International Economics - Intertemporal Trade and Current Account Balance

7/30/2019 International Economics - Intertemporal Trade and Current Account Balance

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InternationalEconomics

1. IntertemporalTradeandtheCurrentAccountBalance2

1.1. SmallTwo-PricedEndowmentEconomy.....................2

1.1.1. TheConsumerProblem.................................................2

1.1.2. EquilibriumoftheSmallOpenEconomy...............7

1.1.3. International Borrowing and Lending, the Current

Account,andtheGainsfromTrade.........................................7 1.1.4. Autarky Interest Rates and the Intertemporal Trade

Pattern..............................................................................................10

1.1.5. TemporaryversusPermanentOutputChanges10

1.1.6. CurrentaccountwithGovernmentconsumption11

1.1.7. ADigressiononIntertemporalPreferences......11

1.2. TheRoleofInvestment......................................................11

1.2.1. AddingInvestmenttotheModel............................12

1.2.2. BudgetConstraintandIndividualMaximization13

1.2.3. ProductionPossibilitiesandEquilibrium...........17

1.2.4. TheModelwithGovernmentConsumption......17

1.3. ATwo-RegionWorldEconomy......................................17

1.3.1. AGlobalEndowmentEconomy...............................17


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1.Inter-temporal Trade and the Current AccountBalance

1.1. SmallTwo-PricedEndowmentEconomy1.1.1. TheConsumerProblem

Hypothesis:

Basicmodelwithtwoperiods,t=1,2 1goodworld(fullytradable) Openeconomywitharepresentativehousehold(agent) Small open economy (no market power, i.e. takes

internationalpricesasgives,interestrateinthiscase)

1asset(homogenous1periodbond)

RepresentativeAgentmaximizes:

U(C1,C2) Ct:consumptionint

s.t. the two budget constraints faced by the agent (budget of

period1and2)

1)C1+A2=y1 yt:outputint

A2 = NFA at the end of t = 1

(Savings = net foreign position of the country at the end of

period1,canalsobenegative)

2)C2=y2+A2*(1+r) r:interestrate


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Assume

U(C1,C2)=U(C1)+*U(C2) U(C1)=periodutility

0


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Solvingthemaximizationproblem:

From(1)

A2=y1-C1

Into(2):

C2=y2+(y1-C1)*(1+r)

!! +!!

!!!= !! + !!

!!!

With!

!!!priceint=1(inunitsofoutputatt=1)of1unitofoutput

int=2

Givesusanewoptimizationproblemwithonlyoneconstraint:

MaxU(C1)+*U(C2)

s.t. !! +!!

!!!= !! + !!

!!!

C2=C1*(1+r)+C2-C1*(1+r)

MaxU(C1)+*U[C1*(1+r)+C2-C1*(1+r)]

C1: U(C1)+*U[C1*(1+r)+C1-C1*(1+r)]=0

U(C1)=(1+r)**U(C2)

1+ ! !! !!!! !!

= 1 This is the Intertemporal Euler

Equation

Thisequationisthekeyofdynamiceconomics!


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Eulerassumptionsexplainedbyagraph:

Cistheoptimalchoice,i.e.C1andC2aresuchasU(C1)=(1+r)**

U(C2)

NB:IntuitionthatunderlinestheEulerequation

Assume U(C1)>(1+r)**U(C2)

Ifthisinequalityholdswelfarebenefitsexceedswelfarecostsby

consuming in C1. As long as it holds, its easy for the agent to

increasewelfare(lifetimeutility)byincreasingC 1andcuttingC2.

ThismeanstheagentwillincreaseC1.


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With !!!!

,Assume(1+r)*=1

Thismeansr=

If(1+r)*=1: U(C1)=U(C2)C1=C2

That means the agent/country wants to stable out consumption

overthetwoperiods.Thisiscalledconsumptionsmoothing.This

waytheconsumptionofacountrycanbemuchsmootherthanthe

incomebylendingorborrowing.

Ifr>: U(C1) > U(C2) C1


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1.1.2. EquilibriumoftheSmallOpenEconomyThissectiononlygivessomefurtherexplanations

1.1.3. International Borrowing and Lending, theCurrentAccount,andtheGainsfromTrade

1.1.3.1.DefiningtheCurrentAccountInternational trade acrosscountries is recorded in the Balance of

Payments (BoP) captures borrowing and lending between

countries. A country is the aggregate of the residents of that

country (aggregate perspective) that have external assets and

liabilitiestowardsforeigncountriesandtheirresidents.

Externalassets=lendingtotheforeigners

Externalliabilities=weborrowoutside.Foreignershold

sharesandbonds.

Difference between the external assets and liabilities (A L) is

calledNetforeignAssets(NFA),writtenBt.Ifitispositive,claims

are larger than what the country owes to the rest of the world

(Germany, Japan, China). Assets and liabilities are a stock

variable,observedatacertaintime.

This leads to the notion of Current Account (CA). The current

accountisavariablemeasuredoveragivenperiod.Itmeasuresthe

changeoftheNFAoveracertainperiod.


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CAt=SI=Bt+1Bt=Yt+rtBtCt

Low saving and high investments gives you a negative current

account. If CA is negative over several periods the NFA will

probablybenegative.

NB: Financial crisis: capital flowed into the US boom in the

housing sector highly indebt banks etc. massive current

accountdeficit

1.1.3.2.GNPandGDPThis section is about the difference between GNP and GDP. Not

importantforus?

1.1.3.3.The Current Account and the Budget Constraint intheTwo-periodModel

Usingtheoldconstraints:

(1)C1+A2=y1 & (2)C2=y2+A2*(1+r)

Weknowthat:

CA1=A2=y1C1 using(1)

Wherey1C1isthetradebalance=netexports

Thusweget: !"

!=

!! !!! !!!!!!

!! !!!!


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And by rearranging we get:

Thismeansthat:

CA1>0y1>y2

CA1=0y1=y2

CA1


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Consumption smoothing assumes that a country will lend to the

restoftheworldifcurrentoutputislargerthanfutureoutput.

1.1.4. Autarky Interest Rates and the IntertemporalTradePattern

Didntcoverthispartinthelectures?

1.1.5. TemporaryversusPermanentOutputChangesCaseofaone-timeshockonoutputs

Ify1 increases, CA1 increases. If output in period 1 increases the

countrygetswealthier.Itthereforconsumesmoreinperiod1and

2 (because of the consumption smoothing logic). But in order to

increaseC2wehavetosavemoreinperiod1andthuslendtothe

restof theworld.Theresult is anincreaseof CA1.Similarly,ifwe

anticipatethaty2willincrease(discoveryofrawmaterial)andthe

agent/countryfeelswealthier.Theresultisthattheagentwantsto

consume more in 1 and 2 (because she wants to smooth out

consumption).Finally the CA1decreasesbecausethecountrywill

borrowformtherestoftheworld.

Caseofapermanentshocktooutput

y1=y2>0CA1=0

This means that permanent shocks dont have any effect on the

current account. Why? The reason again is consumption

smoothing, because it can be achieved without needing funding


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from the rest of the world, but we just consume the additional

outputreceivedin1and2.

1.1.6. Current account with Governmentconsumption

What we have seen until now was the first model of current

account.

Wewillnowinclude:

Government Physicalinvestment(changingcapitalstockanthusoutput)

Gt:governmentconsumption

The government is not productive. But it can take output (levy

taxes)fromtheagenttofunditsconsumption.G tisfinancedusingtaxrevenuesTt.

G1=T1+D2 whereD2ispublicdebtattheendoft=1

G2+D2*(1+r)=T2

1.1.7. ADigressiononIntertemporalPreferences???

1.2. TheRoleofInvestmentInvestments=Savings(I=S)inaclosedeconomy

NB:Physicalinvestments=/=financialinvestment


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1.2.1. AddingInvestmenttotheModelConsumershavetolowerconsumptiontobeabletosaveandthis

wayabletoinvest.Factsobservedinpraxis:

Net exports and current account are countercyclical, i.e.negativelycorrelatedwithoutput(GDP)

Investment is pro-cyclical, i.e. positively correlated withoutput.

Usingourmodel,ifoutputgoesuptoday(boom)Iwillsavemore

(C1 doesnt improve the same way than Y1 consumption

smoothing),andCAbalancewillimprove.However,thisisnotwhat

actually happens, i.e. something is missing. When conditions

improvetoday,conditionstomorrowwillbegoodtoobutabitless

(meanreversion).

(?) NX(goesup)=Y(goesup)C(goesupless)I(increasesa

lot)

PhysicalinvestmentintheCA:

Yt=t*F(Kt) withKt=optimalstockint

tisaparameter

K2=K1+I1


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1.2.2. BudgetConstraintandIndividualMaximizationInvestment competes with consumption as a use of resources.

Thebudgetconstraintconsequentlyis:

!! + !! +1

1 + ! !! + !! = !!

1

1 + ! !!

This is a two-period economy. It does not make sense for a

householdtohaveapositivecapitalstockattheendofperiodtwo,

becausethereis noperiod3 (optimalK3=0optimalI2=-K2).

Consumption can be transformed 1 to 1 into investment and

investmentcanbenegative.(Example:agriculture:I=grainputin

storage,outputandK(capital)canbeeaten,storedorsold.Atthe

endofthefarmerslifehewilluseupallthestock.)

Thebudgetconstraintinfunctionofthecapitalstockis:

!! + !! !! +1

1 + ! !! + !!

= ! ! !! +1

1 + ! ! !(!!)

Theobjectiveisstilltomaximisetotalwelfare:MaxU(C 1)+*U(C2)

inregardstoC1,C2&K2.(ThistimeusingaLagrange,i.e.L=U(C1)+

*U(C2))

Wetakethederivative


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! {!! + !! !! +1

1 + ! !! + !! [! ! !! +

1

1 + ! !

! !! ]}

!

!!!= !

!!! + ! = 0

!

!!!= !

!!! +

!

1 + != 0

!

!!!= ! 1

1

1 + !

1

1 + ! ! !

!!! = 0

1 1

1 + !=

1

1 + ! ! !

!!!

! = ! !

!!! EulerEquationforCapital

whichisthemarginalproductofcapitalatt=2

NB:IntuitionthatunderlinestheEulerequationforcapital

Assume r>2*F(K2)

Wewouldratherinvestinbondsbecausereturnrishigherthan

returnoncapital.

if r


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Each unit that the agent puts into capital in period 1 raises the

resources in period 2 by1 + ! !!!! . Thus,1 + ! !

!!! =

1 + !

Decisionrule:Theagentwillinvestintocapitalaslongasitsreturn

ishigherthanr.Thecapitalstockdoesnotdependonconsumption,

on preferences or on the patience of the country. The optimal

choiceofK2thusequalizesthisequation.

! = ! !!!! !!

Eulerstillholds: 1 + ! !! !!!! !!

= 1

Nowassume:(1+r)=1C1=C2(perfectconsumptionsmoothing)

NX1=Y1-I1-C1=CA1itisequaltoCAbecauseY 1=C1+I1+A2and

A2=CA1

!"! =(!! !!) (!! !!)

2 + !

Possiblescenarios:

1. if 1 increases Y1 increases, I1 doesnt change, CA1increases

2. if2 increases (anticipated in t=1 i.e. a news shock) Y1doesntchange,I1increases(graph),I2decreasesi.e.becomes

more negative (graph), CA2 drops. We expect higher


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productivity in 2, thus we consume less today and invest

moreandconsumetheadditionalcapitalstockin2.

OptimalK2

3.PermanentincreaseinAssume:1=2(shockisthesameforbothperiods)

Assume:K1=K2andY1=Y2beforetheshock

!! = ! ! !!

!! = ! ! !!

Becausebothincrease(andK2becauseof2)bothoutputs

rise.(Attention:noderivativesintheseequations)

!"! =(!! !!) (!! !!)

2 + !=

(!! !!) !! + !!

2 + !


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Y2 increases more than Y1andI1 increases, I2 decreases the CA1

decreases. In other words, permanent increase in CA1

decreases.

CAiscountercyclical

Didnotcover:(?)

1.2.3. ProductionPossibilitiesandEquilibrium1.2.4. TheModelwithGovernmentConsumption

1.3. ATwo-RegionWorldEconomy1.3.1. AGlobalEndowmentEconomy

??

International Economics - Intertemporal Trade and Current Account Balance

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