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Balance of Payments: Accounting and Analysis. Thorvaldur Gylfason. Outline. Balance of payments accounting How BOP accounts are put together and how they relate to monetary, fiscal, and national income accounts Balance of payments analysis Economics of exports, imports, exchange rates, etc. - PowerPoint PPT Presentation
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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
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
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
Recording external Recording external transactionstransactions
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
Foreign exchangeForeign exchange
Real
exc
hang
e ra
teRe
al e
xcha
nge
rate
Imports
Exports
OvervaluationDeficit
OvervaluationOvervaluationRR R moves
when e is fixed
Foreign exchangeForeign exchange
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
Conceptual Conceptual frameworkframework
0
Saving
World interest rate
Investment
World equilibrium
Domestic equilibrium
A
B
CD
Borrowing
Conceptual Conceptual frameworkframework
Real interest rate
Saving, investment
0
Saving
Investment
World equilibrium
Domestic equilibrium
A
Consumer surplusbefore borrowing
C
B
Producer surplusbefore borrowing
Real interest rate
Saving, investment
Conceptual Conceptual frameworkframework
0
Saving
World interest rate
Investment
World equilibrium
Domestic equilibrium
A
Consumer surplusafter borrowing
B DC
Producer surplusafter borrowing
Borrowing
Conceptual Conceptual frameworkframework
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
Conceptual Conceptual frameworkframework
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
0tT dtΔDD at time 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
0tT dtΔDD at time 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
Debt as the sum of Debt as the sum of past deficits past deficits
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
Debt as the sum of Debt as the sum of past deficits past deficits
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
Debt as the sum of Debt as the sum of past deficits past deficits
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
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Numerical example, Numerical example, againagain
Suppose that r = 0.06 (as before)
D/Y = 2D/Y = 2 (our new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before) Heavy Heavy burden, still!burden, still!
85.00.2
20.060.05q
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Numerical example, Numerical example, againagain
Suppose that r = 0.06 (as before)
D/Y = 1D/Y = 1 (new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before) Heavy Heavy burden, still!burden, still!
55.00.2
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Numerical example, Numerical example, againagain
Suppose that r = 0.06 (as before)
D/Y = 0.4D/Y = 0.4 (new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before) Heavy Heavy burden, still!burden, still!
37.00.2
4.00.060.05q
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Numerical example, Numerical example, againagain
Suppose that r = 0.06 (as before)
D/Y = 0.4D/Y = 0.4 (as before)
A/Y = 0.05 (as before)
X/Y = 0.30 (new number)Heavy burden, Heavy burden, but but manageable!manageable!
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Numerical example, Numerical example, againagain
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