Knowledge sourcing by multi-plant firms in Europe

ABSTRACT

Research on geographies of knowledge sourcing examines the organizational structure of innovation activities within the firm, the mechanisms by which knowledge is extracted from various external sources and the geography of these different activities. We augment this literature by exploring knowledge sourcing within multi-plant firms operating in Europe. Analysis makes use of linked patent-firm data recording the location of knowledge production and its ownership. The results add value to existing research in three ways. First, the establishments of multi-plant firms are shown to produce different kinds of knowledge in different locations. Second, the patents generated within a firm's establishments are linked to the knowledge stocks of the regions where they operate, supporting a vision of geographical knowledge sourcing. Third, the complexity of knowledge produced within firms is positively related to the number of plants in which they innovate.

KEYWORDS:

• Knowledge sourcing
• complexity
• technology
• economic geography
• multi-plant firms

Introduction

Successful competition for individual firms, especially over the long-run, depends heavily on access to new technological know-how. That knowledge can be developed within the firm through learning and dedicated processes of research and development (Arrow 1962; Pavitt 1991), and it can be sourced from outside the firm through more or less formal market and non-market interactions (Von Hippel 1988; Chesbrough 2003). While incremental innovations can be generated by economic agents in many locations, more complex and valuable innovation relies on the recombination of knowledge subsets that are not widely available (Mewes 2019). Indeed, Balland et al. (2020) report that more complex forms of knowledge are increasingly confined to larger cities, sites where highly specialized economic agents with diverse sets of capabilities are more likely to be found. Coupled with the difficulty of moving complex technological ideas (see Sorenson, Rivkin, and Fleming 2006 and Balland and Rigby 2017), a relatively small number of innovative regions have become locational targets for firms engaged in knowledge sourcing. Recent research confirms that the production of complex knowledge confers growth advantages on firms located within a limited number of sub-national regions in advanced and emerging economies alike (Mewes and Broekel 2022; Pintar and Scherngell 2022; Rigby et al. 2022; Li and Rigby 2022).

A rapidly growing literature on knowledge sourcing explores how firms access and utilize external sources of knowledge (Almeida 1996; Chung and Alcácer 2002; Tödtling, Lehner, and Trippl 2006; Huggins et al. 2015). For the majority of firms that are single-plant businesses, external knowledge sourcing means tapping into local networks of workers, firms and other research producing organizations, while also looking to access networks of economic agents that reach into non-local knowledge pools (Amin and Cohendet 1999; Bathelt, Malmberg, and Maskell 2004). Within economic geography, research on knowledge sourcing (Bathelt, Malmberg, and Maskell 2004; Lorentzen 2007; Fitjar and Rodríguez-Pose 2013) has been directed at long-standing claims of the local bias of knowledge flows (Marshall 1890; Jaffe, Trajtenberg, and Henderson 1993; Storper and Venables 2004), on whether the ‘buzz and pipelines’ model of Bathelt, Malmberg, and Maskell (2004) is sufficient to capture the heterogeneity of knowledge sourcing practices over space (Trippl, Tödtling, and Lengauer 2009), on knowledge flows in different regional innovation systems and across knowledge bases (Asheim and Gertler 2005; Martin and Moodysson 2013; Tödtling, Grillitsch, and Hoeglinger 2012), and on the benefits of combining local and non-local forms of knowledge (Bathelt 2007).

We seek to add to the literature above through examining the knowledge sourcing practices of multi-locational firms operating within Europe. Unlike most single-plant businesses, multi-plant firms have the capacity to embed themselves within different local knowledge bases, raising the possibilities for combining heterogeneous sets of valuable knowledge. Furthermore, multi-locational firms generate internally many of the different sources of proximity outlined by Boschma (2005) and so face lower costs of knowledge integration than others. Still, we do not have much information about the knowledge sourcing practices of multi-plant firms, especially at the subnational level. We ask three questions regarding the geography of innovation within multi-plant firms. First, do these firms produce different kinds of knowledge across their geographically disparate operational units? Second, is the knowledge they produce at these locations linked to the character of the local knowledge base? That is, do we see evidence of geographical knowledge sourcing by multi-plant firms? Third, are these firms able to integrate the knowledge sourced from different sites and increase the average value of the technologies they generate?

The research questions are addressed by using patent records matched to firm-level ownership and geographical data covering multi-locational firms in Europe. Our focus is placed on the knowledge production activities of these firms across European NUTS2 regions. Results show that close to 70% of firms investigated produce patents in knowledge classes that are significantly different across the locations in which they operate. This share reaches close to 100% for firms with more than 10 establishments, as compared to slightly below 40% for firms with only two establishments. We find that the patents generated within the establishments of multi-unit organizations reflect the broader technological character of the regions in which they are located. This adds to the body of evidence that multi-plant firms strategically locate their operations in order to access place-specific stocks of knowledge. Finally, analysis reveals that the number of establishments across which the firm distributes its innovative activities is positively associated with the production of more complex and valuable patents.

The rest of the paper is divided into four sections. Section two reviews the economic geography literature on knowledge sourcing. In Section three we outline construction of a linked firm-patent data set and provide summary statistics for our sample of multi-unit firms. Section four presents the results of our analysis and Section five summarizes the research findings.

Knowledge sourcing in economic geography

For many firms and regions in the contemporary market economy competitive advantage increasingly rests on the production of non-ubiquitous, tacit knowledge (Maskell and Malmberg 1999). Within the firm, knowledge mainly originates from processes of research and development (Pavitt 1991) and learning (Arrow 1962). For Von Hippel (1988) and Chesbrough (2003), technological knowledge is also acquired outside the firm through market-based interaction, formal and informal exchanges, spillovers and learning from others. Cohen and Levinthal (1990) lay the foundations of firm knowledge development at the intersection of internal and external knowledge sources.

There is growing evidence that different sites of economic activity produce distinct subsets of knowledge whether measured by firm and industry product and process technologies (Rigby and Essletzbichler 1997), in terms of broad knowledge bases (Asheim and Gertler 2005; Martin and Moodysson 2011), or in the mix of patents generated (Kogler, Rigby, and Tucker 2013). Much of this knowledge is not easily moved (Jaffe, Trajtenberg, and Henderson 1993; Audretsch and Feldman 1996), especially that which is tacit (Polanyi 1966; Maskell and Malmberg 1999; Gertler 2003; Nonaka and Takeuchi 1995) and complex (Sorenson, Rivkin, and Fleming 2006; Balland and Rigby 2017). The geographical knowledge landscape then is highly uneven, a low-level surface of widely available codified knowledge interspersed by jagged peaks representing concentrations of complex and tacit knowledge that are broadly aligned with larger cities (Balland et al. 2020).

Regardless of how knowledge is developed, spatial clusters of firms, workers and related organizations tend to dominate innovation (Feldman 1994). In industries and knowledge fields where innovation largely occurs within the firm, access to venture capital funding (Sorenson and Stuart 2001), basic research from universities and labs (Fritsch and Schwirten 1999; Bramwell and Wolfe 2008; Laursen, Reichstein, and Salter 2011), and the availability of teams of specialized knowledge workers (Alcácer and Chung 2014) and specialized service providers (Muller and Doloreux 2009; Shearmur and Doloreux 2019) limit locational possibilities. Where innovation results more from external exchanges with customers and suppliers, the density of partners plays a critical role (Duranton and Puga 2001). To varying degrees, these arguments sustain a long literature within economic geography from Marshall’s (1890) agglomerations and Porter’s (1990, 1998) clusters, to the industrial districts and milieu of Brusco (1986), Becattini (1991) and Camagni (1991), through to learning regions (Lundvall and Johnson 1994; Cooke 2002; Morgan 2007) and the regional innovation systems they develop (Braczyk and Heidenreich 1998; Cooke, Boekholt, and Tödtling 2000). The takeaway from much of this literature is that firms and other economic agents who are part of an innovative cluster are advantaged in ways that outsiders are not. ‘Being there’, as Gertler (2003) notes, smoothes the sharing of ideas, whether they are generated by ‘local buzz’ (Storper and Venables 2004), delivered in the form of spillovers (Jaffe, Trajtenberg, and Henderson 1993; Sonn and Storper 2008), through worker mobility (Almeida and Kogut 1999) or networks of economic agents (Giuliani 2013). For Saxenian (1994) and Storper (1995), following Brown and Duguid (1991), place-specific communities of practice and institutional development foster trust, collective learning (Lawson and Lorenz 1999), shared capabilities and various forms of proximities (Boschma 2005) that reduce the cost of interaction.

More recent work challenges the local bias of the knowledge exchange literature (Bathelt, Malmberg, and Maskell 2004). That access to external knowledge plays a central role in firm innovation is the foundation for a vibrant literature in economic geography on knowledge sourcing. Combining arguments from the regional innovation systems literature (Cooke, Boekholt, and Tödtling 2000; Asheim and Gertler 2005), from knowledge-base ideas (Asheim and Coenen 2005 and Martin and Moodysson 2011) and research on modes of learning (Jensen et al. 2007), this work explores how firms in different industries acquire external knowledge, focusing on the sources of that knowledge, the mechanisms through which it is obtained and the geographical scales at which those mechanisms operate (Tödtling, Lehner, and Trippl 2006; Trippl, Tödtling, and Lengauer 2009; Fitjar and Rodríguez-Pose 2013; Grillitsch and Trippl 2014; Isaksen and Trippl 2017). Much of this work pushes beyond the buzz and pipelines binary to examine how different forms of interaction for knowledge exchange are organized, from informal linkages to more durable network collaborations (see also Powell, Koput, and Smith-Doerr 1996 and Ter Wal and Boschma 2009), involving value-chain partners, universities, research labs and competitors located in a single cluster, or distributed more widely over space.

Although, it is not straightforward to summarize the results of this literature, it is safe to say first, that different types of knowledge, market and technological, product and process, tacit and codified appear to circulate in different ways (Tödtling, Grillitsch, and Hoeglinger 2012; Fitjar and Rodríguez-Pose 2020). Second, knowledge-based interactions appear to be at least as likely to occur between non-local as local partners, though this seems to rest heavily on industrial sector and the fecundity of local/regional innovation systems (Tödtling, Lengauer, and Höglinger 2011 and Trippl 2011). Third, the nature of the underlying knowledge base (analytical, synthetic or symbolic) is correlated with the geography of knowledge circulation (Martin and Moodysson 2013), though the interaction of the innovation system and the knowledge base complicate simple readings (Tödtling, Grillitsch, and Hoeglinger 2012). Grillitsch and Trippl (2014) and Isaksen and Trippl (2017) synthesize the key insights from many of the aforementioned studies in their analysis of knowledge sourcing and patterns of regional innovation.

The knowledge sourcing literature within economic geography is very much focused upon the acquisition of external knowledge by firms that are considered, at least implicitly, as single establishment businesses that operate from a fixed location. This literature says relatively little about how the structure of the firm might evolve to exploit the geography of technological heterogeneity. However, it is clear from the literature in international business and management that increasing numbers of multinational enterprises (MNEs) have divided their operations, at least in part, to embed themselves within different sites of knowledge production (Ghoshal and Bartlett 1988; Cantwell 1989; Dunning 1998; Chung and Alcácer 2002; Almeida and Phene 2004; Cantwell and Mudambi 2011). These locations are often well-connected global city-regions (Cantwell and Iammarino 2003; Goerzen, Asmussen, and Nielsen 2013; Iammarino and McCann 2013; Castellani et al. 2022) containing relatively dense clusters of innovative economic agents (Berry 2015; Li and Bathelt 2018) with high potentials for knowledge acquisition (Alcácer and Chung 2014; Jindra, Hassan, and Cantner 2016). Of course, access to multiple sources of knowledge is not the only reason for the multi-locational structure of many business organizations. Following Dunning (1977) there is a vast literature on the factors shaping the organization of MNEs and the geography of their activities (see Dunning 1998 and Neilsen, Asmusen, and Goerzen 2018).

We extend the knowledge sourcing discussion within economic geography by examining the activities of multi-unit firms operating within Europe. Value is added to earlier work by tracing connections between the establishments of multi-locational firms and the technological capabilities found in different regions (Cantwell and Iammarino 2001; Lo Turco and Maggioni 2016, 2019; Neffke et al. 2018; Elekes, Boschma, and Lengyel 2019 and Crescenzi, Dyèvre, and Neffke 2022). While recent work on the geography of knowledge sourcing restricts the technological search of firms in different sectors to broad knowledge types, we show that individual firms access different kinds of technological knowledge in different places and that they benefit from this practice.

Data

Knowledge sourcing and technological diversification in multi-locational firms operating in Europe are explored by combining patent data from the European Patent Office (EPO) with firm-level data from the Bureau Van Dijk (BVD)'s Orbis database. Patent assignees (firms in our sample) are regrouped by corporate ownership. Company groups in the sample include branches, that are fully-owned legal extensions of the firm, and majority-owned subsidiaries. For the latter, we collect merger and acquisition data from Zephyr to track changes in ownership. Patents generated by subsidiaries are linked to a parent firm only if the application year corresponds to the period of actual ownership.

Utility patent records from the EPO and associated locational information are used to distribute knowledge production across the establishments of the firm, while the nature of technologies is assessed through Cooperative Patent Classification (CPC) technology classes. We focus on patents owned by multi-locational firms operating in the EU27 plus Switzerland, Iceland, Norway and the UK. EPO records do not directly link inventors to unique establishments in multi-unit firms. This can be an issue when the location of an inventor does not correspond with any of the locations over which a firm's establishments are distributed. We use establishment-level information from the BVD to identify all European locations in which multi-locational firms are active. A patent is assigned to one or more establishments of an assignee if the location of the patent inventor (or co-inventor) coincides with one of the locations of the assignee organization. In cases where a patent is assigned to firm X and a co-inventor on the patent is located in region A, if region A contains no establishment associated with firm X, then the patent is not allocated to region A. The geographical matching was performed at the NUTS2 level. Note that NUTS2 regions vary in size and in terms of the political units they represent. While some NUTS2 regions may demarcate city-regions, they more commonly capture broader subnational spaces, and in limited cases represent entire countries. The heterogeneity of these spatial units means that ascribing causation to the locational decisions of multi-plant businesses is difficult and thus some caution must be exercised interpreting the results presented.

The final sample covers 633 unique firms, 3045 establishments and 114,717 patents covering the years 2001–15. Note that some patents are produced by co-inventors located in different establishments within the firm. The sample includes firms with a minimum of two establishments that have patented in at least two consecutive 3-year time periods between the years 2001–15. Multi-year activity is required to generate measures of technological variance within establishments, required by MANOVA tests. The multi-locational firms in our sample account for over 25% of all patents granted in Europe in each time period.¹ Summary statistics for firms in the sample are presented in Table 1. On average, sample firms control three establishments, distributed across two countries. Those firms produce an average of 52 patents with 62 different inventors.

Table 1. Summary statistics.

	# Patents	# Inventors	# Establishments	# Countries
Median	52	62	3	2
Std. dev.	521.67	658.27	5.41	2
Range	2–8687*	4–9192	2–49	1–9

Notes: *The minimum patent count of 2 represents a case where a firm has 2 establishments that have collaborated on a patent in two consecutive 3-year time periods.

Empirical analysis

Do firms produce different technologies across their establishments?

The first part of the empirical analysis investigates whether there are statistically significant differences in the technological portfolios of establishments belonging to a multi-locational firm. That is, do firms produce different kinds of knowledge across the establishments that they control? A standard test would be an analysis of variance to compare the distribution of patents across technology classes within the establishments of a single firm. Because patents are distributed across 652 CPC technology classes, a multivariate analysis of variance (MANOVA) is required. However, a large majority of technology classes contain zero patents in most establishments and thus the assumptions of a standard MANOVA are violated. We therefore turn to a permutation based MANOVA (PERMANOVA), a non-parametric test that operates over a geometric partitioning of the variation in a dataset that may be linked to multiple factors. In our case, analysis focuses upon the variance in patent counts across CPC technology classes that is distributed within and between the establishments that comprise a single firm.

The geometric partitioning of patents across technology classes is defined in the space of a dissimilarity index. The dissimilarity measure employed in this paper is based on the technological relatedness between patent classes (Breschi, Lissoni, and Malerba 2003; Kogler, Rigby, and Tucker 2013). A relatedness score is generated for each pair of technology classes based on the co-occurrence of those classes across EPO patent records. The co-classification counts for CPC classes i and j $(N_{ij})$ are standardized in the form of a cosine index, yielding a measure of the relatedness or technological proximity between classes i and j in a given period: $S_{ij}={\displaystyle \frac{N_{ij}}{\sqrt{N_i\ast N_j}}}$The standardized proximity matrix $(S_{ij})$ is subsequently used to calculate a dissimilarity score between all pairs of establishments by measuring the (inverse) average relatedness distance between the patents they generate across CPC classes. Class counts are aggregated into five three-year periods (2001–03, 2004–06, … , 2013–15) to smoothe annual fluctuations in patenting behaviour and to yield measures of the variance in technology within individual establishments.

The within-group variance is given by the technological dissimilarity of individual establishments between time periods, while the between-group variance is represented by the distance between the centroids of the establishments of a given multi-locational firm. Statistical inference is obtained by the permutation of patent observations across a firm's plants, from which we obtain a distribution of randomly generated F statistics. The null hypothesis is that the observed differences between the centroids of a firm's establishments are not statistically different than what would be observed if the patents were randomly distributed across establishments (Anderson 2017).

Due to the large size of the dissimilarity matrix and the limitations associated with interpreting a single test with a large number of firms, we perform separate PERMANOVA tests for each firm. The raw p-value and an adjusted p-value are reported because of repeated hypothesis testing. The adjusted p-value is calculated from the false discovery rate approach (fdr), which is similar to the Bonferroni correction but generally better suited to large-scale multiple testing. The PERMANOVA tests were performed using the ‘vegan’ package in R (Oksanen et al. 2020).

Table 2 presents the results of the PERMANOVA tests grouped by firm size. Using the adjusted p-value, 68% of firms show differences in technology production across the plants they operate that are significant at the 0.1 level. However, the percentages vary considerably across group sizes. For firms with two patenting establishments, close to 40% produced significant results, and that percentage increased steadily with firm size to reach approximately 97% for firms with 11–20 establishments, and 100% for firms with more than 20 establishments. The results therefore indicate that firms controlling larger numbers of establishments tend to produce more differentiated subsets of knowledge across their plants than do firms controlling fewer establishments.

Table 2. Summary of firm-level PERMANOVA results.

Firm size # of establishments	# of firms	# (%) of firms with signif pmanova (perms = 999)		# (%) of firms with signif pmanova Adjusted for fdr (perms = 999)
2	150	74 (49.3)	p < 0.1	59 (39.3)	p < 0.1
		56 (37.3)	p < 0.05	22 (14.7)	p < 0.05
		11 (7.3)	p < 0.01	0 (0)	p < 0.01
3–5	204	146 (71.6)	p < 0.1	141 (69.1)	p < 0.1
		139 (68.1)	p < 0.05	124 (60.8)	p < 0.05
		111 (54.4)	p < 0.01	78 (38.2)	p < 0.01
6–10	93	87 (93.5)	p < 0.1	86 (92.5)	p < 0.1
		85 (91.4)	p < 0.05	81 (87.1)	p < 0.05
		75 (80.6)	p < 0.01	69 (74.2)	p < 0.01
11–20	39	38 (97.4)	p < 0.1	38 (97.4)	p < 0.1
		38 (97.4)	p < 0.05	37 (94.9)	p < 0.05
		37 (94.9)	p < 0.01	37 (94.9)	p < 0.01
>20	19	19 (100)	p < 0.1	19 (100)	p < 0.1
		19 (100)	p < 0.05	19 (100)	p < 0.05
		19 (100)	p < 0.01	19 (100)	p < 0.01
All firms	505	364 (72.1)	p < 0.1	343 (67.9)	p < 0.1
		337 (66.7)	p < 0.05	283 (56.0)	p < 0.05
		253 (50.1)	p < 0.01	203 (40.1)	p < 0.01

Notes: Results are shown for tests that generated a total of 999 distinct permutations; 128 tests were not reported because they did not meet that criterion.

Do the establishments of firms produce technologies that are related to the knowledge stocks of the regions where they are located (evidence of geographical knowledge sourcing)?

Using secondary data, it is difficult to test whether firms locate plants in particular regions to access specific kinds of knowledge. Indeed, it is likely that many factors shape the location decisions of multi-unit firms. However, if we can link the technologies generated within a firm's establishments to the knowledge stocks of regions where the establishments are located then we have at least identified a pattern of location consistent with the practice of geographical knowledge sourcing. We examine this linkage using a logistic regression model. To understand the structure of the model, assume that a firm comprises three establishments each located in a different city. From these data we generate nine observations where each establishment is associated with each of the three cities. For that set of observations, the dependent variable is coded 0 when the establishment is linked with a NUTS2 region that does not match its actual location, and the dependent variable is coded 1 when the establishment is linked with the NUTS2 region in which it is located. Our task is to predict when the dependent variable will assume the value 1. The key independent variable for this task is a measure of the technological similarity between the patents generated within each of the establishments and those generated within the set of NUTS2 regions with which the establishments are associated. The technological similarity variable is measured for each of the three-year time periods between 2001 and 2015 when a firm's establishments are producing patents.

The measure of technological similarity employed is a standardized count of the number of patent classes in which both the establishment and NUTS2 region exhibit revealed technological advantage (RTA). Following standard practice, RTA is recorded for a technology class in an establishment (region) when the share of patents in that class exceeds the share of a reference group. The reference group for establishments (regions) comprises the set of all establishments (regions) in our sample. The count of overlapping RTA values between establishments and regions is standardized as a cosine index (see Eck and Waltman 2009). The model of geographical knowledge sourcing, as applied to multi-plant businesses, suggests that firms distribute establishments to locations in order to access specific pools of knowledge. Thus, we anticipate a positive sign for the measure of technological similarity in our logit model. Table 3 reveals the results of this statistical test.

Table 3. Logit model predicting region-establishment pairings based on technological similarity between establishments and NUTS2 regions.

Dependent variable: location	Coefficient (Standard Error)	Number of observations
Technological Similarity (standardized)	6.4922*** (0.1740)	84,954
Constant	−1.1456 (0.3982)
Firm fixed effects: Yes
Time fixed effects: Yes

Notes: *** significant at the 0.01 level.

The logit model is estimated with firm and time fixed effects and with robust standard errors. The results in Table 3 show that there is a strong, positive relationship between the technological similarity of establishments and the NUTS2 regions in which they are located. This finding is significant at the 0.01 level and provides support for the idea that multi-unit firms distribute their R&D establishments over space to access specific knowledge subsets. While these results alone cannot confirm the practice of geographical knowledge sourcing, it is difficult to imagine an alternative scenario that would generate the results above alongside a pattern of knowledge development consistent with the technological demands of the firms examined.

Does geographical knowledge sourcing raise the complexity value of firm patents?

In general, we know that firms benefit from developing new technologies (Bettis and Hitt 1995; Roberts 1999). Those technologies may be generated entirely in-house, ‘sourced’ externally through various mechanisms, or developed as a hybrid of internal and external practices. More valuable forms of complex and tacit knowledge are difficult to move across geographical, organizational and institutional spaces (Amin and Cohendet 2004; Gertler 2003; Boschma 2005; Balland and Rigby 2017). As a consequence, it is argued that multi-unit firms exploit their organizational structure to embed establishments in different locations in order to access place-specific repositories of knowledge and lower the cost of integrating heterogeneous knowledge subsets (Cantwell 1989; Cantwell and Mudambi 2005; Meyer, Mudambi, and Narula 2011). An important question is whether multi-unit firms benefit from this activity. The empirical literature has so far provided mixed results on this issue. For instance, Singh (2008) reported that the geographical dispersion of R&D in large multinational firms was negatively associated with the value of innovative output, as measured by the average number of forward citations to firm patents. Scalera, Perri, and Hannigan (2018) report a positive relationship between the geographical dispersion of R&D and the technological scope of patents in US firms, both domestic and multinational, though this relationship is bounded by managerial bandwidth at the subnational level.

We contribute to this debate using a similar methodology to Singh (2008). Unlike Singh (2008), who uses forward citations to capture the (tacit knowledge) value of patents, we measure the value of patents using the complexity of the classes into which they are placed. We suspect that tacit knowledge dampens citations precisely because it is so difficult to move across spatial, organizational and institutional distances. The concept of economic complexity has recently been developed by Hidalgo and Hausmann (2009) to value different kinds of economic activity. For them, complexity reflects the difficulty of producing various types of goods. Countries that have developed broad sets of capabilities specialize in the production of many types of goods, while countries with relatively few capabilities tend to specialize in only a few different sectors. Complex, high-value goods require many capabilities for their production and so tend to be produced in a relatively small number of countries. Conversely, less complex, lower valued goods tend to be produced in a much larger number of locations reflecting the broad availability of a smaller range of capabilities across different countries.

Measuring complexity requires patent data for CPC classes that are distributed over regions of interest. These data are used to build a bipartite (sector-by-region) network of innovation. The complexity measure of Hidalgo and Hausmann (2009) represents the eigenvector centrality for such a bipartite network (He et al. 2016). Following Hidalgo and Hausmann (2009), we estimate complexity scores for the 652 technology classes of the CPC. Individual patents make knowledge claims across a series of these classes. We calculate the complexity value of individual EU patents as the weighted average complexity of the technology classes in which their knowledge claims are reported. The resulting patent complexity values are standardized to fall over the interval 0–1. We argue that this proxy for the value of knowledge comes close to the idea of tacit knowledge, as it captures dimensions of rarity and non-replicability that benefit firms in their search for competitive advantage (Kogut and Zander 1992; Alcácer and Zhao 2012). A review of new work on economic complexity is provided by Balland et al. (2022).

If multi-locational firms are able to integrate the knowledge developed across different localized knowledge pools, we expect that greater levels of geographical dispersion in knowledge sourcing will be positively associated with the production of more complex patents. We examine this issue using an OLS regression model where patents are linked to the firms and establishments in which they were created. The observations in the model are individual patents. We do not aggregate the value of patents by firm because we wish to control for a number of individual patent characteristics that are known to influence their value, such as the number of co-inventors (Ln inventor_count), the number of technology classes (Ln class_count) and the number of knowledge claims (Ln claim_count) they make (Breitzman and Thomas 2015). We measure the geographic distribution of R&D by counting the number of establishments over which a multi-plant firm distributes its patent production (Ln estab_count).

Sourcing knowledge from foreign locations could potentially broaden the scope of technologies and expertise involved in the innovation process. This is captured by a dichotomous variable taking the value 1 if there is a foreign inventor on a patent. If headquarters (HQ) establishments are the locations at which firms do most intra-firm knowledge integration (Mudambi 2002), we anticipate that HQ units might generate more valuable knowledge. Adding a dichotomous variable (HQ) indicating whether a patent is generated within an HQ establishment controls for this effect. Similarly, a binary variable indicates whether the plant where a patent is generated is a subsidiary (Sub) or not. A control for the size of the firm, the total number of patents generated (Ln firm_count), separates the influence of firm size from the spatial dispersion of a firm's R&D activities. Regional patent counts for each NUTS2 region where establishments are located (Ln nuts2_count), control for spatial variations in opportunities for knowledge sourcing, while the standardized measure of technological similarity between establishment and region knowledge stocks captures the influence of the quality of knowledge matching between establishment and region on patent value (Tech_similarity). This measure might also be thought of as a proxy for firm absorptive capacity (Cohen and Levinthal 1990). The regression models include fixed effects for the time-period and the primary class of patents to control for variations in patent complexity value over time and across technological sectors. Firm fixed effects help control for unobserved heterogeneity at the firm level. All continuous independent variables in the models are logged to handle issues of skew and standard errors are robust to heteroscedasticity. Table 4 provides summary statistics for the continuous variables employed in the regression analysis. These statistics are generated for raw variables, before logging.

Table 4. Summary statistics for continuous variables in the regression analysis.

Variables	Mean	Std. Devtn.	Minimum	Maximum
Average complexity	0.485	0.224	0.00004	1.0
# establishments	14.385	12.809	2	49
# classes	1.942	1.190	1	16
# inventors	2.963	1.980	1	26
# claims	0.691	1.235	0	35
Tech_similarity (standardized)	0.247	0.161	0	0.696
# pats_firm	382.217	552.245	1	2495
# pats_region	3768.754	2845.808	2	9860.959

Notes: Total number of observations = 114,717.

Results from the regression analysis are shown in Table 5. Note that these regressions are run across the full set of 114,717 patent observations. In cases where patents were split across co-inventors located in different establishments, the location of the first-listed co-inventor is used. Table 5, Model 1 shows that in the absence of covariates there is a positive and significant relationship between the log number of establishments over which a firm conducts its knowledge production and the average complexity value of the firm's patents. Model 2 adds covariates to Model 1 showing that larger numbers of CPC classes and larger numbers of inventors on individual patents are positively associated with complexity, while the number of knowledge claims on patents is negatively related to complexity. Patents that are produced with a foreign co-inventor tend to be significantly more complex. Model 2 also shows that there is no statistically significant relationship between HQ plants and average patent complexity, while subsidiaries tend to produce patents that are less complex than average within the firm. Greater levels of technological similarity between establishments and the regions where they are located increases patent complexity. Firm size, measured by the number of patents produced, is positively associated with more complex patents, while host region size is not significantly related to patent complexity. In Model 2, the relationship between the number of establishments over which a firm's R&D is distributed and the average complexity of patents produced remains positive and significant.

Table 5. Knowledge complexity and the extent of knowledge sourcing.

	Dependent variable: patent complexity
	Model 1	Model 2	Model 3
Ln estab_count	0.2073*** (0.0107)	0.2085*** (0.0107)	0.2083*** (0.0107)
Ln class_count		0.0125*** (0.0007)	0.0125*** (0.0007)
Ln inventor_count		0.0036*** (0.0007)	0.0036*** (0.0007)
Ln claims_count		−0.0077*** (0.0009)	−0.0069*** (0.0010)
Foreign_inventor		0.0077*** (0.0009)	0.0077*** (0.0015)
HQ		−6.68E-06 (0.0018)	−0.00003 (0.0018)
Subsidiary		−0.0045** (0.0018)	−0.0045** (0.0018)
Tech_similarity (standardized)		0.0181*** (0.0056)	0.0180*** (0.0056)
Ln firm_count		0.0050*** (0.0011)	0.0050*** (0.0011)
Ln nuts2_count		−0.0008 (0.0006)	−0.0008 (0.0006)
Intra_firm citation			−0.0048 (0.0029)
Intra-firm collabtn			−0.0053 (0.0041)
Ln estab_count*Intra_firm citatn			0.0007 (0.0013)
Ln_estab count*Intra_firm collabtn			0.0020 (0.0016)
Constant	0.0166 (0.0147)	−0.0003 (0.0167)	0.0011 (0.0167)
Firm FE	Yes	Yes	Yes
Time period FE	Yes	Yes	Yes
Primary class FE	Yes	Yes	Yes
Adj R2	0.6990	0.7004	0.7004
# Obs	114,717	114,716	114,716

Notes: The model was estimated as an OLS regression. Significance levels are * = 0.1, ** = 0.05 and *** = 0.01. Standard errors are shown in parentheses and are robust to heteroscedasticity.

Following Singh (2008), measures of intra-firm knowledge integration are proxied by dummies indicating whether the establishment that generates a patent cites patents produced by other establishments within the firm over the previous five years (Intra-firm citation), and whether the establishment that generates a patent has inventors that collaborated with inventors from other establishments of the firm in the preceding five years (Intra-firm collaboration). Examining these variables within the regression model should tell us whether integration of knowledge production activities within firms raises the value of knowledge output, and whether one of these measures of integration is more important than the other. The dummy variables for knowledge integration within the firm were also interacted with the firm's establishment count. Model 3 reveals that there is no statistically significant influence of within firm integration on patent complexity, measured by citations or co-inventor collaboration. The interaction effects of establishment count and the integration measures are similarly insignificant. These results suggest that higher levels of patent complexity are generated by firms when they locate establishments in places where the value of patents is higher than average, rather than as the outcome of integrating subsets of knowledge from different establishments. However, it may be the case that our analysis has not captured all forms of knowledge integration within the multi-unit firm. More work is required to investigate the origins of more complex and valuable patents, how and why knowledge complexity varies over space.

We ran a series of robustness checks on these results. A hierarchical regression model with establishments and firms representing two aggregate levels above the patent observations (captured as random effects) produced qualitatively similar findings. Including individual patents across the different locations at which their co-inventors are located increases the number of observations to 124,480. Running the regressions over this set of observations and using sample weights that give individual patents an equal value produced almost identical results to those reported in Table 5. Finally, using forward citations to measure patent value generated a negative and significant coefficient on the measure of a firm's R&D dispersion, echoing the results of Singh (2008). Clearly, forward citations and patent complexity are not capturing the same form of knowledge value.

Conclusions

As we seek to understand the competitive advantage of firms and regions within the contemporary capitalist economy, the knowledge sourcing literature has taken on added importance. Within economic geography, that literature has tended to ignore the operations of multi-unit firms. This is surprising because firms likely adopt a multi-unit organizational structure, at least in part, to exploit the heterogeneous knowledge sourcing possibilities found in different places. The first research goal of this paper was to explore how multi-unit firms distribute their knowledge production/knowledge sourcing practices across establishments in different locations. Using a firm-patent database that allowed us to track the ultimate corporate ownership of patents, we found that firms use their branch plants and subsidiaries to develop different kinds of technologies. We have not identified earlier research that shows statistically significant evidence of subnational technological variations in patent production within the same firm. These differences become more pronounced as the number of establishments within the firm increase. How this technological variety is distributed between branches of the firm and its subsidiaries, and how it shapes the geography and history of firm and region knowledge stocks are important questions for future research.

A second research question examined links between the types of technology generated within the establishments of multi-unit firms and the knowledge stocks of the regions in which those establishments were located. Results revealed that the location of establishments within the firm could be predicted by the technological similarity of the patents produced in those establishments and that of the regions in which the firm's plants were located. This suggests to us that multi-unit firms take the geographic distribution of knowledge assets into account as they plan the location of their R&D activities. However, this does not mean that geographical knowledge sourcing is the only factor that might have influenced the locational choices of the multi-unit firms in our sample.

That our interpretation of the geography of patent data in multi-unit firms is credible would be strongly supported if these firms could be shown to benefit from knowledge sourcing. In economic geography, there is scant evidence that geographies of knowledge sourcing benefit firms. Within the international business literature, that evidence is mixed. The most compelling results from Singh (2008) show that the international dispersion of firm R&D activities does not raise the forward citation value of firm patents. A third research question in this paper revisits this issue at the subnational level. We question the usefulness of forward citations as a proxy measure of tacit knowledge and suggest that the complexity of technology is a better measure of patent value. Our results show that the more a firm spreads knowledge production across establishments located in different NUTS2 regions of Europe, the greater the average complexity value of the firm's patents. There are at least two mechanisms that might explain this finding. First, that the integration of knowledge produced across establishments leads to more complex patents on average. Second, that by spreading technology development across different centres of innovation, firms might be able to tap into more complex and valuable subsets of knowledge. The integration story is not supported by citation or collaboration linkages between a firm's establishments. More work is clearly required to understand how complex knowledge is discovered and captured by the firm.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Before applying the restrictions to generate the final sample for the analysis, multi-locational firms account for about half of all patents generated in Europe, as defined, between 2001 and 2015.