Exercise 3 Short Run Determination of Output, the Interest Rate, the Exchange Rate and the Current Account in a Mundell Fleming Model

Transcription

1 Fletcher School, Tufts University Exercise 3 Short Run Determination of Output, the Interest Rate, the Exchange Rate and the Current Account in a Mundell Fleming Model E212 Macroeconomics Prof. George Alogoskoufis

2 The Mundel Fleming Model A short run Mundell Fleming model of an open economy: Aggregate demand Disposable Income Consumption Function Investment Function Real Government Purchases Taxes net of Transfers Net Exports Function D = C + I + G + NX Y D = Y T C = C + cy D I = I + by di G = G T = T NX = NX x 1 Y + x 2 Y * x 3 S Interest Rate Target of Central Bank Uncovered Interest Parity i = i + e(y Y F 1+ i S = S f 1+ i *!2

3 Definitions of Variables and Parameters D denotes real aggregate demand, Y denotes real aggregate output and income, Y D denotes real aggregate disposable income, C denotes real aggregate private consumption expenditure, I denotes real aggregate gross investment expenditure, G denotes real aggregate government purchases and T denotes real aggregate taxes, net of government transfers, NX net exports, i the domestic nominal interest rate, Y* aggregate real output and income in the rest of the world, i* the nominal interest rate in the rest of the world and S the nominal exchange rate (units of foreign currency per unit of domestic currency and S f is the expected future nominal exchange rate, assumed exogenous. A bar above a letter denotes the autonomous (exogenous component of the corresponding variable, assumed to be positive. c and b denote the marginal propensities to consume and to invest respectively. Both are assumed positive and in addition it is assumed that b+c<1. d>0 is the responsiveness of investment to the nominal interest rate (note that there is a minus sign in front of d. 0 < x 1 < 1 is the marginal propensity to import, 0< x 2 <1 is the marginal propensity to import of the rest of the world, and x 3 > 0 is the responsiveness of net exports to the nominal exchange rate (note that there is a minus sign in front of x 3.!3

4 Definitions of Internal and External Balance Assuming that prices are fixed in the short run, continuous equilibrium in the output market implies that current real output adjusts to aggregate demand to ensure that, Y = D Equilibrium in the money market is maintained through open market operations of the central bank, which adjust the money supply in order to ensure that the nominal interest rate is equal to its target nominal interest rate. e > 0 is the sensitivity of the nominal interest rate to deviations of current output from full employment output Y F. Internal balance is defined as a situation in which Y = Y F, and external balance is defined as a situation in which NX = 0.!4

5 A. Discuss the structure of the model distinguishing between endogenous and exogenous variables, identities, behavioral equations and equilibrium conditions. Endogenous Variables: C, I, NX, Y, i, S Exogenous Variables: G, T, Y*, i*, S f, Y F Behavioral Equations: Consumption Function, Investment Function, Net Export Function, Interest Rate Rule Identities: Definition of Aggregate Demand, Definition of Disposable Income Equilibrium Conditions: Y=D!5

6 B. Using simple algebra solve for the endogenous variables real output Y, the nominal interest rate i, net exports NX and the nominal exchange rate S, as functions of the exogenous variables and the behavioral and policy parameters. Explain your findings. Using the equilibrium condition in the output market, that Y=D,, we get that, Y = C + I + G + NX Substituting the consumption function, the investment function and the net exports function in the right hand side, and solving for Y, we get that output is determined by, Y = 1 C + I + G ct + x 1 c b + x 2 Y * 1 {( di x 3 S} This is the equilibrium condition in the output market, as a function of exogenous variables, the interest rate and the exchange rate. To convert it into an IS curve, we substitute for the exchange rate from the uncovered interest parity condition. We then get, Y = 1 S f C + I + G ct + x 1 c b + x 2 Y * x i * d + x S f 3 1+ i * i This is the open economy IS curve.!6

7 The solution of the model is now straightforward. To determined output and the nominal interest rate we use the open economy IS curve and the interest rate rule of the central bank. This gives the following two equations in two unknowns, Y and i. Y = 1 S f C + I + G ct + x 1 c b + x 2 Y * x i * d + x S f 3 1+ i * i i = i + e(y Y F These two equations determined the equilibrium level of output and the nominal interest rate. These satisfy the equilibrium conditions in the domestic output market, the domestic money market and the foreign exchange market. Having solved for the two key endogenous variables, output Y and the nominal interest rate i, the solution for the rest of the endogenous variables is straightforward. We go to the uncovered interest parity condition, and substituting the solution for the nominal interest rate, we get the solution for the exchange rate. We then substitute the solution for output and the exchange rate in the net exports equation, and get the solution for net exports. Consumption and investment can be determined by substituting the solution for output and the interest rate in the consumption and investment functions.!7

8 C. Depict the determination of equilibrium output, the nominal interest rate, net exports and the exchange rate using an IS-LM-NX diagram and a diagram depicting the uncovered interest parity condition. Explain your findings. Nominal Interest Rate, i,t 0,Y*,i*,S e i=i 0 E i E NX (Y*,i*,S e =0 Y E =Y F Real Output Y!8

9 Nominal Interest Rate, i i 2 >i 0 >i 1 UIP (i*,s e i 2 i 0 i 1 S 1 S 0 S 2 Exchange Rate S!9

10 D. Describe the properties of short run macroeconomic equilibrium in words. Short-run macroeconomic equilibrium in an open economy is determined at the level of output, the domestic interest rate and the exchange rate where, 1. The market for goods and services is in equilibrium, in the sense that aggregate demand equals output (aggregate supply. 2. The domestic money market and international financial markets are in equilibrium, in the sense that the demand for money equals the supply of money and uncovered interest parity holds. If this equilibrium implies full employment, then short run macroeconomic equilibrium implies internal balance. If this equilibrium implies a zero current account, then this macroeconomic equilibrium also implies external balance. In general, short run macroeconomic equilibrium is not characterized by this divine coincidence, and may imply neither internal nor external balance.!10

11 E. Assume that the economy is at a short run equilibrium implying less than full employment and a trade deficit. How can monetary and fiscal policy be used to achieve internal and external balance? Use a diagrammatic analysis. Nominal Interest Rate, i,t 0,Y*,i*,S e i=i 0 i=i 1 i E i E' E E' NX (Y*,i*,S e =0 Y E Y F Real Output Y!11

12 Nominal Interest Rate, i,t 0,Y*,i*,S e i=i 0 i=i 2,T 1,Y*,I*,S e i E NX (Y*,i*,S e =0 E i E' E' Y E Y F Real Output Y!12

13 As shown in the previous two diagrams, a monetary expansion (reduction in the interest rate in the central bank rule will move the economy towards both internal and external balance in this case. If this does not suffice to achieve both internal and external balance (full employment with zero net exports, then a combination of a monetary expansion with a fiscal contraction may do the trick, as in the second diagram. In general, internal and external balance can be achieved in principle through an appropriate mix of monetary and fiscal policy, depending on the initial short run equilibrium. However, in reality, fiscal policy is much less flexible than monetary policy and also subject to political constraints and delays. This is the reason that monetary policy is used much more extensively than fiscal policy in order to stabilize the economy. Yet, there are instances, such as the great recession of that both monetary and fiscal policy has been used. In this exercise we assume that both monetary and fiscal policy can be used under floating exchange rates.!13

14 F. Assume that the economy is at a short run equilibrium implying less than full employment and a trade surplus. How can monetary and fiscal policy be used to achieve internal and external balance? Use a diagrammatic analysis. Nominal Interest Rate, i,t 0,Y*,i*,S e,t 1,Y*,I*,S e i=i 0 i E' E i E NX (Y*,i*,S e =0 E' Y E Y F Real Output Y A fiscal expansion ( T 1 < T 0 or G 1 > G 0 will increase aggregate demand and output and increase interest rates. This will cause an exchange rate appreciation and will bring about an improvement in the trade surplus. If this is not sufficient, it could be combined with an appropriate change in monetary policy that will shift the interest rate rule.!14

15 G. Assume that the economy is at a short run equilibrium implying full employment and a trade deficit. How can monetary and fiscal policy be used to achieve internal and external balance? Use a diagrammatic analysis. Nominal Interest Rate, i,t 0,Y*,i*,S e i=i 0 i=i 1,T 1,Y*,I*,S e i E NX (Y*,i*,S e =0 E i E' E' Y F Real Output Y A monetary expansion ( i 1 < i 0 and a fiscal contraction ( T 1 > T 0 or G 1 < G 0 can leave aggregate demand and output unchanged, but reduce interest rates. This will cause an exchange rate depreciation and will bring about a reduction in the trade deficit, without moving the economy from full employment.!15

16 H. Assume that the economy is at a short run equilibrium implying full employment and a trade surplus. How can monetary and fiscal policy be used to achieve internal and external balance? Use a diagrammatic analysis. Nominal Interest Rate, i,t 0,Y*,i*,S e,t 1,Y*,I*,S e i=i 1 i=i 0 i E' E' i E E NX (Y*,i*,S e =0 Y F Real Output Y A monetary contraction ( i 1 > i 0 and a fiscal expansion ( T 1 < T 0 or G 1 > G 0 will leave aggregate demand and output unchanged, but increase interest rates. This will cause an exchange rate appreciation and will bring about a reduction in the trade surplus, without moving the economy from full employment.!16

17 I. Assume that the economy is at a short run equilibrium implying more than full employment and a trade deficit. How can monetary and fiscal policy be used to achieve internal and external balance? Use a diagrammatic analysis. Nominal Interest Rate, i,t 0,Y*,i*,S e i=i 0,T 1,Y*,I*,S e NX (Y*,i*,S e =0 i E E i E' E' Y F Y E Real Output Y A fiscal contraction ( T 1 > T 0 or G 1 < G 0 will reduce aggregate demand and output, and reduce interest rates. This will cause an exchange rate depreciation and will bring about a reduction in the trade deficit. If this is not sufficient it could be complemented by a shift in the monetary policy rule.!17

18 K. How are you answers to questions E-J modified if the economy has adopted a fixed exchange rate regime? Under fixed exchange rates monetary policy cannot be used. Then fiscal policy is the only remaining policy instrument, unless the country can also revert to a devaluation. In case E, a fiscal expansion can shift the economy towards full employment, but this will cause a widening of the trade deficit. There is a conflict between internal and external balance. A devaluation could resolve this conflict, by reducing the trade deficit. In case F, there is no conflict between internal and external balance for fiscal policy. A fiscal expansion causes both an expansion of output and employment and a reduction in the trade surplus. A possible revaluation may help better achieve internal and external balance. In case G what is needed is a devaluation and a fiscal contraction, to keep output unchanged and reduce the trade deficit. If case H, what is needed is a revaluation (appreciation of the fixed exchange rate and a fiscal expansion to leave output unchanged and reduce the trade surplus. In case I what is needed is a fiscal contraction. The fiscal contraction will reduce the over employment problem and the trade deficit. There is no conflict between internal and external balance. If the fiscal contraction cannot fully achieve both objectives, a devaluation may help. In case J fiscal policy implies a conflict between internal and external balance. What is needed is a fiscal contraction and a revaluation. The fiscal contraction will reduce the over employment problem but will increase the trade surplus. The revaluation will help reduce the trade surplus.!18