poole model

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: 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 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   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   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.                                    Figure 3                                                                         Figure 4   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.

 

Policymakers
can also choose to adopt fiscal policy as an attempt to stabilize the economy.
Fiscal policy has a stabilizing effect on the economy if the budget balance,
the difference between revenue and expenditure, decrease when output falls and
increase when output rises. For example, if output begins to fall, policymakers
can allow tax revenues to fall with income, or even purposely cut tax rates
themselves. This sustains purchasing power and income for individuals and
supports demand. Policymakers could also choose to stimulate demand more by
directly spending more. In any case, a lower surplus or higher deficit essentially
cushions the blow on output.