Technology Entry in the Presence of Patent Thickets IFS Working Paper W16/02 Bronwyn H. Hall Christian Helmers Georg von Graevenitz TechnologyEntryinthePresence ofPatentThickets* BronwynH.Hall(UCBerkeley,NBER,IFS,andNIESR)§ ChristianHelmers(SantaClaraUniversity) GeorgvonGraevenitz(QueenMaryUniversityofLondon,CCP,CREATe) January16,2016 Abstract Weanalyzetheeffectofpatentthicketsonentryintotechnologyareasbyfirmsinthe UK. We present a model that describes incentives to enter technology areas characterized by varying technological opportunity, complexity of technology, and the potentialforhold‐upinpatentthickets.Weshowempiricallythatourmeasureofpatent thicketsisassociatedwithareductionoffirsttimepatentinginagiventechnologyarea controlling for the level of technological complexity and opportunity. Technological areascharacterizedbymoretechnologicalcomplexityandopportunity,incontrast,see moreentry.Ourevidenceindicatesthatpatentthicketsraiseentrycosts,whichleadsto lessentryintotechnologiesregardlessofafirm’ssize. JELcodes:O34,O31,L20,K11 Keywords:IPR,patents,entry,technologicalopportunity,technologicalcomplexity, hold‐up *WearegratefultotheIntellectualPropertyOfficeoftheUnitedKingdomforresearchsupportandtothe NationalInstituteofEconomicandSocialResearchforhospitalitywhilethispaperwasbeingwritten.The viewsexpressedherearethoseoftheauthors.TheyarenotnecessarilythoseoftheUKIntellectual PropertyOfficeorNIESR. TherevisionofthispaperhasbenefittedfromcommentsbyparticipantsinseminarsattheUKIPO,the USPTO,theNBERSummerInstitute,theUniversityofCaliforniaatBerkeley,TILEC,TilburgUniversity, theUniversityofWuppertalandtheTIGERconference2014inToulouse.Wewouldliketothank JonathanHaskel,ScottStern,DietmarHarhoff,StefanWagnerandMeganMacGarvieforcomments,and IainCockburn,DietmarHarhoff,andStefanWagnerforverygeneroussupportwithadditionaldata. §Correspondingauthor:[email protected] 1 Introduction Thepasttwodecadeshaveseenanenormousincreaseinpatentfilingsworldwide(Fink etal.,2013).Therearesignsthatthelevelofpatentingincertainsectorshasbecomeso highastodiscourageinnovation(FederalTradeCommission,2011;BessenandMeurer, 2008;JaffeandLerner,2004;FederalTradeCommission,2003).Themainreasonisthat companies inadvertently block each other’s innovations because of multiple overlappingpatentrightsinso‐called“patentthickets”(Shapiro,2001).Patentthickets arise where individual products draw on innovations protected by hundreds or even thousands of patents, often with fuzzy boundaries. These patents belong to many independent and usually competing firms. Patent thickets can lead to hold‐up of innovations, increases in the complexity of negotiations over licenses, increases in litigation, and they create incentives to add more and weaker patents to the patent system(Allisonetal.,2015).Thisincreasestransactioncosts,reducesprofitsthatderive from the commercialization of innovation, and ultimately may reduce incentives to innovate. There is a growing theoretical (Bessen and Maskin, 2009; Clark and Konrad, 2008; FarrellandShapiro,2008;FershtmanandKamien,1992)andlegalliteratureonpatent thickets (Chien and Lemley, 2012; Bessen etal., 2011). Related work analyzes firms’ attemptstoformpatentpoolstoreducehold‐up(JoshiandNerkar,2011;Lerneretal., 2007; Lerner and Tirole, 2004) and the particular challenges posed in this context by standardessentialpatents(LernerandTirole,2013). The existing empirical evidence on patent thickets is largely concerned with showing that they exist and measuring their density (Graevenitz etal., 2011; Ziedonis, 2004). There is less evidence on the effects patent thickets have for firms. Cockburn and MacGarvie(2011)demonstratethatpatentinglevelsaffectproductmarketentryinthe software industry. They show that a 1 per cent increase in the number of existing patentsisassociatedwitha0.8percentdropinthenumberofproductmarketentrants. ThisresultechoesearlierfindingsbyLerner(1995)whoshowedforasmallsampleof U.S.biotechcompaniesthatfirst‐timepatentinginagiventechnologyisaffectedbythe presence of other companies’ patents. Bessen and Meurer (2013) suggest that patent thickets also lead to increased litigation related to hold‐up. Patent thickets have remainedaconcernofantitrustagenciesandregulatorsintheUnitedStatesforovera decade (Federal Trade Commission, 2011, 2003; USDoJ and FTC, 2007). Reforms that addresssomeofthefactorscontributingtothegrowthofpatentthicketshaverecently beenintroducedintheU.S.(AmericaInventsAct(AIA)of2011)1andbytheEuropean PatentOffice(EPO). 1For further informationsee http://www.gpo.gov/fdsys/pkg/BILLS-112hr1249enr/pdf/BILLS-112hr1249enr.pdf 1 Inspiteoftheavailabletheoreticalandempiricalevidence,itisfrequentlyarguedthat patentthicketsareafeatureofrapidlydevelopingtechnologiesinwhichtechnological opportunitiesabound(Teeceetal.,2014).Thicketsarethusseenasareflectionoffast technological progress that is paired with increased technological complexity (Lewis andMott,2013).Thissuggeststhatatrade‐offbetweentechnologicalopportunityand growthontheonehandandincreasedtransactioncostsduetotheemergenceofpatent thicketsontheothermayexist.Thechallengeinassessingthistrade‐offistodevelopa frameworkthatcapturesthemainincentivesthatleadtopatentthicketsaswellasthe mostimportanteffectsofthickets. This paper contributes to the literature by analyzing the effect of patent thickets on entryintonewtechnologyareas.Ourfocusonentryintopatentingcapturesthepositive effectsofgreatertechnologicalopportunityandnegativeeffectsofgreatertransaction costsimposedbyacomplexpatentlandscapecharacterizedbythickets.Weareableto quantifybotheffectsempirically. Thepapermakestwocontributions:first,weextendthetheoreticalmodelofpatenting in complex technologies introduced by Graevenitz etal. (2013) to free entry and the interaction between incumbents and entrants. Our model shows that technological complexity and technological opportunity increase entry in the context of patent thickets, while potential for hold‐up in patent thickets reduces entry. Whereas complexity and opportunity are shown to have countervailing effects on patenting incentivesinGraevenitzetal.(2013),wefindthatbothfactorsincreasetheincentives to enter. However, hold‐up potential clearly reduces entry incentives. These findings reflectthefactthatpatentthicketsariseduetoincreasedtechnologicalopportunityand complexitybutcreateapotentialforhold‐up. Thesecondcontributionofthepaperconsistsofanempiricaltestofthesepredictions usingfirm‐leveldataonUKfirmsandtheirpatentingintheUKandEurope.Weexploit patent data at both the EPO and the USPTO in order to construct measures of technological opportunity, technological complexity and hold‐up potential and relate thesetoentryintonewtechnologyareasbyUKfirms. Ourempiricalanalysisconfirmsthatentryincreasesintechnologyareascharacterized by greatertechnological opportunity and complexity. However, we also show that the hold‐uppotentialof patentthicketshasnegativeandsubstantiveeffectson entry into patenting. While we cannot quantify the overall net welfare effect, our results do suggestthatthicketsraiseentrycostsforlargeandsmallfirmsalike.Totheextentthat moreoriginalandradicalratherthanincrementalideascomefromnewentrantsrather than incumbents, this is likely to have negative long‐run consequences on innovation andproductmarketcompetition. Theremainderofthispaperisorganizedasfollows.Section2presentsamodelofentry into patenting in atechnology area and derives several testable predictions. Section 3 2 describes the data, and the empirical measurement of the key concepts in the model. Section4discussesourresultsandSection5providesconcludingremarks. 2 TheoreticalModel Thissectionsummarizesthemainresultsofatwo‐stagemodelofentryintopatenting and of subsequent patenting decisions. The model shows how complexity of a technology, technological opportunity and the expectation of hold‐up affect firms’ decisions to enter a technology area. The incentives to patent in such a setting are analyzed by Graevenitz etal. (2013). We generalize their model to analyze entry into technologyareasbyincumbentsandnewentrants. Patentsystemsprovideprotectionofinnovationsintechnologiesthatvarysignificantly intheircomplexityandforwhichthedegreeoftechnologicalopportunitychangeswith the underlying science base. We model varying complexity and opportunity across technology areas as follows: each technology area is divided into technological opportunities. Firms invest in R&D per opportunity to develop new products. Having invested,firmscanchoosetoprotecttheiracquiredknowledgebyapplyingforpatents on facets of each opportunity. Where the technology is discrete, e.g. chemistry, an opportunity consists of one facet. Opportunities in complex technologies comprise multiplefacets.Anincreaseintechnologicalopportunitycorrespondstoanincreasein the number of opportunities in a technology area. An increase in complexity correspondstoanincreaseinthenumberoffacetsperopportunity. Weassumethatallfacetsandopportunitiesaresymmetrical.Thenfirmscanrandomly select which facets and opportunities to patent. The role of the patent office in this model is to randomly assign facets to firms, when multiple firms apply for the same facet. Firms only decide how many technological opportunities to invest in and how manyfacetsineachopportunitytopatent. Thevalueofafirm’spatentportfoliowithinagiventechnologicalopportunitydepends onthenumberoffacetsofanopportunitythathavebeenpatentedoverallandtheshare ofthosepatentsheldbythefirm.Indecidinghowmanypatentapplicationstosubmit eachfirmtakesintoaccountcostsofresearchinganopportunity,costsofupholdingthe patentandlegalcostsofexploitingthepatentportfolio. In this model opportunity increases incentives to patent in discrete technologies, but reduces these incentives in complex technologies. Opportunity relaxes firms’ competition to patent all facets per opportunity in complex technologies. However, given the level of opportunity, greater complexity leads firms to patent more as they seek to ensure that they can exploit the opportunity fully and as they seek to protect theirbargainingpositionamongfirmsholdingpatentsonanopportunity.Thisleadsto countervailingeffectsofopportunityandcomplexityonpatentingincentivesincomplex 3 technologies.Graevenitzetal.(2013)provideevidenceofthisusingdataonEuropean patenting. The countervailing effects of complexity and opportunity on patenting incentives in complex technologiesraisethequestionhowcomplexityandopportunity affectentry. We show below that complexity and opportunity both increase incentives to enter complextechnologies.Itisperhapssurprisingthat,conditionalonthenumberoffirms, more opportunity should reduce patenting incentives, while increasing incentives to enterintopatenting.Asweshowbelowoneeffectisthepreconditionfortheother. Greater complexity increases incentives to enter a technology area as firms are less likelytocompeteforthesamepatentswithineachopportunitywhencomplexityrises. Complexity is frequently associated with increased potential for hold‐up. Hold‐up potential derives tosomedegreefromtheallocationofpatentswithin anopportunity thatresultsfromfirms’patentingefforts.Wheremorethantwofirmsholdasubstantial stake on an opportunity the complexity of bargaining increases. We account for the threatofhold‐upseparatelyandshowthatincreasesinthatreducepatentingandentry. Thereforewemeasurecomplexityandhold‐upseparatelyinourempiricalmodel. 2.1 NotationandAssumptions The key variables of the model are the complexity of a technology k, measured by ( Fk 0 ) ,thedegreeoftechnologicalopportunity,measuredby (Ok 0 ) ,andhold‐up potentialhk.ThevalueofallFkpatentsinanopportunityisVk.Inthesimplestdiscrete setting this is the value of the one patent (facet) that covers each technological opportunity. In more complex technologies this is the value of controlling all patents (facets) on a technological opportunity. Firms (indexed by i) choose the number of opportunitiesoitoinvestinandthenumberoffacetsfiperopportunitytopatent. In equilibrium only Fk (1 (1 ( fˆk / Fk ) N0 1 )) facets are patented, where fˆk is the equilibriumnumberoffacetschosenbyapplicantsandNOisthenumberoffirmsthat havechosenaspecificopportunity.2Since Fk maybesmallerthanFkthetotalvalueof patenting in a technology is V ( Fk ) V ( Fk ) . Graevenitz et al. (2013) assume that the value function Vk ( Fk ) is convex in covered facets. In Appendix C we show that this assumptioncanberelaxed.Wegeneralizethemodelbyintroducingaconcavefunction relatingtheshareofpatentsthefirmholdsonanopportunity(sik)totheproportionof the value Vk the firm can extract through licensing and its own sales: Δ(sik). This capturesthebenefitsthatapatentportfolioconfersinthemarketfortechnology. 2ThepropertiesofN 0aresummarizedinAppendixC. 4 Insumtheassumptionswemakeonthevaluefunctionandportfoliobenefitsare: (VF ): V (0) ( PB): 0, (0) 0, V Fk 0 d ( sik ) dsik 0 and d 2 ( sik ) dsik2 0 (1) (2) Themodelcontainsthreetypesofpatentingcosts: • Costs of R&D per opportunity, which depend on overall R&D activity in that technologyarea: C0 NO j o j . • Costsofmaintainingeachgrantedpatentinforce,Ca. • CostsofcoordinatingR&DondifferenttechnologicalopportunitiesCc(oi),where Cc oi 0 (3) TheseassumptionsimplythatR&Dcostsarefixedcosts.3Weallowfortheendogenous determination of the level of R&D fixed costs, which rise as more opportunities are researchedsimultaneouslybyrivalfirms.ThisreflectscompetitionforinputsintoR&D thatarefixedintheshortrun.CoordinatingdifferentR&Dprojectsalsolimitsthescope ofthefirm’sR&Doperations. Wheremultiplefirmsownfacetsonanopportunity,theirlegalcostsL(γik,sik,hk)depend ontheabsolutenumberofpatentedfacets(γik),ontheshareofpatentsperopportunity thatafirmholds(sik),andontheextenttowhichtheyfacehold‐up(hk).Thefirsttwo channels capture the costs of defending a patent portfolio as the number of patents increases,whileleavingscopeforeffectsonbargainingcoststhatderivefromtheshare of patents owned:4The hold‐up parameter captures contexts in which several firms’ core technologies become extremely closely intertwined. Then each firm has to simultaneously negotiate with many others to commercialize its products, which significantlyraisescosts. 3 Italsoimpliesthatthereisnotechnologicaluncertainty.However,introducingtechnologicaluncertainty intothemodeldoesnotchangethemaincomparativestaticsresults. 4 Graevenitz et al. (2013) analysealternativeassumptionsonlegalcosts. 5 ( LC ): L( ik , sik , hk ), where L 2 0, L 2 ik ik L hk 0, 2 0, L sik 2 0, L sik2 0, (4) 2 L ik hk L 0, sik hk 0 Allremainingcrosspartialderivativesofthelegalcostsfunctionarezero. Inwhatfollows,weusethefollowingdefinitions: k oi , Ok k fi , Fk k Fk V ( Fk ) , V ( Fk ) Fk k sk d ( sk ) , and ( sk ) dsk k fi Fk . Fk fi 2.2 PatentingandEntry Firm i’s profits in technology k, ik (oi , fi , Fk , Ok , Nk , hk ) is a function of the number of opportunities oi in which the firm invests, the number of facets per opportunity fi the firm seeks to patent, the total number of patentable facets per opportunity Fk, the number of technological opportunities a technology offers Ok, the number of firms enteringthetechnologyNk,andthedegreeofhold‐upinthattechnologyhk. Inthissectionweanalyzethefollowingtwo‐stagegameG*: Stage1:Firmsenteruntil ik (oi , fi , Fk , Ok , Nk , hk ) 0 ;5 Stage2:Firmssimultaneouslychoosethenumberofopportunities,oi,toinvestinand thenumberoffacetsperopportunity,fi,topatentinordertomaximizeprofitsπik. Wesolvethegamebybackwardinductionandderivelocalcomparativestaticsresults for the symmetric extremal equilibria of the second stage game. For the subsequent analysis it is important to note that all equilibria of this second stage game are symmetric.Incasethatthesecondstagegamehasmultipleequilibriawefocusonthe properties of the extremal equilibria when providing comparative statics results (Milgrom and Roberts, 1994; Amir and Lambson, 2000; Vives, 2005). Equilibrium valuesofthefirms’choicesaredenotedbyasuperscriptandwedropthefirmspecific subscriptsinwhatfollows,e.g., ˆ . k Atstagetwoofthegameeachfirmmaximizesthefollowingobjectivefunction: ik (oi , fi ) oi V ( Fk ) ( sik ) L( ik , sik , hk ) C0 ( NO j oj ) fi pk Ca Cc (oi ) (5) 5 WetreatNkasacontinuousvariablehere,whichisanabstractionthatsimplifiesouranalysis. 6 This expression shows that per opportunity k, the firm derives profits from its share sik pk fi / Fk ofpatentedfacets,whilefacinglegalcostsLtoappropriatethoseprofits, aswellascostsofR&DC0,costsofmaintainingitspatentportfolioCa,andcoordination costsacrossopportunitiesCc. 2.3 SimultaneousEntrywithMultipleFacets 2.3.1 Comparativestaticsofpatenting Weshowthatthesecondstageofthisgameissmoothsupermodular: Proposition1 The second stage patenting game, defined in particular by assumptions (VF, eq. 2), (PB, eq.3)and(LC,eq.5)issmoothsupermodularif k ik andifownershipofthetechnology isexpectedtobefragmented. This result generalizes Proposition 1 derived by Graevenitz etal. (2013).6Given this resultwecanshowthat: Proposition2 Thepotentialforhold‐upincomplextechnologiesreducespatentingincentives. InAppendixDweshowthattheexpectedlegalcostsofhold‐upreducethenumberof opportunities that firms invest in. In addition, firms with larger portfolios are more exposed to hold‐up and benefit less from the share ofpatents they have patented per opportunity.Botheffectscombinetoreducethenumberoffacetseachfirmappliesfor. 2.3.2 Comparativestaticsofentry In Appendix C we show that there is a free entry equilibrium. In this equilibrium the followingpropositionshold: Proposition4 Underfreeentrygreatercomplexityofatechnologyincreasesentry. In the model, complexity has countervailing effects: first of all it increases profits, because it is less likely that duplicative R&D arises making each opportunity more valuable, this clearly increases incentives to enter. Next, given the level of patent applications( f̂k ),complexityreducestheprobabilitythateachfacetispatented,which reduces profits and entry incentives. Finally, complexity reduces competition for each facet,whichincreasestheprobabilityofpatentingandincreasesinnovationincentives. 6Inourversionofthemodel,itisnolongerthecasethatthevaluefunctionhastobeincreasinginthe numberofpatentedfacetsforsupermodularityofthepatentinggame.Werelegatefurtherdiscussionof thisresulttoAppendixC. 7 Overall weshow that the positive effects outweigh thenegative effects and incentives forentryrisewithcomplexityofatechnology. To derive Proposition 4, consider how equilibrium profits are affected by the complexity of the technology Fk, the degree of technological opportunity Ok, and the potentialforhold‐uphk: (oˆ, fˆ ) Fk oˆ (oˆ, fˆ ) Ok oˆ (oˆ , fˆ ) hk sk ( Fk Fk , Fk NO sˆk ( Ok NO oˆ L hk pk , Fk Fk , NO ˆk ) V ( Fk ) pk , NO (sˆk ) ( sˆk k ( sˆk ) ( sˆk ˆk ) V ( Fk ) 0 ˆ) k k L sˆk 0 ˆ) k L sˆk (6) CO NO oˆ NO oˆ sˆk 0 (7) (8) Proposition4followsfromtheImplicitFunctiontheoremonceweknowthesignofthe derivativeofprofitsw.r.t.F.Underfreeentryfirms’profitsdecreasewithentry: N Fk Fk Nk (9) Therefore, the Implicit Function theorem implies that the sign of the effect of complexityFonentrydependsonthesignoftheeffectofcomplexityonprofits. Equation (6) shows that the effect of complexity on profits depends on the difference betweentheelasticities Fk , Fk and ˆk .Theelasticity pk , F isderivedinAppendixC.1: ˆ k pk , Fk N O2 1 1 1 2 NO ˆ 1 (10) k Thiselasticityisnegativefor ˆk 1/ 2 .Theresultimpliesthatthefirstterminbrackets inequation(6)ispositive.ThesecondtermispositivewhengameG*issupermodular. Overall this implies that greater complexity induces entry. ˆ 1/ 2 is one of two k restrictions required for supermodularity of game G*. This demonstrates that complexityincreasesentryinsettingsinwhichfirmsareplayingasupermodulargame andinwhichcomplexityalsoinducesmorepatenting.7 7When ˆ k 1/ 2 wenolongerhavetheassumptionsnecessarytoshowsupermodularity.Thissituation correspondstothecasewhereonefirmhasmorethanhalfthepatentsinaparticulartechnology opportunitywithinatechnologyarea.Thusourresultsmaynotholdwhenaspecificopportunityishighly 8 Proposition5 Underfreeentrygreatertechnologicalopportunityincreasesentry. For any given number of entrants an increase in technological opportunity reduces competition between firms for patents. This increases firms’ expected profits and increasesentry. ContinuingfromtheproofofProposition4above,bytheImplicitFunctiontheoremthe signofthederivativeofprofitsw.r.t.technologicalopportunitydeterminestheeffectof technologicalopportunityonentry: N Ok Ok Nk (11) Anincreaseintechnologicalopportunityincreasesprofitsandentry.InAppendixCwe show that the term in brackets in Equation (7) is negative under free entry. Profits increase as technological opportunity increases, because fewer firms enter per opportunity. Proposition6 Underfreeentrythepotentialforhold‐upreducesentry. Anincreaseinthepotentialforhold‐upraisesfirms’expectedlegalcosts.Thisreduces expectedprofitsandlowerspotentialforentry. To derive this prediction, note that by the Implicit Function theorem the sign of the derivativeofprofitsw.r.t.thelevelofhold‐upinatechnologyareadeterminestheeffect ofhold‐uponentry: N hk hk Nk (12) Hence,equation(8)showsthattheeffectofhold‐uponentryderivesfromtheincreased legalcoststhatthepossibilityofhold‐upimposesonaffectedfirms. 2.4 Entry and Incumbency Theprevioussection setsoutamodelin whichallfirms enteredandtheninvestedin patents.Atbothstagesfirms’decisionsweresimultaneous.InAppendixD.5weextend themodeltoasettinginwhichsomefirms,theincumbents,facelowercosts( CO where , 0 ) of entering opportunities. This captures the fact that incumbents have concentrated.Ingeneralthiswillnotbethecase,especiallyatourlevelofempiricalanalysis,butitwould beinterestingtoexplorethispossibilityinfuturework. 9 previous experience of doing R&D in a technology area. We demonstrate that our resultsarerobusttothisextensionofthemodel. 2.5 Predictions of the Model Ourmodelpredictshowtheprobabilityofentryintopatentingdependsonopportunity, complexity, hold‐up potential and incumbents’ experience. Here we summarize these predictions,whicharetestedempiricallybelow:8 Prediction1 Greatertechnologicalopportunityincreasestheprobabilityofentry. Greater technological opportunity reduces competition for facets per opportunity, whichraisesexpectedprofitsandtherebyattractsentry. Prediction2 Greatercomplexityofatechnologyincreasestheprobabilityofentry. Greatercomplexityhascountervailingeffects:itreducescompetitionperfacetas well as duplicative R&D, attracting entry. It also increases the likelihood that some of a technologyremainsunpatented,reducingitsoverallvalueandentry.Ourmodelshows thatoverallcomplexityincreasesentry. Prediction3 Greaterpotentialforhold‐upreducestheprobabilityofentry. Hold‐uppotentialincreasesexpectedcostsofentry,reducingit. Prediction4 Moreexperiencedincumbentsaremorelikelytoentertechnologicalopportunitiesnewto them. We show that incumbency advantage raises the number of opportunities that incumbentsenter.Thisimpliesthattheyalsoenternewopportunities,whichtheyhave not previously been active in. This expansion of activity by incumbents crowds out entrybynewentrants. 3 DataandEmpiricalModel This section of the paper describes the data we use in the empirical test of our theoreticalpredictions.Inparticular,wediscusshowwemeasureentry,howthesetof potentialentrantsisidentified,andwhichmeasuresandcovariatesareused. 8Graevenitzetal.(2013)testedpredictionsfromamorerestrictiveversionofthemodelonthelevelof patentapplicationsusingdatafromtheEuropeanPatentOffice. 10 Ourempiricalmodelisahazardratemodeloffirmentryintopatentinginatechnology area as a function of technological opportunity, technological complexity, hold‐up potentialthatcharacterizeatechnologyarea.Wetestthepredictionssetoutattheend oftheprevioussectionforthesevariablesandfortheeffectofafirm’spriorexperience in patenting. Additional firm level covariates include the age and size of firms. The modelsweestimatearestratifiedattheindustrylevel.Thatis,theunitofobservation for each entry hazard is a firm‐technology area, but the hazard shapes and levels are allowed to vary by the industry that the firm is in. This approach recognizes that patentingpropensitiesvaryacrossindustriesforreasonsthatmaynotbetechnological (e.g.,strategicreasons,orreasonsarisingfromthehistoricaldevelopmentofthesector). WeuseacombinationoffirmleveldatafortheentirepopulationofUKfirmsregistered withCompaniesHouseanddataonpatentingattheEuropeanPatentOfficeandatthe Intellectual Property Office for the UK. The firm data comes from the data held at Companies House provided by Bureau van Dijk in their FAME database. European patent registers do not include reference numbers from company registers, nor does Bureau van Dijk provide the identification numbers used by patent offices in Europe. Linking the data from patent registers to firm register data requires matching of applicant names in patent documents and firm names in firm registers. In our work bothafirm’scurrentandpreviousname(s)wereusedformatchinginordertoaccount for changes in firmnames. For more details on the matching of firm‐ and patent‐level dataseeAppendixA. Economic studies of entry are frequently hampered by the problem of identifying the correctsetofpotentialentrants(BresnahanandReiss,1991;Berry,1992).Inourcase this problem is slightly mitigated by the fact that one set of potential entrants into patentinginaspecifictechnologyareaconsistsofallthosefirmsthatcurrentlypatentin other technology areas. We complement this group of firms with a set of comparable firmsfromthepopulationofUKfirmsthathavenotpatentedpreviously. To construct thesample we deleted all firms fromthe data forwhichwe have no size measure, because of missing data on assets. We select previously non‐patenting firms from the population of all UK firms in two steps: 1) we delete all firms in industrial sectorswithlittlepatenting(amountingtolessthan2percentofallpatenting);and2) wechooseasampleofnon‐patentingfirmsthatmatchesoursampleofpatentingfirms by industry, size class, and age class. In principle, this approach will result in an endogenous (choice‐based) sample. However our focus is on industry and technology arealeveleffectsratherthanfirm‐leveleffects.Thereforewedonotexpectthesampling approach we adopt to introduce systematic biases into the estimates we report. We provide a number of robustness checks to ensure that our results are stable. These reveal that sample composition does not affect the key results we present below. All 11 estimatesarebasedondataweightedbytheprobabilitythatafirmisinoursample.9 The sample that results from our selection criteria is a set of firms with non‐missing assets in manufacturing, oil and gas extraction and quarrying, construction, utilities, trade, and selected business services including financial services that includes all (approximately 10,000) firms applying for a patent at the EPO or UKIPO during the 2001‐2009periodandanother10,000firmsthatdidnotapplyforapatent. Thedefinitionoftechnologyareasthatweuseisbasedonthe2008versionoftheISI‐ OST‐INPItechnologyclassification(denotedTF34classes).ThelistisshowninTable1, alongwiththenumberofEPOandUKIPOpatentsappliedforbyUKfirmswithpriority datesbetween2002and2009.Acomparisonofthefrequencydistributionofpatenting acrossthetechnologyareasfromthetwopatentofficesshowsthatfirmsaremorelikely to apply for patents in Chemicals at the EPO, while Electrical and Mechanical Engineeringpredominateinthenationalpatentdata(seethebottompanelinTable1). We treat entry into each technology area as a separate decision made by firms. More thanhalfoffirmswe observepatentinmorethanone area and10percentpatentin more than four. From the 20,000 firms observed, each of which can potentially enter intoeachoneofthe34technologyareas,weobtainabout700,000observationsatrisk. We cluster the standard errors by firm, so our models are effectively firm random effects models for entry into 34 technology areas. Allowing firm choices to vary by technology area is sensible under the assumption that firms’ patenting strategies are contingentupontechnologyandindustrylevelfactorsandarenothomogeneousacross technologyareas.Weconfirmedthevalidityofthisassumptionthroughinterviewswith leadingUKpatentattorneys. There are some technology‐industry combinations that do not occur, e.g. audio‐visual technology and the paper industry, telecommunications technology and the pharmaceutical industry. In order to reduce the size of the sample, we drop all technology‐industrycombinationsforwhichLybbertandZolas(2014)findnopatenting in their data and for which there was no patenting by any UK firm from the relevant industryinthecorrespondingtechnology category.This removesabout30 per centof observations from the data. We provide a robustness check for this procedure in AppendixB. [Table1here] 9Tocheckthis,weestimatedthemodelwithandwithoutweightsbasedonoursamplingmethodology andfindlittledifferenceintheresults. 12 3.1 Variables DependentVariable‐Entry The dependent variable is a dichotomous variable taking the value one if a firm has entered a technology area k at time t and otherwise the value zero. Entry into a technologyareaismeasuredbythefirsttimeafirmappliesforapatentthatisclassified inthattechnologyarea,datedbythepriorityyearofthepatent. Technologicalopportunity Our first prediction from the theoretical model is that there will be more entry in technology areas with greater technological opportunity. Additional reasons that a sector may have more or less patenting include sector “size” or “breadth” and the propensityoffirmstopatentinparticulartechnologiesforstrategicreasonsorbecause of varying patent effectiveness in protecting inventions. To control for both technological opportunity and these other factors, we include the logarithm of the aggregateEPOpatentapplicationsinthetechnologysectorduringtheyear.Tocapture opportunity more specifically we also include the past 5‐year growth rate in the non‐ patent(scientificpublication)referencescitedinpatentsinthattechnologyclassatthe EPO.10Wehavefoundthatthegrowthrateinnon‐patentreferencesisabetterpredictor of entry than the level of non‐patent references, which has been used previously. Presumably the growth rate is a better indicator because it capture new or expanded technologicalopportunity. Technologycomplexity The second prediction of the theoretical model is that technological complexity increases entry, other things equal. Our interpretation of complexity is that it implies manyinterconnectionsbetweeninventionsinaparticularfield,ratherthanaseriesof fairlyisolatedinventionsthatdonotconnecttoeachother.Toconstructsuchameasure, weuse theconcept of network density applied to citations among all the patents that have issued in the particular technology area during the 10 years prior to the date of potentialentry.WeusecitationsattheU.S.patentoffice,bothbecausethesearericher (averaging7orsocitesperpatentduringthisperiodversus3fortheEPO)andalsoto minimizecorrelationwiththethicketsmeasure,whichisbasedonEPOdata.11 Thenetworkdensitymeasureiscomputedasfollows:inanyyeart,thereareNktpatents thathavebeenappliedforintechnologyareakbetween1975andyeart.Eachofthese patentscanciteanyofthepatentsthatwereappliedforearlier,whichimpliesthatthe 10SeeGraevenitzetal.(2013)foramoreextensivediscussionofthisvariableintheliterature. 11Itisimportanttoemphasizethatalthoughpatentofficescooperateandsharesearchreportscitations listedonU.S.patentsarelargelyproposedbytheapplicant,whilstthecitationslistedonEPOandIPO patentsareinsertedbytheexaminer.Thisexplainswhythetwomeasuresarenothighlycorrelated. 13 maximum number of citations within the technology area is given by Nkt(Nkt‐1)/2. We counttheactualnumberofcitationsmadeandnormalizethembythisquantity,scaling themeasurebyonemillionforvisibility,givenitssmallsize. PatentThickets Thethirdpredictionofourmodelisthatgreaterpotentialforhold‐upreducesentry.We measurethepotentialforhold‐upinpatentthicketsusingthetriplescountproposedby von Graevenitz etal.(2011).This isa narrowerinterpretation ofthis measurethan in several previous papers, where it has been used as a proxy for complexity of a technology. In those papers complexity and hold‐up potential have the same effect. In contrast, our model provides opposite predictions for the effects of complexity of a technologyandpotentialforhold‐up. Thetriplesmeasurecorrespondstoacountofthenumberoffullyconnectedtriadson thesetoffirms’criticalpatentcitations.Attimeteachunidirectionallinkbetweentwo firmsAandBcorrespondstooneormorecriticalreferencestofirmA’spatentsinthe setofpatentsappliedforbyfirmBintheyearst,t‐1andt‐2.Weusethesamemeasure oftriplesasHarhoffetal.(2015),whichcontainsalltriplesineachtechnologyarea.The citation data used is extracted from PATSTAT (October 2011 edition).12We normalize thecountoftriplesbyaggregatepatentinginthesamesector,sothatthetriplesvariable represents the intensity with which firms potentially hold blocking patents on each otherrelativetoaggregatepatentingactivityinthetechnology. The triples measure has been used in a number of papers since it was suggested by Graevenitz et al. (2011). They show that counts of triples by technical area are significantly higher for technologies classified as complex than for areas classified as discrete by Cohen et al. (2000). Fischer and Henkel (2012) find that the measure predictspatentacquisitionsbyNon‐PracticingEntities.Graevenitzetal.(2013)usethe measuretostudypatentingincentivesinpatentthicketsandHarhoffetal.(2015)show thatoppositiontopatentapplicationsfallsinpatentthickets,particularlyforpatentsof thosefirmsthatarecaughtupinthethickets. Asarobustnesscheck,wehavealsoexploredtheuseofduples,i.e.thecountofmutual blockingrelationships,tomeasurehold‐uppotential.Combiningbothmeasuresinone regression leads to thorny problems of interpretation. Taken alone the measure has similareffectsasthetriplesmeasureinthiscontext. [Table2here] 12TriplesdatawaskindlyprovidedbyHarhoffetal.(2015). 14 Covariates Itiswellknownthatfirmsizeandindustryareimportantpredictorsofwhetherafirm patents at all (Bound et al. 1984 for U.S. data). Hall et al. (2013) show this for UK patentingduringtheperiodstudiedhere.Therefore,inallofourregressionswecontrol forfirmsize,industrialsector,andyearofobservation.Weincludethelogarithmofthe firm’sreportedassetsandasetofyeardummiesinalltheregressions.13Tocontrolfor industrialsector,westratifybyindustry,whicheffectivelymeansthateachindustryhas itsownhazardfunction,whichisshiftedupordownbytheotherregressors. We also expect the likelihood that a firm will enter a particular technology area to depend on its prior patenting experience overall, as well as its age. Long‐established firmsarelesslikelytobeexploringnewtechnologyareasinwhichtocompete.Thuswe includethelogarithmoffirmageandthelogarithmofthestockofpriorpatentsapplied forinanytechnologybythefirm,laggedoneyeartoavoidanyendogeneityconcerns. ThevariablesonfirmsizeandpatentstockalsoallowustotestPrediction4aboutthe effectofincumbencyadvantageonentry. 3.2 DescriptiveStatistics Our estimation sample contains about 20,000 firms and 700,000 firm‐TF34 sector combinations. During the 2002‐2009 period there are about 10,000 entries into patenting for the first time in a technology area by these firms. Table A‐2 shows the distributionofthenumberofentriesperfirm:2,531enteroneclass,andtherestenter morethanone.TableA‐2showsthepopulationofUKfirmsobtainedfromFAMEinour industries, together with the shares in each industry that have applied for a UK or European patent during the 2001‐2009 period. These shares range from over 10 per centinPharmaceuticalsandR&DServicestolessthan0.1percentinConstruction,Oil andGasServices,RealEstate,Law,andAccounting. EmpiricalModel Weusehazardmodelstoestimatetheprobabilityofentryinto atechnologyarea.The models express the probability that a firm enters into patenting in a certain area conditionalonnothavingenteredyetasafunctionofthefirm’scharacteristicsandthe time since the firm was “at risk,” which is the time since the founding of the firm. In somecases,ourdatadonotgobackasfarasthefoundingdateofthefirm,andinthese casesthedataare“left‐censored.”Whenwedonotobservetheentryofthefirmintoa particular technology sector by the last year (2009), the data is referred to as “right‐ censored.” In Appendix B, we discuss the choice of the survival models that we use for analysis, 13Thechoiceofassetsasasizemeasurereflectsthefactthatitistheonlysizevariableavailableforthe majorityofthefirmsintheFAMEdataset. 15 how to interpret the results, and present some robustness checks. We estimate two classesoffailureorsurvivalmodels:1)proportionalhazard,wherethehazardoffailure over time has the same shape for all firms, but the overall level is proportional to an index that depends on firm characteristics; and 2) accelerated failure time, where the survivalrateisacceleratedordeceleratedbythecharacteristicsofthefirm.Inthebody ofthepaperwepresentresultsusingthewell‐knownCoxproportionalhazardsmodel stratifiedbyindustry.Resultsfromtheacceleratedfailuretimemodelsweresimilarbut theestimatedeffectsaresomewhatlarger(showninAppendixB). As indicated earlier, our data for estimation are for the 2002‐2009 period, but many firmshavebeenatriskofpatentingformanyyearspriortothat.Theoldestfirminour datasetwasfoundedin1856andtheaveragefoundingyearwas1992.BecausetheEPO wasonlyfoundedin1978,wechosetousethatyearastheearliestdateanyofourfirms isatriskofenteringintopatenting.Thatis,wedefinedtheinitialyearasthemaximum of the founding year and 1978. Table B‐2 in the appendix presents estimates of our modelusing1900insteadof1978astheearliestatriskyearandfindslittledifference in the estimates.14We conclude that the precise assumption of the initial period is innocuous.Ourassumptionamountstoassumingthattheshapeofthehazardforfirms foundedbetween1856and1978butotherwiseidenticalisthesameduringthe2002‐ 2009period. AppendixTableB‐1showsexploratoryregressionsmadeusingvarioussurvivalmodels. None of the choices made large differences to the coefficients of interest, so that we focus here on the results from the Cox proportional hazards model, estimated with stratificationbytwo‐digitindustry.Theeffectofthestratificationisthatweallowfirms in each of the industries to have a different distribution of the time until entry into patentingconditionalontheregressors.Thatis,eachindustryhasitsown“failure”time distribution, where failure is defined as entry into patenting in a technology area, but the level of this distribution is also modified by the firm’s size, aggregate patenting in thetechnology,networkdensity,andthetriplesdensity. 4 Results Our estimates of the model for entry into patenting are shown in Table 3. All regressionscontrolforsize,age,andindustry.Bothsizeandagearestronglypositively associated with entry into patenting in a new technological area. Our indicator of technological opportunity and technology class size, the log of current patent 14Themaindifferenceisinthefirmagecoefficient.Becausethemodelsarenonlinear,thiscoefficientis identifiedeveninthepresenceofyeardummiesandvintage/cohort(whichisimpliedbythesurvival modelformulation).Howeveritwillbehighlysensitivetotheassumptionsaboutvintageduetotheage‐ year‐cohortidentity. 16 applications in the technology class, is also positively associated with entry into that class,aspredictedbyourmodel. Column 3 of Table 3 contains the basic result from our data and estimation, which is fullyconsistentwiththepredictionsofourmodel:greatercomplexityasmeasuredby citation network density increases the probability of entry into a technology area, as does technological opportunity, measured both as prior patenting in the class and as growthintherelevantscienceliterature.Controllingforbothtechnologicalopportunity and complexity, firms are discouraged from entry into areas with a greater density of triplerelationshipsamongexistingfirms.Weinterpretthislatterresultasanindicator of the discouraging effect of holdup possibilities or the legal costs associated with negotiationofrightsordefenseinthecaseoflitigation. Wewereconcernedthatournetworkdensity(complexity)andtriplesdensity(hold‐up potential)measuresmightbetoocloselyrelatedtoconveyseparateinformation,butwe foundthattherawcorrelationbetweenthesetwovariableswas‐0.001.Tocheckforthe impactofpotentialcorrelationconditionalonyear,industry,andtheothervariables,in columns 1 and 2 of Table 3 we included these two measures of complexity/thickets separatelyandfoundthatalthoughthecoefficientswereveryslightlylowerinabsolute value,theresultsstillhold,althoughitisclearthattheaggregateclasssizeiscorrelated negatively with the triples density via the denominator of the density (compare the changeinthelog(patentsinclass)coefficientbetweencolumns1and2). AsweshowinAppendixB,theestimatedcoefficientsinthetableareestimatesofthe elasticityoftheyearlyhazardratewithrespecttothevariable,anddonotdependon theindustryspecificproportionalhazard.Aonestandarddeviationincreaseinthelog of network density is associated with a 32 percent increase in the hazard of entry (0.13*2.78), while a one standard deviation in the log of triples density is associated with a 20 percent decrease in the hazard of entry (0.14*1.44). Thus the differences across these technology areas in the willingness of firms to enter them is substantial, bearinginmindthattheaverageprobabilityofentryisonlyabout1.5percentinthis sample. [Table3here] Therearefixedcoststopatenting,andafirmmaybemorelikelytoenterintopatenting inanewareaifitalreadypatentsinanotherarea.Totestthisidea,inthefourthcolumn of Table 3, we add the logarithm of past patenting by the firm. Firms with a greater prior patenting history are indeed more likely to enter a new technology area – doublingafirm’spastpatentsleadstoanalmost100%higherhazardofentry. In the last column we interact the log of assets with the log of patents, the log of network density, the growth of non‐patent literature, and the log of triples density to seewhethertheseeffectsvarybyfirmsize.Theresultsshowthatthenetworkdensity andtechnologicalopportunityeffectsdeclineslightlywithfirmsize.Thetriplesdensity effectdoesnotshowanysizerelationship,suggestingthathold‐upconcernsaffectfirms 17 of all sizes proportionately. We show this graphically in Figure 1, which overlays the coefficientsasafunctionoffirmsizeontheactualsizedistributionofourfirms.From thegraphonecanseethattheimpactofaggregatepatentinginasectorishigherand morevariablethantheimpactofthenetworkdensity,andthatbothfalltozeroforthe largest firms. Growth in non‐patent literature is positively associated with technology entry for small firms, but negatively for large firms, suggesting the role played by the smaller firms in newer technologies based on science. Large firms seem not to be as active in these areas. Controlling for all these features of a technology, the impact of triples density is uniformly negative across firm size, which contradicts the view that thepotentialforhold‐updiscouragesentrybysmallerfirmsmorethanbylargerfirms. 4.1 Robustness TableB‐2intheappendixexploressomevariationsofthesampleusedforestimationin Table3.Column1ofTableB‐2isthesameascolumn4ofTable3forcomparison.The first change (column 2) was to add back all the technology‐industry combinations whereLybbertandZolas(2012)findnopatentingintheirdataandwheretherewasno entry by any UK firm from the relevant industry into that technology category. These observations are about 20 per cent of the sample. The impact of network density on entry is weaker, but the impact of triples density and the technological opportunity variablesisconsiderablystronger.Thatis,technologyarea‐industrycombinationswith no patenting are also those where the technology area displays low technological opportunity. Next we removed all the firms with assets greater than 12.5 million pounds, to check whetherlargefirmswereresponsibleforourfindings.15Thisremovedabout2percent ofthe20,000firms.Column3ofTableB‐2showsthattheresultsdonotchangeagreat deal, although they are somewhat stronger. In column 4, we removed the telecommunications technology sector from the estimation, because it is such a large triplesoutlier.Onceagain,therewaslittlechangetotheestimates.Thelastcolumnof Table B‐2 shows the results of defining the minimum entry year as 1900. With the exception of firm age, the coefficients are nearly identical to those in column 1 of the table. 1512.5millionpoundsisacutoffbasedonthedefinitionofSmallandMedium‐sizedEnterprises(SMEs) asfirmswithfewerthan250employees.Wedonothaveemploymentforallourfirms,soweassumethat assetsareapproximately50thousandpoundsperemployeeinordertocomputethismeasure.Forsmall firmsonly,thisyieldsanassetscutoffof2.5millionpounds. 18 5 Conclusion Patentthicketsariseforamultitudeofreasons;theyaremainlydrivenbyanincreasein thenumberofpatentfilingsandconcomitantreductionsinpatentquality(thatis,the extent to which the patent satisfies the requirements of patentability) as well as increasedtechnologicalcomplexityandinterdependenceoftechnologicalcomponents. Thetheoreticalanalysisofpatentthickets(Shapiro,2001)andthequalitativeevidence provided by the FTC in a number of reports (FTC, 2003; 2011) suggest that thickets impose significant costs on some firms. The subsequent literature has focused on the measurement of thickets (e.g. Graevenitz etal. 2011; Ziedonis, 2004) and has linked thicketstochangesinfirms’IPstrategiesinanumberofdimensions.Thereisstillalack ofevidenceontheeffectofpatentthicketsaswellastheirwelfareimplicationsatthe aggregatelevel. The empirical analysis of the effects of patent thickets must contend with two challenges: first, patent thickets have to be measured and secondly, effects of thickets mustbeseparatedfromeffectsofotherfactorsthatarecorrelatedwiththegrowthof thickets,inparticulartechnologicalcomplexity. This paper confronts both challenges. We show that our empirical measure for the densityofthicketscaptureseffectsofpatentthicketspredictedbytheory.Thissupports resultsbyvonGraevenitzetal.(2011,2013)andHarhoffetal.(2015)showingthatthe coefficients on the triples measure capture predicted effects of patent thickets on patenting and opposition. The paper also separates the impact of patent thickets on entryfromeffectsoftechnologicalopportunityandcomplexityandshowsthatthehold‐ up potential created by thickets reduces entry into patenting. Controlling for technologicalopportunityandcomplexityisimportantbecausebotharecorrelatedwith entryintopatentingandthepresenceofthickets.Itisalsoworthemphasizingthatour measureofthicketsispurgedofeffectsthataredrivenbypatentingtrendsinparticular technologies.Thatis,ourresultsarenotduetothelevelofinventionandtechnological progresswithinatechnologyfield. Our results demonstrate that patent thickets significantly reduce entry into those technology areas in which growing complexity and growing opportunity increase the underlying demand for patent protection. These are the technology areas, which are associated most with productivity growth in the knowledge economy. However, the welfare consequences of our finding are unclear. Reduced entry into new technology areas could be welfare‐enhancing: As is well known from the industrial organization literature, entry into amarket may be excessive if entry creates negative externalities for active firms, for instance due to business stealing. This is likely to be true of patentingtoo.Furthermore,Aroraetal.(2008)showthatthepatentpremiumdoesnot coverthecostsofpatentingfortheaveragepatent(exceptforpharmaceuticals).These andrelatedfactsmightleadonetoconcludethatlowerentryintopatentingislikelyto increasewelfareandthatthicketsraisewelfarebyreducingentry. 19 Incontrast,reducedentryintopatentinginnewtechnologyareasmayalsobewelfare‐ reducing,foratleasttworeasons.First,thereistheobviousargumentthatthebenefits from more innovation may exceed any business stealing costs (as has been shown empirically in the past by others, e.g., Bloom et al. 2013), so that some desirable innovationmaybedeterredbyhighentrycosts.Evenifthiswerenottrue,thereisno reasontobelievethatfirmsthatdonotenterintopatentingduetothicketsarethosewe wishtodeter.Giventheincumbencyadvantage,itislikelythatthefailuretoenterinto patenting in these areas reflects less innovation by those who bring the most original ideas,thatis,bythosewhoareinventing“outsidethebox.” 20 References AmirR,andV.E.Lambson,2000.OntheeffectsofentryinCournotmarkets.TheReview ofEconomicStudies67(2),235–254. 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WIPO,2011.TheSurgeinWorldwidePatentApplications(No.4/4).WIPO.Availableat http://www.wipo.int/edocs/mdocs/pct/en/pct_wg_4/pct_wg_4_4.pdf Ziedonis,R.H.,2004.Don'tFenceMeIn:FragmentedMarketsforTechnologyandthe PatentAcquisitionStrategiesofFirms.ManagementScience50,804–820. 24 Appendix A: Data OuranalysisreliesonanupdatedversionoftheOxford‐Firm‐Level‐Database,which combinesinformationonpatents(UKandEPO)withfirm‐levelinformationobtained fromBureauvanDijk’sFinancialAnalysisMadeEasy(FAME)database(formoredetails seeHelmersetal.(2011)fromwhichthedatadescriptioninthissectiondraws). Theintegrateddatabaseconsistsoftwocomponents:afirm‐leveldatasetandIPdata. Thefirm‐leveldataistheFAMEdatabasethatcoverstheentirepopulationofregistered UKfirms.16Theoriginalversionofthedatabase,whichformedthebasisfortheupdate carriedoutbytheUKIPO,reliedontwoversionsoftheFAMEdatabase:FAMEOctober 2005andMarch2009.ThemainmotivationforusingtwodifferentversionsofFAMEis thatFAMEkeepsdetailsof“inactive”firms(seebelow)foraperiodoffouryears.Ifonly the2009versionofFAMEwereused,intellectualpropertycouldnotbeallocatedtoany firmthathasexitedthemarketbefore2005,whichwouldbiasthematchingresults. FAMEisavailablesince2000,whichdefinestheearliestyearforwhichtheintegrated datasetcanbeconstructedconsistently.TheupdateundertakenbytheUKIPOusedthe April2011versionofFAME.However,sincetherearesignificantreportingdelaysby companies,evenusingtheFAME2011versionmeansthatthelatestyearforwhich firm‐leveldatacanbeusedreliablyis2009. FAMEcontainsbasicinformationonallfirms,suchasname,registeredaddress,firm type,industrycode,aswellasentryandexitdates.Availabilityoffinancialinformation variessubstantiallyacrossfirms.IntheUK,thesmallestfirmsarelegallyrequiredto reportonlyverybasicbalancesheetinformation(shareholders'fundsandtotalassets). Thelargestfirmsprovideamuchbroaderrangeofprofitandlossinformation,aswell asdetailedbalancesheetdataincludingoverseasturnover.Lackofthesekindsofdata forsmallandmedium‐sizedfirmsmeansthatourstudyfocusesontotalassetsasa measureoffirmsizeandgrowth. ThepatentdatacomefromtheEPOWorldwidePatentStatisticalDatabase(PATSTAT). DataonUKandEPOpatentpublicationsbyBritishentitiesweredownloadedfrom PATSTATversionApril2011.Duetotheaverage18monthsdelaybetweenthefiling andpublicationdateofapatent,usingtheApril2011versionmeansthatthepatent dataarepresumablyonlycompleteuptothethirdquarterin2009.Thiseffectively meansthatwecanusethepatentdataonlyupto2009underthecaveatthatitmightbe somewhatincompletefor2009.Patentdataareallocatedtofirmsbytheyearinwhicha firmappliedforthepatent. 16FAMEdownloadsdatafromCompaniesHouserecordswherealllimitedcompaniesintheUKare registered. 25 Sincepatentrecordsdonotincludeanykindofregisterednumberofacompany,itis notpossibletomergedatasetsusingauniquefirmidentifier;instead,applicantnames intheIPdocumentsandfirmnamesinFAMEhavetobematched.Bothafirm'scurrent andpreviousname(s)wereusedformatchinginordertoaccountforchangesinfirm names.Matchingonthebasisofcompanynamesrequiresnamesinbothdatasetstobe `standardized'priortothematchingprocessinordertoensurethatsmall(butoften systematic)differencesinthewaynamesarerecordedinthetwodatasetsdonot impedethecorrectmatching.FormoredetailsonthematchingseeHelmersetal. (2011). [TablesA‐1,A‐2,andA‐3here] 26 Appendix B: Estimating survival models Thisappendixgivessomefurtherinformationaboutthevarioussurvivalmodelswe estimatedandtherobustnesschecksthatwereperformed.Weestimatedtwogeneral classesoffailureorsurvivalmodels:1)proportionalhazard,wherethehazardoffailure overtimehasthesameshapeforallfirms,buttheoveralllevelisproportionaltoan indexthatdependsonfirmcharacteristics;and2)acceleratedfailuretime,wherethe survivalrateisacceleratedordeceleratedbythecharacteristicsofthefirm.We transform(2)toahazardratemodelforcomparisonwith(1),usingtheusualidentity betweentheprobabilityofsurvivaltotimetandtheprobabilityoffailureattgiven survivaltot‐1. Thefirstmodelhasthefollowingform: Pr i first patents in j at t | i has no patents in j s t , X i h( X i , t ) h t exp( X i , ) whereidenotesafirm,jdenotesatechnologysector,andtdenotesthetimesinceentry intothesample.h(t)isthebaselinehazard,whichiseitheranon‐parametricora parametricfunctionoftimesinceentryintothesample.Theimpactofanycharacteristic xonthehazardcanbecomputedasfollows: h Xi,t xi h t exp X i , or h Xi,t xi 1 Xi,t Thusifxismeasuredinlogs,βmeasurestheelasticityofthehazardratewithrespectto x.Notethatthisquantitydoesnotdependonthebaselinehazardh(t),butisthesame foranyt.Weusetwochoicesforh(t):thesemi‐parametricCoxestimateandtheWeibull distributionptp‐1.ByallowingtheCoxh(t)orptovaryfreelyacrosstheindustrial sectors,wecanallowtheshapeofthehazardfunctiontobedifferentfordifferent industrieswhileretainingtheproportionalityassumption. Inordertoallowevenmoreflexibilityacrossthedifferentindustrialsectors,wealso usetwoacceleratedfailuretimemodels,thelog‐normalmodelandthelog‐logistic model.Thesehavethefollowingbasicform: log-normal: S (t ) 1 log( it ) j log-logistic: S (t ) 1/ 1 ( it ) j 1 whereS(t)isthesurvivalfunctionandλi=exp(Xiβ).Weallowtheparametersσ(log‐ normal)orγ(log‐logistic)tovaryfreelyacrossindustries(j).Thatis,forthesemodels, boththemeanandthevarianceofthesurvivaldistributionarespecifictothe2‐digit 27 industry.Inthecaseofthesetwomodels,theelasticityofthehazardwithrespecttoa characteristicxdependsontimeandontheindustry‐specificparameter(σorγ), yieldingamoreflexiblemodel.Forexample,thehazardrateforthelog‐logisticmodelis givenbythefollowingexpression: h(t ) 1/ i d log S (t ) dt j t 1 1/ j 1/ j 1 ( it ) j Fromthiswecanderivetheelasticityofthehazardratewithrespecttoaregressorx:17 log hij (t ) xi (1 1/ i t) j Oneimplicationofthismodelisthereforethatboththehazardandtheelasticityofthe hazardwithrespecttotheregressorsdependont,thetimesincethefirmwasatriskof patenting.Wesamplethefirmsduringasingledecade,the2000s,butsomeofthefirms havebeeninexistencesincethe19thcentury.Thisfactcreatesabitofaproblemfor estimation,becausethereisnoreasontothinkthatthepatentingenvironmenthas remainedstableduringthatperiod.Weexploredvariationsintheassumedfirstdateat riskinTableB‐2,findingthatthechoicemadelittledifference.Accordingly,wehave usedaminimumatriskyearof1978forestimationinthemaintableinthetext. [TablesB‐1andB‐2here] 17Weassumethatxisinlogarithms,asistrueforourkeyvariables,sothiscanbeinterepretedasan elasticity. 28 C Previous Results To help the reader this appendix summarizes a number of results derived by Graevenitz et al. (2013) as well as some additional results that are useful. C.1 The Probability of Patenting a Facet The probability pk that a firm obtains a patent on a facet is: pk (f6k , F, NO (O, o6k , N )) = NO X j=0 ✓ ◆ NY O j ✓ 1 NO 1 j+1 j l=0 fl Fk ◆ NO Y m=NO j fm Fk . (C.1) Then, the expected number of patents a firm owns when it applyies for fi facets is k ⌘ pk fi . For the comparative statics of entry stage it is useful to know that the elasticity of pk w.r.t. F is negative if ˆk < 12 : ✓ ◆ NO @pk X 1 NO = (1 @Fk i+1 i i=0 ˆk )NO i ˆi k( 1) ✓ NO Fk NO F i fˆ ◆ (C.2) Then the elasticity ✏pk ,Fk is: ✏pk ,Fk =NO2 C.2 ⇣ ˆk 1 (1 2 + 1 ) NO ˆk 1 ⌘ (C.3) The Expected Number of Rival Investors The expected number of rival firms NO that undertake R&D on the same technology opportunity as firm i can be expressed as a sum of products: ✓ ◆ NYj N X N NO = j (1 j j=0 l=0 !l ) N Y !m . (C.4) m=N i Graevenitz et al. (2013) show that NO is increasing in !n , where n 2 {l, m}. In the second stage equilibrium NO can be rewritten as: ✓ ◆ N X N NO = j (1 j j=0 ! ˆ k )(N j) ! ˆ kj . (C.5) Incumbency Advantage In the case in which there are incumbents and entrants the expected number of rival firms NO has to rewritten slightly. To do this define: !nI ⌘ oIi O !nE ⌘ oE i O 1 (C.6) We assume that in a previous period N p firms entered and of these a fraction are still active. Then the expected number of rival firms ÑO that undertake R&D on the same technology opportunity as firm i is: ◆ NP ✓ X NP ÑO = j (1 j j=0 C.3 ! ˆ kJ )(N j) (ˆ !kJ )j ✓ ◆ N X N + j (1 j j=0 ! ˆ kE )(N j) (ˆ !kE )j . (C.7) The Expected Number of Facets Covered In the second stage equilibrium the expected number of facets covered through the joint efforts of all firms investing in a technological opportunity is: h ˜ Fk = F 1 (1 ˆk )(NO +1) The derivative of this expression with respect to F is positive: @ F˜k =1 @Fk ⇣ ˆk 1 ⌘NO ⇣ i 1 + ˆk NO (C.8) ⌘ 0. (C.9) The elasticities of F˜k with respect to fk and F are: ⌘ˆk = ✏ˆF̃k ,Fk = ˆk (1 ˆk )NO (C.10) 1 (1 ˆk )(NO +1) 1 (1 ˆk )(NO ) (1 + ˆj NO ) 1 (1 ˆk )(NO +1) (C.11) . which shows that 1 ✏F˜k Fk 0 as the denominator in the fraction is always greater than the numerator. It is useful to observe that the upper bound of the elasticity ⌘ˆk is decreasing in NO . To see this note that the elasticity can be expressed as: ⌘ˆk = (1 ˆk )NO (No + 1) 1 ˆk N2!o + ˆ2k No (N3!O ⇣ 1) ... ⌘. (C.12) This shows that the upper bound of the elasticity decreases in NO : lim ˆk !0 ⌘k = 1 (NO + 1) 1. Here we use the binomial expansion of (1 ˆk )No +1 . The expression also shows that the lower bound of ⌘k | ˆk =1 is zero. 2 D Results This appendix contains derivations for the propositions set out in Section 2 of the paper. D.1 Supermodularity of the Second Stage Game This section sets out the main results needed to show that the second stage of game G⇤ is supermodular. Consider the first order conditions that determine the equilibrium number of facets (fˆ) and technological opportunities (ô): @⇡ik = V (sik ) L( ik , sik ) @oi ✓ @⇡ik o i pk (sik ) = V µk ⌘ik ˜ @fi s Fk ik @Cc o Co (⌃N =0 , ik Ca j=1 oj ) @oi ✓ ◆ h d @L @L i ˜ Fk + Ca + V (1 @ ik dsik @sik (D.13) ⌘ik ) ◆ =0 (D.14) . Now, consider the cross-partial derivatives which must be positive, if the second stage game is supermodular. First, we derive the cross partial derivative with respect to firms’ own actions: @ 2 ⇡ik pk = @oi @fi F˜k ✓ V µk ⌘ik (sik ) sik F˜k ✓ @L + Ca @ ik ◆ h d + V dsik @L i (1 @sik ⌘ik ) ◆ . (D.15) = 0 This expression corresponds to the first order condition (D.14) for the optimal number of facets. Now consider effects of rivals’ actions on firms’ own actions: " # " ✓ ◆# @ 2 ⇡k @ F˜k sik @L @pk fi ⇣ d @L ⌘ @L = V (µk ⇠ik ) + + V F˜k + Ca @oi @om @om F˜k sik @sik @om F˜k dsik @sik @ ik @ 2 ⇡k @oi @fm @Co , o @⌃N j=1 oj " @ F˜k sik = V (µk @fm F˜k sik # " @L @pk fi ⇣ d ⇠ik ) + + V @sik @fm F˜k dsik " @L ⌘ @sik # F˜k ✓ @L + Ca @ ik ◆# @ 2 ⇡k @ F˜k @V @ 2V ˜ @L @ 2 L sik = + Fk ⌘ik Ca + (1 ⌘ik ) 2 @fi @om @om @ F˜k @ F˜k @ ik @sik 2 F˜k " # @⌘ik ⇣ @L ⌘ @pk @ 2 L @ 2 L fi + V (µk ⇠ik ) + fi + (1 ⌘ik ) , @om sik @sik @om @ ik 2 @sik 2 F˜k " @ 2 ⇡k @ F˜k @V @ 2V ˜ @L @ 2 L sik = ⇠ik (1 ✏F˜k ,f ) + ✏F˜k ,f + F ⌘ C + (1 k ik a 2 @fi @fm @fm @ F˜k sik sik @ ik @sik 2 F˜k @ F˜k " # @⌘ik ⇣ @L ⌘ @pk @ 2 L @ 2 L fi + V (µk ⇠ik ) + fi + (1 ⌘ik ) . @fm sik @sik @fm @ ik 2 @sik 2 F˜k (D.16) , (D.17) (D.18) ⌘ik ) # (D.19) The second stage game is supermodular, if the equations (D.16)-(D.19) are non-negative. The fol3 lowing results show that the conditions noted in Section 2 above must hold simultaneously if the game is supermodular. Using the first order condition (D.14), which will hold for any interior equilibrium, it can be shown that: " ! ✓ ◆# ⇣ d @L ⌘ @L @L V F˜k + Ca = ⌘ik V (µk ⇠ik ) + . (D.20) dsik @sik @ ik sik @sik @L If V sik (µk ⇠ik )+ @s > 0, then the second term in the cross-partial derivatives (D.16) and (D.17) is the ik product of two negative expressions, and then equation (D.17) is positive. Equation (D.16) is also positive in a free entry equilibrium: the negative term at the end is less than the negative term in the derivative of @Co @Co profits w.r.t. Nk in Section 2, which is otherwise the same as equation (D.16): @N ô > @N . o ô o ô Turning to equations (D.18) and (D.19) we can show that: @⌘ik @ 2 F˜k fi = @om @fi @om F˜k @⌘ik @ 2 F˜k fi = @fm @fi @fm F˜k @ F˜k @ F˜k fi = @fi @om F˜k 2 @ F˜k @ F˜k fi = @fi @fm F˜k 2 F˜k F˜k ˜k 1 @F ✓ k @om 1 ˜k ✓ 1 @F @fm 1 + ⌘ik k k + ⌘ik k ◆ (D.21) ◆ (D.22) This result allows us to rewrite equations (D.18) and (D.19) as follows: "✓ @ 2 ⇡k 1 @ F˜k = V (µk ⇠ik ) + @fi @om sik F˜k @om " @pk @ 2 L @ 2 L fi f + (1 i @om @ ik 2 @sik 2 F˜k "✓ @ 2 ⇡k 1 @ F˜k = V (µk ⇠ik ) + @fi @fm sik F˜k @fm " @pk @ 2 L @ 2 L fi f + (1 i @fm @ ik 2 @sik 2 F˜k @L @sik ◆✓ 1 2⌘ik # 1 ◆ @ 2V ˜ @ 2 L sik + F ⌘ + (1 k ik 2 @sik 2 F˜k @ F˜k (D.23) ⌘ik ) , @L @sik ◆✓ 1 ⌘ik ) # ⌘ik ) # 2⌘ik 1 ◆ @ 2V ˜ @ 2 L sik + F ⌘ + (1 2 k ik @sik 2 F˜k @ F˜k ⌘ik ) # (D.24) . Given assumptions (VF) and (LC) these two equations will be positive if V ⇣ ⌘ 1 2⌘ik 1 > 0. We analyze each condition in more detail next: sik (µk ⇠ik ) + @L @sik > 0 and @L k) 1. Given our assumptions on the legal cost function (LC, eq. 4) the condition V 4(ŝ (µk ⇠ˆk + @ŝ > ŝk k 4(ŝk ) @L 0 , V ŝk (µk ⇠ˆk > @ŝk implies that µk > ⇠ˆk . The elasticity of the value function w.r.t. additional covered patents must exceed the elasticity of the portfolio benefits function w.r.t. the share of patents held by the firm. This condition is less restrictive than the assumption in Graevenitz et al. (2013) that µk > 1, since we are assuming that ⇠ˆk < 1. ˆ 2. (1 2ˆ ⌘k ) 1 kˆ > 0 , (1 2 ˆ) > (1 ˆ)(NO +1) . This holds for any ˆk < 12 and No suffik ciently large. These restrictions imply a setting in which the ownership of patents belonging to each opportunity is fragmented amongst many firms. It is more likely to arise if the technology is highly complex, otherwise the condition that ˆk < 12 is less likely to hold. 4 In Appendix D.4 we derive the conditions under which the equilibrium of game G⇤ is unique. If there is a unique solution to the optimization problem of the firm at which profits are maximized, then this requires that @ 2 ⇡k /@ fˆ2 < 0. The restrictions that i) µk < 1 and ii) the share of overall profits which the firm obtains is decreasing at the margin in the share of patents the firm holds (@ 2 /@ŝ2k < 0) ensure that there is always such a unique interior solution. In this game G⇤ the comparative statics of patenting are the same as in the main model analyzed in Graevenitz et al. (2013). Specifically we can show that the following effects hold in this game: @ 2⇡ @ 2⇡ @ 2⇡ @ 2⇡ > 0, > 0, < 0, <0 @oi @Fk @fi @Fk @oi @Ok @fi @Ok (D.25) This implies that complexity of the technology increases firms’ patent applications while increased technological opportunity reduces firms’ patenting applications. D.2 Effect of Hold-up on Patenting Here we show that Proposition 2 holds. Consider the following cross-partial derivatives for the effects of higher legal costs L due to hold-up: @ 2 ⇡k = @ ô@hk @ 2 ⇡k = @ fˆ@hk @L(ˆk , ŝk , hk ) <0 , @h ✓ k✓ 2 ◆ ôpk ˜ @ L @ 2L Fk + (1 @ˆk @hk @ŝk @hk F˜k (D.26) ⌘ˆk ) ◆ <0 . (D.27) The first of these conditions shows that the expected legal costs of hold-up reduce the number of opportunities a firm invests in, in equilibrium. The second condition shows that firms with larger portfolios will be more exposed to hold up and will benefit less from the share of patents they have patented per opportunity. Both of these effects reduce the number of facets each firm applies for. D.3 Free Entry Equilibirum Proposition 3 There is a free entry equilibrium at which the marginal entrant can just break even, if R&D fixed costs per opportunity (Co ) increase in the number of entrants. In a free entry equilibrium it must be the case that the following conditions hold: ⇡k (ôk , fˆk , N̂k ) > 0 ⇡k (ôk , fˆk , N̂k + 1) < 0 . ^ The effect of entry on profits at the first stage of game G⇤ can be shown to be: @⇡(ô, fˆ) @NO = ô @Nk @Nk ŝk @ F˜k (ŝk ) Vµ ˜ ŝk Fk @NO ✓ @ V (F˜k ) @ŝk 5 @L @ŝk ◆ (D.28) "✓ @pk fˆ @ + V (F˜k ) @NO F˜k @ŝk @L @ŝk ◆ F˜k ✓ ⇠ˆk ⌘ @L + Ca @ˆk ◆# @Co ô @No ô ! . (D.29) This expression can be further simplified: @⇡(ô, fˆ) ŝk = ô✏NO ,N @Nk N ✏F˜k ,No ✏pk ,No ⌘ˆk (ŝk ) ⇣ µk ŝk V @L + @ŝk @Co No ô @No ô ŝk ! . (D.30) The first two terms in brackets in this derivative are positive and so is the third term. We can show that the limits of ✏F˜k ,No and ✏F˜k ,f in No are both zero. Therefore the above derivative is negative as long as the R&D fixed costs per opportunity are increasing in No . This is the condition set out in Proposition 3. D.4 Uniqueness of the second stage equilibrium We show that stage 2 of game G⇤ is supermodular. This implies that there exists at least one equilibrium of the stage game. An alternative way of deriving existence of the second stage equilibrium for game G⇤ is to analyze the conditions under which the Hessian of second derivatives of the profit function (H⇡ ) is negative semidefinite. This matrix consists of four derivatives of which only one leads to additional restrictions on the model. @2⇡ It is easy to see that @o 2 < 0 due to the coordination costs Cc (oi ) and the restrictions we impose with i assumption (FVC). The two cross-partial derivatives are both zero in equilibrium - refer to equation D.15. @2⇡ Therefore, the only expression that remains to analyze is @f 2. i " @ 2⇡ o i pk @ 2 V = @fi 2 F˜k @ F˜k 2 @ F˜k @fi !2 F˜k @V @ F˜k d d 2 pk +2 (1 ⌘ik ) + V 2 (1 ⌘ik )2 pk sik F˜k @ F˜k @fi dsik ✓ ◆2 ✓ ◆ @ 2L 2 @ 2 L @sik d @L (1 p 2 V @ ik 2 k @sik 2 @fi dsik @sik ⌘ik ) ⌘ik fi # . This can be further simplified: " @ 2⇡ o i pk @ 2 V = @fi 2 F˜k @ F˜k 2 @ F˜k @fi !2 F˜k d 2 pk @ 2L 2 +V 2 (1 ⌘ik )2 p pk sik F˜k @ ik 2 k ✓ ◆ @ 2 L pk @L (1 2 (1 ⌘ ) 2 V ⇠ (1 µ ) ik ik k @sik 2 F˜k sik @sik ⌘ik ) ⌘ik fi # . (D.31) If we impose the restriction that the second derivative of the value function is negative and that the elasticity of the value function, µk < 1, then the first and the last terms in the above expression are @2 negative. The sign of the second term in the expression depends on sign{ @s 2 }, which we will assume is ik negative. The third and fourth terms in the above expression are negative given the conditions imposed on the legal cost function above. 6 D.5 Entry and Incumbency In this section we analyze a game in which incumbents have lower costs of entry and demonstrate that our main predictions are robust. We assume that a fraction (0 < < 1) of the previously active N P firms remain as incumbents. The firms enter until the marginal profit from entry is reduced to zero. Objective Functions First, consider the objective functions of incumbents and entrants and the patenting game they are involved in. We analyze this game and show when it is supermodular. Given symmetry of technological opportunities (Assumption S) the expected value of patenting for entrant and incumbent firm’s in a technology area k is: 0 I ⇡ik (oIi , fiI ) =oIi @V (F̃k ) (sIik ) E E ⇡ik (oi , fiE ) =oE i 0 @V (F̃k ) (sE ik ) L( L( I I ik , sik ) E E ik , sik ) 0 NP @C o ( Co ( 1+N X E oj ) j=1 NP X +N E 1 j=1 oj ) 1 A 1 fiI pk Ca A 1 fiE pk Ca A Cc (oE i ) Cc (oIi ) . (D.32) . (D.33) Define a game GE in which: • There are N P incumbent firms and the number of entrants, N E , is determined by free entry. • Entrants and incumbents simultaneously choose the number of technological opportunities oIi , oE i 2 n I E n [0, O ] and the number of facets applied for per opportunity fi , fi 2 [0, F ]. Firms’ strategy sets Sn are elements of R4 . • Firms’ payoff functions ⇡ik , defined at (D.32,D.33), are twice continuously differentiable and depend only on rivals’ aggregate strategies. • Assumptions (VF, eqn. 1) and (LC, eqn. 4) describe how the expected value and the expected cost of patenting depend on the number of facets owned per opportunity. Firms’ payoffs depend on their rivals’ aggregate strategies because the probability of obtaining a patent on a given facet is a function of all rivals’ patent applications. Note that the game is symmetric within the two groups of firms as it is exchangeable in permutations of the players. This implies that symmetric equilibria exist, if the game can be shown to be supermodular (Vives, 2005).1 1 Note also that only symmetric equilibria exist as the strategy spaces of players are completely ordered. 7 First order conditions for game GE : I @⇡ik =V @oIi (sik ) I @⇡ik o I pk = i I @fi F˜k E @⇡ik =V @oE i ✓ ik , sik ) V µ✏F˜k fi (sik ) E @⇡ik o E pk = i E @fi F˜k L( ✓ L( 4(sik ) sik ik , sik ) V µ✏F˜k fi 4(sik ) sik 0 NP @C o ( F˜k Co ( ✓ 1+N X F˜k @L + Ca @ ik ✓ A oj ) j=1 NP X +N E 1 1 E ◆ oj ) j=1 @L + Ca @ ik h @4(s ) ik + V @sik ik Ca ◆ ik Ca @Cc =0 @oE i h @4(s ) ik + V @sik @Cc =0 @oIi , @L i (1 @sik ⌘ik ) (D.34) ◆ =0 (D.35) (D.36) , @L i (1 @sik , ⌘ik ) ◆ =0 . (D.37) Proposition 7 In game GE the equilibrium number of facets chosen by incumbents and entrants is the same: fˆI = fˆE . We show in Appendix C.2 that in the game with incumbents the number of rivals per opportunity ÑO becomes a function of both ôI , ôE . The first order conditions determining fˆI , fˆE both depend on the total number of entrants per technological opportunity ÑO and so both on ôI , ôE . This is the only way in which rivals’ choices of the number of opportunities to pursue enter these first order conditions2 . Therefore the two conditions are identical and Proposition 7 holds. Proposition 8 The second stage of game GE is smooth supermodular under the same conditions as game G⇤ . Comparative statics results for game G⇤ also apply to game GE . The first order conditions characterizing the game with incumbents and entrants are identical to those for the game without incumbents as long as = 0. As this variable is a constant it does not enter into the second order conditions which we analyze to establish supermodularity and which underpin the comparative statics predictions in Propositions 4-6. Proposition 9 In the second stage of game GE incumbents enter more technological opportunities, if they have a cost advantage in undertaking R&D ( > 0). The first order conditions determining the equilibrium number of opportunities chosen by incumbents and entrants are identical if firms R&D fixed costs per opportunity are the same ( = 0). Therefore ôI| =0 = ôE . As the cost advantage of incumbents in undertaking R&D grows this increases the number of opportunities chosen by incumbents: I @ 2 ⇡ik =1>0 @oI @ . (D.38) 2 Clearly the factors outside the brackets in equations (D.35), (D.37) also depend on these variables, but these do not affect the equilibrium values of fiE , fjI . 8 Proposition 10 In the second stage of game GE the number of entrants decreases as the cost advantage of incumbents increases. Due to the supermodularity of the second stage game, increases in incumbents’ choices of the number of opportunities to invest in will raise the number of opportunities entrants invest in as well as the numbers of facets entrants and incumbents seek to patent in equilibrium. The increases in ôI and ôE will raise the fixed costs of entry into new opportunities, Co , which then reduces entry. References G RAEVENITZ , G., S. WAGNER , AND D. H ARHOFF (2013): “Incidence and Growth of Patent Thickets: The Impact of Technological Opportunities and Complexity,” The Journal of Industrial Economics, 61, 521–563. V IVES , X. (2005): “Complementarities and Games: New Developments,” Journal of Economic Literature, XLIII, 437–479. 9 Table 1 Patenting by Fame firms on Patstat (priority years 2002‐2009) Technology categories Elec machinery, energy Audio‐visual tech Telecommunications Digital communication Basic comm processes Computer technology IT methods for mgt Semiconductors Optics Measurement Analysis bio materials Control Medical technology Organic fine chemistry Biotechnology Pharmaceuticals Polymers Food chemistry Basic materials chemistry Materials metallurgy Surface tech coating Chemical engineering Environmental tech Handling Machine tools Engines,pumps,turbine Textile and paper mach Other spec machines Thermal process and app Mechanical elements Transport Furniture, games Other consumer goods Civil engineering Total Electrical engineering Instruments Chemistry Mechanical engineering Other Fields Weighted by #owners & #classes* GB pats EP pats Total 1,321 1,101 2,422 633 549 1,182 1,181 1,206 2,386 590 732 1,323 302 146 447 1,481 1,302 2,783 256 224 480 269 248 518 392 481 873 1,216 1,458 2,674 132 426 557 592 542 1,134 996 1,561 2,558 182 1,538 1,720 193 950 1,143 277 1,876 2,153 114 280 394 88 458 547 314 1,050 1,363 161 318 479 287 284 571 507 724 1,231 296 344 640 996 813 1,809 428 356 784 887 942 1,829 235 304 539 742 623 1,365 410 261 671 1,149 854 2,002 1,063 930 1,993 1,064 612 1,675 630 507 1,137 2,237 960 3,196 21,619 24,959 46,578 6,032 5,508 11,540 3,328 4,468 7,796 2,418 7,822 10,240 5,910 5,083 10,993 3,930 2,079 6,009 Sector shares GB pats EP pats 6.1% 4.4% 2.9% 2.2% 5.5% 4.8% 2.7% 2.9% 1.4% 0.6% 6.8% 5.2% 1.2% 0.9% 1.2% 1.0% 1.8% 1.9% 5.6% 5.8% 0.6% 1.7% 2.7% 2.2% 4.6% 6.3% 0.8% 6.2% 0.9% 3.8% 1.3% 7.5% 0.5% 1.1% 0.4% 1.8% 1.5% 4.2% 0.7% 1.3% 1.3% 1.1% 2.3% 2.9% 1.4% 1.4% 4.6% 3.3% 2.0% 1.4% 4.1% 3.8% 1.1% 1.2% 3.4% 2.5% 1.9% 1.0% 5.3% 3.4% 4.9% 3.7% 4.9% 2.5% 2.9% 2.0% 10.3% 3.8% 27.9% 15.4% 11.2% 27.3% 18.2% 22.1% 17.9% 31.3% 20.4% 8.3% * Weighting by owners does not affect the numbers, since they all get added back into the same cell. Weighting by classes means that a patent in multiple TF34 sectors is downweighted in each of the sectors. Table 2 UKIPO and EPO patents: numbers, triples and network density 2002‐2009 Technology categories Elec machinery, energy Audio‐visual tech Telecommunications Digital communication Basic comm processes Computer technology IT methods for mgt Semiconductors Optics Measurement Analysis bio materials Control Medical technology Organic fine chemistry Biotechnology Pharmaceuticals Macromolecular chemistry Food chemistry Basic materials chemistry Materials metallurgy Surface tech coating Chemical engineering Environmental tech Handling Machine tools Engines,pumps,turbine Textile and paper mach Other spec machines Thermal process and app Mechanical elements Transport Furniture, games Other consumer goods Civil engineering Total Electrical engineering Instruments Chemistry Mechanical engineering Other Fields Aggregate Number of Triples per EPO patents EPO triples@ 1000 patents 56,714 7751 136.7 34,131 13268 388.7 62,288 27049 434.3 36,975 16529 447.0 10,035 2289 228.1 60,577 21956 362.4 9,312 34 3.7 24,544 9974 406.4 28,458 7767 272.9 44,320 2503 56.5 11,787 26 2.2 17,612 308 17.5 66,062 4411 66.8 41,137 3993 97.1 33,192 365 11.0 52,671 11222 213.1 21,307 3722 174.7 9,955 140 14.1 27,679 1929 69.7 16,935 405 23.9 17,429 363 20.8 24,494 443 18.1 12,708 858 67.5 30,343 252 8.3 24,040 508 21.1 32,602 6678 204.8 23,145 2640 114.1 29,826 319 10.7 15,290 335 21.9 32,716 1301 39.8 48,875 10929 223.6 19,847 206 10.4 19,734 301 15.3 28,817 171 5.9 1,025,555 160,945 156.9 294,575 98,850 335.6 168,239 15,015 89.2 257,507 23,440 91.0 236,836 22,962 97.0 68,398 678 9.9 US Citation Average non‐ network patent density# references 39.4 0.420 63.5 0.449 79.1 1.235 178.5 1.397 110.8 1.162 54.3 1.529 144.2 0.920 94.0 1.070 58.0 0.806 45.6 1.000 319.4 7.040 112.1 0.445 206.2 0.614 32.9 5.253 89.6 17.332 76.6 6.391 92.7 1.236 326.3 2.701 84.8 1.498 91.7 1.130 59.4 0.803 66.2 0.797 206.9 0.487 66.9 0.137 64.0 0.191 85.4 0.210 84.9 0.312 65.7 0.422 146.3 0.189 57.8 0.168 68.3 0.203 107.6 0.166 105.6 0.194 117.1 0.150 100.3 0.800 60.4 1.042 96.3 1.181 71.1 4.977 70.1 0.227 110.8 0.167 @ Triples based on all EPO patenting, priority years 2002‐2009 (see text for definition and further explanation). # Network density is 1,000,000 times the number of within technology citations between 1976 and the current year divided by the potential number of such citations. Table 3 Hazard of entry into patenting in a TF34 Class 538,452 firm‐TF34 observations with 10,665 entries (20,384 firms) Cox Proportional Hazard Model Variable Log (network density) 0.115*** 0.127*** 0.107*** 0.184*** 0.317*** (0.025) 0.060*** (0.022) 0.270*** (0.011) 1.135*** (0.104) ‐0.138*** (0.011) 0.506*** (0.031) 0.084*** (0.022) 0.270*** (0.011) 1.135*** (0.104) (0.023) ‐0.139*** (0.011) 0.545*** (0.030) 0.072*** (0.022) 0.270*** (0.011) 1.136*** (0.104) (0.021) ‐0.101*** (0.010) 0.514*** (0.027) ‐0.009 (0.021) 0.142*** (0.013) 0.773*** (0.130) 0.836*** (0.021) stratified# yes ‐65.96 12 1270.6 stratified# yes ‐65.86 12 1429.1 stratified# yes ‐65.84 13 1517.2 stratified# yes ‐58.69 14 3465.1 (0.052) ‐0.100*** (0.023) 0.822*** (0.071) 0.103* (0.056) 0.513*** (0.083) 0.767*** (0.131) 0.836*** (0.021) ‐0.010* (0.006) ‐0.001 (0.003) ‐0.040*** (0.008) ‐0.015** (0.006) stratified# yes ‐58.67 18 3458.6 (0.024) Log (triples density in class) Log (patents in class) 5‐year growth of non‐ patent refs in class) Log assets Log firm age in years Log (pats applied for by firm previously) Log (network density) * Log assets Log (triples density) * Log assets Log (patents in class) * Log assets Log (average NPL refs) * Log assets Industry dummies Year dummies Log likelihood Degrees of freedom Chi‐squared The sample is matched on size class, sector, and age class. Estimates are weighted by sampling probability. Coefficients for the hazard of entry into a patenting class are shown. Standard errors are clustered on firm. *** (**) denote significance at the 1% (5%) level. Time period is 2002‐2009 and minimum entry year is 1978. Sample is UK firms with nonmissing assets, all patenting firms and a matched sample of non‐patenting firms # Estimates are stratified by industry ‐ each industry has its own baseline hazard. Table A1 Number of TF34 sectors entered between 2002 and 2009 Number of sectors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 or more Total Number of firms 2,531 1,347 647 271 155 71 45 29 20 14 4 2 3 0 13 5,152 Number of entries 2,531 2,694 1,941 1,084 775 426 315 232 180 140 44 24 39 0 240 10,665 Table A‐2 Sample population of UK firms, by industry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Industry Basic metals Chemicals Electrical machinery Electronics & instruments Fabricated metals Food, beverage, & tobacco Machinery Mining, oil&gas Motor vehicles Other manufacturing Pharmaceuticals Rubber & plastics Construction Other transport Repairs & retail trade Telecommunications Transportation Utilities Wholesale trade Business services Computer services Financial services Medicalservices Personal services R&D services inactive Total Number of firms 2,836 3,834 2,948 9,298 24,681 8331 9,365 83,491 2,337 94,952 1,008 6,094 295596 3,292 128,266 14,348 60,837 12,880 138,398 689,942 177,319 183,042 38,424 94,791 7,915 37,525 2,131,750 Number of patenters 2001‐2009 52 246 281 561 606 102 608 15 117 1362 105 398 372 89 251 133 75 75 728 1639 716 219 103 196 713 271 10,033 Share Number of patenting patents 2001‐2009 2001‐2009 1.83% 231 6.42% 126 9.53% 727 6.03% 444 2.46% 70 1.22% 29 6.49% 313 0.02% 96 5.01% 22 1.43% 150 10.42% 551 6.53% 590 0.13% 59 2.70% 6274 0.20% 2324 0.93% 2096 0.12% 621 0.58% 428 0.53% 3608 0.24% 6757 0.40% 1132 0.12% 4930 0.27% 1419 0.21% 1194 9.01% 168 0.72% 5673 0.47% 40,032 Table A3 Entry into techology area 2002‐2009 Numbers Technology Elec machinery, energy Audio‐visual tech Telecommunications Digital communication Basic comm processes Computer technology IT methods for mgt Semiconductors Optics Measurement Analysis bio materials Control Medical technology Organic fine chemistry Biotechnology Pharmaceuticals Polymers Food chemistry Basic materials chemistry Materials metallurgy Surface tech coating Chemical engineering Environmental tech Handling Machine tools Engines,pumps,turbine Textile and paper mach Other spec machines Thermal process and app Mechanical elements Transport Furniture, games Other consumer goods Civil engineering Total Electrical engineering Instruments Chemistry Mechanical engineering Other Fields Total patenting in sector by GB firms 1763.7 788.3 1874.4 1054.0 256.5 2167.2 283.2 347.2 584.7 1765.3 339.0 712.1 1668.4 1569.4 701.6 1700.7 224.4 492.7 1020.2 360.8 400.7 842.7 446.6 1326.3 577.8 1443.4 442.0 847.4 455.7 1445.9 1288.2 1239.2 788.1 2045.8 33263.6 8534.5 5069.5 7760.0 7826.7 4073.0 First time patenter 214 148 146 92 21 291 117 38 55 226 39 165 184 36 41 54 27 36 85 54 77 142 106 274 106 82 77 180 105 223 213 288 194 463 4599 1067 669 658 1260 945 Shares Patented previously in another tech Total entry 250 26.3% 192 43.1% 179 17.3% 141 22.1% 93 44.4% 251 25.0% 157 96.7% 118 44.9% 130 31.6% 269 28.0% 111 44.3% 241 57.0% 209 23.6% 83 7.6% 99 20.0% 80 7.9% 112 61.9% 87 25.0% 144 22.4% 109 45.2% 195 67.9% 213 42.1% 166 60.9% 290 42.5% 180 49.5% 160 16.8% 137 48.4% 234 48.9% 159 57.9% 317 37.3% 236 34.9% 223 41.2% 246 55.8% 255 35.1% 6066 32.1% 1381 28.7% 960 32.1% 1288 25.1% 1713 38.0% 724 41.0% First time patenter 12.1% 18.8% 7.8% 8.7% 8.2% 13.4% 41.3% 10.9% 9.4% 12.8% 11.5% 23.2% 11.0% 2.3% 5.8% 3.2% 12.0% 7.3% 8.3% 15.0% 19.2% 16.9% 23.7% 20.7% 18.3% 5.7% 17.4% 21.2% 23.0% 15.4% 16.5% 23.2% 24.6% 22.6% 13.8% 12.5% 13.2% 8.5% 16.1% 23.2% Patented previously in another tech 14.2% 24.4% 9.5% 13.4% 36.3% 11.6% 55.4% 34.0% 22.2% 15.2% 32.7% 33.8% 12.5% 5.3% 14.1% 4.7% 49.9% 17.7% 14.1% 30.2% 48.7% 25.3% 37.2% 21.9% 31.2% 11.1% 31.0% 27.6% 34.9% 21.9% 18.3% 18.0% 31.2% 12.5% 18.2% 16.2% 18.9% 16.6% 21.9% 17.8% Table B‐1 Hazard of entry into patenting in a TF34 Class ‐ Comparing models 538,452 firm‐TF34 observations with 10,665 entries (20,384 firms) Proportional hazard AFT Variable Cox PH Weibull Log logistic Log normal Log (network density) 0.108*** 0.111*** 0.308*** 0.247*** (0.021) (0.021) (0.096) (0.040) Log (triples density ‐0.100*** ‐0.098*** ‐0.511*** ‐0.258*** in class) (0.010) (0.010) (0.071) (0.024) Log (patents in class) 0.513*** 0.513*** 2.177*** 1.095*** (0.027) (0.027) (0.304) (0.089) 5‐year growth of non‐ (0.013) ‐0.001 ‐0.077 ‐0.039 patent refs in class) (0.022) (0.021) (0.084) (0.038) Log assets 0.149*** 0.130*** 0.529*** 0.198*** (0.013) (0.013) (0.082) (0.024) Log (pats applied for 0.848*** 0.860*** 5.685*** 3.973*** by firm previously) (0.021) (0.019) (0.917) (0.368) Industry dummies stratified# stratified# stratified# stratified# Year dummies yes yes yes yes Log likelihood ‐58.8 ‐96,051.0 ‐114,127.0 ‐111,662.1 Degrees of freedom 13 38 38 38 Chi‐squared 3183.2 4560.1 168.4 300.1 All estimates are weighted estimates, weighted by sampling probability. For the Cox and Weibull models, coefficients shown are elasticities of the hazard w.r.t. the variable. For the log‐logistic, ‐beta is shown. *** (**) denote significance at the 1% (5%) level. Time period is 2002‐2009 and minimum entry year is 1978. Sample is all UK firms with nonmissing assets. AFT ‐ Accelerated Failure Time models # Estimates are stratified by industry ‐ each industry has its own baseline hazard. Table B‐2 Hazard of entry into patenting in a TF34 Class ‐ Robustness Variable Log (network density) Log (triples density in class) Log (patents in class) 5‐year growth of non‐ patent refs in class) Log assets Log firm age in years Log (lagged firm‐level patent stock) Year dummies (1) 0.107*** (0.021) ‐0.101*** (0.010) 0.514*** (0.027) ‐0.009 (0.021) 0.142*** (0.013) 0.773*** (0.130) 0.836*** (0.021) yes (2) ‐0.008 (0.019) ‐0.183*** (0.008) 0.623*** (0.024) ‐0.196*** (0.020) 0.138*** (0.013) 0.588*** (0.145) 0.947*** (0.019) yes (3) 0.114*** (0.024) ‐0.114*** (0.011) 0.605*** (0.031) ‐0.002 (0.025) 0.186*** (0.018) 0.739*** (0.155) 0.954*** (0.033) yes (4) 0.107*** (0.021) ‐0.103*** (0.009) 0.520*** (0.027) ‐0.012 (0.021) 0.139*** (0.013) 0.778*** (0.131) 0.840*** (0.021) yes (5) 0.108*** (0.021) ‐0.103*** (0.009) 0.518*** (0.027) ‐0.012 (0.021) 0.146*** (0.013) 0.021 (0.246) 0.878*** (0.021) yes 538,452 20,384 10,665 1.98% ‐58.69 14 3465.1 692,038 20,384 10,665 1.54% ‐54.60 14 5065.8 452,313 17,993 8,149 1.96% ‐40.59 14 1688.8 523,547 20,384 10,340 1.97% ‐56.94 14 3459.1 538,452 20,384 10,665 1.98% ‐53.81 14 3137.4 Observations Firms Entries Entry rate Log likelihood Degrees of freedom Chi‐squared All estimates are weighted estimates, weighted by sampling probability. Coefficients shown are negative of the estimates (larger coefficient increases entry probability). *** (**) denote significance at the 1% (5%) level. Time period is 2002‐2009 and minimum entry year is 1978. Sample is UK firms with nonmissing assets, all patenting firms and a matched sample of non‐patenting firms Weibull model stratified by industry. (1) Estimates from Table 3, for comparison. (2) Observations for tech sectors of firms whose industry has no such patenting (Lybbert‐Kolas) and where there is no entry by any UK firm in that industry are included. (3) SMEs: firms with assets>12.5 million GBP removed. (4) The Telecom tech sector is removed. (5) The minimum founding year is 1900 instead of 1978.
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