Mundell–Fleming model

The Mundell–Fleming model, also known as the IS-LM-BoP model (or IS-LM-BP model), is an economicmodel first set forth (independently) by Robert Mundelland Marcus Fleming.[1][2] The model is an extensionof the IS-LM Model. Whereas the traditional IS-LMModel deals with economy under autarky (or a closedeconomy), the Mundell–Fleming model describes a smallopen economy. Mundell’s paper suggests that the modelcan be applied to Zurich, Brussels and so on.[1]

The Mundell–Fleming model portrays the short-run rela-tionship between an economy’s nominal exchange rate,interest rate, and output (in contrast to the closed-economy IS-LM model, which focuses only on the re-lationship between the interest rate and output). TheMundell–Fleming model has been used to argue thatan economy cannot simultaneously maintain a fixed ex-change rate, free capital movement, and an indepen-dent monetary policy. This principle is frequently calledthe "impossible trinity,” “unholy trinity,” “irreconcilabletrinity,” “inconsistent trinity” or the “Mundell–Flemingtrilemma.”

1 Basic set up

1.1 Assumptions

Basic assumptions of the model are as follows:[1]

• Spot and forward exchange rates are identical, andthe existing exchange rates are expected to persistindefinitely.

• Fixed money wage rate, unemployed resources andconstant returns to scale are assumed. Thus domes-tic price level is kept constant, and the supply of do-mestic output is elastic.

• Taxes and saving increase with income.• The balance of trade depends only on income andthe exchange rate.

• Capital mobility is perfect and all securities are per-fect substitutes. Only risk neutral investors are in thesystem. The demand for money therefore dependsonly on income and the interest rate, and investmentdepends on the interest rate.

• The country under consideration is so small that thecountry can not affect foreign incomes or the worldlevel of interest rates.

1.2 Variables

This model uses the following variables:

• Y is GDP

• C is consumption

• I is physical investment

• G is government spending (an exogenous variable)

• M is the nominal money supply

• P is the price level

• i is the nominal interest rate

• L is liquidity preference (real money demand)

• T is taxes

• NX is net exports

1.3 Equations

The Mundell–Fleming model is based on the followingequations.The IS curve:

Y = C + I +G+NX

where NX is net exports.The LM curve:

M

P= L(i, Y )

A higher interest rate or a lower income (GDP) level leadsto lower money demand.The BoP (Balance of Payments) Curve:

BoP = CA+KA

where BoP is the balance of payments surplus, CA is thecurrent account surplus, andKA is the capital account sur-plus.

1

2 2 MECHANICS OF THE MODEL

1.4 IS components

C = C(Y − T (Y ), i− E(π))

where E(π) is the expected rate of inflation. Higher dis-posable income or a lower real interest rate (nominal in-terest rate minus expected inflation) leads to higher con-sumption spending.

I = I(i− E(π), Y−1)

where Y−₁ is GDP in the previous period. Higher laggedincome or a lower real interest rate leads to higher invest-ment spending.

NX = NX(e, Y, Y ∗)

where NX is net exports, e is the nominal exchange rate(the price of domestic currency in terms of units ofthe foreign currency), Y is GDP, and Y* is the com-bined GDP of countries that are foreign trading partners.Higher domestic income (GDP) leads to more spendingon imports and hence lower net exports; higher foreign in-come leads to higher spending by foreigners on the coun-try’s exports and thus higher net exports. A higher e leadsto lower net exports.

1.5 Balance of payments (BoP) compo-nents

• CA = NX

• where CA is the current account and NX is netexports. That is, the current account is viewedas consisting solely of imports and exports.

• KA = z(i− i∗) + k

• where i∗ is the foreign interest rate, k is the ex-ogenous component of financial capital flows,z is the interest-sensitive component of capi-tal flows, and the derivative of the function zis the degree of capital mobility (the effect ofdifferences between domestic and foreign in-terest rates upon capital flows KA).

1.6 Variables determined by the model

After the subsequent equations are substituted into thefirst three equations above, one has a system of threeequations in three unknowns, two of which are GDP andthe domestic interest rate. Under flexible exchange rates,the exchange rate is the third endogenous variable whileBoP is set equal to zero. In contrast, under fixed exchangerates e is exogenous and the balance of payments surplusis determined by the model.

Under both types of exchange rate regime, the nominaldomestic money supply M is exogenous, but for differ-ent reasons. Under flexible exchange rates, the nominalmoney supply is completely under the control of the cen-tral bank. But under fixed exchange rates, the moneysupply in the short run (at a given point in time) is fixedbased on past international money flows, while as theeconomy evolves over time these international flows causefuture points in time to inherit higher or lower (but pre-determined) values of the money supply.

2 Mechanics of the model

The model’s workings can be described in terms of anIS-LM-BoP graph with the domestic interest rate plot-ted vertically and real GDP plotted horizontally. The IScurve is downward sloped and the LM curve is upwardsloped, as in the closed economy IS-LM analysis; theBoP curve is upward sloped unless there is perfect capitalmobility, in which case it is horizontal at the level of theworld interest rate.In this graph, under less than perfect capital mobility thepositions of both the IS curve and the BoP curve dependon the exchange rate (as discussed below), since the IS-LM graph is actually a two-dimensional cross-section of athree-dimensional space involving all of the interest rate,income, and the exchange rate. However, under perfectcapital mobility the BoP curve is simply horizontal at alevel of the domestic interest rate equal to the level of theworld interest rate.

2.1 Under a flexible exchange rate regime

In a system of flexible exchange rates, central banks al-low the exchange rate to be determined by market forcesalone.

2.1.1 Changes in the money supply

An increase in money supply shifts the LM curve to theright. This directly reduces the local interest rate relativeto the global interest rate. A decrease in the money supplycauses the exact opposite process.

2.1.2 Changes in government spending

An increase in government expenditure shifts the IS curveto the right. The shift causes both the local interest rateand income (GDP) to rise. A decrease in governmentexpenditure reverses the process.

2.2 Under a fixed exchange rate regime 3

2.1.3 Changes in the global interest rate

An increase in the global interest rate shifts theBoP curveupward and causes capital flows out of the local econ-omy. This depreciates the local currency and boosts netexports, shifting the IS curve to the right. Under less thanperfect capital mobility, the depreciated exchange rateshifts the BoP curve somewhat back down.Under perfectcapital mobility, the BoP curve is always horizontal at thelevel of the world interest rate. When the latter goes up,the BoP curve shifts upward by the same amount, andstays there. The exchange rate changes enough to shiftthe IS curve to the location where it crosses the new BoPcurve at its intersection with the unchanged LM curve;now the domestic interest rate equals the new level of theglobal interest rate.A decrease in the global interest rate causes the reverseto occur.

2.2 Under a fixed exchange rate regime

In a system of fixed exchange rates, central banks an-nounce an exchange rate (the parity rate) at which theyare prepared to buy or sell any amount of domestic cur-rency. Thus net payments flows into or out of the countryneed not equal zero; the exchange rate e is exogenouslygiven, while the variable BoP is endogenous.Under the fixed exchange rate system, the central bankoperates in the foreign exchange market to maintain aspecific exchange rate. If there is pressure to depreciatethe domestic currency’s exchange rate because the sup-ply of domestic currency exceeds its demand in foreignexchange markets, the local authority buys domestic cur-rency with foreign currency to decrease the domestic cur-rency’s supply in the foreign exchange market. This keepsthe domestic currency’s exchange rate at its targeted level.If there is pressure to appreciate the domestic currency’sexchange rate because the currency’s demand exceeds itssupply in the foreign exchange market, the local authoritybuys foreign currency with domestic currency to increasethe domestic currency’s supply in the foreign exchangemarket. Again,this keeps the exchange rate at its targetedlevel.

2.2.1 Changes in the money supply

In the very short run the money supply is normally pre-determined by the past history of international paymentsflows. If the central bank is maintaining an exchange ratethat is consistent with a balance of payments surplus, overtime money will flow into the country and the money sup-ply will rise (and vice versa for a payments deficit). If thecentral bank were to conduct open market operations inthe domestic bondmarket in order to offset these balance-of-payments-induced changes in the money supply — aprocess called sterilization, it would absorb newly arrived

money by decreasing its holdings of domestic bonds (orthe opposite if money were flowing out of the country).But under perfect capital mobility, any such sterilizationwould be met by further offsetting international flows.

2.2.2 Changes in government expenditure

An increase in government spending forces the monetary author-ity to supply the market with local currency to keep the exchangerate unchanged. Shown here is the case of perfect capital mobil-ity, in which the BoP curve (or, as denoted here, the FE curve)is horizontal.

Increased government expenditure shifts the IS curve tothe right. The shift results in an incipient rise in the inter-est rate, and hence upward pressure on the exchange rate(value of the domestic currency) as foreign funds start toflow in, attracted by the higher interest rate. However,the exchange rate is controlled by the local monetary au-thority in the framework of a fixed exchange rate system.To maintain the exchange rate and eliminate pressure onit, the monetary authority purchases foreign currency us-ing domestic funds in order to shift the LM curve to theright. In the end, the interest rate stays the same but thegeneral income in the economy increases. In the IS-LM-BoP graph, the IS curve has been shifted exogenously bythe fiscal authority, and the IS and BoP curves determinethe final resting place of the system; theLM curve merelypassively reacts.The reverse process applies when government expendi-ture decreases.

2.2.3 Changes in the global interest rate

To maintain the fixed exchange rate, the central bankmust accommodate the capital flows (in or out) which arecaused by a change of the global interest rate, in order tooffset pressure on the exchange rate.If the global interest rate increases, shifting theBoP curveupward, capital flows out to take advantage of the oppor-tunity. This puts pressure on the home currency to de-

4 4 CRITICISM

preciate, so the central bank must buy the home currency— that is, sell some of its foreign currency reserves —to accommodate this outflow. The decrease in the moneysupply resulting from the outflow, shifts the LM curve tothe left until it intersect the IS and BoP curves at theirintersection. Once again, the LM curve plays a passiverole, and the outcomes are determined by the IS-BoP in-teraction.Under perfect capital mobility, the newBoP curve will behorizontal at the new world interest rate, so the equilib-rium domestic interest rate will equal the world interestrate.If the global interest rate declines below the domesticrate, the opposite occurs. The BoP curve shifts down,foreign money flows in and the home currency is pres-sured to appreciate, so the central bank offsets the pres-sure by selling domestic currency (equivalently, buyingforeign currency). The inflow of money causes the LMcurve to shift to the right, and the domestic interest ratebecomes lower (as low as the world interest rate if thereis perfect capital mobility).

3 Differences from IS-LM

It is worth noting that some of the results from this modeldiffer from those of the IS-LM model because of theopen economy assumption. Results for a large open econ-omy, on the other hand, can be consistent with those pre-dicted by the IS-LM model. The reason is that a largeopen economy has the characteristics of both an autarkyand a small open economy. In particular, it may notface perfect capital mobility, thus allowing internal policymeasures to affect the domestic interest rate, and it maybe able to sterilize balance-of-payments-induced changesin the money supply (as discussed above).In the IS-LM model, the domestic interest rate is akey component in keeping both the money market andthe goods market in equilibrium. Under the Mundell–Fleming framework of a small economy facing perfectcapital mobility, the domestic interest rate is fixed andequilibrium in both markets can only be maintained byadjustments of the nominal exchange rate or the moneysupply (by international funds flows).

3.1 Example

The Mundell–Fleming model applied to a small openeconomy facing perfect capital mobility, in which thedomestic interest rate is exogenously determined by theworld interest rate, shows stark differences from theclosed economy model.Consider an exogenous increase in government expendi-ture. Under the IS-LM model, the IS curve shifts up-ward, with the LM curve intact, causing the interest rate

and output to rise. But for a small open economy withperfect capital mobility and a flexible exchange rate, thedomestic interest rate is predetermined by the horizon-tal BoP curve, and so by the LM equation given previ-ously there is exactly one level of output that can makethe money market be in equilibrium at that interest rate.Any exogenous changes affecting the IS curve (such asgovernment spending changes) will be exactly offset byresulting exchange rate changes, and the IS curve willend up in its original position, still intersecting the LMand BoP curves at their intersection point.The Mundell–Fleming model under a fixed exchange rateregime also has completely different implications fromthose of the closed economy IS-LMmodel. In the closedeconomy model, if the central bank expands the moneysupply the LM curve shifts out, and as a result incomegoes up and the domestic interest rate goes down. Butin the Mundell–Fleming open economy model with per-fect capital mobility, monetary policy becomes ineffec-tive. An expansionary monetary policy resulting in an in-cipient outward shift of theLM curve would make capitalflow out of the economy. The central bank under a fixedexchange rate system would have to instantaneously in-tervene by selling foreign money in exchange for domes-tic money to maintain the exchange rate. The accommo-dated monetary outflows exactly offset the intended risein the domestic money supply, completely offsetting thetendency of the LM curve to shift to the right, and theinterest rate remains equal to the world rate of interest.

4 Criticism

4.1 Exchange rate expectations

One of the assumptions of the Mundell–Fleming modelis that domestic and foreign securities are perfect substi-tutes. Provided the world interest rate i⋆ is given, themodel predicts the domestic rate will become the samelevel of the world rate by arbitrage in money markets.However, in reality, the world interest rate is differentfrom the domestic rate. Rüdiger Dornbusch consideredhow exchange rate expectations made an effect on the ex-change rate.[3] Given the approximate formula:

i = i⋆ +e′

e− 1

and if the elasticity of expectations σ , is less than unity,then we have

di

de= σ − 1 < 0 .

Since domestic output is y = E(i, y) + T (e, y) , thedifferentiation of income with regard to the exchange ratebecomes

5

dy

de=

∂E

∂i

di

de+

∂E

∂y

dy

de+

∂T

∂e+

∂T

∂y

dy

de

dy

de=

1

1− Ey − Ty

(Ei

di

de+ Te

).

The standard IS-LM theory gives us the following basicrelations:

Ei < 0 , Ey = 1− s > 0

Te > 0 , Ty = −m < 0 .

Investment and consumption increase as the interest ratesdecrease, and currency depreciation improves the tradebalance.

dy

de=

1

s+m

(Ei

di

de+ Te

)dy

de=

1

s+m(Ei(σ − 1) + Te) .

Then the total differentiations of trade balance and thedemand for money are derived.

dT =∂T

∂ede+

∂T

∂ydy = Tede+ Tydy

dL =∂L

∂idi+

∂L

∂ydy = Lidi+ Lydy

Li < 0 , Ly > 0

and then, it turns out that

dT

dL=

Te(s+m) + Ty(Ei(σ − 1) + Te)

Li(σ − 1)(s+m) + Ly(Ei(σ − 1) + Te)

dT

dL=

Tes+ TyEi(σ − 1)

Li(σ − 1)(s+m) + Ly(Ei(σ − 1) + Te).

The denominator is positive, and the numerator is pos-itive or negative. Thus, a monetary expansion, in theshort run, does not necessarily improve the trade balance.This result is not compatible with what the Mundell-Fleming predicts.[3] This is a consequence of introducingexchange rate expectations which the MF theory ignores.Nevertheless, Dornbusch concludes that monetary policyis still effective even if it worsens a trade balance, be-cause a monetary expansion pushes down interest ratesand encourages spending. He adds that, in the short run,fiscal policy works because it raises interest rates and thevelocity of money.[3]

See also: interest rate parity and Overshooting modelSee also: exchange rate and Capital asset pricing model

5 See also• Optimum currency area

• Marshall–Lerner condition

6 References[1] Mundell, Robert A. (1963). “Capital mobility and stabi-

lization policy under fixed and flexible exchange rates”.Canadian Journal of Economic and Political Science 29(4): 475–485. doi:10.2307/139336. Reprinted inMundell, Robert A. (1968). International Economics.New York: Macmillan.

[2] Fleming, J. Marcus (1962). “Domestic financial policiesunder fixed and floating exchange rates”. IMF Staff Pa-pers 9: 369–379. doi:10.2307/3866091. Reprinted inCooper, Richard N., ed. (1969). International Finance.New York: Penguin Books.

[3] Dornbusch, R. (1976). “Exchange Rate Expectations andMonetary Policy”. Journal of International Economics 6(3): 231–244. doi:10.1016/0022-1996(76)90001-5.

7 Further reading• Young, Warren; Darity, William, Jr. (2004),“IS-LM-BP: An Inquest” (PDF), History ofPolitical Economy 36 (Suppl 1): 127–164,doi:10.1215/00182702-36-Suppl_1-127 (Tellsthe difference between the IS-LM-BP model and theMundell–Fleming model.)

• Carlin, Wendy; Soskice, David W. (1990),Macroe-conomics and the Wage Bargain, New York: OxfordUniversity Press, ISBN 0-19-877245-9

• Mankiw, N. Gregory (2007), Macroeconomics (6thed.), New York: Worth, ISBN 978-0-7167-6213-3

• Blanchard, Olivier (2006), Macroeconomics (4thed.), Upper Saddle River, NJ: Prentice Hall, ISBN0-13-186026-7

• DeGrauwe, Paul (2000), Economics of MonetaryUnion (4th ed.), New York: Oxford UniversityPress, ISBN 0-19-877632-2

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