Reversed citations and the localization of knowledge spillovers

Reversed citations and the localization of knowledge spillovers Abstract Spillover of knowledge is considered to be an important cause of agglomeration of inventive activity. Many studies argue that knowledge spillovers are localized based on the observation that patents tend to cite nearby patents disproportionately. Specifically, patent citations are typically interpreted as marking the transmission of knowledge from the cited invention to the citing invention. The localization of patent citations is therefore taken as evidence that such knowledge transmission is also localized. Localization of knowledge transmission, however, may not be the only reason that patent citations are localized. Using a set of citations that are unlikely to be associated with knowledge transmission from the cited to the citing invention, we present evidence that challenges the view that localization of citations is driven by localized knowledge transmission. While we are silent on the question of whether knowledge transmission is localized, to the extent that such localization exists, we argue that it is unlikely to be captured by patent citations. 1. Introduction Regional clusters of economic activity are important sources of innovation and economic growth (Porter, 1990; Martin and Sunley, 2003). In the USA, there are over 40 clusters, accounting for more than 50% of traded employment in U.S. Economic Areas (Porter, 2007). At the same time, clusters vary in their economic and inventive output (Porter, 2003; Delgado et al., 2008; Suire and Vicente, 2009; Agrawal et al., 2014, 2017). These differences have attracted scholars to explore potential mechanisms that contribute to their success including labor market pooling (Krugman, 1991; Audretsch and Feldman, 1996; Rosenthal and Strange, 2001; Delgado et al., 2014), specialized resources (Swann, 1998; Porter, 1990, 2003) and knowledge spillovers (Jaffe et al., 1993; Audretsch, 1998; Giuliani, 2007). Other scholars have attributed the differences to cultural, institutional and ecological factors (e.g., Saxenian, 1994; Bathelt and Glückler, 2014; Sorenson, 2017). The growing importance of innovation and improved access to patent data have led scholars to use patent citations to study the localization of knowledge spillovers. In a seminal paper, Jaffe et al. (1993) find that a citing patent is 5–10 times more likely to be in the same SMSA as the cited patent than a matched non-citing patent. The authors and most subsequent studies (a) view patent citation as a marker for knowledge spillovers and (b) interpret the finding that citing and cited patents are co-located as evidence that knowledge spillovers are localized (Almeida and Kogut, 1999; Alćacer and Gittelman, 2006; Thompson, 2006; Belenzon and Schankerman, 2013; Singh and Marx, 2013; Murata et al., 2014). The current paper presents evidence inconsistent with the interpretation that localization of citations is driven by localized transmission of knowledge from the cited invention to the citing invention. While our paper is silent on the question of whether knowledge transmission across inventions is localized, to the extent that such localization exists, we argue that it is unlikely to be captured by patent citations. Our empirical test is as follows. We identify a set of citations that are unlikely to reflect knowledge transmission from the cited invention to the citing invention, which we label as ‘citation reversals’, and use these citations as a benchmark to compare the localization of citations for which knowledge transmission is possible, ‘citation non-reversals’. Citation reversals typically occur during the patent examination process when an inventor or an examiner cites a relevant patent. Because ascertaining priority dates (the earliest filing date of a patent on a specific invention) is not always straightforward, citation reversals might occur. If localization of citations is driven by localized knowledge transmission, we expect citation non-reversals to be more localized than citation reversals. There are at least two broad interpretations for the relationship between patent citations and knowledge spillovers. The first is that a citation from citing patent A to cited patent B indicates that A builds on B (e.g., Belenzon, 2012; Williams, 2013; Galasso and Schankerman, 2014). Patent citations are localized if inventors are more likely to learn from the inventions of nearby inventors. In other words, a citation indicates that inventions A and B are sequentially linked, and localization in this context means that sequential innovation is localized. By definition, the citing invention must come after the cited invention; thus, the temporal structure of the citation sequence is key. According to this view, our empirical test should shed new light on the interpretation of localized citations. The second interpretation builds on the view that knowledge is ‘in the air’. Accordingly, a citation from patent A to patent B indicates that some background knowledge embodied in invention B is relevant for invention A. Roughly speaking, a citation from A to B implies that the inventors of A are working on a similar problem as the inventors of B. Localization of citations means that inventors in the same locality are working on related problems, not that knowledge spillovers among inventions are necessarily localized.1 A variant of this interpretation is that a patent citation is a noisy signal of local unobserved interactions among inventors. These interactions can manifest as patent citations regardless of whether the citing and cited inventions are actually linked. Clearly, the temporal structure of citations is irrelevant in this case, rendering our empirical test not meaningful.2 However, this interpretation does not explain examiner-added citations, in contrast to where both A and B draw upon the same background knowledge. Moreover, this interpretation of citations as markers of interactions among inventors is at odds with the legal interpretation of citations as limiting the scope of the invention claimed in the patent. The distinction between drawing upon shared background knowledge and learning from specific inventions is important for several streams of research. An inventor whose invention is built upon by subsequent inventions can potentially extract licensing revenues from the latter. Indeed, the key questions analyzed in models of cumulative innovation are how to divide rents between sequential inventors (Green and Scotchmer, 1995), choosing patentability criteria or determining patent length and breadth (O’Donoghue et al., 1998; Bessen and Maskin, 2009). If, instead, the invention draws upon a common pool of knowledge, although the innovation may be cumulative, it would be very difficult for the inventor to identify subsequent inventions that build upon her invention (Laitner and Stolyarov, 2013). Other studies within cumulative innovation examine whether intellectual property rights hinder sequential innovation (Williams, 2013; Galasso and Schankerman, 2014). Their key assumption is that inventors build on the knowledge contained in specific inventions rather than on background knowledge. These studies interpret citations as sequential links between inventions. The distinction is also relevant for the study of entrepreneurial spinoffs and regional clusters. Inventors leaving existing employers to start their own firms could build upon either specific inventions (Anton and Yao, 1995) or more general background knowledge (Chatterji, 2009). If spinoffs, which are often co-located with parents, capitalize on discoveries employees make in the course of their employment, firms have the ability to design contracts to protect themselves. Such contrivances are less useful if spinoffs exploit more general knowledge learned in the course of their employment. The distinction being drawn is vital for innovation management and strategy scholarship. Firms concerned about protecting inventions from spillover to outsiders may try to disperse inventors (Zhao, 2006; Alćacer and Zhao, 2012) or locate them away from competitors (Shaver and Flyer, 2000; Alćacer and Chung, 2007). This strategy is likely to be more effective if inventors are in fact more likely to build upon co-located inventors. If, on the other hand, co-location of citation reflects a reliance upon common knowledge, dispersing inventive activity will merely hurt the firm. Using 1,356,738 USPTO citations and an equal number of control citations, we confirm the stylized fact that patent citations are localized. Our estimates imply that a 50-mile increase in distance between inventors is associated with a 19% reduction in the probability of citation (close to 40% of the sample’s average citation probability). However, when we compare non-reversals to reversals, we find that the two citation groups are equally as localized. That is, the probability of citations falls with distance at the same rate for both groups of citations. This finding is robust to a battery of tests and is inconsistent with the view that citations are localized because inventions are more likely to build on other close by inventions. The rest of the paper is organized as follows: Section 2 discusses the related literature, Section 3 describes the conceptual framework, Section 4 discusses the data, Section 5 presents the non-parametric results, Section 6 presents the estimation results and Section 7 concludes. 2. Related literature The study of knowledge spillovers using patent citations can be traced back to Jaffe et al. (1993) who argue that knowledge spillovers are localized because, as they demonstrate, patent citation pairs are significantly more likely than controls to be in the same geographic area. However, the relationship between citations and spillovers remains unclear in the Jaffe et al.’s (1993) paper and in most follow-up research. If a citation from inventor A to inventor B means that A builds on B, localization of citations would indicate that closely located inventors are more likely to build on one another. Thus, localization of citations would indicate that knowledge spillovers are localized. On the other hand, a citation might indicate that A and B are working on similar problems. Under this interpretation, localization of citations would reflect regional specialization, in that local inventors work on similar problems and draw from common background knowledge. These inventors might cite one another not because the citing invention builds on the cited invention, but because a citation is used to demarcate the citing invention from the cited invention. The present paper proposes an empirical test to help clarify the interpretation of localized citations. At a minimum, it pushes authors to take a clearer stand on whether they view citations as a sequential link between patented inventions or as a noisy measure of related inventive activity whereby the citing patent may not necessarily build on the cited patent. Our discussion in Section 1 explains why this distinction is important. There are numerous studies on knowledge spillovers and regional clusters that utilize patent citations to examine whether knowledge spillovers are localized (e.g., Verspagen and Schoenmakers, 2004; Belenzon and Schankerman, 2013; Nomaler and Verspagen, 2016) and whether co-located firms benefit from localized knowledge spillovers (e.g., Zhao, 2006; Alćacer and Zhao, 2012; Menon, 2015). While these studies demonstrate that citations are localized, they are usually unclear on whether this localization is due to local transmission of knowledge from the cited to the citing patent (localized sequential innovation), or due merely to co-location of related inventive activities. Consequently, empirical results interpreted as indicating localized knowledge spillovers may instead reflect unmeasured factors that make some regions better suited for a certain type of inventive activity relative to other regions. For instance, Verspagen and Schoenmakers (2004) examine whether regional concentration of R&D activities is beneficial to large multinational corporations. The study uses patent citations to argue that knowledge spillovers are localized. Although the study shows that patents citing each other are located closer than otherwise similar patent pairs that do not cite each other, its argument relies on the assumption that patent citations reflect knowledge spillovers from the cited to the citing inventors. In a more recent study that looks at spatial characteristics of technology trajectories, Nomaler and Verspagen (2016) use citation pairs and citation sequences linking multiple patents to show that, although direct citations tend to be geographically localized, citation sequences run across clusters. The authors interpret inter-cluster citations as knowledge flows between the clusters where citing and cited patents are generated. In exploring how firms might benefit from localized knowledge spillovers, Menon (2015) examines the extent to which the presence of highly innovative firms in a region, measured by the number of patents generated, influences the number of patents generated by other firms in the same region. The study shows that locally cited patents generated by the most innovative firms is positively associated with patents generated by other firms in the same MSA. Menon (2015) argues that the greater patenting activity of a region in the presence of highly innovative firms is due to knowledge spillovers. Additionally, Alćacer and Zhao (2012) examine how multinational firms might minimize knowledge outflow from their inventive activities when the activities are co-located with those of their competitors. They find that strong intra-firm interdependence between inventive activities across different regions can reduce expropriation of their knowledge by their competitors. The study uses self-citations and citations made to a firm’s patent by other firms to measure knowledge appropriation and expropriation. In particular, it interprets a citation made by A to B as reflecting the use of B’s knowledge by A. Other studies try to uncover potential mechanisms underlying the localization of citations. An influential stream of research examines inventor mobility. This line of work identifies inventors’ intra-regional mobility based on inventor addresses and patent assignees and examines the relationship between mobility and localized citations. The studies show that citations are local partly because inventor mobility is local. Almeida and Kogut (1999) identify the top 20 inventors in terms of number of forward citations and estimate the effect of their mobility on intra-regional citations. The authors find a positive relationship between mobility of top inventors within a region and the probability that a patent cites another patent in the same region. This finding is interpreted as evidence that inventors’ tendency to stay in a specific region drives the localization of knowledge spillovers in that region. In a related study, Breschi and Lissoni (2009) use patent citations data from the European Patent Office to examine the contribution of inventor mobility to localized knowledge spillovers. The study compares the probability that citing and cited patents are in the same MSA with and without inventor self-citations (inventors citing their own patents) after excluding firm self-citations (where the citing and the cited patent are generated by the same firm). They find that the localization effect drops substantially when inventor self-citations are excluded and interpret this finding as evidence that knowledge spillovers are localized because inventors tend to stay within the same geographical region. Another reason why citations might be localized is that they can be added by local intermediaries. Wagner et al. (2014) argue that patent attorneys build their knowledge repositories while interacting with their clients and reference patents from those repositories when they prepare new patent applications. If patent attorneys are engaged primarily with local inventors and knowledge repositories are built using the inventions of those local inventors, then patent citations added by patent attorneys would likely be localized. Yet other studies utilize examiner-added citations to test whether inventor-added citation pairs exhibit localization patterns as documented in prior studies. Thompson (2006) utilizes examiner-added citations, which is argued to be less likely to reflect knowledge spillovers than inventor-added citations (unless, of course, the examiner is merely correcting for willful omission or oversight on the part of the inventor) and shows that inventor-added citations are more localized than examiner-added citations. Nonetheless, the crucial assumption of the study is that patent citations reflect knowledge spillovers. Alćacer and Gittelman (2006) also focus on examiner citations to see whether any systematic differences exist between inventor-added and examiner-added citations that might bias the widespread finding that knowledge spillovers are localized. They find that while examiner-added citations tend to track inventor-added citations fairly closely in terms of distance between citing and cited patents, including examiner-added citation pairs in the study of knowledge spillovers could bias the results under certain conditions. In recent years, some studies have cast doubt on the interpretation of patent citations and the notion of localized knowledge spillovers. In their critical review of the localized knowledge spillovers literature, Breschi and Lissoni (2001) argue that prior studies have not been clear about the notion of localized knowledge spillovers and that the conceptual framework of localized knowledge spillovers needs to be reassessed and improved. They also argue that more studies should examine the mechanisms underlying localized knowledge spillovers, such as labor mobility and role of university and research institutions. More recently, Sorenson (2017) argued that temporal changes in region-specific entrepreneurial vibrancy, which is closely tied to both economic and inventive output of the region, can be explained more logically by ecological factors than by access to knowledge. To support this argument, Sorenson (2017) points out that while improvements in a region’s knowledge capital require decades, changes in the regional level of entrepreneurial activities can occur in a matter of years. Furthermore, Thompson and Fox-Kean (2005) argue that the matching approach in Jaffe et al. (1993) is too coarse and does not adequately control for existing regional specialization. Imposing stricter matching criteria, they find that the localization effect almost disappears at the SMSA and state levels. In a response to this criticism, Henderson et al. (2005) argue that the lack of localization in Thompson and Fox-Kean (2005) is likely to be due to selection bias arising from inability to match a substantial portion of patents at the subclass level, which in turn drastically reduces sample size. In their re-examination of the findings from Jaffe et al. (1993) and Thompson and Fox-Kean (2005), Murata et al. (2014) use distance-based K-density tests to show that citation pairs are more localized than control pairs in about 30% of technology areas when citing and control patents are matched on six-digit technology classification codes. There is also a broader debate on the meaning of patent citations (Jaffe et al., 2000; Duguet and MacGarvie, 2005; Roach and Cohen, 2013; Moser et al., 2017). Using survey data, Roach and Cohen (2013) show that patent citations are likely to underestimate knowledge transmission from university research and overestimate knowledge transmission between firms when firms engage in strategic citation to mitigate patent invalidation risk. In another survey, Duguet and MacGarvie (2005) show that citations are associated with technology flows through some channels (e.g., equipment sales), but not through others (e.g., R&D outsourcing). Additional survey evidence by Jaffe et al. (2000) shows that one-third of inventors did not learn about the inventions they cited until the citing invention was completed and that close to one-third of inventors did not learn about the cited inventions until the time of the survey. In other words, two-thirds of the citations did not reflect knowledge transfer between the cited and citing inventions. Using data from field trials for hybrid corn, Moser et al. (2017) show that self-citations are likely to capture follow-on inventions, but not citations added by examiners. In summary, patent citations have been widely used in the literature to study knowledge spillovers within and across inventors, firms and regions. However, the assumption that patent citations reflect knowledge spillovers has not been thoroughly tested. As a result, conclusions that use patent citations as a measure of knowledge transmission between the cited and citing patents are open to question. In this paper, we focus on the notion that knowledge spillovers are localized because patent citations are localized. We argue that the evidence presented in this paper is inconsistent with the view that patent citations are localized because inventions are more likely to build on other local inventions. Put differently, our results imply that either patent citation is a poor measure of knowledge spillover or that knowledge spillover is not localized. 3. Preliminary concerns 3.1. Reversed citations and local interactions To test whether the localization of citations is driven by localized knowledge transmission, we identify a set of citations that are not likely to be driven by knowledge transmission, ‘citation reversals’. If localization of citations is driven by localized knowledge transmission, we expect citation non-reversals to be more localized than citation reversals. An important concern about our methodology is that citation reversals might reflect highly localized knowledge transmission among local inventors who share knowledge about new ideas and inventions that have not been disclosed to the public. If this were true, reversed citations would be localized due to highly localized knowledge transmission and our key assumption that reversed citations are not associated with knowledge transmission would be violated. Table 1 summarizes different mechanisms through which both knowledge about inventions and background knowledge could be transmitted, including those that might lead to citation reversals. There are three main learning mechanisms indicated by Columns 1–3. The first is learning from patent documents—learning about inventions by reading published patent documents. There is no reason to expect this type of learning to be localized. Thus, we are not concerned that learning from patent documents would generate localized citation reversals. The second mechanism is learning about inventions from inventors. In this case, inventors might share among themselves knowledge about new inventions. Such learning might be localized if inventors tend to discuss their inventions more frequently with nearby inventors than faraway inventors. The third source of learning is patent intermediaries, such as patent attorneys. By using the same patent attorneys, inventors might learn about new inventions before they are disclosed to the public. Because inventors are more likely to use the same patent attorneys if they are near one another, engaging with patent attorneys might generate localized citation reversals. Table 1 Types and sources of knowledge Notes: This figure shows the types and sources of knowledge distinguished in the paper. Knowledge about invention is knowledge directly related to the invention while background knowledge is knowledge that might underlie the invention and can be drawn upon from a common knowledge pool. Knowledge can also have multiple sources that can influence temporal and geographical characteristics of knowledge transmission. The six inner cells indicate whether knowledge tends to be localized given its type and source. Table 1 Types and sources of knowledge Notes: This figure shows the types and sources of knowledge distinguished in the paper. Knowledge about invention is knowledge directly related to the invention while background knowledge is knowledge that might underlie the invention and can be drawn upon from a common knowledge pool. Knowledge can also have multiple sources that can influence temporal and geographical characteristics of knowledge transmission. The six inner cells indicate whether knowledge tends to be localized given its type and source. Section 6 presents several tests aiming at mitigating the concern that reversals are generated through highly localized learning. 3.2. Comparing the localization effect of reversed and non-reversed citations We propose the following motivation for why localized knowledge transmission might lead to a stronger negative effect of distance on citation probability for citation non-reversals than for reversals. We distinguish between citations that reflect knowledge transmission, i.e., where one invention builds upon another, improving or extending it, and citations that reflect other relationships, where no such knowledge transmission takes place. A patent may cite another patent because both draw upon a common pool of knowledge. Patents may be related in other ways as well. For instance, the citing patent may accomplish the same outcome as the cited patent using a different method or use similar methods to accomplish different goals. The distinction bears on whether the citing invention benefited from the knowledge created in the form of the cited invention. The citing inventions that are related would be unaffected. The citing invention that builds upon the cited invention would have had to acquire the knowledge created by the cited invention. The extant literature has implicitly or explicitly assumed that, when patent class is controlled for, citations reflect knowledge transmission. We argue that citation reversals, by construction, cannot reflect knowledge transmission from the cited invention to the citing invention.3 It is conceivable that the inventor may have learned useful knowledge from the inventor of the cited invention, but it is far more likely that a citation reversal represents the recognition of a related invention, albeit one that should not have been cited because it is not prior art.4 We do not observe whether a citation represents transmission of knowledge or merely some type of relatedness. Instead, we propose a simple structure that clarifies how one can infer the relative importance of the two types of citations in generating the observed pattern of localization of patent citations. If citation reversals reflect relatedness, and if knowledge transmission falls with distance, then citation reversals should be less localized than non-reversals. Consider a pair of patents i and j, where i is the focal patent and j is invented after i. Patent j can build upon patent i with probability πn if it is near and πf if it is far. With probability θn, patent j can be related to patent i if they are near each other and θf if they are far apart. For simplicity, assume a patent that builds upon another will cite it with probability α. Similarly, a patent that is related to another will cite with probability β. The probability that j cites i if they are near is απn + βθn.5 Similarly, the probability of a citation if they are far apart is απf + βθf. The difference in probability of citation between patents located near each other and patents located far is α(πn−πf) +β(θn−θf).6 This difference has two components: πn−πf representing the extent to which knowledge transmission decreases with distance, and θn−θf representing the extent to which patents near each other are related relative to those far apart. Each component is weighted by the relevant citation propensity. The consensus is that both components are positive. That is, nearby inventions are more likely to be related and knowledge transmission is more likely among nearby inventions. Now consider the probability that i cites j, that is, a citation reversal. Since i cannot have built upon j, the probability of the patents being related is simply θn if they are near each other and θf if they are far. If the propensity to cite is β as before, difference in probability of citation between near and far is simply β(θn−θf). The effect of proximity on the probability of citation for non-reversals is α(πn−πf) +β(θn −θf) so that the difference in the effect of proximity with respect to reversals is α(πn−πf). The extant literature has asserted that knowledge transmission increases with proximity, that is, α(πn− πf) > 0. This implies that the effect of proximity on the probability of a citation reversal should be smaller than the effect of proximity on the probability of a non-reversal citation. In the empirical analysis we use distance, so that we expect that distance should have a smaller absolute effect on reverse citations than on normal or non-reversal citations. The validity of our test hinges on the assumption that the underlying knowledge described in a patent cannot be changed as the patent moves forward in the examination process. This assumption assures that the priority date is the date when the invention is created and allows us to determine whether knowledge could have been transmitted from one invention to another. This assumption is validated by the two statutory provisions, 35 U.S.C. 132 and 35 U.S.C. 251, which prohibit introduction of new matter in amendments and the application for reissuance. Examiners are obligated to reject new matters introduced into the abstract, specification or drawings of a patent application once it is filed. The only changes permitted are rephrasing of a passage without changes in meaning and fixing obvious errors whose correction can be foreseen by a person skilled in the given art.7 If so, the transmission of knowledge cannot take place in citation reversals. 4. Data 4.1. Sample Our main sample is from the 2014 version of EPO Worldwide Patent Statistical Database (PatStat) with inventor distances extracted from Google Maps. We follow previous literature and limit our dataset to USPTO patents with inventors residing in the contiguous USA. Thus, we exclude Hawaii, Alaska and offshore U.S. territories, such as Puerto Rico and Guam. The publication years of the citing patents range from 2001 to 2014. (Sample years are based on the availability of examiner citations, which as we later explain are an important part of our analysis.) Whenever multiple inventors are listed for a single patent, we take the city–state combination that occurs most frequently in our distance calculation. If there is an equal number of different city–state combinations, we randomly choose a location from them. Finally, we retain only the citations with a priority lag (difference in years between the priority dates of citing and cited patents) less than 5 years. This restriction is to account for the fact that citation reversals have short priority lags and in turn to ensure that reversals and non-reversals remain comparable. This procedure yields 1,356,738 actual citations. For each pair of patents connected by a citation, we match the citing patent with another patent, to create a control pair. We construct the control group by matching each citing patent in the actual citations with a randomly selected, non-citing patent on four-digit IPC and publication year (Jaffe et al., 1993; Belenzon and Schankerman, 2013). These control patents are paired with the cited patents from the actual citations to form control citations. The sample includes 2,713,476 observations consisting of both actual and control citations. 4.2. Variable definitions We proceed to describe the main variables used in the analysis. Online Appendix Table A1 summarizes their definitions and sources. 4.2.1. Priority date A central piece in our analysis is identifying priority dates, which are used to determine whether a citation is a reversal. Priority date is the earliest application date of the patents that relate to the same underlying invention (also known as a patent family). It is the date when the invention was first recognized by a patent issuing authority to be in existence. A patent can claim as its priority date the application filing date of an earlier patent if the two patents describe the same invention and share at least one inventor. Priority dates can be claimed via different types of patent applications. Among the most common are applications taking advantage of a provisional application filed for the same invention; continuing applications that extend a prior application8; and applications filed in the USA within 12 months of filing a foreign application for the same invention. In all of these cases, to claim an application filing date of an earlier patent as the priority date, the specifications of the underlying invention described in the earlier and subsequent patents must be the same. For example, US 7333597 is a patent on technology that enables telephone synchronization with software applications and documents. The inventors on the patent are Edward M. Silver, Linda A. Roberts and Hong T. Nguyen. The application for this patent was filed on 2 November 2004. However, the priority date of the patent is 29 March 2002, based on an earlier patent, US 6873692, which relates to the same invention and has the same inventors. Because US 7333597 is a continuation of US 6873692 and because the underlying invention and at least one inventor are the same between the two patents, the more recent patent (US 7333597) can claim as priority date the application filing date of the earlier patent (US 6873692). Identifying an earlier patent application from which to take the priority date is not always trivial because an invention may be associated with multiple patent applications with different application filing dates. For this particular example, we went to the USPTO’s patent application information retrieval website to look up all of the patents in the patent family of US 7333597 and looked for the patent application with the earliest filing date. (Online Data Appendix describes how we find the priority dates of the patents in our sample using PatStat). In our sample, 61% of citing patents and 35% of cited patents claim priority dates from an earlier patent application. Of the 61% of citing patents, 59% claim priority based on a provisional application, 40% on a continuing application and 1% on a foreign application. Of the 35% of cited patents, 59% claim priority based on a provisional application, 39% on a continuing application and 2% on a foreign application. Thirty-nine percent of citing patents and 65% of cited patents that do not claim priority dates from an earlier application (Online Appendix Figure A1 presents a breakdown of applications based on the types of priorities they claim). 4.2.2. Citation reversal We construct citation reversals for which transmission of knowledge from the cited to the citing patent is unlikely. The primary type of citation reversals occurs when the priority yearof the citing patent is earlier than the priority year of the cited patent. We refer to this type of citations as ‘priority reversals’. Priority reversals are not likely to reflect knowledge transmission because the cited invention does not exist at least until the citing invention is created. (We explore a secondary type called ‘disclosure citations’ in Table 5 of the robustness section.) Priority reversals occur in about 4% (58,983) of all actual citations in our sample. Priority reversals occur because priority dates are not always transparent to applicants without an extensive search. Although examiners are supposed to review applicant citations for accuracy and appropriateness, the examination process is not fully automated and thus a related patent may be incorrectly cited as prior art when it is not. According to our conversations with patent attorneys and patent examiners, priority reversals can arise when patent applicants include citations on the information disclosure statement or when patent examiners add additional citations during the patent examination process that begins after the patent application is filed. Some patents have a priority date earlier than their filing date, for instance, because they are related to a foreign patent or they are continuations of an earlier patent. These types of patents require more effort in identifying priority dates, and thus applications involving them are more prone to having priority reversals. An example of a priority reversal is patent US 8484303 citing patent US 8073918 (a graphical illustration and transaction highlights are also shown in Online Appendix Figure A4). Patent US 8484303 was filed on 20 September 2011 and US 8073918 was filed on 6 August 2010. However, the invention described in US 8484303 was created on 17 February 2000 while the invention described in patent US 8073918 was created on 21 April 2004. Thus, the priority year of the citing patent is prior to the priority year of the cited patent. We illustrate priority reversals using the timeline in Figure 1. The horizontal line going from left to right represents the progression of time, and the vertical lines extending below the timeline represent the priority date and the earliest publication date of a cited patent. The two vertical lines extending above the timeline represent possible instances of the citing patent’s priority date. A priority reversal occurs when an invention references another invention that has not been created, as demonstrated by the first instance of the citing patent’s priority date coming before the priority date of the cited patent. A non-reversal occurs when an invention references another invention that has been created and disclosed to the public, as demonstrated by the second instance of the citing patent’s priority date falling after the earliest publication date of the cited patent. In this case, knowledge is more likely to have been transmitted from the cited to the citing invention. Figure 1 View largeDownload slide Priority reversal. Notes: This figure presents how priority reversals occur. Priority reversals are citations where the priority date of the citing patent comes before the priority date of the cited patent. The priority date of the citing patent in non-reversals comes after both the priority date and the earliest publication date of the cited patent. Figure 1 View largeDownload slide Priority reversal. Notes: This figure presents how priority reversals occur. Priority reversals are citations where the priority date of the citing patent comes before the priority date of the cited patent. The priority date of the citing patent in non-reversals comes after both the priority date and the earliest publication date of the cited patent. 4.2.3. Geographical distance We calculate distances between citation pairs using PatStat’s inventor addresses dataset and Google Maps API. We first extract inventor city and state information from PatStat’s inventor addresses dataset and then use a custom software application that communicates with Google Maps Geocoding API to obtain geographical coordinates and straight-line distances between inventors of citing and cited patents.9 In addition to continuous distance, we construct dummy variables for distance ranges to examine the nonlinear effect of distance on citation probability. The reference range is 0–25 miles and the rest of the distance ranges are as follows: 25–50, 50–100, 100–150, 150–250, 250–500, 500–1000, 1000–1500, 1500–2500 and >2500. 5. Non-parametric evidence Table 2 presents summary statistics for the main variables used in the analysis. The average distance between patents linked by a citation is 950 miles with a standard deviation of 892 miles. Four percent of the citations are priority reversals and 33% of the citations are added by examiners. On average, a citing patent receives 6 and cited patents receive 48 forward citations. Of the citations, about 14% are coast-to-coast citations and thus we add dummies to control for citations between research clusters that are located in the opposite coasts. Table 2 Summary statistics for main variables Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Notes: This table provides summary statistics for the main variables used in the econometric analysis of the effect of distance on citation probability for the main sample. The sample consists only of actual patent citations. The publication years of citing patents in the sample covers years 2001–2014. Priority lag is the difference between the priority years of the citing and cited patents. Dummy for reversal is a variable that takes 1 if the priority date of the citing patent is earlier than the priority date or the earliest publication date of the cited patent and indicates that knowledge transmission is unlikely. Dummy for examiner citation is a variable that takes 1 if a citation was added by a patent examiner. Dummy for self-citation is a variable that takes 1 if the citing and cited patents are assigned to the same assignee. Table 2 Summary statistics for main variables Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Notes: This table provides summary statistics for the main variables used in the econometric analysis of the effect of distance on citation probability for the main sample. The sample consists only of actual patent citations. The publication years of citing patents in the sample covers years 2001–2014. Priority lag is the difference between the priority years of the citing and cited patents. Dummy for reversal is a variable that takes 1 if the priority date of the citing patent is earlier than the priority date or the earliest publication date of the cited patent and indicates that knowledge transmission is unlikely. Dummy for examiner citation is a variable that takes 1 if a citation was added by a patent examiner. Dummy for self-citation is a variable that takes 1 if the citing and cited patents are assigned to the same assignee. Table 3 presents the mean comparisons of the main variables used in the analysis for citation reversals and non-reversals. The comparison of geographical distances shows that reversals are at least as localized as non-reversals. The average distance between citation pairs is 860 miles for reversals and 954 miles for non-reversals. The share of citations with citing patents that are within 50 miles of the cited patent is 33% for reversals and 25% for non-reversals. These findings are inconsistent with the view that localization of citations is driven by localized knowledge transmission. Table 3 Comparisons of main citation characteristics: non-reversals vs. reversals (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 Notes: This table presents mean comparisons of main variables between non-reversals and reversals. The sample consists of actual patent citations. The publication years of citing patents covers years 2001–2014. **p < 0.01, *p < 0.05. Table 3 Comparisons of main citation characteristics: non-reversals vs. reversals (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 Notes: This table presents mean comparisons of main variables between non-reversals and reversals. The sample consists of actual patent citations. The publication years of citing patents covers years 2001–2014. **p < 0.01, *p < 0.05. Figure 2 presents comparisons of average distances between citing and cited inventors across various types of citations as well as the share of citations with citing inventors within 50 miles of cited inventors. The general pattern shows that the average distance is greater for non-reversals than for reversals. Furthermore, the fraction of citing inventors within 50 miles of the cited inventors is greater for reversals than for non-reversals. These results provide further evidence inconsistent with the notion that localization of citations reflects localized knowledge transmission. Figure 2 View largeDownload slide Average distance between inventors by citation type. Notes: This figure compares localization of citations across different citation types. ‘Fraction within 50 miles’ is the fraction of citations whose inventors reside within 50 miles of each other. The sample contains actual citations with citing patents covering years 2001–2014 and includes only priority reversals. Figure 2 View largeDownload slide Average distance between inventors by citation type. Notes: This figure compares localization of citations across different citation types. ‘Fraction within 50 miles’ is the fraction of citations whose inventors reside within 50 miles of each other. The sample contains actual citations with citing patents covering years 2001–2014 and includes only priority reversals. 6. Econometric analysis Our empirical analysis tests the implication of the model from Section 3.2. We examine whether the effect of distance on citation probability is smaller in magnitude for reversals than for non-reversals. As shown in the model, this relationship will hold if localization of citations is driven by localized knowledge transmission. We follow Jaffe et al. (1993) and match each citing patent with a control, non-citing, patent with the same four-digit IPC code and publication year. Our results are robust to matching at the six-digit IPC code and publication year, though a finer matching naturally reduces the sample size (cf. Online Appendix Table A5). We use a linear probability model to estimate the effect of distance on citation probability for non-reversals and reversals. Our main empirical specification is as follows: Pr(Cij = 1) = β1 ln Dij + β2 ln Dij × Reversalij + β3Reversalij + Z′γ + ηj + εij, where i and j denote citing and cited patents, respectively, Cij is a dummy variable that receives the value of 1 for an actual citation and zero for a control (non-)citation, Dij is the distance in miles between the location of citing and cited inventors and Reversalij is a dummy variable that receives the value of 1 for a citation reversal (and for the matched control non-citing patent). Z is a vector of dyadic dummies indicating citations between leading research clusters (i.e., Austin, TX; Route 128, MA; Raleigh-Durham, NC; San Diego, CA and Silicon Valley, CA). These dyadic research cluster dummies are important because patents produced in clusters specializing in similar inventions are likely to cite one another and the clusters are often located on opposite coasts. The stochastic components are represented by ηj, a cited patent-fixed effect and an iid error term εij. Standard errors are always clustered at the cited patent level. If localization of citations is driven by localized transmission of knowledge, we expect the effect of distance on citation probability to be larger in magnitude for non-reversals than for reversals. Thus, we expect β̂1< 0 to confirm previous evidence on localized citations and β̂2> 0 to support the view that citations with potential knowledge transmission (non-reversal) are more localized than citations where knowledge transmission is unlikely (reversal). 6.1. Results 6.1.1. Reversal vs. non-reversal localization effect Table 4 presents the results from our main test for localized transmission of knowledge in patent citations. Column 1 presents the estimation results for the effect of distance on the probability of citation. Consistent with previous findings in the literature, the results show that patent citations are localized. The coefficient estimate on the distance between citing and cited patents is negative and statistically significant, indicating that two inventors who are geographically close to each other are more likely to cite than inventors who are far away from each other. Column 2 explores the effect of distance on citation probability using distance dummies. The reference distance is 0–25 miles. Based on our estimates, moving from 0 to 50 miles between inventors lowers the probability of citation by about 19 percentage points, or close to 40% of the sample average. Table 4 The effect of distance on the probability of citation for citation non-reversals vs. reversals Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Notes: This table presents the effect of distance on citation probability for non-reversals and priority reversals. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. Publication years of the citing patents range from 2001 to 2014. Distance dummies are included to show non-linear effect of distance for different distance ranges. (The reference category is 0–25 miles.) The time lag between priority years of the citing and cited year is limited to ±5 years. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors are robust to heteroskedasticity and clustered at the cited patent application level to allow for correlation among patents citing the same patent. **p < 0.01, *p < 0.05. Table 4 The effect of distance on the probability of citation for citation non-reversals vs. reversals Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Notes: This table presents the effect of distance on citation probability for non-reversals and priority reversals. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. Publication years of the citing patents range from 2001 to 2014. Distance dummies are included to show non-linear effect of distance for different distance ranges. (The reference category is 0–25 miles.) The time lag between priority years of the citing and cited year is limited to ±5 years. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors are robust to heteroskedasticity and clustered at the cited patent application level to allow for correlation among patents citing the same patent. **p < 0.01, *p < 0.05. Columns 3–5 present our key findings from comparing the estimated effect of distance on citation probability between non-reversals and reversals. If localization of citations reflects localized transmission of knowledge, then we would observe a significantly larger effect of distance on citation probability for non-reversals than for reversals. Column 3 reveals that the effect of distance on citation probability is −0.08 for non-reversals and −0.10 for reversals, indicating that citation reversals are at least as localized as citation non-reversals. Columns 4 and 5 also show no difference in the effect of distance on citation probability for subsamples consisting separately of non-reversals and reversals. Columns 6 and 7 explore the robustness of the results by allowing for non-linear distance effects. The same pattern of results emerges. For example, moving from 0 to 50 miles reduces the citation probability by 18.2 percentage points for non-reversals and 22.5 percentage points for reversals. These findings are inconsistent with the interpretation that localization of citations reflects localized knowledge transmission since citations do not become more localized as transmission of knowledge becomes more likely. They are consistent with the view that local inventors tend to work on similar technical problems, but not necessarily disproportionately learn from one another. 6.1.2. Do inventor interactions drive localized reversals? An important concern about our analysis is that citation reversals might be driven by interactions among local inventors and/or patent intermediaries. If citation reversals are driven by inventors sharing knowledge about new inventions before the inventions are publicly disclosed, then reversals would reflect highly localized knowledge transmission. For instance, it is possible that two local inventors work on related ideas and that knowledge is transmitted from one invention to the other. If, however, the invention building on the other invention is filed for a patent before the invention being built on and a citation is made from the former to the latter, then this priority reversal would capture knowledge transmission.10 In such cases, reversals could not be used as a benchmark for the localization of non-learning citations against which citation non-reversals are compared. This section presents several tests to mitigate this concern. 6.1.2.1. Self-citations If local inventors interact with one another to share knowledge about unpublished inventions, such interactions are more likely to occur within firms than across firms. Thus, if citation reversals were driven by highly localized inventor interactions, self-citations would be more prevalent within reversals than within non-reversals and more localized than external citations. This bias will prevent us from rejecting the null hypothesis that the localization effect of non-reversals is the same as that of reversals. The share of self-citations is 28% for reversals and 19% for non-reversals. Self-citations are also more localized than external citations. The share of citations whose citing patent is within 50 miles of the cited patent is 75% for self-citations and 14% for external citations. (These differences are statistically significant at the 1% level.) Within citation reversals, self-citations are also more localized than external citations (80% of citing patents being with 50 miles of cited patents for self-citations relative to 15% for external citation reversals). These findings are consistent with the concern that reversals might be driven by highly localized knowledge transmission. To mitigate the potential bias caused by self-citations, we exclude them from our sample. Columns 1 and 2 of Table 5 present the estimation results. The results show that the effect of distance on citation probability is still quite similar between citation non-reversals (−0.045) and reversals (−0.035) and thus confirm our main finding that citation reversals are as localized and as non-reversals. Table 5 Priority reversals and local inventor interactions Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Notes: This table presents results from comparing localization of citation non-reversals with different subsets of priority reversals and disclosure citations. Disclosure citations are citations that occur when the priority date of the citing patent comes before the priority date but after the earliest publication date of the cited patent. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. All columns exclude self-citations. Publication years of the citing patents range from 2001 to 2014. The time lag between priority years of the citing and cited year is limited to ±5 years. Standard errors are clustered at the cited patent level to allow for correlation among patents citing the same patent. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors, in parenthesis, are robust to heteroskedasticity. **p < 0.01, *p < 0.05. Table 5 Priority reversals and local inventor interactions Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Notes: This table presents results from comparing localization of citation non-reversals with different subsets of priority reversals and disclosure citations. Disclosure citations are citations that occur when the priority date of the citing patent comes before the priority date but after the earliest publication date of the cited patent. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. All columns exclude self-citations. Publication years of the citing patents range from 2001 to 2014. The time lag between priority years of the citing and cited year is limited to ±5 years. Standard errors are clustered at the cited patent level to allow for correlation among patents citing the same patent. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors, in parenthesis, are robust to heteroskedasticity. **p < 0.01, *p < 0.05. 6.1.2.2. Patent attorneys Patent attorneys are another potential source of highly localized knowledge transmission that might generate citation reversals. Wagner et al. (2014) argue that patent attorneys tend to cite known patents from their knowledge repositories which they develop based on their interactions with their clients. Thus, if local inventors engage with the same attorneys who share knowledge about unpublished local inventions, then such interactions might result in citation reversals that reflect highly localized knowledge transmission. In this case, same-attorney citations (i.e., citing and cited patents are prepared by the same attorney) would be more prevalent within citation reversals than within non-reversals and more localized than different-attorney citations (i.e., citing and cited patents are prepared by different attorneys). This bias will prevent us from rejecting the null hypothesis that the localization effect of non-reversals is the same as that of reversals. To perform this analysis, we extracted attorney information from the weekly compilations of patent publications released by the USPTO for years 2001–2014. We standardized attorney names and removed any corporate legal offices. In our sample, the share of same-attorney citations is 5% for non-reversals and 11% for reversals. Same-attorney citations are also more localized than different-attorney citations. The share of citations that take place within 50 miles of the cited patent is 79% for same-attorney citations and 23% for different-attorney citations (statistically significant at the 1% level). These findings are consistent with the concern that reversals might be driven by highly localized knowledge transmission. To mitigate this concern, we exclude from our sample the same-attorney citations. Columns 1 and 3 in Table 5 show that even after excluding same-attorney citations, the effect of distance on citation probability is similar between citation non-reversals (−0.045) and reversals (−0.031). This finding is consistent with our main finding and mitigates the concern that citation reversals capture highly localized knowledge transmission driven by interactions among inventors and patent attorneys. 6.1.2.3. Examiner reversals To further mitigate the concern that citation reversals might capture highly localized knowledge transmission, we compare the localization of citation non-reversals to that of citation reversals added by patent examiners, which arguably are even less prone to biases that could arise from local inventor interactions. If reversals arise due to local interactions among inventors, we expect inventors to generate proportionally more reversals than examiners and that inventor reversals would be more localized than examiner reversals. Despite the concern, the share of reversals for inventor and examiner citations in our sample is quite similar (4.4% for inventor citations and 4.2% for examiner citations). The share of citing inventors who are within 50 miles of the cited inventors is 33.7% for inventor reversals and 31.1% for examiner reversals, indicating that inventor-added reversals are somewhat more localized than examiner-added reversals. This observation is consistent with the possibility that reversals are driven by inventor interactions. To further explore this concern, we test whether citation non-reversals are more localized than examiner reversals in Columns 1 and 4 of Table 5. The estimation results show that examiner reversals (−0.043) are as localized as non-reversals (−0.045), evidence that localization of patent citations is not likely to be driven by localized knowledge transmission. 6.1.2.4. Disclosure citations If citation reversals capture highly localized inventor interactions, we expect the highest degree of localization to exist for citations made to inventions that have been created but have not been published. To test this hypothesis, we introduce into our sample another citation type, ‘disclosure citation’, which occurs when the priority year of the citing patent comes after the priority year but before the earliest publication year of the cited patent. This time sequence is due to overlapping patent examination periods where a prior-art patent is published while the citing patent application is being examined. (Online Appendix Figure A3 demonstrates disclosure citation on a timeline and Online Appendix Figure A5 provides an example of a disclosure citation.) Because the cited patent was not known to the public at least until the citing inventor applied for a patent on his invention, the only way that the citing inventor would have known about the cited invention is through a local interaction with the cited inventor. Thus, if local inventors share knowledge about their inventions before the inventions are publicly disclosed, then we expect disclosure citations to be substantially more localized than both citation non-reversals and priority reversals. Columns 1, 2 and 5 in Table 5 compare the localization of citations across citation non-reversals, priority reversals and disclosure citations. The results show that disclosure citations (−0.044) are essentially as localized as priority reversals (−0.035) and non-reversals (−0.045). In Online Appendix Table A8, we further present non-linear effect of distance on the citation probability for citation non-reversals, priority reversals and disclosure citations. The results continue to show that the effect of distance on citation probability is quite similar across non-reversals, priority reversals and disclosure citations. These results are inconsistent with the notion that highly localized knowledge transmission via inventor interaction is a major concern. Overall, the results in Table 5 show that, although citation reversals are more frequent for citation pairs filed by the same organization and for citation pairs with a common patent attorney, excluding them from the sample does not change the broad conclusion that localization of patent citations is unlikely to reflect transmission of knowledge from the cited to the citing invention. Additionally, focusing only on citation reversals added by examiners yields a similar effect of distance on citation propensity between reversals and non-reversals. Lastly, the results show that disclosure citations are not particularly more localized than priority reversals and non-reversals, evidence inconsistent with the concern that highly localized knowledge transmission from local inventor interactions is responsible for citation reversals. 6.1.3. Other robustness checks 6.1.3.1. Changes to the underlying invention over time Our main test of comparing the localization of citation non-reversals with reversals relies on the assumption that the underlying invention does not change over time during the examination process. There are some instances where this assumption might be violated. They include filing CIP applications and applications extending provisional applications. Thus, we test whether our main finding is robust to the exclusion of patents issued from these two types of applications. CIP applications are filed when new subject matter is added to the original application for an invention, and thus the original material and the newly added material may have different priority dates. The multiple priority dates might cause mis-categorization of reversals because it is difficult to determine whether a citation is made to (or from) the old or the new material. To mitigate this concern, we examine whether our main findings hold with the CIP applications excluded from our sample. Columns 1 and 3 in Online Appendix Table A2 show that, even with CIP applications excluded, the localization effects are similar between non-reversals (−0.044) and reversals (−0.035). Another way by which the subject matter of an invention could change over the course of the patent application process involves provisional applications. Unlike regular patent applications, a provisional application can be filed with an incomplete invention, which can later be supplemented using a non-provisional application once the invention is completed. To mitigate the concern that the underlying invention could change when a non-provisional application is filed to supplement a provisional application, we test whether our main findings are robust to the exclusion of applications related to provisional applications. Columns 2 and 4 in Online Appendix Table A2 show that the extent of localization is similar between citation non-reversals (−0.042) and reversals (−0.029) even after excluding applications relating to provisional applications. 6.1.3.2. Alternative specifications We address the concern that the use of control patents might miss an important variation that is correlated with distance. Online Appendix Table A3 presents results from an alternative specification in which localization of citation reversals are compared directly with that of non-reversals without the control citations. For each citation reversal, we find a non-reversal with the same cited patent and with the citing patent in the same IPC and publication cohort. To control for potential differences across citing patents, we also add citing patent technology area and publication year-fixed effects. Columns 1–3 show that a citing patent in citation reversals is at least as likely to be within 50-mile radius of the cited patent as it is in citation non-reversals. The results are robust to using 25-mile radius (Columns 4–6). Thus, our main finding, that localization of citations is not likely to be driven by localized knowledge transmission, continues to hold. 6.1.3.3. Extended sample period For our main results, we used a sample that contains citations with citing patents published over years 2001–2014 because examiner citations became identifiable only in 2001. Online Appendix Table A4 presents results from a test that uses a sample whose citing patents cover years 1977–2014 to make sure that our results are not biased by factors inherent to more recent citations. The results from this larger sample are consistent with our main finding and provide additional support that localization of citations is not likely to reflect localized knowledge transmission. For instance, Columns 2 and 3 show that going from 0 to 50 miles reduces the citation probability by 16.8 percentage points for non-reversals and 21.8 percentage points for reversals. 6.1.3.4. Six-digit IPC We further examine robustness of our findings by replicating our test with a sample whose controls are matched on six-digit technology classification codes. This test addresses the concern raised by Thompson and Fox-Kean (2005) that matching on broad technology classification code might not be adequate to control for existing regional specialization. Online Appendix Table A5 presents the results from the sample matched on six-digit technology classification code. As shown in Column 1, patent citations are localized, consistent with the findings in Murata et al. (2014). Also, consistent with our main finding, the results show that citation reversals are at least as localized as non-reversals. For instance, Columns 2 and 3 show that going from 0 to 50 miles reduces citation probability by 18 percentage points for non-reversals and 21 percentage points for reversals.11 These results are consistent with our main finding that, while citations are localized as indicated by prior studies, localization of citations is not likely to be driven by localized knowledge transmission. 6.1.3.5. Patent citation lag When two inventions are generated during the same time period, it is possible that the patent application of the invention building on the other invention gets filed before the patent application of the invention being built on. Under this scenario, citation reversals with short citation lags would reflect knowledge transmission and our test would produce spurious results. However, the possibility of reversals being generated by this process should be reduced as the reversal lag (i.e., difference between the priority years of citing and cited patents in citation reversals) widens. We address this concern by testing our results after re-categorizing reversals with up to 1-year priority lag as non-reversals and performing separate tests for reversals with different reversal lags. Online Appendix Table A6 presents results from the tests performed after re-categorizing reversals with up to 1-year priority lag as non-reversals. The pattern of results is consistent with our main finding and thus mitigates the concern that our main results might be driven by citation reversals generated by reversed timing of patent application filings. 6.1.3.6. Technology areas The importance of inventor interactions for learning from invention is likely to vary across technology areas. For example, inventions in complex technology areas such as telecommunications are likely to require more tacit knowledge than those in discrete technology areas such as chemicals. Such tacit knowledge might be more localized. To test whether reversals are driven by localized inventor interactions, we first compare the share of reversals across six technology areas: Chemistry, Pharmaceutical, Biotechnology, Medical Technology, Computer Technology and Telecommunications. If technology areas characterized by tacit knowledge are more prone to inventor interactions, then we expect to see higher shares of citation reversals for complex technology areas than for discrete technology areas. Inconsistent with the view that reversals are driven by transmission of tacit knowledge, we find that the share of reversals is fairly consistent across the six technology areas, ranging from 4% (Pharmaceuticals) percent to 10% (Medical Technology). We also examine whether the difference between the localization effect for non-reversals and reversals varies by technology area. If reversals in complex technology areas are more localized because inventor interactions are more important for learning, we expect our test to bias against finding a difference in the localization effect between non-reversals and reversals in complex technology areas, but not in discrete technology areas. Online Appendix Table A7a,b presents the results from comparing localization of citation non-reversals and that of reversals. Inconsistent with the expectation, the overall pattern does not show any systematic variation according to our expectation. For instance, going from 0 to 50 miles reduces the citation probability by 22 percentage points for non-reversals (Column 5 of Online Appendix Table A7a) and 51 percentage points for reversals (Column 6 of Online Appendix Table A7a) in Biotechnology and by 21 percentage points for non-reversals (Column 1 of Online Appendix Table A7b) and 23 percentage points for reversals (Column 2 of Online Appendix Table A7b) in Medical Technology. These results provide evidence that localization of citations is not likely to be driven by localized knowledge transmission in complex or discrete technology areas. 7. Concluding remarks This study examines whether localization of patent citations is driven by localized knowledge transmission. Our results show that the effect of distance on citation probability is similar for citation non-reversals and reversals, implying that localized knowledge transmission from the cited to the citing invention is not likely to be a major driver of localized citations. The concern that citation reversals might reflect highly localized knowledge transmission between inventors, either through direct interactions among themselves or through intermediaries, is addressed by comparing localization of non-reversals with various subsets of reversals that are even less likely to be driven by localized knowledge transmission. Our findings imply that either patent citations do not measure knowledge transmission, or that knowledge transmission is not localized, or both. Our findings are consistent with the growing evidence pointing to the inadequacy of using patent citations as a measure of knowledge flows. Patents may cite other patents because they are solving common problems or drawing upon similar techniques. It may well be that the bulk of citations arise from such circumstances rather than from knowledge flows between inventions linked by citations. If so, we need better ways to track such knowledge flows. Fortunately, the growth in computing power and machine-learning methods offer new possibilities. For instance, measuring textual similarity between patents is be a promising way to infer overlap between patents, and perhaps a way to infer knowledge transmission. Other methods include in-text citations to patents instead of relying upon front page citations (Ozcan and Bryan, 2017). We are agnostic about the importance of knowledge spillovers across space. Our findings do point to the potentially important role that organizational links play in knowledge transmission, and the important interactions between geographical and organizational proximity. Further, the role of specialized intermediaries, such as patent agents, and of the providers of specialized technical inputs, such as R&D and engineering services, may be promising avenues for future research. Methodologically, this study provides a way to isolate citations that are unlikely to be associated with knowledge transmission. We identify these special citations by checking whether the citing patent’s priority date comes before the priority date of the cited patent. We use these citations to benchmark localization of knowledge transmission as reflected in patent citations. Patent citations could reflect direct transmission of knowledge from the citing to the cited invention. However, it could also reflect commonalities in domain or solution to a specific technical problem. That is, the patents linked by citation may be linked not by knowledge transmission but by a body of knowledge that is common ground for both inventions. The distinction between an invention building on the cited invention and inventions drawing upon common, or background knowledge is important for both policy and firms. An inventor whose invention is built upon by another inventor might extract licensing revenues from the latter. However, if the subsequent inventor draws upon the background knowledge, then it would be difficult even to identify inventions that build on such knowledge. The distinction also provides insights into entrepreneurial spin-offs and regional clusters. If founders of spin-offs draw knowledge from specific discoveries during their employment at the parent company, then employers can develop contracts to prevent loss of rents. However, if knowledge drawn by the former employees is more general and cannot specifically be identified, then it would be more difficult for employers to protect themselves from former employees utilizing the knowledge. Furthermore, it would be difficult for firms to prevent background knowledge from spilling over to competitors even if they try to disperse inventors or R&D operations across different geographies. Indeed, to the extent that the background knowledge is useful for invention, such dispersion may be counter-productive. In summary, our findings force an uncomfortable choice between two very appealing and widely accepted beliefs, namely that knowledge transmission is less likely over longer distances and that patent citation is a good measure of knowledge transmission. Our empirical setup does not allow us to weigh in on this tradeoff. We look forward to future research for help. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Acknowledgements We would like to thank Wes Cohen for helpful discussions. All remaining errors are ours. Footnotes 1 This explanation leaves open the question of why people working on related problems are located close to each other. One reason could be that such problem solving requires specialized skills (i.e., labor pooling), or access to specialized knowledge that is available only in that region, such as from a local university. If the latter, there may well be knowledge spillovers at work, but not across inventors. 2 In fact, proponents of the ‘noisy signal’ interpretation of citations might even argue that finding a high degree of localization among reversed citations is consistent with the noisy signal view. If citations are just a noisy signal of inventive activity and do not mark actual sequential links between inventions, reversed links are likely and might be even expected. 3 A citation implies that the inventor, the patent agent or the examiner became aware of the cited invention. However, in citation reversals, the citing invention could not have benefited from this knowledge although the citing patent application may have been modified. 4 The issue is subtle. The inventor of a citing patent may acquire the required knowledge from the inventor of the cited patent. Alternatively, the inventor may learn from the cited patent, or the inventor of the cited patent, knowledge that is not unique to the cited invention. We address many of these issues in greater detail in Section 6, where we analyze the localization patterns in self-citations, citations inserted by examiners and citations made to unpublished patents. 5 We are assuming, for simplicity, that these are mutually exclusive outcomes. However, a citation may reflect both building upon and relatedness. In that case, the probability that j cites i if they are near is απn + βθn− αβπnθn. Both απn and βθn are very small in magnitude, so that the product term αβπnθn can be neglected. 6 Existing studies have tried to use patent classes to control for relatedness: It is implicitly or explicitly assumed that two patents in the same class are equally likely to be related independently of whether they are far or near. Formally, for patents in the same patent class, θn−θf =0. 7 The literature on submarine patents discusses how inventors can keep their inventions secret for an extended period of time and change claims using continuation applications (Graham and Mowery, 2004; Reitzig et al., 2007). The change described by the literature pertains to claims rather than inventions and is thus consistent with our assumption that the underlying invention does not change. 8 Continuing applications can be further broken down into continuation, divisional and continuation-in-part (CIP). Continuation applications make additional claims based on an existing invention specified in an earlier patent application while divisional applications are filed to separate out distinct inventions from an earlier application usually because the earlier one fails to meet the ‘unity of invention’ requirement. CIP applications can add extensions to an earlier invention, with claims on new subject matter taking as their priority date the application filing date of the CIP application. The prospect of adding extensions to an underlying invention is concerning since our test relies on the assumption that the underlying invention does not change over time. In Section 6, we run robustness tests after excluding CIP applications and applications claiming priority dates from a provisional application—two sources of potential changes in underlying inventions. Our main finding remains robust to these exclusions. 9 In cases with multiple inventor locations for a single patent, we use the city–state combination that occurs most frequently. If there is an equal number of different city–state combinations, we randomly choose a location among them. 10 Under ‘Patent citation lag’ in Section 6.1.3, we perform tests targeted specifically to address this timing issue. Given that the reversals in patent application filing time would be more likely to occur when inventions are created close in time, we test whether our main finding still holds if we re-categorize reversals with up to 1-year priority lag as non-reversals and at the same time use different citation lags. 11 For the sample matched on six-digit technology classification code, the average distance between citing and cited patents is 977 miles for citation non-reversals and 904 miles for reversals, with the difference statistically significant at the 1% level. 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( 2006 ) Conducting R&D in countries with weak intellectual property rights protection . Management Science , 52 : 1185 – 1199 . Google Scholar CrossRef Search ADS © The Author(s) (2018). Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Economic Geography Oxford University Press

Reversed citations and the localization of knowledge spillovers

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Abstract

Abstract Spillover of knowledge is considered to be an important cause of agglomeration of inventive activity. Many studies argue that knowledge spillovers are localized based on the observation that patents tend to cite nearby patents disproportionately. Specifically, patent citations are typically interpreted as marking the transmission of knowledge from the cited invention to the citing invention. The localization of patent citations is therefore taken as evidence that such knowledge transmission is also localized. Localization of knowledge transmission, however, may not be the only reason that patent citations are localized. Using a set of citations that are unlikely to be associated with knowledge transmission from the cited to the citing invention, we present evidence that challenges the view that localization of citations is driven by localized knowledge transmission. While we are silent on the question of whether knowledge transmission is localized, to the extent that such localization exists, we argue that it is unlikely to be captured by patent citations. 1. Introduction Regional clusters of economic activity are important sources of innovation and economic growth (Porter, 1990; Martin and Sunley, 2003). In the USA, there are over 40 clusters, accounting for more than 50% of traded employment in U.S. Economic Areas (Porter, 2007). At the same time, clusters vary in their economic and inventive output (Porter, 2003; Delgado et al., 2008; Suire and Vicente, 2009; Agrawal et al., 2014, 2017). These differences have attracted scholars to explore potential mechanisms that contribute to their success including labor market pooling (Krugman, 1991; Audretsch and Feldman, 1996; Rosenthal and Strange, 2001; Delgado et al., 2014), specialized resources (Swann, 1998; Porter, 1990, 2003) and knowledge spillovers (Jaffe et al., 1993; Audretsch, 1998; Giuliani, 2007). Other scholars have attributed the differences to cultural, institutional and ecological factors (e.g., Saxenian, 1994; Bathelt and Glückler, 2014; Sorenson, 2017). The growing importance of innovation and improved access to patent data have led scholars to use patent citations to study the localization of knowledge spillovers. In a seminal paper, Jaffe et al. (1993) find that a citing patent is 5–10 times more likely to be in the same SMSA as the cited patent than a matched non-citing patent. The authors and most subsequent studies (a) view patent citation as a marker for knowledge spillovers and (b) interpret the finding that citing and cited patents are co-located as evidence that knowledge spillovers are localized (Almeida and Kogut, 1999; Alćacer and Gittelman, 2006; Thompson, 2006; Belenzon and Schankerman, 2013; Singh and Marx, 2013; Murata et al., 2014). The current paper presents evidence inconsistent with the interpretation that localization of citations is driven by localized transmission of knowledge from the cited invention to the citing invention. While our paper is silent on the question of whether knowledge transmission across inventions is localized, to the extent that such localization exists, we argue that it is unlikely to be captured by patent citations. Our empirical test is as follows. We identify a set of citations that are unlikely to reflect knowledge transmission from the cited invention to the citing invention, which we label as ‘citation reversals’, and use these citations as a benchmark to compare the localization of citations for which knowledge transmission is possible, ‘citation non-reversals’. Citation reversals typically occur during the patent examination process when an inventor or an examiner cites a relevant patent. Because ascertaining priority dates (the earliest filing date of a patent on a specific invention) is not always straightforward, citation reversals might occur. If localization of citations is driven by localized knowledge transmission, we expect citation non-reversals to be more localized than citation reversals. There are at least two broad interpretations for the relationship between patent citations and knowledge spillovers. The first is that a citation from citing patent A to cited patent B indicates that A builds on B (e.g., Belenzon, 2012; Williams, 2013; Galasso and Schankerman, 2014). Patent citations are localized if inventors are more likely to learn from the inventions of nearby inventors. In other words, a citation indicates that inventions A and B are sequentially linked, and localization in this context means that sequential innovation is localized. By definition, the citing invention must come after the cited invention; thus, the temporal structure of the citation sequence is key. According to this view, our empirical test should shed new light on the interpretation of localized citations. The second interpretation builds on the view that knowledge is ‘in the air’. Accordingly, a citation from patent A to patent B indicates that some background knowledge embodied in invention B is relevant for invention A. Roughly speaking, a citation from A to B implies that the inventors of A are working on a similar problem as the inventors of B. Localization of citations means that inventors in the same locality are working on related problems, not that knowledge spillovers among inventions are necessarily localized.1 A variant of this interpretation is that a patent citation is a noisy signal of local unobserved interactions among inventors. These interactions can manifest as patent citations regardless of whether the citing and cited inventions are actually linked. Clearly, the temporal structure of citations is irrelevant in this case, rendering our empirical test not meaningful.2 However, this interpretation does not explain examiner-added citations, in contrast to where both A and B draw upon the same background knowledge. Moreover, this interpretation of citations as markers of interactions among inventors is at odds with the legal interpretation of citations as limiting the scope of the invention claimed in the patent. The distinction between drawing upon shared background knowledge and learning from specific inventions is important for several streams of research. An inventor whose invention is built upon by subsequent inventions can potentially extract licensing revenues from the latter. Indeed, the key questions analyzed in models of cumulative innovation are how to divide rents between sequential inventors (Green and Scotchmer, 1995), choosing patentability criteria or determining patent length and breadth (O’Donoghue et al., 1998; Bessen and Maskin, 2009). If, instead, the invention draws upon a common pool of knowledge, although the innovation may be cumulative, it would be very difficult for the inventor to identify subsequent inventions that build upon her invention (Laitner and Stolyarov, 2013). Other studies within cumulative innovation examine whether intellectual property rights hinder sequential innovation (Williams, 2013; Galasso and Schankerman, 2014). Their key assumption is that inventors build on the knowledge contained in specific inventions rather than on background knowledge. These studies interpret citations as sequential links between inventions. The distinction is also relevant for the study of entrepreneurial spinoffs and regional clusters. Inventors leaving existing employers to start their own firms could build upon either specific inventions (Anton and Yao, 1995) or more general background knowledge (Chatterji, 2009). If spinoffs, which are often co-located with parents, capitalize on discoveries employees make in the course of their employment, firms have the ability to design contracts to protect themselves. Such contrivances are less useful if spinoffs exploit more general knowledge learned in the course of their employment. The distinction being drawn is vital for innovation management and strategy scholarship. Firms concerned about protecting inventions from spillover to outsiders may try to disperse inventors (Zhao, 2006; Alćacer and Zhao, 2012) or locate them away from competitors (Shaver and Flyer, 2000; Alćacer and Chung, 2007). This strategy is likely to be more effective if inventors are in fact more likely to build upon co-located inventors. If, on the other hand, co-location of citation reflects a reliance upon common knowledge, dispersing inventive activity will merely hurt the firm. Using 1,356,738 USPTO citations and an equal number of control citations, we confirm the stylized fact that patent citations are localized. Our estimates imply that a 50-mile increase in distance between inventors is associated with a 19% reduction in the probability of citation (close to 40% of the sample’s average citation probability). However, when we compare non-reversals to reversals, we find that the two citation groups are equally as localized. That is, the probability of citations falls with distance at the same rate for both groups of citations. This finding is robust to a battery of tests and is inconsistent with the view that citations are localized because inventions are more likely to build on other close by inventions. The rest of the paper is organized as follows: Section 2 discusses the related literature, Section 3 describes the conceptual framework, Section 4 discusses the data, Section 5 presents the non-parametric results, Section 6 presents the estimation results and Section 7 concludes. 2. Related literature The study of knowledge spillovers using patent citations can be traced back to Jaffe et al. (1993) who argue that knowledge spillovers are localized because, as they demonstrate, patent citation pairs are significantly more likely than controls to be in the same geographic area. However, the relationship between citations and spillovers remains unclear in the Jaffe et al.’s (1993) paper and in most follow-up research. If a citation from inventor A to inventor B means that A builds on B, localization of citations would indicate that closely located inventors are more likely to build on one another. Thus, localization of citations would indicate that knowledge spillovers are localized. On the other hand, a citation might indicate that A and B are working on similar problems. Under this interpretation, localization of citations would reflect regional specialization, in that local inventors work on similar problems and draw from common background knowledge. These inventors might cite one another not because the citing invention builds on the cited invention, but because a citation is used to demarcate the citing invention from the cited invention. The present paper proposes an empirical test to help clarify the interpretation of localized citations. At a minimum, it pushes authors to take a clearer stand on whether they view citations as a sequential link between patented inventions or as a noisy measure of related inventive activity whereby the citing patent may not necessarily build on the cited patent. Our discussion in Section 1 explains why this distinction is important. There are numerous studies on knowledge spillovers and regional clusters that utilize patent citations to examine whether knowledge spillovers are localized (e.g., Verspagen and Schoenmakers, 2004; Belenzon and Schankerman, 2013; Nomaler and Verspagen, 2016) and whether co-located firms benefit from localized knowledge spillovers (e.g., Zhao, 2006; Alćacer and Zhao, 2012; Menon, 2015). While these studies demonstrate that citations are localized, they are usually unclear on whether this localization is due to local transmission of knowledge from the cited to the citing patent (localized sequential innovation), or due merely to co-location of related inventive activities. Consequently, empirical results interpreted as indicating localized knowledge spillovers may instead reflect unmeasured factors that make some regions better suited for a certain type of inventive activity relative to other regions. For instance, Verspagen and Schoenmakers (2004) examine whether regional concentration of R&D activities is beneficial to large multinational corporations. The study uses patent citations to argue that knowledge spillovers are localized. Although the study shows that patents citing each other are located closer than otherwise similar patent pairs that do not cite each other, its argument relies on the assumption that patent citations reflect knowledge spillovers from the cited to the citing inventors. In a more recent study that looks at spatial characteristics of technology trajectories, Nomaler and Verspagen (2016) use citation pairs and citation sequences linking multiple patents to show that, although direct citations tend to be geographically localized, citation sequences run across clusters. The authors interpret inter-cluster citations as knowledge flows between the clusters where citing and cited patents are generated. In exploring how firms might benefit from localized knowledge spillovers, Menon (2015) examines the extent to which the presence of highly innovative firms in a region, measured by the number of patents generated, influences the number of patents generated by other firms in the same region. The study shows that locally cited patents generated by the most innovative firms is positively associated with patents generated by other firms in the same MSA. Menon (2015) argues that the greater patenting activity of a region in the presence of highly innovative firms is due to knowledge spillovers. Additionally, Alćacer and Zhao (2012) examine how multinational firms might minimize knowledge outflow from their inventive activities when the activities are co-located with those of their competitors. They find that strong intra-firm interdependence between inventive activities across different regions can reduce expropriation of their knowledge by their competitors. The study uses self-citations and citations made to a firm’s patent by other firms to measure knowledge appropriation and expropriation. In particular, it interprets a citation made by A to B as reflecting the use of B’s knowledge by A. Other studies try to uncover potential mechanisms underlying the localization of citations. An influential stream of research examines inventor mobility. This line of work identifies inventors’ intra-regional mobility based on inventor addresses and patent assignees and examines the relationship between mobility and localized citations. The studies show that citations are local partly because inventor mobility is local. Almeida and Kogut (1999) identify the top 20 inventors in terms of number of forward citations and estimate the effect of their mobility on intra-regional citations. The authors find a positive relationship between mobility of top inventors within a region and the probability that a patent cites another patent in the same region. This finding is interpreted as evidence that inventors’ tendency to stay in a specific region drives the localization of knowledge spillovers in that region. In a related study, Breschi and Lissoni (2009) use patent citations data from the European Patent Office to examine the contribution of inventor mobility to localized knowledge spillovers. The study compares the probability that citing and cited patents are in the same MSA with and without inventor self-citations (inventors citing their own patents) after excluding firm self-citations (where the citing and the cited patent are generated by the same firm). They find that the localization effect drops substantially when inventor self-citations are excluded and interpret this finding as evidence that knowledge spillovers are localized because inventors tend to stay within the same geographical region. Another reason why citations might be localized is that they can be added by local intermediaries. Wagner et al. (2014) argue that patent attorneys build their knowledge repositories while interacting with their clients and reference patents from those repositories when they prepare new patent applications. If patent attorneys are engaged primarily with local inventors and knowledge repositories are built using the inventions of those local inventors, then patent citations added by patent attorneys would likely be localized. Yet other studies utilize examiner-added citations to test whether inventor-added citation pairs exhibit localization patterns as documented in prior studies. Thompson (2006) utilizes examiner-added citations, which is argued to be less likely to reflect knowledge spillovers than inventor-added citations (unless, of course, the examiner is merely correcting for willful omission or oversight on the part of the inventor) and shows that inventor-added citations are more localized than examiner-added citations. Nonetheless, the crucial assumption of the study is that patent citations reflect knowledge spillovers. Alćacer and Gittelman (2006) also focus on examiner citations to see whether any systematic differences exist between inventor-added and examiner-added citations that might bias the widespread finding that knowledge spillovers are localized. They find that while examiner-added citations tend to track inventor-added citations fairly closely in terms of distance between citing and cited patents, including examiner-added citation pairs in the study of knowledge spillovers could bias the results under certain conditions. In recent years, some studies have cast doubt on the interpretation of patent citations and the notion of localized knowledge spillovers. In their critical review of the localized knowledge spillovers literature, Breschi and Lissoni (2001) argue that prior studies have not been clear about the notion of localized knowledge spillovers and that the conceptual framework of localized knowledge spillovers needs to be reassessed and improved. They also argue that more studies should examine the mechanisms underlying localized knowledge spillovers, such as labor mobility and role of university and research institutions. More recently, Sorenson (2017) argued that temporal changes in region-specific entrepreneurial vibrancy, which is closely tied to both economic and inventive output of the region, can be explained more logically by ecological factors than by access to knowledge. To support this argument, Sorenson (2017) points out that while improvements in a region’s knowledge capital require decades, changes in the regional level of entrepreneurial activities can occur in a matter of years. Furthermore, Thompson and Fox-Kean (2005) argue that the matching approach in Jaffe et al. (1993) is too coarse and does not adequately control for existing regional specialization. Imposing stricter matching criteria, they find that the localization effect almost disappears at the SMSA and state levels. In a response to this criticism, Henderson et al. (2005) argue that the lack of localization in Thompson and Fox-Kean (2005) is likely to be due to selection bias arising from inability to match a substantial portion of patents at the subclass level, which in turn drastically reduces sample size. In their re-examination of the findings from Jaffe et al. (1993) and Thompson and Fox-Kean (2005), Murata et al. (2014) use distance-based K-density tests to show that citation pairs are more localized than control pairs in about 30% of technology areas when citing and control patents are matched on six-digit technology classification codes. There is also a broader debate on the meaning of patent citations (Jaffe et al., 2000; Duguet and MacGarvie, 2005; Roach and Cohen, 2013; Moser et al., 2017). Using survey data, Roach and Cohen (2013) show that patent citations are likely to underestimate knowledge transmission from university research and overestimate knowledge transmission between firms when firms engage in strategic citation to mitigate patent invalidation risk. In another survey, Duguet and MacGarvie (2005) show that citations are associated with technology flows through some channels (e.g., equipment sales), but not through others (e.g., R&D outsourcing). Additional survey evidence by Jaffe et al. (2000) shows that one-third of inventors did not learn about the inventions they cited until the citing invention was completed and that close to one-third of inventors did not learn about the cited inventions until the time of the survey. In other words, two-thirds of the citations did not reflect knowledge transfer between the cited and citing inventions. Using data from field trials for hybrid corn, Moser et al. (2017) show that self-citations are likely to capture follow-on inventions, but not citations added by examiners. In summary, patent citations have been widely used in the literature to study knowledge spillovers within and across inventors, firms and regions. However, the assumption that patent citations reflect knowledge spillovers has not been thoroughly tested. As a result, conclusions that use patent citations as a measure of knowledge transmission between the cited and citing patents are open to question. In this paper, we focus on the notion that knowledge spillovers are localized because patent citations are localized. We argue that the evidence presented in this paper is inconsistent with the view that patent citations are localized because inventions are more likely to build on other local inventions. Put differently, our results imply that either patent citation is a poor measure of knowledge spillover or that knowledge spillover is not localized. 3. Preliminary concerns 3.1. Reversed citations and local interactions To test whether the localization of citations is driven by localized knowledge transmission, we identify a set of citations that are not likely to be driven by knowledge transmission, ‘citation reversals’. If localization of citations is driven by localized knowledge transmission, we expect citation non-reversals to be more localized than citation reversals. An important concern about our methodology is that citation reversals might reflect highly localized knowledge transmission among local inventors who share knowledge about new ideas and inventions that have not been disclosed to the public. If this were true, reversed citations would be localized due to highly localized knowledge transmission and our key assumption that reversed citations are not associated with knowledge transmission would be violated. Table 1 summarizes different mechanisms through which both knowledge about inventions and background knowledge could be transmitted, including those that might lead to citation reversals. There are three main learning mechanisms indicated by Columns 1–3. The first is learning from patent documents—learning about inventions by reading published patent documents. There is no reason to expect this type of learning to be localized. Thus, we are not concerned that learning from patent documents would generate localized citation reversals. The second mechanism is learning about inventions from inventors. In this case, inventors might share among themselves knowledge about new inventions. Such learning might be localized if inventors tend to discuss their inventions more frequently with nearby inventors than faraway inventors. The third source of learning is patent intermediaries, such as patent attorneys. By using the same patent attorneys, inventors might learn about new inventions before they are disclosed to the public. Because inventors are more likely to use the same patent attorneys if they are near one another, engaging with patent attorneys might generate localized citation reversals. Table 1 Types and sources of knowledge Notes: This figure shows the types and sources of knowledge distinguished in the paper. Knowledge about invention is knowledge directly related to the invention while background knowledge is knowledge that might underlie the invention and can be drawn upon from a common knowledge pool. Knowledge can also have multiple sources that can influence temporal and geographical characteristics of knowledge transmission. The six inner cells indicate whether knowledge tends to be localized given its type and source. Table 1 Types and sources of knowledge Notes: This figure shows the types and sources of knowledge distinguished in the paper. Knowledge about invention is knowledge directly related to the invention while background knowledge is knowledge that might underlie the invention and can be drawn upon from a common knowledge pool. Knowledge can also have multiple sources that can influence temporal and geographical characteristics of knowledge transmission. The six inner cells indicate whether knowledge tends to be localized given its type and source. Section 6 presents several tests aiming at mitigating the concern that reversals are generated through highly localized learning. 3.2. Comparing the localization effect of reversed and non-reversed citations We propose the following motivation for why localized knowledge transmission might lead to a stronger negative effect of distance on citation probability for citation non-reversals than for reversals. We distinguish between citations that reflect knowledge transmission, i.e., where one invention builds upon another, improving or extending it, and citations that reflect other relationships, where no such knowledge transmission takes place. A patent may cite another patent because both draw upon a common pool of knowledge. Patents may be related in other ways as well. For instance, the citing patent may accomplish the same outcome as the cited patent using a different method or use similar methods to accomplish different goals. The distinction bears on whether the citing invention benefited from the knowledge created in the form of the cited invention. The citing inventions that are related would be unaffected. The citing invention that builds upon the cited invention would have had to acquire the knowledge created by the cited invention. The extant literature has implicitly or explicitly assumed that, when patent class is controlled for, citations reflect knowledge transmission. We argue that citation reversals, by construction, cannot reflect knowledge transmission from the cited invention to the citing invention.3 It is conceivable that the inventor may have learned useful knowledge from the inventor of the cited invention, but it is far more likely that a citation reversal represents the recognition of a related invention, albeit one that should not have been cited because it is not prior art.4 We do not observe whether a citation represents transmission of knowledge or merely some type of relatedness. Instead, we propose a simple structure that clarifies how one can infer the relative importance of the two types of citations in generating the observed pattern of localization of patent citations. If citation reversals reflect relatedness, and if knowledge transmission falls with distance, then citation reversals should be less localized than non-reversals. Consider a pair of patents i and j, where i is the focal patent and j is invented after i. Patent j can build upon patent i with probability πn if it is near and πf if it is far. With probability θn, patent j can be related to patent i if they are near each other and θf if they are far apart. For simplicity, assume a patent that builds upon another will cite it with probability α. Similarly, a patent that is related to another will cite with probability β. The probability that j cites i if they are near is απn + βθn.5 Similarly, the probability of a citation if they are far apart is απf + βθf. The difference in probability of citation between patents located near each other and patents located far is α(πn−πf) +β(θn−θf).6 This difference has two components: πn−πf representing the extent to which knowledge transmission decreases with distance, and θn−θf representing the extent to which patents near each other are related relative to those far apart. Each component is weighted by the relevant citation propensity. The consensus is that both components are positive. That is, nearby inventions are more likely to be related and knowledge transmission is more likely among nearby inventions. Now consider the probability that i cites j, that is, a citation reversal. Since i cannot have built upon j, the probability of the patents being related is simply θn if they are near each other and θf if they are far. If the propensity to cite is β as before, difference in probability of citation between near and far is simply β(θn−θf). The effect of proximity on the probability of citation for non-reversals is α(πn−πf) +β(θn −θf) so that the difference in the effect of proximity with respect to reversals is α(πn−πf). The extant literature has asserted that knowledge transmission increases with proximity, that is, α(πn− πf) > 0. This implies that the effect of proximity on the probability of a citation reversal should be smaller than the effect of proximity on the probability of a non-reversal citation. In the empirical analysis we use distance, so that we expect that distance should have a smaller absolute effect on reverse citations than on normal or non-reversal citations. The validity of our test hinges on the assumption that the underlying knowledge described in a patent cannot be changed as the patent moves forward in the examination process. This assumption assures that the priority date is the date when the invention is created and allows us to determine whether knowledge could have been transmitted from one invention to another. This assumption is validated by the two statutory provisions, 35 U.S.C. 132 and 35 U.S.C. 251, which prohibit introduction of new matter in amendments and the application for reissuance. Examiners are obligated to reject new matters introduced into the abstract, specification or drawings of a patent application once it is filed. The only changes permitted are rephrasing of a passage without changes in meaning and fixing obvious errors whose correction can be foreseen by a person skilled in the given art.7 If so, the transmission of knowledge cannot take place in citation reversals. 4. Data 4.1. Sample Our main sample is from the 2014 version of EPO Worldwide Patent Statistical Database (PatStat) with inventor distances extracted from Google Maps. We follow previous literature and limit our dataset to USPTO patents with inventors residing in the contiguous USA. Thus, we exclude Hawaii, Alaska and offshore U.S. territories, such as Puerto Rico and Guam. The publication years of the citing patents range from 2001 to 2014. (Sample years are based on the availability of examiner citations, which as we later explain are an important part of our analysis.) Whenever multiple inventors are listed for a single patent, we take the city–state combination that occurs most frequently in our distance calculation. If there is an equal number of different city–state combinations, we randomly choose a location from them. Finally, we retain only the citations with a priority lag (difference in years between the priority dates of citing and cited patents) less than 5 years. This restriction is to account for the fact that citation reversals have short priority lags and in turn to ensure that reversals and non-reversals remain comparable. This procedure yields 1,356,738 actual citations. For each pair of patents connected by a citation, we match the citing patent with another patent, to create a control pair. We construct the control group by matching each citing patent in the actual citations with a randomly selected, non-citing patent on four-digit IPC and publication year (Jaffe et al., 1993; Belenzon and Schankerman, 2013). These control patents are paired with the cited patents from the actual citations to form control citations. The sample includes 2,713,476 observations consisting of both actual and control citations. 4.2. Variable definitions We proceed to describe the main variables used in the analysis. Online Appendix Table A1 summarizes their definitions and sources. 4.2.1. Priority date A central piece in our analysis is identifying priority dates, which are used to determine whether a citation is a reversal. Priority date is the earliest application date of the patents that relate to the same underlying invention (also known as a patent family). It is the date when the invention was first recognized by a patent issuing authority to be in existence. A patent can claim as its priority date the application filing date of an earlier patent if the two patents describe the same invention and share at least one inventor. Priority dates can be claimed via different types of patent applications. Among the most common are applications taking advantage of a provisional application filed for the same invention; continuing applications that extend a prior application8; and applications filed in the USA within 12 months of filing a foreign application for the same invention. In all of these cases, to claim an application filing date of an earlier patent as the priority date, the specifications of the underlying invention described in the earlier and subsequent patents must be the same. For example, US 7333597 is a patent on technology that enables telephone synchronization with software applications and documents. The inventors on the patent are Edward M. Silver, Linda A. Roberts and Hong T. Nguyen. The application for this patent was filed on 2 November 2004. However, the priority date of the patent is 29 March 2002, based on an earlier patent, US 6873692, which relates to the same invention and has the same inventors. Because US 7333597 is a continuation of US 6873692 and because the underlying invention and at least one inventor are the same between the two patents, the more recent patent (US 7333597) can claim as priority date the application filing date of the earlier patent (US 6873692). Identifying an earlier patent application from which to take the priority date is not always trivial because an invention may be associated with multiple patent applications with different application filing dates. For this particular example, we went to the USPTO’s patent application information retrieval website to look up all of the patents in the patent family of US 7333597 and looked for the patent application with the earliest filing date. (Online Data Appendix describes how we find the priority dates of the patents in our sample using PatStat). In our sample, 61% of citing patents and 35% of cited patents claim priority dates from an earlier patent application. Of the 61% of citing patents, 59% claim priority based on a provisional application, 40% on a continuing application and 1% on a foreign application. Of the 35% of cited patents, 59% claim priority based on a provisional application, 39% on a continuing application and 2% on a foreign application. Thirty-nine percent of citing patents and 65% of cited patents that do not claim priority dates from an earlier application (Online Appendix Figure A1 presents a breakdown of applications based on the types of priorities they claim). 4.2.2. Citation reversal We construct citation reversals for which transmission of knowledge from the cited to the citing patent is unlikely. The primary type of citation reversals occurs when the priority yearof the citing patent is earlier than the priority year of the cited patent. We refer to this type of citations as ‘priority reversals’. Priority reversals are not likely to reflect knowledge transmission because the cited invention does not exist at least until the citing invention is created. (We explore a secondary type called ‘disclosure citations’ in Table 5 of the robustness section.) Priority reversals occur in about 4% (58,983) of all actual citations in our sample. Priority reversals occur because priority dates are not always transparent to applicants without an extensive search. Although examiners are supposed to review applicant citations for accuracy and appropriateness, the examination process is not fully automated and thus a related patent may be incorrectly cited as prior art when it is not. According to our conversations with patent attorneys and patent examiners, priority reversals can arise when patent applicants include citations on the information disclosure statement or when patent examiners add additional citations during the patent examination process that begins after the patent application is filed. Some patents have a priority date earlier than their filing date, for instance, because they are related to a foreign patent or they are continuations of an earlier patent. These types of patents require more effort in identifying priority dates, and thus applications involving them are more prone to having priority reversals. An example of a priority reversal is patent US 8484303 citing patent US 8073918 (a graphical illustration and transaction highlights are also shown in Online Appendix Figure A4). Patent US 8484303 was filed on 20 September 2011 and US 8073918 was filed on 6 August 2010. However, the invention described in US 8484303 was created on 17 February 2000 while the invention described in patent US 8073918 was created on 21 April 2004. Thus, the priority year of the citing patent is prior to the priority year of the cited patent. We illustrate priority reversals using the timeline in Figure 1. The horizontal line going from left to right represents the progression of time, and the vertical lines extending below the timeline represent the priority date and the earliest publication date of a cited patent. The two vertical lines extending above the timeline represent possible instances of the citing patent’s priority date. A priority reversal occurs when an invention references another invention that has not been created, as demonstrated by the first instance of the citing patent’s priority date coming before the priority date of the cited patent. A non-reversal occurs when an invention references another invention that has been created and disclosed to the public, as demonstrated by the second instance of the citing patent’s priority date falling after the earliest publication date of the cited patent. In this case, knowledge is more likely to have been transmitted from the cited to the citing invention. Figure 1 View largeDownload slide Priority reversal. Notes: This figure presents how priority reversals occur. Priority reversals are citations where the priority date of the citing patent comes before the priority date of the cited patent. The priority date of the citing patent in non-reversals comes after both the priority date and the earliest publication date of the cited patent. Figure 1 View largeDownload slide Priority reversal. Notes: This figure presents how priority reversals occur. Priority reversals are citations where the priority date of the citing patent comes before the priority date of the cited patent. The priority date of the citing patent in non-reversals comes after both the priority date and the earliest publication date of the cited patent. 4.2.3. Geographical distance We calculate distances between citation pairs using PatStat’s inventor addresses dataset and Google Maps API. We first extract inventor city and state information from PatStat’s inventor addresses dataset and then use a custom software application that communicates with Google Maps Geocoding API to obtain geographical coordinates and straight-line distances between inventors of citing and cited patents.9 In addition to continuous distance, we construct dummy variables for distance ranges to examine the nonlinear effect of distance on citation probability. The reference range is 0–25 miles and the rest of the distance ranges are as follows: 25–50, 50–100, 100–150, 150–250, 250–500, 500–1000, 1000–1500, 1500–2500 and >2500. 5. Non-parametric evidence Table 2 presents summary statistics for the main variables used in the analysis. The average distance between patents linked by a citation is 950 miles with a standard deviation of 892 miles. Four percent of the citations are priority reversals and 33% of the citations are added by examiners. On average, a citing patent receives 6 and cited patents receive 48 forward citations. Of the citations, about 14% are coast-to-coast citations and thus we add dummies to control for citations between research clusters that are located in the opposite coasts. Table 2 Summary statistics for main variables Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Notes: This table provides summary statistics for the main variables used in the econometric analysis of the effect of distance on citation probability for the main sample. The sample consists only of actual patent citations. The publication years of citing patents in the sample covers years 2001–2014. Priority lag is the difference between the priority years of the citing and cited patents. Dummy for reversal is a variable that takes 1 if the priority date of the citing patent is earlier than the priority date or the earliest publication date of the cited patent and indicates that knowledge transmission is unlikely. Dummy for examiner citation is a variable that takes 1 if a citation was added by a patent examiner. Dummy for self-citation is a variable that takes 1 if the citing and cited patents are assigned to the same assignee. Table 2 Summary statistics for main variables Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Distribution Variables Number of observation Mean Standard deviation 10th 50th 90th Citing priority year 1,356,738 2004 3.3 1999 2004 2008 Cited priority year 1,356,738 2000 3.2 1996 2000 2005 Citations per citing patent 1,356,738 6.4 14.1 0 2 16 Citations per cited patent 1,356,738 48.0 80.6 4 22 115 Priority lag in years 1,356,738 3.2 1.6 1 3 5 Dummy for priority reversal 1,356,738 0.04 0.20 0 0 0 Dummy for examiner citation 1,356,738 0.33 0.47 0 0 1 Dummy for self-citation 1,356,738 0.20 0.40 0 0 1 Distance (miles) 1,356,738 950.4 891.6 6 707 2414 Dummy for 0≤Distance<25 miles 293,769 7.9 7.6 0 7 19 Dummy for 25≤Distance<50 miles 53,786 34.1 6.6 26 33 44 Dummy for 50≤Distance<100 miles 23,256 73.3 14.4 54 73 94 Dummy for 100≤Distance<150 miles 21,960 125.1 15.2 104 125 146 Dummy for 150≤Distance<250 miles 48,873 201.7 28.9 161 202 241 Dummy for 250≤Distance<500 miles 121,888 370.5 66.3 280 362 466 Dummy for 500≤Distance<1000 miles 250,952 737.4 144.6 545 715 944 Dummy for 1000≤Distance<1500 miles 147,507 1270.3 165.0 1043 1271 1473 Dummy for 1500≤Distance<2500 miles 300,460 2026.6 326.2 1572 2057 2430 Dummy for Distance≥2500 miles 94,287 2593.0 60.3 2527 2568 2682 Notes: This table provides summary statistics for the main variables used in the econometric analysis of the effect of distance on citation probability for the main sample. The sample consists only of actual patent citations. The publication years of citing patents in the sample covers years 2001–2014. Priority lag is the difference between the priority years of the citing and cited patents. Dummy for reversal is a variable that takes 1 if the priority date of the citing patent is earlier than the priority date or the earliest publication date of the cited patent and indicates that knowledge transmission is unlikely. Dummy for examiner citation is a variable that takes 1 if a citation was added by a patent examiner. Dummy for self-citation is a variable that takes 1 if the citing and cited patents are assigned to the same assignee. Table 3 presents the mean comparisons of the main variables used in the analysis for citation reversals and non-reversals. The comparison of geographical distances shows that reversals are at least as localized as non-reversals. The average distance between citation pairs is 860 miles for reversals and 954 miles for non-reversals. The share of citations with citing patents that are within 50 miles of the cited patent is 33% for reversals and 25% for non-reversals. These findings are inconsistent with the view that localization of citations is driven by localized knowledge transmission. Table 3 Comparisons of main citation characteristics: non-reversals vs. reversals (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 Notes: This table presents mean comparisons of main variables between non-reversals and reversals. The sample consists of actual patent citations. The publication years of citing patents covers years 2001–2014. **p < 0.01, *p < 0.05. Table 3 Comparisons of main citation characteristics: non-reversals vs. reversals (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 (1) (2) (3) (4) (5) (6) (7) Difference in means Non-reversals Reversals Variables (3)−(6) Number of observation Mean Standard deviation Observation Mean Standard deviation Distance (miles) 94.21** 1,297,755 954.49 890.89 58,983 860.28 901.55 % of citations within 50 miles −0.08** 1,297,755 0.25 0.43 58,983 0.33 0.47 Citing priority year 4.05** 1,297,755 2004 3.17 58,983 2000 3.41 Cited priority year −1.20** 1,297,755 2000 3.18 58,983 2001 3.26 Citations per citing patent 0.75** 1,297,755 6.41 14.06 58,983 5.66 15.02 Citations per cited patent 10.54** 1,297,755 48.43 81.18 58,983 37.89 64.69 Citation lag in years 5.25** 1,297,755 3.39 1.23 58,983 −1.86 1.12 Dummy for examiner citation 0.01** 1,297,755 0.33 0.47 58,983 0.32 0.47 Fraction of self-citations −0.09** 1,297,755 0.19 0.40 58,983 0.28 0.45 Fraction of citations in the same IPC −0.05** 1,297,755 0.20 0.40 58,983 0.25 0.43 Notes: This table presents mean comparisons of main variables between non-reversals and reversals. The sample consists of actual patent citations. The publication years of citing patents covers years 2001–2014. **p < 0.01, *p < 0.05. Figure 2 presents comparisons of average distances between citing and cited inventors across various types of citations as well as the share of citations with citing inventors within 50 miles of cited inventors. The general pattern shows that the average distance is greater for non-reversals than for reversals. Furthermore, the fraction of citing inventors within 50 miles of the cited inventors is greater for reversals than for non-reversals. These results provide further evidence inconsistent with the notion that localization of citations reflects localized knowledge transmission. Figure 2 View largeDownload slide Average distance between inventors by citation type. Notes: This figure compares localization of citations across different citation types. ‘Fraction within 50 miles’ is the fraction of citations whose inventors reside within 50 miles of each other. The sample contains actual citations with citing patents covering years 2001–2014 and includes only priority reversals. Figure 2 View largeDownload slide Average distance between inventors by citation type. Notes: This figure compares localization of citations across different citation types. ‘Fraction within 50 miles’ is the fraction of citations whose inventors reside within 50 miles of each other. The sample contains actual citations with citing patents covering years 2001–2014 and includes only priority reversals. 6. Econometric analysis Our empirical analysis tests the implication of the model from Section 3.2. We examine whether the effect of distance on citation probability is smaller in magnitude for reversals than for non-reversals. As shown in the model, this relationship will hold if localization of citations is driven by localized knowledge transmission. We follow Jaffe et al. (1993) and match each citing patent with a control, non-citing, patent with the same four-digit IPC code and publication year. Our results are robust to matching at the six-digit IPC code and publication year, though a finer matching naturally reduces the sample size (cf. Online Appendix Table A5). We use a linear probability model to estimate the effect of distance on citation probability for non-reversals and reversals. Our main empirical specification is as follows: Pr(Cij = 1) = β1 ln Dij + β2 ln Dij × Reversalij + β3Reversalij + Z′γ + ηj + εij, where i and j denote citing and cited patents, respectively, Cij is a dummy variable that receives the value of 1 for an actual citation and zero for a control (non-)citation, Dij is the distance in miles between the location of citing and cited inventors and Reversalij is a dummy variable that receives the value of 1 for a citation reversal (and for the matched control non-citing patent). Z is a vector of dyadic dummies indicating citations between leading research clusters (i.e., Austin, TX; Route 128, MA; Raleigh-Durham, NC; San Diego, CA and Silicon Valley, CA). These dyadic research cluster dummies are important because patents produced in clusters specializing in similar inventions are likely to cite one another and the clusters are often located on opposite coasts. The stochastic components are represented by ηj, a cited patent-fixed effect and an iid error term εij. Standard errors are always clustered at the cited patent level. If localization of citations is driven by localized transmission of knowledge, we expect the effect of distance on citation probability to be larger in magnitude for non-reversals than for reversals. Thus, we expect β̂1< 0 to confirm previous evidence on localized citations and β̂2> 0 to support the view that citations with potential knowledge transmission (non-reversal) are more localized than citations where knowledge transmission is unlikely (reversal). 6.1. Results 6.1.1. Reversal vs. non-reversal localization effect Table 4 presents the results from our main test for localized transmission of knowledge in patent citations. Column 1 presents the estimation results for the effect of distance on the probability of citation. Consistent with previous findings in the literature, the results show that patent citations are localized. The coefficient estimate on the distance between citing and cited patents is negative and statistically significant, indicating that two inventors who are geographically close to each other are more likely to cite than inventors who are far away from each other. Column 2 explores the effect of distance on citation probability using distance dummies. The reference distance is 0–25 miles. Based on our estimates, moving from 0 to 50 miles between inventors lowers the probability of citation by about 19 percentage points, or close to 40% of the sample average. Table 4 The effect of distance on the probability of citation for citation non-reversals vs. reversals Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Notes: This table presents the effect of distance on citation probability for non-reversals and priority reversals. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. Publication years of the citing patents range from 2001 to 2014. Distance dummies are included to show non-linear effect of distance for different distance ranges. (The reference category is 0–25 miles.) The time lag between priority years of the citing and cited year is limited to ±5 years. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors are robust to heteroskedasticity and clustered at the cited patent application level to allow for correlation among patents citing the same patent. **p < 0.01, *p < 0.05. Table 4 The effect of distance on the probability of citation for citation non-reversals vs. reversals Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) (6) (7) Distance effect Nonlinear distance effect Variables All All All Non-reversal Reversal Non-reversal Reversal Log(Distance) −0.083** −0.080** −0.081** −0.079** (0.000) (0.000) (0.000) (0.002) Log(Distance)×dummy for reversal −0.020** (0.001) Dummy for reversal −0.138** (0.006) Dummy for 25≤Distance<50 miles −0.189** −0.182** −0.225** (0.003) (0.003) (0.023) Dummy for 50≤Distance<100 miles −0.396** −0.386** −0.414** (0.004) (0.005) (0.030) Dummy for 100≤Distance<150 miles −0.439** −0.424** −0.495** (0.004) (0.005) (0.029) Dummy for 150≤Distance<250 miles −0.455** −0.443** −0.478** (0.003) (0.003) (0.022) Dummy for 250≤Distance<500 miles −0.482** −0.467** −0.489** (0.003) (0.003) (0.016) Dummy for 500≤Distance<1000 miles −0.476** −0.464** −0.471** (0.002) (0.002) (0.014) Dummy for 1000≤Distance<1500 miles −0.521** −0.507** −0.508** (0.002) (0.003) (0.015) Dummy for 1500≤Distance<2500 miles −0.516** −0.501** −0.510** (0.002) (0.002) (0.012) Dummy for Distance≥2500 miles −0.470** −0.455** −0.476** (0.003) (0.003) (0.016) Tech cluster controls Yes Yes Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Yes Yes Number of reversals 196,256 196,256 196,256 0 196,256 0 196,256 Observations 2,713,476 2,713,476 2,713,476 2,517,220 196,256 2,517,220 196,256 R2 0.079 0.083 0.093 0.096 0.728 0.100 0.730 Notes: This table presents the effect of distance on citation probability for non-reversals and priority reversals. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. Publication years of the citing patents range from 2001 to 2014. Distance dummies are included to show non-linear effect of distance for different distance ranges. (The reference category is 0–25 miles.) The time lag between priority years of the citing and cited year is limited to ±5 years. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors are robust to heteroskedasticity and clustered at the cited patent application level to allow for correlation among patents citing the same patent. **p < 0.01, *p < 0.05. Columns 3–5 present our key findings from comparing the estimated effect of distance on citation probability between non-reversals and reversals. If localization of citations reflects localized transmission of knowledge, then we would observe a significantly larger effect of distance on citation probability for non-reversals than for reversals. Column 3 reveals that the effect of distance on citation probability is −0.08 for non-reversals and −0.10 for reversals, indicating that citation reversals are at least as localized as citation non-reversals. Columns 4 and 5 also show no difference in the effect of distance on citation probability for subsamples consisting separately of non-reversals and reversals. Columns 6 and 7 explore the robustness of the results by allowing for non-linear distance effects. The same pattern of results emerges. For example, moving from 0 to 50 miles reduces the citation probability by 18.2 percentage points for non-reversals and 22.5 percentage points for reversals. These findings are inconsistent with the interpretation that localization of citations reflects localized knowledge transmission since citations do not become more localized as transmission of knowledge becomes more likely. They are consistent with the view that local inventors tend to work on similar technical problems, but not necessarily disproportionately learn from one another. 6.1.2. Do inventor interactions drive localized reversals? An important concern about our analysis is that citation reversals might be driven by interactions among local inventors and/or patent intermediaries. If citation reversals are driven by inventors sharing knowledge about new inventions before the inventions are publicly disclosed, then reversals would reflect highly localized knowledge transmission. For instance, it is possible that two local inventors work on related ideas and that knowledge is transmitted from one invention to the other. If, however, the invention building on the other invention is filed for a patent before the invention being built on and a citation is made from the former to the latter, then this priority reversal would capture knowledge transmission.10 In such cases, reversals could not be used as a benchmark for the localization of non-learning citations against which citation non-reversals are compared. This section presents several tests to mitigate this concern. 6.1.2.1. Self-citations If local inventors interact with one another to share knowledge about unpublished inventions, such interactions are more likely to occur within firms than across firms. Thus, if citation reversals were driven by highly localized inventor interactions, self-citations would be more prevalent within reversals than within non-reversals and more localized than external citations. This bias will prevent us from rejecting the null hypothesis that the localization effect of non-reversals is the same as that of reversals. The share of self-citations is 28% for reversals and 19% for non-reversals. Self-citations are also more localized than external citations. The share of citations whose citing patent is within 50 miles of the cited patent is 75% for self-citations and 14% for external citations. (These differences are statistically significant at the 1% level.) Within citation reversals, self-citations are also more localized than external citations (80% of citing patents being with 50 miles of cited patents for self-citations relative to 15% for external citation reversals). These findings are consistent with the concern that reversals might be driven by highly localized knowledge transmission. To mitigate the potential bias caused by self-citations, we exclude them from our sample. Columns 1 and 2 of Table 5 present the estimation results. The results show that the effect of distance on citation probability is still quite similar between citation non-reversals (−0.045) and reversals (−0.035) and thus confirm our main finding that citation reversals are as localized and as non-reversals. Table 5 Priority reversals and local inventor interactions Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Notes: This table presents results from comparing localization of citation non-reversals with different subsets of priority reversals and disclosure citations. Disclosure citations are citations that occur when the priority date of the citing patent comes before the priority date but after the earliest publication date of the cited patent. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. All columns exclude self-citations. Publication years of the citing patents range from 2001 to 2014. The time lag between priority years of the citing and cited year is limited to ±5 years. Standard errors are clustered at the cited patent level to allow for correlation among patents citing the same patent. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors, in parenthesis, are robust to heteroskedasticity. **p < 0.01, *p < 0.05. Table 5 Priority reversals and local inventor interactions Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Dependent variable Dummy for an actual citation (1) (2) (3) (4) (5) Non-reversals Priority reversals Disclosure citations Variables Excl. self- citation Excl. self- citation Excl. PA cites Examiner reversals Excl. self- citations Log(Distance) −0.045** −0.035** −0.031** −0.043** −0.044** (0.001) (0.003) (0.003) (0.010) (0.001) Tech cluster controls Yes Yes Yes Yes Yes Cited patent-fixed effects Yes Yes Yes Yes Yes Observations 2,237,179 177,682 176,758 62,150 735,519 R2 0.098 0.720 0.721 0.795 0.391 Notes: This table presents results from comparing localization of citation non-reversals with different subsets of priority reversals and disclosure citations. Disclosure citations are citations that occur when the priority date of the citing patent comes before the priority date but after the earliest publication date of the cited patent. The sample consists of actual USPTO citations and non-citing, control citations that are randomly matched to citing patents on publication year and four-digit IPC code. All columns exclude self-citations. Publication years of the citing patents range from 2001 to 2014. The time lag between priority years of the citing and cited year is limited to ±5 years. Standard errors are clustered at the cited patent level to allow for correlation among patents citing the same patent. Cited patent-fixed effects are included to control for invariant patent-level characteristics that may influence citation probability. Dyadic dummies indicating citations between leading tech/research clusters (i.e., Austin, MA Route 128, Raleigh-Durham, San Diego and Silicon Valley) are included. Standard errors, in parenthesis, are robust to heteroskedasticity. **p < 0.01, *p < 0.05. 6.1.2.2. Patent attorneys Patent attorneys are another potential source of highly localized knowledge transmission that might generate citation reversals. Wagner et al. (2014) argue that patent attorneys tend to cite known patents from their knowledge repositories which they develop based on their interactions with their clients. Thus, if local inventors engage with the same attorneys who share knowledge about unpublished local inventions, then such interactions might result in citation reversals that reflect highly localized knowledge transmission. In this case, same-attorney citations (i.e., citing and cited patents are prepared by the same attorney) would be more prevalent within citation reversals than within non-reversals and more localized than different-attorney citations (i.e., citing and cited patents are prepared by different attorneys). This bias will prevent us from rejecting the null hypothesis that the localization effect of non-reversals is the same as that of reversals. To perform this analysis, we extracted attorney information from the weekly compilations of patent publications released by the USPTO for years 2001–2014. We standardized attorney names and removed any corporate legal offices. In our sample, the share of same-attorney citations is 5% for non-reversals and 11% for reversals. Same-attorney citations are also more localized than different-attorney citations. The share of citations that take place within 50 miles of the cited patent is 79% for same-attorney citations and 23% for different-attorney citations (statistically significant at the 1% level). These findings are consistent with the concern that reversals might be driven by highly localized knowledge transmission. To mitigate this concern, we exclude from our sample the same-attorney citations. Columns 1 and 3 in Table 5 show that even after excluding same-attorney citations, the effect of distance on citation probability is similar between citation non-reversals (−0.045) and reversals (−0.031). This finding is consistent with our main finding and mitigates the concern that citation reversals capture highly localized knowledge transmission driven by interactions among inventors and patent attorneys. 6.1.2.3. Examiner reversals To further mitigate the concern that citation reversals might capture highly localized knowledge transmission, we compare the localization of citation non-reversals to that of citation reversals added by patent examiners, which arguably are even less prone to biases that could arise from local inventor interactions. If reversals arise due to local interactions among inventors, we expect inventors to generate proportionally more reversals than examiners and that inventor reversals would be more localized than examiner reversals. Despite the concern, the share of reversals for inventor and examiner citations in our sample is quite similar (4.4% for inventor citations and 4.2% for examiner citations). The share of citing inventors who are within 50 miles of the cited inventors is 33.7% for inventor reversals and 31.1% for examiner reversals, indicating that inventor-added reversals are somewhat more localized than examiner-added reversals. This observation is consistent with the possibility that reversals are driven by inventor interactions. To further explore this concern, we test whether citation non-reversals are more localized than examiner reversals in Columns 1 and 4 of Table 5. The estimation results show that examiner reversals (−0.043) are as localized as non-reversals (−0.045), evidence that localization of patent citations is not likely to be driven by localized knowledge transmission. 6.1.2.4. Disclosure citations If citation reversals capture highly localized inventor interactions, we expect the highest degree of localization to exist for citations made to inventions that have been created but have not been published. To test this hypothesis, we introduce into our sample another citation type, ‘disclosure citation’, which occurs when the priority year of the citing patent comes after the priority year but before the earliest publication year of the cited patent. This time sequence is due to overlapping patent examination periods where a prior-art patent is published while the citing patent application is being examined. (Online Appendix Figure A3 demonstrates disclosure citation on a timeline and Online Appendix Figure A5 provides an example of a disclosure citation.) Because the cited patent was not known to the public at least until the citing inventor applied for a patent on his invention, the only way that the citing inventor would have known about the cited invention is through a local interaction with the cited inventor. Thus, if local inventors share knowledge about their inventions before the inventions are publicly disclosed, then we expect disclosure citations to be substantially more localized than both citation non-reversals and priority reversals. Columns 1, 2 and 5 in Table 5 compare the localization of citations across citation non-reversals, priority reversals and disclosure citations. The results show that disclosure citations (−0.044) are essentially as localized as priority reversals (−0.035) and non-reversals (−0.045). In Online Appendix Table A8, we further present non-linear effect of distance on the citation probability for citation non-reversals, priority reversals and disclosure citations. The results continue to show that the effect of distance on citation probability is quite similar across non-reversals, priority reversals and disclosure citations. These results are inconsistent with the notion that highly localized knowledge transmission via inventor interaction is a major concern. Overall, the results in Table 5 show that, although citation reversals are more frequent for citation pairs filed by the same organization and for citation pairs with a common patent attorney, excluding them from the sample does not change the broad conclusion that localization of patent citations is unlikely to reflect transmission of knowledge from the cited to the citing invention. Additionally, focusing only on citation reversals added by examiners yields a similar effect of distance on citation propensity between reversals and non-reversals. Lastly, the results show that disclosure citations are not particularly more localized than priority reversals and non-reversals, evidence inconsistent with the concern that highly localized knowledge transmission from local inventor interactions is responsible for citation reversals. 6.1.3. Other robustness checks 6.1.3.1. Changes to the underlying invention over time Our main test of comparing the localization of citation non-reversals with reversals relies on the assumption that the underlying invention does not change over time during the examination process. There are some instances where this assumption might be violated. They include filing CIP applications and applications extending provisional applications. Thus, we test whether our main finding is robust to the exclusion of patents issued from these two types of applications. CIP applications are filed when new subject matter is added to the original application for an invention, and thus the original material and the newly added material may have different priority dates. The multiple priority dates might cause mis-categorization of reversals because it is difficult to determine whether a citation is made to (or from) the old or the new material. To mitigate this concern, we examine whether our main findings hold with the CIP applications excluded from our sample. Columns 1 and 3 in Online Appendix Table A2 show that, even with CIP applications excluded, the localization effects are similar between non-reversals (−0.044) and reversals (−0.035). Another way by which the subject matter of an invention could change over the course of the patent application process involves provisional applications. Unlike regular patent applications, a provisional application can be filed with an incomplete invention, which can later be supplemented using a non-provisional application once the invention is completed. To mitigate the concern that the underlying invention could change when a non-provisional application is filed to supplement a provisional application, we test whether our main findings are robust to the exclusion of applications related to provisional applications. Columns 2 and 4 in Online Appendix Table A2 show that the extent of localization is similar between citation non-reversals (−0.042) and reversals (−0.029) even after excluding applications relating to provisional applications. 6.1.3.2. Alternative specifications We address the concern that the use of control patents might miss an important variation that is correlated with distance. Online Appendix Table A3 presents results from an alternative specification in which localization of citation reversals are compared directly with that of non-reversals without the control citations. For each citation reversal, we find a non-reversal with the same cited patent and with the citing patent in the same IPC and publication cohort. To control for potential differences across citing patents, we also add citing patent technology area and publication year-fixed effects. Columns 1–3 show that a citing patent in citation reversals is at least as likely to be within 50-mile radius of the cited patent as it is in citation non-reversals. The results are robust to using 25-mile radius (Columns 4–6). Thus, our main finding, that localization of citations is not likely to be driven by localized knowledge transmission, continues to hold. 6.1.3.3. Extended sample period For our main results, we used a sample that contains citations with citing patents published over years 2001–2014 because examiner citations became identifiable only in 2001. Online Appendix Table A4 presents results from a test that uses a sample whose citing patents cover years 1977–2014 to make sure that our results are not biased by factors inherent to more recent citations. The results from this larger sample are consistent with our main finding and provide additional support that localization of citations is not likely to reflect localized knowledge transmission. For instance, Columns 2 and 3 show that going from 0 to 50 miles reduces the citation probability by 16.8 percentage points for non-reversals and 21.8 percentage points for reversals. 6.1.3.4. Six-digit IPC We further examine robustness of our findings by replicating our test with a sample whose controls are matched on six-digit technology classification codes. This test addresses the concern raised by Thompson and Fox-Kean (2005) that matching on broad technology classification code might not be adequate to control for existing regional specialization. Online Appendix Table A5 presents the results from the sample matched on six-digit technology classification code. As shown in Column 1, patent citations are localized, consistent with the findings in Murata et al. (2014). Also, consistent with our main finding, the results show that citation reversals are at least as localized as non-reversals. For instance, Columns 2 and 3 show that going from 0 to 50 miles reduces citation probability by 18 percentage points for non-reversals and 21 percentage points for reversals.11 These results are consistent with our main finding that, while citations are localized as indicated by prior studies, localization of citations is not likely to be driven by localized knowledge transmission. 6.1.3.5. Patent citation lag When two inventions are generated during the same time period, it is possible that the patent application of the invention building on the other invention gets filed before the patent application of the invention being built on. Under this scenario, citation reversals with short citation lags would reflect knowledge transmission and our test would produce spurious results. However, the possibility of reversals being generated by this process should be reduced as the reversal lag (i.e., difference between the priority years of citing and cited patents in citation reversals) widens. We address this concern by testing our results after re-categorizing reversals with up to 1-year priority lag as non-reversals and performing separate tests for reversals with different reversal lags. Online Appendix Table A6 presents results from the tests performed after re-categorizing reversals with up to 1-year priority lag as non-reversals. The pattern of results is consistent with our main finding and thus mitigates the concern that our main results might be driven by citation reversals generated by reversed timing of patent application filings. 6.1.3.6. Technology areas The importance of inventor interactions for learning from invention is likely to vary across technology areas. For example, inventions in complex technology areas such as telecommunications are likely to require more tacit knowledge than those in discrete technology areas such as chemicals. Such tacit knowledge might be more localized. To test whether reversals are driven by localized inventor interactions, we first compare the share of reversals across six technology areas: Chemistry, Pharmaceutical, Biotechnology, Medical Technology, Computer Technology and Telecommunications. If technology areas characterized by tacit knowledge are more prone to inventor interactions, then we expect to see higher shares of citation reversals for complex technology areas than for discrete technology areas. Inconsistent with the view that reversals are driven by transmission of tacit knowledge, we find that the share of reversals is fairly consistent across the six technology areas, ranging from 4% (Pharmaceuticals) percent to 10% (Medical Technology). We also examine whether the difference between the localization effect for non-reversals and reversals varies by technology area. If reversals in complex technology areas are more localized because inventor interactions are more important for learning, we expect our test to bias against finding a difference in the localization effect between non-reversals and reversals in complex technology areas, but not in discrete technology areas. Online Appendix Table A7a,b presents the results from comparing localization of citation non-reversals and that of reversals. Inconsistent with the expectation, the overall pattern does not show any systematic variation according to our expectation. For instance, going from 0 to 50 miles reduces the citation probability by 22 percentage points for non-reversals (Column 5 of Online Appendix Table A7a) and 51 percentage points for reversals (Column 6 of Online Appendix Table A7a) in Biotechnology and by 21 percentage points for non-reversals (Column 1 of Online Appendix Table A7b) and 23 percentage points for reversals (Column 2 of Online Appendix Table A7b) in Medical Technology. These results provide evidence that localization of citations is not likely to be driven by localized knowledge transmission in complex or discrete technology areas. 7. Concluding remarks This study examines whether localization of patent citations is driven by localized knowledge transmission. Our results show that the effect of distance on citation probability is similar for citation non-reversals and reversals, implying that localized knowledge transmission from the cited to the citing invention is not likely to be a major driver of localized citations. The concern that citation reversals might reflect highly localized knowledge transmission between inventors, either through direct interactions among themselves or through intermediaries, is addressed by comparing localization of non-reversals with various subsets of reversals that are even less likely to be driven by localized knowledge transmission. Our findings imply that either patent citations do not measure knowledge transmission, or that knowledge transmission is not localized, or both. Our findings are consistent with the growing evidence pointing to the inadequacy of using patent citations as a measure of knowledge flows. Patents may cite other patents because they are solving common problems or drawing upon similar techniques. It may well be that the bulk of citations arise from such circumstances rather than from knowledge flows between inventions linked by citations. If so, we need better ways to track such knowledge flows. Fortunately, the growth in computing power and machine-learning methods offer new possibilities. For instance, measuring textual similarity between patents is be a promising way to infer overlap between patents, and perhaps a way to infer knowledge transmission. Other methods include in-text citations to patents instead of relying upon front page citations (Ozcan and Bryan, 2017). We are agnostic about the importance of knowledge spillovers across space. Our findings do point to the potentially important role that organizational links play in knowledge transmission, and the important interactions between geographical and organizational proximity. Further, the role of specialized intermediaries, such as patent agents, and of the providers of specialized technical inputs, such as R&D and engineering services, may be promising avenues for future research. Methodologically, this study provides a way to isolate citations that are unlikely to be associated with knowledge transmission. We identify these special citations by checking whether the citing patent’s priority date comes before the priority date of the cited patent. We use these citations to benchmark localization of knowledge transmission as reflected in patent citations. Patent citations could reflect direct transmission of knowledge from the citing to the cited invention. However, it could also reflect commonalities in domain or solution to a specific technical problem. That is, the patents linked by citation may be linked not by knowledge transmission but by a body of knowledge that is common ground for both inventions. The distinction between an invention building on the cited invention and inventions drawing upon common, or background knowledge is important for both policy and firms. An inventor whose invention is built upon by another inventor might extract licensing revenues from the latter. However, if the subsequent inventor draws upon the background knowledge, then it would be difficult even to identify inventions that build on such knowledge. The distinction also provides insights into entrepreneurial spin-offs and regional clusters. If founders of spin-offs draw knowledge from specific discoveries during their employment at the parent company, then employers can develop contracts to prevent loss of rents. However, if knowledge drawn by the former employees is more general and cannot specifically be identified, then it would be more difficult for employers to protect themselves from former employees utilizing the knowledge. Furthermore, it would be difficult for firms to prevent background knowledge from spilling over to competitors even if they try to disperse inventors or R&D operations across different geographies. Indeed, to the extent that the background knowledge is useful for invention, such dispersion may be counter-productive. In summary, our findings force an uncomfortable choice between two very appealing and widely accepted beliefs, namely that knowledge transmission is less likely over longer distances and that patent citation is a good measure of knowledge transmission. Our empirical setup does not allow us to weigh in on this tradeoff. We look forward to future research for help. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Acknowledgements We would like to thank Wes Cohen for helpful discussions. All remaining errors are ours. Footnotes 1 This explanation leaves open the question of why people working on related problems are located close to each other. One reason could be that such problem solving requires specialized skills (i.e., labor pooling), or access to specialized knowledge that is available only in that region, such as from a local university. If the latter, there may well be knowledge spillovers at work, but not across inventors. 2 In fact, proponents of the ‘noisy signal’ interpretation of citations might even argue that finding a high degree of localization among reversed citations is consistent with the noisy signal view. If citations are just a noisy signal of inventive activity and do not mark actual sequential links between inventions, reversed links are likely and might be even expected. 3 A citation implies that the inventor, the patent agent or the examiner became aware of the cited invention. However, in citation reversals, the citing invention could not have benefited from this knowledge although the citing patent application may have been modified. 4 The issue is subtle. The inventor of a citing patent may acquire the required knowledge from the inventor of the cited patent. Alternatively, the inventor may learn from the cited patent, or the inventor of the cited patent, knowledge that is not unique to the cited invention. We address many of these issues in greater detail in Section 6, where we analyze the localization patterns in self-citations, citations inserted by examiners and citations made to unpublished patents. 5 We are assuming, for simplicity, that these are mutually exclusive outcomes. However, a citation may reflect both building upon and relatedness. In that case, the probability that j cites i if they are near is απn + βθn− αβπnθn. Both απn and βθn are very small in magnitude, so that the product term αβπnθn can be neglected. 6 Existing studies have tried to use patent classes to control for relatedness: It is implicitly or explicitly assumed that two patents in the same class are equally likely to be related independently of whether they are far or near. Formally, for patents in the same patent class, θn−θf =0. 7 The literature on submarine patents discusses how inventors can keep their inventions secret for an extended period of time and change claims using continuation applications (Graham and Mowery, 2004; Reitzig et al., 2007). The change described by the literature pertains to claims rather than inventions and is thus consistent with our assumption that the underlying invention does not change. 8 Continuing applications can be further broken down into continuation, divisional and continuation-in-part (CIP). Continuation applications make additional claims based on an existing invention specified in an earlier patent application while divisional applications are filed to separate out distinct inventions from an earlier application usually because the earlier one fails to meet the ‘unity of invention’ requirement. CIP applications can add extensions to an earlier invention, with claims on new subject matter taking as their priority date the application filing date of the CIP application. The prospect of adding extensions to an underlying invention is concerning since our test relies on the assumption that the underlying invention does not change over time. In Section 6, we run robustness tests after excluding CIP applications and applications claiming priority dates from a provisional application—two sources of potential changes in underlying inventions. Our main finding remains robust to these exclusions. 9 In cases with multiple inventor locations for a single patent, we use the city–state combination that occurs most frequently. If there is an equal number of different city–state combinations, we randomly choose a location among them. 10 Under ‘Patent citation lag’ in Section 6.1.3, we perform tests targeted specifically to address this timing issue. Given that the reversals in patent application filing time would be more likely to occur when inventions are created close in time, we test whether our main finding still holds if we re-categorize reversals with up to 1-year priority lag as non-reversals and at the same time use different citation lags. 11 For the sample matched on six-digit technology classification code, the average distance between citing and cited patents is 977 miles for citation non-reversals and 904 miles for reversals, with the difference statistically significant at the 1% level. 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Journal of Economic GeographyOxford University Press

Published: Mar 30, 2018

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