li such services is lumpy for anindividual, it is relatively smoothinthe aggregate. 1, '. d utility function u(C IS.c th tura1generalizationofUtl ty over, the peno. th th njusttWO penods, ena occurringover1 ra er a 8. ITGOisanymonotonicallyincreasingfunction,thentheutilityfunction function(1)is (9) T '" f3t-lu(Ct). VI == i-J 'lity function are t=1 additive lifetime UtI . naturallyrepresents the same preferences as VI does, i.e., a monotonically increasing transforma th t canbe representedby an rtyimpliedbymtertem- tion of the lifetime utility function does not affect the consumer's underlying preference order Preferences a .. references.Thekeyprope m tion on ing over different consumption paths. Intertemporally additive preferences take the general form calledintertemporallyaddltlvep. a1rate of substitutionbetween cons~ ~scribed G[UI(CI)+...+UT(CT)](withperiodutilityfunctionspossiblydistinct).Theyalsogobythename :~~s-tul(Cs)/ul(Cr) preTf:~ncr:perty stronglyintertemporaUyseparablepreferences.Forfurtherdiscussionoftheirimplications,seeDeaton ponti additivity is that the f?r the isre- andMuellbauer(1980,ch.5.3). two dates t and s Ieq . on any third date. P ::eq. (9)) is independentofconsumpuon 14 futertemporalTradeandtheCurrentAc.countBalance 15 1.2 TheRoleoffuvestment Peoplegetmarriedall the time. Similarly, peoplemay take vacation trips only at producedwithoutcapital: F(O) = o. Wewillthinkoftherepresentativeconsumer infrequentintervals, burthis is notthe casein the aggregate. (Seasonality can be ashavingtheadditionalroleofproducerwithdirectaccesstothistechnology.9 importantineitheroftheseexamples,butsucheffectsareeasilydealtwith.) Aunitofcapitaliscreatedfromaunitoftheconsumptiongood.Thisprocessis 5. Fundamentally, a very general intertemporally nonadditive utility function reversible, sothataunitofcapital, afterhavingbeen usedtoproduceoutput, can would yield few concrete behavioral predictions. IT consumptions on different be"eaten."You may findthese assumptions unrealistic, buttheyhelp us sidestep dates aresubstitutes,onegetsdramaticallydifferentresultsfromthecaseinwhich sometechnicalissuesthataren'treallycentralhere. Onekeysimplificationdueto they are complements. Because maximal generality would lead to an unfalsifi ourassumptionsisthattherelativepriceofcapitalgoodsintermsofconsumption able macroeconomic theory with little empirical content, macroeconomists have alwaysequals 1. found it more fruitful to begin with a tractable basic setup like eq. (9), which Introducinginvestmentrequiresthatwerethinkthebudgetconstraintsindividu has very sharp predictions. The basic setup can then be amended in parsimo als face, becausenow savingcanflow intocapitalas wellas foreign assets. Total nious and testable ways ifits implications seem counterintuitive or counterfac domesticprivatewealthattheendofaperiodt isnowBt+1+Kt+1,thesumofnet tual. foreignassetsBt+1andthestockofdomesticcapitalKt+1.10 6. Inanyevent,whileempiricalresearchhasraisedinterestingquestionsaboutthe Howis capitalinvestmentreflectedinthe date t currentaccount? Thestockof simplesttime-additivepreferencemodel, itdoesnotyetclearlypointtoasuperior capitalKt+1accumulatedthroughtheendofperiodtisthesumofpreexistingcap nonadditivealternative. ital Ktandnewinvestmentduringperiodt, It (weignoredepreciationofcapital): + Kt+1 = Kt It· (11) 1.2 TheRoleofInvestment Nothingrestrictsinvestmenttobenonnegative,soeq.(11)allowspeopletoeatpart oftheircapital. Historically, oneofthemainreasonscountrieshaveborrowedabroadistofinance Next,thechangeintotaldomesticwealth,nationalsaving,is productiveinvestmentsthatwouldhavebeenhardtofinance outofdomestic sav ings alone. In the nineteenthcentury, therailroad companiesthathelpedopenup Bt+1+Kt+1- (Bt+Kt)=Yt+rtBt - Ct- Gt. the Americas drew on European capital to pay laborers and obtain rails, rolling Finally, rearranging terms in this equation and substituting (11) shows that the .stock, andotherinputs. To take amorerecentexample, Norwayborrowedexten currentaccountsurplusis sivelyinworldcapitalmarkets todevelopits NorthSeaoilresourcesinthe 1970s afterworldoilpricesshotup. (12) Sofar wehavefocused onconsumption smoothinginourstudyofthe current A veryuseful waytointerprettheprecedingcurrentacCountidentityis tolabel account,identifyingthecurrentaccountwithnationalsaving.Ingeneral,however, nationalsavingas St: the current account equals saving minus investment. And because, in reality, in vestmentusuallyismuchmorevolatilethansaving,toignoreinvestmentistomiss (13) muchoftheaction. 1.2.1 AddingInvestmenttotheModel 9. Aswediscussinlaterchapters,itisreasonabletothinkoflaborasbeinganadditionalproduction inputalongsidecapital.Aproductionfunctionoftheform(10)stillisvalidaslongaslaborissupplied Let's modify ourearliermodeleconomyto allowforinvestment.Wenow assume inelasticallybytheindividualproducer.Weassume thatoutputis producedusingcapital, which, intum, canbeaccumulatedthrough lim F'(K)=00 K...O investment.Theproductionfunctionfornewoutputineitherperiodis toensureapositivecapitalstock. Y= F(K). (10) 10. Itissimplesttosupposethatalldomesticcapitalisownedbydomesticresidents.Thestatement thattotaldomesticwealthequalsB+K istrueevenwhenforeignersownpartofthedomesticcapital As usual production is strictly increasing in capital but subject to diminishing stock,however,becausedomesticcapitalownedbyforeignersissubtractedincalculatingnetforeign marginalproductivity: F'(K) > 0 and F"(K) < O.Furthermore,outputcannotbe assetsB.Aslongasperfectforesightholds,sothattheexpostreturnstoassetsareequal,theownership ofthedomesticcapitalstockisirrelevant.Theownershippatternisnotirrelevant,asweseelater,when unexpectedshockscanoccur. 16 Intertempora1TradeandtheCurrentAccountBalance 17 1.2 TheRoleofInvestment FractionofGDP leadingtoidentifyaspecificexpostinvestmentorsavingshiftasthe"cause"ofa currentaccountchange.Ourmodelwithinvestmentwillshowhowvariousexoge 0.4 Investment nous shockscansimultaneouslyaffectallthreevariablesinthesaving-investment identity. 0.3 1.2.2 BudgetConstraintandIndividualMaximization 0.2 To derive the intertemporal budget constraint analogous to eq. (8) when there is bothgovernmentspendingandinvestment, wesimplyaddthe asset-accumulation 0.1 identitiesforperiods 1and2.Forperiod1,currentaccounteq.(12) gives = B2 Yl - Cl - Gl - II o (recallthatBl = 0).Forperiod2,eq. (12) gives -0.1 - B2= Y2+rB2- C2- G2- Iz (recall that B3 = 0). Solve this equation for B2, and substitute theresultinto the -0.2 1973 1976 1979 1982 1985 1988 1991 1994 equationthatprecedesit.Onetherebyarrivesattheintertemporalbudgetconstraint FNiOgluwraey1's.2saving-investmentbalance,1973-94.(Source:OEeD) Cl +II +-Cl2+-+r-I2 =Yl- Gl + Y12+- Gr2 (15) Now itis thepresent valueofconsumptionplusinvestmentthatislintited by the Theneq. (12)statesthatinaneconomywithinvestment, presentvalueofoutput. In this economy with investment, a representative individual maxintizes Ul = (14) + U(Cl) fJU(C2) subjecttoeq. (15), whereeq. (10) replaces Y with F(K) andeq. Nationalsavinginexcessofdomesticcapitalfonnationflowsintonetforeignasset (11) is used to replace I with the changein K. To simplifyfurther, observe that accumulation. peoplewillneverwishto carrycapitalpasttheterntinalperiod2.Thuscapital K2 Thesaving-investmentidentity (14) discloses thatthecurrentaccountisfunda accumulatedin period 1will beconsumedatthe endofperiod2 and K3 will be mentally an intertemporalphenomenon. Simple as itis, theidentity CA = S- I zero,implyingthat is vitalfor analyzing how econontic policies anddisturbances changethecurrent account.Willaprotectivetariff,oftenimposedtoimprovethecurrentaccount,suc Iz= K3 - K2=0- K2=-K2. ceedinitsaim?Theanswercannotbedeterntinedfrompartial-equilibriumreason Usingeq. (15) toelintinateC2fromUl thereforetransfonnstheindividual'sprob ing,butultimatelydependsinsteadonhowthetariffaffectssavingandinvestment. lemto Figure 1.2 returns to the Norwegian case mentioned at the start of this sec tion, graphing recent data on saving, investment, and the current account. In the ntid-1970s, theNorwegiancurrentaccountregisteredhugedeficits, touching -14 percentofGDPin 1977.Inan accountingsense, higherenergy-sectorinvestment + fJu{(1 +r) [F(Kl) - Cl - Gl - II] + FUl + Kl) - G2+II + Kr}. (16) is "responsible" for much of the deficit, although saving simultaneously fell in (Kl isgivenbyhistoryandisnotsubjecttochoiceondate1.)Thetwocorrespond the ntid-1970s, possibly in anticipation ofhigher future oil revenues. Subsequent ingfirst-orderconditionsaretheEulerequation(3) and surpluses through 1985, reflecting higher saving and lower investment, enabled Norwaytorepaymuchofthedebtincurredinthe 1970s. F'(K2) = r, (17) TheNorwegiandata illustrate an importantpoint. Thesaving-investmentiden wherewehaveusedtheidentity K2=Kl +/r. .tity is a vital analytical tool, but because CA, S,and I are jointly deterntined Anextraunitofoutputinvestedondate 1canbefully consumed, togetherwith endogenous variables thatrespond to commonexogenous shocks, it may be ntis- its marginal contribution to output, F'(K2), on date 2. Equation (17) says that 18 IntertemporalTradeandtheCurrentAccountBalance 19 1.2 TheRoleofInvestment Box1.1 period 1investment should continue to the point at which its marginal return is NominalversusRealCurrentAccounts the sameas thatonaforeignloan. Acriticalfeature ofeq. (17) is itsimplication thatthedesiredcapitalstockisindependentofdomesticconsumptionpreferences! Our use in Figure 1.2 ofdata from official national income and product accounts Otherthings equal, wouldn't aless patientcountry, one with alowervalue of{3, raisesanimportantmeasurementproblemthatyoushouldrecognizeasyoureadthis wishtoinvestless?Notnecessarily,ifithas accesstoperfectinternationalcapital book.Unfortunately,theproblemiseasiertounderstandthantocure,soinmostcases wereluctantlycontinuetorelyontheofficialdata. markets. A country that can borrow abroad at the interest rate r never wishes to Ideally, the currentaccountshouldmeasure thechangein aneconomy'snetreal passupinvestmentopportunitiesthatofferanetrateofreturnabover. claimsonforeigners. Inpractice, however, governmentstatistical agencies measure Severalkey assumptions underpinthe separation ofinvestmentfrom consump the currentaccount and GDPby addingup the values oftransactions measuredin tion decisions in thiseconomy. First, theeconomyis small. Thesavingdecisions nominalterms, thatis, in units ofdomestic money. Thispracticeposes no concep ofits residents don'tchange the interestrate atwhichinvestmentprojects canbe tualhazardswhenmoneyhasa stablevalueintermsofrealoutput, but,forreasons wewillunderstandbetterafterlearningaboutmonetaryeconomicsinChapters8-10, financed in the world capital market. Second, the economy produces and con real-worldeconomies arealmostalways afflictedbyatleastsomeprice-levelinfla sumes a single tradable good. When the economy produces nontraded goods, as tion,atendencyforthemoneypricesofallgoodsandservicestoriseovertime.Such in some ofChapter4's models, consumption shifts can affect investment. Third, inflationwouldnotbeaproblemifallinternationalborrowingandlendinginvolved capital markets are free ofimperfections that might act to limit borrowing. We theexchangeofoutput-indexedbonds, as ourtheoretical model assumes. Butmost shall see later (in Chapter 6) that when factors such as default risk restrict ac bonds traded betweencountries havereturns andface values that are contractedin cess to international borrowing, national saving can influence domestic invest termsofcurrencies,implyingthatinflationcanaffecttheirrealvalues. Ahypotheticalexampleillustratestheproblem. SupposeUnitedStatesGDPis$7 ment.ll trillion dollars and the U.S. netforeign debt is $700 billion. Suppose also that all In thepresentsetup, investmentis independentofgovernmentconsumptionas international debts are linked to dollars, that the interestrate ondollarloans is 10 well. In particular, governmentconsumptiondoes notcrowd outinvestmentin a percentperyear,andthatU.S.GDPequalsthesumofconsumption,investment,and smallopeneconomyfacingaperfectworldcapitalmarket. governmentspending. Undertheseassumptionsthe U.S. DepartmentofCommerce would.reportthecurrentaccountbalanceasthenominalinterestoutflowonnetfor 1.2.3 ProductionPossibilitiesandEquilibrium eignassets,or(0.1) x ($700billion)=$70billion.Someasured,thecurrentaccount deficitis 1percentofGDP. Let's assume temporarily that government consumption is zero in both periods. Suppose,however, thatall dollarprices arerisingat5 percentperyear. Overthe ThenFigure1.3showshowthecurrentaccountisdeterminedwhenthereisinvest course ofthe year, the U.S. externaldebtdeclines inreal value by (0.05) x ($700 ment. To theinformationinFigure 1.1,Figure 1.3 adds an intertemporalproduc billion)=$35billionasaresultofthisinflation.Thusthedollarvalueofthechange tion possibilitiesfrontier (PPF) showing the technological possibilities available inU.S. realnetforeignassetsisnot$70billion, but$70billion-$35billion= $35 billion.ThissmallernumberdividedbyGDP,equalto0.5percent,showsthechange inautarkyfortransformingperiod1consumptioninto period2consumption.The in the economy's real netforeign assets as a fraction ofreal output. Naive use of PPFisdescribedbytheequation nominalofficialnumbersmakesthedeficitlooktwiceaslargerelativetoGDPasit reallyis! Cz= F [Kr +F(Kl) - Cd+Kl+F(K[) - Ct. (18) Whileitwaseasytomeasurethecurrentaccountcorrectlyinourexample,doing Whatdoesthiseq\lationimplyaboutthePPF'spositionandshape?Iftheecon soinpracticeismuchharder.Internationalfinancial transactionsaredenominatedin many currencies. Changesin currencyexchangerates as well as.innational money omychosethelowestpossibleinvestmentlevelondate1byeatingallitsinherited pricelevels therefore enterinto the real currentaccount, but, because the currency capital immediately (setting Ir = -Kr), it would enjoy the highest date I con compositionofacountry'snetforeigndebtisdifficulttomonitor,accuratecorrection sumptionavailableinautarky, Cl = Kl +F(K[).Inthis casedate2consumption isproblematic.Manyinternationallyheldassets,suchasstocks,long-termbonds,and realestate,canfluctuatesharplyinvalue.Accountingforthesepricechangesinvolves similarproblems. 11. Onceweallowfor uncertainty, asinChapters2and5, restrictions onthetra~ilityofcertain Caveatemptor. Unlessotherwisestated,theratiosofthecurrentaccounttooutput assetsalsocanupsettheseparationofinvestmentfromconsumption.Wehaven?tyetmtroducedI~bor asanexplicitfactorofproduction,butifthesupplyoflaborinfluencesthemar~al~~oductof.cap~tal, thatyouencounterinthisbookaretheroughapproximationsonegleansfromofficial theseparationcanalso fail whenconsumptionandlaboreffortenterthepenodutilityfunctionm a nationalaccounts.Thesameistrueofrelatedwealthflows, suchassaving-to-output nonadditivemanner. ratios. Evenifconsumptionshiftsdon'talterinvestment, the converseproposition.nee~not?~t:nel As budgetconstraint(15)shows, inves~ent enters theconsum~'s bUd~et constramtmeqwlibnum, so ingeneralfactorsthatshiftdomesticmvestmentcanaffectnationalsavmgtoo.