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The ISLM model in an Open Economy

January 25, 2012 Comments off

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.

Categories: ISLM, Macro

The ISLM model

June 25, 2011 Leave a comment

The ISLM model is one of the most useful basic short-run models in macro. It is a great tool for answering questions related to the effects of fiscal and monetary policy because quickly sketching out the model will give you some answers straight away as to the likely effects on output and the interest rate – which are after all two pretty important consequences of any policy.

Basically you have an IS relation which tells you how the interest rate determines the level of output that will bring the goods market into equilibrium. You have an LM relation which tells you how output determines the interest rate that will bring the money market into equilibrium. Both the goods market and money market will naturally end up in equilibrium, so the equilibrium level of output and interest rate in the economy will be determined by the point at which both these markets are in equilibrium, ie where the IS curve and the LM curves meet.

So you have a simple model like this:

Now we can start answering some questions…

What will be the effect of a fiscal expansion?

The fiscal expansion shifts the IS curve out to the right.

So output rises and so does the interest rate.

If you did it the other way round, a fiscal contraction would mean shifting the IS curve to the left, so output and the interest rate would both fall.

What will be the effect of a monetary expansion?

The monetary expansion shifts the LM curve down.

So output rises and the interest rate falls.

Again if you did the opposite, a monetary contraction would mean the LM curve shifts up, so output falls and the interest rate rises.

Show how a fiscal contraction can be combined with a monetary expansion to prevent a loss of output.

Here we keep output at the same level and have a fall in interest rates.

You can use the ISLM analysis to show why the UK faces a difficult time ahead. George Osborne wants to cut the fiscal deficit, so he is carrying out a fiscal contraction. At the same time, monetary policy is constrained by the fact that interest rates are already pretty much as low as they can go (0.5%) and with inflation exceeding the Bank of England’s target for a while now, it means the next change in monetary policy from the B of E is going to have to be a rise in interest rates (monetary contraction) rather than a monetary expansion.

Here the fiscal contraction has placed downward pressure on interest rates and the Central Bank has contracted monetary policy in order to raise them, both effects have combined to magnify the loss of output.

Categories: ISLM, Macro

The IS relation

June 24, 2011 Leave a comment

The IS relation is the other building block of the ISLM model, along with the LM relation. The LM relation shows us how the interest rate depends on income in the economy through the relationship between supply and demand in the money market. At higher levels of income, the money market requires a higher rate of interest to bring the supply and demand for money into equilibrium, which is why the LM curve is upward sloping.

The IS relation now shows us how income in the economy depends on the interest rate, through the relationship between supply and demand in the goods market. The key channel here to think about, is investment, in the simplified Keynesian model of AD, Y=C+I+G. Investment depends negatively on the interest rate, firms are more willing to invest when interest rates are low, so high interest rates will mean investment is lower and low interest rates will mean investment is higher. If you increase or decrease I in the Keynesian model, you will increase or decrease Y. So you get a downward sloping relationship between interest rates and output, the IS relation:

What the IS curve is telling you, is that given a certain rate of interest, i, the goods market will come into equilibrium at a certain level of income, Y. The lower the rate of interest is, the more investment there will be in the economy, so the supply and demand comes into equilibrium at a higher level of output (or income).

You need to think about the Keynesian Cross model to understand the IS relation. Remember the effect of increasing I on the Keynesian Cross, means you shift the planned expenditure curve up, and you get a higher equilibrium level of Y. So higher I = higher Y. This is basically what happens when you move down the IS curve. The interest rate is getting lower so firms are investing more, higher I means higher income.

The Keynesian Cross also tells us about what to do on the IS curve if we get changes in autonomous consumption, government spending or taxation. Remember that an increase in a or an increase in G, or a decrease in T, shifts the planned expenditure curve up, so you get a higher equilibrium level of Y. This tells us that if we increase a or G, or decrease T, then we need to be at a higher level of Y on the IS relation – but those factors don’t depend on the interest rate, so they are not captured in the downward sloping line. So if you increase a or G, or decrease T, you have to shift the whole IS curve over to the right. The IS relation is basically telling us what level of Y will put the goods market into equilibrium at any given level of interest rate. So if we shift the curve over to the right, it means we have a higher level of Y at any given of interest rate – so if the interest rate stays constant, and I stays constant, but G for instance is higher, then we will get higher Y.

And what about if b, the marginal propensity to consume increases? Remember that b gives us the slope of the planned expenditure curve in the Keynesian Cross. If b increases, then this slope gets steeper. So if you start from the same point where the planned expenditure curve intersects the vertical axis, and draw a steeper line, it will intersect the 45 degree line, at a higher level of Y. So an increase in marginal propensity to consume also increases Y – another thing that we can capture in the IS relation by shifting the whole curve to the right (unless we take the mpc to be endogenous, ie dependent on the interest rate, which it may well be, but it is not treated as such in this model, just to keep it simple.)

So to sum up:
The IS curve is downward sloping, as the interest rate increases, income in the economy decreases
The IS curve shifts out to the right when there is an increase in government spending (a fiscal expansion) or an increase in consumer confidence that would increase autonomous consumer spending or increase the marginal propensity to consume.
The IS curve shifts in to the left when there is a decrease in government spending (a fiscal contraction) or an decrease in consumer confidence that would decrease autonomous consumer spending or decrease the marginal propensity to consume.

Categories: ISLM, Macro

The LM relation

June 24, 2011 Leave a comment

The downward sloping money demand curve can be written like this: \frac {M}{P}=YL(i). What this means is real money balances = the level of income (Y) in the economy multiplied by the liquidity preference (L). The liquidity preference is basically the steepness of the curve, it shows how much people prefer to hold bonds (or other illiquid assets) rather than money, at a higher interest rate, if the liquidity preference schedule is steep then it means demand for money is less elastic with respect to interest rate, if it is fairly flat then it means demand for money is elastic with respect to interest rate (ie a small fall in interest rate means a large increase in the amount of money people want to hold rather than holding bonds). The reason there is an (i) in brackets after the L means that liquidity preference is a function of i, the nominal interest rate. It will of course depend negatively on i, because the higher the interest rate, the lower is M.

Money supply and demand

L(i) determines the steepness of the curve, and Y determines where the curve is, if you increase Y, then you push the whole curve up. This is the principle behind the LM relation. We can basically think of a relationship between i, the nominal interest rate, and Y, the level of income in the economy. As Y increases, then you shift up the money demand curve, so if you keep the money supply constant (the vertical line) then the point of intersection on the diagram is higher. This means that the new interest rate which brings the money market into equilibrium (money supply = money demand) is higher. So if money supply is constant, increasing Y means you get an increase in i; decreasing Y means you get a decrease in i. This is the LM relation – and it is upward sloping:

Think of movements along the LM curve as being what happens when you shift money demand curve up and down in the money supply/money demand diagram. Higher Y means money demand shifts up so you get higher i in equilibrium, that’s a movement up the LM curve.

What shifts the LM curve up or down is movements in the money supply curve. If you shift the money supply curve out (to the right) on the money supply/money demand diagram then you will get a lower i in equilibrium, at all levels of income, that’s the equivalent to shifting the LM curve down. If you shift the money supply curve in (to the left) on the money supply/money demand diagram then you will get a higher i in equilibrium at all levels of income, that’s the equivalent to shifting the LM curve up.

Remember that prices also affect the position of the money supply curve, because we are thinking about real money balances (M/P). As P is on the denominator, an increase in P makes (M/P) smaller, so an increase in P (rising prices) has the same effect as a decrease in M (reducing nominal money supply), so it moves the money supply curve to the left.

So to sum up:
The LM curve is upward sloping, as income in the economy increases, the interest rate increases
The LM curve shifts down when there is an increase in nominal money supply (a monetary expansion) or a fall in prices (rare!)
The LM curve shifts up when there is a reduction in the nominal money supply (a monetary contraction) or a rise in prices (inflation)

The Central Bank can stop inflation from pushing the LM curve up and increasing interest rates, by increasing nominal money supply in a proportionate amount that keeps (M/P) constant when P is rising.

Categories: ISLM, Macro, Money