Mundell-Fleming Model PDF [PDF]

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Mundell–Fleming model The Mundell–Fleming model, also known as the IS- 1.2 Variables LM-BoP model (or IS-LM-BP model), is an economic model first set forth (independently) by Robert Mundell This model uses the following variables: and Marcus Fleming.[1][2] The model is an extension of the IS-LM Model. Whereas the traditional IS-LM • Y is GDP Model deals with economy under autarky (or a closed economy), the Mundell–Fleming model describes a small • C is consumption open economy. Mundell’s paper suggests that the model • I is physical investment can be applied to Zurich, Brussels and so on.[1] The Mundell–Fleming model portrays the short-run relationship between an economy’s nominal exchange rate, interest rate, and output (in contrast to the closedeconomy IS-LM model, which focuses only on the relationship between the interest rate and output). The Mundell–Fleming model has been used to argue that an economy cannot simultaneously maintain a fixed exchange rate, free capital movement, and an independent monetary policy. This principle is frequently called the "impossible trinity,” “unholy trinity,” “irreconcilable trinity,” “inconsistent trinity” or the “Mundell–Fleming trilemma.”

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• 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

Basic set up

1.1

The Mundell–Fleming model is based on the following equations.

Assumptions

The IS curve:

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

• Spot and forward exchange rates are identical, and the existing exchange rates are expected to persist Y = C + I + G + N X indefinitely. where NX is net exports. • Fixed money wage rate, unemployed resources and constant returns to scale are assumed. Thus domes- The LM curve: tic price level is kept constant, and the supply of domestic output is elastic. M = L(i, Y ) • Taxes and saving increase with income. P • The balance of trade depends only on income and A higher interest rate or a lower income (GDP) level leads the exchange rate. to lower money demand. • Capital mobility is perfect and all securities are per- The BoP (Balance of Payments) Curve: fect substitutes. Only risk neutral investors are in the system. The demand for money therefore depends only on income and the interest rate, and investment BoP = CA + KA depends on the interest rate. • The country under consideration is so small that the where BoP is the balance of payments surplus, CA is the country can not affect foreign incomes or the world current account surplus, and KA is the capital account surplus. level of interest rates. 1

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2 MECHANICS OF THE MODEL

1.4

IS components

Under both types of exchange rate regime, the nominal domestic money supply M is exogenous, but for differC = C(Y − T (Y ), i − E(π)) ent reasons. Under flexible exchange rates, the nominal money supply is completely under the control of the cenwhere E(π) is the expected rate of inflation. Higher distral bank. But under fixed exchange rates, the money posable income or a lower real interest rate (nominal insupply in the short run (at a given point in time) is fixed terest rate minus expected inflation) leads to higher conbased on past international money flows, while as the sumption spending. economy evolves over time these international flows cause future points in time to inherit higher or lower (but predetermined) values of the money supply. I = I(i − E(π), Y−1 ) where Y−₁ is GDP in the previous period. Higher lagged income or a lower real interest rate leads to higher investment spending.

N X = N X(e, Y, Y ∗)

2 Mechanics of the model The model’s workings can be described in terms of an IS-LM-BoP graph with the domestic interest rate plotted vertically and real GDP plotted horizontally. The IS curve is downward sloped and the LM curve is upward sloped, as in the closed economy IS-LM analysis; the BoP curve is upward sloped unless there is perfect capital mobility, in which case it is horizontal at the level of the world interest rate.

where NX is net exports, e is the nominal exchange rate (the price of domestic currency in terms of units of the foreign currency), Y is GDP, and Y* is the combined GDP of countries that are foreign trading partners. Higher domestic income (GDP) leads to more spending on imports and hence lower net exports; higher foreign income leads to higher spending by foreigners on the coun- In this graph, under less than perfect capital mobility the try’s exports and thus higher net exports. A higher e leads positions of both the IS curve and the BoP curve depend on the exchange rate (as discussed below), since the ISto lower net exports. LM graph is actually a two-dimensional cross-section of a three-dimensional space involving all of the interest rate, 1.5 Balance of payments (BoP) compo- income, and the exchange rate. However, under perfect capital mobility the BoP curve is simply horizontal at a nents level of the domestic interest rate equal to the level of the world interest rate. • CA = N X • where CA is the current account and NX is net exports. That is, the current account is viewed 2.1 as consisting solely of imports and exports.

Under a flexible exchange rate regime

• KA = z(i − i∗) + k

1.6

In a system of flexible exchange rates, central banks allow the exchange rate to be determined by market forces • where i∗ is the foreign interest rate, k is the ex- alone. ogenous component of financial capital flows, z is the interest-sensitive component of capital flows, and the derivative of the function z is the degree of capital mobility (the effect of 2.1.1 Changes in the money supply differences between domestic and foreign interest rates upon capital flows KA). An increase in money supply shifts the LM curve to the right. This directly reduces the local interest rate relative to the global interest rate. A decrease in the money supply Variables determined by the model causes the exact opposite process.

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

2.1.2 Changes in government spending An increase in government expenditure shifts the IS curve to the right. The shift causes both the local interest rate and income (GDP) to rise. A decrease in government expenditure reverses the process.

2.2 2.1.3

Under a fixed exchange rate regime

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Changes in the global interest rate

money by decreasing its holdings of domestic bonds (or the opposite if money were flowing out of the country). An increase in the global interest rate shifts the BoP curve But under perfect capital mobility, any such sterilization upward and causes capital flows out of the local econ- would be met by further offsetting international flows. omy. This depreciates the local currency and boosts net exports, shifting the IS curve to the right. Under less than perfect capital mobility, the depreciated exchange rate 2.2.2 Changes in government expenditure shifts the BoP curve somewhat back down.Under perfect capital mobility, the BoP curve is always horizontal at the level of the world interest rate. When the latter goes up, the BoP curve shifts upward by the same amount, and stays there. The exchange rate changes enough to shift the IS curve to the location where it crosses the new BoP curve at its intersection with the unchanged LM curve; now the domestic interest rate equals the new level of the global interest rate. A decrease in the global interest rate causes the reverse to occur.

2.2

Under a fixed exchange rate regime

In a system of fixed exchange rates, central banks announce an exchange rate (the parity rate) at which they are prepared to buy or sell any amount of domestic currency. Thus net payments flows into or out of the country need not equal zero; the exchange rate e is exogenously given, while the variable BoP is endogenous.

An increase in government spending forces the monetary authority to supply the market with local currency to keep the exchange rate unchanged. Shown here is the case of perfect capital mobility, in which the BoP curve (or, as denoted here, the FE curve) is horizontal.

Under the fixed exchange rate system, the central bank operates in the foreign exchange market to maintain a specific exchange rate. If there is pressure to depreciate the domestic currency’s exchange rate because the supply of domestic currency exceeds its demand in foreign exchange markets, the local authority buys domestic currency with foreign currency to decrease the domestic currency’s supply in the foreign exchange market. This keeps the domestic currency’s exchange rate at its targeted level. If there is pressure to appreciate the domestic currency’s exchange rate because the currency’s demand exceeds its supply in the foreign exchange market, the local authority buys foreign currency with domestic currency to increase the domestic currency’s supply in the foreign exchange market. Again,this keeps the exchange rate at its targeted level.

Increased government expenditure shifts the IS curve to the right. The shift results in an incipient rise in the interest rate, and hence upward pressure on the exchange rate (value of the domestic currency) as foreign funds start to flow in, attracted by the higher interest rate. However, the exchange rate is controlled by the local monetary authority in the framework of a fixed exchange rate system. To maintain the exchange rate and eliminate pressure on it, the monetary authority purchases foreign currency using domestic funds in order to shift the LM curve to the right. In the end, the interest rate stays the same but the general income in the economy increases. In the IS-LMBoP graph, the IS curve has been shifted exogenously by the fiscal authority, and the IS and BoP curves determine the final resting place of the system; the LM curve merely passively reacts.

2.2.1

The reverse process applies when government expenditure decreases.

Changes in the money supply

In the very short run the money supply is normally predetermined by the past history of international payments flows. If the central bank is maintaining an exchange rate that is consistent with a balance of payments surplus, over time money will flow into the country and the money supply will rise (and vice versa for a payments deficit). If the central bank were to conduct open market operations in the domestic bond market in order to offset these balanceof-payments-induced changes in the money supply — a process called sterilization, it would absorb newly arrived

2.2.3 Changes in the global interest rate To maintain the fixed exchange rate, the central bank must accommodate the capital flows (in or out) which are caused by a change of the global interest rate, in order to offset pressure on the exchange rate. If the global interest rate increases, shifting the BoP curve upward, capital flows out to take advantage of the opportunity. This puts pressure on the home currency to de-

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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 money supply resulting from the outflow, shifts the LM curve to the left until it intersect the IS and BoP curves at their intersection. Once again, the LM curve plays a passive role, and the outcomes are determined by the IS-BoP interaction.

and output to rise. But for a small open economy with perfect capital mobility and a flexible exchange rate, the domestic interest rate is predetermined by the horizontal BoP curve, and so by the LM equation given previously there is exactly one level of output that can make the money market be in equilibrium at that interest rate. Any exogenous changes affecting the IS curve (such as government spending changes) will be exactly offset by resulting exchange rate changes, and the IS curve will Under perfect capital mobility, the new BoP curve will be horizontal at the new world interest rate, so the equilib- end up in its original position, still intersecting the LM and BoP curves at their intersection point. rium domestic interest rate will equal the world interest rate. The Mundell–Fleming model under a fixed exchange rate If the global interest rate declines below the domestic regime also has completely different implications from rate, the opposite occurs. The BoP curve shifts down, those of the closed economy IS-LM model. In the closed foreign money flows in and the home currency is pres- economy model, if the central bank expands the money sured to appreciate, so the central bank offsets the pres- supply the LM curve shifts out, and as a result income sure by selling domestic currency (equivalently, buying goes up and the domestic interest rate goes down. But foreign currency). The inflow of money causes the LM in the Mundell–Fleming open economy model with percurve to shift to the right, and the domestic interest rate fect capital mobility, monetary policy becomes ineffecbecomes lower (as low as the world interest rate if there tive. An expansionary monetary policy resulting in an incipient outward shift of the LM curve would make capital is perfect capital mobility). flow out of the economy. The central bank under a fixed exchange rate system would have to instantaneously intervene by selling foreign money in exchange for domes3 Differences from IS-LM tic money to maintain the exchange rate. The accommodated monetary outflows exactly offset the intended rise It is worth noting that some of the results from this model in the domestic money supply, completely offsetting the differ from those of the IS-LM model because of the tendency of the LM curve to shift to the right, and the open economy assumption. Results for a large open econ- interest rate remains equal to the world rate of interest. omy, on the other hand, can be consistent with those predicted by the IS-LM model. The reason is that a large open economy has the characteristics of both an autarky 4 Criticism and a small open economy. In particular, it may not face perfect capital mobility, thus allowing internal policy 4.1 Exchange rate expectations measures to affect the domestic interest rate, and it may be able to sterilize balance-of-payments-induced changes One of the assumptions of the Mundell–Fleming model in the money supply (as discussed above). is that domestic and foreign securities are perfect substiIn the IS-LM model, the domestic interest rate is a key component in keeping both the money market and the goods market in equilibrium. Under the Mundell– Fleming framework of a small economy facing perfect capital mobility, the domestic interest rate is fixed and equilibrium in both markets can only be maintained by adjustments of the nominal exchange rate or the money supply (by international funds flows).

3.1

Example

tutes. Provided the world interest rate i⋆ is given, the model predicts the domestic rate will become the same level of the world rate by arbitrage in money markets. However, in reality, the world interest rate is different from the domestic rate. Rüdiger Dornbusch considered how exchange rate expectations made an effect on the exchange rate.[3] Given the approximate formula:

i = i⋆ +

e′ −1 e

and if the elasticity of expectations σ , is less than unity, The Mundell–Fleming model applied to a small open then we have economy facing perfect capital mobility, in which the domestic interest rate is exogenously determined by the world interest rate, shows stark differences from the di =σ−1 0

Te > 0 ,

Ty = −m < 0 .

Investment and consumption increase as the interest rates decrease, and currency depreciation improves the trade balance.

dy 1 = de s+m

( ) di Ei + T e de

dy 1 = (Ei (σ − 1) + Te ) . de s+m Then the total differentiations of trade balance and the demand for money are derived.

dT =

∂T ∂T de + dy = Te de + Ty dy ∂e ∂y

dL =

∂L ∂L di + dy = Li di + Ly dy ∂i ∂y

Li < 0 ,

Ly > 0

and then, it turns out that dT Te (s + m) + Ty (Ei (σ − 1) + Te ) = dL Li (σ − 1)(s + m) + Ly (Ei (σ − 1) + Te ) dT Te s + Ty Ei (σ − 1) = . dL Li (σ − 1)(s + m) + Ly (Ei (σ − 1) + Te ) The denominator is positive, and the numerator is positive or negative. Thus, a monetary expansion, in the short run, does not necessarily improve the trade balance. This result is not compatible with what the MundellFleming predicts.[3] This is a consequence of introducing exchange rate expectations which the MF theory ignores. Nevertheless, Dornbusch concludes that monetary policy is still effective even if it worsens a trade balance, because a monetary expansion pushes down interest rates and encourages spending. He adds that, in the short run, fiscal policy works because it raises interest rates and the velocity of money.[3] See also: interest rate parity and Overshooting model See also: exchange rate and Capital asset pricing model

• Optimum currency area • Marshall–Lerner condition

6 References [1] Mundell, Robert A. (1963). “Capital mobility and stabilization policy under fixed and flexible exchange rates”. Canadian Journal of Economic and Political Science 29 (4): 475–485. doi:10.2307/139336. Reprinted in Mundell, Robert A. (1968). International Economics. New York: Macmillan. [2] Fleming, J. Marcus (1962). “Domestic financial policies under fixed and floating exchange rates”. IMF Staff Papers 9: 369–379. doi:10.2307/3866091. Reprinted in Cooper, Richard N., ed. (1969). International Finance. New York: Penguin Books. [3] Dornbusch, R. (1976). “Exchange Rate Expectations and Monetary 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 of Political Economy 36 (Suppl 1): 127–164, doi:10.1215/00182702-36-Suppl_1-127 (Tells the difference between the IS-LM-BP model and the Mundell–Fleming model.)

• Carlin, Wendy; Soskice, David W. (1990), Macroeconomics and the Wage Bargain, New York: Oxford University Press, ISBN 0-19-877245-9 • Mankiw, N. Gregory (2007), Macroeconomics (6th ed.), New York: Worth, ISBN 978-0-7167-6213-3 • Blanchard, Olivier (2006), Macroeconomics (4th ed.), Upper Saddle River, NJ: Prentice Hall, ISBN 0-13-186026-7 • DeGrauwe, Paul (2000), Economics of Monetary Union (4th ed.), New York: Oxford University Press, ISBN 0-19-877632-2

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