Balance of Payments: Accounting and Analysis

Balance of Balance of Payments: Payments: Accounting and Accounting and AnalysisAnalysis

Thorvaldur Gylfason

OutlineOutline1.1. Balance of payments accountingBalance of payments accounting

– How BOP accounts are put How BOP accounts are put together and how they relate to together and how they relate to monetary, fiscal, and national monetary, fiscal, and national income accountsincome accounts

2.2. Balance of payments analysisBalance of payments analysis– Economics of exports, imports, Economics of exports, imports,

exchange rates, etc.exchange rates, etc. 3.3. Current account sustainabilityCurrent account sustainability

– Foreign debt, and how to keep it Foreign debt, and how to keep it in checkin check

Accounting system for Accounting system for macroeconomic analysis in four macroeconomic analysis in four partsparts

1.1. Balance of paymentsBalance of payments2.2. National income accountsNational income accounts3.3. Fiscal accountsFiscal accounts4.4. Monetary accountsMonetary accounts

First look at balance of payments First look at balance of payments accounts, and then look at accounts, and then look at linkageslinkages

Balance of Balance of payments payments accountingaccounting1

External External transactionstransactions

GoodsGoods ServiceServicess

CapitalCapital

ExportExportss XXgg XXss FFxx

ImportImportss ZZgg ZZss FFzz

ExamplesReal transactions

Financial transactions

Balance of paymentsBOP = Xg + Xs + Fx – Zg – Zs – Fz

= X – Z + F = current account + capital accountHereX = XX = Xgg + X + Xss Exports of good and services Exports of good and servicesZ = ZZ = Zgg + Z + Zss Imports of good and servicesImports of good and servicesF = FF = Fxx – F – Fzz Net exports of capital = Net exports of capital =

Net capital inflowNet capital inflow

Recording external Recording external transactionstransactions

Balance of paymentsBalance of paymentsBOP = Xg + Xs + Fx – Zg – Zs – Fz

= X – Z + F = current account + capital accountHereX = Xg + Xs Exports of good and servicesZ = Zg + Zs Imports of good and servicesF = Fx – Fz Net exports of capital =

Net capital inflow




Net capital inflow




Net capital inflow


AgainAgainBOP = X – Z + F = = RR

where where R = reservesR = reservesNote:Note:

X, Z, and F are flowsX, Z, and F are flowsR is a stock, R is a stock, R is a flowR is a flow

Balance of Balance of payments and payments and reservesreserves

R = R – RR = R – R-1-1

AgainAgainBOP = X – Z + F = = RR

where where R = R – RR = R – R-1-1

ImplicationsImplicationsXX RRFF RRZZ RR

In practiceIn practiceZZ FF or or RR

Balance of Balance of payments and payments and reservesreserves

From trade From trade balance to current balance to current accountaccount Trade balanceTrade balance

TB = XTB = Xgg + X + Xnfsnfs – Z – Zgg – Z – ZnfsnfsXXnfsnfs = X = Xss – X – Xfsfs = exports of nonfactor services = exports of nonfactor servicesZZnfsnfs = Z = Zss – Z – Zfs fs = imports of nonfactor services= imports of nonfactor services

Balance of goods and servicesBalance of goods and servicesGSB = TB + YGSB = TB + Yff

YYff = X = Xfsfs – Z – Zfsfs = net factor income = net factor income Current account balanceCurrent account balance

CAB = GSB + TR = TB + YCAB = GSB + TR = TB + Yff + TR + TRTR = unrequited transfers from TR = unrequited transfers from

abroadabroad

Importance of net Importance of net factor income factor income Net factor income from laborNet factor income from labor

– Remittances from domestic workers Remittances from domestic workers abroad (e.g., Turks in Germany)abroad (e.g., Turks in Germany) minus those of foreign workers at minus those of foreign workers at home home

Net factor income from capitalNet factor income from capital– Interest receipts from domestic assets Interest receipts from domestic assets

held abroad minus interest payments held abroad minus interest payments on foreign loans (e.g., Argentina) on foreign loans (e.g., Argentina)

– Includes also profits and dividends Includes also profits and dividends Transfers also matterTransfers also matter

YYff > 0 in Turkey > 0 in TurkeyYYff < 0 in Argentina < 0 in Argentina

Capital accountCapital accountAlso called capital and financial Also called capital and financial

accountaccountFour main itemsFour main items

1.1. Direct investmentDirect investment– Involves control by ownersInvolves control by owners

2.2. Portfolio investmentPortfolio investment– Includes long-term foreign borrowingIncludes long-term foreign borrowing– Does not involve control by ownersDoes not involve control by owners

3.3. Other investmentOther investment– Includes short-term borrowingIncludes short-term borrowing

4.4. Errors and omissionsErrors and omissions– Statistical discrepancyStatistical discrepancy

Overall balance of Overall balance of paymentspaymentsFour main items below the lineFour main items below the line

1.1. GoldGold2.2. SDRsSDRs3.3. Reserve position in IMFReserve position in IMF4.4. Foreign exchangeForeign exchange

Convenient to measure gross foreign Convenient to measure gross foreign reserve holdings in terms of months reserve holdings in terms of months of import coverage – e.g., 3 months of import coverage – e.g., 3 months of importsof imports

Y = C + I + G + X – ZY = C + I + G + X – Z= E + X – Z= E + X – Zwhere E = C + I +Gwhere E = C + I +G

CAB = X – Z = Y – E CAB = X – Z = Y – E Ignore YIgnore Yff and TR for simplicity and TR for simplicity

S = I + G – T + X – Z S = I + G – T + X – Z CAB = S – I + T – GCAB = S – I + T – GCAD = Z – X = E – Y = I – S + G – TCAD = Z – X = E – Y = I – S + G – T

National income National income accountsaccounts

Private sector deficit

Public sector deficit

Y = C + I + G + X – Z Y = C + I + G + X – Z GDP = C + I + G + TBGDP = C + I + G + TBGNP = C + I + G + CABGNP = C + I + G + CABGNP – GDP = CAB – TB = YGNP – GDP = CAB – TB = Yff (if TR = 0) (if TR = 0)GNP = GDP + YGNP = GDP + Yff

GNP > GDP in TurkeyGNP > GDP in Turkey GNP < GDP in ArgentinaGNP < GDP in Argentina

GNDI = GNP + TR = GDP + YGNDI = GNP + TR = GDP + Yff + TR + TR

Links between BOP Links between BOP and national and national accountsaccounts

Links between BOP Links between BOP and national and national accountsaccountsYY X - ZX - Z DefinitionDefinition

GDPGDP Trade Trade balancebalance

Goods and Goods and nonfactor nonfactor servicesservices

Links between BOP Links between BOP and national and national accountsaccountsYY X - ZX - Z DefinitionDefinition

GDPGDP Trade Trade balancebalance

Goods and Goods and nonfactor nonfactor servicesservices

GNPGNP Current Current account account excl. excl. transferstransfers

Goods and Goods and servicesservices

Links between BOP Links between BOP and national and national accountsaccountsYY X - ZX - Z DefinitionDefinitionGDPGDP Trade Trade

balancebalanceGoods and Goods and nonfactor nonfactor servicesservices

GNPGNP Current Current account account excl. excl. transferstransfers

Goods and Goods and servicesservices

GNDIGNDI Current Current account account incl. incl. transferstransfers

Goods and Goods and services services plus plus transferstransfers

Fiscal accounts Fiscal accounts and links to BOPand links to BOP PublicPublic sector sector

G – T = G – T = B + B + DDGG + + DDFF

PrivatePrivate sector sectorI – S = I – S = DDPP –– M M –– BB

Now, add them upNow, add them upG – T + I – S = G – T + I – S = B + B + DDGG + + DDF F + + DDPP –– M M –– B =B = DDGG + + DDF F + + DDPP –– M =M = D D –– M + M + DDFF = - = -R + R + DDFF = Z - X = Z - X

ExternalExternal sector sectorX – Z = X – Z = R - R - DDFF

M = D + R

DG + DP = D

X – Z + F = X – Z + F = RR

F = DF

Monetary accounts Monetary accounts and links to BOPand links to BOPMonetary surveyMonetary survey

M = D + RM = D + RFrom stocks to flowsFrom stocks to flows

M = M = D + D + RRSolve for Solve for RR

R = R = M M –– DDMonetary approachMonetary approach to balance to balance

of paymentsof paymentsStill holds that Still holds that RR = X – Z + F= X – Z + F

Foreign exchangeForeign exchange

Real

exc

hang

e ra

teRe

al e

xcha

nge

rate

Imports

Exports

2

Earnings from Earnings from exports of goods, exports of goods, services, and services, and capital capital

Payments for Payments for imports of goods, imports of goods, services, and services, and capitalcapital

EquilibriumEquilibrium

Balance of Balance of payments analysispayments analysis

*PePQ

Q = real exchange ratee = nominal exchange rateP = price level at homeP* = price level abroad

Increase in Q means real appreciation

ee refers to foreign currency content of domestic currency

Real exchange rateReal exchange rate

*PePQ

Q = real exchange ratee = nominal exchange rateP = price level at homeP* = price level abroad

Devaluation or depreciation of e makes Q also depreciate unless P rises so as to leave R unchanged

RealReal exchange rate exchange rate


Real

exc

hang

e ra

teRe

al e

xcha

nge

rate

Imports

Exports

OvervaluationDeficit

OvervaluationOvervaluationRR R moves

when e is fixed


Price

of f

orei

gn e

xcha

nge

Price

of f

orei

gn e

xcha

nge

Supply (exports)

Demand (imports)

Overvaluation

Deficit

Overvaluation works like a price ceiling

Overvaluation, Overvaluation, againagain

SupplySupply

DemandDemand

EE

ProducerProducersurplussurplus

ConsumeConsumerrsurplussurplus

Quantity

Price

AA

BB

CC

Total Total welfare gainwelfare gain associated associatedwith market equilibrium equalswith market equilibrium equalsproducer surplus (= ABE) plusproducer surplus (= ABE) plusconsumer surplus (= BCE)consumer surplus (= BCE)

WelfareWelfareR = 0, so R is fixed when e floats

SupplySupply

DemandDemand

Price ceilingPrice ceilingEE

FF

GG

Quantity

Price WelfareWelfarelossloss

Price ceiling imposes aPrice ceiling imposes awelfare losswelfare loss equivalent to equivalent tothe triangle the triangle EFGEFG

AA

BB

CC

Consumer surplus = AFGHConsumer surplus = AFGH

HH

JJ

Producer surplus = CGHProducer surplus = CGHTotal surplus = AFGC

Welfare, againWelfare, again

SupplySupply

DemandDemand

Price ceilingPrice ceilingEE

FF

GG

Quantity

Price WelfareWelfarelossloss

Price ceiling imposes aPrice ceiling imposes awelfare losswelfare loss that results that results from shortage (e.g., deficit)from shortage (e.g., deficit)

AA

BB

CC

HH

JJ

Shortage

WelfareWelfare, again, again

Governments may try to keep the national currency overvaluedTo keep foreign exchange cheapTo have power to ration scarce

foreign exchangeTo make GNP look larger than it is

Other examples of price ceilingsNegative real interest ratesRent controls

Causes and costs of Causes and costs of overvaluationovervaluation

Inflation can result in an overvaluation of the national currencyRemember: R = eP/P*

Suppose e adjusts to P with a lagThen R is directly proportional to

inflationNumerical example

Inflation and Inflation and overvaluationovervaluation

Time

Real exchange rate

100

110105 Average

Suppose inflation is 10 percent per year

InflationInflation and and overvaluationovervaluation

Time

100

120

Real exchange rate

110 Average

Hence, increased inflation increases the real exchange rate as long as the nominal exchange rate adjusts with a lag

Suppose inflation rises to 20 percent per year

InflationInflation and and overvaluationovervaluation

How to correct overvaluation

Under a floating exchange rate regimeAdjustment is automatic: e moves

Under a fixed exchange rate regimeDevaluation will lower e and thereby

also Q – provided inflation is kept under control

Does devaluation improve the current account?The Marshall-Lerner condition

The Marshall-Lerner condition: Theory

T = eeX – Z = eX(e) – Z(e)Not obvious that a lower e helps TLet’s do the arithmeticBottom line is:Devaluation improves the current

account as long as

1ba

Suppose prices are

fixed, so that e = Q

a = elasticity of exportsb = elasticity of imports

Valuation Valuation effecteffect arises arises from the from the ability to ability to affect affect foreign foreign pricesprices

The Marshall-Lerner condition

ZeXB )()( eZeeXB

dedZ

dedXeX

dedB

eZ

Ze

dedZ

eX

Xe

dedXeX

dedB

1 1

a b

- +

Export elasticityExport elasticity ImportImportelasticityelasticity

The Marshall-Lerner condition

eZ

Ze

dedZ

eX

Xe

dedXeX

dedB

XbabXaXXdedB

1

0dedB 1baif

X

The Marshall-Lerner condition: Evidence

Econometric studies indicate that the Marshall-Lerner condition is almost invariably satisfied

Industrial countries: a = 1, b = 1Developing countries: a = 1, b =

1.5Hence,

1ba Devaluation improves the current account

Empirical evidence from developing countries

Elasticity of Elasticity ofexports imports

Argentina 0.6 0.9Brazil 0.4 1.7India 0.5 2.2Kenya 1.0 0.8Korea 2.5 0.8Morocco 0.7 1.0Pakistan 1.8 0.8Philippines 0.9 2.7Turkey 1.4 2.7Average 1.1 1.5

Small countries: A special case

Small countries are price takers abroadDevaluation has no effect on the

foreign currency price of exports and imports

So, the valuation effect does not arise

Devaluation will, at worst, if exports and imports are insensitive to exchange rates (a = b = 0), leave the current account unchanged

Hence, if a > 0 or b > 0, devaluation improves the current account

The importance of appropriate side measuresRemember:

It is crucial to accompany devaluation by fiscal and monetary restraint in order to prevent prices from rising and thus eating up the benefits of devaluation

To work, nominal devaluation must result in real devaluation

*PePQ

Equilibrium between demand and supply in foreign exchange market establishesEquilibrium real exchange rateEquilibrium in the balance of

paymentsBOP = X + Fx – Z – Fz

= X – Z + F = current account + capital

account = 0

Balance of Balance of payments payments equilibriumequilibrium

Current account Current account sustainability and sustainability and debtdebt3There are two ways to finance a There are two ways to finance a

deficit on current accountdeficit on current account1.1. Run down foreign reservesRun down foreign reserves

But there is a limitBut there is a limit Rule of thumb: Do not bring reserves Rule of thumb: Do not bring reserves

below three months of imports below three months of imports 2.2. Run up debts abroadRun up debts abroad

Where is the limit? Where is the limit? Is foreign debt bad?Is foreign debt bad?

Not necessarily if the borrowed funds Not necessarily if the borrowed funds are used for profitable investmentsare used for profitable investments

If the world interest rate is lower If the world interest rate is lower than the domestic interest rate, than the domestic interest rate, the country will be a the country will be a borrowerborrower in in world financial markets world financial markets

Domestic firms will want to borrow Domestic firms will want to borrow at the lower world interest rateat the lower world interest rate

Domestic households will reduce Domestic households will reduce their saving because the domestic their saving because the domestic interest rate moves down to the interest rate moves down to the level of the world interest ratelevel of the world interest rate

Conceptual Conceptual frameworkframework

Real interest rate

0 Saving, investment

Saving

Investment

World interest rate

World equilibrium

Domesticsaving

Domesticinvestment

Domestic equilibrium

Borrowing


0

Saving

World interest rate

Investment

World equilibrium


A

B

CD

Borrowing


Real interest rate

Saving, investment

0

Saving

Investment

World equilibrium


A

Consumer surplusbefore borrowing

C

B

Producer surplusbefore borrowing

Real interest rate

Saving, investment


0

Saving

World interest rate

Investment

World equilibrium


A

Consumer surplusafter borrowing

B DC

Producer surplusafter borrowing

Borrowing


Real interest rate

Saving, investment

The area D shows the increase in total surplus and represents the gains from borrowing

Before trade After trade Change Consumer surplusConsumer surplus A A + B + D + (B + D) Producer surplusProducer surplus B + C C - B Total surplusTotal surplus A + B + C A + B + C + D + D


Borrowers are better off and Borrowers are better off and savers are worse offsavers are worse off

Borrowing raises the economic Borrowing raises the economic well-being of the nation as a whole well-being of the nation as a whole because the gains of borrowers because the gains of borrowers exceed the losses of saversexceed the losses of savers

If world interest rate is If world interest rate is aboveabove domestic interest rate, savers are domestic interest rate, savers are better off and borrowers are worse better off and borrowers are worse off, and nation as a whole still off, and nation as a whole still gainsgains

Gains from trade: Gains from trade: Three main Three main conclusionsconclusions

Debt stockDebt stockUsually measured in dollars or other Usually measured in dollars or other

international currenciesinternational currenciesbecause because debt needs to be debt needs to be

servicedserviced in foreign currency in foreign currencyDebt ratioDebt ratio

Ratio of external debt to GDPRatio of external debt to GDPRatio of external debt to exportsRatio of external debt to exports

More useful for some purposes, More useful for some purposes, because because export earnings reflect the export earnings reflect the ability to service the debtability to service the debt

External debt: External debt: Key conceptsKey concepts

External debt: External debt: Key Key conceptsconceptsDebt burdenDebt burden

Also called Also called debt service ratiodebt service ratioEquals the ratio of amortization Equals the ratio of amortization

and interest payments to and interest payments to exportsexports

q = debt service ratioA = amortizationr = interest rate DF = foreign debtX = exports

XrDAq

F

Interest burdenInterest burdenRatio of interest payments to Ratio of interest payments to

exportsexports

XAa q = a + bq = a + b

Amortization burdenAmortization burdenAlso called Also called repaymentrepayment burden burdenRatio of amortization to Ratio of amortization to

exportsexports

XrDb

F

External debt: External debt: Key conceptsKey concepts

Magnitude of the debtMagnitude of the debtDebt should not become too largeDebt should not become too large

How large is too large?How large is too large?Measurement of the debtMeasurement of the debt

Gross or net?Gross or net?May subtract foreign reserves in excess May subtract foreign reserves in excess

of three months of imports of three months of imports Composition of the debtComposition of the debt

FDI, portfolio equity, long-term loans, FDI, portfolio equity, long-term loans, short-term loansshort-term loans

External debt: External debt: Magnitude and Magnitude and compositioncomposition

Composition of the debtComposition of the debtForeign direct investmentForeign direct investment

Least likely to flee, most desirableLeast likely to flee, most desirablePortfolio equityPortfolio equityLong-term loansLong-term loansShort-term loansShort-term loans

Most volatile, least desirableMost volatile, least desirableAs a rule, outstanding short-term As a rule, outstanding short-term

debt should not exceed foreign debt should not exceed foreign reservesreserves

External debt: External debt: Magnitude and Magnitude and compositioncomposition

Indonesia Indonesia and Korea and Korea broke this broke this rule in rule in 19961996

How can we figure out a How can we figure out a country’s debt burden?country’s debt burden?Divide through definition of Divide through definition of qq by by

incomeincomeNow we have expressed Now we have expressed the debt service ratio in the debt service ratio in terms of familiar terms of familiar quantities: the interest quantities: the interest rate rate rr, the debt ratio , the debt ratio DDFF/Y/Y, and the export , and the export ratio ratio X/YX/Y as well as the as well as the repayment ratio repayment ratio A/YA/Y

YX

YDr

YA

q

F

External debt: External debt: NumbersNumbers

Suppose that Suppose that r = 0.06r = 0.06DDFF/Y = 0.50/Y = 0.50A/Y = 0.05A/Y = 0.05X/Y = 0.20X/Y = 0.20

4.02.008.0

0.25.006.005.0q

Here we have a Here we have a country that has to country that has to use use 40% of its export 40% of its export earningsearnings to service to service its external debtits external debt

Heavy burden!Heavy burden!

YX

YDr

YA

q

F

Numerical exampleNumerical example

Debt accumulation is, by its Debt accumulation is, by its nature, a nature, a dynamicdynamic phenomenon phenomenonA large stock of debt involves high A large stock of debt involves high

interest payments which, in turn, interest payments which, in turn, add to the external deficit, which add to the external deficit, which calls for further borrowing, and so calls for further borrowing, and so on on Debt accumulation can develop into a Debt accumulation can develop into a

vicious circlevicious circleHow do we know whether a given How do we know whether a given

debt strategy will spin out of control debt strategy will spin out of control or not?or not?To answer this, we need a little To answer this, we need a little

arithmetic arithmetic

External debt External debt dynamics dynamics

Recall balance of payments Recall balance of payments equation:equation:BOP = X – Z + FBOP = X – Z + F

wherewhereFF = capital inflow = capital inflow = = DDFF

where where DDFF = foreign debt = foreign debtCapital inflow, F, thus involves an Capital inflow, F, thus involves an

increase in the stock of foreign increase in the stock of foreign debt, Ddebt, DFF, or a decrease in the stock , or a decrease in the stock of foreign claims (assets)of foreign claims (assets)

So, F is a So, F is a flowflow and D and DF F is a is a stockstock

External External debtdebt dynamicsdynamics

Now assumeNow assumeZ = ZZ = ZNN + r + rDDFF

ZZ = total imports= total importsZZNN = non-interest imports = non-interest importsrrDDFF = interest payments = interest payments

Further, assumeFurther, assumeX = ZX = ZNN

BOP = 0BOP = 0 A flexible exchange rate ensures A flexible exchange rate ensures equilibrium in balance of payments at all equilibrium in balance of payments at all

times times

Then, it follows thatBOP = X – Z + BOP = X – Z + DDFF = = 00so that DDFF = = rDrDFF

In other words:

rD

ΔDF

F

External External debtdebt dynamicsdynamics

So, now we have:

rD

ΔDF

F

Now subtract growth rate of output from both sides:

g-rY

ΔYD

ΔDF

F

YYg

External debtExternal debt dynamicsdynamics

But what is

This is proportional change in debt ratio:

YΔY

DΔD

F

F

??

YD

YDΔ

YΔY

DΔD

F

F

F

F

This is an application of a simple rule of arithmetic:

%%(x/y) = (x/y) = %%x - x - %%yy

External debtExternal debt dynamicsdynamics

z = x/yz = x/ylog(z) = log(x) – log(y)log(z) = log(x) – log(y)log(z) = log(z) = log(x) - log(x) - log(y)log(y) But what is But what is log(z) log(z) ??

So, we obtain

zΔz

z1

dtdz

dtdlog(z)Δlog(z)

yΔy

xΔx

zΔz

Q.E.D.

Proof Proof

We have shown thatWe have shown that

grd

Δd

where

Debt ratio

Time

r r g g

r = gr = g

r r g g

Need economic Need economic growth to keep growth to keep the debt ratio the debt ratio under controlunder control

YDd

F

Debt, interest, and Debt, interest, and growth growth

It is important to keep It is important to keep economic economic growthgrowth at home at home aboveabove – or at least – or at least not far below – the not far below – the world rate of world rate of interestinterest

Otherwise, the debt ratio keeps rising over Otherwise, the debt ratio keeps rising over timetime

External deficits can be OK, even over External deficits can be OK, even over long periods, as long as external long periods, as long as external debt does not increase faster than debt does not increase faster than output and the debt burden is output and the debt burden is manageable to begin with manageable to begin with

A rising debt ratio may also be OK as A rising debt ratio may also be OK as long as the borrowed funds are long as the borrowed funds are used efficientlyused efficiently

Once again, Once again, high-quality investment high-quality investment is keyis key

What can we learn What can we learn from this? from this?

Let us now study the interaction Let us now study the interaction between trade deficits, debt, and between trade deficits, debt, and growthgrowth

Two simplifying assumptions:Two simplifying assumptions:DDtt = aY = aYt t (omit the superscript F, so D = (omit the superscript F, so D =

DDFF))Trade deficit is constant fraction Trade deficit is constant fraction aa of of outputoutput

YYtt = Y = Y00eegtgt

Output grows at constant rate Output grows at constant rate gg per per yearyear

Y

t

Exponential growth

Debt dynamics: Debt dynamics: Another look Another look

Y

time

Exponential growth implies a linear logarithmic growth path whose slope equals the growth rate

log(Y)

time

1g

Pictures of growth Pictures of growth

T

0tT dtΔDD at time T

Debt as the sum of Debt as the sum of past deficits past deficits

dteaYdtΔDDT

0

gt0

T

0tT

T


DebtDebt as the sum of as the sum of past deficits past deficits

dteaYdtΔDDT

0

gt0

T

0tT

gt0

T

0

gt0

T

0tT e

g1aYdteaYdtΔDD

Evaluate this Evaluate this integral integral between 0 and between 0 and TT

T


DebtDebt as the sum of as the sum of past past deficitsdeficits

dteaYdtΔDDT

0

gt0

T

0tT

gt0

T

0

gt0

T

0tT e

g1aYdteaYdtΔDD

Evaluate this integral between 0 and T

1eg1aYe

g1aYdteaYdtΔDD gT

0gt

0

T

0

gt0

T

0tT

T

0tT dtΔDD So, as T goes to So, as T goes to

infinity, Dinfinity, Dtt becomes becomes infinitely large.infinitely large.But that may be quite But that may be quite OK in a growing OK in a growing economy!economy!

at time T

Debt as the sum Debt as the sum of past deficitsof past deficits

T

0gt

0

T

T

YYeY

ga

YD

Debt as the sum Debt as the sum of past deficits of past deficits

T

0gt

0

T

T

YYeY

ga

YD

T

0

T

0gt

0

T

T

YY1

ga

YYeY

ga

YD


T

0gt

0

T

T

YYeY

ga

YD

T

0

T

0gt

0

T

T

YY1

ga

YYeY

ga

YD

gT

T

0

T

0gt

0

T

T e1ga

YY1

ga

YYeY

ga

YD


So, as T goes So, as T goes to infinity, to infinity, DDTT/Y/YTT approaches approaches the ratio the ratio a/ga/g

T

0gt

0

T

T

YYeY

ga

YD

T

0

T

0gt

0

T

T

YY1

ga

YYeY

ga

YD

gT

T

0

T

0gt

0

T

T e1ga

YY1

ga

YYeY

ga

YD

ga

YD

T

Tlim T


SupposeSupposeTrade deficit is 6% of GNPTrade deficit is 6% of GNP

a = 0.06a = 0.06Growth rate is 2% per yearGrowth rate is 2% per year

g = 0.02g = 0.02Then the debt ratio approachesThen the debt ratio approaches

d = a/g = 0.06/0.02 = 3d = a/g = 0.06/0.02 = 3This point will be reachedThis point will be reached

regardless of the initial regardless of the initial position ...position ...... as long as ... as long as aa and and gg remain remain

unchangedunchanged

Debt ratio

Time

3

Numerical Numerical example example

Suppose that r = 0.06 (as before)

D/Y = 3D/Y = 3 (our new number)

A/Y = 0.05 (as before)

X/Y = 0.20 (as before)

Here we have Here we have a country a country whose entire whose entire export export earnings do earnings do not suffice to not suffice to service its service its debtsdebtsHeavy Heavy burden, burden, indeed!indeed!

15.10.2

30.060.05q

YX

YDr

YA

q

F

Numerical example, Numerical example, againagain


D/Y = 2D/Y = 2 (our new number)


X/Y = 0.20 (as before) Heavy Heavy burden, still!burden, still!

85.00.2

20.060.05q

YX

YDr

YA

q

F



D/Y = 1D/Y = 1 (new number)



55.00.2

10.060.05q

YX

YDr

YA

q

F



D/Y = 0.4D/Y = 0.4 (new number)



37.00.2

4.00.060.05q

YX

YDr

YA

q

F



D/Y = 0.4D/Y = 0.4 (as before)


X/Y = 0.30 (new number)Heavy burden, Heavy burden, but but manageable!manageable!

25.00.3

4.00.060.05q

YX

YDr

YA

q

F


Must adjust policiesMust adjust policiesMust eitherMust either

Reduce trade deficitReduce trade deficit by stimulating by stimulating exports or by reducing imports, orexports or by reducing imports, or

Increase economic growthIncrease economic growthOtherwise, the debt ratio will reach Otherwise, the debt ratio will reach

unmanageable levels, unmanageable levels, automaticallyautomaticallyNo country can afford an external No country can afford an external

debt equivalent to three times debt equivalent to three times annual outputannual output

What to conclude?What to conclude?d = a/gd = a/g

Because the debt burden then Because the debt burden then becomes becomes unbearableunbearableRecall our earlier numerical Recall our earlier numerical

exampleexampleWhere we looked at the relationship Where we looked at the relationship

between the between the debt ratiodebt ratio and the and the debt debt burdenburden

Korea is a case in pointKorea is a case in pointIts Its export-oriented growth strategyexport-oriented growth strategy

reduced the numerator and increased reduced the numerator and increased the denominator of the debt ratio, the denominator of the debt ratio, thereby quickly reducing the country’s thereby quickly reducing the country’s debt burden debt burden

An An import-substitution strategyimport-substitution strategy would would reduce both numerator and denominator reduce both numerator and denominator with an ambiguous effect on the debt with an ambiguous effect on the debt burdenburden

And why not?And why not?

In conclusion

The EndThe EndExternal borrowing is a necessary External borrowing is a necessary

and natural part of economic and natural part of economic developmentdevelopmentThis requires countries that borrow to This requires countries that borrow to

invest the funds borrowed in invest the funds borrowed in high-high-quality capitalquality capital

This is necessary to be able to service This is necessary to be able to service the debt the debt

If debt burden becomes too heavy, If debt burden becomes too heavy, must either must either reduce deficitreduce deficit or or spur spur growthgrowthIt is always desirable anyway to do It is always desirable anyway to do

everything possible to encourage everything possible to encourage economic growtheconomic growth

Rapid growth allows more foreign Rapid growth allows more foreign borrowing without making the debt borrowing without making the debt burden unmanageable burden unmanageable

These slides will be posted on my website: www.hi.is/~gylfason

Documents

Balance of Payments: Accounting and Analysis