Chapter 27 EXPECTATIONS, MONEY, AND THE DETERMINATION OF THE EXCHANGE RATE

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1 Chapter 27 EXPECTATIONS, MONEY, AND THE DETERMINATION OF THE EXCHANGE RATE This chapter places the earlier models in an intertemporal setting by introducing variables such as future prices and future exchange rates into the individual's decision. Because the future is unknown, the way individuals form expectations about the future plays a keypart in the analysis. In the long run, when both goods and asset markets clear, the exchange rate is simply the ratio between the two countries' price levels. However, markets may clear at different rates. In this chapter, asset markets are assumed to clear faster than goods markets. The short-run arbitrage condition thus involves interest rates and exchange rates. In equilibrium, the expected real returns on all assets must be equated, regardless of currency denomination, a condition known as uncovered interest rate parity. Ifforward tradein currencies is possible, arbitrageurs will exploit opportunities for risk-free profit until they bring about the stronger condition, covered interest rate parity. The "overshooting model" addresses the issue of which path the exchange rate must follow when investors are willing to hold both countries' assets and asset markets clear faster than goods markets. Suppose the foreign interest rate were to increase, and the home currency were to jump to its new long-run equilibrium value. This could not be a short-run equilibrium. The expected real returns on the two countries' assets would differ, and investors would desire even more of the foreign asset. To establish equilibrium, the expected return on the domestic asset must increase. This can only happen if the domestic currency appreciates towards its long run equilibrium value. In order for this to happen, the initial jump of the exchange rate must be an even larger depreciation than that implied by the shift to its new long-run equilibrium value, i.e. it must "overshoot" its long-run value. SHORT-ANSWER QUESTIONS 1. True or false: Covered interest rate parity will hold even if assets denominated in different currencies are imperfect substitutes. 2. How would the conditions for interest rate parity between the United States and Japan change if the United States imposed a 10% tax on interest earnings and capital gains resulting from changes in the exchange rate? What would the condition look like if capital gains were not subject to the tax?

2 3. True or false: According to the monetarist theory of exchange rate determination, if purchasing power parity holds, real interest rates should be equalized even if there are persistent differentials between nominal interest rates. 4. True or false: Uncovered interest parity is a stronger hypothesis than is covered interest parity. 5. If the money supply follows a random walk, then the best forecast of tomorrow's money supply is, today's money supply plus some positive error term. today's money supply. a random number. 6. True or false: Under the assumption of rational expectations, an increase in the money supply three months from now has the same effect on the price level as an increase in the money supply that occurs today. 7. What is the effect on the current dollar-pound spot rate if participants in the foreign exchange market anticipate future intervention to support the dollar? 8. Consider an investor who currently holds a 90-day dollar-denominated bond. The investor learns that in six months the Federal Reserve Bank intends to begin a policy of tight money. Is the investor's real return from the bond likely to be affected by this information? If so, how? 9. The assumption of purchasing power parity yields reasonable predictions about exchange rate behavior if the time period under consideration is short. monetary policies are contractionary. price levels change by relatively large amounts.

3 PROBLEMS 1. The Opportunity Cost of Money: When deciding to hold wealth in the form of money or some other asset such as bonds, investors weigh the opportunity costs of these alternative assets. Suppose the market price of a one-year bond with a face value of $1,000 is $925. What is the rate of return on the bond? The expected annual inflation rate is 5%. What is the real interest rate? What is the opportunity cost of holding currency? The rate of return on a one-year bond denominated in German marks is 8% and the expected annual inflation rate in Germany is 6%. What is the opportunity cost of holding deutschemarks relative to holding dollars? 2. Models of Exchange Rate Determination: The equations below list the spot exchange rate as functions of the relative money supplies, the interest rate differential and relative output supplies in the monetarist and Mundell-Fleming models of exchange rate determination. Monetarist model: S = ( M/M*, i - i*, Y/Y* ) Mundell-Fleming model: S = ( M/M*, i - i*, Y/Y* ) For each of the three determinants of the spot rate, indicate whether the spot rate is an increasing function of that variable by marking "+" above it, or a decreasing function of that variable by marking "-" above it. (For example, in the monetarist model, the spot rate rises, or depreciates, as the domestic money supply increases so a "+" should be placed above M/M* in the first equation.) Explain the role of the interest rate differential in the two models. What would the sign over Y/Y* be if, in the Mundell-Fleming model, an increase in national income stimulates demand for the country's export good as well as its demand for foreign imports.

4 3. Real Money Balances and Inflation: Suppose prices are perfectly flexible, and that the central bank's announcements are credible. The central bank announces that last night the money supply doubled. What will happen to the price level? What will happen to real balances? The annual inflation rate has stabilized at 5%. However, the central bank announces that from now the annual rate of monetary expansion will be 10%. What happens to the inflation rate? To the price level? To real money balances? 4. Rational Expectations and the Exchange Rate: Suppose that the current peso-dollar exchange rate is 33 pesos to the dollar, and that traders in the foreign exchange market have the following expectations about next year's price levels in the United States and Mexico: Probability U.S. price level Mexican price level , , ,900 Is the dollar expected to appreciate or depreciate, and by how much? Rumors about changes in the leadership at the Mexican central bank cause traders to assign some weight, albeit a very small one, to the event of a drastic increase in the Mexican price level. Probability U.S. price level Mexican price level , , , ,000 Is the dollar now expected to appreciate or depreciate?

5 5. Announcements and Equilibrium Paths: Consider a two-country world in which foreign and domestic prices are perfectly flexible, there is purchasing power parity, and foreign and domestic assets are perfect substitutes. The diagrams on the next page show the initial levels of the money supply, the price level, the nominal interest rate and real money balances in the domestic economy as well as the spot exchange rate. At time T1 the monetary authority announces that the domestic money supply is going to double at time T2. Show the effect of this announcement in each of the graphs below.

6 6. The Effects of Monetary Policy in a Model with Overshooting: Consider again a two-country world, but in this case, assume that prices do not adjust immediately so that purchasing power parity may not hold in the short run. In the diagrams on the following page, draw in the effects of a one-time increase in the money supply at time T. Explain in words what factors determine the time path of the nominal interest rate. How does this differ from the time path predicted by the monetarist model? Repeat part for the real interest rate and the exchange rate.

7 7. The Flexibility of Fixed Exchange Rates: A colleague argues that the announcement of a fixed exchange rate between the dollar and the pound sterling would eliminate forever any uncertainty about the dollar-pound exchange rate. Do you agree with your colleague? A second colleague joins the discussion and proposes that adopting a gold standard will do the trick to eliminate the uncertainty about exchange rates. As a good student of the gold standard, you question this proposition. How does the gold standard affect exchange rates? What type of reform would be the most effective (and most controversial!) for reducing, if not eliminating, any exchange rate risk? 8. Speculative Bubbles, Overshooting and Expectations: What do you think is meant by "unnecessary" volatility in the exchange rate? Is this consistent with agents having "rational expectations"? In the overshooting model expectations are "regressive." Are regressive expectations also rational expectations? Are rational expectations also regressive? 9. Interest Rates and the Exchange Rate: In the overshooting model of exchange rates, the spot rate, S, can be written as a function of the real interest rate differential and the rate, q, at which the spot rate adjusts to its long-run equilibrium value, S': (S-S')/S' = -(1/q)(r-r*) According to this theory, does a positive real interest rate differential indicate that the exchange rate should appreciate or depreciate? What is the underlying economic reasoning? In the model with flexible prices, investors required a nominal interest rate differential to compensate them for the expected depreciation of the currency. Why do investors require a real interest rate differential as compensation in the overshooting model? What determines q? (d) What is the value of q in the monetarist model?

8 10. Looking for the Model in the Data: The various models of exchange rate determination have different implications for the time-series behavior of macroeconomic variables. (d) What empirical regularities would you look for to determine which of these models best describes exchange rate behavior? What are some of the difficulties in testing these hypotheses? How does the overshooting model explain exchange rate volatility? How does the monetarist model account for exchange rate volatility? 11. Taxing Trade in Currencies: Present the arguments for and against imposing taxes on foreign exchange traders to prevent speculation. What are the possible costs of foreign exchange speculation? What are the benefits?