International Finance and Open Economy Macro Instructor: Konstantin Styrin
Problem Set
I. The FX Market
1. Suppose quotes for the dollar-euro exchange rate, Es/€, are as follows: in New York, $1.50 per euro; and in Tokyo, $1.55 per euro. Describe how investors use arbitrage to take advantage of the difference in exchange rates. Explain how this process will affect the dollar price of the euro in New York and Tokyo.
1. Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands or Great Britain. The (one-year) interest rate on bank deposits is 2% in Britain and 4.04% in the Netherlands. The (one-year) forward euro-pound exchange rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for UIP and CIP as necessary.
a. What is the euro-denominated return on Dutch deposits for this investor?
b. What is the (riskless) euro-denominated return on British deposits for this investor using forward cover?
c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equilibrium in the forward exchange rate market?
d. If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what is the equilibrium forward rate, according to CIP?
e. Suppose the forward rate takes the value given by your answer to (d). Calculate the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound). Is it positive or negative? Why do investors require this premium/discount in equilibrium?
f. If UIP holds, what is the expected depreciation of the euro against the pound over one year?
g. Based on your answer to (f), what is the expected euro-pound exchange rate one year ahead?
II. The Monetary Approach to ERs
3. You are given the following information. The current dollar-pound exchange rate is $2 per British pound. A U.S. basket that costs $100 would cost $120 in the United Kingdom. For the next year, the Fed is predicted to keep U.S. inflation at 2% and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergence to absolute PPP is 15% per year.
a. What is the expected U.S. minus U.K. inflation differential for the coming year?
b. What is the current U.S. real exchange rate, quK/us, with the United Kingdom?
c. How much is the dollar overvalued/undervalued?
d. What do you predict the U.S. real exchange rate with the United Kingdom will be in one year's time?
e. What is the expected rate of real depreciation for the United States (versus the United Kingdom)?
f. What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)?
g. What do you predict will be the dollar price of one pound a year from now?
4. Consider two countries, Japan and Korea. In 1996, Japan experienced relatively slow output growth (1%), whereas Korea had relatively robust output growth (6%). Suppose the Bank of Japan allowed the money supply to grow by 2% each year, whereas the Bank of Korea chose to maintain relatively high money growth of 12% per year. For the following questions, use the simple monetary model (where L is constant). You will find it easiest to treat Korea as the home country and Japan as the foreign country.
a. What is the inflation rate in Korea? In Japan?
b. What is the expected rate of depreciation in the Korean won relative to the Japanese yen?
c. Suppose the Bank of Korea increases the money growth rate from 12% to 15%. If nothing in Japan changes, what is the new inflation rate in Korea?
d. Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, MK; Korea's interest rate; prices, PK; real money supply; and EwoN/v over time. (Plot each variable on the vertical axis and time on the horizontal axis.)
e. Suppose the Bank of Korea wants to maintain an exchange rate peg with the Japanese yen. What money growth rate would the Bank of Korea have to choose to keep the value of the won fixed relative to the yen?
f. Suppose the Bank of Korea sought to implement policy that would cause the Korean won to appreciate relative to the Japanese yen. What ranges of the money growth rate (assuming positive values) would allow the Bank of Korea to achieve this objective?
5. This question uses the general monetary model, in which L is no longer assumed constant and money demand is inversely related to the nominal interest rate. Consider the same scenario described in the beginning of the previous question. In addition, the bank deposits in Japan pay 3% interest; iv = 3%.
a. Compute the interest rate paid on Korean deposits.
b. Using the definition of the real interest rate (nominal interest rate adjusted for inflation), show that the real interest rate in Korea is equal to the real interest rate in Japan. (Note that the inflation rates you calculated in the previous question will apply here.)
c. Suppose the Bank of Korea increases the money growth rate from 12% to 15% and the inflation rate rises proportionately (one for one) with this increase. If the nominal interest rate in Japan remains unchanged, what happens to the interest rate paid on Korean deposits?
d. Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, MK; Korea's interest rate; prices, PK; real money supply; and EwoN/v over time. (Plot each variable on the vertical axis and time on the horizontal axis.)
6. Both advanced economies and developing countries have experienced a decrease in infla¬tion since the 1980s. This question considers how the choice of policy regime has influenced this global disinflation. Use the monetary model to answer this question.
a. The Swiss Central Bank currently targets its money growth rate to achieve policy objec¬tives. Suppose Switzerland has output growth of 3% and money growth of 8% each year. What is Switzerland's inflation rate in this case? Describe how the Swiss Central Bank could achieve an inflation rate of 2% in the long run through the use of a nominal anchor.
b. Like the Federal Reserve, the Reserve Bank of New Zealand uses an interest rate target. Suppose the Reserve Bank of New Zealand maintains a 6% interest rate target and the world real interest rate is 1.5%. What is the New Zealand inflation rate in the long run? In 1997, New Zealand adopted a policy agreement that required the bank to maintain an inflation rate no higher than 2.5%. What interest rate targets would achieve this objective?
c. The central bank of Lithuania maintains an exchange rate band relative to the euro. This is a prerequisite for joining the Eurozone. Lithuania must keep its exchange rate within ±15% of the central parity of 34,528 litas per euro. Calculate the exchange rate values corresponding to the upper and lower edges of this band. Suppose PPP holds. If Eurozone inflation is currently 2% per year and inflation in Lithuania is 5%, calculate the rate of depreciation of the litas. Will Lithuania be able to maintain the band requirement? For how long? Does your answer depend on where in the band the exchange rate currently sits? A primary objective of the European Central Bank is price stability (low inflation) in the current and future Eurozone. Is an exchange rate band a necessary or sufficient condition for the attainment of this objective?
III. The Asset Approach to ERs
7. Use the money market and foreign exchange (FX) diagrams to answer the following questions. This question considers the relationship between the euro (€) and the U.S. dollar ($). The exchange rate is in U.S. dollars per euro, E$1€. Suppose that with financial innovation in the United States, real money demand in the United States decreases. On all graphs, label the initial equilibrium point A.
a. Assume this change in U.S. real money demand is temporary. Using the FX and money market diagrams, illustrate how this change affects the money and FX markets. Label your short-run equilibrium point B and your long-run equilibrium point C.
b. Assume this change in U.S. real money demand is permanent. Using a new diagram, illustrate how this change affects the money and FX markets. Label your short-run equilibrium point B and your long-run equilibrium point C.
c. Illustrate how each of the following variables changes over time in response to a permanent reduction in real money demand: nominal money supply Mus, price level Pus, real money supply MUS/PUS, U.S. interest rate is, and the exchange rate E$1€.
8. This question considers how the FX market will respond to changes in monetary policy. For these questions, define the exchange rate as Korean won per Japanese yen, EwoN/v. Use the FX and money market diagrams to answer the following questions. On all graphs, label the initial equilibrium point A.
a. Suppose the Bank of Korea permanently decreases its money supply. Illustrate the short-run (label the equilibrium point B) and long-run effects (label the equilibrium point C) of this policy.
b. Now suppose the Bank of Korea announces it plans to permanently decrease its money supply but doesn't actually implement this policy. How will this affect the FX market in the short run if investors believe the Bank of Korea's announcement?
c. Finally, suppose the Bank of Korea permanently decreases its money supply but this change is not anticipated. When the Bank of Korea implements this policy, how will this affect the FX market in the short run?
d. Using your previous answers, evaluate the following statements:
i. If a country wants to increase the value of its currency, it can do so (temporarily) without raising domestic interest rates.
ii. The central bank can reduce both the domestic price level and the value of its currency in the long run.
iii. The most effective way to increase the value of a currency is through surprising investors.
9. In the late 1990s, several East Asian countries used limited flexibility or currency pegs in managing their exchange rates relative to the U.S. dollar. This question considers how different countries responded to the East Asian Currency Crisis (1997-1998). For the following questions, treat the East Asian country as the home country and the United States as the foreign country. You may assume these countries maintained a currency peg (fixed rate) relative to the U.S. dollar. Also, you need consider only the short-run effects.
a. In July 1997, investors expected that the Thai baht would depreciate. That is, they expected that Thailand's central bank would be unable to maintain the currency peg with the U.S. dollar. Illustrate how this change in investors' expectations affects the Thai money market and the FX market, with the exchange rate defined as baht (B) per U.S. dollar, denoted EB/$. Assume the Thai central bank wants to maintain capital mobility and preserve the level of its interest rate and abandons the currency peg in favor of a floating exchange rate regime.
b. Indonesia faced the same constraints as Thailand-investors feared Indonesia would be forced to abandon its currency peg. Illustrate how this change in investors' expectations affects the Indonesian money market and the FX market, with the exchange rate defined as rupiahs (Rp) per U.S. dollar, denoted ERp/s. Assume the Indonesian central bank wants to maintain capital mobility and the currency peg.
c. Malaysia had a similar experience, except that it used capital controls to maintain its currency peg and preserve the level of its interest rate. Illustrate how this change in investors' expectations affects the Malaysian money market and the FX market, with the exchange rate defined as ringgit (RM) per U.S. dollar, denoted ERM/$. You need show only the short-run effects of this change in investors' expectations.
d. Compare and contrast the three approaches just outlined. As a policy maker, which would you favor? Explain.
10. Several countries have opted to join currency unions. Examples include the Euro area, the CFA franc union in West Africa, and the Caribbean currency union. This involves sacrificing the domestic currency in favor of using a single currency unit in multiple countries. Assuming that once a country joins a currency union it will not leave, do these countries face the policy trilemma discussed in the text? Explain.