## poole model

The Poole model extends the IS-LMmodel to include uncertainty or shocks. If there were no shocks either settingi, interest rates, or M, money supply, would achieve the target Y, GDP, thereis no problem over the choice of monetary instrument. But, setting M requiresadditional knowledge of money demand, whereas i only requires knowledge of theIS curve. The aim of Monetary Authority is to minimize output volatility, thedifference in output volatility between the two regimes generally depends oncertain characteristics of the economy.

The Central Bank can either choose toset the stock of money and let the interest rate be decided by the interactionof money demand and supply, or it can set the interest rate and let the supplyof money be determined by the demand for money. The IS curve is defined as Y=a0+a1r+m andthe LM curve is defined as              M= b1+b1 Y+b2r+n. Mand 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 threestandard assumptions which apply: b1 >0, b2 <0 and a1<0. The IS and LMequations are expanded with unpredictable shock terms m andn. 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 theshocks is zero, however this does not mean that shocks are not expected and thethird states that their variances are constant. m is a shock to the IS curve, forexample an increase in investor confidence, more positive values of thecoefficient relate to higher levels of investor confidence, this leads toincreased spending and so equilibrium GDP increases all else equal and vice versafor 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 asindividuals have less confidence in a bond being paid back due to thepossibility of the company or government defaulting.                                                                                                                                          Figure 1 Figure1 represents an economy experiencing money demand shocks only. A money demandincrease is a reflection of pessimism as individual’s would rather hold liquidassets, however this is most likely pessimism in real economic terms forexample consumption and investment may be low. In bad times money demand isvolatile so the LM curve is volatile as well, this also means that the IS curvewill have an element of volatility. In economic bad times the increasing demandfor cash causes interest rates to go up endogenously under the money supplyrule which lowers real spending, this only makes the problem worse. However, ifyou fix the interest rate the only financial variable that is driving theeconomic components of GDP is the interest rate, this isn’t changing as it’sfixed so nothing changes as far as GDP is concerned, liquidity preference andstock of money do not matter as they do not enter the determinants.

Thisimplies that volatility in financial markers does not matter, which is a keystrength for the interest rate rule over the money supply rule. If this is howthe economy is working than an interest rate rule would be a better choice thanand a money supply rule.                         Figure 2  Figure2 represents an economy with private spending shocks only. In this case it isthe IS curve giving you volatility rather than the LM curve. This could be dueto economic investment being volatile which there is plenty of evidence tosuggest it is, estimates of it being 17-18% of GDP in the UK.

So in a bad yearno one will invest and the IS curve will be low and in a good year lots ofpeople will so the IS curve will be high. With a fixed money supply rule youhave an advantage of a stabilizing influence to an extent. In good times GDPwill be higher so interest rates will go up, this is beneficial as it offsetsany exuberance from the private sector. Whereas, in bad times interest rateswill fall to offset any pessimism that the private sector may have. There willstill be macroeconomic volatility when there is volatility to the real economybut this offset to an extent by changing interest rates.

As seen in figure 2,fixing interest rates leads to greater macroeconomic volatility as GDP variesbetween Y_’’ to Y+’’, whereas witha fixed money supply rule GDP only varies between Y_’ toY+’.  So in thiscase a fixed money supply rule would be better due to it being an automaticstabilizer of the interest rate.                            Figure 3                                                                        Figure 4  Figures3 and 4 represent uncertainty in both parts of the economy, the money marketsand the real economy. Firstly figure 3 where the IS curve is volatile, under amoney supply rule volatility is less than the interest rate rule as the IScurve shocks are bigger, this is shown by the differences in horizontaldisplacement between Y_’ to Y+’ andY_’’ to Y+’’. This means that interest ratesare acting in the desired way as they are increasing during good times anddecreasing during bad times, to reduce the spending shock. The interest rate isthe key element of why the money supply rule is preferred in this circumstancegiven the objective of minimizing volatility. Now for figure 4 where the LMcurve is volatile, under a money supply rule volatility is greater than theinterest rate rule, this is shown by the differences in horizontal displacementbetween Y_’ to Y+’ and Y_’’to Y+’’. The key point is what the interest rate is doingas this is what links the financial sector to the real economy.

The interestrates are not behaving in a coherent way as they are decreasing in good timesand increasing in bad times which exacerbates the problem. This is why aninterest rate rule is preferred in this circumstance over a monetary supplyrule. Thehorizontal displacement of the IS and LM curves helps to determine which policyyou should choose, as output volatility is costly as it reduces investment inthe long run. The horizontal displacement of the IS curve is equal to m and the horizontaldisplacement 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 LMcurve shifts up when you enter economic bad times which means interest ratesmay be going up and GDP may be going down for other reasons for example the IScurve. If GDP is going down money demand will go down which leads to anoffsetting effect, in bad times n goes up but b1Y goes down.

This means thatif b1 is high enough it couldwrite 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 inthe LM curve. The horizontal displacement of the LM curve depends on therelationship between GDP and interest rates governed by the financial sector.

If < su  then a money supply rule would be preferred,whereas if  > su thenan interest rate rule would be preferred. Money supply rule versus interestrate 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 upthe claim for the use of either rule. Policymakerscan 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 andincrease when output rises. For example, if output begins to fall, policymakerscan allow tax revenues to fall with income, or even purposely cut tax ratesthemselves.

This sustains purchasing power and income for individuals andsupports demand. Policymakers could also choose to stimulate demand more bydirectly spending more. In any case, a lower surplus or higher deficit essentiallycushions the blow on output.

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