# The Mundell-Fleming model revisted.

I. Introduction

As a result of awarding the 1999 Nobel Prize for Economics to Robert Mundell, one of his major contributions, the Mundell-Fleming model, has become a focus of attention. Because of the expansion in international trade and the globalization of international finance, many developing and transitional economies in the world are facing the problem of choosing an appropriate exchange rate regime. In light of the improvement in international capital mobility, many small countries are choosing a pegged (fixed) exchange rate system. As pointed out in Mundell (1963) and Fleming (1962), when a small country tries to maintain a fixed exchange rate in a world of perfect capital mobility, money stock becomes endogenous. This result renders the monetary policy completely ineffective as a stabilization policy instrument.

Why would many small developing and transitional economies choose a fixed exchange rate system in a world dominated by globally floating key currencies? There are many pros and cons, but one fundamental reason may be that the lack (or backwardness) of financial institutions and securities markets makes the execution of the monetary policy ineffective. This situation leaves fiscal policy as the only remaining powerful policy instrument in a fixed exchange rate system. Thus, the understanding of policy effectiveness in an open economy becomes a very important part of any macro and international economics teaching.

This paper first investigates the key role the Mundell-Fleming model plays in the analysis of open economy stabilization policies in most of the major upper-division macro and international economics textbooks. Different models presented in these textbooks are compared. Most models are of the standard IS-LM framework in the original Mundell-Fleming fashion in the (y, i) plane, with y and i being income and the interest rate, respectively. N. G. Mankiw (2000) presents an innovative approach in the (y, e) plane, where e represents the exchange rate, instead.

The major motivation for this synthesis of the Mundell-Fleming model is that, in spite of Mankiw's innovative approach, his conclusion that fiscal expansion has no effect on the trade balance is counter to that of all other texts. Moreover, his unique contribution of adding a trade restriction policy needs further clarification. This is because trade restriction policies may not improve the trade balance under certain circumstances. This situation is clearly evidenced by the experiences of some rapidly expanding Asian countries before the 1997 Asian Crisis. These countries chose to peg their exchange rates to the U. S. dollar, adopted fairly restrictive import policies and experienced amazing GDP growth until 1997, but maintained huge sizes of current account deficits throughout the expansion period as shown in Table 1 below.

This paper first surveys most of the current major macro and international textbooks and presents three major approaches by Dorsbusch/Fisher/Startz, Blanchard, and Mankiw, respectively. Then, a synthesized Mundell-Fleming model is constructed. It is generally believed that trade restriction policies will improve the trade balance. With this model, a necessary condition for such desired effect is derived.

II. Survey of Macro and International Economics Textbooks

The Mundell-Fleming model uses the Hicksian IS and LM framework to analyze the effectiveness of fiscal and monetary policies for small countries under fixed and flexible exchange rates with the assumptions of perfect capital mobility. The analysis belongs to the domain of open macroeconomics as well as international economics. The first appearance of this model in a book was Mundell's (1968) Chapter 18 on capital mobility and stabilization policy under fixed and flexible exchange rates, adapted from his original article (Mundell, 1963). Other major advanced books such as Obstfeld and Rogoff's Foundations of International Macroeconomics (Obstfeld and Rogoff, 1996), present it as the Mundell-Fleming-Dornbusch Model. However, our emphasis in this paper is on the treatment of the Mundell-Fleming model in undergraduate macro and international economics. With this specific focus of the study, Dombusch's Open Economy Macroeconomics (1980) would be too difficult for undergraduate students, even though it provides the most advanced treatment of the Mundell-Fleming model. In this paper, fourteen major macro and international economics textbooks are examined. Surprisingly, six of them (Abel and Bernanke 1998, Barro 1997, Farmer 1999, Gordon 2000, Hall and Taylor 1997, and Krugman and Obstfeld 2000) did not even cite Mundell's contributions, and none of them has analyzed the problem.

Auerbach and Kotlikoff (1998) argues that in a small open economy the IS curve is virtually horizontal which renders the fiscal policy completely ineffective. Thus they argue in favor of a flexible exchange rate regime under which monetary policy is effective.

Baily and Friedman (1995) use the basic IS-LM diagram to discuss the macroeconomic policy in an open economy strictly in terms of a floating exchange rate system. Dombusch, Fischer, and Startz (1998, pp. 283-293) present the essence of the Mundell-Fleming model by arguing that even though later research has refined the Mundell-Fleming analysis, the initial formulation remains intact for the purpose of understanding the basic policy effects under a regime of high capital mobility. With perfect or near perfect capital mobility, the balance of payment (BP) will be at equilibrium at the world interest rate, i.e., BP = 0 at i = [i.sub.f], where i and [i.sub.f] represent the domestic and the foreign (world) interest rates, respectively. Then the standard model will neatly demonstrate that a deviation of domestic interest rate from the world rate due to the monetary expansion (contraction) will create a pressure on currency depreciation (appreciation) through capital outflow (inflow). In order to eliminate this pres sure, a subsequent monetary contraction (expansion) policy will have to be taken. This makes the monetary policy completely ineffective. On the contrary, the fiscal policy is effective under the fixed exchange rate system. Analytically, the monetary policy would regain its independence and become an effective policy under the flexible exchange rate system. Using only the basic tools of the IS-LM analysis, the presentation of Dornbusch, Fischer, and Startz (1998) is actually very appropriate for the undergraduate students in terms of its simplicity.

Froyen (1999) devotes one whole chapter on monetary and fiscal policies in an open economy and states that the chapter is strictly fashioned after the Mundell-Fleming model. However, Froyen provides a neat addition for the case where capital mobility is imperfect so that the BP = 0 curve is upward sloping. (1) He then analyzes the monetary and fiscal policies under such a condition. In the second half of the chapter, the standard Mundell-Fleming small country with perfect capital mobility situation is analyzed.

Blanchard (2000) presents a unique extension of the Mundell-Fleming model. (2) He introduces simple, but very clear, financial investor arbitrage behavior that seeks the highest global expected rate of return so that, at the equilibrium, the interest parity condition (3) must hold. Thus, his general open economy model consists of IS, LM, and the interest parity condition. His fixed exchange rate case will transform the interest parity condition to the condition requiring i = [i.sub.f] and is equivalent to Mundell-Fleming's small country with perfect capital mobility. In other words, the Mundell-Fleming fixed exchange rate case is a very special case in Blanchard's general framework.

In his latest edition, Mankiw (2000) presents a Mundell-Fleming model in the (y, e) plane instead of the traditional IS-LM framework in the (y, i) plane. He calls his model the [IS.sup.*] -[LM.sup.*] model. Since the [LM.sup.*] function is independent of the exchange rate, and with the i = [i.sub.f] condition of perfect capital mobility, a unique level of GDP is obtained from the [LM.sup.*] function M/P = L([i.sub.f], y). The advantage of the Mankiw approach is that the exchange rate, instead of the interest rate, appears explicitly on the vertical axis. This result makes it easier for students to understand the role of the exchange rate, e. He also presents in his framework the effect of trade restriction policies vastly ignored by all others.

In major international economics textbooks, the analysis of external balance, i.e., BP = 0, plays a major role. In general, BP (y, i) = 0 is an upward-sloping function (curve) because as y increases, the current account balance (especially the trade balance) worsens so that BP = 0 resumes only when a higher domestic interest rate, i, attracts capital inflow to offset the deficit. Moreover, the interest sensitivity of international capital flow (i.e., the interest elasticity of BP = 0) can be greater or less than that of the LM function (curve). Lindert and Pugel (1996) and Salvatore (2001) present cases where the BP = 0 curve is steeper than the LM curve, flatter than the LM curve, or is horizontal. Under the fixed exchange rate, as the BP = 0 becomes flatter, the effectiveness of fiscal policy as a stabilization policy will increase. This situation is exactly the case in the Mundell-Fleming model. Appleyard and Field (2001) add another extreme case where BP = 0 is completely interest inelastic (i.e., the BP = 0 curve is vertical). In this case there is a complete capital immobility such that there is only one level of GDP which is commensurate with BP = 0. Thus, any fiscal expansion will create a balance of payments deficit, and the money supply will contract until the original y is restored again. In contrast to the Mundell-Fleming case, the fiscal policy is completely ineffective.

It is clear from this survey that the original contribution of Mundell and Fleming has become a very special case of a general model in most international economics textbooks. Of course, Froyen and Blanchard also generalized the model in their books. In this paper, attention will be focused on the original contribution, i.e., the horizontal BP, as most macroeconomics textbooks do.

III. The Formal Analysis of Various Models

As previously mentioned, all models are based on the Hicksian IS and LM functions for a closed economy. Now, in an open economy with the exchange rate, (e.) (4), playing a central role, one extra equation is needed to complete the model. This requirement is the balance of payments (BP) in most cases, except for the interest parity condition in the Blanchard model.

In general, the following forms of IS and LM functions are used.

IS: y = C(y - T) + I(i) + G + NX(y, [y.sub.f], e) (1)

LM: M/P = L(y, i) (2)

(a) Dornbusch, Fischer, and Startz:

The model strictly follows the assumption of a small country with perfect capital mobility so that BP = 0 at i = [i.sub.f]. i.e., there will not be equilibrium in the balance of payments unless the domestic interest rate equals the world rate. The perfect mobility of capital will guarantee this condition.

BP: i = [i.sub.f] (3)

Figure 1 illustrates these equations.

(b) Blanchard

Blanchard's model involves slightly modified (1) and (2). He makes explicit the income effect of investment and the homogeneity of the money demand function.

IS: y = C(y - T) + I(y, i) + G + NX(y, [y.sub.f], e) (la)

LM: M/P = yL(i) (2a)

The interest parity condition: e = [e.sup.e]/(1 + i - [i.sub.f]) (4)

The important modification is his inclusion of the impact of GDP on investment. This modification makes it possible for the discussion of the policy effect on investment. Equation (4) indicates a negative relationship between the interest rate and the exchange rate. Blanchard discusses the policy effects in his general model where e is flexible, treating the fixed exchange rate with perfect capital mobility as a special case within the general model. Thus, with fixed exchange rate e, [e.sup.e] = e, and (4) becomes

i = [i.sub.f] (3)

This result is demonstrated in Figure 2.

(c) Mankiw

Mankiw's IS function is slightly different from (1) above. His trade balance is expressed as NX = NX(e), with y and [y.sub.f] being excluded. The investment function is I = 1(i), and again without y. Thus, the system consists of:

IS * y = C(y-T) + I(i) + G+NX(e) (1b)

LM * M/P = L(y, i) (2)

BP i = [i.sub.f] (3)

This makes Mankiw's analysis unique in that IS * and LM * are functions of y and e after (3) is being substituted into (ib) and (2), even though LM * is independent of e. From (3) and (2) and given M/P, y is uniquely determined. Further, with (3) and the uniquely determined y, (ib) will yield the equilibrium level for e.

Given the fixed exchange rate, e, and i = [i.sub.f], as soon as G changes, y will change so that M/P has to change to meet the changed demand for money. The money supply is endogenous in the sense that the central bank loses its control over the money supply. This is illustrated in Figure 3.

IV. Fiscal Policy and the Trade Restriction Policy under the Fixed Exchange Rate Revisited

It is unanimously agreed that under a flexible exchange rate system, monetary policies are effective while fiscal policies are not. Under the fixed exchange rate system, the condition under which fiscal policy can be effective in affecting the level of GDP is also agreed upon by all economists. To illustrate this point, first the standard IS-LM model, as illustrated in Figure 1, is used. As G increases, the IS curve shifts to the right by the full size of the multiplier. The corresponding upward pressure of an expansion in government expenditures on the domestic interest, i, will result in i > [i.sub.f] which will attract foreign capital. The domestic currency will appreciate as a consequence of the capital inflow. Under the fixed exchange rate system, the central bank has to purchase the foreign currency with the domestic currency to prevent the exchange rate appreciation. This operation will increase the money supply and the LM curve will shift to the right until i = [i.sub.f] is restored.

In Mankiw's model (Figure 3), the expansionary fiscal policy raises e, i.e., an appreciation, so that under the fixed exchange rate, e, the money supply has to increase to move [LM.sub.1] rightward to [LM.sub.2] However, there has been some disagreement about its effect on the trade balance. Since expansions in government spending essentially have the full multiplier effect due to the reinforcing monetary expansion, so that i = [i.sub.f], all other authors argue that the trade balance would worsen because NX is a negative function of y. But, in Mankiw's model NX = NX(e) so that under the fixed exchange rate [DELTA]e = 0, implying that there will be no change in the trade balance. (See Mankiw p. 328.) Mankiw asks students to reconcile this difference in his problem 4, p. 341, by assuming NX(y, e).

Mankiw is the only one who treats the effect of import restrictions in the Mundell-Fleming model. Under the fixed exchange rate system, an import restriction creates an increase in trade balance initially, so that it will have a positive effect on output y, similar to that of a fiscal expansion. Since e = e, Mankiw concludes that the trade balance increases. His argument is that since i = [i.sub.f], I = I, while S increases because of the increase in y. Therefore, NX = (S - I) increases. Mankiw has claimed that the trade restriction does not affect the trade balance under the flexible exchange rate system. (5)

V. A Synthesis

In this section, a synthesis is attempted for a small country with perfect capital mobility. This synthesis is a static general equilibrium model with assumptions following the original Mundell-Fleming framework. We begin with (la), (2), and (3):

y = C(y - T) + I(y,i) + G + NX(y,[y.sub.f],e) (la)

M/P = L(y,i) (2)

i= [i.sub.f] (3)

Equation (la) includes the effect of y on I. The NX function also includes y as a variable.

Let [gamma] = [partial]I/[partial]y > 0 be the marginal propensity to invest, [theta] = [partial]NX/[partial]y < 0 be the marginal negative trade balance effect (due to the marginal propensity to import), and [alpha] = [partial]S/[partial]y > 0 be the marginal propensity to save.

This synthesis seems to be a minor integration of all three models above, but it will be very useful to analyze the Mankiw trade restriction policy.

As we know, under the fixed exchange rate system the fiscal policy variable, dG or dT, is effective in changing the GDP, or y. Suppose that a fiscal expansion has created an increase in GDP by the size of dy. Then, saving increases by [alpha]dy, investment increases by [gamma]dy, and the trade balance decreases by [theta]dy.

The experience of the emerging economies in Asia before the 1997 Asian Crisis can be used as an illustration of the effect of a fiscal expansion. These Asian countries had maintained pegged (fixed) exchange rate systems and had provided avenues conducive to high capital mobility in order to attract foreign capital. Fiscal expansions have stimulated domestic investments, but huge trade deficits were created because the marginal propensity to save, [alpha], was smaller than the marginal propensity to invest, [gamma], such that dNX = dS - dI = ([alpha] - [gamma])dy < 0. As long as foreign capital inflows continued, growth was sustainable and the big bubble economies were created; however, as soon as capital inflows reversed their direction to become dramatic capital outflows, the economies started to collapse. The Asian Crisis was born (Fan and Fan 1999). Table 1 shows that every year during the booming fixed exchange rate period (from 1990 to the first half of 1997), the NIES all had sizable current account deficits. Then in July of 1997, the run on the Asian currencies collapsed the fixed exchange rate system. After 1997, all current accounts showed sizable surpluses. This is because [alpha] > y (i.e., I < S) so that NX > 0 and a flexible exchange rate has been in effect.

Trade restriction has been a favorite policy instrument of many smaller developing economies. Suppose some trade restriction (import restriction) policies are imposed. Under the fixed exchange rate system with capital mobility, Mankiw concludes that the initial increase in trade balance (due to import reduction) shifts the IS * curve upward and increases the domestic interest rate level, I > [i.sub.f] and e will appreciate. The central bank has to restore i = [i.sub.f] by a monetary expansion so that eventually e = e. The GDP and the trade balance increase. His argument is that an increase in y and the corresponding increase in savings; S(y) while i = [i.sub.f] would imply that I = I ([i.sub.f]), thus, dNX = [dS(y) - d I([i.sub.f])] > 0. (See Mankiw p. 327.) However, unless there is a total ban on a nation's foreign imports, as y increases the marginal propensity to import will worsen the trade balance. Mankiw's conclusion is true in this case because of his extremely restricted NX = NX(e) trade balance equation.

We have derived a more general conclusion in our synthesized model in that although the initial trade restriction policy will create a trade surplus to boost the GDP, whether dNX > 0 or < 0 will depend upon whether the marginal propensity to save exceeds the marginal propensity to invest, i.e., [alpha] > [gamma] or [alpha] < [gamma]. Thus, Mankiw's conclusion would be true only when the marginal propensity to save exceeds the marginal propensity to invest, i.e., [alpha] > [gamma].

VI. Summary

A synthesis of the Mundell-Fleming model, incorporating the income effect on the investment function and the trade balance function, has enabled us to present a simple but important necessary condition which states that in order for an expansionary fiscal policy and a trade restriction policy to have worsening effects on the trade balance, the marginal propensity to save has to be less than the marginal propensity to invest, i.e., [alpha] < [gamma].

The importance of this synthesis can also be seen from the fact that Mankiw concluded that under a fixed exchange rate system, the expansionary fiscal policy does not have any effect on the trade balance because dNX(e) = 0. However, this conclusion contradicts his statement that as y increases, NX(e) = (S - I) > 0 (Mankiw p. 327). In a comparative static model, (S - I) > 0 always implies that net exports have to be positive. In our synthesis, as long as [alpha] < [gamma], the trade balance worsens when an expansionary fiscal policy is undertaken. Thus, Mankiw's conclusion that an expansionary fiscal policy does not change the trade balance is true only when [alpha] = [gamma] is assumed.

The analysis here is carried out for small open economies with perfect capital mobility under a fixed exchange rate regime. Today, many small emerging economies have indeed tried to peg their exchange rates to the U.S. dollar or to other key currencies in order to increase the capital mobility and attract foreign capital inflows to stimulate their economic growth.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Notes

(1.) A simple explanation for the BP curve's being upward sloping is that as income, y, increases, the trade balance worsens such that for BP = 0, the domestic interest, i, has to be higher to attract capital inflows (or reduce capital outflows).

(2.) He states that his model keeps the spirit, but differs in its details from the original Mundell-Fleming model. (Blanchard p. 381)

(3.) The interest parity condition is: i = [i.sub.f] + ([e.sup.e] - e)/e, or e = [e.sup.e]/(1 + i - [i.sub.f]). i is the domestic interest rate, [i.sub.f] is the foreign interest rate, e is the exchange rate, and [e.sup.e] is the given expected depreciation of the exchange rate. This formula omitted a third cross-product term whose order of magnitude is small. However, if the interest/inflation differentials are large, this omitted term may be significant. (See Krugman and Osbtfeld 2000, P. 361.)

(4.) e, the exchange rate is a unit of foreign currency in U.S. dollars, i.e., as e increases, the dollar depreciates. However, Mankiw's e is the number of foreign currency units per dollar, i.e., as e increases, the dollar appreciates.

(5.) See Mankiw p. 328, Table 12-1.

References

Andrew B. Abel and Bernanke, B. S., Macroeconomics, 3rd edition, Addison-Wesley, 1998.

Dennis R. Appleyard and Field, A. J., International Economics, 4th edition, McGraw Hill, 2001.

Alan Auerbach and Kotlikoff, L. J., Macroeconomics: An Integrated Approach, 2nd edition, the MIT Press, 1998.

Martin Baily and Friedman, P. Macroeconomics, 2nd edition, Irwin, 1995.

Robert J. Barro, Macroeconomics, 5th edition, MIT Press, 1997.

Olivier Blanchard, Macroeconomics, 2nd edition, Prentice-Hall, 2000.

Rudiger Dornbusch, Open Economy Macroeconomics, Basic Books, 1980.

Rudiger Dornbusch, Fischer, S., and Startz, R., Macroeconomics, 7th edition, Irwin/McGraw-Hill, 1998.

Liang-Shing Fan and Fan, C. M., "A Fundamental Analysis of Asian Crisis," Proceedings of Academy of Business & Administrative Sciences International Conference, 1999.

Marcus Fleming, "Domestic Financial Policies under Fixed and Under Floating Exchange Rates," International MONETARY Fund Staff Papers 9, Nov. 1962, pp. 369-79.

Roger E. A. Farmer, Macroeconomics, South Western College Publishing, 1999.

Richard T. Froyen, Macroeconomics, 6th edition, Prentice-Hall, 1999.

Robert Gordon, Macroeconomics, 8th edition, Addison-Wesley, 2000.

Robert E. Hall and Taylor, J. B., Macroeconomics, 5th edition, Norton, 1997.

Paul Krugman and Obstfeld, M., International Economics: Theory and Policy, 5th edition, Addison-Wesley, 2000.

Peter H. Lindert and Pugel, T. A., International Economics, 10th edition, Irwin, 1996.

N. Gregory Mankiw, Macroeconomics, 4th edition, Worth, 2000.

Robert Mundell, "Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates," Canadian Journal of Economic and Political Science, 29, Nov. 1963, pp. 475-85.

Robert Mundell, International Economics, MacMillan, 1968.

Maurice Obstfeld and Rogoff, K., Foundations of International Macroeconomics, MIT Press, 1996.

Dominick Salvatore, International Economics, 7th edition, John Wiley, 2001.

Liang-Shing Fan *

Chuen-mei Fan *

* Professors of Economics, Colorado State University, Fort Collins, CO 80523. We appreciate the anonymous referee's comments which have greatly improved our presentation.

As a result of awarding the 1999 Nobel Prize for Economics to Robert Mundell, one of his major contributions, the Mundell-Fleming model, has become a focus of attention. Because of the expansion in international trade and the globalization of international finance, many developing and transitional economies in the world are facing the problem of choosing an appropriate exchange rate regime. In light of the improvement in international capital mobility, many small countries are choosing a pegged (fixed) exchange rate system. As pointed out in Mundell (1963) and Fleming (1962), when a small country tries to maintain a fixed exchange rate in a world of perfect capital mobility, money stock becomes endogenous. This result renders the monetary policy completely ineffective as a stabilization policy instrument.

Why would many small developing and transitional economies choose a fixed exchange rate system in a world dominated by globally floating key currencies? There are many pros and cons, but one fundamental reason may be that the lack (or backwardness) of financial institutions and securities markets makes the execution of the monetary policy ineffective. This situation leaves fiscal policy as the only remaining powerful policy instrument in a fixed exchange rate system. Thus, the understanding of policy effectiveness in an open economy becomes a very important part of any macro and international economics teaching.

This paper first investigates the key role the Mundell-Fleming model plays in the analysis of open economy stabilization policies in most of the major upper-division macro and international economics textbooks. Different models presented in these textbooks are compared. Most models are of the standard IS-LM framework in the original Mundell-Fleming fashion in the (y, i) plane, with y and i being income and the interest rate, respectively. N. G. Mankiw (2000) presents an innovative approach in the (y, e) plane, where e represents the exchange rate, instead.

The major motivation for this synthesis of the Mundell-Fleming model is that, in spite of Mankiw's innovative approach, his conclusion that fiscal expansion has no effect on the trade balance is counter to that of all other texts. Moreover, his unique contribution of adding a trade restriction policy needs further clarification. This is because trade restriction policies may not improve the trade balance under certain circumstances. This situation is clearly evidenced by the experiences of some rapidly expanding Asian countries before the 1997 Asian Crisis. These countries chose to peg their exchange rates to the U. S. dollar, adopted fairly restrictive import policies and experienced amazing GDP growth until 1997, but maintained huge sizes of current account deficits throughout the expansion period as shown in Table 1 below.

This paper first surveys most of the current major macro and international textbooks and presents three major approaches by Dorsbusch/Fisher/Startz, Blanchard, and Mankiw, respectively. Then, a synthesized Mundell-Fleming model is constructed. It is generally believed that trade restriction policies will improve the trade balance. With this model, a necessary condition for such desired effect is derived.

II. Survey of Macro and International Economics Textbooks

The Mundell-Fleming model uses the Hicksian IS and LM framework to analyze the effectiveness of fiscal and monetary policies for small countries under fixed and flexible exchange rates with the assumptions of perfect capital mobility. The analysis belongs to the domain of open macroeconomics as well as international economics. The first appearance of this model in a book was Mundell's (1968) Chapter 18 on capital mobility and stabilization policy under fixed and flexible exchange rates, adapted from his original article (Mundell, 1963). Other major advanced books such as Obstfeld and Rogoff's Foundations of International Macroeconomics (Obstfeld and Rogoff, 1996), present it as the Mundell-Fleming-Dornbusch Model. However, our emphasis in this paper is on the treatment of the Mundell-Fleming model in undergraduate macro and international economics. With this specific focus of the study, Dombusch's Open Economy Macroeconomics (1980) would be too difficult for undergraduate students, even though it provides the most advanced treatment of the Mundell-Fleming model. In this paper, fourteen major macro and international economics textbooks are examined. Surprisingly, six of them (Abel and Bernanke 1998, Barro 1997, Farmer 1999, Gordon 2000, Hall and Taylor 1997, and Krugman and Obstfeld 2000) did not even cite Mundell's contributions, and none of them has analyzed the problem.

Auerbach and Kotlikoff (1998) argues that in a small open economy the IS curve is virtually horizontal which renders the fiscal policy completely ineffective. Thus they argue in favor of a flexible exchange rate regime under which monetary policy is effective.

Baily and Friedman (1995) use the basic IS-LM diagram to discuss the macroeconomic policy in an open economy strictly in terms of a floating exchange rate system. Dombusch, Fischer, and Startz (1998, pp. 283-293) present the essence of the Mundell-Fleming model by arguing that even though later research has refined the Mundell-Fleming analysis, the initial formulation remains intact for the purpose of understanding the basic policy effects under a regime of high capital mobility. With perfect or near perfect capital mobility, the balance of payment (BP) will be at equilibrium at the world interest rate, i.e., BP = 0 at i = [i.sub.f], where i and [i.sub.f] represent the domestic and the foreign (world) interest rates, respectively. Then the standard model will neatly demonstrate that a deviation of domestic interest rate from the world rate due to the monetary expansion (contraction) will create a pressure on currency depreciation (appreciation) through capital outflow (inflow). In order to eliminate this pres sure, a subsequent monetary contraction (expansion) policy will have to be taken. This makes the monetary policy completely ineffective. On the contrary, the fiscal policy is effective under the fixed exchange rate system. Analytically, the monetary policy would regain its independence and become an effective policy under the flexible exchange rate system. Using only the basic tools of the IS-LM analysis, the presentation of Dornbusch, Fischer, and Startz (1998) is actually very appropriate for the undergraduate students in terms of its simplicity.

Froyen (1999) devotes one whole chapter on monetary and fiscal policies in an open economy and states that the chapter is strictly fashioned after the Mundell-Fleming model. However, Froyen provides a neat addition for the case where capital mobility is imperfect so that the BP = 0 curve is upward sloping. (1) He then analyzes the monetary and fiscal policies under such a condition. In the second half of the chapter, the standard Mundell-Fleming small country with perfect capital mobility situation is analyzed.

Blanchard (2000) presents a unique extension of the Mundell-Fleming model. (2) He introduces simple, but very clear, financial investor arbitrage behavior that seeks the highest global expected rate of return so that, at the equilibrium, the interest parity condition (3) must hold. Thus, his general open economy model consists of IS, LM, and the interest parity condition. His fixed exchange rate case will transform the interest parity condition to the condition requiring i = [i.sub.f] and is equivalent to Mundell-Fleming's small country with perfect capital mobility. In other words, the Mundell-Fleming fixed exchange rate case is a very special case in Blanchard's general framework.

In his latest edition, Mankiw (2000) presents a Mundell-Fleming model in the (y, e) plane instead of the traditional IS-LM framework in the (y, i) plane. He calls his model the [IS.sup.*] -[LM.sup.*] model. Since the [LM.sup.*] function is independent of the exchange rate, and with the i = [i.sub.f] condition of perfect capital mobility, a unique level of GDP is obtained from the [LM.sup.*] function M/P = L([i.sub.f], y). The advantage of the Mankiw approach is that the exchange rate, instead of the interest rate, appears explicitly on the vertical axis. This result makes it easier for students to understand the role of the exchange rate, e. He also presents in his framework the effect of trade restriction policies vastly ignored by all others.

In major international economics textbooks, the analysis of external balance, i.e., BP = 0, plays a major role. In general, BP (y, i) = 0 is an upward-sloping function (curve) because as y increases, the current account balance (especially the trade balance) worsens so that BP = 0 resumes only when a higher domestic interest rate, i, attracts capital inflow to offset the deficit. Moreover, the interest sensitivity of international capital flow (i.e., the interest elasticity of BP = 0) can be greater or less than that of the LM function (curve). Lindert and Pugel (1996) and Salvatore (2001) present cases where the BP = 0 curve is steeper than the LM curve, flatter than the LM curve, or is horizontal. Under the fixed exchange rate, as the BP = 0 becomes flatter, the effectiveness of fiscal policy as a stabilization policy will increase. This situation is exactly the case in the Mundell-Fleming model. Appleyard and Field (2001) add another extreme case where BP = 0 is completely interest inelastic (i.e., the BP = 0 curve is vertical). In this case there is a complete capital immobility such that there is only one level of GDP which is commensurate with BP = 0. Thus, any fiscal expansion will create a balance of payments deficit, and the money supply will contract until the original y is restored again. In contrast to the Mundell-Fleming case, the fiscal policy is completely ineffective.

It is clear from this survey that the original contribution of Mundell and Fleming has become a very special case of a general model in most international economics textbooks. Of course, Froyen and Blanchard also generalized the model in their books. In this paper, attention will be focused on the original contribution, i.e., the horizontal BP, as most macroeconomics textbooks do.

III. The Formal Analysis of Various Models

As previously mentioned, all models are based on the Hicksian IS and LM functions for a closed economy. Now, in an open economy with the exchange rate, (e.) (4), playing a central role, one extra equation is needed to complete the model. This requirement is the balance of payments (BP) in most cases, except for the interest parity condition in the Blanchard model.

In general, the following forms of IS and LM functions are used.

IS: y = C(y - T) + I(i) + G + NX(y, [y.sub.f], e) (1)

LM: M/P = L(y, i) (2)

(a) Dornbusch, Fischer, and Startz:

The model strictly follows the assumption of a small country with perfect capital mobility so that BP = 0 at i = [i.sub.f]. i.e., there will not be equilibrium in the balance of payments unless the domestic interest rate equals the world rate. The perfect mobility of capital will guarantee this condition.

BP: i = [i.sub.f] (3)

Figure 1 illustrates these equations.

(b) Blanchard

Blanchard's model involves slightly modified (1) and (2). He makes explicit the income effect of investment and the homogeneity of the money demand function.

IS: y = C(y - T) + I(y, i) + G + NX(y, [y.sub.f], e) (la)

LM: M/P = yL(i) (2a)

The interest parity condition: e = [e.sup.e]/(1 + i - [i.sub.f]) (4)

The important modification is his inclusion of the impact of GDP on investment. This modification makes it possible for the discussion of the policy effect on investment. Equation (4) indicates a negative relationship between the interest rate and the exchange rate. Blanchard discusses the policy effects in his general model where e is flexible, treating the fixed exchange rate with perfect capital mobility as a special case within the general model. Thus, with fixed exchange rate e, [e.sup.e] = e, and (4) becomes

i = [i.sub.f] (3)

This result is demonstrated in Figure 2.

(c) Mankiw

Mankiw's IS function is slightly different from (1) above. His trade balance is expressed as NX = NX(e), with y and [y.sub.f] being excluded. The investment function is I = 1(i), and again without y. Thus, the system consists of:

IS * y = C(y-T) + I(i) + G+NX(e) (1b)

LM * M/P = L(y, i) (2)

BP i = [i.sub.f] (3)

This makes Mankiw's analysis unique in that IS * and LM * are functions of y and e after (3) is being substituted into (ib) and (2), even though LM * is independent of e. From (3) and (2) and given M/P, y is uniquely determined. Further, with (3) and the uniquely determined y, (ib) will yield the equilibrium level for e.

Given the fixed exchange rate, e, and i = [i.sub.f], as soon as G changes, y will change so that M/P has to change to meet the changed demand for money. The money supply is endogenous in the sense that the central bank loses its control over the money supply. This is illustrated in Figure 3.

IV. Fiscal Policy and the Trade Restriction Policy under the Fixed Exchange Rate Revisited

It is unanimously agreed that under a flexible exchange rate system, monetary policies are effective while fiscal policies are not. Under the fixed exchange rate system, the condition under which fiscal policy can be effective in affecting the level of GDP is also agreed upon by all economists. To illustrate this point, first the standard IS-LM model, as illustrated in Figure 1, is used. As G increases, the IS curve shifts to the right by the full size of the multiplier. The corresponding upward pressure of an expansion in government expenditures on the domestic interest, i, will result in i > [i.sub.f] which will attract foreign capital. The domestic currency will appreciate as a consequence of the capital inflow. Under the fixed exchange rate system, the central bank has to purchase the foreign currency with the domestic currency to prevent the exchange rate appreciation. This operation will increase the money supply and the LM curve will shift to the right until i = [i.sub.f] is restored.

In Mankiw's model (Figure 3), the expansionary fiscal policy raises e, i.e., an appreciation, so that under the fixed exchange rate, e, the money supply has to increase to move [LM.sub.1] rightward to [LM.sub.2] However, there has been some disagreement about its effect on the trade balance. Since expansions in government spending essentially have the full multiplier effect due to the reinforcing monetary expansion, so that i = [i.sub.f], all other authors argue that the trade balance would worsen because NX is a negative function of y. But, in Mankiw's model NX = NX(e) so that under the fixed exchange rate [DELTA]e = 0, implying that there will be no change in the trade balance. (See Mankiw p. 328.) Mankiw asks students to reconcile this difference in his problem 4, p. 341, by assuming NX(y, e).

Mankiw is the only one who treats the effect of import restrictions in the Mundell-Fleming model. Under the fixed exchange rate system, an import restriction creates an increase in trade balance initially, so that it will have a positive effect on output y, similar to that of a fiscal expansion. Since e = e, Mankiw concludes that the trade balance increases. His argument is that since i = [i.sub.f], I = I, while S increases because of the increase in y. Therefore, NX = (S - I) increases. Mankiw has claimed that the trade restriction does not affect the trade balance under the flexible exchange rate system. (5)

V. A Synthesis

In this section, a synthesis is attempted for a small country with perfect capital mobility. This synthesis is a static general equilibrium model with assumptions following the original Mundell-Fleming framework. We begin with (la), (2), and (3):

y = C(y - T) + I(y,i) + G + NX(y,[y.sub.f],e) (la)

M/P = L(y,i) (2)

i= [i.sub.f] (3)

Equation (la) includes the effect of y on I. The NX function also includes y as a variable.

Let [gamma] = [partial]I/[partial]y > 0 be the marginal propensity to invest, [theta] = [partial]NX/[partial]y < 0 be the marginal negative trade balance effect (due to the marginal propensity to import), and [alpha] = [partial]S/[partial]y > 0 be the marginal propensity to save.

This synthesis seems to be a minor integration of all three models above, but it will be very useful to analyze the Mankiw trade restriction policy.

As we know, under the fixed exchange rate system the fiscal policy variable, dG or dT, is effective in changing the GDP, or y. Suppose that a fiscal expansion has created an increase in GDP by the size of dy. Then, saving increases by [alpha]dy, investment increases by [gamma]dy, and the trade balance decreases by [theta]dy.

The experience of the emerging economies in Asia before the 1997 Asian Crisis can be used as an illustration of the effect of a fiscal expansion. These Asian countries had maintained pegged (fixed) exchange rate systems and had provided avenues conducive to high capital mobility in order to attract foreign capital. Fiscal expansions have stimulated domestic investments, but huge trade deficits were created because the marginal propensity to save, [alpha], was smaller than the marginal propensity to invest, [gamma], such that dNX = dS - dI = ([alpha] - [gamma])dy < 0. As long as foreign capital inflows continued, growth was sustainable and the big bubble economies were created; however, as soon as capital inflows reversed their direction to become dramatic capital outflows, the economies started to collapse. The Asian Crisis was born (Fan and Fan 1999). Table 1 shows that every year during the booming fixed exchange rate period (from 1990 to the first half of 1997), the NIES all had sizable current account deficits. Then in July of 1997, the run on the Asian currencies collapsed the fixed exchange rate system. After 1997, all current accounts showed sizable surpluses. This is because [alpha] > y (i.e., I < S) so that NX > 0 and a flexible exchange rate has been in effect.

Trade restriction has been a favorite policy instrument of many smaller developing economies. Suppose some trade restriction (import restriction) policies are imposed. Under the fixed exchange rate system with capital mobility, Mankiw concludes that the initial increase in trade balance (due to import reduction) shifts the IS * curve upward and increases the domestic interest rate level, I > [i.sub.f] and e will appreciate. The central bank has to restore i = [i.sub.f] by a monetary expansion so that eventually e = e. The GDP and the trade balance increase. His argument is that an increase in y and the corresponding increase in savings; S(y) while i = [i.sub.f] would imply that I = I ([i.sub.f]), thus, dNX = [dS(y) - d I([i.sub.f])] > 0. (See Mankiw p. 327.) However, unless there is a total ban on a nation's foreign imports, as y increases the marginal propensity to import will worsen the trade balance. Mankiw's conclusion is true in this case because of his extremely restricted NX = NX(e) trade balance equation.

We have derived a more general conclusion in our synthesized model in that although the initial trade restriction policy will create a trade surplus to boost the GDP, whether dNX > 0 or < 0 will depend upon whether the marginal propensity to save exceeds the marginal propensity to invest, i.e., [alpha] > [gamma] or [alpha] < [gamma]. Thus, Mankiw's conclusion would be true only when the marginal propensity to save exceeds the marginal propensity to invest, i.e., [alpha] > [gamma].

VI. Summary

A synthesis of the Mundell-Fleming model, incorporating the income effect on the investment function and the trade balance function, has enabled us to present a simple but important necessary condition which states that in order for an expansionary fiscal policy and a trade restriction policy to have worsening effects on the trade balance, the marginal propensity to save has to be less than the marginal propensity to invest, i.e., [alpha] < [gamma].

The importance of this synthesis can also be seen from the fact that Mankiw concluded that under a fixed exchange rate system, the expansionary fiscal policy does not have any effect on the trade balance because dNX(e) = 0. However, this conclusion contradicts his statement that as y increases, NX(e) = (S - I) > 0 (Mankiw p. 327). In a comparative static model, (S - I) > 0 always implies that net exports have to be positive. In our synthesis, as long as [alpha] < [gamma], the trade balance worsens when an expansionary fiscal policy is undertaken. Thus, Mankiw's conclusion that an expansionary fiscal policy does not change the trade balance is true only when [alpha] = [gamma] is assumed.

The analysis here is carried out for small open economies with perfect capital mobility under a fixed exchange rate regime. Today, many small emerging economies have indeed tried to peg their exchange rates to the U.S. dollar or to other key currencies in order to increase the capital mobility and attract foreign capital inflows to stimulate their economic growth.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

TABLE 1 The Current Account Balance of Asian NIEs (1990-99) (In million US dollars) Year Indonesia Malaysia S. Korea Thailand 1990 -2988 -869.91 -2002.8 -7281.1 1991 -4260 -4182.81 -8317.3 -7571.45 1992 -2780 -2167.32 -3943.35 -6303.41 1993 -2106 -2990.95 989.5 -6363.58 1994 -2792 -4520.14 -3867 -8085.37 1995 -6431 -8643.57 -8506.5 -13554 1996 -7663 -4461.95 -23005.7 -14691.5 1997 * -4889 -5935.25 -8167.2 -3021.08 1998 4096 9528.65 40365.4 14242.5 1999 5785 12605.8 24476.5 12427.9 Source: IMF Financial Statistics June 2000. * Asian Crisis started July 2, 1997.

Notes

(1.) A simple explanation for the BP curve's being upward sloping is that as income, y, increases, the trade balance worsens such that for BP = 0, the domestic interest, i, has to be higher to attract capital inflows (or reduce capital outflows).

(2.) He states that his model keeps the spirit, but differs in its details from the original Mundell-Fleming model. (Blanchard p. 381)

(3.) The interest parity condition is: i = [i.sub.f] + ([e.sup.e] - e)/e, or e = [e.sup.e]/(1 + i - [i.sub.f]). i is the domestic interest rate, [i.sub.f] is the foreign interest rate, e is the exchange rate, and [e.sup.e] is the given expected depreciation of the exchange rate. This formula omitted a third cross-product term whose order of magnitude is small. However, if the interest/inflation differentials are large, this omitted term may be significant. (See Krugman and Osbtfeld 2000, P. 361.)

(4.) e, the exchange rate is a unit of foreign currency in U.S. dollars, i.e., as e increases, the dollar depreciates. However, Mankiw's e is the number of foreign currency units per dollar, i.e., as e increases, the dollar appreciates.

(5.) See Mankiw p. 328, Table 12-1.

References

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Liang-Shing Fan *

Chuen-mei Fan *

* Professors of Economics, Colorado State University, Fort Collins, CO 80523. We appreciate the anonymous referee's comments which have greatly improved our presentation.

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Title Annotation: | economics research |
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Author: | Fan, Liang-Shing; Fan, Chuen-mei |

Publication: | American Economist |

Geographic Code: | 1USA |

Date: | Mar 22, 2002 |

Words: | 4088 |

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