The Poole model is a useful way to

show how to reduce macroeconomic volatility as to show this as it extends the

IS-LM model to include shocks, which can be money shocks, real shocks or a mix

of the two within an economy which all cause volatility. The equation for IS

becomes and LM becomes where u is the shock to IS and v is the shock

to LM. A money supply rule is

where money supply is fixed and interest rates fluctuate. An interest rate rule

is when policymakers fix interest rates and allow money supply to move around

freely depending on money demand. The policymaker wants to minimise the

variance of GDP and so we use a loss function: where Yf is the Natural rate of GDP.

If

an economy faces only money demand shocks then this creates macroeconomic

volatility as it’s the extent to which the financial sector prefers liquidity

to illiquidity. In bad times under a money supply rule quantities of liquid and

illiquid assets are fixed however the opportunity cost of money increases and

so the interest rate resulting in higher money demand and so we get LM+. In

good times then the opposite is true. People have confidence in illiquid assets

and so the price of money goes down decreasing the interest leading to LM-. When

there are money shocks in an economy, if policymakers use a money supply rule

then output can vary between Y- and Y+. By contrast if the policy maker chose

an interest-rate rule they would fix the interest rate at i0 so the expected

level of output is as , and we get a

horizontal LM curve because the LM function can be extended to ‘treat money

supply as interest-elastic… a pegged interest rate, of course is a polar case

in terms of interest elasticity of supply’ (Poole, 1970). This means under an

interest-rate rule actual output will be. If there is are only money

shocks in the economy under an interest rate rule there will be no volatility

as output will always be Y0 geometrically or Yf as . If the economy faces only money demand shocks

then it should use the interest rate rule over the money supply rule to lower macroeconomic

volatility.

More commonly an

economy can face are real shocks, when there is randomness in private spending

affecting the IS curve, with private investment being most volatile component. One

determinant of investment is the interest rate (opportunity cost of investing

in capital stock) which gives a downward sloping investment curve. The

investment curve determines the position of the IS curve as it is government

spending given the amount of investment. In good times people are optimistic

and so invest more and there is a positive spending shock giving IS+. In bad

times there is more uncertainty so people don’t want to invest resulting in a

negative spending shock, IS-.

If policymakers applied a money

supply rule to minimise expected loses then expected output is as . To minimise loses the

policymaker would set the money supply so giving actual output under a money supply rule

as During bad times GDP would be Y1 and

during good times as there is more private spending IS is higher and so GDP is

Y2. If policy makers chose to fix interest rates then we again get the horizontal

LM curve and we can see in bad times, when IS is lower output is Y3 and in good

times it is Y4. We can see from the graph that the amount Y varies when fixing

money stock (Y1-Y2) is smaller than the when fixing interest rates (Y3-Y4). If

an economy faces only private spending shocks it should adopt the money supply

rule to reduce macroeconomic volatility.

In the

real world economies are more likey to be vulnerable to both financial shocks

and real shocks at the same time. If the economy is facing bad times and

policymakers use a money supply rule it will be at the point where the two blue

lines cross. There is pessimism in financial

markets, as people have liquidity preference so Md increases

resulting in a higher LM(+). If there is pessimism in the money market then it

is more than likely that there is also uncertainty in real terms i.e.

Consumption and Investment. Financial institutions distrust of markets will

make consumers and business wearier to invest and so we get IS-. Under a fixed

money supply in bad times output will be Y1.

Oppositely in good times under a money supply rule people have

confidence in their illiquid assets we have a lower Md and a lower

LM curve (LM-). Additionally the real market will we in boom and so there will

be more consumption and investment resulting in a higher IS curve (IS+). In

good times using a money supply rule is Y2.

Conversely the policymakers could a fixed interest rate when there are money

and real shocks. We can see that in bad times GDP would be Y3 due to

significantly lower investment (and/or consumption) and in good times GDP would

be Y4 due to more spending. In this graph real shocks (to IS curve) are larger

than the shocks to the money market, and so we can see from the graph that the

policy makers should use the money supply rule because here interest rates are

acting coherently and going up in good times which offsets it and so

macroeconomic volatility is lower Y1-Y2 than with a fixed interest rate Y3-Y4.

If on the economy was in the position where the LM shocks were greater than the

IS shocks then the opposite would be true. This is because if you were to use a

fixed money supply then the interest rates are not having the desired effect;

they decrease when the economy is in good times and so this encourages more

investment and worsen the situation. Here the policymaker should use an

interest rate rule to lower macroeconomic volatility.

This could also be shown by

comparing losses because as stated earlier the objective of the policymaker is

to minimise the variance of GDP. We know under a fixed interest rate and under fixed money supply. The loss functions

are and with a money supply rule . To compare the

policies we find the ratio of the losses (look at the relative losses. . If the expression ?

is greater than 1 then the loss under a money supply rule is greater and so the

policymaker will chose a fixed interest rate, however if ? is less than

one then the loss under a fixed interest rate is greater so the policy maker

will fix the money supply to reduce macroeconomic volatility. If we assume that

?=-1 then simplifying to . The term in the square brackets is

now very similar to the denominator (Pickering, 2017) and so the interest

elasticity of money demand (?2) is less relevant. What is more

important is ?1, income elasticity of money demand, ?v

and ?u. If ?1 is greater than then

the loss from having a fixed money supply will be smaller than the loss from

having a fixed interest rate. A money shock may not matter much if ?1 is high. LM

shift left in bad times Md increases and GDP falls which feeds back

into the Md function. In economic bad times interest rates may be

increasing for other reasons such as the IS curve. This means than Md increases,

so volatility increases and GDP falls, if ?1 is

high enough it will have a corrective effect on the initial increase that

happens in bad times and counteracts what is happening to v.

An alternative is to

use fiscal policy (taxation and government spending) to reduce volatility. If

the economy is facing positive shocks real shocks then that means people are

optimistic and so IS shifts right. However if the policymaker uses

contractionary fiscal policy and increases income tax and corporation tax then this

will shift IS left again and reduce volatility in the economy. In addition to

this if money demand is very sensitive to interest rates i.e. ?2

is very high then the LM curve becomes horizontal and so fiscal

policy is more attractive.

Combination policy is another alternative where values are set for c’1 and

c’2 in the money supply equation however for certain values the denominators of

optimal c’1 and c’2 vanish so we use . Again we want to minimise losses so get , ) , and . This gives us the

minimum expected loss as . When there is a pure interest rate policy and when there is a pure money stock policy. Except

these two cases combination policy is better than both pure policies (Poole,

1970) because expected losses are lower. For combination policy to be successful

there has to be more knowledge of the parameters than the pure policies.

Overall both the money

supply rule and the interest rate rule are effective at reducing macroeconomic volatility