Lecture Notes 7

Exchange Rate Overshooting

International Economics: Finance Professor: Alan G. Isaac

7 Exchange Rate Overshooting 1

7.1 Overshooting: Core Considerations . . . . . . . . . . . . . . . . . . . . . . . 3

7.1.1 Covered Interest Parity with Regressive Expectations . . . . . . . . . 4

7.1.2 Liquidity Effects and Overshooting . . . . . . . . . . . . . . . . . . . 8

7.1.3 The Algebra of Overshooting . . . . . . . . . . . . . . . . . . . . . . 10

7.2 Implied Real Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.2.1 CIPRE : Real Version . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.2.2 Liquidity Effects and Non-Neutrality of Money . . . . . . . . . . . . . 15

7.3 The Long Run In Sticky-Price Models . . . . . . . . . . . . . . . . . . . . . 17

7.3.1 The Real Interest Differential Model . . . . . . . . . . . . . . . . . . 19

7.4 Money Market Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7.4.1 Overshooting with Sticky Prices . . . . . . . . . . . . . . . . . . . . . 25

7.5 Simple Empirical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . 30

7.5.1 Can We See the CIPRE Relationship? . . . . . . . . . . . . . . . . . 30

1

7.5.2 Forward Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7.5.3 VAR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Terms and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Problems for Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.7 Dornbusch (1976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

7.7.1 Regressive Expectations . . . . . . . . . . . . . . . . . . . . . . . . . 35

7.7.2 Rational Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7.7.3 Unanticipated Policy Shocks . . . . . . . . . . . . . . . . . . . . . . . 41

7.7.4 Anticipated Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Bibliography 45

2 LECTURE NOTES 7. EXCHANGE RATE OVERSHOOTING

In chapter 3, our development of the monetary approach to flexible exchange rates relied

on two key ingredients: the Classical model of price determination, and an exogenous real

exchange rate. We found that the monetary approach had some notable early empirical

successes. But we also found that as data accumulated under the new flexible exchange rate

regimes, the simple monetary approach appeared increasingly unsatisfactory. The present

chapter considers whether the problem lies in attempting to use the monetary approach

model, which has a long-run orientation, to describe short-run exchange-rate movements.

The widespread adoption of floating exchange rates in the early 1970s brought unexpected

volatility of the nominal exchange rate. The large movements of the nominal exchange rate,

coupled with the relative inertia of the price level, produced large fluctuations in the real

exchange rate (and therefore large deviations from purchasing power parity). The monetary

approach model of chapter 3 treats such real exchange rate movements as exogenous, but it

is clearly desirable to explain them.

Increasing the scope of our models seldom comes without costs, and our attempt to

endogenize the real exchange rate is no exception. The most popular models of short-run

real-exchange-rate movements abandon the simplifying Classical assumption of perfectly

flexible prices. These models treat the price level as sticky in the short run. This chapter

develops such a sticky-price exchange-rate model. We find we must therefore abandon

two key simplifying assumptions of the monetary approach model: the exogeneity of the

real interest rate, and the exogeneity of the real exchange rate. Our sticky-price model will

predict large short-run deviations from purchasing power parity, such as those described in

chapter 5.

In sticky-price models, monetary policy influences real interest rates and the real exchange

rate. When prices are sticky, any change in the nominal money stock becomes a change

in the real money stock, which will generally imply a change in the interest-rate. Similarly,

short-run nominal-exchange-rate fluctuations will imply corresponding real exchange rate

fluctuations. There is an immediate benefit for our exchange rate models: we are no longer

2015 Alan G. Isaac

7.1. OVERSHOOTING: CORE CONSIDERATIONS 3

forced to treat persistent deviations from purchasing power parity, such as those we discussed

in chapter 5, as purely exogenous. Instead our explanation short-run nominal-exchange-rate

movements becomes an explanation of short-run real-exchange-rate movements. Sticky-price

models also offer new insights into the sources of exchange-rate volatility. In particular, they

offer an explanation of why exchange rates may be much more volatile than monetary policy.

7.1 Overshooting: Core Considerations

Suppose an economy is disturbed by an unanticipated exogenous change, which we call a

shock . This might be a change in monetary or fiscal policy, but it need not be policy

related. We say the endogenous variable exhibits overshooting in response to this shock if

its short-run movement exceeds the change in its steady-state value.

For example, given the long-run neutrality of money, a one-time, permanent increase in

the money supply will eventually lead to a proportional depreciation of the steady-state value

of the currency. If the short-run depreciation is more than proportional, then the short-run

depreciation of the spot rate is greater than the depreciation of its steady-state value. We say

such an economy exhibits exchange-rate overshooting in response to money-supply shocks.

Popular models of such exchange rate overshooting have three key ingredients: covered

interest parity, regressive expectations, and a liquidity effect of money supply changes. You

are already familiar with the covered interest parity relationship: it is just the requirement

that domestic assets bear the same rate of return as fully hedged foreign assets. This means

that i = i + fd . If we decompose the forward discount on the domestic currency into

expected depreciation and a risk premium, then we can write this as i = i + se + rp.

Once again we see that we must deal with exchange-rate expectations if we wish to

discuss the determination of exchange rates. Instead of the rational-expectations assumption,

this chapter will adopt the slightly more general regressive-expectations assumption.

Expectations are regressive when the exchange rate is expected to move toward its long-

2015 Alan G. Isaac

4 LECTURE NOTES 7. EXCHANGE RATE OVERSHOOTING

run value. This is intended to capture the common-sense idea that if you think that the

exchange rate is currently overvalued, then you also expect it to depreciate toward its long-

run value.

The final key ingredient is that monetary policy has a liquidity effect in the short run.

This means, for example, that expansionary monetary policy lowers the real interest rate

in the short run. These three ingredientscovered interest parity, regressive expectations,

and short-run liquidity effectscan be combined to illustrate why the exchange rate may

overshoot in response to monetary policy changes.

7.1.1 Covered Interest Parity with Regressive Expectations

The first ingredient in our exchange-rate overshooting models is covered interest parity. In

chapter 2 we saw that covered interest parity is implied by perfect capital mobility in the

assets markets. Recall that covered interest parity is just the requirement of equivalent

returns on equivalent assets. This is the first core ingredient of overshooting models.

i i rp = se (7.1)

Here i is the domestic nominal interest rate, i is the foreign interest rate, rp is the expected

excess return on the domestic asset, and se is the expected rate of depreciation of the

spot exchange rate. Note the presence of the expected rate of depreciation. As with the

simple monetary approach model, this makes consideration of exchange rate expectations

unavoidable. Holding all else constant, covered interest parity implies that the domestic

interest rate must be higher when expected depreciation is higher. This implied positive

correlation between interest rates and expected depreciation is summarized in figure 7.1.

The second ingredient in our exchange-rate overshooting models is regressive expectations.

Expectations formation is called regressive when a variable is expected to close any gap

between its current level and its long-run equilibrium level. So if exchange-rate expectations

2015 Alan G. Isaac

7.1. OVERSHOOTING: CORE CONSIDERATIONS 5

se

i

0

i + rp

CIP

Figure 7.1: Covered Interest Parity

are regressive, a spot rate that is above its long-run equilibrium level is expected to fall

towards that level. The expected rate of real depreciation depends on the gap between the

current exchange rate and its long-run equilibrium level.1

se = (S/S) (7.2)

Here S is the full-equilibrium value of the spot rate, which we will discuss more below. The

function determines the expected speed of adjustment of the real exchange rat