Journal of Informetrics 16 (2022) 101256
Contents lists available at ScienceDirect
Journal of Informetrics
journal homepage: www.elsevier.com/locate/joi
Female inventors over time: Factors affecting female Inventors’
innovation performance
Leila Tahmooresnejad∗, Ekaterina Turkina
HEC Montréal, 3000 Côte-Sainte-Catherine Road, Montréal, QC H3T 2A7, Canada
a r t i c l e
Keywords:
Gender
Network analysis
Patents
Citations
i n f o
a b s t r a c t
The aim of this paper is to explore the collaboration of female inventors, how it affects their innovation production and whether it influences their innovation impact. Empirical knowledge of how
inventors collaborate in co-patenting collaborations holds an important key to innovation development. In this article, we report on an analysis of international inventors and patents granted by
the European Patent Office (EPO) between 1978 and 2019. We investigate the structure of inventors’ networks—particularly those of female inventors—over time using social network analysis
and address the gender patterns of collaboration. It can be observed that while female inventors’
overall involvement in patenting activity is not that high, the share of female inventors increases
over the time period in question from 1.2% to 8.9%. We also estimate panel data regressions on
the number of patents and the citation rates of the patents at an individual level. Our results show
that although all inventors benefit from a more central network position within the co-patenting
network in terms of their innovation output, the positive influence is greater for male inventors
than female inventors. In addition, when inventors collaborate with inventors from more diversified countries and regions they contribute to more patents and their patents are more cited.
1. Introduction
The gender gap in science, technology and innovation has received considerable attention in the past two decades from researchers who argue that there is strong evidence of gender inequality in scientific research and patenting activities (Bendels, Müller,
Brueggmann, & Groneberg, 2018; Filardo et al., 2016; Lariviere, Ni, Gingras, Cronin, & Sugimoto, 2013; Long, Leszczynski, Thompson, Wasan, & Calderwood, 2015; Symonds, Gemmell, Braisher, Gorringe, & Elgar, 2006). For instance, Ding, Murray, and Stuart (2006) conducted interviews with faculty members to determine the scope of the gender gap in patenting among life scientists.
Their study demonstrated that female faculty members patent at about 40% of the rate of their male peers. Jensen, Kovacs, and
Sorenson (2018) studied gender differences in obtaining and maintaining patent rights by examining the maintenance histories of
approximately 2.7 million US patent applications and found that women had less favorable outcomes than men. Additionally, existing studies demonstrate that in all countries, across all sectors and all fields, the percentage of women obtaining patents is not only
smaller than that of their male counterparts, but it is smaller than the percentage of women in science, technology, engineering and
mathematics (STEM) in the country (Rosser, 2009).
This indicates that women are not equal participants in new areas of research and innovation. Existing studies have focused
mostly on establishing gender-related differences in science and innovation as well as the reasons for the gender gap and factors
that contribute to it. Earlier explanations focused on the phenomenon of underrepresentation of women in science related to gender
∗
Corresponding author.
E-mail addresses: leila.tahmooresnejad@polymtl.ca (L. Tahmooresnejad), ekaterina.turkina@hec.ca (E. Turkina).
https://doi.org/10.1016/j.joi.2022.101256
Received 30 June 2021; Received in revised form 28 December 2021; Accepted 22 January 2022
Available online 12 February 2022
1751-1577/© 2022 Elsevier Ltd. All rights reserved.
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
discrimination in grant and manuscript reviewing, interviewing, and hiring (Ceci & Williams, 2011). Later studies explained underrepresentation by educational context, where, despite the general reversal of the gender gap in education, women still pursue STEM
study plans at lower rates than their male peers do (Lariviere et al., 2013; Legewie & DiPrete, 2014).
While we have a generally good understanding of the existence of a gender gap in innovation and the factors that explain it,
we have much less knowledge about the trends and patterns in the evolution of women-led innovation over time, the economic
geography of female innovation and the factors that contribute to the success of female innovation. In this study, we aim to contribute
to the emerging literature on this topic by conducting a longitudinal study of women’s patenting activities and examining the factors
that explain women’s patent productivity. To this end, we first develop a theoretical framework of female innovation that draws
on the literature about innovation and social networks. In the past decade, there has been substantial research on co-authorship
networks, however, it has mostly analyzed the issues of network distance between scientists and how patterns of collaboration vary
between subjects and over time (Newman, 2004) and the stability of such networks over time (Cugmas, Ferligoj, & Kronegger,
2019). Despite the increasing importance of scientific collaboration and the collaborative character of scientific research and patent
production, the impact of research collaboration on innovation productivity, and in particular women’s innovation productivity, has
been largely understudied. There is one study that analyzed the propensity to collaborate on Italian academic research that found
that, in general, women have become more prone to collaborate with the exception of international collaboration, where there is
still a gap in comparison to male colleagues (Abramo, D’Angelo, & Murgiac, 2013). However, it was carried out on a small sample.
Whittington (2018) used a big sample from a Bioscan database to explore co-patenting trends and collaborations in biotechnology
and found important differences in male and female network roles. To date, we have not had good knowledge of the structure of
global co-patenting networks across different industries, how positioning in these networks relates to women’s innovation output or
geographic differences in gender-related collaboration patterns. Moreover, a previous study (Whitington, 2017) focused exclusively
on differences in male and female innovation measured by the number of patents. There is, however, extensive research on innovation
that argues that it is important to look at not only the number of innovations, but innovation quality and impact (patent citations)
as well. In raw patent counts, identical weight is given to very important patents and secondary patents; therefore, it is extensively
argued in the literature that patent citations are a more accurate measure of innovation since they represent the impact and quality
of patenting activity and the value of the invention (Almeida & Phene, 2004; Frost, 2001). In this paper, we therefore explore the
structure of global co-patenting networks and female collaboration strategies and analyze network effects on both the number and the
impact of innovations. We build on the social network analysis literature to account for innovation network indicators and proceed
with econometric models using panel data. We empirically investigate global female co-patenting networking using data on 3497,675
patents and 6419,197 inventors from 235 countries covering the period from 1978 to 2019.
This paper is structured as follows. The next section presents the literature review and theoretical framework. The following
section presents the data, methodology and empirical analysis. The last section includes a discussion about the findings and the
conclusion.
2. Literature review and theoretical framework
The innovation literature (Hidalgo, 2015) argues that the complexity of innovation grows over time: earlier innovation was mainly
driven by talented individuals, then collective arrangements emerged, such as research laboratories and firms, and recently, innovation
increasingly demands broader collective intelligence and is driven by large-scale collaborations. Researchers have been using social
network analysis more and more to understand different aspects of innovation, including the transfer of ideas, technology, and
knowledge (Dhanaraj, Lyles, Steensma, & Tihanyi, 2004; Ferrier, Reyes, & Zhu, 2016; Turkina & Van Assche, 2018; Turkina, Oreshkin,
& Kali, 2019). Scholars have increasingly explored the relationship between scientists’ social ties and their performance in creating
technology and knowledge (Adams, 2012; Rost, 2011; Walsh & Maloney, 2007). However, studies on gender-related differences in
innovation networks are rare and limited.
Existing research demonstrates that women do not have inferior skills and capabilities to innovate and patent their research
(Swede, 2003). Nevertheless, there are some controversies in the literature exploring gender-related differences in patent productivity
and citation distribution. While most studies that analyze gender and research citation distribution report average differences in favor
of male authors (Aksnes, Rorstad, Piro, & Sivertsen, 2011; Caplar, Tacchella, & Birrer, 2017; Eagly & Miller, 2016; Maliniak, Powers,
& Walter, 2013), some studies report no discernible gender differences (Slyder et al., 2011). Nielsen (2017) even found some benefits
for female management scholars. However, most of the studies were conducted on limited samples either with limited geographic
scope or in a particular research field. Moreover, it is important to distinguish between patent citations and journal publication
citations, as they have different dynamics. Most patent citation research reports that men are more productive in terms of generating
more patents and have a higher technological impact because they receive more patent citations (Koning, Samila, & Ferguson, 2021;
Sugimoto, Ni, West, & Lariviere, 2015). Sugimoto et al. (2015) also demonstrate that, in every technological area, female patenting
is proportionally more likely to occur in academic institutions than in corporate environments.
The literature suggests that gender inequalities in patent productivity and quality can be the result of several social factors, such
as social beliefs and discrimination in hiring (Ceci & Williams, 2011; Van den Brink, 2011), as well as education, as fewer women
choose to study in STEM fields (Lariviere et al., 2013; Legewie & DiPrete, 2014; Rosser, 2009). Additionally, the literature mentions
that gender imbalances occur due to significant obstacles in women’s career progress, including sometimes hostile work climates
(Pololi, Civian, Brennan, Dottolo, & Krupat, 2013), and societal cultures in which the gendered division of domestic labor is expected
(Jolly et al., 2014).
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Journal of Informetrics 16 (2022) 101256
More recent studies also call our attention to the patterns of women’s participation in innovation networks, the phenomenon of
social network structures and women’s positioning in these networks (Whittington, 2018), because lacking important ties impedes
access to resources such as new ideas and information, and knowledge of industrial and technological advancements, commercial
processes, and the steps and procedures necessary to patent research. Therefore, more attention should be devoted to women’ social
ties to understand women’s positioning and strategies in social networks in order to better understand the logic behind the gender
gap and develop approaches to narrow it.
Existing research on female participation in social networks has primarily focused on academics and their publication productivity
because doctoral-level female scientists tend to work in educational institutions (Fox, 2001). Meng (2016) investigated collaborations
and the gender gap in academic patenting and suggests that having collaboration ties with industry could significantly increase the
probability of female academic scientists being involved in patenting. There are very few studies that explore gender-related differences in patenting in corporate and industrial settings. Whittington (2018) argues that the share of women involved in biotechnology
patenting is increasing over time; at the same time, we do not know the trends and tendencies in other fields.
In sum, there is a need for large-scale studies on gender-related differences in co-inventor networks and the relationship between
network properties and patent productivity across multiple fields with a longitudinal perspective.
Below we mobilize concepts from the social network literature, as well as insights from the educational, psychological and sociological studies in order to develop a comprehensive framework of the relationship between different network indicators and innovation
from gender-based perspective.
2.1. Network centrality
A social network provides valuable information to actors about the specific capabilities and reliability of potential partners (Sultana
& Turkina, 2020). A network structure encodes a lot of information about connection patterns, and existing research argues that
the magnitude of network participants’ success is affected by their positions in the network (Orlic, Hashi, & Hisarciklilar, 2018).
An actor’s position in the network reflects their connectedness to other actors as well as those other actors’ connectedness to one
another (Gulati, 1995; Bonacich, 1987; Benjamin & Podolny, 1999). Therefore, the powerfulness of a position in the network depends on not only the number of direct connections it has that provide access to different resources but also the power of the
other nodes to which a node is connected (Dyer & Sing, 1998). Being central in the network brings several benefits, such as status, prestige, and influence over other actors in the network (Faulk, McGinnis Johnson, & Lecy, 2017; Orlic et al., 2018; Podolny,
1993).
In terms of innovation, inventors who are in central positions may more easily bring together collaborators who have important
boundary-spanning knowledge, and this central position can help them to source a variety of knowledge and ideas and enable
them to recombine this knowledge and produce new innovations (Uzzi & Spiro, 2005; Fleming, Mingo, & Chen, 2007; Lingo &
O’Mahoney, 2010). Tahmooresnejad and Beaudry (2017, 2018) found that the structure of the co-invention network plays a significant
role in technological productivity and quality.
Moreover, researchers distinguish different types of centrality, and there are ongoing debates in the literature about whether it
is more beneficial to be a broker and connect otherwise disconnected nodes or to be connected to nodes that are themselves highly
connected. Turkina and Van Assche (2018) studied inter-firm networks in Bangalore’s tech cluster and found that radical innovations
were generated by firms that acted as brokers between network communities.
As for differences between male and female inventors, emerging research has found indications of substantial differences in their
network behavior, patenting activity and probability of being cited. For instance, Dion, Sumner, and Mitchell (2018) studied gender
gaps in the citation process in political science and found female scholars’ publications were under-cited; they also found male scholars
received more citations from other male scholars. Wittington (2017) explored the effects of position centrality on patent productivity
in co-patenting networks in biotechnology and found that in the aggregate as well as across time and organizational space, women are
less likely than men to be in central positions. No studies explain these recent findings in detail, but it is possible to provide several
explanations by borrowing from the educational, psychological and sociological literature. Studies indicate that in the past, there was
significant hierarchical and gender discrimination in science when interviewing and hiring women as well as reviewing grants and
manuscripts (Ceci & Williams, 2011; Clauset, Arbesman, & Larremore, 2015) that affected not only women’s scientific productivity,
but also the general cultural landscape of society, where science has since become considered not a “woman’s job”; this negatively
influenced women’s motivation to pursue degrees and jobs in science (Lariviere et al., 2013; Legewie & DiPrete, 2014). Even though
recent advances in gender equality have improved the situation for female scientists, path dependency and legacies of the past affect
women’s entry and performance in science. Consequently, female scientists see their research and patents receive fewer citations, it is
more difficult for them to make an impact and they are solicited less for prestigious collaborations. Additionally, existing research on
gender studies indicates that women still bear a more significant burden in parenting, which often interrupts their careers and affects
their visibility and collaborations (Hunter & Leahey, 2010). Moreover, the sociological literature indicates that women focus more on
local connections and are less likely to establish more diverse and long-range network ties (Szell & Thurner, 2013), which affects their
overall centrality in social networks. Finally, there is also evidence in the sociological literature that men are more strategic in their
network behavior and are more prone to use network linkages to their benefit. For instance, Ibarra (1992) explored the networks of
managers and found that while women tended to use their networks more for social support and were more interested in the process
of communication and interaction, men were more focused on results and actively used their linkages for their strategic benefit and
to promote their careers. Therefore, assuming an equal number of linkages and similar centrality in co-inventor networks, men may
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Journal of Informetrics 16 (2022) 101256
be more likely to be strategic with their collaborations and focus on the output, whereas women could be more motivated by the
collaboration process.
Given the above discussion, once we analyze global co-patenting networks across industries, we expect inventors’ network position
to have a positive influence on the number of patents they have and citations they receive. We also expect there to be gender-related
differences in co-patenting networks and in the benefits derived from network centrality. Our first set of propositions are therefore:
Proposition 1a: Inventors who have higher network centrality contribute to more patents than their colleagues.
Proposition 1b: Inventors who have higher network centrality receive more citations than their colleagues.
Proposition 1c: The benefits of being central in a network are smaller for female inventors (who find it more difficult to become
central in a network) than for their male colleagues (who have an easier time becoming central).
2.2. Clustering
Another important network characteristic to consider is network clustering. Clustering in real-world networks is a fundamental
property that helps us understand how nodes interact with the nodes in their immediate environment (Yin, Benson, & Leskovec, 2019).
Clustering is different than centrality because a cluster is a subnetwork in which an inventor is directly linked to any other inventor
in the subnetwork. It represents the likelihood that Inventor A and Inventor B are connected if Inventor A and Inventor C have a
relationship; if they are, there exists a relationship between Inventor B and Inventor C.1 In more general terms, a node that is placed
at the periphery of the overall network can have a high clustering coefficient if it is placed in a local cluster with densely connected
nodes. In contrast, for a node to be central in the network, it must have long-range network ties that lead to distant communities,
not just intense local collaboration (Kadushin, 2012). As another example, a node embedded in a local cluster can have high degree
centrality (many connections to its local partners), but a low clustering coefficient if its partners are not connected among themselves.
The innovation literature points to the important effect network clustering has on different indicators of node performance. For
instance, Kim, Steensma, and Heidl (2020) found that firms that have inventor network configurations in which inventors are heavily
clustered into cohesive subgroups of interconnected inventors are more likely to innovate and build on new venture technologies.
In a study of nanotechnology patents in universities by Tahmooresnejad and Beaudry (2018), the results showed that the density of
collaborative ties among inventors positively influences an academic inventor’s productivity.
As far as gender differences are concerned, female scientists tend to collaborate with fewer scientists than male scientists do,
but their co-authors are more likely to also be linked together (Szell & Thurner, 2013), implying a higher clustering coefficient.
Moreover, female scientists collaborate more often with the same collaborators and are more likely to repeat their past collaborations
(Ductor, Goyal, & Prummer, 2018; Ghiasi, Larivière, & Beaudry, 2017; Lindenlaub & Prummer, 2021). When an inventor begins a
collaboration, it seems female inventors would rather rely on the collaborators currently in their clustered group as opposed to team
up with new co-inventors. Less invention output risk might be associated with them due to there being less uncertainty about the
co-inventor of a current collaborator.
We suspect that while collaboration relationships are beneficial for both male and female inventors, the effect may be stronger
for female inventors than male inventors. Our second set of propositions are:
Proposition 2a: Inventors who are in clustered groups contribute to more patents than their colleagues in sparsely connected
groups.
Proposition 2b: Inventors who are in clustered groups receive more citations than their colleagues in sparsely connected groups.
Proposition 2c: Female inventors benefit more from being in a clustered group in a network than their male colleagues do.
2.3. Tie diversity
While centrality and clustering characteristics focus on nodes, the innovation and social network analysis literature also finds
important effects at the level of ties. It has been argued that linkages that incorporate diversity (ties across social divides) provide
network nodes with important benefits by bringing them complementary information and opportunities as well as giving them access to different pools of resources (Burt, 1992; Granovetter, 2005). In particular, researchers argue for the importance of social
ties spanning different organizational boundaries—including ethnic and gender divides—in transferring tacit knowledge and enhancing creativity in technological and scientific environments (Bozeman, Dietz, & Gaughan, 2001; Dietz & Bozeman, 2005; Heinze &
Bauer, 2007). Martinez and Aldrich (2011) explored entrepreneurial networks and argued that having a variety of ties increases
self‐efficacy and innovation. In this paper, we explore different types of tie diversity and their effects on innovation: gender diversity
among close collaborators, geographical diversity, as well as discipline diversity. Our third set of propositions are:
Proposition 3a: The geographical diversity of co-inventors has a beneficial influence on innovation output.
Proposition 3b: The diversity of disciplines associated with patents has a positive impact on innovation output.
Proposition 3c: Gender diversity positively influences innovation output.
1
To better understand this indicator, we present in Appendix D examples of three simple networks in which the cliquishness for Inventor A varies.
It is higher in Figure A(c) (equals 1) and lower in Figure A(a) (equals 0).
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Table 1
General description of the network data.
Network Overview
Values
Number of Inventors
Number of Male Inventors
Number of Female Inventors
Number of Co-Invention Links
Giant Component (22.65% visible)
Number of Inventors
Number of Male Inventors
Number of Female Inventors
Number of Co-Invention Links
Structural Network Measures
Average Degree
Average Clustering Coefficient
Connected Components
42,312
38,804
3084
89,223
9524
8698
826
47,099
4.217
0.581
18,514
3. Data, methodology and empirical analysis
3.1. Description of the data
We extract our data from the OECD REGPAT database, which provides patent and inventor data and links the data to the applicants’
countries. We use the inventor’s address information to trace the country of the invention to better understand the geography of
innovation. Our database contains information about 3497,675 patents and 6419,197 inventors from 235 countries covering the
period from 1978 to 2019. This database helps us provide unique insights into the network characteristics of inventors and examine
co-patenting networks with a focus on gender differences.
In terms of gender identification, we apply several gender databases one by one to identify the gender of the inventors. One
of the main databases used in this analysis is the WIPO (World Intellectual Property Organization) gender database developed by
Martínez et al. (2015). This database has compiled a worldwide gender dictionary of 6.2 million names from 182 countries using PCT
applications. We develop a model that is trained to use all existing databases and then applied to identify the gender of the inventors’
names. In the end, we could identify the gender of 98% of the inventors in our database, with only 2% returning with an unknown
gender.
From these data, the gender balance shows some degree of progress in the share of female inventors between 1978 and 2019. The
number of female inventors has increased over the years and peaked in 2016. In order to develop a comprehensive understanding
of the evolution of female inventors, we explore co-patenting networks and use time-splitting features to create dynamic networks
employing time intervals for when inventors commenced and ended their invention activities.
A first overall view of the network shows its complexity and usefulness when we take all the patents and inventors into account
due to the high number of nodes and edges. Moreover, to gain a better understanding of the network, we restricted our dataset to
focus on the most productive inventors. We extract from the dataset the most proficient inventors and select the inventors who have
at least ten patents over the time period. This helps us to better illustrate the shape and strength of the network and its relationships.
The entire time period is considered for network visualization to provide a portrait of inventive collaborations over the years.
3.2. Entire network (1978–2019)
In this network, we investigate the evolution of 42,312 inventors, of which 7.29% are female, and the structure of their networks
between 1978 and 2019. Description of the network data are given in Table 1.
It was observed from gender analysis that the 3084 women formed 2355 collaboration links with women and the 38,804 men
formed 69,885 collaboration links with only men. On the other hand, the women formed 16,983 collaboration links with men.
Fig. 1 shows the entire network and its largest (giant) component. Since the focus of our study is on gender differences, nodes
are color-coded blue for male inventors and red for female inventors. As we see in the graph on the left, many individuals are solo
inventors and have no links with others.2
The giant component contains 9524 inventors, 826 of whom are female inventors. Analyzing the aggregate of those invention
relationships makes it possible to investigate more closely the presence of female inventors. To conduct the comparison of female and
male inventors, we choose a narrower sample of individuals who have a high number of connections (node degree of 20 or more).
This narrower sample reveals that while the share of female inventors is low within the entire network (7.3%) and within the giant
2
We used the OpenOrd layout algorithm (from Gephi) to obtain a meaningful representation of our network. OpenOrd is a force-directed layout
and specialized in handling large-scale real-world graphs. The algorithm incorporates edge cutting and a multi-level approach, and groups the nodes
based on force-directed layouts and average-link clustering. According to Martin et al. (2011), the force-directed approach is the most common
algorithm for undirected graphs.
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Journal of Informetrics 16 (2022) 101256
Fig. 1. The complete network of inventors between 1978 and 2019 (on the left) and the giant component of the network (on the right).
Fig. 2. Percentage of female inventors to male inventors in each interval.
component (8.6%), when it comes to the most prolific inventors who have a more central position, the percentage of female inventors
rises to 15%. This is almost two times higher than the presence of female inventors in the giant component or the entire network.
The evolution of female inventors’ networks over time
An analysis of the changes in female inventors’ networks over time reveals interesting findings given the increase in their collaborations. When we change the interval, we observe female inventors continue to collaborate year after year. We look at the presence
of female inventors in five-year time intervals between 1980 and 2019.
For further analysis, it is worth finding out what percentage female inventors represent compared to male inventors in each of the
nine intervals. The results are shown in Fig. 2. As expected, female inventors’ overall involvement in patenting activity is not very
high, but the share of female inventors does increase over time from 1.2% for the first interval (before 1980) to 8.9% for the last
interval (2015–2019).
In Fig. 3, more links between inventors can be identified through the visualization of networks over time. The highest number
of co-patenting links can be observed between 2010 and 2015. While the number of female inventors increases over time, female
inventors are more likely to extend their collaborations with female inventors. As the network graphs show, before 1995, female
inventors were mostly solo inventors or collaborated with male inventors; however, between 1995 and 2000, they started to develop
more relationships with other female inventors, and later, there are more collaborations between female inventors.
We remove male inventors from the networks to better observe the position of female inventors in co-patenting networks as shown
in Fig. 4. The networks are presented from 1990 on as there are very few female inventors in the early years of the time period studied.
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Journal of Informetrics 16 (2022) 101256
Fig. 3. The evolution of inventors over time.
The findings show that although patenting has been primarily dominated by male inventors, female inventors started to contribute
before 1980 and have contributed more and more over time since then. Table 2 shows that the contribution of female inventors is
highest between 2010 and 2015.
It is not surprising to see that female inventors develop more connections with male inventors. In the long run, however, as the
number of female inventors increases, they find more patenting partners from their own gender as evidenced by Table 2.
The number of female inventors was very low before 1990, with only 13 female inventors between 1978 and 1980, 44 female
inventors between 1980 and 1984, and 100 female inventors between 1985 and 1989. Most of the female inventors were not connected
to a female inventor as their co-patenting partner at that time. We can observe only one connection between female inventors before
1990. However, we found very strong links between female inventors after 2000.
With respect to connections between female inventors, there was a considerable increase in links between 2000 and 2004; the
number of links of female inventors with male inventors peaked later, between 2010 and 2014.
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Fig. 4. The evolution of female inventors over time (1990–2019).
Table 2
The number of inventors and co-invention links in the overall network by interval.
Time intervals
Number of male
inventors
Number of
female inventors
The links between
female inventors
The links of female inventors
with male inventors
Number of total
co-invention links
Before 1980
1980–1984
1985–1989
1990–1994
1995–1999
2000–2004
2005–2009
2010–2014
2015–2019
1108
2527
4134
5511
11,605
17,739
20,699
20,693
13,790
13
44
100
266
707
1213
1582
1760
1223
1
1
1
19
260
1373
672
851
562
61
193
256
788
2785
6871
7445
9148
5700
2067
4885
6413
5264
14,633
32,964
41,703
45,717
27,494
The extent of female inventors’ relationships is depicted in Fig. 5. The blue line represents the links of female inventors with male
inventors over time, and the red line presents the links between female inventors. These lines provide an insightful snapshot of the
participation intensity of female inventors over 40 years.
3.3. Gender differences in the influence of network characteristics on innovation performance and impact
With the focus of this study being on female inventors, we use longitudinal data about 42,312 inventors over forty years to address
the importance of collaborations and network structure on inventors’ performance when controlling their other characteristics.
One of the dependent variables of this study is the number of patents over the past five years in each given year (NumPatents5),
which is used as the measure of invention performance. For every patent application, we identify and extract the citations the patent
receives in the past three years (NumCitations3). Tahmooresnejad and Beaudry (2019b) used the number of forward citations in the
first three years to capture the economic value of patents and found equivalent results using the overall number of citations and the
number of citations in the three years.
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Fig. 5. The number of links of female inventors with female inventors and with male inventors.
Using social network analysis, it is possible to examine the structural positions within the network and determine the impact
inventors’ key position has on invention performance. We create five-year subnetworks for a given year3 that take into account
inventors’ ties over the past five years to reflect active collaborations across time. All the variables are calculated on a yearly basis
for each individual. The most common network characteristics are network centrality measures, which include degree centrality,
betweenness centrality, closeness centrality, and eigenvector centrality, whose impact on inventors’ performance we aim to determine.
We examine the impact of network centrality measures and the clustering coefficient on innovation productivity and quality.
Degree centrality is the number of co-patenting connections that an inventor has, and it is measured as the sum of inventors
adjacent to a specific inventor. This determines an inventor’s importance and role within the network to some extent. Eigenvector
centrality, on the other hand, takes the degree centrality of the connected inventors into account. In other words, it is the extent
to which inventors are connected to other inventors who themselves have high degree centrality (Freeman, 1979). The Degree and
Eigenvector variables are used in our models4 for empirical illustration in this study. We find that while the share of female inventors
seems to be small compared to that of male inventors, the average degree of female inventors is higher than that of male inventors.
This illustrates that the relatively few female inventors in the co-patenting network are expected to spread knowledge more quickly
and broadly. But female inventors have less influential neighbors according to eigenvector centrality.
Closeness centrality measures how close a particular inventor is to another inventor and how long it takes information and
knowledge to spread from one inventor to other accessible inventors in the network.5 We turn to a peculiar role of inventors in
transmitting knowledge and use betweenness centrality, which identifies how inventors are bridged within the network.6 This measure
is defined as the number of times one inventor falls along the shortest path between two other inventors. It determines an inventor’s
importance based on the flow of knowledge within the network (Tahmooresnejad and Beaudry, 2017).
Comparing closeness centrality and betweenness centrality in our sample network shows that male inventors have more influence
in the network due to their higher closeness centrality. Female inventors tend to be slightly less “close” to other inventors than male
inventors on average, but the difference is very small. The expected influence of male inventors in the network is greater than that
of female inventors due to their betweenness centrality. Inventors with higher betweenness centrality can be crucial for the network
as they act like bridges connecting different regions of the network. Male inventors are indeed more likely to be more effective since
closeness and betweenness can better capture an inventor’s ability to spread knowledge than degree centrality. As we observe in our
data, female inventors are less likely to be in strategic positions as they are not involved in the high number of shortest paths that
exist between other inventors in the network.
The other network characteristic that we aim to investigate in the network is the clustering coefficient. An inventor’s clustering
coefficient indicates the tendency that their neighbors connect to one another (Watts & Strogatz, 1998).
3
We calculate the network measures using inventors’ co-links during the four years prior to the given year and the given year.
Degree centrality can be calculated using the following equation, where deg(xi ) is computed by counting the neighbors of each node. In the
standardized form, it is divided by (N-1).𝐷𝑒𝑔𝑟𝑒𝑒(𝑥𝑖 ) = deg(𝑥𝑖 ) (1)
5
The Closeness variable in our models is defined to account for closeness centrality. Closeness for node xi is calculated using the following formula,
1
where distance (xi ,xj ) indicates the distance from node xi to node xj .𝐶𝑙𝑜𝑠𝑒𝑛𝑒𝑠𝑠(𝑥𝑖 ) = ∑ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
(2)
(𝑥 ,𝑥 )
4
𝑖≠𝑗
6
𝑖
𝑗
The Betweenness variable is defined to take betweenness centrality into account. Betweenness centrality can be obtained for node (i) using the
following equation, where gjk is the number of shortest paths from node xj to node xk , and gjik is the number of shortest paths from node xj to node
∑ ∑ 𝑔𝑗𝑖𝑘
𝑖 ≠ 𝑗 ≠ 𝑘 (3)
xk that pass through node xi .𝐵𝑒𝑡𝑤𝑒𝑒𝑛𝑛𝑒𝑠𝑠(𝑥𝑖 ) =
𝑔
𝐽 ,𝑘
𝑗𝑘
9
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
An interesting feature of the clustering coefficient7 is that it is closely related to an inventor’s importance as a high clustering
coefficient shows that the inventor belongs to the dense part of the network. The Clustering variable has been defined for this network
measure in this study. Our results of comparing the average clustering coefficients of male and female inventors in each of the
intervals studied illustrate that female inventors have higher average clustering coefficients. This means that the female inventors
in our dataset are more able to cluster co-inventors. Our focus is on prolific inventors, and this higher clustering ability shows that
female inventors are likely to be in clusters that are connected to each other.
Furthermore, the model used in our study includes a set of control variables related to inventor characteristics and patenting
activity. Innovation performance might be further affected by time-varying factors like the number of years that a specific inventor
remains in the network. To take this effect into account, we add a variable that denotes the number of years between the first and
the last patenting activity. However, an inventor’s total number of patents shows whether they were productive over the years they
were in the collaboration network (ActiveTimePat). Moreover, the proportion of patents that are withdrawn compared to the total
number of patents can be related to inventors’ patenting activity (WithdrawalPat).
Given the importance of inventors’ geographical diversity, we are interested in their affiliations to understand how geographically
diversified their co-inventors are in terms of region and country and whether this diversity could correspond to an increase in their
patenting activity. To test the impact of diversity, we include the average number of countries and regions of co-inventors of patents
at a given inventor level in the model over the past five years in a given year (AvgCtryDiversity5 and AvgRegDiversity5).
In addition, to examine the difference between the impact of the network structure of male and female inventors, we include a
dummy variable for female inventors (dFemale) that is 1 if an inventor is female and 0 if an inventor is male. Because part of our
story relates to collaboration between female inventors, we use another variable related to female inventors to account for the female
diversity of the patent inventors to whom a specific inventor is a co-inventor. We add the percentage of female inventors compared
to all co-inventors of a patent (AvgFemaleDiversity5) to investigate the extent to which they may have an effect on an inventor’s
performance and citations.
Discipline diversity may appear to be related to patenting activity and patent visibility. To account for that, we utilize the International Patent Classification (IPC) code reported in the patent documents and calculate the average number of IPC codes assigned
to an inventor’s patents each year. We use the average of discipline diversity over the past five years in a given year to all of an
inventor’s patents that year (AvgDiversityIPC5). All variables are averaged at the individual level for a given year or for a group of
years when we include the average for the past five years. A list of all variables that we use in this analysis and their definitions are
presented in Table 3. 8
As different network measures may be collinear and strongly correlated with one another, we choose to introduce variables
with higher correlation in separate models to prevent two independent variables affecting each other. All the network variables
and inventor-related variables remain consistent across various models in terms of their sign and significance, which suggests that
the results are robust. The results for the dependent variable NumPatents5 are presented in Tables 4 and 5. We incorporate negative
binomial count estimates as our dependent variables are count data. Individual-level effects are not appropriately modeled by randomeffect models. In our regressions, the Hausman specification test systematically rejected the random-effect models in favor of the
fixed-effect models,9 and we used the fixed effect in our models.
3.4. Regression results
In terms of the impact of network positioning on the number of patents, we utilize the temporal nature of our panel data and lags
for the network characteristics. In the models presented, we consider the dependent variable NumPatents5 at time t given the network
positions at time t-1.
A one-year lag10 of network positions has been found to significantly positively impact the number of patents, which means the
collaboration ties among inventors influence patenting activity in the subsequent year. In the models, we control for the average
number of years that an inventor has been active in the network for one patent, withdrawn patents, an inventor’s average inventor
share among the other co-inventors, female diversity, geographical diversity (region and country), and discipline diversity. We include
the variables separately and as interaction variables with the dummy variable dFemale.
The results in Tables 4 and 5 highlight that degree centrality and eigenvector centrality are significantly positively related to the
number of patents. This suggests that inventors seem to promote their performance when they are more central and connected to
other inventors who have a high number of connections.
7 The clustering coefficient can be calculated as follows:
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟 𝑛𝑜𝑑𝑒𝑠 𝑐 𝑜𝑛𝑛𝑒𝑐 𝑡𝑒𝑑 𝑏𝑦 𝑒𝑑𝑔𝑒𝑠
)
𝐶𝑙𝑢𝑠𝑡𝑒𝑟𝑖𝑛𝑔 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚
(4)𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑑𝑔𝑒𝑠 existing among 𝑁 𝑛𝑜𝑑𝑒𝑠 = 𝑁 ∗(𝑁−1
We also test some in𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑑𝑔𝑒𝑠 𝑡ℎ𝑎𝑡 𝑚𝑎𝑦 𝑒𝑥𝑖𝑠𝑡 𝑎𝑚𝑜𝑛𝑔 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟𝑠
2
teraction variables (dFemale × Degreet , dFemale × Eigenvectort , dFemale × Closenesst , dFemale × Betweennesst , dFemale × Clusteringt , dFemale × AvgCtryDiversityInv5t , dFemale × AvgDiversityIPC5t and dFemale × AvgRegDiversityInv5t ) in the models. The results are available upon request.
8
Heteroskedasticity and auto-correlation issues were treated in the models by using the Wooldridge test for autocorrelation in panel data and a
Modified Wald statistic for groupwise heteroskedasticity in the fixed-effect models.
9
We also tested a two-year lag; the results were the same and supported the hypotheses. These results are presented in Appendix C (Tables C3
and C4).
10
We also tested the interaction variables of the dummy variable for female inventors with network measures (dFemale × Degreet , dFemale × Eigenvectort , dFemale × Closeness, dFemale × Betweennesst , dFemale × Clusteringt , dFemale × AvgCtryDiversity5t , dFemale × AvgRegDiversity5t ,
and dFemale × AvgDiversityIPC5t ), and the results showed the same impact. Some of the results are presented in Appendix C.
10
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Table 3
Description of the variables.
Variables
Dependent variables
NumPatents5t
NumCitations3t
Network variables
Degreet
Eigenvectort
Closenesst
Betweennesst
Clusteringt
Inventor variables
AvgnbInventors5t
AvgFemaleDiversity5t
AvgCtryDiversity5t
AvgRegDiversity5t
AvgCtryDiversityInv5t
AvgRegDiversityInv5t
AvgInventorShare5t
AvgDiversityIPC5t
ActiveTimePat
WithdrawalPat
dFemale
Year dummies
Description
The number of patents an inventor has had over the past five years in a given year t.
The total number of patent citations an inventor has received over the past three years in a given year t.
The inventor’s degree centrality in a five-year subnetwork in year t.
Transformation: [ln(103 x Degreet + 1)]
The inventor’s eigenvector centrality in a five-year subnetwork in year t.
Transformation: [ln(108 x Eigenvectort + 1)]
The inventor’s closeness centrality in a five-year subnetwork in year t.
Transformation: [ln(Closenesst + 1)]
The inventor’s betweenness centrality in a five-year subnetwork in year t.
Transformation: [ln(1010 x Betweennesst + 1)]
The inventor’s clustering coefficient in a five-year subnetwork in year t.
Transformation: [ln(10 x Clusteringt + 1)]
The average number of inventors associated with the patents invented by the inventor over the past five years in year t.
Transformation: [ln(AvgnbInventors5t + 1)]
The average proportion of female inventors to all inventors associated with the patents invented by the inventor over the past five
years in year t.
Transformation: [ln(AvgFemaleDiversity5t + 1)]
The average number of countries associated with the inventor list for the patents invented by the inventor over the past five years in
year t.
Transformation: [ln(AvgCtryDiversityt + 1)]
The average number of regions associated with the inventor list for the patents invented by the inventor over the past five years in
year t.
Transformation: [ln(AvgRegDiversityt + 1)]
The average number of countries associated with the inventor list for the patents invented by the inventor over the past five years
divided by the average number of inventors over the past five years in year t.
Transformation: [ln(AvgCtryDiversityInvt + 1)]
The average number of regions associated with the inventor list for the patents invented by the inventor over the past five years
divided by the average number of inventors over the past five years in year t.
Transformation: [ln(AvgRegDiversityInvt + 1)]
The inventor’s average inventor share for the patents they invented over the past five years in year t.
Transformation: [ln(AvgInventorShare5t + 1)]
The average of discipline diversity over the past five years in a given year t to all of an inventor’s patents that year.
Transformation: [ln(DiversityIPCt + 1)]
The proportion of the number of years between the inventor’s first and last patents to the total number of patents the inventor invented
over the entire time period.
Transformation: [ln(ActiveTimePat + 1)]
The proportion of the number of the inventor’s patents that are withdrawn to the total number of patents invented by the inventor.
Transformation: [ln(WithdrawalPat + 1)]
The dummy variable for female inventors.
A dummy variable for each year that accounts for any time trends in an inventor’s performance.
Interestingly, the positive impact of betweenness and closeness is relatively strong, which shows the shortest paths between
inventors in the network are of great importance to facilitate knowledge flow and positively influence inventors’ performance. We
also observe from the network characteristics that clustering has a positive effect on innovation performance.
There is a positive relationship between the average number of co-inventors and the number of patents. When an inventor collaborates with many other inventors on each patent, they tend to contribute to more patents. Inventors should therefore value
co-invention rather than being solo inventors to achieve higher performance. In essence, developing ties with a greater number of
inventors increases the chance of finding suitable co-inventors for future collaboration.
Our results suggest that the number of years between an inventor’s first and last patents does not play an important role in terms
of their performance. The impact is especially strong and negative when we normalize the number of years per patent. This is not
very surprising given that the time between patenting cannot be considered years of experience if it is too long. However, the number
of withdrawn patents could negatively influence inventors’ patenting performance.
We include the country and region diversity variables separately in models in order to be able to compare inventors’ performance
when they are from the same or different geographical locations. The results show that increasing the number of domestic and
international collaborations results in more patents.
The additional control measure for the discipline diversity variable adds more insight to the analysis by highlighting that when
co-inventors are from different disciplines and technological fields, they are more likely to have a greater number of innovative
outcomes.
Based on these findings, we accept that collaborative connections enhance innovative outcomes, but the influence of network
structure on innovation performance could be different for female inventors as compared to male inventors. One of the goals of this
11
L. Tahmooresnejad and E. Turkina
Table 4
The regression results of the impact of network measures (Degree, Eigenvector, and Closeness) on the number of patents.
Variables
Models
NumPatents5t
(1)
3
ln(10 × Degreet-1 )
0.240
(0.004)
(2)
∗∗∗
0.193
(0.004)
(3)
∗∗∗
0.292
(0.004)
(4)
∗∗∗
0.292
(0.004)
(5)
(6)
(7)
(8)
(9)
ln(108 × Eigenvectort-1 )
0.035
(0.001)
∗∗∗
0.027
(0.001)
∗∗∗
0.040
(0.001)
∗∗∗
0.045
(0.001)
0.664
(0.007)
∗∗∗
ln(AvgInventorShare5t )
ln(ActiveTimePat)
12
−1.886
(0.014)
ln(WithdrawalPat)
−0.135
(0.015)
ln(AvgFemaleDiversity5t ) 0.320
(0.040)
ln(AvgCtryDiversityInv5t ) 2.604
(0.034)
ln(AvgRegDiversityInv5t )
∗∗∗
∗∗∗
∗∗∗
0.364
(0.007)
0.455
(0.003)
−1.989
(0.015)
−0.209
(0.016)
0.610
(0.040)
∗∗∗
0.311
(0.006)
∗∗∗
−1.889
(0.013)
∗∗∗
∗∗∗
0.177
(0.037)
∗∗∗
Year dummies
Constant
lnalpha_constant
Loglikelihood
∗∗∗
∗∗∗
∗∗∗
−0.175
(0.013)
Yes
1.830
(0.014)
−1.616
(0.013)
173,426
30,493
31,206
0.0934
−513,828
0.490
(0.036)
1.363
(0.027)
0.466
(0.007)
∗∗∗
∗∗∗
∗∗∗
−2.078
(0.017)
−0.091
(0.018)
0.362
(0.048)
2.438
(0.035)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−2.129
(0.018)
−0.162
(0.018)
0.633
(0.048)
∗∗∗
−0.027
(0.013)
Yes
1.796
(0.010)
−2.151
(0.017)
173,426
30,493
51,760
0.1434
−485,483
∗∗
∗∗∗
∗∗∗
0.469
(0.006)
0.412
(0.004)
−2.123
(0.016)
∗∗∗
∗∗∗
∗∗∗
−0.102
(0.015)
Yes
0.858
(0.019)
−1.682
(0.015)
173,426
30,493
28,935
0.1033
−444,830
∗∗∗
∗∗∗
∗∗∗
−0.162
(0.015)
Yes
1.717
(0.015)
−1.546
(0.014)
173,426
30,493
25,138
0.0879
−452,467
−2.097
(0.017)
∗∗∗
∗∗∗
∗∗∗
0.251
(0.047)
∗∗∗
∗∗∗
∗∗∗
0.624
(0.044)
0.883
(0.028)
∗∗∗
∗∗∗
−2.061
(0.016)
−0.060
(0.017)
0.344
(0.046)
2.326
(0.034)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−2.146
(0.017)
−0.139
(0.018)
0.617
(0.045)
0.579
(0.019)
−0.020
(0.015)
Yes
1.664
(0.012)
−1.926
(0.017)
173,426
30,493
37,440
0.127
−433,096
∗∗∗
0.0106
(0.010)
0.559
(0.007)
0.024
(0.011)
∗∗
∗∗∗
0.395
(0.004)
−2.077
(0.017)
∗∗∗
0.668
(0.044)
0.554
(0.028)
∗∗∗
0.419
0.006
−0.179
(0.015)
Yes
2.181
(0.015)
−1.493
(0.014)
173,426
30,493
23,124
0.08
−519,971
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.372
0.006
−0.175
(0.015)
Yes
1.646
(0.014)
−1.569
(0.014)
173,426
30,493
23,770
0.090
−451,572
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
∗∗∗
−2.081
(0.016)
∗∗∗
0.222
(0.046)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.096
(0.015)
Yes
1.174
(0.017)
−1.628
(0.015)
173,426
30,493
27,807
0.10
−510,829
∗∗∗
∗∗∗
∗∗∗
−0.154
(0.015)
Yes
1.863
(0.017)
−1.521
(0.014)
173,426
30,493
24,501
0.09
−518,190
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.1479
(0.011)
0.546
(0.007)
∗∗∗
∗∗∗
∗∗∗
0.0827
(0.010)
0.838
(0.008)
∗∗∗
∗∗∗
0.516
(0.020)
0.343
(0.005)
−0.171
(0.013)
Yes
1.564
(0.013)
−1.723
(0.013)
173,426
30,493
32,220
0.103
−508,313
(12)
∗∗∗
∗∗∗
∗∗∗
−0.015
(0.015)
Yes
2.011
(0.011)
−1.834
(0.017)
173,426
30,493
36,815
0.12
−498,758
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Journal of Informetrics 16 (2022) 101256
Nb of observations
Nb of groups
𝜒2
R2 _pseudo
−0.113
(0.013)
Yes
0.935
(0.017)
−1.792
(0.014)
173,426
30,493
35,824
0.1123
−503,138
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
−1.850
(0.013)
∗∗∗
∗∗∗
0.509
(0.018)
0.768
(0.008)
∗∗∗
∗∗∗
(11)
∗∗∗
ln(Closenesst-1 )
ln(AvgnbInventors5t )
(10)
∗∗∗
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Table 5
The regression results of the impact of network measures (Betweenness and Clustering) on the number of patents.
Variables
Models
NumPatents5t
(1)
ln(10
10
× Betweennesst-1 )
0.021
(0.001)
(2)
∗∗∗
0.0188
(0.001)
(3)
∗∗∗
0.0218
(0.001)
(4)
∗∗∗
0.025
(0.001)
(5)
ln(10 × Clusteringt-1 )
ln(AvgnbInventors5t )
0.772
(0.008)
∗∗∗
0.472
(0.007)
∗∗∗
ln(AvgInventorShare5t )
ln(ActiveTimePat)
−1.998
(0.015)
ln(WithdrawalPat)
−0.095
(0.017)
ln(AvgFemaleDiversity5t ) 0.300
(0.045)
ln(AvgCtryDiversityInv5t ) 2.323
(0.033)
ln(AvgRegDiversityInv5t )
∗∗∗
∗∗∗
∗∗∗
−2.065
(0.016)
−0.175
(0.017)
0.565
(0.044)
∗∗∗
0.497
(0.006)
0.396
(0.004)
−2.030
(0.015)
∗∗∗
0.177
(0.044)
∗∗∗
∗∗∗
Year dummies
Constant
lnalpha_constant
Nb of observations
Nb of groups
𝜒2
R2 _pseudo
Loglikelihood
−0.086
(0.015)
Yes
1.211
(0.017)
−1.695
(0.015)
173,426
30,493
31,197
0.1041
−507,784
∗∗∗
∗∗∗
∗∗∗
−0.148
(0.014)
Yes
1.991
(0.015)
−1.566
(0.013)
173,426
30,493
27,143
0.0892
−516,196
∗∗∗
∗∗∗
−2.002
(0.015)
∗∗∗
0.572
(0.041)
0.718
(0.026)
∗∗∗
∗∗∗
−2.009
(0.016)
−0.072
(0.017)
0.344
(0.046)
2.480
(0.035)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.026
(0.002)
0.511
(0.007)
−2.104
(0.017)
−0.155
(0.018)
0.614
(0.045)
0.555
(0.019)
−0.004
(0.014)
Yes
2.011
(0.010)
−1.924
(0.017)
173,426
30,493
42,009
0.1268
−494,896
∗∗∗
∗∗∗
0.385
0.006
−0.159
(0.014)
Yes
2.092
(0.013)
−1.578
(0.013)
173,426
30,493
26,443
0.090
−515,681
(8)
∗∗∗
∗∗∗
∗∗∗
0.0702
(0.002)
0.496
(0.007)
0.419
(0.004)
−2.031
(0.015)
∗∗∗
0.073
(0.002)
∗∗∗
∗∗∗
−2.013
(0.016)
∗∗∗
0.227
(0.045)
∗∗∗
0.638
(0.043)
0.856
(0.029)
∗∗∗
0.406
0.006
−0.182
(0.015)
Yes
2.009
(0.014)
−1.528
(0.014)
173,426
30,493
25,253
0.086
−517,989
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
(7)
∗∗∗
∗∗∗
0.435
(0.019)
0.0528
(0.002)
0.805
(0.008)
∗∗∗
∗∗∗
(6)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.102
(0.015)
Yes
1.119
(0.017)
−1.647
(0.015)
173,426
30,493
28,210
0.101
−509,830
∗∗∗
∗∗∗
∗∗∗
−0.160
(0.015)
Yes
1.924
(0.015)
−1.523
(0.014)
173,426
30,493
24,270
0.086
−518,211
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.021
(0.015)
Yes
1.971
(0.010)
−1.878
(0.018)
173,426
30,493
39,901
0.124
−496,551
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
study is to address the difference between the impact of female inventors’ and male inventors’ network position on their patenting
activity when controlling for their other characteristics. To investigate the gender difference impact, we include the dummy variable
for female inventors in the models. We find that our dummy variable for female inventors is negatively significant in all the models,
which indicates that the influence of network centrality on the number of patents invented is greater for male inventors than female
inventors. Despite the lower impact for female inventors, our findings reveal that inventors generally benefit from collaborating with
female inventors, as our AvgFemaleDiversity5 variable is positively significant. Using the average proportion of female inventors in
the inventor list to the number of patents invented by an inventor helps to get closer to measuring the influence of collaborating with
female inventors on the patenting activity of all co-inventors. According to the results, we observe that inventors may end up with a
greater number of patents if they get involved in more gender-diverse collaborations.
In the second set of analyses, we examine the influence of network position on the citation score of patents. Tables 6 and 7
demonstrate the results. As expected, inventors’ network position has a positive impact on the visibility of their patents. This confirms
that the likelihood of receiving citations increases when inventors are in a better position in the network, namely when inventors
have high degree centrality or have extended ties with inventors who have high degree centrality.
Closeness centrality and betweenness centrality estimate the extent to which each inventor is involved in the co-patenting collaboration, and the findings of our study show that these measures positively influence patents’ forward citations. Inventors with higher
betweenness centrality are more influential when it comes to attracting other inventors and play an important broker role. In sum,
inventors with more direct connections to all the other inventors, inventors who are close to all the other inventors in the network,
and inventors with higher betweenness centrality have the power to control knowledge flow and can attract more new inventors and
increase the citation score of patents. In accordance with the clustering effect, inventors’ propensity to link to the most connected
individuals may be beneficial for patent visibility by increasing the likelihood of forming interconnected networks and enhancing
trust in the inventions of their collaborators. It appears that clustering facilitates ties within the network and enhances collaborators’
visibility.
Regarding the impact of inventor-related measures, we find that collaborating with a foreigner has a positive impact on citations.
It is also more likely that inventors who collaborate with other inventors from different regions can enhance the visibility of their
patents. As for the other variables, active time in the network per patent and the number of withdrawn patents are both found to
negatively affect citations. It is possible that more active time per patent is not fruitful for citations as it may be an indicator of lower
13
L. Tahmooresnejad and E. Turkina
Table 6
The regression results of the impact of network measures (Degree, Eigenvector, and Closeness) on the number of citations.
Variables
Models
NumCitations3t
(1)
3
ln(10 × Degreet )
0.361
(0.014)
(2)
∗∗∗
0.273
(0.015)
(3)
∗∗∗
0.300
(0.016)
(4)
∗∗∗
0.419
(0.015)
(5)
(6)
(7)
(8)
(9)
ln(108 × Eigenvectort )
0.0732
(0.004)
∗∗∗
0.057
(0.004)
∗∗∗
0.066
(0.004)
∗∗∗
0.056
(0.004)
0.5306
(0.048)
ln(AvgInventorShare5t )
ln(ActiveTimePat)
14
−1.559
(0.063)
ln(WithdrawalPat)
−0.771
(0.071)
ln(AvgFemaleDiversity5t ) 2.510
(0.138)
ln(AvgCtryDiversity5t )
4.931
(0.081)
ln(AvgRegDiversity5t )
∗∗∗
−2.555
(0.063)
∗∗∗
2.081
(0.040)
1.187
(0.026)
−1.179
(0.066)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
3.373
(0.127)
∗∗∗
1.646
(0.147)
∗∗∗
Year dummies
Constant
lnalpha_constant
1.159
(0.028)
Loglikelihood
∗∗∗
∗∗∗
∗∗
∗∗∗
−0.529
0.0496
Yes
−21.79
(1.660)
1.7078
(0.009)
197,002
31,253
0.0672
−263,448
−1.834
(0.063)
−0.722
(0.071)
2.729
(0.142)
4.991
(0.081)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−2.760
(0.062)
∗∗∗
3.519
(0.130)
∗∗
∗∗∗
∗∗∗
∗∗∗
1.670
(0.149)
∗∗∗
∗∗∗
−0.2865
0.0579
Yes
−26.040
(13.430)
1.5743
(0.0102)
197,002
31,253
0.0874
−257,757
∗∗∗
∗
∗∗∗
−0.5374
0.0512
Yes
−21.910
(13.43)
1.7111
(0.0094)
197,002
31,253
0.0667
−263,607
∗∗∗
∗∗∗
−1.073
(0.076)
3.434
(0.175)
∗∗∗
∗∗∗
−1.804
(0.063)
−0.597
(0.073)
2.989
(0.140)
5.043
(0.083)
∗∗∗
∗∗∗
∗∗∗
−0.1213
0.059
Yes
−25.5402
(13.42)
1.4764
(0.0119)
197,002
31,253
0.1001
−254,162
∗∗∗
∗∗
∗∗∗
∗∗∗
1.477
(0.024)
−0.503
0.071
Yes
−24.334
(12.430)
1.720
(0.010)
197,002
31,253
0.067
−263,618
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
−2.795
(0.062)
∗∗∗
0.495
(0.052)
2.268
(0.039)
1.097
(0.026)
−1.397
(0.066)
∗∗∗
∗∗∗
3.684
(0.129)
∗∗∗
1.384
(0.028)
∗∗∗
1.743
(0.148)
∗∗∗
∗∗∗
−0.3011
(0.057)
Yes
−25.0724
(6.115)
1.587
(0.0100)
197,002
31,253
0.0856
−258,260
∗∗∗
−1.019
(0.075)
3.606
(0.178)
∗∗∗
1.499
(0.024)
−0.509
(0.071)
Yes
−23.875
(2.086)
1.732
(0.010)
197,002
31,253
0.065
−264,012
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.249
(0.051)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.8582
(0.048)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
1.225
(0.027)
−0.120
0.0585
Yes
−24.75
(1.66)
1.475
(0.012)
197,002
31,253
0.1004
−254,074
∗∗∗
2.167
(0.039)
1.157
(0.026)
−1.412
(0.067)
∗∗∗
∗∗∗
1.409
(0.024)
−0.484
0.067
Yes
−26.25
(1.630)
1.692
(0.010)
197,002
31,253
0.070
−262,580
(12)
∗∗∗
∗∗∗
∗∗∗
−0.539
(0.050)
Yes
−21.4798
(6.1146)
1.7089
(0.0091)
197,002
31,253
0.0671
−263,488
∗∗∗
∗∗∗
∗∗∗
−0.1244
(0.058)
Yes
−24.9661
(6.11)
1.4847
(0.0118)
197,002
31,253
0.0989
−254,518
∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Journal of Informetrics 16 (2022) 101256
Nb of observations
Nb of groups
R2 _pseudo
−0.275
0.0562
Yes
−25.77
(10.33)
1.5657
(0.010)
197,002
31,253
0.0887
−257,390
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
−1.147
(0.074)
3.080
(0.164)
(11)
∗∗∗
ln(Closenesst )
ln(AvgnbInventors5t )
(10)
∗∗∗
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Table 7
The regression results of the impact of network measures (Betweenness and Clustering) on the number of citations.
Variables
Models
NumCitations3t
(1)
ln(10
10
× Betweennesst )
0.0177
(0.002)
(2)
∗∗∗
0.0086
(0.002)
(3)
∗∗∗
0.0153
(0.002)
(4)
∗∗∗
0.029
(0.002)
(5)
ln(10 × Clusteringt )
0.179
(0.010)
ln(AvgnbInventors5t )
ln(AvgInventorShare5t )
ln(ActiveTimePat)
−1.729
(0.064)
ln(WithdrawalPat)
−0.688
(0.073)
ln(AvgFemaleDiversity5t ) 2.915
(0.146)
ln(AvgCtryDiversity5t )
4.983
(0.083)
ln(AvgRegDiversity5t )
∗∗∗
−2.697
(0.063)
∗∗∗
2.221
(0.039)
1.121
(0.026)
−1.319
(0.067)
3.617
(0.132)
∗∗∗
1.715
(0.153)
∗∗∗
∗∗∗
Year dummies
Constant
lnalpha_constant
Nb of observations
Nb of groups
R2 _pseudo
Loglikelihood
−0.2991
(0.057)
Yes
−25.144
(12.582)
1.5908
(0.0102)
197,002
31,253
0.0853
−258,348
−1.095
(0.075)
3.507
(0.182)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.5396
(0.050)
Yes
−21.723
(12.58)
1.7213
(0.0094)
197,002
31,253
0.0655
−263,936
−1.635
(0.063)
−0.673
(0.072)
2.780
(0.142)
5.0425
(0.0827)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.1249
(0.058)
Yes
−24.748
(12.6)
1.489
(0.0120)
197,002
31,253
0.0985
−254,611
∗∗
∗∗∗
∗∗∗
1.460
(0.024)
−0.501
(0.073)
Yes
−23.85
(12.582)
1.725
(0.010)
197,002
31,253
0.066
−263,762
(8)
0.109
(0.010)
∗∗∗
−2.641
(0.062)
∗∗∗
0.128
(0.012)
2.178
(0.039)
1.158
(0.027)
−1.256
(0.066)
∗∗∗
∗∗∗
3.561
(0.130)
∗∗∗
1.253
(0.028)
∗∗∗
1.744
(0.152)
∗∗∗
∗∗∗
−0.308
(0.057)
Yes
−25.0724
(6.115)
1.5801
(0.0102)
197,002
31,253
0.0867
−257,941
∗∗∗
−1.055
(0.074)
3.356
(0.170)
∗∗∗
1.467
(0.023)
−0.515
(0.067)
Yes
−23.875
(2.086)
1.716
(0.010)
197,002
31,253
0.067
−263,429
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.204
(0.011)
∗∗∗
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
∗∗∗
∗∗∗
∗∗∗
1.269
(0.029)
(7)
∗∗∗
∗∗∗
∗∗∗
(6)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.5507
(0.050)
Yes
−21.4798
(6.1146)
1.717
(0.0094)
197,002
31,253
0.0661
−263,782
∗∗∗
∗∗∗
∗∗∗
−0.1362
(0.059)
Yes
−24.9661
(6.11)
1.4847
(0.0119)
197,002
31,253
0.0991
−254,458
∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
patent quality. We control for the average number of co-inventors associated with patents, and the results show that having more
inventors on a patent application can impact patent citation.
Regarding the technological fields measured by IPC diversity, we find collaborating with inventors in other technological fields
helps with knowledge flow between inventors and increases the likelihood that patents are seen by experts from other fields. Interestingly, average female diversity has a significantly positive influence on the number of citations received. However, including the
dummy variable for female inventors proves that male inventors seem to receive more citations in the three years after a patent is
granted when they extend their collaborations and have a better network position.
In the third set of analyses, we introduce interaction variables in the models as we thought that the diversity and network measures
might have a different effect on female inventors than male inventors that we could test with interaction terms. We observe that the
previous results remain consistent overall in sign and significance. Our models characterize several significant main and interaction
effects inventor characteristics have on the number of patents and the number of citations.11 All interaction variables show less impact
on patenting activity over the past five years for female inventors than for male inventors.
We now turn to marginal effects to try to better understand the important factors for improving innovative outcome between female
and male inventors. Tables 8 and 9 present the marginal effects of select corresponding regression results found in Tables 6 and 7. For
each of the variables, they present the marginal effect of increasing the value of the explanatory variable by one unit. For the Men
rows, it is the marginal effect of increasing the dependent variable by one unit while keeping all the other covariates constant and the
dummy variable for female inventors at 0 (dFemale = 0). The Women rows present the marginal effect of increasing the independent
variable by one unit while keeping all the other covariates constant and the dummy variable for female inventors at 1 (dFemale = 1).
In regard to the number of patents, network measures and diversity variables play a very fundamental role in explaining the
number of patents for male inventors. Increasing each of these explanatory variables by one unit is generally associated with more
patents for both male and female inventors, and the increase is slightly higher for male inventors. This suggests that male inventors
with higher network centrality have more patents. While the results for the marginal effects in terms of the number of citations are
less significant, we still see that increasing the network centrality, clustering, and region diversity variables by one unit yields more
citations for male inventors than female inventors.
11
Note that these are from different models selected from the regression results in Tables 6 and 7.
15
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Table 8
Marginal effects of the regression results – number of patents.12
Variables
Marginal Effects
Number of Patents (selected models)
ln(103 × Degreet )
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
2.49
2.27
0.36
0.34
0.85
0.80
0.22
0.21
0.55
0.52
27.03
24.70
5.44
5.01
3.58
3.25
ln(108 × Eigenvectort )
ln(Closenesst )
ln(1010 × Betweennesst )
ln(10 × Clusteringt )
ln(AvgCtryDiversity5t )
ln(AvgRegDiversity5t )
ln(AvgDiversityIPC5t )
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
1.99
1.83
0.28
0.26
1.52
1.44
0.194
0.187
0.27
0.25
24.17
22.88
6.18
5.87
4.37
3.78
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
3.01
2.73
0.46
0.40
0.25
0.21
0.26
0.22
0.76
0.66
25.17
23.60
5.49
5.13
3.85
3.35
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗
∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
2.96
2.67
0.28
0.22
1.59
1.41
0.19
0.16
0.27
0.22
24.07
23.57
4.70
4.54
3.99
3.43
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Table 9
Marginal effects of the regression results – number of citations.
Variables
Marginal Effects
Number of Citations (selected models)
ln(103 × Degreet )
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
Men
Women
1.26
0.96
0.26
0.19
1.86
1.38
0.06
0.05
0.64
0.47
17.20
13.06
3.114
1.829
3.43
3.23
ln(108 × Eigenvectort )
ln(Closenesst )
ln(1010 × Betweennesst )
ln(10 × Clusteringt )
ln(AvgCtryDiversity5t )
ln(AvgRegDiversity5t )
ln(AvgDiversityIPC5t )
∗∗∗
∗∗∗
0.73
0.43
0.15
0.09
2.25
1.27
0.022
0.013
0.29
0.01
17.70
13.10
3.62
2.04
3.47
3.10
∗∗∗
∗∗∗
∗
∗
∗∗∗
∗∗∗
∗
∗
0.99
0.92
0.19
0.17
1.00
0.89
0.06
0.05
0.41
0.37
17.48
13.13
3.23
1.85
3.43
3.07
0.99
1.68
0.46
0.38
1.48
0.66
0.06
0.03
0.39
0.21
17.30
12.83
3.31
1.87
3.36
2.97
∗∗∗
∗∗∗
At the beginning of this paper, we set out to validate three sets of propositions about network centrality, clustering, and tie
diversity. We assessed all these propositions, and the results support all of them except Proposition 2c about the impact of clustering
on female inventors. We had anticipated that female inventors with a higher clustering rate would contribute to more patents and
receive more citations, but we cannot prove this proposition. Our results show that this effect is still higher for male inventors in our
dataset. We suspect that this result can be partly explained by the low share of female inventors in our sample. Moreover, patenting
activity is a male-dominated area, and all the inventors studied prefer developing and repeating collaborations with a male inventor.
Although female inventors benefit from clustering to some degree, they are under the influence of the male inventors in their group.
4. Discussion and conclusion
This paper involved a longitudinal investigation of the effects of global co-inventor network properties on innovation output
and specifically analyzed gender-related differences in the effects of co-inventor networks. In doing so, it addressed the call to
explore gender gap in science empirically with large-scale data (Legewie & DiPrete, 2014; Rosser, 2009). Previous empirical studies
exploring gender-related differences in innovation focused predominantly on publications and publication citations (Caplar et al.,
2017; Symonds et al., 2006); this paper analyzed large-scale industrial patent data across multiple fields. Our study advanced the
work of Wittington (2018) on the gender aspects in co-inventor networks in biotechnology patenting in that it extended the study to
all available industries at a global level and evaluated the effects of different network properties on innovation. Additionally, while
Wittington (2018) focused only on patent productivity (the number of patents), our paper also analyzed effects on the quality of
innovations (measured by the number of patent citations).
The evidence from the global patenting data analyzed in this paper provides important theoretical contributions to the literature
on gender-related differences in innovation. First, the paper offers novel insights by highlighting the changing landscape of gender
differences in patenting over time. While we find that female inventors’ overall involvement in patenting activity is not very high, we
observe that the share of women involved in patenting increases over time across different fields. Additionally, there are important
nuances and differences in the patterns of female collaboration. We notice an interesting trend that while female inventors collaborated
16
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
heavily with male inventors initially, over time, there is a tendency towards increasing collaboration among women. While these
findings are novel for the innovation literature, insights from the sociological literature (Ibarra, 1992; Szell & Thurner, 2013) and
network literature (Kim & Altmann, 2017) can help to explain this phenomenon. According to the sociological studies, women usually
form long-term and repeated collaborations and perform well in situations of trust and shared vision and values; therefore, it is usually
easier for them to collaborate with others of their own gender. When women started to actively patent their research, there were very
few of them, so they naturally collaborated with men. At the same time, once more women entered the field, they started to form
dense collaborative groups among themselves. As far as the network literature is concerned, according to the concept of homophily,
nodes that share similar attributes (in our case, gender), tend to cluster together over time in large scale complex networks.
Second, the paper offers novel insights by using the network perspective to explain the effects of collaborations on innovation
and respective gender-related differences. It explored three network characteristics that are claimed to be of fundamental importance
in network science: network centrality, clustering and tie diversity. Our analysis revealed that network centrality, clustering and tie
diversity generally have a significant positive impact on innovation output (the number of patents) and the quality of innovations
(measured by the number of citations). The positive impact of node centrality is in line with the emerging research on co-inventor
networks (Tahmooresnejad & Beaudry, 2018, 2019a). At the same time, the fact that clustering and tie diversity both have a significant
positive impact too is novel and indicates that not only is overall position centrality in the network important for innovation, but
the node’s immediate local environment is as well. Inventors located in cohesive groups of interconnected inventors will see better
innovative outcomes. However, for these cohesive groups to function well and avoid lock-in, tie diversity is a critical element, meaning
it is important for inventors to collaborate with colleagues of different genders and from different geographic areas and technological
fields.
As far as gender-related differences are concerned, our results indicate that even though both male and female inventors benefit
significantly from such network properties as centrality and clustering, these properties’ influence on the number of patents invented
and the number of citations received is stronger for male inventors than for female inventors. Our results also indicate that female
inventors are less likely than male inventors to be in strategic positions of centrality. These findings are in line with the sociological
literature and gender studies (Ibarra, 1992; Szell & Thurner, 2013) that argue there are gender-related differences in social network
behavior and men are more result-oriented and strategic in using their linkages for their benefit, while women tend to focus more on
local connections, which leads to the lack of more diverse and long-range network ties in their environment (Szell & Thurner, 2013).
Taken together, these findings highlight important inequalities in the structural position of female inventors and call for further
investigation of the factors that lead to this outcome. In the theoretical part of the paper, we mention a number of plausible explanations for this phenomenon including the existence of certain obstacles for women in science in terms of education, societal culture
and the division of labor. Future studies could explore these reasons empirically and in further detail.
On the up side, the results of the analysis also indicate that the share of female inventors has increased significantly over time
and that women have gradually become more active in global collaboration networks.
It is interesting to note that while gender diversity in collaborations is a predictor of male innovation, it is less critical for female
innovation.
Future studies could advance this research by considering various factors or combinations of inventor and patent characteristics
(triadic patents, higher patent value, etc.) to identify highly qualified inventors. Moreover, including other factors that can be studied
in terms of female inventors may provide a more accurate portrait. For instance, some factors that are not included in this study
are the inventor’s age, their marital status, the number of children they have, cultural factors of their country/region, and the
type of organization they are affiliated with (industry, research lab, university, government). Taking these important attributes into
consideration will make it possible to investigate their role in gender-related differences in inventor network behavior. The attributes
can help to further explain the nuances of differences.
This study has a number of limitations, with the sample chosen being the most obvious one. Our research focuses solely on the
most prolific inventors, those with at least 10 patents over the time period studied. While our data sample helps us to better visualize
the innovation network, the picture presented may not reflect the reality of all inventors. Hence, the findings of our analyses are
likely to be relevant for the more productive inventors. Second, we limited our sample by using the number of patents to identify
prolific inventors, however, it is likely the results would be affected if other inventor characteristics or some patent features were
used to identify the more productive inventors. Third, there are so many reasons a statistical gender difference may exist; it could
be a natural or cultural division of inventors by society, or it could be related to women’s interest in STEM. While we provided some
plausible explanations in the theoretical part of the paper for the structural network differences that we found, we did not explore
these factors (e.g., female motivation, number of kids) empirically. Therefore, future studies could focus on explaining why these
structural differences occur and explore a variety of psychological, sociological and economic factors. The findings of this paper
should not be overgeneralized, and it is necessary to include all the factors, otherwise we cannot generally claim there is a patenting
gap between male and female inventors.
A final limitation of our study is that since we had a discipline diversity variable (IPC code technological diversity), we did not use
technology fixed effects. There may, however, be a relationship between the amount and quality of innovations and the technological
field. Future studies could examine this in detail.
Author Contributions
Leila Tahmooresnejad: Conceived and designed the analysis; Collected the data; Contributed data or analysis tools; Performed
the analysis; Wrote the paper. Ekaterina Turkina: Conceived and designed the analysis; Contributed data or analysis tools; Performed
the analysis; Wrote the paper.
17
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Appendix A
Table A1
Descriptive statistics.
Variables
Obs.
Mean
Std. Dev.
Min.
Max.
NumPatent5
NumCitation3
Degree
Eigenvector
Closeness
Betweenness
Clustering
AvgnbInventors5
AvgInventorShare5
ActiveTimePat
WithdrawalPat
AvgFemaleDiversity5
AvgCtryDiversity5
AvgRegDiversity5
AvgCtryDiversityInv5
AvgRegDiversityInv5
AvgDiversityIPC5
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
9.733
2.283
4.340
21.778
0.544
0.123
0.423
3.352
0.221
0.431
0.287
0.067
0.823
1.806
0.296
0.580
3.908
9.129
14.000
6.157
151.893
0.357
2.882
0.410
2.376
0.148
0.305
0.239
0.112
0.404
1.262
0.141
0.234
4.391
1
0
0
0
0
0
0
0.2
0.002
0
0
0
0.2
0.2
0.018
0.018
0.2
264
1768
109
2043
1
257
1
46.39
1
3.33
1
1
8
15
1
1
149
18
L. Tahmooresnejad and E. Turkina
Appendix B
Table B1
Correlation matrix.
19
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
1
1.000
2
NumPatent5
NumCitation3
ln(103 × Degreet )
ln(108 × Eigenvectort )
ln(Closenesst )
ln(1010 × Betweennesst )
ln(10 × Clusteringt )
ln(AvgnbInventors5t )
ln(AvgInventorShare5t )
ln(ActiveTimePat)
ln(WithdrawalPat)
ln(AvgFemaleDiversity5t )
ln(AvgCtryDiversity5t )
ln(AvgRegDiversity5t )
ln(AvgCtryDiversityInv5t )
ln(AvgRegDiversityInv5t )
ln(AvgDiversityIPC5t )
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0.127
0.412
0.115
−0.087
0.260
0.148
0.213
0.203
−0.409
0.042
0.133
0.235
0.162
−0.007
−0.048
0.185
1.000
0.086
0.040
0.010
0.024
0.050
0.143
0.045
−0.089
0.029
0.091
0.130
0.108
−0.039
−0.033
0.140
1.000
0.589
−0.166
0.538
0.607
0.448
−0.188
−0.163
0.095
0.164
0.178
0.340
−0.368
−0.112
0.185
1.000
0.156
0.268
0.443
0.211
−0.109
0.081
0.080
0.058
0.076
0.198
−0.196
−0.002
0.157
1.000
−0.382
−0.083
−0.117
0.032
0.155
−0.053
−0.076
−0.091
−0.182
0.053
−0.092
−0.033
1.000
0.127
0.208
0.026
−0.081
0.052
0.040
0.165
0.275
−0.113
0.094
0.164
1.000
0.302
−0.209
−0.118
0.056
0.103
0.057
0.177
−0.340
−0.155
0.114
1.000
−0.004
−0.131
0.112
0.319
0.646
0.734
−0.569
−0.255
0.541
1.000
−0.038
−0.108
0.003
0.535
0.159
0.577
0.255
0.251
1.000
−0.084
−0.116
−0.105
−0.019
0.035
0.145
−0.101
1.000
0.097
0.014
0.111
−0.098
0.004
0.184
1.000
0.236
0.190
−0.142
−0.142
0.252
1.000
0.666
0.191
0.104
0.497
1.000
−0.242
0.438
0.463
1.000
0.440
−0.140
1.000
−0.044
1.000
Journal of Informetrics 16 (2022) 101256
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Appendix C
Table C1
The regression results of the impact of network measures (interaction variables) on the number of patents.
Variables
ln(NumPatents5t )
Models
(1)
ln(103 × Degreet-1 )
0.193
(0.004)
(2)
(3)
(4)
(5)
(6)
(7)
∗∗∗
ln(108 × Eigenvectort-1 )
0.0275
(0.001)
∗∗∗
0.027
(0.001)
∗∗∗
ln(Closenesst-1 )
0.1471
(0.011)
∗∗∗
ln(1010 × Betweennesst-1 )
0.0189
(0.001)
∗∗∗
0.0181
0.0006
∗∗∗
ln(10 × Clusteringt-1 )
ln(AvgnbInventors5t )
ln(ActiveTimePat)
ln(WithdrawalPat)
ln(AvgFemaleDiversity5t )
ln(AvgRegDiversityInv5t )
dFemale
0.363
(0.007)
−1.989
(0.015)
−0.208
(0.016)
0.619
(0.041)
0.528
(0.018)
−0.084
(0.031)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.465
(0.007)
−2.128
(0.018)
−0.162
(0.018)
0.644
(0.048)
0.535
(0.0205)
−0.068
(0.036)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗
0.466
(0.007)
−2.128
(0.018)
−0.164
(0.018)
0.636
(0.048)
0.516
(0.020)
−0.241
(0.026)
∗∗∗
0.006
(0.002)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.545
(0.007)
−2.146
(0.017)
−0.139
(0.018)
0.627
(0.045)
0.5996
(0.0201)
−0.052
(0.035)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.471
(0.007)
−2.065
(0.016)
−0.174
(0.017)
0.576
(0.044)
0.458
(0.019)
−0.036
(0.033)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.472
(0.007)
−2.066
(0.016)
−0.173
(0.017)
0.567
(0.044)
0.435
(0.019)
−0.178
(0.014)
∗∗∗
0.009
0.0025
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.026
(0.002)
0.510
(0.007)
−2.104
(0.017)
−0.155
(0.018)
0.625
(0.046)
0.5779
(0.0197)
−0.051
(0.035)
∗∗∗
−0.2752
(0.0743)
1.914
(0.015)
−1.5234
(0.014)
Yes
173,426
30,493
24,247
0.086
−518,178
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
dFemale × Eigenvectort-1
dFemale × Betweennesst-1
dFemale × AvgRegDiversityInv5t
Constant
lnalpha_constant
Year dummies
Nb of observations
Nb of groups
𝜒2
R2 _pseudo
Loglikelihood
−0.230
(0.067)
1.821
(0.014)
−1.616
(0.013)
Yes
173,426
30,493
31,181
0.094
−513,804
∗∗∗
∗∗∗
∗∗∗
−0.2384
(0.0767)
1.709
(0.015)
−1.5464
(0.014)
Yes
173,426
30,493
25,118
0.088
−452,445
∗∗∗
∗∗∗
∗∗∗
1.723
(0.015)
−1.546
(0.014)
Yes
173,426
30,493
25,256
0.088
−452,456
20
∗∗∗
∗∗∗
−0.2596
(0.0746)
1.854
(0.017)
−1.5218
(0.014)
Yes
173,426
30,493
24,483
0.0858
−518,161
∗∗∗
∗∗∗
−0.2844
(0.0701)
1.981
(0.015)
−1.5663
(0.013)
Yes
173,426
30,493
27,117
0.0893
−516,159
∗∗∗
∗∗∗
∗∗∗
1.9926
(0.015)
−1.567
(0.013)
Yes
173,426
30,493
27,287
0.089
−516,150
∗∗∗
∗∗∗
∗∗∗
∗∗∗
L. Tahmooresnejad and E. Turkina
Table C2
The regression results of the impact of network measures (interaction variables) on the number of patent citations.
Variables
ln(NumCitations3t )
3
ln(10 × Degreet )
Models
(1)
0.361
(0.014)
(2)
∗∗∗
0.367
(0.014)
(3)
∗∗∗
0.618
(0.017)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
ln(108 × Eigenvectort )
0.073
(0.004)
∗∗∗
0.073
(0.004)
∗∗∗
0.225
(0.006)
0.529
(0.048)
∗∗∗
0.384
(0.042)
0.018
(0.002)
∗∗∗
0.024
(0.002)
∗∗∗
0.036
(0.002)
ln(10 × Clusteringt )
ln(WithdrawalPat)
ln(AvgFemaleDiversity5t )
ln(AvgCtryDiversity5t )
∗∗∗
−2.214
(0.059)
∗∗∗
−1.318
(0.065)
∗∗∗
2.800
(0.134)
∗∗∗
21
ln(AvgDiversityIPC5t )
dFemale
0.259
0.1224
∗∗
dFemale × Degreet
1.276
(0.021)
−0.061
0.101
∗∗∗
−0.643
(0.076)
∗∗∗
−0.804
(0.088)
∗∗∗
2.701
(0.162)
4.695
(0.089)
∗∗∗
−1.833
(0.063)
∗∗∗
−0.723
(0.072)
∗∗∗
2.797
(0.141)
∗∗∗
5.081
(0.085)
∗∗∗
−2.491
(0.058)
∗∗∗
−1.283
(0.065)
∗∗∗
2.998
(0.138)
∗∗∗
∗∗∗
0.289
(0.107)
−0.427
(0.051)
∗∗∗
−0.065
(0.032)
∗∗
1.307
(0.021)
−0.5584
(0.111)
∗∗∗
−0.911
(0.081)
∗∗∗
−0.655
(0.094)
∗∗∗
2.883
(0.181)
4.847
(0.100)
∗∗∗
−1.803
(0.063)
∗∗∗
−0.598
(0.073)
∗∗∗
3.052
(0.140)
∗∗∗
5.130
(0.087)
∗∗∗
−2.449
(0.059)
∗∗∗
−1.209
(0.066)
∗∗∗
3.228
(0.141)
∗∗∗
∗∗∗
∗∗∗
0.051
(0.181)
1.338
(0.021)
−0.113
(0.106)
0.188
(0.127)
∗∗∗
−1.728
(0.064)
∗∗∗
−0.689
(0.073)
∗∗∗
2.981
(0.145)
5.072
(0.087)
∗∗∗
−2.371
(0.060)
∗∗∗
−1.286
(0.066)
∗∗∗
3.126
(0.144)
∗∗∗
∗∗∗
1.308
(0.021)
−0.126
(0.106)
0.204
(0.127)
∗∗∗
−1.075
(0.075)
∗∗∗
−0.674
(0.090)
∗∗∗
3.313
(0.170)
4.928
(0.092)
∗∗∗
0.179
(0.010)
∗∗∗
−1.633
(0.063)
∗∗∗
−0.675
(0.072)
∗∗∗
2.846
(0.141)
∗∗∗
5.134
(0.087)
∗∗∗
0.153
(0.009)
∗∗∗
−2.312
(0.058)
∗∗∗
−1.253
(0.066)
∗∗∗
3.043
(0.139)
∗∗∗
∗∗∗
−0.315
(0.069)
∗∗∗
−0.025
(0.008)
∗∗∗
1.321
(0.021)
−0.106
(0.105)
0.2026
(0.128)
−0.034
(0.014)
dFemale × Clusteringt
lnalpha_constant
Year dummies
Nb of observations
Nb of groups
R2 _pseudo
Loglikelihood
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.290
(0.092)
∗∗∗
−0.061
(0.029)
∗∗
−0.580
(0.117)
∗∗∗
−0.550
(0.116)
∗∗∗
−0.567
(0.116)
∗∗∗
−0.576
(0.118)
∗∗∗
−0.258 ∗ ∗ ∗
−0.234 ∗ ∗ ∗
−0.238 ∗ ∗ ∗
−0.225 ∗ ∗ ∗
−0.245 ∗ ∗ ∗
(0.053)
(0.055)
(0.053)
(0.053)
(0.054)
−25.840 ∗ ∗ ∗ −25.39 ∗ ∗ ∗ −25.33 ∗ ∗ ∗ −26.103 ∗ ∗ ∗ −24.379 ∗ −26.511
−25.03 ∗ ∗ ∗ −23.04 ∗ ∗ ∗ −25.20 ∗ ∗ ∗ −22.96 ∗ ∗ ∗ −24.965 ∗ ∗ ∗ −25.13 ∗ ∗ ∗ −23.341 ∗ ∗ ∗ −23.816
(2.900)
(2.90)
(2.411)
(5.201)
(12.582)
(11.930)
(19.28)
(18.27)
(12.58)
(3.314)
(4.734)
(2.09)
(2.1)
(2.000)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
1.643
1.573
1.628
1.647
1.586
1.644
1.590
1.642
1.695 ∗ ∗ ∗ 1.5793 ∗ ∗ ∗ 1.638
1.687
1.5648 ∗ ∗ ∗ 1.618
(0.0104)
(0.009)
(0.012)
(0.010)
(0.009)
(0.013)
(0.010)
(0.009)
(0.010)
(0.009)
(0.011)
(0.010)
(0.009)
(0.011)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
197,002
197,002
197,002
197,002
197,002
197,002
197,002
197,002
1,970,026
197,002
197,002
197,002
197,002
197,002
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
31,253
0.0888
0.080
0.094
0.088
0.078
0.1006
0.086
0.076
0.104
0.090
0.087
0.0869
0.077
0.0883
−257,352
−259,969
−194,652
−257,721
−260,381
−16,563
−258,227
−260,950
−258,314
−260,849
−19,617
−257,906
−260,686
−195,934
Journal of Informetrics 16 (2022) 101256
Constant
0.236
(0.012)
∗∗∗
−1.005
(0.072)
∗∗∗
−0.658
(0.090)
∗∗∗
3.236
(0.167)
5.047
(0.091)
∗∗
dFemale × Betweennesst
∗∗∗
∗∗∗
∗∗∗
dFemale × Eigenvectort
dFemale × AvgCtryDiversity5t −0.604
(0.114)
dFemale × AvgDiversityIPC5t
(14)
∗∗∗
ln(1010 × Betweennesst )
−1.557
(0.063)
−0.773
(0.071)
2.580
(0.137)
5.025
(0.085)
(13)
∗∗∗
ln(Closenesst )
ln(ActiveTimePat)
(12)
∗∗∗
L. Tahmooresnejad and E. Turkina
Table C3
The regression results of the impact of network measures (Degree, Eigenvector, and Closeness) on the number of patents (two-year lag for network variables).
Variables
NumPatents5t
Models
(1)
ln(103 × Degreet-2 )
0.154
(0.005)
(2)
∗∗∗
0.097
(0.005)
(3)
∗∗∗
0.220
(0.004)
(4)
∗∗∗
0.219
(0.004)
(5)
(6)
(7)
(8)
(9)
ln(108 × Eigenvectort-2 )
0.0295
(0.001)
∗∗∗
0.0191
(0.001)
∗∗∗
0.0363
(0.001)
∗∗∗
0.044
(0.001)
0.854
(0.008)
∗∗∗
ln(AvgInventorShare5t )
ln(ActiveTimePat)
22
−2.018
(0.015)
ln(WithdrawalPat)
−0.191
(0.017)
ln(AvgFemaleDiversity5t ) 0.361
(0.044)
ln(AvgCtryDiversityInv5t ) 2.786
(0.037)
ln(AvgRegDiversityInv5t )
∗∗∗
∗∗∗
∗∗∗
0.548
(0.007)
0.480
(0.004)
−2.118
(0.016)
−0.277
(0.018)
0.682
(0.045)
∗∗∗
0.457
(0.006)
∗∗∗
−2.022
(0.014)
∗∗∗
∗∗∗
0.192
(0.041)
∗∗∗
Year dummies
Constant
lnalpha_constant
Loglikelihood
∗∗∗
∗∗∗
∗∗∗
−0.176
(0.014)
Yes
1.792
(0.015)
−1.664
(0.015)
173,426
30,493
31,764
0.1008
−447,762
0.659
(0.040)
1.185
(0.029)
0.586
(0.008)
∗∗∗
∗∗∗
∗∗∗
−2.125
(0.017)
−0.141
(0.018)
0.338
(0.050)
2.669
(0.037)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−2.165
(0.018)
−0.227
(0.019)
0.647
(0.050)
∗∗∗
−0.018
(0.013)
Yes
1.757
(0.010)
−2.299
(0.021)
173,426
30,493
52,247
0.1586
−418,990
∗∗∗
∗∗∗
0.550
(0.007)
0.439
(0.004)
−2.184
(0.017)
∗∗∗
∗∗∗
∗∗∗
−0.097
(0.016)
Yes
0.753
(0.020)
−1.828
(0.017)
173,426
30,493
30,871
0.1189
−377,700
∗∗∗
∗∗∗
∗∗∗
−0.165
(0.015)
Yes
1.687
(0.016)
−1.647
(0.016)
173,426
30,493
27,011
0.0992
−386,151
−2.116
(0.017)
∗∗∗
∗∗∗
∗∗∗
0.226
(0.049)
∗∗∗
∗∗∗
∗∗∗
0.698
(0.047)
0.884
(0.030)
∗∗∗
∗∗∗
−2.159
(0.017)
−0.132
(0.018)
0.385
(0.048)
2.574
(0.036)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−2.230
(0.018)
−0.225
(0.019)
0.703
(0.047)
0.602
(0.020)
−0.010
(0.015)
Yes
1.644
(0.013)
−2.145
(0.022)
173,426
30,493
40,464
0.1475
−365,448
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.425
0.006
−0.193
(0.015)
Yes
1.621
(0.015)
−1.630
(0.014)
173,426
30,493
23,950
0.097
−387,258
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
∗∗∗
0.0213
(0.011)
0.628
(0.007)
0.428
(0.004)
−2.198
(0.016)
∗∗
0.059
(0.012)
∗∗∗
∗∗∗
−2.153
(0.017)
∗∗∗
0.229
(0.047)
∗∗∗
0.795
(0.045)
0.585
(0.030)
∗∗∗
0.474
0.006
−0.202
(0.016)
Yes
2.126
(0.015)
−1.580
(0.015)
173,426
30,493
23,555
0.093
−451,697
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
0.2172
(0.012)
0.640
(0.007)
∗∗∗
∗∗∗
∗∗∗
0.1213
(0.011)
0.952
(0.009)
∗∗∗
∗∗∗
0.560
(0.020)
0.425
(0.006)
−0.196
(0.014)
Yes
1.644
(0.014)
−1.707
(0.014)
173,426
30,493
29,906
0.104
−446,242
(12)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.098
(0.015)
Yes
1.009
(0.018)
−1.798
(0.017)
173,426
30,493
29,391
0.1174
−439,500
∗∗∗
∗∗∗
∗∗∗
−0.165
(0.015)
Yes
1.757
(0.017)
−1.644
(0.016)
173,426
30,493
26,220
0.0998
−448,259
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.012
(0.015)
Yes
1.962
(0.011)
−2.086
(0.021)
173,426
30,493
40,275
0.1446
−425,942
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
Journal of Informetrics 16 (2022) 101256
Nb of observations
Nb of groups
𝜒2
R2 _pseudo
−0.107
(0.014)
Yes
0.838
(0.018)
−1.871
(0.016)
173,426
30,493
36,448
0.1228
−436,830
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
−1.948
(0.015)
∗∗∗
∗∗∗
0.537
(0.019)
0.901
(0.009)
∗∗∗
∗∗∗
(11)
∗∗∗
ln(Closenesst-2 )
ln(AvgnbInventors5t )
(10)
∗∗∗
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
Table C4
The regression results of the impact of network measures (Betweenness and Clustering) on the number of patents (two-year lag for network variables).
Variables
NumPatents5t
Models
(1)
ln(1010 × Betweennesst-2 )
0.0126
(0.001)
(2)
∗∗∗
0.0095
(0.001)
(3)
∗∗∗
0.0144
(0.001)
(4)
∗∗∗
0.017
(0.001)
(5)
ln(10 × Clusteringt-2 )
ln(AvgnbInventors5t )
0.916
(0.008)
∗∗∗
0.596
(0.007)
∗∗∗
ln(AvgInventorShare5t )
ln(ActiveTimePat)
−2.109
(0.016)
ln(WithdrawalPat)
−0.162
(0.018)
ln(AvgFemaleDiversity5t ) 0.341
(0.047)
ln(AvgCtryDiversityInv5t ) 2.595
(0.036)
ln(AvgRegDiversityInv5t )
∗∗∗
∗∗∗
∗∗∗
−2.167
(0.017)
−0.258
(0.018)
0.652
(0.046)
∗∗∗
0.591
(0.006)
0.432
(0.004)
−2.157
(0.016)
∗∗∗
0.186
(0.045)
∗∗∗
∗∗∗
Year dummies
Constant
lnalpha_constant
Nb of observations
Nb of groups
𝜒2
R2 _pseudo
Loglikelihood
−0.090
(0.015)
Yes
1.044
(0.017)
−1.827
(0.017)
173,426
30,493
32,294
0.1192
−438,594
∗∗∗
∗∗∗
∗∗∗
−0.161
(0.015)
Yes
1.890
(0.016)
−1.651
(0.015)
173,426
30,493
28,179
0.0999
−448,238
∗∗∗
∗∗∗
−2.090
(0.016)
∗∗∗
0.711
(0.044)
0.705
(0.029)
∗∗∗
∗∗∗
−2.121
(0.017)
−0.145
(0.018)
0.372
(0.048)
2.664
(0.037)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.0023
(0.002)
0.626
(0.008)
0.0486
(0.002)
0.584
(0.007)
0.447
(0.004)
−2.153
(0.016)
∗∗∗
0.226
(0.046)
−2.202
(0.018)
−0.242
(0.019)
0.676
(0.047)
0.547
(0.020)
−0.002
(0.015)
Yes
1.956
(0.010)
−2.142
(0.021)
173,426
30,493
45,640
0.1481
−424,233
∗∗∗
∗∗∗
0.454
0.006
−0.186
(0.015)
Yes
2.070
(0.013)
−1.623
(0.014)
173,426
30,493
26,011
0.096
−449,968
(8)
∗∗∗
∗∗∗
0.049
(0.002)
∗∗∗
∗∗∗
−2.096
(0.017)
∗∗∗
∗∗∗
0.759
(0.045)
0.802
(0.031)
∗∗∗
0.467
0.006
−0.203
(0.016)
Yes
2.016
(0.015)
−1.598
(0.015)
173,426
30,493
24,319
0.095
−450,874
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
ln(AvgDiversityIPC5t )
dFemale
(7)
∗∗∗
∗∗∗
0.496
(0.020)
0.0259
(0.002)
0.934
(0.009)
∗∗∗
∗∗∗
(6)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
−0.100
(0.015)
Yes
1.008
(0.018)
−1.801
(0.017)
173,426
30,493
29,154
0.1176
−439,424
∗∗∗
∗∗∗
∗∗∗
−0.165
(0.015)
Yes
1.876
(0.016)
−1.635
(0.016)
173,426
30,493
25,755
0.0988
−448,787
∗∗∗
∗∗∗
∗∗∗
−0.015
(0.015)
Yes
1.934
(0.010)
−2.115
(0.022)
173,426
30,493
41,501
0.1468
−424,850
∗∗∗
∗∗∗
Note: ∗ ∗ ∗ , ∗ ∗ , and ∗ show significance at the 1%, 5%, and 10% levels, respectively, and standard errors are presented in parentheses.
Appendix D– Additional Figures
Fig. D1. Examples of three networks with different clustering coefficients.
23
∗∗∗
∗∗∗
∗∗∗
∗∗∗
L. Tahmooresnejad and E. Turkina
Journal of Informetrics 16 (2022) 101256
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