1) The document discusses external wealth and a country's long-run budget constraint. It defines external wealth as the net assets a country owns abroad minus the foreign assets owned within the country. 2) A country's change in external wealth equals its current account balance plus net factor income from abroad plus capital gains or losses. In the long run, for a small open economy, external wealth must equal zero if all debts are to be paid off. 3) The document provides a two-period example of a country's budget constraint. It shows that a creditor country with positive initial wealth can run trade deficits on average in the future, while a debtor country must run trade surpluses on average.

1. Eco 328
External wealth and the long run budget constraint

2. 2
Do government deficits cause current account deficits?
Often they go together - “twin deficits”. Foreigners finance our deficits.
They sell goods and services to us and then accumulate US assets rather than
buying US goods and services. Many of these assets are treasury securities.
The current account can be expressed
The theory of Ricardian equivalence asserts that a fall in public saving is fully offset
by a contemporaneous rise in private saving.
From the data, however, we see private saving does not fully offset government
saving in practice.
The current account might move independently of saving (public or private) due to
changes in the level of investment.

CA  Sp  Sg  I

3. 3
External Wealth
• Just as a household is better off with higher wealth, all else
equal, so is a country.
• “Net worth” or external wealth with respect to the rest of
the world (ROW) can be calculated by adding up all of the
foreign assets owned by the home country and subtracting
all of the home assets owned by ROW.
• In 2012, the United States had an external wealth of about
–$4,474 billion. This made the United States the world’s
biggest debtor.

4. 4
• The level of a country’s external wealth (W) equals
• A country’s level of external wealth is also called its net
international investment position or net foreign assets.
If W > 0, home is a net creditor country: external assets
exceed external liabilities.
If W < 0, home is a net debtor country: external liabilities
exceed external assets.
The Level of External Wealth
    
  
LA
W












ROWbyowned
assetsHome
homebyowned
assetsROW
=wealthExternal

5. 5
• There are two reasons a country’s level of external wealth
changes over time.
1. Financial flows: As a result of asset trades, the country
can increase or decrease its external assets and liabilities.
Net exports of home assets cause an equal increase in the
level of external liabilities and hence a corresponding
decrease in external wealth.
2. Valuation effects: The value of existing external assets
and liabilities may change over time because of capital
gains or losses. In the case of external wealth, this change
in value could be due to price effects or exchange rate
effects.
Changes in External Wealth

6. 6
• Adding up these two contributions to the change in external
wealth (ΔW), we find
• Since −FA = CA + KA, substituting this identity
Changes in External Wealth
    
lossescapitalminusgainsCapital
=
effectsValuation
=
assetsofexportNet
wealthexternal
ongainsCapital
account
Financial
wealthexternal
inChange



















FA
W
    
lossescapitalminus
gainsCapital
=
effectsValuation
receivedtransfers
capitalNet
=
income
Unspent
=
wealthexternal
ongainsCapital
account
Capital
account
urrentC
wealthexternal
inChange
























 KACAW

7. a country can increase its external wealth in one
of only three ways:
o Through its own thrift (a CA surplus, so expenditure is
less than income)
o By the charity of others (a KA surplus, by receiving net
gifts of wealth)
o With the help of windfalls (having positive capital
gains)
Similarly, a country can reduce its external wealth by
doing any of the opposites.
7

8. 8

9. 9
Are these valuation effects significant?
• For the past 30 years the United States has almost always had a
financial account surplus, reflecting a net export of assets to the
rest of the world to pay for chronic current account deficits.
• If there were no valuation effects, then the change in the level of
external wealth should equal the cumulative net import of assets
over the intervening period.
• But valuation effects or capital gains can generate a significant
difference in external wealth.
• From 1988 to 2012 these effects reduced U.S. net external
indebtedness in 2012 by more than half compared with the level
that financial flows alone would have predicted.
• Capital gains always have a “zero sum” property—by symmetry, an
increase in the dollar value of the home country’s external assets is
simultaneously an increase in the dollar value of the rest of the
world’s external liabilities.

10. Capital gains have cut hour external debt in half!
10
-8000000
-7000000
-6000000
-5000000
-4000000
-3000000
-2000000
-1000000
0
1000000
NFA CumCA

11. 11
• External wealth is only part of a country’s total wealth, the
sum of the home capital stock (all nonfinancial assets in the
home economy, denoted K) plus amounts owed to home by
foreigners (A) minus amounts owed foreigners by home (L):
• Changes in the value of total wealth can then be written as
follows:
External Wealth and Total Wealth
 
wealthExternal
assetsalnonfinanciHome
)-(+=wealthTotal LAK
    
losses)minus(gainseffectsValuationdisposals)minusns(acquisitoAdditions
–on
gainsCapital
+
on
gainsCapital
+
–to
Additions
+
to
Additions
=
wealthtotal
inChange






























LAKLAK

12. 12
• Additions to the domestic capital stock K are simply
investment, denoted I. Additions to external wealth, A – L,
equal net additions to external assets minus net additions to
external liabilities
• Now, using the BOP identity, we know that CA + KA + FA = 0
so that minus the financial account –FA must equal CA + KA,
hence we can write
External Wealth and Total Wealth

  

losses)minus(gainseffectsValuation
economyhometheinto
assetsofimportNet
=
toAdditions
economyhomein the
assetstoAdditions
=
KtoAdditions –on
gainsCapital
+
on
gainsCapital
+)(
wealthtotal
inChange



















LAK
FAI
LA
  
losses)minus(gainseffectsValuation
–on
gainsCapital
+
on
gainsCapital
wealthtotal
inChange


















LAK
KACAI

13. 13
• The BOP identity makes the connection between external asset trade
and activity in the current account.
• Take the connection one step further using the current account
identity, S = I + CA,
• There are only three ways to get more (or less) wealthy: do more (or
less) saving (S), receive (or give) gifts of assets (KA), or enjoy the
good (bad) fortune of capital gains (losses) on your portfolio.
• What is true about individuals’ wealth is also true for the wealth of a
nation in the aggregate.
External Wealth and Total Wealth
  
losses)minus(gainseffectsValuation
–on
gainsCapital
+
on
gainsCapital
wealthtotal
inChange


















LAK
KAS

14. Countries face shocks all the time, and how they are able to cope
with them depends on whether they are open or closed to
economic interactions with other nations.
Hurricane Mitch battered Central America from
October 22, 1998, to November 5, 1998. It was
the deadliest hurricane in more than 200 years
and the second deadliest ever recorded.
Hurricanes are tragic human events,
but they provide an opportunity for
research.
The countries’ responses illustrate
some of the important financial
mechanisms that help open
economies cope with all types of
shocks, large and small.
14
NOAA/SatelliteandInformationService

15. The Macroeconomics of Hurricanes The figure shows the average response (excluding transfers)
of investment, saving, and the current account in a sample of Caribbean and Central American
countries in the years during and after severe hurricane damage. The responses are as expected:
investment rises (to rebuild), and saving falls (to limit the fall in consumption); hence, the current
account moves sharply toward deficit.
15

16. • Suppose the interest rate is 10% annually, :
Case 1 A debt that is serviced. You pay the interest but you
never pay any principal.
Case 2 A debt that is not serviced. You pay neither interest
nor principal. Your debt grows by 10% each year.
• Case 2 is not sustainable.
• In the long run, lenders will not allow the debt to keep
growing larger and larger.
• Nations face a similar constraint.
16
Consider two cases of a $100,000 loan – neither pays it back

17. Make some simplifying assumptions:
• Prices are perfectly flexible. Analysis can be done in terms of
real variables, and monetary aspects of the economy can be
ignored.
• The country is a small open economy. The country cannot
influence prices in world markets for goods and services.
• All debt carries a real interest rate r*, the world real interest
rate, which is constant. The country can lend or borrow an
unlimited amount at this interest rate.
How The Long-Run Budget Constraint Is Determined
17

18. Couple more:
• The country pays a real interest rate r* on its start-of-period debt liabilities
L and is paid the same interest rate r* on its start-of-period debt assets A.
Net interest income payments equal to r*A − r*L, or r*W, where W is
external wealth (A − L).
• There are no unilateral transfers (NUT = 0), no capital transfers (KA = 0),
and no capital gains on external wealth.
 Therefore, there are only two nonzero items in the current account:
the trade balance and net factor income from abroad, r*W.
• If r*W is positive, the country is earning interest and is a lender/creditor
with positive external wealth. If r*W is negative, the country is paying
interest and is a borrower/debtor with negative external wealth.
How The Long-Run Budget Constraint Is Determined
18

19. Calculating the Change in Wealth Each Period
We can write the change in external wealth from end of year
N − 1 to end of year N as follows:
Calculating Future Wealth Levels
 
wealthexternalsperiod'laston
vedpaid/receiInterest
1–
*
periodthis
balanceTrade
periodthis
wealthexternalinChange
1– NNNNN WrTBWWW 
We can compute the level of wealth at any time in the future by
repeating the above.
Rearranging, we can solve for wealth at the end of year N:
19

20. External wealth equals the sum of three terms: the
current account, the capital account, and capital gains on
external wealth.
For now, the last two terms are zero.
In this simplified world, external wealth can change for
only two reasons: surpluses or deficits on the trade
balance in the current period,
or surpluses and deficits on net factor income arising from
interest received or paid.
20

21. Suppose all debts owed must be paid off, and the country must
end that year with zero external wealth, i.e. settle up with
everybody.
At the end of year 1:
Then:
The two-period budget constraint equals:
01
*
0 )1( TBWrW  At the end of year 0,
10
*
1 )1(0 TBWrW 
10
*
1
2*
1 )1()1(0 TBTBrWrW  
(1 r*
)2
W1  (1 r*
)TB0  TB1
The Budget Constraint in a Two-Period Example
21

22. The two-period budget constraint tells us that a creditor
country with positive initial wealth (left-hand-side
negative) can afford to run trade deficits “on average” in
future;
conversely, a debtor country (left-hand-side positive) is
required to run trade surpluses “on average” in future.
22

(1 r*
)2
W1  (1 r*
)TB0  TB1

23. The present value of X in period N is the amount that would
have to be set aside now, so that, with accumulated interest, X is
available in N periods. If the interest rate is r*, then the present
value of X is X/(1 + r*)N.
Present Value Form
23
By dividing the previous equation by (1 + r* ), we find a more
intuitive expression for the two-period budget constraint:
The Budget Constraint in a Two-Period Example

24. Extending the Theory to the Long Run
If N runs to infinity, we get an infinite sum and arrive at the
equation of the LRBC:
  


balancestradefutureandpresentallofluePresent va
4*
4
3*
3
2*
2
*
1
0
periodlastfromwealth
ofluepresent vatheMinus
1
*
)1()1()1()1(
)1( 







 
r
TB
r
TB
r
TB
r
TB
TBWr
A debtor (surplus) country must have future trade balances that
are offsetting and positive (negative) in present value terms.
24
The Budget Constraint in a Two-Period Example

25. A Long-Run Example: The Perpetual Loan
The formula below helps us compute PV(X) for any stream of
constant payments:
For example, the present value of a stream of payments on a
perpetual loan, with X = 100 and r* = 0.05, equals:
25

26. If the amount loaned by the creditor is $2,000 in year 0,
and this principal amount is outstanding forever, then
the interest that must be paid each year to service the
debt is 5% of $2,000, or $100.
Under these conditions, the present value of the future
interest payments equals the value of the amount loaned
in year 0 and the LRBC is satisfied.
26

27. Implications of the LRBC for Gross National Expenditure and
Gross Domestic Product
The LRBC tells us that in the long run, a country’s national
expenditure (GNE) is limited by how much it produces (GDP). To
see how, consider the previous equation and the fact that
.GNEGDPTB 
27

28. The left side of this equation is the present value of
resources of the country in the long run:
the present value of any inherited wealth plus the
present value of present and future product.
The right side is the present value of all present and
future spending (C + I + G) as measured by GNE.
28

29. The long-run budget constraint says that in the long run, in
present value terms, a country’s expenditures (GNE) must equal
its production (GDP) plus any initial wealth.
The LRBC shows how an economy must live within its means in
the long run.
29

30. The Favorable Situation of the United States
“Exorbitant Privilege”
The U.S. has been a net debtor with W = A − L < 0 since the
1980s. Negative external wealth leads to a deficit on net factor
income from abroad with r*W = r*(A − L) < 0. However, U.S. net
factor income from abroad has been positive throughout this
period. How can this be?
• The only way a net debtor can earn positive net interest
income is by receiving a higher rate of interest on its assets
than it pays on its liabilities.
• In the 1960s French officials complained about the United
States’ “exorbitant privilege” of being able to borrow cheaply
while earning higher returns on U.S. external assets.
30

31. “Manna from Heaven”
The U.S. enjoys positive capital gains, KG, on its external wealth.
Some skeptics call these capital gains “statistical manna from
heaven.”
• Others think these gains are real and may reflect the United
States acting as a kind of “venture capitalist to the world.”
• As with the “exorbitant privilege,” this financial gain for the
United States is a loss for the rest of the world.
31
The Favorable Situation of the United States

32. When we add the 2% capital gain differential to the 1.5% interest
differential, we end up with a U.S. total return differential
(interest plus capital gains) of about 3.5% per year since the
1980s. For comparison, in the same period, the total return
differential was close to zero in every other G7 country.
We incorporate these additional effects in our model as follows:
 
  

  

effectsAdditional
wealthexternalon
gainsCapital
aldifferentirateinterestto
dueIncome
0*
effectsalConvention
wealthexternalsperiod’laston
vedpaid/receiInterest
1–
*
periodthis
balanceTrade
periodthis
wealthexternalinChange
1– )( KGLrrWrTBWWW NNNNN 
32
The Favorable Situation of the United States

33. How Favorable Interest
Rates and Capital Gains
on External Wealth Help
the United States The
total average annual
change in U.S. external
wealth each period is
shown by the dark pink
columns. Negative
changes were offset in
part by two positive
effects. One effect was
due to the favorable
interest rate differentials
on U.S. assets (high)
versus liabilities (low).
The other effect was
due to favorable rates of
capital gains on U.S.
assets (high) versus
liabilities (low). Without
these two offsetting
effects, the declines in
U.S. external wealth
would have been much
bigger.
33

34. The Difficult Situation of the Emerging Markets
The United States borrows low and lends high. For most poorer
countries, the opposite is true.
Because of country risk, investors typically expect a risk premium
before they will buy any assets issued by these countries,
whether government debt, private equity, or FDI profits.
34

35. Sovereign Ratings and
Public Debt Levels:
Advanced Countries Versus
Emerging Markets and
Developing Countries The
data shown are for the
period from 1995 to 2005.
The advanced countries
(green) are at the top of
the chart. Their credit
ratings (vertical axis) do
not drop very much in
response to an increase in
debt levels (horizontal
axis). And ratings are
always high investment
grade.
The emerging markets and
developing countries
(orange) are at the bottom
of the graph. Their ratings
are low or junk, and their
ratings deteriorate as debt
levels rise.
35

36. Sudden Stops in Emerging Markets On occasion, capital flows can suddenly stop,
meaning that those who wish to borrow anew or roll over an existing loan will be
unable to obtain financing. These capital market shutdowns occur frequently in
emerging markets
In a sudden stop, a borrower country sees its financial account
surplus rapidly shrink.
36