Expectations and Exchange-rate overshooting

Expectations and Exchange-Rate Overshooting In Chapter 35 we discuss the determination of exchange rates, and in a box on page 905 we examine why exchange rates are so volatile, and the role that “news” plays in this volatility. In this web-based section we present a famous theory of exchange rates that seeks to carefully explain why exchange rates are more volatile than the economic “fundamentals”—such as interest rates, money supplies, and commodity prices—and why they often “overshoot” in the short run what will ultimately be their long-run response to a change in one of these fundamental economic variables.

A Little Background Following the Second World War, the major countries of the world established a system of fixed exchange rates that was based on both the U.S. dollar and gold. It was not quite as pure as the Gold Standard that existed until 1914, but it was similar, and was based on two elements. First, the price of gold was fixed at $35 (U.S.) per ounce, and the U.S. Treasury stood ready to buy or sell any amount of gold required to peg this price. Second, countries then pegged their individual currencies to the U.S. dollar. The International Monetary Fund was created to oversee the necessary payments, and to deal with whatever imbalances occurred, during the operation of this “gold-exchange” standard. This system worked relatively well until the late 1960s when the United States, with considerable fiscal expenditures directed at funding the Vietnam War, and with considerable monetary growth, began to experience inflation. With inflation, the underlying freemarket price of gold began to rise, but the system required the price to be pegged at $35 per ounce. The result was that the United States began losing gold to buyers around the world; in August 1971 President Richard Nixon closed the “gold window” and thereby stopped pegging the price of gold. The gold-exchange standard came to a close and the world entered a new regime of flexible exchange rates. It is no surprise that the new system of flexible exchange rates was more volatile than the fixed system—this is true by definition. But what surprised many economic observers was that exchange rates appeared to be more volatile than any of the important economic variables that theory and experience suggested were the fundamental determinants of exchange rates. As we discuss in Chapter 35, such variables include price levels, interest rates, and commodity prices. Beginning a few years earlier, the role of expectations was being discussed seriously by macroeconomists—Milton Friedman, for example, had recently written an important paper in which he explained how expectations of the private sector restricted the long-run impact of monetary policy. The time was therefore ripe for the incorporation of expectations into a theory of exchange-rate changes.

Expectations and the Real Exchange Rate The late Rudiger Dornbusch, for many years a professor at MIT and one of the world’s leading macroeconomists, developed a theory to explain the volatility of exchange rates. His 1976 paper “Expectations and Exchange-Rate Dynamics” is now considered to be a classic in the field. His theory is based on two central ideas: the long-run neutrality of money, and the role of expectations in financial markets. We cover the basics in turn.

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Expectations and Exchange-rate overshooting

The Real Exchange Rate and Long-Run Money Neutrality The nominal exchange rate is the price in domestic currency of one unit of foreign currency—for example, the Canadian–U.S. exchange rate in June of 2004 was 1.38, indicating that it then required 1.38 Canadian dollars to purchase one U.S. dollar. A rise in this exchange rate is a depreciation of the Canadian dollar because it takes more Canadian dollars to purchase a single U.S. dollar. The nominal exchange rate is the price of one currency in terms of another, but it is not the relative price of goods in two countries. The real exchange rate is a measure of the international relative price of goods and here is represented by R. The real Canadian–U.S. exchange rate is given by: R = ePUS/PC

(1)

where e is the nominal Canadian–U.S. exchange rate, PUS is the U.S. aggregate price level, and PC is the Canadian aggregate price level. Note that each national price level is measured in units of the respective national currency and so R is itself unit-free. The real exchange rate is a measure of (aggregate) relative prices between two countries. A rise in the real exchange rate, caused either by a nominal depreciation of the Canadian dollar or by an increase in U.S. prices relative to those in Canada, is a real depreciation of the Canadian dollar. The interpretation of a real depreciation of the Canadian dollar is that Canadian goods are becoming cheaper relative to U.S. goods, either because the Canadian currency gets cheaper (e rises) or because Canadian domestic prices are falling relative to those in the United States (PUS/PC rises). Conversely, a fall in the real exchange rate—a real appreciation of the Canadian dollar—means that Canadian goods are becoming more expensive relative to U.S. goods, either because the Canadian dollar is becoming more expensive or because Canadian domestic prices are rising relative to U.S. prices. So much for the real exchange rate. Now consider the idea of long-run money neutrality that we discuss in detail in Chapter 28. The economy’s adjustment mechanism following aggregate demand or aggregate supply shocks involves an adjustment of factor prices in response to output gaps. This adjustment process continues until the level of real GDP is returned to the level of potential output. If the shock in question is a monetary contraction or expansion (a shift of the AD curve), the long-run effect of the shock, as we discuss in Chapter 28, falls only on nominal variables, including the price level, nominal wages, and the nominal exchange rate. But if money is neutral in the long run, monetary policy will have no effect on any real variables, such as output, employment, investment, real wages, and other relative prices. Note the mention of relative prices in the previous sentence. If money is neutral in the long run, then relative prices—including international relative prices—will be unaffected in the long run by changes in monetary policy. Thus changes in monetary policy will have no long-run effect on the real exchange rate. So if a Canadian monetary expansion, for example, has the long-run effect of increasing the Canadian price level, it must also have the long-run effect of depreciating the Canadian dollar (raising e), thus keeping the real exchange rate unchanged. Indeed, this long-run depreciation of the Canadian dollar is exactly the international manifestation of the same forces that cause the longrun increase in the Canadian price level.

The Role of Expectations in Financial Markets Financial capital is highly mobile across international borders, and the rise of the computer over the past three decades and of the Internet over the past decade have increased this mobility considerably. In general, financial capital seeks the highest possible rate

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Expectations and Exchange-rate overshooting

of return, but also as much security as possible. One might think, therefore, that rates of return on Canadian government bonds and U.S. government bonds would be very close, if not exactly the same, for the simple reason that both federal governments are extremely safe credit risks—that is, neither government is at all likely to renege on its formal debt commitments. In fact, however, interest rates on similarly risky financial assets can deviate considerably for long periods of time; the reason is that the expectations of exchangerate changes are an important component of an investment’s total rate of return. This observation brings us to the theory of uncovered interest parity. Consider an investor choosing between buying a Canadian government bond or a U.S. government bond, both of which have a maturity of one year. Given the current purchase price of the Canadian bond, the annual interest rate (yield) on that bond is iC. Similarly, the annual interest rate on the U.S. bond is iUS. Now suppose that the Canadian government is viewed by creditors as being a slightly more risky borrower than is the U.S. government (U.S. government bonds are typically considered to be the safest bonds in the world). In this case, if creditors expected the Canadian–U.S. exchange rate to be stable over the coming year, arbitrage (buying high-yield bonds and selling low-yield bonds) in financial markets would result in the following equality: iC = iUS + 

(2)

where  is the risk premium on Canadian bonds. Equation (2) says that Canadian interest rates will be equal to U.S. rates plus a premium to reflect the greater risk on the Canadian bonds. In a world of flexible exchange rates, however, exchange rates are usually not expected to be stable, for the simple reason that various policies are changing and various shocks are occurring (or expected to occur in the near future). Participants in financial markets form their expectations about how exchange rates are likely to move, and these expectations affect their choices regarding which financial assets to purchase. For example, if people expect the Canadian dollar to appreciate relative to the U.S. dollar over the coming year, they will be prepared to purchase Canadian bonds even at a lower interest rate than available in the United States; in contrast, if people expect the Canadian dollar to depreciate over the coming year, they will only be prepared to purchase Canadian bonds if they are compensated with a higher interest rate than that on U.S. bonds. This logic suggests a modification of Equation (2) as follows: iC = iUS +  + E(∆e)

(3)

where E(∆e) is the expected change in the Canadian–U.S. exchange rate over the coming year. This modified equation expresses what is called uncovered interest parity— “uncovered” because it is an equality that should hold as a result of arbitrage by participants in the financial market who are not “covering” their purchases of foreign exchange by using the forward exchange market (a futures market in foreign currencies). As Equation (3) states, the more the Canadian dollar is expected to depreciate over the coming year, the higher Canadian interest rates must be relative to U.S. rates before investors are indifferent between purchasing the two different assets.

Exchange-Rate Overshooting We can now put these two different pieces together to understand the volatility of flexible exchange rates. Figure 1 can be used to illustrate the path of the exchange rate over time. Suppose that the economic fundamentals such as interest rates, money supplies, and commodity prices are not changing, and that there is no inflation either in Canada or in

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FIGURE 1

Expectations and Exchange-rate overshooting

Exchange-Rate Overshooting Following a Monetary Expansion e e3

Exchange Rate

Path 2 e1

short-run depreciation

Path 1

e2

long-run depreciation

e0

0

t*

Time

Exchange rates often change more in the short run than they do in the long run. Until t* the economic fundamentals are constant and thus the exchange rate is constant. At t* there is a domestic monetary expansion that reduces domestic interest rates. The lower interest rates cause a capital outflow and a sudden depreciation of the currency (rise in the exchange rate). But in order to be consistent with uncovered interest parity, the rise in the exchange rate must be so large that it is followed by an expected decline (appreciation of the currency). Thus Path 1 is not possible; the only possible path following a monetary expansion is one like Path 2 where the exchange rate in the short run “overshoots” its long-run level. This overshooting is one popular explanation for the volatility of exchange rates.

the United States. In such a setting, the Canadian–U.S. exchange rate will be stable at some level like e0, as it is in Figure 1 up to time t*. Suppose the Bank of Canada embarks on an unanticipated monetary expansion at time t*. We know from the analysis in Chapter 28 that the short-run effects of the monetary expansion are to reduce Canadian interest rates, stimulate an outflow of financial capital, and thus depreciate the Canadian dollar. As a result, the Canadian exchange rate will rise—and it will do so almost immediately since financial markets are very fluid. Furthermore, we also know that the long-run effect of the monetary expansion (assuming that money is neutral in the long run) is to increase the Canadian price level and also to depreciate the Canadian dollar. Suppose the long-run effect on the Canadian– U.S. exchange rate is that it rises to e1 (enough so that, given the long-run change in the Canadian price level, the real exchange rate is unaffected). At first pass, one might think that the path followed by the exchange rate would be one like Path 1, with a sudden depreciation to e2 followed by a more gradual depreciation as the Canadian price level also rises in the long run. In this case, the nominal depreciation would lead to a sudden real depreciation, but in the long run there would be no effect on the real exchange rate. The problem with Path 1, and this was precisely Dornbusch’s central insight, is that this path violates the uncovered interest parity condition and thus cannot be consistent with a world in which investors are rationally choosing between alternative financial assets. Dornbusch agreed that the short-run effects of the Canadian monetary expansion

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Expectations and Exchange-rate overshooting

must involve a sudden depreciation of the Canadian dollar because the lower Canadian interest rates will lead to a capital outflow. But those reduced Canadian interest rates can only be consistent with Equation (3) if the Canadian dollar is expected to appreciate over the coming year. Thus, Dornbusch reasoned that following a Canadian monetary expansion there must be three phases: first, there must be a sudden depreciation; second, there must be a subsequent expected appreciation; and third, the long-run nominal depreciation must be such that the real exchange rate is unaffected (money neutrality). The only possible path is therefore one like Path 2, one that shows immediately how Dornbusch’s model explains why exchange rates can be more volatile than the underlying economic fundamentals. The exchange rate rises immediately to e3 because of the capital outflow caused by the reduced Canadian interest rates. Those lower Canadian interest rates, however, can only be sustained so long as the Canadian dollar is expected to appreciate against the U.S. dollar, thus the exchange rate gradually falls toward its long-run level, e1. The long-run nominal depreciation (the difference between e1 and e0) is determined by the long-run influence of the monetary expansion on the Canadian price level (to keep the real exchange rate unchanged). For what should be obvious reasons, the behaviour shown by Path 2 is now called “exchange-rate overshooting” because the initial change in the exchange rate is greater than the long-run change —that is, the exchange rate “overshoots” its long-run level. *** Dornbusch’s insights regarding expectations and exchange-rate changes have made a lasting impact on the way economists think about the relationship between economic fundamentals and movements in exchange rates. His insights, combined with those contained in the box on page 905, provide a solid foundation for understanding why exchange rates are so volatile.

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