Construction of data
To test the hypotheses in the previous section, our empirical analysis utilizes data for patent-holding firms in the world, taken from the Orbis dataset compiled by Bureau van Dijk (BvD). It includes various firm attributes, in addition to information on patents granted to each firm that is originally provided by PATSTAT. PATSTAT contains detailed information of patents, such as the patent identification number, date of filing, name and address of applicants and owners, country code, international patent classification, abstract, and identification numbers of patents cited by the focal patent.
In this study, we utilize data for patents that were applied for from 1991 to 2010 and granted by 2014, the final year in our dataset. We exclude patents applied for in the most recent four years because it takes several years for an applied patent to be actually granted. Harhoff and Wagner (2009) report that the average duration from the application of a patent to EPO to its grant was 4.36 and 5.10 years in 1991 and 1998, respectively. Therefore, many patents applied for in recent years have not been granted and thus are not included in our data.
BvD aggregates the patent data at the firm level. This is possible because BvD assigns an identification number to each firm in the Orbis data and identifies the identification number of each patent owner firm in PATSTAT, by matching firm names reported in PATSTAT and the Orbis. Therefore, the Orbis data can identify co-patenting networks among firms quite accurately. However, it should be noted that because BvD focuses on companies as their business target, non-firm patent owners, such as universities, public research institutions, and individuals, are excluded from our sample.
In this study, we focus on firms that were granted any patent during the period 1991–2010. The total number of patents owned by any firm with an identification number assigned by BvD in this period is 26,181,824, and the number of firms that have been granted any patent is 534,569.
To locate each firm, we use its addresses recorded in the Orbis data. Thus, a patent can be assigned to multiple countries because of possible multiple owners. The number of patents for firms located in each of the top six countries is 8,506,558 for Japan, 6,528,207 for the United States (US), 2,833,394 for Germany, 1,547,916 for South Korea, 1,043,371 for France, and 972,034 for China. These six countries account for approximately 80% of all patents.
Although patent-holding firms are generally larger than non-patent holders, we should note that our sample includes many SMEs, as the number of workers of the bottom 10% firm in our sample is just five whereas its median is 128. Accordingly, most firms in our sample do not apply for patents frequently but rather once every few years. Therefore, rather than using annual panel data, we divide the whole 20-year period into four five-year periods, 1991–1995, 1996–2000, 2001–2005, and 2006–2010.
Our rich dataset allows us to construct a measure of the citations the patents of each firm receive. Because a patent cites another patent when the former is influenced by the latter, the number of forward citations and the number of forward citations per patent are often regarded as an indicator of the quality of innovation (Griliches 1998; Nagaoka et al. 2010; Trajtenberg 1990) and are used in the literature on the effect of the firm network on innovation (Belderbos et al. 2014; Briggs 2015; Rost 2011). We first count the number of forward citations that the focal patent received from subsequent patents, excluding self-citations. A citation of patent A by patent B is defined as a self-citation if patents A and B share any firm as their owners.
Our key measure of innovation quality is the number of citations at the firm level. We count the number of citations each patent receives during the whole period in our entire data, i.e., from 1991 to 2014. Some studies fix the period (window) in which patents receive citations, e.g., for four or seven years after the application (Belderbos et al. 2014; Phelps 2010). However, we find that some patents are cited for a long period after their applications. For example, 49% of citations to patents applied for in 1991 were cited 10 years after the application or later. To incorporate the long duration of patent citations, we count all citations that each patent receives during the whole period in our data when we measure the quality of each patent. However, the number of citations tends to be smaller for more recent patents than for earlier ones. For example, a patent applied for in 1991 receives more citations than that with the same quality applied for in 2010, simply because of the longer time period after the application for the former. To account for the differences in the number of citations stemming from differences in application years, we standardize the number of citations by dividing it by the average number of citations in each year and summing it up over the 5-year period. Specifically, the standardized measure of the number of citations for firm i in 5-year period t, CITATIONit, is given by
$$\begin{array}{c}{\mathrm{C}\mathrm{I}\mathrm{T}\mathrm{A}\mathrm{T}\mathrm{I}\mathrm{O}\mathrm{N}}_{it}=\sum\limits_{y\in t}\frac{{\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_{iy}}{{\mathrm{a}\mathrm{v}\mathrm{g}\_\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_{y}}, \end{array}$$
(1)
where citationiy is the number of citations that patents applied for in year y and owned by firm i receive from year y to 2014 and avg_citationy is the average number of citations to patents applied for in year y from y to 2014. Therefore, \({\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_{iy}/{\mathrm{a}\mathrm{v}\mathrm{g}\_\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_{y}\) represents the number of citations to patents applied for in a particular year standardized by its average.
Using the data, we also create measures of the co-patenting network of firms, i.e., the network in which firms are connected through the co-ownership of patents. Identifying the co-patenting network is possible because each owner firm of a patent is provided with an identification number in the Orbis dataset. The number of patents with more than one owner is 959,363, or 3.7% of the total number of patents, whereas the number of firms that co-own any patent with other firm or institution is 89,175, or 17% of those that own any patent. The total number of links in the co-patenting network is 166,183. The number of patents whose owners are located in more than one country, or internationally co-owned patents, is 248,909, or 0.95% of all patents, whereas the number of firms that co-own any patent with a foreign firm or institution is 20,445, or 3.8% of patent-holding firms.
We regard a co-patenting relationship between two firms as an indication of their research collaboration, because research collaboration can result in co-ownership of its outcomes, i.e., patents (Belderbos et al. 2014; Briggs 2015; Hagedoorn et al. 2003). In practice, however, firms may not co-own patents generated from their research collaboration because of their strategic decision to avoid possible legal and institutional complications in co-patenting (Hagedoorn 2003). Empirically, Hagedoorn et al. (2003) fail to show a significant correlation between research collaboration and co-patenting. Belderbos et al. (2014) find that co-patenting does not necessarily improve Tobin’s q of firms, suggesting that this may be because values from co-patenting are difficult to appropriate to patent co-owners. Therefore, some existing studies utilize firm-level data in which research collaboration and alliances are identified from surveys, news media, and business reports (Ahuja 2000; Owen-Smith and Powell 2004; Phelps 2010; Rost 2011; Whittington et al. 2009), such as the community innovation surveys (CIS) (Belderbos et al. 2006; Ebersberger and Herstad 2013; Haus-Reve et al. 2019) and the CATI database of MERIT (Gilsing et al. 2008; Hagedoorn et al. 2003). However, the present study relies on co-patenting links to identify research collaboration to cover a large number of firms around the world, following Belderbos et al. (2014) and Briggs (2015).
Firm attributes, such as sales and the number of employees, are included in the Orbis dataset. However, these attributes for most firms are available only from 2007 to 2014, while for a small sub-sample of firms they are also available from 1991 to 2010, our sample period. Therefore, our benchmark estimation does not use any firm attribute information from Orbis but only use the location and industry classification of each firm. To overcome possible shortcomings from not using standard firm attributes, we will use fixed effects at the firm level and at the country-industry-year level, as we will explain later in detail. To check the robustness of the benchmark estimations, we will also experiment with the sub-sample of firms with firm attributes.
Changes in the global co-patenting network over time by country
In this subsection, we highlight changes in the global co-patenting network over time and differences across countries so that we can later obtain more adequate interpretation and implication from our estimation results on the relationship between the network structure and innovation. In particular, we focus on the top six countries in terms of the number of patent grants, which represent approximately 80% of all patent grants.
Figure 1 shows changes in the number of patents granted by application year from 1991 to 2010. Japanese firms are granted the largest number of patents throughout the period, whereas the US is granted the second-largest number. However, in the last few years of the period examined, the number of patents in both Japan and the US declined, while China emerged as the third-largest country. These dynamics in the number of patents for each country presented here are mostly consistent with what is reported by the five largest intellectual property offices, EPO, JPO, USPTO, the Korean Intellectual Property Office, and the State Intellectual Property Office of the People's Republic of China (IP5 Offices 2012, Fig. 3.2). There are slight differences because we focus on patents granted to firms and institutions included in the firm-level Orbis dataset. Notably, the number of patents granted to China reported in IP5 Offices (2012), 312,507, is larger than that in Fig. 1.
Figure 2 indicates the changes in the ratio of the average number of citations per patent for a country to the overall average number of citations per patent. Note that the ratio is standardized so that the average of this ratio in each year is one. Thus, Fig. 2 illustrates the average quality of innovation in each country relative to other countries. Then, we can see that the US has created innovations of the highest quality, while its relative quality declined from 1991 to 2003. This decline is partly because the relative quality of patents granted to Japan increased during the same period. However, the relative quality for Japan decreased after 2003, associated with an increase in the US. Thus, we conclude that both the quantity and quality of innovation generated by Japanese firms have recently deteriorated. By contrast, Chinese firms have recently increased both the quantity and quality of innovation, although the quality measure is the lowest among the six countries at the time of the year 2010.
Looking at the dynamics in the extent of co-patenting for each country, we illustrate changes in the share of co-owned patents in all patents in Fig. 3. The overall co-patenting share at the patent level has been increasing from 3% in 1990 to 4.3% in 2010, indicating that research collaboration has been increasingly performed over time, possibly because of the spreading recognition of the effectiveness of open innovation (Chesbrough 2003). The share has been the highest for France in most years during the period examined, increasing substantially. The recent increase in the share of China is also prominent.
Furthermore, we focus on the dynamics of international co-patenting in Fig. 4. We find that the share of patents internationally co-owned in all patents has also been increasing over time. However, there is a substantial gap in the share between Japan and South Korea, the lowest two countries, and the others. Because the other four countries, France and China in particular, considerably increased the share of international co-patenting in the 2000s, while Japan and South Korea were stagnant, the gap has been widened over time. This feature of Japan and South Korea will be confirmed in the visualization of the global network in the next subsection.
Structure of the global co-patenting network
To provide an overview of the structure of the global co-patenting network of firms, we visualize the network using an algorithm, ForceAtlas2 (Jacomy et al. 2014), in Gephi, open-source software for network visualization. ForceAtlas2 assumes gravity between linked nodes and repulsion between unlinked nodes. Accordingly, a set of nodes linked with each other are located closely together and form a group. Consequently, nodes linked with many others, or hubs, tend to be located in the center of the network.
Figure 5 shows the visualization in the period 1991–1995 (panel [A]) and 2006–2010 (panel [B]) for comparison across periods. The figure uses different colors for firms located in each of the top six countries in terms of the number of patents granted, Japan (red), the US (blue), Germany (green), South Korea (light blue), France (yellow), and China (black), while other firms are colored in gray. In the visualization, we pick up the largest connected component, i.e., the largest sub-network in which firms are directly or indirectly linked with each other. This is because there are many fragmented sub-networks separated from the largest connected component and located far away from the center of the visualized space, and they are less important in the big picture of the network. However, we use all firms in the estimations conducted in later sections. The share of firms in the largest connected component is 48% and 63% in the periods 1991–1995 and 2006–2010, respectively. This share varies across countries. In the period 2006–2010, 91% of Japanese firms are in the largest connected component, while the shares are substantially smaller for other countries: 69% for South Korea and China, 64% for France, 60% for Germany, and 59% for the US.
Figure 5 also illustrates that firms are likely to be linked within each country. In particular, firms in Japan and South Korea form two groups that are remarkably separated from firms in other countries. While firms in the US, Germany, and France are also located closely together, these clusters are located closely with each other. This finding implies that firms in the US, Germany, and France collaborate more across national borders with each other, while firms in Japan and South Korea mostly collaborate with other firms in the same country.
The comparison between panels (A) and (B) further indicates the following. First, the isolation of Japanese and South Korean firms has remained over time. Second, US, German, and French clusters are more closely linked with each other in the period 2006–2010 than in the period 1991–1995, implying that firms in these countries have become more active in international collaboration. Finally, Chinese firms, the black dots, are not clearly visible in the period 1991–1995 but form a cluster located closer to the combination of the US, German, and French clusters than to the Japanese and South Korean clusters in the period 2006–2010.
We further show the distribution of the number of firms linked with the focal firm, or the degree centrality (Newman 2010), in Fig. 6. The degree distribution is of great interest because if it follows the power law, i.e., there are a few nodes with an extremely large number of links or hubs, the network is classified as a scale-free network. It is well known that because in a scale-free network, most nodes are indirectly connected with each other with a small number of steps through hub nodes, diffusion of information can be quick (Barabási 2016). Many types of networks have been found to be scale free, including firms' transaction networks (Fujiwara and Aoyama 2010; Saito 2015).
Panels (A) and (B) of Fig. 6 show the cumulative density function (CDF) of the degree centrality by period and by country, respectively. Panel (A) illustrates the linear relationship between the log of the cumulative density and the log of degree, indicating that the global research collaboration network in any period is scale free. The gradient of the linear relationship is similar, while the size of the network (the total number of firms) increases over time. Because a larger gradient (or a smaller gradient in absolute values) of the log–log relationship indicates larger heterogeneity in the degree centrality among nodes, and a similar gradient over time implies that such heterogeneity is unchanged for the 20 years examined.
In panel (B) of Fig. 6, we observe that the gradient is different across countries. The gradient calculated by a linear regression is the largest (or the smallest in absolute values) for Japan, − 0.91, and the smallest for the US, − 1.42. This implies that there are more hubs with many links in Japan than in the US and that the median firm in Japan has more links than that in the US. These results suggest that the structure of the research collaboration network differs substantially across countries. In addition, we examine the variation across the country in assortativity of nodes, i.e. whether nodes are likely to be connected with others with a similar value of degree centrality, finding a large variation across countries. Appendix shows the details of the analysis.
Variables for co-patenting networks
This study considers three measures that represent the characteristics of the ego network of each firm in each period: the degree centrality, the local clustering coefficient, and Burt's constraint measure. When we construct the network measures, we exclude isolates, i.e., firms that do not co-own any patent with others, because the measures cannot be defined for isolates. The co-patenting network is regarded as an undirected graph, i.e., a network in which links have no direction.
The degree centrality in a network is the number of nodes directly linked to the focal node. In the co-patenting network examined in this study, degree centrality represents the number of firms that co-own any patent with the focal firm. The degree centrality is a widely used index that measures the centrality of the focal firm in the network (Ahuja 2000; Whittington et al. 2009). When we use the degree centrality in the estimations, we take its log because its distribution has a fat tail, as shown in Fig. 6.
The local clustering coefficient is an index to measure how densely each firm's partners are also connected. It is defined as the ratio of the number of pairs of firms that are connected with the focal firm and are also connected with each other to the number of all possible pairs of firms that are connected with the focal firm. When a firm is linked with only one firm, we define that its clustering coefficient is zero, following the standard literature (Barabási 2016). Because this definition is rather arbitrary, we will include a dummy variable for firms with only one link in the estimations. The clustering coefficient ranges from zero to one, and its higher value indicates that a firm's research collaboration partners are also collaborating with each other. This measure has been used in the literature on the effect of network characteristics on innovation (Fleming et al. 2007b; Gonzalez-Brambila et al. 2013; Phelps 2010; Rost 2011).
The constraint measure of Burt (1992) for node i is defined as follows:
$$\begin{array}{c}C\left(i\right)=\sum\limits_{j\in {V}_{i}, j\ne i}{\left({p}_{ij}+\sum\limits_{q\in {V}_{i}, q\ne i,j}{p}_{iq}{p}_{qj}\right)}^{2},\end{array}$$
(2)
where Vi represents the set of nodes in i's ego network, pij is the relative link strength between nodes i and j and is assumed to be 1/Ni for any j Vi. Ni represents the degree centrality of i, assuming the same weight across links. Everett and Borgatti (2018) show that Eq. (2) can be rewritten as
$$\begin{array}{c}C\left(i\right)=\frac{1}{{N}_{i}}+\frac{2}{{N}_{i}^{2}}\sum\limits_{j\in {V}_{i}, j\ne i}\sum\limits_{q\in {V}_{i}, q\ne i,j}{p}_{qj}+\frac{1}{{N}_{i}^{2}}\sum\limits_{j\in {V}_{i}, j\ne i}{\left(\sum\limits_{q\in {V}_{i}, q\ne i,j}{p}_{qj}\right)}^{2}.\end{array}$$
(3)
Thus, the constraint measure for node i is smaller when (a) node i is connected with more nodes (Ni is larger), (b) i's direct neighbors are not connected with each other (pqj is zero), or (c) i's direct neighbors are connected with many more others beyond i's ego network (pqj is smaller). In other words, this measure is small when the focal node is connected with a variety of nodes directly and indirectly, bridging between different clusters of nodes. When a firm is linked with only one firm, we assume that pqj is zero although there is, in fact, no firm j and thus that this measure is one. Because this definition is arbitrary, similar to the case of the clustering coefficient when the degree is one, we will include a dummy for firms with one link in the estimations. This measure ranges from zero when a node is connected with an infinite number of nodes to 1.125 when a node is connected with two nodes that are also connected (Everett and Borgatti 2018). Burt's constraint measure is also used in the literature on the effect of networks on innovation (Ahuja 2000; Gonzalez-Brambila et al. 2013; Guan et al. 2017; Rost 2011). Figure 7 illustrates examples of the three cases (a), (b) and (c) as described above. The arrows (a), (b) and (c) in Fig. 7 correspond to the above three cases that affect the constraint measure for node i. The upper center example (C(i) = 1.125) in Fig. 7 is the case of the largest value of Burt’s constraint measure, and the value decreases as it follows each arrow.
Descriptive statistics
In our estimation, we drop firm-period observations in singleton groups, i.e., groups with only one observation, to fully exploit the benefits of using fixed effects at the firm level and at the country-industry-period level (Correia 2015). Note that the results are essentially the same if we do not drop singletons. In addition, when we estimate the effect of the three network measures on innovation performance, we restrict the observations to firms with any co-patenting relationship because these measures can be defined only for these firms. Then, our sample contains 356,397 and 48,910 firm-period observations for the estimation of the effect of research collaboration and the three network measures, respectively.
Table 1 shows the descriptive statistics of the variable used in the estimations for the sample for estimations. Among all firms, the average number of patents granted is 63.8, although its distribution is quite skewed, as its median is only 5 and its maximum is 139,275. The number of citations is also skewed: its mean is 63.9, whereas its median is 2.41. The number of citations per patent, which can be considered as an indicator of innovation quality at the firm level, is 1.32, on average. The dummy for firms with any co-patenting relationship with other firms or institutions is 0.20, on average. The dummy for firms with any co-patenting relationship with foreign firms or institutions is 0.05, on average, indicating that international research collaboration is quite rare. It should be noted that the dummy for co-patenting and the dummy for international co-patenting are not exclusively defined. In other words, when a firm engages in international co-patenting, both dummies are one. When a firm engages in domestic co-patenting, the dummy for co-patenting is one while the dummy for international co-patenting is zero. The correlation coefficient between the dummy for co-patenting and its first lag is 0.52, whereas the corresponding figure for international co-patenting is 0.46. These figures suggest that while co-patenting behaviors are persistent, we still have sufficient variations in these key variables over time for the estimations of their effects. The dummy for firms in the largest connected component of the co-patent network, i.e., the largest sub-network of firms linked directly and indirectly with each other, is 0.13, on average. Therefore, the share of firms in the largest connected component among firms in the sample firms in the co-patenting network is approximately 65% (= 0.13/0.20). The lower rows of Table 1 show that firms with a co-patenting relationship are more likely to be granted more patents and receive more citations in total and citations per patent. Thus, it is inferred that firms that engage in research collaboration with other firms innovate more in terms of both quantity and quality. We will test this inference by econometric analysis later.
Table 1 Descriptive statistics at the firm-period level In addition to the summary statistics of the three network measures in Table 1, we present histograms of the distributions for firms in the sample for the estimations in Fig. 8. The distribution of the degree is shown by a logarithmic scale in panel (A) of Fig. 8. We confirm a power-law distribution, as found for all firms in our data before singletons are dropped in Fig. 6. The median and mean of the number of partners are 2 and 5.36, respectively, indicating that most firms have only a few co-patenting partners. Panels (B) and (C) of Fig. 8 illustrate the distribution of the clustering coefficient and Burt's constraint measure, respectively. In these figures, we exclude firms with only one partner, which represent 43% of all firms in the estimation sample, because the clustering coefficient and Burt's constraint measure of those firms are arbitrarily defined as zero and one, respectively. Neither distribution is standard bell-shaped. The clustering coefficient is zero for 32% of firms, whereas it is one for 17%, of which 78% have two partners. Firms with a clustering coefficient between 0.5 and one are scarce. Burt's constraint is 0.5 for 20% of firms, among which all have two partners. Firms with Burt's constraint measure between 0.6 and one are scarce.
Table 2 indicates the correlation coefficients between the three network measures. Here, as mentioned before, we exclude firms with only one link in common with panels (B) and (C) of Fig. 8. As implied by Eq. (3), Burt's constraint measure includes the inverse of the degree centrality by definition. Accordingly, the correlation coefficient between the two measures is − 0.758 and quite high. We also find a negative correlation between the degree and the clustering coefficient, as often found in the literature (Barabási 2016). In addition, the correlation coefficient between Burt's constraint measure and the clustering coefficient is 0.588, a reasonably high value, because the former is related to the latter, as shown by the second term of Eq. (3).
Table 2 Correlation coefficients between network measures (firms with two or more links [N = 27,700]) Table 3 shows the international comparison in the number of firm-period observations, the number of patents per firm, and the three measures of the global co-patenting network at the firm-period level. This table conspicuously shows that Japanese firms are different from firms in other countries. The number of firm-period observations for Japan is small, compared with its large number of patents granted. Accordingly, the number of patents per firm is substantially larger for Japan than for other countries. The average of the logarithm of the degree centrality and the clustering coefficient is the largest for Japan. By contrast, Burt's constraint measure, which is smaller when the focal firm bridges different groups of firms, is the smallest for Japan. The evidence reveals that in Japan, a limited number of large firms are densely connected with many other domestic firms.
Table 3 International comparison of descriptive statistics at the firm-period level