QUEEN S UNIVERSITY FINAL EXAMINATION FACULTY OF ARTS AND SCIENCE DEPARTMENT OF ECONOMICS APRIL 2017

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1 Page 1 of 5 QUEEN S UNIVERSITY FINAL EXAMINATION FACULTY OF ARTS AND SCIENCE DEPARTMENT OF ECONOMICS APRIL 2017 ECONOMICS 426 International Macroeconomics Gregor Smith Instructions: The exam is three hours in length. Answer two (2) of the six questions in Part A. Each question in Part A is worth ten (10) marks. Answer three (3) of the five questions in Part B. Each question in Part B is worth fifteen (15) marks. For questions in Part B that involve a numerical part be sure to show your calculations and intermediate steps. Read the questions carefully. Put your student number on each answer booklet. Please answer all questions in the answer booklets. Start each question on a new page. You may use the allowed hand calculator: the Casio 991. No other aids are allowed. Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer the exam questions as they are written. This material is copyrighted and is for the sole use of students registered in Economics 426 and writing this exam. This material shall not be distributed or disseminated. Failure to abide by these conditions is a breach of copyright and may also constitute a breach of academic integrity under the University Senate s Academic Integrity Policy Statement.

2 Page 2 of 5 PART A Answer two (2) of the following six (6) questions as true, false, or uncertain. Your grade will depend mainly on your explanation. Each question is worth ten (10) marks. 1. The Canada-US exchange rate can be both statistically explained contemporaneously and predicted in advance using oil prices. 2. Departures from uncovered interest parity (for example in the Yen-USD market) mean that there are riskless profits from the carry trade and that the forward rate is a biased predictor of the future spot exchange rate. 3. The current value of the real exchange rate can help predict the rate of real depreciation and the rate of nominal depreciation. 4. There are several ways for emerging market economies to avoid the negative effects of loose US monetary policy. 5. For most countries the costs of a currency union outweigh the benefits. 6. The problem of global imbalances continues to worsen, partly due to China s exchangerate policy.

3 Page 3 of 5 PART B Answer three (3) of the following five (5) questions. Each question is worth fifteen (15) marks. 1. This question uses a two-period model of a small, open economy with no investment to predict some of the effects of a decrease in government spending. Suppose that the country has net foreign assets labelled B 0 = 10. Output is given by Y 1 = 100 and Y 2 = 110. The world interest rate is r = Households smooth consumption so that C 1 = C 2. (a) Suppose government spending is G 1 = G 2 = 20. Solve for the value of the current account in each time period. (b) Suppose that government spending in period 1 falls to G 1 = 18. But G 2 = 20 still. Solve for the value of the current account in each time period. (c) Suppose that government spending in period 1 falls to G 1 = 18 but now the effect can persist: G 2 = 20 2ρ, so that ρ [0, 1] describes the persistence in this change. Find formulas that give the current account in each time period as function of ρ. 2. Suppose that PPP holds between Turkey (the home country) and the euro area (the foreign, starred country), so that in logs: s t + p t p t = 0. Also suppose that UIP holds. Money demand in Turkey is given by: m t p t = 0.5i t, and in the euro area by m t p t = 0.5i t. (a) Derive the fundamental equation of the monetary model of the exchange rate. (b) Suppose that the relative money supply in logs is given by x t m t m t, and that x t = x t 1 + ɛ t, where ɛ t is white noise with mean zero. Solve for the exchange rate s t in terms of the current value of x t. (c) Find expressions for the international interest differential and also for f t, the log of the one-period-ahead forward rate.

4 Page 4 of 5 3. Suppose that asset returns satisfy this Euler equation: 1 = E t 0.94(1 + r t+1 ) C t 1 C t+1 where r t+1 denotes the return from period t to period t + 1 and C is real consumption in the US. For simplicity suppose there is no inflation. Suppose that in any period C can take on two values, 1.00 and 1.02, each with probability 0.5. There is no autocorrelation in consumption. (a) Call h t the price of a one-period bond that pays 1 in all states of the world in period t + 1. Find the interest rate on this bond first when C t = 1 and second when C t = (b) Call h jt the price of a one-period bond (issued by a sovereign government in an emerging economy) that pays 1 in period t+1 with probability 1 λ and pays 0.8 with probability λ. The event of this partial default is uncorrelated with the value of consumption in period t + 1. Solve for the expected return on this bond first when C t = 1 and second when C t = (c) How could an analyst estimate the value of the default probability λ? 4. Suppose that in the target zone between the Hong Kong and the US dollars the log price of the USD in HKD is given by: s t = 1 3 x t E ts t+1, where x t m t m t. Also suppose that x t can be described as a discrete random variable. It can take on the values 1 or 3, each with probability 0.5, and is independently distributed over time. (a) Find the two possible values of s t. (b) Find the variance of x t and the variance of s t. (c) If UIP holds, find the two possible values of the international interest rate differential, i t i t. Also find the value of the log forward exchange rate f t.

5 Page 5 of 5 5. This question studies the real exchange rate between eastern Europe (the home region) and the western European countries that also are in the euro zone (the foreign, starred region). Suppose the real exchange rate is given by: q = SP P T PN 0.5 PT 0.5P N 0.5 = SP 0.5, where T and N denote the traded and non-traded sectors respectively. Suppose that the Balassa-Samuelson model applies (where the LOP holds for traded goods) and that labour productivity in the N-sector is the same in both regions. In the T -sector, labour productivity in the east is half the value in the west, but it is catching up. In growth rates: A T = 4% per year and = 1% per year. A T (a) Where are prices (as measured by the price index) lower and by how much? Find the rate of real appreciation or depreciation in eastern Europe. (b) Consider Slovenia, which is in the euro zone and also in eastern Europe. If western Europe in the euro zone has an inflation rate of 2% per year then what will the inflation rate in Slovenia be? (c) Consider Poland, which has a floating exchange rate against the euro and is in eastern Europe. Its inflation rate is the same as the inflation rate in the western European countries of the European zone (2% per year). What will be happenning to its nominal exchange rate over time?

6 Economics 426 Final Exam 2017 Answer Guide Part B 1. (a) We know that: (1.02)( 10) = = C 1[1.98] + G 1 + G So now if G 1 = G 2 = 20 then C 1 = C 2 = Thus and so CA 2 = CA 1 = 0.02( 10) = 0.02, (b) Now with x = 2 we have C 1 = C 2 = Thus CA 1 = 0.02( 10) = 0.97, and so CA 2 = (Notice that a temporary decline in government spending leads to an increase in the current account balance.) (c) Now the constraint is: Rearranging gives: And then and = C 1 (1.98) ρ C 1 = ρ [ ]. CA 1 = 81.8 C 1, CA 2 = 10 CA 1. (If you are paitent you can consolidate and cimplify these formulas.) 2. (a) With α = 0.5 the fundamental equation is: s t = 2 3 x t E ts t+1 (b) Using either solution method with this drifting random walk gives: s t = αµ + x t = x t.

7 (c) Notice that E t s t+1 = s t = x t = f t and i t i t = µ. 3. (a) The bond price is: h t = 0.94C t [ ]. When C t = 1 then h t = 0.93 so r = 7.5%. When C t = 1.02 then h t = so r = 5.3% (b) We know that h jt = h t [1 0.2λ] There are now two possible values for the interest rate for each starting value of C t, but the expected returns are the same as in part (a). E[ 1 h jt 1] = (1 λ)[ 1 h jt 1] + λ0.8[ 1 h jt 1] = 1 h t 1 (c) The ratio of the two bond prices provides information on λ. Rearranging: λ = 5[1 h jt h t ]. 4. (a) We know that the expected value of s is the expected value of x, which is 2. Thus: s t = 1 3 x t When x = 1 we find s = 5/3 = When x = 3 we find s = 7/3 = (b) The mean of x is 2 and the variance is 1. To find the variance of s we can use the two values, or work from the formula in part (a). σ 2 s = σ 2 x = (c) The log forward rate is just f t = E t s t+1 = 2. So the two possible values for the interest differential come from: i t i t = E t s t+1 s t = 2 s t, which can be or

8 5. (a) The assumptions in the preamble tell us that: so prices are lower in the east. Also q t = ( A T A T ) 0.5 = = q = 0.5( A T A T ) = 0.5( 3) = 1.5 and the east experiences a real appreciation of 1.5% per year. (b) The inflation rate in Slovenia will be 3.5% per year. (b) The zloty will appreciate by 1.5% per year.