Economics Chapter 17 Homework Comments This chapter makes heavy use of present value

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17 Balance of Payments I: The Gains from Financial Globalization

Notes to Instructor

Chapter Summary

This chapter connects the balance of payments to long-run economic growth and

highlights the benefits of international finance for consumption smoothing, investment,

and risk sharing. The key lessons from this chapter are as follows:

■ An open economy is able to smooth consumption through borrowing or lending,

affecting its current account and external wealth position.

■ An open economy is able to invest in productive capital projects without reducing

Comments

This chapter makes heavy use of present value and intertemporal trade–offs. Students

may find this material unfamiliar. Instructors will find it useful to review the basic

concept of present value and to highlight the difference between thinking in a dynamic

model and thinking in a static one. Also, students may be intimidated by the math used in

this chapter because it is somewhat technical.

The section is broadly organized as follows:

1. The Limits on How Much a Country Can Borrow: The Long-Run Budget

Constraint

a. How the Long-Run Budget Constraint Is Determined

i. Calculating the Change in Wealth Each Period

ii. Calculating Future Wealth Levels

iii. The Budget Constraint in a Two-Period Example

iv. Present Value Form

v. A Two-Period Example

vi. Extending the Theory to the Long Run

b. A Long-Run Example: The Perpetual Loan

c. Implications of the LRBC for Gross National Expenditure and Gross

Domestic Product

d. Summary

e. Application: The Favorable Situation of the United States

i. “Exorbitant Privilege”

2. Gains from Consumption Smoothing

a. The Basic Model

b. Consumption Smoothing: A Numerical Example and Generalization

i. Closed Versus Open Economy: No Shocks

ii. Closed Versus Open Economy: Shocks

iii. Generalizing

iv. Smoothing Consumption When a Shock Is Permanent

c. Summary: Save for a Rainy Day

d. Side Bar: Wars and the Current Account

3. Gains from Efficient Investment

a. The Basic Model

b. Efficient Investment: A Numerical Example and Generalization

i. Generalizing

c. Summary: Make Hay While the Sun Shines

d. Application: Delinking Saving from Investment

e. Can Poor Countries Gain from Financial Globalization?

i. Production Function Approach

ii. A Benchmark Model: Countries Have Identical Productivity Levels

iii. The Lucas Paradox: Why Doesn’t Capital Flow from Rich to Poor

Countries?

iv. An Augmented Model: Countries Have Different Productivity Levels

f. Application: A Versus k

i. More Bad News?

4. Gains from Diversification of Risk

a. Diversification: A Numerical Example and Generalization

i. Home Portfolios

ii. World Portfolios

iii. Generalizing

iv. Limits to Diversification: Capital Versus Labor Income

b. Application: The Home Bias Puzzle

c. Summary: Don’t Put All Your Eggs in One Basket

5. Conclusion

6. Appendix: Common Versus Idiosyncratic Shocks

An alternative organization for class lecture is given in the following. This combines

1. The Limits on How Much a Country Can Borrow: The Long-Run Budget

Constraint

a. How the Long-Run Budget Constraint Is Determined

i. Calculating the Change in Wealth Each Period

ii. Calculating Future Wealth Levels

b. A Long-Run Example: The Perpetual Loan

c. Implications of the LRBC for Gross National Expenditure and Gross

Domestic Product

2. Gains from Consumption Smoothing

3. Gains from Efficient Investment

a. The Basic Model

b. A Numerical Example and Generalization

c. Summary: Make Hay While the Sun Shines

4. Linking the LRBC to Economic Growth and Investment

a. Can Poor Countries Gain from Financial Globalization?

i. Production Function Approach

ii. A Benchmark Model: When Countries Have Identical Productivity Levels

iii. An Augmented Model: When Countries Have Different Productivity

Levels

5. Linking the Model to Risk Diversification

6. Appendix: Common Versus Idiosyncratic Shocks

Lecture Notes

Now that we have covered the accounting of international transactions, we are prepared

to analyze their meanings in two different contexts: the long run (this chapter) and the

short run (the following chapter).

When a country seeks to increase investment, this involves a difficult trade–off.

Although investment is key to economic growth and prosperity, investing in capital

resources today requires giving up consumption. In the same way that an individual takes

out a loan to pay for her education or to buy a home, a country can borrow from abroad

(or lend to other countries).

S = I + CA

This chapter shows how open economies can benefit from financial globalization

through borrowing or saving with other countries to (1) smooth consumption and (2)

1 The Limits on How Much a Country Can Borrow: The Long–Run Budget

Constraint

We know from the previous chapter that borrowing or lending internationally has

implications for external wealth. This chapter extends the analysis of external wealth to

study how this variable evolves over time, using the intertemporal approach.

Understanding how countries lend and borrow is easy once household lending and

borrowing are understood. When a household borrows, the usual arrangement is a fully

amortized loan. Each month the household makes a payment, usually the same dollar

amount. Each payment has two parts: the principal repayment and the interest. Since the

loan amount is reduced with each payment, over the life of the loan, the fraction of each

payment that is principal rises, while the fraction that is interest falls. The final payment

is mostly principal with just a bit of interest. Consider two cases:

■ Case 1 A debt that is serviced. The household makes interest payments on the

debt, but never pays down the principal amount borrowed. At the end of each

■ Case 2 A debt that is not serviced. The household pays neither the interest owed

Case 2 is not sustainable because it assumes one can borrow a larger and larger amount

each year by rolling over the amount owed each period. This is also known as a pyramid

scheme, or a Ponzi game. In the real world, this is not possible. All debts must be paid

off eventually.

How the Long–Run Budget Constraint Is Determined

We begin with the assumptions used in the model:

■ Prices are perfectly flexible. This means the model can be defined in real terms,

ignoring the monetary aspects of the model. All quantities are expressed in

inflation–adjusted terms.

Calculating the Change in Wealth Each Period Consider the change in external wealth

in a given period, N:

Calculating Future Wealth Levels Adding WN−1 to both sides yields the following

expression for external wealth in period N:

WN = TBN + (1 + r*)WN−1

The Budget Constraint in a Two–Period Example Suppose there are two periods in the

economy. The current period denoted is 0 (= N) and the previous period is denoted −1 (=

N − 1):

Substituting in the expression for current external wealth, W0, we get

Note that the country’s external wealth in period 1 depends on the amount of external

wealth accumulated through net interest income earned and the trade balance each period

Present Value Form The previous expression can be rewritten by dividing both sides by

(1 + r*):

A Two–Period Example The previous expression shows that the present value of future

trade balances must be equal to the negative of the present value of wealth from the last

period, −(1 + r*)W−1. In other words:

then this country is a net debtor and therefore must run trade surpluses to pay off

its debts.

Extending the Theory to the Long Run It’s straightforward to extend the two-period

case to N periods. The LRBC becomes

If students feel comfortable with summation notation, it can be expressed as

A Long–Run Example: The Perpetual Loan

This example considers a perpetual loan in which a country pays a fixed amount, X, each

period, beginning in period 1 and lasting forever. This is a useful case to study because it

is equivalent to Case 1 from the beginning of the chapter (e.g., the principal is rolled

Subtracting the first expression from the second one, we see PV(X) = X/r*:

Implications of the LRBC for Gross National Expenditure and Gross Domestic

Product

Now that we are familiar with how external wealth changes over time and how this

relates to trade balances, we can use the LRBC to understand the link between GNE = C

The LRBC says that in the long run, in present value terms, a country’s expenditures

(GNE) must equal its production (GDP), plus any initial wealth.

This shows how a country is able to finance the differences between its production

and its spending by borrowing or lending over time.

Summary

In a closed economy, TB = 0, so production and expenditure must be equal. In an open

economy, a country can spend more than it produces by borrowing, or it can produce

APPLICATION

The Favorable Situation of the United States

Recall two key assumptions from the LRBC: the same, constant real interest rate, r*,

applies to assets and liabilities, and there are no capital gains from external wealth.

“Exorbitant Privilege” Since the 1980s, the United States has been a net debtor, r*W <

0, yet net factor income from abroad has been positive during this period. How does a net

debtor earn positive interest income?

“Manna from Heaven” In addition to the difference in interest rates on assets and

liabilities, the United States has consistently enjoyed capital gains on external wealth.

Summary The United States has earned about 3.5% per year more than the rest of the

world (earning 2% in capital gains plus 1.5% more in interest). This has been going on

since the 1980s. The total return differential was near zero for every other G7 country.

Too Good to Be True? The two additional effects in the previous expression show how

the United States is able to offset the negative effects of trade deficits on external wealth.

diminishing over time.

APPLICATION

The Difficult Situation of the Emerging Markets

In the previous application, we saw that applying the LRBC model to the United States

required relaxing some assumptions. If we consider emerging markets, we similarly must

relax the model’s assumptions to account for special situations in these countries. This

application considers two assumptions: (1) the interest rates paid on assets and liabilities,

and (2) that countries are able to borrow and lend freely as long as they satisfy the LRBC.

a country can borrow—a debt limit. These limits can be observed in the data as sudden

stops in the flow of external finance. When a debtor country hits a debt limit, its financial

account rapidly shrinks, forcing a decrease in its current account deficit and a sudden

change in expenditures (GNE) and production (GDP).

2 Gains from Consumption Smoothing

This section uses the LRBC together with a simple model of an economy to illustrate

The Basic Model

This section uses the same assumptions as outlined at the beginning of the LRBC section.

In addition:

■ GDP = Q produced using a single input: labor.

■ Consumption takes place in identical representative households, so “household” is

used interchangeably with “country.” The household prefers a smooth level of

consumption.

■ No other sources of demand, I = G = 0, so GNE = C and Q = C + TB.

■ Analysis begins in period 0, with given initial wealth equal to zero, W−1 = 0.

Consumption Smoothing: A Numerical Example and Generalization

We consider two cases to see how a country can smooth consumption:

■ Closed economy: TB = 0, Q = C in all periods, so LRBC is automatically

satisfied.

Closed Versus Open Economy: No Shocks

■ Closed economy: Q = 100 = C

PV(Q) = 100 + 100/0.05 = 2,100 = PV(C)

■ Open economy: TB = 0; Q = 100 = C

Closed Versus Open Economy: Shocks Suppose there is a temporary negative shock to

output, or −21 units. Output is equal to 100 units in every period afterward.

■ Closed economy: Q0 = 79 = C0

How to solve for the numerical values. We can use the LRBC equation:

Because the country begins with initial external wealth equal to zero, the present value of

PV(Q) = PV(C)

Steps to computing numerical values for Q, C, TB, NFIA, and W over time are as follows:

1. Identify the initial level of output (as a result of the shock). From the example, we