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:bhhall@berkeley.edu
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.
Arora,A.,Ceccagnoli,M.,&Cohen,W.M.(2008).R&DandthePatentPremium.
InternationalJournalofIndustrialOrganization,26(5),1153‐1179.
Arundel,A.,Patel,P.,2003.StrategicPatenting,BackgroundReportfortheTrendChart
PolicyBenchmarkingWorkshopNewTrends.Availableat
http://proinno.intrasoft.be/reports/documents/TCW15_background_paper.pdf.
Berneman,L.P.,Cockburn,I.,Agrawal,A.,Shankar,I.,2009.U.S./CanadianLicensingIn
2007‐08:SurveyResults.lesNouvelles1–8.
Berry,S.,1992.Estimationofamodelofentryintheairlineindustry,Econometrica,60,
889‐917.
Bessen,J.,Maskin,E.,2007.SequentialInnovation,Patents,andImitation.RANDJournal
ofEconomics40,611‐635.
Bessen,J.,Meurer,M.,2013.ThePatentLitigationExplosion.LoyolaUniversityChicago
LawJournal45(2):401‐440.
Bessen,J.,Meurer,M.,2008.Patentfailure:howjudges,bureaucrats,andlawyersput
innovatorsatrisk.Princeton,NJ:PrincetonUniversityPress.
Bloom,N.,M.Schankerman,andJ.vanReenen,2013.Idenitfyingtechnologyspillovers
andproductmarketrivalry,Econometrica81(4),1347–1393.
Bound,J.,Cummins,C.,Griliches,Z.,Hall,B.,Jaffe,A.,1984.WhodoesR&Dandwho
patents?R&DPatentsandproductivity,Z.Griliches(ed.).Chicago,Universityof
ChicagoPress.
BresnahanT.,ReissP.,1991.Entryandcompetitioninconcentratedmarkets,Journalof
PoliticalEconomy,99,977‐1009.
Cockburn,I.M.,MacGarvie,M.J.,2011.EntryandPatentingintheSoftwareIndustry.
ManagementScience57,915–933.
Cockburn,I.M.,MacGarvie,M.J.,Muller,E.,2010.Patentthickets,licensingand
innovativeperformance.IndustrialandCorporateChange19,899–925.
Cohen,W.M.,Nelson,R.R.,Walsh,J.P.,2000.ProtectingtheirIntellectualAssets:
AppropriabilityConditionsandWhyU.S.ManufacturingFirmsPatent(orNot).
Cambridge,MA:NBERWorkingPaperNo.7552.
Farrell,J.andMerges,R.P.(2004).IncentivestoChallengeandtoDefendPatents:Why
LitigationWon’tReliablyFixPatentOfficeErrorsandWhyAdministrativePatent
ReviewMightHelp,BerkeleyTechnologyLawJournal,19(3),943‐970.
Farrell,J.,Shapiro,C.,2008.Howstrongareweakpatents?AmericanEconomicReview
21
98,1347–1369.
FederalTradeCommission,2003.ToPromoteInnovation‐TheProperBalanceof
CompetitionandPatentLawandPolicy.Washington,DC:GPO.Availableat
http://www.ftc.gov/reports/innovation/P040101PromotingInnovationandCompet
itionrpt0704.pdf
FederalTradeCommission,2011.TheEvolvingIPMarketplace:.AligningPatentNotice
andRemediesWithCompetition.Washington,DC.Availableat
http://www.ftc.gov/os/2011/03/110307patentreport.pdf
Fischer,T.,&Henkel,J.,2012.Patenttrollsonmarketsfortechnology–Anempirical
analysisofNPEs’patentacquisitions.ResearchPolicy,41(9),1519‐1533.
Graevenitz,vonG.,Wagner,S.,Harhoff,D.,2011.Howtomeasurepatentthickets—A
novelapproach.EconomicsLetters111,1–4.
Graevenitz,vonG.,Wagner,S.,Harhoff,D.,2013.Incidenceandgrowthofpatent
thickets:theimpactoftechnologicalopportunitiesandcomplexity.Journalof
IndustrialEconomics,61(3),521‐563.
Grindley,P.C.,Teece,D.J.,1997.ManagingIntellectualCapital:LicensingandCross‐
LicensinginSemiconductorsandElectronics.CaliforniaManagementReview39,8–
41.
Hall,B.H.,2005.ExploringthePatentExplosion.JournalofTechnologyTransfer30,35–
48.
Hall,B.H.,Harhoff,D.,2004.PostGrantReviewSystemsattheU.S.PatentOffice‐Design
ParametersandExpectedImpact.BerkeleyTechnologyLawJournal19,981–1015.
Hall,B.H.,Helmers,C.,vonGraevenitz,G.,Rosazza‐Bondibene,C.,2012a.Astudyof
patentthickets.DraftReporttotheUKIPO,1–66.
Hall,B.H.,Helmers,C.,Rogers,M.,Sena,V.,2013.Theimportance(ornot)ofpatentsto
UKfirms.OxfordEconomicPapers65(3):603‐629.
http://dx.doi.org/doi:10.1093/oep/gpt012
Hall,B.H.,Ziedonis,R.H.,2001.Thepatentparadoxrevisited:anempiricalstudyof
patentingintheUSsemiconductorindustry,1979‐1995.RANDJournalofEconomics
101–128.
Harhoff,D.andM.Reitzig(2004).DeterminantsofOppositionagainstEPOPatent
Grants–TheCaseofBiotechnologyandPharmaceuticals,InternationalJournalof
IndustrialOrganization,22(4),443‐480.
Harhoff,D.,2006.PatentQuantityandQualityinEurope‐TrendsandPolicy
ImplicationsCollection.InB.KahinandF.Foray(eds),AdvancingKnowledgeandthe
KnowledgeEconomy.Cambridge,MA:MITPress,331‐350.
Harhoff,D.,Graevenitz,von,G.,Wagner,S.,2015.ConflictResolution,PublicGoodsand
22
PatentThickets.ManagementScience,forthcoming.
http://dx.doi.org/10.1287/mnsc.2015.2152
Harhoff,D.,Hall,B.,Graevenitz,G.V.,Hoisl,K.,Wagner,S.,Gambardella,A.,Giuri,P.,2007.
TheStrategicUseofPatentsanditsImplicationsforEnterpriseandCompetition
Policies.FinalreportforECTenderNoENTR/05/82,1–307.
Hegde,D.,Mowery,D.C.,Graham,S.J.H.,2009.PioneeringInventorsorThicketBuilders:
WhichU.S.FirmsUseContinuationsinPatenting?ManagementScience55,1214–
1226.
Helmers,C.,RogersM.,SchautschickP.,2011.IntellectualPropertyattheFirm‐Levelin
theUK:TheOxfordFirm‐LevelIntellectualPropertyDatabase.UniversityofOxford,
DepartmentofEconomicsDiscussionPaperNo.546.
Lemley,M.,Shapiro,C.,2005.Probabilisticpatents.JournalofEconomicPerspectives19,
75–98.
Lemley,M.,Shapiro,C.,2007.PatentHoldupandRoyaltyStacking.TexasLawReview
85:1991.
Lerner,J.,1995.Patentingintheshadowofcompetitors.JournalofLawandEconomics
38,463‐495.
Lerner,J.andJ.Tirole,2013.Standard‐EssentialPatents,NBERWorkingPaper19664.
Lewis,J.I.D.andR.M.Mott,2013.Theskyisnotfalling:Navigatingthesmartphone
patentthicket,WIPOMagazine,February2013,
http://www.wipo.int/wipo_magazine/en/2013/01/article_0002.html
Lybbert,T.J.,Zolas,N.J.2014.GettingPatents&EconomicDatatoSpeaktoEachOther:
An‘AlgorithmicLinkswithProbabilities’ApproachforJointAnalysesofPatenting&
EconomicActivity.ResearchPolicy43(3),530‐542.
MilgromP.andJ.Roberts,1994.Comparingequilibria.AmericanEconomicReview
84(3),441–459.
Palmer,J.A.andK.Kreutz‐Delgado,2003.Ageneralframeworkforcomponent
estimation.Proceedingsofthe4thInternationalSymposiumonIndependent
ComponentAnalysis.
Reitzig,M.,Henkel,J.,Heath,C.,2007.Onsharks,trolls,andtheirpatentprey—
Unrealisticdamageawardsandfirms’strategiesof“beinginfringed.”Research
Policy36,134–154.
Schmoch,U.,2009.DocumentIPC/CE/41/5,Annex,ConceptionofaTechnology
ClassificationforCountryComparisons,41thsessionoftheIPCCommitteeofExperts.
1–15.
Shapiro,C.,2000.Navigatingthepatentthicket:Crosslicenses,patentpools,and
standardsetting.Innovationpolicyandtheeconomy1:119–150.
23
Somaya,D.,2003.Strategicdeterminantsofdecisionsnottosettlepatentlitigation.
StrategicManagementJournal24,17–38.
Teece,D.,E.Sherry,andP.Grindley,2014.Patentsand"PatentWars"inWireless
Communications:AnEconomicAssessment,DigiworldEconomicJournal95,85‐98.
U.S.DepartmentofJustice,FederalTradeCommission,2007.AntitrustEnforcementand
IntellectualPropertyRights:PromotingInnovationandCompetition,1–217.
Vives,X.,2005.Complementaritiesandgames:Newdevelopments.JournalofEconomic
LiteratureXLIII(2),437–479.
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.