The to illiquidity. In bad times under a money

 The Poole model is a useful way toshow how to reduce macroeconomic volatility as to show this as it extends theIS-LM model to include shocks, which can be money shocks, real shocks or a mixof the two within an economy which all cause volatility. The equation for ISbecomes  and LM becomes  where u is the shock to IS and v is the shockto LM.  A money supply rule iswhere money supply is fixed and interest rates fluctuate. An interest rate ruleis when policymakers fix interest rates and allow money supply to move aroundfreely depending on money demand.

The policymaker wants to minimise thevariance of GDP and so we use a loss function:  where Yf is the Natural rate of GDP. Ifan economy faces only money demand shocks then this creates macroeconomicvolatility as it’s the extent to which the financial sector prefers liquidityto illiquidity. In bad times under a money supply rule quantities of liquid andilliquid assets are fixed however the opportunity cost of money increases andso the interest rate resulting in higher money demand and so we get LM+. Ingood times then the opposite is true. People have confidence in illiquid assetsand so the price of money goes down decreasing the interest leading to LM-. Whenthere are money shocks in an economy, if policymakers use a money supply rulethen output can vary between Y- and Y+. By contrast if the policy maker chosean interest-rate rule they would fix the interest rate at i0 so the expectedlevel of output is   as , and we get ahorizontal LM curve because the LM function can be extended to ‘treat moneysupply as interest-elastic… a pegged interest rate, of course is a polar casein terms of interest elasticity of supply’ (Poole, 1970). This means under aninterest-rate rule actual output will be.

If there is are only moneyshocks in the economy under an interest rate rule there will be no volatilityas output will always be Y0 geometrically or Yf as .  If the economy faces only money demand shocksthen it should use the interest rate rule over the money supply rule to lower macroeconomicvolatility. More commonly aneconomy can face are real shocks, when there is randomness in private spendingaffecting the IS curve, with private investment being most volatile component. Onedeterminant of investment is the interest rate (opportunity cost of investingin capital stock) which gives a downward sloping investment curve. Theinvestment curve determines the position of the IS curve as it is governmentspending given the amount of investment.

In good times people are optimisticand so invest more and there is a positive spending shock giving IS+. In badtimes there is more uncertainty so people don’t want to invest resulting in anegative spending shock, IS-. If policymakers applied a moneysupply rule to minimise expected loses then expected output is  as . To minimise loses thepolicymaker would set the money supply so  giving actual output under a money supply ruleas   During bad times GDP would be Y1 andduring good times as there is more private spending IS is higher and so GDP isY2.

If policy makers chose to fix interest rates then we again get the horizontalLM curve and we can see in bad times, when IS is lower output is Y3 and in goodtimes it is Y4. We can see from the graph that the amount Y varies when fixingmoney stock (Y1-Y2) is smaller than the when fixing interest rates (Y3-Y4). Ifan economy faces only private spending shocks it should adopt the money supplyrule to reduce macroeconomic volatility.  In thereal world economies are more likey to be vulnerable to both financial shocksand real shocks at the same time. If the economy is facing bad times andpolicymakers use a money supply rule it will be at the point where the two bluelines cross.

 There is pessimism in financialmarkets, as people have liquidity preference so Md increasesresulting in a higher LM(+). If there is pessimism in the money market then itis more than likely that there is also uncertainty in real terms i.e.Consumption and Investment. Financial institutions distrust of markets willmake consumers and business wearier to invest and so we get IS-. Under a fixedmoney supply in bad times output will be Y1. Oppositely in good times under a money supply rule people haveconfidence in their illiquid assets we have a lower Md and a lowerLM curve (LM-). Additionally the real market will we in boom and so there willbe more consumption and investment resulting in a higher IS curve (IS+).

Ingood times using a money supply rule is Y2. Conversely the policymakers could a fixed interest rate when there are moneyand real shocks. We can see that in bad times GDP would be Y3 due tosignificantly lower investment (and/or consumption) and in good times GDP wouldbe Y4 due to more spending. In this graph real shocks (to IS curve) are largerthan the shocks to the money market, and so we can see from the graph that thepolicy makers should use the money supply rule because here interest rates areacting coherently and going up in good times which offsets it and somacroeconomic volatility is lower Y1-Y2 than with a fixed interest rate Y3-Y4. If on the economy was in the position where the LM shocks were greater than theIS shocks then the opposite would be true. This is because if you were to use afixed money supply then the interest rates are not having the desired effect;they decrease when the economy is in good times and so this encourages moreinvestment and worsen the situation.

Here the policymaker should use aninterest rate rule to lower macroeconomic volatility. This could also be shown bycomparing losses because as stated earlier the objective of the policymaker isto minimise the variance of GDP. We know under a fixed interest rate   and under fixed money supply. The loss functionsare   and with a money supply rule . To compare thepolicies we find the ratio of the losses (look at the relative losses. .

If the expression ?is greater than 1 then the loss under a money supply rule is greater and so thepolicymaker will chose a fixed interest rate, however if ? is less thanone then the loss under a fixed interest rate is greater so the policy makerwill fix the money supply to reduce macroeconomic volatility. If we assume that?=-1 then  simplifying to . The term in the square brackets isnow very similar to the denominator (Pickering, 2017) and so the interestelasticity of money demand (?2) is less relevant. What is moreimportant is ?1, income elasticity of money demand, ?vand ?u. If ?1 is greater than   thenthe loss from having a fixed money supply will be smaller than the loss fromhaving a fixed interest rate.

A money shock may not matter much if ?1 is high. LMshift left in bad times Md increases and GDP falls which feeds backinto the Md function. In economic bad times interest rates may beincreasing for other reasons such as the IS curve. This means than Md increases,so volatility increases and GDP falls, if ?1 ishigh enough it will have a corrective effect on the initial increase thathappens in bad times and counteracts what is happening to v.

An alternative is touse fiscal policy (taxation and government spending) to reduce volatility. Ifthe economy is facing positive shocks real shocks then that means people areoptimistic and so IS shifts right. However if the policymaker usescontractionary fiscal policy and increases income tax and corporation tax then thiswill shift IS left again and reduce volatility in the economy. In addition tothis if money demand is very sensitive to interest rates i.e. ?2is very high then the LM curve becomes horizontal and so fiscalpolicy is more attractive.

Combination policy is another alternative where values are set for c’1 andc’2 in the money supply equation  however for certain values the denominators ofoptimal c’1 and c’2 vanish so we use  . Again we want to minimise losses so get ,                   ) , and . This gives us theminimum expected loss as . When  there is a pure interest rate policy and when  there is a pure money stock policy. Exceptthese two cases combination policy is better than both pure policies (Poole,1970) because expected losses are lower.

For combination policy to be successfulthere has to be more knowledge of the parameters than the pure policies. Overall both the moneysupply rule and the interest rate rule are effective at reducing macroeconomic volatility