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 March 4, 2013 Abstract We stuy the eterminants of patent quality an the volume of patent applications when inventors care about perceive patent quality. We examine the e ects of various policy reforms, in particular, a proposal to establish a two-tiere patent system. In the two-tiere system, applicants can choose between a regular patent an a more costly an possibly more thoroughly examine gol-plate patent. Introucing a secon patent-tier can reuce patent applications an the incience of ba patents, it sometimes increases welfare. The gol-plate tier attracts inventors with high ex-ante probability of valiity, but not necessarily applicants with innovations of high economic value. Keywors: patent, patent quality, gol-plate patent, two-tiere patent system, innovation, research an evelopment, prior art. JEL classi cation coes: D83, O31, O34 We are grateful to Haim Bar for his help with programming, for his time, helpful comments an support. We are thankful to Kaushik Basu, Phoebe Chan, Mahumita Datta, Corinne Langinier, Aija Leiponen, Tapan Mitra, Weny Zeng an seminar participants at Drexel University, at the 2009 International Inustrial Organization Conference in Boston, an at the 2011 Royal Economic Society Annual Conference in Lonon, for valuable comments. This research was conucte using the resources of the Cornell University Center for Avance Computing. y Department of Economics an Finance, Montclair State University, Montclair, NJ atalvmail.montclair.eu z Department of Economics, 903 Library Tower, Binghamton University, Vestal, NY taliabar97gmail.com 1

2 1 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 existing patents. 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 herself 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. Patent examination only provies an imperfect public signal on the existence of invaliating prior art. If a patent system allows many ba patents, the perceive quality of patents is low an so is the value of holing patents. This limits the ability of the patent system to rewar true inventors. We stuy the eterminants of patent quality the probability that a patente innovation is goo (novel an non-obvious in light of the prior art). The true valiity of an innovation is unknown, but every inventor has private information on the ex-ante (before examination) probability of valiity of her own invention. In equilibrium, there is a threshol probability of valiity above which inventors apply for a patent. This threshol an the perceive patent quality are jointly etermine in equilibrium. An increase in patent quality lowers the threshol, but a lower threshol results in a lower patent quality. Concerns over patent quality an the backlog problem 1 prompte several propos- 1 Accoring to recent USPTO ata, the unexamine patent applications backlog (i.e. patents which are awaiting First O ce Action at any given time) is over 600,000 applications, see (last accesse October 23, 2012). 2

3 als for patent system reforms, for example, a patent opposition system (Merges, 1999), patent bounties (Thomas, 2001), community patent review (Noveck, 2006) an golplate patents (Lemley, Lichtman an Sampat, 2005; Lemley an Lichtman, 2007). Our paper provies insights on the potential e ects of such policies on the volume of patent applications an on the quality of patents. We show that an increase in the patenting fee reuces the number of patent applications that have 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. Making the examination process more stringent has a positive e ect on patent quality, but interestingly, it has an 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. We stuy the proposal to establish a two-tiere patent system. Applicants woul be allowe to gol-plate their patents by paying a higher fee an being subject to a more thorough review process. Accoring to Lemley et al. (2005), this woul ramatically improve the quality of economically signi cant patents. The proposal has also attracte the attention of the current 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 peer-review 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. 2 Our paper formally moels a two-tiere patent system an examines its outcomes compare to the stanar (single-tiere) system. We show that in equilibrium in a twotiere system, innovators with high ex-ante probability of valiity apply for gol-plate patents, intermeiate applicants apply for regular patents (the lower tier) an the lowest probability of valiity innovators o not apply. If economically more signi cant patents 2 See Barack Obama on Technology an Innovation at 3

4 ten to have higher probability of valiity than the less signi cant ones (for example, ue to more intensive prior art search), then their innovators will be more likely to apply for gol-plate patents. However, since the choice of patent tier can also epen on the bene ts from patenting, sorting base on economic signi cance (which is one of the intene consequences of the two-tiere system) is not guarantee. We consier a family of two-tiere systems in which the lower tier has the same examination intensity an fees as the single-tiere system, an the higher tier o ers equally or more intense examination for a higher fee. We call this an ae-tier system. We show that introucing an ae tier will reuce the volume of patent applications an of ba patents. Intuitively, the gol-plate tier attracts the highest probability of valiity applicants, making the quality of regular patents lower than in the single-tiere system. Thus, the equilibrium in this ae-tier system exclues the worst applicants to apply uner the single-tiere system. Gol-plate patents are of better quality than in the single-tiere system (because of better selection of applicants an more thorough examination). In the ae-tier system, there are fewer ba patents. We exten the moel to consier the incentive to invest in R&D. The set of innovators then becomes enogenous, an epens on the incentives that the patent system provies. We e ne a simple welfare function that accounts for the surplus of innovators an consumers. We n that an ae-tier system oes not always o er a welfare improvement over the single-tiere system. Intuitively, reucing the volume of ba patents might come at the cost of ecrease incentive to innovate. Welfare uner an optimal two-tiere system is at least as high as the welfare uner an optimal single-tiere system. We show that when the bene t from having the highest patent quality is su ciently large, the optimal two-tiere system results in strictly higher welfare than the optimal single-tiere system. Intuitively, the two-tiere system ienti es a subset of high quality patents an when these o er su ciently high bene ts, the twotiere system can increase welfare. It allows bene ting from the high quality of gol-plate patents without increasing examination costs. The rest of this paper procees as follows. In Section 2, we iscuss the relate literature. In Section 3, we escribe the moel. In Section 4, we focus on the analysis of the stanar single-tiere patent system. In Section 5, we analyze the two-tiere patent system. Section 6 consiers welfare an incentives to invest in R&D. Section 7 o ers a 4

5 iscussion on economic signi cance of innovations an the incentive to gol-plate patents. Section 8 conclues. 2 Relate Literature This paper relates to a large boy of literature on innovation an patent policy (see Scotchmer, 2006, for a etaile review). Speci cally, our paper contributes to a boy of literature that recognizes imperfections in the functioning of the patent examination process. Farrell an Shapiro (2008) propose a moel of licensing in the shaow of patent litigation. They e ne a patent s strength as the probability that it woul be foun vali an infringe if teste in court, an ientify conitions uner which weak patents impose a greater social cost. Langinier an Marcoul (2009) concentrate on incentives to search an isclose prior art given an imperfect examination process. Caillau an Duchêne (2011) examine the impact of the patent o ce on rms incentives to innovate an to apply for patents, an the overloa problem patent examiners face. They consier the role of the patent fees as a policy instrument. From a theoretical perspective, there is no consensus on the optimal level of the patent application fees. Rassenfosse an van Pottelsberghe e la Potterie (2010) review the economic literature on the role of the patent fees. They present stylize facts on the patent fees of thirty patent o ces worlwie, illustrating high heterogeneity in the level an structure of the patent fees. Accoring to their paper, [p]atent fees are generally applicant frienly an their setting appears to be governe by the imperative to balance buget or to ajust to the level of other patent o ces... an only recently policy-makers have... realize that the patent fees can be use as a policy tool. Base on a survey of R&D labs in the U.S. manufacturing sector, Cohen et al. (2000) report that 36.7 percent of responents inicate application costs as a reason that gure into their ecision not to patent. In our paper, patent tiers i er in the fees an examination intensities. Patent systems may o er tiers that i er along other imensions. A patent renewal system can be unerstoo as a multi-tier patent system in which innovators can choose to pay more for a longer patent life. 3 Crampes an Langinier (1998) suggest that renewals convey 3 We focuse on the application fees. Renewal fees are pai conitional on the patent being grante, 5

6 information an hence an incumbent may prefer not to pay the renewal fee for the patent to signal low market pro tability. Cornelli an Schankerman (1999) show that when rms have i erent R&D prouctivities, patent renewal systems can improve welfare. Scotchmer (1999) suggests a moel with asymmetric information on the costs an bene ts of research. She shows that all implementable ecision rules can be implemente with renewal mechanisms. Versions of tiere systems are alreay in place or being consiere in some countries. Christie an Moritz (2005) escribe Australia s two-tiere system. Patents in the lower tier ( innovation patents ) are require a lower threshol of inventiveness an are not subject to opposition prior to grant. Innovation patents are grante a maximum of eight year term an permit up to ve claims. In Japan, applications are not examine unless there is a request for examination (for a fee) within three years of application. If a request for examination has not been mae within the time limit, the application is eeme withrawn. 4 Yamauchi an Nagaoka (2009) stuy the patent system reform in Japan. Patent o ces in other countries incluing Canaa, China, Germany, Inia, Korea, Romania, Russia an Thailan also o er eferre examination or some form of elaye examination request (see Norman et al. 2010). 5 One can view applications for which innovators i not request examination as belonging to a lower tier. 6 Our paper also relates to a literature on testing an certi cation in the presence of asymmetric information. Our moel has a certi er (the patent o ce) who can etect low quality (a non-patentable innovation) with some probability (etermine by the examination intensity). Accoring to Dranove an Jin (2010) who review the literature on quality isclosure an certi cation, [m]ost of the theoretical work focuses on the incentives for rms to voluntarily isclose quality an for certi ers to provie unbiase certi cation about prouct quality. The role of the patent o ce is not only to reveal information, but to grant legal intellectual property rights. This a ects the incentives of an can be capture in our moel by the bene t functions. 4 Article 48(3) of the Japanese Patent Law. See 5 Examination elays occur also in systems that o not o er eferre examination. In a moel of the US patent system, Regibeau an Rockett (2010) explain the relationship between the importance of inventions an elays in examination. 6 In the eferre system, applicants can switch from the lower tier (that o ers no examination) to the higher tier by requesting examination. They cannot stay in the lower tier for too long. 6

7 innovators to apply for patents an etermines the nature of isclosure of information by the patent o ce. In some moels in the certi cation literature (e.g., Lizzeri, 1999), the certi er perfectly observes quality. In other moels (e.g., Gill an Sgroi, 2008), the certi- er observes a signal of quality, but oes not become perfectly informe that the quality is ba. In our moel, the patent o ce oes not have full information about quality. The test (examination) can ientify ba applications, but unless the examination is perfect, some ba applications remain unetecte. Farhi, Lerner an Tirole (2010) is relevant to ours in its examination of tiere certi cation. In their paper, sellers (analogous to innovators in our moel) want to be rate highly. They start uninforme, but can learn about the quality of their prouct. Their paper investigates the questions of transparency (shoul failure to be certi e be reveale?) an the coarseness of rating. One important i erence is that, in their paper, a seller who faile to be certi e in the higher tier can go own the pecking orer to be certi e by a lower tier (e.g., journal submissions). In contrast, in the context of patents, if invaliating prior art was reveale in the gol-plate patent examination process, the applicant cannot apply for the lower patent tier. 3 The Moel There exists a large heterogeneous population of inventors. Each inventor has one invention which can be goo or ba, but the true state is unknown. The inventor has private information an ex-ante (before ling for a patent) probability that the invention is goo, 2 [0; 1]. That is, is the probability that there oes not exist any invaliating prior art. 7 Inventor types are inepenently rawn, the cumulative istribution function F () is i erentiable, with a positive ensity f () > 0: An inventor can choose whether to apply for a patent. The patent application fee is P: Each application is examine in the patent o ce. For simplicity, we assume that patentability only epens on whether invaliating prior art is foun in the examination process or not. 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 : If no invaliating 7 Patent applications often inclue several claims. Valiity is etermine claim by claim. We simplify here by assuming that the patent is either vali all its claims are vali or it is not. 7

8 prior art is foun, a patent is grante. 8 Hence, a ba innovation is grante a patent with probability (1 ) an a goo innovation is always grante a patent. By making the assumption that invaliating prior art is foun with a known probability, we implicitly assume that the patent o ce is committe to (in expectation) a certain examination intensity. We n this assumption to be reasonable because the patent o ce is a government agency that interacts with inventors repeately (creating a reputation); the information on its buget, the number of employees an the time allocate to patent examination (at least on average) can be mae public. Accoring to Cockburn et al. (2002), the USPTO operates various internal systems to ensure quality control through auiting, reviewing an checking examiner s work. Thus, 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. 9 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. In equilibrium, perceive quality is correct it is the probability that a patente innovation is goo (i.e., there oes not exist any invaliating prior art): q = Pr [goo patent j patent was grante] : The bene t from holing a patent epens on whether it is goo or ba, an on the perceive quality of patents. Let G(q) enote the bene t from a goo patent an B(q) enote the bene t from a ba patent. 10 An inventor oes not know for sure if her invention is goo an if it will be grante a patent. Her expecte payo from a patent application is: V (; q) = G (q) (1 )(1 )B (q) P: (1) 8 This simplifying assumption allows us to focus on the granting of ba (not truly novel) patents. In reality, the patent o ce may reject novel innovations, for example, ue to misunerstaning of prior art that was foun, or for reasons unrelate to the prior art. 9 For moels that account for examiners incentives, see Langinier an Marcoul (2010) an Schuett (2011). 10 We think of these bene ts as capturing the value of holing a patent, this can inclue not only the value from market power in the market for a patente prouct, but also other bene ts that a patent holer might enjoy, such as improve bargaining position, reputation, facilitation in cross-licensing agreements, etc. 8

9 The functions G(q) an B(q) are i erentiable an satisfy the following assumptions: G(q) B(q) 0 an B 0 (q); G 0 (q) > 0 for all q: (2) We assume that the bene t from a ba patent is lower because if a ispute arises, it is less likely to be uphel in court. Bene ts increase with perceive patent quality for several reasons. A higher perceive patent quality makes infringement less likely, an puts the patentee in a better position in negotiations over licensing or infringement isputes. A higher perceive quality also makes the patent more valuable as a signal to the investors an rival rms. Finally, for simplicity, the value to the inventor from an invention which is not protecte by a patent is assume to be zero 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 patent protection or not to apply, but have no choice regaring the intensity of the examination process. 4.1 Equilibrium The inventor applies for a patent if her expecte bene t from applying excees that from not applying, V (; q) 0: Using (1), we n that for any quality q; there exists a cut-o probability 1 (q); e ne by: 8 >< 1 (q) = >: 1 if P > G(q) P (1 )B(q) G(q) (1 )B(q) if G(q) P (1 )B (q) 0 if P < (1 )B (q) ; so that inventors with ex-ante probability of valiity 1 apply for the patent an those with < 1 o not apply. If P > G(q); then patents are too costly an no one applies for a patent. If P < (1 )B (q) ; then the patenting fee is lower than the expecte bene t of 11 If secrecy allows innovators to bene t from non-patente innovations, the value of not patenting can be positive an might epen on the innovator s ex-ante probability of valiity. In this case, the bene t from secrecy woul nee to be subtracte from the current expression V (; q) : Our analysis remains qualitatively the same as long as the resulting net bene t from patenting is still increasing in ; which woul require the bene t from secrecy not to be too steep as a function of : (3) 9

10 applying even if the patent is ba, so everyone applies for a patent. In the interior range, the threshol 1 (q) ecreases with q: That is, the higher the perceive patent quality is, the more inventors apply for patents. Taking into account a threshol ex-ante probability of valiity 1 < 1; above which inventors apply for a patent, the probability that a grante patent is goo is given by: q 1 ( 1 ) = Pr(goo j grante) = Pr(goo an grante) Pr(grante) = 1R f () 1 : (4) 1R [1 (1 )] f () 1 1R Aitionally, q 1 (1) = The lowest value q 1 can obtain is f () ; if all inventors apply for a patent ( 1 = 0) an examiners never n invaliating prior art ( = 0); the highest value it can obtain is q 1 = 1, when examination is perfect ( = 1). If < 1; then q 1 ( 1 ) is increasing in 1 ; because a higher 1 inicates an overall better pool of applicants. Equilibrium in the single-tiere system is e ne as follows. 0 De nition 1 Equilibrium in the single-tiere system is characterize by a pair ( 1; q1) ; such that: 1 = 1 (q1) an q1 = q 1 ( 1); (5) where 1 (:) an q 1 (:) are e ne in (3) an (4). Inventors of type 1 apply for a patent an inventors of type < 1 o not apply for a patent. The equilibrium is interior if 1 2 (0; 1): It is easy to verify that a unique (not necessarily interior) equilibrium exists. This hols true because the equilibrium is an intersection between a ecreasing function 1 (q 1 ) an a strictly increasing function q 1 ( 1 ). 4.2 Simple Policy Interventions The equilibrium pair ( 1; q 1) epens on the examination intensity, on the patenting fee P; an on the bene t functions G(:) an B(:). 13 In our rst proposition, we examine 12 By the l Hospital rule, the limit of (4) as 1! 1 is The bene t functions can be a ecte by increase patent breath an longer patent term. These policies were stuie for example by Gilbert an Shapiro (1990), Klemperer (1990), O Donoghue (1998), O Donoghue, Scotchmer an Thisse (1998). 10

11 how changes in policy-levers a ect the volume of patent applications [1 patent quality q 1. F ( 1)] ; an Proposition 1 Assuming an interior equilibrium, (i) an increase in the patenting fee (P ) results in an increase in patent quality an a ecrease in patent applications; (ii) an increase in the examination intensity () results in an increase in patent quality, but has an ambiguous e ect on the volume of patent applications. Figure 1 illustrates two equilibrium points E 1 (; P 1 ) an E 2 (; P 2 ) which correspon to two systems with the same examination intensity but i erent levels of the patent fee P 1 < P 2. A higher patent fee results in fewer patent applications for every q 1 (i.e., 1 (q 1 ) shifts right), but no change in perceive quality q 1 ( 1 ) for any 1. The equilibrium E 2 has fewer patent applications (higher 1) an higher patent quality q1. 14 No Patent Patent Figure 1: The e ect of an increase in patent fee Figure 2 illustrates two equilibrium points for two i erent examination intensities E 1 ( 1 ; P ) an E 2 ( 2 ; P ) with 1 < 2. A higher examination intensity results in fewer patent applications for a given quality (i.e., 1 (q 1 ) shifts right), but also results in a higher quality for the given pool of applicants (q 1 ( 1 ) shifts up). The equilibrium E 2 ( 2 ; P ) has a higher patent quality than E 1 ( 1 ; P ). In the gure, the volume of applications increases, but this is not always the case. Tougher examination reuces the probability of any 14 A similar argument implies that a strengthening of patent protection (an increase in G(:) an B(:)) results in a lower patent quality an more patent applications. In contrast, a post-grant opposition system (Merges, 1999) or a weakening of the presumption of valiity are likely to lower the bene t functions resulting in an equilibrium with fewer patent applications an a higher patent quality. 11

12 applicant to secure a patent, making a patent application less attractive, particularly to low probability of valiity inventors; but the increase in perceive quality makes patents more valuable. When the bene t from a patent is sensitive enough to perceive patent quality, then the volume of applications coul increase with examination intensity. Thus, a policy reform that woul open patent examination to the public (e.g. Noveck, 2006) is expecte to result in an increase in patent quality, but its e ect on the volume of patent applications is ambiguous. No Patent Patent Figure 2: The e ect of an increase in examination intensity Our analysis throughout the paper assumes that the patent o ce can commit to its examination intensity. It is possible that examiners woul intensify their examination if they face a worse pool of applicants (lower 1 ) as there is a greater nee for examination to maintain quality. Alternatively, examiners might respon to a higher volume of applications with less intensive examination, ue to the increase work-loa. Consier the e ects of an increase in the patent fee. We preicte fewer patent applications an a higher patent quality. If examiners intensify their examination, the e ect woul be to further increase patent quality. However, if examiners relax their examination intensity, this woul moerate the positive e ect that the increase in the fees has on patent quality. As long as the examiners response to a higher volume of applications is small, we expect the preictions of our moel to be relevant. Our moel has heterogeneous probabilities of valiity, but uniform bene t functions. In a moel with two imensions of heterogeneity, quality an value, Koenen (2011) shows that there are conitions uner which an increase in the patent fee may result in a ecrease in average patent quality. In his moel too, an increase in the fee increases the threshol 12

13 for application, so that fewer invali ieas are submitte. However, there is an aitional e ect not present in our analysis. Koenen explains, [a]s the private value of patents ecreases, the quality cuto level for which patents are pro table increases, until at the margin only the best patents survive...raising patent fees therefore generically kills o high-quality patent application over-proportionally. 5 The 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). 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 high presumption of valiity. They suggeste that inventors woul likely pay for serious review of their inventions which are economically most important. Therefore, 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. In this section, we exten our basic moel to analyze a twotiere patent system. We examine inventors equilibrium selection of a patent tier an how it is a ecte by patent policy. 5.1 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. Following the proposal of Lemley et al. (2005), we assume that a gol-plate patent is associate with a higher fee: P gp > P r ; an a more thorough examining proceure: gp r > Patent tier (a regular or a gol-plate patent) is 15 It is possible to esign a system with two tiers such that P 1 > P 2 an 1 < 2. Depening on the value of these policy controls, we coul have an equilibrium in which low probability of valiity applicants pay more to avoi tough examination, or an equilibrium in which high probability of valiity applicants pay high fees to enjoy being part of a high quality patent tier. However, our characterization of a threshols equilibrium an other results use the assumption that gp r.an P gp P r : 13

14 public information. 16 The value of a patent to an inventor epens on both its ex-ante probability of valiity an on the quality of patents of its tier (q r for a regular patent, or q gp for a golplate patent). 17 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. 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 ) (1 )(1 i )B (q i ) P i : (6) 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. When the set of applicants is non-empty, patent quality the probability that a patent in tier i 2 fr; gpg is goo is q i = Pr(goojpatent-tier i grante) which is erive using Bayes rule. When the set is empty, we set q i = Thus we e ne: 8 >< q i = >: R R i f() i [1 i (1 )]f() if i 6= Ø, (7) 0 if i = Ø. We now e ne the 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; 1] an patent qualities q r an q gp such that: 16 The patent o ce can make information on patent tiers available. The policy is not likely to be e ective if this information is not mae public. We also note that in the case of the peer-to-patent project (see it is publicly known who participates in the special examination process, as these applications are mae public to solicit information from the public. 17 In our moel, innovators have the same bene t functions G (:) an B (:) in either tier. In practice, bene ts in the gol-plate tier might be higher. For example, in Australia s reform, the lower tier patents are grante for a shorter uration. We conjecture that most of our nings woul remain the same qualitatively. 18 One can e ne the perceive quality of an empty set of innovators in i erent ways. Since we mostly focus on interior equilibria, we o not elaborate on this issue. 14

15 1. 2 r ; if an only if V r (; q r ) 0 an V r (; q r ) V gp (; q gp ); 2. 2 gp ; if an only if V gp (; q gp ) > 0 an V gp (; q gp ) > V r (; q r ); 3. q r an q gp satisfy equation (7). 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 will show 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 in which there exist 0 1 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 < < < 1. In an interior threshols-equilibrium, at least some inventors apply for each patent tier, an some o not apply for a patent. 19 exists, we assume a single crossing conition for all q: To guarantee that a threshols-equilibrium G 0 (q) (1 r )B 0 (q) > 0: (8) This conition states that the cross-erivative of the payo functions with respect to the inventor s type an patent quality q is positive. moerately steeper than G: 20 It hols when B is atter or only In an interior threshols-equilibrium, the quality of gol-plate patents is higher than that of regular patents, q gp > q r : Otherwise, for all ; a regular patent gives a higher value V r (; q r ) V gp (; q gp ) as e ne in (6) an the equilibrium woul not be interior. It is easy to verify that any interior equilibrium is a threshols-equilibrium. This hols because for given equilibrium qualities q gp > q r ; the payo functions V r (:) an V gp (:) are 19 Non-interior equilibria are also possible. If patent fees are very small (large), it is possible that all innovators apply (no one applies). A two-tiere system coul collapse into a single-tiere system with all innovators applying either to the regular tier, or to the gol-plate tier. 20 Existence of equilibrium (not necessarily interior) can be shown using a xe point argument. We omit the proof as the argument is stanar, but it is available from the authors. 15

16 linear in. If a type innovator prefers to gol-plate her patent, any higher type woul prefer the same. An interior threshols-equilibrium is characterize by threshol levels ; an patent qualities q r an q gp such that H ( ; ; q r ; q gp ) = 0 where the function H = (h 1 ; h 2 ; h 3 ; h 4 ) ; is e ne as follows: 8 h 1 := G (q r ) (1 ) (1 r ) B (q r ) P r = 0; >< h 2 := [G (q gp ) G (q r )] (1 ) [(1 gp )B (q gp ) (1 r )B (q r )] (P gp P r ) = 0; R h 3 := [ (1 q r ) (1 r ) (1 ) q r ] f() = 0; 1R >: h 4 := [ (1 q gp ) (1 gp ) (1 ) q gp ] f() = 0: (9) The rst two equations e ne the threshols: h 1 (:) = 0 implies that an applicant with ex-ante probability of valiity is ini erent between applying for a regular patent an not applying for a patent, V r ( ; q r ) = 0; h 2 (:) = 0 implies that an applicant with ex-ante probability of valiity is ini erent between applying for a regular patent an for a gol-plate one, V gp ( ; q gp ) = V r ( ; q r ). The next two equations e ne the quality of regular an gol-plate patents, as obtaine from rearranging equation (7). To erive the e ects of the fees an examination intensities on equilibrium, we implicitly i erentiate the system of equations H in (9). We assume that the eterminant of the Jacobian matrix (the matrix of partial erivatives) of this system is positive. We refer to this as the Jacobian Conition, an write it formally in the Appenix, in De nition 5. In Lemma 1 (Appenix A), we provie a su cient conition for the Jacobian conition to hol in a special case use in proposition 6 an in Lemma 2 (Appenix B), a su cient conition for it to hol for a linear moel. 21 Consier the e ects of changes in the patenting fees. 9 >= >; Proposition 2 Uner the Jacobian Conition, aroun an interior equilibrium, (i) As the gol-plate patent fee (P gp ) increases, the overall volume of patent applications increases; the volume of gol-plate patent applications ecreases; the quality of 21 By the implicit function theorem, the eterminant of the Jacobian matrix, J, appears as the enominator of each of the comparative statics erivatives. It consists of mostly positive terms an we foun it to be positive in numeric solutions of the moel. If J < 0, the e ects we report in the proposition are exactly reverse. 16

17 gol-plate patents an the quality of regular patents increase; the prevalence of ba patents increases as well; (ii) As the regular patent fee (P r ) increases, the overall volume of patent applications ecreases. The e ects of the regular patent fee on the other equilibrium variables an the e ects of examination intensities are in general ineterminate, but in Appenix B we state aitional results in the special case of a linear moel. 5.2 The Ae-Tier System Consier a special family of two-tiere systems in which the regular tier has the same fee an examination intensity as the single-tiere system. We refer to such two-tiere system as an ae-tier system. De nition 4 Given a single-tiere system with examination intensity an a patent fee P; an ae-tier system is a two-tiere system with P gp > P r = P an gp r = : We compare the single-tiere system with an ae-tier system. Proposition 3 Consier a single-tiere system an an ae-tier system. Assume each system has an interior equilibrium. Then in the ae-tier system, (i) there are fewer patent applications than in the single-tiere system ( > 1 ); (ii) the quality of regular patents is lower than in the single-tiere system (q r q 1 ); (iii) the quality of a golplate patents is higher (q gp q 1 ); (iv) overall, there are fewer ba patents than in the single-tiere system. Proposition 3 establishes that an ae tier results in a ecline in the overall volume of patent applications. The reason for this is that applicants with the highest probability of valiity choose to gol-plate their patents, leaving an averse selection of applicants for the regular patent-tier. Hence regular patents have lower perceive quality than the patents in the single-tiere system, an therefore are less attractive. Gol-plate patents have higher perceive quality than patents in the single-tiere system. Overall there are fewer ba patents because there is a ecline in low probability of valiity patent applications an a more thorough examination of gol-plate patent applications. 17

18 An ae-tier system involves more intense examination. This potentially increases the patent o ce s expeniture. To assure that the expeniture of the patent o ce oes not excee that in the single-tiere system, the gol-plate patent fee coul be set to cover the aitional cost of examination: P gp P r [c ( gp ) c ( r )] : If the examination intensity of gol-plate patents is not much higher ( gp r is small), then increase in the fee can be small enough so that some inventors woul inee apply for a gol-plate patent. In an ae-tier system, innovators with probability of valiity either o not apply for a patent, or apply for a patent that has a lower quality than a patent in the single-tiere system. Thus, these innovators are either as well o or worse o. Only innovators who have a high ex-ante probability of valiity > might be better o ue to the higher quality of gol-plate patents. However, since examination intensity is higher an the fee is higher, it is not guarantee that they are better o. The e ect of the introuction of an ae tier on the payo s of innovators is negative unless the bene t from increase quality of gol-plate patents is su ciently large to o set the loss of all lower ex-ante probability of valiity applicants. 6 R&D Investment an Welfare An important goal of the patent system is to provie incentives to innovate. We have so far assume a xe set of innovators. In this section, we exten the moel to consier the incentives to invest in R&D an social welfare. Suppose each rm has one iea for innovation. The necessary R&D investment of each innovation is a ranom variable I uniformly istribute over [0; I]: The probability of valiity is rawn from a istribution F on [0; 1]: We assume that the probability of valiity is reveale to the innovator after investment but before patenting. Uner this assumption, the probability istribution F before investment is the same as the probability istribution conitional on R&D investment. We therefore keep the same notation for this istribution. We iscuss the known case in the conclusion. Welfare captures the surplus of innovators, an the aitional social surplus that result from patente an non-patente innovation a ecting consumers an other proucers. We enote by S C the social surplus when a rm investe in R&D, the resulting innovation 18

19 was goo an the innovation was not patente. We enote by S G an S B the ae (i.e. not capture by the patentee) social surplus from a goo an a ba patent respectively. Ba innovations that are not patente have no ae social surplus. We assume, S C S G 0 S B : 22 Innovators invest if their expecte bene t from investment excees the cost. Because is yet unknown at the time the innovator has to ecie on R&D investment, an innovator invests if the R&D cost is lower than her expecte payo from an innovation. We enote the expecte payo of innovators by IS (innovators surplus). Innovators invest in R&D if I IS. 23 The innovators surplus can be interprete as a measure for the incentive to invest in R&D. We e ne welfare as: 8 9 ZIS net innovators surplus 1 < z } { = W = CCS I : {z } {z} R {z} IS I I: (10) ; 0 conitional consumers surplus PTO s net revenue innovators surplus = 1 I CCS R IS IS: (11) 2 {z } conitional social surplus We e ne each of the components of this welfare function for the two-tiere system. The same e nitions apply to the single-tiere system, where = 1 an = 1: The conitional consumers surplus is e ne by: CCS = Z 0 Z 1 S C f() Z [S G (1 )(1 r )S B ] f() (12) [S G (1 )(1 gp)s B ] f(): The rst integration term captures surplus from goo innovations that were not patente, an the secon an thir integration terms capture surplus from innovations that have receive regular patents an gol-plate patents, respectively. The net revenue of the patent o ce captures the patent fees collecte from regular 22 For simplicity, we o not explicitly moel the source of surplus an abstract from potential gains from better information about patent quality an from litigation costs. 23 Our innovators surplus is similar to the concept of sellers welfare use by Farhi, Lerner an Tirole (2010) in their analysis of markets for certi cations. In the context of a patent race, Grossman an Shapiro (1987) examine the e ects of policy changes on the inustry s expecte pro ts an state conitions uner which inustry pro ts measure welfare. 19

20 an gol-plate patents, net of the costs of examination. It is given by: R = Z [P r c( r )] f() Z 1 [P gp c( gp)] f(): The innovators surplus is e ne by: IS = Z [G (q r ) (1 )(1 r )B (q r ) P r ] f() Z 1 [G (q gp) (1 )(1 gp)b (q gp) P gp] f(): The rst line in IS captures the surplus attaine by innovators who choose to apply for the regular tier an the secon line captures the surplus from the gol-plate tier. It is easy to see that, for a given patent policy, welfare increases when the social value of patente or non-patente innovation increases an when the loss from ba patents ecreases (S G ; S C or S B increase), an when the cost of examination c() ecreases. Given patent policy, the social surplus an the examination cost o not irectly a ect the equilibrium in a single-tiere or a two-tiere system. Therefore, these comparative statics results also hol for welfare at the optimal patent policy. 6.1 Innovators Surplus an Welfare in Single-Tiere System An increase in the patent fee is typically thought to reuce the incentive to innovate. Our moel suggests, however, that in aition to the irect negative e ect of an increase in the patent fees, there is an inirect positive e ect. An increase in the patent fees reuces applications from low probability of valiity applicants an results in higher perceive patent quality. Taking into account that innovators bene ts increase with patent quality, there is an inirect positive e ect of an increase in the patent fee which at least partially o sets the negative irect e ect. This can be seen by i erentiating the single-tiere system innovators surplus (IS 1 ) with respect to P: By the e nition of 1 ; the inirect e ect of P on IS 1 through 1 is zero, therefore we have: (IS 1 ) P = Z 1 Z 1 f() [G 0 (q 1 ) (1 )(1 )B 0 q 1 (q 1 )] f() : P 1 {z } 1 {z } irect fee e ect 0 quality increase e ect 0 20

21 Proposition 4 For uniformly istribute ; if [G (q) (1 ) B (q)] is concave (or linear) in q, innovators surplus ecreases with the patent fee. There exist convex bene t functions for which innovators surplus increases in a range of the patent fees. By (6), [G (q) (1 ) B (q)] represents the slope of the value function V (; q 1 ) with respect to : When this expression is concave (or linear) in q, the inirect e ect of an increase in quality on the innovators surplus is smaller in magnitue than the irect (negative) e ect, so that innovators surplus eclines. 24 As a self-fune agency, the USPTO relies on the fees to cover its costs. Shoul the patent o ce set a fee that exactly covers, excees or subsiizes its examination costs? This questions is particularly relevant in light of the recent patent reform act which gives the patent o ce fee setting authority. 25 We show that in the range where P c () ; the net innovator s surplus (NIS = IS R) increases with the fee. Intuitively, by pricing at the social cost of examination, the marginal patent applicant generates no value, but lowers the average quality of all patents, an therefore if the patent o ce sets the net innovators surplus as its objective function, the fee shoul be raise. An increase in the patent fees also increases conitional consumer surplus, because xing the incentive to innovate, unpatente innovations generate more surplus than patente ones. Proposition 5 (i) The conitional consumers surplus increases with the patent fees. (ii) In the range where P c () ; the net innovators surplus an the conitional social surplus also increase with the patent fees. From (11) we know that welfare equals W 1 = CSS IS 1 : The e ect of the increase in I the patent fee on welfare is W 1 P = CSS P IS 1 I {z } e ect on conitional social surplus CSS IS 1 : I {z P } e ect on incentive to innovate 24 For an increase in examination intensity, we also have a negative irect e ect an a positive inirect e ect ue to the increase in quality. (IS 1 ) = Z 1 (1 )B (q 1 ) f() 1 {z } irect examination intensity e ect 0 Z 1 [G 0 (q 1 ) (1 )(1 )B 0 q 1 (q 1 )] f() : 1 {z } quality increase e ect 0 25 See 21

22 By Proposition 5, in the range P c () conitional consumers surplus increases with the patent fee. However, an increase in the fee has an aitional, potentially negative e ect on the incentive to innovate. Thus, the welfare maximizing patent fee can, but oes not necessarily, excee the cost of examination. 6.2 Welfare Improving Two-Tiere System Welfare in an optimal two-tiere system is at least as high as welfare in the optimal single-tiere system because the two-tiere system can be esigne to mimic the best single-tiere system. We show that when G (1) (the bene t from having a goo patent when perceive patent quality is high) is su ciently large, welfare is strictly higher in the optimal two-tiere system. Intuitively, a subset of high probability of valiity innovators apply for gol-plate patents, these have a very high perceive quality an thus enjoy the very high bene ts. In the single-tiere system, a very high quality coul only be obtaine with either high examination intensity (which woul be costly) or with a high patent fee that woul exclue all but the very high valiity applicants (which coul reuce the incentive to innovate). With a two-tiere system on the other han, the high quality of gol-plate patents can be enjoye without excluing a signi cant volume of low ex-ante probability of valiity applicants, because these applicants can still apply for the regular (low fee) tier. To establish more formally that a two-tiere system can result in higher welfare, we consier an ae-tier system that i ers from the single-tiere system only in the golplate patent fee: r = gp = an P r = P; but P gp > P: There is a threshol gol-plate patent fee P gp so that for P gp P gp ; no innovator applies for a gol-plate patent an the two-tiere system results in the same equilibrium as the single-tiere system. When G (1) is high enough, compare to the bene t of a goo patent in the single-tiere system G (q 1 ) ; welfare woul increase with a small reuction in the gol-plate patent fee below P gp, which results in a two-tiere system with higher welfare. In the proof of Proposition 6, we formalize the conition on G (1) : We note that the conition never hols for linear bene t functions, but hols for other (convex) functions The proof of the proposition uses an ae-tier system. We coul not rule out the possibility that there exist other two-tiere systems that improve welfare even in a linear moel, but numeric solutions we pursue i not yiel welfare improvements when using linear bene t functions. 22

23 Proposition 6 Welfare uner an optimal two-tiere system is at least as high as welfare uner the optimal single-tiere system. The optimal two-tiere system can result in strictly higher welfare than the optimal single-tiere system when G (1) is su ciently high compare to G (q 1 ). To gain further insight on welfare improving two-tiere systems, we solve the moel numerically. We informally escribe some insights we gaine. 27 Using a uniform istribution of types () an quaratic bene t functions, we foun two-tiere systems that increase welfare above that of an optimal single-tiere system. The improvement in welfare was higher for higher costs of examination. Intuitively, convex bene t functions o er particularly high bene ts to the applicants with high patent qualities. If the cost of intense examination is low, high quality patents can be achieve with high examination intensity even in a single-tiere system. But when examination is more costly, the two-tiere system allows ientifying a subset of high quality patents while keeping examination intensities relatively low. In the numeric examples we solve, optimal two-tiere systems feature i erential application fees P gp > P > P r, but examination intensities that were equal or close across the two tiers, an were lower than in the single-tiere system. The assumption that gp r (which was part of the policy reform propose by Lemley et al., 2005) might be too restrictive. It is possible that welfare coul be even higher with lower examination intensity in the gol-plate tier. The intuition why gp shoul not be too high is that patents with higher ex-ante probability of valiity sort into the gol-plate patent tier. Therefore, at least ex-post stringent examination of gol-plate patents is not e cient. We note, however, that our moel i not take liquiity constraints into account. If many applicants with high probability of valiity cannot a or the high golplate patent fees, it might be better to esign a system with high examination intensity for gol-plate patent applications instea of high fees so as not to exclue buget constraine high probability of valiity applicants from the gol-plate tier. 27 We use the publicly available software R available at to compute numeric solutions. Programs an more etaile results are available upon request from the authors. 23