## Application Changes in the Equilibrium Exchange Rate Two Examples

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Our analysis has revealed the factors that affect the value of the equilibrium exchange rate. Now we use this analysis to take a close look at the response of the exchange rate to changes in interest rates and money growth.

Changes in Changes in domestic interest rates iD are often cited as a major factor affect-

Interest Rates ing exchange rates. For example, we see headlines in the financial press like this one: "Dollar Recovers As Interest Rates Edge Upward." But is the view presented in this headline always correct?

Not necessarily, because to analyze the effects of interest rate changes, we must carefully distinguish the sources of the changes. The Fisher equation (Chapter 4) states that a (nominal) interest rate equals the real interest rate plus expected inflation: i = ir + tc e. The Fisher equation indicates that an interest rate i can change for two reasons: Either the real interest rate ir changes or the expected inflation rate tc e changes. The effect on the exchange rate is quite different, depending on which of these two factors is the source of the change in the nominal interest rate.

Suppose that the domestic real interest rate increases so that the nominal interest rate iD rises while expected inflation remains unchanged. In this case, it is reasonable to assume that the expected appreciation of the dollar will be unchanged because expected inflation is unchanged, and so the expected return on foreign deposits will remain unchanged for any given exchange rate. The result is that the RF schedule stays put and the RD schedule shifts to the right, and we end up with the situation depicted in Figure 5, which analyzes an increase in i D, holding everything else constant. Our model of the foreign exchange market produces the following result: When domestic real interest rates rise, the domestic currency appreciates.

When the nominal interest rate rises because of an increase in expected inflation, we get a different result from the one shown in Figure 5. The rise in expected domestic inflation leads to a decline in the expected appreciation of the dollar (a higher appreciation of the euro), which is typically thought to be larger than the increase in the domestic interest rate iD5 As a result, at any given exchange rate, the expected return on foreign deposits rises more than the expected return on dollar deposits. Thus, as we see in Figure 6, the RF schedule shifts to the right more than the RD schedule, and the exchange rate falls. Our analysis leads to this conclusion: When domestic interest rates rise due to an expected increase in inflation, the domestic currency depreciates.

Because this conclusion is completely different from the one reached when the rise in the domestic interest rate is associated with a higher real

5This conclusion is standard in asset market models of exchange rate determination; see Rudiger Dornbusch, "Expectations and Exchange Rate Dynamics," Journal of Political Economy 84 (1976): 1061-1076. It is also consistent with empirical evidence that suggests that nominal interest rates do not rise one-for-one with increases in expected inflation. See Frederic S. Mishkin, "The Real Interest Rate: An Empirical Investigation," CarnegieRochester Conference Series on Public Policy 15 (1981): 151-200; and Lawrence Summers, "The Nonadjustment of Nominal Interest Rates: A Study of the Fisher Effect," in Macroeconomics, Prices and Quantities, ed. James Tobin (Washington, D.C.: Brookings Institution, 1983), pp. 201-240.

FIGURE 6 Effect of a Rise in the Domestic Nominal Interest Rate as a Result of an Increase in Expected Inflation

Because a rise in domestic expected inflation leads to a decline in expected dollar appreciation that is larger than the resulting increase in the domestic interest rate, the expected return on foreign deposits rises by more than the expected return on domestic (dollar) deposits. RF shifts to the right more than RD, and the equilibrium exchange rate falls from E, to E2.

Expected Return (in \$ terms)

interest rate, we must always distinguish between real and nominal measures when analyzing the effects of interest rates on exchange rates.

### Changes in the Money Supply

Suppose that the Federal Reserve decides to increase the level of the money supply in order to reduce unemployment, which it believes to be excessive. The higher money supply will lead to a higher American price level in the long run (as we will see in Chapter 25) and hence to a lower expected future exchange rate. The resulting decline in the expected appreciation of the dollar increases the expected return on foreign deposits at any given current exchange rate and so shifts the RF schedule rightward from RF, to RF2 in Figure 7. In addition, the higher money supply will lead to a higher real money supply M/P because the price level does not immediately increase in the short run. As suggested in Chapter 5, the resulting rise in the real money supply causes the domestic interest rate to fall from iD to iD2, which lowers the expected return on domestic (dollar) deposits, shifting the RD schedule leftward from RD to RD2. As we can see in Figure 7, the result is a decline in the exchange rate from E, to E2. The conclusion is this: A higher domestic money supply causes the domestic currency to depreciate.

### Exchange Rate Overshooting

Our analysis of the effect of an increase in the money supply on the exchange rate is not yet overâ€”we still need to look at what happens to the exchange rate in the long run. A basic proposition in monetary theory, called monetary neutrality, states that in the long run, a one-time percentage rise in the money supply is matched by the same one-time percentage rise in the price level, leaving unchanged the real money supply and all other economic variables such as interest rates. An intuitive way to understand this proposition is to think of what would happen if our government announced overnight that an old dollar would now be worth 100 new dollars. The money supply in new dollars would be 100 times its old value and the price level would also be 100 times higher, but nothing in the economy would really have changed; real and nominal interest rates and the real money supply would remain the same. Monetary neutrality tells us that in the long run, the rise in the money supply would not lead to a change in the domestic interest rate and so it would return to iD in the long run, and the schedule for the expected return on domestic deposits would return to RD. As we can see in Figure 7, this means that the exchange rate would rise from E2 to E3 in the long run.

The phenomenon we have described here in which the exchange rate falls by more in the short run than it does in the long run when the money supply increases is called exchange rate overshooting. It is important because, as we will see in the following application, it can help explain why exchange rates exhibit so much volatility.

Another way of thinking about why exchange rate overshooting occurs is to recognize that when the domestic interest rate falls in the short run, equilibrium in the foreign exchange market means that the expected return on foreign deposits must be lower. With the foreign interest rate given, this lower expected return on foreign deposits means that there must be an expected appreciation of the dollar (depreciation of the euro) in order for the expected return on foreign deposits to decline when the domestic interest rate falls. This can occur only if the current exchange rate falls below its longrun value.

FIGURE 7 Effect of a Rise in the Money Supply A rise in the money supply leads to a higher domestic price level in the long run, which in turn leads to a lower expected future exchange rate. The resulting decline in the expected appreciation of the dollar raises the expected return on foreign deposits, shifting the RF schedule rightward from RF1 to RF2. In the short run, the domestic interest rate iD falls, shifting RD from RD to RD2. The short-run outcome is that the exchange rate falls from E1 to E2. In the long run, however, the interest rate returns to iD1 and RD returns to RD1. The exchange rate thus rises from E2 to E3 in the long run.

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