Movements of the IS and LM curves are triggered by changes in money demand, which are influenced by one of two states of the economy: good or bad.
During good periods, increased confidence of financial markets causes higher demand for illiquid assets, as investors are confident in being paid back.
Conversely, in bad times (characterised by increased amounts of uncertainty) demand for liquid assets rises due to the greater likelihood of high-risk asset defaults. Monetary authorities cannot directly control money demand, therefore when attempting to stabilise the economy a choice of two policies exists: the interest rate or the money supply.
The interest rate rule consists of setting the interest rate at a desired level, r*, so to achieve the policymakers’ target output level. Money supply adjusts endogenously and the equilibrium found at the intersection point of r* and money supply determines the new level of money demand. Money demand shocks will not affect the LM curve, as it is horizontal, so the new output level is determined by movements of IS.
When using the money supply rule, the policymaker fixes money supply precisely at a desired level, M*.1 The intersection between money demand and M* will establish the new interest rate, and at what point on the LM curve the economy is operating.
Poole’s analysis is based on a closed economy IS-LM model, which has been modified to include stochastic shock variables u and v as shown:2
LM: Rearranged for:
This incorporates macroeconomic volatility and uncertainty into the model, making it a truer reflection of how the economy operates. It is assumed that the price-level is fixed so the variables in this model are in real terms.3 Policymakers must then choose between the two aforementioned tools at their disposal – crucially, they are unable to use both in conjunction because of the inverse relationship between interest rates and money supply.4 Assuming that policymakers have both the freedom of choice and ability to implement their chosen policy exactly,5 Poole’s analysis concludes that optimal policy choice is found by minimising the squared deviation of real output (Y) from the target level of real output through the following loss function:6
By substituting the interest rate rule into the loss function we obtain:
Whilst using the money supply rule gives:
Once the loss functions have been found, Poole obtains the ratio of losses which in its simplest form is given by:
By comparing the ratio of losses, Poole specifies the conditions for preferring one policy over the other; if >1, the variation in output under the money supply rule is greater so the interest rate rule is preferred, whilst if