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SIEPR  Discussion  Paper  No.  15-­‐005    

Zvi  Griliches  and  the  Economics  of  Technology  Diffusion:  Linking  innovation  adoption,  lagged  investments,  and  productivity  growth          

By    

   Paul  A.  David    

   

Stanford  Institute  for  Economic  Policy  Research  Stanford  University  Stanford,  CA  94305    (650)  725-­‐1874  

 The  Stanford  Institute  for  Economic  Policy  Research  at  Stanford  University  supports  

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ZviGrilichesandtheEconomicsofTechnologyDiffusion:Linkinginnovationadoption,laggedinvestments,andproductivitygrowth

By

PaulA.David

Firstversion:August2003Secondversion:December2005Thirdversion:March312009Fourthversion:March20,2011Thisversion:April4,2015

Acknowledgements

Thepresentversion isarevisionof theStanford Institute forEconomicPolicyResearch(SIEPR)DiscussionPaperNo.10‐029 (March),2011.The firstversionof thisworkwaspresentedtotheConferenceonR&D,EducationandProductivity,heldinMemoryofZviGriliches (1930 –1999) on 25‐27th, August 2003 at CarrJ des Sciences,Ministère de laRecherche,Paris,France.GabrielGoddardfurnishedcharacteristicallyswiftandaccurateassistancewiththesimulations,andthegraphicsbaseduponthemthatappearinSection4.IamgratefultoWesleyCohenforhisperceptivediscussionoftheconferenceversion,particularlyinregardtothesupply‐sidefacetofGriliches’1957articleinEconometrica.ThewisecounselandextraordinarypatienceofJacquesMairesseandManuelTrajtenbergintheircapacitiesaseditorsofthe2003conferenceproceedingswasvitalinlaunchingmeonthe extended courseof revisions thathasbrought thepaper to itspresent state.At theoutsetof that journey Ihad thebenefitofmanyhelpful suggestionsby twoanonymousrefereesfortheabridgmentandthoroughrestructuringoftheconferencepaper,onlysomeof which (evidently) have been implemented. More recently, I incurred further debts,firstly, to Bronwyn Hall for comments that clarified several points regarding Griliches’redirectionofhisempiricalresearchintheearly1970’sawayfromexplicittreatmentofdiffusionphenomena,andtowardaspectsoftechnologicalchangeandtheimpactofR&Donfirm‐levelproductivity,aswellasimprovingtheappearanceofFigure5. SubsequentpresentationsofthematerialtotheMERITWorkshoponInformationTechnologyandNewIndustry and Labour Market Dynamics (held on 3‐4 June 2004) at the University ofMaastricht, and at the seminar of the Eindhoven Centre for Innovation Studies (on 17November 2004) at Eindhoven University of Technology, provided stimuli from BartVerspagenandotherstoundertakestillmoreimprovements–whichcontributedtofurtherlengthenthepaper.StillmorerecentconversationswithH.PeytonYoungonthegeneralclass “heterogeneous threshold” models of adoption have contributed to the presentexposition of the challenges posed to empirical identification of alternative diffusionmechanisms.MyintellectualdebtstoTrondOlson,PaulStonemanandGavinWright,whosecontributions to our co‐authored works (referenced herein) have been important inshapingmyresearchonthissubjecttoadegreethatthefootnotecitationsinadequatelyconvey.Whilegratefultoallthosewhohaveofferedtheirhelp,Iinsistthatnoneshouldbeheldtoblameforwhateverdefectsanddeficienciesneverthelesspersistinthesepages.

ABSTRACT

ThescientificlegacyofZviGriliches’contributiontotheeconomicanalysisofthediffusionoftechnological innovations is the subject of this paper. It beginswith an examination of therelationshipbetweenGriliches’pioneeringempiricalworkontheintroductionandadoptionofhybridcornandthesubsequentdevelopmentoftheoreticalmodelsandeconometricresearchonthemicroeconomicdeterminantsofdiffusion.Next,itformalizesthewaythatthedynamicsofdiffusionobservedattheaggregatelevelisshapedbystructuralconditionsatthemicro‐level–onboththesupplyandthedemandsidesofthemarketforproductsembodyingtechnologicalinnovations, both of which were addressed by Griliches (1957). It then points out thereflectionsofthoseprocessesinlaggedbehaviorofaggregateinvestmentindurablecapital‐embodiedinnovations–oftenregardedasanindependentsubjectofGriliches’analyticalandeconometricresearch.Thelatterconnection,anditslinkwithproductivitychangesstemmingfrom embodied technical change, are made explicit by the model of micro‐to‐macrorelationshipsaffectingthetotalfactorproductivity(TFP)growthratethatispresentedinthethirdmajorsectionofthepaper(andtheAppendix).Thethreeforegoingdynamicphenomena– diffusion, durableinvestmentlags,andTFPgrowth–werethetopicsofGriliches’threemostwidely cited journal articles, respectively. The connections among themhave not beengenerallynoticedbyeconomists,and,indeedtheyremainedimplicitin hiswritingsuntillateinhiscareer,whenheemphasizedthediffusion‐productivitynexusasakeyproximatedeterminantofthepaceofeconomicgrowth–aperceptionwhoseimportanceremainsinsufficientlyappreciatedin currentpolicydiscussions that focusattentionon “innovation”as thedriverof intensivegrowth.Havingdirectedattentiontothemicroeconomicsoftechnologyadoptionunderlyingthe‘transitions’duringwhichthediffusionofmajorinnovationsgeneratesurgesininnovation‐embodying capital formation, and to the consequent waves in the TFP growthrate at the industryandsectorallevels,shouldbeseenasprominentamongtheimportantandenduringcontributionsthatZviGrilichesmadetomoderneconomics.

Keywords:technologyadoption,innovations,diffusion,investmentlags,learning‐by‐doing, heterogeneous adopters, contagion model, threshold model, micro‐macromodels,laborproductivityandTFPgrowth‐surges.JELClassificationNos.:D22,D24,O33,O4.ContactAuthor:PaulA.Davidpad@stanford.edu

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ZviGrilichesandtheEconomicsofTechnologyDiffusion:Linkinginnovationadoption,laggedinvestments,andproductivitygrowth

1. Introduction

This essay considers the scientific legacy of Zvi Griliches’ contribution to the economicanalysis of the diffusion of technological innovations by examining the relationship between hispioneering empiricalwork on the introduction and adoption of hybrid corn and the subsequentdevelopmentoftheoreticalmodelsandeconometricresearchonthemicroeconomicdeterminantsofdiffusion.Thosedevelopmentshaveexposedthewaysinwhichstructuralconditionsatthemicro‐levelonthedemandsideofmarketsfornewprocessinnovations,anddynamicfeedbacksaffectingthesupplysideofthemarketsforinnovativeproductscaninteracttoshapethespecificsofdiffusionphenomena that are observed at the level of industries and sectors. Further elaboration of thisanalyticalperspectivebringsintoclearerfocusthemicro‐to‐macroconnectionsbetweendiffusionand the laggedbehavior of aggregate investment in capital‐embodied innovations, aswell as theimpact of diffusion dynamics on the pace of growth of aggregate total factor productivity (TFP).Directing the attention of empirical and theoretical research to examine the microeconomicmechanismsthatunderlietechnological‘transitions’drivenbythediffusionofmajorinnovationshasrevealed processes that can generate wave‐like surges of innovation‐embodying capitalaccumulation,andcorrespondingwavesinthegrowthratesof industrialandsectoraltotal factorproductivity (TFP). The impetus his pioneering study of hybrid corn imparted to subsequentresearch aimed at identifying the roles of structural conditions anddynamic linkages among thepopulationofpotentialadoptersandthesuppliersofinnovation‐embodyingproducergoods,deserverecognition among the most important enduring legacies of Griliches’ contributions tomoderneconomics.

1.1Diffusion,distributedlagsandthegrowthofmeasuredTFP:ZviGriliches’threebiggestjournalpublication“hits”

The three most widely cited journal articles by Zvi Griliches deal, respectively, with theeconomicsofthediffusionoftechnologicalinnovations,theeconometricsofdistributedlagsandthesourcesofmeasuredchangesintotalfactorproductivity(acollaborativepaperwithDaleJorgenson).Obviously, citation statistics are but one means of gauging the intellectual impact of researchcontributions–andalimitedoneatthat.1Nevertheless,itistestimonytothesignificanceofthemainsubjectofthisessaythatthe1957Econometricapaperontheintroductionandacceptanceofhybridcorn among U.S. farmers comes first in the rank ordering of the many journal articles whosecumulativeannual journalcitationshavebeencompiled inDiamond’s (2003)surveyofGriliches’contributionstotheeconomicsof technologyandgrowth.Moreover, theremarkable fact thattheannual flowof citations to thisparticular articlehas continued to trendupwards throughout the 1Thethreepaperstoptheall‐timecitationrankingof110journalarticleswhoseannualcitationcountsfrom1956 to 2002were compiled from theWeb of Science journals, supplementing in some cases bymaterialcoveredintheSocialScienceCitationIndex.TherespectivetotalcitationcountsreportedinDiamond(2003:TableII)forthesearticlesare:Griliches(1957)–548.8;Griliches(1967)–214;GrilichesandJorgenson(1967)–106.BecauseDiamond(2003) interpolatedmonthlycounts forSeptember‐Decemberof the finalyearbyapplyingmultiplierof1.5tothedataforthemonthsthroughtoAugust2002,hisproceduregeneratedsomefractionaltotals,suchtheonethatappearsforthefirstpaperinthislist.Onthegeneraltopicofthelimitationsofpublicationcitationsasindicatorsofscientificimportance,vanRaan(1988)remainsanexcellentplacetostart.

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forty‐fiveyearsfollowingitspublication–andmostprobablyforthefullhalf‐century‐‐bearsstrikingtestimony to the lively interest among economists in the phenomena that it brought within thepurviewoftheirdiscipline,andtothesustainedinfluenceofthatpath‐breakingstudy.2 Althoughthesethreetop‐citedpublicationsgenerallyhavebeenviewedasunrelatedcontributions(somuchsothattheirjointsalienceineconomicsliteratureowesvirtuallynothingtocross‐citationsamongthem),therearesignificantsubstantiveconnectionsamongthesetopics.Thatcontentionmotivatesthediscussionpursuedinthefollowingpages.

Necessarily,itbeginsbyreviewingthespecificdetailsofGriliches’path‐breakingpaperontheintroductionandadoptionofhybridcorn,anditsinfluenceuponsubsequentresearchbyotherson the diffusion of innovations. This did not stimulate explicit considerations of economicrelationships among the three dynamic phenomena that have just been bracketed here; theconnections among them remained largely unexplored in the literature, including Griliches ownresearchwheretheyremainedimplicit,atbest.Indeed,thisreflectedthefactthatbythemid‐1960’shis attention had turned away from the study of specific technological innovations and thephenomenaassociatedwiththeirdiffusionintouse,andhedidnotreturntothesubjectempiricalstudiesofdiffusion–apartfromGriliches’(1980),thebrief(butnonethelesssignificant)commentspromptedbyDixon’s (1980)re‐examinationof theavailableU.S.dataon thecaseofhybridcorn.Nevertheless, clear recognition of the broader importance of understanding the dynamics oftechnologyadoptionresurfacedinGriliches’reflectivewritings.Thatthenexusdiffusion‐productivitygrowth nexus figuredprominently in his approachduring the 1990’s to understanding themainproximatedeterminantsofthepaceofeconomicgrowth,andthereforwarrantedcloserattentionfrom economists, is evident from the following passage in Griliches’ R&D and Productivity: theEconometricEvidence(1998):

“Realexplanations[ofproductivitygrowth]willcomefromunderstandingthesourcesof scientific and technological advances and from identifying the incentives andcircumstancesthatbroughtthemaboutandthatfacilitatedtheirimplementationanddiffusion.”3

Onthestrengthofthatendorsement,thispaperundertakestocounter‐balancethetendencyoftheendogenouslygrowthmodelliteraturetoglossoverthedynamicprocessesthroughwhichthediffusion of innovations is implicated in the realized pace of aggregate total factor productivitygrowth.

1.2 Organizationandoverview

Theorganizationofthediscussionproceeds,accordingly,“frommicrotomacro.”Chapter2beginswith a review of the approach that Griliches (1957) adopted in studying themicro‐level

2 Corroborative reassurance is available, from theNewYorkTimes (5November 1999: p. 11) obituary byMichaelWeinstein,which reportsDale Jorgenson’s reference to this study, alongwith the1958 JPE article(measuringthesocialrateofreturnonR&Dinhybridcorn)asthebestknownandmost‐mentionedofGriliches’contributions.Diamond(2004)alsonotesArielPakes’(2000)descriptionofthe1957Econometricaarticleas“seminal.”

3 Emphasis added. This passage is reprinted in Griliches, 1998: pp.89‐90 from Griliches (1994)AmericanEconomicReviewarticleonproductivity,R&Dand“thedataconstraint.”Histextgoesontosaythatrecognitionoftheseconnectionswould–oratleastshould‐‐leadeconomists“backtothestudyofthehistoryofscienceandtechnologyandthediffusionoftheirproducts,atopicthatwehaveleftlargelytoothers.”

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economicdeterminantsoftheintroductionandadoptionofdiffusionofhybridcornonU.S.farms.Thediscussion (in sect. 2.2) considers the impetus thatwas imparted to economists’ subsequentempiricalresearchonthediffusionofprocessinnovationsbytheemphasisGriliches’commitmenttothe rational‐actormodel inwhich profitability considerationswere themain determinant of thespeedwithwhichtheinnovationhadbeenacceptedwithindifferentfarmingregions.Ittracesthewaythattheparticularempiricalstrategythathehademployeddirectedthesubsequentcourseoftheoreticalmodel‐buildingtowardaccounting for the logisticshapeofdiffusionpaths in termsof“contagion”effects,althoughthesewerenotfeaturedinhis1957discussionoftheroleofinformationpropagationlagsintheadoptionprocess. Section2.3returnstore‐examinethecontroversywithruralsociologistswhohadbeenprovokedbyGriliches’treatmentofthesubjectintermsthatallowlittleifanyexplanatoryimportancetotheaspectsofitonwhichtheirapproach(informedbysocialpsychologyandsociometry)had focused, and the respects inwhich that stanceunderwent someaccommodating transformations in the course of responding to criticisms from that quarter(Griliches 1960, 1962). As a result, what is seen to have emerged from the controversy wassubstantive agreementbetween the emphasis accordedby sociologists and economists to socialcommunicationsasthecentraldynamicprocessdrivingoftechnologyadoption,accompaniedbyagrowingdisjunctionbetweentheconceptualandempiricalframeworkswithinwhichworkonthesubjectproceededinthetwodisciplines.As

AsSection2.4shows,theparadoxicalstateofaffairsjustreferredtobecamemanifestintheliteraturewiththerisingpopularityamongeconomistsoftheformalversionofthecontagionmodelthat was introduced by Mansfield (1961), and the evident commonality between the latter’seconometricstrategyandthatwhichGriliches(1957)hadintroduced.Section2.5 takesupothermattersthathadnotbeensubjectsofdisciplinarycontroversybutwerenonethelessrecognizedtobeproblematic‐‐yetnotreadilyresolvedwithineitherGriliches’(1957)explanatoryframeworkorthatoftheruralsociologistswhoviewedthestructureschannelingsocialinfluencetobethekeytounderstandingadoptionbehaviors.Centralamongthesewastheexistenceofheterogeneityinthecircumstances of potential adopters, and its connection with the behavior of the suppliers ofinnovation‐embodyinginputs‐‐sucnashybridcornseeds,whichGriliches’studyhadundertakentoexplainalsointermsofrationalprofit‐seekingaction.BothofaspectsofGriliches’originalworkweremarginalizedintheliteraturebythegrowingpopularityofthe“informationcontagion”model,butemergedduring the later1960’s in an alternative, thebasic “thresholdmodel.”This approach toexplainingdiffusion(David1966,1969,1971)wasbasedonrecognitionthatmanyinnovationswerebiased in their relative factor‐usevis‐à‐vis theestablishedproduction technologies,and thereforeexplicitlyconsideredthewaythiswouldinteractwithheterogeneitiesamongpotentialadopterstoaffect their choices among the alternative availableproductionprocesses. It opened anew routethroughwhichempiricalmodelscouldaccountforaggregate‐levellagsindiffusionlagsbyallowingfortheeffectsofsupply‐sidetechnicalchangethatalteredtherelativeprice‐performanceratioofinnovation‐embodyingproducts,andtherebyinducedsequentialdemand‐sideswitchingfromoldtonewprocesstechnologies.

Chapter2’sdiscussionclosesbyconsidering(in2.6)theimplicationsforempiricalresearchoftheresultingproliferationintheliteratureof“diffusionmodels”thatappeartobeobservationallyequivalent, all being capable of generating the same form of aggre gate diffusion curves. To thecontagion,andthethresholdmodelswasaddedwhichishereseentobeanincipientevolutionary,replicatormodelthatappearedinNelson(1958)–althoughnotconstruedexplicitlyinevolutionarytermsuntil the early 1980s.All threemodels are seen to be capable of generating the canonicallogisticformofS‐shaped(ogive)diffusioncurvetowhichtheattentionofmodel‐buildershadbeendirectedbyGrilichesandMansfield.There it isshownthat theirobservationalequivalenceat the

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aggregatelevelissuperficial,asitmaskstheabsenceofmicro‐levelobservationsthatwouldpermitidentification of the quite distinct underlying specifications of in these models of behavioralresponses,structuralconditionsandrelatedtimeconstantsofthedynamicprocessesgoverningthetemporaldistributionofadoptiondecisionstakingplaceamongthepopulationofpotentialadopters.

Chapter 3 presents a more complete account of the “threshold” approach to themicroeconomicsof technology adoptionsbaseduponexplicitmodelling of the role of populationheterogeneities.Griliches(1980),inabriefreflectivecommentcontrastingtreatmentsofdiffusion,characterized this recognition of the implications of heterogeneities among the potential userseconomic and environmental circumstances as a useful “moving equilibrium” alternative to theparadigmofa“disequilibrium”transitiongovernedbyinformationconstraints. Theexpositioninsection3.1isbasedmainlyuponDavidandOlsen(1984,1986),whichexpandsthebasic“thresholdmodel’s”analysisofan informedrationalagent’s choice‐of‐techniquedecisions(betweenanovel,evolvingtechnologyandanfamiliar,maturetechnology),bytakingintoaccountthedynamiceffectsofanticipatedfeedbacksfromchangesinsupplyconditionsaffectingthecostsofadoption.ThelatterformulationabsorbedStonemanandIreland’s(1983)introductionofsupply‐sidelearningeffectsinthe“threshold”framework,butwentfurtherbyconsideringtheimplicationsoflearningexternalitiesor“spill‐overeffects”onthepricingofdurableproductionassetswhenpotentialusers(aswellasproducers) could anticipate the future trajectory of the relative prices of innovation‐embodyinggoods.WhereasGriliches’(1957)viewedthesupplyofinnovation‐embodyinginputsasaffectingonlythetimingofthefirstsignificantcommercialintroductionofthenewtechnology,inthemorefullyelaboratedmodelsofthe1980’sthebehaviorsofagentsonboththesupply‐sideanddemand‐sideareseentocontinuouslyshapethedynamicsofdiffusionpath.Moreover,togetherwithconditionsin themarket for the goodswhat it is used to produce, these endogenous forces can generate amovingupperceiling,orsaturationlevelintheextentofdiffusion‐‐towardswhichtheactualpathofdiffusion’sconvergencedrivestheceilingupwardsuntilthenichesintowhichtheinnovationcanspreadareexhausted.

Thesourcesandformsofthedistributionsoftheputativeheterogeneitiesamongpotentialadopters that canbeadmitted inmodelsof thisgeneral class,and their relationship to the time‐constants of themicro‐level diffusion process are discussed in Section 3.3. This serves tomakeexplicit the connections between the structural conditions underlying such processes and thedistributedlagdynamicsthatdiffusioncouldgeneratesinthevolumeofaggregateindustry‐levelorsector‐levelinvestmentsincapitalequipmentandstructuresthatembodytheinnovation.ThereitisnotedthattheexplicitdynamicanalysisofadoptiondecisionspresentedinChapter3underscoresaproposition that ina sense is thecorollaryof thepointemphasized insection2.6: fully specifiedmodelsofdiffusionbelongingtothelargeclassthatposittheexistenceofheterogeneitiesamongthepopulationofpotentialadopterscangenerateverydistinctivedifferencesinaggregateleveldiffusiondynamics,evenwherethehypothesizedeconomicmicro‐levelmechanismsareidentical.

Aforward‐lookingmessagethatemergesinsection3.4isthateconometrictestingoftheseandstillrichertheoreticalmodelsoftechnologydiffusionwillnotbepossiblewithoutmuchgreaterconcerted efforts to develop extensive bodies of consistent micro‐level cross‐section data andaggregate time‐series observations that allow controlling for confounding effects on each of thedistinctsubprocessesthatarerecognizedbythearrayofalternativediffusionmechanisms.Itisnotedthattheinabilitytomeetthatexactingchallengeunderminedearlysociounderminedsociometricresearch by Coleman, Katz and Menzel (1957, 1966) that was long taken by sociologists toempiricallysupporttheclaimsofthe“sociallearnthoroughinformationcontagion”explanationofdiffusionphenomena–andtoanextentthathasonlyrecentlybeenappreciated.Clearly,paneldata

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providingobservationsnotonlyonadoptionbehaviorbutinternvenningnon‐pecuniaryinteractions,includingsocialcommunicationsamongactualandpotentialusersoftheinnovation,arewhatwillbe required empirical identification of the micro‐level processes and measurement of theircharacteristictimeconstantsandrelativeimpactsonthecourseofchangesintheaggregateextentofdiffusion.

Chapter4buildsupontheanalysisofthegeneralthresholdmodelofdiffusionpresentedinSection3,andexaminestheimplicationsofitsunderlyingdeterminantsfortheratesofgrowthlaborproductivityandtotalfactorproductivityattheaggregatelevelofanindustryinwhichanew,capital‐usingprocesstechnologyisdisplacingapre‐existingmethodproducingaconsumer‐goodusingonlylabor.Themainstructural featuresandrationalizingassumptionsof thesimulationmodel that isconstructedforthispurposeareoutlinedinsection4.1(relegatingtheformaldetailstothepaper’sAppendix).Section4.2examinesthemainpointsthatemergefromthesimulationexercises,whichexhibit the distinct ways in which underlying structural parameters affect the amplitude anddurationsofwave‐likemovements that theprocessof the innovation’sdiffusiongenerates in theaggregatelevelgrowthrateslaborproductivityandTFP.

Having completed the announced task of showing the connections between micro‐leveladoptionbehaviors,thedynamicsofdistributedlagsinindustrylevelinvestment,andthediffusion‐drivensourcesofaggregateTFPgrowth,thepaperconcludesinsection5bycommentingbrieflyonapossibly important set of connections thatmaywarrant investigation and inclusion in a futureelaborationofthesimulationstructurepresentedhere.Theseconcernthelinkagesbetweendiffusionprocesses and the behavior of R&D investment in the industries that supplying the innovation‐embodyingcapitalgoods,andtranslateknowledgegainedfromexperienceinproducingthosegoods,aswellasfromthefirmsthatadoptedpreviousvintagesoftheirinnovativeproductsintonewerandmoreeffectiveinputsthatcangainacceptanceamongthemarketnichesthattheinnovationhasnotyetpenetrated.LittleappearstobeknowaboutthisaspectofthenexusthatmayindirectlyconnectR&D and productivity growth, and such an exploration of the diffusion‐R&D connection mightusefullyroundouttheprogramofresearchthatbecamethemainfocusofZviGriliches’sustainedcontributionstotheempiricalstudythesourcesofeconomicgrowthinthemodernera.

2.TheNatureoftheLegacy—EconomicsandTechnologyDiffusion

TheapproachtakenheretoassessthenatureofZvi'sGriliches’(1957)seminalcontributiontotheliteratureontheeconomicsofdiffusionmustconsidernotonlywhathadbeenaccomplishedinthatwork,andhowitshapedtheensuingdevelopmentoftheliteraturedevotedtothissubject,butalsowhathadlefttobedonebylatercontributors.ThissectionthereforefocusesuponboththeachievementandthelimitationsofthisfamousstudyoftheintroductionandacceptanceofhybridcornbyU.S.farmers.

2.1Thehybridcornstudy—aneconometricparadigmisborn

ZviGriliches’earlyeconometricstudyofthecommercialintroductionanddiffusionofhybridcornintheU.S.wasinfluentialfortworeasonsthatweresomewhatintensionwitheachother.First,heconstruedthephenomenonofdiffusionineconomicratherthansociologicalterms,andsoopenedanewavenuetoexaminingtheeconomicsoftechnologicalchange.Second,thequantitativeapproachheadoptedwasprimarilyinductive,ratherthandependentuponformulatingaparticulartheoretical

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modelfromwhichdeductivepropositionscouldbederivedandsubjectedtostatisticaltests.Instead,hisworkhadgivenothersasimplewaytoquantitativelycharacterizethreeaspectsofthegenericphenomenonoftechnologydiffusionobservedattheaggregate(population)level–thelengthoftheintroductionlag,thespeedoftheinnovation’sadoption(or“acceptance”),andtheterminalextentofitsdiffusion.Thisprovidinganintuitivelyappealingandtractableempiricalmethodologythatprovedtobewidelyapplicable,andattractiveinleavingroomformanyalternativeexplanatoryhypothesesconcerningtheunderlyingbehaviorsoftheadoptingagents.

Both aspects of Griliches’ approach are reflected in his implicit characterization of thediffusionprocessasonethatoccurredsuccessivelywithindistinctgeographicalregions,andinhisselectionofastatisticallyconvenientdescriptivespecificationforthediffusionpath–namely,thecumulativelogisticdistribution.Hecouldthenproceedimmediatelytohypothesizethatthespeedofdiffusion(andhencetheoverallshapeoftheS‐shapedpathdeterminedbytheslopeparameterinthe diffusion function) would reflect economic conditions having to do with the innovation'sprofitabilityforarepresentativeadopter.Similarly,economicfactorscouldbesupposedtoaffectthelocationoftheonsetdateforthediffusionprocessunderexamination,andthereforetobereflectedstatisticallyinthevalueofthatsecond(scaling)parameterofthelogistic.4

Grilichestherebywasabletocharacterizethediffusionpathintermsoftworeadilyobtainedparameters–theslopecoefficientofthelogisticfunction,andthe‘intercept’coefficient(whichsetstheinitialorconventionallyperceptible)proportionofadoptersfromwhencetheobserveddiffusionprocessproceeds.5Theeleganceof this simplificationhadamajor initial influence in stimulatingeconometric research on diffusion: characteristics of various technological innovations, or of theindustriesandmarketsintowhichthesehadbeenintroduced,couldsimplybeenteredasregressorsthatmightaccountforinter‐innovationvariationsofthelogisticslopecoefficients.

Aswillbeseen, thissoonwasseizeduponbyeconomistsasan“obvious”wayproceedinquantitative studies of the role of demand‐side conditions in determining the adoption of newproduction techniques and new goods. But, an equally novel aspect of Griliches’ paper inEconometrica (1957)was concernedwith factors operating on the supply sideof themarket forhybridcornseedintheU.S.Likemanyotherinnovations,hybridplantsaremostefficientaselementsofaproductionsystemwhentheyhavebeendesignedforaspecificenvironment.Insomecasestherelevant“environment”iseconomic,inthesenseofbeingdefinedbythestructureofrelativepricesof thearrayof inputsusedby theproductionsystem; inothers, it is thephysicalenvironment towhichtheprocessrequiredbeingadapted.Inthecaseofhybridcorn,Grilichesnoted,localvariationsinsoiltypes,climate,andpestscalledforthesuppliersofseedstodevelopparticularvarietiesthatwouldbebestsuitedtotherequirementsoffarmerinthevarioussub‐regionsoftheU.S.,rangingsouthwardsfromWisconsinandIowa,toTexasandAlabama(seeFig.2).

4When theupper asymptote of thediffusionpath is taken to be unity (universal adoption), signifying theassumptionmadebyGriliches’(1957),thereareonlytwofreeparameterstofiteconometricallyforthelogisticdistribution.Buttheconventionalapproachistoestimateaslopeparameterandaninterceptconstantfroma(linear)modelofthelog‐oddsratio.Seediscussionbelow,inthissection.

5Griliches(1957:p.504,esp.n.10)obtainedtheseparameterestimatesbyunweightedleast‐squaresregression,basedonthelog‐oddstransformofthelogisticgrowthcurve,rejectingtheweightingmethodologyproposedby Berkson (1955) to correct for heteroskedasticity, on the grounds that the bio‐assay context in whichBerkson’sprocedurehadbeenproposedwasofdoubtfulapplicabilityinthe(time‐series)contextinwhichhewasworking.

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Consequently, considerations of the profitability of the incremental “development”investmentsthisentailed–suchastheextentoftheexistingcorn‐acreageinthesub‐region,andthetypicalsizeofthefarmthatthecompany’sseed‐salesmenwouldhavetovisit–wouldbeexpectedtoaffectthespatio‐temporalsequencingoftheinnovation’sintroduction.Inthispartofhisanalysis,Grilichesclearlyhadanticipatedtheeffortsoflaterbuildersofmicroeconomicmodelstoincorporatetheeffectsof incrementalsupply‐sideadaptationsuponthediffusionprocess.Yetatthetimethisaspect of his path‐breaking study, about which I will want to say something more, attractedcomparativelylittlenotice.

Muchmorenotice,andevensomecross‐disciplinarycontroversythatheighteneconomistsattention,wasfocusedonaspectofhisworkthatsupportedtheconclusionthatadoptionbehaviorexhibiteda“rational”responsetotheavailabilityofasuperiormethodofproduction,onethatwas“consistentwiththeideaofprofitmaximization.”Althoughthelaggedadoptionofhybridcornbythefarmersinaparticularregionofthecountryreflectedthefactthat“thespreadofknowledge1snotinstantaneous”(1957:p.522),thespeedwithwhichtheregion’simperfectlyinformedfamerscameto“realizethatthingshadinfactchanged”inthetechnologyofcorncultivation,andadjustedtheirmethodsaccordingly.

Griliches’ classic (1957) paper on hybrid corn did not undertake to develop a formaltheoreticaljustificationforitsrelianceonthelogisticspecificationintheeconometricanalysis;nordid itemphasizeaneconomic(orsociological)explanation for the failureof the innovation tobetakenupinstantaneouslyanduniversallyassoonasitwasintroducedinanyparticularregion.Itisreasonabletosupposethatsuchemphasiswasnotthoughttobenecessary,inviewofthecompellingempiricalpatternsexhibitedinthatfamouschartoftheS‐shapedcurvestracingtherisingproportionof corn acreage planted with hybrid seed in each of the major‐corn growing states. There are,however,severalpassagesthatclearlyindicateGriliches’viewthattheuncertaintiessurroundingthedecisionas towhether toadoptanovelmethodofproduction,suchashybridcorn,couldnotbeimmediatelydispelled;itwouldtaketimeforfarmersindividuallytoaccumulateinformationthatsuccessivelyreinforcedconfidencetheinnovations’allegedbeneficial(profitable)properties.Hereisthewayheputsit(Griliches,1957,p.516):“Also,inaworldofimperfectknowledge,ittakestimetorealizethatthingshaveinfactchanged.Thelargertheshift thefasterwillentrepreneursbecomeawareofit,“finditout,”andhencetheywillreactmorequicklytolargershifts.”

Attheendofthatsentenceappearafootnotethathasbeenlargelyoverlookedbymostofthecommentaries on this frequently citedpaper, butwhich is nonetheless significant in reveal thatGrilichesenvisagedtheindividualprocessofdecisionmakingunderuncertainlyasinherentlytimeconsuming, because sufficient confirmatory data had to be accumulated in order to justifyabandoninganestablishedroutine.Heexplicitlyreferstothestatisticalmethodofsequentialsampleanalysis for quality control decision, and the procedure for this (based on the Average SampleNumber)thatWald(1947)haddevised,takingthatassupportforhisinterpretativehypothesisthattherewouldbeaninverseassociationbetweenthesizeofthestimulus(intheformofdifferentiallygreaterprofitability)andlengthoftimethatwouldelapsebeforetheadeliberatingfarmerrespondedbyacceptingthenewmethod.TheAverageSampleNumberastheexpectednumberofitemsthatwouldneedtobesampledforagivenbatchbeforebeingable(withaspecifiedlevelofconfidence)torejectthebatchasbelongingtoa loweraveragequalitypopulationthanthestandardthatwasdesired.Grilichesthuslikenedthefarmer’sdecisionunderuncertaintytoaqualitycontroldecision,inwhichinformationwouldhavetobeaccumulatedsequentiallyinordertoattaintherequisiteASNfordiscardingopenpollinatedcorninfavorthethehybridalternative::

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“ThisisanalogoustotothesituationinSequentialAnalysis.TheASN(averagesamplenumber) isan inverse functionof,amongother things, thedifferencebetween thepopulationmeans.Thatis,thelargerthedifferencebetweenthetwothingswhichwearetesting,thesoonerwewillaccumulateenoughevidencetoconvinceusthatthereisadifference.”Griliches(1957:p.516,n.33)

AnumberofnotablepointsemergefromcloserconsiderationofGriliches’somewhatarcanestatistical analogy.First, thisexplanation for thephenomenon thatnewandsupposedly superiormethodsarenotadopted instantaneously is fullyconsistentwithGriliches’ approach toadoptionphenomena as reflecting rational decision‐making – in this caseunder conditionsof uncertainty.Secondly, insofar as there is a decisionmodel, it is framed at the individual level and thereforeinvokesarepresentativeagent’sbehaviortoexplainwhytheobservedtransitiontohybridcornbyatypicalfarmerwouldbefoundtoproceedmorequicklywheretheprofitdifferentialofferedbytheinnovationwasbigger.Notably,thereisnoindicationthatthearrivalofconfirmatoryinformationisavariablethatcoulddependuponinteractionsorcommunicationsamongneighboringfarmers;inthesequentialanalysisset‐upthedecisionisbeingmadecompletelyindependentlyofothers,andbasedentirelyonthereceiptofinformationthatisgeneratedautonomously–perhaps,intheactualcaseathand,beingbroadcastbytheUSDAagriculturalextensionservice.

Thirdly, micro‐level explanatory framework accounts for the delay in adoption, and fordifferencesinthelengthofthatdelayfollowingtheintroductionofanadapted(andhenceprofitable)hybridintheregion.Butthisdoesnotexplainthephenomenonofacontinuousriseintheproportionoffarmersthathavejoinedtheranksoftheadopters.Somethingismissing,withoutwhichthetimepath of diffusion a given corn‐growing region would take the “bang‐bang” form of adjustment:nothingwouldhappenfollowingtheintroductionoftheinnovation,andeventuallyallthefarmerswouldadoptatonce–supposingtherewasnoconstraintontheavailablesupplyofthehybridseeds.6

Fourthandlast,theproximatesourceofthisproblemistherepresentativeagentapproachthathasbeenseentobeimplicitinGriliches’interpretationofhisempiricalresults.Ifthedecisiontoadoptaninnovationposesabinarychoice,then,inordertoaccountforthecontinuityoftheobservedtransitiontoawidespreadacceptanceofthenewtechnologyamongthepopulation,itisnecessaryto posit some heterogeneity among the agents. Within the framework suggested by Griliches’discussion of sequential analysis, one could readily introduce differences in the rate at whichinformationwouldreachdifferentfarmers;orsupposethatthelossfunctions,orconfidencelevelscharacterizingdifferentagentswouldresultinacontinuousdistributionofaveragesamplenumbers,sothatifbroadcastmessagesaboutthebenefitsofswitchingtohybridcornwerereachingeveryoneat the same rate, the dates at which different farmers attained their respective ASNs would bedistributedcontinuouslythroughtime.But,thepullofrepresentativeagentmodellingwasstrong,andthepathtowardsmodelsbasedonexplicitrecognitionofheterogeneitiesinthepopulationofpotentialadopterswasnottakenimmediatelybytheeconomistswhofollowedGriliches’lead.

6Strictlyspeaking,thiswouldnotnecessarybethecase,givenGriliches’choiceoftheproportionofregionalcornacreageplantedwithhybridcornseedsasthemeasureoftheextentofdiffusion.Theadoptiondecisioncouldbetoplantsomeofthefarm’sacreagewithhybridcorn,andadjustthisupwardsovertime.Thereforethebinarydecisionframeworkdoesnotnecessaryapplyinthesecircumstances,whereasitwouldiftheindexofdiffusionmeasuredtheproportionoffarmsorfarmersonwhichhybridseedhadbeplantedatall.Mansfield(1963a,1963b)distinguishedbetweeninter‐firmandintra‐firmdiffusion,withappropriatedifferentmeasureoftheextentofadoption.

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2.2 Towardbehavioralinterpretations:the“contagionmodel”emerges

Notlongthereafter,EdwinMansfield’s(1961,1963a,1963b,1966,1968b)inquiriesintothediffusionof industrial innovationsbegan toerectan impressiveempiricaledificebyapplying thedescriptive statistical approach that Griliches (1957) had pioneered. Mansfield (1961) venturedbeyond Griliches’ work, by proposing a formal economic rationale for his econometric studies’employmentofthelogistic formincharacterizingthetimepathofmeasuresoftheproportionateextendofdiffusion‐‐explicitlyhypothesizingthatinformationimperfectionseffectivelyconstrainedadoption,butwouldbegraduallyeliminatedasknowledgeaboutoftheinnovationbecamemoreandmorewidelydisseminatedbysocialcommunicationwithintherelevantcircleofpotentialadopters.Thesupposedmechanismofdisseminationwasasocialcontact,‘word‐of‐mouth’transmissionoftherelevantknowledge,ratherthanonebaseduponeconomicconsiderationofthebenefitsandcostsofsearchesforinformationfirmsforwhichthenewindustrialprocesseswerepotentiallyrelevant.Thiswasviewedasnatural, andessentially costless,unlike thebroadcastingof informationabout thebenefits of the innovation by the producers and vendors of the inputs that would enable theinstallationandoperationoftheoftherequirednewfacilitiesandmethod’soperation–knowledgeintermediaries such as the publicly funded agricultural extension agents, and the marketingpersonneloftheprivatehybridseedcompanies.

Ratherthantryingtoexplainwhysuchinformationseemedtoflowalongparticularchannelswithinanetworkofsocialcommunications‐‐ofthesorttowhichstudiesbyruralsociologists’tendedincreasinglyassignimportance,(1961:pp.746‐748)producedaversionoftheso‐called‘contagion’modelofinformationdiffusion,bystartingfromageneralconceptualizationinwhichtheprobabilityofadoptionisafunctionofperceptionsofthemagnitudesofthegreaterprofitabilityenjoyedbyusersof the innovation interacted with information about the extent of its adoption among others(“competitors”)intheindustry,andworkinghiswaytowardthewell‐knownseparableformofthedifferential equation for the logistic “information propagation” process.7 This classic “socialcontagion” or random “word‐of‐mouth” process of information dissemination, separates theexpected effect upon a non‐adopter of learning about the relative advantages of an innovativemethodfromthelikelihoodofanon‐adopter(inasymmetricallyinteractiveandcompletelyinter‐penetrating population of agents) becoming informed by others about the innovation’s putativebenefits.8

7ThisderivationinvolvedbeginningwithaTaylorseriesexpansionofangeneralmultivariatefunction,andproceededbysuccessivearbitrarysuppressionsofhigher‐orderterms,andanequallyadhoc impositionoflimiting initial conditions, to arrive eventually at a deterministic expression for the increased number ofadopterswhoseseparableformexpressedtheprobabilityofanincrementaladoptionastheproductoftwocomponents:theprobabilityofarandomlydrawnagentbecoming informed,andtheconditional likelihoodthataninformedagentwouldbecomeanadopter.TherationaleforthiscumbersomeprocedurenowhereisstatedbyMansfield.Butitspalpableeffectistoconveytheappearanceofarrivingatthelogisticregressionmodelfromacompletelygeneraltheoryoftherepresentativefirm’sadoptionbehavior,ratherthanfromthebehavioralhypothesisthatthehazardofthemarginal“hold‐out”adoptingtheinnovationisatime‐invariantfunctionofinnovation’scomparativeprofitability(and,possiblysomeconstraints).Thisroutetothelogistic,asfarmoredirect,asthefollowingtextpointsout.But,whateverthereasonforMansfield’smoreroundaboutapproach,itseffectenhancedthecontrastbetweenhiscontributionandtheearlierpaperofGriliches(1957).8 This and othermore complicated, mixed broadcast and social contagion processes originated andwereelaboratedinthefieldofmathematicalepidemiology‐‐notablybyBailey(1957),uponwhoseworkMansfield(1961) had drawn. See also, Bailey (2nd Ed., 1975) for further refinements. The implicit constrast with“completelyinterpenetrating”isapopulationthatisstratifiedbysocialclass,income‐relatedstatus,orother

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Bypositingthatinformationistransferred(asaninfection)throughrandomsocialcontactsbetweenthosewhohadalreadyadoptedtheinnovationandthosewhohadnot,onearrivesalmostimmediatelyatthedifferentialequation:dP=n{P(1‐P)},whereP isthemeanprobabilitythatarandomly drawnmember of the population of potential adopterswill already have adopted theinnovation and hence possess information as to its benefits. Under conditions of complete andrandomsocialinter‐mixing,theproductterm{P(1‐P)}istheprobabilityofarandomdyadiccontactateach“moment”thatwillalterthenon‐adopter’sinformationstatetothatof“sufficientlyinformed.”If the constantn is themean probability that a newly informed non‐userwill join the ranks ofadopters, the left hand‐side of the equation represents the resulting increase in the expectedincrementintheshareofadoptersamongthepopulation.9ThenP(t),thusdefined,isameasureofDn(t) the extent of the innovation’s diffusion at time t, and so, by integration of the differentialequationfordP/dt,onemayarriveimmediatelyattheresultthatDn(t)isalogisticfunctionoft,withslopeparametern.

MansfieldthencouldfollowGriliches’(1957)empiricalstrategyandhisgeneralemphasisonthe centrality of profitability considerations in adoption behavior, hypothesizing that whereexpected profitability of adoptionwas higher, therewould be a highermean probability that aninformed non‐adopterwould immediately accept the innovation.10 He first foundn as the slopeparameterof the logisticequations fittedbyweighted leastsquaresregression to the time‐seriesobservationsontheactualextentofdiffusion(Dn(t))foreachof12processinnovationsthathadbeenintroducedintheperiodbetween1900andtheimmediatepost‐WorldWarIIyears,andeventuallywereadoptedbyallthemajorfirmsin4industries‐‐rangingfrombituminouscoalmining,tobeerbrewing,ironandsteelandrailroads).

Mansfieldtookasameasureofthe“profitability”ofthei‐thinnovationinthej‐thindustrytheinverseoftheratiobetweentheaverage“payback”periodthatthemajorfirmsinthej‐thindustryhad experienced when they installed that innovation (for all the major firms in his dataset dideventually adopt these technologies), and the average payback period that his managementinformantsfromthatindustryreportedwasusedbyfirmsinevaluatingallsuchinvestmentprojects.Thiswasoneofapairofright‐handvariablesheenteredinalinearregressionmodeltoaccountforthevariationsamongtheinnovationsinthe(slopeparameter)estimatesoftheirrespective“speedofacceptance”(touseGriliches’terminology)‐‐orwhatMansfield,focusingupontheadoptingfirms,termedthe“rateofimitation.”Thesecond“explanatory”variablemeasuredtherelative“lumpiness”oftherequiredinvestmentoutlayastheratiobetweentheaverageinitialexpenditureforthei‐thinnovation in the j‐th industry and themean asset size of themajor companies in that industry. ascriptive bases for preferential social attachments, or otherwise partially “balkanized” within essentiallydisconnectednetworksofcommunication.Coleman(1964:Ch.17)treatsthemathematicsofsuchprocessesundertheheadingof“diffusioninincompletesocialstructures”.

9If0<n<1,asisusualinthesemodel,inthedeterministicequivalentversionofthesemodelsonemustallowthepossibilitythattheaverage“contacted”agentwillhavebeencontactedandhence“informed”but(withsomepositiveprobability)remainanon‐adopter.Implicitlyitisassumedthattheinformationaleffectofthecontactisimmediatelydissipated,sothattheexpectedeffectofthenextcontactisthatsameasthatofthefirst,oranyamongthosethatprecededit.Theforegoingtextisphrasedaccordingly.

10Mansfield(1961:p.746)offeredthesamerationaleforthehypothesizedeffectofprofitability,referringtoGriliches’ (1957) study: “As the difference between the profitability of this investment and that of otherswidens, firms tend tonoteandrespond to thedifferencemorequickly.Both the interviews [theMansfieldconductedwithindustrypersonnelfromwhomheobtainedsomeofhisinnovationspecificdata,e.g.,onthepaybackperiod]andthefewotherstudiesregardingtherateofimitationsuggestthatthisisso.”

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Mansfield(1961:p.747)includedthisvariableontheargumentthat“firmstendtobemorecautiousbeforecommittingthemselvestosuchprojectsandthattheyoftenhavemoredifficultyinfinancingthem.”

Totesttheabilityoftheforegoingpairofindustry‐specificvariablestoaccountfortheinter‐innovation variations in the speed of imitation,Mansfield estimated the linear (log‐odds logistictransform) regressionmodel for the 12 “rate of imitation” (slope) parameters, constraining thecoefficientsonthesevariablestobethesameforeachoftheinnovationsadoptedwithineachoftheindustries.11Findingastatisticallysignificantnegativeestimateofthecoefficientforthis“investmentsize”variable,alongwiththesignificantpositiveregressioncoefficientfortherelativebrevityofthe(expost)“paybackperiod”,Mansfieldconcludedthat–someunexplainedinter‐industryvariationsnotwithstanding–thehypothesisthatprocessinnovationsdiffusedintousemorequicklywhentheyweremoreprofitable,holdingconstantthegreaterrisksandfinancingconstraintsassociatedgreaterrequiredinvestmentsize,stooduptothedata“surprisinglywell.”12

2.3GrilichesandMansfieldandthe‘disequilibrium’conceptualizationofdiffusion

11ThisparalleledtheprocedureofGriliches(1957:TablesVI,VII),inconstrainingtheestimatedeffectsonthelogistic slope parameters of the variables (average corn acreage per farm, pre‐hybrid average yields, etc.)indicativeofhybridcorn’sdifferentialprofitabilitytobeconstantacrossthestates,andacrosscrop‐reportingdistricts.

12Describing this approachasbasedupon the “deterministic” versionof the information contagionmodel,becauseitsoughttoexplaintherateofimitationbasedupon(thelogisticparameterestimatedfrom)theactualtimingofadoptionsbyfirmsinthecaseofeachinnovation,Mansfield(1961:sect.6)triedasecondeconometricstrategy, estimating a “stochastic version” of themodel. In effect, thismethod obtained an estimate of the(hypothesized)aconstanthazardofadoptionfromthemeanoftheobservedproportionsof(previous)non‐adoptersthatjoinedtheranksofadoptersateachsuccessivedate.Mansfield(pp.359‐360)reportedthattheexpectednumberofnewadoptersateachdate,obtainedbyusingthatvalueoftheslopeparameter,showedgreaterdeviationsfromtheactualobservationsthantheresidualsobtainedfromtheweightedleast‐squaresestimates of the (deterministic) logistic model; but that the results of regressing the estimated slopeparametersforeachinnovationontheprofitabilityandinvestmentsizevariableswerevirtuallyidenticaltothosehehadobtainedbyweightedleastsquaresregressionestimationofthelog‐oddsequation.Thereisasmall detail of econometric methodology that differentiates Mansfield’s empirical approach from that ofGriliches,butappearstohavepassedwithoutnoticeinthesubsequentliterature.WhereasGriliches(1957:p.505)explicitlyjustifiedhisuseofthelogisticcurvesimplyasadescriptivedevice(reducinganextensivebodyofdatatothreesetsofparameters–origins,slopesandceilings,Mansfieldpresentedhisregressionmodelasbaseduponthe“deterministic”logisticequationderivedfromabehavioraltheoryofdiffusiondrivenbysocialcontagion,addingadisturbancetermtothelog‐oddstransformationoftheequationfortheexpectednumberofnewadoptersineachperiod.Inthiscase,however,mimimumChi‐squareestimationwouldhavebeenmoreappropriatethanthemaximumlikelihood(weightedleastsquares)estimationprocedurethatMansfieldhademployed,inviewoftheproblemofserialcorrelationthatwouldbeinducedbydisturbancesinthebehaviouralmodel(seeBerkson(1955):thus,anegativeshockattwouldreducethenumberofadoptersinthepopulationatt+1,which–underthehypothesizedinformationcontagionprocess‐‐wouldresultinasmallerexpectednumber of new adopters at t+1. Onemay note that during the early phase of the process (i.e., before theinflectionpointofthelogistic)thepersistingnegativeeffectsofanegativeshockswouldbegreaterthanthepersistingcorrespondingeffectsofashockofequalmagnitudebutoppositesign,sothatinadditiontoserialcorrelationof thedisturbancesauniformdistributionof randomdisturbancesalsocouldgiverise tosomedegreeofheteroskedasticityintheresiduals,but.howseriouslyMansfield’sestimateswereaffectedbytheseproblemsremainsunclear.

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Two sets of remarks now are in order concerning the foundational phase of empiricalresearchontheeconomicsoftechnologydiffusion,representedbytheworksofGriliches(1957)andMansfield(1961).Thefirstoftheseconcernstheroleassignedtoinformationalconstraints,andthereliance upon the passage of time as a proxy for the unobserved improvements in the state ofknowledge among the population of potential adopters about the economic benefits of theinnovation. The second concerns the assumption that the population of firms (and farms) isessentiallyhomogeneousinregardtotheirsituations,exceptinregardtotheirinformationstate,sothatarepresentativeagentmodelissufficienttocharacterizeindividualbehaviorandthetranslationbetween the analysis ofmicro‐level behavior and phenomena observed at the aggregate level ofindustriesorsectorsiseasyandimmediate.Whilethesecommentsmightbereadascritical,theyarenot“faultfinding”andtakenothingawayfromtheseminalachievementsofthepioneersinthisfield.Rather, thepurposehere is to indicatehowthesubsequent flowofanalyticalandempiricalresearch contributionswas channeled by the paths that had been opened during this formativephase,andthosethatremainedtobeexplored.

2.3.1Informationpropagationandtimeinthediffusionofinnovations:

InhisbriefcommentsonDixon’s(1980)“revisit”tothesubjectofthediffusionofhybridcorn,Griliches(1980:pp.1463‐1464)remarksthatsincemuchoftherelevantdatadescribingandaffectingindividualadoptersofnewtechnologiesareunobservable,“timewasbroughtintotheanalysisasaproxy” for one or another of the forces thatwere viewed to be responsible for the innovation’sgraduallywideningacceptance.Hisownworkisdescribedashavingfeaturedthe“‘disequilibrium’interpretation”of thesituationcreatedbythe introductionofcommerciallyavailablehybridcornseed in each region, and taking “time” to proxy for “the spread of information about the actualoperating characteristics of the technology and the growth in the available evidence as to itsworkabilityandprofitability.”Thesameapproach,takingtheadopters’informationstatestosubjecttoalterationwiththepassageoftimecharacterizedMansfield’sresearch,althoughheexplicitlycitedsocialcommunicationsasinfluentialsourcesofinformationtransmissionfrom(successful)adoptersto non‐adopters, whereas Griliches (1957) remained non‐committal about the specifics of theinformation‐transmissionmode.Rather,ashasbeenseen,Griliches’ reference to the “ASNeffect”implies that the content of the information would affect the representative agent’s speed ofacceptance of the innovation, whatever the source: the larger was the associated profitabilityadvantagereportedby the flowof information, the fewerwouldbe theexpectednumberofsuchreports(i.e.,theaveragesamplenumber),and(bysurmise)theshorterwouldbethetimerequiredtopersuadetheindividualtoadopttheinnovationinquestion.13

The contrast between theway these two foundational research contributions treated thequestionofhowthesupposedinformationconstraintuponadoptioncametoberemovedmaywellhavereflectedadifferenceintherealitiesofthesituationstheystudying,andconsequentlyinthesource materials that were available in each case. Footnote reference in his article footnotereferencesleavelittleroomfordoubtthatGrilicheswasthoroughlyawareoftheexistenceofactivebroadcastsourcesofinformationabouttheadvantagesofhybridcornemanatingfromtheU.S.D.A.agricultural extension service and the private seed companies; whereas nothing of equivalentsalience is inevidenceregarding “marketing”effortsby thevendorsofanyamong thediverseof

13Uniformmessagingspeed,independentofthecontent,isthereforeimpliesbythis–andthesocialcontagionmodels,anassumptionthatisquiteplausiblewhenconsideringdiffusionphenomenathatextendoveraspanofmonthsorseveralyears.But,whentheprocessofacceptancestretchesoverdecades,thetime‐invarianceassumptionbecomesmoredubious.

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processequipmentembodyingtheindustrialinnovationsstudiedbyMansfield.But,perhapsmoresignificantly,thelatter’sproposalofan“informationcontagion”interpretationofthedeterministiclogisticequationappearstobeenshapedatleastinpartbythepublication‐‐coincidentintimewithGriliches (1957) ‐‐ of Coleman, Katz and Menzel’s (1957) article on the adoption of the broadspectrumantibioticTetracyclineamongprescribingphysiciansinaNewEnglandcity.14Thiswasthefirstinalineofinfluentialquantitativesociologicalstudiesbytheseauthorsthatfocusedontheroleinthediffusionofinnovationsofpersonalcommunicationsand“socialcontagion”processes.15

There is nothing to suggest that Mansfield equated the circumstances of the medicalinnovationstudiedbyColeman,KatzandMenzel(1957,1966),andtheirconclusionsabouttheroleofword‐of‐mouthtransmissionofinformation,wereimmediatelygermanetotheeconomicorsocialcircumstancesoftheindustrialinnovationsinhissample.16Themarkeddifferencesbetweenthe6‐monthperiodwithinTetracyclinewentfrommarginalacceptancetonearuniversaladoptionwithinthe communitiesofphysicians studiedbyColeman,Katz andMenzel (1957,1966), anddiffusionprocessesthatMansfield’sdatadescribedasextendingnotonlyforyears,butoverdecades,wouldbeenoughtoraisedoubtsthatsameunderlyingdynamicofinformationpercolationwasresponsibleinallofthem.17Mansfielddidnotremarkonthatparticulardisparity,however,butremarked(1961:p.744,andn.8)thatwhilethediffusionofanewtechniquegenerallywasaslowprocess,therewerewidevariationsamonginnovationsinthe“rateofimitation”:onaverage7.8yearselapsedfollowinganinnovation’sintroductionbeforehalftheindustry’s(major)firmshadadoptedit,buttherangeof 14Mansfield(1961:pp.745‐746)referencedthisworkinsupportofhisargumentthatadoptionswouldbecomemorelikelyas“asmoreinformationandexperienceaccumulate,”adding:“Competitivepressuresmountand“bandwagon”effectsoccur.Wheretheprofitabilityofusingtheinnovationisverydifficulttoestimate,themerefact that a large proportion of its competitors have introduced itmay prompt a firm to consider it morefavorably.” This, however, says nothing explicit about social communications, and the footnote discussion(p.746,n.8)focusedon“thesnow‐balleffect”notedbyColeman,etal.,remarkingthe“almostalltheexecutivesweinterviewedconsideredthiseffecttobepresent.”

15Coleman,KatzandMenzel(1957),andtheimmediatesequelinKatz(1961),representedthefirstfruitsofaneffort to substantiate thecontention inKatzandLazarsfeld (1955) thatpersonal communicationswereanimportant influence in individuals’ willingness to try new products. A more elaborate monograph onTetracycline’s adoption among the physicians in four small Illinois cities, was published subsequently byColeman,KatzandMenzel(1966)underthetitleMedicalInnovationandbecamewidelyinfluential.ashavingestablishedthecriticalroleinformationpropagationbyofword‐of‐mouththroughsocialnetworks(see,e.g.,Rogers,1995).

16Indeed,Mansfield’s(1961:p.746,andfn.8)referredtothisarticleinthecontextofarguingthat“themerefactthatalargeproportionofitscompetitorshaveintroduceditmaypromptafirmtoconsideritmorefavourably,”andinthefootnotecommentedonlythat“Coleman,etal.[6]noteda‘snow‐ball’effect.Forwhatitisworth,almostalltheexecutivesweinterviewedconsideredthiseffecttobepresent.”

17EvenwithinMansfield’scollectionofinnovation,therearelargevariationsaroundthemeandurationofxyearsfromfirstintroductiontoadoptionbyallthe(major)firmsintherespectiveindustries–thepopulationforwhichMansfield’sdiffusionmeasureswerecalculated.Forexample,fromthegraphsinMansfield(1961:Fig. 1) is seen that 30 years or more elapsed before all among the major railroads had adopted installcentralizedtrafficcontrol,andautomaticcarretarders;thatwasthecasealsoregardtotheacceptanceofby‐productcoke‐ovens,thecontinousannealingprocessbythemajorironandsteelfirms:whereas10yearsorfewer elapsed before all the major firms had installed the pallet‐loading machine, the tin container, andcontinuous mining machinery. These variations did not merely reflect inter‐innovation differences in theextremeright‐handtailofthedistributionofadoptionlags(measuredfromtherespectiveintroductiondates.Halfofthemajorpig‐ironproducerswereusingby‐productcokeovenwithin15years,whereashalfofthemajorcoalproducerswereusingthecontinuousminingmachinewithin3years.

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inter‐innovationvariationaroundthatsamplemeanwasfrom0.9to15years.Onemightwonderhowplausibleitistosupposethat15or16yearselapsedbeforethelasthalfofthemajorpig‐ironproducers heardbyword‐of‐mouth about the proven advantages of installing by‐product cokingovens,whereas only5 yearswere required for the correspondingmessage about thebenefits ofcontinuousminingmachinestopercolateintothenon‐adoptinghalfofthemajorcoalcompanies.

Nevertheless,Mansfield’sempiricalstrategysoughttoaccountforthosevariationsintermsofdifferencesamongthe(fixed)characteristicsoftheinnovationsthatwouldaffecttheprofitabilityand,recognizingthatinstallationoflumpyindustrialfacilitieswasrequiredinsomecases,therisksor financing obstacles involved in their installation. This supposed (implicitly, in endorsing the“contagion” model) that when an innovation was insufficiently attractive to win acceptance bysubstantialportionoftheindustry,itwouldtakelongerfornon‐adopterstogetthenews,andasmallproportionofthosewhowouldactuponitpositively.

The“epidemic”or“socialcontagion”modelofdiffusionhasgainedanenduringplaceinboththeeconomicandthesociologicalliteraturesontheadoptionofinnovations,and,withoutwarrant,asbeenseenisnowcasuallyassociatedwithmicro‐levelbehavioralinterpretationsthatareadducedto account for both Griliches’(1957) and Mansfield’s findings about the relationship betweenprofitability and speed of acceptance or imitation. Moreover, in view of the foregoing skepticalobservationsconcerningtherelevanceofinformation‐constraineddelaysinadoption–whichwouldhavehadtopersistfordecadeswithinsomeindustriesbeforegraduallybeingallieviatedthroughtheslow dissemination of knowledge carried by word‐of‐mouth ‐‐ this represents one of moderneconomics’moreremarkabletriumphsof“nicetheory”over“empiricalplausibility.”

2.4Conflictsovereconomicrationalityandtheheterogeneityofpotentialadopters

AsecondfeaturethatGriliches(1957)andManfield’s(1961)contributionsshare,inadditionto(andasthedualof)theircommonemphasisontheslowpercolationofinformationrequiredtopersuade rational managers of the benefits of new techniques, is that both worked within arepresentativeagentframework.Consequently,theirexplanationsofthediffusionphenomenapaidlittleifanyattentiontotherolethatcouldbeplayedbytheexistenceamongtheagents(farmersorfirmmanagers)populatingtherelevant industriesofdifferencesbearingupontheprofitabilityofadoptingaparticularinnovationatagivenpointintime.

ThiscommitmenttotherepresentativeagentmodelingapproachlurkedbeneaththesurfaceofthecontroversiesintowhichGrilichesfoundhimselfdrawnbythereactionsofruralsociologiststohisEconometricaarticle. Theinterestofeconomistsinthetopicofdiffusionoftechnology,andtheirappreciationofyoungGriliches,undoubtedly,wasraisedfurtherbythatcontroversyandtheconfidentanddeftwayinwhichhedeflectedthepointsofhiscritics.Grilicheshadpresentedassocompellingtobebeyondcavilhisconclusionsthat“takingaccountofuncertaintyandthefactthatthespreadofknowledgeisnotinstantaneous,farmershavebehaviedinafashionconsistentwiththeidea of profit maximization.” But he e may have underestimated the extent to which his plainexpressionofthemwouldbereadinsomequartersasfightingwords.Anyway,hereiswhathesaidinafootnoteattheveryendofthe1957paper:

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“Itismybeliefthatinthelongrun,andcross‐sectionally,[sociological]variablestendtocancelthemselvesout,leavingtheeconomicvariablesasthemajordeterminantsofthepatternoftechnologicalchange.”

Among rural sociologists, and especially those approaching the study of diffusion in theresearch tradition that had developed from Ryan and Gross’s (1943) pioneering study of Iowafarmers’responsestotheintroductionofhybridcorn,thosefightingwordswouldcontinuetorankleformanyyearsafterwards.TheyarequotedinthereviewofthiscontroversythatappearedinEverettM.Rogers’subsequentsurveysofresearchonthediffusionof innovations18—tobe immediatelydismissedinthosepagesasexemplifyinga“ridiculous”subscriptiontothenaievehomoeconomicusconceptualizationpopularamongmembersofthe“ChicagoSchool.”Intruth,Rogers(1983,andinthe two preceding editions of that book) completely missed the point of the position taken byGriliches(1957,1960,1962)inturningasidethecomplaintsofthiscritics.Howeverrashlyphrased,hispartingremarksinthe1957articlereallywerenotaboutwhetherhumanactionwasorwasnotinfluenced by non‐economic considerations; instead, they concerned the statistical question ofwhethernon‐economic influencesupon individuals’behaviours weresufficientlycorrelatedovertime,orinthecross‐section,toexertasignificantinfluenceontheobservedaggregateoutcomes.

AtleasttwoaspectsofwhatpassedbetweenGrilichesandtheruralsociologistsinthatnowremote controversy over the diffusion of hybrid corn usefully be “revisited” in the presentconnection.ThefirstexposesmorefullypointsofcommonalityaswellasthedisagreementsbetweentheapproachtodiffusionphenomenainwhatbecametheGriliches‐Mansfieldtraditionineconomics,andthedefendersoftheruralsociologicaltradition.Thesecondilluminatestheeventual,reflectiverapproachment with the sociologists’perspective that that can be read in Griliches (1980)“Comments”onRobertDixon’s(1980)paper“HybridCornRevisited”.

In the following paragraphs these two threads are taken up in turn, and shown to beentangledintheirimplicationsforthewaythateconomicresearchondiffusionhasdevelopedfromtheseedsplantedbyGriliches.Thereis,inaddition,animportantrelationshipbetweenthetwopoint,inasmuchasbothwerecompletelyalignedwiththesameimplicitly“pro‐innovation”dispositionthatcanbefoundinthestudiesbyGriliches,andlaterbyMansfield–and,forthatmatter,intheresearchtraditionondiffusionestablishedamongruralsociologistsintheU.S.Thecommonviewwasthattheinnovationinquestion,whetheritwasboilingdrinkingwater,plantingsorghum,tractor‐ploughing,or theoxygenprocess in the ironandsteel industry,wasuniversallysuperior insome importantobjective sense vis‐à‐vis the “traditional” techniques that were in used farms or firms underexamination. Further, that superioritywas taken to be established from the firstmoment of theinnovation’s introduction, and to persist thereafter. Implicitly this assumed away objectivedifferencesinthecircumstancesofpotentialadoptersthatmighthaveabearingontheir(rational)decisions.

The issue in contention between the rural sociologists and Griliches’ supporters andfollowers, therefore, was simply whether or not the index of that superiority was comparativeprofitability. Yett, there was nothing in the structure of Griliches’ (1957) presentation of thedescriptive,statisticalmodeloflogisticdiffusionitselfthatconnectedrelativeprofitabilitydirectlytothepaceofdiffusionasmeasuredbytheestimateoftheslopeparameterofthelogisticcurve.Thelogistic formwas an a priori specification that had yet to be statistically against other possiblediffusion paths. Mansfield’s proposed interpretation, which suggested that relatively higher 18See,forexample,Rogers(1983:pp.32‐34,56,214‐215).

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profitabilitywouldincreasethelikelihoodthatinformedpotentialadopterwouldactuallyaccepttheinnovation,afterlearningaboutitfromacurrentuser,alsowasnottestedempirically;althoughitmighthavebeen,byconsideringwhethertheorderofadoptionofagiveninnovationwaspositivelyassociatedwithitsrelativelyprofitabilityfortheadopters.19

2.4.1‘Congruence’,‘compatibility’andvariationsinadopter’sobjectivecircumstances

The second point to be noted concerns the awkward implications that follow fromacknowledging,asGriliches’rejoinderhaddone,thataninnovation’sprofitabilitymightbeaffectedbyits“congruence”and“compatibility”withotherelementsintheestablishedfarmingregime–asthesociologistshadcontended.Inotherwords,thecomparisoninthecaseunderdebatemightnotbeproperlycharacterizedmerelyby lookingat thecostsandyieldsofhybridcornseedsandtheopen‐pollinatedalternatives.

Hybridization in effect had created a more efficient pump for nutrients, and, as theagriculturalextensionofficersofthedaywereexplainingtofarmers–albeitindifferentterms–thispumpwouldnotdeliverwhatitcouldunlessitfirstwasproperlysetup.Chemicalfertilizerswouldhavetobesupplied,andthatmeantfertilizertankswouldneedtobepurchasedandinstalled;morewaterwouldberequiredtogoalongwiththefertilizer,andthatmightmeandiggingnewwells,orotherwiseimprovingirrigationcapacity.Providingmorenutrientswouldheightentheproblemofweeds, and so chemical or mechanical means would need to be introduced to suppress thesecompetitorsfortheexpensivenourishmentthatthehybridplantsweresupposedtopumpup.Eventhatwasnottheendofthematter.Inadditiontothedirectfinancialcostsofthosefixedinputs,accesstoworkingcapitalwouldbecriticalwhenawholesaleswitchwasmadetohybridseed,becauseifbadweatherorpestsspoiledtheharvest,thewherewithaltopurchasenewseedforfollowingyearwouldbecomeacriticalconditionforthefarmfamily’ssurvivalontheland.

Looked at from this angle, the “representative agent” version of Griliches’ “profitabilitycounts”storyabouthybridcornappearsrather too facile.Objectiveeconomicdifferencesexistedamong the farmsof theMidwest in thisera,quitenoticeably in regard to their currentand theirexpected futurecornacreage, the termsof theiraccess tobank finance, their family laborsupplysituation,andalsointheeducationalattainmentsofthefarms’operators–whichmightwellaffecttheir capabilities to grasp and manage critical aspects of the new, more intricate system ofcultivation.20Surelytheheterogeneityofthepopulationintheserespectsmightbeexpectedtoshowupincost,realizedyield,andfarmrevenuedifferences.Hence,bytheverysameargumentthatZvihadusedtodeflectthecriticismsfromhissociologicalantagonists,thedeterminantsofperceivedprofitabilitymightwellbesaidtogoverntheextenttowhichtheinnovationwouldbeadoptedwithinafarmingcommunity.Butprofitabilitywasnotsimplyafunctionofseedyieldsandpricesthatwereessentiallythesameforeveryone.

Supposing,then,thatawarenessoftherequirementsforcommerciallysuccessfuldeploymentofhybridcornhadbecomethoroughlydisseminatedasaresultoftheeffortsofthoseagriculturalextension officers, there could nonetheless be “rational non‐adopters.” If that was the case, 19 Instead,Mansfield (1968) studied a number of different innovations, and sought to relate the speed of(logistic) adoption to characteristics of the typical firms in the industry that couldbe viewed as having abearingontheprofitabilityoftheinnovationinquestion.

20ThesignificanceofhumancapitalintensityamongthesourcesofthegrowthofU.S.farmproductivitywouldemergeasanotablefindinginGriliches’(1964),anaggregateproductionfunctionstudy.

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somethingelseintheobjectivesituationwouldhavetochangeinorderfortheretobethefurtherexpansionintheproportionofacreageunderhybridcorn.That,atleast,wasthewayitappearedtothiscity‐boywhen,withouteverhavingsetfootonanIowacorn‐farm,hestartingtothinkaboutthedeterminantsof thediffusionof grainharvesting in the antebellumMidwest, and cameupon thedebatethathadgoneonbetweenGrilichesiandhiscritics.21

Therewasanotherbothersomematter—notunrelatedtotheonejustnoticed,buthavingtodowiththeneatempiricalstrategythatGrilicheshaddevised.Thefamilyofdiffusionpathsexhibitedinthe1957papersclearlyisanartifactoftheU.S.DepartmentofAgriculture’sstatisticalreportingpractices:totalcornacreageundercultivation,andacreageunderhybridcornwerecollectedatthecountylevel,aggregatedandpublishedforthestates.Surelythesepoliticalunitshadtobeviewedasratherarbitraryaggregationsfromaneconomicstandpoint;therewerenotevenanyapparentstate‐level farmpolicy issues thatwould render it of economic interest to concern ourselveswith thedynamics of the diffusion of hybrid corn on a state‐wide basis. But, what was the theoreticallyappropriatelevelofaggregation?Supposingthatthedatacouldbeobtainedonacounty‐by‐countybasis,wouldthatbeamore‘natural’populationunitwithinwhichtoexaminethecourseofdiffusion?Orshouldthecounty‐leveldatabere‐aggregatedtoformsomeeconomicallydistinctlargerregionswithinwhichtherecouldbesaidtobesubstantialhomogeneity?Wouldsuchathingbefeasible,letaloneappropriateforanalyticalpurposes?

Theanswerswerenotobvious. Itwasnotevenclearthatthe ideaofregionaldifferencescouldbespecifiedclearly,andifso,whetherornotitshouldbeindependentoffixedfeatures–suchasclimate,orsoiltypes–thatmighthaveabearingonmicro‐leveladoptiondecisions.Whatdidseemclearisthatifallthestatedataforcornfarmerswasaggregated,itwouldexhibitanadoptionpathwhichwasfarmoreprotractedthanthoseshownfortheindividualstates,apointcommentedonbyGriliches(1980:Further,becausethatdiffusioncurvewouldhaveauniqueinceptiondate,theslopeparameterestimatedfromthelogisticregressionwouldneedtodescribethemoreprotractedtimepath,andconsequentlywouldbesmallerthanthat formanyof thesub‐regions.OntheGriliches‐Mansfield interpretation, however, differential profitability of hybrid cornwould affect the slopecoefficientofthelogisticandconsequentlygovernthespeedofthecontagionprocess;hence,forthelarger aggregate if would have to be said that the differential profitability of the innovation forfarmerswasweakerintheaggregate(andafortioriweakerinthelateadoptionregions)thanwasthecaseintheearlyadoptingsub‐regions.

ButGriliches(1957)hadprovidedadifferentexplanationfortheseparationbetweenearly‐andlate‐adopters:itwassupposedtohavestemmedfromthedifferencesintheinnovation‐suppliers’expectedprofitability,whichgaverisetothesequenceofintroductiondates.Lookingattheprocessfromtheaggregatelevel,itnowseemedthattheheterogeneityofcorn‐growingconditionsacrosstheU.S.playedarole in thediffusionprocess thatwasnotacknowledgedwhenGriliches focusedhisempiricalanalysisatthestatelevel.Yet,ifthiswasavalidconclusion,mightitnotalsobeonethat

21Theinfluenceofthosedoubtsaboutthesufficiencyofthe‘contagion’modelfounditswayintotheapproachtaken inDavid (1966).But, as that publicationwasmeant to be a contribution to economichistory – in afestschriftforAlexanderGerschenkron,theadvisorofmyyetunfinisheddoctoraldissertation—andnotaboutdiffusion theory, its pages contained no explicit references to Griliches’ study of hybrid corn and thecontroversyithadignited.Suchmatterswouldwaituntilmyincipientheterodoxycouldbeformalizedforadifferentaudience,inDavid(1969).

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wouldholdinregardtothediffusionprocessatthestatelevel?Andthen,whynotalsoatthecounty‐level,andbelow?

Perhapsnotaltogethersurprisingly,ruralsociologists–evenbeforetheyreachedthefightingwordsattheendofGliches’Econometricaarticle–werefindingitdifficulttosquarethecomplexandnuancedpicturethathadbeenprojectedbyRyanandGross’s(1943)influentialstudyoftheresponseof Iowa’s farmers to the introduction of hybrid corn,22 with Griliches’ stark emphasis upon thedifferential profitability of hybrid corn as the principal systemic factor affecting the speed of itsdiffusion. Ryan and Gross (1943) had reported a complicated array of objective and subjectiveconsiderationsaffecting the social communicationof influential informationwithin Iowa farmingcommunities as having shaped the reception of hybrid corn cultivation as a substitute for thetraditionalfarmingregimebasedonopen‐pollinatedcorn‐seed.Furthermore,thecriticalresponsestoGriliches(1957)thatappearedinRuralSociologyfromBabcock(1960),andHavensandRogers(1962) in defending the research tradition stemming from Ryan and Gross’s pioneering studyactuallywentbeyond it andemphasized the rolesof the “congruence” and “compatibility”of theinnovationwiththepre‐existingfarmingregimenandbeliefsabouttheirefficacyofthosepractices.These underlying structures were held to be the real determinants of the alacrity with whichindividualsembraced.23

Griliches’(1960,1962)sequentialrejoinderstoBabockandHavensandRogers,respectively,werespiritedbutactuallyavoidedcounter‐attacking;hisrebuttalsadroitlysoughttodeflectpointsthey offered in criticism of his emphasis on profitability as the determinant of the speed of thediffusionprocessinanygivenfarminglocale.Essentially,hepointedoutthattheconsiderationstheyraised(whichwillbeexaminedmoreexplicitlyinsection3)wouldaffectboththerealityandtheperceptionoftheinnovation’sprofitability;therefore,toportraytheirinfluencesasdistinctfromthatofprofitabilitywasa“falsedichotomy”,and“anotherfalsedichotomy.”Ononeface,thiscouldbereadas something of a retreat from the blunt dismissal of the relevance of “sociological factors” inGriliches’1957text,whileonitsotherface,itservedtoenlargethetentofthe“profitability”approachto explaining farmers’ behaviors – so that everything could be taken in beneath it, and no realconcessionneedbemadetothecritics.Bothsideswithdrew,and,amongthemselvesthesociologistsandtheeconomistsalikeeachdeclaredtotalvictory.

OnestrandinthesubsequentdevelopmentofmodelsofinnovationcanbetracedbacktothelivelycontroversywithruralsociologiststhatGrilicheshadsparkedbyconceptualizingtheadoptionof innovations as amatter of rational, profit‐seeking individual behavior, rather than as a social 22Thishadbeenalandmarkcontributiontothemethodologyandsubstanceofinterview‐basedresearchontheadoptionofinnovations.Indeed,thetraditionamongquantitativesociologistsspringingfromtheworkofRyanandGross (1943) continues to shapeempirical studies in the fieldofmarketing,aswell as academicsociologicalinquiriesintotheadoptionoftechnologicalandotherinnovationsamongruralcommunitiesinthedevelopingeconomies.TherewasnoreferencetothisworkinGriliches’Econometricaarticle,althoughit isimplausibletosupposehecouldhavebeenunawareofitsexistence.ThefollowingquotationfromRyan(1948:p.273)wasofferedbyGriliches(1957,p.516(n.31)tosupporthiscontentionthattheavailablesupplyofthehybridseedinthe1930’swasnotabindingconstraintduringthatearlystageofitsdiffusion:“therapidityofadoptionapproximatedtherateatwhichfarmer’sdecidedfavorablyuponthenewtechnique.”

23See,forexample,Babcock(1962),RogersandHavens(1962).RogersandShoemaker(1971)andRogersandKinkaid(1981)havecarriedforward,andconsiderablyelaboratedandgeneralizedtheemphasisthatRyanandGross(1943)placedontheimportanceforthedynamicsoftechnologyadoptionofstructuresocialinteractionsamongthepotentialadopterpopulationthataffectedaccess topersuasive informationabouthybridcorn’sadvantages.

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process.Thatcross‐disciplinaryencounterinitselfpromotedtheinterestsofeconomistsinextendingtheapplicationoftheirfamiliarparadigmofmicroeconomicbehaviorintoanewareaofempiricalandtheoreticalanalysis,therebycontributingtotheemergenceof“the“economicsoftechnologicalinnovation”asanimportantemergingtopicfortheprofessionduringthelatter1950sandtheearly1960s.24

2.4.2Reflectionsonthelegacy

ZviGriliches’1957articleontheadoptionofhybridcornestablishedhispositionasthepath‐breakingeconomistintheareaofempiricalresearchonthediffusionofinnovationsandthesourceofinspirationformuchofthefollowingresearchonthesubject. Theliteratureeventuallymovedbeyondhisinitialcontribution,bothinthetheoreticalanalysisoftechnologyadoptionandkindredphenomena,andinthespecificseconometrictoolsthathavebeenemployed,isonlytobeexpected.In the history of science certainly it is not uncommon for the formative legacies of a majorbreakthroughtoberapidlyoutgrownasothersareattractedtoanewlyopened,promisinglineofinquiry.But,inthiscase,progresstowardstheintegrationofmoreintricatetheoreticalanalysiswithmore sophisticated empirical studies has turned out to be more modest than might have beenexpectedattheoutset.

Grilicheshimselfcommenteduponthis,suggestingthathoweverimportantthephenomenonof“diffusionlags”mightbeasapracticalmatter,itwasanawkwardanomalyforeconomicanalystsaccustomedtothinkingrationalagentsandcollectivitiesofagentsthatwereoperatingat,orinthenearneighborhoodofequilibrium.InaninterviewconductedbyKruegerandTaylor(2000:p.181),hewentfurthersuggestedthateconomists’over‐ridingpreoccupationwithmodelsofequilibriumhad contributed to limiting further development of his initial empirical workof the diffusioninnovations:

“Weneverhavehadagoodtheoryoftransitions.Andthefield,byandlarge,movedtowardan interpretationwhereeverythingwas inequilibrium,all the time.So thediffusionstory,assuchdidn’tseemlikethemodelpeoplewantedtodevelop….[M]ostof the economy is quite far away from the boundaries of the current state ofknowledge.Someofitisbecauseitisequilibrium—it’snotprofitableatheexistingcoststructures.Butsomeofitisbecauseit’snewandithasn’tbeenfullydevelopedyet.It’sintheprocessofbeingadopted.”

24Seeforexample,theseminalarticlebyNelson(1959)onthe“appropriabilityproblem”inR&Dinvestment,andthewiderangeofnewresearchontherateanddirectionof“inventiveactivity”representedintheNBERconferencevolumeeditedbyNelson(1962).MuchofthenovelfocusofthatNBERconferencereflectedtherecentformationofaninformedandinfluentialaudiencethathadformedamongeconomists(outsidethesub‐filedofagriculturaleconomics),andwhowereespeciallyappreciativeof thesteprepresentedbyGriliches’(1957,1958)publications.Thisaudience,fortuitouslyfortheyoungGriliches’career,hadbeencreatedbythemajorprogramofresearchontheeconomicsoftechnologicalinnovationconductedatRAND(inSantaMonica)during1942‐1962.Thisearlyworkintheearly1950sfeaturedformativememorandaontopicssuchastheinformation‐theoretic formulationof theeconomicsofresearch,andthe implicationsofempirical “learningcurves”forcost‐functionsintheairframeindustry–drawingcontributionsfromKennethArrow,andSelmaSchweitzerArrow,ArmenAlchian,andmanyotherswhowentontohavedistinguishedcareersinotherfields,asdidRichardNelsonwhocametoRANDlaterinthatdecade.ButforthediscoveriesofHounshell(2000)intheRANDarchives,littlewouldbeknownaboutthisimportantintellectualepisode–apartfromthepersonalrecollectionsimpartedbysomeamongtheparticipants.

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Butanotherexplanationforthis“disappointment”wouldseemtolieinadifferentproblem,aboutwhichGrilicheswasoutspokeninotherresearchcontexts.Itsoonbecameapparentthattherewere very exacting, and costly data requirements if consistent econometric studies were to bepursued at the aggregate level at which his hybrid corn research had been pitched, and at themicroeconomicleveltowardwhichboththeoreticalmodellingandempiricalresearchonadoptionbehaviorbegantoshiftsoonthereafter.

WhereasGrilicheshadbeenabletoconstructdiffusiondetailedregion‐specifictime‐seriesfromtheavailablevoluminousdataontotalU.S.farmacreagesplantedwithcorn,andtheacreageplanted with hybrid corn – and using some unpublished data obtained from Department ofAgriculture,Mansfieldsetouttobuildadatasettracethepenetrationoftherangeofnewtechniquesthroughavarietyoftradepublications,andprivateindustrysources.MuchoftheimpactofManfield’s(1963a,b, 1966, 1968b ) later publications resulted from the sustained data collection effort hemounted, focused on the adoption of new technology bothwithin firms and across firms in themanufacturing and transport sectors, and much of what came to be known about the centraltendencies and variations in the patterns of diffusion of industrial processes stemmed from thisresearchprogram,inwhichseveralgenerationsofMansfield’sgraduatestudentsattheUniversityofPennsylvaniawereenlisted.25

Withtheexceptionofafewoutstandingcontributors,theeconomicsprofessionrespondedweaklytothe“dataconstraint”challenge.Theresulthasbeenthatsystematiceconometricresearchondiffusion continues constrainedby the lackof suitablemicro‐level data, and the gapbetweentheoreticalmodellingandempiricalstudieshastendedtowiden.26Oneofthemanifestationsofthisgaphasbeentheprofusionofmodelsthathavemultiplied,unconstrainedbythedata.Theothersideofthe“dataconstraint”oneconometricworkinthefieldofdiffusionhasbeencomparativeabsenceoftheimpositionof“datadiscipline”upontheoreticalelaborationsofmodelsthataredesignedtobeobservationallyequivalentwithinthelimitedsphereof“stylizedfacts”thatsubstituteextensiveandvarieddatasetsaboutactualdiffusionexperience.Thefollowingsectionismeanttounderscorethispointwithconcreteexamples.

2.5Multiplyingmodelsoflogisticdiffusion

Mansfield’s(1961)invocationofarandomcontactprocessofcontagionwasonlyoneamongthemultiplicity of interpretations thatmight equally have been attached to the phenomenon oflogisticdiffusion.Atthereducedformlevelatwhicheconometricworkinthisareawasconducted,mostofthealternativeformulationswereobservationallyequivalent.InthefollowingparagraphsIdemonstratethisexplicitlywithoutattemptingtobeexhaustive.

2.5.1:An‘evolutionary’economicinterpretation?

Consider, forexample,avariantthathasadistinctlyevolutionaryflavor;notsurprisingly,perhaps,asithasitsrootsinthemathematicsofpopulationgenetics.LuccaCavalli‐SforzaandMarcFeldman(1981)provideageneticmodelbaseduponrandompopulationinter‐mixing,inwhichtheproportionofthepopulation(again,wemaylabelitP)carryingthemutanttraitevolvesaccordingto

25 In the U.K. Nabseth andRay (1974), andDavies (1979), similarly contributed to building the empiricalfoundationsforthestudyofdiffusion,butthisefforthasnotcontinued.

26Recentexceptionsprovetherule:seeForman,GoldfarbandGreenstein(2003);BresnahanandYin(2007).

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alogisticfunctionoftime.Theyshowthattheslopecoefficientofthelogistic(again,callitn)inthiscaseissimplyn=ln(km/ko),wheretheratiokm/komeasurestheDarwinianfitnessofthemutantgenerelativetotheoldgene.Translatingthisintomorefamiliarterms,wecouldsaythattheslopecoefficient is a log‐transform of the ‘fitness’ measure of the innovation’s advantage vis‐à‐vis theestablished(cultural)trait.

Togofromthismetaphortoaformal“evolutionaryeconomics”‐stylemodelofdiffusionsomefurtherbitsmusttoadded,makingthereplicatordynamicsexplicit.Thisisnotsohard:supposethattheinnovation(mutantculturaltrait)isaproductionmethodthatreducesunitproductioncostsfortheadoptingfirms,andthatthelatterareoperatinginacompetitivemarket.Next,supposetherateofcapacitygrowthviainvestmentinthefacilitiesrequiredbytheinnovationisequaltotheprofitrate.27Sincethefirmsenjoyingthelowerunitcostswillgetmoreprofitperunitofcapacityprofits,thecapacityof the firmsadopting the innovationwillgrowrelative to thatof thenon‐innovatingremnantbykm/ko.Theresultwillbealogisticpathfortheproportionof(fullcapacityutilization)outputthatisproducedwiththenewtechnique.Viewedfromthisunaccustomedangle,ZviGriliches’intuitive identification of the slope parameter of the logistic with somemeasure of the relativeprofitabilityoftheinnovationinquestionmightentitlehimtofurtheresteem–surprisinglyinthiscase,asapioneeringevolutionaryeconomistinspiteofhimself!28

The‘evolutionaryeconomics’overtonesoftheforegoingsketch‐modelnotwithstanding,itfollowstheworkofGrilichesandMansfieldfaithfullyinitsassumptionthatthecoefficientofrelativefitnessfortheinnovation(i.e.,thenew‘culturaltrait’inquestion)isinherentintheinnovationitself.Anobviousjustificationforthissuppositionistodismissasinconsequentialthepossiblevariationsoftheenvironmentsencounteredbythosewhoacquirethetrait.Morecomplexmodelsofpopulationgenetics subsequently have abandoned that simplification, allowing both heterogeneity ofenvironments and their dynamic transformation as a consequence of the diffusion of the new(behavioral)traitwithinthepopulation.

In a sense, the literature on themicroeconomics of diffusion began tomove in the samedirection(althoughnotconsciouslyregardingtheevolutionaryparallels).Thisdevelopmentturnedupon a more formalized acknowledgment of the implications of heterogeneities in the adopterpopulation,andbiasesinthepropertiesofinnovations.Together,theseempiricalrealitiesposedachallengetothecasualassumptionthatinnovationswereuniversallydominantvis‐à‐vispre‐existingtechnologies. They therefore pointed to the possibility that diffusion lags were not necessarilyexplainedby incomplete information.This, in turn, raisedquestionsabout therationaleofpolicyprograms designed to promote technology adoption by providing demonstration programs andidentifyingefficientchannelsforthepropagationofinformationabouttheinnovationinquestion.29

27Ifweareentertainingevolution,whynotalsohaveaCambridge‐Pasinettistyletheoryofsavings,inwhichthecapitalistssaveeverythingandtheworkersnothing?

28ThisMolière‐likedenouementshouldnotobscurethecreditforthereplicatordynamicinthisformulation,whichwasintroducedmuchlaterbyNelsonandWinter(1982),whocreatedastochasticversionofasystemwith this structure and examined its path of adjustment (through selection) in response to the recurrentemergenceofmutationscharacterizedbyvaryingdegreesof“relativefitness.”

29 See e.g., Rogers andShoemaker (1971);Rogers andKincaid (1981) forprogramsof that genre, and theimplicitcritiquebyStonemanandDavid(1986).

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The approach finding itsway into corners of the economics literature focused less uponinformationcontagions,andmoreupon the implicationsofpopulationheterogeneities, combinedwithfixedcostsofadoptionandvariableinput‐savingbiasesinprocessinnovations.Itallowedforthe possibility that expected scale of operationsmight enter into investment decisions involvingchoicesbetweennewandoldtechniques,such,thatgiventherelativepricesofthefixedandvariableinputs,therewouldbea“threshold”outputscalebelowwhichadoptionwouldnotoccur,solongasthedecisionagentsweremyopiccost‐minimizers.

2.5.2Movingequilibrium:thresholdmodelsandlogisticdiffusion

Myinitialandsubsequentcontributiontothemodellingofdiffusioninnovationsintroducedandgeneralizedthatapproachforthecaseofprocessinnovations.But,thishardlyistheoccasiononwhichtoreviewthedetailsofallthosepapers.30Rather,thepointinbringingupthematterhereissimplytounderscorethepreviousassertionthattherearemanydifferentmodelsthatwillaccountforthephenomenoncharacterizedoflogisticandlogistic‐likediffusionatthemacro‐level.Theclassofso‐called‘thresholdmodels’–inwhichavarietyofformulationsissubsumed–canperformthattrick without having any recourse to imperfections in the information states of the agents.Furthermore, their simpler formulations suppose that adopters and non‐adopters alike at eachmoment are in profit‐maximizing (or, at least, cost‐minimizing) equilibrium. The essence of theapproachistoviewthediffusionpathitselfasamovingequilibrium,thedynamicsofwhichcanhaveexogenousorendogenousdrivers,orboth.

In this light, onemight re‐phraseGriliches’ comment (quotedabove) about the economicprofession’spenchantforthinkingaboutequilibriumratherthanabouttransitions:theprofession’spredilection for modelling the behavior of agents in equilibrium terms posed an obstacle toexplaining macro‐transitions simply in terms micro‐level disequilibrium. Models of temporallyextendeddiffusionprocessesthatallowfeedbackfromtheprocessitselftoprovidedynamicdriversforamovingequilibriumthereforecouldrestoretheconceptualizationofthemacro‐phenomenonasatransition.Butthecosttotheneoclassicalworldviewofpursuingthelatterinterpretationwastheacceptanceof externalities (suchas various formsof “learning”) as a vital sourceof the system’sdynamics.

Inordertofixideasherewemaystartwiththebasicformalizationofthe“threshold”modeloftechnologyselection,anddevelopasimplespecificationthatallowsthismodeltomimicthetimeseriesimplicationsofthebasiccontagionmodel—bygeneratingalogisticdiffusionpath.Itisbestatthisstagenottoburdentheexpositionwithmathematicalformalism,sothenotationhereiskepttoaminimum—evenatthecostofleavingsomelooseendsthatcanbetidiedupafterward.

Thebasicnotionofanadoption“threshold”isthatthereisavariatezthatentersthediscretechoiceproblemof individualagent iwhoischaracterizedbythevaluezi,suchthattheagentwillselectthenoveloption—theinnovation—overotherswhen(zi)<z*.Thus,z*isimplicitlydefinedasthe“thresholdadoptionlevel”ofthekeyvariate.Letusassumethatthetechnologychoiceisfor

30SeeDavid(1969,1986,1991,1997);DavidandOlsen(1984,1986,1992).Idonotreviewheretoaseparatelineofmypublicationsthatareconcernedwithmodelsofinter‐innovationrivalry,particularlythosedrivenbynetworkexternalities.

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allintentsandpurposesirreversible,perhapsbecausethedecisiontoadopttheinnovationentailsacquisitionofahighlydurableandindivisiblephysicalasset.31

Ifwethensupposethatthecriticalvariatezhasacontinuousfrequencydensityfunctioninthe population of potential adopters, f(z) , the proportion of the population among which thecondition for adopting the innovation is not fulfilledwill be just the value of the corresponding(stationary) cumulativedensity function,F(z*). Therefore,wehave as ameasureof theextentofdiffusiontheproportionofthepopulationthatshouldadopt:

D(z*)=1‐F(z*).

UndertheassumptionthatF(z) isstationary,D(z*)canincreaseifandonlyifz*becomessmaller.Inotherwords,thethresholdpointhastopassdownwardsthroughthez‐distribution.

If we know the shape of F(z), and can characterize the dynamics of z*(t) = g(t), it isstraightforwardtodeducehowthelatter’smotionmustre‐mapF(z*)YF(t),therebygeneratinga’moving equilibrium’ path for the diffusion index in the time domain, D(t). It’s really no morecomplicatedthanthat!

All sortsof diffusionpaths, andallmannerofmicro‐level processesgenerating aggregateleveltime‐seriesmeasuresofdiffusioncanberationalizedintermsofthisbasicframework.Puttingittheotherway‘round,byspecifyingf(z)andg(t)onemayderivetheshapeofthediffusionpath.Thus,letuspositthatthez‐distributionisthelog‐logistic,andthatg(t)declinesexponentiallywithtimeattheinstantaneousrate8,andseewhathappens.Wenowmaywrite

D(z)=1‐F(z*)=exp{‐((lnz)}[1‐D(z)]=(z)‐([1‐D(z)],

and

z*(t)=g(t)=z*(0)[exp{‐8t}].

Upon finding ln(z*(t))andsubstituting this in theexpression forD(z=z*),we immediatelyobtainalogisticfunctionint ,theslopeparameterofwhichnowisrevealedtoben=(8 .Thisisreadilyconfirmedbyformingtheresultingexpressionforthefamiliarlog‐oddsratio:

( )) { *( )}

[1 ( )]{ D t

t ln z oD t

ln

.

Thismodeloflogisticdiffusionaffordsaninterestinginterpretationofthecoefficientoftthatmaybeestimatedbylinearregressionmethods;itreflectsboththerateatwhichthethresholdpointisfalling,andtheshapeoftheunderlyingz‐distribution.Givenanextraneousestimateforz*(0)–thevalueobservedfortheinitialadopters–bothofthemodel’sstructuralparameterscanberecoveredfromtheinterceptandslopecoefficientsofthislinearexpression.Formulatedasaregressionmodelby the addition of a disturbance term, the parameters of interest may be estimated by linear

31 See Sect. 3, for discussion of the specific contexts in which this formalization first developed, andsubsequentlywaselaborated.

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regressionmethods.32Obviously,differentspecificationsoftheunderlyingheterogeneity,i.e.ofthedistribution function for z*, would generate different regression models, and correspondinglydifferent interpretations of their coefficients.33 It may be noticed that although profitabilityconsiderations obviously can enter into the marginal agent’s micro‐level decision functions, theestimatedparameternsaysnothingatallabouttherelativeprofitabilityoftheinnovation.

2.6Amultiplicityofmodelsandtheirimplicationsforempiricalresearch

The specifics of the underlying adoption process for the innovation cannot be uniquelyidentifiedsimplyfromtheshapeofthediffusionpaththatemergesattheaggregatelevel.Thethreesimplemodels just reviewed are observationally equivalent if one is restricted to looking at thetimes‐seriesof thechangingproportionof adopters in thepopulation,or,asGrilichespioneeringstudy of hybrid corn has done, at the proportion of aggregate output produced with the noveltechnology in a given region. This spotlights the the formidable challenges that are posed forempiricalresearcherswhoseektoidentifythespecificmechanism,orgroupsofmechanismsthatareresponsible for the temporally distributed uptake of particular innovations in one or anotherhistorical time and place. The requirement to collect consistent micro‐level cross‐section andaggregatedtime‐seriesobservationsnotonlyonadoption,butonthevariableshypothesizedtobecriticaldeterminantsofindividuals’decisionsregardingtheirchoicesamongavailabletechniques,certainlyimposesaheavyburdenontheindividualresearcherwhowouldundertakeaneconometricinvestigationofthiskind.InthislightwemayrecallZviGriliches’(1994)expressionofconcernthattheeconomicsprofession’s internal rewardstructurescontinueto inhibitourcollectiveability toeasethe“dataconstraint”onempiricalresearchintoimportantquestionsaffectingeconomicgrowth:34

“Weourselvesdonotputenoughemphasisonthevalueofdataanddatacollectioninourtrainingofgraduatestudentsandintherewardstructureofourprofession.Itisthepreparationskilloftheeconometricchefthatcatchestheprofessionaleye,notthequalityoftherawmaterialsinthemeal,ortheeffortthatwentintoprocuringthem.”

Butthe“observationalequivalence”ofalternativemechanismsgeneratingdiffusionpathsatthe aggregate level is not the whole of the identification challenge. Consider one class of thesemechanisms,the“thresholdmodel”,andassumethatadynamicdriversetsaspecifictime‐pathforthefallinthe“break‐even”variatez*(t).Itwillthenbeseenthatdifferentdistributionsofz‐‐thecriticalheterogeneityinthepopulationofpotentialadopters–maygeneratedistinctivemappingsofdiffusioninthetime‐domain.Whenthethresholdvariateisfallingexponentially,ithasbeenseen

32Awordofcautionisinorderforthosewhowouldfollowcommoneconometricpracticeandestimatethelog‐oddsequationbyOLS.methods.Inthistime‐seriesrelationshiptheproblemofautocorrelateddisturbancessuggestsrelyinginsteadonminimumChi‐squareestimatorsfortheslopecoefficient.

33The thresholdmodeldeveloped inDavid (1969) featuredexpectedoutput as thekeyvariable (z) in theadoption of a fixed input‐using technology, and specified this to be distributed lognormally within thepopulationofpotentialadopters.Withthethresholdfallingataconstantexponentialrate,8,aoneobtainsaprobitregressionmodel.Theslopecoefficientofthatlinearrelationshipintissimply8/F , whereF isthestandarderrorofN(0,F),thestandardnormaldistributionofln(z).34Reprintedfromthe1994AmericanEconomicReviewarticleinGriliches,(1998):p.364.

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thatalog‐logisitcdistributionofzinthepopulationofpotentialadoptersgeneratesadiffusiontime‐series that is logistic and symmetrical. Yet, were z to be distributed log‐normally the sameexponentiallydecreasingthresholdz(t)*givesrisetoatransformedcumulativenormal(TCN)time‐pathfortheproportionofadoptersinthepopulation.35 Alternatively,onemightpositthatthez‐distributionwaslog‐Gompertz,sothatthetime‐seriesobservationsonproportionofadoptersinthepopulationwouldturnouttobethecumulativeGompertzdistribution,andthetimeprofileoftheincrementalincreasesintheextentofdiffusion()D(t))followtheinnovation’sintroductionwouldresembledistributedlagsoftheKoyckform.Withoutbeingabletodirectlyexaminethehypothesizedz‐variate’s distribution, it would not be possible to attribute the variant diffusion paths to thedifferingspecificationsofthesamestructure,ratherthantopossiblyfundamentaldifferencesintheunderlyingadoptionmechanism.36

Toestablishtheconnectionbetweentechnologydiffusionseenasacontinuoustime‐seriesprocessattheaggregatelevel,andasaquantalresponseattheleveloftheindividualadoptingagents,onemustanappropriatecharacterizationoftheproductiontechnologiesandbothkindsofdata.37To

35TheTNCdiffusioncurvedoesnothavea traceableclosed‐formexpression,as it involvesevaluationofadefiniteintegral,but,ontheotherhand,theproportionofadoptersinthepopulationatsuccessivepointsintime lies along a straight line when plotted on normal probability scales, and the underlying parametersdescribingthelog‐normaldistributionandtherateatwhichthethresholdisfallingcanbeestimatedbyprobitregression analysis. These implications are derived in David (1969: section III.3), and Davies (1979)subsequently–butapparentlyquiteindependently‐‐madeextensiveuseofprobitregressionshisempiricalstudiesofdiffusion.David(1969)showsthatifthecriticalvariatezisoutputscale,themeasureoftheextentofdiffusionDv(t)‐‐denotingtheshareoftotalindustryoutputthatisproducedusingtheinnovation–neednottakethefamiliarogiveformofthecumulativenormal.Whenthediffusionprocesscommenceswithadoptionbyproductionunitswhoseoutputscalesaremuchabovethemeanoftheoutputscale inthe industry, it ispossiblethatDv(t)1withoutexhibitinganinflexion.

36Unlikethelogistic, theGompertzdistributiondoesnotgeneratesymmetricS‐shapeddiffusionpaths,andDixon(1980), followingtheempiricalstrategydevisedbyGriliches(1957),pointedtotheobserved lackofsymmetryintheupdatedregionaltimeseriesoftheextentofcornacreageunderhybridcornashisgroundsfor estimating theparameters of theGompertz function rather than the logistic. Griliches (1980: p. 1463),however,questionedthisonthegroundsthatitwasmerelycurve‐fittingtoaccommodatetheobserved“slowuppertail”,which,hesuspected,wasduetodelayedsupply‐adaptationsinhybridseeds‐‐requiredforthemtobeprofitablyuseinthecertainareasthatwereill‐usedtotheinitiallyavailablevarieties.

37 Tempting as it may be to adopt a “representative agent” framework and introduce mathematicallyconvenientaggregativeproductionrelationshipstofinessetheneedtounderstandaggregatelevelphenomenaat the underlyingmicroeconomic level, using appropriatemicro‐level data, succumbing to that temptationyieldsatbest a “simulatedunderstanding”of theeconomic realities.Anexampleofwhat fromthepresentperspectivemustbeseenasanerrorofaggregationinrepresentingtheeconomicsofthetransitiontoamajortechnological innovation isprovidedbyarecentattempttoapplya“representativeagent”modelofcapitalaccumulation in characterizing the diffusion of mechanized production as a moving equilibrium process.Manuelli andSeshadri (2003) construct a simulationmodelbasedonaone‐sectorneoclassical productionfunctionwhichtheyusetotoportraythegrowthofthestockoffarmtractors(andthedeclineofthatofhorsesand mules) in U.S. agriculture during 1880‐1930 as “friction‐less technology adoption” – i.e., pure factorsubstitution‐‐inresponsetotheeffectofrisingrealwages.Therecanbenoobjectionheretothechoice‐of‐technique framework, or the abstraction from short‐term lags due to “frictions” in the transmission ofinformationabouttheadvantagesoftractors.ButManuelliandSashadri’sanalysis,unfortunately,remainsun‐informedbyanyoftherecentresearchonthesubjectof“tractorization”intheU.S.‐‐e.g.,Sargen(1979),Ankli(1980), Fite (1980), Whatley (1985, 1987). Consequently, it takes no notice of the wealth of micro‐levelinformationabouttechnicalchangesininputusageandinputprices(especiallyrelativepricesofhorsefodderandtractorfuel),aswellassuchcriticalmattersastheconstraintsthatclimateimposedonthedurationof

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beconsistent,moreover,thetimeseriesshouldbeaggregatedfromasuccessionofcross‐sectionsofthepopulation.But,ifwhatiswantedisatime‐seriesmeasureofdiffusionexpressingtheproportionofaggregateoutputproducedwiththenoveltechniques,orwitheachoftherelevantnewandoldtechniques towhich theagentshadaccess, then there isa further requirement:onemusthaveameasureoftheoutputsoftheproductionfacilitiesforwhichchoicesamongtheavailabletechniquesare beingmade. Griliches (1957)wasworkingwith ameasure defined in reference to the cornacreageplantedineachregion,but,fromthataloneitwouldnotbepossibleidentifyaneconomicdiffusionmechanismthatinvolvedthepropagationofinformation,orotherinfluencestransmittedintheinteractionsamongthefarmers.Theplotsofarablelanddonotswitchfrombeingunderopen‐pollinatedcorntobeingplantedwithhybridseedbecausetheyseewhat’sgoingonintheadjoiningacreages, or pass messages to one another. Perhaps that “data constraint” served to restrainGriliches from explicitly discussing the views that had emerged from the local studies of ruralsociologists,concerningtheimportanceofsocialcommunicationsamongthesourcesofinformationinfluencingfarmers’acceptanceofnewproductionmethods.

Consequently,itisimportanttostressthatatthestartofhiseconometricresearchcareer,in

his study of the diffusion of hybrid corn, Grilicheswas (characteristically) careful in observing adistinctionbetweentwokindsofempiricalresearchstrategies.Oneistoestablishthenatureoftheregularitiesthatarepresentintheaggregateleveloutcomesofeconomicagents’behaviors,andofferone or more hypotheses that are in effect “conjectured interpretations” of the sources andsignificance of those established statistical regularities. A quite different research strategyundertakes to specify alternative hypothesized mechanisms governing the behaviors of theindividualactors,and,whereappropriatethetemporalpropagationofinfluencesamongthemthatconnectthesequenceofthoseactions.Thegoalofthelatter,structuralapproachistomakeitpossibleto uniquely identify which among the alternative mechanisms had generated the observedphenomenon – in principle, at least, given the requisite datawhose relevance is implied by themodel(s). Clearly, Griliches’(1957) path‐breaking contribution opened up a path thatwould leadotherstofollowhisworkandthatofMansfieldintakingthesecond,structuralmodellingapproachin econometric studies of the diffusion of process technologies.38 But he did not embark upon ithimself.

3.HeterogeneousandtheMicroeconomicEquilibriumApproachtoDiffusion: TheoreticalandEmpiricalImplications

An inclusively broad and diverse class of diffusion models that possess a commonfundamental structure is opened up by abandoning the representative agent approach andcharacterizingthepopulationofpotentialadoptersasheterogeneousinoneormorerespectsthatimpingeupontheoutcomeofarationalmicro‐levelassessmentoftheeconomicbenefitsandcostsofselecting among available production techniques. Analysis of those decision as irreversibleinvestmentsinthedurablefacilitiesrequiredtoinstallanovelprocessofproduction–whetherina availabletimeintervalsforpost‐harvestploughingandthecomparativespeedsoftractorsvs.horse‐teams(onthenorthernplains);orabouttheimpedimentstomechanizationposedbylabormarketinstitutions(inthepre‐WWIIcottonSouth).Theresult isa“explanation”that“simulates”thegrowthof theaggregatestockoftractorswithoutbeinginanywayenlighteningabouttheprocessesthatunderlaythatdevelopmentindifferentregionsofthecountryduringdifferentperiodsofthehalf‐centuryunderexamination.

38Seee.g.,Trajtenberg(1990),KarshenasandStoneman(1992),Stoneman(2002),BresnahanandYin(2007),tonameonlyafewleadingexemplars.

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businessfirm,orahousehold–callsforexplicitlydynamicspecificationofthepotentialadopter’sopportunityset,andthewayinwhichthelattermaybechangedasaconsequenceoffeedbacksandinteractions with suppliers of the innovation‐embodying goods, and interactions with otheradopters.

3.1GeneralizingandElaboratingtheThresholdModel

Suchconsiderations,alreadytoucheduponintheexpositionofthebasic“thresholdmodel”ofdiffusion(insection2.5.2),havecarriedthetheoreticalliteraturewellbeyondtheframeworkofthepioneeringcontributionstotheeconomicsoftechnologydiffusionrepresentedbytheworkofGrilichesandMansfield.Thenewconceptualandanalyticaldepartureofthisapproachconsistsinexplicitlyassumingthatthepopulationofpotentialadoptersisheterogeneousinsomerespectthatisrelevanttotheindividualagents’rationalandinformedchoice‐of‐techniquedecisionregardingtheadoptionofanovelproductiontechnology,andseekingtocharacterizethedynamicconditionsunderwhichtherewillbeanequilibriumpathforthatinnovation’sdiffusion..

Theexistenceofdifferencesamongpotentialadoptersinavariable(denotedbyzinsection2.5b)affectingdecisionsastowhetherornottoadoptthenovelautomationequipment,andwillhastheeffectofpartitioningthepopulationateachmomentintimebetweenthoseforwhomacceptingtheinnovationisoptimal,andthoseforwhomitisnot.Ifthecriticalvaluez*atthatmoment‐‐theso‐calledadoption“threshold”–remainsunchanged,theprocessofdiffusionwouldhalt.But,withasecularlyfallingthreshold,theeffectoftheheterogeneityofthepopulation(withregardtoz)istospread out the dates on which different members of the population choose to install the newproduction facilities. In the hypothesized circumstances, therefore, following the “shock” of theinnovation’s introduction thedynamicsof diffusionwill have the appearance ofadistributed lagprocess of investment in automation equipment by the ensemble of “progressive” (innovationaccepting)firmsintheconsumer‐goodssector.

In thesimplest formulationof thismodel the innovation‐embodyingcapitalequipment isassumed tobe an infinitelydurable “machine” that is indivisible and sufficiently “lumpy”,havingsufficiently large capacity to obviate the need for any of the adopting firms tomake subsequentfurtherinvestmentsinequipmentofthesametype.Consequently,thelagsobservedinrealgrossinvestmentattheindustrylevelwouldreflectthetimedistributionoftheadvancingextensivemarginoftheinnovation’sacceptanceintheindustry.Theshapeofthatdistribution,liketheshapeofthediffusionpath,wouldreflectthetheunderlyingfrequencydistributionofzinthepopulation,andthedynamicsofthethresholdvalue,z*(t).Ashasbeenpreviouslynoted,withz*(t)fallingataconstant(exponential)rateandzbeingdistributedinthepopulationaslog‐Gompertz,grossinvestmentintheindustry would exhibit a Koyck lag distribution following the innovation’s initial commercialintroduction.39

39Afurtherpointmaybenotedinthisconnection.Ifonesupposedthatz(i)representedthei‐thfirm’sunittransportcosttoshiptheadoptingfirms’respectiveoutputstothenearestmarket,then,aswillbeseenfromsection 3.2 (below), the distribution of the expected (and realized) volume of saleswould be determinedendogenouslybytheprofitmaximizingadopters’choicesofproductionmethods.Outputwouldshiftupwardsasaresultofthereducedunitcostofproductionforinfra‐marginaladopters,and(ceterisparibus)wouldalsofollowtheunderlyingzdistribution.Becausetheeffectoftheinnovationwouldbeseeninariseintheleveloftotalindustryoutput(aswellasaveragefirmoutput),andifaveragetransportcostswerefallingsecularly,thetime‐seriesofthelevelofoutputintheindustryandthegrossflowofcapitalformation(needtoimplementtheinnovation)wouldbepositivelycorrelated.Since,ifzweredistributedaslog‐Gompetz,grossinvestmentwould

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To fix ideas here it is convenient to give a brief exposition of the generalized “thresholdapproach” to modelling technology diffusion by following David and Olsen’s (1984, 1986)presentation,inwhichthedynamicsoftransitiontoanewtechnologyisenvisagedasaprocessofcapital‐using“automation”ofproductionmethodsinaconsumer‐goodsindustry.Thismodel, likethat developed contemporaneously by Ireland and Stoneman (1986), introduces an endogenoussourceofdynamicsbyallowingforincrementalsupply‐sidemodificationsthatlowerthecostsoftherequiredinnovation‐embodyingcapitalassets(or,equivalently,increasethesavingsinunitvariablecostsofproductionwithequipmentofconstantprice).Recognitionofthesupply‐sideofdiffusionphenomenaisverymuchinthespiritofGriliches’(1957)examinationoftheroleofthehybridcornseedcompanies,whichsoughttoexpandtheirmarketbysuccessivelyre‐adaptingtheirproducttosuittheconditions(ofsoil,climateandinsectpopulations)indifferentcorn‐growingregions.40Theseincremental innovations are assumed to be embodied in successive vintages of a new class ofindivisible capital equipment (“machines”), the first vintage of which is treated as having beenintroducedbyanexogenousdiscreteinnovation.The“movingequilibrium”modelofadoptionofthenovelmethodofproductionparticularizesthegeneralobservationthatinnovationsseldomremainintheiroriginalform,andthatimprovementsbythesuppliersplayanimportantpartinwideningthefieldoftheirapplicationandeventualadoption(see,e.g.,Rosenberg,1972).41

followaKoycklag‐distribution,casualeconometricanalysismightwellyieldtheappearanceofsupportfora“representativeagent” formulationofthe familiarcapitalstockadjustmentmodel.Butappearancesmaybemisleading,andinthecaseenvisaged,theunderlyingmicroeconomicrealityisthatthesequentialdecisiontoadopttheinnovationandundertaketherequiredinvestmentwascausingtheinvestment.

40Inthecaseofhybridcorn,thepricesofseesweremuchthesameforallregions,althoughtheperformancecharacteristicsofthenewerseedwereimprovedvis‐à‐visthosethathadbeenintroducedearlier(seeGriliches(1957,p.507,n.19).But theresemblance to thesituationenvisaged inDavidandOlsen(1984,1986)andStoneman‐Ireland(1983)modelsisnotcompleteintworespects..Firstly,eachmodificationofhybridcorn‐seedwasintendedtosuittheneedsoffarmersinaspecificgeographicalenvironmentotherthanthosewhereithadpreviouslyfoundacceptance,andsecondly,Griliches’(1957:esp.pp.507‐509)depictsthesechangesastheresultofdistinct“introduction”decisionsbycommercialseedproducersastothemostprofitableorderinwhichtoenterthedifferentgeographicalmarkets.Therefore,eachofthesesuccessive“innovations”–basedonpubliclyfundedexperimentstations’researchandprivateR&Dbytheseedcompanies–wouldhavehadlittleifany“spillover”consequencesforcorn‐growinginotherregions(except,perhaps,throughtheeffectsonthe eventual market price of corn itself). Both the David‐Olsen and the Stoneman‐Ireland models specifylearningeffectsinsupplyfollowingthecommercialintroductionofthenewtechnology.Astheselowertheunitcostofproducingthecapitalgood,evenwithimperfectcompetitiononthesupplysidethepricesinthemarketfortheeinnovative‐embodyinginputwouldtendtofallrelativetotheoutputofthefinalgoodsproducers.Thisdrivesthediffusionof the innovationamongthem,andhencecontinues theaccumulationof the vendors’experience inproducingthecapital‐good.Stoneman‐Irelandassumesupply ismonopolized,themonopolistfollowsaoptimalinter‐temporalprice‐discriminationstrategy,reducingthemarketpriceovertime;whereasDavid‐Olsen assumes learning effects are not internalized and spillover among the firms in a competitivesupply,forcingthesupply‐pricetofallasdiffusionproceeds.(Theso‐called“Coaseconjecture”–questioningtheviabilityofintertemporalprice‐discriminationbythemonopolistvendorofadurablegood,suchasisisassumedbyStonemanandIreland(1983),promptsDavidandOlsen(1992)reformulationthemodelunderthesuppositionthat(likeIBM,andtheUnitedShoeMachineryCompany)themonopolysupplierrented,ratherthansoldtheinnovativeproducerdurable.

41 Rosenberg (1972) emphasizes the generality of this phenomenon and its importance in the eventualdisplacementofformerlydominanttechnologiesbynewonesthat,intheiroriginalformulationsoftenwerecrude, and harboured defects that circumscribed their sphere of effective commercial application. Thisperspective in effect blurs the conceptual distinction been dynamic processes of diffusion and innovation,

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Theforminwhichthemodelwillbesetoutheretakesafurtherstep,however,bylinkingtheprocess of incremental improvements in the innovation’s formulation with an an endogenous“learningprocess”inthesectorthatsuppliesthe“automationequipment”,i.e.,adurablereproducibleasset that embodies the basic innovation. It is assumed that this novel type of capital‐good iscompetitivelysupplied,andtheimprovementsthataremadeonthebasisofaccumulatingexperiencewith “field operation” of this type of equipment, for with its construction, is not privatelyappropriatedbythe“learningentities”.Instead,theknowledgeisa“spill‐over”,beingsharedbyallthevendorsoftheinnovativecapitalgoodsandthereforeisfullytranslatedintoreductionsoftheirunitprice‐performanceratio.Sinceexperience‐basedlearningeffectsofthiskinddependuponthecumulativeprocessesofproducing(and/orinstallingandusing)thenewequipment,theyrepresentafeedbackeffectfromtheinnovation’sdiffusionandthereforeconstituteanendogenousdriverofthe sequential adoption of the innovation by the heterogeneous firms in the machine‐usingindustry.42

Endogenous generation of incremental innovations is conventionally represented as alearningprocessthatresultsinacontinuousreductionoftheunitreproductioncostof“machinesofa constant kind.”43 This reduction proceeds at a pace governed by the rate of accumulation ofcollective experience among the ensemble of firms engaged in the business of supplying thosemachines.Assumingconditionsofperfectcompetitionprevailinthelatterindustry,theserealcostreductions equivalent to a relative decline in the hedonic price of the indivisible capital goodsembodying the new technology.44 Because the pace at which this kind of learning can proceedremainslimitedbytherateatwhichthenewtechnologyisbeingadopted,expectationsaboutthefuturetrajectoryofincrementalinnovationsandthecontinuationofdiffusionprocessitself,ineffect,becomehostagetooneanother.

Treatingthiscomplicationduetothefeedbackfromuse‐experienceinthemicrolevelmodelmakes it essential to take account of the effects of anticipations (or expectations) of continued

although it isnot inconsistentwith insistenceondistinguishingbetween themicro‐leveladoptiondecision(involvingachoiceamongexistingproductsormethodsofproduction),andtheinnovator’simprovementoftheperformanceattributesofanexistingproductorproductiontechnique.

42 It is importanttoemphasizethatwhiletheinducedimprovementsintheprice‐performanceratiooftheinnovation‐embodying equipmentmaybe regardedaspositive feedbackeffect that is an externalityof theadoptiondecisionsofthefirmsintheconsumer‐goodssector,thelatterisapecuniaryexternality.Thisavoidscomplications would arise were the feedback effects of adoption to take the form of non‐pecuniaryexternalities, such as class “network effects” or interdependences among agents’ preferences due to“demonstrationeffects.” cesarise inanexternalityof capital.Aswillbenotedbelow, thepresenceofnon‐pecuniaryexternalities,whenagainstarefullyinformed,cangiverisetoamultiplicityofequilibriumdiffusionpaths,includingpathsthatexhibitdiscontinuitiesratherthanacontinuouslyriseintheextentofdiffusion.

43 The ubiquitous nature of the latter phenomenon supports the plausibility of supposing that a majortechnological breakthrough would establish a potential for many subsequent incremental improvementswhosecumulativeeffectuponproductioncostsmightwellovershadowthatoftheinitiatinginnovation.See,e.g.,Enos(1962,2001)onpetroleumrefining;Hollander(1965)onrayon.But,seealsoCohenandKlepper(2001)ontherolethatpurposiveR&D–ratherthanexperience‐basedlearning—mayplayinthegenerationofincrementaltechnicalprogress.

44 Another connection may thus be noted – between studies of diffusion dynamics and the theory andapplicationofhedonicprices,towhichGrilichesmadepioneeringcontributions(seetheassessmentbyPakes(2003).

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technologicalinnovationuponthetimingofadoptiondecisions,45aswillbeseenfromthefollowingformalizationofthegeneralizedthresholdmodel.

3.2Thegeneralizedthresholdmodel

Consideranindustrycomprisedoffirmsproducingahomogeneousfinaloutput,denotedbyX,andmarketingitcompetitivelyatpricep.Further,thereisacapital‐goodsindustrythatsuppliesmachinery used in the production of this final good under conditions of perfect competition. Tosimplifymatters,wemayassumethattheremainingsectoroftheeconomyislargeinrelationtotheformer two, and its product is the numeraire of the system; machinery from the capital‐goodsindustryisnotusedbythis(residual)sector.

Themachinesembodyingtheinnovationinthissetuparetakentobesuppliedonlyaslargeandindivisibleunitsofcapacity,attheunitpurchasecostk.Althoughonlyoneunitofthisautomationequipmentneedbe installedbyanyfirminorder for it toacquireaccesstothe latestproductiontechnology,inthisgeneralformulationonemayallowthepossibilitythattheacquiringfirmsareabletooperateitoverawiderangeofoutputscales.

Wemayabstractfromthepossibleeffectsofimperfectinformationanduncertaintyupontheprocess of diffusion, and assume instead that all firms in the final goods industry have identical(costless)knowledgeconcerningthebenefitsandcostsassociatedwithuseofthenewproductiontechnology.Thepopulationof firms in the industry is taken tobe fixed, implying thatonly firmsalready established when the new equipment first becomes available will have access to theinnovation.46 Ratherthancomplicatethepresentationbyintroducingrealisticconsiderationssuchasthedepreciationofcapitalgoods,andthepossibilityofreplacementofobsolescentequipmentatsomefuturedate,onemaymakethefollowingfurtherassumptions:(a)allinvestmentisirreversible,which is to say that there isnomarket forusedmachineryof any type; (b) capital equipment isinfinitelydurable;and(c)therecentlyintroducedlineofmachinesistheonlymajortechnologicalinnovationrelevantforthefinalgoods‐producingindustrywithintheforeseeablefuture.47

45 See Rosenberg’s (1976) discussion of the latter in a context where “learning effects” are kept in thebackground.

46Thisassumptionisnotaseriousrestrictionupontheanalysis,inasmuchastheextantfirmsareleftfreetovarytheirrespectiveproductionscales;yet,itgreatlysimplifiesmatters,byequatingthestockofthenewesttypeofcapitalequipment(measuredinstandardmachineunits)withanindexoftheproportionofthefirmsthathaveadoptedautomation.

47WithoutradicallyalteringtheDavidandOlsen(1984)model,themoreglaringunrealismofsimplifications(b)and(c)canbeavoided,puttingintheirplacetheassumptionsofstochasticdepreciationofthe“one‐horseshay”variety,andstochastictechnologicalobsolescence,bothfollowingexponentialprocesses.Undertheonehorseshayassumption,depreciationoccurscompletelyand instantaneously. It thus takesexactly thesameformastechnologicalobsolescenceduetothesuddenavailabilityofasuperiortypeofmachine.Ifthestochasticprocessesgoverningtheseeventsyieldexponentialdistributionsofthedepreciationandobsolescencedates,andifthosedistributionsareindependent,thentheconstanthazardratesforbotheventsmaybeaddedtofindthehazardratefortheterminationofthebenefitstreamassociatedwithagivenpieceofcapitalequipment.Assumingriskneutrality,theexpectedpresentvalueofthebenefitstreammaythenbefoundsimplybyusingthelatter(constant)hazardrateasa“riskpremium”addedtothe(riskless)timediscountrate, leavingtheanalysis otherwise undisturbed. Ireland and Stoneman (1983), use this approach to model the effect ofvariations in obsolescence risks. The difficulty in treating physical depreciation the same way is that

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3.2.1Productiontechnologiesandtheadopter’sinvestmentdecision

Eachfirminthefinalgoodssectormustdecideifandwhentoadoptthenewtechnology,andwillmakethisdecisiononthebasisofthenetpresentvalueoftheinvestmentrepresentedbyanewlyinstalledautomatedplant.SupposeafirmhasdecidedtoinvestatdateT.Itshouldthenproducesoastomaximizeinstantaneousprofitsateachpointintime,usingtheoldtechnology(whichmaybeembodiedinexistingcapitalgoods)beforedateT,andthenewtechnologythereafter.Assumethatinstantaneousnetoperatingrevenuefunctionsarewelldefinedforbothtechnologies—atleastovertherangeofoutputvolumesconsideredhere.Forconveniencethelattercanbereferredtoas“profitfunctions”,rememberingthattheprofitsinthiscasearegrossoffixedcostcharges.

This specification of a profit function, denoted asRi( . ) for the i‐th technology, impliesdecreasingreturnstoscaleintheutilizationofvariableinputsintheproductionprocesses.Lettheinstantaneousprofitfunctionsfortheold(i=1)andnew(i=2)technologies,respectively,be

Ri(p)=maxx

{px–Ci(x)}i=1,2 (2.1)

whereCi(.)denotestherespectivevariablecostfunctionsandpistheproductprice.Notethat the firm’s optimal output x is now given for each technology by the derivative of the profitfunction:

xi(p)=Rpi(p)i=1,2. (2.2)

Thesecostfunctionsremainstationaryovertime,byassumption.Thisimplicitlyimposesthesimplifyingassumptionthatfactorinputpricesaretime‐stationary.Forthesakeofconcretenessandconvenience, let us refer to the new technology (i = 2) as “computer automation.” Then,enhancementsintheefficiencyofautomationequipmentwillbetreatedasequivalentreductionsintheunit reproductioncostof “machinesofa constantkind”, i.e.,machinescharacterizedby time‐stationaryvariablecostsofoperation.

Theautomationtechnologycanonlybeofinteresttothefirmiftheprofitdifference

B(p)=R2(p)–R1(p)>0 (2.3)

foratleastsomerangeoffutureprices.Thisdifference(theundiscountedgrossbenefitfromadoption)istakentobepositiveforalloutputpricesconsideredhere.Itdoesnogreatviolencetotheengineering realities to posit also that this gross benefit function is increasing inp. The latter isequivalenttosupposingthatthemarginalcostschedulefortechnology2lieseverywherebelowthatfortechnology1,andthatthefirm’soptimumsupply(holdingthemarketstructureunaltered)thusishigherundertheregimeofautomation.Thislastimplicationfollowsdirectlyfrom

Bp(p)=x2(p)–x1(p)>0. (2.4)

replacement demands break immediate correspondence between cumulative sales of the newest type ofmachineandthediffusionindex.

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As in all equilibriummodels of diffusionunderperfect competition, it is essential for thisanalysis that therebesomeobjective, identifiableheterogeneity in thepopulationof firmswhichresults in the benefit function varying across the firms of the industry. This proposition wasdemonstratedbyDavid[1969]).Possiblesourcesofheterogeneitywillbementionedshortly,butforthepresentitissufficientsimplytonotethattheprofitfunction(s)willbeindexedbyafirm‐specificcharacteristic,z.

Nowconsidertheinvestmentdecisionfacingthefirmoftypezatdatet,whenthecostofinstallinganew,automatedplantiskt.Thelatterpriceisnotindexedbyz,sinceatanymomentoftimeauniformpriceprevailsinthe(competitive)marketforcapitalequipment.Theproblemtobesolvedbythez‐thfirmthereforeistochooseanadoptiondateTthatwillmaximizethenetpresentvaluefunction

V(T,z)= ( B ( ) - -rT -rTT tp , z e d t k e

, (2.5)

inwhichristherateoftimediscount.

Assumingsmoothpricepaths,thenecessaryfirstorderconditionis

V(T,z)‐B(pT,z)+rkT– Tk

=0. (2.6)

Thishasastraightforwardandfamiliar interpretation: thecostofmarginallydelayingtheadoption(i.e.,investment)datebeyondTisthelossofinstantaneousprofitsequaltoB(.),whereasthemarginalgain is thesumof theavertedcosts,namely therendcosts,rk, and theanticipated

capitalloss,‐ Tk,thatotherwisewouldbeincurredduetotheinstantaneousdropinthereproduction

costofthenew,automatedplantfollowingdateT.48Implicitly,theinclusionofallowanceforachangeinthevalueofthefixedassetrequiredbytheinnovativeprocesspresupposesthatrationaladopterswouldformexpectationsregardingthefuturecourseoftheprice(andhencethereproductioncostvaluation)ofthatasset.49

48DavidandOlsen’s(1984,1986)formulationofthepotentialadopter’sproblemasthemaximizationofV(T,z),definedasanetpresentvaluefunction,representedadeparturefromDavid’s(1966,1969)treatmentofthe demandproblem as that of short‐run profitmaximization by competitive agents in themachine‐usingindustry, thereby reducing the choice‐of‐technique problem to that of myopic cost‐minimization. Theintroduction of expected changes in the price of the capital good in the derived demand function for theinnovationateachpointintimedistinguishedDavidandOlsen’s(1984)analysisfromthatofStonemanandIreland(1983,and1986),whichfollowsDavid(1969)inmodellingthedemandsideofthemarket.

49InadditiontothetheoreticalmeritofthisbelatedimprovementuponbasicthresholdmodelformulatedinDavid(1966,1969),Lew(2000)suggestsitmaybeempiricallyrelevant.InhisstudyofthediffusionoftractorsontheCanadianprairiesduringthelate1920s,theparameterizedversionofthebasicthresholdmodelover‐predicted the rate of adoption. Lew suggests that this discrepancy resulted from the model’s failure toincorporatefarmers'expectationsoffutureprices,andthevolatilityinwheatpricesandfallingtractorpricesareshowntomakedelayingatractorpurchasearationaldecisionforwheatfarmersinSaskatchewaninthelate1920s.Ontheotherhand,itmustbenotedthatthesuccessofusingthethresholdmodel(inanyversion)tosimulatechangesinthe(aggregate)extentofdiffusionorthegrowthofthetractorstockinaregionduringa specific time interval shoulddependalso on the accuracywithwhich thepertinent heterogeneity in the

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AdditionalsufficientconditionsfordateTtobeoptimalforthez‐thfirmarestraightfoward:

v(t,z)>or<0fort>or<T (2.7a)

and

v(T,z) 0. (2.7b)

Evidently, because rationaldecisions regardingadoptionof thenew technologywouldbeinfluenced by expectations regarding the future real costs of the innovation‐embodying capitalequipment,andanticipateddecreasesinitsprice‐performanceratio–whetherduetoanautonomoustrendoftechnologicaladvancesaffectingfirmsinthemachine‐buildingindustry,orspecific“learningeffects”intheproductionofnovelcapital‐equipmentinquestion‐‐wouldtendtodelayadoptionbymarginal firms. But,where incremental improvementsof thiskindcanbeanticipatedtoariseasfeedbackfromthediffusionprocessitself,furtheradoptionwoulddependuponthebalancebetweennegativeeffectofanticipatedcapitallossesandthepositiveeffectofarealizedreductionofthefixedcapitalinput’spricevis‐à‐visthatofthevariableinputrequiredbythenovelprocess.50

Thepresentformulationfollows(1983)inexplicitlyrecognizingtheroleindiffusionofpost‐innovationdevelopmentsonsupplysideofthemarketfortheembodiedinnovation.Inthisrespectthesemodelsbear somekinshipwithGriliches’original analyisof caseofhybrid corn,butwithasignificantdifference. In the lattersituation thesub‐marketswerespatiallyaswellas temporallyseparated,andanticipationsofeventual“improvements”inseed‐qualitywouldnotexertthesamedelayingeffortsonadoption,becausetheywouldn’tbepertinenttotheconditionsofthefarmersintheinitialregionswheretheinnovationhadalreadybeenintroduced.

3.2.2Modelling“learningeffects”asasupply‐sidedriverofthedynamicprocess

Introducinglearning‐by‐doingexternalitiesamongcompetitivefirmsthatsupplytheinnovation‐embodyingcapitalgoodimpliesthatthemarginalcostofproducingthelatter,c(t),willbe a monotone increasing function of the cumulative production experience of that industry.Experience,however,maybetakentobeindexedbyS(t),thecumulativevolumeoftheindustry’sshipments(measuredin“machineunits”fromthefirstunitsoldatt=0).Thus,wehavealearningfunctionc(t)=L{},which,undertheassumedcompetitiveconditionsofsupplyintheinnovativecapital‐goodsindustry,determinesthedynamicsofitsproductprice:

kt=c(t)=L{S(t)},whereLS<0. (2.8)

Given the infinitedurabilityof the innovation‐embodying “machines,” the indexofexperience S also indexes the stock of automation equipment which adopters collectively have adopterpopulationischaracterised–whichinthiscasewouldbetherelevantportionofthedistributionofarablewheatacreagesonSaskatchewanfarmsatthetime.50SeeRosenberg(1976) foradiscussionof theroleofexpectations indecisionsregardingtheadoptionofinnovations,whichconsidersawiderangeofanticipations,includingthoseofchangesintheperformanceoruser‐costs of substitute and complementary technologies. David and Olsen (1986) show conditions underwhichthecombinationofahighinitialuser‐costofcapital,andtoorapidanexpectedinitialrateoffalloftheprice‐performanceratiooftheinnovation‐embodyingcapitalgood–duetotheinitialsteepnessofthelearningcurve‐‐wouldpreventthediffusionprocessfromstartingautomatically.

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installed,oneperfirm,byassumption.SincethesizeofthepotentialadopterpopulationmaybeheldconstantatN,onemaywrite

S(t)=NC{D(t)}, (2.9)

0<D<1,beingthemeasuredextentoftheinnovation’sdiffusionamongthefirmscomposingthefinalgoodssector.Now,followingtherepresentationofthethethresholdmodelininsection2.5,wehaveD(t)=[1–F(z(t)],whenz=z*.Substitutingthisineq.(2.9),thefunctiondeterminingktcanbeexpressedas

kt=L{[1–F(z*(t))]}.

Givenamappingz*(t)=y,whereyindexesthemarginaladopteratt,thisrelationshipcanbewrittenmorecompactlyas:

kt=F(y), (2.10)

so that the supply price of the innovation‐embodying capital goodwould tend to declinerelative to thatof theoutputof the sectoradopting thenew technology (assumingnoequivalenttechnologicalprogressaffectingotherinputsinthefinalgoodssector.Withtherealinterestrate(r) constant, the real “user‐cost”of the innovation‐embodyingcapital,rkt, mustbe fallingas thethresholdlevelmovesdownwardinthedistributionofpotentialadopterstofirmsoflowerrank(y)..

3.2.3Heterogeneityandthe“z‐distribution”offirms

Iffirmswereidentical,theyallwouldchoosethesameadoptiondate,andatthatdatenewplantswouldgointoproductionasrapidlyastheycouldbeinstalled.Insofarasanydiffusionpathwasobservable,itwouldonlyreflectthesequenceoftemporary,“rationingequilibria”inthemarketforautomationequipment.Tocreatethepossibilityofmarket‐clearingequilibriumdiffusionpathsinthepresentmodel,DavidandOlsen(1984)makeacrucialassumption:firmsinthefinalgoodssectorcanbeorderedaccordingtoasingleparameter,orindex,z,suchthatthegrossprofitdifferenceB(.)isacontinuousandmonotonicallydecreasingfunctionofz:

Bz(p,z)<0,forallpricespintherelevantrange. (2.11)

One possible interpretation of the z‐parameter is that it indexes an intangible attributeaffecting costs, such as managerial efficiency.51 But z also may be taken to represent inter‐firmdifferencesinmoreobjective,anddirectlyverifiableconditionsimpinginguponoperatingprofits,suchastransportcostsdifferencesaffectingthef.o.b.pricesoftheirfinalproduct.52Thefirm‐specificvariate z alsomaybe interpreted as thepriceof oneof the inputsused in the firm’s production

51Inthiscaseweshouldcallit“z‐efficiency”,byanalogywithHarveyLeibenstein’sfamous“x‐efficiency”.

52Thedifferentialtransportcostinterpretationofzappearstobequitegermaneindiscussionsofthediffusionofautomatedassemblytechnology,inviewofthenecessityofconcentratingproductioninplantsthatwillbeintensivelyutilizedthroughmultipleshift‐working.

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process, thereby permitting recognition of factor market imperfections as a source of theheterogeneityamongthepopulationofpotentialadopters.53

Itisofcourseadrasticsimplificationtosupposethatfirmscanberank‐orderedalongauni‐dimensional scale. But while working with multivariate distributions is straightforwardconceptually, it requires further specification of the co‐variances among the several sources ofheterogeneity,andthese–howeverrelevanttothefine‐grainempiricaldetails‐‐soonbegintoclutteruptheanalysis.Nevertheless,itisworthremarkingalsothatthez‐parameterintheforegoingcasewouldturnout tobecorrelatedwith thescaleofoutputundereachtechnologicalregime.Hence,therecouldbepositiverankcorrelationsbetweentheorderofadoptionamongfirmsandtheirexante or ex post (output) size, just as in the scale‐constrained models presented by numerousempiricalstudies.54

Indeed,acloserexaminationoftheresultsobtainedinMansfield’s(1961,1968)studiesofthediffusionofindustrialinnovationssuggeststhattheinformation‐contagionrationaleofferedforhiseconometricspecificationnotwithstanding,thestatisticallysignificant“profitabilityeffects”onthe rate of adoption that he reported could have altogether different underlying causes. Thestatistically significant effects found in Mansfield’s regression estimates of the logistic slopecoefficientsaregeneratedbythesubsetofindustrycaseswheretheinnovationsinquestionwerefixed‐capitalusing,andtheindexesoffirmcharacteristics(supposedlybearingontheinnovation’sprofitabilityincludedmeasuresthatinalllikelihoodwerepositivelycorrelatedwithdifferencesinexpectedoutputscale.Thatmightimplythatadoptiondecisionsoccurredwherescalewassufficientto bring the firms across the break‐even threshold level, rather than as a response to higherprospectiveratesofreturnontherequiredfixedcapitaloutlay.

Inthemodeljustpresented,however,zmaybeamorefundamentalsourceofheterogeneitythatexplainsobservabledifferencesinoutputscale,includingtheadjustmentofproductionscaleinresponsetotheavailabilityoftheinnovationitself. Moreover,thefactor‐usebiasoftechnologicalchangemayswitchbetweenonemajorwaveof innovationsandthenext,sothatthefirmswhichenjoyedinput‐priceadvantagescausingthemtobelargestinscaleofoutputundertheoldtechnologywouldnotnecessarilybefirsttoadoptthenew.55

UnderthemoregeneralconditionsDavidandOlsen(1984,1986and1992)obtainfortheexistenceofarationalforesightequilibriumpathofdiffusion,thetime‐profileoftheproportionoffirmsthathavealreadyinstalledequipmentofthenewtype—themeasureoftheextentofdiffusiondenotedbyDn(t)—mayexhibittheclassicogive,orS‐shape.Nonetheless,therearecircumstances

53Forthisinterpretation,notethatwhenzisafactor’sprice,Hotelling’slemmatellsusthatBz(p,z)=Rz2(p,z)–Rz1(p,z)=‐[L2(p,z)–L1(p,z)],whereLi(p,z)aretheinputdemandfunctionsforthatparticularfactorunderthealternativetechnologies.Thus,fthenewtechnologyresultsinthefirmexpandingitsdemandforthefactorattheprevailingpricez—atleastovertherelevantrangeofoutputpricep—condition(A8)willindeedbesatisfied.

54 David (1966, 1971), Sargen (1979), Davies (1979), Stoneman and Ireland (1983) andWhatley (1983).Stoneman(2002:Ch.8)developsannestedeconometricmodelingapproachtodistinguishingamong“rank,”(capital)“stock,”temporal“order”and“epidemic”effectsinthediffusionofnewprocesstechnologies.

55Instead,thesizeorderingoffirmsintheindustrymayundergonon‐monotonictransformationinthecourseof the diffusion process. To appreciate this, one would have to look more closely at the product marketequilibriumconditions.

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in which the diffusion curve would be concave over its entire range.With this class of models,universaladoptionor“complete”diffusionisbynomeansanecessary,foreordainedoutcomethatresemblesthegradualbutinevitablefillingupofabottle.

Althoughtherearesolutions(dynamicequilibria)inwhichthediffusionandlearningwillgetunderwayandcontinueuntilitapproachesuniversalacceptance‐‐thesituationdepictedinFigure1,itisalsoquitepossibleforthediffusionprocesstobebroughttoastopshortofuniversaladoption,whichthecasedepictedbyFigure2.

[Figures1and2here]

Thereasons for thisareseveral. (i)The innovationmayshift theusing‐industryaggregatesupplyschedulerelativetothemarketdemandschedule,leadingtofallingmarginalrevenueandthedisappearanceofapositivegapbetweenanticipatedbenefitsandanticipatedcostsofadoptionattheextensivemarginal.(ii)Itispossiblethatproductionofthecapitalgoodembodyingtheinnovationrequires an exhaustible resource input,whose risingmarginal supplyprice checks the fall in therelative price of the capital good, stopping the break‐even threshold for adoption from movingdownwardthroughthez‐distribution.(iii)Partialdiffusionismorelikelytoarise,therefore,ifthedynamicdriverofthethresholdlevelisentirelyendogenous,anddependentuponpositivefeedbackfromthemovementoftheextensivemarginofadoption—asinthelearningmodel.

Inthefullinformationthresholdmodeltheheterogeneityofthepopulationrequiresthatweabandonthenotionthatattimettherearepotentialadoptersbeyondtheextensivemargin:ifthethreshold ceased to fall, the processwould be at a stationary equilibrium.This iswhatGriliches(1980)pointedtowhenhecommentedthatamodelof“amovingupperlimit”–suchasthatinDavid(1969)–couldreplacehisspecificationofanexantefixedupperlimitthatcouldbeobservationallyidentified. Inaddition,andofpossiblygreater interest, is theresult that insomeconjunctionsofinitialsupply‐sideanddemand‐sideconditions,thestartofadiffusion‐cum‐learningprocessdrivenbyperfectcompetitionmayremainblocked.Thiscanbethecaseevenwherethepositive‐feedbackprocessdrivenbylearningeffectscouldtakeoveroncethelevelofadoptionandcapitalgoodspriceshad been brought to a critical “take‐off” point, presumably by non‐market interventions. Moregenerallystill,underfull‐employmentconditions,optimumsocialmanagementofanewtechnology’sadoptioninthepresenceoflearningexternalitiesmaycallforfasterdiffusionthanwouldoccurevenwithcompleteinformation(perfectforesight)andperfectcompetitionprevailinginalltherelevantmarkets.56

Complicationsofthisnaturebegintotakeongreatereconomicpolicysignificancewhenoneturns,asIdonow,toconsidertheconnectionbetweenthemicroeconomicsoftechnologyadoptionandthemacro‐industry‐levelcourseofproductivitygrowth.

3.3Sourcesofadopterheterogeneitiesandtime‐constantsofdiffusionprocesses

Althoughtheemphasisoftheforegoinghasbeenplaceduponthecommonstructureoftheexplanationofdiffusionphenomenaprovidedbythethresholdadoptionmodelsandtheconsequent

56Theimplicationsofthislatterpointforpatentpolicyasasecond‐bestpublicstrategyareexaminedinDavidandOlsen(1992).

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homomorphismthatispresentacrossthearrayofspecificdiffusionprocesses,itisimportantnottoclosethisdiscussionwithoutcallingattentiontotheempiricallyobserveddifferencesinthetime‐constantsthatareanimportantidentifyingvariable.Thisispointthathastendedtobeoverlookedintheeconomicsliterature57.

Finally,itisappropriatetoconcludebyrecallingthatthegenericstructureoftheadopters’heterogeneity approach to understandingdiffusionphenomena is so inclusive that unobservablepsychological resistances or other behavioral impediments to action under uncertainty can beformulatedwithinthisframework.Ifonestartswiththesuppositionthatsuchdirectlyunobservableimpediments, often described in the rural sociology literature as “resistances to novelty” or“psychologicalinertia”differamongindividuals,thenshapeofthedistributionofsuchresistancesthen becomes a relevant structure affecting the dynamics of the novelty’s acceptance in thepopulation (see, e.g. David 1969). For example, Young (2005) proposes to use the shape of theaggregatediffusionpathstoidentifywhethertheprocessunderlyingthediffusionofhybridcornwassimple contagion model involving information transmission (generating a logistic), and or by a“sociallearningprocess”ofthekindfirstsuggestedbyGranovetter(1978)–whichhasbeennoticedcanbeformulatedaamemberofthefamilyof“thresholdmodels.”

The information propagation process can be specified in both cases as proceeding by arandomcontactsinacompletelyintermixedpopulation,sothattheonlystructuraldifferenceisthemodels is whether there is a uniform degree of “a priori resistance” among the agents, or adistributionofresistancesthatmustineachcasebeovercomebyacorrespondinglystrongersignalregarding thenetbenefit of adoption.Given the specificationof a randomcontactprocess, if theexperienceofadopterswereheldtobeuniformitcouldbesupposedthatsomecumulativenumberofcontactsbyadopterswouldberequiredtoovercomeresistanceineachpotentialadopter’scase.

Whileamuchinthisveinispossible,therelevantpracticalquestioniswhetherthespeedofthese information transmission processes is not so rapid, compared with the transition ratesinvolvedwhenirreversibleinvestmentdecisionsaboutnewtransportinfrastructures,ordurableandlumpyadvancedwaferfabricationequipment(“steppers”)inthesemiconductorsareatstake,thatthefinegraindifferencesamongthemwillnotsubstantiallyaffecttheimpactofthediffusionprocessupon productivity growth. It is to empirical questions of this kind that the following section isdirected.

57Butonemayaskwhetheritreallyisplausiblethatinformationpropagationlagsandsociallearningaboutagiven,universallysuperiortechnologycouldaccount for theseobserved lags?.Even in thecaseofGrilicheshybridcornstudy,thedifferencesbetweenIowaandotherstates,e.g.Kentuckyis4vs9yearstogofrom10%to90%adoption.AsimplycontagionprocessofthekindproposedbyMansfieldwouldhavetoexplainwhythetimerateofcontactsbetweenadoptersandnon‐adopterswassomuchhigherinIowathanelsewhere.ThealternativeASNmechanismforthetransitionofindividualfarmer’stothenewmethodwouldencounterthesameproblem: if individuals need repeated exposures to reportsof the innovation’s economic advantagesbeforebecomingconvinced,whyisthesupportofthedistributionofpsychological“resistances”somuchmorecompactamongthefarmersinsomeregionsthanelsewhere.Grilichescommentsonheterogeneitiesamongthecropreportingregionswithinstatesasasourceof loweracceptanceratesat thestate level.Withinhisframework of explanation those difference would have to correspond to differences in the observedprofitabilityofadoption,andthesourcesofthelatterremainidentifiedbutitisreasonabletosupposethatthiswouldbeofthesamevemagnitudeasthedifferencesintheobservedratesofacceptance.(Giventhepowerofthetestandtheerrorlevelforfalsepositives,theASNisaninversefunctionofthedifferencebetweensamplemeans.)

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4.DiffusionandProductivityGrowth:FromMicrotoMacro

A portion of the comparative neglect of empirical research on the microeconomics oftechnology choice and innovations’ adoption histories may be attributed to the fact that theconnectionbetweendiffusionandaggregateproductivitygrowthhasnotbeendevelopedformally.Ashasbeenpointedoutelsewhere(David1986;andalsoDavid&Foray1995),thepoliticaleconomyofgrowthpolicyhaspromotedexcessiveattentiontoinnovationasadeterminantoftechnologicalchangeandproductivitygrowth,totheneglectofattentiontotheroleofconditionsaffectingaccesstoknowledgeof innovationsandtheiractual introduction intouse.The theoretical frameworkofaggregateproductionfunctionanalysis,whetherinitsearlyformulationorinthemorerecentgenreofendogenousgrowthmodels,hassimplyreinforcedthattendency.Totrytocorrectthatimbalanceby explicitly modelling the connections between productivity growth and diffusion dynamics issomethingthatZviGrilichesmightwellhavedone,hadhadhecontinuedtopursuehisearlyinterestinthediffusionofprocessinnovationsratherthanfocusinghisresearchtoempiricalstudiesoftherelationshipsproductivitychange,R&Dinvestment,andpatentingactivity.

Themodelconsideredheresufficestocapturethedirectandindirecteffectsofthediffusionofamajoror“radical”process‐innovationuponthemeasuredgrowthofinputproductivity.Whileitserves to highlight several general propositions that are simple but often overlooked about therelationshipbetweenthepaceofproductivitygrowthandthepaceatwhichproductivity‐enhancinginnovationsareadopted,58thisheuristicexercise’smainvalueistoidentifyexplicitlykeymicro‐leveldeterminants of the dynamics of diffusion among the proximate factors governing the aggregateproductivitygrowthrateintheadoptingsectoroftheeconomy.

Thecomponentsofthemodelarereducedformrelationshipsthatembedasetofunderlyingthemicroeconomicconditionsgoverningfirms’decisionstoadoptanew,fix‐inputusingandvariable(labor)input‐savingtechnologyforconsumer‐goodsproduction,andtheinducedprocessesthroughwhichsuppliersandusersofthenewprocess‐equipmentmodifyitsdesignandmodeofapplicationonthebasisof fieldexperience.Beingbasedon“learningbydoing”and“learningbyusing,”suchmodifications are driven by the innovation’s diffusion and, in turn, contribute both directly andindirectlytoenhancingproductivityintheconsumer‐good’ssector.Theirdirectimpactisduetothereducedlabor‐inputrequirementswiththenewtechnologywiththattechnique,whichareassumedto result from labor‐training effects and organizational changes that spill‐over throughout the“progressive,” innovation‐adopting segment of the consumer‐goods industry, thereby raising itsaveragelevelofproductivity.Theirindirectimpactstemsfromtheloweredprice‐performanceratioofthecapitalequipment,whichexpandstheextensivemarginofadoptioninthatindustry,increasingthe relativeweight of the industry’s “progressive” segment in total industry output, and therebyraisingtheindustry’soverallleveloflaborproductivity.

58These relationships have previously been explored in the specific historical context of the effects of thediffusion of the electrical dynamo (and secondary electric motors in particular) on the surge of U.S.manufacturing productivity growth during the 1920s. See David (1991:Technical Appendix), an OECDpublicationthathasbeencitedmorewidelythanithasbeenread;apdfversionmaybeobtainedonrequestfromtheauthor. SeealsoDavidandWright (2003) for comparativeevidenceon thediffusion‐productivitygrowthlinkinthecaseofU.S.,BritishandJapaneseindustrialelectrificationduringtheInterwarera.

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Inthebasicformulationexhibitedhere,thesimulationstructuredoesn’tpretendtocapturethe entire range of complex interdependences that could exist between the pace of the newtechnology’sdiffusionandtherateof(endogenous)improvementsstemmingfromexperiencewiththenewtechnology,but itconveysanempiricallyplausiblepictureofadynamictransitionintheindustrythat isbeingdrivenendogenously,by feedbackfromtheprocessofdiffusion itself.Eventhoughtheremayexistothersourcesofchangeaffectinguser‐costsofthenewtechnology,inadditionto the experience‐based improvements in input efficiency explicitly represented in themodel asdependingdirectlyuponcontinueddiffusion,thespecificationsemployedinthesimulationswillbeseentoplausiblyallowforotherindirectdynamicfeedbackeffectsonthegrowthofaggregatelaborproductivityandTFPintheconsumer‐goodsindustry.

Presentation of the details of the micro‐to‐macro simulation model is relegated to theAppendix,andtextthatfollowscomplementstheformalderivationsfoundtherebydiscussingtheplausibility (if not the “realism”) of the main assumptions and specifications (in sect. 4.1), andcommentingupontheinterpretationofthesimulationexercises(insect.4.2).59

4.1 Assumptions, model specifications and implications for the diffusion‐driven aggregateproductivitygrowthrate:

For these purposes one may envisage a discrete process innovation embodied in anindivisiblecapital‐good(“machine”)thatisassumedtobeoffixedcapacityandinfinitedurability.The production process using this new technique is characterized by lower unit labor inputrequirementsthanareobtainedwiththepre‐existing,purelylabor‐usingmethodofproducingtheconsumer good, and it is assumed that the respective unit labor requirement for each of thetechniquesareinvarianttothescaleofproduction(uptothecapacitylimitofthemachineinthecaseofthenewerone).Specifically,denotingtherealoutputflowperunitoflaborinputusingthej‐th technique at time t as tj , where j = o represents the “old” technique and j =N, the “new”

technique, it is assumed: (a)that the innovative technique is characterized by higher laborproductivity: ( ) ( )N ot t forallt;(b)theoldtechnologyusesonlylabor,anditsunitlaborinput

requirementsremainunaltered: ( )t 0 0 ,forallt.

Further,thereisan“incrementalimprovementfunction”fortheinnovation,arisingfromtheaccumulationofexperienceincommercialapplicationsofthenewtechniquewhichyield“learningspill‐overs” within the progressive segment of the consumer‐goods industry. These “learningexternalties”leavetheoutputcapacityofthemachineunchangedbuthavetheeffectofraising N(t),theaveragelaborproductivityofallofthefacilitiesintheprogressivesegmentoftheindustry,thatistosay,ofallproductionentitiesthathaveadoptedtheinnovation.60Becausethecapacityoftheinnovation‐embodying“machines”isassumedtobefixed,andthelatterareperpetuallydurable,

59Thefollowingtextrefersreaderstospecificequations,usingthenumberingthatappearsintheAppendix..60The context of the innovation’s applicationhere refers todifferentproduction facilities, all ofwhich areassumedtoinvolveessentiallythesameproductionoperations.Thisabstractionfromrealityisworthnoting,especiallywhenoneconsidersthediffusionofso‐called“generalpurposetechnologies.”AdaptationofGPTstotherequirementsofdifferentindustrialapplicationstypicallyhasentailedsignificantcollateralinvestmentintechnicalimprovements,ancillarycapitalformationandorganizationalchange‐‐ashasbeendocumentedforspecific cases as different as electrification and ICTs (see, e.g., David ,1991; David and Wright (2003);Brynjolfsson(2000);Bresnahan,BrynjolfssonandHitt(2002)..

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cumulativeproductionexperiencegrowsparipassuwiththestockofmachines.Further,underthesimplifyingrestrictionthatthetotalnumberofproductionfacilities(firms)inthesectorisconstant,theshareofthesector’soutputproducedbyitsinnovation‐adoptingfirmsisthemeasureD(t)=Dn(t),whereDndenotestheproportionofadoptersamongNfirmsofthissector.Astheinnovationcomesintomorewidespreaduseintheconsumer‐goodssector,thisresultsinmicro‐levelaverageunitlaborrequirementsdecreasingforalladopters,bothabsolutelyandvis‐à‐visthe“old”technique.61

Atagivenmomentintimethelevelofaveragelaborproductivityinthesectoroftheeconomytowhichtheinnovationisapplicablecanberepresentedasafunctionoftheshareofthesector’soutput being produced by its “progressive”, innovation‐adopting segment and the relative laborinputrequirementofthenewandtheoldtechniques.Theoutputshareoftheindustry’s“progressive”segmentistherelevantmeasureoftheextentoftheinnovation’sdiffusion,D(t),62andtheaveragelevelof laborproductivitythroughouttheconsumer‐goodsindustryisfoundastheinverseoftheweighted harmonic average of the unit labor requirements of adopters and non‐adopters of theinnovation (eqs.A.1,A.2) ‐‐ theweightsbeingD(t) and [1–D(t)], respectively. Consequently, anincreaseintheextentofdiffusionhasadirect,compositionalshifteffectonthegrowthrateofaveragelaborproductivityinconsumption‐goodssector,andmayhave“indirecteffects”throughthevarietyofchannelsthroughwhichmorewidespreaduseofthenewtechnologyalters itsunit laborinputrequirements—vis‐à‐visthatofthe“old”technology‐‐inallapplications(eq.A.1a).Improvementsthatlowertheunitlaborrequirementsassociatedwiththeinnovation,intermareasourceof“self‐reinforcing”feedback”thatsustainsitswideningacceptance.

Afurther,generalempirical implicationmayberemarkeduponatthispoint.It isevident(from eq. A.5) that the average rate of growth of labor productivity in the innovation‐adoptingindustrycannotbestrictlyproportional to therateofgrowthof theoutput‐sharemeasureof theextent of diffusion,D(t).When the time‐path ofD(t) takes the classic, symmetric S‐shaped formdescribedbythecumulativelogistic(orthenormal)distribution,theannualchangeintheextentofdiffusion(dD)willreachamaximum(theinflectionpointofthecurve)whereD=0.5,butthethepeak in the proportional growth rate of labor productivity necessarily occurs after the extent ofdiffusion had passed its peak ‐‐ the “half‐way” mark, under the stated symmetry conditions.Moreover,furtherpostponementoftheproductivitygrowthpeakwouldresultwheretheelasticityoftheinnovation’sindirecteffectsisnotconstant,butinsteadincreasesastheinnovationbecomes

61BecausetheprocessenvisagedisoneinwhichD(t)increasesmonotonically,itisnotnecessarytoformallyspecifythattheenhancementeffectsduetolearningareirreversible,sothattheratio( ( ) / ( )N ot t )isnon‐

decreasing.

62 ThedomainofD is [0,1], but theupper limit is definitional and the attained limit ofD(t) is taken to beendogenous,forreasonsdiscussedinconnectionwithFigure2,above,inSection3,but,undertheassumptionsmadehere,productionfacilitiesusing“themachine”alwaysareoperatedatthelatter’sfixedcapacity(specifiedintermsofoutput).Further,itisconvenienttoassumethatthereisa“managementconstraint”ontheuseoflaborintheoldtechnology,sothattheoutputofindividualproductionfacilities(firms)inthenon‐progressivesegment isboundedat a constantuniform level thatneverexceeds thatof themachine‐using firms.TheseassumptionssupporttheequivalenceofthemeasuresD=Dn.NotethatGriliches(1957)alsoworkswithanoutputrelatedmeasureofD(t)–theproportionoftotalcornacreagethatwasplantedwithhybridcornseeds.Hadhe sought todefine an appropriate (output share)measure forderiving averageproductivity in corn‐productionas a functionof the acceptanceofhybrid corn seed, itwouldhavebeennecessary toallow fordifferenceinyieldperacrebetweenhybridandopen‐pollinatedcornineachofthecrop‐reportingregions.ButthatwasnotGriliches’purpose,andhesimplyacceptedtheavailableU.S.AgricultureDepartmentstatisticsofacreagesplantedbytypeofseed.

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the dominant technology within the sector. Such “delayed positive feedback effects” on thedifferentialbetweenproductivitylevelscharacterizingthenewandoldtechnologiesarequitelikelyto be important where there are significant network externalities, and labor force trainingexternalitiesthataccompanymorewidespreadadoptionoftheinnovation.

Forconvenienceofimplementation,thesimulationmodelisspecifiedundertheassumptionsthat:

(i)thereisastationarylog‐logisticfrequencydistributionofanunderlyingcriticalvariatez

among the firmbelonging to thepopulationofpotential adopters (e.g., their respective expectedoutputscales,ordistancesfromthemarketfortheiroutput);

(ii)thethresholdvalueforagentstoselectthenewtechniqueisz*(t)attimet,anditdeclinesattheexponentialrate8;

(iii)that,sincethenewtechniqueisembodiedinafixeddiscreteinput‐bundle,onlyoneunit

ofwhichisacquiredbyeachadoptingagent,firmsworkingwithaunitoftheinnovativetechnologyallwillhaveidenticalandconstantflowoutputcapacitykN ,whereasnon‐adoptingfirmswillhaveconstantflowoutputcapacitykO.<kN.

Theseassumptionsleadimmediatelytotworesultsthatareusefulinsimplifyingtheexposition.Theindexoftheextentofdiffusionattimet,D(t),definedasproportionofthepopulationthathasadoptedtheinnovation,willbealogisticfunctioninthet‐domain,withasymptoticsaturationatD()=1(eq.A.6).Secondly,theinstantaneousgrowthratealongthediffusionpathwillbedirectlyproportionalto[1‐D(t)],wherethefactorofproportionalityis >0(seeeq.A.7b).

Theparameter8 ,ashasbeennoted,istheexponentialrateatwhichthethresholdvariatez*(t) isdecreasing,whereas is the slopeparameterof the cumulative logisticdistribution, andvariesdirectlywiththekurtosis(peaked‐ness)ofthefrequencydistributionofzandinverselywithitsvarianceamongthefirmsformingthepopulationofpotentialadopters intheconsumer‐goodssector. Variations of this parameter pair, reflecting alterative underlying conditions affecting themicroeconmicsofadoptionoftheinnovationthereforewilltranslateintoalternativeshapesofthediffusionpath,D(t),andthenceintocorrespondingalternativeproductivitygrowthpaths.

Afurthersimplifyingspecificationoftheendogenous“improvement function”forthenewtechnologyresultsin (iv)aconstantelasticityofaveragelaborproductivityamongadoptingfirmswithrespecttotheextentofdiffusionintheindustry): ( )t = 0( ) = ,forallt.

BecauseD(t)istantamounttoanindexoftheextentofthecumulativeexperiencewiththeproductionand theutilizationof the innovation‐embodyingcapital goods, this constantelasticityconditionissatisfiedbytheclassiclearningcurveor“progressfunction”suggestedbyHirsch(1952)andArrow(1962)–asisseenfrom(eq.A.8).Thatinterpretationisentirelystraightforwardwhenthe “learning” involving integrating the novel capital goods into production operations and theacquisition byworkers of skills in its use, as a function of operating the infinitely durable fixed‐capacitymachines.Aswasnotedabove,giventheproportionofoutputrepresentedbythecapacityof the new machine stock then would vary directly with the cumulated output of the industry

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supplyingsuchequipment,andalsowiththecumulatedvolumeofgrossinvestmentrepresentedbythosemachines.63

Itisnecessarytopausehereandtonoticeanimplicationofhavingpreviouslyspecifiedthatthemicro‐level“break‐even”thresholdwasbeingdrivendownwardsthroughthedistributionF(z)ataconstant(exponential)rate(8).Consistencybetweenthatspecificationandthespecificationofa constant elasticity of “learning” with respect to D(t) ‐‐ which, by lowering the unit laborrequirementsforusersofthenew(mechanized)techniquewillreducethecriticalthreshold(z*)ata slowing pace as diffusion proceeds, implies that some other forces in addition to the assumeddiffusion‐induced “learningeffects”mustalsobeactingonz*(t) Theseauxiliarydynamicdriverswould have operate so as to reduce z*(t) at a compensating pace that was increasing inD(t) ‐‐although less‐than‐proportionately – in order tomaintain the over‐all constancy of the specifiedexponentialrate(8)ofthethreshold’sdownwardpassagethroughthez‐distribution.

Plausiblecandidatesareavailabletofillthatrole,andtheinterpretationofthereducedformsimulationmodel can be enriched by briefly describing a particular set ofmechanisms that areconsistent with the previous analysis of diffusion dynamics in a heterogeneous population ofpotentialadopters.64Theaccumulationofprocessinnovationsinthecapital‐goodssectorthatwassupplying the machines ‐‐ deriving from the shared cumulative experience gained in machine‐building, could generate cost‐savings advances in machine‐building at a rate that would beaugmentedbyrecombinationoftheresultingincrementalprocessimprovements.65Theimplicationofrecombinantnoveltyinthiscase,assumingcompetitionamongthefirmsinthemachinerysupplysector,isthattherateatwhichtheratiobetweenrealwageandthecompetitivesupply‐priceofthemachinewouldtendtorisemorequicklyasthediffusionprocessproceeded–becausethecumulativenumberofmachinesinstalledwouldriseparipassuswiththerisingextentofdiffusion‐‐undertheassumption that the number of establishment in the population of potential adopter remainedunchanged.

Therefore,wemayposittheoperationofthissecondfeedbackloop‐‐fromtheprogressofdiffusiontoprocessinnovationsinmachine‐buildingthatarecost‐savingforthefirmsinthatsector.Theeffectofthelaterwillbetoincreasetherateatwhichthethresholdforadoptionintheconsumer‐goodssectorisreducedoverthecourseoftheinnovation’sdiffusion.Thisinducedconcomitantof

63This follows immediately fromtheassumptions that the ‘’learningeffect” in theuseofmachines isbothHarrod‐neutral and disembodied. The former of these assumed conditions leaves the per period outputcapacityofadditionstothestockofthenovelcapitalgoodunaltered,sothattheratioofaggregateoutputtothestockofmachinesinstalledremainsconstant,and,giventheinfinitedurabilityassumption,overtimethecumulativevolumeofproduction risesparipassuswith cumulative investment in thenewequipment.Thelatterconditionimpliesthatit“spillsover”,providinganexternalityforalltheenterprisesthathaveadoptedtheinnovation–intheformofthereducedunitlabor‐requirementsinproductionoftheconsumergood(asnoticedinfootnote37,above).

64Harkingback to themulti‐sectormodelpresented in section3, itwill be recalled that thepopulationofestablishmentsintheconsumer‐goodsindustrymaybeheterogeneouswithrespecttotheirexpectedscalesofproduction,andthethresholdscaleforadoptionz*wouldthentendtobedrivendownwardbyincreasesintheratiooftheunitlaborcoststotheusercostofthefixedcapitalequipment(theindivisible“machine”).

65Onrecombinantgenerationoftechnological(andother)novelties,see,e.g.,Weitzman(1998),andShapiroandVarian(1999),andtheconceptualizationaprocessofincremental“recombinantinnovation”generatingarising–albeitbounded‐‐rateoftechnologicalchange.Thisisassumedheretoyieldanacceleratedpaceofgainsintheefficiencywithwhichtheinnovation‐embodyingmachinescanbeproduced..

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continueddiffusioncouldcombinewithanexogenousconstanttrendrateofgrowthofeconomy‐widerealwagerateduetodevelopmentsarisingoutsidetheinnovationadoptingconsumergoodsindustry,andtherebysufficetoexactlyoffsetthedeceleratingrateoffallinthethresholdduetothefeedbackfromthedirectandindirecteffectsoftheinnovation’swideningadoption.Indeed,itisnotdifficulttofindtheconditionsunderwhichthejointoperationoftheseexogenousandendogenousdriverswouldjustsufficetomaintaintheconstancyoftheexponentialratefallinthethresholdforadoption,fulfillingthesimulationmodel’sabilitytogenerateadiffusionpaththathastheclassicallogisticform.66

Theforegoinginterpretationofthereducedformlabor‐productivityimprovementfunctionfor the innovation clearly shares somethingwith the conventional suppositions that learning‐by‐producing and learning‐by‐using new investment have effects on productivity that are Harrod‐neutral.Consequently,itisconceivabletheseendogenouseffectscouldbeincorporatedingrowthmodels that are consistentwith the existence of a balanced, or steady‐state growth path for theeconomy.But,aswillbeseen,thetransitionfollowingtheintroductionofaninnovationinagivenindustryorsectoroftheeconomygeneratesawaveinthegrowthrateofaggregateproductivity.Tomaintaintheeconomy’saggregateproductivitygrowthatsteadyrateswouldrequireasuccessionoffortuitouslytimedinnovationsappearinginvarioussectors,orasequenceoftransitionsdrivenbytheoverlappingdiffusionofsuccessivelyintroducedgeneral‐purposetechnologies.

Suchconstructions,however,liebeyondtheaspirationsofthepresentsimulationexercise,whichaimstoestablishmorelimitedpropositionsthediffusion‐productivitygrowthnexus.Itshouldbeequallyobviousthatthepresentformulationhassoughttoavoidthecomplicationsofallowingforless‐than‐universalandinstantaneouslearningexternalities,suchaswouldbepresentwereonetosuppose that the learning effects resultedmachines that improved in quality continuously fromvintage‐to‐vintage.67Werethelattertobethecase,however,thelatestincrementalreductioninlabor

66Fromthespecificationofthelearningfunctionineq.A8,andeq.A7bitcanbeseenthattherateatwhichz*(t) would be falling due to the endogenous learning effects within the adopting industry is 8e(t)= [

(log{ ( )} / )D t t ]. This rate, obviously, is decreasing in D(t). The simplest specification of an offsetting

endogenouslygenerateddownwardforceontheadoptionthresholdwouldrequirethatratetobe:8`(t)=8‐8e(t)=8 (1 )[1 ( )]D t ,i.e.,aratethatisincreasingwithD(t),butless‐than‐proportionately..Inthepresentcontextofaninnovationthatisrelativelyfixedfactorintensiveandvariableinput‐(labor‐)saving,thejoint candidates for this roleare (1)anexogenousconstantupward trend in therealwage (8 at therate [(1 ) )–due todevelopmentsexogenous toboth themachine‐building industryand theparticular finalgoodsindustry,andanendogenousfeedbackfromcumulative“learningeffects”inthemachine‐buildingsector.Thelattermustcontinuouslyreducetheratiobetweenthepriceoftheinnovation–embodyingcapital‐goodandthewageratethroughoutthediffusionprocess–aratethatisincreasingwithcumulativeincreaseinthestockofmachinesthathadbeeninstalled:(8[ (1 ) ]D(t)).

67CominandHobjin(2008)havemadeanefforttointroducecontinuousvintageimprovementofembodiedinnovationsintoaone‐sectormodelofsteady‐stategrowth,whileallowingforthegrowthrateofaggregatelaborproductivity tobeaffectedby technology‐specific “diffusion lags”.As theirs is a representativeagentmodellingapproach,theconceptofdiffusiondepartsfromthedefinitionofincreasingextentofacceptanceofthe innovation among a heterogeneous population of potential adopters, or of the rising proportion ofaggregateoutputproducedwiththenewtechnology.Curiously,therefore,“lags”intheirmodeldonotmeasurethe time elapsed between commercial introduction and substantial saturationof themarket for particularinnovations.Instead,theydefinethe“diffusionlag”unconventionallyasthe(constant)delaybetweeninventionand commercial introduction of each vintage of the family of innovations ‐‐including the first). The latter

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requirements would be confined only to the current extensive margin of adopting firms in theconsumergoodssector—whichisnotthecasehere.68

The foregoing log‐logistic heterogeneity specifications, and the expression for the growthrateofaggregatelaborproductivityasadirectandindirectfunctionofD(t),leadtoanexpression(eq.A.9)fortheproportionalrateofgrowthofaggregatelaborproductivityintheconsumer‐goods

sector‐‐denotedby ( )LL t

:

where

( )(1 )( ) ( ( )[1 ( )]( )),

1 [ ( )] ( )

( ) 1 [ ( )] ,

LLt

t D t D tt D t

t D t

and 0 ( )( )N o

,

>0beinganormalizationparameterinthelearningfunction.

ItisevidentthatthatthegrowthrateisquadraticinD(t)‐‐whetherornotthereareindirectlearningeffectsfromdiffusion(i.e.,for0< )–whichleadsonetoanticipatethefindingthatthemonotonicriseofthelogisticdiffusioncurvewillgenerateasingle‐peakedwaveinthegrowthrateoflaborproductivity.Further,theproductofthemicro‐levelparameters, ,willactsasascalarmultiplier affecting the slope of the diffusion curve and hence the the amplitude of the wavegenerated in theproductivity growth rate.The first aspectof thismaybe seendirectly from thesimulationsdisplayedinFigure3,whichshowsthreealternativediffusionpathsontheleft‐sideofthepanel,correspondingtodifferentheterogeneityspecificationscorrespondingtothevalueofthevarianceofthez‐distribution,whileholdingconstant8,therateoffallinthethresholdz*(t).Ontheright‐side of Figure 3 appear the corresponding waves that are induced in the growth rate ofaggregatelaborproductivity.69

Fromthepositivevalueof2thatappearsinthenotesbeneathFigure3,itcanbeseenthatthesegrowthratesimulationsallowforlearningeffectswiththenewtechnology.Thetiminginthepeakintheaggregatelaborproductivitygrowthrate,whichoccursafterthemaximumintheslope

correspondstowhatGriliches(1957),Mansfield(1962)andthefollowingliteraturelabelasthe“introduction”lag,distinguishingitfromthe“acceptance”or“diffusion”lag.

68Withouta complete specificationof themicro‐level adoptiondynamics it isnotpossible to compare theimplicationsforthepathofaggregateproductivechangeofavintagemodelwithembodiedlearningeffects,ratherthanthepresentmodelofdiffusionwithdisembodiedaugmentationofthebenefitsaccruingtoalltheadoptersoftheinnovation.

69FromthetoppanelofFigure4(below)italsomaybeseenthatalthoughthebehavioroftheaveragelaborproductivitygrowthrateisnon‐monotonic,theunderlyingdiffusionrate(i.e.,theproportionalgrowthofD,isundergoingcontinuousretardationalongthelogisticpath.Agoodbitofsurprise,andsomeconfusiononthispointstemsfromthecasualsuppositionthattherateofproductivitygrowthshouldreflectimmediatelyreflecttherateofdiffusion,whereasitistheabsoluterateofchangeinDthatmatters.

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ofthediffusioncurve–attheinflexionofthelogistic(D(t)=.5),ashasbeenseen,isageneralpropertythatholdswhetherornotthereareindirect,feedbacksfrom“experienced‐basedlearning”.

[Figure3here]

Figure3exhibitsathirdpoint,uponwhichPart2remarked:theinfluenceoftheshapeofthedistribution of underlying population heterogeneity upon diffusion dynamics, and hence uponaggregateproductivitygrowthintheindustry.Otherthingsbeingequal,thelowerthevalueofthelogistic parameter(, the greater is the variance (and the lower is the Kurtosis) of the frequencydistribution of the population characteristic (z) that enters the micro‐level choice of techniquedecisions.Thus,withthe“break‐even”assumedtobefallingexponentiallyatthesame(fast)rateinall three situations, its is seen that lowervaluesof(stretchout thediffusionprocess, lower theproductivitygrowthprofilesanddisplacethe(attenuated)peaksubstantiallyintothefuture.70

Twoimplicationsfollowimmediatelyfromthislatterobservation.First,oneisonlyseeinghalf thepictureby focusingon thedeterminantsof thepaceatwhich the thresholdpointz*(t) ispushed downward through the z‐distribution. Putting this more concretely, the essentiallyneoclassicalfactor‐substitutionstorythateconomiststodayliketotellaboutthewaythatanewformofcapitalraisesaggregatecapital‐intensityandtherebyraiseslaborproductivity,moreoftenthannotisaninadequate“representativeagent”tale.Alltheemphasisisplacedontheforcescausingtherelativefalloftherealuser‐costsoffixedcapitalinputs(suchascomputerequipment)vis‐à‐vislaborinputs—asthedriveroffactorsubstitution,andhencethedeterminantofthegrowthrateoflaborproductivity.Butifthez‐distributiondifferedfromonesectoroftheeconomytothenext,therewouldbequitedifferentpatternsofdiffusionandcorrespondinglydifferentlaborproductivityperformance– for which the hypothesized representative agent “model” would have, at best, only ad hocexplanations.71

Secondly, it is worth noticing that the measured pace of diffusion and the dynamics ofproductivitymaywellbeaffectedbythealterationoftheunderlyingz‐distribution,asaresultoftheeconomicpressuresemanatingfromtheadoptionoftheinnovationbysomefirmsintheindustry.Itisquiteconceivablethatcompetitivepressuresonthenon‐adoptingremnantoftheindustrywouldforceoutfirmsatthelowzendofthedistribution,therebytendingtoraisetheparameter(overthecourseoftheprocess.Theresultwouldnolongerbeastrictlylogisticdiffusionpath.Topreservethelatterform,itwouldbenecessaryforthez‐distributiontobetransformedbya(‐preservingupwardshiftinitsmean.Supposethatevolutionofthefirstmomentofzproceededataconstantproportionalrate,:.Itissimpleenoughtoshowthattheslopecoefficientoftheresultinglogisticdiffusionpathwouldthenbecome{((8+:)}.Consequently,theworkingofcompetitiveforcesattheindustrylevelcanquiteneatlybe formally assimilated into this richer accountof long‐runproductivity growthdynamics.

70Notethattheabsolutevaluesof(and8usedinthissimulationareratherarbitrary;thesameresultscouldbeobtainediftheannualrateofdeclinein8weretakentobehalfasfast–approximatingthe15%perannumtrendinthehedonicpricesofcomputerandcommunicationsequipment—iftheunderlyingheterogeneitydistributionwashalfasspreadout(i.e.,(={0.6,0.9and1.2}).

71 The resemblance of this picture to the now‐popular line of interpretation of the computer‐revolution’scontribution to aggregate productivity (developed in the influentialwork of Jorgenson (2000) and his co‐authors)isnotentirelycoincidental.

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4.2 Simulating effects onmicro‐level deteminants of diffusion on the growth rate ofmeasuredTFP

Explicitmodellingof themicroeconomicsofdiffusiondecisionsshedfurtheranddifferentlightuponthesourcesofthe“productivityresidual.”Quiteclearlythiscannotbethewholepicture,becausetheeffectsofthediffusionprocessinthecaseofeachinnovation(orfamilyofimprovableinnovation)aretransitional.Whenthenewtechniquefindsitswayintoalltheavailablenichesofuse, the impetus imparted to productivity improvement is exhausted. Diffusion thus resemblesevolutionaryprocessesofselection, inbeing“a firethatconsumes itsownfuel.”This transparentconsiderationcertainlyissufficientwarrantfortheattentionthatZviGriliches’empiricalresearchprogramdevoted to thenexus between firm‐levelR&D investment andmulti‐factor productivitygrowth. But perhaps something was lost by working at that very low level of aggregation: itsuppressedattentiontotheindustry‐andsector‐levelproductivityeffectsthatdependeduponthediffusion of the novelties created in company laboratories, and by publicly funded research inuniversitiesandgovernmentmission‐agencies.

Granting while sustained advances in total factor productivity do depend upon thegenerationoffurtherinnovations,tothedegreethatsubstantialproductivityraisingtechniquesarenot being introduced continuously in time, the pace of TFP growthwill be subject to wave‐likeimpulses that reflect the dynamics of the overlapping diffusion of sequential innovations.Technological breakthroughs that yield potentially large and ubiquitous gains unit laborrequirements for theadopters,and induceclustersof innovation innumerous technicallyrelatedindustries,consequentlymaywellgeneratepronouncedsurgesintheproductivitygrowthratesomeconsiderabletimeafterthekeyinnovationisfirstintroduced.

ThesimulationmodeldevelopedintheAppendixgenerateschangesintheTFPgrowthratebyexpressingthelatterasinverseoftheweightedaverageoftheratesofchangeintheunitlaborinputandunitcapitalinputrequirementsintheprogressive,innovation‐adoptingsegment,andtherateofchangeintheunitlaborinputrequirementsofthepartoftheatindustrythatcontinuestoworkwiththeold(un‐mechanized)techniques.Theweightsforthosetwosegments,asbefore,arefound from the measure of the extent of diffusionD(t) (see eq. A.11). In order to calculate theweightedaverageofthegrowthratesofcapitalandlaborproductivityinthe“progressive”segmentof the industry, however, is necessary also toweight the latter by the elasticities of outputwithrespecttoeachofthefactorinputs.Thesimplestapproachavailableistheonethathasbeenadoptedforthepresentsimulationexercises,namely,positingthatthesegmentofthefinalgoodsindustrycomprisingproductionfacilitiesthathaveadoptedtheinnovationischaracterizedbyanaggregateproductionfunctionoftheCobb‐Douglassform,aspecificationthatis,atleast,notinconsistentwiththerestrictionsthathavebeenplacedonthenewtechniqueofproduction.72

72ACobb‐Douglass aggregateproduction function for this (growing) sectorwouldbe implied if the fixed‐coefficientproductiontechniquesbeingusedbytheconstituentfirms(eachtechniquebeingcharacterizedbyacapital‐laborratio)variedaccordingtoaParetodistribution.SeeHouthakker(1955‐56).Suchapossibilityisnotobviouslyinconsistentwiththeassumptionsthathavebeenmadeaboutthenoveltechnology,becausethewhilethecapacityoftheindivisiblecapitalgoodembodyingtheinnovationisassumedtobeconstant,theunitlabor input requirements are subject to change over time, as are the associated production scales of the

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Itfollowsthattheelasticityofoutputwithrespecttolaborinputintheadoptingsegmentoftheindustrywillbeconstantovertime.Underconditionsofcompetitionintheproductandfactormarkets, this implies that the share of labor in aggregate output of the adopting segment of theindustryalsowillbeaconstant,0< N <1.73Butintheconsumer‐goodsindustryasawhole,labor’s

sharewillbecontractingasthediffusionoftherelativelycapital‐usinginnovationproceedsandtheaggregatecapital‐outputratiointheindustryispushedupwards(seeeq.A.14).

Therearetwoalternativespecialassumptionsofinterestinregardtotherateofchangein

output‐capitalratiowiththenew,mechanizedtechnology, )(tN

:undertheassumptionofHarrod‐neutralityitiszero,whereasundertheassumptionofHicks‐neutralityisequalitytotherateofchangeinlaborproductivity.Correspondingly,therearetwoalternativeexpressions(eqs.A.15andA.16)hatrelatetherateofchangeoftheindustry‐wideaverageproductivityofcapitalintheconsumergoodssectortothegrowthrateinthemeasureofdiffusion.

Because it has been assumed that a Cobb‐Douglass aggregate function describes therelationshipbetweenlaborandcapitalinputsintheprogressive,innovation‐adoptingsegmentoftheportion of the consumer‐goods industry, Harrod‐neutrality and Hicks‐neutrality are equivalentspecificationsfortheeffectsoftechnologicalchangewithinthatportionofsegmentindustry,butthatis not the case for the industry as a whole. Consequently, there are two alternative simulationequationsforthegrowthrateofTFP,intheHarrod‐neutralitycase:

2( ) | ( ) 1 1 ( ) ( )(1 ) ( )[1 ( )]N NHarrod NA t t D t D t D t

adoptingfirmsattheextensivemargin.But,thatalonedoesnotsufficetoguaranteethatthedistributionofmicro‐leveltechnicalcoefficientswouldhavetheParetoform.

73Inasmuchastheoutputcapitalratio,vistakentobeconstantforadoptingfirms,assumingtheyproduceatthecapacityof“themachine”,constancyoftherealrateofinterest(r)intheeconomywouldsettheshareofoutputimputedtocapital,and,underconstantreturntoscale,thisfixes N =[1‐rv],whereas,fortheindustry

asawholetheshareoflaborisdecreasingasthediffusionoftherelativelycapital‐usingtechnologyproceeds(eq.A.12)andcanbefoundfrom ( )L t =1–D(t)[rv].Onecannotsupposethatattheleveloftheindividual

firmstheshareofoutputgoingtocapitalwastheelasticityofoutputwithrespecttocapitalinputservices,sincewithfixedcoefficientsthatelasticityisnotdefined.But,theassumptionmadehereappliestotheaggregateproductionfunctionfortheinnovatingsegmentasawhole.Oneisthenfreetoassumethatatthemicroandaggregate level of the ensemble of adopters in the consumer‐goods sector, the average rate of return to(infinitely durable) capital is the real interest rate in the economy. This, however, does constrain theinterpretationthatcanbeplacedonthesourceofheterogeneityinthepopulationofadopters.Forexample,itwouldbedifficulttoconsistentlysupposethatathresholdmodelbasedupondifferencesamongfirmsintheirexpectedoutputrateaccountedfornon‐adoptionbyfirmsthatwerebelowthebreak‐evenscaleofproductionforaninnovationthatwasfixed‐factor‐using,andvariable‐factor–saving–assuggestedinthediscussionofsection3.Firmsatthemarginofadoptionwouldbe“breakingeven”,andearningtheopportunitycostrateofreturnontheirinvestments,butasdiffusionproceeded(withthethresholddeclining)agrowingfractionoftheadopterswouldbeearningsupernormalreturnsontheir investment–as theiroutputscalewasabovethebreakevenpoint.Diffusionwoulddriveariseintheshareofoutputthatcametoownersofcapitalwithintheconsumer‐goodssector’s“progressive”segment,andafortioriinthesectorasawhole–becausetheaggregatecapital‐outputratiotherewasrisingasmoreandmorefirmsadoptedthecapital‐usinginnovation.

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andtheHicks‐neutralitycase:

( ) | ( ) | ( ) 1 [1 ( )]NHicks NA t A t HaN D t

,

derivedaseqs.A.19andA.20,respectively.

Otherthingsbeingequal,simulationsofequation(A3.20)produceTFPgrowthratesthatlieeverywhereabovethosefromequation(A.19),sincethesecondoftheright‐handtermsinthefirstoftheseequationsispositive.

Onereadilycanfindthefirst‐orderconditionforthepeakTFPgrowthrate,d ( ( ) | )A t HiN

=0(fromeqs.A.9andA.18,andThepositivevalueofD(t)**whichsatisfiesthatconditionisfoundtobeafunctionofthemodel’sfourparameters(",2,8, N ),andthenormalizingconstant,6.Given

D**(t), and the parameter , which is a constant reflecting the initial position of the thresholdvariableinthez‐distributionatt=0.,itisstraightforwardtosolveforageneralexpressiongivingthedatet**atwhichthepeakgrowthrateofTFPoccurs.ThenumericalsimulationsdisplayedinFigure4,however,conveytheessentialpointsofthestoryrathermoreimmediately.

[Figure4here]

The top panel in Figure 4 presents alternative diffusion paths generated by variantspecifications regarding the rate of decline in the “break‐even” threshold level z*, and thecorresponding time profiles of the proportionate rate of diffusion, which is seen to undergonecontinuous retardation. The latter is more pronounced when the process is being driven by acomparativelyfastdeclineinz*(t).

Simulation results for the growth rate of average labor productivity and themulti‐factorproductivityresidualappearontheleft‐andrighthandsideofthelowerpanel,respectively.Thesecalculationshavebeenmadeusingthreealternativespecificationsofthestrengthoftheimpactoflearningfromdiffusionexperienceontheincrementalimprovementofthenewtechnology’srelativeefficiency.Inthebasecase,condition2=0signifiestheabsenceofanysuchlearningeffects.Undertheassumptionofafastrateofdeclineinthethresholdvaluez*(t),theinflectionpointofthediffusionpathoccursatD=0.5,indicatedbythedottedverticallineatthet=30date.Onecanseethatthepeaksin the labor productivity growth rate are displaced to the right of that, the ‘delay’ being morepronouncedthestrongeraretheendogenouslearningeffects.

TheresultsshowthatthepeakoftheTFPgrowthrateissimilarlydisplacedintimebeyondthedateoftheinflectionpointofthediffusionpath.Thisrightwardsshiftismorepronouncedthanthat observed in the case of the growth rate of labor productivity. The latter reflects the strongcontributions of increasing fixed input (capital) deepening during the phase when the absolutechangesintheextentofdiffusionbecomelarge.

The alternative cases presented by Figure 4 display the time profile of the multi‐factorproductivity residual under the assumption that there are positive Hicks‐neutral efficiencyimprovementsinthenewtechnologythatproceedpari‐passuswiththewideningofexperienceintheuseofthenewtechnology(i.e.,withtheextentofdiffusion).Intuitionissatisfiedbyobservingthat

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the greater is the elasticity of these learning effects on efficiency with respect to the extent ofdiffusion,thestrongertheupwardeffectontheprofileoftheTFPgrowthrate.

Werethelearnedimprovementsinfactorefficiencytobeconfinedtoenhancementsintheefficiencyoflabor,asisthecaseunderHarrod‐neutrality,thegeneralleveloftheTFPprofilewouldbelower;alsoitspeakwouldbereachedstilllaterinthediffusionprocessthanthesimulationresultsshowtheHicks‐neutralityspecification.Theintuitionforthisisquitedirect:underHarrodneutralityimprovements there is no source of capital efficiency improvements to offset the decline in thesector‐wideaverageproductivityofcapitalasdiffusionproceeds.

Note that some special conditions are required in order for the foregoing assumption ofincrementalimprovementintherelativeefficiencyofthenewtechniquetobeconsistentwiththe(unchanged) specification of the diffusion path. The effects upon either the heterogeneitydistribution,orthemovementoftheadoptionthresholdmustchangeinanoffsettingmannerandsokeep the threshold falling over time at a constant exponential rate, as the simulations posit.Alternatively,onemaysupposethatthedistributionofcriticalheterogeneitiesinthepopulationisdisplacedataratethatoffsetsthedecliningpaceofgrowthoflabor‐andcapital‐inputefficiencydueof experience‐based learning. It is not implausible that the pace of upward shift in the expectedoutput size distribution could be accelerating over time in such a fashion. Similarly, it is quiteconceivablethattherelativeuser‐costofthenewcapitalintheindustrymightfallataquickeningpace,eitherbecausetheeconomy‐widelevelwasbeingforcedupwardsorbecausescaleeffectswereloweringtherealcostsofproducingthenewfixedinputs.Ofcourse,theconstantrateoffallintheadoptionthresholdhasbeenassumedhereprimarilyforexpositionalconvenience.

5.Conclusion:Goingforwardwithempiricalresearchondiffusion

As has been seen, the class of microeconomic models of new technology adoption thatrecognized the existence of underlying, critical heterogeneities in the population of potentialadopters,andtherelationshipthelatter’sdistributioninthepopulationandthedistributionoftheagentsadoptiondecisionsintime,offersaquitecomprehensiveframeworkforstudyingdiffusionphenomenawheredecisionsbytheagentsdonotinvolvestrategicconsiderations. Thethresholdmodelisnotsomuchatheoryofthediffusionofinnovationsasitisaparadigmwithinwhichonemay articulate a variety of distinct theoretical models involving both the demand‐side and thesupply‐sideof themarket fornewtechnologies.Thus, it iscapableofsubsumingaquitedifferenteconomicmechanisms,anditsvariantformulationscaninprincipleaccountfordiffusionprocessesthat follow different lag structures that are very protracted, as well as those which are highlycompressedintime.

By “connecting the dots” between the seminal contributionsmade in Zvi Griliches to theeconomicsoftechnologydiffusion,thestudyofdistributedadjustmentlags,andthegrowthrateofmeasuredTFP,theprecedingpaperraisestwosetsofissuesforempiricalresearchthatcanbeseentocutacrossthesethreefields.Thefirstissueisthatofthe“dataconstraint”onempiricaleffortstoidentifyparticularmicro‐levelmechanisms thatgenerate time‐seriesphenomenaobservedat thelevelofpopulationaggregates.Theexactingdatarequirements‐‐consistenttime‐seriesdataattheaggregate levelandcross‐sectionobservationsat themicro‐level–havebeenpointedout(in theconclusion of section 2) as a serious obstacle to econometric identification andmeasurement of

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specificsub‐processesthatmaybecontributingtoslowingthespeedofinnovation’sdiffusionintowidespreadacceptance.

Whethertheincentivesandmaterialresourcescanbemobilized,inordertocarrythroughan extensive program of data collection and data preparation that will be needed if empiricalresearchinthisfieldistomoveforwardintandemwiththeelaborationofnewanalyticalmodelsisanimportantpracticalissue.Unfortunately,littlehashappenedtoalterthefundamentalsourcesofthe“dataconstraint”inthisarea,which,asZviGrilichespointedoutinanotherconnection,stemasmuchfromtheinternalrewardstructureoftheacademiceconomicsastheydofromthepoliciesofpublicandprivateresearchfundingagencies.

Butthisrealismdoesnotcounselresignationanddespair:thereismuchthatcanbedone,andisworthdoingthatdoesnotrequiretheeconometricallyconclusiveidentificationofthedomainsofempiricalrelevanceofthemanydistinctivetheoreticalstructuresthathavebeenandstillcouldbeproposedinthisfield.Evenwiththeavailabledataitseemsitwouldbeusefulandnotatallinfeasiblesystematicallytodistinguishempiricallybetweentwobroadclassesofdiffusionphenomena.Ontheonehand,wouldbethosethatdonotinvolvesignificantirreversibleinvestmentexpenditures,andaredrivenprimarilybytherelativerapidpropagationofinformation–theprimaryeffectofwhichistodispeluncertaintiesaboutthenetbenefitsofadoptiononthepartoftheagents.Ontheotherhand,one expects to find diffusion phenomena whose dynamics involve temporally more prolongedtransitions from restricted to widespread application of the new technology, and it may beconjecturedthatoncarefulexaminationoftheirindividualcircumstances,thesecaseswillbefoundtoreflecttheinducedmodificationoftheeconomicandtechnicalcharacteristicofthenewtechnologyinresponsetofeedbackinducedbytheprocessofdiffusion,therebypermittingthenewtechnologicalsystemtobecomeattractivetoanincreasingproportionofaheterogeneouspopulationofrationalandalreadyinformedeconomicagents.

Logically,therecanbeamixedcategory,wherebothinformationpropagationandamovingequilibriumoftechnologyadoptionbyinformedagentsbothmustbeviewedasofmoreorlessequalquantitative importance in setting the time constant for the overall diffusion process. It seemsreasonabletosupposethatmostofthedatathathasbeencollectedwillbefoundtobelonginthepolar categories, andmoreover, that what is conventionally measured as growth in total factorproductivity at the aggregate industry and sectoral levels, and imputed to “innovation” will beattributabletothecompositionaleffectswithinindustriesandsectorsofthediffusionprocessesthatbelonginthecategoryofhe“lowfrequency”feedbackdynamics.

Stillotherempiricalenquirieswouldappeartobebothfeasibleandusefulinexploringlinksbetween diffusion processes and sub‐field of the economics of technological change where ZviGriliches’work openedmajor research thoroughfares that others have been able to travel. TheconnectionbetweenchangesinmeasuredproductivityattheleveloftheenterpriseandinnovativeactivitiesassociatedwithR&DexpendituresandpatentingwasacentralpreoccupationofGriliches’research,aboutwhichtheprecedingpagesofthispaperhaveremainedsilent.74Havingherefulfilledthepromisetoexhibittheconnectionsthatmayandshouldbedrawnbetweenresearchondiffusion,

74SeeGriliches(1998),andnotablyinthiscontext,GrilichesandMairesse(1984),Griliches,HallandHausman(1986),GrilichesandRegev(1995),forthelegacyofthisprogramofmico‐leveleconometricinvestigationisevidentinthecontributionsofHall(2009),Mairesse,MohnenandKremp(2009),Regev(2009),andothersthatappearinPartIVofthisIssue.

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distributed lags and TFP growth, perhaps a further feasible task for the future is the empiricalexplorationofthenexusbetweendiffusionandR&D.

Itseemsentirelyreasonabletosupposethattheremaybesomeidentifiablefeedbackfromchangesinthesalesrevenuesreceivedbysuppliersofproducer(orconsumer)goodsthatembodyinnovativeproductionprocesses,andtheinternalfinancingofR&Dinvestmenttofurtherdeveloptheir products innovation ‐‐ improving the performance, or maintainability of later vintages oftheoriginalinnovation'sdesign?Figure5summarizestheseveraldynamicconnectionsthatwerealready represented in the simulation structure discussed in Section 4, and ventures to indicate(conjecturally, with a question‐mark) that a fourth set of dynamic relationships bear closerinvestigation:theseinvolve“post‐innovationR&Dexpenditures”thatarebothdependentupontheprogress of an innovation’s diffusion, and in turn affect the speed and eventual extent of itsacceptance.

Thisopensa topic thathasremainedmoreor lessuntouched in thediffusion literatureandbarelynoticedineconometricresearchthathasfocusedonthedeterminantsofR&Dexpendituresatthefirmlevelandtheirimpactsuponproductivitygrowth.Hereonecanonlyspeculatebrieflyaboutthreepossiblelinesalongwhichfutureresearchintotheexistenceandimportanceofsuchmicro‐levelconnectionsmightunfold.

First, one can start by examining the possible diffusion‐R&D nexus based upon therelationshipbetweengrosssalesrevenuesfromtheinnovativeproductline,andthelatter’seffectthe firm’snetearnings,which in turnmightpositivelyaffectR&Dbudgetingdecisions,especiallysmallerenterpriseswhereR&Dwastightlyconstrainedbyretainedearnings,or lendersrationedcredit to supportR&Don thebasisofnewproduct salesgrowth. As second,variant connection,perhapsmorerelevantwherealargerfirmatanypointoftimehadanumberofproductlinesthatdiffered in their degree of novelty, and the question of funding further improvement in a newlyintroducedproduct(embodyinganinnovativeproductiontechnology)wasprimarilyoneallocatingavailable retained earnings for R&D among the claimant product lines. In this case, attention isdirectedtothepossibilitythattherearelifecyclesinR&Dbudgetingattheleveloftheindividualproductline:intheearlyphasesofanewproduct’sdiffusion,risingsalesvolume–howeversmallinabsoluteterms–maystrengthensthecaseforthefirmtocontinueR&Dexpenditurestoimproveanemerging("proven")additiontotheproductline,andsoworktofurtherexpandthedimensionsofthemarketnicheintowhichitisbeingaccepted.But,bythesametoken,onceaninflectionpointinthediffusionpathispassed,quiteconceivablytherewillbesomewaningofthecapitalbudgetingcommittee’senthusiasmforcontinuingtotrytopushtheinnovationintomarginalportionsofthemarket, and the higher absolute level of sales revenues from the maturing product will beincreasinglydivertedtosupportingtheimprovementofyoungerproductlines.75

Aseconddistinctlineofinquirywouldleadtowardbetterunderstandingofthemechanismsinvolved the user‐producer feedback, generating suggestions for further improvement in

75NotethatwherefundsforR&Darenotconstrainedbysalesofthenewproductitselftheoverlappinglife‐cyclesinproductlines,asjustdescribed,wouldgeneralfeedbackswhoseimplicationsforthedynamicsofthethresholdlevelforadoptionaresharplydistinguishablefromthosewhereproductperformanceimprovementsdrivenimplementingby‐productlearningbasedupontheaccumulatedexperienceamongeitherthesuppliersortheadoptersoftheinnovation.Inparticularitwouldtendtoimpartamorepronouncedsigmoidpatterntothechanges in the relativeattractivenessof thespecific innovative technique to thepotentialadopters.Bycontrast,inthemodelofSect.4,the(new)machine‐buildingfirms’movementsdowntheirexperience‐basedlearning curves yields decreasing incremental gains in the price‐performance ratio of the innovation‐embodyingproduct.

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performance based upon reports from field use through dealership and maintenance servicenetworksforproducerdurable,orinformationreturnedtothefirmbysalespersonnel.Theliteraturein industrial organization economics and management, with few exceptions, has conceptualizedlearning‐by‐doing in production activities not as an object of management and the deliberateallocationofresources,butratherastheopportunisticimplementationofincrementalmodificationsin product design, fabrication methods, or modes of use that are essentially by‐products of theoperationofestablishedproductionroutinesandthereforecanberegardedascostless.Thus,theyareheldtobeanalyticallydistinctfromR&Dinvestments,whicharetreatedastemporalprecursorstotheestablishmentofproduction.Yet,thereisamplereasontothinkotherwise,andthereforetoentertain the idea that somesignificantpartof theexpenditures reportedasR&Dmayrepresentdeliberate investmentsofdesignandengineeringresources,andcostlyorganizational integrationand analysis of information flowing from interactions between sales and service personnel intomanagerial processes intended to optimize and capture the benefits of experience‐driven“learning.”76Clearlythereisevidencethatthisisthecaseinsomeindustrieswherethereistechnicalsupportformarketingofnewcomplexproducts,andthecontrolofqualityandyieldinfabricationisan important determinant of unit costs.77

Thirdly, consider the role of the information revealed by sales reports about "structuralholes"inthemarket‐‐areaswheretheinnovationsurprisinglyfailstopenetrate,whichareidentifiedbyreportsfromthefieldandpointstoproblematicfeaturesoftheexistingdesign?Thisisavariantof the "focusing devices" for technological change argument ‐‐ a la Rosenberg (1972), but thefeedbackaboutdysfunctional features ismarketmediated,rather thantechnicaland takingplacewithintheinnovatingfirm‐‐whichismainlywhatNatehadinmind.Doweknowanythingaboutanyofthis?Shouldn'twe?Itwouldthenbepossibletotakeaccountofanotherfeed‐backloopthatlinksR&Dintothesystemalongwith"diffusion","laggedinvestment",andTFPgrowth.

76Hatch andMowery (1998), in addition to providing a surveyof the literatureon learningbydoing thatsupports the foregoing characterization, present an analysis of deliberate practices in the semiconductorfabricationindustrythatallocateresourcestomanagingthelearningprocessinordertoincreaseyieldswhilemaintainingquality.Seealso,inthisvein,AdlerandClark(1991),andPisano(1997).

77Theliteratureonproducer‐userinteractions,startingwithRosenberg(1982)Ch.6on“learningbyusing”–particularlyinreferencetooptimizationofaircraftperformance,mightbefruitfullyharvestedforadditionalevidencethattranslatingtheinformationcapturedduringfielduseintoproductivity‐orproductperformance‐enhancingengineeringmodificationentailsbothfixedandvariableresourceexpenditures,somepartofwhichsurelywindupasexpensedbythesupplyingfirmbutreportedas“Development”underR&Dfortaxpurposes.

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2

Figure 4 Simulation parameter values: SLOW = 0.2 ; FAST = 0.3 ; = {0, 0.2 0.4} ; N = 0.5; = 0.5 ; 0N

o

= 0.4; = 60; where 11

teetD .

(Note: normalizes the initial value of tD to 0.01.)

Figure 3 (a) Figure 3 (b) Effect on diffusion of greater variance Effect on aggregate labor productivity (smaller ( ) of the underlying heterogeneity growth of greater variance (smaller ( ) of the distribution. underlying heterogeneity distribution.

0.5

0

1

0 30 60Time

D t

0 .3

2.5 %

0%

5 %

0 30 60 Time

FAS Tln t

0 .45

0 .6

0 .3

0.45

0 .6

Extent of diffusion Growth rate of labor productivity

3

Figure 4 Simulation parameter values: SLOW = 0.2 ; FAST = 0.3 ; = {0, 0.2 0.4} ; N = 0.5; = 0.5 ; 0N

o

= 0.4; = 60; where 11

teetD .

(Note: normalizes the initial value of tD to 0.01.)

Figure 4 : Effects of alternative values for 8 -- the rate of fall of the adoption ‘threshold level z*(t) – on the diffusion path, and on the growth rates of labor productivity ( )ln B(t) ) and multifactor productivity ( ) ln A(t) ), with

alternative diffusion-driven (Hicks-neutral) “learning effects” the relative productivity of the new technology

TimeTime

2.5%

0%

5%

0 30 60

2.5%

0%

5%

0 30 60

F A S Tln t F A S Tln A t H iN ,

= 0 .2

= 0 .4 = 0

= 0 .2 = 0 .4

= 0

0.5

0

1

0 30 60

5%

0%

10%

0 30 60Time Time

D t ln D t

F A S T

F A S T S L O W

S L O W

4

A‐1APPENDIX

AHeuristicModelLinkingAggregateProductivityGrowthRatesto

Micro‐levelDeterminantsofTechnologyDiffusionDynamics

A.1Definitionsandassumptions

Thefollowingnotationreferstoanindustryorsectorproducingahomogeneousgood,V:

tj : isoutputperunitoflaborinputusingthej‐thtechniqueattimet,wherej=orepresentsthe

“old”techniqueandj=N,the“new”technique; ( ) ( )N ot t forallt.

tD : istheproportionofaggregateoutputproducedusingtechniqueN,attimet;

)t( : isaggregatelaborproductivityattimet.Aggregatelaborproductivity )t( maybeexpressedas:

1

0 0( ) ( ) 1 ( ){1 ( ( ) / ( ))}Nt t D t t t .(A.1)

A‐2 There are two simplifying assumptions that restrict the dynamics of the technique‐specific laborproductivityrate: Assumption1: 00 )( t forallt.

Assumption2: 2

2( ) ( ) , 0, 0.N N

N Nt D tD D

A.2Determinantsofthegrowthrateofaggregatelaborproductivity

Thegeneralexpressionforthedependenceoftheproportionalgrowthrateoflaborproductivityonchangesintheextentoftheinnovation’sdiffusionisobtainedbyrewriting(A.1)as

,)()]([1

)( 0

tDt

t

(A.2)

wherewedefine:

)(1)( 0

tt

N

.

The proportionate growth rate of labor productivity, ( ) ln ( ) /t t t

, is then found by

differentiationof(A.2):

1 ( ) ( ) [1 ( )] ( ) ( )

( )1 [ ( )] ( ) 1 [ ( )] ( )

d t dD t t t dD tt

dt t D t dt t D t dt

, (A.3)

wheretheelasticityparameterintheendogenousinnovation‐improvementfunction,isdenotedby

2

A‐2

( ) ( )

( )( ) ( )

N

N

t D tt

D t t

.

ThefirsttermontheRHSof(A.3)givesusthedirecteffectofdiffusiononproductivitygrowth,whichisthetotaleffectinthesimplestcasewhereneitherthenewnortheoldtechnologiesundergoanychangeintheirrespectiveunitlaborinputrequirements,i.e.where ( )t =0and ( )N Nt forallt.Thesecondterm

on the RHS, obviously, gives the indirect effect. For future reference, the time‐path of aggregate laborproductivitywillbedenotedby 1( ) ( )t t inthesimplifiedcase( N =0)wherethediffusionof the

innovationdoesnotinducefurtherreductionsintheunitlaborrequirementsforthosefirmsthathaveadoptedit.

Itisnowstraightforwardtoshowthataggregatelaborproductivitydoesnotgrowmostrapidlywhentheextentofdiffusion is risingat its fastestpace. Thispropositionholdsgenerally, but it ismost readilyunderstoodbyexaminingthecasewhere ( )t =0and )()( ot NN ,sothat (t)= >0forallt.ThegeneralexpressioninequationA.3simplifiesto

1( )

( ) , 01 ( )

dD tt

D t dt

. (A.3a)

Evidently, 1

isnotsimplyproportionaltothechangeintheextentofdiffusion(dD),andthereforeit

willnotreachamaximumwhendD/dtreachesitsmaximum.Thisisreadilyshownbydifferentiating )(1 t

withrespecttotime:

22

11'2

( )

1 ( )

d t d D

dt D t dt

, (A.4)

fromwhichitfollowsthatat22

1'1'

2

( )max , 0, and

dD d D d t

dt dt dt

.

Forthetypicalcase,[max(dD)]occursintheinterval(0,1),implyingthat1 | m ax ( )d D

cannotbeat

amaximum.Sincetheterminbrackets()ontheRHSofequation(A3a)isincreasingmonotonicallyinD(t),max 1( )t mustbereachedlaterthanmax(dD).

It isnowstraightforward toshowthat this result ismoregeneralwhen thereaconstantelasticityparameter that describes the dependence of the indirect “learning effects” upon changes in D(t), i.e.,

( ) ( )t forall.Onemaythendefineanewparameter,

(1 ) /k ,

3

andnotice that thebasicdifferentialequation(A.3) for thesumofdirectand indirecteffects thenmaybewritteninthealternativeform:

A‐3

( )( ) , 0, 0

1 ( )

dD tt k k

D t dt

. (A.5)

From this it follows immediately that the value ofD(t) at which the whole expression for the laborproductivitygrowthratereachesitsmaximumwillcoincidewiththatobtainedforthespecialcasewhenonlydirecteffectsarepresent: 1m a x m a x

.

A.4Diffusionmodelspecificationsandthetime‐pathofaveragelaborproductivityintheindustry

Foreventualcomputationalconvenience,drawinguponthediscussioninSection2.3ofthetext,wemayintroduce3specifyingassumptionsforthemicro‐leveldynamicsofthediffusionprocess:

Assumption3:Thereisastationaryunderlyingdistributionofthecriticalvariatezinthepopulationofpotentialadopters that is log‐logistic in form,and the thresholdvalue foragents toselect thenewtechniqueisz*(t)attimet,whichdeclinesattheexponentialrate8.

Assumption4:Thenewtechniqueisembodiedinafixeddiscreteinput‐bundle,onlyoneunitofwhichisacquiredbyeachadoptingagent.Firmsworkingwithaunitoftheinnovativetechnologyallhaveidenticalandconstantflowoutput‐flowcapacitykN,whereasnon‐adoptingfirmshaveconstantoutput‐flowcapacitykO.

Fromthesespecificationitfollowsthatanindexoftheextentofdiffusionattimet,D(t),definedasproportionofthepopulationthathasadoptedtheinnovation,willbealogisticfunctioninthet‐domain,withasymptotic saturation atD()=1. This yields closed‐form expressions for the level, the absolute and theproportionalchangesinD(t):

First,wehavetheformalreadyfamiliarfromthederivation(seesection2.4ofthetext):

1( 0, 0*( ) 1 , ;)( tzD t e (A.6)

where *z = isaconstantreflectingtheinitialpositionofthethresholdvariableinthez‐distributionatt=0.

Second,forall >0,weobtain

( )

( )[1 ( )] ( );dD t

D t D tdt

(A.7a)

( ) ( )[1 ( )].D t D t

(A.7b)

Assumption5:Thereisanendogenous“improvementfunction”fortheaveragelaborproductivityofworkersusingthenewtechnologywhichischaracterizedbyaconstant(less‐thanunitary)elasticityofresponsetotheincreasedextentofdiffusion.

4

Thisspecifyingassumptionissatisfiedby:

( )( ) ( ) , 0 1,N N

D tt o

(A.8)

A‐4

where isanarbitrarynormalizationconstant.

The foregoing log‐logistic diffusion specifications, in conjunction with equation (A.3), lead to thefollowingsimulationequationsforthedirectandindirecteffectscombined:

( )(1 )( ) ( ( )[1 ( )]( )),

1 [ ( )] ( )

( ) 1 [ ( )] ,

LLt

t D t D tt D t

t D t

(A.9)

where 0 ( )( )N o

,and ( )LL t

denotestheaggregategrowthrateoflaborproductivityfortheunderlying

diffusionprocessbasedonthelog‐logisticheterogeneityspecification.

Inthespecialcaseinwhichthereareno“learningeffects”,i.e. 0)( t ,thesimulationequationreducesto:

1 ( ) ( )[1 ( ) ( )1 ( )

LL t D t D tD t

. (A.10)

A.5DiffusiondynamicsandthegrowthrateofaggregateTFP

As the simulation model developed here maintains the underlying specifications that generate alogistictimepathforthediffusionindex, ( )D t ,theLLsubscriptonvariablesdenotingtheproductivitygrowthratesintheindustrywillbesuppressedinthefollowingexposition.

AcceptingtheconventionalAbramovitz(1956)‐Solow(1957)computationoftherateofgrowthofthetotalfactorproductivity(TFP)residual,thelattermaybeexpressedasthefactorshare‐weightedaverageoftheaveragelaborproductivityandcapitalproductivitygrowthrates:

))t(()]t(1[)t()t(A LL

, (A.11)

giventheexpressionfortheproportionalgrowthrateofTFP,oncewehaveexpressionsforthetimeratesof

changeofoutputperunitofcapitalinput,denoted(

),andfortheshareoflaborintheaggregateoutputofthesectorinquestion, )(tL .

A.5(a)Labor’sshareinaggregateoutput:

5

Assumption 6: The segment of the final goods industry comprising production facilities that haveadopted the innovation ischaracterizedbyanaggregateproduction functionof theCobb‐Douglassform.

Fromthatspecification(theplausibilityofwhichisdiscussedinSection4.1ofthetext,particularlyinfootnote56)itfollowsthattheelasticityofoutputwithrespecttolaborinputintheadoptingsegmentoftheindustry

A‐5

will be constant over time. Thus, under conditions of competition in the product and factor markets,Assumption6impliesthattheshareoflaborinaggregateoutputoftheadoptingsegmentoftheindustryalsowillbeaconstant,0< N <1.

AsindicatedbytheremarksonAssumption1,theshareoflaborintheoldtechnology‐sectoroftheeconomyistakentobeunity,sothattheshareoflaborintheindustryasawholeis:

NL 1)t(D1)t( . (A.12)

A.5(b)Thegrowthrateofcapitalproductivity:

The aggregate capital productivity growth rate depends upon the rate of change in the extent ofdiffusion, and the level and changes occurring in the productivity of capital used in the new technologysegmentoftheindustry(orsector).Denotingthelatterbyvn(t),andrecallingthattheoldtechnologyusesonlylabor,theaggregatecapitalproductivityintheindustryisgivenby

1( ) ( ) / ( ) ( ) / ( )N Nt D t t t D t . (A.13)

Fromequation(A.13),bydifferentiation,andmultiplicationofbothsidesoftheresultingexpressionby1/(t),thegrowthrateofaggregatecapitalproductivityissimply:

)t(D)t()t( N (A.14)

Twoalternativespecificationsareofinterestinregardto )(tN

:

Assumption7a:Improvementsintheefficiencyofthenewtechnologyduetoendogenous,diffusion‐

dependentchangesareHarrod‐neutral(denotedHaN)‐‐theyraise ),t(N but,leave 0)t(N

forall

t.

Consequently,Harrod‐neutralityintheinnovation‐usingsectorimpliesthat

( ) | ( )t H aN D t

(A.15)

Alternatively,onemayentertain

Assumption7b:Improvementsintheefficiencyofthenewtechnologyduetoendogenous,diffusion‐dependentchangesareHicks‐neutral(denotedHiN),i.e.theyresultin

)t()t( NN forallt.

Makinguseofeq.(A.8),Assumption7bimplies:

6

( ) | ( ) ( ) (1 ) ( )t H iN D t D t D t

(A.16)

For the industry as a whole, where measured aggregate TFP changes (interpreted as ‘efficiencygrowth’) result from the direct compositional effects of the innovation’s diffusion, and endogenousimprovements the productivity of the adopters. Consequently, the variant specifications of the way that

“learning”orother externalitiesof the innovation’sdiffusioneffects ( ( )N t , ( )N t

),will yielddifferent

industry‐widegrowthratesformeasuredTFP.

A‐6

A.6SimulationequationsfortheaggregateTFPgrowthrate

Combiningtheresultsgivenbyequations(A.11)and(A.15)or(A.16),alternatively,weobtainfortheHarrod‐neutralityandHicks‐neutralitycases,respectively:

2( ) | ( ) ( ) 1 ( ) ( )L L

Harrod - NA t t t t D t

(A.17)

and

2( ) | ( ) ( ) 1 ( ) (1 ) ( )L L

Hicks - NA t t t t D t

(A.18)

Substitutingfor )t(L fromequation(3.12),for )t(D

from(3.7b),theseexpressionsmayberewrittenintheform:

2( ) | ( ) 1 1 ( ) ( )(1 ) ( )[1 ( )]N NHarrod NA t t D t D t D t

, (A.19)

and

( ) | ( ) | ( ) 1 [1 ( )]NHicks N Harrod NA t A t D t

. (3.20)

Fromequations(3.18)and(3.9),onereadilycanfindthefirst‐orderconditionforthepeakTFPgrowth

rate,d ( ( ) | )A t HiN

=0.ThepositivevalueofD(t)**whichsatisfiesthatconditionisafunctionofthefour

parameters(",2,8, N )andthenormalizingconstant,6.

GivenD**(t),andtheparameter definedinequation(3.6),itisstraightforwardtosolveforageneral

expressiongivingthedate(t**)atwhichwhichthepeakgrowthrateofTFPoccurs.