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US Current Account Balances: Share of GDP
2.0%
1.0%
0.0%
-1.0%
-2.0%
-3.0%
-4.0%
-5.0%
-6.0%
-7.0%
Sustainability
• What does it mean to say that the CA is
sustainable?
– Can the economy continue to borrow?
– When will it be cut off from further borrowing?
• Start with the current account expression:
– (note that K  NFA i.e, net foreign assets)
– Which we can write as,
f
t
– And thus
t
Substitution
• Thus,
• Now use this in the CA expression to eliminate
• And repeat the process:
Result
• If we keep doing this indefinitely, we obtain:
– This should look familiar
– The first term on RHS is PV of net imports
– Second term is PV of NFA some time very far in the future
• Call this the terminal value of NFA. Let’s examine this first
• If finite horizon
– PV of terminal assets = 0
• If infinite horizon then let T go to infinity,
• Why is this our terminal condition Why does it make sense?
Terminal Value of NFA
• If
we are running a Ponzi game
– We never pay back our debts – free lunch
• If
we are forgoing some utility
– => we are gifting foreigners, not optimal
• Hence, we must have
• So, our intertemporal constraint must be:
Intertemporal constraint
• This means that,
• The economy’s net debt today = PV of future trade
surpluses
– So key to sustainability is economy’s ability to generate future
surpluses
• Is it rational to believe that we can earn sufficient future surpluses?
• Key is thus expectations of future spending and income
– Not much of a criteria
• Can’t we say more than this?
Second try at criteria
• When is debt non-increasing?
– That is, when does Debt/GDP not grow?
• We cannot have a steady state with exploding debt
• Why is this important?
• Let the growth rate be defined by
• Start with
• Then we can show that the change in NFA/GDP is,
How do we get this
• Start with
• Then,
and divide by Yt+1
Implication
• Why is this expression important?
– Decompose the growth in debt ratio to:
• Primary component – the trade balance
• Feedback component – the weight of the past debt
– If r > g then burden of past debt is growing
– If r < g then we can have a party today and the
burden still decreases over time
» Dynamic inefficiency
• So debt is sustainable if debt ratio is not growing
Sustainability
• What does this imply?
– If we have negative NFA, then r > g implies it will grow
• Faster growth means it will decrease
• Or, if we have positive trade balances debt will fall
• Suppose, r = .05 and g = .03
– If tb gradually goes to zero we get debt crisis
– We need tb to go to 1.5% of GDP to escape
• If r = .06 and g = .03 things are worse
• If r = .08 and g = .03 we are in real trouble
• Problem: r depends on kf
Simulations (r = .05, g = .03)
Simulations (r = .06, g = .03)
TB declines at constant rate
Simulations (r = .08, g = .03)
TB declines at constant rate
Dollar price of a Euro
Yen Price of a Dollar
NFA and Ability to Repay
• Notice that even if NFA gets more negative
what matters is ability to repay
– For US, net wealth has been rising relative to net
debt
• Foreign debt is still small relative to total US
debt
– In industrialized countries foreigners cannot be
treated differently from residents
– So US is better credit risk than one might fear
US Net Wealth and Debt Positions
Valuation

• You might think of NFAt   CAt i , i.e., as the
i 1
sum of all past current accounts
– Think of a bathtub. Level of water is the sum of all
the water that has ever been poured in, minus all the
water that ever drained out
• Would be true if we lived in one-good economy
• But NFA made up of many assets and liabilities,
and their relative prices change over time
– This => US indebtedness can change even without
CA reversal
Valuation Effects
• We need to add valuation effects
– NFA may differ from cumulative
current accounts

VEt  NFA* t   CAt i
i 1
– If US earns positive net foreign income this adds to
our consumption possibilities
• Where do they come from?
– Differences in rates of return
– Capital gains and losses on foreign assets
• Interest income is reported capital gains are not realized
• Postpone why, and first adjust our analysis
NFA and Valuation
• Suppose US stock market rises
– Then value of foreign holdings of US assets rises
• So NFA decreases
– But has US ability to finance debt fallen? Probably not, if the
stock market rose due to higher productivity etc.
– Example, Finland and Nokia
• Nokia widely held by foreigners was a huge share of
Finnish wealth
• When Nokia’s stock price surged, Finnish NFA
approached minus 170% of GDP, when the price fell
NFA recovered
Finland’s NFA and Nokia Price
Adjusting for Valuation
• Separate out income on NFA in the CA expression
• We want to express everything in ratios again
• or
Capital Gains
• We need to do something about the term, KG
– Suppose they are proportional to assets and liabilities
– Then,
– If we let real returns be
then,
Valuation
• Now we know that
• So,
• or
Implications
• The first and last term are familiar from before
• The middle term is the valuation term
– If
obviously no valuation effect
– Excess return on assets allows NFA to grow even
when GDP growing slow or tb is too small
• If we earn excess returns the scale of NFA matters
– Since NFA for US is roughly 25% of GDP this is big
• How does it impact sustainability?
Simulations with Valuation
US Net Foreign Assets
Is it Ending?
Role of Size
• Size of net debt matters
• We know that net interest income is
• For this to be positive we require
• So,
Implications
• We are assuming that
• Let’s suppose that
• Thus,
so
and
• What about RHS? In US, L is about equal to Y
– So
is approximately equal to -.26
– So the condition for positive net income is satisfied, since
0.33  (0.26)
– But what if net debt rises to -.35?
– Or if rA falls to .05?
Why was this calculation interesting?
• We showed that even though US NFA < 0, it is
still possible to earn positive interest income
– This is possible because returns on assets we hold
are greater than returns paid on our liabilities
• But it also requires that liabilities not be too much greater
than assets
– Why this is the case is interesting.
Valuation Effect: Causes
• What causes this?
– Imperfect substitutability
• If assets and liabilities were perfect substitutes, returns
would be equalized
– Risk could be a factor
– Exorbitant privilege
• We borrow in our own currency
– Liability mismatch
• US is like a bank, borrow short lend long
• From Central Banker to venture capitalist
– Share of portfolio in risk assets has risen
– But liquidity mismatch can be trouble
– Future Triffin Problem?
World Banker to Venture Capitalist
Net Income and Government Interest Payments
Dark Matter
• In 1980 NFA of US$365bn and net foreign investment
income of US$30bn.
• Cumulative current account deficits between 1980 and
2004 were US$4.5tn, but net income relatively constant
– Yet the US net foreign factor income in 2004 was still
US$30bn
– Seems paradoxical
– Especially if we assume that the net foreign investment
income data is to be trusted more than trade balance and net
foreign assets data
Dark Matter
• HS assume that the latter miss systematic income streams
– Global liquidity services
– Insurance services
– Knowledge services
• These do not show up in historical capital flow data, or in market
value data
– Why? went unrecorded, is that these services were bundled with financial
instruments:
• US currency, US sovereign debt and US-originated FDI.
• But once abroad they produce income streams
• US has been so good at exporting these services that
conventional current account balance data is irrelevant
– Notice this is opposite to the savings glut type or investment boom
hypothesis
Dark Matter
• Suppose that the $30 billion in net income is real
• Discount this at 5%
– Equals $600 billion
– Since, measured NFA = $-2.5 trillion, HS conclude that there must be
missing $3.1 trillion in assets
– This is Dark Matter
• Curious that H-S apply discount factor to net rather than gross
income
– Gross income in 2004 was $376 billion, so by their procedure, gross
assets = $7.52 trillion, less than measured official gross assets of $10 trillion
• Perhaps there is dark anti-matter!
– Since foreign assets in US generated $340 billion, by H-S this implies $6.8
trillion, so dark anti-matter for foreign assets is $5.7 trillion!
Dark Matter: Assessment
• Perhaps FDI income is mis-measured, but why should we trust
net income measures more than asset trade balance data?
• Why is the mis-measurement one way?
– US has had lots of inward FDI too
– Does the historical cost of foreign direct investment in the US understate
the fair value of the assets it created by less than the historical cost of
outward US direct investment abroad understates the fair value of the
assets thus created?
• Why are receipts always larger than liabilities?
•
Dark matter or cold fusion?
– Seems pretty clear that the paradox is going away
– Implies adjustment will be necessary
• Even less exotic theories justifying massive capital inflows seem
problematic in hindsight
Valuation Effect
• This does not mean that the valuation effect is
irrelevant
– Valuation effects do lessen the need for adjustment
– Consider an unexpected 10% depreciation of the $
• Suppose that A/Y = .7, and that 85% is held in dollars
– Assume all liabilities are in dollars
• This implies a transfer of 5.9% (0.7*0.85*0.1) of GDP from the rest
of the world to the US
– This would more than cover the trade deficit.
– But why would foreigners hold $ if they expect it to
depreciate?
Real Exchange Rate
• For adjustment to occur the real exchange rate
must change
• Why can’t an increase in r solve the problem?
– Increases CA surpluses for all countries
– A differential change in relative price is needed
• Real exchange rate is the relative price of foreign
goods relative to our goods
• Big swings since 1973
– Not just volatile, but not mean-reverting
US Real Exchange Rate,
(Trade-weighted Broad )
Real Exchange Rate
• Define the real exchange rate as
– It is the relative price of foreign goods
• Nominal exchange rate is the relative price of monies
– An appreciation of the real exchange rate thus means
that we are more competitive
– changes in Q will impact net exports, and hence, the
current account.
– If a current account deficit is to be reversed an
appreciation of the real exchange rate may be one of
the mechanisms of adjustment.
An Important Detour: PPP
• Suppose all goods tradable and that US and
Japan produce identical basket of goods
• Then arbitrage, “LOP,” implies that dollar price
of goods will be equal, net of transport costs, so
– SP* = P
– but this implies that Q = 1, and S = P/P*
• So nominal exchange rate is driven by price differences
• Or movements in the exchange rate are driven by relative
inflation rates,
More PPP
• Big Mac Index
• Predicts
– Euro depreciation, Rand appreciation, Yen appreciation
• So not perfect, why?
– Not all goods are tradable
– Consumption baskets differ
– Theory based on trade flows, ignores capital flows
• Relative prices not independent of income
– Why?
International Prices
• International prices differ from domestic prices
– International prices refers to common prices for the same
goods
– Differ from domestic because of the presence of non-traded
goods
• Haircuts are cheaper in poor countries
• Leads to differences in the relative prices of tradable goods across
countries
• Differences can be significant
– in 2004 Chinese per-capita income measured at market exchange rates
was $1272, but at international prices it was $6200. At international prices
China is the second largest economy in the world. Only about 7th at
market exchange rates.
– Japan, on the other hand had per-capita income of $37,600 at market
prices, but at international prices it was only $31,400.
Simple Example
• 2 countries (A and B), 2 goods (T and N)
• Country B is richer
– Identical preferences for simplicity
– GDP at market prices in country A is
– Assume market exchange rates cause
– Ratio of GDP’s is
in the figure
• Notice that N is relatively more expensive in B
International Prices
• Now use a common set of relative prices to
value the consumption baskets
• At common international prices the choices of
A are more expensive. We have
• People in poor countries spend more of their
income on N because these are relatively
cheaper
GDP at Market Exchange Rates
N
A
B
MER
A
MER B
T
Market versus PPP exchange rates
N
A
B
MER
A
IP A
IP B
MER B
T
Hyperinflation
• Germany after World War I.
– The ratio price index in November 1923 to the price index in August
1922 was 1.02 × 1010.
• Equivalent to a monthly inflation rate of 322 percent.
• On average, prices quadrupled each month
• Hungary after WW2
– Between August 1945 and July 1946 the general level of prices rose at the
rate of over 19,000 percent per month, or 19 percent per day.
• Extremes were even higher
– In October 1923, German prices rose at the rate of 41 percent per day.
– And in July 1946, Hungarian inflation reached the rate of 4.19 × 1016
percent per month (prices double every 15 hours)
• Led to the issue of the 100 quintillion pengo note
Largest banknote ever
Real Exchange Rate and the Current Account
Trade Deficit and the real value of the dollar
Real Exchange Rate
• Why does Q vary?
– One factor, trade costs
• Trade cost, c, assumed to be equal to some fraction of
the unit cost of the good at its source.
• Price of good exported at home is P, but when sold in the
foreign country price is: P(1+c).
– Existence of trade costs affects arbitrage incentives
of traders.
• Difference in prices in the two locations.
– Arbitrage occurs only if difference in prices are large
enough to compensate for trade cost.
Trade costs in practice
• Transportation costs
• U.S. imports: freight costs from 1% to 27% of unit cost.
• Landlocked countries: prices 55% higher (vs. coastal)
– Trade policy
• Average tariffs: 5% (advanced), 10% (developing)
– Summary of estimates for advanced economies
Deviations in PPP are not random
• Big Macs less expensive in poorer countries.
• Big Macs are 21% cheaper in Mexico and 53% less in
Malaysia (vs. U.S.)
– Similar pattern with Starbucks tall lattes.
• Lattes cost 15% less in Mexico and 25% less in Malaysia,
compared with the U.S. price.
• Explained by existence of nontraded goods.
– Big Mac is produced using a combination of traded
goods (flour, beef and special sauce) and nontraded
goods (cooks, cleaners, etc.).
Big Mac and Incomes
• Dollar price of the Big Mac is strongly
correlated with the local hourly wage (in dollars).
General Case
• This association is true in general
– Most goods have nontraded and traded components,
so the economy-wide price level should follow the
same patterns observed above.
• Strong positive relationship between U.S. price level and
GDP per person.
• Deviations in PPP vary systematically.
• Explain this with simple model that has traded
and non-traded goods
GDP and Price Levels
Non-traded goods and the real exchange rate
• How does Q depend on the presence of N?
• Let the price level be given by
• Then we write the real exchange rate as
• But LOP applies to traded goods, so
• Thus,
  P*   
n
 *
  Pt 
Q

  Pn 
  Pt 





Implications
• Q changes if relative prices change in either country
• Q changes if consumption basket changes
• Take logs of Q to get
– Then the rate of change of the real exchange rate is
– If
• Then
or
Implications
• Movements in Q depend on differential growth in nontraded goods prices.
– If non-traded goods prices rise faster in the foreign country
then the real exchange rate will appreciate and foreign prices
will rise faster than domestic prices.
• This real appreciation occurs with development and is
called the Balassa-Samuelson effect
– economic growth is associated with increased productivity in
traded goods, so that they fall relative to the price of nontraded goods.
– Why does economic growth cause the relative price of
tradables to fall?
• Key point, labor market equilibrium
Balassa-Samuelson
• Again start with
• Profit maximization implies
• And given LOP for tradables,
we have,
• So ratio of dollar wages depends on ratio of
marginal products of tradables
Labor market equilibrium
• Labor market equilibrium implies wt  wn  w
• Profit maximization implies
• So,
• Now assume that
or
MPLn  MPL*n if   1
– Simplifying assumption => all productivity differences are in
traded goods
• Then
– but we know that Q depends on the LHS, and that RHS
depends on productivity differences
• because of labor market equilibrium condition
Put the pieces together
• Put the pieces together
– So Q depends on the ratio of the marginal product
of labor in tradables, the B-S proposition, or
Yen Price of a Dollar
Implications
• First, if all goods tradable,   0 , then Q is constant
• The higher the share of non-tradables, the greater the
impact of differential productivity on the change in Q
• Explains rising yen
– Differential productivity and catchup
• After WW2 non-tradables very cheap
• Recovery meant rising productivity in tradables
• Led to rise in relative price of non-tradables
– More noticeable for CPI based measures than WPI based measures
• Same holds true in transition economies
Balassa-Samuelson Effect
RER and the Current Account Deficit
• We know that Q must change to close deficit
– But by how much?
• Two key issues
– Home bias
• How difficult to shift consumption towards domestic
goods
– Tradables versus non-tradables
• How hard is it to shift to production of tradable goods
Role of non-traded goods
• Consider a small economy so the country is a price
taker in traded goods.
– Then we can treat foreign and domestic traded goods as a
composite good, T.
– The country can transform capital and labor into traded and
non-traded goods given the PPF
• Suppose the country initially received a transfer from
the rest of the world equal to NX.
– Then consumption initially takes place at Q0
• the transfer allowed consumption of T to be larger than what
the economy produced
– Now suppose the transfer is withdrawn
• this is the equivalent to improving the trade balance by the
amount, NX
– PPF shifts down by NX
Adjustment to withdrawal of the transfer
• Production is now at P0
• If no change in RER, we prefer to be at
– But this is infeasible, it is outside the PPF – there is
an excess demand for tradables
– Relative price of tradables must rise, we move to
• The higher price of traded goods causes production to
shift towards traded goods and reduces the consumption
of them.
• So the real exchange rate increases — the real value of
domestic currency falls.
Size of Adjustment
• Required change in RER depends on
– How difficult it is to switch production to T
• If PPF were flat it would require no change in RER to
shift production
• In short run it requires even more change
– Overshooting
– Depends on Preferences between T and NT
• Elasticity of substitution
• If low
is farther to northwest – greater excess demand
• If people were indifferent, no need for change in RER
RER and openness
• If the economy is more open a smaller change in
RER is required
– In that case more goods are tradable
– So initial consumption are farther to the northeast
• PPF is flatter in that region
• Key point is that we cannot trade NT
– Greater the share of NT in GDP the larger the
required change in Q to cause production to shift
• And to cause the rest of the world to buy our exports
Key Point
• Greenspan and others argue that greater capital market
integration eliminates need for RER adjustment
– Improved financial integration means we can borrow more
easier
• But this misses the whole point
– It is imperfect integration of goods markets that is the reason
why Q must change
– Impact of capital-market integration is on amount we can
borrow to finance CA deficits.
• Thus, it effects the timing of when the dollar will depreciate.
– How much the dollar must decline in real terms depends on
how easy it is to increase net exports
Subtle Conclusion
• We have seen that for CA to improve Q must rise
• This does not mean that Q rising (or dollar falling in
real terms) means CA will improve
– These are two different questions!!
– CA improvement requires S to rise relative to I
• We did not show that Q rising causes S to rise relative to I
– We showed that if S is to rise relative to I then Q must rise
• That is, whether savings can rise relative to investment without the dollar
having to depreciate
• Adjustment required depends on how open the
economy is and how easy it is to shift to tradables.
– Real exchange rate puzzle: why is deficit so large given the current weak
dollar?
Real Exchange Rates and Global Imbalances: Two Views
• The transfer problem refers to the question of
how the trade balance will adjust to correct
global imbalances.
• Do large changes in the trade balance necessitate
large adjustments in the real and nominal
exchange rates?
• How to think about this?
– Immaculate transfer, vs.
– differentiated goods
Steady State Trade Balance
• Determine the steady state trade balance
– Country chooses trade balance to offset borrowing (or
lending). At steady state, TB is equal in each period:
TB  r W
W
– Based on initial external wealth, W0, make predictions
about its future trade balance:
• A debtor country (W0 < 0) must run a trade surplus from now
and into the future.
• A creditor country (W0 > 0) must run a trade deficit from now
and into the future.
Immaculate Transfer
• Identical Economies, Purchasing Power Parity,
and the “Immaculate Transfer”
– Scenario: Foreign borrows $1 from Home
• Foreign income and spending and increase. Home income
and spending decrease.
• Demand for each of the goods is unchanged, so the price
of the two goods is unchanged.
• This leaves the real exchange rate, Q, unchanged.
• Home external wealth decreases and trade balance is
positive.
Identical Economies, Purchasing Power Parity,
and the “Immaculate Transfer”
• Decrease in Home consumption
offset by decrease in foreign
consumption
• As Home TB rises, there is no
change in the real exchange rate,
Q  0
Differentiated Goods and Home Bias
• Goods are differentiated across Home and
Foreign, spending patterns are not the same
across countries.
– Home bias: Home prefers Home goods and Foreign
prefers Foreign goods).
– Same scenario: Foreign borrows $1 from Home
• Demand for Foreign goods increases relative to demand
for Home because Foreign prefers Foreign goods.
• Relative price of Foreign increases, so real exchange rate
rises as the Home trade balance increases.
Differentiated Goods and Home Bias
• Patterns of demand
across two countries
change, adjustment in
real exchange rate
• Home real depreciation
and Foreign real
appreciation, i.e., Q rises
Implications
• Real and Nominal Exchange Rates during
Adjustment
– If the assumption of differentiated goods is correct, then
large changes in real exchange rates are needed to
correct global imbalances.
– These adjustments will happen through:
• adjustment in the nominal exchange rate, and/or
• adjustment in relative prices
– If both countries have similar inflation targets, then the
adjustment will work through the nominal exchange rate.
Conclusions: Two Views
• Pessimists
– Benchmark calculations
• Debt service requirements: 0.5% of real GDP.
• IMF report estimates a 1% (of GDP) trade surplus would
require a 27% depreciation of the U.S. dollar.
– Implications for U.S. spending and production
• Dollar depreciation may occur slowly.
• Hard landing scenario would mean a dramatic shift in U.S.
consumption and production.
– J-curve effects might prolong and exacerbate adjustment, as foreign
return increases, bidding up U.S. interest rates.
Conclusion: Optimists
• Optimists
– Additional factors that will mitigate the effects:
• Same IMF report estimates a trade surplus equal to 1% of
GDP would require only a 7% depreciation.
• U.S. received higher interest payments on its foreign assets than
it has paid on its domestic assets owned by foreigners,
supporting the trade deficit.
– Large nominal depreciations would cause large valuation
effects in favor of the U.S. because:
• nearly all U.S. external liabilities are denominated in dollars, but
• most external assets are denominated in foreign currency.
Real Dollar Indices
140
130
120
110
100
90
80
70
1975
1980
1985
1990
Major Currencies
1995
2000
Broad Index
2005
Weighting and the Real Exchange Rate
Adjustment in more open economy
Greater share of tradables
in consumption basket for
the open economy
Adjustment with short-run rigidity
Production
possibilities are
more inelastic in the
short run
PPF
T
Axes are traded goods
and non-traded goods
NT
Adjustment with non-traded goods
At this point there is an
excess demand for
tradable goods
Rising Yen
B-S effect stronger with CPI based RER
1.26
1.24
1.22
1.2
Dollars per Euro
Dollars per Euro
1.3
1.28
1.18
1.16
06
20
06
20
06
20
06
20
06
20
06
20
06
20
06
20
06
20
05
20
05
20
05
20
05
20
09
08
07
06
05
04
03
02
01
12
11
10
09
Rand/$
114
112
Yen per Dollar
Yen has weakened
120
118
116
110
108
106
06
20
06
20
06
20
06
20
06
20
06
20
06
20
06
20
06
20
05
20
05
20
05
20
05
20
09
08
07
06
05
04
03
02
01
12
11
10
09
Relative price levels and per-capita incomes
Relative GDP and Relative Price levels
B-S and the transition economies
Yen and PPP
Euro and PPP
Midterm One
18
mean =63
standard deviation = 13.75
16
14
12
10
8
6
4
2
0
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100