Download and the Exchange Rate

CHAPTER 20. 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 home and foreign bonds. Fixed
and floating 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 19 by dropping the assumption that the exchange rate
(under floating rates) is a policy variable. Thus, it allows for 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. This treatment differs from the canonical
model by assuming that the expected future exchange rate is fixed, rather than equal to the current rate.
ii.
A devaluation is an decrease in the level of a fixed exchange rate. A revaluation is an increase
in the level of a fixed exchange rate. Under fixed rates the exchange rate changes infrequently (but
usually traumatically). Under flexible rates the exchange rate changes continuously in response to supply
and demand.
iii. An appendix to the chapter discusses the central bank balance sheet, in the context of monetary
policy under fixed exchange rates.
2.
Assumptions
i.
The home and foreign price levels are assumed to be fixed. Accordingly, expected inflation is
assumed to be zero, so the real interest rate equals the nominal rate.
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. Home and foreign bonds are considered perfect substitutes and there is perfect capital mobility, so
uncovered interest parity holds.
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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
Given that NX=X(Y,)-IM(Y,)/, the goods market equilibrium condition can be written
Y=C(Y-T)+I(Y,r)+G+NX(Y,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,i)+G+NX(Y,Y*,E).
2.
(20.1)
Equilibrium in Financial Markets
Foreign currency is assumed to have no transactions value for domestic residents, so the choice between
domestic money and bonds can be summarized by the LM relation,
M=YL(i),
(20.2)
which was introduced in Chapter 4.
Under the assumptions of perfect asset substitutability (i.e., no risk premium) and perfect capital
mobility, the expected return on home 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.
(20.3)
The chapter assumes that the expected future exchange rate is fixed at E e . Under this assumption and
dropping time subscripts, uncovered interest parity can be rewritten as
E  Ee
(1  i )
(1  i*) (20.4)
The home currency tends to appreciate (E tends to increase) when the expected exchange rate increases,
when the home 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 home currency is not expected to gain or
lose value, the home interest rate equals the foreign interest rate. When the home currency is expected to
depreciate (so that E  E e \), the home interest rate is greater than the foreign interest rate. In this case,
financial investors will only purchase home bonds if they are compensated with an interest rate higher
than i*. When the home currency is expected to appreciate, the home interest rate is less than the foreign
interest rate. In this case, financial investors will only purchase foreign bonds if they are compensated
with a higher foreign interest rate.
3.
Putting Goods and Financial Markets Together
Substituting equation (20.3) into equation (20.1) gives the open economy IS relation:
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Y=C(Y-T)+I(Y,i)+G+NX(Y,Y* E e [1+i]/[1+i*]).
(20.5)
The LM relation is given by equation (20.2). 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, the position of the IS curve is affected by
foreign output and the foreign interest rate.
4.
The Effects of Policy in an Open Economy
The effects of an increase in government spending are depicted graphically in Figure 20.1. 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. Since the
expected future exchange rate is fixed, uncovered interest parity (equation (20.4)) 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.
Figure 20.1: Expansionary Fiscal Policy in an Open Economy with Floating Exchange Rates
A decrease in the money supply shifts the LM curve to the left. Output falls, the interest rate increases,
and the exchange rate appreciates. Investment definitely falls, but the effect on the trade balance is
ambiguous, because the fall in output tends to increase it, but the exchange rate appreciation tends to
reduce it.
5.
Fixed Exchange Rates
If policymakers fix the exchange rate (credibly) at E , then expected depreciation is zero, and i=i* by
uncovered interest parity. As a result, the IS and LM relations become
Y=C(Y-T)+I(Y,i*)+G+NX(Y,Y*, E )
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M=YL(i*).
Given fiscal policy, foreign output, and the foreign interest rate, output is fully determined by the fixed
exchange rate and the IS curve. As a result, 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 fixed exchange rate.
Although policymakers lose control over monetary policy under fixed exchange rates, 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
home currency is expected to depreciate. However, the home currency will appreciate 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.
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. It might be worthwhile 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 plus foreign exchange
reserves. The liabilities side is high powered money or the monetary base. The money supply is a
multiple of the monetary base, as described in Chapter 5. 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 reserves to buy its currency. As foreign exchange reserves fall, the money
supply falls. Ultimately, 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
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some freedom to pursue independent monetary policy, at least temporarily. It may still lose 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 home country, a
reluctance on the part of international investors to substitute between home 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
home country can affect foreign income and the foreign interest rate. For example, an increase in
government spending in the home economy tends to increase home output and cause a home
appreciation. This implies an increase in foreign net exports, foreign output, and the foreign interest rate,
effects that in turn affect the home 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 home economy is small, so that the changes in foreign variables are small,
or that the effects on the home economy arising from changes in foreign variables are small 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 expansion in the
leader implies a fall in the leader’s interest rate and an increase in the leader’s output. The increase in
output implies an increase in net exports for other members of the system and a shift of their IS curves to
the right. The other members must undertake monetary expansion to match their interest rates to the
leader, i.e., they must shift their LM curves to the right. The net result is an expansion in these
economies. On the other hand, 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 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 causes a recession 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-) E ,
(20.5)
where E is a constant, all of the qualitative results hold when 0<1. When =1, fiscal policy can
longer affect output under floating exchange rates. 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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