ECM134 International Money and Finance 2012/13 Exam Paper Model Answers

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1 ECM34 International Money and Finance 202/3 Exam Paper Model Answers Alexander Mihailov Department of Economics University of Reading 5 January 202 TWO hours; answer TWO of the five questions that follow. Equilibrium Exchange Rate under Asset Arbitrage Assume the framework of the simple asset market model of the nominal exchange rate where the equilibrium condition is ensured by limitless arbitrage. You are given the following data for the Home (H) and F oreign (F ) interest rates, announced to hold at a horizon of one year, respectively ι t = 5% and ι t = 3%. (a) If you also consider that the corresponding forward rate of the Home currency (HC) with respect to the F oreign currency (FC) is F t = (using the price or academic quotation, as in the lectures), calculate the equilibrium spot exchange rate S t of the HC consistent with Covered Interest Parity (CIP). Explain whether the Home currency is sold in the market at a forward discount or premium and by how much (in % terms) it is expected to depreciate or appreciate. (0 marks) (b) Calculate the expected HC nominal exchange rate (NER), E t [S t+ ], which corresponds to the following 5 equally probable outcomes for S t+ :.02, 0.98, 0.95, 0.93, 0.90 (according to the academic quotation of the NER we stick to). What is the implied equilibrium spot exchange rate consistent with Uncovered Interest Parity (UIP) and by how much (in % terms) is the Home currency expected to depreciate or appreciate? (20 marks) (c) Do CIP and UIP hold in the data? Why or why not? (20 marks) (a) Covered Interest Parity (CIP) S t = +ι t +ι t F t S t = +3 + ι t = ( + ι t ) Ft S t +5 = the HC is sold at a forward discount in the market, as F t S t > 0. =.094 2% (net) HC depreciation is expected in the market. F t S t = (b) Uncovered Interest Parity (UIP) 5 ( ) = is the expected NER of the HC. + ι t = ( + ι t ) Et[St+] S t S t = +ι t +ι t E t [S t+ ] S t = = the implied equilibrium S t = , and so the market expects depreciation of the HC (since E t [S t+ ] S t > 0). =.094 2% is the expected (net) HC depreciation rate in the market. E t[s t+] S t =

2 (c) Empirical Evidence on CIP and UIP Many papers have tested CIP. Overall, the empirical evidence confirms CIP to perform pretty well. Occasional violations occur after accounting for transaction costs, but they are short-lived and typical for periods of high market volatility. However, violations of UIP are common in the data, and they present one of the empirical puzzles for international economists. The most common explanation that has been suggested is the risk premium optimally required by risk-averse investors to invest in a riskier asset. 2 Multiple Equilibria and Stability in the Forex Market E, price of foreign currency E 2 H 2 H E S(E) D(E) quantity of foreign currency Figure : Multiple Equilibria and Stability in the Forex Market Figure presents two possible equilibria in the market for foreign exchange. The spot exchange rate, E, defined as the domestic currency price of (a unit of) foreign currency, is measured along the vertical axis. The quantities of foreign exchange demanded, D(E), or supplied, S(E), at any given exchange rate level are measured along the horizontal axis. It is, furthermore, assumed that demand for foreign currency and supply of foreign currency both originate only because of the underlying demand for imports and supply of exports of goods. (a) Why, under producer currency pricing (PCP), the supply curve for foreign currency S(E) may be initially an increasing function but subsequently a decreasing function of the exchange rate? Why this peculiarity does not arise for the demand curve D(E)? (30 marks) (b) Which of the possible equilibria, H and H 2 in Figure, is stable and which unstable, and why? (20 marks) (a) In many models of the 940s and the 950s, the (foreign-currency) values of the demand, supply and excess demand for foreign exchange as a function of the NER, E, under fixed prices have been written as, respectively: 2

3 D (E) = PIM Q IM (E), S (E) = }{{} E P EXQ EX (E), () }{{} FC value of IM demand by H FC value of IM demand by F ED (E) D (E) S (E) = P IM Q IM (E) E P EXQ EX (E). (2) Hence, a positive (negative) excess demand for foreign exchange in the domestic economy is equivalent to a trade (BoP) deficit (surplus): ED (E) 0 CA 0. (3) Such demand and supply functions for foreign currency, D (E) and S (E), in the forex market of a country, here H, are said to be derived or indirect functions. The reason is that they arise from the underlying demand functions for goods: demand for foreign goods by residents (import demand by H), Q IM (E), and demand for domestic goods by nonresidents (import demand by F ), Q EX (E). The derived nature of the functions originates in the key assumption in earlier models of the forex market that transactors demand and supply foreign currency only in relation with purchases or sales of goods abroad (e.g. not in relation with asset transactions). The important consequence of such an assumption is that even if the underlying schedules for goods are well-behaved, the resulting schedules for foreign exchange may have unusual shape and give rise to multiple equilibria. To illustrate this, take the traditional case of PCP (LCP implies an inverse logic), looking at equations (). Under PCP, it is the abnormal shape of the supply schedule for foreign currency, S (E), that may lead to multiple equilibria. We assume a well-behaved demand for imports, Q IM (E), i.e. such that monotonically decreases as the exchange rate, E, increases; since the foreign-currency price of imports, PIM, is assumed constant, the domestic-currency price of imports, EPIM, moves in the same direction as the NER, E. We also assume a well-behaved demand for imports by F or, equivalently, demand for exports of H goods, Q EX (E), i.e. such that monotonically increases as the exchange rate, E, increases; since the domestic-currency price of exports, P EX, is assumed constant, the foreign-currency price of exports, E P EX, moves in the opposite direction to the NER, E. Hence, in the first case, the demand for foreign currency in the H forex market, D (E), moves in the same direction as the underlying demand for H imports of goods, Q IM (E). In the second case, however, the supply of foreign currency in the H forex market, S (E), and the underlying demand for H exports by F, Q EX (E), do not necessarily move in the same direction: under price-elastic H export demand by F (i.e. with η EX > ), a domestic currency depreciation (E ) of % would bring about an increase in the volume of exports, Q EX (E), greater than %, which more than offsets the decrease in the foreign-currency price of exports, E P EX (given their constant domestic-currency price, P EX ): the foreign-currency value of the proceeds from H exports that emerges as supply of foreign currency in H s forex market, S (E) = E P EXQ EX (E), therefore increases (S (E) ); hence, S (E) has a positive slope; under price-inelastic H export demand by F (i.e. with η EX < ), a domestic currency depreciation (E ) of % would bring about an increase in the volume of exports, Q EX (E), smaller than %, which cannot fully offset the decrease in the foreign-currency price of exports, E P EX (given their constant domestic-currency price, P EX ): the foreign-currency value of the proceeds from H exports that emerges as supply of foreign currency in H s forex market, S (E) = E P EXQ EX (E), therefore decreases (S (E) ); hence, S (E) has a negative slope. Consequently, two cases should be distinguished in the analysis of equilibrium in the forex market:. The import demand curve in F, i.e., the demand curve for exports of H goods, Q EX (E), has everywhere an elasticity either greater than one or smaller than one. 2. Alternatively, it has an elasticity greater than one in some of its region(s) and smaller than one in other region(s). 3

4 (b) We can detect in Figure quickly which of the two possible equilibria of the forex market is stable and which not. Let us begin with the lower-exchange rate equilibrium H (the one where the home currency is relatively appreciated). Take, first, a still lower NER level, say, E. As evident in the graph, at a level of the exchange rate of E,the excess demand causes an appreciation of the foreign currency, which is the same as depreciation of the home currency, i.e. there will be market forces (mark an upward arrow below E ) naturally and progressively returning the forex market toward point E where the excess demand is fully absorbed, so there the very cause of the adjustment (upwards in the graph) is annihilated and the process stops at a rest. Now doing the same kind of analysis but starting with a level of the exchange rate above E, say, E, the inverse logic would apply (and so an arrow above H would point downwards). That is why we can conclude that point H, to which the forex market (model) tends to return from initial positions both (slightly) above and (slightly) below, is a stable equilibrium, also known as a fixed point or a rest point of the system analysed. Repeating the exercise in the neigbourhood of the higher exchange rate equilibrium at point H 2, corresponding to a NER level of E 2, one could easily see that this equilibrium is (dynamically) unstable. The reason is that neither a bit below, nor a bit above that point there are natural market forces that drive the system back to E 2. On the contrary, excess supply of foreign currency below H 2 pushes the NER down and away from E 2, and excess demand above H 2 pushes the NER up and away from E 2 again (mark an upward arrow). Thus, H 2 is an unstable equilibrium, not a rest (or fixed) point for the system. 3 The Monetary Approach to the Balance of Payments The monetary approach to the balance of payments (BoP) was developed in the 960s, in part within the research department of the IMF under the intellectual leadership of Jacques Polak and in the context of the Bretton Woods system of fixed exchange rates. (a) (b) Enumerate its main assumptions. (20 marks) Analyse and interpret its equilibrium condition, which we wrote in the lectures as: θir t = s + p t + φy t λι t + ɛ t ( θ) d t, (4) }{{} =m d t where ir t is (the log of) international reserves, s is (the log of) the nominal exchange rate, p t is (the log of) the F oreign price level, y t is (the log of) Home output, ι t is the F oreign interest rate, d t is (the log of) domestic credit, m d t is (the log of) money demand, 0 < θ < is the fraction of international reserves in the total assets of the central bank, φ > 0 is the income elasticity of money demand and λ > 0 is the interest-rate semi-elasticity of money demand. (30 marks) (a) Main Assumptions. PPP is a key assumption in the monetary approach, justified as an aggregation of the law of one price (LOP) in the markets for goods and services. 2. UIP is assumed to hold as well, so we have perfect substitutability between home and foreign assets. 3. All prices are assumed flexible under the monetary approach. 4. The focus of the monetary approach is on conditions for stock equilibrium in the money market: the BoP is essentially a monetary phenomenon, and should therefore be analysed in terms of adjustment of money stocks. 4

5 5. Production is assumed at the level of full employment, so real income is fixed. This assumption, together with the flexible prices ensure no short-run output-inflation trade-off (i.e. a vertical Phillips Curve). 6. A stable money demand function is taken to exist. 7. The small open economy (SOE) case rather than the two-country version of the model is usually considered (as we did in the lectures). (b) Analysis and Interpretation of Equilibrium Equation (4) summarises the main insights of the monetary approach to the balance of payments, or, which is the same, of the monetary model (of the balance of payments) under peg. It is evident from the money demand function in (4) that if the SOE in question experiences any of the following: positive income growth, y t ; declining interest rates, ι t ; rising prices, p t ; the demand for nominal money balances will grow, m d t. Equation (4) further shows the following. If this increased demand for money is not satisfied by an accommodating increase in domestic credit, d t, so that m d t > ( θ) d t in (4), the public will obtain the additional money it desires to hold by running an overall BoP surplus, i.e., an increase in international reserves, ir t. If, on the other hand, the central bank engages in a domestic credit expansion that exceeds the growth of money demand, so that m d t < ( θ) d t in (4), the public will eliminate the excess supply of money (it does not wish to hold) by spending or investing it abroad and thus running a(n overall) BoP deficit, i.e., a decrease in international reserves. Consequently, the money supply, m s t ( θ) d t + θir t, in the monetary model under peg is endogenous, that is, determined by expression (4). 4 The S-Curve The horizontal S-curve, first documented in Backus et al. (994), is presented in Figure 2 using annual data between 960 and 2007 for six countries, namely, Brazil, Chile, France, South Korea, Thailand and the UK. Define this S-curve. For which 3 countries in the sample here the S-curve stands out in the clearest way? What is the important fact the S-curve highlights (valid for 5 countries in the panels of the figure, but not for one country which)? The horizontal S-curve illustrates the correlation between de-trended (log) net exports, N X, (relative to GDP, nx NX GDP ) and de-trended (log) T ot P IM P EX, corr (T ot, nx) on the vertical axis, contemporaneously (at t = 0, on the horizontal axis) at various lags of T ot behind NX (e.g. t = 3, 2, ) and at various leads of T ot (e.g. t = +, +2, +3). 5

6 0.4 Brazil 0.2 Chile France 0.2 Skorea Thailand UK Figure 2: The S-Curve. Source: Leon-Ledesma and Mihailov (OUP book), calculations using World Bank data. Sample period is and the annual data is detrended using the HP filter as in the original Backus et al. (994) paper. In particular, for a sample of developed economies Backus et al. (994) found that the cross-correlation function between current terms of trade and future (lagged) values of the trade balance is positive, but between current terms of trade and past (lead) values of the trade balance it is negative. As also documented in the figure here, these correlations resemble a horizontal S shape, meaning that the two variables under analysis are negatively correlated in the current period and in the more distant past/future but positively correlated over some medium run (of 2 to 6 quarters, roughly speaking). One can see that the S-curve is especially clear in the case of South Korea and, to a lesser degree, Brazil and France. With the exception of Thailand, the negative correlation at time 0 or and the positive correlation at time 2 and 3 appears in all countries. This cross-correlation pattern reminds as well of the J-curve, as a deterioration in the T ot (T ot ) leads to an improvement in NX after a lag of 2-3 years in the figure. 5 Monetary Expansion in the Static Mundell-Fleming Model The static Mundell-Fleming model of the early 960s can be represented by the following system of two equations: dm = dy = δ γ ds σ γ dι + dg, (5) γ ( ) λ + dι + φδ γ ds φσ γ φ dg. (6) γ 6

7 All variables except the world interest rate, ι, are in logarithms and d denotes a small change. y is output, s is the exchange rate, g is government expenditure and m is the stock of money. All parameters (δ, γ, σ, λ, φ) are assumed positive, with 0 < γ <. (a) Derive analytically and interpret the effects of a monetary expansion on output under pegged versus under floating exchange rates. Draw graphs to support your interpretation. (40 marks) (b) What can you conclude about the effectiveness of monetary policy as a stabilisation tool under the alternative exchange-rate regimes? (0 marks) (a) Deriving and Interpreting the Effects of a Monetary Expansion The effects of monetary policy on output, which are of interest when judging the effectiveness of this type of macropolicy as a stabilisation tool, can be derived analytically from (5), and those on the stock of money from (6). Under (Credible) Peg In this case ds = 0. Moreover, under the ceteris paribus condition of our comparative statics analysis here, dι = 0 and dg = 0 too. Therefore, looking at the expressions of (5) and (6), one could verify that dm = 0 and dy = 0. The intuition is as follows (see Figure 3). An expansionary monetary policy, identified by a rise in domestic credit, DC, on the asset side of the central bank s balance sheet, will not be able to affect the monetary base, M B, on the liability side (and, ultimately, via the money multiplier, the money supply, MS), as under a peg regime it will be fully offset by a commensurate fall in the net foreign assets, NF A C, on the asset side of the balance sheet of the central bank. This complete offsetting arises because the increase in DC puts downward pressure on the domestic interest rate and residents are not willing to hold the additional money available in the economy, so they spend them to buy foreign assets (running a temporary BoP deficit, i.e., causing capital outflow) while the domestic interest rate remains the same as the foreign interest rate (ensured by perfect capital mobility). This means that the central bank, operating in a peg regime, has to accommodate the demand for foreign assets by selling out of its international reserves, so that NF A C decreases exactly by the initial increase in DC. Again, taking the central bank s balance sheet, DC + NF A C = MB, and as DC = NF A C, the final effect on the monetary base is nil. Graphically, the LM curve first shifts out but then returns to its initial position: output is, thus, not changed (neither is the interest rate). Figure 3: Mundell-Fleming Model Monetary Expansion under Peg 7

8 Under (Pure) Float Now ds 0, and we have to take into account the effect on output of the (instantaneous) variation in the exchange rate, itself caused by the monetary expansion. Thus, the monetary expansion (dm > 0), in addition to shifting out the LM curve, depreciates the exchange rate under float (since the central bank does not intervene, selling foreign assets to defend the peg, as in the previous analysis), which can be seen from (6): ds dm = γ φδ The depreciation causes, in turn, expenditure switching (residents buy less foreign goods whereas foreigners buy more domestic goods, which is cheaper for them at the depreciated exchange rate) and an expansion of domestic output, while the domestic interest rate remains the same as the foreign interest rate (ensured by perfect capital mobility), i.e., a shift out of the IS curve, which can be seen from (5): > 0, The overall effect will therefore be: dy ds = δ γ > 0. dy ds ds dm = δ γ γ φδ = φ > 0. This interpretation is illustrated in Figure 4. It is clear from the analytic results as well as from their graphical representation that a monetary expansion under float increases output. Figure 4: Mundell-Fleming Model Monetary Expansion under Float (b) Effectiveness of Monetary Policy as a Stabilisation Tool Summarising the results above, in the original Mundell-Fleming model under perfect capital mobility:. monetary policy is completely ineff ective as a stabilisation tool under a fixed exchange rate regime; 2. but is eff ective under a flexible exchange rate regime. 8