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.

The Model

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

IS:

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 <1 the opposite is true.7 We obtain an equivalent conclusion when comparing the ratio of the standard deviations, if then an interest rate rule should be applied. If then a money supply rule is superior. Policymakers should also consider the parameters of the model as they can help predict how the economy will react to changes in policy. represents income elasticity of money demand, which is significant as it is part of the volatile component of financial sector behaviour given by affects the horizontal displacement of the LM curve. The higher the denominator (), the more it has the ability to reduce money demand shocks represented by v. Furthermore, Poole showed that when (the interest elasticity of money demand) was low, then the expected loss when using a money supply rule, , would also be smaller. 8 Having a low creates a trade off: a smallwill result in greater stability of the means but will lead to greater shifts in the interest rate.9 However, such changes in the interest rate may help overcome the destabilising effects of shocks: a low will cause a significant drop in the interest rate, which may help the economy recover from a repression.10 Thus, the result of the loss function will be lower because the variation in Y has been minimised. The shocks Greater liquidity preference in the financial sector during bad times causes a positive shock to money demand, shifting to . If the monetary authorities were to fix money supply, then interest rates would increase, causing an exacerbation of economic instability. The increase in interest rates would have a negative consequence on consumer and investor spending, as they are most responsive to its change.11 Hence, the variance of Y would be greater and overall output would drop to .12 In such circumstances an interest rate rule would be more desirable (as shown by the horizontal LM) as it would have a stabilising effect on the real economy. (Poole, p.202) An alternative scenario emerges when a positive private spending shock, likely to be caused by the volatile investment component of IS, shifts to . An income over because it pushes up prices and leads to a misallocation of resources.13 In such environment, policymakers obtain a lower loss function by implementing the money supply rule to reduce volatility. This is shown by the smaller dispersion of output from relative to . Fixing money supply when there is a high demand for money causes interest rates to rise. To some extent this will curb the effect of an unsustainable boom as money becomes more expensive for the real economy, thus the output volatility will be reduced.14 Although, the extent of this will depend on how wealth is allocated between money and assets.15 (Poole, p.201) In reality, policymakers will likely be faced with an economy that is experiencing shocks in both the IS and LM. The relative size of the shock will help policymakers conclude which market is most volatile and which policy is most appropriate. This is demonstrated by the horizontal displacement of the IS curve, caused by its u term, or the LM curve caused by its term. Hence, policymakers can rely on the following rule: when the horizontal displacement of IS is greater than that of LM, as above, they should use a money supply rule. When the opposite holds, policymakers should use an interest rate rule. In choosing the correct instrument they will minimise the dispersion of Y along the x-axis. Limitations & Alternatives In Poole's model, monetary policy is passive; it is implemented after a shock is observed.16 A problem arises for policymakers due to the time lag between the shock occurring and data becoming available, as only then they will only be able to adjust the policy instruments exactly.17 Orphanides and Williams agree that given the presence of imperfect information on shocks and their parameters, restricting the extent to which policymakers may stabilise the economy is.18 In addition, policy's 'double-lag structure'19 means its full effect will only materialise following two time-periods. This is problematic because the state of the economy is likely to have evolved, causing changes in the structure of the model. Hence, the policy choice is no longer optimal.20 Moreover, it incorrectly assumes that policymakers can always intervene immediately to rectify the effect of a shock.21 An alternative form of monetary policy has been proposed: a policy "determined by rules rather than discretion".22 Here, policymakers make binding commitments (in an attempt to be seen as credible central bankers) to operate monetary policy following a target rule taking expectations into account.23 This could take the form of a Taylor-type rule, which is thought to be successful in stabilising the economy given that its goals are "appropriately defined".24 Alternatively a precise inflation-targeting zone could be adopted, as is the case with the European Central Bank where monetary policy is conducted with the aim of operating within its 0-2% target boundary.25 Given that most economic agents are to some degree forward-looking, should a shock occur they will foresee a change in monetary policy given the explicit inflation target, and will correct their behaviour to complement the policymaker's objectives, reducing volatility further.26 Conclusion To conclude, through stochastic modelling Poole produces guidelines for policymakers to implement optimal monetary policy in response to random shocks. In order to stabilise the economy they must consider the kind of shock that affected the economy and its magnitude, as well as the variance of the error terms, and the parameters that characterise the model. Nonetheless, it is not without limitations, namely choosing the right policy instrument given the lags involved in the data collection and implementation process.27 This led us to consider an active monetary policy as an alternative. While appealing, active rules only partially resolve the above limitation. Indeed, Kyland and Prescott concede that relying entirely on rules limits a policymaker's ability to deal with extraordinary crises.28 "History dependent"29 rules and forecasts are built on past parameters that may not consistently represent the best fit for the economy. Therefore, rules will only solve the problem of delay if their parameters have been continually assessed to ensure that they have remained valid. 1 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.198 2 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.204 3 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.203 4 Stephen J Turnovsky, 'Optimal choice of monetary instruments in a linear economic model with stochastic coefficients', Journal of Money, Credit and Banking, vol. 7, issue 1 (Ohio State University Press, 1975), p.51 5 Ray C Fair, Optimal Choice of Monetary Policy Instruments In a Macroeconomic Model, NBER Working Paper Series, Working Paper No. 2150 (1987), p.1 6 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.204 7 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.206 8 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.205 9 Hiroshi Yoshikawa, 'Alternative Monetary Policies and Stability in a Stochastic Keynesian Model', International Economic Review, Vol. 22, No. 3 (Oct., 1981), p.563 10 Hiroshi Yoshikawa, 'Alternative Monetary Policies and Stability in a Stochastic Keynesian Model', International Economic Review, Vol. 22, No. 3 (Oct., 1981), p.555 11 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.200 12 Ray C Fair, 'Optimal Choice of Monetary Policy Instruments In a Macroeconomic Model', NBER Working Paper Series, Working Paper No.2150 (1987), p.12 13 William Poole, 'Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model', The Quarterly Journal of Economics, vol.84, no.2 (May, 1970), p.203 14 Wendy Carlin and David Soskice, 'Consumption, Investment and Money', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006), p.139 15 Wendy Carlin and David Soskice, 'Consumption, Investment and Money', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006), p.275 16 Stephen J Turnovsky, 'Optimal choice of monetary instruments in a linear economic model with stochastic coefficients', Journal of Money, Credit and Banking, vol. 7, issue 1 (Ohio State University Press, 1975), p.55 17 Stephen J Turnovsky, 'Optimal choice of monetary instruments in a linear economic model with stochastic coefficients', Journal of Money, Credit and Banking, vol. 7, issue 1 (Ohio State University Press, 1975), p.55 18 Athanasios Orphanides and John C Williams, 'Robust monetary policy with imperfect knowledge', Working Paper Series No 764 (ECB, June 2007), p.35 19 Wendy Carlin and David Soskice, 'Monetary Policy', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006) p.153 20 Finn E Kyland and Edward C Prescott, 'Rules Rather than Discretion: The inconsistency of Optimal Plans', The Journal of Political Economy (1977), p.480 21 Stephen J Turnovsky, 'Optimal choice of monetary instruments in a linear economic model with stochastic coefficients', Journal of Money, Credit and Banking, vol. 7, issue 1 (Ohio State University Press, 1975), p.55 22 David Romer, Advanced Macroeconomics, 3rd edition, Chapter 10: Inflation and Monetary Policy (Boston: McGraw-Hill/Irwin, 2006), p.510 23 David Romer, Advanced Macroeconomics, 3rd edition, Chapter 10: Inflation and Monetary Policy (Boston: McGraw-Hill/Irwin, 2006), p.515 24 Michael Woodford, 'The Taylor Rule and Optimal Monetary Policy', The American Economic Review, vol. 91, no. 2 (May, 2001), p. 236 25 Wendy Carlin and David Soskice, 'Applications: Europe, the USA and Asia', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006), p.168 26 Wendy Carlin and David Soskice, 'Applications: Europe, the USA and Asia', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006), p.170 27 Wendy Carlin and David Soskice, 'Monetary Policy', Macroeconomics: imperfections, institutions and policies (New York: Oxford University Press, 2006), p.139 28 David Romer, Advanced Macroeconomics, 3rd edition, Chapter 10: Inflation and Monetary Policy (Boston: McGraw-Hill/Irwin, 2006), p.510 29 Michael Woodford, 'The Taylor Rule and Optimal Monetary Policy', The American Economic Review, vol. 91, no. 2 (May, 2001), p. 236