# Mundell-Fleming model

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Mundell-Fleming model

The Mundell-Fleming model is an economic model first set forth by Robert Mundell and Marcus Fleming. The model is an extension of the IS-LM model. Whereas IS-LM deals with economy under autarky, the Mundell-Fleming model tries to describe a small open economy.

Typically, the Mundell-Fleming model portrays the relationship between the nominal exchange rate and the economy output (unlike the relationship between interest rate and the output in the IS-LM model) in the short run. 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 Unholy Trinity," the "Irreconcilable Trinity," the "Inconsistent trinity" or the Mundell-Fleming "trilemma."

Basic set up

The traditional model is based around the following equations.

*$Y=C+I+G+NX$ ("The IS Curve")
**Where $Y$ is GDP, $C$ is consumption, $I$ is investment, $G$ is government spending and $NX$ is net exports.

*$frac\left\{M\right\}\left\{P\right\}=L\left(i, Y\right)$ ("The LM Curve")
**Where $M$ is money supply, $P$ is average price, $L$ is liquidity, $i$ is the interest rate and $Y$ is GDP.

*$BoP=CA+KA$ ("The BoP Curve (Balance of Payments)")
**Where $CA$ is the current account and $KA$ is the capital account.

IS components

*$C=C \left(Y-T, i-E\left( pi \right)\right)$
**Where $C$ is consumption, $Y$ is GDP, $T$ is taxes, $i$ is the interest rate, $E\left(pi\right)$ is the expected rate of inflation.

*$I=I\left(i-E\left(pi\right), Y_\left\{-1\right\}\right)$
**Where $I$ is investment, $i$ is the interest rate, $E\left(pi\right)$ is the expected rate of inflation, $Y_\left\{-1\right\}$ is GDP in the previous period.

*$G=G$
**Where $G$ is government spending, an exogenous variable.

*$NX=NX \left(e, Y, Y*\right)$
**Where $NX$ is net exports, $e$ is the real exchange rate, $Y$ is GDP, $Y*$ is the GDP of a foreign country.

BoP components

*$CA=NX$
**Where $CA$ is the current account and $NX$ is net exports.

*$KA=z\left(i-i*\right)+k$
**Where $z$ is the level of capital mobility, $i$ is the interest rate, $i*$ is the foreign interest rate, $k$ is capital investments not related to $i$, an exogenous variable

Mechanics of the model

One important assumption is the equalization of the local interest rate to the global interest rate.

Under flexible exchange rate regime

We speak of a system of flexible exchange rates when governments (or central banks) allow the exchange rate to be determined by market forces alone.

Typically this means governments (or central banks) announce an interest rate target which they are prepared to buy or sell any amount of domestic currency to maintain.

Changes in money supply

An increase in money supply will shift the LM curve to the right. This directly reduces the local interest rate and in turn forces the local interest rate lower than the global interest rate. This depreciates the exchange rate of local currency through capital outflow. The depreciation makes local goods cheaper compared to foreign goods and increases export and decreases import. Hence, net export is increased. Increased net export leads to the shifting of the IS curve to the right to the point where the local interest rate will equalize with the global rate. This increases the overall income in the local economy.

A decrease in money supply will cause the exact opposite of the process.

Changes in government spending

An increase in government expenditure shifts the IS curve to the right. The shift will cause the local interest rate to go above the global rate. The increase in local interest will cause capital inflow and the inflow will make the local currency stronger compared to foreign currencies. Strong exchange rate also makes foreign goods cheaper compared to local goods. This encourages greater import and discourages export and hence, lower net export. As a result, the IS will return to its original location where the local interest rate is equal to the global interest rate. The level of income of the local economy stays the same. The LM curve is not at all affected.

A decrease in government expenditure will reverse the process.

Changes in global interest rate

An increase in the global interest rate will cause an upward pressure on the local interest rate. The pressure will subside as the local rate closes in on the global rate. When a positive differential between the global and the local rate occurs, holding the LMB curve constant, capital will flow out of the local economy. This depreciates the local currency and helps boost net export. Increasing net export shifts the IS to the right. This shift will continue to the right until the local interest rate becomes as high as the global rate.

A decrease in global interest rate will cause the reverse to occur.

Under fixed exchange rate regime

We speak of a system of fixed exchange rates when governments (or central banks) announce an exchange rate (the parity rate) at which they are prepared to buy or sell any amount of domestic currency.

Changes in money supply

Under the fixed exchange rate system, the local central bank or any monetary authority will only change the money supply in order to maintain a level of exchange rate. If there is a pressure to appreciate the exchange rate, the local authority will increase its foreign reserve by purchasing foreign currencies with the local currency. This will return the exchange rate to its previous level. When there is a depreciation pressure, the authority will purchase its own currency in the market with its foreign reserve to return the currency to its pre-pressure state.

A revaluation occurs when there is a permanent increase in exchange rate and hence, decrease in money supply. Devaluation is the exact opposite of revaluation.

Changes in government expenditure

Increased government expenditure shifts the IS curve to the right. The shift encourages the interest rate to go up and hence, appreciation of the exchange rate. However, the exchange rate is controlled by the local monetary authority in the framework of a fixed system. In order to maintain the exchange and alleviate the pressure on the exchange rate, the monetary authority will purchase foreign currencies with local currencies until the pressure is gone i.e. back to the original level. Such action shifts the LM curve in tandem with the direction of the IS shift. This action increases the local currency supply in the market and lowers the exchange rate &mdash; or rather, return the rate back to its original state. In the end, the exchange rate stays the same but the general income in the economy increases.

The reverse is true when government expenditure decreases.

Changes in global interest rate

To maintain the fixed exchange rate, the central bank must offset the capital flows (in or out) which are caused by the change of the global interest rate to the domestic rate. The central bank must restore the situation where the real domestic interest rate is equal to the real global interest rate to stop net capital flows from changing the exchange rate.

If the global interest rate increases above the domestic rate, capital will flow out to take advantage of this opportunity. This would depreciate the home currency, so the central bank must buy the home currency and sell foreign currency reserves to offset this outflow. This decrease in the money supply shifts the LM curve to the left until the domestic interest rate is the global interest rate.

If the global interest rate declines below the domestic rate, the opposite occurs. Money flows in, the home currency would appreciate, so the central bank must offset this by increasing the money supply (sell domestic currency, buy foreign), the LM curve shifts right, and the domestic interest rate becomes the global interest rate.

Differences from IS-LM

It is worth noting that some of the result from this model differs from the IS-LM because of the open economy assumption. Result for large open economy on the other hand falls within the result predicted by the IS-LM and the Mundell-Fleming models. The reason for such result is because a large open economy has both the characteristics of an autarky and a small open economy.

In the IS-LM, interest rate will be the key component in making both the money market and the good market in equilibrium. Under the Mundell-Fleming framework of small economy, interest rate is fixed and equilibrium in both market can only be achieved by a change of nominal exchange rate.

Example

A much simplified version of the Mundell-Fleming model can be illustrated by a small open economy, in which the domestic interest rate is exogenously predetermined by the "world interest rate" (r=r*).

Consider an exogenous increase in government expenditure, the IS curve will shift upward, with LM curve intact, causing the interest rate and the output to rise (partial crowding out effect) under the IS-LM model.

Nevertheless, as interest rate is predetermined in a small open economy, the LM* curve (of exchange rate and output) is vertical, which means there is exactly one output that can make the money market in the equilibrium under that interest rate. Even though the IS* curve still shift up, it will result in a higher exchange rate and same level of output (complete crowding out effect, which is different in the IS-LM model).

The example above makes an implicit assumption of flexible exchange rate. The Mundell-Fleming model can have completely different implications under different exchange rate regimes. For instance, under a fixed exchange rate system, with perfect capital mobility, monetary policy becomes ineffective. An expansionary monetary policy resulting in an outward shift of the LM curve would in turn make capital flow out of the economy. The central bank under a fixed exchange rate system would have to intervene by selling foreign money in exchange for domestic money to depreciate the foreign currency and appreciate the domestic currency. Selling foreign money and receiving domestic money would reduce real balances in the economy, until the LM curve shifts back to the left, and the interest rates come back to the world rate of interest i*.

Further reading

* Optimal currency area
* Carlin and Soskice, Macroeconomics and the Wage Bargain
* Mankiw, Macroeconomics
* Blanchard, Macroeconomics
* Paul de Grauwe, Economics of Monetary Union, 2007

References

* DARITY, William Jr. and YOUNG, Warren. IS-LM-BP: an inquest. (Tells the difference between the IS-LM-BP model and the Mundell-Fleming model.) [http://www.econ.ucdavis.edu/faculty/kdhoover/pdf/Hope/Young.pdf]

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