The Poole model extends the

IS-LM model to include uncertainty or shocks. If there were no shocks either

setting i, interest rates, or M, money supply, would achieve the target Y, GDP,

there is no problem over the choice of monetary instrument. But, setting M

requires additional knowledge of money demand, whereas i only requires

knowledge of the IS curve. The aim of Monetary Authority is to minimize output

volatility, the difference in output volatility between the two regimes

generally depends on certain characteristics of the economy. The Central Bank

can either choose to set the stock of money and let the interest rate be

decided by the interaction of money demand and supply, or it can set the

interest rate and let the supply of money be determined by the demand for

money.

The IS curve is defined as Y=a0+a1r+m and the LM curve is defined as M= b1+b1 Y+b2r+n. M and Y are defined as the logarithms of money supply and output. b0, b1, b2, a0 and a1 are parameters and r is the

interest rate. There are three standard assumptions which apply: b1 >0, b2 <0 and a1<0. The IS and LM equations are expanded with unpredictable shock
terms m and n. These unpredictable shock terms have the five following properties: Em=0, En=0, Em2=s2m, En2=s2n and Emn=smn=rsmsv. The first and second assumptions state that the mean of the shocks is
zero, however this does not mean that shocks are not expected and the third
states that their variances are constant. m is a shock to the IS curve, for example an increase in investor
confidence, more positive values of the coefficient relate to higher levels of
investor confidence, this leads to increased spending and so equilibrium GDP
increases all else equal and vice versa for negative values. n is a shock to the LM curve
and money demand in particular. However, in this case more positive values
correspond to economic bad times, this is due to money demand being part of the
IS-LM model liquidity preference. In bad times liquid assets are preferred, so
money demand is higher as individuals have less confidence in a bond being paid
back due to the possibility of the company or government defaulting.
Figure
1 represents an economy experiencing money demand shocks only. A money demand
increase is a reflection of pessimism as individual's would rather hold liquid
assets, however this is most likely pessimism in real economic terms for
example consumption and investment may be low. In bad times money demand is
volatile so the LM curve is volatile as well, this also means that the IS curve
will have an element of volatility. In economic bad times the increasing demand
for cash causes interest rates to go up endogenously under the money supply
rule which lowers real spending, this only makes the problem worse. However, if
you fix the interest rate the only financial variable that is driving the
economic components of GDP is the interest rate, this isn't changing as it's
fixed so nothing changes as far as GDP is concerned, liquidity preference and
stock of money do not matter as they do not enter the determinants. This
implies that volatility in financial markers does not matter, which is a key
strength for the interest rate rule over the money supply rule. If this is how
the economy is working than an interest rate rule would be a better choice than
and a money supply rule.
Figure
2 represents an economy with private spending shocks only. In this case it is
the IS curve giving you volatility rather than the LM curve. This could be due
to economic investment being volatile which there is plenty of evidence to
suggest it is, estimates of it being 17-18% of GDP in the UK. So in a bad year
no one will invest and the IS curve will be low and in a good year lots of
people will so the IS curve will be high. With a fixed money supply rule you
have an advantage of a stabilizing influence to an extent. In good times GDP
will be higher so interest rates will go up, this is beneficial as it offsets
any exuberance from the private sector. Whereas, in bad times interest rates
will fall to offset any pessimism that the private sector may have. There will
still be macroeconomic volatility when there is volatility to the real economy
but this offset to an extent by changing interest rates. As seen in figure 2,
fixing interest rates leads to greater macroeconomic volatility as GDP varies
between Y_'' to Y+'', whereas with
a fixed money supply rule GDP only varies between Y_' to
Y+'. So in this
case a fixed money supply rule would be better due to it being an automatic
stabilizer of the interest rate.
Figures
3 and 4 represent uncertainty in both parts of the economy, the money markets
and the real economy. Firstly figure 3 where the IS curve is volatile, under a
money supply rule volatility is less than the interest rate rule as the IS
curve shocks are bigger, this is shown by the differences in horizontal
displacement between Y_' to Y+' and
Y_'' to Y+''. This means that interest rates
are acting in the desired way as they are increasing during good times and
decreasing during bad times, to reduce the spending shock. The interest rate is
the key element of why the money supply rule is preferred in this circumstance
given the objective of minimizing volatility. Now for figure 4 where the LM
curve is volatile, under a money supply rule volatility is greater than the
interest rate rule, this is shown by the differences in horizontal displacement
between Y_' to Y+' and Y_''
to Y+''. The key point is what the interest rate is doing
as this is what links the financial sector to the real economy. The interest
rates are not behaving in a coherent way as they are decreasing in good times
and increasing in bad times which exacerbates the problem. This is why an
interest rate rule is preferred in this circumstance over a monetary supply
rule.
The
horizontal displacement of the IS and LM curves helps to determine which policy
you should choose, as output volatility is costly as it reduces investment in
the long run. The horizontal displacement of the IS curve is equal to m and the horizontal displacement of the LM curve
is equal to –(n/b1), where
b1 is the income elasticity of money demand.
Money demand shocks may not matter that much if b1 is high enough. The LM curve shifts up when you
enter economic bad times which means interest rates may be going up and GDP may
be going down for other reasons for example the IS curve. If GDP is going down
money demand will go down which leads to an offsetting effect, in bad times n goes up but b1Y goes down. This means that if b1 is
high enough it could write off the increase in n. Level
of income is another determinant of the position of the LM curve, so in bad
times income levels fall which offsets to an extent the increase in the LM
curve. The horizontal displacement of the LM curve depends on the relationship
between GDP and interest rates governed by the financial sector. If < su then a
money supply rule would be preferred, whereas if > su then an interest rate rule would be preferred.

Money supply rule versus interest rate rule is highly dependent on the model

parameters b1 and

the volatility of n

and m,

empirical evidence should also be used if possible to back up the claim for the

use of either rule.