TY - JOUR
AU - Hohberger,, Jan
AB - Abstract Innovation research widely acknowledges that most inventions are recombinations of existing ideas and technologies. Following this stream of research, this study analyses how the values of prior inventions used to develop a subsequent invention influence the value of the new invention. Building on evolutionary theory and research on technological search and technological paradigms, this article proposes a positive relationship between prior inventions’ value and subsequent invention value. The analysis of a large-scale patent data set of pharmaceutical and semiconductor firms largely confirms this notion; however, it also shows that the effect weakens when prior inventions are of “higher” value. Valuable prior inventions are also positively related to the likelihood that subsequent inventions are “breakthroughs”; however, while this effect also decreases when prior inventions hold higher values, the decreasing effect occurs only at particularly high levels of prior invention value. In contrast, combining valuable inventions limits the likelihood of generating poor invention outcomes value. In summary, while the results lend support to theories of evolutionary and cumulative technological progress, they also show that despite the recombination potential of technical knowledge, there are practical limits to the benefits of valuable inputs. 1. Introduction A well-established idea in innovation research is that many inventions are recombinations of existing technology and knowledge (Schumpeter 1939; Weitzman 1998) and that the characteristics of such knowledge influence invention types and their values (Nelson and Winter 1982; Fleming 2001; Phene et al., 2006; Carnabuci and Operti 2013; Kaplan and Vakili 2014). This view has led to a stream of research on the characteristics of prior inventions and their influence on invention results, such as knowledge age (Ahuja and Lampert 2001; Katila 2002; Miller et al., 2007), scope (Katila and Ahuja 2002), organizational origin (Katila 2002; Miller et al., 2007), geographic origin (Rosenkopf and Almeida 2003; Phene et al., 2006), technological diversity and distance (Rosenkopf and Nerkar 2001; Phene et al., 2006), and complexity (Fleming 2001). Despite the array of studies examining knowledge characteristics and the increasing reliance of the economy on the production, refinement, and accumulation of ideas (Powell and Snellman 2004), gaps in understanding remain on how inventions build on previous ideas, as well as the mechanisms that drive the accumulation of knowledge (Carnabuci and Bruggeman 2009). In particular, knowledge of how the value of prior inventions influences the value of new inventions is limited. When exploring combinations of prior inventions, previous studies have often referred to the value of an invention, but without directly measuring the value of inputs into the innovative process (Ahuja and Lampert 2001; Fleming and Sorenson 2001; Carnabuci and Operti 2013; Kaplan and Vakili 2014). The current study addresses this issue by investigating how prior invention value relates to the values of subsequent inventions. It applies the logic of evolutionary economics and technological search to argue that the value of a prior invention—embedded in innovation—is positively related to subsequent invention value. However, it also reasons that this effect is subject to diminishing returns and becomes weaker at higher levels of prior invention value. Furthermore, prior research shows that the relationship between the characteristics of a prior invention and performance outcomes is not salient, nor uniform, across the distribution of performance (Anderson and Tushman 1990; Christensen 1997; Tripsas 1997; Ahuja and Lampert 2001; Conti et al., 2013). As such, research has mostly investigated the top end of invention performance (“breakthrough inventions”), as these types of inventions can set the direction of future inventions and are linked to economic progress, firm survival, and business growth (Christensen 1997; Ahuja and Lampert 2001). However, more recent studies have also investigated the lower end of performance distribution (often called “invention failures”) and compared it with other parts of the invention value distribution (Singh and Fleming 2010; Mata and Woerter 2013; Conti 2014). These investigations not only are relevant from a managerial perspective, as they provide a more nuanced picture of invention outcomes and potentially help develop strategies to avoid or minimize invention failures, but also inform theoretical discussion, as they uncover different cause–effect relationships between invention activities and outcomes along the distribution of invention performance. Following this logic, this study explores the importance of prior invention value of both significant inventions (i.e., breakthroughs) and invention failures. In line with the arguments of technological paradigms, the underlying expectation is that the relationship between prior invention value and breakthrough inventions will be positive but diminish over time and be negative for “low-value inventions.” The empirical strategy adopted in this study aligns with that of previous innovation research, which has typically used patent references (i.e., backward citations) to assess the influence of prior invention characteristics on new invention outcomes and forward citations to measure invention value (Ahuja and Lampert, 2001; Fleming, 2001; Carnabuci and Operti, 2013; Gruber et al., 2013; Arts and Veugelers, 2014; Kaplan and Vakili, 2014). However, rather than applying a forward citation measure only to patents (i.e., the outcomes of invention processes), the study also applies it to prior inventions (i.e., patent references), and thus, the knowledge base in the innovation process. By providing an in-depth analysis of the value of prior inventions, this study contributes to previous technological search research by presenting a complementary view of prior knowledge and invention combinations and how they can influence invention outcomes (Fleming, 2001; Ahuja and Lampert, 2001; Carnabuci and Operti, 2013; Phene et al., 2006). From a theoretical perspective, this study contributes to bodies of literature related to the limits of recombinant knowledge growth (Weitzman, 1998; Olsson and Frey, 2002; Carnabuci, 2010) and technological search (Laursen, 2012). Guided by the established idea that subsequent inventions are the outcomes of recombinations of previous inventions and that each new idea can be recombined to generate multiple new ideas, Weitzman (1998) argues that knowledge growth increases in scale and is not subject to diminishing returns. However, several researchers have criticized the idea of an unconstrained combinatorial process as unrealistic and have proposed the existence of constraining factors that affect recombinant growth (Olsson and Frey, 2002; Carnabuci and Bruggeman, 2009; Carnabuci, 2010). The uncertainty of invention activities (Fleming, 2001), combined with the boundaries of the information-processing capacity of humans (Simon, 1991), limits the potential recombination of technical knowledge and results in path-dependent and idiosyncratic invention patterns within a given research trajectory or paradigm (Dosi, 1982; Nelson and Winter, 1982; Dosi and Nelson, 2010). To date, few empirical studies have examined the recombination potential of technologies and/or its limitations (Carnabuci and Bruggeman, 2009). The current research provides an invention-level examination of the potential limits of growth. The concepts of “prior invention value” and “path dependency” enable detailed investigation into the cumulative development of ideas and technologies—within trajectories and technological paradigms—by linking the success of current inventions to the success of “ancestor” inventions. However, this research also argues that in rare cases of breakthrough inventions, prior invention values may not translate into successful inventions, but rather limit the growth potential of knowledge. From a managerial perspective, the limited attention to the value of prior inventions is surprising given that their value provides insights into the effectiveness and efficiency of invention activities. Therefore, the value of prior inventions is crucial for managers and innovators who want to gain a better understanding of how to optimize searching for and combining prior inventions to develop new inventions. At the same time, such an understanding also reduces the uncertainty of new invention processes, particularly for breakthrough inventions, which are the foundations of subsequent inventions and are strongly related to social progress and organizational performance (Anderson and Tushman, 1990; Christensen, 1997; Tripsas, 1997; Ahuja and Lampert, 2001; Phene et al., 2006; Singh and Fleming, 2010; Conti et al., 2013). This understanding also aids in reducing inefficient and ineffective innovation processes and, thereby, the generation of low-value inventions. After all, many invention activities do not create value, and low-value outputs are common (Fleming, 2007). Therefore, reducing the likelihood of innovation failures—as well as their associated costs and business risks—should be of key interest to firms. 2. Theory and hypothesis 2.1 Invention and knowledge inputs Scholars have long recognized that many scientific and technological developments are based on cumulative and local extensions of previous ideas within a given trajectory (Kuhn, 1962; Merton, 1973; Dosi, 1982; Nelson and Winter, 1982; Murray and O’Mahony, 2007). Perhaps the most well-known expression of this is the concept of “paradigms,” introduced by Thomas Kuhn (1962) in his work on the evolution of scientific fields. With regard to the cumulativeness of scientific developments, Kuhn (1962) argued that successful scientific research results in changes to normal science (i.e., science characterized as slowly accumulating work with an established theory or paradigm)—where normal science produces the building blocks of scientific research and is continuously adding to the growing stock of scientific knowledge. Kuhn’s work has had a significant influence on innovation and technological progress research (Teece, 2008; Dosi and Nelson, 2010). In his work on technological trajectories, Dosi (1982) wrote: As “normal science” is the “actualization of a promise” contained in a scientific paradigm, so is “technical progress” defined by a certain “technological paradigm.” We will define a technological trajectory as the pattern of “normal” problem solving activity (i.e., of “progress”) on the ground of a technological paradigm. More recently, Furman and Stern (2006) argued that modern capitalism is characterized by a self-perpetuating and cumulative process and that scientific productivity—across a wide range of industries and technologies—is upheld by researchers exploiting an ever-growing set of knowledge pertinent to their fields. The emphasis on the cumulativeness of innovation within trajectories and technological paradigms might seem to clash with ideas on the disruptive nature of innovation (Christensen, 1997). However, the cumulative nature of invention refers to “normal” invention activity, which forms the majority of all invention activity. This is where “success breeds success” or the extent “to which innovative advances are made by dwarfs standing on the shoulders of past giants” (Dosi and Nelson 2010: 73). With this cumulative view of progress, new inventions build on successful ideas from the past and therefore lead to inherent serial correlations in both successes and failures (Dosi and Grazzi, 2006). There are two key explanations for the cumulative nature of invention activities. First, research on the sociology of science and innovation stresses the significance of institutions, practices, and communities in science and technology (Merton, 1973; Latour, 1987). Social norms and conventions build frames of reference and normative pressures to encourage remaining within those frames. These “frames” capture how inventors make sense of technologies; they shape how inventors perceive technologies and which performance criteria and standards they use to evaluate them. Thus, technological frames guide inventors in determining which technology is useful (Kaplan and Tripsas, 2008). Furthermore, innovating within an existing frame of reference—by using established inventions—makes new inventions more likely to be accepted in the community responsible for the prior inventions. Second, the cumulative nature of invention activity also stems from the uncertainty and complexity of the discovery process (Fleming, 2001), combined with the cognitive and mental limitations of humans (Simon, 1991). The ever-growing number of potential combinations of ideas and inventions can overwhelm the imagination and mental power of human beings (Fleming, 2001). In addition, many potential combinations do not yield valuable outcomes, and therefore predicting the success of an invention is difficult. However, in a positive sense, building on valuable combinations reduces search possibilities by relying on a successful path of ideas, which increases the likelihood of success and future value generation. Fleming (2001) also notes that when inventors disregard unsuccessful past ideas, they are likely to reduce the size of combinative search possibilities and eliminate fruitless avenues. Thus, while reliance on valuable prior inventions is likely to be beneficial, arguments regarding the ecology of innovation and the need to balance exploitation and exploration reveal that an excessive use of such inventions may result in diminishing, marginal contributions of prior invention value to subsequent invention value. 2.1.1 Ecology of innovation Research on the ecology of innovation has shown that competitive intensity within and between technological areas can negatively affect invention outcomes. For example, Podolny and Stuart (1995) show that competition within a technological area (i.e., a technological niche) negatively affects the likelihood that subsequent inventions will build on any prior ones. They argue that whether an invention becomes successful or not is a function of the crowdedness of the technological area. Similarly, Podolny et al. (1996) show that the more a firm competes for knowledge within the same area as other firms, the less it tends to grow. Carnabuci (2010) demonstrates that the growth of technologies is negatively related to competitive pressures from related technological areas. In addition to the competitive pressure within popular niches, these findings are grounded in the bounded rationality of the inventor and the scarcity of organizational resources. In situations of technological competition, technologies must compete for inventors’ limited attention, as well as organizational investments (Podolny and Stuart, 1995; Carnabuci, 2010). These findings are related to the issue of prior invention value, as the value potential of a market or technological area is a key factor attracting competitive entries to a niche (Siegfried and Evans, 1994). However, new entries (or increased research activity from existing firms) increase competition, which then negatively affects future invention outcomes (Podolny and Stuart, 1995; Carnabuci, 2010). In other words, areas with high-value inventions attract competition, which in turn can negatively affect the outcomes of the inventions built on the prior high-value technology. 2.1.2 Balancing exploitation and exploration Building on March (1991), various studies on invention performance show that risk taking, variation (i.e., exploration), and the use of established ideas (i.e., exploitation) must be balanced to achieve breakthrough invention outcomes (Ahuja and Lampert, 2001; Phene et al., 2006). While the use of successful and established ideas ensures continuity and security, knowledge variation and risk taking are also necessary to develop new and alternative ideas for successful innovation (March 1991). An excess of one type of activity—at the expense of the other—will most likely lead to suboptimal performance outcomes. This implies that an over-reliance on high-value prior inventions, which are an indicator of established and low-risk knowledge inputs, can lead to suboptimal performance outcomes. Therefore, because they are particularly salient for higher levels of prior invention value, the ecology of innovation and the need to balance exploitation and exploration represent the “recombination potential of high-value inventions.” H1: The recombination of valuable prior inventions positively influences the value of subsequent inventions; however, this effect decreases at higher levels of prior invention value. 2.2 Exploring the impact of prior invention value for high- and low-value inventions Previous research has challenged the notion that the effects of invention activities and prior invention characteristics are constant, or uniform, for the entire distribution of invention performance. Multiple studies have shown that the top percentage of inventions are created with different inputs and processes from standard inventions (Anderson and Tushman, 1990; Christensen, 1997; Tripsas, 1997; Ahuja and Lampert, 2001; Conti et al., 2013; Hohberger, 2016b). In addition, several recent studies have investigated low-performing inventions and compared them with other parts of the invention value distribution. For example, Conti (2014) shows that the stricter enforcement of non-competition agreements increases the likelihood of both breakthroughs and invention failures. Thus, the enforcement of non-competition agreements has a similar effect at both ends of the invention value distribution. Conversely, Singh and Fleming (2010) show that the relationship between inventor team size and invention outcomes differs at the upper and low end of the invention value distribution. While team- and/or organization-based invention activities increase the likelihood of breakthrough inventions, they also decrease the likelihood of a patent without citations (Singh and Fleming, 2010). In a similar vein, Mata and Woerter (2013) investigate the link between internal and external R&D activities on firm profits. They show that internal and external R&D are related only to specific upper parts of the firm profit distribution and have no significant effects on other parts. Common among these three studies is their provision of a more nuanced picture of innovation-driven phenomena. Thus, to test the robustness of results and to explore specific theoretical arguments related to invention value distribution, the current study also explores the importance of prior invention value at the lower and upper ends of the invention value distribution. 2.2.1 Breakthrough inventions In cases of higher value inventions, the positive effects of prior invention value on subsequent innovation value diminish because value judgements are less transferable from one successful technological trajectory to another. While standard inventions undergo cumulative progress along an existing technological trajectory, breakthrough inventions often cross these trajectories or create new ones (Anderson and Tushman, 1990). Breakthrough inventions are based on the combination of novel, emerging, and pioneering technologies (Ahuja and Lampert, 2001) and require radical and broad changes to “technological frames” (Kaplan and Tripsas, 2008). This is in line with Kuhn’s (1962: 6–7) views on paradigm changes and world views, in which he argues that in the realm of science, Revolutionary changes […] involve discoveries that cannot be accommodated within the concepts in use before they were made. In order to make or to assimilate such a discovery one must alter the way one thinks about and describes some range of natural phenomena. When referential changes of this sort accompany change of law or theory, scientific development cannot be quite cumulative. One cannot get from the old to the new simply by an addition to what was already known. This change of trajectory implies that the old heuristics and underlying basic technological frames do not match the new invention and its establishment of a new trajectory (i.e., old criteria for assessing performance; value and quality do not fit the new trajectory). That is, valuation of a prior invention entails a different valuation logic, and thus, past value appraisals of inventions are negatively related to breakthrough inventions. Furthermore, value judgements about an existing invention cannot aid in making inferences about the new invention. Ahuja and Lampert (2001) describe technological progress as continuous improvements in fitness along a technology trajectory. Thus, the fitness of a technology is understood as a close matching of all important performance characteristics of a technology, as well as the performance characteristics of a technological trajectory. Within a trajectory of fitness values of specific new technologies, values are closely correlated to the fitness values of previous technologies. In such cases, inventions that build on prior inventions are more likely to share the same technological trajectory and subsequently result in similar fitness values to those of their “parent” inventions (Ahuja and Lampert, 2001). Following this logic, in cases of standard inventions, which follow existing technological trajectories, prior invention values are positively related to values of new inventions. However, because prior and new inventions are based on different fitness profiles, the serial correlation of prior invention values with new invention values is reduced in cases of breakthrough inventions. In addition, high prior invention values indicate a particularly strong fit with a past technological trajectory, and therefore a positive fit with a new trajectory is less likely. 2.2.2 Low-value inventions On the other end of the invention performance distribution are low-value inventions, which are important to explore for two reasons. First, in a general sense, the notion that the relationship between dependent variables differs at various points along the distribution of the dependent variable holds equally true for both lower and upper parts of the distribution. Second, and more important from a theoretical standpoint, the use of valuable prior inventions within technological trajectories has opposite implications at the lower end of the distribution of invention value. For example, while the combination of valuable prior inventions may not influence the production of breakthroughs—because valuable prior inventions represent an established paradigm and breakthrough inventions require the pursuit of new and riskier technologies—they may provide a potential safeguard against invention failure, as well as reduce the probability of extremely poor invention outcomes. Thus, testing this relationship can significantly shed light on invention processes and strengthen the theoretical precision of search theories. 3. Method 3.1 Sample This study draws from a sample of US Patent and Trademark Office (USPTO) patent data, from US-based firms in the pharmaceutical and semiconductor industries. These two industries were chosen for three reasons. First, invention and technological recombination are central aspects of these industries, for both optimal organizational performance and survival. Second, both industries rely heavily on patents and thus have frequently appeared in patent-based studies (Rothaermel and Hess, 2007; Corredoira and Rosenkopf, 2010; Phene et al., 2012). Third, testing the hypothesis in two high-technology industries with different institutional norms, appropriability strategies, technological requirements, and industry dynamics improves the validity and generalizability of the results (Sorensen and Stuart, 2000; Laursen and Salter, 2014). The semiconductor industry is characterized by rapid technological changes and short product life cycles. Semiconductor firms also typically rely on lead times, secrecy, and manufacturing or design capabilities, in addition to patent protection, and their research is driven by developments in physical and material sciences (Sorensen and Stuart, 2000; Hall and Ziedonis, 2001). Conversely, research generated by pharmaceutical firms lies at the intersection of molecular biology, genetics, immunology, and chemistry. It is also influenced by biotechnology developments (Pisano, 2002) and strongly linked to basic research. As a result, pharmaceutical firms rely strongly on basic scientific research and actively collaborate with universities and research institutes (Almeida et al., 2011). All main constructs are measured with variables based on patent data. Despite some inherent limitations (Gittelman 2008), patent data provide a unique tool to investigate invention, knowledge sourcing, and technological change (Jaffe et al., 1993; Sorensen and Stuart, 2000; Almeida et al., 2011; Hohberger et al., 2015). As patents provide citations to “prior art” (i.e., references to relevant previous patents), which are established proxies for “built-on” knowledge in the innovation process (Caballero and Jaffe, 1993), patent data are particularly useful for research into the development of inventions. Patent references can be used to identify the extent to which inventors build on previously developed technological areas (Fleming, 2001; Katila and Ahuja, 2002; Phene et al., 2006; Carnabuci and Operti, 2013). Furthermore, the forward citations of patents are an acceptable means of measuring the impact, quality, and value of an invention, which is crucial for the current study (Lanjouw et al., 1998; Trajtenberg, 1990; Harhoff et al., 2003; Hall et al., 2005). However, it is important to note that patent references cannot serve as direct knowledge inputs. Although inventors are legally required to list “prior art,” the references are not without bias. Patent citations are related to financial implications, which may create incentives to omit references (Schettino, 2007; Lampe, 2012), and patent officers frequently add citations to patents (Thompson, 2006; Alcacer et al., 2009). However, studies on the overall validity and reliability of patent data have shown that citations are good proxies for knowledge spillover and flow (Jaffe et al., 2000; Duguet and MacGarvie, 2005). In assessing the strategic behavior of inventors during the patent application process, Lampe (2012) also argues that it is favorable to include examiner citations in any analysis. The data for the current study were collected in five steps. First, using Standard Industrial Classification (SIC) codes, firms from both industries were identified from the Compustat database. Pharmaceutical firms came from SIC codes 2834 (pharmaceutical preparations) and 2836 (biological products, except diagnostics), while semiconductor firms fell in code 3674 (semiconductors and related devices) (Hall and Ziedonis, 2001; Higgins et al., 2011; Srivastava and Gnyawali, 2011). The Compustat database was also used to extract financial data on the firms. In the second step, the sample firms were matched with all their USPTO patents. While excluding non-US firms and non-USPTO patents is an inherent limitation of this study, it is also in line with most related studies focusing on one patent system. The reason for this exclusion is the limited comparability between international patent systems due to differences in their application of standards and processes. The use of USPTO patents also enables patents to be matched to firms by employing dynamic matching procedure of the NBER PDP Project. The third step extracted detailed information for each USPTO patent from the PATSTAT database (version 2015b). PATSTAT is issued by the European Patent Office, but it also provides detailed access to international patents, including USPTO patents. In addition, it provides easy database access to raw data of individual patents, which was particularly useful during the fourth and fifth steps of data collection. In these steps, the cited references for each of the focal patents were collected, and forward citations for the focal and cited patents were captured to calculate subsequent and prior invention value. The years spanning 1985–2006 were selected for data extraction, as the NBER PDP Project patent-matching procedure is only available up to 2006, and patent activities across firms, technology classes, and industries are relatively limited before 1985. Overall, the sampling procedure yielded a focal sample of 552 firms with 139,529 patents. 3.2 Dependent variables 3.2.1 Invention value As in previous patent-based studies, the value of an invention is approximated by the number of patent forward citations (Ahuja and Lampert, 2001; Phene et al., 2006; Rothaermel and Hess, 2007; Singh and Fleming, 2010; Almeida et al., 2011). In patent and technology-based studies, forward citations are a well-established proxy for invention value because they correlate positively with the market value of firms, patent renewals, patent quality, intellectual property values, and technological importance (Trajtenberg, 1990; Lanjouw et al., 1998; Jaffe et al., 2000; Harhoff et al., 2003; Hall et al., 2005). However, independent of content and perceived value, older patents have more time to receive citations (e.g., a patent created 5 years ago has far less time to receive citations than a patent created 20 years ago). Therefore, it is important to account for the length of the time-to-cite window. Similar to previous research, this study accounted for this window by incorporating year dummies for the publication date of the focal patents. 3.2.2 Breakthrough and low-value inventions The value of inventions varies significantly, and most inventions yield only limited value and thus are technological dead ends (Singh and Fleming, 2010). The limited number of inventions that are the basis of many subsequent inventions can be interpreted as breakthroughs because they entail technological progress and contain substantial technological and economic value (Fleming, 2001; Phene et al., 2006; Singh and Fleming, 2010). Accordingly, breakthrough inventions capture the importance of an idea and the subsequent ideas built on it (Ahuja and Lampert, 2001; Rosenkopf and Nerkar, 2001; Phene et al., 2006; Singh and Fleming, 2010; Conti et al., 2013). Thus, breakthrough inventions constitute a fraction of the most cited patents in a given period and are measured with the forward citations of patents (Ahuja and Lampert, 2001). In line with previous research, the top 2% of cited patents are considered breakthroughs (Ahuja and Lampert, 2001; Phene et al., 2006); however, all regressions are performed with the top 1% and 5% of cited patents and yield similar results. The measurement of low-value inventions is similar to the estimations for breakthrough inventions, but it differs in terms of its focus on the lower end of the invention value distribution. Low-value inventions are inventions without any forward citations and are measured with a dummy that takes the value of 1 if a patent has no forward citations and the value of 0 if it has at least one forward citation (see Conti, 2014; Singh and Fleming, 2010). 3.3 Prior invention value Patent references (i.e., backward citations) were used to identify prior inventions (Fleming, 2001; Katila and Ahuja, 2002; Phene et al., 2006; Carnabuci and Operti, 2013; Gruber et al., 2013; Kaplan and Vakili, 2014), and in line with the logic of measuring the value of a patent by using its forward citations, the value of prior inventions was also measured with the forward citations of prior inventions. Although the time-to-cite correction is particularly important for the value of prior inventions—as these patents have a longer time-to-cite period and, therefore, more variance in their windows—it is not advisable to use fixed effects to account for the possible time-to-cite windows for all the possible citation lags. Thus, the forward citations were corrected by using an exponential decay factor that accounts for the loss and decay of knowledge over time (Fleming, 2001): e−(application date of citing patent−publication date of focal patenttime constant of knowledge loss) ⁠. The decay factor is set at 5 years, which implies that approximately one-third of the knowledge remains after 5 years and is equivalent to a yearly reduction rate of 18%. To analyze the robustness of the results, various sensitivity analyses were performed, with loss rates ranging from 3 to 7 years; the raw citation count and the results remained stable. The final measure of prior invention value is the average value of prior inventions (i.e., time-to-cite-corrected forward citations) of a focal patent. 3.4 Control variables Patents are constructed in a complex institutional environment and are built by strategic actors (Gittelman, 2008). Therefore, it is important to include a broad set of invention- and patent-related control variables, such as those that account for the heterogeneity of the focal patent, the cited patent references (i.e., prior inventions), and firm-generated patents. Industry and technological differences can have a strong influence on patenting behavior (Cohen et al., 2000; Sorensen and Stuart, 2000). Thus, technological dummies for the 13 most common technological fields within the sample were used to control for technological differences between patents. Schmoch (2008) classification was used to define technological fields according to International Patent Classification (IPC) codes. The number of inventors is an indicator of a project's size and the efforts underlying an invention (Gittelman and Kogut, 2003), and it can influence the generation of average and breakthrough inventions (Singh and Fleming, 2010); therefore, the number of inventors was included in all models. Previous studies have shown that the involvement of star inventors can have a significant influence on invention outcomes (Kehoe and Tzabbar, 2015; Hohberger, 2016b). Therefore, the current study used a dummy variable if a patent was created with the help of a star inventor. Star inventors are those within the top 2% of inventors—as measured by patent citations—in the 5 years before the development of a focal patent. The number of prior inventions (i.e., patent references) of a focal patent was used to approximate the knowledge input into subsequent inventions. Basic science-based inventions can have a different citation pattern than more applied science-based inventions (Fabrizio, 2007; Hohberger, 2016a). Therefore, the number of scientific references of a focal patent was used to capture the amount of scientific input into an invention. Furthermore, the ratio of patent references to scientific references served as an indicator of the overall “science orientation” of a patent. Although the focal patents used in the study were exclusively US-based patents, patent references can be international. As the geographic origin of references can influence invention performance (Phene et al., 2006; Lahiri, 2010), a Blau index helped control for international references diversity, 1−∑pi2 ⁠, where (ρ) is the percentage of patents from a patent authority in a given region (i). High scores indicate that the patent is based on more geographically diverse patent references. Similarly, the technological diversity of the references can influence the performance and value of inventions (Almeida and Kogut, 1997). Therefore, a second Blau index was calculated on the basis of the technological diversity of prior inventions. In this case, (ρ) represents the percentage of IPC subclasses (i) across all patent references of a focal patent. The numbers of IPC subclasses (six-digit level) also served to control for the technological scope of an invention. This is important because the technological scope may be related to the value of inventions and diffusion (Katila, 2002; Hohberger, 2016a). In accordance with previous studies, the average citation lag of patent references for the focal patent served to control for the prior invention age (Ahuja and Lampert, 2001). This measure assumes that an invention based on old technology is more likely to cite older patents, while inventions that cite more recent patents are more likely to pertain to current issues (Ahuja and Lampert, 2001). Thus, prior invention age is measured as the time span between the application date of the priority patent and the average publication date of all patent references. The variance of prior invention age is also taken into account. Another control variable is the technological distance between the prior invention and the focal patent, D=∑(pi−ci)2 ⁠, where (ρ) represents the proportion of IPC subclasses (i) of the focal patent and (c) represents the average proportion of IPC subclasses (i) of all references. The measure uses IPC classes to capture the technological distance between a focal patent and its patent references and accounts for the multiple IPC classes of patents. This distance measure ranges from a low of zero (very high in technological similarity) to a theoretical maximum that is slightly above 1.414 (the square root of two) for technological dissimilarity. This measure has the advantage of weighting the different IPC classes on the basis of their usage across all references and taking their relative importance into account. Various related studies capturing technological distance have also applied this measure (Rosenkopf and Almeida, 2003; Song et al., 2003; Vasudeva and Anand, 2011; Hohberger et al., 2015). A final measure of the level of prior inventions is the variance of their values. To control for time variations at the firm level, several firm-level controls were included to complement the fixed firm effects, which account for time-invariant firm differences. The number of patents per year controls for the patenting activity and the level of a firm's research activity. In line with previous discussions on firm size and invention (Sorensen and Stuart, 2000), firm size reflects the number of employees, while the return on assets (ROA) per year controls for firm profitability. A firm's capability of combining knowledge depends on its R&D intensity; thus, the ratio of R&D expenditure to net sales serves as a control. In addition, the number of R&D alliances helps account for the external research of a firm. Alliances were downloaded from the SDC Platinum database and coded into R&D-focused alliances, as well as marketing- and distribution-oriented alliances. With the focus on innovation activities, the R&D-focused alliances served as control variables in the estimation. Finally, year dummy variables accounted for any systematic differences in the sample period of the application of the focal patents. 3.5 Estimation Invention performance was measured as a non-negative count variable and estimated with a quasi-maximum likelihood (QML) Poisson regression with cluster (by firm) robust standard errors. The QML Poisson offers multiple advantages over a negative binomial regression (NBR) with fixed firm effects, which is often used in patent research. Among other things, the estimation results in a more conservative estimation—due to larger standard errors—and imposes fewer constraints on the underlying data distribution than NBR. However, as a robustness check, all models were also run with an NBR with fixed firm effects and a classic ordinary least squares (OLS) regression with fixed firm effects and a log-transformed dependent variable. When modeling the extreme ends of the invention value distribution, the objective was to estimate the likelihood that a patent fell in a category that exhibited extremely high or low citation counts. Thus, in line with previous research, a logit regression model was used for dichotomous outcomes (Phene et al., 2006; Singh and Fleming, 2010; Conti et al., 2013). However, it is important to note that breakthrough inventions are relatively rare events and not all firms within the sample created breakthroughs (or low-value inventions). Therefore, to avoid losing large parts of the observations—because of missing variances in the dependent variable—the models were tested using random firm effects rather than fixed firm effects. To account for inherent limitations of the random-effects specification, the logit models were also estimated using a linear probability model with fixed effects as a robustness check. 4. Results Table 1 presents the descriptive statistics and correlation matrix and displays notable differences among patents, firms, and industries. For example, patents cited between 0 and 163 prior patents, with an average number of 13.87 prior patents, and pharmaceutical patents have, on average, a greater number of prior patents (15.08) than semiconductor patents (13.20). The industry differences are even greater for technological scope; pharmaceutical firms incorporate an average of 8.78 IPC classes, while semiconductor patents have only 3.12. Furthermore, semiconductor patents have shorter citation lags than patents from pharmaceutical firms (pharmaceutical patents = 6.92 years; semiconductor patents = 4.37 years). These results lend support to the idea that semiconductor firms are more reliant on recent developments and have shorter development time frames; the differences are comparable to previous studies in related industries (Sorensen and Stuart, 2000). Table 1 also shows that all correlations are at moderate levels. However, to examine the threat of multi-collinearity, the variance inflation factors (VIFs) were also calculated. The VIFs of the full model are below 3 and the VIF of each variable is below 4, indicating that multi-collinearity is not a serious problem. Table 1. Descriptive statistics and correlation matrix Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 1 Invention value 1.00 2 Value prior inventions 0.30 1.00 3 Industry dummy −0.02 0.04 1.00 4 Number of patents −0.06 0.05 0.48 1.00 5 Firm size −0.04 −0.03 −0.21 0.21 1.00 6 ROA 0.02 0.00 0.00 0.08 0.32 1.00 7 R&D intensity 0.00 0.00 −0.12 −0.09 −0.11 −0.26 1.00 8 R&D alliances 0.11 0.06 −0.02 0.01 0.25 0.17 −0.04 1.00 9 Star inventor 0.18 0.16 0.02 0.15 −0.12 −0.01 −0.01 −0.03 1.00 10 Technological distance −0.02 −0.03 0.25 0.18 0.15 0.11 −0.10 0.07 −0.15 1.00 11 Variance value prior inventions 0.15 0.57 −0.03 −0.02 −0.01 −0.01 0.01 0.01 0.03 −0.01 1.00 12 Number of prior inventions 0.06 0.04 −0.05 0.07 −0.04 −0.05 0.04 −0.06 0.18 −0.08 0.00 1.00 13 Number of scientific references 0.02 0.02 −0.28 −0.12 0.00 −0.06 0.07 0.01 0.07 −0.16 0.02 0.21 1.00 14 Science orientation −0.03 −0.03 −0.27 −0.14 0.04 −0.01 0.03 0.05 −0.03 −0.10 0.01 −0.23 0.48 1.00 15 Number of inventors 0.02 0.00 −0.27 −0.15 0.07 0.00 0.04 −0.01 0.18 −0.17 0.01 0.09 0.13 0.06 1.00 16 International diversity 0.01 −0.07 −0.40 −0.22 0.08 −0.02 0.07 0.00 0.00 −0.18 0.01 0.16 0.27 −0.07 0.17 1.00 17 Techn. diversity (prior inv.) 0.04 0.04 −0.26 −0.11 0.04 −0.04 0.05 −0.01 −0.01 −0.05 0.03 0.26 0.16 −0.24 0.09 0.32 1.00 18 Age prior inventions −0.03 −0.21 −0.25 −0.14 0.08 0.01 0.01 −0.01 −0.06 0.02 −0.02 0.17 0.05 −0.12 0.03 0.20 0.19 1.00 19 Variance age prior inventions 0.01 −0.06 −0.09 −0.05 0.04 0.00 0.00 −0.01 −0.03 0.03 −0.01 0.05 −0.01 −0.05 −0.01 0.06 0.09 0.57 1.00 20 Technological scope 0.01 −0.02 −0.38 −0.19 0.09 −0.02 0.06 0.00 0.07 −0.40 0.01 0.10 0.19 0.11 0.27 0.27 0.17 0.08 0.01 1.00 Overall (n = 139,529) M 22.75 31.84 0.64 473.70 29.45 0.02 0.45 1.53 0.32 0.63 3.57 13.87 0.53 0.08 2.63 0.16 0.52 5.28 39.53 5.15 SD 42.85 48.86 0.48 518.53 27.36 0.25 3.12 3.19 0.00 0.24 66.45 17.31 0.52 0.15 1.91 0.23 0.30 4.91 138.92 7.09 Min 0.00 0.00 0.00 1.00 0.00 −17.23 −1.73 0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 1.0 1892.0 122.0 4.2 210.4 22.0 0.2 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 8844.5 166.0 Pharmaceuticals (n = 50,051) M 23.92 29.46 0.00 137.64 36.96 0.95 0.95 1.61 0.29 0.55 5.99 15.08 0.73 0.13 3.31 0.29 0.63 6.92 57.07 8.78 SD 52.92 67.76 0.00 112.42 30.17 5.17 5.17 2.37 0.45 0.24 109.80 19.47 0.47 0.21 2.38 0.26 0.28 5.98 166.05 10.35 Min 0.00 0.00 0.00 1.00 0.00 −1.73 −1.73 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 0.0 431.0 122.0 210.4 210.4 11.0 1.0 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 6612.5 166.0 Semiconductor (n = 89,478) M 22.10 33.17 1.00 661.68 25.25 0.02 0.17 1.49 0.31 0.68 2.22 13.20 0.42 0.05 2.25 0.09 0.47 4.37 29.72 3.12 SD 35.99 33.91 0.00 560.08 24.68 0.18 0.23 3.57 0.46 0.23 11.70 15.94 0.51 0.09 1.47 0.17 0.30 3.90 120.00 2.65 Min 0.00 0.00 1.00 1.00 0.00 −4.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 1503.0 857.5 1.0 1892.0 99.9 4.2 9.2 22.0 1.0 1.0 805.2 153.0 9.0 1.0 26.0 0.8 1.0 83.8 8844.5 153.0 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 1 Invention value 1.00 2 Value prior inventions 0.30 1.00 3 Industry dummy −0.02 0.04 1.00 4 Number of patents −0.06 0.05 0.48 1.00 5 Firm size −0.04 −0.03 −0.21 0.21 1.00 6 ROA 0.02 0.00 0.00 0.08 0.32 1.00 7 R&D intensity 0.00 0.00 −0.12 −0.09 −0.11 −0.26 1.00 8 R&D alliances 0.11 0.06 −0.02 0.01 0.25 0.17 −0.04 1.00 9 Star inventor 0.18 0.16 0.02 0.15 −0.12 −0.01 −0.01 −0.03 1.00 10 Technological distance −0.02 −0.03 0.25 0.18 0.15 0.11 −0.10 0.07 −0.15 1.00 11 Variance value prior inventions 0.15 0.57 −0.03 −0.02 −0.01 −0.01 0.01 0.01 0.03 −0.01 1.00 12 Number of prior inventions 0.06 0.04 −0.05 0.07 −0.04 −0.05 0.04 −0.06 0.18 −0.08 0.00 1.00 13 Number of scientific references 0.02 0.02 −0.28 −0.12 0.00 −0.06 0.07 0.01 0.07 −0.16 0.02 0.21 1.00 14 Science orientation −0.03 −0.03 −0.27 −0.14 0.04 −0.01 0.03 0.05 −0.03 −0.10 0.01 −0.23 0.48 1.00 15 Number of inventors 0.02 0.00 −0.27 −0.15 0.07 0.00 0.04 −0.01 0.18 −0.17 0.01 0.09 0.13 0.06 1.00 16 International diversity 0.01 −0.07 −0.40 −0.22 0.08 −0.02 0.07 0.00 0.00 −0.18 0.01 0.16 0.27 −0.07 0.17 1.00 17 Techn. diversity (prior inv.) 0.04 0.04 −0.26 −0.11 0.04 −0.04 0.05 −0.01 −0.01 −0.05 0.03 0.26 0.16 −0.24 0.09 0.32 1.00 18 Age prior inventions −0.03 −0.21 −0.25 −0.14 0.08 0.01 0.01 −0.01 −0.06 0.02 −0.02 0.17 0.05 −0.12 0.03 0.20 0.19 1.00 19 Variance age prior inventions 0.01 −0.06 −0.09 −0.05 0.04 0.00 0.00 −0.01 −0.03 0.03 −0.01 0.05 −0.01 −0.05 −0.01 0.06 0.09 0.57 1.00 20 Technological scope 0.01 −0.02 −0.38 −0.19 0.09 −0.02 0.06 0.00 0.07 −0.40 0.01 0.10 0.19 0.11 0.27 0.27 0.17 0.08 0.01 1.00 Overall (n = 139,529) M 22.75 31.84 0.64 473.70 29.45 0.02 0.45 1.53 0.32 0.63 3.57 13.87 0.53 0.08 2.63 0.16 0.52 5.28 39.53 5.15 SD 42.85 48.86 0.48 518.53 27.36 0.25 3.12 3.19 0.00 0.24 66.45 17.31 0.52 0.15 1.91 0.23 0.30 4.91 138.92 7.09 Min 0.00 0.00 0.00 1.00 0.00 −17.23 −1.73 0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 1.0 1892.0 122.0 4.2 210.4 22.0 0.2 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 8844.5 166.0 Pharmaceuticals (n = 50,051) M 23.92 29.46 0.00 137.64 36.96 0.95 0.95 1.61 0.29 0.55 5.99 15.08 0.73 0.13 3.31 0.29 0.63 6.92 57.07 8.78 SD 52.92 67.76 0.00 112.42 30.17 5.17 5.17 2.37 0.45 0.24 109.80 19.47 0.47 0.21 2.38 0.26 0.28 5.98 166.05 10.35 Min 0.00 0.00 0.00 1.00 0.00 −1.73 −1.73 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 0.0 431.0 122.0 210.4 210.4 11.0 1.0 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 6612.5 166.0 Semiconductor (n = 89,478) M 22.10 33.17 1.00 661.68 25.25 0.02 0.17 1.49 0.31 0.68 2.22 13.20 0.42 0.05 2.25 0.09 0.47 4.37 29.72 3.12 SD 35.99 33.91 0.00 560.08 24.68 0.18 0.23 3.57 0.46 0.23 11.70 15.94 0.51 0.09 1.47 0.17 0.30 3.90 120.00 2.65 Min 0.00 0.00 1.00 1.00 0.00 −4.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 1503.0 857.5 1.0 1892.0 99.9 4.2 9.2 22.0 1.0 1.0 805.2 153.0 9.0 1.0 26.0 0.8 1.0 83.8 8844.5 153.0 Table 1. Descriptive statistics and correlation matrix Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 1 Invention value 1.00 2 Value prior inventions 0.30 1.00 3 Industry dummy −0.02 0.04 1.00 4 Number of patents −0.06 0.05 0.48 1.00 5 Firm size −0.04 −0.03 −0.21 0.21 1.00 6 ROA 0.02 0.00 0.00 0.08 0.32 1.00 7 R&D intensity 0.00 0.00 −0.12 −0.09 −0.11 −0.26 1.00 8 R&D alliances 0.11 0.06 −0.02 0.01 0.25 0.17 −0.04 1.00 9 Star inventor 0.18 0.16 0.02 0.15 −0.12 −0.01 −0.01 −0.03 1.00 10 Technological distance −0.02 −0.03 0.25 0.18 0.15 0.11 −0.10 0.07 −0.15 1.00 11 Variance value prior inventions 0.15 0.57 −0.03 −0.02 −0.01 −0.01 0.01 0.01 0.03 −0.01 1.00 12 Number of prior inventions 0.06 0.04 −0.05 0.07 −0.04 −0.05 0.04 −0.06 0.18 −0.08 0.00 1.00 13 Number of scientific references 0.02 0.02 −0.28 −0.12 0.00 −0.06 0.07 0.01 0.07 −0.16 0.02 0.21 1.00 14 Science orientation −0.03 −0.03 −0.27 −0.14 0.04 −0.01 0.03 0.05 −0.03 −0.10 0.01 −0.23 0.48 1.00 15 Number of inventors 0.02 0.00 −0.27 −0.15 0.07 0.00 0.04 −0.01 0.18 −0.17 0.01 0.09 0.13 0.06 1.00 16 International diversity 0.01 −0.07 −0.40 −0.22 0.08 −0.02 0.07 0.00 0.00 −0.18 0.01 0.16 0.27 −0.07 0.17 1.00 17 Techn. diversity (prior inv.) 0.04 0.04 −0.26 −0.11 0.04 −0.04 0.05 −0.01 −0.01 −0.05 0.03 0.26 0.16 −0.24 0.09 0.32 1.00 18 Age prior inventions −0.03 −0.21 −0.25 −0.14 0.08 0.01 0.01 −0.01 −0.06 0.02 −0.02 0.17 0.05 −0.12 0.03 0.20 0.19 1.00 19 Variance age prior inventions 0.01 −0.06 −0.09 −0.05 0.04 0.00 0.00 −0.01 −0.03 0.03 −0.01 0.05 −0.01 −0.05 −0.01 0.06 0.09 0.57 1.00 20 Technological scope 0.01 −0.02 −0.38 −0.19 0.09 −0.02 0.06 0.00 0.07 −0.40 0.01 0.10 0.19 0.11 0.27 0.27 0.17 0.08 0.01 1.00 Overall (n = 139,529) M 22.75 31.84 0.64 473.70 29.45 0.02 0.45 1.53 0.32 0.63 3.57 13.87 0.53 0.08 2.63 0.16 0.52 5.28 39.53 5.15 SD 42.85 48.86 0.48 518.53 27.36 0.25 3.12 3.19 0.00 0.24 66.45 17.31 0.52 0.15 1.91 0.23 0.30 4.91 138.92 7.09 Min 0.00 0.00 0.00 1.00 0.00 −17.23 −1.73 0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 1.0 1892.0 122.0 4.2 210.4 22.0 0.2 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 8844.5 166.0 Pharmaceuticals (n = 50,051) M 23.92 29.46 0.00 137.64 36.96 0.95 0.95 1.61 0.29 0.55 5.99 15.08 0.73 0.13 3.31 0.29 0.63 6.92 57.07 8.78 SD 52.92 67.76 0.00 112.42 30.17 5.17 5.17 2.37 0.45 0.24 109.80 19.47 0.47 0.21 2.38 0.26 0.28 5.98 166.05 10.35 Min 0.00 0.00 0.00 1.00 0.00 −1.73 −1.73 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 0.0 431.0 122.0 210.4 210.4 11.0 1.0 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 6612.5 166.0 Semiconductor (n = 89,478) M 22.10 33.17 1.00 661.68 25.25 0.02 0.17 1.49 0.31 0.68 2.22 13.20 0.42 0.05 2.25 0.09 0.47 4.37 29.72 3.12 SD 35.99 33.91 0.00 560.08 24.68 0.18 0.23 3.57 0.46 0.23 11.70 15.94 0.51 0.09 1.47 0.17 0.30 3.90 120.00 2.65 Min 0.00 0.00 1.00 1.00 0.00 −4.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 1503.0 857.5 1.0 1892.0 99.9 4.2 9.2 22.0 1.0 1.0 805.2 153.0 9.0 1.0 26.0 0.8 1.0 83.8 8844.5 153.0 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 1 Invention value 1.00 2 Value prior inventions 0.30 1.00 3 Industry dummy −0.02 0.04 1.00 4 Number of patents −0.06 0.05 0.48 1.00 5 Firm size −0.04 −0.03 −0.21 0.21 1.00 6 ROA 0.02 0.00 0.00 0.08 0.32 1.00 7 R&D intensity 0.00 0.00 −0.12 −0.09 −0.11 −0.26 1.00 8 R&D alliances 0.11 0.06 −0.02 0.01 0.25 0.17 −0.04 1.00 9 Star inventor 0.18 0.16 0.02 0.15 −0.12 −0.01 −0.01 −0.03 1.00 10 Technological distance −0.02 −0.03 0.25 0.18 0.15 0.11 −0.10 0.07 −0.15 1.00 11 Variance value prior inventions 0.15 0.57 −0.03 −0.02 −0.01 −0.01 0.01 0.01 0.03 −0.01 1.00 12 Number of prior inventions 0.06 0.04 −0.05 0.07 −0.04 −0.05 0.04 −0.06 0.18 −0.08 0.00 1.00 13 Number of scientific references 0.02 0.02 −0.28 −0.12 0.00 −0.06 0.07 0.01 0.07 −0.16 0.02 0.21 1.00 14 Science orientation −0.03 −0.03 −0.27 −0.14 0.04 −0.01 0.03 0.05 −0.03 −0.10 0.01 −0.23 0.48 1.00 15 Number of inventors 0.02 0.00 −0.27 −0.15 0.07 0.00 0.04 −0.01 0.18 −0.17 0.01 0.09 0.13 0.06 1.00 16 International diversity 0.01 −0.07 −0.40 −0.22 0.08 −0.02 0.07 0.00 0.00 −0.18 0.01 0.16 0.27 −0.07 0.17 1.00 17 Techn. diversity (prior inv.) 0.04 0.04 −0.26 −0.11 0.04 −0.04 0.05 −0.01 −0.01 −0.05 0.03 0.26 0.16 −0.24 0.09 0.32 1.00 18 Age prior inventions −0.03 −0.21 −0.25 −0.14 0.08 0.01 0.01 −0.01 −0.06 0.02 −0.02 0.17 0.05 −0.12 0.03 0.20 0.19 1.00 19 Variance age prior inventions 0.01 −0.06 −0.09 −0.05 0.04 0.00 0.00 −0.01 −0.03 0.03 −0.01 0.05 −0.01 −0.05 −0.01 0.06 0.09 0.57 1.00 20 Technological scope 0.01 −0.02 −0.38 −0.19 0.09 −0.02 0.06 0.00 0.07 −0.40 0.01 0.10 0.19 0.11 0.27 0.27 0.17 0.08 0.01 1.00 Overall (n = 139,529) M 22.75 31.84 0.64 473.70 29.45 0.02 0.45 1.53 0.32 0.63 3.57 13.87 0.53 0.08 2.63 0.16 0.52 5.28 39.53 5.15 SD 42.85 48.86 0.48 518.53 27.36 0.25 3.12 3.19 0.00 0.24 66.45 17.31 0.52 0.15 1.91 0.23 0.30 4.91 138.92 7.09 Min 0.00 0.00 0.00 1.00 0.00 −17.23 −1.73 0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 1.0 1892.0 122.0 4.2 210.4 22.0 0.2 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 8844.5 166.0 Pharmaceuticals (n = 50,051) M 23.92 29.46 0.00 137.64 36.96 0.95 0.95 1.61 0.29 0.55 5.99 15.08 0.73 0.13 3.31 0.29 0.63 6.92 57.07 8.78 SD 52.92 67.76 0.00 112.42 30.17 5.17 5.17 2.37 0.45 0.24 109.80 19.47 0.47 0.21 2.38 0.26 0.28 5.98 166.05 10.35 Min 0.00 0.00 0.00 1.00 0.00 −1.73 −1.73 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 5005.0 4179.4 0.0 431.0 122.0 210.4 210.4 11.0 1.0 1.0 9500.0 163.0 12.0 1.0 32.0 0.9 1.0 93.0 6612.5 166.0 Semiconductor (n = 89,478) M 22.10 33.17 1.00 661.68 25.25 0.02 0.17 1.49 0.31 0.68 2.22 13.20 0.42 0.05 2.25 0.09 0.47 4.37 29.72 3.12 SD 35.99 33.91 0.00 560.08 24.68 0.18 0.23 3.57 0.46 0.23 11.70 15.94 0.51 0.09 1.47 0.17 0.30 3.90 120.00 2.65 Min 0.00 0.00 1.00 1.00 0.00 −4.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 Max 1503.0 857.5 1.0 1892.0 99.9 4.2 9.2 22.0 1.0 1.0 805.2 153.0 9.0 1.0 26.0 0.8 1.0 83.8 8844.5 153.0 Table 2 depicts the results for the QML Poisson regression for the average invention value. Model 1 shows the results for the control variables. For example, the number of star inventors, the number of prior inventions, and the technological scope are all positive and significant (P < 0.01). In addition to the number of patents and R&D alliances, most of the firm-level controls have only a limited influence on the models. Furthermore, though not shown in detail, the technology dummies are mostly significant, which implies that citation propensity differs across technological areas. In Model 2, the main effect of the value of prior inventions is tested, and its coefficient is positive (P < 0.05), while in Model 3, the logarithmic-transformed term is positive and strongly significant (P < 0.01). Model 3 also has a lower log-likelihood and better Akaike (AIC) and Bayesian (BIC) information criterion fit statistics, thereby providing support for H1. As an alternative specification, Model 4 tests the inverted U-shaped relationship by adding the quadratic term of prior invention value to its main effect. In this model, the main effect is positive and significant (P < 0.01), but the quadratic term is negative, not significant, and very small. However, the logarithmic transformation in Model 3 shows a better fit with AIC and BIC statistics; therefore, this specification is preferred. Table 2. Regression analysis of invention values Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . NBR . OLS . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Number of patents 0.000** 0.000** 0.000*** 0.000*** −0.001*** 0.000*** 0.000*** 0.000** 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size −0.001 −0.001 −0.001 −0.001 0.004 0.001 0.000 −0.001 −0.001*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.003 −0.002 −0.002 −0.002 0.000 0.000 ROA 0.038 0.076 0.032 0.064 0.025 0.055 0.012 0.043 0.027** 0.061*** −0.045 −0.074 −0.036 −0.059 −0.035 −0.043 −0.032 −0.042 −0.014 −0.023 R&D intensity 0.003 0.002 0.002 0.001 0.001 0.023 0.001 0.002 0.002 0.001 −0.002 −0.002 −0.002 −0.002 −0.002 −0.025 −0.003 −0.002 −0.001 −0.002 R&D alliances −0.003 −0.004 −0.004 −0.005 0.009 −0.003 −0.005 −0.004 −0.004*** −0.003** −0.004 −0.004 −0.003 −0.003 −0.009 −0.004 −0.003 −0.004 −0.001 −0.002 Star inventor 0.550*** 0.514*** 0.421*** 0.483*** 0.531*** 0.356*** 0.401*** 0.472*** 0.203*** 0.330*** −0.031 −0.031 −0.024 −0.032 −0.049 −0.022 −0.024 −0.025 −0.005 −0.008 Technological distance 0.072 0.102 0.147** 0.118* 0.306*** −0.067 0.123 0.090 0.244*** 0.188*** −0.076 −0.074 −0.064 −0.066 −0.086 −0.067 −0.064 −0.064 −0.014 −0.021 Variance value prior inventions 0.000*** 0.000 0.000 0.000** 0.000 0.000 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.003*** 0.003*** 0.003*** 0.003*** 0.005*** 0.001 0.003*** 0.003*** 0.002*** 0.004*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 0.000 Number of scientific references 0.106*** 0.101*** −0.063*** 0.087*** −0.112*** −0.012 −0.072*** −0.003 −0.007 −0.056*** −0.018 −0.018 −0.019 −0.018 −0.033 −0.025 −0.021 −0.019 −0.006 −0.008 Science orientation −0.399*** −0.401*** 0.868*** −0.320*** 0.768*** 0.774*** 1.025*** 0.395*** 0.078*** 0.707*** −0.120 −0.119 −0.128 −0.114 −0.146 −0.131 −0.138 −0.112 −0.028 −0.034 Number of inventors 0.014*** 0.015*** 0.015*** 0.015*** 0.011* 0.020*** 0.016*** 0.015*** 0.010*** 0.018*** −0.004 −0.004 −0.004 −0.004 −0.006 −0.002 −0.003 −0.004 −0.001 −0.002 International diversity −0.028 0.028 0.214*** 0.073 0.304*** 0.187*** 0.224*** 0.073** 0.089*** 0.234*** −0.038 −0.043 −0.030 −0.055 −0.042 −0.034 −0.030 −0.036 −0.013 −0.017 Techn. diversity (prior inv.) 0.174*** 0.165*** 0.024 0.123** −0.151** 0.092*** −0.009 0.023 −0.078*** −0.079*** −0.063 −0.057 −0.042 −0.051 −0.063 −0.030 −0.041 −0.057 −0.009 −0.013 Age prior inventions −0.029*** −0.022*** 0.029*** −0.013*** 0.024*** 0.034*** 0.031*** 0.000 0.012*** 0.017*** −0.003 −0.004 −0.004 −0.004 −0.004 −0.005 −0.003 −0.004 −0.001 −0.001 Variance age prior inventions 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope 0.011*** 0.011*** 0.010*** 0.010*** 0.010*** 0.015*** 0.010*** 0.011*** 0.006*** 0.010*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.004 −0.002 −0.002 0.000 −0.001 Value prior inventions 0.002** 0.004*** −0.001 −0.001 Value prior inventions (ln) 0.440*** 0.385*** 0.488*** 0.448*** 0.283*** 0.390*** −0.024 −0.027 −0.037 −0.024 −0.003 −0.004 Value prior inventions (sq) −0.000 0.000 Value prior inventions (ln) (alt.) 0.249*** −0.023 Constant −0.870*** 1.405*** −0.022 −0.034 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Full Firm-level control Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Observations 138,876 138,876 138,876 138,876 49,509 89,367 137,470 138,876 138,876 138,876 AIC 3,824,507 3,744,129 3,481,733 3,658,099 1,371,038 2,078,448 3,332,817 3,628,597 1,077,600 432,820 BIC 3,825,000 3,744,631 3,482,235 3,658,610 1,371,488 2,078,928 3,333,319 3,629,099 1,078,112 433,331 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . NBR . OLS . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Number of patents 0.000** 0.000** 0.000*** 0.000*** −0.001*** 0.000*** 0.000*** 0.000** 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size −0.001 −0.001 −0.001 −0.001 0.004 0.001 0.000 −0.001 −0.001*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.003 −0.002 −0.002 −0.002 0.000 0.000 ROA 0.038 0.076 0.032 0.064 0.025 0.055 0.012 0.043 0.027** 0.061*** −0.045 −0.074 −0.036 −0.059 −0.035 −0.043 −0.032 −0.042 −0.014 −0.023 R&D intensity 0.003 0.002 0.002 0.001 0.001 0.023 0.001 0.002 0.002 0.001 −0.002 −0.002 −0.002 −0.002 −0.002 −0.025 −0.003 −0.002 −0.001 −0.002 R&D alliances −0.003 −0.004 −0.004 −0.005 0.009 −0.003 −0.005 −0.004 −0.004*** −0.003** −0.004 −0.004 −0.003 −0.003 −0.009 −0.004 −0.003 −0.004 −0.001 −0.002 Star inventor 0.550*** 0.514*** 0.421*** 0.483*** 0.531*** 0.356*** 0.401*** 0.472*** 0.203*** 0.330*** −0.031 −0.031 −0.024 −0.032 −0.049 −0.022 −0.024 −0.025 −0.005 −0.008 Technological distance 0.072 0.102 0.147** 0.118* 0.306*** −0.067 0.123 0.090 0.244*** 0.188*** −0.076 −0.074 −0.064 −0.066 −0.086 −0.067 −0.064 −0.064 −0.014 −0.021 Variance value prior inventions 0.000*** 0.000 0.000 0.000** 0.000 0.000 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.003*** 0.003*** 0.003*** 0.003*** 0.005*** 0.001 0.003*** 0.003*** 0.002*** 0.004*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 0.000 Number of scientific references 0.106*** 0.101*** −0.063*** 0.087*** −0.112*** −0.012 −0.072*** −0.003 −0.007 −0.056*** −0.018 −0.018 −0.019 −0.018 −0.033 −0.025 −0.021 −0.019 −0.006 −0.008 Science orientation −0.399*** −0.401*** 0.868*** −0.320*** 0.768*** 0.774*** 1.025*** 0.395*** 0.078*** 0.707*** −0.120 −0.119 −0.128 −0.114 −0.146 −0.131 −0.138 −0.112 −0.028 −0.034 Number of inventors 0.014*** 0.015*** 0.015*** 0.015*** 0.011* 0.020*** 0.016*** 0.015*** 0.010*** 0.018*** −0.004 −0.004 −0.004 −0.004 −0.006 −0.002 −0.003 −0.004 −0.001 −0.002 International diversity −0.028 0.028 0.214*** 0.073 0.304*** 0.187*** 0.224*** 0.073** 0.089*** 0.234*** −0.038 −0.043 −0.030 −0.055 −0.042 −0.034 −0.030 −0.036 −0.013 −0.017 Techn. diversity (prior inv.) 0.174*** 0.165*** 0.024 0.123** −0.151** 0.092*** −0.009 0.023 −0.078*** −0.079*** −0.063 −0.057 −0.042 −0.051 −0.063 −0.030 −0.041 −0.057 −0.009 −0.013 Age prior inventions −0.029*** −0.022*** 0.029*** −0.013*** 0.024*** 0.034*** 0.031*** 0.000 0.012*** 0.017*** −0.003 −0.004 −0.004 −0.004 −0.004 −0.005 −0.003 −0.004 −0.001 −0.001 Variance age prior inventions 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope 0.011*** 0.011*** 0.010*** 0.010*** 0.010*** 0.015*** 0.010*** 0.011*** 0.006*** 0.010*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.004 −0.002 −0.002 0.000 −0.001 Value prior inventions 0.002** 0.004*** −0.001 −0.001 Value prior inventions (ln) 0.440*** 0.385*** 0.488*** 0.448*** 0.283*** 0.390*** −0.024 −0.027 −0.037 −0.024 −0.003 −0.004 Value prior inventions (sq) −0.000 0.000 Value prior inventions (ln) (alt.) 0.249*** −0.023 Constant −0.870*** 1.405*** −0.022 −0.034 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Full Firm-level control Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Observations 138,876 138,876 138,876 138,876 49,509 89,367 137,470 138,876 138,876 138,876 AIC 3,824,507 3,744,129 3,481,733 3,658,099 1,371,038 2,078,448 3,332,817 3,628,597 1,077,600 432,820 BIC 3,825,000 3,744,631 3,482,235 3,658,610 1,371,488 2,078,928 3,333,319 3,629,099 1,078,112 433,331 Table 2. Regression analysis of invention values Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . NBR . OLS . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Number of patents 0.000** 0.000** 0.000*** 0.000*** −0.001*** 0.000*** 0.000*** 0.000** 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size −0.001 −0.001 −0.001 −0.001 0.004 0.001 0.000 −0.001 −0.001*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.003 −0.002 −0.002 −0.002 0.000 0.000 ROA 0.038 0.076 0.032 0.064 0.025 0.055 0.012 0.043 0.027** 0.061*** −0.045 −0.074 −0.036 −0.059 −0.035 −0.043 −0.032 −0.042 −0.014 −0.023 R&D intensity 0.003 0.002 0.002 0.001 0.001 0.023 0.001 0.002 0.002 0.001 −0.002 −0.002 −0.002 −0.002 −0.002 −0.025 −0.003 −0.002 −0.001 −0.002 R&D alliances −0.003 −0.004 −0.004 −0.005 0.009 −0.003 −0.005 −0.004 −0.004*** −0.003** −0.004 −0.004 −0.003 −0.003 −0.009 −0.004 −0.003 −0.004 −0.001 −0.002 Star inventor 0.550*** 0.514*** 0.421*** 0.483*** 0.531*** 0.356*** 0.401*** 0.472*** 0.203*** 0.330*** −0.031 −0.031 −0.024 −0.032 −0.049 −0.022 −0.024 −0.025 −0.005 −0.008 Technological distance 0.072 0.102 0.147** 0.118* 0.306*** −0.067 0.123 0.090 0.244*** 0.188*** −0.076 −0.074 −0.064 −0.066 −0.086 −0.067 −0.064 −0.064 −0.014 −0.021 Variance value prior inventions 0.000*** 0.000 0.000 0.000** 0.000 0.000 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.003*** 0.003*** 0.003*** 0.003*** 0.005*** 0.001 0.003*** 0.003*** 0.002*** 0.004*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 0.000 Number of scientific references 0.106*** 0.101*** −0.063*** 0.087*** −0.112*** −0.012 −0.072*** −0.003 −0.007 −0.056*** −0.018 −0.018 −0.019 −0.018 −0.033 −0.025 −0.021 −0.019 −0.006 −0.008 Science orientation −0.399*** −0.401*** 0.868*** −0.320*** 0.768*** 0.774*** 1.025*** 0.395*** 0.078*** 0.707*** −0.120 −0.119 −0.128 −0.114 −0.146 −0.131 −0.138 −0.112 −0.028 −0.034 Number of inventors 0.014*** 0.015*** 0.015*** 0.015*** 0.011* 0.020*** 0.016*** 0.015*** 0.010*** 0.018*** −0.004 −0.004 −0.004 −0.004 −0.006 −0.002 −0.003 −0.004 −0.001 −0.002 International diversity −0.028 0.028 0.214*** 0.073 0.304*** 0.187*** 0.224*** 0.073** 0.089*** 0.234*** −0.038 −0.043 −0.030 −0.055 −0.042 −0.034 −0.030 −0.036 −0.013 −0.017 Techn. diversity (prior inv.) 0.174*** 0.165*** 0.024 0.123** −0.151** 0.092*** −0.009 0.023 −0.078*** −0.079*** −0.063 −0.057 −0.042 −0.051 −0.063 −0.030 −0.041 −0.057 −0.009 −0.013 Age prior inventions −0.029*** −0.022*** 0.029*** −0.013*** 0.024*** 0.034*** 0.031*** 0.000 0.012*** 0.017*** −0.003 −0.004 −0.004 −0.004 −0.004 −0.005 −0.003 −0.004 −0.001 −0.001 Variance age prior inventions 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope 0.011*** 0.011*** 0.010*** 0.010*** 0.010*** 0.015*** 0.010*** 0.011*** 0.006*** 0.010*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.004 −0.002 −0.002 0.000 −0.001 Value prior inventions 0.002** 0.004*** −0.001 −0.001 Value prior inventions (ln) 0.440*** 0.385*** 0.488*** 0.448*** 0.283*** 0.390*** −0.024 −0.027 −0.037 −0.024 −0.003 −0.004 Value prior inventions (sq) −0.000 0.000 Value prior inventions (ln) (alt.) 0.249*** −0.023 Constant −0.870*** 1.405*** −0.022 −0.034 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Full Firm-level control Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Observations 138,876 138,876 138,876 138,876 49,509 89,367 137,470 138,876 138,876 138,876 AIC 3,824,507 3,744,129 3,481,733 3,658,099 1,371,038 2,078,448 3,332,817 3,628,597 1,077,600 432,820 BIC 3,825,000 3,744,631 3,482,235 3,658,610 1,371,488 2,078,928 3,333,319 3,629,099 1,078,112 433,331 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . QML Poi. . NBR . OLS . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Number of patents 0.000** 0.000** 0.000*** 0.000*** −0.001*** 0.000*** 0.000*** 0.000** 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size −0.001 −0.001 −0.001 −0.001 0.004 0.001 0.000 −0.001 −0.001*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.003 −0.002 −0.002 −0.002 0.000 0.000 ROA 0.038 0.076 0.032 0.064 0.025 0.055 0.012 0.043 0.027** 0.061*** −0.045 −0.074 −0.036 −0.059 −0.035 −0.043 −0.032 −0.042 −0.014 −0.023 R&D intensity 0.003 0.002 0.002 0.001 0.001 0.023 0.001 0.002 0.002 0.001 −0.002 −0.002 −0.002 −0.002 −0.002 −0.025 −0.003 −0.002 −0.001 −0.002 R&D alliances −0.003 −0.004 −0.004 −0.005 0.009 −0.003 −0.005 −0.004 −0.004*** −0.003** −0.004 −0.004 −0.003 −0.003 −0.009 −0.004 −0.003 −0.004 −0.001 −0.002 Star inventor 0.550*** 0.514*** 0.421*** 0.483*** 0.531*** 0.356*** 0.401*** 0.472*** 0.203*** 0.330*** −0.031 −0.031 −0.024 −0.032 −0.049 −0.022 −0.024 −0.025 −0.005 −0.008 Technological distance 0.072 0.102 0.147** 0.118* 0.306*** −0.067 0.123 0.090 0.244*** 0.188*** −0.076 −0.074 −0.064 −0.066 −0.086 −0.067 −0.064 −0.064 −0.014 −0.021 Variance value prior inventions 0.000*** 0.000 0.000 0.000** 0.000 0.000 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.003*** 0.003*** 0.003*** 0.003*** 0.005*** 0.001 0.003*** 0.003*** 0.002*** 0.004*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 0.000 Number of scientific references 0.106*** 0.101*** −0.063*** 0.087*** −0.112*** −0.012 −0.072*** −0.003 −0.007 −0.056*** −0.018 −0.018 −0.019 −0.018 −0.033 −0.025 −0.021 −0.019 −0.006 −0.008 Science orientation −0.399*** −0.401*** 0.868*** −0.320*** 0.768*** 0.774*** 1.025*** 0.395*** 0.078*** 0.707*** −0.120 −0.119 −0.128 −0.114 −0.146 −0.131 −0.138 −0.112 −0.028 −0.034 Number of inventors 0.014*** 0.015*** 0.015*** 0.015*** 0.011* 0.020*** 0.016*** 0.015*** 0.010*** 0.018*** −0.004 −0.004 −0.004 −0.004 −0.006 −0.002 −0.003 −0.004 −0.001 −0.002 International diversity −0.028 0.028 0.214*** 0.073 0.304*** 0.187*** 0.224*** 0.073** 0.089*** 0.234*** −0.038 −0.043 −0.030 −0.055 −0.042 −0.034 −0.030 −0.036 −0.013 −0.017 Techn. diversity (prior inv.) 0.174*** 0.165*** 0.024 0.123** −0.151** 0.092*** −0.009 0.023 −0.078*** −0.079*** −0.063 −0.057 −0.042 −0.051 −0.063 −0.030 −0.041 −0.057 −0.009 −0.013 Age prior inventions −0.029*** −0.022*** 0.029*** −0.013*** 0.024*** 0.034*** 0.031*** 0.000 0.012*** 0.017*** −0.003 −0.004 −0.004 −0.004 −0.004 −0.005 −0.003 −0.004 −0.001 −0.001 Variance age prior inventions 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope 0.011*** 0.011*** 0.010*** 0.010*** 0.010*** 0.015*** 0.010*** 0.011*** 0.006*** 0.010*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.004 −0.002 −0.002 0.000 −0.001 Value prior inventions 0.002** 0.004*** −0.001 −0.001 Value prior inventions (ln) 0.440*** 0.385*** 0.488*** 0.448*** 0.283*** 0.390*** −0.024 −0.027 −0.037 −0.024 −0.003 −0.004 Value prior inventions (sq) −0.000 0.000 Value prior inventions (ln) (alt.) 0.249*** −0.023 Constant −0.870*** 1.405*** −0.022 −0.034 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Full Firm-level control Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Fixed Effect Observations 138,876 138,876 138,876 138,876 49,509 89,367 137,470 138,876 138,876 138,876 AIC 3,824,507 3,744,129 3,481,733 3,658,099 1,371,038 2,078,448 3,332,817 3,628,597 1,077,600 432,820 BIC 3,825,000 3,744,631 3,482,235 3,658,610 1,371,488 2,078,928 3,333,319 3,629,099 1,078,112 433,331 To aid the interpretation and check of the validity of the findings, multiple additional models were performed. First, because the previous models could not be performed with an industry dummy (due to its time invariance), the sample was divided between the two industries. Models 5 and 6 show the results from these observations. Despite some changes in the control variables, the effects of the prior invention value variables are consistent with previous results. Second, the descriptive statistics show a wide distribution of several key variables, including prior invention value. Thus, to examine the influence of outliers, which can be particularly influential in non-linear models (Haans et al., 2015), Model 7 was performed without outliers. The outliers refer to the top percentile of prior invention values, which roughly coincides with the definition of outliers as “mean plus four times the standard deviation.” The results for the reduced sample are in line with previous findings. Third, because the value of an invention can affect the citation pattern of prior inventions—and as a consequence, the value of prior inventions—the models needed to account for this. Therefore, the potential endogeneity was addressed by performing all models with an adjusted variable for prior invention value, which only uses the forward citations of prior inventions up to the application year of the focal invention. This procedure truncates the citation counts but also ensures that the popularity of a focal patent does not confound the value of prior inventions. Model 8 shows the results for the fully specified procedure, with an adjusted value for the prior invention variable. Under these conditions, the logarithmic transformation remains positive and significant (P < 0.01). Fourth, all models were also performed with NBR and OLS regression (both with fixed firm effects). However, the different estimation methods did not change the interpretation of the main findings, as Models 9 and 10 show.1 To ease the interpretation of non-linear effects, Figure 1 graphically presents the main results. The graphs depict the relationship between prior invention values and subsequent invention values, on the basis of the transformed estimation for both industries up to (approximately) the 99th percentile of prior invention values. The graph clearly shows the positive but diminishing relationship, which is relatively similar in both industries. Figure 1. Open in new tabDownload slide Invention values by industry. Figure 1. Open in new tabDownload slide Invention values by industry. 4.1 Breakthrough inventions Table 3 presents the results of the logit regression of breakthrough inventions. Again, because breakthrough inventions are relatively rare events, not all firms in the sample had breakthroughs each year; therefore, breakthrough inventions were performed with random firm effects and not fixed firm effects. As such, it was possible to perform the estimation with an industry dummy to account for the differences between the two industry subsamples. After testing the control variables in Model 1, Model 2 illustrates that prior invention value has a positive and significant (P < 0.01) relationship to breakthrough inventions. From this, Model 3 shows that the logarithmic transformation of prior invention value is negative and significant (P < 0.01). Comparison of the two models shows that Model 3 is preferable because of its lower log-likelihood and better AIC and BIC fit statistics. Model 4 tests the alternative quadratic specification and shows that the main effect is positive and significant (P < 0.01). By depicting a curvilinear (inverted U-shaped) relationship, Model 4 also shows that the estimate for the transformed variable is negative, significant, and relatively small (P < 0.01). However, also in this case, the logarithmic transformation yields a better model fit (i.e., based on AIC and BIC criteria). Table 3. Regression analysis of breakthrough inventions Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy 0.247 0.405* 0.602*** 0.446** − − 0.461** 0.481** − −0.221 −0.224 −0.210 −0.211 – – −0.216 −0.212 – Number of patents 0.000 0.000 0.000 0.000 −0.003*** 0.000** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Firm size −0.006** −0.006** −0.005* −0.006** −0.006 0.001 −0.003 −0.005 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.004 −0.003 −0.003 0.000 ROA 0.056 0.101 0.064 0.028 0.307 −0.045 −0.087 0.086 0.000 −0.169 −0.174 −0.174 −0.167 −0.283 −0.283 −0.165 −0.174 −0.002 R&D intensity 0.010 0.011 0.010 0.009 0.010 0.067 −0.011 0.010 0.000 −0.008 −0.008 −0.007 −0.008 −0.008 −0.132 −0.020 −0.007 0.000 R&D alliances 0.002 0.000 −0.009 −0.022* 0.075*** −0.018 −0.005 −0.001 0.000 −0.011 −0.011 −0.012 −0.012 −0.027 −0.014 −0.013 −0.012 0.000 Star inventor 1.955*** 1.887*** 1.583*** 1.780*** 2.025*** 1.392*** 1.594*** 1.719*** 0.018*** −0.073 −0.073 −0.074 −0.074 −0.138 −0.089 −0.078 −0.073 −0.001 Technological distance 0.203 0.272 0.386** 0.313* 0.920*** −0.215 0.278 0.270 0.006*** −0.172 −0.173 −0.176 −0.175 −0.273 −0.237 −0.187 −0.174 −0.002 Variance value prior inventions 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.009*** 0.009*** 0.006*** 0.008*** 0.011*** 0.002 0.005*** 0.008*** 0.000*** −0.001 −0.001 −0.001 −0.001 −0.002 −0.002 −0.002 −0.001 0.000 Number of scientific references 0.347*** 0.352*** 0.249*** 0.377*** 0.150 0.284*** 0.165* 0.164** −0.003*** −0.070 −0.072 −0.082 −0.075 −0.147 −0.105 −0.087 −0.079 −0.001 Science orientation −0.861** −1.091*** −0.174 −1.365*** −0.313 0.221 1.246** 0.789* 0.032 −0.357 −0.394 −0.494 −0.463 −0.719 −0.697 −0.503 −0.461 −0.003 Number of inventors 0.028** 0.033** 0.040*** 0.033** 0.037** 0.050** 0.044*** 0.036*** 0.000* −0.013 −0.013 −0.014 −0.014 −0.019 −0.020 −0.014 −0.013 0.000 International diversity −0.026 0.118 0.638*** 0.392** 0.779*** 0.461** 0.668*** 0.326** 0.002 −0.158 −0.160 −0.167 −0.163 −0.253 −0.233 −0.176 −0.163 −0.002 Techn. Diversity (prior inv.) 0.792*** 0.747*** 0.290** 0.637*** −0.280 0.436*** 0.214 0.386*** 0.001 −0.130 −0.131 −0.134 −0.133 −0.258 −0.160 −0.142 −0.133 −0.001 Age prior inventions −0.117*** −0.123*** 0.050*** −0.046*** −0.008 0.100*** 0.072*** −0.016 0.001*** −0.011 −0.011 −0.012 −0.011 −0.019 −0.016 −0.013 −0.012 0.000 Variance age prior inventions 0.001*** 0.001*** 0.000 0.001** 0.000 −0.001* −0.001* 0.000 0.000*** 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Technological scope 0.022*** 0.022*** 0.020*** 0.021*** 0.019*** 0.029*** 0.019*** 0.020*** 0.000*** −0.004 −0.004 −0.004 −0.004 −0.004 −0.009 −0.004 −0.004 0.000 Value prior inventions 0.002*** 0.013*** 0.000 −0.001 Value prior inventions (ln) 1.328*** 1.017*** 1.584*** 1.471*** 0.010*** −0.044 −0.063 −0.064 −0.061 0.000 Value prior inventions (sq) −0.000*** 0.000 Value prior inventions (ln) (alt.) 0.768*** −0.034 Constant −6.611*** −6.996*** −12.356*** −7.568*** −11.044*** −12.362*** −12.839*** −9.556*** −0.040*** −0.281 −0.289 −0.354 −0.288 −0.525 −0.462 −0.410 −0.321 −0.003 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,442 89,336 137,471 138,876 138,876 AIC 13,305 13,134 12,264 12,726 4,267 7,935 11,231 12,712 −248,735 BIC 13,826 13,666 12,795 13,267 4,716 8,423 11,762 13,243 −248,223 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy 0.247 0.405* 0.602*** 0.446** − − 0.461** 0.481** − −0.221 −0.224 −0.210 −0.211 – – −0.216 −0.212 – Number of patents 0.000 0.000 0.000 0.000 −0.003*** 0.000** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Firm size −0.006** −0.006** −0.005* −0.006** −0.006 0.001 −0.003 −0.005 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.004 −0.003 −0.003 0.000 ROA 0.056 0.101 0.064 0.028 0.307 −0.045 −0.087 0.086 0.000 −0.169 −0.174 −0.174 −0.167 −0.283 −0.283 −0.165 −0.174 −0.002 R&D intensity 0.010 0.011 0.010 0.009 0.010 0.067 −0.011 0.010 0.000 −0.008 −0.008 −0.007 −0.008 −0.008 −0.132 −0.020 −0.007 0.000 R&D alliances 0.002 0.000 −0.009 −0.022* 0.075*** −0.018 −0.005 −0.001 0.000 −0.011 −0.011 −0.012 −0.012 −0.027 −0.014 −0.013 −0.012 0.000 Star inventor 1.955*** 1.887*** 1.583*** 1.780*** 2.025*** 1.392*** 1.594*** 1.719*** 0.018*** −0.073 −0.073 −0.074 −0.074 −0.138 −0.089 −0.078 −0.073 −0.001 Technological distance 0.203 0.272 0.386** 0.313* 0.920*** −0.215 0.278 0.270 0.006*** −0.172 −0.173 −0.176 −0.175 −0.273 −0.237 −0.187 −0.174 −0.002 Variance value prior inventions 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.009*** 0.009*** 0.006*** 0.008*** 0.011*** 0.002 0.005*** 0.008*** 0.000*** −0.001 −0.001 −0.001 −0.001 −0.002 −0.002 −0.002 −0.001 0.000 Number of scientific references 0.347*** 0.352*** 0.249*** 0.377*** 0.150 0.284*** 0.165* 0.164** −0.003*** −0.070 −0.072 −0.082 −0.075 −0.147 −0.105 −0.087 −0.079 −0.001 Science orientation −0.861** −1.091*** −0.174 −1.365*** −0.313 0.221 1.246** 0.789* 0.032 −0.357 −0.394 −0.494 −0.463 −0.719 −0.697 −0.503 −0.461 −0.003 Number of inventors 0.028** 0.033** 0.040*** 0.033** 0.037** 0.050** 0.044*** 0.036*** 0.000* −0.013 −0.013 −0.014 −0.014 −0.019 −0.020 −0.014 −0.013 0.000 International diversity −0.026 0.118 0.638*** 0.392** 0.779*** 0.461** 0.668*** 0.326** 0.002 −0.158 −0.160 −0.167 −0.163 −0.253 −0.233 −0.176 −0.163 −0.002 Techn. Diversity (prior inv.) 0.792*** 0.747*** 0.290** 0.637*** −0.280 0.436*** 0.214 0.386*** 0.001 −0.130 −0.131 −0.134 −0.133 −0.258 −0.160 −0.142 −0.133 −0.001 Age prior inventions −0.117*** −0.123*** 0.050*** −0.046*** −0.008 0.100*** 0.072*** −0.016 0.001*** −0.011 −0.011 −0.012 −0.011 −0.019 −0.016 −0.013 −0.012 0.000 Variance age prior inventions 0.001*** 0.001*** 0.000 0.001** 0.000 −0.001* −0.001* 0.000 0.000*** 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Technological scope 0.022*** 0.022*** 0.020*** 0.021*** 0.019*** 0.029*** 0.019*** 0.020*** 0.000*** −0.004 −0.004 −0.004 −0.004 −0.004 −0.009 −0.004 −0.004 0.000 Value prior inventions 0.002*** 0.013*** 0.000 −0.001 Value prior inventions (ln) 1.328*** 1.017*** 1.584*** 1.471*** 0.010*** −0.044 −0.063 −0.064 −0.061 0.000 Value prior inventions (sq) −0.000*** 0.000 Value prior inventions (ln) (alt.) 0.768*** −0.034 Constant −6.611*** −6.996*** −12.356*** −7.568*** −11.044*** −12.362*** −12.839*** −9.556*** −0.040*** −0.281 −0.289 −0.354 −0.288 −0.525 −0.462 −0.410 −0.321 −0.003 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,442 89,336 137,471 138,876 138,876 AIC 13,305 13,134 12,264 12,726 4,267 7,935 11,231 12,712 −248,735 BIC 13,826 13,666 12,795 13,267 4,716 8,423 11,762 13,243 −248,223 Notes: *** P < 0.01, ** P < 0.05, * P < 0.1. Table 3. Regression analysis of breakthrough inventions Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy 0.247 0.405* 0.602*** 0.446** − − 0.461** 0.481** − −0.221 −0.224 −0.210 −0.211 – – −0.216 −0.212 – Number of patents 0.000 0.000 0.000 0.000 −0.003*** 0.000** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Firm size −0.006** −0.006** −0.005* −0.006** −0.006 0.001 −0.003 −0.005 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.004 −0.003 −0.003 0.000 ROA 0.056 0.101 0.064 0.028 0.307 −0.045 −0.087 0.086 0.000 −0.169 −0.174 −0.174 −0.167 −0.283 −0.283 −0.165 −0.174 −0.002 R&D intensity 0.010 0.011 0.010 0.009 0.010 0.067 −0.011 0.010 0.000 −0.008 −0.008 −0.007 −0.008 −0.008 −0.132 −0.020 −0.007 0.000 R&D alliances 0.002 0.000 −0.009 −0.022* 0.075*** −0.018 −0.005 −0.001 0.000 −0.011 −0.011 −0.012 −0.012 −0.027 −0.014 −0.013 −0.012 0.000 Star inventor 1.955*** 1.887*** 1.583*** 1.780*** 2.025*** 1.392*** 1.594*** 1.719*** 0.018*** −0.073 −0.073 −0.074 −0.074 −0.138 −0.089 −0.078 −0.073 −0.001 Technological distance 0.203 0.272 0.386** 0.313* 0.920*** −0.215 0.278 0.270 0.006*** −0.172 −0.173 −0.176 −0.175 −0.273 −0.237 −0.187 −0.174 −0.002 Variance value prior inventions 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.009*** 0.009*** 0.006*** 0.008*** 0.011*** 0.002 0.005*** 0.008*** 0.000*** −0.001 −0.001 −0.001 −0.001 −0.002 −0.002 −0.002 −0.001 0.000 Number of scientific references 0.347*** 0.352*** 0.249*** 0.377*** 0.150 0.284*** 0.165* 0.164** −0.003*** −0.070 −0.072 −0.082 −0.075 −0.147 −0.105 −0.087 −0.079 −0.001 Science orientation −0.861** −1.091*** −0.174 −1.365*** −0.313 0.221 1.246** 0.789* 0.032 −0.357 −0.394 −0.494 −0.463 −0.719 −0.697 −0.503 −0.461 −0.003 Number of inventors 0.028** 0.033** 0.040*** 0.033** 0.037** 0.050** 0.044*** 0.036*** 0.000* −0.013 −0.013 −0.014 −0.014 −0.019 −0.020 −0.014 −0.013 0.000 International diversity −0.026 0.118 0.638*** 0.392** 0.779*** 0.461** 0.668*** 0.326** 0.002 −0.158 −0.160 −0.167 −0.163 −0.253 −0.233 −0.176 −0.163 −0.002 Techn. Diversity (prior inv.) 0.792*** 0.747*** 0.290** 0.637*** −0.280 0.436*** 0.214 0.386*** 0.001 −0.130 −0.131 −0.134 −0.133 −0.258 −0.160 −0.142 −0.133 −0.001 Age prior inventions −0.117*** −0.123*** 0.050*** −0.046*** −0.008 0.100*** 0.072*** −0.016 0.001*** −0.011 −0.011 −0.012 −0.011 −0.019 −0.016 −0.013 −0.012 0.000 Variance age prior inventions 0.001*** 0.001*** 0.000 0.001** 0.000 −0.001* −0.001* 0.000 0.000*** 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Technological scope 0.022*** 0.022*** 0.020*** 0.021*** 0.019*** 0.029*** 0.019*** 0.020*** 0.000*** −0.004 −0.004 −0.004 −0.004 −0.004 −0.009 −0.004 −0.004 0.000 Value prior inventions 0.002*** 0.013*** 0.000 −0.001 Value prior inventions (ln) 1.328*** 1.017*** 1.584*** 1.471*** 0.010*** −0.044 −0.063 −0.064 −0.061 0.000 Value prior inventions (sq) −0.000*** 0.000 Value prior inventions (ln) (alt.) 0.768*** −0.034 Constant −6.611*** −6.996*** −12.356*** −7.568*** −11.044*** −12.362*** −12.839*** −9.556*** −0.040*** −0.281 −0.289 −0.354 −0.288 −0.525 −0.462 −0.410 −0.321 −0.003 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,442 89,336 137,471 138,876 138,876 AIC 13,305 13,134 12,264 12,726 4,267 7,935 11,231 12,712 −248,735 BIC 13,826 13,666 12,795 13,267 4,716 8,423 11,762 13,243 −248,223 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy 0.247 0.405* 0.602*** 0.446** − − 0.461** 0.481** − −0.221 −0.224 −0.210 −0.211 – – −0.216 −0.212 – Number of patents 0.000 0.000 0.000 0.000 −0.003*** 0.000** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Firm size −0.006** −0.006** −0.005* −0.006** −0.006 0.001 −0.003 −0.005 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.004 −0.003 −0.003 0.000 ROA 0.056 0.101 0.064 0.028 0.307 −0.045 −0.087 0.086 0.000 −0.169 −0.174 −0.174 −0.167 −0.283 −0.283 −0.165 −0.174 −0.002 R&D intensity 0.010 0.011 0.010 0.009 0.010 0.067 −0.011 0.010 0.000 −0.008 −0.008 −0.007 −0.008 −0.008 −0.132 −0.020 −0.007 0.000 R&D alliances 0.002 0.000 −0.009 −0.022* 0.075*** −0.018 −0.005 −0.001 0.000 −0.011 −0.011 −0.012 −0.012 −0.027 −0.014 −0.013 −0.012 0.000 Star inventor 1.955*** 1.887*** 1.583*** 1.780*** 2.025*** 1.392*** 1.594*** 1.719*** 0.018*** −0.073 −0.073 −0.074 −0.074 −0.138 −0.089 −0.078 −0.073 −0.001 Technological distance 0.203 0.272 0.386** 0.313* 0.920*** −0.215 0.278 0.270 0.006*** −0.172 −0.173 −0.176 −0.175 −0.273 −0.237 −0.187 −0.174 −0.002 Variance value prior inventions 0.000*** 0.000 0.000*** 0.000*** 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions 0.009*** 0.009*** 0.006*** 0.008*** 0.011*** 0.002 0.005*** 0.008*** 0.000*** −0.001 −0.001 −0.001 −0.001 −0.002 −0.002 −0.002 −0.001 0.000 Number of scientific references 0.347*** 0.352*** 0.249*** 0.377*** 0.150 0.284*** 0.165* 0.164** −0.003*** −0.070 −0.072 −0.082 −0.075 −0.147 −0.105 −0.087 −0.079 −0.001 Science orientation −0.861** −1.091*** −0.174 −1.365*** −0.313 0.221 1.246** 0.789* 0.032 −0.357 −0.394 −0.494 −0.463 −0.719 −0.697 −0.503 −0.461 −0.003 Number of inventors 0.028** 0.033** 0.040*** 0.033** 0.037** 0.050** 0.044*** 0.036*** 0.000* −0.013 −0.013 −0.014 −0.014 −0.019 −0.020 −0.014 −0.013 0.000 International diversity −0.026 0.118 0.638*** 0.392** 0.779*** 0.461** 0.668*** 0.326** 0.002 −0.158 −0.160 −0.167 −0.163 −0.253 −0.233 −0.176 −0.163 −0.002 Techn. Diversity (prior inv.) 0.792*** 0.747*** 0.290** 0.637*** −0.280 0.436*** 0.214 0.386*** 0.001 −0.130 −0.131 −0.134 −0.133 −0.258 −0.160 −0.142 −0.133 −0.001 Age prior inventions −0.117*** −0.123*** 0.050*** −0.046*** −0.008 0.100*** 0.072*** −0.016 0.001*** −0.011 −0.011 −0.012 −0.011 −0.019 −0.016 −0.013 −0.012 0.000 Variance age prior inventions 0.001*** 0.001*** 0.000 0.001** 0.000 −0.001* −0.001* 0.000 0.000*** 0.000 0.000 0.000 0.000 −0.001 0.000 0.000 0.000 0.000 Technological scope 0.022*** 0.022*** 0.020*** 0.021*** 0.019*** 0.029*** 0.019*** 0.020*** 0.000*** −0.004 −0.004 −0.004 −0.004 −0.004 −0.009 −0.004 −0.004 0.000 Value prior inventions 0.002*** 0.013*** 0.000 −0.001 Value prior inventions (ln) 1.328*** 1.017*** 1.584*** 1.471*** 0.010*** −0.044 −0.063 −0.064 −0.061 0.000 Value prior inventions (sq) −0.000*** 0.000 Value prior inventions (ln) (alt.) 0.768*** −0.034 Constant −6.611*** −6.996*** −12.356*** −7.568*** −11.044*** −12.362*** −12.839*** −9.556*** −0.040*** −0.281 −0.289 −0.354 −0.288 −0.525 −0.462 −0.410 −0.321 −0.003 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,442 89,336 137,471 138,876 138,876 AIC 13,305 13,134 12,264 12,726 4,267 7,935 11,231 12,712 −248,735 BIC 13,826 13,666 12,795 13,267 4,716 8,423 11,762 13,243 −248,223 Notes: *** P < 0.01, ** P < 0.05, * P < 0.1. These results hold true for the various robustness checks, including the split industry regressions in Models 5 and 6, the regression with fewer excluding outliers (Model 7), the model in which prior invention values are adjusted to account for possible endogeneity (Model 8), and when the estimation is replicated with a linear probability model with fixed firm effects (Model 9). Interpretation of the non-linear relationships in the logit models is not intuitive; therefore, Figure 2 plots their results. To ease interpretation, the graphs are based on the predicted probabilities, not the log odds. Predicted probabilities are easier to interpret and closer to the intended meaning of the model because they represent the likelihood of a breakthrough invention occurring depending on a given level of prior invention value.2 In the case of the pharmaceutical industry, the curve shows a slightly diminishing rate. Conversely, in the semiconductor industry, the curve is relatively steeper and does not depict a diminishing shape, as much of the diminishing part of the function lies outside the data. These findings add an important qualifier to the regression results, as they indicate that the relationship between prior invention value and breakthrough inventions is largely linear. Figure 2. Open in new tabDownload slide Breakthrough inventions by industry. Figure 2. Open in new tabDownload slide Breakthrough inventions by industry. 4.2 Low-value inventions Table 4 shows the results for the logit estimation for low-value inventions. The modeling approach and the sequence of the models are similar to the estimation of the breakthrough inventions in Table 3. After an initial estimation, which depicts only the control variables (see Model 1), Model 2 shows the main effects of prior patent values. As expected, the effects are negative and significant (P < 0.01). Model 3 tests the logarithmic transformation; in this estimation, the transformed coefficient is negative and significant (P < 0.01). Model 4 tests the alternative quadratic specification of prior invention values, and the results are also significant and indicate a non-linear relationship. However, as in the previous tables, estimation of the logarithmic specification in Table 4 shows the best model fit. The results also remain stable for the split industry regressions shown (Models 5 and 6), the regression with a smaller sample that excludes extreme prior invention values (Model 7), the estimation with the endogeneity-adjusted prior invention values (Model 8), and the estimation in the form of a linear probability model (Model 9). Figure 3 illustrates that the predicted probability of a patent having zero citations decreases with increasing prior invention values. The graph depicts negative effects of prior invention value on the likelihood of low-value inventions for both industries. It also shows the diminishing effects occurs relatively early within the range of data. Table 4. Regression analysis of low-value inventions Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy −1.057*** −1.097*** −0.998*** −1.098*** – – −0.936*** −1.038*** – −0.102 −0.100 −0.09 −0.100 – – −0.098 −0.099 – Number of patents 0.000*** 0.000*** 0.000*** 0.000*** 0.001*** 0.000* 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size 0.001 0.001 0.002 0.001 0.002 0.010*** 0.002 0.002 0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.003 −0.001 −0.001 0.000 ROA 0.125* 0.135** 0.140** 0.136** 0.271*** −0.194 0.128** 0.135** 0.003 −0.065 −0.065 −0.064 −0.065 −0.097 −0.153 −0.065 −0.065 −0.005 R&D intensity −0.001 −0.001 0.000 −0.001 0.002 −0.283* 0.001 0.000 0.000 −0.004 −0.004 −0.004 −0.004 −0.004 −0.155 −0.004 −0.004 0.000 R&D alliances −0.021*** −0.019*** −0.018** −0.019*** 0.003 −0.008 −0.016** −0.020*** 0.001*** −0.007 −0.007 −0.007 −0.007 −0.011 −0.014 −0.007 −0.007 0.000 Star inventor −0.396*** −0.348*** −0.300*** −0.347*** −0.236*** −0.323*** −0.603*** −0.333*** −0.016*** −0.029 −0.030 −0.030 −0.030 −0.043 −0.041 −0.044 −0.029 −0.002 Technological distance −0.234*** −0.274*** −0.277*** −0.275*** −0.482*** 0.112 −0.261*** −0.245*** −0.032*** −0.070 −0.070 −0.070 −0.070 −0.094 −0.108 −0.070 −0.070 −0.005 Variance value prior inventions 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions −0.010*** −0.009*** −0.010*** −0.009*** −0.013*** −0.006*** −0.009*** −0.009*** −0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 Number of Scientific references −0.186*** −0.148*** 0.061** −0.146*** 0.258*** 0.019 0.069** −0.041 0.001 −0.028 −0.028 −0.029 −0.028 −0.046 −0.044 −0.029 −0.029 −0.002 Science orientation 0.948*** 0.775*** −0.600*** 0.767*** −0.693*** −1.493*** −0.673*** 0.117 −0.007 −0.084 −0.084 −0.095 −0.084 −0.121 −0.248 −0.095 −0.087 −0.007 Number of Inventors −0.024*** −0.027*** −0.025*** −0.027*** −0.022*** −0.028** −0.024*** −0.025*** −0.001*** −0.006 −0.006 −0.006 −0.006 −0.007 −0.011 −0.006 −0.006 0.000 International diversity −0.179*** −0.257*** −0.380*** −0.259*** −0.463*** −0.163* −0.381*** −0.270*** −0.027*** −0.057 −0.057 −0.057 −0.057 −0.074 −0.093 −0.057 −0.057 −0.004 Techn. Diversity (prior inv.) 0.068 0.112** 0.243*** 0.115** 0.146* 0.162*** 0.269*** 0.274*** 0.011*** −0.045 −0.045 −0.046 −0.045 −0.077 −0.058 −0.046 −0.046 −0.003 Age prior inventions 0.037*** 0.036*** −0.007** 0.036*** −0.012*** 0.005 −0.010*** 0.013*** 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.005 −0.003 −0.003 0.000 Variance age prior inventions −0.001*** −0.001*** 0.000* −0.001*** −0.001*** 0.000 0.000 −0.001*** 0.000* 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope −0.013*** −0.013*** −0.013*** −0.013*** −0.013*** −0.010 −0.013*** −0.013*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.007 −0.002 −0.002 0.000 Value prior inventions −0.004*** −0.004*** 0.000 0.000 Value prior inventions (ln) −0.420*** −0.353*** −0.499*** −0.452*** −0.027*** −0.014 −0.018 −0.023 −0.015 −0.001 Value prior inventions (sq) 0.000*** 0.000 Value prior inventions (ln) (alt.) −0.281*** −0.010 Constant −3.157*** −2.933*** −1.882*** −2.926*** −1.865*** −3.333*** −1.822*** −2.525*** 0.135*** −0.129 −0.129 −0.133 −0.129 −0.154 −0.297 −0.134 −0.129 −0.007 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm-level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,473 89,359 137,471 138,876 138,876 AIC 64,527 64,286 63,595 64,275 28,571 34,627 63,186 63,758 11,486 BIC 65,048 64,807 64,127 64,816 29,029 35,116 63,717 64,290 11,998 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy −1.057*** −1.097*** −0.998*** −1.098*** – – −0.936*** −1.038*** – −0.102 −0.100 −0.09 −0.100 – – −0.098 −0.099 – Number of patents 0.000*** 0.000*** 0.000*** 0.000*** 0.001*** 0.000* 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size 0.001 0.001 0.002 0.001 0.002 0.010*** 0.002 0.002 0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.003 −0.001 −0.001 0.000 ROA 0.125* 0.135** 0.140** 0.136** 0.271*** −0.194 0.128** 0.135** 0.003 −0.065 −0.065 −0.064 −0.065 −0.097 −0.153 −0.065 −0.065 −0.005 R&D intensity −0.001 −0.001 0.000 −0.001 0.002 −0.283* 0.001 0.000 0.000 −0.004 −0.004 −0.004 −0.004 −0.004 −0.155 −0.004 −0.004 0.000 R&D alliances −0.021*** −0.019*** −0.018** −0.019*** 0.003 −0.008 −0.016** −0.020*** 0.001*** −0.007 −0.007 −0.007 −0.007 −0.011 −0.014 −0.007 −0.007 0.000 Star inventor −0.396*** −0.348*** −0.300*** −0.347*** −0.236*** −0.323*** −0.603*** −0.333*** −0.016*** −0.029 −0.030 −0.030 −0.030 −0.043 −0.041 −0.044 −0.029 −0.002 Technological distance −0.234*** −0.274*** −0.277*** −0.275*** −0.482*** 0.112 −0.261*** −0.245*** −0.032*** −0.070 −0.070 −0.070 −0.070 −0.094 −0.108 −0.070 −0.070 −0.005 Variance value prior inventions 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions −0.010*** −0.009*** −0.010*** −0.009*** −0.013*** −0.006*** −0.009*** −0.009*** −0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 Number of Scientific references −0.186*** −0.148*** 0.061** −0.146*** 0.258*** 0.019 0.069** −0.041 0.001 −0.028 −0.028 −0.029 −0.028 −0.046 −0.044 −0.029 −0.029 −0.002 Science orientation 0.948*** 0.775*** −0.600*** 0.767*** −0.693*** −1.493*** −0.673*** 0.117 −0.007 −0.084 −0.084 −0.095 −0.084 −0.121 −0.248 −0.095 −0.087 −0.007 Number of Inventors −0.024*** −0.027*** −0.025*** −0.027*** −0.022*** −0.028** −0.024*** −0.025*** −0.001*** −0.006 −0.006 −0.006 −0.006 −0.007 −0.011 −0.006 −0.006 0.000 International diversity −0.179*** −0.257*** −0.380*** −0.259*** −0.463*** −0.163* −0.381*** −0.270*** −0.027*** −0.057 −0.057 −0.057 −0.057 −0.074 −0.093 −0.057 −0.057 −0.004 Techn. Diversity (prior inv.) 0.068 0.112** 0.243*** 0.115** 0.146* 0.162*** 0.269*** 0.274*** 0.011*** −0.045 −0.045 −0.046 −0.045 −0.077 −0.058 −0.046 −0.046 −0.003 Age prior inventions 0.037*** 0.036*** −0.007** 0.036*** −0.012*** 0.005 −0.010*** 0.013*** 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.005 −0.003 −0.003 0.000 Variance age prior inventions −0.001*** −0.001*** 0.000* −0.001*** −0.001*** 0.000 0.000 −0.001*** 0.000* 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope −0.013*** −0.013*** −0.013*** −0.013*** −0.013*** −0.010 −0.013*** −0.013*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.007 −0.002 −0.002 0.000 Value prior inventions −0.004*** −0.004*** 0.000 0.000 Value prior inventions (ln) −0.420*** −0.353*** −0.499*** −0.452*** −0.027*** −0.014 −0.018 −0.023 −0.015 −0.001 Value prior inventions (sq) 0.000*** 0.000 Value prior inventions (ln) (alt.) −0.281*** −0.010 Constant −3.157*** −2.933*** −1.882*** −2.926*** −1.865*** −3.333*** −1.822*** −2.525*** 0.135*** −0.129 −0.129 −0.133 −0.129 −0.154 −0.297 −0.134 −0.129 −0.007 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm-level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,473 89,359 137,471 138,876 138,876 AIC 64,527 64,286 63,595 64,275 28,571 34,627 63,186 63,758 11,486 BIC 65,048 64,807 64,127 64,816 29,029 35,116 63,717 64,290 11,998 Notes: *** P < 0.01, ** P < 0.05, * P < 0.1. Table 4. Regression analysis of low-value inventions Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy −1.057*** −1.097*** −0.998*** −1.098*** – – −0.936*** −1.038*** – −0.102 −0.100 −0.09 −0.100 – – −0.098 −0.099 – Number of patents 0.000*** 0.000*** 0.000*** 0.000*** 0.001*** 0.000* 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size 0.001 0.001 0.002 0.001 0.002 0.010*** 0.002 0.002 0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.003 −0.001 −0.001 0.000 ROA 0.125* 0.135** 0.140** 0.136** 0.271*** −0.194 0.128** 0.135** 0.003 −0.065 −0.065 −0.064 −0.065 −0.097 −0.153 −0.065 −0.065 −0.005 R&D intensity −0.001 −0.001 0.000 −0.001 0.002 −0.283* 0.001 0.000 0.000 −0.004 −0.004 −0.004 −0.004 −0.004 −0.155 −0.004 −0.004 0.000 R&D alliances −0.021*** −0.019*** −0.018** −0.019*** 0.003 −0.008 −0.016** −0.020*** 0.001*** −0.007 −0.007 −0.007 −0.007 −0.011 −0.014 −0.007 −0.007 0.000 Star inventor −0.396*** −0.348*** −0.300*** −0.347*** −0.236*** −0.323*** −0.603*** −0.333*** −0.016*** −0.029 −0.030 −0.030 −0.030 −0.043 −0.041 −0.044 −0.029 −0.002 Technological distance −0.234*** −0.274*** −0.277*** −0.275*** −0.482*** 0.112 −0.261*** −0.245*** −0.032*** −0.070 −0.070 −0.070 −0.070 −0.094 −0.108 −0.070 −0.070 −0.005 Variance value prior inventions 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions −0.010*** −0.009*** −0.010*** −0.009*** −0.013*** −0.006*** −0.009*** −0.009*** −0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 Number of Scientific references −0.186*** −0.148*** 0.061** −0.146*** 0.258*** 0.019 0.069** −0.041 0.001 −0.028 −0.028 −0.029 −0.028 −0.046 −0.044 −0.029 −0.029 −0.002 Science orientation 0.948*** 0.775*** −0.600*** 0.767*** −0.693*** −1.493*** −0.673*** 0.117 −0.007 −0.084 −0.084 −0.095 −0.084 −0.121 −0.248 −0.095 −0.087 −0.007 Number of Inventors −0.024*** −0.027*** −0.025*** −0.027*** −0.022*** −0.028** −0.024*** −0.025*** −0.001*** −0.006 −0.006 −0.006 −0.006 −0.007 −0.011 −0.006 −0.006 0.000 International diversity −0.179*** −0.257*** −0.380*** −0.259*** −0.463*** −0.163* −0.381*** −0.270*** −0.027*** −0.057 −0.057 −0.057 −0.057 −0.074 −0.093 −0.057 −0.057 −0.004 Techn. Diversity (prior inv.) 0.068 0.112** 0.243*** 0.115** 0.146* 0.162*** 0.269*** 0.274*** 0.011*** −0.045 −0.045 −0.046 −0.045 −0.077 −0.058 −0.046 −0.046 −0.003 Age prior inventions 0.037*** 0.036*** −0.007** 0.036*** −0.012*** 0.005 −0.010*** 0.013*** 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.005 −0.003 −0.003 0.000 Variance age prior inventions −0.001*** −0.001*** 0.000* −0.001*** −0.001*** 0.000 0.000 −0.001*** 0.000* 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope −0.013*** −0.013*** −0.013*** −0.013*** −0.013*** −0.010 −0.013*** −0.013*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.007 −0.002 −0.002 0.000 Value prior inventions −0.004*** −0.004*** 0.000 0.000 Value prior inventions (ln) −0.420*** −0.353*** −0.499*** −0.452*** −0.027*** −0.014 −0.018 −0.023 −0.015 −0.001 Value prior inventions (sq) 0.000*** 0.000 Value prior inventions (ln) (alt.) −0.281*** −0.010 Constant −3.157*** −2.933*** −1.882*** −2.926*** −1.865*** −3.333*** −1.822*** −2.525*** 0.135*** −0.129 −0.129 −0.133 −0.129 −0.154 −0.297 −0.134 −0.129 −0.007 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm-level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,473 89,359 137,471 138,876 138,876 AIC 64,527 64,286 63,595 64,275 28,571 34,627 63,186 63,758 11,486 BIC 65,048 64,807 64,127 64,816 29,029 35,116 63,717 64,290 11,998 Variable . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Logit . Logit . Logit . Logit . Logit . Logit . Logit . Logit . LPM . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . B./St.Er. . Industry dummy −1.057*** −1.097*** −0.998*** −1.098*** – – −0.936*** −1.038*** – −0.102 −0.100 −0.09 −0.100 – – −0.098 −0.099 – Number of patents 0.000*** 0.000*** 0.000*** 0.000*** 0.001*** 0.000* 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Firm size 0.001 0.001 0.002 0.001 0.002 0.010*** 0.002 0.002 0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.003 −0.001 −0.001 0.000 ROA 0.125* 0.135** 0.140** 0.136** 0.271*** −0.194 0.128** 0.135** 0.003 −0.065 −0.065 −0.064 −0.065 −0.097 −0.153 −0.065 −0.065 −0.005 R&D intensity −0.001 −0.001 0.000 −0.001 0.002 −0.283* 0.001 0.000 0.000 −0.004 −0.004 −0.004 −0.004 −0.004 −0.155 −0.004 −0.004 0.000 R&D alliances −0.021*** −0.019*** −0.018** −0.019*** 0.003 −0.008 −0.016** −0.020*** 0.001*** −0.007 −0.007 −0.007 −0.007 −0.011 −0.014 −0.007 −0.007 0.000 Star inventor −0.396*** −0.348*** −0.300*** −0.347*** −0.236*** −0.323*** −0.603*** −0.333*** −0.016*** −0.029 −0.030 −0.030 −0.030 −0.043 −0.041 −0.044 −0.029 −0.002 Technological distance −0.234*** −0.274*** −0.277*** −0.275*** −0.482*** 0.112 −0.261*** −0.245*** −0.032*** −0.070 −0.070 −0.070 −0.070 −0.094 −0.108 −0.070 −0.070 −0.005 Variance value prior inventions 0.000*** 0.000*** 0.000 0.000 0.000 0.000 0.000*** 0.000 0.000*** 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Number of prior inventions −0.010*** −0.009*** −0.010*** −0.009*** −0.013*** −0.006*** −0.009*** −0.009*** −0.001*** −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 −0.001 0.000 Number of Scientific references −0.186*** −0.148*** 0.061** −0.146*** 0.258*** 0.019 0.069** −0.041 0.001 −0.028 −0.028 −0.029 −0.028 −0.046 −0.044 −0.029 −0.029 −0.002 Science orientation 0.948*** 0.775*** −0.600*** 0.767*** −0.693*** −1.493*** −0.673*** 0.117 −0.007 −0.084 −0.084 −0.095 −0.084 −0.121 −0.248 −0.095 −0.087 −0.007 Number of Inventors −0.024*** −0.027*** −0.025*** −0.027*** −0.022*** −0.028** −0.024*** −0.025*** −0.001*** −0.006 −0.006 −0.006 −0.006 −0.007 −0.011 −0.006 −0.006 0.000 International diversity −0.179*** −0.257*** −0.380*** −0.259*** −0.463*** −0.163* −0.381*** −0.270*** −0.027*** −0.057 −0.057 −0.057 −0.057 −0.074 −0.093 −0.057 −0.057 −0.004 Techn. Diversity (prior inv.) 0.068 0.112** 0.243*** 0.115** 0.146* 0.162*** 0.269*** 0.274*** 0.011*** −0.045 −0.045 −0.046 −0.045 −0.077 −0.058 −0.046 −0.046 −0.003 Age prior inventions 0.037*** 0.036*** −0.007** 0.036*** −0.012*** 0.005 −0.010*** 0.013*** 0.000 −0.003 −0.003 −0.003 −0.003 −0.004 −0.005 −0.003 −0.003 0.000 Variance age prior inventions −0.001*** −0.001*** 0.000* −0.001*** −0.001*** 0.000 0.000 −0.001*** 0.000* 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Technological scope −0.013*** −0.013*** −0.013*** −0.013*** −0.013*** −0.010 −0.013*** −0.013*** −0.001*** −0.002 −0.002 −0.002 −0.002 −0.002 −0.007 −0.002 −0.002 0.000 Value prior inventions −0.004*** −0.004*** 0.000 0.000 Value prior inventions (ln) −0.420*** −0.353*** −0.499*** −0.452*** −0.027*** −0.014 −0.018 −0.023 −0.015 −0.001 Value prior inventions (sq) 0.000*** 0.000 Value prior inventions (ln) (alt.) −0.281*** −0.010 Constant −3.157*** −2.933*** −1.882*** −2.926*** −1.865*** −3.333*** −1.822*** −2.525*** 0.135*** −0.129 −0.129 −0.133 −0.129 −0.154 −0.297 −0.134 −0.129 −0.007 Year dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Patent technology dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Sample Full Full Full Full Pharma. Semic. Reduced Full Full Firm-level control Random E. Random E. Random E. Random E. Random E. Random E. Random E. Random E. Fixed Effect Observations 138,876 138,876 138,876 138,876 49,473 89,359 137,471 138,876 138,876 AIC 64,527 64,286 63,595 64,275 28,571 34,627 63,186 63,758 11,486 BIC 65,048 64,807 64,127 64,816 29,029 35,116 63,717 64,290 11,998 Notes: *** P < 0.01, ** P < 0.05, * P < 0.1. Figure 3. Open in new tabDownload slide Low-value inventions by industry. Figure 3. Open in new tabDownload slide Low-value inventions by industry. 5. Discussion Building on concepts of evolutionary economics and technological search (Nelson and Winter, 1982; Dosi and Grazzi, 2006), and the idea that each invention is the recombination of previous knowledge and technologies (Schumpeter, 1939; Weitzman, 1998), this study explored the relationship between the value of prior inventions and the value of inventions that build on that knowledge. The analysis of a large-scale patent data set, in two high-technology industries, shows that the presence of valuable prior inventions is positively associated with the values of subsequent inventions (i.e., those based on the prior inventions). However, the relationship becomes weaker with increasing values of prior inventions. Similarly, the study also finds a positive relationship between the likelihood of generating particularly valuable inventions (i.e., breakthroughs) and the value of prior inventions. Again, the relationship shows a weakening effect at higher levels of prior invention value. However, particularly for breakthrough inventions in the semiconductor industry, the flattening of the function only occurs at relatively high levels of prior invention value and therefore affects only a small number of inventions. Conversely, combining valuable inventions reduces the likelihood of generating poor invention outcomes already at low levels of prior invention value. In general, these findings uphold the idea of cumulative and path-dependent invention patterns in technological paradigms, as proposed by proponents of technological search and evolutionary economics (Dosi, 1982; Nelson and Winter, 1982; Fleming 2001; Dosi and Nelson, 2010). The non-linearity of the effects not only provides a more detailed and nuanced picture of technological search but also represents a qualifier for the recombination potential of technologies. While mathematical recombination of knowledge might be limitless (Weitzman 1998), this study shows that the outcomes of the combinatorial activities are dependent on the underlying characteristics and values of technology inputs. However, the values generated by large numbers of valuable prior inventions may not justify their use and therefore constrain the use of previous inventions. As such, the study indicates that if the values of prior inventions are considered, the recombination of technological knowledge is subject to diminishing returns. It is also important to note that combining large numbers of valuable inventions is potentially more difficult and costly and could further constrain recombination potential. However, the finding that the relationship between prior invention value and breakthrough inventions is largely linear and only diminishing at relatively high levels of prior invention value provides an important nuance to the results. Because technological value is difficult to transfer between technological paradigms, the non-linear effects were expected be more pronounced for breakthrough inventions; however, other than for the extreme values of prior inventions, this was not the case. A possible explanation is that the high value of prior invention inputs is applicable to a wider technological space and, thus, across paradigms and invention types. The finding that the technological diversity of prior inventions is positively related to breakthrough inventions (see Table 3) corroborates this line of reasoning. The argument is that breakthroughs not only are based on more diverse inputs but also are more applicable to a wider set of inventions. This is opposite to general inventions, which are based on less diverse inputs and thus have potentially less applicability across technological domains. The magnitude of these results indicates that the findings not only are statistically significant but have economic relevance as well. For example, in the pharmaceutical industry, use of the mean citation level—as a basis to compare the levels of one standard deviation below and above the mean—increases the number of citations by 5.1. However, in the semiconductor industry, the number of citations increases by 3.5. Although it is difficult to accurately quantify the economic impact of these relationships, other studies have provided measures for the value of forward citations (Hall et al., 2005; Bessen, 2008). These studies are based on different samples, but they can still be used to approximate the economic impact of the presented results. For example, Bessen (2008) estimates that an additional patent citation increases the net value of a patent by approximately 4%–7%, which in his sample reflects an economic impact, per patent citation, of USD 78,000 (in 1992 USD). Thus, using Bessen’s finding to cast projections on the results from the current study, an increase of prior invention value from one standard deviation below to one standard deviation above the mean would increase the net value of a patent by 6.16%–33.3%. This corresponds to an economic impact of approximately USD 397,300 in the pharmaceutical industry and USD 273,000 in the semiconductor industry (in 1992 USD). However, the overall impact of patent citations is likely to be higher because the technologies embodied in a patent may be much greater than the value of the patent itself (Bessen, 2008). Hall et al. (2005) show that an increase of the citation/patent ratio, by a factor of one for all the patents of a given firm, increases the firm’s market value by 2.7%. This corresponds to an average increase in firm value of approximately USD 327,000 (in 1992 USD) for every additional citation received by a single patent. Using these firm-level estimates and a greater prior invention value (i.e., from one standard deviation below to one standard deviation above the mean), the firm value increases by USD 1,667,700 in the pharmaceutical industry and USD 1,144,500 in the semiconductor industry (in 1992 USD). The impact of prior invention value on the ends of the invention value distribution is also noteworthy. For example, increasing prior invention value from one standard deviation below the mean to one standard deviation above the mean increases the predicted likelihood of a breakthrough invention by 1.11% in the pharmaceutical industry and 1.3% in the semiconductor industry. When interpreting these values, it is important to note that breakthrough inventions, by definition, are rare events (i.e., top 2% of patents by citations). Similarly, increasing the prior invention value from one standard deviation below the mean to one standard deviation above the mean decreases the predicted likelihood of a low-value invention by 11.4% in the pharmaceutical industry and by 5.2% in the semiconductor industry. Furthermore, by analyzing prior invention values, the current study opens the field for future research to examine the value of technology inputs in the innovation process, to answer central questions with regard to invention and strategy research. A large stream of research investigates how organizations combine technology and knowledge to innovate and achieve competitive advantages (Cohen and Levinthal, 1990; Rothaermel and Hess, 2007). For example, Kogut and Zander (1992) identify combinative capabilities as a cornerstone of the knowledge-based view of a firm, and Cohen and Levinthal (1990) discuss an organization’s capacity to absorb external knowledge. However, to access and investigate concepts such as combinative capabilities and absorptive capacities, it is important to account for the value and quality of the knowledge inputs. For example, anecdotal evidence suggests that some firms can use less valuable technologies and combine them into highly valuable outcomes while other organizations possess valuable technologies but are unable to achieve valuable outputs. To examine the differences between these firms, researchers need to capture the value of technology inputs. As with all empirical research, the current research has several limitations, which should be considered in its interpretation. Although patent data validly enabled the modeling of invention value, it imposes limitations. For example, inherent selection issues affect patent data—that is, not all inventions are patentable, nor are all patentable inventions patented. Every patent represents, even if only at minimal levels, a successful invention, as firms are unlikely to apply for a patent if they believe that the invention does not bear a minimum value. Similarly, patent offices only grant patents for novel, useful, and non-obvious developments. In addition, patent data are criticized as only measuring explicit knowledge, while most significant knowledge inputs are often of a tacit nature. Finally, the study was limited to patents based on the USPTO patents system. However, these limitations are somewhat attenuated by (i) the complementary and closely correlated nature of codified and tacit knowledge (Mowery et al., 1996), (ii) the selection of industries in which patenting is an important and widespread way to protect intellectual property, and (iii) the use of a large and frequently investigated patent system. Another issue in using patent data is that patent references are unable to capture all the knowledge and ideas embedded in an invention, nor are the references a direct instance of knowledge transfer or, indeed, done by the inventors themselves (Alcacer et al., 2009). Nevertheless, studies on the applicability of reference measures in invention studies confirm their overall validity and reliability as proxy and indirect measures for inputs in the patenting process (Jaffe et al., 2000). Finally, while the measurement of breakthrough inventions—through forward citations—is in line with multiple studies on patent inventions (Ahuja and Lampert, 2001; Phene et al., 2006; Singh and Fleming, 2010; Conti et al., 2013), research has also used alternative measures (Dahlin and Behrens, 2005; Zhou et al., 2005). Therefore, it would be desirable to connect stronger measures with actual product performance. However, this was not possible in the current study because of limitations to the underlying data set. Against this background, this study provides a unique contribution to the literature. It is a large-scale examination of the relationship between the value of prior inventions and subsequent invention outcomes. Relying on well-established patent data measurements, the study produced robust and compelling results that advance both theory and practice. Footnotes 1 " NBR and OLS models are performed for all regressions, and all estimations support the presented results. 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TI - Combining valuable inventions: exploring the impact of prior invention value on the performance of subsequent inventions
JO - Industrial and Corporate Change
DO - 10.1093/icc/dtw056
DA - 2017-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/combining-valuable-inventions-exploring-the-impact-of-prior-invention-FGDZBzpvtO
SP - 907
VL - 26
IS - 5
DP - DeepDyve
ER -