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International Economics - Intertemporal Trade and Current Account Balance
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Transcript of 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
??