EC201 – International Macroeconomics
1.1: International Macroeconomics: Global Imbalances: Current Account:
Balance of payments has two main components: the current account and the financial
account. Current Account = trade balance + income balance + net unilateral transfers.
The financial account measures changes in a country’s net foreign asset position.
Financial account = Increase in foreign owned assets in the U.S – Increase in U.S. owned
assets abroad
Thus, in the case of the import of a smartphone, the U.S. resident pays with US currency,
then a South Korean resident (Samsung) is buying U.S. assets (currency) for $500 so the U.S.
financial account receives a positive entry of $500 and current account a negative $500.
This illustrates the principle known as double entry bookkeeping. Each transaction enters
the balance of payments twice, once with a positive sign and once with a negative sign.
It can be one on the current account and one on the financial account or two on one
account – for example, the purchase of shares (financial assets) enters twice on the financial
account (the money from the shares, and the assets going in the other direction). Foreign
aid represents an export of goods and a unilateral transfer to waive the payment.
Therefore, current account balance = - financial account balance.
Trade balance = Goods balance + service balance
Income Balance = Net Investment Income + Net International Compensation to Employees
Net income from capital is called Net Investment Income and consists of dividends,
interests, profits, etc. Net income from labour is called Net International Payments.
Net unilateral transfers: is the difference between gifts received from the rest of the world
and gifts given to the rest of the world. These gifts can involve private agents or gov.
Net unilateral transfers = private remittances + government transfers
If the current account is negative, all other things equal, the net external debt of the country
goes up, and if the current account is positive, the external debt falls.
It must be the case that CAUS + CAROW = 0
The country with the biggest accumulated current account deficit is the US. The countries
that have been financing these deficits are China, Japan, Germany and oil exporting
countries (Russia, members of OPEC and Norway). Overall, the picture is one of unbalanced
accumulated trade.
1.3: The Net International Investment Position: NIIP is used to refer to a country’s net
foreign wealth = Difference between a country’s foreign assets (A) and its foreign liabilities
(L) – value of the country’s assets owned by foreign residents. NIIP = A – L
NIIP is a stock, while the current account is a flow.
NIIP is negative, then the country has debt. NIIP positive, country is a net creditor.
∆ NIIP=CA+ valuation changes
Valuation changes is changes in the market value of the country’s foreign assets and liability
positions (due to currency fluctuations, changes in stock prices, interest rates etc)
In the absence of valuation changes, the level of the current account must equal the change
in the net international investment position.
You can find the hypothetical NIIP by removing valuation changes from the actual NIIP.
To do this you start with the NIIP of the initial year and add all of the CA balances until the
year of interest. This yields the hypothetical NIIP.
In spite of large CA deficits, the U.S. reduced its external debt due to:
,Large depreciation of the U.S. dollar (20%). Most of the U.S. foreign liabilities are in dollars,
whereas most of the U.S. holdings of foreign assets are in foreign currency.
Large increases in the price of foreign stocks.
1.4: The Negative-NIIP-Positive-NII Paradox: Even though the U.S. has had a negative net
international investment position (NIIP < 0) for the past quarter century, it receives
investment income from the rest of the world (NII > 0).
How could it be that a debtor country, instead of having to make payments on its debt,
receives income on it?
There are two suggested explanations for this: Dark Matter and Return Differentials.
The Dark Matter hypothesis maintains that the Bureau of Economic Analysis may
underestimate the net foreign asset holdings of the United States (e.g. intangibles which are
not correctly reflected in the official BoP e.g. the value of U.S. brands which does not show
up in the raw investments).
However, the argument goes, these intangibles would generate income for the U.S. which
would be appropriately recorded. It thus becomes possible that the U.S. could display a
negative NIIP and at the same time a positive NII.
TNIIP = the ‘true’ net international investment position.
TNII Pt =NII Pt + Dark Matter t
Net investment income is the return on the TNIIIP. So letting r denote the interest rate, we
have: NII = rTNII P t−1
However, this theory can yield such a high number it seems unrealistic
Return Differentials: Explanation could be that the U.S. earns a higher interest rate on its
foreign asset holdings (shares – riskier but earn relatively high returns) than foreigners earn
on their U.S. asset holdings (mostly safe U.S. treasury bills).
NIIP = A – L. Let rA be the interest rate (return) on A, and rL the interest rate on L.
The question is how large does the interest rate differential on assets and liabilities, r A – rL,
have to be to explain the paradox.
NII must equal the difference between investment income and investment payments:
NII = rAA – rLL
Small interest rate differentials can generate very large effects on net investment income
because gross positions are so large. Hence just a small rate of return differentials can lead
to a positive NII even though the NIIP is negative.
At a global level, all current account balances must add up to zero.
2.1: Current Account Sustainability: Sustainability in 2 periods: Can a country run a
perpetual trade balance deficit? It depends on whether the country is a net debtor or a net
creditor (positive NIIP). If it is a net debtor, its NIIP is negative, then no. As in this case, the
country will have to run a trade balance surplus at some point to service its debt.
If the country is a net creditor of the rest of the world, NIIP positive, then it can run a
perpetual trade deficit and finance it with the interest generated by its net investments
abroad.
For example, consider an economy that lasts for two periods. It starts period 1 with a net
¿
foreign asset position of B0. Let r denote the interest rate. Then the country’s NII in period 1
¿
is given by r B0. Let the trade balance be denoted TB1.
¿ ¿ ¿
C A1 =r B0 +T B 1 but at the same time with no valuation changes: C A1 =B 1−B 0
,C A 2=B ¿2−B ¿1 which combining and remembering B¿2=0 yields B¿0=−C A 1−C A 2 This
formula says that a country’s initial net foreign asset position must be equal to the sum of
its present and future current account deficits which implies that the country can run
current account deficits in both periods only if the initial net asset position is positive.
Then the country’s net international investment position at the end of period 1:
¿ ¿ ¿ ¿
B1=( 1+r ) B 0 +T B1 Similarly, B2=( 1+r ) B1+ T B 2
There are 2 assumptions: 1) net payment to employees = 0 2) net unilateral transfers = 0
Now at the end of period 2, the country cannot hold assets or debts, because no one will
¿
be alive in period 3 to collect (the world ends in period 2). This means that B2=0
¿ T B2
Combining these equations: ( 1+r ) B 0=−T B1− which states that the net foreign asset
(1+ r )
position (including interest) equals the present discounted value of its future trade deficits.
¿
It is clear from this expression that if the country is a net debtor, B0 < 0, then it must run a
trade balance surplus at some point. However, if the country is a net creditor of the rest of
¿
the world, B0 >0 , then it can afford running trade deficits in both periods. This result holds
not just for two period economies, but for economies lasting any number of periods,
including an infinite number of periods but in this case the country must not violate the no-
ponzi condition (debt grows at a rate less than the interest rate).
Note, that the current account is the trade balance + NII so we are only interested in the
payment on the debt not the absolute debt.
2.2: Math of Current Account: Savings, Investment and the Current Account: In any period
savings, investment and the current account are linked by the identity C A1 =S 1−I 1
Savings in excess of what is needed to finance domestic investment must be allocated to
purchases of foreign assets. Therefore, according to this relation, a deficit in the current
account occurs when a country’s investment exceeds its savings.
¿
Current Account Deficits as Reflections of Trade Deficits: C A t=T Bt +r B t−1
Current Account as the Gap between National Income and Domestic Absorption: A country’s
absorption, which we denote by At, is defined as the sum of private consumption,
government consumption and investment: At =C t + I t +G t
Combining this expression with the formulas above, CA can be expressed as the difference
between income and absorption: C A t=Y t − At
Thus the current account is in deficit when domestic absorption of goods and services
exceeds national income.
So to conclude the CA can be viewed four ways:
C A t=B¿t −B¿t−1, C A t=rB ¿t−1 +T Bt , C A t=St −I t , C A t=Y t − At
¿ ¿
2.3: Sustainability in infinite periods: B1=( 1+r ) B 0 +T B1 ≈ the change in NIIP = ∆ CA
¿
¿ B 1 T B1
B0= −
1+r 1+ r
¿
B T B2
Now shifting one period forward: B¿1= 2 −
1+ r 1+r
¿
¿ B2 T B1 T B2
Substituting in: B0= − −
( 1+r ) 1+r ( 1+r )2
2
, Repeating this iterative procedure T times results in the relationship:
¿ B¿T T B1 T B2 T BT
B0= − − …
( 1+r ) 1+r ( 1+ r )
T 2
( 1+r )T
¿
The no-Ponzi-game constraint tells us that you need to pay your debts. Bt ≥ 0
In an infinite horizon economy no-Ponzi-game condition tells you that the amount of debt
BT
that you can have, cannot grow at a faster rate than your interest rate: lim T
≥0
T → ∞ ( 1+r )
BT
Optimality constraint: lim T
≤0 - this is the opposite of the above. You do not want to
T → ∞ ( 1+r )
save so much that you give so much credit that you will never get it back from the rest of
the world.
This restriction and the no Ponzi-game constraint can be simultaneously satisfied only if the
BT
transversality condition holds: lim T
=0
T → ∞ ( 1+r )
Letting T go to infinity and using the transversality condition, this becomes:
−T B1 T B2
B¿0= − …
1+r ( 1+ r 2 )
Therefore, can a country run a perpetual trade deficit? If it is a foreign debtor, no! The same
as in the two period model. If the initial asset position is negative, then it is impossible to
run perpetual trade deficits as the two negative signs would cancel out and the right hand
side would then be positive.
What about the current account? Can a country run perpetually current account deficits?
¿ ¿
Assume the country is initially a net debtor. Law of motion: Bt =( 1+ r ) Bt −1+ T B t
Consider an example in which each period the country generates a trade balance surplus
¿
sufficient to pay a fraction α of its interest obligations. That is, T Bt =−αr Bt −1 where the
factor α is between 0 and 1.
¿ ¿
Bt =( 1+ r−αr ) B t−1 (substituted in)
¿
Recall the definition of Current Account: C A t=r Bt −1 +T Bt
¿
Therefore, we have C A t=r ( 1−α ) Bt−1 <0
And so the current account will always be negative
Does this country satisfy the Transversality/No Ponzi scheme conditions?
¿ t ¿
Law of motion of debt given above implies: Bt =( 1+ r−αr ) B0
[ ]
t
B ¿t 1+r ( 1−α ) ¿
It follows that: = B 0, which converges to zero as t becomes large because
( 1+ r )
t
1+r
1 + r > 1 + r(1−α ¿
Notice that under the assumed policy the trade balance evolves according to:
t−1 ¿
T B1=−αr [ 1+r ( 1−α ) ] B o
That is the trade balance is positive and grows unboundedly over time at the rate r(1 - α ¿. In
order for a country to be able to generate this path of trade balance surpluses, its GDP must
be growing over time at a rate equal or greater than r(1 - α ¿. If this condition is satisfied, the
repayment policy described in this example would support perpetual current account
deficits even if the foreign initial net foreign asset position is negative.
3.1: Endowment SOE: Theory of Current Account Determination:
1.1: International Macroeconomics: Global Imbalances: Current Account:
Balance of payments has two main components: the current account and the financial
account. Current Account = trade balance + income balance + net unilateral transfers.
The financial account measures changes in a country’s net foreign asset position.
Financial account = Increase in foreign owned assets in the U.S – Increase in U.S. owned
assets abroad
Thus, in the case of the import of a smartphone, the U.S. resident pays with US currency,
then a South Korean resident (Samsung) is buying U.S. assets (currency) for $500 so the U.S.
financial account receives a positive entry of $500 and current account a negative $500.
This illustrates the principle known as double entry bookkeeping. Each transaction enters
the balance of payments twice, once with a positive sign and once with a negative sign.
It can be one on the current account and one on the financial account or two on one
account – for example, the purchase of shares (financial assets) enters twice on the financial
account (the money from the shares, and the assets going in the other direction). Foreign
aid represents an export of goods and a unilateral transfer to waive the payment.
Therefore, current account balance = - financial account balance.
Trade balance = Goods balance + service balance
Income Balance = Net Investment Income + Net International Compensation to Employees
Net income from capital is called Net Investment Income and consists of dividends,
interests, profits, etc. Net income from labour is called Net International Payments.
Net unilateral transfers: is the difference between gifts received from the rest of the world
and gifts given to the rest of the world. These gifts can involve private agents or gov.
Net unilateral transfers = private remittances + government transfers
If the current account is negative, all other things equal, the net external debt of the country
goes up, and if the current account is positive, the external debt falls.
It must be the case that CAUS + CAROW = 0
The country with the biggest accumulated current account deficit is the US. The countries
that have been financing these deficits are China, Japan, Germany and oil exporting
countries (Russia, members of OPEC and Norway). Overall, the picture is one of unbalanced
accumulated trade.
1.3: The Net International Investment Position: NIIP is used to refer to a country’s net
foreign wealth = Difference between a country’s foreign assets (A) and its foreign liabilities
(L) – value of the country’s assets owned by foreign residents. NIIP = A – L
NIIP is a stock, while the current account is a flow.
NIIP is negative, then the country has debt. NIIP positive, country is a net creditor.
∆ NIIP=CA+ valuation changes
Valuation changes is changes in the market value of the country’s foreign assets and liability
positions (due to currency fluctuations, changes in stock prices, interest rates etc)
In the absence of valuation changes, the level of the current account must equal the change
in the net international investment position.
You can find the hypothetical NIIP by removing valuation changes from the actual NIIP.
To do this you start with the NIIP of the initial year and add all of the CA balances until the
year of interest. This yields the hypothetical NIIP.
In spite of large CA deficits, the U.S. reduced its external debt due to:
,Large depreciation of the U.S. dollar (20%). Most of the U.S. foreign liabilities are in dollars,
whereas most of the U.S. holdings of foreign assets are in foreign currency.
Large increases in the price of foreign stocks.
1.4: The Negative-NIIP-Positive-NII Paradox: Even though the U.S. has had a negative net
international investment position (NIIP < 0) for the past quarter century, it receives
investment income from the rest of the world (NII > 0).
How could it be that a debtor country, instead of having to make payments on its debt,
receives income on it?
There are two suggested explanations for this: Dark Matter and Return Differentials.
The Dark Matter hypothesis maintains that the Bureau of Economic Analysis may
underestimate the net foreign asset holdings of the United States (e.g. intangibles which are
not correctly reflected in the official BoP e.g. the value of U.S. brands which does not show
up in the raw investments).
However, the argument goes, these intangibles would generate income for the U.S. which
would be appropriately recorded. It thus becomes possible that the U.S. could display a
negative NIIP and at the same time a positive NII.
TNIIP = the ‘true’ net international investment position.
TNII Pt =NII Pt + Dark Matter t
Net investment income is the return on the TNIIIP. So letting r denote the interest rate, we
have: NII = rTNII P t−1
However, this theory can yield such a high number it seems unrealistic
Return Differentials: Explanation could be that the U.S. earns a higher interest rate on its
foreign asset holdings (shares – riskier but earn relatively high returns) than foreigners earn
on their U.S. asset holdings (mostly safe U.S. treasury bills).
NIIP = A – L. Let rA be the interest rate (return) on A, and rL the interest rate on L.
The question is how large does the interest rate differential on assets and liabilities, r A – rL,
have to be to explain the paradox.
NII must equal the difference between investment income and investment payments:
NII = rAA – rLL
Small interest rate differentials can generate very large effects on net investment income
because gross positions are so large. Hence just a small rate of return differentials can lead
to a positive NII even though the NIIP is negative.
At a global level, all current account balances must add up to zero.
2.1: Current Account Sustainability: Sustainability in 2 periods: Can a country run a
perpetual trade balance deficit? It depends on whether the country is a net debtor or a net
creditor (positive NIIP). If it is a net debtor, its NIIP is negative, then no. As in this case, the
country will have to run a trade balance surplus at some point to service its debt.
If the country is a net creditor of the rest of the world, NIIP positive, then it can run a
perpetual trade deficit and finance it with the interest generated by its net investments
abroad.
For example, consider an economy that lasts for two periods. It starts period 1 with a net
¿
foreign asset position of B0. Let r denote the interest rate. Then the country’s NII in period 1
¿
is given by r B0. Let the trade balance be denoted TB1.
¿ ¿ ¿
C A1 =r B0 +T B 1 but at the same time with no valuation changes: C A1 =B 1−B 0
,C A 2=B ¿2−B ¿1 which combining and remembering B¿2=0 yields B¿0=−C A 1−C A 2 This
formula says that a country’s initial net foreign asset position must be equal to the sum of
its present and future current account deficits which implies that the country can run
current account deficits in both periods only if the initial net asset position is positive.
Then the country’s net international investment position at the end of period 1:
¿ ¿ ¿ ¿
B1=( 1+r ) B 0 +T B1 Similarly, B2=( 1+r ) B1+ T B 2
There are 2 assumptions: 1) net payment to employees = 0 2) net unilateral transfers = 0
Now at the end of period 2, the country cannot hold assets or debts, because no one will
¿
be alive in period 3 to collect (the world ends in period 2). This means that B2=0
¿ T B2
Combining these equations: ( 1+r ) B 0=−T B1− which states that the net foreign asset
(1+ r )
position (including interest) equals the present discounted value of its future trade deficits.
¿
It is clear from this expression that if the country is a net debtor, B0 < 0, then it must run a
trade balance surplus at some point. However, if the country is a net creditor of the rest of
¿
the world, B0 >0 , then it can afford running trade deficits in both periods. This result holds
not just for two period economies, but for economies lasting any number of periods,
including an infinite number of periods but in this case the country must not violate the no-
ponzi condition (debt grows at a rate less than the interest rate).
Note, that the current account is the trade balance + NII so we are only interested in the
payment on the debt not the absolute debt.
2.2: Math of Current Account: Savings, Investment and the Current Account: In any period
savings, investment and the current account are linked by the identity C A1 =S 1−I 1
Savings in excess of what is needed to finance domestic investment must be allocated to
purchases of foreign assets. Therefore, according to this relation, a deficit in the current
account occurs when a country’s investment exceeds its savings.
¿
Current Account Deficits as Reflections of Trade Deficits: C A t=T Bt +r B t−1
Current Account as the Gap between National Income and Domestic Absorption: A country’s
absorption, which we denote by At, is defined as the sum of private consumption,
government consumption and investment: At =C t + I t +G t
Combining this expression with the formulas above, CA can be expressed as the difference
between income and absorption: C A t=Y t − At
Thus the current account is in deficit when domestic absorption of goods and services
exceeds national income.
So to conclude the CA can be viewed four ways:
C A t=B¿t −B¿t−1, C A t=rB ¿t−1 +T Bt , C A t=St −I t , C A t=Y t − At
¿ ¿
2.3: Sustainability in infinite periods: B1=( 1+r ) B 0 +T B1 ≈ the change in NIIP = ∆ CA
¿
¿ B 1 T B1
B0= −
1+r 1+ r
¿
B T B2
Now shifting one period forward: B¿1= 2 −
1+ r 1+r
¿
¿ B2 T B1 T B2
Substituting in: B0= − −
( 1+r ) 1+r ( 1+r )2
2
, Repeating this iterative procedure T times results in the relationship:
¿ B¿T T B1 T B2 T BT
B0= − − …
( 1+r ) 1+r ( 1+ r )
T 2
( 1+r )T
¿
The no-Ponzi-game constraint tells us that you need to pay your debts. Bt ≥ 0
In an infinite horizon economy no-Ponzi-game condition tells you that the amount of debt
BT
that you can have, cannot grow at a faster rate than your interest rate: lim T
≥0
T → ∞ ( 1+r )
BT
Optimality constraint: lim T
≤0 - this is the opposite of the above. You do not want to
T → ∞ ( 1+r )
save so much that you give so much credit that you will never get it back from the rest of
the world.
This restriction and the no Ponzi-game constraint can be simultaneously satisfied only if the
BT
transversality condition holds: lim T
=0
T → ∞ ( 1+r )
Letting T go to infinity and using the transversality condition, this becomes:
−T B1 T B2
B¿0= − …
1+r ( 1+ r 2 )
Therefore, can a country run a perpetual trade deficit? If it is a foreign debtor, no! The same
as in the two period model. If the initial asset position is negative, then it is impossible to
run perpetual trade deficits as the two negative signs would cancel out and the right hand
side would then be positive.
What about the current account? Can a country run perpetually current account deficits?
¿ ¿
Assume the country is initially a net debtor. Law of motion: Bt =( 1+ r ) Bt −1+ T B t
Consider an example in which each period the country generates a trade balance surplus
¿
sufficient to pay a fraction α of its interest obligations. That is, T Bt =−αr Bt −1 where the
factor α is between 0 and 1.
¿ ¿
Bt =( 1+ r−αr ) B t−1 (substituted in)
¿
Recall the definition of Current Account: C A t=r Bt −1 +T Bt
¿
Therefore, we have C A t=r ( 1−α ) Bt−1 <0
And so the current account will always be negative
Does this country satisfy the Transversality/No Ponzi scheme conditions?
¿ t ¿
Law of motion of debt given above implies: Bt =( 1+ r−αr ) B0
[ ]
t
B ¿t 1+r ( 1−α ) ¿
It follows that: = B 0, which converges to zero as t becomes large because
( 1+ r )
t
1+r
1 + r > 1 + r(1−α ¿
Notice that under the assumed policy the trade balance evolves according to:
t−1 ¿
T B1=−αr [ 1+r ( 1−α ) ] B o
That is the trade balance is positive and grows unboundedly over time at the rate r(1 - α ¿. In
order for a country to be able to generate this path of trade balance surpluses, its GDP must
be growing over time at a rate equal or greater than r(1 - α ¿. If this condition is satisfied, the
repayment policy described in this example would support perpetual current account
deficits even if the foreign initial net foreign asset position is negative.
3.1: Endowment SOE: Theory of Current Account Determination:
