The Poole model was first hypothesized by William Poole in 1970. The Poole model builds on the stochastic IS-LM model to incorporate unexpected shocks to investment and the money market. The model works under the assumption that policymakers primary objective is to minimise output volatility (Poole, 1970). To achieve this primary goal of minimised volatility, policymakers can adopt a monetary approach. Under this approach they can either set the money supply and control interest rates or set interest rates and control money supply. Policymakers have a trade-off between these two options as they can change the money supply and interest rates, however cannot do these independently of one another.Firstly, take the scenario where an economy experiences an unexpected increase in money demand (MD) and investment is fixed (IS curve stationary). Under a fixed money supply rule the change in MD (M’D to MD”, Figure 1) would subsequently cause an increase in real interest rates as Money supply is set as constant causing a shift in the LM curve and a change in output (LM’ to LM”, Y0 to Y- Figure 1) . Figure 1.When policymakers decide to set interest rates and there is a shock to MD, money supply can subsequently be changed to maintain the set interest rate and counteract the shock. As shown in Figure 2, the shift in MS means the interest rate remains constant, thus the LM curve is perfectly elastic and Y does not fluctuate when adverse shocks to the money demand occur.Figure 2.In the case of an economy which is exclusively affected by shocks to MD, policymakers should always choose to set interest rates and control the money supply. This eliminates any output changes (Y?Y0) compared to fluctuating interest rates and maintained money supply (Figure 3, Y can fluctuate from Y0 to Y+/ Y-). Figure 3.In the scenario of a shock only to investment policymakers favour a money supply rule. Interest rates can efficiently fall or rise to counteract the adverse shift in the IS curve however there will still be some variation in Y (Figure 4, Y’+/ Y’-). However, the variation is smaller in comparison to the fixed IR rule which sees output vary from Y”+/ Y”-.Figure 4.Furthermore, when there is a shock to both MD and Investment the choice for policymakers is not straightforward. As an interest rate rule counteracts a shock to MD more efficiency and a money supply rule counteracts a shock to the Investment more efficiently, policymakers must quantify which policy will reduce the effect of the shocks to output the most.To explore which route central banks should take we must first express the IS/LM curves mathematically: IS: Y= ?0 + ?1i + uLM: M= ?0 + ?1Y + ?2i + v Where u and v are stochastic random variables (the respective shocks to the IS/LM curve) and it is assumed ?1<0 and ?1>0 and ?2<0.Since u and v are shocks we assume their means to be zero and have constant variances:E(u) = 0 and E(v) = 0E(u2) = ?2 and E(v2) = ?2We must now consider the role of the central bank. The primary objective of the central bank is to minimise volatility thus its loss function is the variation of output from equilibrium levels of output. L = E(Y-Yf)2 If the central bank follows an interest rate rule, output is affected only by shocks to investment as money supply can be altered to counteract any unexpected changes in MD. Y= ?0 + ?1i + uE(Y) = ?0 + ?1i (since E(u) = 0)The central bank will set i to ensure: E(Y) = YfYf = ?0 + ?1i*This can be rearranged to provide the optimal IR:i* = (Yf - ?0) / ?1Solution for Y:Y = Yf + uIf the central bank choses to the fix money supply they must take into account both u and v:IS: Y= ?0 + ?1i + u LM: M= ?0 + ?1Y + ?2i + vFirstly we must rearrange to solve for Y in terms of M:Y=1?1?1+ ?2(?0?2+ ?1(M- ?0)+ ?2u- ?1v) Since E(u) = 0 and E(v) = 0:Y=1?1+ ?2(?0+ ?1(M- ?0)To minimise the loss function, M will be set so that E(Y) = Yf:Y=Yf= 1?1?1+ ?2(?0?2+ ?1(M*- ?0)Final output:Y=Yf+ 1?1?1+ ?2(?2u- ?1v) Now that the two respective output functions have been derived they can be substituted into the central banks loss function.Interest rate rule:Li=E(Y-Yf)2 Y=Yf + uLi = E(Yf+u-Yf)2Li = Eu2Li = ?2uMoney supply rule:LM = E(Y-Yf)2 Y=Yf+ 1?1?1+ ?2(?2u- ?1v))LM = E(Yf+ 1?1?1+ ?2(?2u- ?1v)- Yf)2LM = E( 1?1?1+ ?2(?2u- ?1v)2By expanding the brackets the following loss function is derived:LM=E( 1(?1?1+ ?2)2(?12?v2-2?1?2??u?v+ ?22?u2) Since the two loss functions for both the money supply and interest rate rule have been derived the two policies can be compared through the ratio of the respective losses: Li = ?u2 LM=E( 1(?1?1+ ?2)2(?12?v2-2?1?2??u?v+ ?22?u2) ?=LM/Li=1(?1?1+ ?2)2(?12?v2/?u2-2?1?2?v/?u)+ ?22)If ?>1 then the central bank will choose the interest rate rule (as LM>Li), if ?<1 money supply rule (LM