National accounting in an indebted open

economy

Gianni Vaggi

April 2014

The national accounting in an indebted open economy

Suppose D0 = 100 to be repaid in 10 years and i = 5%,

each year:

iD interest payments = 5

ΔD principal repayment = 10

iD + ΔD = DS Debt Service

The national accounting in an indebted open economy

Remember: FA = NCF = Net Capital Flows = (Inflows – Outflows)

FA = [(Inflows - Other Outflows) -ΔD] = dD/dt

• ΔD<0 in an indebted economy ΔD is an outflow because debt must be repaid

• dD/dt is the change of the debt stock during the year, which depends also on inflows and other outflows in the FA.

CA = [(X-M) + (NPI – iD) + NSI]

The national accounting in an indebted open economy

CA+FA = 0

Suppose an indebted economy where there are only foreign debt related flows:

(Inflows - Other Outflows) = 0

and no other item in NPI and NSI other than –iD

[(X-M) - iD] - ΔD = 0

(X-M) = iD + ΔD = DS

Take the example: DS = 5 +10 = 15

(X-M) - iD = ΔD

The national accounting in an indebted open economy

IF IF the trade balance is 15 and exactly covers the debt service, thenthen the overall debt decreases by ΔD = D0 - D1 , according to the original scheduled payments or:

-ΔD = 90 -100 = -10 = -dD/dt

IF IF the trade balance is 5 and covers interests only, thenthen ΔD = 0 and the overall debt does not change:

dD/dt=0

IF IF the trade balance is less than 5 and, thenthen the overall debt increases:

dD/dt=>0

The Current Account Balance

Now suppose there are other financial flows in the CA

In the BoP the Current account balance (CA) is the sum of three items:

Trade balance (X-M)

Net income transfers (interest payments, dividends, etc.;)= Net Primary Income = NPI

Net unilateral transfers (remittances, international aid, etc.)= Net Secondary Income = NSI

The national accounting in an indebted open economy

Net primary income: Net primary income: Interests on foreign debt

Dividends (on portfolio investments);

Earnings of FDIs, profit repatriation

Rents on land and natural resources;

Compensation of employees (cross-border workers).

Net secondary income:Net secondary income:

Personal transfers (i.e. remittances);

Current) International cooperation,ODA

The national accounting in an indebted open economy

Consider the following flows:

-iD are outflows in NPI = -5

Compensation of employees are often included in remittances

NSI includes -remittances

-international aid , ODA

The national accounting in an indebted open economy

Remember:

[(X-M) + NPI + NSI] = CA Current Account Balance

and CA + FA = 0

[(X-M) - iD + NSI] + (-ΔD) = 0

[(X-M) + NSI] = iD + ΔD = DS = 15

Debt sustainability - 1

D = overall foreign debt

Y = GDP

gn = (dY/dt)/Y is the nominal growth rate

Thresholds d(D/Y)/dt < 0< 0

The latter: Domar 1944

Debt sustainability - 2

By total differentiation of D/Y:

d(D/Y)/dt = [ (dD/dt)*Y - (dY/dt)*D ]/ Y2

= (dD/dt)Y - [ (dY/dt)/Y ] * (D/Y)

= (1/Y) [dD/dt - gn * D ]

But dD/dt = [inD - (X – M)]

Debt sustainability - 3

i = (in - dp/dt) and g = (gn - dp/dt)

dp/dt inflation rate on debt

d(D/Y)/dt = (i - g)D/Y - (X - M)/Yd(D/Y)/dt = (i - g)D/Y - (X - M)/Y

i, g are the real interest rate and the GDP growth rate

d(D/Y)/dt = inD/Y - gnD/Y - (X - M)/Y

Debt sustainability - 4

But there are also other financial flows:

Current Account (CA)= [(X-M) + NPI + NSI ]

NICA = [CA – iD] = Non-Interest Current Account

NICA = [CA – iD] = [(X-M) + NPI + NSI] - iD

NICA largely depends on the trade balance, but not only.

Debt sustainability - 5

The correct sustainability formula is

d(D/Y)/dt = (i - g)D/Y - d(D/Y)/dt = (i - g)D/Y - NICANICA/Y/Y

Debt sustainability – 6- and national public debt

NICA is the equivalent for foreign debt of the concept of Primary surplus (net of interests) for domestic(public) debt

(T – G) = Primary surplus

[(T – G) – iD] (<0) = overall Fiscal Deficit = FD

FD/Y must not exceed 3%