International Finance Lecture 4 Autumn 2011 The Mundell Fleming Model The Mundell Fleming Model is a simple open economy version of the IS LM model. I. The Model A. The goods market Goods market equilibrium in the IS LM model is characterised graphically by the IS curve. In this section I derive an open economy version of the IS curve. I assume that there is a single home good and a single good produced by the rest of the world. The home currency price of the home good is denoted by P and the foreign currency price of the foreign good is denoted by P*. I assume that both of the prices are constant and, as we can pick the units that the home and foreign goods are measured in, we can assume that both are equal to one. I will denote the exchange rate by e and interpret it as the home currency price of foreign currency. This is how it is usually defined in the economics literature. This means that we have: Floating exchange rate Fixed exchange rate e goes up depreciation devaluation e goes down appreciation revaluation a. The national accounting identity and the law of one price The national accounting identity for an open economy is (1) Y = C + I + G + X, Where X is net exports, or exports minus imports. In the closed economy version with a fixed price, P, normalised to one, it did not matter whether we thought of the variables as being measured in units of the good or in the home currency value of the good. Here we will be explicit and say that it is measured in units of the home good. I assume that the Law of One Price holds. The Law of One Price The law of one price says that goods should cost the same amount, whether you buy them in home currency or convert the home currency into foreign currency and buy them with foreign currency. As an example, if a sweater sells for 100 at Harrods and the pound is worth two dollars, then the same sweater at Saks Fifth Avenue should cost $200. Of course trade restrictions and transportation costs mean that this is not always true so the law is more of a rule of thumb. More generally, we can express the law of one price at p = ep*, where p is the home currency price of a good, e is the exchange rate, expressed as the homecurrency price of foreign currency and p* is the foreign currency price of a good.
b. net exports The value of net exports in terms of home currency is equal to the value of exports in terms of home currency minus the value of imports in terms of home currency. The value of exports in terms of home currency is equal to P times the volume of exports. The value of imports in terms of home currency is equal to the home currency price of the foreign good multiplied by the volume of imports. By the law of one price the home currency price of the foreign good is equal to the exchange rate times the foreign currency price. Thus, the value of imports in terms of home currency is ep* times the volume of imports. So, dividing through by P, we have that the volume of net exports (X) is equal to the volume of exports minus (ep*/p) times the volume of imports. Since P = P* = 1 we have that X = volume of exports e x volume of imports. We can also interpret X as X = foreign demand for home goods e x home demand for foreign goods. I assume that X is a function of Y and e. I further assume that the foreign demand for home goods is not a function of Y and that an increase in Y increases the home demand for foreign goods. Thus, X is a decreasing function of Y. We have that ep*/p = e is the relative price of foreign goods in terms of home goods. Thus an increase in e (a depreciation or devaluation) causes the foreign demand for home goods to go up and the home demand for foreign goods to go down. However, it does not necessarily cause e times the home demand for foreign goods to go down. This depends on the elasticity of demand for foreign goods with respect to the price. So it is not clear if X goes up or down. This ambiguity led to a huge literature that tested whether devaluation causes net exports to go up or down. The conclusion was that in the very short run demand does not respond much to devaluation and the direct effect of the change in the exchange rate dominates: devaluation worsens the trade balance. However, after some time, demand responds sufficiently that the trade balance improves. This phenomenon is called a J Curve. I assume here that an increase in e improves the trade balance. Thus we have: (2) X = X(Y,e), X Y < 0, X e > 0. c. equilibrium in the goods market Substituting (2) and the assumptions I made about C and I in the last lecture into equation (1) yields (3) Y = C(Y) + I(r) + G + X(Y,e). I will continue to graph this with Y on the horizontal axis and r on the vertical axis. Given G, we will have a different IS curve for every value of e. An expansionary fiscal policy (an increase in G) shifted the IS curve out. So, an increase in e (since it increases X) also shifts the IS curve out. B. The money market
Only domestic residents hold money and home residents do not hold foreign money. Thus the condition for money market equilibrium is the same as in the previous lecture. The LM curve has the same properties as in Lecture 3. C. Uncovered interest parity Denote the world interest rate by r*. It is assumed that the home country is small in the sense that it takes the world interest rate as given. Both home and foreign investors hold home and foreign bonds. I assume that they care solely about their expected return from holding these bonds. An investor can take one unit of home money and invest in a home bond. At the end of the period he gets 1 + r units of home money. Alternatively, he can take one unit of home money, exchange it for 1/e units of foreign money and invest it in a foreign bond. At the end of the period he will have (1 + r*)/e units of foreign money. He can exchange this for (1 + r*)(e /e) units of home money, where e is the end of period exchange rate. I assume that investors have myopic, or adaptive, expectations. They expect that the end of period exchange rate will be the same as the current exchange rate. Thus their expectation of e is that it equals e and they expect they will get 1 + r* units of home currency if they invest in home bonds. Thus, for investors to be willing to hold both home and foreign bonds it must be true that 1 + r = 1 + r*, or that r = r*. Graphically we have: If the home interest rate is greater than the world interest rate, all investors would want to hold only home bonds and all of the world s capital would be on the verge of flowing into the home country: a balance of payments surplus. If home interest rate is less than the foreign interest rate then no investor would want to hold home bonds and all of the capital in the home country would be on the verge of flowing out: a balance of payments deficit. II. Floating Exchange Rates
A. Equilibrium with floating exchange rates When the exchange rate floats we want to find the combination (Y,r,e) such that the goods market clears (equation (3)), the money market clears (4) M = L(Y,r) and there is balance of payments equilibrium: (5) r = r*. That is, we want to find a value of e such that all three curves (the IS curve, the LM curve and the BP curve) intersect. If there were just two curves it is easy to see how they would intersect, but how do we get all three to intersect? Suppose that they do not: In the above picture, the intersection of the IS and LM curves occurs at an interest rate that is greater than the world interest rate: r > r*. I assume that the exchange rate adjusts to keep r = r*. I assume: If r > r* (there is a balance of payments surplus), e (the exchange rate appreciates) If r < r* (there is a balance of payments deficit), e (the exchange rate depreciates). We have that e (the exchange rate depreciates) implies the IS curve shifts in. e (the exchange rate appreciates) implies the IS curve shifts out. So, the exchange rate changes in the way that causes the IS curve to shift so that it intersects with the other two curves. In the above case the exchange rate depreciates and the IS curve shifts in to intersect with the LM and BP curves.
B. Monetary policy with floating exchange rates The only curve that depends on M is the LM curve. An expansionary monetary policy (an increase in M) shifts the LM curve out. This is seen to the right. The new intersection of the IS and LM curves is at an r < r*. Thus we are in the region of balance of payments deficit and the exchange rate depreciates. This causes the IS curve to shift out until it intersects with the new LM curve and the BP curve. This is seen in the figure below. Thus, an expansionary monetary policy causes output to go up, the exchange rate to depreciate and the interest rate to remain unchanged. Consumption goes up because output goes up and investment is unchanged because the interest rate is unchanged. What happens to net exports? The increase in output tends to decrease net exports and the depreciation tends to increase net exports. However we have that Y C = I + G + X. Both Y and C go up, but because the marginal propensity to consume is less than one we have that Y C goes up. So, I + G + X must go up. I and G are unchanged, so X must go up. The story can be told in words. An expansionary monetary policy causes excess supply in the money market and the interest rate declines to clear the money market. The decline in the interest rate
leads to a balance of payments deficit and the exchange rate depreciates to restore balance of payments equilibrium. The depreciation of the exchange rate causes net exports to rise and output must rise to restore goods market equilibrium. C. Fiscal policy with floating exchange rates An expansionary fiscal policy is an increase in G. The only curve that depends on G is the IS curve and it shifts out. This is seen in the figure below. The intersection of the LM and new IS curve is now in the region of balance of payments surplus and the exchange rate appreciates, shifting the IS curve back to its original position. Thus, an expansionary monetary policy with a floating exchange rate is ineffective. Both the interest rate and output are unchanged. Thus, consumption and investment are unchanged. If output, consumption and investment are unchanged and government spending goes up, then by equation (1), net exports must go down by the amount that government spending goes up. An expansionary fiscal policy has no effect on output: the government spending just crowds out net exports. III. Fixed Exchange Rates A. Equilibrium with fixed exchange rates Suppose that the government pegs the exchange rate at e. Suppose as before that the three curves did not intersect. This is seen in the figure below. In this figure, the intersection of the IS and LM curves occurs at an interest rate that is greater than the world interest rate: r > r*. As before, if the government does not act, the exchange rate will appreciate. To keep the exchange rate from appreciating the central bank intervenes in the foreign exchange market, selling home currency and buying foreign currency. This causes the home money supply to expand and the LM curve shifts out until the three curves intersect.
We have the following rules: If r > r* the central bank intervenes, selling home money and buying foreign money. Thus, M and the LM curve shifts out. If r < r* the central bank intervenes, buying home money and selling foreign money. Thus, M and the LM curve shifts in. With floating exchange rates the exchange rate adjusts so that the IS curve moves so that all three curves intersect. With fixed exchange rates the money supply adjusts so that the LM curve moves so that all three curves intersect. B. Monetary policy with fixed exchange rates The only curve that depends on M is the LM curve. An expansionary monetary policy (an increase in M) shifts the LM curve out. This is seen to the right. This is seen below.the new intersection of the IS and LM curves is at an r < r*. Thus we are in the region of balance of payments deficit and the central bank must intervene to keep the exchange rate from depreciating. This causes the LM curve to shift back to its original position. This is seen in the figure below. Output is unchanged. The only thing that happens is reserves
fall. If the government runs out of reserves doing this then it can no longer maintain the fixed exchange rate. This is a fundamental result in international finance. A country with internationally mobile capital and a fixed exchange rate cannot follow an independent monetary policy. This is clear from equations (3) (5). We have three equations to solve, so there must be three endogenous variables. If e is fixed, then one of the variables that was exogenous in the floating case must be endogenous in the fixed regime. G cannot adjust as quickly as M so it is natural to think of M as the new endogenous variable. C. Fiscal Policy with Fixed Exchange Rates An expansionary fiscal policy is an increase in G. Only the IS curve is affected by a change in G and it shifts out as seen below: : The new intersection of the IS and LM curves is in the region of balance of payments surplus. According to our rule, this causes the central bank to intervene by buying reserves and selling its own currency. This causes the LM curve to shift out. The outcome is that Y goes up, r is unchanged, C goes up, I is unchanged, and reserves rise. Because Y goes up, X goes down.
D. Devaluation with Fixed Exchange Rates Suppose that the central bank increases (devalues) the fixed exchange rate. By equations (3) (5), we know only the IS curve is affected. The IS curve shifts out as seen below: The new intersection of the IS and LM curves is in the region of balance of payments surplus. According to our rule, this causes the central bank to intervene by buying reserves and selling its own currency. This causes the LM curve to shift out. The outcome is that Y goes up, r is unchanged, C goes up, I is unchanged, and reserves rise. Because Y goes up and I is unchanged, X goes up. (See equation (3))