Inflation/unemployment regimes and the instability of the Phillips curve

Ormerod, Paul; Rosewell, Bridget; Phelps, Peter Working Paper Inflation/unemployment regimes and the instability of the Phillips curve Economics Discussion Papers, No. 2009-43 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Ormerod, Paul; Rosewell, Bridget; Phelps, Peter (2009) : Inflation/unemployment regimes and the instability of the Phillips curve, Economics Discussion Papers, No. 2009-43, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/28249 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Discussion Paper Nr. 2009-43 | October 7, 2009 | http://www.economics-ejournal.org/economics/discussionpapers/2009-43 Inflation/Unemployment Regimes and the Instability of the Phillips Curve Paul Ormerod Volterra Consulting, London Bridget Rosewell Volterra Consulting, London Peter Phelps Volterra Consulting, London, and University of Cambridge Abstract Using the statistical technique of fuzzy clustering, regimes of inflation and unemployment are explored for the United States, the United Kingdom and Germany between 1871 and 2009. We identify for each country three distinct regimes in inflation/unemployment space. There is considerable similarity across the countries in both the regimes themselves and in the timings of the transitions between regimes. However, the typical rates of inflation and unemployment experienced in the regimes are substantially different. Further, even within a given regime, the results of the clustering show persistent fluctuations in the degree of attachment to that regime of inflation/unemployment observations over time. The economic implications of the results are that, first, the inflation/unemployment relationship experiences from time to time major shifts. Second, that it is also inherently unstable even in the short run. It is likely that the factors which govern the inflation/unemployment trade off are so multidimensional that it is hard to see that there is a way of identifying periods of short run Phillips curves which can be assigned to particular historical periods with any degree of accuracy or predictability. The short run may be so short as to be meaningless. The analysis shows that reliance on any kind of trade off between inflation and unemployment for policy purposes is entirely misplaced. JEL: C19, E31, N10 Keywords: Phillips curve, inflation, structural change, fuzzy clustering Correspondence Corresponding author Paul Ormerod, Volterra Consulting, London, UK, e-mail: [email protected]; Bridget Rosewell, Volterra Consulting, London, UK, e-mail: [email protected]; Peter Phelps, Volterra Consulting and University of Cambridge, UK, e-mail: [email protected] © Author(s) 2009. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany 2  1.Introduction  Fromatheoreticalstandpoint,Friedman(1968)arguedthatinthelong‐runthereisnoconnection betweeninflationandthestateofdemand.Insofarasthereisconsensusonthesemattersamongst economists,thisisit.However,the‘longrun’isatheoreticalconcept,andeconomictheoryoffersno guidanceastohowlongthelongrunmightbeinpractice(thoughseeAtkinson(1969)fora fascinatinganalysis).  Atanypointintime,however,itisusuallypostulatedthatthereisaconnectionbetweentherateof inflationandthelevelofdemandintheeconomy.Thestrongerisdemand,thehighertherateof inflationislikelytobe.Yetdiscoveringsucharelationshipinpracticehasprovedfraughtwith difficulties.  Forexample,thereisnoconsensusastothevariableorvariableswhichshouldbeusedempiricallyto expressthelevelofdemand.Unemploymentisfrequentlyused,andwasindeedchosenforthe seminalarticleonthePhillipscurveattemptingtodescribetherelationshipbetweeninflationandthe levelofdemandinpre‐FirstWorldWarBritain(Phillips,1958).Buteventhen,differentresearchers mayestimatedifferentfunctionalformsforanyparticularempiricalrelationship.  Muchmoreimportantly,suchrelationshipsarewellknownnottobetimeinvariant.Inotherwords,a reasonablerelationshipmaybediscoveredtoholdinagiveneconomyoversomeparticularperiod. However,atsome(unknown)pointinthefuture,itwillbreakdown.Thispaperinvestigateswhether itispossibletoidentifypointsofbreakdownandwhetheritmakessensetotalkaboutadistinction betweenshortrunandlongrunbehaviouroftheeconomyinthiscontext.  TheflatteningofthePhillipscurveinrecentdecadeshasbeenacknowledgedglobally.The InternationalMonetaryFund(IMF)reportsthatinmanycountriesacrosstheworld,inflationisless sensitivetobusinesscyclesinthe1990sthanbefore(IMF,2006).Variousaspectsoftheinstabilityin therelationshipbetweeninflationandoutputhavebeenhighlightedinthepostwarera.Inthecase 3  oftheUS,AtkesonandOhanian(2001)showthatbetween1970and1999,thereisnomeaningful relationshipbetweeninflationandunemployment.Inanotherstudy,Roberts(2006)reportsanear halvingoftheslopeoftheUSPhillipscurvebetween1960‐1983and1984‐2002.Furthermore,King, StockandWatson(1995)findthatonlyuponintroducingtime‐varianceintothemodeldoesthere appeartobeanyclearnegativerelationshipbetweeninflationandunemploymentintheUSduring thepost‐SecondWorldWarera.Ithasalsobeensuggestedthatthesamenegativeslopeofthe Phillipscurvehasshiftedovertime(KingandWatson,1994).Thesefindingsindicatethatinstability potentiallyliesinboththeslopeandlevelofthePhillipscurve. Stabilityassessments,includingstructuralbreakandrecursiveestimationtestsforthePhillipscurve inGermanyandtheeuroarea,indicatethatsubstantialparameterinstabilityispresentintheearly 1980sandalsoaroundthetimeofreunification(Barkbuetal.,2005).Theauthorsfindthatthe PhillipscurveisrelativelymoreunstableinGermany,comparedtotheUS.Itissuggestedthatthere‐ unificationinGermanyincreasedtheinstabilityofinflation‐unemploymentrelationshipintheeuro areaintheearly1990s.TheflatteningofthePhillipscurveoverrecentdecadesintheUKhasalso beendocumented(Iakova,2007). Reasonsforthisinstabilitythathavebeensuggestedarenotalwaysindependentofeachother,but generallyrelatetosomeformofstructuralchangeintheeconomy.Forexample,greaterlabour marketcompetitionmayreducethecyclicalsensitivityofprofitmargins.Businessesaremorelimited intheirabilitytoraisetheirpricesinresponsetoincreaseddemand(Batini,JacksonandNickell, 2005). Ithasalsobeensuggestedthatproductioncostshavebecomelesssensitivetothebusinesscycle.In thecaseofdevelopedwesterneconomies,therehasbeenanincreasingtrendinbusinesses transferringsomeoftheiractivitiestocountriessuchasChinaandIndia.Thishasmadeworkersless inclinedtopushforhigherwagesasunemploymentratesfall.Thereforetheimpactofeconomic activityonmarginalcostoflabourmayhavechangedinthemodernera.Theabilityoffirmstohire workersfromAccessioncountriesofEasternEuropeandtheincreasedflowofimmigrationfromsuch countriesisalsolikelytohavehadsimilareffects(Bean,2006). 4  Thefamous“LucasCritique”,originatingfromapaperbyRobertLucasin1976,isalsorelevantwhen consideringtheinstabilityofparametersineconomicmodels.The“LucasCritique”concernsthe behaviourofthepolicymakerinfluencingtheeconomicagents’behaviour.Considerachangein monetaryregimefromaninflation‐targetingregimetoanalternativeone,wherethecentralbank attemptstopermanentlyclimbthePhillipscurve(bytradingoffhigherinflationforlower unemployment).Thechangeinbehaviourofthecentralbankwould,atsomepoint,influencethe behaviourofeconomicagents.Forexample,firmswouldforeseehigherinflationinthefutureand makenewdecisionsoveremploymentlevels.Thusthepolicychangewouldlikelyaltertheestimated parametersofthePhillipscurve. Althoughtheempiricalsupportforthe“LucasCritique”israthermixed,researchershavepointed towardsmonetarypolicyregimechangesashavinganimpactonthePhillipscurve.Itisconsidered thatcrediblemonetarypolicyhasimprovedtheabilityofcentralbankstoanchorinflation expectations,thusdampeningtheimpactofrealeconomicactivityoninflationandflatteningthe Phillipscurve(Mishkin,2007). Therehavebeennumerouscountry‐specificstructuralchangesinthemoderneconomywhichhave potentiallyalteredtherelationshipbetweeninflationandrealeconomicactivity.InGermany,there‐ unificationandadoptionoftheEurocurrencyaretworelativelyrecentstructuralchangestohave occurred.IntheUS,theFederalReservebecamemoreaggressiveinthefightagainsthighinflation followingtheeconomicdistressofthe1970s.IntheUK,theindependenceoftheBankofEnglandis thoughttohavemademonetarypolicymorecredible. Allofthesepropositionsareessentiallyposthocjustificationsforchangesinarelationshipwhichhas itsrootsinanempiricalassociationofeconomicaggregates.Animportantimplicationofthe literatureonempiricalPhillipscurvesisthatthereisnosettledviewastohowandwhytheybreak down,withmanyreasonsbeingputforward,bothofageneralandacountry‐specificnature.But breakdowntheyundoubtedlydo. Inthispaper,wecharacterisetheinherentinstabilityoftheempiricalPhillipscurveusingannualdata inthreemajoreconomies,theUnitedStates,theUnitedKingdomandGermanyovertheperiod1871 5  –2009.TherearetwoinherentreasonsfortheinstabilityofempiricalPhillipscurves.First,these majorcapitalisteconomieseachoperateatanypointintimeinoneofthreedistinctregimesin inflation/unemploymentratespace.Theprobabilityofremainingattime(t+1)intheregimewhich obtainsattimetishigh,butthereisaprobabilityofswitchingtoadifferentregime.Weobtain empiricalestimatesofthetransitionprobabilitymatrices.  Weusethestatisticaltechniqueoffuzzyclusteringtoillustratethesepoints,usinglongrundatafor Germany,theUnitedKingdomandtheUnitedStates.Thisapproachhastheimportantattributeof expressingthestrengthofassociationofanygivenobservationwithaparticularregimeratherthan creatingasimpleclassification.  ThisbringsustothesecondreasonfortheinstabilityofthePhillipscurves.Notonlydoeconomies movefromoneregimetoanother,buttheobservationswithinanygivenregimehavedifferent degreesofmembershipofit.Anobservationisallocatedtoaparticularregimebecauseits attributes,onwhichtheclusteringiscarriedout,havemoreincommonwiththoseobservationsin thisregimethaninotherregimes.However,thedegreetowhichthisisthecasevaries,frombeing onlymarginallyclosertoonegroupthantoanother,tobeingunequivocallyinonegrouptothe exclusionofothers.Thedegreesofmembershipsofinflation/unemploymentregimesconstantly fluctuateovertimewithinanygivenregime.  Theeconomicimplicationsoftheresultsdescribedherearethatthereareoccasionalmajor shocks/changesineconomicbehaviourwhichmoveeconomiesfromoneinflation/unemployment regimetoanother.Andimportantly,inaddition,thereisacontinuoussequenceofsmallshocks whichchangethedegreetowhichobservationscanbecharacterisedasbelongingtothesame regime.  Section2describesthedata,section3thetechniqueoffuzzyclustering,andsection4setsoutthe results.  6  2.Data ThemainsourcesforthehistoricaldataareMaddison(1995)andMitchell(1978).UnitedStatespre‐ SecondWorldWarunemploymentdataistakenfromRomer(1986)andCoen(1973).Datasince 1994isavailableintheIMFdatabase. Astrikingfeatureofthedataoverthe1871‐2009periodisthesimilarityofthedistributionsin inflationratesbetweenthethreecountries,whereinflationisdefinedasthepercentagechangein theconsumerpriceindex.ThereisofcoursethequiteexceptionalperiodinGermanyintheearly 1920s,culminatinginthehyperinflationof1924.Weexcludetheseyearsfromtheanalysis.To anticipate,weidentifythreeregimesininflation/unemploymentspaceineachcountry,sostrictly speakingweidentifyfourregimes,withthemassiveGermaninflation1920‐24constitutingaseparate regime.  Table1setsoutthesummarystatisticsforinflation1871‐2009inthethreecountries(excluding1920‐ 1924forGermany,apointwedonotrepeatbelow)   Table1Summarystatisticsofinflation,1871‐2009 Min1stquartilemedianmean3rdquartilemax US  ‐10.50 1.7 2.13.6 18 UK‐150.1 2.0 3.14.9 22.5 Germany ‐110.6 1.9 3.03.5 49 ThesimilarityevidentinTable1isconfirmedonaformaltest.ThenullhypothesisthattheUSandUK distributionsarethesameisonlyrejectedonaKolmogorov‐Smirnovtestatap‐valueof0.509.The p‐valuesfortherejectionofthenullhypothesesthattheUSandGermanyandtheUKandGermany arethesameare0.169and0.423respectively. Purelyforinterest,Figure1belowshowsthesimplePhillipscurvesobtainedbyregressinginflation onunemploymentineachofthethreecountriesovertheentiredataset.However,westressthat theseareforinterestonlyandourconclusionsdonotrelyinanywayonthem. US    UK    Germany -20 -10 0 10 20 30 40 50 0 4 8 12 16 20 UNEMPLOYMENT INFLATION INFLATION vs. UNEMPLOYMENT -20 -10 0 10 20 30 40 50 04812 16 20 UNEMPLOYMENT INFLATION INFLATION vs. UNEMPLOYMENT -20 -10 0 10 20 30 40 50 0 4 8 12 16 20 UNEMPLOYMENT INFLATION INFLATION vs. UNEMPLOYMENT  Figure1:Regressionofinflationontheunemploymentrateineachofthethreecountriesfrom1871‐ 2009.  Theslopesoftheregressionsareverysimilarineachcase,being‐0.315withstandarderror0.104for theUS,‐0.509and0.127fortheUKand‐0.503and0.180forGermany. ReturningtothedatainTable1,the‘fattail’natureofthedataisevident.Theratioofthemeanto themedianrangesbetween1.24and1.58comparedtothetheoreticalvalueof1,andisfarinexcess ofanyempiricalratiowhichisobtainedfromarandomnormallydistributedvariablewiththesame samplelength.Thenullhypothesisthatthedataaredistributednormallyisrejectedforeachcountry onaKolmogorov‐Smirnovtestatap‐valueof0.000. 3.Methodology 7  8  Clusteringisastandardtechniquewhichisusedwidelyacrossarangeofdisciplines.Itexaminesthe attributesofeachparticularobservationinadataset,andgroupstogetherthoseobservationswith similarattributes.Inthiscase,eachyearhasarateofinflationandarateofunemployment associatedwithit.Thesearetheprimaryrequirements.  Atoneextreme,iftheattributeswereverysimilaracrossallobservations,thedatawouldbegrouped intoasinglecluster.Attheother,ifeachobservation(year)hadverydifferentattributes,therewould beasmanyclustersasthereareobservations.  Neitheroftheseextremeswouldbeofmuchuse.Inpractice,wewouldliketofindasmallnumberof distinctclustersinthedata.Withineachcluster,theattributesofeachobservationhavemorein commonwitheachotherthantheydowithotherobservations,andthereisacleardistinction betweeneachoftheclusters.  Classicalclusteringgroupseachobservation,onthebasisofitsattributes,unequivocallyintooneor otheroftheclusters.Weoverlayclassicalclusteringtechniqueswithfuzzylogicandusefuzzy clustering.  Fuzzyclusteringassignseachobservationtosomedegreetoeachoftheclusters.Inthejargon,each observationhasamembershipofeachcluster.Membershipiscalculatedasaproportion,sothesum ofthemembershipsofeachobservationis1.Anobservationwhichisverytypicalofaparticular clusterwillhaveamembershipofthatclusterofcloseto1,andclosetozerofortheotherclusters. Ontheotherhand,anobservationwhichisamoremarginalmemberwillhaveasimilarmembership valuefortwo(orveryoccasionallymore)clusters.Itwillbeallocatedtotheclusterforwhichits membershipishighest,butithasattributeswhichplaceitonthemarginbetweenclusters.  Fuzzyclusteringthereforecontainsmoreinformationinitsoutputthanclassicalclustering.The conceptofmembershipandhowthismightevolveinfutureisakeypartofthecalculationsofthe potentialrangeofinflation. 15  otherwords,ifaneconomyisinclusteriinyeart,wecancalculatetheprobabilitiesofitremaining inclusteriinyeart+1,andofitmovingtoeitherclusterjorclusterk.Table4setsthisout. Table4Probabilityoftransitionfromoneclustertoanother,US1871‐2009 TransitionMatrix UST2 Cluster SteadyWeakDisruption Steady0.870.020.11 Weak0.120.820.06 T1 Disruption 0.240.030.73  Thediagonalvaluesofthematrixthereforerepresenttheprobabilitiesofeconomypersistinginthe threeclustersforsubsequenttimeperiods.Itisclearthatthedegreeofpersistenceishigh,although the‘disruption’clusteristheleastso. Thereisagreaterchanceofswitchingfroma‘steady’toa‘disruption’cluster,thantoa‘weak’ cluster.A‘steady’yearismuchmorelikelyfollowingayearof‘disruption’thanamovetowardsa ‘weak’cluster.Aprobabilityof0.24isgivenforreturningtoastableeconomyfollowingayearof ‘disruption’.   .2UKClusterAnalysis TheclustercentresarequalitativelysimilartothoseoftheUS Table5ValuesforUKinflationandunemploymentratesatclustercentres,averagedacross 500separatesolutionsofthefuzzyclusteringalgorithm. ClusterDescriptionInflationUnemployment Observations 16  Steady 2.13.070 Weak 0.38.951 Disruption 13.13.718  Thefirstisthe‘steady’clusterwithreasonablylowlevelsofinflationandunemployment.The majorityofobservationsfallintothiscluster.Thesecondisthe‘weak’clusterandhashigh unemploymentandlowinflation.ThisissimilartotheUS‘weak’cluster,althoughintheUKthis accountsformorethanathirdoftotalmemberships.Thefinalclusterischaracterisedbyhigh inflationandmoderateunemploymentandisthuslabelled‘disruption’.Thisclusterisapparent duringtheFirstandSecondWorldWarsaswellasthe1970soilcrisis. Whereasmostofthepast15yearshavefallenintothe‘steady’category,therehasrecentlybeena noticeableshifttowardsthe‘weak’cluster.  Figure3:FuzzyclustermembershipofeachyearintheUK1871‐2009ofthethreeclusters,‘steady’, ‘weak’and‘disruption’.  ThetransitionmatrixrevealsasimilarlyhighdegreeofpersistenceofstatesaswiththeUS.The ‘weak’and‘steady’clustersarethemostpersistent.      17  18  Table6Probabilityoftransitionfromoneclustertoanother,UK1871‐2009 TransitionMatrix UKT2 Cluster SteadyWeakDisruption Steady0.840.090.07 Weak0.140.860.00 T1 Disruption 0.170.110.72  4.3GermanyClusterAnalysis Thedetailsoftheclustercentresaredisplayedinthetablebelow. Table7ValuesforGermaninflationandunemploymentratesatclustercentres,averaged across500separatesolutionsofthefuzzyclusteringalgorithm  Cluster DescriptionInflation Unemployment Observations Steady2.12.275 Weak1.57.654 Disruption31.12.610  TheclustersareagainnotdissimilartothoseidentifiedintheUSandUK,withsteady,weakand disruptioneconomicclustersidentified. Thedominantcluster,with75members,islabelled‘steady’,withstableeconomiccharacteristicsof moderatetolowunemploymentandinflation. The‘weak’clusterisfairlysizeablewith54ofthe139yearsbeingassociatedwiththiscluster.Itis labelledas‘weak’duetoitshighlevelofunemployment.Inflationremainslowinthisregime. Thefinalclusteriscategorisedbyveryhighinflationandgenerallylowunemployment.This ‘disruption’clusterisfairlysmall,withonly10members.Itisassociatedmostwiththepost‐First WorldWartomid1920shyperinflation.   Figure5:FuzzyclustermembershipofeachyearinGermany1871‐2009ofthethreeclusters,‘steady’, ‘weak’and‘disruption’.  19  20  ThetransitionmatrixrevealsthatthedegreeofpersistenceofeconomicregimesinGermanyis higherthanintheUSandUK.However,incommonwiththeothercountries,transitionfrom‘weak’ or‘disruption’clustersaremorelikelytobetowardsthe‘steady’cluster. Table8Probabilityoftransitionfromoneclustertoanother,Germany1871‐2009  TransitionMatrix GERT2 Cluster SteadyWeakDisruption Steady0.880.120.00 Weak0.130.850.02 T1 Disruption 0.100.000.90  5. Discussion Thecountrieshavegenerallybeeninsimilarregimesthroughoutthesample.Althoughthenatureand precisetimingsofthestructuralchangesmaydifferfromcountrytocountry,theresultsindicatethat manyofthestructuralchangeswerecommontoall.Table7setsouttheresults.Wemeasurethe probabilityofdifferentnumbersofcountriesallbeinginthesameclusterinanygivenyear. Table7Probabilitesofthethreecountriesbeinginthesameorindifferentregimesinany givenyear CommonalityProbabilityRandom 0countriesinsamecluster0.060.22 2countriesinsamecluster0.570.67 3countriesinsamecluster0.370.11  Wecomparetheempiricalprobabilitieswiththoseofapurelyrandomprocessofallocatingcluster membership.Assumingapurelyrandomassignment,eachcountryhasaoneinthreechanceinbeing 21  inaparticularclusterinagivenyear.Therefore,theprobabilitythateachcountryisin,say,the steadyclusteris(1/3)3.Therearethreedifferentoutcomes:allcountriescouldbeineitheraSteady, Weak,orDisruptioncluster,hence(1/3)3ismultipliedbythree:3x(1/3)3=0.11Conversly,ifno countriesareinthesameclusterinagivenyear,thenwehave6x(1/3)3=0.22Theprobabilitythat twocountriesareinthesameclusterinagivenyearistheonlyotherpossiblesituation,therefore giving:1‐0.11‐0.22=0.67.  Theclusteranalysismembershipspermitcalculationofthelikelihoodofnocountriesbeinginthe sameclusterinanygivenyear.Thisisfoundtobeverysmall,withtherebeingonlya6percent chanceofthishappening.Comparedtoa22percentchanceunderrandomlyswitchingclusters,this suggestsadegreeofsynchronisationbetweentheeconomicconditionsinthedifferentcountries.In addition,itisfoundthatthemostcommonnumberofcountriesbeinginthesameclusterinany givenyearistwo,withtheprobabilityofthishappeningat57percent.In37percentofthesample allthreecountrieswereinthesamecluster.Sofor94percentofthetimeatleasttwooutofthe threecountriessharedacommonregime. Theresultsaboveshowtwokeythings.First,economiesmovefromoneclusterin inflation/unemploymentspacetoanother.Second,thereisaconsiderabledegreeofcommon experienceintheclustermembershipofthesethreemajorcapitalisteconomiesovertime.The implicationhereisthatthereareshockswhoseimpactissufficientlylargeastoshiftthePhillipscurve dramatically.WeillustratethisinFigure6below.  1880 1900 1920 1940 1960 1980 2000 Date 0 1 0 1 0 1 weak by date steady by date disruption by date Average Memberships 1871-2009 Membership  Figure6:Averagemembershipof‘weak’,‘steady’and‘disruption’clusters,1871‐2009. ItisapparentfromFigure6thatthereareseveralcommonalities.TheFirstWorldWarcreatedmuch ‘disruption’forallthreeeconomies,withsubstantiallevelsofinflationbeingrecorded.Theyears aroundtheGreatDepressionshowupas‘weak’inallcountries,withunemploymentlevelsveryhigh andsubstantialdeflationexperiencedbyall. TheperiodbeforetheFirstWorldWarshowslittlemembershipofthedisruptionregimebutrapid swingsbetweenmembershipofthe‘steady’and‘weak’group.Onaveragethe1960sshowthemost consistentlystrongmemberships. Aprolongedperiodofrelativestabilitywasexperiencedforaround20yearsfollowingtheSecond WorldWar.ThisstabilitypersistedforlongerinGermany,whilstboththeUSandUKsuffereda decadeofdisruptionwhichwasmarkedbystagflation. 22  23  Notably,itisdifficulttoidentifysignificantperiodswithhighmembershipsofoneregimepersisting. Mixturesareprevalentaswellchangesinthesemixtures. Thenaturalinstinctofeconomistswhenconfrontedbyevidenceofadistinctshiftinanimportant empiricalrelationshipistototrytoidentifyamajorchangewhichcanaccountforthis.Sometimes, thiswillbesuccessful.However,wenoteinthiscontextthatrecentresearchinnetworktheory, describingthepercolationofshocksacrossasystemofinterconnectedagents,suggeststhatitis possibleforevenminorshockstohavedramaticconsequences(forexample,Watts,2002;Ormerod andColbaugh,2006).AnexampleisthemassivestockmarketcrashinOctober1987,forwhichno majorcausehaseverbeenidentified. AfurtherimplicationofFigure6,however,isthatalthoughtransitionsfromone inflation/unemploymentregimetoanotherarerelativelyrare,therearepersistentfluctuationsinthe degreesofmembershipofaregime,eveninperiodsofrelativestabilityintermsofthedominant regime.Theseimplyinturnthattheinstabilityoftheshort‐runempiricalPhillipscurveisendemic. Thefactorswhichgoverntheinflation/unemploymenttradeoffaresomulti‐dimensionalthatitisnot reallypossibletoidentifythemempirically.Theremaybeperiodswhenanestimatedrelationship appearstoexist,butofnecessityitwillbreakdownevenintheabsenceofanymajorshockwhich mightenablethebreakdowntobeidentified. InthiscontextitishardtoseethatthereisawayofidentifyingperiodsofshortrunPhillipscurves whichcanbeassignedtoparticularhistoricalperiodswithanydegreeofaccuracyorpredictability. Theshortrunmaybesoshortastobemeaninglessandinadditiontheclusteringshowshow unpredictabletransitionstonewregimemembershipswillbe.Ifnothingelse,thisanalysisshows thatrelianceonanykindoftradeoffbetweeninflationandunemploymentforpolicypurposesis entirelymisplaced.    24  References  1. A.AtkesonandL.Ohanian,2001,“ArePhillipsCurvesUsefulforForecastingInflation?", FederalReserveBankofMinneapolisQuarterlyReview,25(1),pp.2‐11. 2. B.Barkbu,V.Cassino,A.Gosselin‐Lotz,LPiscitelli,2005,“TheNewKeynesianPhillipsCurvein theUnitedStatesandtheEuroArea:AggregationBias,StabilityandRobustness,”Bankof EnglandWorkingPaperNo.285. 3. N.Batini,B.Jackson,andS.Nickell,2005,“AnOpenEconomyNewKeynesianPhillipsCurvefor theUK”,JournalofMonetaryEconomics,52,pp.1061‐1071. 4. C.Bean,“GlobalisationandInflation”,SpeechtoLSEEconomicsSociety,Oct.2006. 5. R.Coen1973,“LaborForceandUnemploymentinthe1920sand1930s:ARe‐examination basedonPostwarExperience”,TheReviewofEconomicsandStatistics,55(1):46‐55. 6. M.Friedman,1968,"TheRoleofMonetaryPolicy",AER,58(1),pp.1‐17. 7. D.Iakova,2007,“FlatteningofthePhillipsCurve:ImplicationsforMonetaryPolicy”,IMF WorkingPaper07/76. 8. InternationalMonetaryFund,WorldEconomicOutlook,IMF,April2006. 9. L.Kaufman,andP.Rousseeuw,FindingGroupsinData:AnIntroductiontoClusterAnalysis, 1990Wiley,NewYork. 10. R.KingandM.Watson,1994,“Thepost‐warU.S.Phillipscurve:ARevisionistEconometric History”,Carnegie‐RochesterConferenceSeriesonPublicPolicy,Vol.41,pp.157–219. 11. R.King,J.Stock,andM.Watson,1995,“TemporalInstabilityoftheUnemployment‐Inflation Relationship”,FederalReserveBankofChicagoEconomicPerspectivesVol.19,pp.2‐12. 12. R.Lucas,1976,“EconometricPolicyEvaluation:ACritique,”Carnegie‐RochesterConference SeriesonPublicPolicy,1,pp.19‐46. 13. A.Maddison,DynamicForcesinCapitalistDevelopment,OxfordUniversityPress,1991. 14. F.Mishkin,2007,“InflationDynamics”,NBERWorkingPaperNo.13147. 15. B.Mitchell,EuropeanHistoricalStatistics1750‐1970,ColumbiaUniversityPress,1978. 16. P.OrmerodandR.Colbaugh,2006,“CascadesofFailureandExtinctioninEvolvingComplex Systems”,JournalofArtificialSocietiesandSocialSimulation,Vol.9,4.