Patent Quality and a Two-Tiered Patent System

Transcription

1 Patent Quality an a Two-Tiere Patent System Viya Atal y an Talia Bar z October 2, 200 Abstract We stuy the eterminants of patent quality an the volume of patent applications in a moel where innovators care about perceive patent quality. We examine the e ects of various reforms on patent quality, in particular a proposal to establish a two-tiere patent system in which applicants can choose a more costly an more stringent examination process gol-plate patents. Introucing a secon patent-tier can reuce patent applications, an the incience of ba patents. We claim that innovators with high exante probability of valiity will more likely apply for the gol-plate patents, but sorting in the imension of economic signi cance is not obvious. Keywors: innovation, patent, prior art, research an evelopment, golplate patents, two-tiere patent system. JEL classi cation coes: D83, O3, O34 We are grateful to Haim Bar, Kaushik Basu, Phoebe Chan, Mahumita Datta, Corinne Langinier, Aija Leiponen, Tapan Mitra an seminar participants at Drexel University an at the 2009 International Inustrial Organization Conference in Boston for valuable comments. y Department of Economics & Finance, Montclair State University. atalv@mail.montclair.eu z Department of Economics, Cornell University. tb97@cornell.eu.

2 Introuction The quality of patents has been a subject of growing concerns. Ba patents patents that woul have faile the novelty or non-obviousness patentability requirements ha their examiners been more informe likely have averse e ects on our society. Patents, goo or ba, have social costs. Patent holers can exclue others from use of inventions which might hiner future innovations an commercialization of proucts, or inuce unnecessary costs of uplication an inventions aroun an existing patent. In the case of goo patents, such social costs may be o set by the bene ts of increase incentives to innovate an to isclose new information. But bearing the social cost of a patent can harly be justi e for ba patents. Moreover, ba patents are presumably more likely to be associate with litigation costs (for a more etaile iscussion on the social costs of ba patents see Merges, 999). Our paper highlights an aitional, largely overlooke, cost of ba patents the negative externality impose by ba patents on all patent holers. We argue that ba patents unermine the goals of the patent system because they reuce the value of holing patents. Thir parties (competitors, investors, etc.) are likely less informe than the inventor about the probability of valiity of a speci c issue patent, but they have an overall perception of patent quality. How thir parties perceive the quality of patents may a ect a patentee s ability to eter entry, negotiate licensing fees, bargain, or secure venture capital funing. For example, if patent quality is perceive to be low, a potential entrant might be less worrie about infringement an an investor might be less impresse by the fact that a start-up company hols a patent. We think of the perceive quality of a patent (or its reputation) as the probability that an issue patent is goo (or truly vali). If a patent system allows many ba patents, the perceive quality of patents eclines lowering the value of holing patents an thus limiting the ability of the patent system to rewar true inventors. Our paper stuies the eterminants of patent quality. Patent quality is en- 2

3 ogenously etermine in equilibrium together with inventors ecisions whether to apply for a patent. In our moel, every inventor has private information on the ex-ante (before examination) probability of valiity of his own invention. A patent gives its owner a larger bene t if others believe that patents are of high quality. Quality epens on all inventors ecisions to apply for patents as well as on the examination process. For any given perceive patent quality, we n that inventors will apply for patents if the probability of valiity of their patent applications excee a certain threshol. An increase in patent quality lowers the threshol. However, a lower threshol implies lower quality because the pool of applicants becomes inferior. Hence, the quality of patents an the ecision to apply for patents are jointly etermine in equilibrium. We stuy the e ects of patent system reforms on the volume of patent applications an on the quality of patents. Particularly, we examine how changes in patenting fees an in the intensity of examination a ect equilibrium outcomes. We n that an increase in patenting fee reuces the number of patent applications that have a low ex-ante probability of valiity. It also increases the quality of patents (that is, the probability that grante patents are goo) an thus, their value. Interestingly, making the examination process more stringent coul have ambiguous e ects on the volume of patent applications. On one han, stringent examination reuces the probability of any applicant to receive a patent, which eters low probability of valiity applicants. On the other han, the increase in expecte patent quality makes holing a patent more valuable an thus more attractive. Concerns about the abunance of ba patents prompte several proposals for patent system reforms such as establishing a patent opposition system (Merges, 999), patent bounties (Thomas, 200), gol-plate patents (Lemley, Lichtman an Sampat, 2005; Lemley an Lichtman, 2007), an community patent review (Noveck, 2006). Our paper provies insights on the potential e ects of such policies. Particularly, we focus on an analysis of the Lemley et. al. (2005) proposal to establish a two-tiere patent system which, accoring to the authors, woul 3

4 ramatically improve the quality of economically signi cant patents. In such system, applicants woul be allowe to gol-plate their patents by paying a higher fee an being subject to a more thorough review process. This proposal has also attracte the attention of the new aministration: [w]ith better informational resources, the Patent an Traemark O ce coul o er patent applicants, who know they have signi cant inventions, the option of a rigorous an public peerreview that woul prouce a gol-plate patent much less vulnerable to court challenge. Where ubious patents are being asserte, the PTO coul conuct low-cost, timely aministrative proceeings to etermine patent valiity. Our paper formally moels a two-tiere patent system an examines its outcomes compare to the stanar (single-tiere) system. We show that introucing a two-tiere system, in which the lower tier is the same as the original patent system but a secon more stringently examine patent tier is also o ere, results in a ecline in the volume of patent applications, with low quality applicants less likely to apply. The volume of ba patents issue woul ecline for two reasons, the more stringent examination in the secon tier, an the reuce number of low ex-ante probability of valiity applicants. Sorting of applicants between regular an gol-plate patents epens on the inventor s ex-ante probability of valiity. Inventors of higher ex-ante probability of valiity are more likely to gol-plate their patents. The sorting of inventors between the two tiers coul aitionally epen on the economic value of the invention. We examine, in the context of our moel, the hypothesis raise by Lemley et. al. (2005) that economically signi cant patents will sort into the gol-plate tier. Finally, we stuy the e ect of changes in patent policies on the overall volume of patent applications an on gol-plate patents. This paper relates to a large boy of literature on innovation an patent policy. An excellent review of many of these contributions can be foun in Scotchmer (2006). More speci cally, our paper contributes to a egling boy of litera- See Barack Obama on Technology an Innovation at 4

5 ture which recognizes imperfections in the functioning of the patent examination process. Among such theoretical contributions is the article by Caillau an Duchêne (2007). They examine the impact of the patent o ce on rms incentives to innovate an to apply for patent protection, an the overloa problem patent examiners face. They show that given imperfections in the examination process, some granting of ba patents are inevitable. They also consier the role of patent fees as a policy instrument an examine their e ects on R&D investment an on incentives to apply for patents. Langinier an Marcoul (2008) concentrate on incentives to search an isclose prior art given an imperfect examination process. Atal an Bar (200) focus on inventors timing an intensity of prior art search. Our current paper procees as follows. In Section 2, we escribe the moel. In Section 3, we focus on the analysis of the stanar single-tiere patent system. In Section 4, we analyze the two-tiere patent system. Section 5 conclues. 2 The Moel There exists a large heterogeneous population of inventors. Each inventor has one invention which is characterize by a parameter 2 [0; ] that represents the exante (before patent application) probability that the invention is goo. That is, is the probability that there oes not exist prior art that invaliates this invention. 2 Inventors types are inepenently rawn from a istribution escribe by the cumulative istribution function F () on [0; ] ; an positive ensity f () > 0: An inventor can choose whether or not to apply for a patent. Patent application fee is given by P: Any application is examine in the patent o ce to etermine if it is patentable. For simplicity, we assume patentability only epens on whether or not invaliating prior art is foun in the examination process. The examiner searches for prior art exerting search e ort such that, if there exists invaliating prior art, it woul be foun with a probability p: If no invaliating prior art is 2 Patent applications often inclue several claims. Valiity is etermine claim by claim. We simplify here by assuming the patent is either vali all its claims are vali or it is not. 5

6 foun, a patent is grante. Hence, a goo innovation is always grante a patent an a ba invention is grante a patent with probability ( p). By making the assumption that invaliating prior art is foun with a known probability p, we implicitly assume that the patent o ce is committe to (in expectation) this examination intensity. The patent o ce is a government agency an it interacts with inventors repeately. Thus it is likely to be able to create a reputation on examination proceures. The buget of the patent o ce, the number of its employees an the time allocate to patent examination (at least on average) can be mae public. Accoring to Cockburn et al., examiners are allocate xe amounts of time for completing the initial examination of the application, an for isposal of the application. Iniviual examiners are heterogenous an may use i erent examination technologies, but a patent examiner is assigne to each application, not chosen by the inventor. Cockburn et al. also ocument that USPTO operates various internal systems to ensure quality control through auiting, reviewing an checking examiner s work. Aitionally, for the rst several years of their career, examiners are routinely reviewe by a more senior primary examiner. It seems reasonable that by an large the patent o ce can make sure its employees follow the guiance provie to them for examination proceure an intensity. We assume that the value of a patent to an inventor epens on the quality it is perceive to have by less informe thir parties. Our moel captures such epenence in a simple stylize way. Let q be the probability that an innovation is goo (i.e., there exists no invaliating prior art) conitional on it having been grante a patent: q Pr [goo patent j patent was grante] : We will refer to this probability as the perceive patent quality, or simply as patent quality. An inventor oes not know if he will be grante a patent an if the patent is goo, but he forms an expectation taking into account the ex-ante probability of valiity an the examination process. Bene ts from goo or ba patents 6

7 epen on perceive patent quality q: An inventor s expecte payo from a patent application is given by V (; q) G (q) ( )( p)b (q) P () where G(q) an B(q) enote the bene t from a patent as a function of perceive quality q conitional on the innovation being goo or ba respectively. We assume G(q) B(q) 0 for all q. The assumption that the bene ts from patents are lower if the patent is ba coul capture the probability that a patent woul fail to be efene in the case of a ispute. We also assume that the functions B an G are i erentiable an that the value of a ba patent is more sensitive to the perceive quality of patents, B 0 (q) > G 0 (q) 0: If perceive quality is low, thir parties may be more likely to infringe the patent, which woul be more etrimental to the holer of a ba patent. For a patent quality q ; we assume B() G(); that is, if perceive patent quality is perfect, the values of a goo an a ba patent are the same. Finally, for simplicity, the value to the inventor from an invention which is not protecte by a patent is normalize to be zero. 3 The Single-Tiere Patent System In this section, we examine the single-tiere patent system the stanar patent system in which inventors face the ecision to apply for a patent protection or not to apply, but have no choice regaring the intensity of the examination process. 3. Equilibrium The ecision to apply for a patent epens on the inventor s expecte bene t. The inventor applies for a patent if this expecte bene t excees that of not applying, V (; q) 0: Using (), we n that for any quality q; there exists a cut-o probability (q) e ne by 8 if P > G(q) >< P ( p)b(q) (q) G(q) ( p)b(q) if G(q) P ( p)b (q) >: 0 if P < ( p)b (q) 7

8 so that inventors with ex-ante probability of valiity apply for the patent an those with < o not apply. If P > G(q); then patents are too costly an no one applies for a patent. If P < ( p)b (q) ; then patenting fee is low enough an the expecte bene t of holing even a ba patent is high enough so that everyone applies for a patent. In the interior range, the threshol (q) ecreases with q; that is, the higher the perceive patent quality is, the more inventors apply for patents. Particularly, more low ex-ante probability of valiity applicants woul n it worthwhile to apply. Taking into account a threshol ex-ante probability of valiity above which inventors apply for a patent, the probability that a grante patent is goo is given by q ( ) Pr(goo j grante) Pr(goo an grante) Pr(grante) R R h p e f e e e i f : e e This is the belief that an uninforme person has on the probability that a patent is goo. The possible values of q are in the range [E(); ] : The lowest value q E() is obtaine if all inventors apply for a patent an examiners never n invaliating prior art (p 0); an the highest value q is obtaine if the examination is perfect (p ). Note here that when p < ; the perceive quality of patents increases with the threshol. A higher threshol implies an overall better pool of applicants an thus a higher probability that a grante patent is goo. We now e ne an equilibrium in our moel. De nition (Patenting Equilibrium) A patenting equilibrium is characterize by a pair f ; q g; such that (q ) an q q ( ): (2) Inventors of type apply for a patent an inventors of type < o not apply for a patent. The equilibrium is interior when 2 (0; ): 8

9 Our rst result establishes existence of an equilibrium an erives conitions for an interior equilibrium where some but no all inventors apply for patents. We also show that given our assumptions, when an interior equilibrium exists, it is unique. Proposition If P > G(); then in equilibrium no one applies for a patent ( ). If P < ( p) B (q (0)) ; then in equilibrium all inventors apply for a patent ( 0). For intermeiate levels of the patenting fee, there exists a unique interior equilibrium f ; q g. Detaile proofs are provie in the appenix. To prove this proposition, we show that the equilibrium is e ne as an intersection between two functions (q) which is ecreasing in q (because with a higher perceive quality more inventors apply) an q () which is increasing in (because quality increases when fewer low probability of valiity applicants apply.) When these two functions intersect, there is a unique interior equilibrium. Figure illustrates the equilibrium, it epicts the ownwar sloping (q); the upwar sloping q () an their intersection which e nes the equilibrium. 3.2 Policy 3.2. Simple interventions The equilibrium pair f ; q g epens on the patent policy parameters p (examination intensity) an P (patenting fee). Equilibrium also epens on the bene t functions G(:) an B(:). These functions re ect the economic value of the innovation, an can be a ecte by patent policies that strengthen patent protection (such as increase patent breath an longer patent term). 3 In our secon proposition, we examine the relationship between policy levers an equilibrium outcomes. We 3 Patent breath an patent length are extensively iscusse in the literature on patents; see, for example, Gilbert an Shapiro (990), Klemperer (990), O Donoghue (998), O Donoghue, Scotchmer an Thisse(998). 9

10 examine how changes in these! policies a ect which etermines the volume of R patent applications f() an the quality of patents q. Proposition 2 In the range of an interior equilibrium, (i) the equilibrium volume of patent applications ecreases with patenting fee (P ) an the quality of patents increases with patenting fee; (ii) patent quality increases with the examination intensity (p) but the e ect of examination intensity on the equilibrium volume of patent applications is ambiguous; (iii) a policy that strengthens patent protection to increase G(:) an B(:) woul result in lower patent quality an more patent applications. The e ect of an increase in patenting fee is intuitive. A higher patenting fee makes patent applications less attractive. Therefore, fewer low ex-ante probability of valiity inventors apply for the patent an thus the quality of patents increases. The increase in patent quality makes applying for a patent more attractive, but not enough to reverse the ecline in applications ue to the increase in fee. Figure 2 illustrates two equilibrium points E (p; P ) an E 2 (p; P 2 ) which correspon to two systems with the same examination intensity p but i erent levels of patent fee P < P 2. A higher patent fee results in a shift of the curve (q ) to the right, but no change in the curve q ( ). The intersection E 2 has less applications (higher ) an higher patent quality q. The e ect of an increase in examination intensity is more complex. Figure 3 illustrates equilibria for two i erent examination intensities E (p ; P ) an E 2 (p 2 ; P ) with p < p 2. A higher examination intensity results in a shift of the curve (q ) rightwar, but also a shift up of the curve q ( ) to the right. The equilibrium E 2 (p 2 ; P ) has a higher patent quality q ; but the e ect on patent applications is ambiguous. On one han, tougher examination reuces the probability of any applicant to secure a patent, making a patent application less attractive, particularly to low probability of valiity inventors; on the other han, one can expect an increase in the perceive quality of patents ue to the tougher examination process making patent applications more attractive (when inventors 0

11 care about the perceive quality of a patent). The overall e ect on the volume of patent applications is ambiguous. If the bene ts from a patent were not sensitive to perceive patent quality, then the increase in examination intensity woul only reuce the probability of securing a patent an hence the volume of applications woul ecline. However, when the bene t from a patent is sensitive enough to perceive patent quality, then the volume of applications might increase with examination intensity. The perceive quality of patents must increase, whether or not the volume of application ecreases. If perceive quality were to ecrease, there woul necessarily be a ecline in patent applications which in turn woul imply higher quality. Changes in the bene t functions G(q) an B(q) change the function (q) but o not have an e ect on q (): A strengthening of patent protection, for example by increasing patent length or breath, increases the conitional bene t functions G(q) an B(q): As a result, more inventors apply an the quality of patents eclines. In contrast, a post grant opposition system as propose by Merges (999), or a weakening of the presumption of valiity are likely to lower B(q): 4 This will shift (q) up resulting in an equilibrium with less patent applications an a higher patent quality. However, accounting for more invaliation of ba patents post patent granting suggests an aitional e ect which is similar to that of increase examination intensity. In this case, the combine e ect woul be an increase in patent quality, but an ambiguous e ect on the volume of applications. Noveck (2006) avocates a Community Patent Review system. In this proposal, for each patent application, there woul be a winow of time uring which patent examination is open to the public. Facilitating the aition of prior art by the public pre-granting of the patent can be seen as an increase in the probability that invaliating prior art woul be etecte when it exists, that is, an increase in p: Hence, this reform is expecte to result in an increase in patent quality, but 4 In the USA, patents are presume vali. This implies that the buren of establishing invaliity of a patent rests on the party asserting invaliity. We iscuss this issue futher in Section 4.4.

12 an ambiguous e ect on the volume of patent applications. 5 Caillau an Duchêne (2007) propose a policy in which the patent o ce woul penalize rejecte applicants to inuce more investment in R&D which is assume to increase the probability that the innovation quality is high. Thomas (200) proposal combines a pre-examination perio in which informants might submit pertinent prior art, with a bounty to any party who succees in proviing invaliating prior art. The bounty woul be nance by charging a ne to the applicant, thus, in Thomas proposal, a penalty for a ba patent is combine with an increase in the probability of ning invaliating prior art p. In the context of our moel, a penalty for a ba patent P B woul appear in the applicant s payo function as V (; q) G (q) ( )( p)b (q) ( )pp B P: The penalty for a ba patent results in an e ect that is similar to that of an increase in patenting fee P. Increasing the penalty will result in less patent applications an higher patent quality. However, a one ollar increase in patenting fee woul result in a larger reuction in patent applications an in the volume of ba patents than the same increase in penalty. The reason is that the patent applicants in our moel o not know for sure if they have a goo or a ba application. The ex-ante probability of valiity is ; an so, for any applicant, an increase of one ollar in patenting fee results in an increase of one ollar in the cost of patenting, but an increase of one ollar in the penalty for a rejecte application only results in an expecte cost increase of ( )p: We note however that our moel oes not account for the e ect fees might have on the incentive for R&D an hence it oes not fully capture the potential bene ts from penalties. In Section 4, we will more closely examine one more policy reform, the Lemley, Lichtman an Sampat s (2005) proposal of a two-tiere patent system. Before 5 Allowing public review also requires that the patent application be mae public. In the current US system, applications are typically publishe 8 month after the e ective ling ate. If in implementing this reform this perio is shortene, there woul be an aitional ambiguous e ect on the value of patent applications which we have not accounte for. 2

13 oing so, we consier welfare an the optimal examination intensity an patenting fee in the single-tier patent system. 3.3 Welfare Suppose that in terms of social welfare, the value of a goo patent is at least as large as its private value, G(q) e G(q); but the social value of a ba patent is lower than its private value, B(q) e B(q). This epicts the iea that private inventors cannot capture the full bene ts of their innovation, nor o they take into account the social costs of ba patents. Social welfare in the single-tiere system is W Z h G e (q ) ( )( p) B e i (q ) c(p) f() where c (p) is the social cost of patent examination such that the probability of ning an invaliating prior art reference is p if there exists any. Assume, for any ; welfare increases with patent quality. This hols for example when the social bene t functions increase with quality G e0 (:) > 0; B e0 (:) > 0, or when the weaker su cient conition Z 0 h G e0 (q ) ( )( p) B e i 0 (q ) f() > 0 (3) hols. In an optimal policy with P > 0 an > p > 0 that maximize the social welfare, the following conitions hol: W p 0 an W P 0: We focus on the rst orer conition with respect to patenting fee. Di erentiating welfare with respect to P; we n that for any examination intensity p; the corresponing optimal patent fee solves the following rst orer P c(p)f( ) h P G e (q ) ( )( p) B e i (q )) f( ) P : (4) This conition for an optimal policy re ects the balance between marginal costs an marginal bene ts of changes in patent fee. The marginal bene ts of an increase 3

14 in patent fee inclue the increase in social bene ts ue to the increase in patent quality ( rst term on left han sie), as well as the save examination costs on marginal applicants (secon term on left han sie). The marginal cost of the increase in patent fee is the lost surplus from marginal applicants (right han sie). We make two observations base on the conition (4) for optimal patenting fee. Proposition 3 Given an examination intensity p; if patenting fee is chosen optimally, then (i) the net social surplus from the marginal applicant is positive: h G e (q ) ( )( p) B e i (q ) c(p) > 0; (ii) if the private expecte bene t of the marginal applicant excees the social bene t of his application, i.e., if G (q ) ( )( p)b (q ) e G (q ) ( )( p) e B (q ) ; (5) then the optimal patenting fee is larger than the cost of examination, P > c(p): The marginal applicant,, is the applicant who, in equilibrium, is ini erent between applying for a patent or not applying for a patent. The rst claim in the proposition follows immeiately from (4). It implies that from a social perspective, patent fee shoul be set high enough so that some socially bene cial patents are not applie for. Forgoing the social surplus from these patents increases patent quality an the welfare generate by the patent system. The secon claim in the proposition implies that (uner conition (5)) patent fee nees to be set high enough so that it more than o sets the cost of examination. The conition (5) is more likely to hol when ba patents are costly for the society an the volume of patent applications is high (low ). The conition hols, for example, if private an social bene ts of a goo project are the same, G(q) e G(q); but ba projects have a lower social value, B(q) e B(q). Examining the rst orer conitions, as we i above, help unerstan some of the forces involve in setting an optimal policy, however, as a practical matter, 4

15 patent policy is not likely to be set to its optimal levels. Lack of information an resource constraints may be among the reasons why an optimal policy is not feasible. Moreover, in practice, patent policy is often by an large uniform, it is practically har to tailor it to its optimal level by sector or by other criteria. 4 Two-Tiere Patent System In an article title What to Do about Ba Patents? Lemley et. al. (2005) propose to establish a two-tiere patent system. The proposal was further iscusse in Lemley an Lichtman (2007). Their rationale is that the two-tiere system will allow the patent o ce to focus its examination resources on important patents an pay little attention to the rest. The two-tiere patent system woul give applicants a choice between a low cost patent application which is not examine thoroughly, an a high cost patent application which woul be subject to a thorough examination an earn a presumption of valiity. They suggeste that inventors woul likely pay for serious review of their inventions which are economically most important. This self selection mechanism woul allow the patent o ce to focus resources on most important patents (those whose inventors choose to apply for the upper tier). In this section, we exten our basic moel to analyze a two-tiere patent system. We examine inventors equilibrium selection of a patent tier an how it is a ecte by the patent policy parameters. 4. Extening the Moel We maintain most of our assumptions from the previous section, but now we introuce the two-tiere patent system. Inventors can choose to apply for a regular patent, or for a gol-plate patent. A gol-plate patent is associate with a higher fee P gp > P r an a more thorough examining proceure p gp > p r. We assume that p gp is su ciently high (or B only moerately steeper than G) so that G 0 (q) ( p gp )B 0 (q) > 0: (6) 5

16 This conition will help us establish the existence of equilibrium in the two-tiere system. The conition clearly hols when p gp : Which patent was grante is public information. The value of a patent to an inventor epens on both its ex-ante probability of valiity an on the perceive quality of patents of its tier (q r for a regular patent or q gp for a gol-plate patent). Perceive patent quality epens on the patent tier for two reasons: the i erent examination intensities an the i erent enogenously etermine selection of patent applicants. Given patent policy parameters an choices by all other inventors, an inventor whose ex-ante probability of valiity is an who applies for a patent-tier i 2 fr; gpg ; obtains a value: V i (; q i ) G (q i ) ( )( p i )B (q i ) P i : (7) An inventor woul le for a regular patent if the value of a regular patent is greater than zero (value of not patenting), V r (; q r ) 0 an also greater than the value of a gol-plate patent, V r (; q r ) V gp (; q gp ): Let us enote the set of inventors who apply for a regular patent by r an the set of inventors who le for a gol-plate patent by gp. The probability that a patent of type i 2 fr; gpg is goo is then given by R f() q i Pr(goo j patent-tier i grante) i R [ p i ( )] f() : (8) i Uner the assumption of rational expectations, the probability q i is the belief others hol about the quality of a patent-tier i: As before, we refer to q i as perceive patent quality, or simply patent quality. We now e ne an equilibrium in our moel. For simplicity (an without loss of generality), we assume that when ini erent between patenting or not patenting, inventors choose to patent an when ini erent between a regular patent an a gol-plate patent, inventors apply for the regular patent. De nition 2 A two-tiere patent system equilibrium is given by two isjoint sets of inventors r an gp in [0,] an patent qualities q r an q gp such that: 6

17 . for all 2 r ; V r (; q r ) 0 an V r (; q r ) V gp (; q gp ); 2. for all 2 gp ; V gp (; q gp ) 0 an V gp (; q gp ) > V r (; q r ); 3. q r an q gp satisfy equation (8). The rst two conitions imply that inventors choose optimally between applying for a regular patent, a gol-plate patent or no patent; the thir conition states that expectations about patent quality are rational given all inventors choices an the existing patent policy. We n that in any equilibrium the sets r an gp can be e ne using threshols so that high types apply for gol-plate patents, an intermeiate types apply for a regular patent. De nition 3 (i) A threshols equilibrium is a two-tiere patent system equilibrium such that there exist 0 so that in equilibrium inventors with types > apply for a gol plate patent, inventors with types in the range ( ; ) apply for a regular patent an inventors with types < o not apply for a patent. (ii) A threshols equilibrium is interior if 0 < < <. In an interior threshols equilibrium, at least some inventors apply for each patent tier, an some o not apply for a patent. The next proposition states initial results about equilibria in the two-tiere system. Proposition 4 An equilibrium for the two-tiere system exists. Any interior equilibrium is a threshols equilibrium. Moreover, in the interior equilibrium, the probability that a patent is goo is higher for gol-plate patents, q gp > q r : In the interior equilibrium, the inventor with ex-ante probability of valiity is ini erent between applying for a regular patent an not applying for the patent at all. Hence, if q r is the equilibrium perceive quality of regular patents, then V r ( ; q r ) 0: An inventor with ex-ante probability of valiity is ini erent between applying for a regular patent an applying for a gol-plate patent. 7

18 Hence, V gp ( ; q gp ) V r ( ; q r ). Payo s V r (:) an V gp (:) are e ne in (7). By the e nition of interior equilibrium an by Proposition 4, to n an interior equilibrium, we nee to n,, q r an q gp such that the following system is satis e: 8 >< >: Pr ( pr)b(qr) G(q r) ( p r)b(q r) ; (Pgp Pr) [( pgp)b(qgp) ( pr)b(qr)] [G(q gp) G(q r)] [( p gp)b(q gp) ( p ; r)b(q r)] R f() q r ; R [ p r( )]f() R f() q gp : R [ p gp( )]f() The rst equation states the ini erence of an applicant with an ex-ante probability of valiity between applying for a regular patent or not applying; the secon states the ini erence of an applicant with an ex-ante probability of valiity between applying for a regular patent or for a gol-plate one; the last two equations e ne perceive patent qualities for regular an gol-plate patents base on the equilibrium choices of inventors. 9 > >; (9) 4.2 Consequences of Gol-plating Patents In this section, we consier the e ect of introucing gol-plate patents to a stanar single-tiere patent system. We compare a two-tiere system with a benchmark single-tiere system in which the patenting fee an the examination intensity are the same as those in the regular patent-tier. But in the two-tiere system, the inventors have an aitional choice: they can gol-plate their patents which provies a more thorough examination process at a higher fee. Suppose that in the single-tiere patent system, in equilibrium, inventors with ex-ante probability of valiity apply for the patent, an average patent quality is given by q : Suppose now that the patent o ce aopts the new twotiere system. Let us consier the e ect of the availability of the secon patent-tier 8

19 on the volume of patent applications an on the quality of patents. We assume (the more interesting case) that the new system woul result in an interior equilibrium, where both patent-tiers are applie for. As escribe earlier, an enote the cut-o ex-ante probabilities of valiity for regular patent applications an for golplate patent applications, respectively (see (9)). The next proposition escribes the e ects of introucing a two-tiere system. Proposition 5 Consier a single-tiere system with examination intensity p an a patent fee P an consier a two-tiere system where regular patents have the same fee an examination intensity as the single-tiere system (P r P an p r p). Assume each system has an interior equilibrium. Then, (i) in the two-tiere system, the volume of patent applications is lower than in the single-tiere system ( > ); (ii) the perceive quality of a regular patent is lower than that of a patent in the single-tiere system (q r q ); (iii) the perceive quality of a golplate patent is higher (q gp q ); (iv) overall, there are less ba patents in the two-tiere system. Proposition 5 establishes that the aition of the secon patent-tier results in a ecline in the overall volume of patent applications (with less low quality patents being applie for). The reason for this ecline is that when the secon patent-tier option exists, the highest quality applicants choose to gol-plate their patents, leaving an averse selection of applicants for the regular patent-tier. Hence, regular patents woul be of lower quality than a patent in the single-tiere system, an therefore less attractive. But gol-plate patents woul be of higher quality. The overall quality of patents woul increase as a result of this policy change. The latter e ect results from the ecline in low quality patent applications as well as the more thorough examination of gol-plate patents. A two-tiere system involves more intense examination. This potentially increases the patent o ce s expeniture. Because the patent o ce is self-fune, the cost may nee to be o set with higher fees. If the gol-plate patent fee is set high enough to cover the higher examination costs, the expeniture of the patent o ce 9

20 woul not increase. For a very stringent gol-plate patent examination process, this cost may be prohibitively high so that no interior equilibrium exists. However, (uner a technical conition) we show that if the single-tiere system has an interior equilibrium an imperfect examination (p < ), then there is a two-tiere patent system with an interior equilibrium in which the expeniture of the patent o ce oes not excee that of the single-tiere system. Proposition 6 Consier a single-tiere system with examination intensity p an a patent fee P that has an interior equilibrium f ; q g : Assume the Jacobian matrix of the system of equations (9) has a positive eterminant 6 at the point ( ; ; q r q ; q gp ): Then there exist p gp > p an P gp > P such that the two-tiere system, where P r P an p r p, has an interior equilibrium in which the expeniture of the patent o ce oes not excee that of the single-tiere system. Intuitively, to assure that the expeniture of the patent o ce oes not excee that in the single-tiere system, we coul set gol-plate patent fee to cover the aitional cost of examination: P gp P r [c (p gp ) c (p r )] : A su ciently small increase in examination intensity p gp in the secon tier woul allow a small enough gol-plate patent fee so that there is an interior equilibrium in the two-tiere system. 4.3 Patent Policy an Its E ect on the Two-Tiere System In this section, we consier the e ect of changes in patent policy on the two-tiere patent system, particularly, the e ect of changes in patenting fees an the intensity of examination on the volume of patent applications, on the choice between regular an gol-plate patents an on patent quality. Accoring to the propose 6 The Jacobian matrix is the matrix of rst erivatives of the system of equilibrium equations. A positive Jacobian guarantees that the solution to the system of equilibrium equations exists an is locally unique. In Proposition 7, we emonstrate that the conition hols, for example, in the linear moel we analyze. 20

21 policy reform, gol-plate patents are intene to be thoroughly examine. To simplify the analysis while capturing this iea, we will consier the extreme case in which examination of gol-plate patents is perfect, p gp : With such stringent examination, the perceive quality of gol-plate patents is maximize, q gp, because any ba application for a gol-plate patent is rejecte. The system of equilibrium equations (9) is then reuce to q r P r ( p r )B (q r ) G (q r ) ( p r )B (q r ) ; (0) (P gp P r ) ( p r )B (q r ) [G() G (q r )] ( p r )B (q r ) ; () R R f() [ p r ( )] f() : (2) There exists an interior equilibrium when there is a solution to the system of equilibrium equalities with ( ; ; q r ) 2 (0; ) 3. Interior equilibria exist for some functional forms (of G; B an F ); an parameter values (P gp ; P r ; p r ) ; but not always. From conition (), it is easy to see that a necessary conition for the existence of an interior equilibrium is that G () G (0) > (P gp P r ) : (3) That is, the increase in bene t from applying for a goo plate patent must surpass the aitional cost for gol plating the patent. If this conition fails, then no inventor applies for a gol-plate patent. If inventors payo s are inepenent of perceive quality, then G () G (0) an the two-tiere system fails. We now investigate how patenting fees P gp an P r an the examination intensity for regular patents p r a ect the (interior) equilibrium outcomes in the two-tiere patent system. To simplify erivations, from now on, restrict to a linear version of the moel which is e ne as follows. De nition 4 (Linear moel) In the linear moel, the istribution of inventors types is uniform: F () ; the bene t-functions are linear: G (q) (G G 0 q) 2

22 an B (q) (B B 0 q) ; with parameters that satisfy (G G 0 ) (B B 0 ) an 2G 0 B 0 > G 0 > 0 (i.e., the bene t from a goo patent is at least as high as that from a ba patent, these bene ts are equal at q, an B(q) is moerately steeper than G(q).). Consier rst the e ect of an increase in the fee for a gol-plate patent. With a rise in cost of applying for a gol-plate patent, we can expect some applicants to apply for a regular patent instea of a gol-plate patent. This woul result in a ecline of gol-plate patent applications ( increases). Applicants who switch from gol-plate patents to regular patents are of higher ex-ante probability of valiity than those who applie for regular patents when the fee is lower. Therefore the perceive quality of regular patents (q r ) increases. If bene ts from patent applications i not epen on the perceive quality, there woul be no reason for the overall volume of patent applications to change. However, because bene- ts increase with perceive quality, with higher gol-plate patent fee there is an increase in perceive quality of regular patents which results in an increase in regular patent applications also from marginally low quality applicants (a ecline in ): Hence, overall there is an increase in the number of patent applications. Because there is a ecline in (stringently examine) gol-plate patents an rise in low-quality applications, the number of ba patents grante increases. However, the quality of regular patents increases espite the possible increase in number of applications. An increase in the fee for a regular patent woul make regular patents less attractive for some high ex-ante probability of valiity inventors who woul now prefer a gol-plate patent instea, as well as from some low ex-ante probability of valiity inventors who woul now prefer not to apply for a patent at all. Therefore, the prevalence of ba patents woul ecline both ue to the ecrease in applications by some low ex-ante probability of valiity inventors an because of the increase in applications for the more stringently examine gol-plate patents. The perceive quality of a regular patent increases. The e ect of an increase in patent examination intensity is more complex. On 22

23 one han, the increase in examination e ort reuces the probability that a patent is grante which lowers the value of applying for regular patents. On the other han, because patentees bene t from a higher perceive value, if the quality of patents increases with examination intensity, it woul have a positive e ect on the value of applying for regular patents. In our analysis, the rst e ect (which makes regular patents less attractive) ominates for low ex-ante probability of valiity inventors, thus there will be a ecline in overall applications for patents. However, an increase in examination intensity or regular patents has an ambiguous e ect on the volume of gol-plate patent applications. The e ect of an increase in examination intensity on the prevalence of ba patents is negative an the e ect on the perceive quality of a regular patent is positive. We summarize these nings in the following proposition. Proposition 7 In the linear moel, if regular patent examination intensity is not too high (p r 2 ), an gol-plate patents are perfectly examine (p gp ) ; then in an interior equilibrium, (i) the overall volume of patent applications increases ( eclines) with golplate patenting fees (P gp ), it ecreases with regular patents fees (P r ) an with the intensity of the examination process (p r ); (ii) the volume of gol-plate patent applications increases ( eclines) with the fees of regular patents; it ecreases with gol-plate patenting fees. The e ect of the intensity of examination of regular patents is ambiguous; (iii) the quality of regular patents (q r ) increases with gol-plate patenting fees, with regular patents fees an with its examination intensity; (iv) the prevalence of ba patents increases with gol-plate patenting fees an ecreases with regular patents fees an with their examination intensity. 4.4 Presumption of Valiity The patent system is a part of the executive branch of the government. Its ecisions are subject to review by courts. Patent law states however that a patent 23

24 shall be presume vali an that the buren of establishing invaliity of a patent or any claim thereof shall rest on the party asserting such invaliity (35 USC 282). Lemley an Lichtman (2007), in their examination of the two-tiere patent system proposal iscuss at length the issue of presumption of valiity. They suggest that in the two-tiere system, gol-plate patent holers shoul enjoy a presumption of valiity as their patents were thoroughly examine, but patents in the other tier shoul not be presume vali. They explain further that [w]e know far less than we shoul about how presumptions a ect litigation ecisions.... it is far from a simple matter to preict how changes in a legal presumption woul change actual case outcomes. Our moel of the two-tiere patent system therefore focuse on the main characteristics of the two-tiere system more thorough examination an higher fees for gol-plate patents, but i not explicitly aress the issue of presumption of valiity. To some extent, presumption of valiity may be capture in our moel by the fact that we took into account perceive patent quality an its positive e ect on the value of patents. Bene t functions were assume to have the same functional forms G(q) an B(q); but gol-plate patents have a higher perceive quality (q gp > q r ) which we can think of as also capturing a presumption of valiity. Another way to think about moeling more explicitly a legal change in presumption of valiity is to assume i erent bene t functions in the two tiers G i (q) an B i (q) for i 2 fr; gpg ; with higher bene ts in the case of gol-plate patents because of the stronger presumption of valiity. In our system of equilibrium inequalities, the change woul be re ecte in the equation e ning the threshol between types who apply for the regular an the gol-plate patents. For simplicity of the notation an analysis, we chose not to incorporate this in the moel. We conjecture that reucing presumption of valiity for regular patents an increasing it for gol-plate patents, to the extent that this is escribe by tier-speci c values for holing a patent, woul make gol-plate patents at least marginally more attractive an regular patents less attractive. As long as the i erence in bene ts is not large, we o not expect selection patterns into the two tiers to change. 24

25 4.5 Economic Importance an Gol-Plate Patents Lemley et. al. (2005) state that most likely applicants woul pay for serious review with respect to their most important patents but conserve resources on their most speculative entries. To examine this claim in light of our moel, we rst nee to ask what characterizes the economically most important patents? If one thinks of these as being innovations that are ex-ante most likely to be vali, then our previous analysis establishes the suggeste relation. This hols because we foun that only inventors with a high enough ex-ante probability of valiity apply for a gol-plate patent. However, economic importance is probably better interprete in terms of the economic value of the innovation rather than in terms of the probability of it being goo. In our moel, the values of a patent conitional on it being goo or ba are given by the functions G(q) an B(q). We have assume that these two functions are increasing in the perceive quality of patents q, that the value of a ba patent is steeper but that at q ; G() B(): What woul istinguish the values associate with an economically important patent from a less important one? It seems reasonable to assume that the value of the patent conitional on it being goo woul be higher for an economically more signi cant patent. Denoting two innovations an 2, the rst being more signi cant, we expect G (q) > G 2 (q): It also seems reasonable that for economically signi cant innovations, the value of at least a ba patent is more sensitive to perceive quality. This is because if the patent is economically signi cant, a competitor woul have more to lose from being exclue an perhaps more to gain from trying to invaliate it. How likely the competitor is to challenge the patent can epen on the perceive value of patents. Hence, our secon assumption is that for economically signi cant patents, B(q) is steeper (B 0 (q) B0 2 (q)), an possibly also G(q) (or, G0 (q) G0 2 (q)). For low perceive patent quality, the value of a ba patent may be lower. But for high perceive patent quality, the value is higher: B () > B 2 (): Figure 4 illustrates this comparison between the values of an economically signi cant patent an an economically insigni cant one. 25

26 Proposition 8 If economic signi cance is characterize by higher bene t functions an steeper value of ba patents, the e ect of economic signi cance on the volume of gol-plate patent applications is ambiguous. We show this ambiguity in the appenix using two numerical examples. In both examples, we assume a linear moel. We vary the egrees of increase in the bene t an the change in slope of the function B(q): The examples establish that applicants with economically more signi cant patents are not necessarily more likely to apply for gol-plate patents than the applicants with economically less signi cant patents Heterogenous Bene t Functions So far, we compute an equilibrium for innovations that are heterogenous in their ex-ante probability of valiity, but have homogeneous bene t functions. This best escribes a situation in which inventors an their competitors can observe innovations economic values, even if the patent o ce oes not. Allowing unobserve (by thir parties) heterogenous bene t functions woul make the analysis signi cantly more complex because each innovator s ecision woul epen on his ex ante probability of valiity as well as on the economic values of his innovation. However, to get a sense of what the potential e ect of economic signi cance might be when applicants have heterogenous bene t functions, we assume there is an equilibrium in a two-tiere system with some equilibrium levels of perceive patent qualities qgp > qr: We consier a simple example in which we capture the heterogeneity of economic signi cance with a parameter : bene t functions are of the form G (q) G (q) an B (q) B (q). Thus, here a more signi cant patent has bene t functions which are a parallel shift up of those of a less signi cant patent. The i erence between an inventor s payo from applying for a gol plate 26