Economics 826 International Finance Final Exam: April 2005 ...

Economics 826 International Finance Final Exam: April 2005

Answer 4 questions from Part A and 4 questions from Part B. Part A is worth 60%. Part B is worth 40%. You may write in english or french. You may use a hand calculator.

Part A: Analytical Answer 4 of the following questions. (15 marks each)

1. This question looks at one reason why a forward exchange rate might be a biased predictor of the corresponding spot rate. Suppose that the spot rate evolves this way: st+1 = 0.9st +
t+1 , and that
t+1 has a mean of zero and is uncorrelated with st . But market participants do not know this pattern. They form expectations as follows: Et st+1 = st . Finally, suppose that UIP holds: ft = Et st+1 . (a) An economist tries to test UIP by assuming rational expectations, and hence running a least-squares regression: st+1 = βft . ˆ Will the economist conclude that Find an expression for the population value of β. UIP holds? (b) How could the economist test whether a risk premium is present? 1

2. How much scope do target zones leave for international interest-rate differentials? This question uses the monetary model of the exchange rate to outline an answer to this question. Suppose that the nominal exchange rate always satisfies: st = 0.5xt + 0.5Et st+1 , where x is a fundamental. The fundamental is random, like this: xt = 1 ± 0.2, where the two outcomes are equally likely. By confining x to this range, the authorities confine s to a target zone. (a) What is the variance of x? (b) Find the two possible values for st (these will be s and s), one when xt = 1.2 and the other when xt = 0.8. (c) What is the variance of s? (d) Suppose that t counts months. Find the two possible values for the expected rate of depreciation of the currency. If UIP holds, then what are the corresponding international interest-rate differentials, on an annualized basis?

3. A financial economist is studying the 1929 stock-market crash. She hypothesizes that the log stock price index can be explained this way: pt = dt + 0.2Et (pt+1 − pt ), where dt is the aggregate stream of log dividends. (a) Show that this theory implies that the log stock price can be written as an expected present-value of log dividends, if you ignore the remainder term in solving this equation forwards. (b) Suppose that the pattern in log dividends until 1929 was this: dt = µ + dt−1 + ηt . Solve for the log price, pt . (c) Then also solve for the price-earnings ratio in levels. (This ratio often is used to summarize stock-price values.) How does this ratio depend on µ, the dividend growth rate? (d) Call your solution to part (b) the fundamental solution, pt∗ . Suppose that the actual stock price index seemed to behave like this: pt = pt∗ + 6t . 2

What would we call this additional term? Is it rational for a price to behave in this way?

4. An economist writes: “A boom in commodity prices should lead to an increase in the Canadian current account balance.” This question uses economic theory to shed light on this claim. Suppose that there are two time periods. Canada begins with net foreign assets B0 , imports one good to consume, and exports a second good (primary commodities, say) in amount Y x at relative price P (the terms of trade) to pay for that: C1 +

P2 Y2x C2 = (1 + r )B0 + P1 Y1x + . 1+r 1+r

The endowments are given, as are r and P . (a) With consumption smoothing, will the current account respond more to temporary changes in the terms of trade or to permanent ones? (b) Imagine trying to forecast export earnings using an autoregression: P2 Y2x = ρ1 P1 Y1x , with a coefficient ρ1 . Show how the value of ρ1 affects the current account. (c) Outline how you would extend the theory to include an infinite horizon, rather than a horizon of one year.

5. This question investigates the effect of productivity growth in a non-traded sector on the real exchange rate. Imagine a small, open economy with two sectors. In the non-traded sector, Y N = AN LN and in the traded sector Y T = AT LT , are the production functions. Both sectors are competitive. There is no capital. Workers can move between sectors to equalize wages. The price of traded goods, P T , is given from the world market. (a) Show how differential productivity growth in the two sectors would affect the country’s real exchange rate. (b) In reality, do non-traded goods explain a large part of variations in real exchange rates?

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6. This question studies a ‘first-generation’ model of a speculative attack on a fixed exchange rate. Suppose that we approximate the central bank’s balance sheet using logarithms (lower-case letters): m = b + r, and that the central bank’s bond holdings grow this way: bt+1 = µ + bt . The exchange rate is determined by this model: st = mt + γEt (st+1 − st ). (a) If reserves are zero then solve for the floating exchange rate, st . (b) Next suppose that reserves are not zero, and that the central bank tries to hold the exchange rate constant at s, while b continues to grow. Show how the timing of a speculative attack depends on (i) µ and (ii) initial foreign exchange reserves. (c) If UIP holds, describe the international interest rate differential (at a very short maturity) as the scenario in part (b) unfolds.

7. Imagine that bonds are priced by risk-neutral investors, so that consumption growth does not appear in real interest rates. The price of a one-period, nominal discount bond is: Pt . Qt1 = Et β Pt+1 Let β = 0.98. Consider an open economy with inflation targeting (like Canada, the UK, or Sweden). Suppose that the expected rate of inflation is 2% and that the inflation rate is uncorrelated from period to period. From one period to another, ⎧ ⎨ 1.03 Pt+1 = 1.02 ⎩ Pt 1.01

w.p. 0.2 w.p. 0.6 w.p. 0.2

(a) Solve for Qt1 . (b) What does the yield curve look like in this country? (c) If we also observed the U.S. yield curve, could we reliably combine them to forecast changes in the value of the local currency?

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Part B: Empirical Discuss 4 of the following statements or questions. (10 marks each)

1. A country with a fixed exchange rate has no scope for independent monetary policy. 2. Low consumption correlations are an indicator of incomplete, international risk sharing. 3. Why does the IMF require that highly indebted countries reduce government spending as a precondition to receiving IMF grants or loans? 4. Briefly discuss both parts of this statement: “Most countries’ foreign exchange reserves are too small to defend their fixed exchange rates against attacks by large speculators, so they tend to either float or join a currency union.” 5. Do country-specific changes in productivity help us understand either (a) the current account or (b) the real exchange rate? 6. Explain the low-test-power problem in testing for PPP and briefly explain what responses are available to this problem. 7. In the Lucas two-country model, can there be a correlation between real and nominal exchange rates? 8. Bretton Woods II will not be sustainable without a remnimbi revaluation. 9. Evidence on pass-through suggests that rich countries should choose fixed exchange rates and poor ones floating exchange rates, exactly the opposite of what we generally observe.

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