# “Monetary so lies between IS1 and IS2 and the

“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.

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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.