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## The ISLM model in an Open Economy

January 25, 2012

The IS relation is flatter in the case of an open economy than a closed economy. This is because output is more sensitive to changes in the nominal interest rate, because we are taking net exports into account.

The uncovered interest parity condition, $(1+i_t)=(1+i*_t)\frac{E_t}{E^e_{t+1}}$, implies that, an increase in the domestic interest rate $i$ will increase the nominal exchange rate $E$ when other factors like the foreign interest rate $i*$ and the expected future exchange rate $E^e$. This means that the currency will appreciate in value.

Alternatively, a decrease in the domestic interest rate will decrease the nominal exchange rate, and mean that the currency will depreciate in value.

The IS relation is a downward sloping relation, meaning as the interest rate falls, output increases. In the closed economy this is simply due to the effect on investment, in the Keynesian model of aggregate demand Y = C + I + G, where I depends negatively on the interest rate. Lower interest rates mean businesses are more likely to invest and so I rises.

In the open economy we also start to consider net exports, so the Keynesian model of aggregate demand becomes Y = C + I + G + NX where NX (net exports) depends on domestic income, foreign income and the exchange rate. When domestic incomes are higher, imports will be higher. When foreign incomes are higher, exports will be higher. When the exchange rate rises, imports will be higher and exports lower because it becomes cheaper for domestic consumers to afford foreign goods whilst it becomes more expensive for foreign consumers to import the goods our economy produces. When the exchange rate falls, imports will be lower and exports higher because it becomes more expensive for domestic consumers to afford foreign goods so they substitute away from imports and instead purchase domestic produced goods. However foreigners will find the goods we produce cheaper so are likely to buy more of our exports.

A higher exchange rate (caused by a higher interest rate) means more imports and less exports, so NX falls and AD rises.

A lower exchange rate (caused by a lower interest rate) means less imports and more exports, so NX rises and AD rises.

This magnifies the effect interest rates have on output.

When interest rates fall, investment increases and net exports increase, so output increases by more in an open economy than it would in a closed economy.

When interest rates rise, investment falls and net exports fall, so output decreases by more in an open economy than it would in a closed economy.

This means the IS relation will be flatter in an open economy than in a closed economy.

The LM relation is unchanged in the open economy. Exchange rates do not affect demand for domestic money as foreign investors would rather hold interest bearing bonds than non interest bearing domestic currency anyway.