“Monetary policy

concerns the decisions taken by central banks to influence the cost and availability

of money in an economy” (European Central Bank, 2015). The monetary authority’s

main objective is to minimise output volatility, allowing for more accurate and

effective forecasting and policy regarding the economy. The monetary authority

accomplishes this by using either an interest rate rule or a money supply rule.

An interest rate rule is when the monetary authority runs a fixed interest

rate; usually r* which is the interest rate that leads to target

output and let money supply vary naturally. A money supply rule is when the

monetary authority sets the level of money stock and allows interest rates to

vary naturally. The money stock can be increased at a steady rate, usually

equal to the rate of growth of real GDP. If there wasn’t uncertainty in the economy,

the monetary authority could achieve a target level of output by setting either

the interest rate or the money supply. However, as there is uncertainty in the

economy, the choice of monetary instrument affects the level of macroeconomic

volatility.

The Poole model

shows the differing effects of the two approaches and allows us to calculate

which approach leads to the least amount of volatility and therefore which

monetary instrument to use. In the Poole model, the IS relationship is

determined by the equation Y= a0 +

a1r + u where Y is the logarithm of output and u is the value

of any potential shock, such as changes in investor confidence whereby more

positive terms means there is higher confidence, leading to increasing GDP. The

LM curve uses the equation M=b0 + b1Y

+ b2r + v where M is the

logarithm of money supply and v is the value of any potential shock in the

economy whereby positive values suggest poor economic performance. The answer

to which policy should be used to minimise output volatility depends on the

values of the parameters in the IS-LM model.

In this diagram (Poole,

1970) where the IS curve has experienced a shock and so lies between IS1

and IS2 and the money supply has been fixed so that the LM curve

lies as LM1; as a result, output lies between Y1 and Y2.

If interest rates are fixed at r*, meaning that the LM curve will be

at LM2, meaning that output lies between Y0 and Y3.

Consequently, in this example it is clear to see that the best course of action

would be for the monetary authority to set the money supply at a fixed level

and let interest rates fluctuate naturally as the interest rate rule leads

potentially to greater volatility as the gap between Y0 and Y3

is much larger than the gap between Y1 and Y2.

This diagram (Poole,

1970) depicts a situation in which money demand has experienced a shock. If a

money supply rule was employed, the LM function will lie somewhere between LM1

and LM2, meaning that output will lie between Y1 and Y2.

However, if an interest rate rule was used and was fixed at r*, then

the LM function will be at LM3, meaning that output will lie at Yf.

Thus, in this example, it is clear to see that the best course of action here

would be to set interest rates at r* and allow money supply to

fluctuate naturally as output is unaffected, meaning that there is no

volatility in output under an interest rate rule.

In general, to

decide which policy is the most effective at reducing output volatility, we

must look at the loss function; L = E(Y-Yf)2, and

compare the expected values using the two rules to determine which approach leads

to the least volatility. It can be assumed that E(v) and E(u) = 0 as shocks can

be either positive or negative, averaging to 0; it is also assumed that both v

and u have a constant variance. With the interest rate rule, E(Y) = a0 + a1r as E(u)=0. Since E(Y) = Yf as the

interest rate is set to achieve Yf. Therefore a0 + a1r* =

Yf and so, r* = .

Substituting this into the IS relationship gives the equation; Y=Yf

+ u. Thus, the loss function under the interest rate rule is Li = E

(Yf + u – Yf)2 = Eu2 = s2u.

With a money supply rule, the expected value of the loss function is; E(Yf

+ b2u – a1v

– Yf )2 which equals Eb2u – a1v2

which simplifies to b22su2

+ a12sv2

– 2b2a1rsusv. Comparing

the loss functions, letting l = = b22

+ a12 – 2b2a1 and assuming that r = -1 ( in other words that the covariance is -1 ),then

l = b2 +a1 2. Therefore, l

is less than 1 (LM is less than Li and therefore there is

less output volatility) when is

less than b1.

This shows that the monetary authority should be using a money supply rule when

<
su and
an interest rate rule when > su.

In

diagrammatical terms, if the horizontal displacement of the LM curve is greater

than that of the IS curve, then running an interest rate rule will lead to a

lower level of output volatility, the reverse is also true i.e. if the

horizontal displacement of the LM curve is less than that of the IS curve, then

running a money supply rule will lead to a lower level of output volatility. The horizontal shift in the IS curve equals u

from the IS equation, similarly the horizontal shift in the LM curve equals – from the LM equation. The values of the

parameters in the IS and LM equations are also important; since the model is

log-linear, b1

represents the income elasticity of money demand and corrects any change in

income on the overall level of money demand. Similarly, b2 represents the

interest elasticity of money demand and has a similar effect as b1. This is significant

as the lower b2

is, the lower the expected loss is under a money supply rule.

However,

evaluating this, it is often difficult for the monetary authority to know the

exact values for s, b or

a. This means that it is hard for the monetary authority to

figure out with certainty whether an interest rate rule or a money supply rule

would be more effective at reducing output volatility.

Alternatively, the monetary authority could

use a combination policy to minimise output volatility. This can be done by

making the money supply interest sensitive, either positively or negatively

depending on the slope of the LM curve. If the values of the money supply

equation are set such that M= c1′ + c2’r, knowing that

the denominators of c1′ and c2′ can be removed with the

correct parameter values, an additional term can be added to the equation, c0

(the common denominator of c1′ and c2′) such that coM=c1

+ c2r. Adding this equation to the model and as the expected loss is

minimised by equating the partial derivatives of c1 and c2

to 0 means that the loss function can be expressed as; Lc = . Therefore it can be seen that when c0

= 0, the combination policy becomes a pure interest rate rule and when c2*

= 0, it becomes a pure money supply policy. The loss function also implies that

except for these two scenarios, the combination policy minimises output

volatility more effectively than either the money supply policy or the interest

rate policy. However, the combination policy depends on knowledge of more parameters

than either of the two pure strategies and therefore may be harder to employ if

the monetary authority doesn’t have full information, which is often the case

due to time lags and revisions of data.

A

final method that can be used to stabilise the economy and reduce output

volatility is to use discretionary monetary or fiscal policy. This is when the monetary

authority (monetary policy) or the government (fiscal policy) change policy on

an ad hoc basis to reflect the current economic situation. This is beneficial because it means that

policy can be specifically designed to react to the current economic climate.

Fiscal policy can still lead to output volatility because there are time lags

associated with fiscal policy changes affecting the economy as consumers are

often slow to react to changes in taxation.

To

conclude, the decision as to whether monetary policy should be conducted using

a money supply rule or interest rate rule to reduce output volatility is

dependent on the parameters within the Poole model. Using the loss function and

comparing the expected values of the two, the monetary authority should use a

money supply rule when <
su and
an interest rate rule when > su.

There are other alternative methods that can be used such as using a

combination or using discretionary monetary or fiscal policy. Overall, it can

be advised to use either a money supply rule or interest rate rule, depending

on the parameters within the model.