The or below the target of Yf. This is:

The Poole Model was created by Poole in 1970; his analysis builds on the deterministic macro IS-LM model to become a stochastic model, which includes uncertainty and shocks to the economy. Each nation’s monetary authority may use the Poole model in order to set monetary policy within an economy, by setting interest rates or directly setting the money supply. Most monetary authorities have the objective of minimizing macroeconomic volatility since it “adversely disrupts the lives of many people” and therefore is an undesirable state for an economy. (Kahn, 2016) High macroeconomic volatility is a “fundamental concern” for countries, especially developing countries. (Loyza et al, 2007, p343). The IS (investment saving) is a variation of the income-expenditure model incorporating market interest rates (Amighini and Giavazzi, 2013).  In the IS equations, this is:?0+?1r+u=YWhere Y is the logarithms of output, r is the interest rate, ? is the parameters and u is the unpredictable shock term. The shock term relates to any shock to the IS curve. For example, using investor confidence, higher confidence will increase equilibrium GDP. (3)The LM (liquidity money supply) represents the amount of money available for investment. (Amighini and Giavazzi, 2013). In the LM equation:?0+?1+?2r+v=MWhere M is the logarithm of the money supply, ? is the parameters and v is the unpredictable shock term. The unpredictable shock terms are expected to have a negative correlation. These unpredictable shock terms have specific properties. E(u) and E(v) both equal 0:  without loss of generality, on average the shock terms are 0. However, this does not mean that shocks are not expected. (3)The analysis continues with a Central Bank objective, which is to minimise the loss function. This loss function shows that equivalent losses arise if the economy’s output is above or below the target of Yf. This is: (3)L=E(Y-Yf)² Monetary policy “refers to actions taken by central banks to affect monetary and other financial conditions in pursuit of the broader objectives of sustainable growth of real output, high employment and price stability.” (Palgrave Dictionary of Economics). The target problem for the monetary authorities is that, with the current parameters explained above, they may operate through either interest rate changes or money supply changes, but not through both independently. (Poole, 1970) The interest rate rule is where the bank sets the interest rate, therefore the level of output is determined only by the IS equation. The bank will set the interest rate so that the expected level of output of an economy is Yf. This would mean EY=?+??r as Eu=0. The optimal interest rate is:r*=Y*-????Actual output becomes Y=Y*-u. (3). Monetary authorities increase interest rates in a boom and decrease them in a recession, whilst the money supply is allowed to fluctuate. (Poole, 1970) Diagrammatically, the monetary authority will set the interest at r*, which causes the LM function to become horizontal. This would be set so that it intercepts the IS curve at the full employment level of income, Yf.LMr*rISYfY The money-supply rule is for the monetary authority to fix the money supply to minimise its expected losses. (3) This is set by the equation to minimise expected losses to the Central bank. This is found by, firstly, Y being solved in terms of M:Y=1?1?1+???0?2+?1M-?0+?2u-??vThen, expected output is found by the equation:EY=1?1?1+???0?2+?1M-?0Therefore, the monetary authority will set M so that the expected level of output is equal to Yf. This equation is:EY=1?1?1+???0?2+?1M*-?0M*=?0-?0?2?1+?1?1+?2?1YfIn order to minimise expected losses, M=M*. So actual output becomes (3) :Y=Yf1?1?1+????u-??vTherefore, in words, the money supply rule works by fixing the money supply. The monetary authority wants to achieve a constant rate of growth of the money supply or respond to the current state, including volatility, of the economy by adjusting the growth in the money supply. Therefore, the money supply will increase more rapidly in a recession and less in a boom. (Poole, 1970)Diagrammatically, this would be setting the money supply at the level so that the LM function will cut the IS function at Yf, the full employment level of income (which is also the expected level of output given the set money supply). (Poole, 1970) LMrISr*YfYThe optimal policy depends on the relative importance of the shocks to the economies and the elasticity of the IS and LM functions. It should be determined by which instrument minimizes the expected losses the most, therefore reducing economic volatility. The difference in the optimum instrument occurs when stochastic terms are added, therefore the shocks of u and v to the IS-LM model. (Poole, 1970)The interest rate rule could be seen as the optimal policy for reducing macroeconomic volatility depending on the interest sensitivity of the demand for money. The higher the interest sensitivity, the lower the minimum expected loss from a money supply policy (Poole, 1970). The interest rate rule can also stabilize inflation. This could be done by using a ‘Taylor rule’ where interest rates are adjusted in response to output and inflation. When there are variations in the LM function, if money demand is randomly shocked then the money supply rule will only increase the variation in output, whilst interest rates set it at a certain fixed point. It is also controllable, and key in influencing investment and spending behaviour. (Kahn, 2016)A study by Friedman (1960) showed that where money supply was made to grow at a given rate, it would provide secure stability irrespective of business cycles. This would be optimal, especially if authorities don’t have information or capacity to know details such as when or how much to increase the growth of the money supply.  The IS-LM function also shows that if output deviates from its equilibrium, because the IS curve shifts, output can be stabilized by changing money supply growth and not interest rates. (Kahn, 2016)However, it is possible that a combination policy could occur, where the interest rate and money supply are kept in a certain relationship to each other; this relationship would depend on the values of the parameters of both the IS and LM equations. (Poole, 1970) In the money supply policy, there is an optimal value for the parameter for the interest sensitivity of the demand for money. However, since it is unlikely that this parameter would equal the optimal value, it should be possible that the optimal slope of the LM function could be obtained. (Poole, 1970) This optimal slope would determine whether the relationship between the money supply and the interest rate was negative or positive. The optimal combination can be proved by considering an equation, starting with the money supply function:c0M=c1+c?rWhere c?, c? and c? are parameters, M is the money supply and r is the interest rate. The expected loss is minimized by setting the partial derivatives of the loss equal to 0. The policy instruments are said to be the values of c? and c? and the optimal policy is:c0M=c1*+c2*rIf c?=0, it becomes a pure interest rate policy, and when c?*=0, it becomes a pure money supply policy. It is likely that the combination policy is the optimal policy as the expected losses may be lower than the other two policies. However, the superiority depends on the knowledge of more parameters than either the money supply or interest rate policies. (Poole, 1970)Policymakers may endeavour to stabilise economies using other methods, such as a fiscal policy.  Fiscal policy is the use of changing taxes and government spending to reduce macroeconomic volatility; for example, by deliberately changing public spending and tax instruments to offset business cycle fluctuations.  (Debrun and Kapoor, 2010)  This automatic stabilisation occurs due to tax revenues tending to be proportional to national income and expenditure, while as public spending reflects the government’s commitments regardless of the state of the economy, except when it comes to entitlement programmes, such as unemployment benefits.  It can also reduce it by making sure the structure of the tax and transfer system is designed to maximise economic efficiency and market flexibility, decreasing the effect of shocks on the economy. (Debrun and Kapoor, 2010)A problem with using Fiscal Policy is that “velocity is more stable than the investment multiplier.” ( Friedman-Meiselman) Another problem is that it depends greatly on where the government sets income tax, either by setting income tax rates (which allow tax revenues to be an endogenous variable) or setting tax receipts (so implicit income tax would be endogenous). (Poole, 1970)Overall, in order to achieve optimal monetary policy and reduce macroeconomic volatility, monetary authorities need to have a direct or inverse relationship between the money supply and the interest rate in whichever policy they choose. (Poole, 1970) Both a money supply policy or an interest rate policy could be more optimal depending on the parameters and other factors which occur in the economy.  However, it is likely that the superior will be a combination policy, that takes into account the relationship between money supply and interest rates of an economy. This is more likely to lead to a stable and growing economy and to reduce macroeconomic volatility. However, there is uncertainty in that each of the parameters of the model may be treated as a random variable, which renders it analytically impossible due to the number of variances and co-variances involved in the equations. (Poole, 1970) Knowing what the right policy is can never be certain, and also will vary with time and the state of the economy.  Fiscal policy can also be an effective policy in an economy, but is unlikely to be used in isolation and is generally less stable.

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