Tiroplastia

Interesting insights into the behaviour of exchange rates are obtained by writ-ing out full employment equilibria such as A in terms of algebraic equations.

Let us be more general than we were in Figure 5.17. There we assumed that financial investors do not expect the exchange rate to change, so that was the foreign exchange market equilibrium condition. In general, if for whatever reason the exchange rate is expected to depreciate, open inter-est parity in the general form given in equation (5.1) above holds. Introducing some shorthand, this foreign exchange market equilibrium condition can be written as

Open interest parity or FE curve (5.4) where is the expected rate of depreciation from today until next period. As long as expected depreciation remains the same, the economy’s full employment equilibrium is at point C (Figure 5.18).

Point C, or other equilibria on the vertical line over Y* that would result if the world interest rate or expected depreciation changed, may be thought to obtain either in the long run, after prices have had enough time to adjust, or even in the short run, if prices are very quick to adjust.

At equilibrium point C the interest rate and income remain unchanged. In order to keep the IS curve in the position that passes through C, the real

e^e+1 K (E^e+1 - E)>E i = i^World + e+^e1

i = i^World

Income

Interest rate

Y*

Potential income i ^World

Money-supply increase shifts LM to the right

Induced depreciation shifts IS to the right IS0

IS₁

FE

LM₀

LM₁

Price increase lowers real money supply and real exchange rate, shifting both LM and IS to the left Old and new

equilibrium

2 3

3 1

A

B

Figure 5.17 Under flexible exchange rates, a money-supply increase leads from A to B.

Since B is above potential income Y*, prices rise. This reduces the real money supply, shifting LM back to the left. The real exchange rate is also reduced, moving IS back to the left and the economy back to A.

Income, real money circulation and the real exchange rate are the same as before.

5.7 Today’s exchange rate and the future 143

exchange rate must remain unchanged. Suppose the real exchange rate required to make IS pass through C is 1, so that or, taking logarithms (denoted by lower-case letters)

Long-run IS curve (5.5) At C the money market is also in equilibrium. Suppose the money demand function is semi-logarithmic (that means, the logarithm of real money demand depends on Y and i):

Semi-logarithmic LM curve (5.6) Now let and (we can do this, since these exoge-nous variables may be at any arbitrary value anyway). Then substitute equa-tion (5.5) into (5.6) for p and (5.4) into (5.6) for i to obtain . Solving this equation for e gives

(5.7) The present exchange rate responds one-to-one to changes in the money sup-ply, but it also reflects depreciation expected to occur tomorrow. This can be brought out in a slightly different form if we note that , which means that the expected rate of depreciation equals the difference between the logarithm of tomorrow’s expected exchange rate and the logarithm of the current exchange rate. Substituting this into equation (5.7) and solving for e gives

(5.8) where The equation makes the important statement that today’s exchange rate is a weighted average of today’s money supply and the exchange rate expected to prevail tomorrow. So whatever the market expects to happen to the exchange rate in the future (an appreciation or a deprecia-tion) in an almost self-fulfilling fashion already happens today.

a = 1>(1 + h).

e = am + (1 - a)e^e+1

e^e+1 = e^e+1 - e e = m + he^e+1

m - e = -he^e+1

i^World = 0 Y* = 0, p^World = 0

m - p = kY* - hi e + p^World = p

EP^World = P, EP^World>P

Income

Interest rate

Y*

Potential income i ^World+ eε₊₁

i ^World IS₀

IS₁

FEgeneral case

LM₀

LM₁

Old and new equilibrium

1 3

3 2 C

A

D

Figure 5.18 (Flexible exchange rates.) Expected depreciation drives a wedge between the domestic and the world interest rate. FE is in the blue position and the new long-run equilibrium is in C. Just as described in Figure 5.17 for the case of zero depreciation expectations, attempts to stimulate income by increasing the money supply are sooner or later nullified by price increases of equal magnitude.

Using this equation, the 2009 exchange rate depends on the concurrent money supply and on the exchange rate expected for 2010:

(5.9) Does this mean that the investors’ time horizon ends in 2010? No, for if we know that one year’s exchange rate always depends on next year’s exchange rate and the current money supply, we should anticipate that equation (5.8) also links the 2010 exchange rate to the exchange rate expected for 2011:

(5.10) Taken together, equations (5.9) and (5.10) provide a link between 2011 and the exchange rate in 2009. Equation (5.10) leaves it open, though, how is being determined. This is not difficult to find out, however. Since equation (5.10) links any two periods in time, we can move it one year ahead to see that

depends on and two years ahead to see that depends on Actually, we can do this as often as we want. By doing it ten more times, we notice that the 2009 exchange rate depends on the exchange rate expected for the year 2023. And this once again depends on what we expect for 2024.

The important lesson to be learned from this exercise is that today’s exchange rate is linked to all expected future developments. If we come to expect the exchange rate to depreciate two years from now, this will make the exchange rate depreciate today.

This chapter’s second look at booms and recessions leaves much of Chapter 2’s and Chapter 3’s bottom lines intact. Small changes in autonomous spending may cause large changes in income, and thus may be a cause of as well as a potential remedy for business cycle fluctuations. A refined picture has emerged, however. First, large income responses may not only be triggered by direct changes in autonomous spending. Indirect stimulation of spending via an expansion of the money supply may serve the same purpose. While we had already seen this result in Chapter 3, monetary policy works via the exchange rate in the open economy rather than directly via the interest rate. Second, which policy measures work and which do not crucially depends on the exchange rate system. The government spending multiplier of Chapter 2 only then reappears in the Mundell–Fleming model if exchange rates are fixed.

Under flexible exchange rates government spending is completely crowded out by a fall in exports. Then monetary policy takes its place as an effective means of stimulating demand and income. Third, if the economy already operates at potential income, rising prices are likely to nullify efforts to stimu-late income, no matter which instrument is being used.

CHAPTER SUMMARY

■ The Mundell–Fleming model explains demand-side equilibria in the open economy as an interaction between the goods market, the money market and the foreign exchange market.

■ Fiscal policy (that is, a change in government spending or a tax change) affects income when exchange rates are fixed. Under flexible exchange rates there is complete crowding out.

e^e₂₀₁₃. e^e₂₀₁₂

e^e₂₀₁₂, e^e₂₀₁₁

e^e₂₀₁₁ e^e₂₀₁₀ = am^e₂₀₁₀ + (1 - a)e^e₂₀₁₁

e₂₀₀₉ = am₂₀₀₉ + (1 - a)e^e₂₀₁₀

Exercises 145

■ Monetary policy affects output when exchange rates are flexible. When exchange rates are fixed, monetary policy is ineffective. The central bank is forced to sterilize (neutralize) any attempted money-supply increase immediately through foreign exchange market intervention.

■ During the transition from one equilibrium to another, individuals may expect the exchange rate to change. Depreciation expectations affect the FE curve and, hence, the specifics of the adjustment process.

■ Because after a disturbance the foreign exchange market and the money market adjust faster than the goods market, the exchange rate may be forced to overreact, that is, it overshoots its long-run equilibrium level.

■ If the economy operates at potential output, there is full crowding out via price increases. In the case of a money-supply increase, the price increase drives the real money supply back to its original level. In the case of a gov-ernment expenditure increase, the price increase makes the real exchange rate appreciate just enough to drive down net exports by as much as government expenditures increased.

comparative static analysis 134 crowding out 126

dynamic analysis 134

exchange rate overshooting 139 fiscal policy 125

fixed exchange rates 127 flexible exchange rates 126 monetary policy 128

Mundell–Fleming model 124 stable equilibrium 134

Key terms and concepts

E X E R C I S E S

5.1 Suppose the government raises the income tax rate. What are the effects on income, the inter-est rate and the exchange rate

(a) with a flexible exchange rate?

(b) with a fixed exchange rate?

(Derive your results graphically, assuming perfect international capital mobility.)

5.2 The central bank reduces the money supply.

What are the consequences for income, the interest rate and the exchange rate (a) with a flexible exchange rate?

(b) with a fixed exchange rate?

(Derive your results graphically, assuming perfect international capital mobility.)

5.3 Analyze the consequences of an increase of the world interest rate. Assume fixed exchange rates and perfect international capital mobility. What might be the reason for the increasing foreign interest rate? What does the result tell you about problems of international policy coordination?

5.4 How does a devaluation of the domestic cur-rency in a system with fixed exchange rates and perfect capital mobility affect the domestic interest rate and output?

5.5 Your country is exposed to a positive demand shock (say, foreign demand for domestic goods increases) and you are in charge of monetary

and fiscal policy. Formally, your country main-tains a regime of flexible exchange rates with all trading partners, but for some reason you wish to keep the exchange rate where it was before the shock. What can you do? Use the graphical apparatus of the Mundell-Fleming model to explain your answer.

5.6 Suppose that investors suddenly lose confidence in the domestic currency and expect it to depre-ciate by 5% every period from now on. Trace the consequences in the Mundell–Fleming model. What does the result tell you about ’self-fulfilling prophecies’? Will the induced changes in income and the (flexible) exchange rate last?

(Hint: Work with the general equilibrium condition )

5.7 Consider Figure 5.19, which depicts returns to US and German government bonds since 1960.

What do these time series tell us about investors’

expectations concerning the Deutschmark/dollar exchange rate?

i = i^W +e^e+1.

5.8 Consider the macroeconomic situation shown in Figure 5.20 in which the FE curve is vertical.

(a) Discuss the conditions under which the FE curve might be vertical.

(b) Describe the mechanisms that bring about a macroeconomic equilibrium in which all three lines intersect under flexible exchange rates, and under fixed exchange rates.

(c) Analyze the effect of expansionary monetary and fiscal policy in a system of flexible exchange rates with perfect capital immobility.

5.9 Suppose investment is independent of the inter-est rate and the FE curve is vertical. Sketch the macroeconomic equilibrium under fixed and flexible exchange rates and describe the mecha-nisms that help achieve it.

United States

Germany

2 4 6 8 10 12

1960 1965 1970 1975 1980 1985 1990 1994

Interest rate

Figure 5.19

Y LM

IS i FE

Figure 5.20

The original sources for the Mundell–Fleming model are the following:

■ J. Marcus Fleming (1962) ‘Domestic financial policies under fixed and floating exchange rates’, IMF Staff Papers 9: 369–79.

■ Robert A. Mundell (1962) ‘Capital mobility and stabilization policy under fixed and flexible exchange rates’, Canadian Journal of Economic and Political Science 29: 475–85.

A more recent view on the flexible vs fixed exchange rates controversy is offered by Stanley Fischer (2001)

‘Exchange rate regimes: is the bipolar view correct’, Journal of Economic Perspectives 15: 3–24.

An excellent example of how flexible the

Mundell–Fleming apparatus is in terms of permitting the incorporation of new research results is Luis Céspedes, Roberto Chang and Andrés Velasco (2003)

‘IS-LM-BP in the Pampas’, IMF Staff Papers 50, Special issue: 143–56.

Recommended reading

Applied problems 147

A P P L I E D P R O B L E M S

RECENT RESEARCH