978-0133780581 Chapter 19 Lecture Note

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OUTPUT, THE INTEREST RATE, AND THE EXCHANGE RATE 88

Chapter 19. Output, the Interest Rate,

and the Exchange Rate

I. MOTIVATING QUESTION

How are output, the interest rate, and the exchange rate determined

simultaneously in the short run in an open economy?

Output, the interest rate, and the exchange rate are determined jointly by simultaneous equilibrium in the

goods market and the domestic and world financial markets. In the open economy, goods demand

includes net exports. The world financial market allows trade between domestic and foreign bonds.

Fixed and flexible exchange rate regimes have different implications for the relative effectiveness of

fiscal and monetary policy in stimulating output.

II. WHY THE ANSWER MATTERS

This chapter generalizes the model of Chapter 18 by dropping the assumption that the exchange rate

(under a flexible exchange rate regime) is a policy variable. Thus, the model allows for the joint

determination of output, the nominal interest rate, and the exchange rate, and illustrates the importance of

the exchange rate as a transmission mechanism in the open economy. These considerations are required

for a realistic treatment of modern market economies.

III. KEY TOOLS, CONCEPTS AND ASSUMPTIONS

1. Tools and Concepts

i. The chapter introduces a modern version of the Mundell-Fleming model, which is the IS-LM

model in an open economy under perfect capital mobility. The treatment in the text differs from the

canonical model by assuming that the expected future exchange rate is fixed, rather than equal to the

current exchange rate.

ii. A devaluation is a decrease in the level of a fixed exchange rate (akin to a depreciation). A

revaluation is an increase in the level of a fixed exchange rate (akin to an appreciation).

iii. An appendix to the chapter discusses the central bank balance sheet, in the context of monetary

policy under fixed exchange rates.

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2. Assumptions

i. The domestic and foreign price levels are assumed to be fixed. Accordingly, expected domestic

inflation and expected foreign inflation are assumed to be zero, which implies that the real interest rate

equals the nominal interest rate throughout the world.

ii. Production is assumed to respond to changes in demand without changes in price, so demand

determines output.

iii. Foreign currency is assumed to have no transactions value for domestic residents.

iv. Domestic and foreign bonds are considered perfect substitutes, and there is perfect capital mobility,

so uncovered interest parity holds.

v. The expected future exchange rate is assumed to be constant. As long as the expected future

exchange rate changes less than one-for-one with the current exchange rate, this assumption does not

affect the qualitative results of the chapter.

IV. SUMMARY OF THE MATERIAL

1. Equilibrium in the Goods Market

Equilibrium in the goods market equilibrium can be written as

Y=C(Y–T)+I(Y,r)+G –IM(Y*,)/ + X(Y*,).

(+) (+,-) (+,-) (+,-)

In the short run, assume that P and P* are fixed and (for convenience) equal to one, so that E=. Since

P is fixed, assume that expected inflation is zero, so that r=i. Under these assumptions, goods market

equilibrium can be rewritten as

Y=C(Y–T)+I(Y,r)+G+NX(Y,Y*,). (19.1)

(+) (+,-) (-,+,-)

2. Equilibrium in Financial Markets

Initially when we looked at financial markets in the IS-LM model we assumed there were only two

possible assets, money and bonds. However, in an open economy we can now also choose foreign bonds.

Under the assumptions of perfect asset substitutability (i.e., no risk premium) and perfect capital mobility,

the expected return on domestic and foreign bonds must be the same. This arbitrage condition is called

the uncovered interest parity condition, and can be written as

(1+it)=(1+i*t)Et/Eet+1. (19.3)

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The chapter assumes that the expected future exchange rate is fixed at e. Under this assumption and

dropping time subscripts, uncovered interest parity can be rewritten as

E= [(1+i)/(1+i*)] e. (19.5)

The domestic currency tends to appreciate (E tends to increase) when the expected exchange rate

increases, when the domestic interest rate increases, and when the foreign interest rate falls. Note that

when the exchange rate equals the expected exchange rate, i.e., when the domestic currency is not

expected to gain or lose value, the domestic interest rate equals the foreign interest rate. When the

domestic currency is expected to depreciate (so that E> e), the domestic interest rate is greater than the

foreign interest rate. In this case, the difference between the domestic and the foreign interest rate

compensates financial investors for the expected depreciation of the domestic currency. When the

domestic currency is expected to appreciate, the domestic interest rate is less than the foreign interest rate.

In this case, the difference between the foreign and the domestic rate compensates financial investors for

the expected depreciation of the foreign currency.

3. Putting Goods and Financial Markets Together

Substituting equation (19.5) into equation (19.1) gives the open economy IS relation:

Y=C(Y–T)+I(Y,i)+G+NX(Y,Y*, e[(1+i)/(1+i*)]).

Graphically, the IS curve slopes down in Y–i space. An increase in the interest rate reduces investment, as

in the closed economy, and in addition, causes the currency to appreciate, reducing net exports.

Moreover, in an open economy, the position of the IS curve is affected by foreign output and the foreign

interest rate.

Since the interest rate is the policy rate set by the central bank the LM relation is given by the equation,

i =

Together the IS and the LM equations determine the interest rate and equilibrium output. Increasing the

interest rate now leads to lower domestic investment and a decrease in output. However, now in an open

economy it causes the currency to appreciate which makes domestic goods relatively more expensive and

also pushes output lower.

A box in the text points out that the uncovered interest parity condition derived in the text ignores risk and

liquidity. Changes in the perceived risk of holding a country’s assets shift the uncovered interest parity

relation and affect the exchange rate, the domestic interest rate, and domestic output. The appreciation of

the dollar in the 1990s, for example, was driven by the perceived safety of U.S. Treasury bonds, and their

high liquidity. Demand for U.S. assets continues to be strong, despite relatively low U.S. interest rates.

4. The Effects of Policy in an Open Economy

The effects of an increase in government spending are depicted graphically in Figure 19-4 on page 400.

The left panel shows the IS–LM curves. The right panel plots the uncovered interest parity condition. An

increase in government spending shifts the IS curve to the right. Output and the interest rate increase.

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Since the expected future exchange rate is fixed, uncovered interest parity implies that the exchange rate

appreciates (E rises). The increase in output and the appreciation of the exchange rate both work to

reduce the trade balance. The effect on investment is ambiguous, because the output effect tends to

increase investment, but the interest rate effect tends to reduce it.

A decrease in the money supply shifts the LM curve upward. Output falls, the interest rate increases, and

the currencyincreases in value (i.e. appreciates). Investment definitely falls. The effect on the trade

balance is ambiguous: the fall in output tends to increase the trade balance while the exchange rate

appreciation tends to reduce the trade balance.

5. Fixed Exchange Rates

Some countries allow exchange rates to float freely (i.e. Canada, U.S., U.K.) while others fix their

currency to another currency (i.e. Argentina, several African countries). Countries that fix, or peg, their

currencies must often intervene in the foreign exchange market to maintain their peg. The dedication to

maintaining the peg varies. Some countries move slowly (i.e. crawling peg) while others move more

rapidly.

Given fiscal policy, foreign output, and the foreign interest rate, output is fully determined by the fixed

exchange rate and the IS curve. Pegging a currency abdicates monetary policy to the foreign currency. In

other words monetary policy is endogenous (i.e., policymakers lose control over the money supply).

Given Y, M must adjust to maintain i*, in order to maintain the fixed exchange rate. If i ever strays from

i*, uncovered interest parity implies that the exchange rate will be expected to appreciate or depreciate.

This is inconsistent with a credibly fixed exchange rate.

Although policymakers lose control over monetary policy under a fixed exchange rate regime, they retain

control over fiscal policy. In fact, the effect of fiscal policy on output is magnified, relative to the case of

flexible exchange rates. An increase in G would ordinarily lead to an increase in i. Under a fixed

exchange rate, this is impossible. To maintain the fixed exchange rate, which requires i=i*, the money

supply must increase. As a result, an increase in G leads to an increase in the money supply as well. So,

the effect of fiscal policy on output is augmented by endogenous changes in the money supply.

V. PEDAGOGY

Confusion over the implications of the uncovered interest parity condition is likely to become an

important issue in this chapter. Suppose the expected exchange rate is fixed. If i rises above i*, the

domestic currency is expected to depreciate in the future, but the domestic currency appreciates now.

Why? An analogy to the physical world is instructive. A roller coaster must rise before it can fall. Thus,

if the exchange rate is expected to fall (depreciate) in the future, it must rise now above its expected future

value.

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VI. EXTENSIONS

1. Fixed Exchange Rates and the Central Bank Balance Sheet

An appendix to the chapter discusses the central bank balance sheet and the management of fixed

exchange rate regimes. Instructors may wish to discuss this point in the main lecture to build intuition for

the endogeneity of the money supply under a fixed exchange rate.

The asset side of the central bank balance sheet consists of domestic bonds and foreign exchange

reserves. The liabilities side consists of high powered money (or the monetary base). The money supply

is a multiple of high powered money, as described in Chapter 4. Consider a monetary expansion in the

form of a purchase of domestic bonds. This transaction creates high powered money, since the central

bank writes a check on itself. The monetary expansion tends to reduce the domestic interest rate. A fall in

the domestic interest rate implies an expected appreciation to maintain uncovered interest parity. If the

expected future exchange rate is fixed, an expected appreciation implies a depreciation of the current

exchange rate, which is incompatible with a fixed exchange rate regime.

To defend the exchange rate, the central bank must sell foreign exchange reserves to buy domestic

currency. As foreign exchange reserves fall, the money supply falls. Ultimately, foreign exchange

reserves fall by enough to offset completely the original monetary expansion. The fixed exchange rate and

the IS curve determine output, which (together with the foreign interest rate) determines money demand.

Since money demand is unaffected by the central bank purchase of bonds, the money supply cannot be

affected either. In the end, the monetary expansion changes only the composition of central bank assets

(more bonds, fewer reserves) and not the size of the money stock.

The amount of time required for the endogenous adjustment of the money supply depends on the degree

of capital mobility. The model presented in the text assumes perfect capital mobility, which implies that

the adjustment of the money supply happens instantaneously. If capital mobility is limited, the adjustment

of the money supply will take more time. In these circumstances, the central bank will have some

freedom to pursue independent monetary policy, at least temporarily. The central bank may still lose

foreign exchange reserves if it attempts an expansion, but it may be able to increase output for some

period of time. Reasons for less than perfect capital mobility include a lack of developed financial

markets in the domestic country, a reluctance on the part of international investors to substitute between

domestic and foreign bonds, and capital controls—government-imposed limits on trade in assets with the

rest of the world.

2. Interdependencies

The chapter takes foreign income and the foreign interest rate as fixed. In fact, changes in policy in the

domestic country can affect foreign income and the foreign interest rate. For example, an increase in

government spending in the domestic economy tends to increase domestic output and cause a domestic

appreciation. This implies an increase in foreign net exports, foreign output, and the foreign interest rate,

effects that in turn affect the domestic economy. A full open-economy model would consider the effects

of policy in the context of world equilibrium. A justification for ignoring effects on foreign output and

the foreign interest rate is that the domestic economy is small, so that the effect on foreign variables are

small, or that the effects on the domestic economy arising from changes in foreign variables are small

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compared to the direct effects. In any event, a full world equilibrium model with flexible exchange rates

is beyond the scope of this text.

Matters are less complicated for fixed exchange rates, as suggested by a box in the text. Assuming that

the strongest partner—call it the leader—in a fixed exchange rate system is free to set interest rates as it

chooses, then the other members of the system must adjust. In this case, a monetary contraction in the

leader implies an increase in the leader’s interest rate and a reduction in the leader’s output. The fall in

output implies a fall in net exports for other members of the system and a shift of their IS curves to the

left. The other members must undertake monetary contractions to match their interest rates to the leader,

i.e., they must shift their LM curves to the left. The net result is a fall in output in these economies. A

fiscal expansion in the leader increases the interest rate and output in the leader’s economy. The increase

in output tends to shift the IS curve to the right in the other economies (through the effect on net exports),

but the increase in the interest rate requires a monetary contraction in the other economies. Assuming that

the interest effect dominates, the fiscal expansion in the leader’s economy also causes a fall in output in

the other economies. For an example of these forces at work, see the box in the text on the effects of

German reunification—which led to an increase in German demand and a monetary contraction in

response—on other members of the European Monetary System.

VII. OBSERVATIONS

The chapter assumes that the expected future exchange rate is fixed. All of the qualitative results for this

chapter hold as long as the expected exchange rate responds less than one-for-one to movements in the

exchange rate. For example, if the expected exchange rate is given by

Ee=E+(1-) ,

where is a constant, all of the qualitative results hold when 0<1. When =1, fiscal policy can no

longer affect output under flexible exchange rates. In this case, an increase in government spending leads

to an appreciation that fully crowds out net exports. The case where =1 is the canonical

Mundell-Fleming model.

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