Eco 328External wealth and the long run budget constraint

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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

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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.

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• 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

ROWby owned

assets Home

homeby owned

assetsROW = wealth External

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• 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

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• 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

losses capital minus gains Capital=

effectsValuation =

assets ofexport Net

wealthexternal

on gains Capital

account

Financial

wealthexternal

in Change

FA

W

losses capital minus gains Capital

=effectsValuat ion

received transfers capitalNet

=

incomeUnspent

=

wealthexternal

on gains Capital

account

Capital

account

urrentC

wealthexternal

in Change

KACAW

a country can increase its external wealth in oneof 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.

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8

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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.

Capital gains have cut hour external debt in half!

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-8000000

-7000000

-6000000

-5000000

-4000000

-3000000

-2000000

-1000000

0

1000000

NFA CumCA

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• 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

assets alnonfinanci Home

)-(+ = wealthTotal LAK

losses) minus (gains effectsValuation disposals) minus ns(acquisito Addit ions

–on

gains Capital+

on

gains Capital+

– to

Additions +

to

Additions =

wealthtotal

in Change

LAKLAK

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• 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 = 0so that minus the financial account –FA must equal CA + KA, hence we can write

External Wealth and Total Wealth

losses) minus (gains effectsValuation

economy home theintoassets ofimport Net

= toAdditions

economy home in theassets toAdditions

=K toAdditions –on

gains Capital+

on

gains Capital+)(

wealthtotal

in Change

LAK

FAI

LA

losses) minus (gains effectsValuation

–on

gains Capital+

on

gains Capital

wealthtotal

in Change

LAKKACAI

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• 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 (gains effectsValuation

–on

gains Capital+

on

gains Capital

wealthtotal

in Change

LAKKAS

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.

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NO

AA

/Sat

ellit

e an

d In

form

atio

n S

ervi

ce

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.

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• 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.

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Consider two cases of a $100,000 loan – neither pays it back

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

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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

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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

wealthexternal speriod'last on

vedpaid/receiInterest

1–

*

period thisbalance Trade

period this wealthexternalin Change

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:

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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.

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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*)2W1 (1 r*)TB0 TB1

The Budget Constraint in a Two-Period Example

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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.

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(1 r*)2W1 (1 r*)TB0 TB1

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

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By dividing the previous equation by (1 + r* ), we find a moreintuitive expression for the two-period budget constraint:

The Budget Constraint in a Two-Period Example

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:

balances tradefuture andpresent all of luePresent va

4*

4

3*

3

2*

2

*

10

periodlast fromwealth of luepresent va theMinus

1

*

)1()1()1()1()1(

r

TB

r

TB

r

TB

r

TBTBWr

A debtor (surplus) country must have future trade balances that are offsetting and positive (negative) in present value terms.

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The Budget Constraint in a Two-Period Example

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:

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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.

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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

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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.

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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.

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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.

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“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.

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The Favorable Situation of the United States

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:

effects Additional

wealthexternal ongains Capital

aldifferenti rateinterest todue Income

0*

effects alConvention

wealthexternal speriod’last onvedpaid/receiInterest

1–

*

period thisbalance Trade

period this wealthexternal in Change

1– )( KGLrrWrTBWWW NNNNN

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The Favorable Situation of the United States

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.

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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.

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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.

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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.

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