Do Capabilities Reside in Firms or in Regions? Analysis of Related Diversification in Chinese Knowledge Production

abstract

Do capabilities reside in firms, in regions, or in both? Within economic geography, most contemporary research on diversification examines how local structures condition regional development possibilities. The underlying logic is that capabilities are generated within regions and sometimes shared between them. We challenge that logic, exploring whether capabilities are more likely to emerge within the firm and to flow across spatial boundaries than they are to be built within the region flowing across firm boundaries. Analysis focuses on technological diversification within the establishments of multilocational firms operating across Chinese cities. Overall, the results demonstrate that the knowledge structure of firms is more important than the knowledge structure of cities in shaping diversification within establishments. We show that rates of technological diversification vary according to plant status (headquarters or not), location (core or peripheral city), and on whether plants are introducing more or less complex knowledge. The influence of plant, firm, and regional characteristics on diversification vary markedly across the analytical samples examined.

Key words:

• related diversification
• patents
• capabilities
• China

Since the pioneering work of Penrose (1959) and Cyert and March (1963), firm heterogeneity has been a cornerstone of attempts to understand competitive advantage. According to the resource-based view, the development of firm-specific assets underpins the heterogeneity that fuels competition (Wernerfelt 1984; Barney 1991). Hamel and Prahalad (1990) build their resource-based model of firm performance around competence and capabilities. Kogut and Zander (1992) and Grant (1996) extend this work into the realm of technology. These arguments are put in motion by Teece et al. (1994) and Teece, Pisano, and Shuen (1997) who explore the dynamics of capabilities, after Nelson and Winter (1982), in processes of search and creative destruction powered by competition. The path dependent nature of learning and the gradual accumulation of capabilities places diversification at the center of these dynamics.

Diversification may be understood as the entry of a firm into new activities (Ramanujam and Varadarajan (1989). Those activities might be new product lines, new markets, new technologies or new forms of organization. Following Penrose (1959), as firms learn to use their resources more efficiently, they build excess capacity and exploit possibilities that are close to their core capabilities. In terms of technology, the local nature of search is well known (Atkinson and Stiglitz 1969; Stuart and Podolny 1996) and, for many, represents the recombination of existing technological competence with new ideas sourced from a technology landscape that is complex and not well mapped (Fleming and Sorenson 2001). Over time, parts of the technology landscape become less of a terra incognita as knowledge complementarities emerge supporting forms of technological lock-in and related trajectories of diversification (Dosi 1982; Breschi, Lissoni, and Malerba 2003; Leten, Belderbos, and Van Looy 2007; Kogler, Essletzbichler, and Rigby 2017).

Within economic geography and related fields, considerable attention has focused on the related diversification of multilocational firms and of the countries and regions in which they are active (Pavitt, Robson, and Townsend 1989; Cantwell and Piscitello 2000; Cantwell and Iammarino 2001). More recent investigation of regional diversification may be traced to the product space research of Hidalgo et al. (2007) and to the paper by Frenken and Boschma on regional branching (2007). Key to these works is the finding that regions do not diversify along random paths; rather they accumulate capabilities that are related to their existing know-how (Boschma and Iammarino 2009; Neffke, Henning, and Boschma 2011; Boschma, Minondo, and Navarro 2013; Boschma, Balland, and Kogler 2015) and to the knowledge sets of neighboring regions with whom they interact more intensively (Rigby 2015).

While the focus of this recent work is on diversification within regions, it is important to acknowledge that regional economies comprise multiple economic actors. Thus, the regional diversification observed results from the decisions of individual agents to alter the range of activities in which they engage, or from dynamics introduced to the region by firm entry and exit. Ignoring the latter for the moment, we are primarily interested in whether the diversification decisions of economic agents are shaped by their own internal (firm-specific) capabilities or whether they result from capabilities that are shared across firms within local and regional economies. Capabilities here are understood as the set of tangible and intangible assets that are employed in processes of competition, including diversification. Those capabilities may be proxied by the range of activities in which economic agents, or groups thereof, are already specialized. This range impacts the potential trajectories of diversification. An active literature on geographies of knowledge sourcing and knowledge flow intersects with the questions raised above (Bathelt, Malmberg, and Maskell 2004; Fitjar and Rodríguez-Pose 2013; Tödtling, Asheim, and Boschma 2013). The focus on the region in much of the diversification literature suggests, at least implicitly, that capabilities are primarily embedded territorially and shared by the economic agents that comprise the regional economy. Yet, is this the case? We know that technology is highly proprietary and closely guarded by the firm. Where then do technological capabilities reside?

New work by Lo Turco and Maggioni (2016, 2019) examining firm and local relatedness on product diversification within Turkey, and the papers by Neffke et al. (2018) and Elekes, Boschma, and Lengyel (2019) on “agents of change” are directed at a more detailed understanding of the forces that shape diversification. The current article extends this research. Our empirical work is separated into two parts. In the first part, we develop a standard model of regional diversification for Chinese cities. We engage in this analysis because most research on regional diversification focuses on the US and Europe, with a relatively small number of exceptions (see Poncet and De Waldemar 2013; Zhu, He, and Zhou 2017; Alonso and Martin 2019). It remains an open question whether the process of regional diversification identified in past studies (Neffke, Henning, and Boschma 2011; Boschma, Balland, and Kogler 2015) operates the same way in different parts of the world, especially within countries at different levels of economic development. The second part of our empirical work returns to the question posed above regarding the location of capabilities. This work focuses on a sample of multilocational firms engaged in knowledge production across Chinese cities. For the branches of these firms, we examine whether the capabilities that influence related technological diversification are located within the branches themselves, within the regions in which the branches are located, or whether they derive from the firm of which the branch is a part.

The first set of results shows that technological diversification within Chinese cities operates in much the same way as regional diversification elsewhere. In aggregate, diversification within Chinese cities is strongly conditioned by the capabilities that have already been established at the city level. Diversification is also positively influenced by the technological characteristics of cities that are linked by patterns of co-inventor collaboration. The second set of results show that the relatedness density of existing technological assets within the branches of multilocational firms, within their parent firms, and within the cities where branches are located all influence diversification. However, firm density effects tend to be at least three times stronger than city density effects in shaping the path of new technological specializations. Separating the headquarters (HQ) branches of multilocational firms from non-HQ branches reveals that the relative influence of firm and city relatedness varies significantly between branch types. We also show significant differences in the impact of firm and local relatedness on diversification in non-HQ establishments separated into core and periphery cities in China and between firm branches that are producing more or less complex patents.

The rest of the article is organized in three sections. In the following section, a short review of the literature highlights the role of relatedness in recent thinking about diversification and discusses a number of extensions to early models of related diversification. Thereafter, we present our data and analysis. We move from an overview of sources, through some descriptive statistics by way of scene setting, to analysis of the standard model of regional related diversification and then to technological diversification within the branches of a sample of multilocational firms. A final section provides a brief conclusion, summarizing the main findings and their implications for potential future research.

Literature Review

Territorial economies comprise assemblages of economic agents, institutions, and resources of various kinds that are interconnected with those elsewhere. Capitalist competition, worker struggle, and political pressures emanating from environmental and other concerns drive continuous change in these assemblages in terms of the mix of products supplied and the technologies used to produce them, in firm organization, interfirm linkages, and institutional forms that operate across multiple spatial scales (Schumpeter 1939; Tushman and Anderson 1986). Many of these changes are nonrandom; they evolve out of existing sets of capabilities, some local and some not, that reflect longer-running trajectories of competition and past choices by boundedly rational economic agents (Rigby and Essletzbichler 1997). Sets of capabilities typically evolve relatively slowly, though in times of crisis economic adjustment can be abrupt and painful as firms and regions are forced to reinvent themselves, raising important questions about resilience (Freeman and Perez 1988; Christensen 1997; Geels 2002; Simmie and Martin 2010). For the most part, market forces select the products that are favored and so direct more aggregate patterns of technological change as well as firm and regional fortunes (Nelson and Winter 1982).

The diversification of regional economies is examined as a branching process by Frenken and Boschma (2007), in which new activities draw on and recombine related local assets. Klepper (2007) privileges the role of the firm in providing such assets, while Saxenian (1996) and Storper (1995) look to particular constellations of local institutions. The broad literature on agglomeration, clusters, and learning regions places more weight on the importance of place-based factors, including the mix of economic agents and their interaction along with local social capital, in driving the pattern of regional economic development (Camagni 1991; Glaeser et al. 1992; Lundvall 1992; Maillat 1995; Giuliani and Bell 2005; Morgan 2007). Others question the significance of the local asset base altogether (Bathelt, Malmberg, and Maskell 2004; Fitjar and Rodríguez-Pose 2017).

Quantitative analysis of regional diversification may be traced to Hidalgo et al. (2007) and their use of the concept of relatedness to explain how the export baskets of countries evolve as part of the process of development. Boschma, Minondo, and Navarro (2013) build on product-based measures of relatedness from export data to trace the emergence of new industries across Spanish regions. Neffke, Henning, and Boschma (2011) utilize a measure of industry relatedness based on overlapping product portfolios to explore the creation of new growth paths within Swedish regions. They show that growth paths linked to the existing industrial base of the region have a higher probability of occurring. Boschma, Balland, and Kogler (2015) build measures of relatedness between patent classes to explain patterns of technological diversification across US cities, to which Rigby (2015) adds geographic spillovers. Colombelli, Krafft, and Quatraro (2014) follow a similar proximity-based approach to explain the emergence of nanotechnology in EU regions. Outside the US and Europe, Alonso and Martin (2019) analyze the process of regional diversification in Mexico and Brazil. Tanner (2016) provides some important correctives to the broader claims of much of this empirical work.

Regardless of the measure of relatedness used, most of the work just examined looks at capabilities as being embedded within regions. This gives rise to models of diversification where existing regional capabilities are the primary drivers of the direction of economic change. For Beugelsdijk (2007), such thinking raises concerns of an ecological fallacy. To be sure, the focus on regional aggregates reflects the difficulty of accessing firm-level data over space, yet much existing work on relatedness and diversification raises old questions about the relative importance of firm and regional characteristics in understanding the economic dynamics of regions (Markusen 1996; Sternberg and Arndt 2001; Boschma 2004).

In evolutionary economic geography, a number of papers have begun the process of unpacking regional economic diversification seeking to identify the “agents of change” (Neffke et al. 2018). Thus, Lo Turco and Maggioni (2016) investigate whether the addition of new products to a firm’s product basket is influenced by local capabilities as well as by the firm’s internal capabilities. In the case of Turkey, they report that local capabilities play a larger role than firm capabilities in shaping product diversification after controlling for a number of firm characteristics. However, they also reveal that firm capabilities are more important than local capabilities in directing new product development in more peripheral eastern provinces of the country. In subsequent papers, Elekes, Boschma, and Lengyel (2019) and Lo Turco and Maggioni (2019) look at the role of foreign multinational enterprises (MNEs) versus local firms in shaping the path of regional economic diversification in emerging economies. They find that extraregional flows of knowledge, transmitted via foreign MNEs, play the dominant role in local economic discovery. This extends the earlier work of Cantwell and Piscitello (2000) and Boschma and Iammarino (2009) on the significance of MNEs in transmitting knowledge over space.

Within the context of China, a number of authors have begun to outline patterns of diversification across firms and regions. In an early study, Zhao and Luo (2002) explore product diversification, the ownership structure, and performance of foreign manufacturing subsidiaries operating in China. They report that related product diversification improves subsidiary performance over unrelated diversification. Lin and Wang (2012) show that regional industrial diversification is linked to latent patterns of comparative advantage. Using firm-level export data for the period 2000–2006, Poncet and De Waldemar (2013) use the measure of product relatedness from Hidalgo et al. (2007) to explore the relationship between the export performance of firms and patterns of comparative advantage at the city level. They reveal that firm-level exports grow faster for products that have higher relatedness density to the product spaces of cities from which exports originate. Wang, Ning, and Prevezer (2015) use Chinese patent data to study how the relationship between the volume of invention and technological diversification in China has evolved, after Archibugi and Pianta (1992) and Cantwell and Vertova (2004). This work is extended by Wang et al. (2016) who link diversification to the innovation capability of Chinese provinces. Using annual firm survey data, Guo and He (2017) examine changes in industry relatedness across different regions in China. They show that related diversification characterizes the evolution of industry space in coastal regions, while more unrelated forms of diversification are found elsewhere. Using city-level export data, Zhu, He, and Zhou (2017) push this work a little further, revealing that extraregional linkages, internal innovation, and state policy have allowed some Chinese regions to engage in new path creation and evolve more rapidly than others. Zhou, Zhu, and He (2019) use the same export data in an attempt to separate region and firm effects on related diversification. However, they assume that each establishment in their data represents a unique firm, and thus they do not capture a firm effect that links diversification within plants that are part of a multilocational firm. Separating firm from regional capabilities thus remains an open question that we tackle explicitly in the second part of our empirical analysis.

There is considerable work left to do on related diversification in China and elsewhere. For all researchers interested in geographies of diversification, related or otherwise, it is important to recognize that regions are not economic agents, even though policy makers can actively shape the political–economic environment within which competition unfolds. Thus, when writing about regional diversification, it should be clear we are referring to change in the activities of firms and other actors that comprise a particular region. Linking such changes to a region’s capabilities is a more complex and more interesting question that speaks to local and nonlocal forms of knowledge sharing. In truth, in much of the earlier research on related diversification within regions, the region itself is little more than a unit of observation. Separating the capabilities that are locked within the boundaries of the firm from those that flow across firm boundaries, within and between regions, might allow us to construct measures of capabilities that are geographic rather than corporate. Indeed, this is part of the task we have set ourselves below.

Data and Analysis

This section of the article comprises three subsections. The first subsection outlines our data sources and presents some basic descriptive statistics. The second subsection examines a standard model of related diversification that links the development of new technology classes within Chinese cities to the relatedness density of their existing patent stocks. This simple model is extended by incorporating technology spillovers between cities linked through firm collaboration. The third subsection extends the literature on place-based capabilities to consider the influence of relatedness density at the branch, firm, and city levels on diversification within the (city-based) branches of multilocational firms.

Sources of Data and Descriptive Statistics

Exploration of the structure of knowledge in Chinese cities makes use of domestic invention patents filed with the Chinese Intellectual Patent Office (SIPO). To the best of our knowledge, this is the first article to examine technological diversification in Chinese cities using patent data. Patents have become the standard means of tracking knowledge production and the pattern of technological diversification at the subnational level, largely because of their availability and the wealth of information they contain (Feldman and Kogler 2010). However, it should be remembered that not all new knowledge is patented and that patent statistics themselves are biased indicators of invention, as pointed out by Pavitt (1985) and Griliches (1990).

We use the filing (application) date on SIPO patents to mark the timing of invention. The nature of the knowledge produced is characterized by the four-digit International Patent Classification (IPC) codes that are listed on each patent. The geography of Chinese patents is indicated by the location of the patent assignee(s). Patents with multiple assignees are fractionally split between the cities where those assignees are located. Note that multilocational firms do not register all their patents at a single HQ location. We exploit this fact in our analysis. The period of investigation runs from 1991 to 2015 and focuses on five-year time steps. The patents examined are all granted. We stop analysis in 2015 because of right censoring in the data that occurs because of the time lag between filing a patent and its grant date.

Table 1 reports the growth of knowledge production in China since 1991, disaggregated into seven major classes after Schmoch (1999). The IPC itself distributes patents across eight main classes, but that classification is not as useful in terms of separating key intellectual claims by a broad sector of applications. Taking the twenty years between the midpoint of our first time period (1991–95) and the midpoint of our last time period (2011–15), the number of inventor patents in China expanded at an annual average compound growth rate of 23.9 percent. That is an astonishing rate of increase. Most gains have occurred since 2000, so the recent growth in knowledge production within China is remarkable. That growth is relatively evenly balanced across the seven main classes reported in Table 1, with drugs and pharma recording the lowest annual average compound rate of growth at 19.6 percent and the electronics sector experiencing the most rapid growth at close to 30 percent per year on average between the early 1990s and 2015.

Table 1 Aggregate Patent Numbers over Three Time Periods

Aggregate Patent Class	1991–95	2001–15	2011–15	Annual Rate of Growth
Electronics	3723.6	53056.8	685869.2	0.298
Computers & Communications	4304.7	22738.4	367063.5	0.249
Chemicals	8935.6	40033.7	425544.2	0.213
Drugs & Pharma	9775.2	47591.6	351120.3	0.196
Industrial Process	4396.7	24751.7	417003.6	0.256
Machinery & Transport	6226.3	34064.9	506056.0	0.246
Miscellaneous	2142.4	9286.1	141820.9	0.233
Total	39504.5	231523.2	2894477.7	0.239

Although different classes of patents have grown relatively evenly in the past thirty years, the spatial structure of invention changed a great deal. Table 2 and Figure 1 reveal the changing geography of Chinese invention since 1991 (see also Sun 2000). The geography of knowledge production in China, at least as measured by patents, has remained relatively concentrated, though it has moved southward. In 1991 to 1995, guided by the national economic development strategy, resource-based cities, such as the old industrial bases in the Northeast and the Bohai Rim, registered relatively high numbers of patents. Some provincial capitals or regional central cities, such as Chengdu, Chongqing, Zhengzhou, Xi’an, Wuhan, Changsha, and Lanzhou, also captured a high share of patent production. In the most recent period (2011–15), invention in China is mainly distributed in the eastern coastal areas, reflecting their diversified industrial structure and abundant human capital. The Beijing–Tianjin area with Beijing as the center, the Yangtze River Delta with Shanghai as the center, and the Pearl River Delta with Shenzhen as the center have become key nodes of knowledge production.

Table 2 Top 10 Sites of Invention in China

Rank	1991–95		2001–05		2011–15
1	Beijing	6,028	Beijing	36,153	Beijing	291,512
2	Shanghai	1,681	Shanghai	29,077	Shanghai	187,058
3	Shenyang	1,296	Shenzhen	21,082	Shenzhen	156,914
4	Tianjin	1,190	Tianjin	14,041	Suzhou(Jiangsu)	118,091
5	Chengdu	1,050	Hangzhou	7,708	Qingdao	90,026
6	Nanjing	960	Changsha	6,599	Nanjing	84,071
7	Xian	893	Guangzhou	6,155	Tianjin	83,523
8	Wuhan	879	Nanjing	5,770	Chengdu	74,821
9	Guangzhou	798	Wuhan	4,909	Changzhou	72,974
10	Dalian	755	Chengdu	4,895	Wuxi	70,255

Figure 1. Patent distribution in Chinese cities, 1991–95 and 2011–15.

Figure 2 highlights patterns of collaboration in knowledge production between assignees located in different Chinese cities in 1991–95 and 2011–15. The ties between each pair of cities reflect the overall number of patent collaborations that link them. The darker the color of the ties, the more cooperation between economic agents within each pair of cities. It is clear from Figure 2 that the Chinese city collaboration network has changed markedly since the early 1990s. In the early period, the inventor collaboration network was dominated by a single central city, Beijing. Today, the collaboration network is polycentric, focused on Beijing, Shanghai, Shenzhen, and Chengdu. While intercity collaborations are dominated by these four cities, it is interesting to note that economic actors in Shanghai and Shenzhen engage in considerable collaboration with regional partners, much more so in fact than agents in Beijing and Chengdu. This may reflect regional policy and industrial structure.

Figure 2. Collaborative structure of Chinese urban invention, 1991–95 (top panel) and 2011–15 (bottom panel).

Investigation of technological diversification within Chinese cities requires construction of a Chinese knowledge space that represents the distance between IPC technology classes as recorded on domestic Chinese patent records. Coclass data gathered from individual patents are used to measure the proximity between all pairs of the 629 IPC classes listed on SIPO data. This technique follows the earlier work of Jaffe (1986), Breschi, Lissoni, and Malerba (2003), and Kogler, Rigby, and Tucker (2013). To measure the proximity, or knowledge relatedness, between patent technology classes we employ the following method. Let P indicate the total number of patent applications in the given subperiod. Then, let $F_{ip}=1$ if patent record p lists the classification code i, otherwise $F_{ip}=0.$ Note that i represents one of the 629 primary technology classes into which the knowledge contained in patents is classified. In a subperiod, the total number of patents that list technology class i is given by $N_i=\sum _p{F}_{ip}$. In similar fashion, the number of individual patents that list the pair of coclasses i and j is identified by the count $N_{ij}=\sum _p{F}_{ip}{F}_{jp}$. Repeating this coclass count for all pairs of IPC classes yields a symmetric technology class cooccurrence matrix C the elements of which are the coclass counts $N_{ij}$. The coclass counts are converted into measures of proximity through division by the square root of the product of the number of patents in each of the two classes, or

$S_{ij}=N_{ij}/\sqrt{N_i\ast N_j}$

where $S_{ij}$ is an element of the standardized cooccurrence matrix (S) that indicates the technological proximity, or knowledge relatedness, between all pairs of patent classes in a given period. The elements on the principal diagonal of S are set to 1. An $S_{ij}$ value of zero would indicate that there are no patents in a given period that contain class codes i and j.

The network of technological relatedness across the 629 IPC patent class nodes is mapped with the aid of UCINET (Borgatti, Everett, and Freeman 2002). The visualizations of the Chinese knowledge space in Figure 3 are generated with the Gower-scaling metric (Gower 1971). The node colors in the figure represent the seven aggregate technology groups identified earlier within the IPC. Node size indicates the number of patents granted within a class. In 1991–95 the largest node is A61K (preparations for medical, dental, or toilet purposes) with 5,289 patents. In 2011–15, the largest node (G06F = electric digital data processing) contains 133,275 patents. Figure 3 shows that technology classes cluster within their more aggregate (color) groupings. The clustering of technology nodes indicates that they share a common knowledge base. The closer the nodes, the higher the relatedness between them and the greater the cognitive overlap. The electronics cluster is clear in Figure 3 for the period 2011–15. The link between the chemicals classes (black) and the drugs and pharma (yellow) technologies is also apparent. The figure also makes clear the relatively rapid shift in the nature of Chinese invention.

Figure 3. Chinese knowledge space, 1991–95 and 2011–15.

Notes: Red = Electronics (1), Green = Computers & Communications (2), Chemicals = Black (3), Yellow = Drugs & Pharma (4), Blue = Industrial Process (5), Purple = Machinery & Transport (6), Grey = Miscellaneous (7).

A Model of Related Diversification

The standard model of related diversification imagines that cities (or regions and countries) will diversify into those technology classes that are related to their existing technological base. The logic underpinning this model is that the economic agents that comprise an urban economy build sets of capabilities over time that allow them to produce distinct types of technological knowledge. The path dependent nature of capability development means that firms and, in aggregate, regions develop industrial and technological repertoires that are not rapidly changed (Grabher 1993; Rigby and Essletzbichler 1997). Thus, over time, they tend to accumulate new sets of capabilities that are closely connected to their existing knowledge cores.

We track technological diversification by tracing measures of revealed technological advantage (RTA) for all technology classes within cities from one time period to the next. RTA is typically expressed as a (0/1) binary variable that takes the value one when the city share of patents in a class exceeds the share of a reference region, typically the sum of geographic units examined. In this case, the reference region comprises the 286 Chinese cities in our data frame. When an RTA value switches from zero to one, then a city has successfully diversified into a new technology. Note that the entry of a city into a technology type previously unoccupied by the agents that constitute the city economy is also examined. We test the impact of relatedness density on technological diversification with a fixed effects regression model that takes the following form:

(1) $RT{A}_{ict}={\beta }_0+{\beta }_{1}Densit{y}_{ict-1}+{\beta }_{\mathit{k}}{X}_{{\mathit{k}}_{cit-1}}+{\gamma }_c+{\gamma }_t+{\epsilon }_{ict}$(1)

In Equation (1)(1) $RT{A}_{ict}={\beta }_0+{\beta }_{1}Densit{y}_{ict-1}+{\beta }_{\mathit{k}}{X}_{{\mathit{k}}_{cit-1}}+{\gamma }_c+{\gamma }_t+{\epsilon }_{ict}$(1) , the dependent variable indicates RTA in city c, technology class i at time t. Equation (1)(1) $RT{A}_{ict}={\beta }_0+{\beta }_{1}Densit{y}_{ict-1}+{\beta }_{\mathit{k}}{X}_{{\mathit{k}}_{cit-1}}+{\gamma }_c+{\gamma }_t+{\epsilon }_{ict}$(1) models the probability of a city developing RTA as a function of the relatedness density of a technology class to the existing knowledge base in the city recorded at time t-1. The relatedness density of technology class i in city c at time t is calculated as

$RelatednessDensit{y}_{ict}=\frac{{\sum }_{j\ne i}{S}_{ijt}\ast RT{A}_{cjt}}{{\sum }_{j\ne i}{S}_{ijt}}$

The relatedness density values range from 0 to 1, with 0 indicating that a city does not have RTA in any of the technology classes j that are related to class i. As the relatedness density index approaches 1, then cities have RTA in knowledge stocks j that are increasingly strongly related to technology in class i. In other words, relatedness density reflects the potential of a region to develop new technological specializations based on existing capabilities (Balland et al. 2019). Theory suggests that the density variable should be positively related to the change in RTA within city–technology pairings.

The term $\beta X$ in Equation (1)(1) $RT{A}_{ict}={\beta }_0+{\beta }_{1}Densit{y}_{ict-1}+{\beta }_{\mathit{k}}{X}_{{\mathit{k}}_{cit-1}}+{\gamma }_c+{\gamma }_t+{\epsilon }_{ict}$(1) represents k = 5 covariates to be estimated. We include two city-size measures, one captured by the city’s population and the second captured by the total number of patents produced in the city. Larger cities tend to be more diverse, though we are agnostic on the expected sign of the city-size variables on the probability of RTA emerging in a specific technology class. The range of technologies generated within a city is measured with a technology class Herfindahl. We hypothesize that the Herfindahl exhibit a negative relationship with RTA, as more specialized cities would tend to have RTA in fewer classes than less specialized cities. A measure of competition over technological rents is proxied by the number of firms and other organizations that patent in a city divided by the number of patents. Competition is expected to increase the probability of RTA and new class entry as diversification is a key competitive strategy. The national rate of growth of patents by technology class captures nationwide technological dynamics and should be positively related to the dependent variable. City and time fixed effects are added to all models in Table 3 and standard errors are robust.

Table 3 Logit Regressions of Related Diversification in Chinese Cities, 1991–2015 (Logits)

	Dependent Variable
	City RTA			City Entry
	Model 1	Model 2	Model 3	Model 4
Lag relatedness density	1.5841*** (0.0171)	1.5861*** (0.0204)	1.5823*** (0.0205)	1.1647*** (0.0215)
Lag city population		−0.0000*** (7.30E-07)	−0.0000*** (7.30E-07)	−8.72E-06*** (6.69E-07)
Lag city Patent sum		−0.0000*** (1.70E-06)	−0.0000*** (1.74E-06)	−0.0001*** (4.29E-06)
Lag city Herfindahl		−1.2742*** (0.1604)	−1.2808*** (0.1605)	−0.4467*** (0.1449)
Lag technology competition		−0.0067 (0.0178)	−0.0065 (0.0178)	−0.0320 (0.0187)
Lag class rate of growth		0.0000 (0.0000)	0.0000 (0.0000)	0.0010*** (0.0001)
Lag city-tech spillover			1.1498** (0.4986)	3.6743** (0.5581)
Constant	−3.2463*** (0.0756)	−2.6348*** (0.0826)	−2.6335*** (0.0826)	−2.7898*** (0.0722)
Time FE	Yes	Yes	Yes	Yes
City FE	Yes	Yes	Yes	Yes
Observations	628,685	602,309	602,309	602,309

Notes: All models are fit with robust standard errors shown in parentheses. *Significant at the 0.1 level, **Significant at the 0.05 level, ***Significant at the 0.01 level. The dependent variable in Model 4 is the presence/absence of a technology class in a city. In all models the dependent variable takes the value 0 in period t-1 and the value 0 or 1 in period t.

Results from estimating slightly different variants of the model in Equation (1)(1) $RT{A}_{ict}={\beta }_0+{\beta }_{1}Densit{y}_{ict-1}+{\beta }_{\mathit{k}}{X}_{{\mathit{k}}_{cit-1}}+{\gamma }_c+{\gamma }_t+{\epsilon }_{ict}$(1) are reported in Table 3. The logit model is used because of the binary nature of the dependent variable. Model 1 is incorporated as a baseline in order to explore changes in the relatedness density coefficient with the addition of various controls. As hypothesized, the lagged value of relatedness density is a positive and significant predictor of technological diversification at the city level. The coefficient in the model represents the impact of a unit change in relatedness density on the log odds of the probability of RTA being established in a technology class.

Model 2 incorporates city level covariates. The city-size variables, population and the sum of patents, have coefficients that are negative and significant. Thus, holding constant the values of other variables, the probability of diversification is lower in larger cities. This result holds regardless of whether population, the sum of patents, or both variables are used as the size measure. The Herfindahl operates as expected, with increases in the technological specialization of cities dampening the probability of diversification. The competition variable has no influence on diversification. The coefficient for the class rate of growth is positive, though not significantly related to technological diversification.

Model 3 adds a collaboration weighted lag of relatedness density between cities. This is built in two steps. First a matrix of standardized values (cosine index) of collaboration strength between all pairs of cities is produced. A second matrix contains measures of relatedness density for all 629 technology classes for each city. The product of these two matrices is a collaboration-weighted lag of relatedness density values for each city–technology class pair. This collaboration-weighted city–technology spillover variable is used to indicate whether there is a substitution or complementarity effect in patterns of related diversification between cities. The positive value of the spillover measure suggests the effect is one of complementarity, indicating that city-specific knowledge flows resulting from collaboration raise the likelihood of diversification in partner cities.

Model 4 employs a different dependent variable, that of entry by a city into a technology class in which it has not previously generated any patents. The related diversification literature is split almost evenly in terms of whether changes in the binary RTA variable or entry into new fields should be the dependent variable. The results for Model 4 are broadly consistent with those already reported, though there are three important variations. First, note that the coefficient on the relatedness density measure is considerably lower in Model 4 than in Model 3. This makes sense, for it is more difficult to move into a brand-new technological field than it is to generate extra patents in an established technology. Second, the influence of the rate of growth of a technology is more than an order of magnitude greater in the case of entry. This is also readily understood, for if there is any growth from 0, entry must occur. Finally, the influence of the city–technology class spillover measure is considerably larger on entry than on the establishment of RTA. This result confirms that collaboration is an important mechanism through which economic agents learn about new technological possibilities.

In terms of economic effects, the coefficients in the model are log odds ratios that report how a one-unit change in an independent variable influences the logarithm of the probability of technological diversification divided by the probability of no technological diversification. The nonlinear nature of the logit estimator means that the partial regression coefficients vary with the scale of the original variables. For Model 3 and using the margins command in STATA, evaluated with independent variables at their means and including fixed effects, an increase of one standard deviation in relatedness density would raise the average probability of diversification by only about six percentage points. For Model 4, this marginal effect is approximately four percentage points. The marginal effects from the logits are small, echoing similar findings for diversification in Swedish regions reported by Neffke, Henning, and Boschma (2011). Note that we get similar results on key variables using the linear probability model. We also get a positive and significant coefficient on relatedness density if we run the model in panel form as a fixed effects conditional logit where the units of observation are technology classes within cities.

Related Diversification within Multilocational Firms: Do Capabilities Reside in Firms or Regions?

The standard model of related diversification is typically operationalized with units of observation that are spatial—countries, cities, or regions. In large part, this reflects the availability of geographic information and the difficulty of assembling firm-level data. Development of the model over spatial units pushes the researcher to assume, at least implicitly, that the capabilities that really count are located within regions, though they may sometimes flow between them as the analysis above indicates. For the most part, then, capabilities are seen as residing in locations rather than in firms, moving across firm boundaries within regions more readily than they move within firms across space. However, there are strong reasons to doubt this assumption, especially when dealing with technologies that tend to be highly proprietary. In this subsection of the article, we explore whether evidence supports the notion that capabilities are located within firms or within regions.

Of course, if capabilities reside in firms, then it might be said that certain capabilities are also located in the regions where specific firms operate. Still, we must be careful on this issue because a great deal of analysis within economic geography assumes that the co-location of economic agents implies some sharing of capabilities and the emergence of place-specific assets and relationships that fuel regional performance. While it is undoubtedly the case that place-specific assets of tangible and intangible kinds do emerge within economic clusters (Storper 1995; Baldwin et al. 2008), the impacts of these assets are heterogeneous (Potter and Watts 2011; Rigby and Brown 2015) and not broadly quantified. In the analysis below, we separate the influence of firm-specific, city-specific, and branch-specific forms of relatedness density on technological diversification.

Investigation focuses upon a subsample of Chinese patents that are connected to multilocational firms. These are firms that have branches in different Chinese cities and that patent in each of those cities. The multilocational firms were identified with firm data from Bureau van Dijk (BVD). Because of the time-intensive nature of identification, our analysis focuses only on the largest 200 multilocational firms operating across Chinese cities. These firms are responsible for generating around 700,000 patents between 1991 and 2015, some 20 percent of the Chinese total. On average, each of these multilocational firms has a branch in five different Chinese cities. The largest firm, State Grid Corporation of China, had sixty-seven branches that generated patents across Chinese cities in the most recent period examined.

In order to explore the location of capabilities, we set up another related diversification model, this one focused on the activities of the branches of multilocational firms. For each branch we note those technologies (IPC classes) in which the branch attained RTA across our five-year time windows. Measures of relatedness density are then built for all observations at the branch, firm, and city level. Note that our reference data set includes only the patent data within the multilocational firms that we examine. This reference set provides the denominator in the RTA calculations. The multilocational firm data includes patent information from all the branches that belong to the firm (through ownership). Subsidiaries and joint ventures are not included with these data.

Somewhat more formally, our dependent variable, RTA, is now defined at the level of a branch as

$RT{A}_{branchi}=\frac{Patent{s}_{ifc}/{\sum }_{i}Patent{s}_{ifc}}{{\sum }_i{\sum }_{f}Patent{s}_{ifc}/{\sum }_i{\sum }_f{\sum }_{i}Patent{s}_{ifc}}$

where i refers to the technology (IPC patent) class, f to the firm, and c to the city. The time subscript is omitted for clarity. Note again that the overall denominator here is the class share in the reference region (the sum of all branches across cities in China that are owned by the two hundred firms that we examined). RTA at the firm level is defined as

$RT{A}_{firmi}=\frac{{\sum }_{c}Patent{s}_{ifc}/{\sum }_i{\sum }_{c}Patent{s}_{ifc}}{{\sum }_c{\sum }_{f}Patent{s}_{ifc}/{\sum }_i{\sum }_f{\sum }_{c}Patent{s}_{ifc}}$

where the overall denominator is the same as in the RTA for the branch. Finally, RTA at the city level is defined as

$RT{A}_{cityi}=\frac{{\sum }_{f}Patent{s}_{ifc}/{\sum }_i{\sum }_{f}Patent{s}_{ifc}}{{\sum }_c{\sum }_{f}Patent{s}_{ifc}/{\sum }_i{\sum }_f{\sum }_{c}Patent{s}_{ifc}}$

These different measures of RTA allow us to define three relatedness density terms in our model, one for the branch, firm and city:

$Densit{y}_{branch,i}=(\sum _{j\ne i}{S}_{ij}\ast RT{A}_{branchi})/\sum _{j\ne i}{S}_{ij}$

$Densit{y}_{firm,i}=(\sum _{j\ne i}{S}_{ij}\ast RT{A}_{firmi})/\sum _{j\ne i}{S}_{ij}$

$Densit{y}_{city,i}=(\sum _{j\ne i}{S}_{ij}\ast RT{A}_{cityi})/\sum _{j\ne i}{S}_{ij}$

where $S_{ij}$ is the relatedness between classes i and j, and where RTA = 0/1. The new model to be estimated is

(2) $\begin{array}{rl}& RT{A}_{branch,it}={\beta }_{branch}Densit{y}_{branch,it-1}+{\beta }_{firm}Densit{y}_{firm,it-1}+{\beta }_{city}Densit{y}_{city,it-1}\\ & +{\beta }_k{X}_{kt-1}+F{E}_{time}+F{E}_{firm}+F{E}_{city}+\epsilon \end{array}$(2)

where $X_{kt-1}$ represents k time-varying measures of the size of firms, cities, and classes, and the remaining terms are defined above. While Equation (2)(2) $\begin{array}{rl}& RT{A}_{branch,it}={\beta }_{branch}Densit{y}_{branch,it-1}+{\beta }_{firm}Densit{y}_{firm,it-1}+{\beta }_{city}Densit{y}_{city,it-1}\\ & +{\beta }_k{X}_{kt-1}+F{E}_{time}+F{E}_{firm}+F{E}_{city}+\epsilon \end{array}$(2) represents the base model in the following analysis, that model is extended by splitting the analytical sample into different binary groupings and capturing the significance of differences in model parameters across groups via interaction effects.

Results from estimating the model of technological diversification within the branches of multilocational firms are shown in Table 4. We add time, firm, and city fixed effects to remove the influence of characteristics that are specific to these units in the analysis. Standard errors are robust throughout the analysis. To ease interpretation, all continuous variables are normalized. Models 5, 7, 8, and 9 examine changes in the binary value of RTA as the dependent variable, while Model 6 looks at entry into technology classes previously unoccupied by individual firm branches. In the analysis below, we focus on the relative importance of firm and city density on diversification as a way of examining the contributions of firm-based and place-based capabilities.

Table 4 Related Diversification in Branch-Level Data, 1991–2015 (Logits)

Dependent Variable	Branch RTA	Branch Entry	Branch RTA	Branch RTA	Branch RTA	Branch RTA
	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10
Branch Density (Normalized)	0.1353*** (0.0032)	0.1440*** (0.0030)	0.1718*** (0.0081)	0.1366*** (0.0041)	0.1123*** (0.0079)	0.1314*** (0.0058)
Firm Density (Normalized)	0.3253*** (0.0040)	0.2721*** (0.0037)	0.3156*** (0.0104)	0.3604*** (0.0041)	0.3709*** (0.0046)	0.3600*** (0.0059)
City Density (Normalized)	0.0480*** (0.0049)	0.0356*** (0.0042)	0.0010 (0.1133)	0.0647*** (0.0057)	0.0790*** (0.0069)	0.0357*** (0.0083)
Inventors per firm	−0.0024 (0.0456)	−0.3294*** (0.0372)	0.3408** (0.1363)	0.0055 (0.0457)	−0.0503 (0.0582)	−0.0991 (0.0613)
Inventors per city	−0.4940*** (0.0314)	−0.4960*** (0.0250)	−0.8821*** (0.0712)	−0.4107*** (0.0399)	−0.8579** (0.3565)	−0.2267*** (0.0687)
Inventors per class	0.1881*** (0.0057)	0.3247*** (0.0056)	0.2311*** (0.0125)	0.2197*** (0.0059)	0.2019*** (0.0068)	0.2395*** (0.0533)
Private Dummy			0.2452 (0.2283)
HQ Dummy				1.4539*** (0.0317)
Core Dummy					0.4581*** (0.1117)
Complexity Dummy						−0.1155*** (0.0241)
Interact branch density			−0.0457*** (0.0088)	−0.0676*** (0.0158)	0.0317*** (0.0092)	−0.0080 (0.0081)
Interact firm density			0.1159 (0.0112)	−0.0640*** (0.0158)	−0.0023 (0.0101)	0.0305*** (0.0078)
Interact city density			0.0579*** (0.0123)	−0.0343** (0.0103)	−0.0538*** (0.0129)	0.0303*** (0.0113)
Interact firm Inventors			−0.3751*** (0.1296)	0.0011 (0.0754)	0.1849*** (0.0535)	0.1893*** (0.0463)
Interact city Inventors			0.4422*** (0.0680)	−0.0423 (0.0413)	0.6185* (0.3155)	0.3590*** (0.0569)
Interact class inventors			−0.0557*** (0.0141)	−0.1680*** (0.0203)	0.0585*** (0.0146)	−0.0199*** (0.0537)
Constant	−4.8269*** (0.2013)	−4.9045*** (0.1912)	−5.1060*** (0.2766)	−5.7443*** (0.2108)	−5.8401*** (0.2887)	−5.2591*** (0.2771)
Time FE	Yes	Yes	Yes	Yes	Yes	Yes
Firm FE	Yes	Yes	Yes	Yes	Yes	Yes
City FE	Yes	Yes	Yes	Yes	Yes	Yes
Observations	3,095,127	3,095,127	3,095,127	3,095,127	2,416,702	3,095,127

Notes: All continuous independent variables are normalized and lagged one period. All models were run with robust standard errors shown in parentheses. *Significant at the 0.1 level, **Significant at the 0.05 level, ***Significant at the 0.01 level. In all models the dependent variable takes the value 0 in period t - 1 and the value 0 or 1 in period t.

Model 5 is the logit for all branches in our sample of multilocational firms. The three coefficients on the different lagged measures of relatedness density, those observed within the branch, within the firm, and within the city are positive and significant, implying that existing knowledge assets at these three levels influence technological diversification within and across the branches of multilocational firms. The density variables are normalized, and thus the partial regression coefficients represent the impact of a one standard deviation increase in relatedness density on the log odds of RTA being developed in the technology class of a firm’s branch. Although the coefficient on firm relatedness density is about seven times larger than that for city density in Model 5, the marginal effect of a one standard deviation unit increase in the firm density coefficient, at 0.7 percent, is about three and a half times greater than that for the city density effect. Though the margins are relatively small, the relative importance of firm capabilities over city capabilities in the diversification process is clear and consistent throughout the models estimated.

Model 6 provides a check on the robustness of the dependent variable in Model 5 and reports the influence of the density measures and covariates on entry into classes previously unoccupied by individual firm branches. Results for the density measures of Model 6 are broadly similar to those for Model 5, with branch, firm, and city relatedness exerting a significant and positive influence on branch diversification. Across the models of Table 4, the time-varying measure of city size has a negative impact on diversification, technology class size has a positive impact, and firm size is largely insignificant. The positive sign on technology class is expected and likely capturing the overall growth of particular technologies driving increases in branch RTA in those same technologies. The negative sign on city size is unexpected, since as cities expand they typically add specializations.

Our sample of Chinese multilocational firms includes companies that are state owned as well as private. In Model 7, we explore whether the three relatedness density measures vary in their impact on branch diversification across the state and private-sector firms examined. When the dummy variable private takes the value 0 in Model 7, the interaction terms drop out of the model, and the results in the top of the table report the influence of the independent variables on diversification in state-owned firms. When the dummy takes the value 1, the interactions in the bottom half of the table report how the impacts of the independent variables change between state-owned and private-sector firms. In Model 7, the coefficient on the dummy variable reports no significant difference in the probability of diversification between state and private-sector firms, holding constant the influence of the remaining independent variables. One interesting finding in Model 7 is that there is no influence of city density on diversification in state-owned firms, while in private-sector firms the city-density variable has a positive and significant influence on diversification.

In Model 8, attention turns to whether the three density variables have a differential impact on diversification between the HQ branches of firms and non-HQ branches. The broader literature on multilocational firms makes clear that the flows of information among different branch types is asymmetric (Gupta and Govindarajan 2000; Hansen 2002). The dummy variable in this case reports that, overall, there is significantly more diversification in HQ branches than non-HQ branches. The coefficient on the HQ dummy is relatively large. Comparing branch types, there is a significant decrease in the influence of branch, firm, and city density on diversification in HQ plants relative to non-HQ plants. However, the relative decline in the city-density coefficient is far greater than in the firm density coefficient as we move from non-HQ to HQ branches. Indeed, the ratio of the marginal effects of firm to city density increases by a factor of six between non-HQ and HQ branches. Thus, firm-based capabilities are, in relative terms, much more important to diversification in HQ branches than in non-HQ branches. More work is required to clearly demonstrate that non-HQ branches are playing a role as listening posts gathering local technological knowledge to be passed to the firm.

Model 9 focuses exclusively on non-HQ branches, exploring whether non-HQ establishments in core cities diversify in different ways than non-HQ establishments in peripheral cities. Core and peripheral cities were identified from networks of intercity collaboration on individual patents (see Figure 2) using the coreness network algorithm of Borgatti and Everett (2000). Borgatti and Everett (2000) develop idealized representations of core-periphery networks using the block modeling approach of Breiger (1976) and measures of the cohesiveness of subgraphs following Wasserman and Faust (1994). In blocking terminology, an ideal core-periphery network is a two-class partition of nodes with the core as a 1-block, the periphery as a 0-block, and where core-periphery ties comprise an (imperfect) 1-block. They explore how to test whether an observed network exhibits a core-periphery structure and how to identify the strongest two-mode partitions of networks by examining the correlation between the structure of ties in an observed network and in the idealized core-periphery network. Running our intercity collaboration networks through the core-periphery model in UCINET (Borgatti, Everett, and Freeman 2002) yields measures of how likely it is that individual cities comprise part of the core in a two-class network. Across the five time periods examined, the core-periphery test places approximately 10 percent of cities into the core of the network. As robustness checks, we experimented with drawing the core-periphery boundary at different points between the seventy-fifth and ninetieth percentiles of the coreness algorithm, and it made little difference to the results.

Model 9 shows that the base probability of diversification for non-HQ branches is greater if they are located in core cities rather than peripheral cities. However, it is also interesting to note that the city density effect is significantly higher in peripheral rather than core cities. This finding does indicate that non-HQ branches in less innovative cities use local knowledge more intensively to diversify their technologies. Note that we lose some observations in Model 9 as we ignore HQ branches.

There is much current interest in the complexity of technology, its geography, and impact on the economy (Balland and Rigby 2017; Mewes and Broekel 2020; Pintar and Scherngell 2021). Measures of technology class complexity were generated for Chinese patent data using the method of Hidalgo and Hausmann (2009) and made binary using the median as cut point. Model 9 explores whether there is any difference in the relative density effects on diversification into more or less complex technology classes. The negative and significant dummy variable in Model 9 supports the view that diversification into complex technology classes is more difficult than diversification into less complex classes. The positive and significant interaction effects for firm and city density indicate that while branch capabilities may be sufficient to diversify into low complex technologies, more help from the firm as a whole and from external sources may be required to diversify into more complex technologies.

The results presented above are based on a relatively small sample of two hundred multilocational firms patenting in China, and so we do not seek to push the generality of our work too hard. Our findings are largely similar if generated with the linear probability model, if we focus on entry into new technology classes, and if we drop the time-varying covariates.

Conclusion

In this article we explored patterns of technological diversification within cities and within the branches of multilocational firms in China. Our purpose was to better understand the process of knowledge sourcing. Much of the related diversification literature in evolutionary economic geography has focused on the region as a unit of analysis. Implicit in much of that work is the claim that the technological structure of the region is a key driver of the direction of diversification. While this argument might raise old questions about the spatial ecological fallacy and the reification of the region, the issue is surely more complex today as we recognize the coevolution of firms and the regional economies of which they are a part. The mobility of workers between firms, the formal and informal relationships between firms, and the institutional structures that are so much a part of the regional economy make it difficult at times to separate that which is created within the firm from that which is learned in the broader environments within which firms operate. Another way of saying this is that the knowledge structure of the region and that of the firms that comprise the region are endogenous. Matters are complicated further by the flow of knowledge between firms located in different regions and by the flow of knowledge within the multilocational firm.

Still, it may be possible to disentangle the influence of the firm from the influence of the region in the process of technological diversification. At least, this was one of the tasks that we set for ourselves. At the city level, consistent with previous work on technological diversification, the knowledge stocks of cities were shown to be a reliable predictor of the pattern of future technological diversification. Intercity flows that capture assignee collaboration were also shown to exert a positive and significant influence on related diversification at the city level. To separate the impacts of firm and city knowledge bases on diversification, a sample of two hundred multilocational firms was generated. We examined patterns of technological diversification within the branches of these firms, linking diversification to measures of relatedness density calculated at the branch, firm, and city levels. Using fixed effects logit models, all three forms of relatedness density were shown to exert a positive and significant influence on branch diversification. Across the models examined, relatedness density within the firm exerted more than three times the impact of relatedness density at the city level on branch diversification. These results suggest that knowledge flows much more readily across the branches of the firm than it does across firm borders within the city. In some degree these findings run counter to those reported by Lo Turco and Maggioni (2016). Clearly, more work is required to unpack the meaning of place-based capabilities, to separate capabilities that are specific to individual economic agents and those that might be shared, and to understand how these different forms of capabilities influence trajectories of change within firms and regions.

Building on the management literature that details asymmetries of information flow between the plants of multiunit firms, the HQ and non-HQ branches of the firms in our sample were separated. We report significantly more diversification in HQ plants than non-HQ plants. The influence of the local (city) knowledge base on patterns of diversification was markedly smaller in HQ branches than in the non-HQ branches of the firm, lending some support, perhaps, to a vision of non-HQ branches as harvesters of local knowledge, or at least that held by economic agents operating in the same city. Separating non-HQ branches of firms into those operating in core and peripheral cities, the plants operating in core cities enjoyed higher levels of diversification, while the role of city capabilities in driving new specializations was significantly greater in peripheral than in core cities. Findings also indicated that city-level capabilities have significantly more impact on diversification in private-sector firms than in state-owned firms, though these differences were insufficient to generate higher overall rates of technological diversification in private-sector businesses. Finally, our results suggest that plant diversification into complex technologies is more difficult than diversification into less complex technologies, as we might expect. Firm and city-level capabilities played a significantly larger role in plant diversification into technology classes that were more complex than average, suggesting that borrowing know-how from the firm as a whole and from local, external partners may be critical for the production of complex knowledge.

In sum, we hope that we have added value to the agents of change literature that has focused on mining firm-level data to help understand the dynamics of diversification that occur within regions and firms. We push that literature into the patent realm focusing on technological diversification at the level of the plant, the firm, and the city within China. Our results suggest that there is a lot more heterogeneity in the diversification data than we have recognized to this point. Much more work is required to see if these patterns hold up in other settings and to decipher their meaning for our understanding of the evolution of relatedness and of firm and region dynamics. Understanding the process of diversification in single-plant firms also demands more attention.

Acknowledgments

The authors thank Anthony Frigon for help in development of this article.