Foundations of International Macroeconomics. Chapter 1A

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by  Obstfeld M., Rogoff K.

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.