Today’s exchange rate and the future

real money supply is the same as before the central bank increased the nomi-nal money supply. So prices rose by just as much as the nominomi-nal money sup-ply. It also means that the real exchange rate is unchanged. So the exchange rate depreciated by just as much as the price level rose.

5.7 Today’s exchange rate and the future

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 5.12. There we assumed that financial investors do not expect the exchange rate to change, so that i = i^World was the foreign exchange market equilibrium condition. In general, if for whatever reason the exchange rate is expected to depreciate, open interest 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 5.13).

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^e+1

Figure 5.12 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.

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

exchange rate EP^World>P must remain unchanged. Suppose the real exchange rate required to make IS pass through C is 1, so that EP^World=P, 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 Y* = 0, p^World=0 and i^World=0 (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 a = 1>(1 + h). 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.

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

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

m - e = -he^e+1

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

Figure 5.13 (Flexible exchange rates.) Expected depreciation drives a wedge between the domestic and the world inter-est rate. FE is in the blue position and the new long-run equilibrium is in C. Just as described in Figure 5.12 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.

Income

Interest rate

Y*

Potential income i ^World+ eε₊₁

i ^World IS₀

IS₁

FE general case

LM₀

LM₁

Old and new equilibrium

1 3

3 2 C

A

D

Chapter summary 135 Using this equation, the 2006 exchange rate depends on the concurrent money supply and on the exchange rate expected for 2007:

(5.9) Does this mean that the investors’ time horizon ends in 2007? 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 2007 exchange rate to the exchange rate expected for 2008:

(5.10) Taken together, equations (5.9) and (5.10) provide a link between 2008 and the exchange rate in 2006. Equation (5.10) leaves it open, though, how e^e₂₀₀₈ 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 e^e₂₀₀₈depends on e^e₂₀₀₉, and two years ahead to see that e^e₂₀₀₉depends on e^e2010. Actually, we can do this as often as we want. By doing it ten more times, we notice that the 2005 exchange rate depends on the exchange rate expected for the year 2020. And this once again depends on what we expect for 2021. 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 stimu-lation 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 com-pletely 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 econ-omy already operates at potential income, rising prices are likely to nullify efforts to stimulate 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^e2007 = am^e2007 + (1 - a)e^e₂₀₀₈ e₂₀₀₆ = am₂₀₀₆ + (1 - a)e^e₂₀₀₇

comparative static analysis 125 crowding out 117

dynamic analysis 125

exchange rate overshooting 130 fiscal policy 116

fixed exchange rates 118 flexible exchange rates 117 monetary policy 119

Mundell–Fleming model 115 stable 125

Key terms and concepts

EXERCISES

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

■ 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 gov-ernment expenditures increased.

Exercises 137

5.8 Consider the macroeconomic situation shown in Figure 5.15 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.

1960 1965 1970 1975 1980 1985 1990 1994

Interest rate

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

■ J. Marcus Fleming (1962) ‘Domestic financial poli-cies 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 current 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 more recent 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

fiscal policy. Formally, your country maintains 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 depreciate. 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?

5.7 Consider Figure 5.14, 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?

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.

Table 5.2

TRAVEL R (March Y^USAin

in $m 1973 = 100) 1987 $ Y^OECD*

1973 -3,158 98.9 3,268.6 69.4

1974 -3,184 99.4 3,248.1 69.1

1975 -2,812 94.0 3,221.7 63.6

1976 -2,558 97.6 3,380.8 68.8

1977 -3,565 93.4 3,533.3 72.0

1978 -3,573 84.4 3,703.5 74.9

1979 -2,935 83.2 3,796.8 78.5

1980 -997 84.9 3,776.3 78.9

1981 144 101.0 3,843.1 79.3

1982 -992 111.8 3,760.3 77.3

1983 -4,227 117.4 3,906.6 78.8

1984 -8,438 128.9 4,148.5 83.8

1985 -9,798 132.5 4,279.8 86.3

1986 -7,382 103.7 4,404.5 87.2

1987 -6,481 90.9 4,539.9 90.3

1988 -1,511 88.2 4,718.6 95.3

1989 5,071 94.4 4,838.0 98.4

1990 8,978 86.0 4,897.3 100.0

1991 17,957 86.5 4,867.6 99.7

1992 20,885 83.5 4,979.3 99.4

1993 20,840 90.0 5,134.5 99.1

1994 18,000 88.6 5,342.3 103.6

*Index of industrial production (1990 = 100)

expected depreciation should equal the difference in expected inflation rates. The positive coefficient of 28.65 states that the more depreciation the market expects, the more the exchange rate depreciates today. The equation explains 80% of the variance of this exchange rate during the sample period.

Note: Frankel’s equation also includes the differ-ence in interest rates. Its coefficient is not significant and is not shown here.

WORKED PROBLEM

In and out of the United States

Net exports as a building block of the

Mundell–Fleming model have been specified in equation (4.2) (Chapter 4) as (after rearranging)

(5.11) This type of equation should explain all net exports, the current account, or certain categories of net exports. Table 5.2 gives data for US net travel and

NX = (x₂ +m₂)R + x₁Y^World-m₁Y

APPLIED PROBLEMS

RECENT RESEARCH

In document Economics - Macroeconomics, 2nd Edition - (Manfred Gartner) Pearson Prentice Hall 2006 (Page 158-163)