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Chapter 12: The IS-LM-BP Model. Constructing the IS-LM-BP Model The Open Economy IS Curve (The ISXM Schedule) The BP curve The Open Economy LM Curve Exchange Rate Regimes Equilibrium in the IS-LM-BP Model Comparative Statics The Mundell-Fleming Model. Learning objectives.
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Chapter 12: The IS-LM-BP Model • Constructing the IS-LM-BP Model • The Open Economy IS Curve (The ISXM Schedule) • The BP curve • The Open Economy LM Curve • Exchange Rate Regimes • Equilibrium in the IS-LM-BP Model • Comparative Statics • The Mundell-Fleming Model
Learning objectives • Extend the traditional IS-LM model to incorporate open economy considerations • Understand the open economy version of this model, the IS-LM-BP model. The BP schedule reflects equilibrium in the balance of payments. • Analyse the various applications of this model. • Evaluate a particular version of the IS-LM-BP model, known as the Mundell-Fleming model. • Understand the impact of different exchange rate regimes on the IS-LM-BP model.
The IS-LM-BP Model • The open economy version of the IS-LM model is the IS-LM-BP model. • This adds a new line: the BP schedule which reflects equilibrium in the balance of payments. Overall equilibrium will now exist where the economy is in real, monetary and external equilibrium. • There are many different variants of the IS-LM-BP model. Different versions make different assumptions about the degree of capital mobility and the exchange rate regime.
The IS-LM-BP Model • A particular version of the IS-LM-BP model which definitely deserves attention is known as the Mundell-Fleming model. This is just the basic IS-LM-BP model with perfect capital mobility. • The second way in which different versions of the model may arise is through the type of exchange rate regime that is assumed. Under a floating regime, the exchange rate is market determined and can fluctuate accordingly. A fixed regime is where the policy maker acts to maintain the exchange rate at a particular level. It will be seen that the effects of different policies is not independent of the exchange rate regime in place.
Constructing the IS-LM-BP Model • Extending the basic IS-LM to the open economy requires two additions. • Firstly, the closed economy IS and LM curves need to be adapted to take into account the foreign influences on the domestic goods and money markets, respectively. • Secondly, the BP schedule represents the combination of income and interest rates where the balance of payments (or the external part of the economy) is in equilibrium.
The open economy IS curve (The ISXM Schedule) • Extending the IS curve to the open economy simply requires the addition of the current account or net exports. • Demand will therefore equal supply when this national income identity holds: (12.1) • C represents domestic consumption, which is represented by a typical Keynesian consumption function consisting of disposable income:
The ISXM Schedule • Investment is a negative function of the interest rate and also a set of exogenous factors: • Government spending is exogenously set: • In the previous chapter, a simple function form for the real value of net exports or the trade balance was given as follows: (12.2)
The ISXM Schedule • There are several parameters and factors here which determine the size of net exports. • The first is the real exchange rate. Providing the Marshall-Lerner condition holds, a depreciation in the real exchange rate will lead to an improvement in net exports, as consumers substitute away from foreign produced goods to domestic produced goods. • Exports are determined by the level of overseas income and the parameter , which is the proportion of foreign income spent on domestic goods. If foreign income rises, or foreigners develop a higher preference for domestic goods, then each of these and net exports will rise.
The ISXM Schedule • The total level of imports is the product of domestic income Y and the marginal propensity to import. As income rises, consumers will tend to spend more – a proportion of which will be on foreign goods and services. Alternatively, if the preferences of domestic consumers were to switch towards foreign goods, then and total imports will rise. • Hence, substituting this into (12.1) gives: (12.3)
The ISXM Schedule • Rearranging this, we can derive the equilibrium level of income as a function of all the parameters and variables: (12.4) • This is the open economy version of the IS curve. To differentiate this from the closed economy version, we can entitle it as the ISXM schedule. • The ISXM curve also slopes downwards, as a rise in interest rates will lead to a fall in investment, and then a multiplied fall in income.
The ISXM Schedule • However, the slope of the ISXM curve will be steeper than that of the standard IS curve. This is because the multiplier is now smaller, following the addition of the marginal propensity to import. • In the closed economy, the multiplier was 1/(1-c). This can be written as 1/s, where s is the marginal propensity to save. • In the open economy, the multiplier is: or . • As long as the marginal propensity to import is positive, the multiplier will be smaller.
The ISXM Schedule • Imports are a leakage from the circular flow of income. As the marginal propensity of import increases, a higher proportion of any additional income will be spent overseas rather than on domestically produced goods and services. Consequently, the multiplier will be lower. • Other than this, the ISXM schedule will behave in exactly the same way as the closed economy version. • A change in anything other than the level of income or the interest rate will lead to a shift in the ISXM curve. Specifically, if exports rise because foreign income or the proportion dedicated to domestic goods and services increase; or imports fall due to a decline in the marginal propensity to import, then equilibrium output will rise and the ISXM curve will shift outwards.
The ISXM Schedule • An important feature of the ISXM curve is that it will be expected to shift if there is a change in the real exchange rate. • Providing that the Marshall-Lerner condition holds, a real appreciation reduces the competitiveness of domestic goods and services. Exports will fall, and imports will rise and the ISXM curve will shift inwards. • If there’s a real depreciation, then the opposite holds true. The improved competitiveness of output produced at home will lead to a fall in imports and a rise in exports, and the ISXM curve will shift outwards. • Strictly speaking, the ISXM curve should also pivot as the multiplier will change due to the exchange rate effect on the marginal propensity to import.
The BP curve • This represents equilibrium in the balance of payments. • The BP schedule plots the combinations of income (Y) and interest rates (r) where total inflows and outflows to and from overseas are equal. • The balance of payments consists of two main parts: the current and capital accounts. • The current account is mainly determined by the trade balance or the value of net exports (X-M). • The capital account is largely driven by financial flows, where international investors move funds around the world in search of the highest returns.
Versions of the IS-LM-BP Model • Different versions of the IS-LM-BP model make varying assumptions about the degree of capital mobility. • If there is no capital mobility, then finance cannot flow across borders and the capital account doesn’t exist. The entire balance of payments position is set by the trade balance. • Where there is perfect capital mobility, capital can flow freely with no restrictions. Given that capital flows are large in comparison to trade (exports and imports), the capital account will then tend to dominate the balance of payments position.
Versions of the IS-LM-BP Model • In constructing the BP curve, we allow for three different levels of capital mobility. • no or zero capital mobility • Perfect capital mobility • capital mobility is neither zero nor perfect
No capital mobility • The balance of payments is represented by only the trade balance or the value of net exports. The BP schedule (equilibrium in the balance of payments) can therefore be substituted by a BT schedule (equilibrium in the balance of trade). • The BT curve is plotted as the combinations of income and interest rates where the trade balance is in equilibrium, BT=0 =X-M.
No capital mobility • The import function relates the domestic level of income to the total amount of imports. Assuming a positive and constant marginal propensity to import, the import function will be an upward sloping function against the domestic level of income. • A real depreciation in the exchange rate will lead to a downward pivot in the import function. As domestic goods become more competitive, consumers will switch their consumption towards them and away from foreign goods; so, the marginal propensity to import will fall. • The import function will pivot, and the total fall in imports will of course depend on the level of income.
No capital mobility • Overall equilibrium in the balance of trade will arise where the export and import functions coincide. This will then determine the BT schedule: (12.6)
No capital mobility • A position to the right of the BT schedule indicates a deficit in the balance of trade. Here, imports exceed exports. Likewise, a position to the left of the BT schedule represents a deficit, exports exceed imports. • We have already seen that a change in the real exchange rate leads to a shift in the export function and a pivot in the import function. • Following a real depreciation, domestic goods become more competitive vis-à-vis those produced abroad. As a result, the export function will shift upwards and the import function will pivot downwards. This means that the level of income where the balance of trade is in equilibrium will increase.
Perfect Capital Mobility • Under conditions of perfect capital mobility, if r is the domestic interest rate and r* is the foreign rate, then the following holds true: • If the domestic interest rate exceeds the foreign interest rate, then capital will flow into the country and the balance of payments will move into surplus. • If the domestic interest rate is less than the foreign interest rate, then capital will flow out of the country and the balance of payments will move into deficit. • Therefore, balance of payments equilibrium will be where r=r*. As only a miniscule deviation from the overseas interest rate is required to generate large capital flows, the BP schedule will hence be flat at the overseas interest rate.
Perfect Capital Mobility • Changes in the exchange rate will not have any impact on this curve. • As the BP schedule is horizontal, a horizontal shift in itself will have no discernable effect. • The other reason is due to the fact that the trade balance is only a small part of the balance of payments. Therefore, changes in exports and imports have a very small effect on the balance of payments relative to the scale of capital flows.
Intermediate Capital Mobility • BP curve is upward sloping. • As income rises, imports and the balance of trade deficit become greater. In turn, larger capital account surpluses will be required to offset this deficit. These capital account surpluses can be achieved by offering higher interest rates. • If a country borrows heavily, however, the increased perception of default is likely to increase the risk premium. • As a result, higher and higher interest rates would be required in order to attract the required capital inflows to maintain the balance of payments.
What Shifts the Furthest: The IS or BP Schedules? • Following a change in the real exchange rate, and assuming that the Marshall-Lerner condition holds, both the IS and BP schedules will shift horizontally and in the same direction. • The answer to the question as to which one shifts the furthest can be answered by looking at the equations that describe the ISXM and the BT schedules. • As we are only interested in what happens following a change in the exchange rate, we can make some simplifying assumptions to the ISXM equation. These are as none of these variables depend on the real exchange rate.
What Shifts the Furthest: The IS or BP Schedules? • The new ISXM schedule is now written as: • Suppose there was a real depreciation in the currency. Exports will rise and produce a multiplier effect on the level of income where the goods market and the trade balance are in equilibrium. • The only difference between the multipliers is the term 1-c in the IS schedule. As long as this is greater than zero, the multiplier attached to the ISXM schedule will be smaller. Given that it is almost certainly the case that 1-c>0, the ISXM schedule will shift by a smaller amount than the BT schedule.
The Open Economy LM Curve • The LM curve in an open economy is exactly the same as its closed economy counterpart. It defines the combinations of income and interest rates where the demand and supply of money are equal to each other. • As we have seen in chapter 7, this is an upward sloping function. • As income rises, the demand for money increases due to the transactions motive. • By increasing interest rates, the excess demand for money is countered, as higher bond yields encourage people to hold less cash and move into bonds.
The Open Economy LM Curve • The open economy, though, can exert a powerful effect on the money market. The conventional closed economy LM curve is derived under the assumption that the money supply is fixed. In a closed economy, the government or the monetary authority is assumed to have complete control over the money supply. • In an open economy, in contrast, this proposition is less likely. As we will see, there is a direct relationship between the money supply and the balance of payments position. • The position of the LM curve is therefore linked to that of the BP schedule.
The Open Economy LM Curve • The factors determining the supply of money are covered in some detail in chapter 5. In brief, the money supply is equal to a multiple of the high powered money stock (H), also known as the monetary base. The money supply, including the demand deposits, will be a multiple of the monetary base. This multiple will be determined by the size of the money multiplier: • In the closed economy, the change in the monetary base is equal to the public sector deficit (PSD) less government sales of bonds. This is essentially the government deficit that is paid for by cash (by printing money) rather than through bond sales:
The Open Economy LM Curve • In an open economy, there will a further determinant to the stock of high powered money. This is the net purchase of foreign reserves (R) by the central bank: • Assuming that the public deficit is entirely financed by bond sales, then in the open economy, the money supply is driven by central bank changes in reserves (foreign assets). The change in reserves now represents the official financing of the balance of payments.
The Open Economy LM Curve • For the sake of simplicity assume that there is no capital mobility, so that the balance of payments position and thus the size of official financing or the change in foreign reserves is determined by the trade balance . • In this case, the high powered money stock can be described as follows: • Any discrepancy between exports and imports will see the domestic monetary base rising or falling in line with movements in the foreign exchange reserves of the central bank. The change in the money supply is:
The Open Economy LM Curve • We are now in a position to describe how the LM and BP (money markets and the balance of payments) interact.
The Open Economy LM Curve • The interaction between the balance of payments and the money supply implies that the central bank, government, or other monetary authority will find it impossible to exert control over the money supply in an open economy. This, though, is not entirely true. • In the above figure, points a and c are not sustainable because adjustments in the money supply will push the economy to a position where the balance of payments is equilibrated. • In an open economy, the money supply can be expressed as follows:
The Open Economy LM Curve • In the above, we simply assumed that the public sector debt was funded entirely by bond sales, leaving the money supply to be driven by the change in foreign reserves. • Bond sales in this case are just sufficient to stop any public sector surplus or deficit from affecting the money supply. However, in the same way, it is possible for bond sales to be used to prevent trade imbalances from affecting the domestic money supply. • In this case, bond sales are set so that: • This process of selling or purchasing excess bonds is known as sterilization.
The Open Economy LM Curve • The balance of payments consists of not only the trade balance (current account) but also the capital account: BP = X – M + net capital inflows. • The change in reserves (R) is determined by the official financing required to achieve BoP equilibrium. • When there is perfect capital mobility, any domestic interest rate above the foreign rate would produce large-scale capital inflows and lead to an increase in the money supply as foreign reserves accumulate (c to d). • Conversely, when the equilibrium in the money market produces an interest below the foreign rate, large capital flows lead to a deficit on the balance of payments. The process of official financing will lead to falling foreign reserves and a fall in the money supply, shifting the LM curve upwards – a movement from a to b.
The Open Economy LM Curve • An important issue which certainly requires some discussion is the ability of the monetary authorities to control the domestic money supply (the position of the LM schedule) in an open economy. • Previously, we mentioned that the monetary policy can do this by sterilizing the impact of official financing on the money supply. This was in the case of there being low capital mobility. • Does the result carry over to the case of perfect capital mobility? The conventional wisdom would argue that the answer to this question is no.
The Open Economy LM Curve • Where there is no capital mobility, sterilization is only required to offset the effects of the trade balance. However, under perfect capital mobility, only very small differences in home and foreign interest rates are required in order to produce very large flows of capital. • It, therefore, comes down to a question of scale. • Sterilization is more realistic when dealing with relatively smaller levels of official financing. For this reason, it has become a well-established phenomenon that policy makers cannot hope to have high capital mobility and also the power to control the money supply (set the position of the LM curve). • Where capital is perfectly mobile, the LM curve effectively disappears, and the money supply is automatically determined so that r*=r.
Equilibrium in the IS-LM-BP Model • The point where the three schedules intersect represents the combination of income and interest rates where the goods market, the money market and the balance of payments are all in equilibrium. • Having established this model, it can now be applied in a number of ways. Fiscal policy will shift the IS schedule, monetary policy the LM schedule, and exchange rate policy the BP schedule.
