This paper argues that the parameters of monetary policy rules affect the persistence of
inflation and output. Persistence is lower if monetary policy emphasises the price level or if
there is an inflation target. A greater emphasis on output increases persistence. There is a
simple New Keynesian interpretation of our findings: monetary policy rules affect persistence
by affecting real rigidities

Bratsiotis, GJ

Martin, C

English

Brunel University Research Archive

1Monetary Policy Rules and the Persistenceof Inflation and OutputGeorge J. BratsiotisSchool of Economic StudiesUniversity of ManchesterDover Street,Manchester M13 9PL,UK.Christopher Martin1Department of EconomicsBrunel UniversityUxbridgeMiddlesex UB8 3PH, UK.September 2002Abstract:This paper argues that the parameters of monetary policy rules affect the persistence ofinflation and output.  Persistence is lower if monetary policy emphasises the price level or ifthere is an inflation target. A greater emphasis on output increases persistence.  There is asimple New Keynesian interpretation of our findings: monetary policy rules affect persistenceby affecting real rigidities.JEL: classification: D4, D5, E5.Keywords: Persistence, Monetary Policy Rules                                           1 Department of Economics and Finance, Brunel University, Uxbridge, Middlesex UB8 3PH,UK; Phone (+33)1895 03171; Fax (+33)1895 203384; Email christopher.martin@brunel.ac.uk21) IntroductionMonetary policy rules have been widely used in recent years todescribe the behaviour of policymakers (eg Taylor, 1993, Clarida et al, 1999)and to analyse optimal policy (Svennson, 1997).  This paper develops thatliterature by arguing that monetary policy rules affect the persistence ofinflation and output and that they do so by affecting real rigidities.We consider a simple macroeconomic model in which policymakersmanipulate aggregate demand using a monetary policy rule in which thenominal money supply responds to the deviations of output and the price levelfrom their target or desired values.  On the supply side, monopolisticallycompetitive firms produce output using labour inputs.  Price adjustment isstaggered and modelled using the familiar Calvo (1983) framework.We show that the parameters of the monetary policy rule affect thepersistence of inflation and output.  Persistence is lower if policymakers attachgreater importance to the price level.  If policymakers have a strict inflationtarget, there is no persistence. By contrast, persistence is high if policymakersgive priority to attaining their target level of output.  Our model has the NewKeynesian property that persistence is higher when real rigidities are stronger(Ball and Romer, 1990).  We argue that the parameters of monetary policyrules affect persistence by affecting the degree of real rigidity.The remainder of the paper is structured as follows. Section 2 outlinesour model.  Section 3 describes how monetary policy rules affect persistence.Section 4 summarises and considers the wider implications of our work.2) The modelThere are a large number of identical monopolistically competitive firmsEach firm has the simple production function(1) it ity l=where ity  is output in firm i at time t, itl  is employment in firm i at time t and allvariables are expressed as natural logarithms.   Each firm also faces thedemand curve3(2) ( )it t it ty y p pη= − −where ty  is aggregate demand, itp  is the price set by firm i, tp  is theaggregate price level and η  is the constant price elasticity of demand.Firms hire labour on the labour market.  We assume the labour marketis imperfectly competitive and that the real wage is(3)  /t t tw p y ρ− =where w is the nominal wage.  Equation (3) is a general expression for thereal wage that can be derived from a number of models of imperfectlycompetitive wage determination such as efficiency wage theories or union-firms bargaining models.  A larger value of ρ implies that real wages are lessresponsive to output.The optimal price for each firm is simply a mark-up over the nominalwage.  Using (3), the optimal price is therefore(4)  * /it t tp p yµ ρ= + +where p* is the optimal price and µ=(η/η-1) is the mark-up of price overmarginal cost.Aggregate demand is(5) ( )t t t ty m p ε= − +where m is the nominal money supply and tε  is an aggregate demand shockthat is assumed for simplicity to be white noise and known at time t.  Monetarypolicymakers manipulate aggregate demand using the monetary policy rule(6) ( ) ( )T Tt t tm m p p y yφ ψ= − − − −4where pT is the target or desired price level and yT is the target or desiredlevel of output.  The parameters φ and ψ reflect the importance policymakersattach to achieving their price and output targets.  If φ→∞ and ψ→0, the over-riding priority of policymakers is to achieve a price level of pT.  In this model,this is equivalent to a policy of strict inflation targeting (Bernanke et al, 1999).If ψ→∞ and φ→0, the only objective of monetary policy is to achieve an outputlevel of yT.  If φ=ψ, policymakers pursue a target for nominal GDP, while ifφ=ψ=0, policymakers target the money supply.Combining (4), (5) and (6), we can express the optimal price as(7)  ˆ* (1 )1it t tp m p βµ β β εφ= + + − + +where ˆ1T Tm p ym φ ψφ+ +=+ and 1(1 )φβρ ψ+=+.We assume that price adjustment is sluggish and use a version of theCalvo (1983) model of staggered price adjustment.  For each firm, prices areadjusted with fixed probability λ and remain constant with probability (1-λ).Then the price level is given by(8) 10(1 ) (1 )iit it j it itip x x pλ λ λ λ∞− −== − = + −∑where p is the aggregate price level, x is the price chosen by firms, The pricechosen when firms adjust is forward-looking:(9) 10(1 ) * * (1 )iit t it j it t itix E p p E xλ λ λ λ∞+ +== − = + −∑where we assume there is no discounting for simplicity.3) Persistence5Combining equations (8) and (9) and aggregating, the aggregate pricelevel is(10)21 12 2(1 ) ( ) *2(1 ) 2(1 )t t t t tp p E p pλ λλ λ λ λ− +−= + +− + − +Aggregating (7) and substituting into (10)(11) 1 1 ˆ( ) (1 2 )( )1tt t t tp A p E p A mεµβ φ− += + + − + + +where 212(1 )A λλ βλ−=− +.  Solving this difference equation, prices can beexpressed as(12) 1 ˆ(1 )( )1tt tp p mεµθ θ β φ−= + − + + +where(13) 2 1B Bθ = − − ;212(1 )B βλ λ= + − .From equation (13) and the definition of β we obtain (14)20; 0; 0;d d dd d d dθ θ θλ β λ β< < < 0ddβφ >  and 0ddβψ< .Based on equation (12) inflation is then simply(15)  1 11 ( )1t t t tθπ θπ ε εφ− −−= + −+6where 1t t tp pπ −= −  is the inflation rate.  Substituting (12) and (6) into (5), wecan also express output as(16) 1 1(1 ) ( )1t t t ty y θθ θ ρµ ε εψ− −= − − + −+Equations (15) and (16) establish our main result, which is that theparameters of the monetary policy rule affect the persistence of inflation andoutput.  If policymakers place greater emphasis on the price level, then φ islarge and ψ is small.  From (7) (13), and (14) this implies that β will be higherand so inflation and output will be less persistent.  A similar argument showsthat a greater emphasis on output creates more persistence.  If policymakershave a strict inflation target there is no persistence (θ→0) and prices are attheir target level (p→pT).We can give our findings a simple New-Keynesian interpretation.Nominal rigidity is measured by (1-λ), the proportion of firms who do notadjust price, and real rigidity is measured by (1-β), the impact of theaggregate price level on each firms’ optimal price (Romer, 2001).   From (14),we note that persistence is greater when nominal rigidity is stronger,(1 ) 0ddθλ− > , and this effect is stronger with stronger rigidities, 2(1 ) (1 ) 0dd dθλ β− − > .Our model therefore has the New Keynesian property that persistence is dueto nominal rigidity and that the impact of nominal rigidity is greater where realrigidity is stronger (Ball and Romer, 1990).From (7), we note that real rigidity is lower when real wages are moreresponsive to output.  Therefore persistence is stronger when real wages areless responsive to output (Ball and Romer, 1990).  But real rigidity is alsoaffected by the parameters of the monetary policy rule.  If policymakersemphasize the price level, or adopt an inflation target, then, from (7), φ is largerelative to ψ, so β is large.  This means that real rigidity is low and, from (13),there is less persistence in inflation and output.  Intuitively, policymakers willrespond to shocks that tend to move prices away from their target value byoffsetting changes in the nominal money supply.  Desired relative prices in (7)7are therefore less responsive to the aggregate price level.  By contrast, ifpolicymakers place greater emphasis on output, then β is small.  Real rigidityis stronger, leading to greater persistence.  In this case, monetary policy willtend to accommodate movements in the price level and so desired relativeprices are more responsive to the aggregate price level.4) ConclusionsThis paper has argued that the parameters of monetary policy rulesaffect the persistence of output and inflation and that a greater emphasis onstabilising prices (for example, through an inflation target) reduces thepersistence of inflation and output.  We also argue that monetary policy rulesaffect persistence by affecting the degree of real rigidity.Our analysis can be extended in a number of ways.  We could considera more complete model where aggregate demand depended on the realinterest rate and where policymakers control the nominal interest rate, inwhich case we could model monetary policy using a Taylor rule (Taylor,1993).  We could consider a more detailed model of nominal rigidity, such asthe staggered adjustment model of Taylor (1979), in which case the frequencyof price adjustment may also be affected by the monetary policy rule. Wecould also analyse a more detailed model of the labour market, allowing wagesetting to be influenced by the monetary policy rule.  We would expect to finda similar link between monetary policy rules and persistence in these moresophisticated models.8ReferencesBall, L, and D Romer, 1990, “Real Rigidities and the Non-Neutrality ofMoney”, Review of Economic Studies,  57, pp 179-98Bernanke, B, T Laubach, F Mishkin and A Posen, 1999, Inflation Targeting:Lessons from the International Experience, Princeton University PressCalvo, G, 1983, "Staggered Contracts in a Utility-Maximizing Framework,"Journal of Monetary Economics, 12, pp 383-98.Clarida, R, J Gali, and M Gertler, 1999, "The Science of Monetary Policy: ANew Keynesian Perspective" Journal of Economic Literature 37 (December)pp. 1,661-1,707.Romer, D, 2001, Advanced Macroeconomics (2nd edition), McGraw-Hill,Svennson, L, 1997, “Optimal Inflation Targets, ‘Conservative Central Bankers’and Linear Inflation Contracts”, American Economic Review, pp 98-114Taylor, J, 1979, "Staggered Wage-Setting in a Macro Model", AmericanEconomic Review, Papers and Proceedings, 69, pp 108-13Taylor, J, 1993, "Discretion versus policy rules in practice", Carnegie-Rochester Conference Series on Public Policy, 39, pp 195-214.

Monetary policy rules and the persistence of inflation and output

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