Mirowski-From Mandelbrot to Chaos in Economic Theory

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Mirowski-From Mandelbrot to Chaos in Economic Theory
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  FromMandelbrot to ChaosinEconomicTheory* PHILIPMIROWSKIUniversityofNotreDameNotreDame,IndianaAn interestnthehistoryf ideas sgoodorthe scientist'soul.[49,21]I. Can Economic Theorists AdmitThatHistoryMatters?We arelivinginthemidst of aprofoundrupturebetween older andemergentnotions of scientificexplanation[67;68; 24; 25;51].Thevery meaningsof order andchaos,the deterministicandthestochastic,arebeingreconceptualizedn thisdecade,andit is fair topresumehatthingswillneverbe the same. Someeconomists,understandably,o not want to be left in thelurch,andhave turned heirprodigiouseffortsto assimilationof some of the new doctrinesand mathematical techniques.But,sofar,what this movement acks is historicalperspective.While it iseasyto beswept upinthe enthusiasmof the momentforwhatisunquestionablyne of the mostsignificantintellectualnnovationsof thecentury,hat still doesnot absolvetheeconomistfromaskingsomeverybasicquestions:Whyshould thisparticularetof ideas or mathematical ormalismsbe well-suitedtoeconomicdiscourse?Whatsit abouthisnew mathematicshatwillnecessarily mproveeconomics?What accounts for thisrushtoappropriateewtechniques?Howwillthey changethewayeconomicsis done?Despitetheappearancef numerousurveyarticles hesequestionshavenotyetbeenadequatelyaddressed5;11;33].The reason thesequestions anguishsthattheyareinherentlyhistoricalrather hannarrowlytechnical. Sincemost economistscannot bepresumedo have afirmbackgroundnthe historiesofphysicsor ofeconomics,andsuchabackgroundannotbeprovidednthespaceof ajournalarticle,most of the statementsmadein this section about thesehistorieswill notbedocumentedhere,althoughthe readers directed to someof the author'swritings[56;57;58;61;62]forthecorroboratingvidence.All that can beaccomplishedhere is to set thestageforthe narrativesnthesubsequentections of thispaper,whichwilldocumenthe historical elationshipor,moretothepoint,the lackthereof)betweenBenoit Mandelbrot'sworkineconomics and thelater workof such authors as J.Grandmont,R.Day,J.Benhabib,W.Brock,J.Scheinkman,W.Barnett,P.Chen and othersinattemptingoimporttheinsightsofchaostheoryinto economics.Thepurposeof this narratives to illustrate hemajorthesis of thispaper,namely,that economists *Thefirstdraftof thispaperwas writtenwiththehelpof agrantrom the NationalEndowment orthe Humanities.The authorsextremelygratefultoWilliamBarnett,William Brock andPingChenforsupplyingunpublishedworkingpapers,and to Benoit Mandelbrotorspendingsome timeansweringwhat must have seemed to him to beverynaiveques-tions.Ihave beenveryfortunate o have receivedextensivecommentson thispaperfrom RandallBausor,JohnBurkett,Clauded'Aspremont,RoyWeintraub,HalVarian,anonymousefereesand Bruce McCulloch. 289  290PhilipMirowskihave notthoughthroughheimplicationsof the chaos literature or theirdisciplinewith sufficientdepthandrigor,becausetheyare notyet readytoadmitfreelythathistorymattersat alllevelsofdiscourse.The intenseattractionwhichthe chaos literatureexertsuponmodemmathematicaleco-nomics can bereadily explained bythehistoryofthatdiscipline.Mathematicaleconomics isessentiallyco-extensivewiththeschool of neoclassicaleconomictheory;and neoclassicaltheorywasdirectly copiedfrom mid-19thcenturyenergy physics[58,chap.5;61].Thepurposeof thattransferofmetaphor,whichequated preferences r utility oa field ofpotentialenergy,wasmulti-levelled:at thegrossestlevel,imitationofphysicswasthoughtorenderconomic discourseintrinsically scientific ;atanotherlevel,constrainedoptimizationover a conservative vectorfield wasthoughttoembodythe deterministicdeal of all scientificexplanationprevalentnthatera;atyeta thirdlevel,some believed thatenergywasthe intermediate erm which allowed thereductionofthe socialto physicallawfrompsychic energydown tomechanicalmotion. Hencemathematicaleconomics,and morespecificallyitsneoclassicalincarnation,hasalong historyof imitation of thephysicalsciences.What ismoreimportantor ourpresentconcerns is theproblemswhich such imitationhas thrownupoverthepastcentury.First,while neoclassical economicsattemptedopartakeof the idealofdeterministicex-planation,t wasnowhereas successful atthisendeavorasitsexemplar,physics.This weaknesscan bedirectlytracedto apersistenttergiversationverwhat,precisely,wasconservedin theeconomicsystem[58,chaps.5-7;62;64].Without ananalagousconservationprinciple,neo-classical economics was blocked fromfollowing physicsintothe realmofaserious formaldy-namics,includingtheformal structureofHamiltonians,'nd instead retreated nto thespuriouspseudo-dynamicsof ceterisparibusconditions. Thisinabilityo emulate thecoreofthe idealofdeterministicxplanationarnished he entireprogramofimitatingphysics.Secondly,theabsenceof alegitimatedynamicsalsocompromisedhe idealofa scientificempiricism[57;59;60].What could it mean toattempto fitneoclassicalrelations otime seriesevidence when the fundamentaldeterminantsfneoclassicalequilibrium isplayednonecessarystabilityfromone moment to the next?Indeed,mostprominentirst- andsecond-generationneoclassicalswerehostiletoattemptsoimportsuchtechniquesasleast-squaresstimationntoeconomics;and the earliest efforts in this area werepioneeredbyindividualsskepticalof neo-classicaltheory[59;60].Suchdisputesoverthemeaningof scientificactivityalsocompromisedthe claimsofneoclassicaltheoryto haveattained scientific tatus.Third,therewastheproblemthatphysicscontinuedtoevolverapidlyafter the mid-19thcentury,whereas the neoclassicalresearchprogramendedtoremainmiredinitssrcinal19thcenturyorientation.nparticular,rom JamesClerkMaxwellonwards,physics increasinglybegantoincorporatetochastic deas intophysical explanations,whereasneoclassicaleconomics did not[66].Thisprogressiveabandonmentfthe ideal ofdeterministicxplanationasbeensummarizedfelicitously by Ilya Prigogine[67,187]:Inthe nineteenthentury,herewas aprofusionfcontroversyetween energeticists nd atomists ,he formerlaiminghe second aw[ofthermodynamics]estroyshemechanicalconceptionftheuniverse,he atter hathesecond aw should e reconciled ithdynamicst 1.Onemay occasionallyfind an economistworkingwithHamiltonians;ut it is clear that(a)theyarenot thefavoredmode ofconceptualizationfdynamicsnneoclassicaltheory[75]and(b)thereisabsolutelynoagreementuponthepropernterpretationsf Hamiltoniansduetotheproblemsmentionedn[58,chap.7;62].As aparentheticalemark,the favored tacticofresort toLiapunovtechniquesto discussdynamicshave never beenplausiblylinked tothe coreneoclassical tenet ofoptimizingbehavior[6].  FROMMANDELBROTTOCHAOS 291 thepriceof some additionalssumptions uchasprobabalisticrguments.What hismeansexactlyannowbe seenmoreclearly.The price snotsmallbecauset involvesfar-reachingmodificationf the structurefdynamics.Now,itis true that neoclassical economicsfinallyadmittedomeaspectsof stochastic con-ceptsintoits ambitwith therise of econometrics andsomewhat furtherwith the rationalexpectationshypothesis )[57; 63];but the curiousaspectof thisdevelopments that thesto-chastictermsweremerelyappendedotheexistingconstrainedptimizationormulas,andwerenotpartandparcelof a fundamentaleconceptualizationfeconomictheory,unliketheparalleleventsinphysics.Moreover,asweshall observebelow,thesestochastic shocks hadlittleornotheoreticalustification,butthemselves seemedonlyan excuse to maintain hepuredeterministicidealofexplanationnthe faceofmassivedisconfirmingvidence.Asoneprominentneoclassicalputthe case:[neoclassicalconomists]aturallyendedo thinkof models n whichhingsettledown o auniqueositionndependentlyf initial onditions.echnicallypeaking,we theoristsopednottointroduceysteresishenomenantoourmodel,astheBibledoeswhen tsays, Wepasshiswayonlyonce and,nsosaying,akeshesubjectutoftherealmfscienceandntoherealmofgenuinehistory71, 184-5].Now,intothisunsatisfactoryituation,we observe the intrusionof the furtherdevelopmentofchaostheoryinphysics.The allure of thisdevelopmentorneoclassical economists isreadilyapparent:t seems to outsiders that thereisnowa technical solutiontomanyof the mostirri-tatingandendemicproblemsof neoclassicaltheoryoverthelastcentury.Here(againwestress)itseems that the mostrigiddeterminismsreconciledwiththepervasive appearanceof randomphenomena.Hereagainitseemsthat thepreviousack of asubstantiveynamicsmayberepairedwithonlyalittle moresophisticatedmathematics.Hereitseemsthat theformalismofstrangeattractorsmay promiselaw-governedbehaviorndependentofhistoricalocation.Here,itseemsthereis aremedyfor thepalpablefailureofahalf-centuryofeconometricendeavor.Further,tmerelyinvolves asimple extrapolationof thesrcinaltendenciesofneoclassicaltheory,since itinvolves furtherdirectimitationof theoriesgeneratedwithin thephysicscommunity.nsummary,chaostheorylookslikeitjustmightbe the salvationof the neoclassicalresearchprogram.Contraryotheseimpressions, nothingcould be further rom thetruth.II. Mandelbrotonthe Irrelevance of ModernEconometricsBenoitMandelbrotwroteanumber ofstunningly srcinal papersin economics fromroughly1962-1972;andthen,afterwards,hewentonto becomefamouselsewhere.AlthoughGleick[25,81-118]writes asthoughMandelbrot'sconomic ideashad agreatimpactupontheprofession,thesimplehistoricalfactisthattheyhave beenbyandlarge ignored,withsome fewexceptions[7; 19; 20; 53;54]which seemtohavebeensubsequentlyabandonedbythose authors.More-over,whileit can be claimedthat theworkon economicswas animportant nputinto his laterinnovationsconcerning fractals which didmake himfamous,onecanfind no indicationofhow the connectionsmightbe madein theexistingliterature.Hence we observe thecurious factthat economists haveconceivedofanenthusiasmorthechaos literaturea decadeor moreafterthis literaturemaybesaidtohave itsroots ineconomics,andyet theyexhibitno interestin orcuriosityabout thoseroots.  292PhilipMirowskiMandelbrot hepersonais at least asfascinatingasMandelbrot he theorist.Hisprimaryidentityis as amathematician,althoughonoccasion mathematicians aveinsisted that what hedoesis notreallymathematics[25, 114].Hehimselfhassaid, Veryoften when Ilistentothelistofmy previousjobsIwonderif I exist.The intersectionofsuch sets issurelyempty [25,86].Heis often volubleconcerningthe viewthathe couldneverhaveaccomplishedhis work inanyconventionalacademicdisciplineordepartment,ndthat he wasextremelyortunate o haveworked forIBM,becausetheylethim followhisinstincts.And,as headmits, Economics isveryfar from whatIplannedto tackle as a scholar [1,214].There are fourspecialtraitsofMandelbrot nd his work which are central o an understand-ingoftheepisodefrom1962to 1972. The first is thatMandelbrotas been aperpetualoutsiderin almosteveryintellectualcontext;andespeciallyoutsideofthehidebounddistinctionsbetweendisciplinesinthe moderuniversity.Thereis aclear connectionnthisrespectbetweenhis ideasandhislife,as he himself has noted: AsIallowedmyselftodrift,Isoon came to viewthe nor-malunpredictabilityf life ascontributingayersor strataofexperiencehatarevaluable,demandnoapology,and addupto auniquecombination 1,208].No rationalmaximizer,he.Second,inan attituderefreshinglyunorthodoxor amathematician,he dismisses Bourbakistormalism,and thinks the fetish for axiomatizationhaslargelyrun its course. To astudent,the reductionto axiomsislargelya matterofsatisfyingtheteacher [1,216].Clearly,such apersonwouldnot be taken with theworkof a KennethArrow ora GerardDebreu. Third,heisapartisanofthe revival of aspecifically geometricintuition nmathematics,o the extentoftherebeingaprofoundphenomenologicalapproachnall of his work(andnotjusttheeconomics)[45, 261].Anyresearchprogramhatregularlydisplaysacertainmethodologicaldisdainfor visual evidencewouldcertainlyfind thisattitudequaint,atbest.Andfourth,Mandelbrothaspersistentlyridi-culed thephysics envyofneoclassicaleconomists;and theironyofmuchofstatisticalheoryfirstsrcinatingnsocialtheoryhasnotbeen loston him. . . .itisnot true hatdifferencesndevelopmentetween ciencesrerelatedo,and here-foreexcusedby,differences f age asmeasuredythe earliestystematicnvestigationf thedifferentopics.Indeed,probabilityheoryaw ts firstriumphsnphysics,but t hadbeenbornelsewhere,n thestudyofproblemsaisedbyeconomic-psychologicalhoice. .Evenas lateas1912,statisticalocialsciencecouldstillbepresenteds a model o befollowedystatisticalphysics51,120].Mandelbrot'sworkinphysics,geology,economicsandmeteorologyhaveallbeenpartof alargerpartiallyhiddenagenda,one whichhe revealednhis 1964 Premature ractalManifesto, only recently published[51].There hearguedhathis efforts shouldberegardednthevanguardofa secondstageofindeterminism, ne that hesuggestedwith hisusualmodesty,was abroadculturalphenomenon.The firststageof indeterminismwas anattemptointroduceprobabilitytheoryinto such areas asphysicsandeconomicsbythepartitioningff of the causal determinis-ticaspectsfromthestochasticdisturbances,neffectsubordinatinghelatterto the former.Thekeyto theplausibilityof thisfirststagewas aresorto theclassicalcentral imit theorem,whichallowed those so inclined toclingto theirpreviousdeterministicworld-views. The secondstagewouldbe markedbytheexplorationofthose areaswheretheclassicalcentralimit theorem ailedtohold:these would beinthe less-developedsciences, theintellectuallums ofdeterministicscience:weatherprediction,turbulence,ensilestrengthandfractures,and ofcourse,economics.Much ofthisresonatedwith the holism vs.reductionism debatewhichwas endemictosocialtheory,whichMandelbrothoughtwasmerelysymptomaticof alarger problem: instudyingeconomicrecords,itmay verywell bepreferableo avoid thetemptationoattackperiodsofcrisis
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