US Current Account Balances: Share of GDP

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US Current Account Balances Share of GDP
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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 i.e, net foreign assets)
• Which we can write as,
• And thus

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Substitution

• Thus,
• Now use this in the CA expression to eliminate
• And repeat the process

4
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. Lets
  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?

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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
• gt we are gifting foreigners, not optimal
• Hence, we must have
• So, our intertemporal constraint must be

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Intertemporal constraint

• This means that,
• The economys net debt today PV of future trade
  surpluses
• So key to sustainability is economys 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
• Cant we say more than this?

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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,

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Hypothetical Path for Debt(growth rate 4)
Is this path sustainable?
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Yes, it is!
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How do we get this

• Start with and
  divide by Yt1
• Then,

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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 gt g then burden of past debt is growing
• If r lt 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

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Sustainability

• What does this imply?
• If we have negative NFA, then r gt 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

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Simulations (r .05, g .03)
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Simulations (r .06, g .03)
TB declines at constant rate
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Simulations (r .08, g .03)
TB declines at constant rate
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Dollar price of a Euro
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Yen Price of a Dollar
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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

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US Net Wealth and Debt Positions
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Valuation

• You might think of , i.e.,
  as the 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 gt US indebtedness can change even without
  CA reversal

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Valuation Effects

• We need to add valuation effects
• NFA may differ from cumulative current accounts
• 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

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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 Nokias stock price surged, Finnish NFA
  approached minus 170 of GDP, when the price fell
  NFA recovered

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Finlands NFA and Nokia Price
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Adjusting for Valuation

• Separate out income on NFA in the CA expression
• We want to express everything in ratios again
• or

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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,

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Valuation

• Now we know that
• So,
• or

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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?

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Simulations with Valuation
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US Net Foreign Assets
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Is it Ending?
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Role of Size

• Size of net debt matters
• We know that net interest income is
• For this to be positive we require
• So,

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Implications

• We are assuming that so
• Lets suppose that and
• Thus,
• 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
• But what if net debt rises to -.35?
• Or if rA falls to .05?

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Why was this calculation interesting?

• We showed that even though US NFA lt 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.

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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?

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World Banker to Venture Capitalist
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Gold vs other US gross foreign assets (share of
GDP)
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US Gross Foreign Assets by Class
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US Gross Foreign Liabilities by Class
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Income Balance Broken Down
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Path of a Debtor
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Net Income and Government Interest Payments
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Dark Matter

• In 1980 NFA of US365bn and net foreign
  investment income of US30bn.
• Cumulative current account deficits between 1980
  and 2004 were US4.5tn, but net income relatively
  constant
• Yet the US net foreign factor income in 2004 was
  still US30bn
• 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

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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

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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!

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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

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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 (0.70.850.1) 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?

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NIIP and Net Income
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Interest-Sensitive Returns
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Equities
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FDI
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Net Income by Asset Class
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Changes in NIIP, Explained

• The -333.0 billion change in the net investment
  position from yearend 2004 to yearend 2005 was
  largely due to record private net foreign
  purchases of U.S. securities, including U.S.
  Treasury securities, and to the depreciation of
  most major foreign currencies against the dollar,
  which lowered the dollar value of U.S.-owned
  assets abroad.
• The impact of these net purchases and
  exchange-rate changes was partly offset by price
  appreciation of U.S.-held foreign stocks that
  surpassed by a large amount price appreciation of
  foreign-held U.S. stocks.
• U.S.-owned assets abroad were 10,008.7 billion
  at yearend 2005, compared with 9,186.7 billion
  at yearend 2004.
• Foreign-owned assets in the United States were
  12,702.5 billion at yearend 2005, compared with
  11,547.4 billion at yearend 2004.

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Real Exchange Rate

• For adjustment to occur the real exchange rate
  must change
• Why cant 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

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US Real Exchange Rate, (Trade-weighted Broad )
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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.

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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,

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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?

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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.

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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 GDPs is in the figure
• Notice that N is relatively more expensive in B

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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

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GDP at Market Exchange Rates
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Market versus PPP exchange rates
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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

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Largest banknote ever
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Real Exchange Rate and the Current Account
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Trade Deficit and the real value of the dollar
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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(1c).
• 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.

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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

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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.).

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Big Mac and Incomes

• Dollar price of the Big Mac is strongly
  correlated with the local hourly wage (in
  dollars).

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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

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GDP and Price Levels
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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,

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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

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Implications

• Movements in Q depend on differential growth in
  non-traded 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 non-traded goods.
• Why does economic growth cause the relative price
  of tradables to fall?
• Key point, labor market equilibrium

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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

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Labor market equilibrium

• Labor market equilibrium implies
• Profit maximization implies
• So,
• Now assume that or
• Simplifying assumption gt 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

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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

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Yen Price of a Dollar
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Implications

• First, if all goods tradable, , 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

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Balassa-Samuelson Effect
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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

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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

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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.

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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

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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

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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

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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?

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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

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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
• Based on initial external wealth, W0, make
  predictions about its future trade balance
• A debtor country (W0 lt 0) must run a trade
  surplus from now and into the future.
• A creditor country (W0 gt 0) must run a trade
  deficit from now and into the future.

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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.

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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,

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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.

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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

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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.

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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.

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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.

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Real Dollar Indices
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Weighting and the Real Exchange Rate
102
Adjustment in more open economy
Greater share of tradables in consumption basket
for the open economy
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Adjustment with short-run rigidity
Production possibilities are more inelastic in
the short run
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PPF
Axes are traded goods and non-traded goods
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Adjustment with non-traded goods
At this point there is an excess demand for
tradable goods
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Rising Yen
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B-S effect stronger with CPI based RER
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Dollars per Euro
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Rand/
110
Yen has weakened
111
Relative price levels and per-capita incomes
112
Relative GDP and Relative Price levels
113
B-S and the transition economies
114
Yen and PPP
115
Euro and PPP
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