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 = b0 + 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: E m = 0, E n = 0, E m2 = s2m,
E n2 = s2n
and E mn = 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 time, 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.