Chapter 8 A Short Run Keynesian Model of Interdependent Economies

George Alogoskoufis, International Macroeconomics, 2016 Chapter 8 A Short Run Keynesian Model of Interdependent Economies Our analysis up to now was related to small open economies, which took developments in the rest of the world as given, since they were too small to influence them. In this chapter we analyze a short run Keynesian model of large interdependent economies. This model is a two country variant of the Mundell-Fleming-Dornbusch model, adapted for the global economy. Policies in one country affect macroeconomics developments in both the country itself, and the rest of the world. Thus, they affect the path of the global economy. We assume that the world economy consists of two identical interdependent economies. Global variables such as international interest rates, international inflation and international output and employment levels are determined by the average of the monetary and fiscal policies of the two economies. Differences in monetary and fiscal policy between the two economies determine the nominal and real exchange rate of the currency of each country relative to that of the other, and the corresponding relative interest rates, relative inflation rates and relative output and employment levels. A coordinated global monetary expansion leads to lower global interest rates, a rise in global output and employment and higher global inflation. A coordinated global fiscal expansion leads to a rise in global output and employment and higher global inflation, but also higher global interest rates. If these policies are perfectly symmetrical, then there is no impact on nominal and real exchange rates and the current accounts of the two economies. A unilateral monetary expansion in one country leads to a short-term nominal and real appreciation of its currency against the rest of the world, resulting in a short-term increase in output and employment in the country, an improvement in its current account, but at the expense of output and employment in the other country, which comprises the rest of the world, whose real exchange rate appreciates and whose current account deteriorates. Thus, a unilateral monetary expansion turns out to be a beggar thy neighbor policy, as it causes a rise in output and employment in the economy that undertakes it, at the expense of the rest of the world. A unilateral fiscal expansion in one country leads to a short and long term real appreciation of its exchange rate, an increase in its inflation and international interest rates, an increase in its output

and employment and a deterioration of its current account. The current account deterioration mitigates the effects of the fiscal expansion on output and employment in the economy undertaking the fiscal expansion, and leads to an increase in output and employment in the other country, which comprises the rest of the world. Thus, a unilateral fiscal expansion turns out to be a locomotive policy in the short run, as it expands output and employment in both countries. The international interdependence of economies, and the international spillovers of macroeconomic policies, constitute grounds for coordination of monetary and fiscal policies worldwide, as the unilateral determination of monetary and fiscal policy by each country, does not take account of the spillovers to the rest of the world. The result is the excessive use of beggar thy neighbor policies, which have negative spillovers in the rest of the world, and the excessive avoidance of locomotive policies, which have positive spillovers in the rest of the world. 8.1 A Short Run Keynesian Model of Interdependent Economies There are two interdependent economies, economy 1 and economy 2. The economies are perfectly symmetrical, meaning that they have exactly the same structure. Therefore, all the parameters that characterize them are the same for both economies. 8.1.1 Short Run Macroeconomic Equilibrium in Output, Money and Foreign Exchange Markets Equilibrium in the market for goods and services in economy 1, the IS curve, is defined by, e! y 1 = αg 1 β(i 1 p 1 ) + γ y 2 + δ(s + p 2 p 1 ) (8.1) where y is the logarithm of real aggregate income, p the logarithm of the price level, g the logarithm of the fiscal stance, and i the nominal interest rate. s is the nominal exchange rate, measured in units of the currency of country 1 per unit of the currency of country 2. α,β,γ and δ are constant positive parameters. α denotes the elasticity of aggregate demand with respect to the fiscal stance, and β the semi elasticity of aggregate demand with respect to the real interest rate. A dot over a variable denotes its first derivative with respect to time, and superscript e the expected value of the relevant variable. γ denotes the semi elasticity of aggregate demand in country 1, with respect to the real income of country 2, while δ denotes the elasticity of aggregate demand with respect to the real exchange rate. Equilibrium in the money market, the LM curve is defined by,! m 1 p 1 = y * 1 εi 1 (8.2) where m is the logarithm of the domestic money supply and y* is full employment income, assumed exogenous. (8.2) is based on the permanent income hypothesis. ε is the semi elasticity of money demand with respect to the nominal interest rate.!2

There is perfect capital mobility, and domestic securities are perfect substitutes for foreign securities. As a result, uncovered interest parity holds continuously. This is the equilibrium condition in the foreign exchange market.! i 1 = i 2 + s (8.3) Domestic interest rates may diverge from international interest rates, only to the extent that there are expectations for a change in the exchange rate s. If a depreciation of the exchange rate is expected, domestic nominal interest rates are higher than international nominal interest rates, in order to compensate investors for their expected loss in terms of the domestic currency. Finally, domestic prices are assumed to adjust gradually. The adjustment depends on the difference between current domestic income and full employment income, and is defined by, p 1! = π 1 + λ(y 1 y * 1 ), λ 0 (8.4) where π is the long run inflation rate of economy 1 and λ the speed of adjustment of prices to excess demand in the market for goods and services. (8.4) denotes that the inflation rate deviates from the equilibrium inflation rate to the extent that current income differs from full-employment income. There is a gradual adjustment of the price level to the level that ensures full employment. The real full employment income is exogenous and its logarithm denoted by y*. Equations (8.1) to (8.4) describe economy 1. Economy 2 is absolutely symmetrical, and described by, e! y 2 = αg 2 β(i 2 p 2 ) + γ y 1 δ(s + p 2 p 1 ) (8.5)! m 2 p 2 = y * 2 εi 2 (8.6) p 2! = π 2 + λ(y 2 y * 2 ), λ 0 (8.7) 8.1.2 The Nature of Short Run Macroeoconomic Interdependence There are three channels of macroeconomic interdependence in this model. The first two operate through the market for goods and services, and the third through financial markets. The first channel of interdependence links aggregate demand and output in the two economies, as the real income of each economy affects aggregate demand in the other economy, through the demand for imports and exports (net exports). The second channel of interdependence operates through the real exchange rate. The relative price of goods in the two economies, expressed in a common currency, affects aggregate demand in the two economies through the demand for net exports. Finally, there is financial interdependence, through the foreign exchange market, as the interest rates in the two economies and the nominal exchange rate must satisfy uncovered interest parity. 8.1.3 Solution of the Model: The Aoki Method!3

!!!! George Alogoskoufis, International Macroeconomics, 2016 Ch. 8 Because of the symmetry that characterizes this model, we can analyze the dynamic behavior of the global economy as the sum (average) of the two economies, and the dynamic behavior of economy 1 relative to economy 2, as the difference between the two economies. For each variable x, we define its value that corresponds to the global economy as, x A = 1 ( 2 x + x 1 2 ) For each variable x, we define its value that corresponds to the difference between economy 1 and economy 2, as, x R = 1 ( 2 x x 1 2 ) After we characterize the behavior of the global economy, and the behavior of economy 1 relative to economy 2, we can then characterize the behavior of economy 1 as, x 1 = (x A + x R ) and the behavior of economy 2 as, x 2 = (x A x R ) In this way, we can characterize the dynamic behavior of both economies, and the global economy. 8.2 Macroeconomic Adjustment in the Global Economy The behavior of the global economy is characterized by the average behavior of the two economies. Averaging (8.1) and (8.5), we get the global demand for goods and services, i.e the IS curve for the global economy.! e y A = αg A β(i A p A ) + γ y A (8.8) Because of the symmetry of the two economies, the real exchange rate has no impact on global demand for goods and services, as it only affects the relative demand for goods and services between the two economies. Averaging (8.2) and (8.6), we get the equilibrium condition in the global money market, i.e the LM curve for the global economy.! m A p A = y * A εi A (8.9) Finally, from the average of (8.4) and (8.7) we get the equation for the adjustment of global inflation.!4

p A! = π A + λ(y A y * A ) (8.10) Equations (8.8) to (8.10), describe a short run keynesian model for the global economy. The real exchange rate and current accounts play no role, as the global economy is a closed economy. Assuming rational expectations for expected inflation in (8.8), we substitute (8.10) for expected inflation, and solving for global output we get, 1! y A = (8.11) 1 βλ γ αg β(i π ) βλy * ( A A A A ) (8.11) is the adjusted IS curve for the global economy. It determines the negative relationship between output and the nominal interest rate that maintains short run equilibrium between global savings and global investment. The dynamic path of this short run equilibrium is described in Figure 8.1. From (8.9), the demand for money is a negative function of the nominal interest rate, but independent of current income, as it only depends on permanent income. Thus, the global LM curve is horizontal. In the short-run equilibrium, for a given money supply, real money balances are given, as the price level is predetermined. Gradually, as the price level adjusts downwards, due to the excess supply of goods and services, the global economy moves towards full employment as the horizontal LM curve shifts downwards, and aggregate output and income adjusts along the adjusted IS curve. Starting from an initial price level, say p0, for a given money supply and equilibrium inflation, income is determined at y0 and the nominal interest rate at i0. Gradually, prices fall in relation to the money supply, the LM curve shifts downwards, and income approaches full employment income. The adjustment process could be speeded up, if there was a one-off increase in the money supply, which would have shifted the LM curve downwards immediately, so as to achieve a faster adjustment towards full employment. In this case, a prolonged period of deflation would not be required. The same could be done through a global fiscal expansion, which would have shifted the IS curve to the right, resulting in a faster adjustment towards full employment. In this case, nominal interest rates would not adjust downwards, as in the case of a monetary expansion. 8.3 The Relative Behavior of the Two Economies and the Exchange Rate We next turn to the determination of the dynamic adjustment of economy 1 relative to economy 2. Subtracting (8.5) from (8.1), we get the difference between aggregate demand for goods and services in economy 1, relative to economy 2. This is given by,! y R = αg R β (8.12) 2 (s e 2 p R ) γ y R + δ (s p R )!5

Correspondingly, we get the difference between the money market equilibrium conditions and the price adjustment equations in the two economies.! m R p R = y * R ε (8.13) 2 s p R! = π R + λ(y R y * R ) (8.14) From (8.13), we get that, ( )! s = 2 (8.15) ε m p y * R R R The expected rate of depreciation of the currency of economy 1 relative to economy 2 depends on the relative excess liquidity in economy 1. Substituting (8.12) in (8.14), and assuming rational expectations, we get,! p = π + λ R R (8.16) 1+ γ + λβ αg + β R ε (m p y * * R R R) + δ ( s p R ) y R The solution of the system of the two differential equations (8.15) and (8.16) can be described using a phase diagram. The equilibrium is a saddle point. The exchange rate is a non predetermined variable, which can adjust immediately, and the relative price level is a predetermined variable, which can only adjust gradually. From (8.15), we get that, ( )! s * = 0 p R = m R y R (8.17) From (8.16) we get that, ( ) p = π, p = 1 R R R β + δε δεs + βm + αεg (β + ε)y * R R R (8.18) The system of (8.17) and (8.18) can be used to characterize the phase diagram of the system of the differential equations (8.15) and (8.16), which is analogous to the one of the Dornbusch (1976) model. The equilibrium and the dynamic adjustment are presented in Figure 8.2. It is worth analyzing some of the properties of the long run equilibrium first.!6

First, the long-run equilibrium is characterized by monetary neutrality. A shift in the relative money supply of one country has no real effects. From (8.17) and (8.18) it follows that in the long-run equilibrium (steady state),! dm R = dp R = ds (8.19) A shift in the relative money supply of one country causes an equiproportiane change to the relative price level and the exchange rate of this country. Therefore, the long run real exchange rate is not affected, nor is any other real variable. This long term monetary neutrality is a desirable feature of this model, as it makes it consistent with any general equilibrium monetary model. Second, the steady state equilibrium is a saddle point, since the system of differential equations (8.15) and (8.16) have one positive and one negative eigenvalue. There is a unique saddle path that leads to this steady state, which is depicted in Figure 8.2. The equilibrium is stable because the relative price level is a predetermined variable and the exchange rate is a non predetermined variable. Third, a change in the relative money supply has short-term real effects, as relative price levels cannot adjust immediately, but only gradually, through (8.16). Only the nominal exchange rate, as a nonpredetermined variable can adjust immediately. In Figure 8.3 we analyze both the short and the long term effects of an increase in the relative money supply in economy 1. The initial equilibrium is at point E. An increase in the relative money supply of country 1 moves both (8.17) and (8.18) to the right. The new long-run equilibrium is at point E, where the exchange rate has depreciated by the same rate as the rate of increase of the the relative money supply, and the relative price level of country 1 has increased by the same rate as well. In the short term, the relative price level cannot change. The adjustment of the relative price level to the new equilibrium is gradual. Thus, the exchange rate, from the point of view of country 1, depreciates immediately (at point E0), and the economies begin to adapt along the saddle path which gradually leads to the new long-run equilibrium E. We see that the initial depreciation is higher than the long run depreciation of the exchange rate. The exchange rate overshoots, so that the domestic money market in economy 1 remains in equilibrium. The overshooting of the exchange rate depreciation creates expectations of a future appreciation of the exchange rate, the nominal interest rate of economy 1 falls relative to the nominal interest rate of economy 2, and the relative money supplies in the two economies are willingly held. As the relative price level of economy 1 gradually rises, relative real money supplies gradually fall, and the economies approach a new long run equilibrium with a higher relative price level and a depreciated nominal exchange rate for country 1. Short run output and employment rise in economy 1, if the exchange rate depreciation causes an improvement in the current account of economy 1. This is an assumption that we shall maintain, although one could imagine configurations of the parameters of the model for which this does not hold. Thus, in the case where a depreciation of the real exchange rate leads to a short term improvement of!7

the current account, aggregate demand rises in country 1 not only because of the reduction of the real interest rate, but also because of the real depreciation of the exchange rate. Let us consider what happens to economy 2. The short run nominal and real depreciation of the currency of economy 1 is a nominal and real appreciation of the currency in economy 2. This, immediately reduces aggregate demand in economy 2, and produces a fall in output. The short run increase in output and employment in economy 1 has been achieved partly through a fall of output and employment in country 2. This policy, is often referred to as a beggar thy neighbor policy, as the improvement in output and employment in country 1 has been achieved at the expense of a deterioration of output and employment in country 2. In Figure 8.4 we analyze the impact of a change of relative fiscal stance gr. A relative fiscal expansion in economy 1 creates excess demand, and moves (8.18) to the right. The nominal exchange rate appreciates immediately, and the economy moves from equilibrium E to the new equilibrium E, which implies an appreciation of both the nominal and the real exchange rate. The real appreciation, and the concomitant increase in the real interest rate, partly offsets the short run increase in relative aggregate demand from the fiscal expansion. Part of the increase in aggregate demand shifts to the rest of the world, because of the real appreciation of the exchange rate. Therefore, output and employment rise in both countries, although the effects on the home country mean that output and employment will rise more in country 1 relative to country 2. In the short run, a fiscal expansion is a locomotive policy, as it can raise output and employment in both countries. It should be noted that the fiscal expansion causes a deterioration of the current account of economy 1 and an improvement in the current account of economy 2, because of the shift it causes to the real exchange rate. If initially the two economies were not at the steady state equilibrium E, but at E0, on the saddle path towards E, the relative fiscal expansion causes an appreciation of the exchange rate to E1, and the economies continue to adjust along the new saddle path leading to E. It is worth noting that in case of a relative fiscal expansion there is no overshooting of the exchange rate. There is an initial real appreciation, which is maintained along the new adjustment path. 8.4 Coordinated versus Uncoordinated Macroeconomic Policies There is no guarantee that uncoordinated unilateral monetary and fiscal policies by each country will lead to socially desirable results. The reason is that if each country acts on their own, they will not take into account the international spillovers of their choice of policy. Assume that the world is in an initial position with low output and high unemployment. The optimal global policy would be a coordinated fiscal and monetary expansion that would speed up the convergence of both economies to full employment. If every country acted unilaterally, there is no guarantee that is optimal policy would be adopted at the world level. For example, it could be the case that both countries tilted their policies towards beggar thy neighbor monetary expansions, at the expense of locomotive fiscal expansions. This would be the case if unilateral monetary expansions caused an improvement in the current account, while!8

unilateral fiscal expansions caused a deterioration in the current account, and countries tended to act taking the current account as a policy goal. We shall return to the problem of policy coordination in the context of a model based on better microeconomic foundations that the standard keynesian model, but the general point that in the presence of macroeconomic interdependence uncoordinated policies are not necessarily optimal is a valid point. There is no guarantee that uncoordinated unilateral initiatives by each country with respect to monetary and fiscal policy will lead to socially desirable results. The reason is that no country will take account of the international spillovers of its choice of policy. Thus, when there is international macroeconomic interdependence, it may be useful and necessary to coordinate monetary and fiscal policies between countries. 8.5 Quantitative Simulations of the Model In this section we present a quantitative simulation of the dynamic behavior of the model of two interdependent economies, for specific values of the parameters. This allows us to have a quantitative feel for the interdependence of the two economies and the impact of monetary and fiscal policy of each economy on the economy itself, the rest of the world and the global economy. We also examine the effects of coordinated changes in monetary and fiscal policy at the world level. We assume, as in the theoretical analysis of two interdependent symmetrical economies 1 and 2, that the short-term behavior of the economies is described by equations (8.1) to (8.7). The values of the parameters in the simulation are as follows: α = 0.5, β = 0.5, γ = 0.25, δ = 0.5, ε = 0.5. The logarithm of full employment output is normalized to zero for both economies, as is the logarithm of the initial money supply m, the initial stance g and the initial nominal (and real) interest rate i. Thus, in the simulations we assume that both economies are in an initial equilibrium where the logarithm of all variables is equal to zero. We first examine the dynamic effects of two unilateral policy shifts on the part of economy 1. First, a permanent increase in the money supply by 10%, i.e m1 increased from 0 to 0.10, and second, a permanent 10% fiscal expansion, i.e an increase of g1 from 0 to 0.10. The effects of these disturbances are presented in Figures 8.5 and 8.6, both for each economy and the global economy. As can be seen from Figure 8.5, an increase in the money supply in country 1 causes an immediate nominal and real depreciation of the exchange rate relative to the currency of country 2, which exceeds 10% and an increase in demand and output in country 1. The exchange rate depreciation initially overshoots the steady state depreciation, and the exchange rate subsequently starts appreciating. Thus, following the initial depreciation of the exchange rate there is a process of gradual increase in the price level of country 1, a gradual nominal and real appreciation of the exchange rate, and a gradual return of aggregate demand and output to their steady state levels. In the new steady state the nominal exchange rate has depreciated by 10%, and the price level has risen by 10%. This policy is beggar thy neighbor in the short run. The real depreciation of the currency of economy 1 is equivalent to a real appreciation of the currency of economy 2, leading to an initial reduction in!9

aggregate demand, output and, after a lag, the price level in economy 2. Thereupon, there is a recovery in both output and the price level in economy two, which leads it back to the original steady state. In the new steady state, its exchange rate has appreciated by 10% to compensate for the increase in the foreign price level, but its real exchange rate is unchanged. The increase in the money supply in country 1 causes a short run expansion of global output, as the increase in real output in country 1 exceeds the reduction of real output in country 2. It also causes a short run reduction in the world nominal interest rate, and a gradual increase in the world price level by 5%, equivalent to the percentage increase in the world money supply. In Figure 8.6 we depict the effects of a 10% fiscal expansion in economy 1. This causes an immediate nominal and real appreciation of its currency relative to the currency of economy 2. This appreciation of the real exchange rate causes a fall in net exports which mitigates the effects of the fiscal expansion on aggregate demand and output in country 1. Aggregate demand and output expand by less than 5%. Because an exchange rate appreciation in country 1 is equivalent to an exchange rate depreciation in country 2, this policy leads to an increase in aggregate demand and output in economy 2 as well, because of the improvement in its own net exports. Because of the expansion of current real output and employment, the price level starts rising in both countries, while the world real interest rate starts rising as well, to compensate for the increase in global aggregate demand and restore equilibrium between global savings and investment. In the new steady state, the nominal and the real exchange rate of economy 1 has appreciated by 5% in order to offset the impact of the fiscal expansion on aggregate demand in country 1. This policy is locomotive in the short run, as it results in a short run expansion of output and employment in the rest of world. In the new steady state, aggregate output has returned to full employment in both countries, but economy 1 has an overvalued real exchange rate, running a persistent current account deficit relative to country 2. Thus, this equilibrium may not be sustainable in the steady state. In addition, global nominal and real interest rates have risen in order to ensure the reduced global savings are equal to global investment. Thus, a fiscal expansion may crowd out global private investment in the steady state. In Figures 8.7 and 8.8 we consider the effects on each country and the global economy of coordinated monetary and fiscal expansions, which are shared between the two countries. Such policies do not affect either the exchange rate or the current account, as they maintain perfect symmetry between the two countries. 8.6 Conclusions about Short Run Macroeconomic Interdependence In this chapter we have analyzed a short run Keynesian model of the global economy. We assumed that the world economy consists of two identical interdependent economies. Global variables, such as international interest rates, international inflation and global output and employment are determined by the average of the monetary and fiscal policies of the two economies.!10

Differences in monetary and fiscal policy between the economies determine the nominal and real exchange rate of each country's currency relative to the rest of the world, and the corresponding national nominal and real interest rates, inflation rates and levels of output and employment. A global monetary expansion leads to an increase in global output and employment in the short run, and temporarily higher international inflation. A global fiscal expansion leads to an increase in global output and employment in the short run, temporarily higher inflation and higher nominal and real interest rates. A unilateral monetary expansion in one country leads to short run nominal and real appreciation of its currency vis-a-vis the rest of the world, resulting in a short increase in its output and employment, an improvement in its current account and a temporary increase in inflation. However, this policy may be beggar thy neighbor in the short run, as it could reduce output and employment in the rest of the world. A unilateral fiscal expansion in one country leads to a short term and long term real appreciation of the exchange rate, a deterioration in its current account, a temporary increase in inflation, and an increase in international nominal and real interest rates. The appreciation of the exchange rate mitigates the impact of the fiscal stimulus the domestic economy, leading to an increase in aggregate demand and output in the rest of the world. In this sense, a unilateral fiscal expansion is a locomotive policy as it increases output and employment in both the country undertaking it, but also in the rest of the world. The short run international macroeconomic interdependence of economies is an important reason for the coordination of monetary and fiscal policies, as the unilateral non coordinated determination of monetary and fiscal policy by each country does not take into account spillovers to the rest of the world. The analysis has also highlighted the disadvantages of short run keynesian models, particularly with respect to fiscal policy, the balance of payments and aggregate investment. These models ignore the inter-temporal aspects of macroeconomic policy, fiscal policy in particular, and the relationship between short-term imbalances and stocks such as the aggregate capital stock and public and external debt of a country. Such a failure can be corrected with the use of long term models, based on the intertemporal approach.!11

Figure 8.1 The Adjustment Path of Global Output, Inflation and Nominal Interest Rates i A IS' IS i 0 0 LM 0 i E E LM E y 0A y* A y A!12

Figure 8.2 The Adjustment Path of the Nominal Exchange Rate and Relative Price Levels s s=0 p R =0 E 45º p R!13

Figure 8.3 The Effects of a Permanent Increase in the Money Supply in Country 1 s s=0 p R =0 Ε 0 E E 45º p R!14

Figure 8.4 The Effects of a Permanent Fiscal Expansion in Country 1 s s=0 p R =0 Ε 0 E Ε 1 E 45º p R!15

Figure 8.5 The Effects of a 10% Increase in the Money Supply in Country 1!16

Figure 8.6 The Effects of a 10% Fiscal Expansion in Country 1!17

Figure 8.7 The Effects of a Coordinated 5% Increase in the Money Supply in both Countries!18

Figure 8.8 The Effects of a Coordinated 5% Fiscal Expansion in both Countries!19

References Aoki M. (1981), Dynamic Analysis in Open Economies, New York, Academic Press. Dornbusch R. (1976), Expectations and Exchange Rate Dynamics, Journal of Political Economy, 84:pp. 1161-76. Mundell R. (1963), Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates, Canadian Journal of Economics and Political Science, 29: pp. 475-85.!20