The Mundell–Fleming model, also known as the IS-LM-BoP model (or IS-LM-BP model), is an economic model first set forth (independently) by Robert Mundell and Marcus Fleming.[1] [2] The model is an extension of the IS–LM model. Whereas the traditional IS-LM model deals with economy under autarky (or a closed economy), the Mundell–Fleming model describes a small open economy.
The Mundell–Fleming model portrays the short-run relationship 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 relationship between the interest rate and output). The Mundell–Fleming model has been used to argue[3] that an economy cannot simultaneously maintain a fixed exchange rate, free capital movement, and an independent monetary policy. An economy can only maintain two of the three at the same time. This principle is frequently called the "impossible trinity," "unholy trinity," "irreconcilable trinity," "inconsistent trinity," "policy trilemma," or the "Mundell–Fleming trilemma."
Basic assumptions of the model are as follows:
This model uses the following variables:
The Mundell–Fleming model is based on the following equations:
The IS curve:
Y=C+I+G+NX
The LM curve:
| M | |
| P |
=L(i,Y)
The BoP (Balance of Payments) Curve:
BoP=CA+KA
C=C(Y-T(Y),i-E(\pi))
I=I(i-E(\pi),Yt-1)
NX=NX(e,Y,Y*)
CA=NX
KA=z(i-i*)+k
i*
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.
Under both types of exchange rate regime, the nominal domestic money supply M is exogenous, but for different reasons. Under flexible exchange rates, the nominal money supply is completely under the control of the central bank. But under fixed exchange rates, the money supply in the short run (at a given point in time) is fixed based on past international money flows, while as the economy evolves over time these international flows cause future points in time to inherit higher or lower (but pre-determined) values of the money supply.
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.
In this graph, under less than perfect capital mobility the positions of both the IS curve and the BoP curve depend on the exchange rate (as discussed below), since the IS-LM graph is actually a two-dimensional cross-section of a three-dimensional space involving all of the interest rate, income, and the exchange rate. However, under perfect capital mobility the BoP curve is simply horizontal at a level of the domestic interest rate equal to the level of the world interest rate.
As explained below, whether domestic monetary or fiscal policy is potent, in the sense of having an effect on real GDP, depends on the exchange rate regime. The results are summarized here.
Flexible exchange rates: Domestic monetary policy affects GDP, while fiscal policy does not.
Fixed exchange rates: Fiscal policy affects GDP, while domestic monetary policy does not.
In a system of flexible exchange rates, central banks allow the exchange rate to be determined by market forces alone.
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. That being said, capital outflows will increase which will lead to a decrease in the real exchange rate, ultimately shifting the IS curve right until interest rates equal global interest rates (assuming horizontal BOP). A decrease in the money supply causes the exact opposite process.
An increase in government expenditure shifts the IS curve to the right. This will mean that domestic interest rates and GDP rise. However, this increase in the interest rates attracts foreign investors wishing to take advantage of the higher rates, so they demand the domestic currency, and therefore it appreciates. The strengthening of the currency will mean it is more expensive for customers of domestic producers to buy the home country's exports, so net exports will decrease, thereby cancelling out the rise in government spending and shifting the IS curve to the left. Therefore, the rise in government spending will have no effect on the national GDP or interest rate.
An increase in the global interest rate shifts the BoP curve upward and causes capital flows out of the local economy. 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 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.
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.
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 devalue 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.
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 balance-of-payments-induced changes in the money supply — a process called sterilization – it would absorb newly arrived money by decreasing its holdings of domestic bonds (or the opposite if money were flowing out of the country). But under perfect capital mobility, any such sterilization would be met by further offsetting international flows.
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-LM-BoP 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.
The reverse process applies when government expenditure decreases.
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 depreciate, 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 intersects 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.
Under perfect capital mobility, the new BoP curve will be horizontal at the new world interest rate, so the equilibrium domestic interest rate will equal the world interest rate.
If the global interest rate declines below the domestic rate, the opposite occurs. The BoP curve shifts down, foreign money flows in and the home currency is pressured to appreciate, so the central bank offsets the pressure by selling domestic currency (equivalently, buying foreign currency). The inflow of money causes the LM curve to shift to the right, and the domestic interest rate becomes lower (as low as the world interest rate if there is perfect capital mobility).
Some of the results from this model differ from those of the IS-LM model because of the open economy assumption. Results for a large open economy, 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 and a small open economy. In particular, it may not face perfect capital mobility, thus allowing internal policy measures to affect the domestic interest rate, and it may be able to sterilize balance-of-payments-induced changes in the money supply (as discussed above).
In 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).
The Mundell–Fleming model applied to a small open economy facing perfect capital mobility, in which the domestic interest rate is exogenously determined by the world interest rate, shows stark differences from the closed economy model.
Consider an exogenous increase in government expenditure. Under the IS-LM model, the IS curve shifts rightward, with the LM curve intact, causing the interest rate 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 end up in its original position, still intersecting the LM and BoP curves at their intersection point.
The Mundell–Fleming model under a fixed exchange rate regime also has completely different implications from those of the closed economy IS-LM model. In the closed economy model, if the central bank expands the money supply the LM curve shifts out, and as a result income goes up and the domestic interest rate goes down. But in the Mundell–Fleming open economy model with perfect capital mobility, monetary policy becomes ineffective. An expansionary monetary policy resulting in an incipient outward shift of the LM curve would make capital 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 domestic money to maintain the exchange rate. The accommodated monetary outflows exactly offset the intended rise in the domestic money supply, completely offsetting the tendency of the LM curve to shift to the right, and the interest rate remains equal to the world rate of interest.
One of the assumptions of the Mundell–Fleming model is that domestic and foreign securities are perfect substitutes. Provided the world interest rate
i\star
i=i\star+
| e' | |
| e |
-1
\sigma
| di | |
| de |
=\sigma-1<0 .
y=E(i,y)+T(e,y)
| dy | |
| de |
=
| \partialE | |
| \partiali |
| di | |
| de |
+
| \partialE | |
| \partialy |
| dy | |
| de |
+
| \partialT | |
| \partiale |
+
| \partialT | |
| \partialy |
| dy | |
| de |
| dy | |
| de |
=
| 1 | |
| 1-Ey-Ty |
\left(Ei
| di | |
| de |
+Te\right) .
Ei<0 , Ey=1-s>0
Te>0 , Ty=-m<0 .
| dy | |
| de |
=
| 1 | |
| s+m |
\left(Ei
| di | |
| de |
+Te\right)
| dy | |
| de |
=
| 1 | |
| s+m |
\left(Ei(\sigma-1)+Te\right) .
dT=
| \partialT | |
| \partiale |
de+
| \partialT | |
| \partialy |
dy=Tede+Tydy
dL=
| \partialL | |
| \partiali |
di+
| \partialL | |
| \partialy |
dy=Lidi+Lydy
Li<0 , Ly>0
| dT | |
| dL |
=
| Te(s+m)+Ty(Ei(\sigma-1)+Te) | |
| Li(\sigma-1)(s+m)+Ly(Ei(\sigma-1)+Te) |
| dT | |
| dL |
=
| Tes+TyEi(\sigma-1) | |
| Li(\sigma-1)(s+m)+Ly(Ei(\sigma-1)+Te) |
.
See also: interest rate parity and Overshooting model.
See also: exchange rate and Capital asset pricing model.
The economic historian Charles Read has pointed out that Sir Robert Peel's economic policies in 1840s Britain closely followed the irreconcilable policies of the policy trilemma predicted by the model:
(i) Fixing the value of British currency to a gold standard, with the paper pound currency freely convertible to gold.
(ii) A limited banknote supply based on a fixed relationship to the gold reserve.
(iii) Free movement of bullion flows from 1819 and lower import tariffs on food and raw materials from 1842 (often loosely referred to as free trade).
(iv) Control of interest rates and a balanced budget in order to reduce the national debt.
The loss of control of interest rates and serious economic crisis every ten years (1847, 1857, 1866) is consistent with this analysis.[5]