most of us look for help beyond our own household We can...

1. INTRODUCTION

1 Introduction

• Now that we have covered the accounting of international transactions in the last chapter, we are prepared toanalyze their meanings in two different context: the long run (this chapter) and the short run (the next chapter)— in this chapter we will study the gains from financial globalization from the "long-run" perspective.

• How does your household cope with economic shocks and the financial challenges they pose?

— Suppose (1) you are self-employed and own a business and (2) a sever storm appears and a flood over-whelms your town.

∗ You suffer from this disaster, so that your income is lower for several months. If your business premisesare damaged, you must also plan to make new investments to repair the damage.

∗ If you have no financial dealings with anyone, your household as a little closed economy face adiffi cult trade-off as your household income falls. Since your income has to equal its consumption plusinvestment, you choose either one:

1. Would you invest to repair the damage and let your household suffer as you cut back drasticallyon consumption?

2. Would you neglect the need to investment, and try to maintain your level of consumption?

∗ However, faced with an emergency like this, most of us look for help beyond our own household:

· We might hope for transfers (e.g., gifts from the government) or we rely on financial markets (e.g.,dip into savings and apply for a loan).

• We can extend the boundary of this story from the household unit to the national level, and applythe same logic.

— Countries face shocks all the time, and how they are able to cope with shocks depends on whether theyare open or closed to economic interactions with other nations.

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1. INTRODUCTION

• When countries faces economic shocks all the time (e.g., 2011 tsunami in japan that could be considered as anegative shock to output), how they are able to cope with shocks depends on whether they are openor closed to economic interactions with other nations.

— For example, consider countries in the Caribbeanand Central America that are hit by hurricanes sooften.

∗ In the years immediately following a hurricane,the increase in investment associated with re-building can be financed through the currentaccount deficit (i.e., international borrowing),even though national saving declines:

· S = I +CA in an open economy (versusS = I in a closed economy).

∗ This figure shows the average responses (ex-cluding transfers) of investment I, saving S,and the current account CA in a sample ofCaribbean and Central American countries inthe years during and after severe hurricanedamage. The responses are as expected:

1. Investment (I) rises (to rebuild).

2. Saving (S = Y −C −G) falls (to limit thefall in consumption).

3. Thus, the current account (CA = S − I)moves sharply toward deficit.

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1. INTRODUCTION

• In this chapter, we see how financially open economies can, in theory, reap gains from "financialglobalization".

1. We first look at the factors that limit international borrowing and lending in the long run.

— We derive the long-run budget constraint that tells us about the limits on how much a country canborrow in the long run.

2. We then see how a nation’s ability to use international financial markets allows it to accomplish threedifferent goals:

(a) Consumption smoothing

— A nation steadies its consumption level when income fluctuates (in response to shocks) by borrow-ing/lending internationally.

(b) Effi cient investment

— International borrowing allows an open economy to build a productive capital stock without sacri-ficing consumption smoothing.

(c) Diversification of (income) risk

— Trading capital assets between countries allows an open economy to smooth fluctuations in itsincome level without any borrowing/lending.

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2. THE LIMITS ON HOW MUCH A COUNTRY CAN BORROW: THE LONG-RUN BUDGET CONSTRAINT

2 The Limits on How Much a Country Can Borrow: The Long-Run Budget Constraint

• Our introductory example shows how international borrowing can help countries better cope with economicshocks. But, like households, there is a limit to how much a country can borrow (or lend).

— Thus, understanding the constraints on how countries might borrow and lend to one another isour first task in this chapter.

∗ With this understanding, we can then examine how financial globalization shapes the economic choicesavailable to a country as economic conditions change over time.

• Because we study an economy as it evolves over time, we are taking a dynamic approach to macroeconomicsrather than a static approach

— The dynamic approach is also known as the intertemporal approach.

— One key element in this approach is to keep track of whether a country is managing its wealth sustainably.

∗ We use changes in an open economy’s external wealth (W ) to derive the key constraint that limits itsborrowing in the long run: the long-run budget constraint (LRBC).

1. The LRBC tells us precisely how and why a country must, in the long run, “live within its means.”

2. A country’s ability to adjust its external wealth through borrowing and lending provides a bufferagainst economic shocks, but the LRBC places limits on the use of this buffer.

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• To develop some intuition on the LRBC, let’s look at a simple household analogy.

— This year (denoted by year 0) you borrow $100, 000 from the bank at an interest rate of 10% annually,assuming that you have no other wealth and inflation is zero. Once you borrow the $100, 000, assumethat there are two different ways in which you can deal with your debt each year:

Case 1 A debt that is serviced.

∗ Every year you pay the 10% interest due on the principal amount of the loan, $10, 000, but never paydown any principal. At the end of each year, the bank as a lender renews the loan (a rollover), so yourwealth remains constant at −$100, 000.

Case 2 A debt that is not serviced.

∗ You pay neither the interest nor the principal, but ask the bank to roll over the principal plus theinterest due on it each year. In this case, the amount owed will grow over time (i.e., by 10% eachyear).

— Case 2 is not sustainable: If the bank allows it, your debt level will explode to infinity.

∗ Sometimes it is called a rollover scheme, a pyramid scheme, or a Ponzi game.

∗ This case illustrates the limits or constraints on the use of borrowing:

· In the long run, lenders will simply not allow the debt to grow beyond a certain point: thatis, debts must be paid off eventually — this requirement is the essence of the LRBC.

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2.1 How The Long-Run Budget Constraint Is Determined

• As is usual when building an economic model, we start with a basic model that makes a number of simplifyingassumptions. Here are the assumptions we make:

1. Prices are perfectly flexible (in the long run).

— Under this assumption, the model can be defined in real terms, ignoring all monetary aspects of themodel (To adjust for inflation and convert to real terms, we could divide all nominal quantities by anindex of prices).

2. The country is a small open economy. The country trades goods and services with the rest of the worldthrough exports and imports and can lend or borrow overseas, but only by issuing or buying debt (bonds).

— Because the country is small, it cannot influence prices in world markets for goods and services orinterest rates.

— All debts carry a real interest rate r∗, the world real interest rate, which we assume to be constant.The country can lend or borrow an unlimited amount at this interest rate.

∗ The country pays r∗ on its start-of-period debt liabilities L and is paid r∗ on its start-of-period debtassets A. Thus, the net interest income received is equal to (r∗A− r∗L) = r∗ (A− L) = r∗W ,where W = (A − L) is external wealth at the start of the period (and external wealth may varyover time). If r∗W > 0 (r∗W < 0), the country is earning (paying) interest and is a lender/creditor(borrower/debtor) with positive (negative) external wealth.

3. There are no unilateral transfers (NUT = 0), no capital transfers (KA = 0), and no capital gains onexternal wealth W .

— CA = TB +NFIA+NUT = TB + r∗W (by assumption NUT = 0 and NFIA = r∗W ).

— ∆W = −FA+Capital gains on W = CA + KA = CA (by assumption capital gains on W = 0 andKA = 0). Thus, ∆W = TB +NFIA = TB + r∗W

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• Mathematically, we now calculate the change in external wealth and its level each period.

— Based on the assumptions we made, we can write the change in external wealth from the end of yearN − 1 (or the beginning of year N) to the end of year N as follows:

∆WN = WN −WN−1︸︷︷︸Change in external wealth

this period

= TBN︸︷︷︸Trade balancethis period

+ r∗WN−1︸︷︷︸Interest paid/received

on last period’s external wealth

Then, we rearrange the preceding equation to find the level of external wealth at the end of year N :

WN︸︷︷︸External wealth

at the end of this period

= TBN︸︷︷︸Trade balancethis period

+ (1 + r∗)WN−1︸︷︷︸Last period’s external wealth

plus interest paid/received on that wealth

∗ We can compute the level of wealth at any time in the future by repeated application of the formula.

· This equation shows that wealth at the end of a period is the sum of the two terms: the tradebalance this period captures an addition to wealth due to net exports (exports minus imports), andwealth at the end of last period times (1 + r∗) captures the wealth from last period plus the interestearned on that wealth.

∗ In the examples in the following sections, we will use this kind of expression to understandthe dynamics of a country’s external wealth and the role of the trade balance.

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2.2 The Budget Constraint in a Two-Period Example and The Long-Run Budget Constraint

• We start with a simplified two-period model that starts in year 0 and ends in year 1. In the model, we assume:

1. A country has some initial external wealth (an inheritance from the past), W−1.

2. The country can borrow or lend in the current period, year 0.

3. All debts owed or owing must be paid off by the end of year 1: that is, the country must end year 1 withzero external wealth, W1 = 0.

• We now apply the formula for the level of external wealth derived previously.

— At the end of year 0,

W0 = (1 + r∗)W−1 + TB0

where W−1 is the level of external wealth at the beginning of year 0. At the end of year 1,

W1 = (1 + r∗)W0 + TB1

Furthermore, substituting for W0 gives:

W1 = (1 + r∗)2W−1 + (1 + r∗)TB0 + TB1

∗ In addition to its initial level of external wealth W−1, two years later at the end of year 1 the countryhas accumulated wealth equal to the trade balance in years 0 and 1 (TB0 and TB1) plus the one yearof interest earned (or paid) on the year 0 trade balance (r∗TB0) plus the two years of interest earned(or paid) on its initial wealth (

(2r∗ + r∗2

)W−1).

By imposing that the country must end year 1 with zero external wealth, i.e., W1 = 0, we have:

0 = (1 + r∗)2W−1 + (1 + r∗)TB0 + TB1

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This is rewritten as:

− (1 + r∗)2W−1 = (1 + r∗)TB0 + TB1

∗ This is the two-period budget constraint. It tells us that:

· A creditor country with positive initial wealth (left-hand-side negative) can afford to run trade deficits"on average" in future.

· A debtor country with negative initial wealth (right-hand-side positive) is required to run tradesurpluses "on average" in future.

— By dividing the previous equation by (1 + r∗), we find a much more intuitive expression for the two-periodbudget constraint:

− (1 + r∗)W−1︸︷︷︸Minus the present value ofwealth from last period

= TB0 +TB1

(1 + r∗)︸︷︷︸Present value of

all current and future trade balances

where every element represents a quantity expressed by its present value term.

∗ By definition, 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 thepresent value of X in period N is X

(1+r∗)N.

· For example, suppose you will receive $121 at the end of year 2 and the interest rate is 10%. Then,the present value of that $121 now, in year 0, equals 121/ (1.1)2 = $100 because $100× 1.1(addinginterest earned in year 1)×1.1(adding interest earned in year 2)= $121.

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— For a two-period example, let’s suppose that W−1 = −$100 million and r∗ = 10%. Then, to pay off $110million in year 0 (i.e., initial debt plus the interest accruing on this debt during period 0), the countrymust ensure that the present value of current and future trade balances is +$110 million. The countryhas many ways to do this:

1. It could run a trade surplus of $110 million in period 0 and balance trade in period 1, or

2. It could wait to pay off the debt until the end of period 1, and run a trade surplus of $121 million inperiod 1 after having balanced trade in year 0 (note $121/ (1 + 0.1) = $110) or

3. It could have any other combination of trade balances in periods 0 and 1 that allows it to pay off thedebt and accumulated interested so that external wealth at the end of period 1 is zero and the budgetconstraint is satisfied.

It is important to note that what matters in the budget constraint is the sum of the trade balancesduring the next two periods "in a present value sense", not trade balances period by period.

∗ For example, if a country is initially a debtor (W−1 < 0), it can run a trade deficit this period, but willneed to run a relatively large trade surplus in the subsequent period.

• Now, by extending the two-period model to N periods and allowing N to run to infinity, we can extend andtransform the two-period budget constraint into the long-run budget constraint (LRBC):

− (1 + r∗)W−1︸︷︷︸Minus the present value ofwealth from last period

= TB0 +TB1

(1 + r∗)+

TB2

(1 + r∗)2+

TB3

(1 + r∗)3+ · · ·︸︷︷︸

Present value ofall current and future trade balances

— The LRBC plays an important role in our analysis of how countries can lend or borrow because it imposesa condition that rules out choices that would lead to exploding positive or negative external wealth —a debtor (creditor) country with a negative (positive) initial wealth must have current/futuretrade balances that are offsetting and positive (negative) in present value terms.

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• Before proceeding, we consider the perpetual loan in which

1. the borrower make a fixed interest payment of X each period beginning in period 1 and lasting forever,

2. but the principal is rolled over forever.

Note that this is equivalent to Case 1: A debt that is served we considered previously.

— The concept of the perpetual loan helps us understand the LRBC and apply it to a case that we revisitin the rest of the chapter to explore how countries that take out an initial loan must make payments toservice that loan in the future.

— The present value of a stream of constant interest payments X denoted by PV (X) is computedas follows:

PV (X) =X

(1 + r∗)+

X

(1 + r∗)2+

X

(1 + r∗)3+ · · ·︸︷︷︸ = X

r∗

∗ This formula helps us compute PV (X) for any stream of constant payments X starting from period1, something we often need to do to verify the LRBC.

∗ For example, suppose that you owe a perpetual loan of $2, 000 at the interest rate of 5% in year 0.

Then, you make interest payments of X = $100 every year starting in year 1 and lasting forever, andthus the present value of these future interest payments is:

PV (X = 100) =100

(1 + 0.05)+

100

(1 + 0.05)2+ · · · = 100

0.05= 2, 000

· It is important to note that the present value of the future constant interest payments ($2, 000)equals the value of the amount loaned in year 0 ($2, 000, the principal that is never paid off), andthus the LRBC is satisfied.

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2.3 Implications of the LRBC for GNE and GDP

• The LRBC tells us that in the long run, a country’s national expenditure (GNE) is limited by how much itproduces (GDP ).

— To see this, we insert TB = GDP −GNE into the LRBC equation and collect terms:

(1 + r∗)W−1︸︷︷︸Present value of

wealth from last period

+GDP0 +GDP1

(1 + r∗)+

GDP2

(1 + r∗)2+ · · ·︸︷︷︸

Present value ofcurrent and future GDP︸︷︷︸

Present value ofthe country’s resources

= GNE0 +GNE1

(1 + r∗)+

GNE2

(1 + r∗)2+ · · ·︸︷︷︸

Present value ofcurrent and future GNE

=Present value of

the country’s spending

∗ The long-run budget constraint says that in the long run, in present value terms, a country’sexpenditure (GNE = C+ I+G) must equal its production (GDP ) plus any initial wealth. TheLRBC therefore shows quite precisely how an economy must "live within its means" in the long run.

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2.4 Summary on the LRBC

• The key lesson of our intertemporal model is that a closed economy is subject to a tighter budget constraintthan an open economy.

1. In a closed economy, "living within means" requires a country to have balanced trade year by year, sothat its expenditure must equal its production in each year.

2. In an open economy, "living within means" requires that a country must maintain a balance between itstrade deficits and surpluses that satisfies the LRBC - they must balance only in a present value sense,rather than year by year.

• This conclusion implies that an open economy ought to be able to do better (or no worse) than aclosed economy in achieving its desired pattern of expenditure over time.

— This is the essence of theoretical argument that there are gains from financial globalization.

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2.5 Applications: Favorable Situation of the U.S. and Diffi cult Situation of the Emerging Markets

2.5.1 The Favorable Situation of the United States

• Two assumptions we made greatly simplified our intertemporal model:

1. The same real interest rate r∗ applied to income received on assets A and income paid on liabilities L.

2. there were no capital gains on external wealth W .

• However, these two assumptions are not satisfied for the United States.

1. Exorbitant privilege

— The U.S. has since the 1980s been a net debtor with W = A−L < 0. Negative external wealth wouldlead to a deficit on net factor income from abroad with r∗W = r∗(A− L) < 0.

Yet as we saw in the last chapter, U.S. net factor income from abroad has been positive throughoutthis period. How can this be?

∗ The only way a net debtor can earn positive net interest income is by receiving a higher rate ofinterest on its assets A than it pays on its liabilities L, which has been consistently true for the U.S.since the 1960s.

∗ In the 1960s French offi cials complained about the United States’“exorbitant privilege”of beingable to borrow cheaply by issuing external liabilities while earning higher returns on U.S.external assets such as foreign equity and foreign direct investment.

— To develop a framework to make sense of this finding, we define net foreign income from abroad as:

NFIA =(r∗A− r0L

)= r∗ (A− L) +

(r∗ − r0

)L = r∗W +

(r∗ − r0

)L

where r∗ > r0 with(r∗ − r0

)= 1.5% and

(r∗ − r0

)L might represent an income bonus the U.S. earns

as a "banker to the world."

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2. Manna from heaven

— The U.S. also has long enjoyed positive capital gains, KG, on its external wealth.

∗ This gain comes from a difference of two percentage points between the large capital gains onseveral types of external assets and the smaller capital losses on external liabilities, which started inthe 1980s.

∗ However, it is hard to pin down the source of these capital gains, not just the result ofprice or exchange rate effects. They are gains that cannot be otherwise measured. As a result,some skeptics call these capital gains “statistical manna from heaven.”

— As with the “exorbitant privilege,” this financial gain for the U.S. is a loss for the rest of the world.As a result, some economists describe the U.S. as more like a “venture capitalist to the world” thana “banker to the world,” given the large contribution of differential profits and capital gains (ratherthan pure interest) on equity to this persistent beneficial wealth effect.

3. Incorporating the extra "bonuses" on external wealth, exorbitant privilege and manna from heaven

— 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.

— To include the effects of the total return differential in our model, we have to incorporate the extra"bonuses" on external wealth, as well as the conventional terms that reflect the trade balance andinterest payments:

∆WN︸︷︷︸Change in

external wealththis period

= TBN︸︷︷︸Tradebalancethis period

+ r∗WN−1︸︷︷︸Interest paid/receivedon last period’sexternal wealth︸︷︷︸

Conventional effects

+(r∗ − r0

)L︸︷︷︸

Income due tointerest ratedifferential

+ KG︸︷︷︸Capital gainson externalwealth︸︷︷︸

Additional effects

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• This figure shows how favorable interest rates andcapital gains on external wealth help the unitedstates.

1. The total average annual change in U.S. ex-ternal wealth each period is shown by the darkred columns.

2. Negative changes were offset in part by twopositive effects.

(a) One effect ((r∗ − r0

)L) was due to the

favorable interest rate differentials on U.S.assets (high) versus liabilities (low).

(b) The other effect (KG) was due to favor-able rates of capital gains on U.S. assets(high) versus liabilities (low).

3. Without these two offsetting effects, thedeclines in U.S. external wealth would havebeen much bigger.

— As the figure indicates, the U.S. has seen theseoffsets increase markedly in recent years, risingfrom 1% of GDP in the late 1980s to an aver-age of about 4% of GDP in the 2000s. Theselarge offsets have led some economists to takea relaxed view of the swollen U.S. trade deficitbecause they finance a large chunk of the coun-try’s trade deficit —with luck, in perpetuity.

— However, we may not be able to count onthese offsets forever: long-run evidence sug-gests that they are not stable and may be di-minishing over time.

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2.5.2 The Diffi cult Situation of the Emerging Markets

• In the previous application, we saw that applying the LRBC model to the U.S. required relaxing some assump-tions.

• If we consider emerging markets and developing countries, we similarly must relax the model’sassumptions to account for special situations in these countries. In this case, two assumptions arerelaxed:

1. The country faces the same real interest rate on A and L.

2. The country is able to borrow or lend freely as much as it wants at the prevailing world real interest rateas long as it satisfies the LRBC.

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1. For most poorer countries, they borrow highand lend low. Because of country risk, investorstypically expect a risk premium before they will buyany assets (e.g., government debt) issued by thesecountries.

• This figure plots government bond ratings(from Standard and Poor’s) against public debtlevels using historical data for a large sampleof advanced countries, emerging markets, anddeveloping countries.

(a) The top of the figure displays the sampleof advanced countries.

i. The government bonds issued by most ofthese countries were rated AA or better.These bonds carried very small risk pre-miums because investors were confidentthat these countries would repay theirdebts.

ii. The risk premiums did not increasemarkedly even as these countries wentfurther into debt.

(b) The bottom half of the figure shows thesample of emerging markets and developingcountries.

i. Only about half of the government bondsissued by these countries were consideredinvestment grade (BBB- and above), and

the rest were considered junk bonds.Investors demanded extra profit ascompensation for the perceived risksof investing in many of these coun-tries: large risk premiums.

ii. Ratings deteriorated rapidly as debt lev-els rose, an effect is not as strong inthe advanced countries. This observationshows the sharp limits to borrowingfor poorer countries: at some stage, thecost of borrowing becomes prohibitive, ifit is possible at all.

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2. On the borrowing side, there are limits to howmuch poorer countries can borrow – a debtlimit.

• These limits can be observed in the data assudden stops in the flow of external finance.

— In a sudden stop, a borrower country seesits financial account surplus rapidly shrink(suddenly nobody wants to buy any moreof its domestic assets) and so the currentaccount deficit also must shrink (becausethere is no way to finance a trade imbal-ance).

• This figure illustrates the remarkable frequencywith which emerging market countries experi-enced sudden stops.

— These capital market shutdowns occurmuch more frequently in emerging markets.

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3. GAINS FROM CONSUMPTION SMOOTHING

3 Gains from Consumption Smoothing

• In the next two sections, we bring together the long-run budget constraint and a simplified model of an economyto see how gains from financial globalization can be achieved in theory.

— In this section, we focus on the gains that result when an open economy uses external borrowing andlending to eliminate an important kind of risk, namely, undesirable fluctuations in aggregate consumption(i.e., smooth consumption).

3.1 The Basic Model

• We retain all of the assumptions we made when developing the LRBC. We also adopt some additional assump-tions that hold whether the economy is closed or open:

1. GDP (or output) is denoted Q. It is produced each period using labor as the only input. Productionof GDP may be subject to shocks: depending on the shock, the same amount of labor input may yielddifferent amounts of output.

2. We use the terms “country”and “household” interchangeably. Preferences of the country/householdare such that it will choose a level of consumption C that is constant over time, or smooth. Thislevel of smooth consumption must be consistent with the country/household’s LRBC.

3. Our analysis begins at time 0, and we assume initial wealth inherited from the past, W−1 = 0.

4. When the economy is open, we look at its interactions with the rest of the world (ROW). We assumethat the country is small, ROW is large, and the prevailing world real interest rate is constant at r∗, say,r∗ = 5% per year in the numerical examples that follow.

5. To keep the rest of the model simple - for now - we assume that consumption is the only source ofdemand, implying that both investment I and government spending G are zero (I = G = 0).

— Under this assumption, GNE = C, so that if the country is open, TB = GDP −GNE = Q− C .

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• Taken all together, these assumptions give us a special case of the LRBC that requires the present value ofcurrent and future trade balances to equal zero (by assumption, because initial wealth is zero, W−1 = 0):

0︸︷︷︸Initial wealth is zero

= Present value of TB = Present value of GDP − Present value of GNE

or equivalently (by assumption, TB = GDP −GNE = Q− C),

Present value of Q︸︷︷︸Present value of GDP

= Present value of C︸︷︷︸Present value of GNE

— This equation says that the LRBC will hold, and the present value of current and future TB willbe zero, if and only if the present value of current and future Q (output) equals the presentvalue of current and future C (consumption).

3.2 Consumption Smoothing: A Numerical Example and Generalization

• Using the basic model we derived previously, we can explore how countries smooth consumption by examiningtwo cases:

1. A closed economy

— In this case, TB = 0 in all periods, external borrowing and lending are not possible, and the LRBC isautomatically satisfied.

2. An open economy

— In this case, TB does not have to be zero, borrowing and lending are possible, and we must verifythat the LRBC is satisfied.

• In the next, we begin with a numerical example that illustrates the gains from consumption smoothing, andthen we will generalize the result later.

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3.2.1 Closed versus Open Economy: No Shocks to Output

• Benchmark numerical values:

— Output is 100 units in each year: QN = 100 for N = 0, 1, 2, · · · .

— The world real interest rate is 5% per year: r∗ = 0.05.

1. When the economy is closed,

• C = Q = 100 in each period: consumption is perfectly smooth.

• PV (C) = PV (Q) = (100 + 100/0.05) = 2, 100 (by applying the perpetual loan formula).

2. If this economy were open rather than closed, nothing would be different.

• C = Q = 100 in each period, which is the country’s preferred consumption path.

— The LRBC is satisfied because there is a zero trade balance TB = 0 at all times: PV (C) = PV (Q)

• There are no gains from financial globalization because this open country prefers to consume only whatit produces each year, and thus has no need to borrow or lend to achieve its preferred consumption path.

3. A closed or open economy with no shocks: output equals consumption, trade balance is zero, andconsumption is smooth.

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3.2.2 Closed versus Open Economy: Shocks

• Suppose there is a temporary unanticipated output shock of —21 units in year 0, that is, output Q falls to 79in year 0 and then returns to a level of 100 thereafter:

Q0 = 79; QN = 100 for N = 1, 2, · · ·

— The change in PV (Q) is simply the drop of 21 in year 0. Thus, PV (Q) falls by 1% from 2,100 to 2,079.

1. In the closed economy, its consumption path isno longer smooth:

• Q0 = C0 = 79 in year 0.

QN = CN = 100 in subsequent years.

— The country can’t achieve consumptionsmoothing.

• The LRBC is automatically satisfied, PV (Q) =PV (C) = (79 + 100/0.05) = 2, 079.

2. In the open economy, a smooth consumption pathis still attainable because the country can borrowfrom abroad in year 0, and then repay over time:

• Q0 = 79, C0 = 99, TB0 = −20 in year 0.

QN = 100, CN = 99, TBN = 1 in sub. years.

— The country is able to smooth consumptionthrough running a trade deficit in a periodwhen a negative shock reduces output (sothat the open economy do better).

• PV (Q) = (79 + 100/0.05) = 2, 079 andPV (C) = (99 + 99/0.05) = 2, 079. So theLRBC is satisfied, PV (C) = PV (Q).

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• We can calculate the path of all the important macroeconomic aggregates for the open economy as follows:

1. PV (Q) = (79 + 100/0.05) = 2, 079 for a new stream of output and PV (C) = C + C/0.05 for a streamof a new constant consumption path. Then, the LRBC should be satisfied, that is, PV (Q) = PV (C):

2, 079︸︷︷︸PV (Q)

= C + C/0.05︸︷︷︸PV (C)

⇒ C = 99 is the new constant level of consumption over time

— Shortcut: PV (Q) has fallen by 1% from 2, 100 to 2, 079. Thus, C must fall by 1% from 100 to 99 inall periods to still be smooth over time and satisfy the LRBC (i.e., PV (C) = 2, 079 = PV (Q)).

2. In year 0,

(a) Q0 = 79 and C0 = 99. Thus, TB0 = Q0 − C0 = −20 (trade deficit).

(b) NFIA0 = r∗W−1 = 0 (W−1 = 0 by the assumption), CA0 = (TB0 +NFIA0) = −20, and W0 =(1 + r∗)W−1 + TB0 = −20.

3. In subsequent years,

(a) QN = 100 and CN = 99. Thus, TBN = QN − CN = 1 (trade surplus).

(b) NFIAN = r∗×WN−1 = 0.05× (−20) = −1 (the country must make net factor income from abroadpayment of −1 in the form of interest paid).

CAN = (TBN +NFIAN) = 1− 1 = 0 (no further borrowing in subsequent years).

WN = (1 + r∗)WN−1 + TBN = WN−1 + (r∗WN−1 + TBN) = WN−1 + (NFIAN + TBN) = −20 (thecountry must borrow 20 in year 0, and then make, in perpetuity, 5% interest payments of 1 unit onthe 20 units borrowed; external wealth does not explode because interest payments are made in fulleach year and no further borrowing is required).

• The lesson is clear: When output fluctuates, a closed economy cannot smooth consumption, but anopen economy can by borrowing and lending internationally.

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3.2.3 Generalizing

• From the previous numerical example, we can draw some general conclusions regarding how consumptionchanges in response to changes in output in the open economy.

— In the open economy, the country is able to spread out the effects of the shock to output over time byborrowing or lending internationally, rather than suffering a one time large adjustment in consumption.

• Suppose, more generally, that:

1. Output Q and consumption C are initially stable at some value with Q = C and external wealth is zero.

2. Now Q unexpectedly falls in year 0 by an amount ∆Q, and returns to its prior value for all future periods

Then, since the loss of output in year 0 reduces the present value of output by the amount ∆Q, the countrymust lower the present value of consumption by the same amount to meet the LRBC.

— The country accomplish this by lowering C uniformly (every year) by a smaller amount, ∆C < ∆Q.

1. The country runs a trade deficit of ∆Q−∆C < 0 in year 0, since C falls less than Q in year 0. Thecountry must borrow from other nations an amount equal to this trade deficit, and external wealthfalls by the amount of that new debt.

2. In subsequent years, Q returns to its normal level but C stays at its reduced level, so trade surplusesof ∆C are run in all subsequent years.

3. Thus, a loan of ∆Q−∆C in year 0 requires interest payments of r∗× (∆Q−∆C) in later years, andthe subsequent trade surpluses of ∆C must cover these interest payments:

r∗ × (∆Q−∆C)︸︷︷︸Amount borrowed in year 0︸︷︷︸

Interest due in subsequent years

= ∆C︸︷︷︸Trade surplus in subsequent years

⇒ ∆C = r∗

1+r∗∆Q

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∗ 0 < r∗

1+r∗< 1, which implies an open economy only needs to lower its steady consumption level

by a fraction of the size of the temporary output loss (in the previous numerical example, ∆C =(0.05/1.05)× (21) = 1, consumption had to fall by 1 unit, while ∆Q0 = −21).

3.2.4 Smoothing Consumption when a Shock Is Permanent

• We just showed how an open economy uses international borrowing to smooth consumption in response to atemporary shock to output.

— However, when the shock is permanent, the outcome is different.

∗ With a permanent shock, output will be lower by ∆Q in all years, so the only way either a closedor open economy can satisfy the LRBC while keeping consumption smooth is to cut consumption by∆C = ∆Q in all years.

• Comparing the results for a temporary shock and a permanent shock, we see an important point:

— Consumers can smooth out temporary shocks —they have to adjust a bit, but the adjustment is far smallerthan the shock itself. But they must adjust immediately and fully to permanent shocks.

3.3 Summary: Save for a Rainy Day

• Financial openness allows countries to "save for a rainy day."

— An open economy can save output when it experiences positive shocks (by running a trade surplus andaccumulating external wealth) and borrow to pay for consumption spending when it experiences negativeshocks (by running a trade deficit and decumulating external wealth): running a trade surplus duringgood times and a trade deficit during bad times. By doing so, the desired smooth consumption path canbe achieved.

∗ In contrast, in a closed economy, consumption must equal output in every period, so output fluctuationsimmediately generate consumption fluctuations.

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