An Encompassing Framework for Evaluating Simple Monetary Policy Rules:

Transcription

1 An Encompassing Framework for Evaluaing Simple Moneary Policy Rules: Ray Barrell, Karen Dury and Ian Hurs Naional Insiue of Economic and Social Research 2 Dean Trench Sree Smih Square London SWP 3HE K.Dury@niesr.ac.uk Absrac Taylor and ohers have argued ha model sabiliy requires ineres rae policy rules have an inflaion feedback parameer greaer han one. In his paper we build an encompassing framework o analyse he sabiliy condiions of various policy rules on Taylor s model and in a world where here are nominal rigidiies in he shor-erm evoluion of demand. We conclude ha wih a combined nominal GDP and inflaion argeing rule, his sabiliy condiion is no necessary. We use sochasic simulaions on NiGEM o evaluae differen parameerisaions of he rules. We discuss he resuling covariance srucures and discuss heir implicaions for he ECB. Key Words: Taylor rules, Inflaion argeing, Moneary policy, feedback rules, Noe: The resuls presened in his paper are provisional and due o he compuaional burden of sochasic simulaions a wider se of resuls are being consruced for he final version of he paper. The suppor of he ESRC under gran R Do small differences maer? is graefully acknowledged. We would like o hank Andy Blake for many helpful commens on his paper. All errors remain ours.

2 . Inroducion The Purpose of his paper is o examine he meris of differen moneary policy rules by using sochasic simulaion echniques on he Naional Insiues Global Economeric model, NiGEM. More precisely, he paper invesigaes he sabilisaion properies of hese rules in erms of reduced variabiliy in cerain main economic ime series, such as oupu and inflaion. We are no only concerned wih looking a differen ypes of policy rules bu also varying he parameers wihin a rule iself o conribue o he debae ha has buil up in he academic lieraure on he mos appropriae size of feedback coefficiens in he rules. Oher issues are covered in he paper, such as he implicaions differen policy rules may have for he European Cenral Bank and he implicaions of including exchange rae uncerainy ino he analysis. In his paper we sar by looking a a simple descripion of he policy environmen as given in Taylor (998a) and a he sabiliy of a small model under a se policy rules ha are nesed wihin a general framework. We look a argeing a nominal aggregae, a mixed nominal aggregae and inflaion argeing regime, pure inflaion arges and a Taylor rule. 2 We he go on o examine if he small model findings hold when applied o a large-scale macro economic model. Large scale macro-models of he economy need moneary closure rules even more han hey need fiscal closure, as many analyses canno be sensibly underaken wihou some knowledge of he response of he moneary auhoriies. There are wo classes of moneary policy rule ha can be used in large models and by policy makers, and hey have slighly differen implicaions for he price level and for he model. There are hose ha ie a nominal aggregae or variable down in he long run, including fixed exchange rae rules, money sock guidelines and nominal GDP argeing 3. There are ohers ha feed back on he inflaion rae, and sabilise i in he long run, bu whose impac on he level of prices depends on he naure of he shocks and he feedback in he policy rule. The disincion beween hese wo classes of rules is brough ou in an annex. 2 In Barrell Dury and Hurs (999a) we look more direcly a commonly used Taylor Rules in he conex of inernaional policy co-ordinaion, alhough hese rules also fi wihin our framework., and in Barrell, Dury and Hurs (999b) we invesigae ou-urns for moneary and fiscal policy in Europe, and discuss he argeing sraegies available o he ECB. 3 The class also includes using he change in he ineres rae o arge he level of inflaion. 2

3 Since Taylor s paper (993), here has been much ineres in he evaluaion of differen moneary policy rules. A subsanial par of his lieraure concenraes on he use of simple policy rules on small sylised models many of which are backward looking closed economy models (see Rudebusch and Svensson (998), Svensson (997) and Ball (997)). They argue, for example, ha he opimal policy is some form of inflaion argeing hrough a Taylor ype rule, in which ineres raes are adjused in response o he deviaion of oupu and inflaion from heir desired pah. Indeed many have advocaed ha ineres feedback rules ha respond o increases in inflaion wih more han one for one increase in he nominal ineres rae, are sabilising4. Taylor (998b) finds ha here is hisorical evidence in he US ha shows here is an unambiguous correlaion beween moneary policy rule and macroeconomic sabiliy. Three eras of US moneary hisory were analysed; firs , where raes were unresponsive o flucuaions in oupu and inflaion: second, , where shor erm ineres raes were more responsive bu he response on ineres raes o changes in inflaion were less han ; hird where he ineres rae response was greaer han. The laer period proved o be he mos economically sable period. Taylor (998a) suggess ha he ECB should follow such a rule where he response coefficien on he inflaion arge is greaer han one. However a recen paper by Benhabib, Schmi-Grohé and Uribe (998) has argued ha such an acive policy rule can lead o insabiliy. They show in an opimisaion framework ha even if here exiss a unique seady sae equilibrium for his rule, here will exis an infinie number of equilibrium rajecories lying near he acive seady sae. They advocae ha using local echniques o analyse he sabiliy of he sysem may lead o inappropriae policy regimes. Chappell and Turner (998) demonsrae ha he Taylor rule can induce insabiliy ino a small macroeconomic model wih Raional Expecaions because i effecively removes he real balance effec from he oupu equaion making excess demand a funcion of only inflaion. In addiion i may be he case ha in large models, small model resuls may no hold. As Chappell and Turner poin ou, in more complex models he Taylor rule may no produce insabiliy as oher facors will make oupu a 4 See Clarida and Gerler (997), Chrisiano and Gus (998) 3

4 funcion of he price level, for insance he effecs of he real exchange rae on compeiiveness, and so sabilise he model. Moneary policy also affecs he economy hrough exchange rae channels as well as hrough he ineres rae effecs on domesic demand. Therefore he choice of a bes moneary policy rule may change when working in an open economy framework. Svensson (998) exends he analysis of inflaion argeing o a small open economy model where he exchange rae plays a prominen role in he ransmission mechanism of moneary policy and shows ha by argeing variables oher han jus inflaion, he variabiliy of oher economic variables is reduced. In order o ake accoun of he variabiliy of hese oher variables i is necessary ha small models are expanded o include hem, and ha we work in an open economy framework, and hence here is a srong case for analysing he ECB s problems using a large open macro-economic model. Taylor does use sochasic simulaions on a seven counry macro-economic model o calculae he variabiliy of cerain economic variables under a Taylor rule. However, he does no analyse how he economic sabiliy is affeced by changing he parameers of he rule. We aim o build on his work by aking a class of moneary policy rules considered in he general framework we have developed and apply differen parameerisaions of he rules o ascerain wheher hese small model findings hold on a large open-economy macro-economeric model. Our aim in his paper is o build an encompassing framework so ha we can analyse he sabiliy properies of a class of simple moneary policy feedback rules where boh he Taylor rule and his descripion of he world is nesed wihin he general framework. We sar wih he Taylor rule and show he heoreical basis for Taylor s resul. We hen consider some alernaive policy rules ha are nesed wihin he general framework of he model and examine he condiions necessary for sabiliy. Wihin he framework we can hen exend he simple Taylor world and examine he sabilisaion properies of he class of rules when wealh effecs are included in he aggregae demand schedule. Following Taylor we will hen go on o apply he heoreical calculaions based on he small model resuls o a large global economeric raional expecaions model. We will use sochasic simulaion echniques on he Naional Insiiues Global Economeric Model, NiGEM, o evaluae he performance of he policy rules. The bes way o evaluae he sabilisaion properies of he rules is o apply a sequence of 4

5 random shocks o he model. Analysing policy rules using deerminisic shocks is useful as i can give a clear comparison of he effecs under a very specific shock o he economy (Barrell, Dury and Pain (998). However, he overall performance of a policy rule will depend on is abiliy o sabilise economic variables given a variey of shocks. To conclude ha one rule is superior o anoher, we mus apply a number of random shocks o he model and measure is overall performance, and hence he mos effecive way o evaluae rules is o use sochasic simulaion echniques. In secion 2 we develop he heoreical framework for analysing a class of moneary policy rules. We discuss 5 ypes of rules ha are nesed wihin he general framework. Wihin he framework we can hen exend he Taylor model o examine how real wealh effecs aler he small model resuls. Secion 3 gives a summary of he echniques used o underake sochasic simulaions on NiGEM and discusses he issue of including shocks o he exchange rae. Secion 4 provides a brief overview of NiGEM and Secion 5 repors he resuls of he simulaions on he variabiliy of cerain economic variables. Secion 6 examines resuls when exchange raes are excluded from he analysis and Secion 7 concludes. 2. An Encompassing Framework In his secion we provide a general framework for evaluaing differen policy rules. Le us expand he simple Taylor model described in Taylor (998a) o include real wealh effecs and a wider class of moneary feedback rules. This simple analyical framework is sufficien o cover he class of models we wish o invesigae, alhough he richness of expecaional elemens is no fully brough ou. In paricular, we do no feel ha i is possible o underake policy analysis wihou he assumpion of raional expecaions a leas being considered, bu Taylor s simple framework excludes hese elemens, and in his secion we herefore do he same. Consider he model, defined in erms of deviaions from baseline: y = β ( w p ) + u ( i π ) + θ () π i π y + e = + β 2 = γ π + γ p y 2 ( ) (2) (3) 5

6 where y is he percen deviaion of real GDP from poenial, π is he inflaion rae, p is he price level, w is nominal wealh and i is he nominal shor-erm ineres rae. e and u are serially uncorrelaed sochasic shocks wih a zero mean. Lower case denoes logarihms. Equaion () is a convenional IS curve which relaes oupu o he real ineres rae and includes he possibiliy of wealh (or real balance) effecs on demand. The parameers of he model are β, β 2 and θ and are assumed o be posiive. Equaion (2) can be inerpreed as a convenional Phillips curve and equaion (3) is he moneary policy rule used o close he model. In he more general model, he nominal ineres rae is assumed o respond o deviaions of inflaion, price level and real GDP from heir desired arge pahs. We shall firs consider he various ypes of rules ha his framework encompasses and hen ake each rule in urn and examine heir sabilisaion properies. Our objecive is o include rules ha can be described as argeing a nominal aggregae such as he money sock or nominal GDP 5 We can expand equaion (3) o give: i = γ π + γ 2 p + γ 22 y Various ypes of rules are nesed wihin his general framework. (4) Parameer values γ = 0, (γ 2 =γ 22 ) γ, γ 2, γ 22 >0, (γ 2 =γ 22 ) γ 2 = γ 22 = 0 ; γ > 0 γ 2 = 0 ; γ 22, γ > 0 Type of rule Money or Nominal GDP argeing rule Combined money or nominal GDP and inflaion argeing rule Pure direc proporional rule on he inflaion rae Taylor rule To examine he properies of he various rules le us firs subsiue equaion 4 ino equaion o ge an aggregae demand relaionship beween inflaion, π, and oupu y. This gives: y β θ e [( γ ) π + γ 2 p ] + ( w p ) + ( + βγ 22) ( + βγ 22) ( + βγ 22) = (5) Noe ha p = p + π 5 We use hese erms as subsiues for each oher, as a velociy de-rended moneary aggregae will move in line wih nominal GDP in he medium erm, and as we are no assuming ha he auhoriies wish o hi heir arge period by period, responses will be similar wih eiher arge. 6

7 Subsiuing his ino 5 and differeniaing wih respec o π gives: dy β θ = [( γ ) + γ 2] dπ ( + βγ 22) ( + βγ 22) The slope of he aggregae demand curve herefore becomes a funcion of he parameers of he policy rule. Sabiliy would require he slope of he AD curve o be negaive, i.e. dy/dπ < 0. This would imply ha a posiive inflaionary shock will resul in a fall in y below zero (i.e. real oupu will be below poenial oupu) and his will end o reduce inflaion and sabilise he model. Afer simplifying, he sabiliy condiion becomes: β [ γ ) + γ ] θ 0 ( 2 < (6) This condiion shows ha he sronger he wealh effecs he less imporan is he feedback coefficien on inflaion. In he simple Taylor model here are no wealh effecs and no direc feedback on prices, so we have γ 2 = θ = 0. Therefore sabiliy requires ha: β [ γ ] 0 < As Taylor poins ou, γ mus be greaer han for he sabiliy condiion o be saisfied. However i is ineresing o look a he sabiliy of he model under differen policy rule assumpions and o examine how argeing nominal aggregaes and including wealh effecs change he resuls. Firs we will consider some alernaive policy rules ha are nesed in his general framework and hen look a how wealh, or real balance, effecs change he resuls. 2. Alernaive policy rules on he simple model. A A pure inflaion argeing rule Le us assume ha a policy rule where shor-erm ineres raes respond direcly o he deviaion of inflaion from is desired pah, i.e. γ 2 = γ 22 = 0. Therefore we have a simple proporional rule on inflaion given by: i = γ π We are also assuming no wealh effecs a his poin (θ=0). Using he sabiliy condiion (6), we find ha he same parameer resricions apply as in he Taylor rule, 7

8 i.e.γ >. Therefore in his model a pure inflaion argeing regime requires a more han a one o one response of ineres raes o an inflaionary shock in order ha he model is sable in response o shocks. B. Nominal GDP argeing rule Wih a nominal GDP argeing or money sock rule, he parameers γ 2 and γ 22 are equal and γ = 0, (θ=0). The sabiliy condiion requires: γ 2 > Therefore for sabiliy wih his rule, he coefficien on he nominal aggregae, hence on boh he price level and real GDP, is greaer han one. C. A combined rule A nominal GDP and inflaion argeing rule We hen consider a combined policy rule of nominal GDP argeing (or money sock rule) and a direc inflaion arge. I appears from Duisenberg (998) ha he ECB has adoped his combinaion and we discuss is furher in Barrell, Dury and Hurs (999b). Wih a nominal GDP argeing rule, he parameers γ 2 and γ 22 are equal. The inflaion argeing componen of he rule requires ha γ >0. Wih he combined rule he sabiliy condiion is given by: β [ γ ) + γ ] 0 ( 2 < which reduces o γ + γ, (θ=0). I is ineresing ha wih he combined rule he 2 > sabiliy condiion does no require he parameer on he inflaion arge, γ, o be greaer han, nor he feedback on he nominal aggregae o exceed. The sabiliy condiion requires ha he sum of he coefficien on direc inflaion and he coefficien on he price level be greaer han one The inclusion of wealh effecs Resaing he sabiliy condiion (6) derived from our general model wih wealh effecs, we have. β [ γ ) + γ ] θ 0 ( 2 < (6) Taylor has shown, and we have re-saed, ha his simple rule in a world where here are no wealh or price level effecs will be sabilising as long as he inflaion feedback 8

9 parameer is greaer han one. We have so far assumed ha θ = 0 and so here are no financial wealh effecs included in he aggregae demand schedule. This is he assumpion ha Taylor uses o derive his sabiliy condiions. However, he body of empirical evidence suggess ha i is likely ha here will be oher variables in he aggregae demand schedule ha are affeced by he price level. In our general framework i is easy o exend he Taylor model o include wealh effecs by simply assuming ha θ >0. The sabiliy condiions for he differen ypes of rules are now: Taylor Rule : θ γ > β For sabiliy he Taylor rule now implies ha he response of oupu o real ineres changes mus be sronger han he real wealh effec in he aggregae demand schedule. Hence, i is no necessary for γ o be greaer han one for he model o display sable responses o shocks. We would in general assume ha real wealh effecs were weaker han real ineres rae effecs, and hence he feedback needs o remain posiive. This cavea holds for all rules ha include his erm. Pure Inflaion Targe The same condiion as he Taylor Rule applies: θ γ > again implying ha γ β does no have o be greaer han one for sabiliy. For he class of model we hink represen he world and analyse in his paper, a feedback of one on inflaion in an inflaion argeing regime should be unambiguously sabilising. 6 Nominal GDP argeing θ γ 2 > β implying he coefficien on he price level arge and he real GDP arge does no have o be greaer han one when wealh effecs are presen. 6 A feedback parameer of uniy on inflaion should no be confused wih a rule ha arges he real ineres rae in he long run. If a shock requires ha he real ineres rae falls in he long run, hen a feedback of one on inflaion in he shor run will be conracionary, and hence inflaion will fall, and ineres raes will follow. They will have o fall enough o sabilise inflaion on he baseline. The argumen is no differen from ha when he feedback coefficien exceeds one. 9

10 The Combined Rule: Nominal GDP and Inflaion Targeing γ θ + γ 2 > β implying he sum of he inflaion feedback coefficien and he price level feedback coefficien does no have o be greaer one. If for insance he effec of real ineres raes on aggregae demand were four imes he size of he real balance effec, hen we could have nominal feedback effecs of, say 0.4, and an inflaion feedback of 0.5, and he model and economy would display sable responses o shocks, as heir sum exceeds 0.75, which is all ha is required for sabiliy. We would argue ha here is a wide class of rules ha can be considered as boh usable and sabilising when considering how o se moneary policy. All mus saisfy he condiion ha hey sabilise he price level in he long run, and hence ha inflaion is sable. The choice of paramerisaion depends upon he welfare effecs of differing rules, and hese can be judged by looking a he effecs of rules on he variabiliy of oupu and inflaion, for insance. 3. Sochasic simulaion echniques The basic procedure There are a number of ways o evaluae he properies of models and he role of policy rules. Policy rules are designed o deal wih shocks o he economy. Differen policy rules can be evaluaed in he conex of a specific shock, such as he change in srucural capial flows o Eas Asia, which we discuss in Barrell, Dury and Pain (998). However, heir abiliy o deal wih repeaed shocks is he mos imporan conex in which hey can be evaluaed. Rules have o be designed for an uncerain world, and echniques, such as sochasic simulaions, have o be uilised in order o analyse he effecs of rules on he variabiliy (and poenially also he level) of variables of ineres o policy makers. Wihin he framework of sochasic simulaions, a variey of shocks are imposed on he model. These shocks are aken a random from a paricular disribuion and are repeaedly applied o he model. Hence he momens of he soluion of he endogenous variables can be calculaed and uncerainy invesigaed. Sochasic simulaion can be eiher in respec o he error erms, 0

11 coefficien esimaes or boh. In his paper we assume ha he coefficien esimaes are known wih cerainy and he sochasic shocks o he model are only applied o he error erms, much as in he res of he economic lieraure. 7 We use he boo srap mehod where he shocks are generaed by repeaedly drawing random errors for individual ime periods for all equaions of he model, NiGEM. The hisorical shocks o he esimaed equaions (and o calibraed ones) can be described as residuals in a regression equaion, and hey can be described by an n equaion by ime periods marix of single equaion residuals (SER). If he equaions are an adequae descripion of he srucure of he economies we observe over he period we draw shock from, hen we have consruced a se of random srucural shocks o hose economies. from he marix of single equaion residuals (SER). The shocks drawn will have he same conemporaneous disribuion as he empirical disribuion of he SER, which is assumed o be normally disribued, N(0,σ 2 ). In his way he hisorical correlaions of he error erms is mainained across variables, bu no hrough ime. If, for example, invesmen shocks across Europe are highly posiively correlaed, he error erms will end o be high ogeher for hese counries. There are a number of oher mehods for drawing he shocks which rely on specifying he variancecovariance marix or generaing pseudo-random shocks which are consisen wih he hisorical residuals (see Ireland and Wesaway 990 for a descripion). One of he main echniques used for generaing shocks is he McCarhy algorihm (See McCarhy 972). This approach uses he formula o generae a vecor of shocks, S: S = T 0.5 ru where S is he vecor of random shocks, r is he x T vecor of random numbers wih disribuion N(0,) and U is he T x M marix of disurbances from T observaions and M srucural equaions. The properies of S end o he rue srucural errors as T ends o infiniy, giving an asympoic esimae of he rue covariance marix. The mehod we are using akes he acual hisorical residuals, picked a random from he SER marix and hen applied as shocks o he model. In his way compuaional requiremens before he model is solved are reduced considerably. 7 Chaper 5 of Clemens and Hendry (998) conains a clear descripion of he echnique used in his paper.

12 There are around 800 sochasic equaions in NIGEM, 500 pos recursive and 500 ideniy equaions. No all sochasic equaions have been esimaed over he same period because of daa limiaions, However, he period 993Q o 997Q4 is common o all sochasic equaions and so is aken as he esimaion period from which o draw he shocks. In general all equaions have been esed for srucural sabiliy, and he parameers for his period represen he se expeced o hold over he fuure 8. Using his period yields 20 vecors of quarerly error erms which can be drawn a random in order o underake he sochasic simulaions. All sochasic equaions in he model are shocked a he same ime, alhough we draw a disincion beween equaions for exchange raes and for oher variables, and we highligh he imporance of shocks o he exchange rae in our analysis. Each sochasic equaion is shocked in he firs period using a random drawing from is errors over he hisorical period and he model is hen solved in forward-looking mode o calculae he expecaions ha he shock would generae. This can be hough of as being equivalen o a single deerminisic simulaion where a number of differen variables are shocked. A second random drawing of error erms is hen made and applied o each sochasic equaion in he following period of he simulaion run, and again he model is solved forward. This is repeaed for all ime periods being sochasically simulaed and is known as a rial. Each rial will consis of T (ime period for which we are sochasically simulaing) draws of X (number of sochasic equaions) values. This can be done as many imes as desired and each rial will yield an esimae of he endogenous variables for each ime period. I is imporan o solve he model far enough ino he fuure so ha he resuls in a rial soluion period are no affeced by he erminal dae. In his paper we sochasically shock he model over he firs 5 years of our forecas baseline bu each ime a shock is applied, he model is solved forward o 207q. For a 5 year soluion period, each rial consiss of 20 simulaions, herefore he oal number of simulaions underaken was 20 imes he number of rials for each policy regime. I should be noed ha we also apply he same shocks o each policy regime in order ha a comparison beween rules can be made wih relaively small se of rials. Seeding he shocks in his way is useful as 8 We have also de-meaned he shocks, as is common in his lieraure. A heoreical basis for his approach can be found in Clemens and Hendry (998), chaper 8, where hey discuss a heory of inercep correcions. 2

13 differences in shocks will produce differen resuls ha canno be ascribed o differen policy regimes. This paper is concerned wih he variabiliy of endogenous ime series such as oupu and inflaion and in order o presen he resuls in a condensed form we concenrae on he Roo Mean Squared Deviaion (RMSD) of variables from heir baseline pah as in Bryan e al (993). For level variables such as oupu and consumpion he mean squared deviaion for period is calculaed: ~2 i J ( y ) 2 j i y B i B σ = (3) J j= y i 2 j Where ~σ i denoes he esimaed variance of he variable i in period, y i is he value of he jh rial of variable i in period, B y i is he value of variable i on he base in period, and J is he number of rials aken. This will give a ime series of esimaed variances for each variable. We hen ake a simple average of his series over N ime periods and ake he square roo o give a simple summary saisic o help assess he performance of he policy rules over he whole ime period. The summary saisic given in he following ables are he RMS%Ds, i.e. J j B ( y i y i ) B 2 N RMS% D( yi ) = (4) N = J j= y i For variables such as ineres raes and he inflaion rae, absolue deviaions are measured in percenage poins, i.e. he RMSD for he ineres rae, r, would be: N J 2 j B RMSDr ( ) = ( r r ) (5) N = J j= where r j is he value of he ineres rae for rial j in period and rb is he value of he ineres rae on he base in period. Shocking he Exchange rae In his paper we include shocks o exchange raes. This is no sandard pracice in hese exercises (See Fair (998)). These shocks have been excluded in he previous lieraure as exchange raes can be inerpreed as policy reacion funcions in he model. In our simulaions we assume ha exchange rae markes are forward looking 3

14 and follow he arbirage pah wih no risk premia and jump when here is news. Hence hey are calibraed, srucural, no policy equaions and have errors on hem, much as esimaed equaions do. An anicipaed and susained fall in ineres raes in, say, Japan, will cause he Yen/dollar rae o jump in he firs period 9. The size of jumps depends on he effecs on ineres raes ha are anicipaed for he fuure, and hence policy rules affec financial markes. However, any exchange rae uncerainy mus be aken accoun of in he model and we do his by including shocks o he exchange rae in he sochasic simulaions. The consrucion of hisorical shocks o serling is clear, as he bilaeral rae agains he dollar exised in he pas, as did he raes for Japan, Canada, Sweden and so on. However, we are simulaing he model wih an exchange rae equaion for he Euro, a currency ha did no exis in he pas. Moving from he a regime where individual Euro area counries have heir own exchange raes o one where here is single exchange rae for EMU members inroduces some uncerainies as o wha shocks o apply o he Euro. We could consruc a se of shocks o he Euro ha was he weighed average of shocks o he individual currencies over he pas. However, his would no necessarily be he correc sraegy, as EMU has been se up, and hence shocks across bilaeral raes wihin he Union are no longer possible. A beer sraegy would be o apply he shocks ha occurred o he core of EMU (Germany, Belgium, Neherlands, France (and Ausria)) over he 993 o 997 period, and we adop his for he Euro. However, his means ha we are applying a subse of hisorical shocks, especially o he European Moneary Union and o he US, as in he laer case shocks o he exchange rae are he resul of shocks o all US dollar bilaeral raes. Sochasic experimens on NiGEM This paper seeks o use he mehod of sochasic simulaions o evaluae he differen ypes of moneary policy rules discussed in Secion on a large economeric open economy model. We focus on using he small model resuls by applying differen parameerisaions of he rules o he model o evaluae heir performance and he implicaion of he resuls for ineres rae deerminaion a he ECB. The mainenance of medium erm price sabiliy in he euro area is of prime concern o he ECB, bu we 9 The forward soluion uilises a soluion algorihm based on and Hall (985), and he erminal condiions on all forward looking variables involve a rae of growh condiion. 4

15 will also look a he degree o which oupu, inflaion and some oher key economic variables flucuae around he forecas baseline or arge pah. We will firs look a he variabiliy of individual ime series across he differen policy rules. A policy ha reduces he variabiliy of hese economic series will be judged o be more effecive. The 5 policy rules considered can all be derived from he general policy rule, equaion (3), resaed here: i = γ π + γ 2 p + γ 22 y (3) Rule : Nominal GDP argeing, or money argeing, where γ = 0 and γ 2 = γ 22 < Rule 2: A combined nominal GDP, or money sock, and inflaion argeing rule where γ 2 = γ 22 = 0.5. Rule 3: A pure inflaion argeing rule where γ = ; γ 2 = γ 22 = 0 Rule 4: A Pure inflaion argeing rule where γ =.5; γ 2 = γ 22 = 0 Rule 5: A Taylor rule where γ =; γ 2 = 0, γ 22 = 0.5 Rule Type of rule Parameer values γ γ 2 γ 22 NOM Nominal GDP argeing rule CR Combined nominal GDP and inflaion argeing rule INFT Inflaion argeing rule INFT.5 Inflaion argeing rule TR Taylor rule In each case we look a we are argeing he curren rae of inflaion and he curren level of a nominal magniude. Rules, 2, 3 and 5 are fully nesed. Rule 2 adds an inflaion arge wih a coefficien of, Rule 3 keeps he inflaion arge wih he same coefficien bu akes away he nominal aggregae and rule 5 keeps he same coefficien on real oupu bu includes an inflaion arge wih a coefficien of. Rule 3 and 4 are direcly comparable in ha he coefficien on he inflaion arge is increased from o.5. Rule 3 and Rule 5 are nesed ogeher, as he same coefficien of is used for he inflaion arge bu Rule 5 adds a feedback on real GDP of 0.5. The performance of he rules will give some insigh ino wheher he small model properies hold on a large model. A single moneary policy is applied o he euro wide 5

16 area in ha ineres raes do no reac o individual counry developmens bu o EMU wide aggregaes. The Unied Kingdom is no in EMU and so follows is own ineres rae reacion funcion and he resuls repored for he UK reflec he effec of changing coefficiens in he UK moneary policy rule. Denmark is no in EMU bu has declared ha i will follow EMU moneary policy and so he resuls for Denmark come from he effecs of changing he moneary policy rule in EMU. Denmark is also used in calculaing he EMU aggregaes. Sweden is also ou of EMU and is policy rule is lef unchanged across he sochasic simulaions. We firs repor he resuls of he sochasic simulaions across he 5 classes of rules where we include shocks o he exchange rae. In Secion 6 we hen go on o presen resuls for each rule where shocks o he exchange rae are excluded in he simulaions. 4. The model NiGEM is an esimaed model which uses a New-Keynesian framework in ha agens are presumed o be forward-looking bu nominal rigidiies slow he process of adjusmen o exernal evens. The heoreical srucure and he relevan simulaion properies of NiGEM are described in Barell and Sefon (997) and NIESR (998). The model conains esimaed srucures for he whole world, wih he major economies having equaion models wih around 20 key behavioural equaions. I has complee demand and supply sides, and here is an exensive moneary and financial secor. All counries in he OECD, including Souh Korea, are modelled separaely, as is China. There are regional blocks for Eas Asia, Lain America, Africa, Miscellaneous Developing counries, and Developing Europe. Shor erm ineres rae changes should have an impac on long erm ineres raes, equiy prices and exchange raes. NiGEM is mos commonly used for scenario analysis under he assumpion ha expecaions in financial markes are raional, in ha hey are fully consisen wih he oucomes of an even given he reacions of policy makers. Hence financial variables can 'jump' in he firs period of a scenario. These assumpions are adoped here. The size of he jump depends upon he ineres differenial ha opens up. The anicipaion of lower shor-erm raes will cause longerm raes o fall by he forward convoluion of shor erm ineres rae changes. Equiy prices will rise when ineres raes are anicipaed o fall. Hence any shock ha is expeced o slow down aciviy will have is effecs parly offse by he auomaic 6

17 shock absorbers in he moneary sysem. The size of he effec will depend upon he moneary rules used by he auhoriies. Forward looking long raes have o look T periods forward ) (+LR ) = Π j=, T (+SR +j ) T We assume ha exchange rae markes are forward looking, and exchange raes jump when here is news. An anicipaed and susained fall in ineres raes in Japan, say, will cause he Yen/dollar rae o jump in he firs period 0. The size of jumps depends on he effecs on ineres raes ha are anicipaed for he fuure, and hence policy rules affec financial markes. Forward looking exchange raes have o look one period forward 2) RX = RX + (+SRH )/(+SRF ) In our analyses labour markes are assumed o embody raional expecaions, a leas where we have evidence ha bargainers use forward expecaions, much as in Anderon and Barrell (995). Conracs are overlapping, and here are forward and backward elemens in he wage equaions, and hey display dynamic homogeneiy in (almos) all cases. The speed of adjusmen of wages and prices is esimaed o vary beween counries, and depends upon insiuions in he labour and produc markes. In general he US and he UK reac more quickly o excess capaciy han do he more regulaed coninenal European markes, and our resuls reflec hese differences, as well as differences in he underlying srucure of wealh and consumpion. Furher deails of he model are available on reques. Wage equaions can be wrien as 3) W/P = λ[(w/p) - PROD] + β U + δ P e +(-δ) P - ec Where W is he nominal wage, P is he price level, PROD is a long erm measure of produciviy and U is unemploymen. However consumers are no assumed o look forward when making heir decisions oday, bu raher hey reac o curren and pas incomes and ne financial wealh. This does no mean ha fuure evens do no affec heir behaviour, as forward looking long raes and equiy prices affec deb ineres paymens and asse values now. 0 The forward soluion uilises a soluion algorihm based on and Hall (985), and he erminal condiions on all forward looking variables involve a rae of growh condiion. 7

18 Hence financial markes bring forward he consequences of fuure evens, acing as agens for more passive households. Changing o forward looking household behaviour does no affec our resuls in any significan way. The model is large, bu wih a common (esimaed and calibraed) underlying srucure across all economies. The whole model is solved simulaneously in forward mode. The forward-looking naure of hese markes is cenral o model properies, and especially in shocks such as ha in Eas Asia and Lain America. The model is solved in a sequence of loops, uilising he sparse srucure of forward links in ime. A shock is applied, and he model is run over he full ime period, and ineres raes are allowed o be endogenous. A fall in demand will, for insance, cu ineres raes. Forward looking agens know his, and we emulae his knowledge by running he model a second ime, bu calculaing he long rae as he forward convoluion of shor raes in he previous run. The model is coninually run forward and sars again, and his is repeaed unil a soluion is found where raes of growh of expeced variables are consan a he erminal dae, and all equaions are converged. In paricular, longerm ineres raes are forward convoluions, and his period s exchange rae depends on ha nex period adjused hrough he arbirage condiion bu shor erm ineres rae differenials. Policy rules are imporan in closing he model and we have hem for fiscal and moneary policy. We assume budge deficis are kep wihin bounds in he longer erm, and axes rise o do his. Governmens are assumed o slowly adjus ax raes o offse any changes in heir defici from is arge rajecory, and hence hey remain solven in he simulaion (See Barrell and Sefon (997)). This simple feedback rule is imporan in ensuring he long run sabiliy of he model. Indeed, as Blanchard, 986, shows, wihou a solvency rule (or a no Ponzi games assumpion) here is no soluion o a forward-looking model. We can describe he simple fiscal rule as Tax = Tax - + φ [GBRT GBR] Where Tax is he direc ax rae, GBR and GBRT are he governmen surplus arge and acual surplus, and φ is he feedback parameer designed o remove an excess defici in less ha five years. 8

19 5 Resuls There are a number of poenial paerns of resuls ha we migh observe. In his secion we show ha when we include a direc inflaion arge ino he policy rule we find ha oupu variabiliy is increased and inflaion variabiliy is reduced compared o a simple nominal argeing rule for he UK. For he US and Euroland boh oupu and inflaion variabiliy are reduced under he combined rule compared o he nominla aggregae rule. Indeed, he more flexible US economy prefers a pure inflaion arge, whereas for he Euro area including some nominal aggregae in he rule is preferred. Our resuls indicae ha he inclusion of a real GDP arge (wih no direc price level arge as in a nominal aggregae) ino he policy rule rule for he ECB is unproducive as inflaion variabiliy increases subsanially more han he fall in oupu variabiliy. We also show, as one would expec ha for he US, as he feedback coefficien on he pure inflaion argeing rule is increased he variabiliy of oupu and inflaion falls. The ables below give summary saisics from he sochasic simulaions underaken on NiGEM in erms of RMSD or RMS%D under he differen policy rules and hey also indicae he saisical significance beween variances 2. Tables,2 and 3 presen he RMSDs for oupu, inflaion and he price level respecively. Each able also conains an index value for Rule 2, 3, 4 and 5 (Rule = 00). Individual counry values are given as well as he EMU aggregaes, he UK, and he US. Resuls are also available for Canada, Japan and individually for all oher OECD members, and he non-oecd blocks on he model. They are omied for reasons of space, and are discussed elsewhere, especially as he resuls for Japan hrow significan ligh on he problems associaed wih operaing an economy so near a poenial liquidiy rap on ineres raes. Our firs se of resuls have been consruced under he assumpion ha exchange raes are shocked. This is uncommon in he lieraure as discussed earlier. However, in Secion 6 we analyse he same se of rules bu we remove exchange rae uncerainy. This maybe he poin where inflaion and oupu are boh miniminsed and increasing he feedback coefficien furher inroduces insabiliies. Furher sochasic simulaions will be presened in he final version of he paper o invesigae his. 2 The F-raio o be esed is formed by aking he larger variance (no he RMSD as shown in he ables) divided by he smaller variance wih he degrees of freedom associaed wih he number of sample poins. This will give a value greaer han uniy. We may say ha if variances differ by more han 6 o 7 percen hen hey are significanly differen from each oher. Only he significance of variances are shown for he UK, US and EL and only for oupu and inflaion. 9

20 Table : Variabiliy of Oupu; Index value for RMS%D of Rule 2, Rule 3 and Rule 4 (Rule = 00) 3 RULE RULE 2 RULE 3 RULE 4 RULE 5 RULE = 00 RULE 2 RULE 3 RULE 4 RULE 5 GE FR * SP IT NL BG PT IR FN * OE UK * US * EL Rule = NOM : Rule 2 = CR : Rule 3 = INFT: Rule 4 = INFT.5: Rule 5 = TR. Oupu variabiliy Rule 2 In general i is no clear wha he effecs of increasing he feedback on inflaion should be on oupu. Inroducing he inflaion feedback ino he nominal rule helps sabilise oupu for he US and Euroland. The fall is significan for he US wih oupu volailiy falling by 6%. The majoriy of EMU member saes benefi from reduced oupu variabiliy under he combined rule compared wih a nominal argeing rule (alhough his is only significan for France and Finland). The variabiliy for Euroland oupu falls alhough i is no significan. The UK sees a rise in oupu variabiliy of 5%. Rule 2 3 The US experiences a furher fall in oupu variabiliy as he regime moves o inflaion argeing alone, bu he UK sees a rise in oupu variabiliy. 3 * indicaes variance is significanly differen o he variance under Rule indicaes variance is significanly differen o he variance under Rule2 indicaes variance is significanly differen o he variance under rule3 (only he comparison of Rule 4 o Rule 3 is shown) indicaes variance is significanly differen o he variance under rule3 (only he comparison of Rule 5 o Rule 3 is shown) 20

21 A pure inflaion argeing rule increases oupu variabiliy for all European counries compared o he combined rule. The increase is significan for all counries wih he excepion of Belgium, Ireland and Ausria. Euroland oupu variabiliy also increases significanly as he nominal aggregae is removed. Rule 3 4 All EMU member saes experience a fall in oupu variabiliy as he inflaion coefficien is increased from o.5, (excep for Belgium and Ireland who experience a sligh rise, alhough his is insignifican, and Ausria who sees no change in oupu variabiliy). However, oupu variabiliy is higher han under eiher he nominal or he combined rule. The difference from he uni coefficien rule is only significan for France, Spain and Finland. The Euro area as a whole also sees a fall of 2% in oupu variabiliy bu his is no significan. The UK experiences a large increase in oupu variabiliy and he US a sligh fall. Rule 3 5 Including a arge on real GDP helps o reduce oupu variabiliy for a number of EMU member counries, significanly. For Euroland as a whole oupu variabiliy is reduced by 6% which is significan. The UK sees a fall of around 9% and Euro area sees a fall of 6%. Table 2: Variabiliy of Inflaion; Index value for RMSD of Rule 2, Rule 3 and Rule 4 (Rule = 00) 4 RULE RULE 2 RULE 3 RULE 4 RULE 5 RULE = 00 RULE 2 RULE 3 RULE 4 RULE 5 GE FR * 08 0 SP IT NL BG PT IR * FN OE UK US * EL * Rule = NOM : Rule 2 = CR : Rule 3 = INFT: Rule 4 = INFT.5: Rule 5 = TR. 4 see foonoe 3 2

22 Inflaion variabiliy Rule 2 Mos of EMU member counries see a fall in inflaion variabiliy under he combined rule compared o he nominal aggregae rule. Ou of he 4 larges economies i is only Ialian inflaion variabiliy ha does no fall. The UK sees a fall of around 2% bu he US inflaion variabiliy is reduced by around %. The Euro area as a whole sees a fall of 6%. Rule 2 3 Moving o a pure inflaion argeing rule wih a feedback coefficien of raises inflaion variabiliy for all counries (wih he excepion of Porugal), and for virually all counries his is significan. For EMU as a whole here is a rise in inflaion variabiliy of over 20% as compared o he combined rule 5. Moving o a pure inflaion argeing rule leaves UK inflaion variabiliy he same bu increases inflaion variabiliy for he US. Rule 3 4 All EMU counries see a fall in inflaion variabiliy when he feedback coefficien on inflaion is increased in he pure inflaion argeing case (wih he excepion of Belgium and Porugal). For EMU as a whole he fall in inflaion variabiliy beween hese wo rules is significan. Increasing he inflaion coefficien from o.5 reduces he inflaion variabiliy for he US significanly bu leaves i unchanged for he UK. Rule 3 5 Generally, he resuls for he member saes show a fall in inflaion variabiliy when he real GDP arge is inroduced o a pure inflaion argeing rule. The fall is only significan for Germany and Spain. For Euroland as a whole inflaion variabiliy falls by 7% which is significan. 5 I is ineresing ha for Euroland as a whole, inflaion variabiliy falls by more han in any individual counry. This is due o he changes in he cross-counry covariance srucure of Euroland inflaion. We discuss his issue in a relaed paper Barrell, Dury and Hurs (2000). 22

23 The UK sees a fall in inflaion variabiliy as he real GDP arge is included in he rule. However he US sees a rise of 5%. Table 3: Variabiliy of Price level; Index value for RMS%D of Rule 2, Rule 3 and Rule 4 (Rule = 00) 6 RULE RULE 2 RULE 3 RULE 4 RULE 5 RULE = 00 RULE 2 RULE 3 RULE 4 RULE 5 GE * FR * SP * IT * NL * BG * PT * IR * FN * OE * UK * US * EL * Rule = NOM : Rule 2 = CR : Rule 3 = INFT: Rule 4 = INFT.5: Rule 5 = TR. Rule 2 All counries experience a significan fall in he variabiliy of he price level, paricularly he UK which sees a fall of 20%. Price level variabiliy in he US and Euorland falls by 8%. Rule 2 3 Moving o a pure inflaion arge resuls in a significan rise for all counries. Only in he UK does price level variabiliy sill remain below ha under Rule (NOM). Euroland sees a very large rise of around 50%. Rule 3 4 As he inflaion arge coefficien is increased o.5 price level variabiliy falls significanly for all counries excep Spain and Porugal. For he US and he UK price level variabiliy falls below ha of Rule (NOM). Rule See foonoe 3 23

24 Under he Taylor rule he variabiliy of he price level falls for virually everyone excep he US compared o a pure inflaion argeing rule. The UK and Euroland see a fall of 5% and 2% respecively. However, he US sees a rise of 3%. The combined rule is clearly he preferred rule for Euroland as oupu, inflaion and price level variabiliy are minimised under his rule. In erms of oupu and inflaion, he US would prefer an inflaion argeing rule wih a coefficien of.5. The resuls for he UK are mixed. The preferred rule in erms of oupu sabilisaion is he nominal aggregae argeing rule, whereas inflaion variabiliy is minimised under he Taylor rule wih a feedback coefficien of on inflaion. However, if boh oupu and inflaion were of concern o he Bank of England, hen he UK may prefer a Taylor rule wih he same coefficien on inflaion, alhough his would depend on he imporance placed on oupu variabiliy. If he concern of he cenral bank was o sabilise he price level hen Euroland, UK and he US would all prefer a combined nominal aggregae and inflaion argeing rule. 7 Shocking he exchange rae. In his secion we show ha shocking he exchange rae can have imporan implicaions in erms of he choice of policy rule and ha he argumens presened in he previous secions are srenghened. We presen resuls for all rules when he exchange raes are no shocked and compare he resuls o he previous resuls under he same rule when exchange raes are shocked. For he experimens underaken above, he shocks drawn from he pas include shocks for he exchange raes. The consrucion of hisorical shocks o serling is clear, as he bilaeral rae agains he dollar exised in he pas, as did he raes for Japan, Canada Sweden and so on. However, we are simulaing he model wih an exchange rae equaion for he Euro, a currency ha did no exis in he pas. Moving from he a regime where individual Euro area counries have heir own exchange raes o one where here is single exchange rae for EMU members, inroduces some uncerainies as o wha shocks o apply o he Euro and indeed wheher hey should be applied a all. This is he approach aken by Fair (998). Table 4 compares he resuls for oupu, inflaion and he price level wih ha when exchange raes are shocked. An index value is given for resuls when exchange raes 24

25 are shocked compared o when hey are no shocked. Therefore a value greaer han 00 indicaes ha shocking he exchange rae resuls in increased variabiliy. Where shocking he exchange rae resuls in lower variabiliy he box is shaded. Table 4: Index for oupu variabiliies when exchange raes are shocked. No shocked = 00. RULE RULE 2 RULE 3 RULE 4 RULE 5 Oupu UK US EL Inflaion UK US EL Price level UK US EL Rule = NOM : Rule 2 = CR : Rule 3 = INFT: Rule 4 = INFT.5: Rule 5 = TR. Shocking he exchange rae resuls in a fall in oupu variabiliy for he UK and he US over mos of he rules, alhough Euroland experiences hardly any change. Exchange rae shocks have a pronounced effec on he variabiliy of UK inflaion, wih he variabiliy rising o over 20% under he inflaion argeing rule. For he US and Euroland he difference in variabiliy is very small compared o he resuls for he UK. This indicaes ha for he smaller more open economies i maers wheher we shock he exchange rae or no bu he large closed economies he differences are no as large. The UK benefis from a fall in he price level variabiliy over every rule and he US benefis under all bu he Taylor rule. Euroland only sees he benefi under he combined rule. To see if excluding exchange rae shocks changes he preferred counry rules he following able presens he rule for each counry which minimises some loss funcion boh wih and wihou exchange rae shocks. I is likely ha policy makers will no focus solely on he variabiliy of one variable and will be concerned wih he variabiliy of boh oupu and inflaion raes and so boh will appear in heir loss funcions. They may also believe ha oher non-price 25