Academy of Science, Beijing, China b School of International Business, Southwestern University of

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3 Technology Analysis & Strategic Management, How do prolific inventors impact firm innovation in ICT: implications from patent co-inventing network Gupeng Zhang a, Xiaofeng Lv b and Hongbo Duan c a College of Technology Management, University of Chinese Academy of Science, Beijing, China; b School of International Business, Southwestern University of Finance and Economics, Chengdu, Sichuan, China; c School of Management, University of Chinese Academy of Science, Beijing, China Prolific inventors not only own higher innovation productivity, but also impact other inventors through innovation networks. This paper contributes to existing literatures by differentiating prolific inventors from non-prolific inventors in the network context, and making an empirical analysis of the effect of prolific inventors. We use the patent filing data from the State Intellectual Property Office of China (SIPO) in investigating the effect of prolific inventors on firm innovation. We use the patents filed by 10 largest Information & Communication Technology firms during and establish the innovation network with patent co-inventing data. The empirical result shows that prolific inventors positively impact their partners who used to co-invent at least one patent with them. Furthermore, prolific inventors positively impact inventors who do not have a close contact with them. The closer the inventors are to prolific inventors, the more patents they produce. Members are thereby more likely to gather around prolific inventors and formulate intensive clusters. In networks centered by prolific inventors, useful knowledge outweighs redundant knowledge, and high clustering that facilitates knowledge flow is proved to be beneficial; while in networks without prolific inventors, high clustering may not be beneficial as there are less inventors holding advanced knowledge. Policy implications are discussed at the end of this study. Keywords: prolific inventors; patent; innovation network; knowledge flow 1. Introduction As an imaginative and uniquely gifted individual, an inventor s creativity is usually affected by contextual factors in the social network, e.g. organisational environment, groups, etc. (Amabile 1988; Choi 2004). The structure of social networks is important in shaping an inventors ability to generate a creative outcome (Cattani and Ferriani 2008). Most existing studies focused on the effect of the network context, which can be classified into the properties of network structure, Corresponding author. zhanggupeng@163.com 2014 Taylor & Francis

4 2 G. Zhang et al. which is examined by Tushman (1977), Cummings and Cross (2003), and Barsky (1999), and the network positioning, which is examined by Ahuja (2000), Nerkar and Paruchui (2005), Paruchuri (2010), and Cattani and Ferriani (2008). They try to find out either effective network structures or advantageous network positions, which are usually based on the networks formulated by the direct and indirect contacts between inventors. 1 Sytch, Tatarynowicz, and Gulati (2011), Cowan, Jonard, and Zimmermann (2007), and Baum, Cowan, and Jonard (2010) focused on these bilateral contacts and their subsequent effect within the innovation network. As inventors own differing performance, they may produce different impacts on each other through the collaboration network. Some elites with higher performance may produce greater effects. By looking into the distribution of patents developed in the R&D department of several major US companies, Narin (1993) and Narin and Breitman (1995) observed that the patent output is highly concentrated on a small number of inventors: top 1% of inventors are 5 10 times as productive as the average inventor and the top 10% of inventors are at least three to four times as productive as the average inventor. A similar trend is also found by Ernst (1996) and Leptien (1996), who made empirical studies of German-speaking countries. Le Bas, Cabagnols, and Bouklia (2010) termed inventors with the capacity of producing high number of patents Prolific Inventors. Prolific inventors, who were also termed Great Inventors by Jones (2010), usually patented a lot of their inventions in order to extract economic return (Le Bas, Cabagnols, and Bouklia 2010). Levine (1986) noted that prolific inventors are recognised as sources of information, top performers valuable to the organisation in meeting its technological objectives. Studies by Gambardella, Harhoff, and Verspagen (2006), Latham, Le Bas, and Touach (2006), and Gay, Le Bas, and Latham (2008) provided empirical evidence that prolific inventors own more citations than the other inventors. Pilkington (2006), Gambardella, Harhoff, and Verspagen (2006), Latham, Le Bas, and Touach (2006), and Gay, Le Bas, and Latham (2008) made an in-depth analysis of the patent productivity of prolific inventors. Since the group members within the network exert substantial influence on each other (Choi 2004; Idson and Kahane 2004), prolific inventors who may produce greater effect should be particularly noted. As the core/periphery structure widely exists in the social network (Barsky 1999), prolific inventors are usually found in the core positions that are key in producing unity (Mintz and Schwartz 1981). They act often as research group leaders and technological goalkeepers who mediate the flow of knowledge into the research organisation. Through professional mobility, prolific inventors can be viewed as knowledge translators or knowledge brokers in between firms, organisations, and communities. They help transferring pieces of knowledge through the different communities they overlap at one or different points of time. Thus, knowledge stays a collective structure in particular within firms (Le Bas, Cabagnols, and Bouklia 2010). On the other hand, prolific inventors, as knowledge workers, also play a prominent role in the design, development, and integration of pieces of knowledge within a department of research as there are people, in invention team, with different technological and scientific specialisations (Le Bas, Cabagnols, and Bouklia 2010). Because of the increasing rate at which individuals and organisations learn and consequently achieve sustainable competitive advantages, the knowledge held by prolific inventors is usually essential to research teams. As group members accumulate experience and competence in the embedded network of relations, prolific inventors play a crucial role in this process by matching the dispersed and fragmented bits of knowledge, and also in the process of transferring their own knowledge to other inventors (Le Bas, Cabagnols, and Bouklia 2010). Prolific inventors may have an enduring effect on other inventors. When prolific inventors move to other locations, they may still have effect on the inventors in the prior location according to Agrawal, Cockburn, and McHale (2006).

5 How do prolific inventors impact firm innovation 3 As there are many studies, e.g. Cummings and Cross (2003), Cattani and Ferriani (2008), and Paruchuri (2010), relevant with the effect of the network positioning and network structure on innovation, e.g. the centrality or the hierarchical network, there should be prolific inventors 2 who hold central positions and play a key role. However, it appears that the above studies did not make a clear identification of these prolific inventors in the network, which makes the effect of network structure and network positioning quite general. It appears necessary to make a disintegration of these effects and a classification of the inventors in the context of network. Other studies, e.g. Pilkington (2006), Gambardella, Harhoff, and Verspagen (2006), Latham, Le Bas, and Touach (2006), and Gay, Le Bas, and Latham (2008), identified prolific inventors, but they lack an indepth investigation of these prolific inventors in the network context. This paper contributes to existing literatures by differentiating the prolific inventors from non-prolific inventors in the network context, and making an empirical analysis of the effect of prolific inventors. We take into account the network distances of non-prolific inventors relative to prolific inventors and study the impact from the perspective of effect recipients, i.e. the non-prolific inventors. We make a disintegration of the network according to the strength of the effect by prolific inventors and analyse this effect in the sub-networks. This would allow us to make a focal analysis of the effects of prolific inventors by removing other noisy effects. This is a new perspective compared with existing studies, which appear to have taken the network as a whole, and the effects appear to be functioning on all the inventors. We examine how prolific inventors impact close and distant nonprolific inventors in terms of the efficiencies of knowledge flow. Many studies, e.g. Cummings (2003), Ambos and Ambos (2009), Li and Scullion (2006), Fischer, Scherngell, and Jansenberger (2006), Singh (2005), and Sorenson, Rivkin, and Fleming (2006) have confirmed the negative role of distance in the efficiencies of knowledge flow. However, as members are more likely to follow prolific inventors, the network centred by prolific inventors may be more clustered, which may lead to a greater intensity of knowledge flow. It appears that the aforementioned studies did not make a particular study of the network structure around prolific inventors, as well as how it functions on the knowledge flow. With the patent co-authorship data from the State Intellectual Property Office of China (SIPO) during , we make an in-depth analysis of the structure of the innovation networks and the role of prolific inventors of 10 largest Information & Communication Technology (ICT) firms. By making a disintegration of the network clusters according to the inclusion of prolific inventors, this study compares the structural differences of these clusters, as well as their subsequent effect on patent productivity. Section 2 presents the hypothesis, Section 3 presents the data and methods, Section 4 provides the empirical result, and Section 5 discusses and concludes. 2. Hypothesis Most members are more likely to learn from members with greater performance, e.g. prolific inventors, who are usually believed to hold greater knowledge. Knowledge originated from prolific inventors may reach distant inventors as they are likely to be in the same innovation network. However, there may be efficiency losses due to distances and knowledge flow may barely benefit distant members. As inventors are in different network positions, the efficiency of knowledge flow from prolific to non-prolific inventors appears to be different. Since not all inventors have a direct contact with prolific inventors, the amount of knowledge they receive from the prolific inventors may be different. This is relevant to the distances between inventors within the network. Many studies have provided evidences that high distances, e.g. geographic distances (Ambos and Ambos

6 4 G. Zhang et al. 2009; Cummings 2003; Fischer, Scherngell, ands Jansenberger 2006; Li and Scullion 2006), cultural and linguistic distances (Ambos and Ambos 2009), and social relationship distances (Singh 2005; Sorenson, Rivkin, and Fleming 2006), negatively impact the effectiveness of knowledge flow. This is because the direct connections allow the recipient to interactively query the original source of the knowledge to correct errors or to fill gaps in the original transmission (Sorenson, Rivkin, and Fleming 2006). In comparison, distant members may thereby learn inaccurate or even no knowledge from prolific inventors. As prolific inventors usually own greater knowledge, members with a close contact with prolific inventors may benefit more from the knowledge flow and thus own higher patent productivity. Accordingly, we draw the following two hypotheses: Hypothesis 1. Members with direct contacts with prolific inventors have higher patent productivity than members with indirect contacts with prolific inventors. Hypothesis 2. Members close to prolific inventors have higher patent productivity than members distant from prolific inventors. Since prolific inventors own more citations than the other inventors (Gambardella, Harhoff, and Verspagen 2006; Gay, Le Bas, and Latham 2008; Latham, Le Bas, and Touach 2006) and usually act as group leaders and technological goalkeepers (Le Bas, Cabagnols, and Bouklia 2010), they are believed to own enriched knowledge and hold more resources. Members may thereby be more likely to be motivated by and gather around prolific inventors to join the R&D object. Prolific inventors are also frequently viewed as knowledge translators or knowledge brokers who facilitate knowledge flow (Le Bas, Cabagnols, and Bouklia 2010); we may therefore find a network with greater connectivity around prolific inventors. Therefore, the group with prolific inventors may be more clustered due to the high connectivity. Accordingly, we make the following hypothesis: Hypothesis 3. Groups with prolific inventors are more clustered than groups without prolific inventors. Most studies have confirmed an inverted U -shaped relationship between network clustering and network performance, e.g. Uzzi and Spiro (2005), Chen and Guan (2010), Fowler (2005), and Guimera et al. (2005), i.e. a middle-level clustered network encourages, but an extremely low- or high-level clustered network discourages innovation. Gulati, Sytch, and Tatarynowicz (2012) gave an explanation for this parabolic relationship by analysing the evolution of network: the accumulation of disparate actors into macro-social structures that benefit organisations by facilitating exchanges of information, knowledge, and other resources. As the network is becoming more clustered, there is a decline in the formation of bridging ties and the clustered architecture contains too much exchange of redundant knowledge. A lack of diversity is coupled with the decreasing innovation potential of the members that have been growing, as the social structure is further characterised by self-containment and fragmentation. The role of a more clustered network may be two sided: on one hand, it may diffuse knowledge that improves innovation, and on the other hand, it may bring too much common or even negative information that hamper creativity (Chen and Guan 2010). As the clusters facilitate knowledge flow (Brusco 1990; Dahl and Pedersen 2004; Russo 1985), it may not be always beneficiary if inventors receive too much knowledge, especially if the knowledge is useless and inventors spare too much time in filtering the knowledge. After passing the medium level, clustering negatively impacts innovation output. Therefore, the role of clustering in innovation may to a great extent depend on the parity between useful and redundant

7 How do prolific inventors impact firm innovation 5 knowledge. As the new and useful knowledge is proved to be always beneficial (e.g. James and Sankaran 2006), it is necessary to encourage the flow of this type of knowledge between group members. In the groups centred by prolific inventors who usually own new and useful knowledge (Le Bas, Cabagnols, and Bouklia 2010), the role of clustering may therefore be quite different. It is likely that a higher clustering that facilitates knowledge flow may increase the patent productivity in the groups centred by prolific inventors. Hence we make the following hypotheses: Hypothesis 4. There is a parabolic relationship between clustering and patent productivity in groups without prolific inventors. Hypothesis 5. There is a positive relationship between clustering and patent productivity in groups with prolific inventors. 3. Data and methods 3.1. Data Many literatures measured the technological performance of R&D personnel objectively on the basis of patenting activity (Ernst 1999). We use the patent filing data from SIPO, which covers totally over 6 million patents by the year The number of patents filed during in SIPO grew at the fastest pace and SIPO has become the second largest database in the world, just behind United States Patent and Trademark Office (USPTO), but greater than Japanese Patent Office (JPO) and European Patent Office (EPO) (Guan and Shi 2012). With such a huge and ever-booming number of patents, it would be very possible to explore representative information about the role of innovation network from the database of SIPO. This study focuses on the network collaboration at the firm level in ICT industry, which is one of the fastest growing and knowledge-intensive industries. By making a rank of patent counts during , we found that Huawei, ZTE, Nokia, IBM, Philips, Intel, Sony, Panasonic, Samsung, and LG filed larger number of patents than any other firms. We chose these top 10 ICT Multinational Corporations because the patent data by these firms are large enough to establish well-structured networks. With relatively large patent applications by each firm, we establish the network with sufficiently large scale, which allows us to make a robust identification of prolific inventors. The Price law, i.e. the number of prolific inventors is smaller than the square root of all inventors (Price 1976), or the method by Pilkington and Dyerson (2001, 2002) and Pilkington, Lee, and Chan (2009), i.e. inventors have higher than twice the average output productivity of others, can be referred in determining the threshold of prolific inventors. However, this threshold may not be sufficient to make a clear differentiation. As inventors file relatively close number of patents, prolific inventors who rank in the last position may file very similar number of patents as non-prolific inventors who rank in the top position. It may therefore not be appropriate to classify the former into prolific group and the latter into non-prolific group. Therefore, we define prolific inventors in the following way: (1) rank the inventors by the number of connections and choose the top 10% inventors, which refers to the lower threshold proposed by Narin (1993) and Narin and Breitman (1995) and (2) identify maximum n inventors ranking in the top 10% as prolific inventors, where the connections of the inventor ranking in the nth position is 10% higher than the n+1th inventor. 3 Obviously, this method contains two thresholds, which produce a relatively low ratio of prolific

8 6 G. Zhang et al. inventors, 4 who also file significantly larger number of patents than any non-prolific inventors. This would make a relatively clear differentiation between prolific and non-prolific inventors. We study the largest connected component 5 of the innovation network with the data of five-year moving windows, which classifies the data into the following 11 cohorts: , , , , , , , , , , and We take the cohort of as an example. As is shown in Figure 1, most inventors file relatively low number of patents, while a small ratio of inventors file large number of patents. The circled spots are composed of prolific inventors who have more coinventing experiences and file much more patents. With the threshold given earlier, Huawei, ZTE, and Nokia did not have prolific inventors during As is shown in Table 1, there are 42 prolific inventors in sum, which is relatively a very small ratio compared with 8059 non-prolific inventors. There are 1002 inventors (about 1/8 of the nonprolific inventors) who are directly connected with prolific inventors, i.e. who have co-invented at least one patent with prolific inventors in the past. Panasonic and LG own the highest number of prolific inventors, which is followed by Sony with eight prolific inventors Variables As patent and patent statistics have been included in many research fields (Griliches 1990) and have been treated as the most important output indicator of innovation for their standardised information relating to new ideas and technological development (Frietsch and Grupp 2006), this study uses patent count in measuring innovation. Following Schilling and Phelps (2007), Fleming, King, and Juda (2007), Chen and Guan (2010), and Zhang, Guan, and Liu (2014), the dependent variable in this study is the number of patent applications by inventors, PatentAppl i,t+1, which measures inventor i s patent productivity at period t + 1 with the number of patent application. This suggests that inventors with higher innovation performance should have higher patent output. To test Hypotheses 1 and 2 that clarify the positive role of prolific inventors, we introduce two independent variables: (1) ConnectPI i,t 4:t, which is 1 if non-prolific inventor i co-invents at least one patent with one of the prolific inventors and 0 other wise. This variable denotes the closeness of cooperation relationships between inventor i and prolific inventors. A positive parameter estimate of ConnectPI i,t 4:t would provide support for Hypothesis 1. (2) AvgPathLengthPI i,t 4:t, which is the average path length from non-prolific inventor i to all the prolific inventors within the firm, i.e. N j=1 AvgPathLengthPI i,t 4:t = AvgPathLengthPI i j,t 4:t, N where N is the number of prolific inventors in the network. AvgPathLengthPI i j,t 4:t is measured by the number of intermediate inventors on the shortest path between non-prolific inventor i and prolific inventor j. Since longer path may lead to efficiency losses of knowledge flow, the negative parameter estimate ofavgpathlengthpi i,t 4:t would provide support for Hypothesis 2. As is shown in Figure 2, the path length distributes log normally and is right-skewed. The average distance from inventors to prolific inventors is about 5, i.e. there are averagely five patentees between non-prolific and prolific inventors, with minor non-inventors being either very distant from or very close to prolific inventors.

9 How do prolific inventors impact firm innovation 7 Figure 1. ln-ln distribution of patents filed in Note: X-axis denotes the number of patents filed by an inventor, Y-axis denotes the density, and circled spots are composed of prolific inventors.

10 8 G. Zhang et al. Table 1. Scale of networks of the largest component in Number of non-prolific Number of Number of Number of inventors with a direct contact non-prolific inventors connections prolific inventors with prolific inventors Total , IBM , Philips , Intel , Sony , Panasonic , Samsung , LG , Huawei , ZTE , Nokia Figure 2. Distribution of the path length from prolific inventors ( ). ClusterCoef i,t 4:t, clustering coefficient, i.e. the ratio of an inventor s cooperators connected to each other, is measured by the following formula (Kolaczyk 2009): ClusterCoef i,t 4:t = τ (i) τ 3 (i), where τ (i) is the number of connected triangles that contain inventor i, the τ 3 (i) is the number of connected triples for which the two edges are both incident to inventor i. The square term of ClusterCoef i,t 4:t is also added to the regression model as there may be a parabolic relationship between clustering and patent output (Chen and Guan 2010; Zhang, Guan, and Liu 2014). The statistics and parameter estimates of ClusterCoef i,t 4:t and its square term would provide a test for Hypotheses 3, 4, and 5. The control variables in this study are referred to the studies by Schilling and Phelps (2007), Fleming, King, and Juda (2007), Gulati, Sytch, and Tatarynowicz (2012), Chen and Guan (2010), and Zhang, Guan, and Liu (2014), who examined the regional level impact of networks by averaging the variables over all the inventors. Different from these studies, we go in more detail into the inventor level and choose the following control variables: AvgPathLength i,t 4:t, the average path length of inventor i to all other inventors (including prolific and non-prolific inventors), which may negatively impact patent output due to the difficulties in knowledge transfer (Chen and Guan 2010; Cowan and Joward 2003; Fleming, King, and Juda

11 How do prolific inventors impact firm innovation ; Hargadon 2003; Schilling and Phelps 2007; Uzzi and Spiro 2005; Verspagen and Duysters 2004; Zhang, Guan, and Liu 2014). Centrality i,t 4:t, which is measured by two methods: closeness centrality, originally proposed by Sabidussi (1966), which takes into account the geodesic distance between inventors, and betweenness centrality, originally proposed by Freeman (1977), which takes into account the extent to which a vertex is located between other pairs of vertices (Kolaczyk 2009). The formula for estimating closeness and betweenness centrality are as follows: CloseCentrality i = j I 1 dist(i, j), where dist(i, j) is the geodesic distance between the vertices i, j I. BetweenCentrality i = s =t =i I σ(s, t i) σ(s, t), where σ(s, t i) is the total number of shortest paths between s and t that pass through i and σ(s, t) = I σ(s, t i). The betweenness centrality may have a positive but not very significant impact on patent output according to Schilling and Phelps (2007). However, there appears to be no studies investigating the impact of closeness centrality on patent output. Degree i,t 4:t, the number of inventors directly connected with inventor i, which is one of the key control variables, since inventors with more connections with others are believed to invent more patents. Gulati, Sytch, and Tatarynowicz (2012) showed that vertex degree has a significant impact on bridging ties, which may in turn increase the patent output. IBM i, Philips i, Intel i, Sony i, Samsung i, Huawei i, ZTE i, Nokia i are dummy variables, which equal 1 if inventor i is in that firm and 0 otherwise. Table 2. Summary statistics of variables. Mean Std. Dev. Min. Max. PatentAppl i,t ConnectPI i,t 4:t AvgPathLengthPI i,t 4:t ClusterCoef i,t 4:t ClusterCoef 2 i,t 4:t AvgPathLength i,t 4:t BetweenCentrality i,t 4:t CloseCentrality i,t 4:t Degree i,t 4:t IBM Philips Intel Sony Panasonic Samsung Huawei ZTE Nokia LG

12 Table 3. Correlation matrix of variables (n = 26, 808). Dependent variable PatentAppl i,t+1 2. ConnectPI i,t 4:t AvgPathLengthPI i,t 4:t ClusterCoef i,t 4:t ClusterCoef 2 i,t 4:t AvgPathLength i,t 4:t BetweenCentrality i,t 4:t CloseCentrality i,t 4:t Degree i,t 4:t IBM Philips Intel Sony Panasonic Samsung Huawei ZTE Nokia LG G. Zhang et al.

13 Table 4. Regression results with all non-prolific inventors. How do prolific inventors impact firm innovation 11 PatentAppl i,t+1 Dependent variable Model 1 Model 2 Model 3 Model 4 Independent variable Coefficient Coefficient Coefficient Coefficient ConnectPI i,t 4:t (0.0510) (0.0531) AvgPathLengthPI i,t 4:t (0.1657) (0.1295) ClusterCoef i,t 4:t (0.0466) (0.0455) (0.0540) (0.0751) ClusterCoef 2 i,t 4:t (0.0033) (0.0008) (0.0113) (0.0035) AvgPathLength i,t 4:t (0.0065) (0.0071) (0.0066) (0.0055) BetweenCentrality i,t 4:t (1.5845) (1.0280) CloseCentrality i,t 4:t (0.5738) (0.1522) Degree i,t 4:t (0.0011) (0.0009) (0.0001) (0.0004) Company (Reference: LG) IBM (0.0502) (0.0613) (0.0990) (0.0027) Philips (0.0499) (0.0501) (0.0021) (0.0004) Intel (0.0908) (0.0891) (0.0023) (0.0010) Sony (0.0470) (0.0472) (0.0231) (0.0096) Panasonic (0.0371) (0.0613) (0.0110) (0.0279) Samsung (0.0431) (0.0432) (0.0158) (0.0214) Huawei (0.0821) (0.2551) (0.0281) (0.0196) ZTE (0.0242) (0.0295) (0.0231) (0.0387) Nokia (0.1721) (0.3374) (0.1981) (0.2031) Constant (0.0564) (0.1034) (0.0171) (0.0990) No. of observations 26,808 26,808 26,808 26,808 Log likelihood 11, , LR chi Prob. > chi Condition index Hausman chi Prob. > Chi Note: Standard error in the parentheses. Parameter estimate is significant at 1% level. Parameter estimate is significant at 5% level. Parameter estimate is significant at 10% level.

14 12 G. Zhang et al. Tables 2 and 3 list the summary statistics and correlation matrix of variables, respectively. The patent application (PatentAppl i,t+1 ) of non-prolific inventors significantly positively correlates with the direct connection with prolific inventors (ConnectPI i,t 4:t ), while significantly negatively correlates with the path length from prolific inventors (AvgPathLengthPI i,t 4:t ), which suggests that, at least for inventor collaboration networks, one cannot ignore the effect of prolific inventors on innovation Statistic model Due to the count nature of the patent filing data, the count model is preferred. Researchers often use Poisson models to analyse count data, but these models constrain the variance to equal the mean. In this study, a test for over dispersion (i.e. the variance exceeds the mean) rejected the constraint of the Poisson model at the 1% level. The over-disperse patent data suggested the need for the negative binomial specification (Fleming, King, and Juda 2007; Hausman, Hall, and Griliches 1984). The basic Poisson model estimates the probability of an observed value conditional on the values of a set of independent variables: P(y x) = e λ λ y. y! To avoid negative predicted values for the mean λ, the negative binomial model replaces the Poisson mean λ with a gamma distribution to allow the predicted mean to vary according to the Table 5. Average clustering coefficient and t-test. Sub-networks without Sub-networks with t-test of H 0 : (1) (2) prolific inventors (1) prolific inventors (2) and H 1 : (1) <(2) (0.1726) (0.3112) (0.2031) (0.4117) (0.3009) (0.2526) (0.2740) (0.2666) (0.3647) (0.2136) (0.2736) (0.2221) (0.3114) (0.2928) (0.2543) (0.3716) (0.3155) (0.4511) (0.3625) (0.2571) (0.2895) (0.3292) Note: Standard error in the parentheses; the whole network may be disintegrated into several sub-networks, since there are several prolific inventors. We estimate the clustering coefficient of each inventor in each sub-network; After removing the prolific inventors and their directly connected inventors, the sub-network without prolific inventors may not be totally connected. We keep the largest component of the sub-network and estimate the clustering coefficient of each inventor in the largest component. Parameter estimate is significant at 1% level. Parameter estimate is significant at 5% level. Parameter estimate is significant at 10% level.

15 Table 6. Regression result with disintegrated networks. How do prolific inventors impact firm innovation 13 PatentAppl i,t+1 Sub-networks without prolific inventors Sub-networks with prolific inventors Dependent variable Model 1 Model 2 Model 3 Model 4 Independent variable Coefficient Coefficient Coefficient Coefficient ClusterCoef i,t 4:t (0.5857) (0.5003) (0.1032) (0.1003) ClusterCoef 2 i,t 4:t (0.0071) (0.0035) (0.1771) (0.1834) AvgPathLength i,t 4:t (0.0311) (0.0139) (0.1828) (0.1922) BetweenCentrality i,t 4:t (0.1029) (1.7131) CloseCentrality i,t 4:t (0.9845) (1.7142) Degree i,t 4:t (0.0121) (0.0026) (0.0015) (0.0009) Company (Reference: LG) IBM (0.0938) (0.1029) (0.1025) (0.1151) Philips (0.0948) (0.1981) (0.0991) (0.1422) Intel (0.0723) (0.0938) (0.1814) (0.1829) Sony (0.0488) (0.0409) (0.1052) (0.1091) Panasonic (0.0288) (0.0113) (0.0472) (0.0551) Samsung (0.0057) (0.0030) (0.1015) (0.1255) Huawei (0.0133) (0.0161) (0.0042) (0.0048) ZTE (0.0032) (0.0008) (0.0009) (0.2742) Nokia (0.0910) (0.0785) (0.2812) (0.3723) Constant (0.0307) (0.0046) (0.1262) (0.2946) No. of Observations 14,281 14, Log Likelihood LR Chi Prob. > Chi Condition Index Hausman Chi Prob. > Chi Note: Standard error in the parentheses. Parameter estimate is significant at 1% level. Parameter estimate is significant at 5% level. Parameter estimate is significant at 10% level.

16 14 G. Zhang et al. distribution of the error term: λ Ɣ(γ, δ). Thus, the probability density function comes to be a negative binomial model with parameters λ and δ: e λ λ y ( ) Ɣ(γ + y) δ γ ( ) 1 γ P(y x) = f (λ) dλ = BN(γ, δ). y! Ɣ(γ)Ɣ(y + 1) 1 + δ 1 + δ 0 The data with subscript i denoting the inventor and t denoting the period are unbalanced panel data, since inventor i may not appear in each period. We thereby use panel model. The fixedeffects negative binomial model is preferred because it considers within-inventor variation, i.e. it controls for time-invariant, national idiosyncratic characteristics (Fleming, King, and Juda 2007; Hausman, Hall, and Griliches 1984). The Hausman tests reject random effects specification at the 1% level in all the regressions (Tables 4 and 6). The conditional mean of the negative binomial patent function for inventor i in year t + 1 is described in the following equation: γ i,t+1 = E(PatentAppl i,t+1 ConnectPI i,t 4:t,AvgPathLengthPI i,t 4:t, ClusterCoef i,t 4:t,AvgPathLength i,t 4:t, Centrality i,t 4:t, Degree i,t 4:t, IBM i, Philip i, Intel i, Sony i, Samsung i, Huawei i, ZTE i Nokia i ) = β 0 + β 1 ConnectPI i,t 4:t + β 2 AvgPathLengthPI i,t 4:t + β 3 ClusterCoef i,t 4:t + β 4 ClusterCoef 2 i,t 4:t + β 5AvgPathLength i,t 4:t + β 6 Centrality i,t 4:t + β 7 Degree i,t 4:t + β 8 IBM i + β 9 Philip i + β 10 Intel i + β 11 Sony i + β 12 Panasonic i + β 13 Samsung i + β 14 Huawei i + β 15 ZTE i + β 16 Nokia i, where γ i,t+1 is the conditional expected number of patents granted to inventor i in year t + 1. In order to estimate the impact of prolific inventors during five-year moving windows on the following year patent output of non-prolific inventors, dependent variable is calculated in year t + 1 while all independent variables are calculated from years t 4tot. 6 Dependent variable PatentAppl i,t+1 is the number of patents filed by inventor i in year t Empirical results Table 4 presents the coefficient estimates for the negative binomial model. All the Hausman tests reject the random effect and the fixed effect settings are thereby utilised in all the regressions. The condition indexes are all lower than 30 but higher than 10, which indicates that there is medium and acceptable level of collinearity. The estimates of control variables are mostly significant and in the expected direction. In Models 1 4, the estimates of ClusterCoef i,t 4:t are significantly positive, while the estimates of ClusterCoef 2 i,t 4:t are significantly negative. This corresponds with Chen and Guan (2010) and Zhang, Guan, and Liu (2014), who also found a parabolic relationship between clustering and patent output. AvgPathLength i,t 4:t negatively impacts patent output, which also corresponds with existing studies, e.g. Chen and Guan (2010), Zhang, Guan, and Liu (2014), and Fleming, King, and Juda (2007). The estimates of Degree i,t 4:t are significantly positive, which partly correspond with Fleming, King, and Juda (2007), who found an insignificantly positive relationship between the degree density and patent output. The betweenness centrality

17 How do prolific inventors impact firm innovation 15 shows a positive but insignificant impact on patent output, which corresponds with Schilling and Phelps (2007). The estimate of ConnectPI i,t 4:t is significantly positive in Model 1 and Model 2, which suggests that inventors directly connected with prolific inventors will have higher patent output, compared with inventors indirectly connected with prolific inventors. This provides support for Hypothesis 1. The estimates of AvgPathLengthPI i,t 4:t is significantly negative in Model 3 and Model 4, which suggests that a shorter path length from prolific inventors will positively impact patent output and thereby supports Hypothesis 2. This empirical result may be expectable, since the estimates of AvgPathLength i,t 4:t is also significantly positive, which suggests that being in close proximity to other inventors would always facilitate knowledge flow and thereby increase patent output. Prolific inventors are more likely to be either the organisers or the leaders of innovation activity. As prolific inventors are more patent productive, others may be urged to learn the knowledge diffused by them. Therefore, non-prolific inventors are more likely to gather around prolific inventors and form intensive clusters. To make a focal analysis of the effects of prolific inventors by removing other uncorrelated effects, we disintegrate the network by the connection with prolific inventors and make a comparison of the sub-networks with and without prolific inventors. Figure 3 presents an example clarifying the rule of disintegration. The totally connected network in Figure 3(a) is formulated by 13 inventors. Inventor 6 (in black) is identified as a prolific inventor and is directly connected by 6 other inventors, i.e. Inventors 1, 4, 7, 8, 9, and 10 (in Figure 3. Disintegration of networks. (a) The whole network, (b) sub-network with prolific inventors, and (c) sub-network without prolific inventors.

18 16 G. Zhang et al. green). We pick up these inventors and form a new network with their connections (Figure 3(b)), leaving other inventors (in red) and their connections forming another network (Figure 3(c)). With this method, we disintegrate each network of each firm in each period and estimate the average clustering coefficient of the disintegrated networks. We run the t-tests to see if there is significant statistical difference of clustering between the two groups. As is shown in Table 5, in 6 periods, i.e , , , , , and , of all the 11 periods, H 0 is rejected and H 1 is accepted, i.e. sub-networks with prolific inventors own statistically higher (at 10% level) clustering coefficient than sub-networks without prolific inventors, while in the other five periods, the differences are not significant. There is no t-test supporting H 0 in Table 5. These results provide evidences that it is more likely to form a more intensive cluster by introducing prolific inventors. Since inventors have a tendency to gather around prolific inventors and form a more clustered network, we may have found support for Hypothesis 3. There are only strong connections between prolific and non-prolific inventors in the subnetworks, since all the prolific inventors are directly connected with the non-prolific inventors. We are therefore able to examine how prolific inventors impact innovation with direct and strong connections. As prolific inventors are usually believed to hold useful knowledge, the knowledge flows beneficial to non-prolific inventors are emphasised. The role of clustering that facilitates knowledge flow in the sub-network may be quite different from that in the whole networks, which appear to diffuse both useful and redundant knowledge. As is shown in Table 4, the parabolic relationships between patent productivity and clustering is confirmed by this study, which also corresponds with Chen and Guan (2010) and Zhang, Guan, and Liu (2014). Model 1 and Model 2 in Table 6 show similar results with that in Table 3, where the estimates of ClusterCoef i,t 4:t are significantly positive and the estimates of ClusterCoef 2 i,t 4:t are significantly negative. This provides evidences for Hypothesis 4, which indicates that the role of clustering without prolific inventors depends on the parity between useful and redundant knowledge. Since most inventors hold partly useful, but partly redundant knowledge, the facilitation of knowledge flow proved to be not always beneficial. This empirical result may therefore be expectable. Model 3 and Model 4 in Table 6 show that the estimates of ClusterCoef i,t 4:t are significantly positive, while those of its square term ClusterCoef 2 i,t 4:t are not significant, which suggests that high clustering with prolific inventors linearly and positively impacts patent output. This empirical result is quite different from that in Model 1 and Model 2, and is also different from that of Chen and Guan (2010) and Zhang, Guan, and Liu (2014). This suggests that in networks centred by prolific inventors who mostly hold useful knowledge, the role of clustering may be quite different. The facilitation of the flow of useful knowledge is beneficial, which may be one of the main determinants of this empirical result. This provides evidences for Hypothesis 5, which suggests that more clustered networks would benefit innovation, in case the clusters are led by prolific inventors who diffuse useful knowledge within the cluster. By making a comparison between Models 1 and 2 and Models 3 and 4 in Table 6, we may find a low significant level of the estimates of ClusterCoef i,t 4:t with low estimate value in Models 1 and 2, compared with that in Models 3 and 4. This suggests that in sub-networks without prolific inventors, the negative role of clustering is emphasised. 7 The estimates of ClusterCoef 2 i,t 4:t in Models 1 and 2 are highly significant and the estimate value is relatively higher, compared with that in Models 3 and 4. This suggests that in sub-networks with prolific inventors, the positive role of clustering is emphasised. In summary, the parabolic relationship between clustering and patent output, which has been confirmed by the empirical results in Table 3 and other studies, may be co-determined by two forces: the contacts with prolific inventors that diffuse useful knowledge,

19 How do prolific inventors impact firm innovation 17 which may lead to a positive relationship, and the contacts with non-prolific inventors that diffuse redundant knowledge, which may lead to a negative relationship. 5. Discussion and conclusions As prolific inventors have higher innovation productivity, which may be more economically valuable, they are believed to hold useful knowledge that is beneficial to other inventors. Knowledge diffused by prolific inventors is transmitted to other inventors through the network, where the clusters in the network play a key role in the knowledge flow. For most ICT firms in most periods, there are prolific inventors who are significantly impacting other inventors. By using the patent co-authorship data from SIPO during , this paper establishes the innovation networks of 10 largest ICT firms. We disintegrate these networks by identifying the direct co-authorship relationships with prolific inventors, so that the role of prolific inventors is more clearly reflected. With the negative binomial model, this paper makes an empirical analysis, which confirms the positive role of prolific inventors by investigating the direct and indirect impact: (1) the direct impact, which shows that members with direct contact with prolific inventors own higher patent output and (2) the indirect impact, which shows that a closer distance from prolific inventors that facilitates knowledge accession would increase the patent output. This is because knowledge diffused by prolific inventors is mostly beneficial, and the proximity would allow members to get more useful knowledge from prolific inventors. Therefore, members are more likely to gather around prolific inventors and formulate more intensive clusters, which in turn would facilitate knowledge flow. Clusters centred by prolific inventors play a quite different role from existing studies that claim that the relationship between clustering and patent output is parabolic. As useful knowledge outweighs redundant knowledge in networks centred by prolific inventors, high clustering that facilitates knowledge flow is proved to be always beneficial. ICT industry is one of the most R&D-intensive industries, where innovation networks play a key role in innovation. As prolific inventors are mostly organisers or leaders of innovation activity, they have a significant impact on the others through the collaboration network. They may, to a great extent, determine the success of an R&D project. Prolific inventors make up very specific human resources that request particular management; hence they are motivated to share the knowledge (Le Bas, Cabagnols, and Bouklia 2010). Since prolific inventors are important to technology innovation, firms should first identify them and then manage them in a particular fashion. A close contact between prolific inventors and others should be encouraged by firms. Since prolific inventors usually produce greater impact, the firm manager should ensure that prolific inventors are leading the research team in the right way and diffusing the right knowledge. Prolific inventors diffusing incorrect knowledge or leading the group in an incorrect way would have worse consequences. As with any studies, there are limitations to this project that could become avenues for future research. The first limitation concerns the selection of only large ICT firms to study. We selected these large firms because our research question required us to select firms that have filed large number of patents so that well-structured networks are established. However, future studies could expand the selection to different kinds of firms such as small firms. Moreover, the ICT industry offers a unique context with distinct characteristics, so the generalisability of these findings to other industries needs to be explored. The third limitation concerns the use of patent data. Although patent data are the most comprehensive data of innovations for ICT firms, they do not capture those collaborations which did not result in patents. Future studies need to examine other kinds of data, such as the field survey data. The fourth limitation is that after making a disintegration