StartingtheStudyofEconomicEvolutionwithNelsonWinter-likeModelsVersion:
12th April
[email protected]://www.business.auc.dk/evolution/esa/DRUID,AalborgUniversity1OverviewPurposesof
the lecture and the slidesIntroductiontoNelsonWintermodelswhich has
a pioneering statusin evolutionary
modellingIntroductiontoevolutionarymodellingby constructing from
scratcha family of NelsonWinter-like
modelsIntroductiontoevolutionarysimulationin relation
toNelsonWinter-like modelsCompendiumof Andersen and Valente (2002),
Andersen (2001) andtosome extentValente and Andersen (2002).
ReferencesarefoundonthelastslideContents of the slides andto some
extentthe lectureTheNelsonWinterbook: background, main models and
problemsThestandardNelsonWintermodel of industrial dynamics
(memberof theAKmodel family)TheNelsonWinter-likeALmodelswith only
labour and knowledge(theAL model family)TheALMarkImodel
withxedproductivitiesandreplicatordynamicsincludingdeductionsandsimulationsTheALMarkIImodels
withendogenouschangeofproductivitiesTheALMarkIIImodels
withemergingmarketsforintermediategoodsandR&DspecialisationTheartofsimulationin
relation to evolutionary models and theLaboratory for simulation
development
(Lsd)2ThehistoryandstateofevolutionaryeconomicsStylisedhistoryinthreestages
(cf. Hodgson 1993 and Andersen 1996):1. Oldevolutionaryeconomics.
The verbal accounts that can now berecognised as covering aspects
of economic
evolutionFromAdamSmithviaMarx,MengerandMarshalltoVeblen,SchumpeterandHayek2.DarkAges
ofevolutionaryeconomics. The crowding out of theverbal approach
when economics reached high standards in static
analysisEspeciallyfromthe1920s. LionelRobbins: theoldstuis
intelligentafter-dinnertalk3. Newevolutionary economics. The modern
studies that are based on abreak-through in evolutionary
modellinga.
Startingpointsnotleastinthreebooks:NelsonandWinter,AnEvolutionaryTheoryofEconomicChange(1982)MaynardSmith,EvolutionandGameTheory(1982)Axelrod,TheEvolutionofCooperation(1984)b.
GrowthanddiversityofnewevolutionaryeconomicsNeo-Schumpeterianstudiesoftechnology-basedindustrialdynamicsandeconomicgrowthEvolutionarygametheoryoftheformaltypethatstudytheevolutionaryselectionofNashequilibriaSimulation-orientedstudiesoftheevolutionofinstitutionsanddominatingstrategiesComplexitystudiesthatemphasisesofthepathdependencyofdominanttechnologies,etc.Andsoon.
. .c.
ContemporaryproblemsandperspectivesTheproductionofsolidresultsofevolutionaryanalysisisstillratherslowRelativelyhighbarrierstoentrytoevolutionarymodellingandsimulationRapiddiusion(e.g.
intothejournalsofbusinesseconomicsandeconomicgeography)beforebasicissueshavebeenclariedThediusionintopolicyaspectsisincreasing,andherethemodellingproblemsareevenlarger3RevisitingtheNelsonWinterbook20yearsafterContents
in brief summaryPartI OverviewandMotivationPartII
Organization-TheoreticFoundationsofEconomicEvolutionaryTheoryPartIII
TextbookEconomicsRevisitedPartIV GrowthTheoryPartV
SchumpeterianCompetitionPartVI EconomicWelfareandPolicyPartVII
ConclusionCharacteristics(cf. Andersen 1996, Ch. 4)The
populationperspective is
fundamentalTheNWevolutionarytheorystartsfromrecognisingthatrmsareheterogeneousandboundedlyrational,sotheyformapopulationwithevolvingcharacteristicsSynthesisofmechanisms.
The NW evolutionary theory is based on asynthesis ofTransmission:
TheoriesofroutinesandtheirreproductioninrmsMutation:
TheoriesofthecreationofnewroutinesinrmsSelection:
TheoriesoftheselectionenvironmentanditsinuenceEmphasisonsimulationmodels.
The synthesis of the evolutionarymechanisms is made by means of
simulation
modelsThestartingpointisPartII,buttheactualsynthesistakesplacebymeansoftheevolutionaryNWmodelsthataredesignedforcomputersimulation(PartsIVandV)Appreciative
approach. All major NW models are designed with aconcrete problem
in mind, although it is especially emphasised in
recenthistory-friendly modelsAnalyticalmodels as servants. Nelson
and Winter make models forwhich mathematical deductions can be made
for the sakeof preparingthe ground for more realistic
models4OverviewofNelsonWintermodels(numberedbychapters)Simpleformalmodelsfor
analytical results:NW6: SectionAParticularModelofEconomicSelection:
NelsonandWinter(1982,Ch. 6,144154)NW7:
SubstitutionAMarkovModelofFactorSubstitution:
NelsonandWinter(1982,Ch. 7,175192)NW10.1:
DevelopmentDevelopmentandBackwardnessinaTwo-TechnologyEvolutionaryModel:
NelsonandWinter(1982,Ch. 10,235240,240245)NW10.2:
GrowthasselectionGrowthasaPureSelectionProcess:
ManyTechniquesandManyVariableInputs: NelsonandWinter(1982,Ch.
10,240245).Growthandindustrymodelsfor simulation results:NW9:
Growthvs.
SolowAnEvolutionaryModelofEconomicGrowth:NelsonandWinter(1982,Ch.
9,209214)NW12:
IndustrialdynamicsIDynamicCompetitionandTechnicalProgress:
NelsonandWinter(1982,Ch. 12,281287,302f.)NW13:
IndustrialdynamicsIIForcesGeneratingandLimitingConcentrationunderSchumpeterianCompetition:
NelsonandWinter(1982,Ch. 13)NW14:
IndustrialdynamicsIIITheSchumpeterianTrade-oRevisited:NelsonandWinter(1982,Ch.
14)Subsequentmodelsby Nelson and WinterXNW84:
RegimesSchumpeterianCompetitioninAlternativeTechnologicalTechnologicalregimes:
Winter(1984).XNW99:
History-friendlymodelsHistory-friendlyModelsofIndustryEvolution:
TheComputerIndustry:
Malerba,Nelson,OrsenigoandWinter(1999).Limitationsof the
overviewFurtherworks
NeitheranalyticalNWmodelspublishedafter1982northecontributionsofotherauthorsarelisted(thelatterarepartlysurveyedinKwasnicki,2001).5TheevolutionarymechanismsandtheNWmodels(I)TwocorequestionsinNWmodelsare:Willtheevolutionaryprocessmovetowardmonopoly?Howcanthis(unrealistic?)
tendencybeavoided?Thesimpleselectionprocessdue to the basic
structure of NW modelsDierentproductivities.
FirmsnormallyhavedierentcapitalproductivitiessothatagivenstockofcapitalcanproducedierentquantitiesindierentrmsUniformprices.
Allrmsfacethesameoutputpriceandthesamefactorprices.Dierentprotrates.
DierentproductivitiesandunitarypricesmeansthatrmshavedierentprotratesSelection
ofrms. Firmsarebeing selected
sincethedierentprotratesleadtodierentgrowthrates.
Supernormalprotscanbeconsideredasrewards for high tness, while
subnormal prots are punishmentsfor low tnessSelectionandtheprocess
ofaccumulation. Investment behaviour maychange the basic selection
mechanismSimplecapacityaccumulationandmonopoly.
Ifrmsinvestalltheirprotsinaccumulationanddonothaveexternalnance,thenthermwiththehighestproductivitywillgrowintoamonopolyMonopolisticrestraint.
InthestandardNWmodelthisfull selection
isavoidedbymonopolisticrestraintoncapacityaccumulation.
ThusthemodelsincludethermsincreasingawarenessoftheoveralldemandcurveasitsmarketshareincreasesEntryofnewrms.
Analternativestrategytocontrolthetendencytowardmonopolyistointroducenewrmsintotheindustry.
Thesenewrmsenterfromanexogenouspoolofrms(cf.
e.g.Winter,1984,283288).Externalnance
couldalsochangethebasicselectionprocessbysuckingprotsoutofdominantrms.
IntheNWmodelsit,however,strengthensthebasicselection6TheevolutionarymechanismsandtheNWmodels(II)Theinnovationimitationprocessboth
produces and controls the varianceof the rms
productivitiesInnovationindependentofrmbehaviour.
Inthiscaseinnovationscomelike mannahfromheaven tosmallandlargerms.
Inthis(unrealistic)waywecanavoidmonopolytSatiscingbehaviourandinnovation.
IntheNW9growthmodel search
forimprovementsisanadhocactivitythatemergescostlesslywhenarmexperiencesunsatisfactoryresults.
ThisbehaviourhelpstoavoidmonopolyImprovementasapermanentstrategy.
ThisistheassumptioninmostoftheNWmodels.
Theinnovationimitationprocessdoesnotremovethelong-termtendencytowardmonopolybecauseofincreasingreturnstotheapplicationofR&Dresults.
Ifrmsshownorestraintontheirexpansion,monopolyemergeswithaprobabilityofoneSchumpeterian
evolutionincludesjumpsinproductivityandquality,sohereweseefurtherpossibilitiestobreakoutofnear-monopolysituations7ThestandardNWmodelofindustrialdynamics(I)1.
Themarketsare simplied to allow a focus on
evolutionCapitalandlabourmarkets
arearesimplycharacterisedbyxedpricesandunlimitedsupplyTheoutputmarket
hasaxeddemandD. TheoutputpricePtissetsothatthemarketclears,i.e.Pt=
D/Qt(1)2. Productionandprotfor rmjin
periodtCapitalandproductivityFromperiodt
1thermhasitsownlevelsofcapitalKj,t1andproductivityAj,t1Output
Additionalinputs(labouretc.) isbought,andtheresultingoutputisQjt=
Aj,t1Kj,t1(2)Prot ThesumoftheoutputofallthermsQt=
nj=1 QjtresultsinthepricePtandtherevenuePtQjt.
Thexedcostsperunitofcapitaliscincludesbothwagesandcapitalrental.
TherearealsoR&Dexpendituresthatperunitofcapitalisrj.
Thustheprotisjt= PtQjt (c + rj)Kj,t1(3)3. Capitalaccumulationis in
principle
simpleDepreciationUnlesstherminvestsitscapitalshrinkswiththerateofdepreciation.Financialconstraint
Themaximuminvestmentisdeterminedbytheprotplusextranancialresourcesfrombanks.
ThusImaxjt= (1 + b)jt.Desiredinvestment
isdeterminedbythesizeofpricerelativetotheunitcosts.Iftheexpectedmarkupislessthanunity,Idesirejtbecomesnegative.
Ifthermhasalargemarketshare,itshowsinvestmentrestraintbecausethewaytheoutputmarketisfunctioning.
ThusIdesirejtisalsodeterminedbythemarketshare.Actualinvestment
perunitofcapitalcomesfromacombinationoftheconstraintandthedesire:Ijt=
min(Imaxjt, Idesirejt) (4)Thenewlevel ofcapital
isonlyforuseinnextperiod. Itis:Kjt= (1 + Ijt
)Kj,t1(5)8ThestandardNWmodelofindustrialdynamics(II)4.
Endogenousproductivitychangeis the core issue of the NW
modelProductivityandR&DCapitalproductivityisdeterminedbyrm-specicknowledgethatisimprovedbyR&Dthatcanbeinnovativeand/orimitative.TheR&Deortperunitofcapitalissplitupaccordingtoaxrulesothatrj=
rINj+
rIMj(6)ImitativeR&DgivesifsuccessfulaccesstothebestproductivityoftheindustryAmaxj.
ThetotaleortofthermisrIMjKj,t1andtheprobabilisticproductivityofresearchisIM.
Theproductofthesetwonumbersgivesthemeannumberofimitationsperperiod.
TheactualnumberisdrawnfromaPoissonprocess.
Ifthenumberisatleastunity,wesetAIMj=
Amaxj;otherwiseitis0.InnovativeR&DgivesifsuccessfulaccesstoaresultdrawfromanormaldistributionwithaxedstandarddeviationandameanthatdierbetweenthedierentNWmodels;inthecumulativeregimeitisequaltotheexistingproductivity.
ThetotalinnovativeeortofrmisrINjKj,t1andtheprobabilisticproductivityofresearchisIN.
Theproductofthesetwonumbersgivesthemeannumberofinnovationsperperiod.
TheactualnumberisthedrawnfromaPoissonprocess.
Ifthenumberisatleastunity,thermgetsadrawfromthenormaldistributionandtheresultisAINj.
IfinnovativeR&Disunsuccessful,thisnumberis0.Newproductivityisdeterminedpreciselyandisavailableinthenextperiod:Ajt=
max(Aj,t1, AIMjt, AINjt ) (7)Appropriabilityregimes
arespecieddirectlybytheproductivityofimitativeresearch.
Ifthisproductivityislow,thentheresultsoftheinnovatorsarewellprotected.Technologicalregimes
arespeciedbythewaythemeanofthenormaldistributionofinnovativeresultsaredetermined:
1. Theregimewithrm-basedcumulationoftechnologyhasameanequaltoAj,t1.
2.
Theregimewithindustry-basedcumulationoftechnologyhasameanequaltoAmeant1.
3.
Theregimewithscience-basedtechnologyhasameanequaltoanexogenouslyknowledgethatisexponentiallygrowing.9StructureofthestandardNWmodelProtPhysicalcapitalVariableinputsCostsInnovation&imitationKnowledgeFirmsoutputRevenueOtherrmsTotaloutputPriceTotaldemandInvestment(dependentonmarketshare)Figure
1:
StructurediagramofthestandardNWmodelofindustrialdynamics10StrategiesformodellingintheNWtraditionResultsandproblemsThe
standard NW model has had a signicantinuence. But there are
problems, e.g.Too manyparameters. Especially the xed demand in
standard NWmodels is problematicAd hocinvestmentrestraintof large
rms is problematic as a startingpointAd hocentryofnewrmsin extended
NW models like Winter (1984)Separatesimpliedmodelsto study
replicator dynamics, etc.
areproblematicDicultiesofextendedsimulationmodelsbecause of
thecomplexitiesDicultiesofteachingbecause of the
complexitiesSolutions. There are dierent ways of coping with the
problems within theNW tradition, e.g.1.
Theback-to-basicsstrategyseeks for highly simplied startingpoints
and then moves very slowly to the real complexity of
evolutionaryprocesses.2. Theextensionsstrategyis largely related to
Winter (1984). It hasrun into decreasing returns . . .3. The
history-friendly strategyof Malerba, Nelson, Orsenigo andWinter
(1999) emphasises the main NW strength: the relationship
toambitious empirical studies4. Thedemandsidestrategyadds a theory
of the complexity ofdemand to reach more realistic industrial
dynamics (partly in relation tothe ChamberlinLancaster
traditions)5. Themultiactivitygeneralisationstarts from complex rms
withintraorganisational diversity to deal with intermediate
exchange,specialisation of R&D, and multisectoral growth and
developmentIn the following strategy 1 is chosen, but it is
intended to support otherstrategies (especially strategy
5).11ConstructingtheALmodelfamilyinthreesteps1. Studytheproblems
oftheNWmodelfamily. This model family maybe called theAKmodels of
economic evolution.aTo sum up, majorproblems are
ThedefactostandardistheAKmodelofindustrialdynamics
TheAKgrowthmodelhasbeenlessdeveloped
SpecialisedAKmodelsanalyseaspectsofformalevolutionindependentlyfromtherestofthemodels
Thesetypesofmodelshouldbeintegrated
Butphysicalcapitalhindersaneasyintroductionofmultipleactivitiesandtheintroductionofssionsandfusionsofrms2.
Developapure-labourversion oftheNWmodelofgrowth. Thismodel family
may be called theAL models
TheALmodelsalsocoverindustrialdynamicsandformalreplicatordynamics
ALmodelsmakeiteasytointroducemultipleactivitiesaswellasssionsandfusions
TheALmodelsishandytoolsforteachingevolutionarymodelsandsimplesimulationtechniques3.
DevelopmultiactivityALmodelsas a generalisation of simple
andwell-studiedAL models
ItinheritsallthecharacteristicsofthesimpleALmodel,butismorecomplex
Itallowsustostartfromastudyofintraorganisationaldiversity
WecangraduallyintroduceintermediateexchangewithoutaddingadhocdemandspecicationsspecialisationofR&DinarichselectionenvironmentmultisectoralgrowthanddevelopmentfromthebottomupaBecauseoftheproductionfunctionQjt=
Aj,t1Kj,t112Thexed-productivityALmodelofgrowth(ALMarkI)Thehouseholdsandthewagerate.
There is an unchanging number ofNhouseholds, which each supply one
unit of labour. The wage rate is xed tounity,w = 1. Households
spend all income on the single product of theeconomy.Therms. There
is a xed number ofn rms. We consider rmjin
periodt.EmployeesandproductivityThermhasastockofemployeesLj,t1andxedproductivityAj.
Allemployeesproduceattheproductivityleveloftherm.
Theunitcostofthermiscj= 1/Aj.Output isproducedaccordingtoQjt=
AjLj,t1(8)Prot
TheoutputofthermissoldatthemarketpricePwiththerevenuePQjtandthecostswLj,t1=
Lj,t1. Thustheprotisjt= PQjt Lj,t1(9)Newemployment
Thepaymentofthermsemployees(Lj,t1)ismadeoutoftherevenuefromperiodt
1,soalltherevenueofperiodtisusedforemployment.
ThustherminperiodtwillemployLjt= PQjt.
ThechangeinthenumberofemployeesisLjt Ljt Lj,t1= PQjt Lj,t1=
jt(10)Themarkets. There are only two markets: the output market and
the
labourmarket.Outputdemandinperiodtissimplytheincomeofthehouseholds.
ThustheoutputmarketsdemandDt=
nj=1 Lj,t1= Lt.Outputsupplyistheaggregateoutputoftherms,Qt=
nj=1 Qjt.Outputprice Thepriceissettoclearthemarket.
TosecurethatthesupplyQisbought,wehavethepricePt=
Dt/QtLaboursupplyissimplythenumberofhouseholdsN.Labourdemandisdeterminedbytherms.
TheaggregatedemandisLt=
nj=1 PtQtjLabourmarketequilibrium.
Sincethemodelprovidesnomechanismtobringthexedsupplyoflabourinaccordancewiththedemandforlabour,thequestioniswhetherN=
Lt. Weshallreturntothisquestion.13SummaryoftheALMarkImodelProtj= Wj
CjLabourLj,t1CostsCj= wLj,t1= Lj,t1FirmsoutputQj= AjLj,t1RevenueWj=
PQjKnowledgeAjOtherrmssactivitiesTotaloutputQ =
QjPriceP= D/QTotaldemandD=
Lj,t1Hiringorring: Lj= jWorkersincomeFigure2: Structurediagramof
theALMarkImodel.
Forsimplicityunlaggedtimesubscriptshavebeenomitted.14DeductionsaboutthedynamicsoftheALMarkImodelSimplicityleadstodeductions.
Since theAL Mark I model is designedaccording to the KISS
principle, we can make formal deductions about itsdynamics:1.
Thetheoremofconstantemployment.
AggregateemploymentandaggregatedemandisunchangingintheALMarkImodel.2.
Thetheoremofdistance-from-meandynamics.
IntheALMarkImodelthegrowthrateofthemarketshareofanyrmisequaltothedistancebetweentheaverageunitcostsanditsunitcosttimesitsmarketshare,i.e.dsjt/dt
= sjt( ct cjt).3. Fishersfundamentaltheoremofnaturalselection.
IntheALMarkImodelthegrowthrateofaverageproductivityisequaltothenegativeofthevarianceofthemarket-shareweightedunitcosts,i.e.
d ct/dt = Var(cjt).Deductionshelpinfurtherwork. Given these
theorems we immediatelycan say a lot about theAL Mark I
model.Replicatordynamics.
Thedistance-from-meandynamicsisalsocalledreplicatordynamics.
Itmeansthatifallrmshavemeanproductivity,thereisnochangeinmarketshares.
Furthermore,thermwiththehighestproductivitywillalwayshavethehighestgrowthrate,soitwillendupasamonopoly.Theimportanceofastatisticalapproach.
ThethirdtheoremisavariantofthetheoremofR.A.Fisher(creatorofmuchofmodernstatisticsandevolutionaryanalysis).
Itemphasisesthatwecanperformouranalysisintermsoftheweightedmeanvarianceoftheunitcosts/productivities.
Asvariancemovestowardszero,thechangeofmarketsharesdisappears.15SimulatingthedynamicsoftheALMarkImodel(I)Table
1: HandsimulationoftheALMarkImodel.Period 0 1 2 . . . 14
15Firm1withA1= 1.2Employment 100.000 120.000 140.260 . . . 273.074
277.441Output 120.000 144.000 . . . 321.468 327.689Marketshare
0.400 0.468 . . . 0.910 0.925Prot 20.000 20.260 . . . 5.185
4.366Firm2withA2= 1.0Employment 100.000 100.000 97.403 . . . 25.523
21.609Output 100.000 100.000 . . . 30.046 25.523Marketshare 0.333
0.325 . . . 0.085 0.072Prot 0.000 -2.597 . . . -4.523
-3.914Firm3withA3= 0.8Employment 100.000 80.000 62.338 . . . 1.403
0.950Output 80.000 64.000 . . . 1.652 1.122Marketshare 0.267 0.213
. . . 0.006 0.004Prot -20.000 -17.662 . . . -0.662
-0.453AggregatedataEmployment 300.000 300.000 300.000 . . . 300.000
300.000Output 300.000 308.000 . . . 353.165 354.334Price/av.
unitcosts 1.000 0.974 . . . 0.849 0.847Aggregateprots 0.000 0.000 .
. . 0.000 0.000Growthaver. costs -0.027 -0.025 . . . -0.003
-0.002Varianceofunitcosts 0.027 0.025 . . . 0.003
0.003Outputdispersion(H) 2.9220 2.706 . . . 1.162
1.134Instability(I) 0.177 0.169 . . . 0.025
0.02216SimulatingthedynamicsoftheALMarkImodel(II)Usingthecomputer.
Even in the simpleAL Mark I model we get helpRunmultiplesteps. Make
a huge number of calculations to follow thedynamics to its
endCheckdierentvarianceofproductivities. Generate distributions
ofproductivities with a known variance and test the
consequencesBepreparedforextensions. The computer makes it easy to
endogeniseproductivity changeMake graphicaloutputfor comparisons
and reporting0 100 200 300 400
5000.1560.1580.160.1620.164PeriodtAj0 100 200 300 400
50000.20.40.60.81PeriodtsjtFigure3: Simulationof theALMarkIamodel
for500periodswithfourrms. Theproductivitiesof theleftpanel
havebeendrawnrandomlyfromadistributionwithameanof0.16.17EconomiclifeonthelatticeThelatticeis
a two-dimensional grid.Householdsinitially employed by the same rm
are placed near to each otherEmploymentchangeis shown during the
simulationProductivitydierencesbetweenemployeesmay be introduced.
Theshift is always from low productivity to high productivity rms.
But duringa period new employees may gradually improve from the low
level to thehigh levelA.After2periods B.After10periods
C.After30periodsD.After80periods E.After125periods
F.After200periodsFigure 4:
EvolutiononthelatticeoftheALMarkImodel.18FromtheALMarkImodeltotheALMarkIImodelsProductionandresearchis
the new topicDivisionoflabour.
ThermdividesitsstockofemployeesLj,t1byaxedparameterj.
LabourforproductionisLprodj= (1 j)Lj,t1andlabourforresearchisLresj=
jLj,t1.Productionfunction. OnlyrmsproductionworkersproduceoutputQj=
AjLprodj(11)Costs. Sincew= 1,thermstotalcostsaresimplyCj= Lprodj+
Lresj= Lj,t1.Prot. ThermsellsallitsoutputatthemarketpriceP.
Thusitobtainstheprotj= PQj Lj,t1= PAjLprodj
Lj,t1(12)TheR&Doutcomeis modelled as a two-stage stochastic
processProbabilityofaresearchsuccess.
Theresearchershaveaxedproductivitythatismeasuredastheaveragenumberofsuccessesperperiodperresearcher,1/.
TheresultofthermstotalresearchactivitiesismodelledasaPoissonprocesswithaveragewaitingtimeforasuccessequaltotimesthenumberofresearchers.Methodsofresearch.
TheresearchworkersapplydierentR&Dmethodsaccordingtoxedparametersthatdeterminethedegreetowhichtheresearchersfocusondierentwaysofimprovingknowledge:
(a)cumulationofthermsownknowledge,(b)imitationoftheleadingrmintheindustry,(c)applicationoftheindustrysaverageknowledge,and(d)applicationofgeneralknowledge.Outcomesofresearch.
Withcumulativeknowledgetheresultisdrawnfromanormaldistributionwithmeandeterminedbythermspresentproductivityandaxedstandarddeviation.Productivitychange.
The rms productivity in periodt is the maximum ofthe existing
productivity inherited from periodt 1 and the potentialproductivity
obtained by R&D, i.e.Aj= max(Aj,t1, Aresj).
(13)19StructureoftheALMarkIImodelswithchangingproductivitiesProtj=
Rj CjLabourLj,t1CostsCj= Lj,t1ResearchersLresj=
rjLj,t1WorkersLprodj= (1
rj)Lj,t1Innovation&imitationAresjFirmsoutputQj=
Aj,t1LprodjRevenueRj= PQjKnowledgeAj,t1PriceLj= Lj,t1 +jAj=
max(Aj,t1, Aresj)Figure 5: Thebasic structureof theAL MarkII family
of growth models with
endoge-nousdeterminationoftheproductivitylevel(cf. gure2).
Thediagramisdrawnfromtheviewpointofaparticularrmj.
Thereadingofthediagramstartsfromthestatevariableslabourand
knowledge(i.e. productivity). After theprothasbeen
found,theemploymentlevel forthenextperiod is determined.
Afterinnovation and imitation
hasbeenperformed,theproductivityofthenextperiodisdetermined.20ThedynamicsofdierentALMarkIImodels(I)A.Thecaseofxedproductivities(ALMarkIa)0
100 200 300 400 5000.1560.1580.160.1620.164PeriodtAj0 100 200 300
400
50000.20.40.60.81PeriodtsjtB.Thecaseofrandom-walkcumulationofproductivities(ALMarkIIa)0
50 100 150 2000.150.20.250.30.35PeriodtAjt0 50 100 150
20000.20.40.60.81PeriodtsjtC.Longerrunofthecaseofrandom-walkcumulationofproductivities(ALMarkIIa)0
200 400 600 800 100024681012PeriodtAjt0 200 400 600 800
100000.20.40.60.81PeriodtsjtFigure 6:
SimpledynamicalpatternsfromsimulationsofALMarkIImodelswithfourrms:(A)Theresearchintensitytozeroforallrms,sowehaveALMarkIamodel.
(B)IntheALMarkIIamodel wehaveproductivityincreasesthat
ineachperiodisdrawnfromarandomdistribution with a mean equal to the
present productivity level of the rm. (C) The
specicationoftheALMarkIIamodelimpliesthataseriesofrandomsuccessescan(withlesserandlesserprobability)changethesituationofpanelB.ThusweinpanelCconsideracontinuationofthepreviousALMarkIIasimulationandseethatpanelBdoesnotrepresentalock-insituation.21ThedynamicsofdierentALMarkIImodels(II)D.ThecaseofR&D-basedcumulationofproductivities(ALMarkIIb)0
50 100 15000.20.40.6PeriodtAjt0 50 100
15000.20.40.60.81PeriodtsjtE.ThecaseoftwormswithR&DandtwormswithoutR&D(ALMarkIIb)0
50 100 1500.160.180.20.220.24PeriodtAjt0 50 100
15000.20.40.60.81PeriodtsjtF.Thecaseofrmsthatarebothinnovatorsandimitators(ALMarkIIc)0
100 200 3000123PeriodtAjt0 100 200
30000.20.40.60.81PeriodtsjtFigure7: Dynamical
patternsfromsimulationsof ALMarkIImodelswithfourrms: (D)Inthe
ALMarkIIbmodel rms mayperformR&D, andthe innovative results
have theirmeanvalueinthepresentproductivityoftherm.
InpanelDallrmsperformhavethesameR&Dintensity. (E)Inpanel
EtwormsperformR&DlikeinpanelsD,
whilethetwootherrmshavenoR&Dandthusobtainsaninitiallyhigherprotability.
(F)IntheALMarkIIcmodel all rms may perform both innovation and
imitation. Imitators can in one step reach
theproductivityleveloftheleadingrm. InpanelFallrmshavethe
sameintensityofinnovativeR&DandthesameintensityofimitativeR&D.22TowardsALMarkIIIwithmultipleproductsBasicidea:
Move from the aggregate activities ofAL Mark I and II rmsto
multiple activities1. Each rmjhasmjt production activities2. A
similar number of R&D activities improve the knowledge on
theproduction activities3. A structural R&D activity increases
the number of production activitiesand the related R&D
activities so thatmj,t+1 = mjt +
1Simpleinterdependenceofactivities:One production activity produces
nal output like in the otherALmodelsmjt 1 production activities
produce intermediate goods used in thenal production activityMore
complex interdependencies can easily be introducedSowhat?We may
start with single-activity rms and let multiple activities
evolveTwo rms with equal aggregate productivities may dier in
activity-levelproductivitiesFirms can specialise into sellers and
buyers of intermediate goodsTransaction costsR&D strategies may
also be specialisedDierent R&D strategies t dierent exchange
regimes23ThermintheALMarkIIImodelsofgrowthandindustrialdynamicsLabourInnovation&imitationIntermediategoodsFinaloutputKnowledgeIntermediategoodspurchasesIntermediategoodspricingandsalesFigure
8: Structure diagram that only covers a single rms activities in
theALMark III
models.24TwotypesofmarketintheALMarkIIImodelsFinalgoodpriceandcostsinanearlyandlaterstage0
10 20 304567890 10 20
30456789Intermediatedemandandsupplyinanearlyandlaterstage0 10 20 30
4022.533.544.50 10 20 30 4022.533.544.5Figure 9:
AcomparisonofbetweenthenalgoodmarketandapotentialintermediategoodmarketintheALMarkIIImodels25TwotypesofR&DstrategyintheALMarkIIImodelsTopstrategy(rm
1)L0,1L1,1L2,1L3,1BeforeinnoL0,1L1,1L2,1L3,1InnoinA3,1L0,1L1,1L2,1L3,1+InnoinA3,1L0,1L1,1L2,1L3,1+InnoinA3,1Bottomstrategy(rm
2)L0,2L1,2L2,2L3,2BeforeinnoL0,2L1,2L2,2L3,2InnoinA0,2L0,2L1,2L2,2L3,2+InnoinA1,2L0,2L1,2L2,2L3,2+InnoinA2,2Figure10:
Comparisonof twotypesof
R&Dstrategywhenthereisnointermediategoods trade. Theareaof
eachpieis thelabour costs of producingoneunit of naloutput.
Theslicesofthepiearethelabourcostsinindividualactivities.26ConclusionsontheconstructionoftheALmodelfamilyThesimpleALMark
Imodel with xed productivities impliesAwhole-economyapproachwith
veryfewparameters.
ThismakesiteasiertounderstandthanthestandardNWmodelApure-labourapproachthatmakesiteasytointroducee.g.
fusionsandssions.
ThisallowsasimplesolutiontotheentryandexitproblemofNWmodelsAdeductiveapproachthatgivesproventheoremsaboutthedynamicsofthemodelAsimulationapproachthatgiveadeeperintuitionaboutthedynamicsofthemodelandpreparesforextensionsAnALmodel
familywasnotexplicitlycreated.
However,entry/exitofrmsandthemodellingoftheproductivitydevelopmentofindividualemployeesaresuchextensionsTheALMark
IImodelswith changing productivities implies
e.g.ThesameapproacheslikeforALMarkI.
ButwedidnothavetimeforthatEasyreductiontotheALmodel
bysettingproductivitychangetozero.ThuswecancheckwhetheroursimulationmodelisconstructedcorrectlyEasyintroductionofdierentregimes
ofproductivitychange.
ThusawholefamilyofALMarkIImodelscanbecreatedquicklyTheALMark
IIImodelsare still described programmatically rather thanin detail.
However, we see e.g.Intermediategoodsratherthancapital.
ThemodelsdonothavetoassumexedpricesoftheproducedinputsResearchspecialisationimpliesbindingsonfuturepossibilities,soitopensupalargeareaofstrategyevolutionTransactioncosts
caneasilybeintroducedalthoughtheyhavebeenleftoutintheNelsonWintertradition(cf.Winter,1991)ThetheoryofthermiscloselyrelatedtomultiactivityrmsanditiscentraltotheverbalNelsonWintertradition(cf.NelsonandWinter,1982,PartII)27ElementsoftheartofsimulationWhatcanbesaid,canbesaidclearly,andwhatyoucantsay,youshouldshutupaboutindependentlybyWittgensteinandtheComputerBasicprinciples
forhandlingbothevolutionarysystemsandthesimulationofthemTheKISSprinciple:
KeepItSimple,Stupid!
EvolutionarymodellingissocomplexthatitmustbehandledwithcareThedivide-and-governprinciple:
DecomposehardtaskssubtasksTheprincipleofsuccessiveapproximations:
Startfromthesimple,andthenmovebytinystepstothecomplexTheunite-and-leadprinciple:
BecomeavirtuosowithbymeansofthesubtasksyouhavemasteredThelevelsofsimulationworksuggestsanaturaltrajectoryModelapplication:
ExploreagivenmodelbyasetofsystematicallyperformedsimulationsModeldevelopment:
ExtendgivenmodelsorcreateanewoneSystemdevelopment: Develop thetools
formodeldevelopmentandapplicationDeningasimulationbyfourlists1.
Alistofmodelequations likeQuantity = Productivity Employment2.
Alistofparametervalues likeProductivity= 1.2(intheALMarkImodel)3.
Alistofinitialvaluesofstatevariables likeInitial employment = 1004.
AlistofsimulationrunspecicationlikeSimulationsteps = 5000But. . .
thecomputerneedsmoretoperformasimulationrun(e.g.
providedbytheLsdsystem)28WorkinginloopsSimulationsettingsSystemdevelopmentValuesofparametersModelequations,andalgorithmsforrunningthemodelEvaluationofsimulationresultsInitialvaluesofstatevariables(5)(4)(1)(2)(3)Figure
11:
Feedbacksinthesimulationofanevolutionarymodel.29Workinginsteps1.
Problemdenition2. Modelspecicationandanalysis3.
Modelimplementation4. Simulationanalysisofsingleruns5.
Simulationstatisticsofmultipleruns6. Parameterexploration7.
Modelspecicationcontrol8. ReportingresultsFigure 12:
Stepsinsimulationwork.
Afewfeedbacksareincluded.30Laboratoryforsimulationdevelopment(Lsd)TheLsdsystemis
a system of simulation tools and evolutionary simulationmodelssee
Andersen and Valente (2002) and Valente and Andersen
(2002)PurposesareFacilitateexplorationofexistingmodels
byawindows-basedinterfacetousersthatcoversallthestepsofmodelexplorationFacilitateextensionofexistingmodels
byawindows-basedinterfacetodevelopersthatcoversallthestepsofmodeldevelopmentandbyasimpliedinterfacetotheC++programminglanguageFacilitatecreationofmodels
bythesamemethodsasforexistingmodelsbutemphasisingthebottom-upmethodologyFacilitatedocumentationandreplicabilityofsimulationresultsthus,perhaps,overcomingthebadreputationofmuchsimulationworkFacilitatethecreationofasimulationcommunitybymore-or-lessenforcingrulesfordocumentationanddistributionofsimulationmodelsImplementationof
the system has been a continuing project by Valente sinceit was
initiated in 1995 by Dosi, Nelson, Winter and
othersTheLsdModelsManager(LMM)
isacomputerapplicationthatisusedfortheselection,compilationandmodicationofstand-alonesimulationmodels.ForusersinterestedonlyinmodelexplorationLMMisatoolforchoosingbetweenpreexistingsimulationmodels.
LMMisalsousedbythedeveloperTheLsdModelExplorers(LMEs)
arestand-aloneapplicationsforthesimulationofmodels.
TheLMEallowsuserstochangethecongurationandthustoperformloops13ofgure11inanecientmanner.
LMEisalsousedbythedeveloper31WorkinginstepsintheLsdsystem:
ModelusersSelectmodelinLMMInspectbasicdocumentationandequationsStarttheLMEWritesimplereportsonthestudyLoadcongurationintheLMEChangecongurationInspectandchangehelplesRunmodelandstudyRunTimePlotAnalyseresultsintheLMEPlotdata
MakestatisticsExportdatatootherapplicationsFigure 13:
ThebasicuseoftheLsdsystem.32Firststep: SelectthemodelFigure 14:
ThewindowoftheLsdsystemthatisrstencounteredbyusers.
ThiswindowisthepartoftheLsdModelsManager(LMM),whereyouchoosethemodelwithwhichtowork.In
the leftpart ofthe windowthere isalistof the modelsthat are found
inthe Lsddirectory ofthe computer. When a model is chosen,its
description is shown in the right part of the
window.33WorkinginLsdsteps: StartandcongurationFigure 15:
ThemainwindowofLMM.Wehavechosentorunthemodelimmediately.Figure 16:
ThebrowserwindowoftheLME(LsdModelExplorer)foranAL-likemodelhasbeenopenedbyLMMandwehaveloadedasimulationspecicationcalledLK1arepldyn.
IntherightpaneltheRunmenuhasbeenpulleddownandwearereadytorunthemodel.34WorkinginLsdsteps:
ModelstructureandresultsFigure17: Themodel structurewindowof
theLMEfortheAL-likemodel. Therearevehierarchicallyorganisedobjects:
World, Economy, Firm, HouseSectorandOptions.
SincethecursorisplacedovertheobjectWorld,weseethevariablesthatarefoundhere.Figure
18: During a simulation run in an LMEapplication it is possible to
follow the dynamicsof selected variables. The have selected the
market shares of the ve rms and see that they showa simple
distance-from-mean dynamics. After the simulation run there are
very rich possibilitiesfor exploring and documenting the results.
Here we can also produce more beautiful and
precisegraphics.35WorkinginLsdsteps:
ModeldevelopersCopyofornewmodelinLMMWriteequationsinLMMDevelopthemodelinLMMMakebasicdocumentationCompileandstarttheLMEofthemodelDevelopconginsyncwithequationsLoadcongurationintheLMEDevelophelponthemodelRunmodelandstudyRunTimePlotAnalyseresultsintheLMEFigure
19: ThedevelopmentofLsdmodels.36WorkinginLsdsteps:
WritingequationsFigure 20: HereLMMisusedforrewritingmodelequations.
ThiscaneitherbedoneintheamixedLsd/C++languageor (ashere)inthe
highlysimpliedLsdmacro language.
Itisonlythedarktextthatismacrocode.
Therestarecomments.37ReferencesAndersen,
E.S.(1996),EvolutionaryEconomics:
Post-SchumpeterianContributions,paperbackedn,Pinter,London.Andersen,
E.S.(2001),TowardamultiactivitygeneralisationoftheNelsonWintermodel,PaperforDRUIDsNelsonandWinterConference,1215June,DRUID,Aalborg.URL:http://www.business.auc.dk/druid/conferences/nw/paper1/andersen.pdfAndersen,
E.S.andValente,M.(2002),Introductiontoarticialevolutionaryprocesses,Chapterforthebookproject
Articial EconomicEvolution: Model
ExplorationandExtensionintheLaboratoryforSimulationDevelopment,
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BasicBooks,NewYork.Hodgson,G.M.(1993),EconomicsandEvolution:
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