## MUNDELL-FLEMING MODEL (Encyclopedia)

The Mundell-Fleming Model (MFM) describes the workings of a small economy open to international trade in goods and financial assets, and provides a framework for monetary and fiscal policy analysis.The basic framework is a static, non-microfounded model extending the Keynesian IS-LM model. Indeed, the MFM shares with the IS-LM model the philosophical and methodological approach, and the basic features: the model is linear and the main assumption is that consumer prices are fixed. As a matter of fact, the MFM nests the IS-LM model as a special case, for a particular parameterisation.

The starting point of the IS-LM model, which describes a closed economy, is the income identity, which requires the equality between the overall output of the economy and the sum of absorption channels: private consumption (C), private investment (I) and public spending (G):

(1)

Rather than being just an identity, the above equation has also an alternative interpretation, since it defines the composition of aggregate demand and the clearing condition for the goods market. Each of the components above, indeed, describes the behaviour of one particular kind of agent that populates the economy. The first component (C) describes the behaviour of the household, and can be cast in the form of the following linear relation:

(2)

Private consumption, therefore, is an increasing function of personal income Y, net of taxes paid to the fiscal authority T: higher income levels make the budget constraint looser and support higher levels of spending. Parameter c defines the income elasticity of private consumption, also known as the "marginal propensity to consume", while C° captures an exogenous component to private consumption. The second component (I) describes the behaviour of firms, and can be cast in the form

(3)

according to which the demand for private investment is decreasing in the interest rate (higher interest rates reduce the number of investment projects that are profitable enough to be preferred to bonds, which in turn pay the interest rate), with elasticity a.^{1}The third component, finally, describes the behaviour of the fiscal authority, controlling the amount of public spending (G = G°), and taxes collected according to the linear rule

(4)

which implies that taxes consist of a lump-sum component (T°) and a component proportional to income, with t being the marginal tax rate.

The MFM, therefore, extends such framework to an open economy. For the goods market, this implies some additional components of aggregate demand. In particular, in an open economy, both consumption and investment goods produced domestically may be demanded and purchased by foreign agents. In this case, we talk about "exports" (X). Similarly, domestic consumers and firms may demand and purchase consumption and investment goods produced abroad. In this case, we talk about "imports" (M). The difference between these components measures the "Net Exports" (NX=X-M). The income identity for the case of an open economy accounts for such an additional component:

(5)

In this case, indeed, C and I capture the total demand of domestic agents for consumption and investment goods, including both domestic and foreign goods. On the other hand, Y measures domestic production of goods, regardless of the fact that the final use of these goods takes place domestically or abroad. The term NX accounts for this discrepancy, by subtracting the part of the domestic demand that involves foreign goods (M) and adding the part of domestically produced goods directed to the foreign market (X).To fully understand this additional component and how it is related to the rest of the macroeconomy, it is necessary at this point to introduce an additional macroeconomic variable, which the IS-LM model lacks, as it is peculiar of a system open to international relations: the exchange rate. The nominal exchange rate (e) defines the price of domestic currency in units of foreign currency.^{2}Given this definition, an increase in e implies an appreciation of the domestic currency (you need more dollars to buy one euro), while on the contrary a reduction in e implies a depreciation of the domestic currency. This additional variable is key to understand the behaviour of the agents that interact in the international markets, because a domestic consumer purchasing a foreign good has to pay a price denominated in a foreign currency. To evaluate how convenient that good is, in relation to a substitute good produced at home, the consumer has to compare the respective prices, and in order to do that he/she has to convert them in a common currency. To this end, he/she is going to use precisely the exchange rate. Moreover, with respect to this additional variable, we also define the monetary regime: in particular, the Central Bank can leave the exchange rate free to fluctuate in response to the varying international economic conditions, or else it can commit to the target of a given value (or interval) for the domestic currency. In the first case we talk about a regime of *flexible* exchange rates; while in the second case, we talk about *fixed* exchange rates. As the exchange rate appreciates, exports fall (since domestic goods are more expensive to foreign consumers) and imports increase (since foreign goods are cheaper to domestic agents). Accordingly, given the definition of the exchange rate specified above, we can represent the net exports as a decreasing function of the exchange rate:

(6)

in which* b* and *q *capture the output and exchange-rate elasticity of net exports, respectively, and NX° measures the exogenous component (depending e. g. upon the level of foreign output).

Using the equilibrium condition (5), and the behavioural equations describing the several components, we can write the open-economy version of the IS schedule as:

(7)

The open-economy IS curve is therefore a decreasing function of both the interest rate (as in the closed-economy framework) and the exchange rate:

Figure 1. The open-economy IS curve, as a function of the interest rate (sx) and exchange rate (dx).

Changes in the exchange rate induce changes in aggregate demand and imply movements along the IS schedule, if the latter is drawn in the plane (Y, e), while they imply parallel shifts of the whole schedule, if it is drawn in the plane (Y, i).

The money market is described by the same equations as in the closed-economy framework. The money demand reflects the three Keynesian determinants and is therefore increasing in total output and decreasing in the interest rate:

(8)

The money supply, in its baseline formulation, is instead exogenous and under the direct control of the Central Bank, and is therefore the monetary policy instrument (M^{s} =M°). The LM schedule, describing the clearing of the money market (M^{d} =M^{s}), defines therefore a positive relation between output and interest rate, just as in the closed-economy version of the model:

(9)

The level of money supply determines the location of the schedule in the plane (Y, i).

In a closed economy, equilibrium in both goods and money markets is sufficient to describe the general equilibrium of the economy (equilibrium in the residual bond market is ensured by the Walras’ law). In an open economy, instead, general equilibrium requires in addition also the equilibrium in the external sector, described by the Balance of Payments, which records all international transactions. In particular, the Balance of Payments consists of the sum of the current account (the trade balance) and the capital account (the capital flow). The trade balance is measured by the net exports, and depends upon domestic output and the exchange rate, as discussed above. The capital flow (CF), instead, is increasing in the differential between domestic and foreign interest rates:

(10)

As the domestic interest rate increases above the foreign one, financial assets denominated in the domestic currency pay relatively better than foreign assets, and the domestic country experiences a capital inflow (CF >0).^{3 }Such inflow is the stronger the higher elasticity.

Therefore, equilibrium in the external sector can be described by the schedule BB, defining the locus of output and interest-rate combinations which ensure:

(11)

Such relation is positively sloped, similarly to the relation described by the LM curve. On the external sector, the MFM imposes specific assumptions. In particular, the model assumes that: 1. the economy is a small open economy; 2. domestic and foreign assets are perfect substitutes for each other; and 3. there are no restrictions of any kind on capital movements across the border. Direct implications of these assumptions are that: 1. the foreign interest rate is exogenous to the domestic conditions; 2. the capital flows depend solely on the interest-rate differential; and 3. the elasticity of capital flows with respect to the interest-rate differential is infinite. These implications are reflected in the position and slope of the BB schedule, describing the equilibrium in the external sector:

Figure 2. The equilibrium condition in the external sector: the BB schedule.

In particular, the BB schedule is horizontal, with intercept equal to the foreign interest rate: even an infinitesimal differential between domestic and foreign interest rates, given perfect substitutability and zero-restrictions to capital movements, would indeed induce an infinite capital flow across the border. Therefore, equilibrium in the external sector requires i = i*.

The general equilibrium is achieved when all markets clear at the same time. In the context of the MFM, this requires a triple of output, interest and exchange rates at which all equilibrium conditions (equations 7, 9, and 11) are satisfied. From a graphical perspective, this requires the intersection of the IS, LM and BB schedules in a single point:

Figure 3. General equilibrium in the Mundell-Fleming Model.

From an analytical perspective, the solution to the model depends on the specific exchange-rate regime. With flexible exchange rates, the system can be solved recursively: equilibrium in the external sector determines the domestic interest rate (i =i*, and therefore the position of the BB curve), equilibrium in the money market determines the level of output Y°, given the equilibrium domestic interest rate (from the intersection of LM and BB), and finally the equilibrium in the goods market, given the levels of output and interest rate found earlier, implies the equilibrium level of the exchange rate (and therefore the position of the IS schedule that ensures a unique intersection among the BB, IS and LM curves). With fixed exchange rates, the Central Bank commits itself to support a specific level of the exchange rate (for example e°). Since the monetary policy instrument is money supply (Ms), this regime implies that the latter is determined endogenously to support the exchange rate target. In this context, the system can also be solved recursively, although following a different order: equilibrium in the external sector determines the domestic interest rate, i =i*; given such value, and the target level for the exchange rate (e°), equilibrium in the goods market determines the equilibrium level for the real output (from the intersection between BB and IS, whose position is determined by e°). Finally, the equilibrium in the money market yields the level of money supply consistent with both equilibrium output Y° and target level of the exchange rate e° (i.e. it determines the position of the LM schedule by ensuring a unique intersection with BB and IS). The specific exchange rate regime has important consequences for the analysis of the effects of monetary and fiscal policy. Specifically, with flexible exchange rates, monetary policy is most effective because it is amplified by the fluctuations of the exchange rate that it induces. On the contrary, fiscal policy has no effect at all on the real activity, because it is completely sterilised by the exchange rate reaction. Indeed, a monetary expansion shifts the LM schedule out in LM’. The excess money supply induces downward pressures on the interest rate, which in a closed economy would raise the speculative demand for money and close the excess supply. In an open economy, however, the downward pressures on the interest rate translate immediately into capital outflow and a consequent depreciation of the domestic currency (given the infinite elasticity of the capital flow to the interest-rate differential). The currency depreciation, in turn, makes domestic goods more competitive on the international markets and the foreign demand for domestic goods thereby increases: net exports rise and the IS schedule shifts out in IS’. The increase in net exports raises equilibrium output from Y° to Y’ and consequently the transactions demand for money: the money market clears even if the interest rate does not move.

Figure 4. The effects of a monetary expansion with flexible exchange rates

The overall effectiveness of monetary policy is stronger than in a closed economy because the transmission mechanism only works through the exchange rate, with no variations in the interest rate: in a closed economy, instead, the interest rate falls, investment and output rise, and the excess money supply is closed by means of an increase in both transactions and speculative money demand. Fiscal policy, on the contrary, is completely ineffective with respect to equilibrium output. An increase in public spending, indeed, shifts the IS curve out into IS’, raising domestic demand. By doing so, however, it induces upward pressures on the interest rate (for a given money supply), which in turn translate into an appreciation of the domestic currency and a reduction of net exports: the fall in foreign demand is exactly the same as the increase in domestic one. Public spending, therefore, crowds out net exports completely, and the IS curve shifts back in IS’’. Interest rate and output do not change and the only effect that fiscal policy exerts is an appreciation of the exchange rate. Although ineffective with respect to output, however, it is worth noticing that fiscal policy is not ineffective altogether: indeed it induces an income redistribution between agents producing goods for the foreign markets and those producing goods for the domestic one.

Figure 5. The effects of a fiscal expansion with flexible exchange rates.

The policy implications are completely reversed with fixed exchange rates. Monetary policy is ineffective because money supply cannot be affected without violating the exchange rate target. A monetary expansion, indeed, by inducing downward pressures on the interest rate, would imply a depreciation of the domestic currency, in contrast with the exchange rate target. To meet the target, then, the Central Bank would have to close the excess supply of domestic currency on the international currency markets by selling foreign currency in exchange for the domestic one: money supply falls and the LM shifts back in. Equilibrium output therefore remains unaffected, just like the interest and exchange rates: the only effect of the monetary expansion would be the replacement, within the assets side of the Central Bank’s balance sheet, of foreign reserves with domestic bonds.

Figure 6. The effects of a monetary expansion with fixed exchange rates.

A fiscal expansion, on the contrary, is amplified by the response that the Central Bank needs to ensure to meet the exchange rate target. An increase in public spending, indeed, induces upward pressures on the interest rate and, consequently, an appreciation of the exchange rate. Such appreciation of the domestic currency makes the domestic Central Bank enter the international currency markets to close the excess demand of domestic currency, by purchasing foreign currency in exchange for the domestic one: the LM schedule shifts out, money supply increases and it accommodates the fiscal expansion. Equilibrium output increases from Y° to Y’, while neither the interest rate nor the exchange rate vary.

Figure 7. The effects of a fiscal expansion with fixed exchange rates.

The effectiveness on equilibrium output is stronger than in a closed economy because the exchange rate target forces the Central Bank to expand the money supply, preventing the domestic interest rate to rise and crowd out private spending, as it would instead happen in a closed economy.

____________________________^{1}Given the assumption of fixed prices, nominal and real interest rates are the same.^{2}Also with respect to the exchange rate, there are two relevant definitions: the nominal exchange rate, as defined in the text, and the real exchange rate, which instead measures the ratio between the foreign and the domestic price indexes, in terms of a common currency. Given the assumption of fixed prices, however, the two definitions coincide, up to an appropriate normalisation (similarly to the case of the interest rate).^{3}In evaluating alternative financial assets denominated in different currencies, investors in financial markets should also consider their expectations about the change in the exchange rate, between the moment in which the asset is purchased and that in which it pays off. In the present context, however, we are considering a static world, in which the expectations about the future level of the exchange rate coincide with the current level. Accordingly, the differential between interest rates is the same as the differential in ex-ante rates of return.

Editor: Salvatore NISTICO'

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