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Economics 456International Macroeconomics and Finance: Section 4

Geoffrey Dunbar

UBC, Winter 2013

February 15, 2013

Geoffrey Dunbar (UBC, Winter 2013) Economics 456 February 15, 2013 1 / 53

Balance of Payments

International borrowing and lending has three possible advantages for acountry.

Consumption smoothing

Efficient investment

Diversification of risk.


Balance of Payments

There are often practical reasons for international borrowing and lending.Climate shocks such as hurricanes or natural disasters such as earthquakestypically require sizeable re-investment. International borrowing can reducethe costs of such investment.


Balance of Payments

As another example, consider a developing country that wishes to invest init’s education system.If the country is still poor, raising money via taxes is costly in welfareterms since the marginal utility of consumption is high.Borrowing and repaying in a future period is welfare improving if thereturns to education are greater than the borrowing costs.


Balance of Payments

One big question is how much can a country borrow?In this section we will derive the long-run budget constraint.A key restriction we will impose is that there is a no-Ponzi scheme.We will also consider the effects of shocks, risk and productivity.


Balance of Payments

Before we begin writing down a model, we should define exactly what weare trying to measure.A countries balance of payments comprises two accounts: the currentaccount and the financial account.The current account measures a country’s net payments and receipts forimports and exports (trade balance), net payments and receipts ofincome (net factor income from abroad) and net unilateral transfers.The capital account measures the net change in a country’s financialassets that transact as gifts. The financial account measures the netchange in asset exports minus asset imports. (Not everyone distinguishesbetween these two, they used to be called just the capital account.)


Balance of Payments

The wonderful part of the balance of payments is that:

current account = −financial account− capital account

To see how this works, consider the purchase of a Samsung Galaxy Phoneby someone in Vancouver for $600. The phone is imported from SouthKorea so imports rise by $600. However, since the payment is in dollarsthen Samsung is receiving a $600 financial asset (the currency), thus thefinancial account falls by this amount.


Balance of Payments

The textbook covers some basic macro aggregates.

GNE Gross National Expenditure: is equal to GDP plus the tradebalance.

GNI Gross National Income: is equal to GDP plus net factorincome from abroad.

NUT Net unilateral transfers: net transfers received (given) from(to) the rest of the world.

GNDI Gross National Disposable Income: GNI plus NUT.


Balance of Payments

The distinction between GDP, GNI and GNDI can lead to differentconclusions regarding an country’s economic progress.For example, Ireland paid a sizeable amount of it’s income to foreigners viafactor payments. Factors can be labour or capital.


Gross National Income


Net Unilateral Transfers

Net unilateral transfers are likewise relatively unimportant for developedcountries but they matter for developing countries.One of the main types of transfers is official development assistance orother charitable gifts, e.g. the Bill and Melinda Gates Foundation.


Gross National Disposable Income


The US Current Account


Current Account and Savings

Although the current account relates to the national income identity:

Y = C + I + G + CA,

it is important to remember that the current account is also the differencebetween savings and investment:

CA = S − I


Global Imbalances

To frame the issue of global imbalances, recall that savings is simplyforegone consumption. It can, in theory, be used for consumption at anymoment and thus there can be large swings in savings.Also note that savings can be either private saving or government savings:

S = Sp + SG

Perhaps it is not surprising that government savings can be volatile.


Global Imbalances


Global Imbalances

The issue with government deficits can be framed through the lens ofRicardian Equivalence. For government deficits to matter, it must be thatRicardian Equivalence does not hold, otherwise private savings wouldadjust to offset government deficits.


Global Imbalances


The Financial Account

We can think of the financial account as:

net export of domestic assets + net import of foreign assets

We have seen that the financial account, the capital account and thecurrent account are related. Although the balance of payments accountingimplies that these sum to zero, this is not often true in practice. Part ofthe problem is accounting for financial derivatives. These are oftenincluded as part of the statistical discrepancy.


Balance of Payments


External Wealth

What we have examined so far are income flows. However, flows over timebecome stocks.It should be no surprise that countries can amass wealth in foreign assets.A country’s external wealth is the difference between it’s holdings of assetsin the rest of the world and the rest of the world’s holding of its assets.Note that there can be a currency mismatch.


External Wealth

Changes in external wealth come from the financial account and valuationeffects, VE . The valuation effects are due to capital gains or losses whichcan be due to interest rate changes or exchange rate changes.If we call the change in external wealth ∆W then:

∆W = −FA + VE = CA + KA + VE

So countries gain external wealth through thrift, gifts or valuation changes.External Wealth is also known as the Net International InvestmentPosition (NIIP).


External Wealth


Valuation Effects Can Matter!


The Long-Run Budget Constraint

The long-run budget constraint (LRBC) of a country is a limit on howmuch debt it can borrow.In this examination of borrowing constraints we are only interested infeasibility. This means we are only interested in whether a country canrepay. This does not imply that it will choose to repay.We have already used examples of LRBC when we examined exchange ratemodels. Here we shall focus on these constraints in more detail.


The Long-Run Budget Constraint: Assumptions

Prices are perfectly flexible.

The country is a small open economy

The interest rate on all debt is r , the world real interest rate.

There are no NUTs.

The capital account is always zero.



Because of our assumptions, the change in wealth each period must comefrom the current account. Here it is the trade balance plus net factorpayments from abroad. Thus,

∆Wt = TBt + rWt−1

where t is the year and TB refers to the trade balance. Note that rWt−1

are the factor payments to the external wealth. Note as well that becauseprices are perfectly flexible and we are using a real model then there are novaluation effects.



Since ∆Wt = Wt −Wt−1 then rearranging the last expression yields:

Wt = TBt + (1 + r)Wt−1

Now note that since we are deriving this equation without reference to aspecific t then we can also write:

Wt−1 = TBt−1 + (1 + r)Wt−2

This is our usual repeated substitution trick.



Now recall that what we are trying to find is the maximum amount acountry can borrow and still repay at some point in the future.Let’s rewrite the expression above as:

−Wt−1 =TBt

1 + r− Wt

1 + r

And now use repeated substitution to replace Wt . We will get:

−Wt−1 =TBt

1 + r+

TBt+1

(1 + r)2+

TBt+2

(1 + r)3+ ...− W∞

(1 + r)∞



This is the same as the LRBC in the textbook, Equation 6-1. To see this,just multiply both sides of the above expression by 1 + r .

−(1 + r)Wt−1 = TBt +TBt+1

(1 + r)+

TBt+2

(1 + r)2+ ...− W∞

(1 + r)∞

This equation is a bit more interesting than perhaps the textbook suggests.



Note that W∞(1+r)∞ → 0 in either of two ways: W∞ = 0 or

(1 + r)∞ →∞ faster than W∞.

Also notice that it is the assumption of a constant r allows us towrite the constraint this way.

Also note that this budget constraint is hard to forecast: is aparticular TB too negative or will future TB’s offset it?



The LRBC also has implications for national income and nationalexpenditure.Recall that: GNE + TB = GDP.So we can substitute in for the trade balance.

−(1+r)Wt−1 = GDPt − GNEt+GDPt+1 − GNEt+1

(1 + r)+GDPt+2 − GNEt+2

(1 + r)2+...− W∞

(1 + r)∞

Our observations from the last slide matter here too. As a pre-cursor tosome of the analysis we will do, consider the following situation.



Suppose that GDP is produced used capital and labour effort. Andsuppose that, for whatever reason, a country is allowed to borrowing avery large amount in a period so that GDP-GNE is negative. Now considerthe perspective of the borrowing country. To repay the debt, the countrymust either save more or work more. These are costly to utility. Or thecountry can default. This is presumably costly too since the country’sfuture borrowing will be affected.So the decision to repay or not involves a trade-off between futuredisutility and current disutility.To throw even more into the mix, suppose that it is an OLG environment.Then the current generation which is deciding to repay or not may not bealive to experience the disutility in the future.



A related but somewhat different situation is also interesting to consider.Suppose that you are the leader of the government and you are concernedthat future gov’ts may make spending decisions of which you do notapprove. One thing you could do to ‘tie the hands’ of a future governmentis to leave office with a large amount of external debt. This will effectivelyforce GNE ≤ GDP and so no future government’s will have the fiscalroom to enact new spending.


The United States and Exorbitant Privilege

Recall our discussion of the simplifying assumptions. One thing weassumed is that the interest rate was constant for both assets andliabilities. This is not always true in practice.For the US, the interest rate it pays on it’s borrowing is historically 1.5-2percentage points lower than it earns on it’s foreign assets. (Perhaps thisis explained by investor’s perceptions of a flight-to-quality.)Thus, even though the US is a net debtor it actually earns net factorincome from abroad.This is unlikely to continue for several reasons, most particularly the factthat it may be increasingly difficult to find new buyers for US debt andalso because development in the rest-of-the-world should lower themarginal returns to such assets.


The United States and Manna fomr Heaven

A second difference for the US is that it has routinely enjoyed capital gainson its external wealth.These capital gains are effectively transfers from the rest of the world tothe US. The average return from 1980 to today is roughly 2 percentagepoints a year.This combined with the interest rate differential gives the US roughly 3.5-4percentage points higher return on its external wealth than other countries.


Balance of Payments


Balance of Payments

Let’s reconsider our LRBC that we derived (somewhat) theoretically a fewslides ago.Do the valuation effects that we observed for the US have any implicationfor the LRBC arguments?Yes!The valuation effects imply that the external wealth position is not simplydue to the trade balance and net factor payments.


Balance of Payments

Of course, the US may be a special case. So perhaps we might want toconsider more evidence before we become skeptical of the LRBC conceptas a whole.Let’s consider emerging markets. The LRBC assumes that all countrieshave access to borrowing and lending at the world interest rate.


Balance of Payments


Balance of Payments

These graphs suggest that emerging markets face different interest rateschedules and face different access to capital markets then advancedcountries.Emerging markets must pay a different risk premium than advancedeconomies. This suggests that the interest rate schedule is not constantfor these countries and depends, at least in part, on the path of tradebalances.Second, emerging markets are more likely to face a ‘sudden stop’ in whichit’s financial account shrinks rapidly. This implies that the current accountbalance must similarly shrink. So how can one model a sudden stop in theLRBC?


Balance of Payments

So now that we have examined the LRBC we must ask the question: why?What role does the LRBC play for a country?The LRBC is a constraint on consumption.Thus, to investigate the effects of the LRBC for an economy, we need todescribe the consumption path for an economy.


Balance of Payments

In general, we shall assume that countries exhibit consumption-smoothingpreferences.Before we begin on this track, I also note that it is not entirely clear thatthe LRBC is unaffected by consumption patterns.There is what we might call an endogeneity problem.


Balance of Payments


Balance of Payments

So, if it is the case that countries choose the level of financial openessbecause of their preferences over consumption smoothing then it is alsodifficult to know how to model the LRBC as a constraint.Basically, in this case the shape of the constraint depends on the desiredconsumption path and then we would need to model this.


Consumption Smoothing and the Current Account

The textbook example (on page 216) considers the case where borrowingis offset by consumption changes in all future periods. In a model whereagents have preferences for consumption smoothing and must repay this isoptimal.Suppose the current account in a particular year falls by ∆Q.



To see the role that the LRBC plays for consumption, let’s examine how achange in income matters for the current account. Recall,

−(1+r)Wt−1 = GDPt − GNEt+GDPt+1 − GNEt+1

(1 + r)+GDPt+2 − GNEt+2

(1 + r)2+...− W∞

(1 + r)∞

Now suppose that, for whatever reason, GDP falls by an amount ∆Q inperiod t but is expected to return to its original level in the subsequentand all future periods.Now, consider the case where agents prefer smooth consumption.



Clearly, the agent will prefer to borrow internationally to offset the fall indomestic income. Otherwise consumption would necessarily fall and thisisn’t optimal given his preferences. Ideally, the agent wants to reduceconsumption in all periods by an amount ∆C . Thus it must be that

∆C < ∆Q.

This is the implication of consumption smoothing.



So for consumption to not fall in period t, it must be that the countryborrows ∆Q −∆C . This allows the agent to only reduce consumption inperiod t by ∆C .This fall in external wealth must be offset by future surplusses so that theLRBC still holds. Because the agent wishes to smooth consumption, thefuture trade surplusses must reduce consumption in all future periods by∆C .



Using the LRBC, it must be that:

0 = −(∆Q −∆C ) +∆C

1 + r+

∆C

(1 + r)2+

∆C

(1 + r)3+ ...

Rearranging:

∆Q −∆C =∆C

1 + r(1 +

1

(1 + r)+

1

(1 + r)2+ ...)

Using our infinite series representation:

∆Q −∆C =∆C

1 + r(

1

1− 1/((1 + r)) = − ∆C

1 + r(

1 + r

r) = −∆C

r



So we can now solve for an expression in terms of consumption.

r(∆Q −∆C ) = ∆C

We can solve this to yield:

∆C =r

1 + r∆Q

This is the fall in consumption in response to a fall of ∆Q in GDPassuming consumption smoothing preferences and that the LRBC issatisfied.


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