The Small Open Economy ISLM Model

Henry Thompson International Economics

Macroeconomics is based on models that describe aggregate economic behavior and the response of the economy to shocks from energy prices, financial system failures, foreign recessions, exchange rate shocks, and government monetary and fiscal policies. The ISLM model is the workhorse macro model and this introduction focuses on the small economy open to international trade and investment. IS indicates investment and saving on the real side of the economy and LM stands for liquidity and money on the monetary or financial side of the economy. The main advantage of the ISLM model is that it includes consumption, investment, government spending, taxes, exports, imports, the interest rate, exchange rate, and national output in a single framework. Unemployment and inflation, the two major policy targets of macroeconomics, are indirectly linked to the ISLM model. The ISLM model does not include optimal decision making by households, firms, and government, and does not include the production and distribution of output, the labor market, or economic growth. Although the ISLM model has shortcomings, its appeal is the overall description of how the major macroeconomic variables in an economy react over time periods of a few quarters or a year. The ISLM model is also worth studying because it remains the primary model used by government policy makers, financial commentators, and macroeconomic consultants. This introduction examines the open economy ISLM model, focusing on the role of government policy to influence output and unemployment. A mix of government policies are considered, fiscal policy in government spending and taxation, monetary policy in control of the money supply, and exchange rate policy in the central bank choice of a fixed or floating exchange rate. Inflation is anticipated in the ISLM model. The small open economy is assumed to be a price taker for the global interest rate in the international credit market. The balance of trade and international investment in the capital account are included in the adjustment process. For the small open macroeconomy the exchange rate, trade, and international investment prove critical to the adjustment process.

A. Production, absorption, and trade along the IS curve Three groups inside the economy (consumers, firms, government) consume aggregate output Y. The three types of spending are C I G household consumption firm investment government spending.
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Absorption A is the sum of these three types of domestic spending, A = C + I + G. The balance of trade BOT = X M is added to A to derive gross domestic product Y. Exports are produced but not consumed and must be added to A, while imports are consumed but not produced and must be subtracted. The complete expenditure accounting framework for gross domestic product is Y = A + BOT = C + I + G + X M, where Y A BOT X M gross domestic product absorption balance of trade export revenue import spending

Short of changing inventories, everything that is produced on the left side of the equation is absorbed by the economy or exported. Imports are consumed but not produced and included on the right hand side. When BOT > 0 there is a trade surplus with the economy producing more than it absorbs, lending to other countries and accumulating wealth, and when BOT < 0 there is a trade deficit with the economy borrowing and spending wealth. The national accounting scheme says nothing about how economic agents in the economy behave and behavioral assumptions are required to build a macro model. The IS curve summarizes these behavioral assumptions and shows combinations of output and the interest rate that balance spending and production. Consumer spending depends on income Y after taxes T and the interest rate, (+) (-) C = C( Y T , r ) . The (+) indicates that an increase in disposable income Y T leads to an increase consumer spending. Consumers typically save a only fixed portion of disposable income. Taxes are exogenous to the ISLM model. While taxes are not explained by the model, it can analyze the effects of exogenous changes in fiscal policy variables T or government spending G. The motivation for government spending and taxes is based on economic and political decisions. Consumption spending also depends on the real interest rate r. A higher interest rate induces consumers to save more as indicated by the (-) sign. Bonds pay a rate of return equal to the nominal interest rate R on the single riskless bond issued by firms or the government to borrow.

The Fischer equation relates the real interest rate r to the nominal interest rate R and expected inflation , r = R . Expected inflation and the real interest rate are critical variables. The ISLM model keeps the price level P fixed making inflation equal to zero and implying r = R. Over long time periods, however, the government controls the money supply and by implication the price level P. A higher growth rate in the money supply leads to a higher price level P. Inflation = P/P is determined by money supply policy, complicating the macro adjustment. Consumption in fact also depends on expectations about future income and prices, average age of the population, changes in the propensity to save, changes in trade protection, and so on. This introduction sticks with the simplest assumptions. If a macro model proves capable of predicting aggregate behavior, it is useful regardless of its assumptions and the ISLM model has proven useful. Investment spending I by firms depends on the interest rate r. Firms consider the opportunity cost of buying bonds when making investment decisions. Firms with retained earnings have the option of investing in an array of projects such as a new assembly line or new delivery trucks, and rank these investment projects according to their rates of return. The most attractive investment projects are those with the highest rates of return, and they are the first ones done subject to liquidity constraints. Any investment project has to offer a higher rate of return than the market interest rate r to be considered. Firms with retained earnings have the option to buy bonds or invest in internal projects, and would invest in any project with a rate of return higher than r. Firms without retained earnings could possibly borrow by selling bonds to raise funds to invest in projects with rates of return higher than r. Investment spending declines with an increase in the real interest rate r since fewer investment projects would be profitable. The investment function is then (-) I = I( r ). The ISLM model does not explain government spending G but examines the effects of fiscal policy when G changes. The basic government budget is tax income less spending, T G. The government also has to pay the interest expense rB on its outstanding bonds B but can print money Ms or sell bonds B to finance a deficit if T < G + rB where means change in. The government budget constraint is G + rB = T + Ms + B. The money supply Ms plays an important role and the government is responsible for controlling it through the Central Bank. The government also sets taxes T and determines whether to sell or buy

bonds B. A drawback from raising funds by selling government bonds B > 0 is the higher spending rB in the future. The next term in the national income expenditure equation is export revenue. The exchange rate plays a role in determining export revenue and import spending as do changing price levels at home and abroad. Suppose there is a single foreign country. The real exchange rate eP*/P is the relative price of imports, or in units eP*/P = ($/)(/m) ($/x) = ($/m) ($/x), where the exchange rate is the price of foreign currency e = $/, P* = /m is the foreign euro currency price of imports m, and P = $/x is the home dollar currency price of exported products x. This relative price of imports is the price of a unit of imports m in terms of a unit of exports x. Depreciation refers to a higher exchange rate eP*/P that raises the home currency price of imports. Depreciation may be due to a higher e, an increase in P*, or a decrease in P. The resulting change in export revenue depends on the import elasticity. Export revenue also increases with foreign income Y* since foreign purchases of home products increase with higher income. The export revenue function is (+) (+) X = X( eP*/P, Y* ). Depreciation raises export revenue X. A higher foreign price level P* raises export revenue since the foreign country would substitute toward cheaper imports. A higher home price level P induces foreign consumers to substitute away from home goods, lowering X. Higher foreign income Y* causes an increase in foreign spending on home exports. Import spending is the mirror image of export revenue, (-) (+) M = M( eP*/P, Y ) . An increase in national income increases import spending M and lowers the BOT = X = M. Depreciation raises the BOT with an increase in X and a decrease in M. Depreciation raises the BOT if exports plus imports are elastic, the Marshall-Lerner condition. Adjustment to depreciation can lead to a J-curve in the BOT. Traders do not immediately respond to the exchange rate since trade contracts are set in advance. The BOT falls with depreciation before rising as traders adjust to the higher price of foreign products. The J-curve refers to this drop then ultimate increase in the BOT over time. Combining absorption A and the BOT into a single equation, (+) (-) (-) (+) (+) (-) (+) Y = C( Y T, r ) + I( r ) + G + X( eP*/P, Y* ) M( eP*/P, Y ).

This equation is the IS curve in Figure 1 graphed with r on the vertical axis and Y on the horizontal axis. The IS curve shows combinations of r and Y that equalize production Y and spending A + BOT. Along the IS curve there is product market equilibrium.
r

IS' IS

Y Figure 1. The IS Curve

The IS curve has a negative slope since an increase in Y is larger on the left side of the equation than the resulting increase on the right side. Only part of an increase in income is consumed since the marginal propensity to consume is less than one. Also increased income raises import spending M. To return to product market equilibrium on the IS curve, r must fall. The IS curve shifts to the right as in Figure 1 due to a number of exogenous changes. The IS curve shifts right due to these changes in exogenous macro variables, e P* P Y* G T depreciation raises X and lowers M higher foreign price level raises X and lowers M lower home price level raises X and lowers M higher foreign income raises X increased government spending, a fiscal policy expansion lower taxes increase disposable income, a fiscal policy expansion.

The IS curve also shifts to the right with the following behavioral changes: C I X M increased propensity to consume structural increase in investment increase in foreign excess demand for home exports decrease in home excess demand for foreign exports

The IS curve is half of the ISLM model. The other side of the economy is based on the money or bond market.

B. The money and bond market along the LM curve The money side of the ISLM model is based on equilibrium between the supply and demand for money. The real money supply is Ms/P where Ms is the nominal money supply and P is the price level. In units Ms = $ and P = $/good implying Ms/P is the money supply in terms of goods. The price level P deflates the nominal money supply Ms in case of inflation. Over years, most economies have inflation. Real money demand L is a function of the transactions demand for money and the opportunity cost of holding money rather than bonds. All agents demand money for transactions, and higher income Y implies more transactions. A higher real interest rate means a higher return on bonds or a higher opportunity cost of holding money. With a zero real interest rate, holding cash would be as productive as holding bonds. With a very high real interest rate, it would be optimal to hold as little cash as possible since future income is lost with idle cash. The money market equilibrium is the equilibrium between money supply and demand, (+) (-) Ms/P = L( Y, r )
Yeni ki, dustura gore, Ms/P-ye Y musbet ve r menfi tesir etdiyinden ve IS-LM modelde Y absis oxu, r ordinat oxu uzre yerleshdiyinden, LM curve upward slopping olmalidir. Diger terefden de LM eyrisi pula telebi ifade edir ve teleb eyrileri upward slopping olurlar.

in Figure 2. The LM curve slopes upward due to the signs of Y and r. An increase in Y raises the demand for money and r would have to increase to lower money demand back to the money market equilibrium along the LM curve.

LM LM'

Y Figure 2. The LM Curve

The LM curve shifts to the right as in Figure 2 due to changes in exogenous variables or a behavioral shift in the demand for money, Ms government expansion of the money supply
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P L

lower price level or deflation structural decline in money demand

endogenous factor

A structural decrease in money demand also shifts the LM curve to the right and can be due to improved bond quality with lower risk increased desire to buy bonds and save lower expected future income saving to smooth consumption over time lower expected prices and desire to wait until prices fall currency substitution, holding foreign currency instead of home currency increased use of credit cards. The interest rate R is linked to the foreign interest rate R* by interest rate parity IRP, 1 + R = [(1/e)(1 + R*)]Ee, where Ee is the expected exchange rate. IRP says that the return on a home bond 1 + R must equal the return on a foreign bond due to arbitrage across the international bond market. The foreign return on one unit of domestic currency 1/e is converted back to domestic currency at the expected rate Ee. Simplifying IRP, the home interest rate is approximately equal to the foreign interest rate plus the expected home currency depreciation, R = R* + (Ee e)/e . The home interest rate is lower than the foreign interest rate when Ee < e or the home currency is expected to appreciate. Investors cover themselves with the forward exchange rate f in the covered interest parity CIP condition R = R* + (f e)/e . The forward discount on domestic currency is (f e)/e. If f > e the home currency is expected to depreciate and R > R*. The forward rate f is an unbiased predictor of e. Inflation plays a role in deciding where to invest. Arbitrage implies exchange rates follow price levels according to purchasing power parity PPP, P = eP*, and PPP implies a link between home and foreign inflation rates, = e/e + * . An inflating currency depreciates. The IRP condition becomes R = R* + ( *). If < * then R < R*. A small open economy takes the global real interest rate r* as given as in Figure 2. The economy adjusts to r* since home savers have the option to buy foreign bonds at r*. The home interest
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rate r might differ temporarily from the foreign interest rate r* but there adjustment to r* occurs in the ISLM equilibrium. The small open economy is open to trade in the BOT along the IS curve and open to foreign investment at r* along the LM curve. The following sections put the IS and LM curves together into the open economy ISLM model.

C. The small open ISLM economy with a flexible exchange rate Figure 3 combines the IS and LM curves into an equilibrium at the international interest rate r* and equilibrium income Ye. At the intersection of the IS and LM curves, there is an equilibrium in both the product market on the IS curve and the money/bond market on the LM curve. Figure 3 includes the full employment level of output Yf. If Ye < Yf there is unemployment and for some reason the wage does not fall to clear the labor market. An increase in output Y would lower unemployment given some slack in the labor market.
r LM

r* IS

Ye Yf Y Figure 3. Equilibrium and Full Employment Output

A primary goal of macro policy is to keep Ye close to Yf although it is far from clear that fiscal or monetary policy can achieve it. Some theory and evidence suggest the economy would adjust more quickly without active policy. Start in the equilibrium in Figure 3 and examine the effects of a change government policy. First consider expansionary monetary policy with an increase in the money supply Ms . The LM curve shifts right to LM as shown in Figure 4. The economy adjusts to the point where the new LM curve intersects the IS curve with a lower interest rate r and higher output Y. The lower interest rate makes foreign bonds attractive to home lenders leading to a flow of funds to the foreign currency that depreciates the home currency. The capital account KA in the balance of payments BOP moves to deficit as the economy lends to the rest

of the world. Depreciation leads to a BOT surplus and the right shift in the IS curve. On the new IS curve the economy returns to BOT = 0.
r LM LM' depreciation Ms increase r*

IS Ye Yf Y Figure 4. Monetary Expansion with Flexible Exchange Rate

The secondary shift moves to its new equilibrium at the world interest rate r* and Yf. Note that Y increases due to the original shift in the LM curve from the increase in Ms and again due to the subsequent shift in the IS curve with the depreciation and expanding BOT. The interest rate r falls but then rises back to the world level r* and IRP implies the currency appreciates as r rises. The exchange rate depreciates and overshoots before appreciating back to its new equilibrium. Overshooting is a characteristic of price adjustment in all asset markets. Given a shock, asset prices overshoot their long term level. PPP implies depreciation if P rises due to the increase in Ms. In an economy near full employment there would be no output increase, only depreciation and inflation due to the increase in the money supply. Even with slack in the economy, it is an open question whether expansionary monetary policy is the best way to eliminate it. Any structural problem in the labor market causing unemployment should be remedied directly. Without any doubt, continued increase in the growth of the money supply leads to depreciation and inflation and has no effect on income. The goal of a stable price level has proven the most sensible and reliable way to conduct monetary policy. Active policy of continuously manipulating Ms to affect unemployment is ill advised and the most sensible monetary policy target is a stable price level. Summarizing, expanding the money supply in a small open economy with flexible exchange rates causes a temporary drop in the interest rate and subsequent return to the world level increased output if there is slack in the economy overshooting depreciation an increase in the BOT
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inflation near full employment. Expansionary fiscal policy refers to an increase in government spending G or a decrease in taxes T shifting the IS curve to the right as shown in Figure 5. The interest rate r increases, attracting foreign investment and appreciating the currency. Appreciation defeats the effect of the expansionary fiscal policy, lowering exports and increasing imports. This BOT deficit shifts the IS curve back to its original position and output returns to Ye. There is no permanent effect on unemployment.
r LM T down G up

appreciation r* IS' IS Ye Y Figure 5. Fiscal Expansion with Flexible Exchange Rate

As a direct result of the expansionary fiscal policy, the economy has become less involved with the rest of the world. The increase in the government deficit G T causes a trade deficit X M < 0. This link is known as the twin deficits. The increase in government borrowing to cover its deficit raises the demand for bonds increasing the interest rate. The increased government borrowing and higher interest rate also decrease private investment in an effect called crowding out. Summarizing the effectiveness of expansionary fiscal policy in a small open economy with a flexible exchange rate, there is no ultimate effect on output or unemployment a temporary rise in the interest rate currency appreciation twin government and trade deficits.

D. The small open ISLM economy with a fixed exchange rate Historically, flexible exchange rates are new. The world economy has operated mostly on metal standards with each currency defined as so many ounces of a particular precious metal and exchange rates frozen by the metallic standard. One dollar was worth this many ounces of gold and by implication so many francs and so many pounds, always and everywhere. Governments exchanged
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currency for metals and were constrained in producing more money by the amount of metals on hand, and coins contained the required amount of the metals. Efforts to loosen constraints with bimetallic standards failed since the official metallic rates could not keep up with the flexible metal prices. Governments moved off metallic standards in the early 20th century but kept exchange rates frozen by trying to define their currencies in terms of metals. The main principle behind a fixed exchange rate regime is that any excess demand for foreign currency must be met by government support for the fixed rate buying or selling foreign exchange, an expensive proposition if the domestic currency is cheap. Governments often simply restrict foreign exchange transactions by import or foreign exchange licenses. Such government interference ultimately fails unless it is consistent with the underlying economy. The fixed exchange rate system set up at the end of World War II collapsed in the early 1970s due to an overvalued dollar, giving way to the present system of floating exchange rates for the major currencies. Fixed exchange rates remain the most popular exchange regime for small economies while the major currencies float. The three major floating currencies are the dollar, yen, and euro. Triangular arbitrage implies the two effective global exchange rates $/ and $/ with their implied /. Most of the other nearly 300 currencies are pegged to one of these. Governments find controlling the foreign exchange rate an effective method of taxation since many have little chance of collecting business or personal taxes. Fixed exchange rates can be set at levels that tax importers and subsidize exporters. Another motivation for fixed exchange rates is that the effectiveness of monetary policy and fiscal policy is reversed. Figure 6 shows the effect of expansionary monetary policy with a fixed exchange rate.
r LM fall in FXR LM'

r*

increse Ms IS

Ye Y Figure 6. Monetary Expansion with a Fixed Exchange Rate

The increase in the money supply shifts the LM curve right. With r falling there is increased demand for foreign bonds and an international cash outflow. Foreign exchange reserves decline in
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order to support the balance of payments deficit and the decrease in reserves lowers the money supply Ms. A government that fixes its exchange rate has no monetary policy. To gain control of the exchange rate the government would have to give up control of its money supply. The money a government prints it gets to spend, an advantage called seignorage. Summarizing, with fixed exchange rates a monetary expansion temporarily lowers the interest rate and raises output leads to cash outflow decreases foreign exchange reserves. In contrast, fiscal expansion under a fixed exchange rate system increases output at least given slack in the economy. Fiscal tax and spend policy might also be more consistent with policy goals of a government wanting to control the exchange rate. Expansionary fiscal policy with an increase in G or decrease in T in Figure 7 shifts the IS curve right. The result is a BOP surplus and a domestic interest rate r higher than r*. Cash flows into the economy and foreign exchange reserves FXR increase raising Ms. The LM curve then shifts out pushing r back to r* and increasing Y further due to the increased FXR. The exchange rate remains fixed and the interest rate returns to the world level r*. If the economy is near full employment the only effect of expansionary fiscal policy will be inflation due to the increased foreign exchange reserves. Ultimately, however, such fiscal expansion cannot be expected to continue to increase output.
r LM FXR up LM'

r*

G up

T down IS

Ye Y Figure 7. Fiscal Expansion with a Fixed Exchange Rate

Expansionary fiscal policy with a fixed exchange rate temporarily raises the interest rate increases foreign investment into the country increases foreign exchange reserves raises output given slack in the economy.

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While there may be some temporary ability of fiscal policy to stimulate output and lower unemployment, there are limits. Continued expansionary fiscal policy has never led to sustained economic growth and rising per capita income.

Conclusion Economists are divided according to whether they are policy activists and if so whether they favor fixed or floating exchange rates, monetary or fiscal policy, and government spending or taxes. The economic approach to fiscal policy is to define the optimal role for the government and levy taxes to support that level of government spending. The optimal role of government is debatable and any tax system will tax some people more than others. Some schools of economic thought favor active monetary policy or fiscal policy to manage economies in some circumstances, while others doubt the ability of government and see government mismanagement as a primary cause of economic downturns. Students of economics should be skeptical of those advocating quick fixes. The main point to remember in this introduction to ISLM is that the choice of a floating or fixed exchange rate regime determines the effectiveness of monetary policy versus fiscal policy. Without any doubt, free trade and free international investment are the best policies for sustained economic growth. Active monetary or fiscal policy may offer short term temporary nudges for the economy but do nothing to improve long term economic performance.

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