## This essay will assess two different monetary

This essay will assess two different monetary policy approaches: the money supply rule means that the monetary authority would set the money supply and leave the interest rate to fluctuate independently, the interest interest-rate rule would mean that the monetary authority would be setting the interest rate and allowing the money supply to move independently. Reducing macroeconomic volatility would mean an increase in the stability of trends in various macroeconomic indicators, the Poole model however only accounts for output, so only this will be examined. The Poole model, as outlined in Poole’s 1970 paper can be used to assess both of these approaches.  The Poole model is based upon the traditional IS-LM model, where the price level is assumed constant, but adapting it to account for economic shocks: (1) Y=0+1r+u                                 (2) M = 0+1Y+2+v                  The equation (1) represents the IS curve and (2) the LM curve. In (1) r represents the interest rate; u and v represent shocks to the IS and LM curves respectively.  In the case of the monetary authority applying the interest rate rule the LM curve would be horizontal as the interest rate is prescribed at a certain level. This means that when applying the interest-rate rule less knowledge is necessary than when applying the money-supply rule; only knowledge of the IS relation is necessary (given that the LM relation is simply a horizontal line at the chosen interest rate).  It would seem as if there is less uncertainty when using the interest-rate approach, given that only shocks on one curve occur, however this depends on the variance in the shocks acting on each curve as well as other parameters in the economy. Within the Poole model the aim of the monetary authority is to minimise its loss function, which is: L=E(Y-Yf)2 Where Y is output, and Yf is  expected output. In words, the smaller the difference between the actual output and the target output, the better for the monetary authority. Assuming that the monetary authority is rational and well informed, so that any goal they set will be realistic. Then the expected difference between the expected output and the actual output is a good measure of macroeconomic uncertainty. Therefore minimising this loss function is equivalent to minimising macroeconomic uncertainty.The Poole model, with shocks both fiscal and monetary, can be easily represented graphically as done below in Fig I and Fig II. In both Fig. I and Fig. II the y-axis labelled i represents the interest rate, the x-axis labelled Y represents output. The curves labelled IS- and IS+ reflect the outermost bounds of possible IS curves subject to shocks, IS+ being the upper end and IS- being the lower end. LM+ and LM- reflect the outermost bounds of possible LM curves subject to shocks. LM(Md=Ms) is the LM curve if the interest-rate rule is adopted. Y’+ and Y’- are the outermost bounds of output when the money supply rule applies and Y”+ and Y”- are the outermost bounds when the interest-rate rule applies (again, true in both Fig. I and II). In Fig. I the gap between IS- and IS+  is greater than the gap between the LM- and LM+ curve. This means that, in this case, the output variation is greater: (Y”+-Y”-) >(Y’+-Y’-) when the money supply rule is used. Preferring the money supply rule in this case means that if there is a recession, the interest rate falls on its own, reducing the impact of the shock to spending. In Fig. II the gap between LM+ and LM- is greater than the gap between the IS+ and IS-. This means that, in this case, the output variation is lower: (Y”+-Y”-) <(Y'+-Y'-) when the money supply rule is used. In this case using the money supply rule would would raise the interest rate in the event of a recession, amplifying the effect of the negative spending shock, and having a very negative effect on macroeconomic volatility.The lower the output variation, the more macroeconomic volatility is reduced. So in the case that the gap between the bounds of LM is greater than the gap between the bounds of IS, the interest-rate rule will lead to greater macroeconomic stability, and in the case that the opposite is true, the money-supply rule will lead to greater macroeconomic stability. Recalling that IS is determined by Y=0+1r+u , the horizontal shift in IS is given by u, the shocks. LM is determined by M = 0+1Y+2+v, solving this for Ygives: Y=-01+11M-21i-11v, and the horizontal shift in LM: -11v. These shocks (and their variances) and 1therefore determine whether the money supply rule or the interest rate rule should be applied. With a fixed interest rate the LM curve would be flat and the IS curve would be the only one affecting the level of output. By finding the expected level of output: EY=0+1r(using the fact that Eu=0) an equation for the optimal interest rate can be derivedr*=(Yf-0)/1and the expected output of the economy will be equal to the actual output, without accounting for shocks. Accounting for shocks: Y=Yf+u (3)If the monetary authority sets the money supply, an expected output value is derived discounting the random shocks (given Ev=Eu=0) , EY=111+202+1(M-0). The monetary authority aims to have expected output equal actual output, and the optimal monetary supplyM*can be substituted into the equation for expected output then Y = Yf+1/(11+22u-1v (4).The expected loss in the case of the interest-rate rule, Lr, and the expected loss in the case of the money-supply rule LM are derived from plugging in the output equations from the above paragraph into the loss function for the monetary authority. The effects of either approach can be compared with the ratio LMLr, whereLMLr=(11+2)-212v2u2-2uv12vu+22If the value of LMLr>1the loss function L = E(Y-Yf)2will be lower if the interest-rate rule is chosen, and therefore macroeconomic volatility will be lower in this case If LMLr<1 then the opposite is true. LMLr(11+2)-212v2u2+22The above inequality (which can be derived from the loss function ratio) shows that if vu is small enough (say less than the value of 1) then the ratio LMLrwill be less than one, so that a money stock policy would be superior to an interest rate policy for both the loss function of a monetary authority and macroeconomic volatility.  So based on this analysis, the smaller the chance of shocks in the goods market ( the smallerv)is compared the chance of shocks in the financial market (the smaller u)the more likely that the money-supply approach will lead to macroeconomic stability and vice versa. Poole wrote that vis commonly held to be smaller than u "at the current state of economic knowledge" in 1970. This view has remained roughly unchallenged over the preceding decades; the monetary sector is more centralised than the expenditure sector, more is held to be known about it and therefore it is considered less uncertain (and would have a lower variance of random shocks) . This would suggest that a money supply rule would lead to lower a lower loss function for the monetary authority, lower output volatility and therefore lower macroeconomic volatility generally. Poole's model however does fail to include forward looking variables. It has an equilibrium at a single point in time, and doesn't hold much predictive power for the future. Other approaches to improving macroeconomic stability are numerous. On method would be fiscal policy. This deals directly with fiscal shocks, negative or positive. If there is a negative shock, the government can raise its spending and if there is a dangerous positive shock taxes can be raised. This of course does nothing to deal with monetary shocks, but this approach could be used in conjunction with a monetary policy. If policy makers are elected by the public on a short term basis, devolving monetary powers to an independent central authority could improve macroeconomic stability in the long run.To reiterate, whether the interest-rate rule or the money-supply rule is the best approach in order to reduce macroeconomic volatility depends upon the relative variability of fiscal and monetary shocks according to the Poole model. As far as modern economics has found, the relative variability is as such that the interest-rate rule should be preferred in the case of a typical developed economy.