# The role of ego network structure in facilitating ego network innovations.

INTRODUCTION

Innovation is generally regarded as the creation or adoption of new ideas for processes or products (Damanpour & Gopalakrishnan, 2001) and is a vital component to a firm's strategy (Azadegan, Dooley, Carter & Carter, 2008). Accordingly, research in the supply chain management domain has identified several dimensions of innovation that play vital roles in its generation and success. One key element in the success of innovation is supply chain integration, both internally and externally, as research suggests that it plays a large role in the service innovation process (Stank, Keller & Daugherty, 2001). Additionally, collaboration with suppliers (Kim, 2000) and the increases in customer service that can arise from the innovation process (Flint, Larsson & Gammelgaard, 2008) have all been noted.

A striking commonality to the research on innovation within supply chains is that it all implicitly relies upon the network in which a firm is embedded to explain its innovative capabilities. Yet, the level of analysis in most of this research is at the firm level, rather than from the broader perspective of the firm's network. Thus, there is a significant gap in the literature regarding the effects of network structure on innovation within a firm's network. Accordingly, a more appropriate level of analysis through which to study innovation is at the network level. Hence, this study contributes to the extant literature by examining the role that network structure plays in generating innovations for the network members. We thus develop a framework for supply chain innovations using social network theory. Social network theory has recently made quite a profound ascendency and impact in supply chain research. Generally, social network theory examines relational dynamics through the lens of structure. That is to say it leverages the connections between and among entities to explain future behavior or actions (Choi & Kim, 2008; Choi & Wu, 2009). For example, scholars have studied the effect that supplier network size has on performance and trust within business relationships (Terpend & Ashenbaum, 2012) and developed conceptual frameworks that have advanced the effects of power within various network configurations (Bastl, Johnson & Choi, 2013). Particularly germane to the present research context is Kim, Choi, Yan and Dooley (2011)'s work wherein they have empirically disentangled the structure of the automotive supply network of major automotive manufacturers and find that, among other things, leveraging social network theory is useful in determining key players in various networks.

From the network perspective, innovations within the network often implicitly arise from components of the "ego network" of a particular firm. An ego network is comprised of an ego (i.e., a social unit such as a manufacturer), the ego's immediate ties (i.e., first-degree connections), and the connections among the nodes to which the ego is connected (Borgatti & Halgin, 2011; Burt, 1980; Freeman, 1982). Ego networks have been applied to various contexts such as power and influence in networks (Burt, 1992), innovation adoption (Ahuja, 2000b), and the role that ego networks have on new joint venture formations (Carnovale & Yeniyurt, 2014).

As noted above, however, most research operationalizes innovation at the firm level, rather than a network level. Thus, a primary goal of this research was to reconcile this issue and study innovation at the network level. We do so by generating the overall network structure of manufacturing-based joint ventures (JVs) in the automotive industry over a 19-year period. A joint venture can be described as the formation of a separate, autonomous entity derived from the collaboration of two or more parent organizations (Kogut, 1988). Joint ventures have long been identified as sources of positive effects on innovation (Inkpen, 1996). We then generate the ego network structures for all firms in the network, including their innovation output over the 19-year period of observation. Thus, in this study, we address the following research question: What role does network structure play in generating innovations for network members and what characteristics of network structure facilitate innovation in global supply chain networks?

The rest of the article is organized as follows. First, we review the relevant literature surrounding innovation. We then articulate several hypotheses that connect network structure to network innovations by examining ego networks in the global automotive industry. Afterward, we describe the empirical context of our study. Finally, a discussion of the results is presented followed by the limitations and future research directions.

LITERATURE REVIEW AND HYPOTHESIS DEVELOPMENT

Innovation Networks

Innovation has long been studied in the management and supply chain management domains. Broadly, innovation is generally regarded as the creation or adoption of new ideas for processes or products (Damanpour & Gopalakrishnan, 2001). Dowling and Midgley (1978) highlight the first-mover advantages to innovation, as they consider a firm to be innovative when they adopt a product or process earlier than other firms in the network. Delbecq and Mills (1985) develop a more precise definition, stating that innovation is a significant change within the organization or its line of services or products that requires a substantial adjustment in functions and/or structures, and is incorporated into the organization. Similarly, Autry and Griffis (2008:159) define the innovation orientation of a firm as "the capacity to make improvements to business processes or outcomes by leveraging new or specialized ideas, methods, or advancements." Furthermore, Soosay, Hyland and Ferrer (2008) highlight a firm's collaborative capabilities (i.e., its potential to interact within the network) as antecedents to innovation output. Accordingly, innovation is a vital component of a firm's overall strategy (Azadegan et al., 2008) and can be dichotomized into process and product innovation. A product innovation refers to a new product that serves to fill an external unmet need, whereas a process innovation refers to the integration of new elements into a firm's operations that are used to produce a product or service (Damanpour & Gopalakrishnan, 2001). Innovation in supply chain management has recently been defined as, "the process of making changes to products, processes, and services that results in new value creation to the organization and its customers by leveraging knowledge efforts of the firm and (or) that of its supply network partners" (Narasimhan & Narayanan, 2013:28). This definition highlights that innovation is an organizational process that leverages knowledge. Cohen and Levinthal (1990) articulate that a firm's ability to leverage prior knowledge significantly impacts its ability to innovate in the future; they term this as absorptive capacity.

Another vital component of the above definition of innovation (Narasimhan & Narayanan, 2013) is the potential peripheral or network effects on innovation. It has been suggested that "networks with a superior capacity for learning and knowledge transfer are able to 'out-innovate' single firms or networks with less effective knowledge-sharing routines" (Billington & Davidson, 2013:1464). Extending beyond the focal firm, Azadegan (2011) examines supplier operational innovativeness and the positive impact it has on manufacturers. In a similar line of inquiry, Wagner (2012) finds that supplier integration has a positive impact on the new product development process. Additionally, Oke, Prajogo and layaram (2013) found that supplier innovativeness has a positive impact on the innovative strategy of the firm. Autry and Griffis (2008) articulate a conceptual framework that derives propositions in support of supply chain structure as an attenuation mechanism of firm innovation and performance. Effectively, viewing the network as a resource (e.g., Zaheer, Gozubuyiik & Milanov, 2010) allows the focal firm to leverage existing tacit knowledge within the network and to integrate it within the boundaries of the firm, essentially, what Kogut and Zander (1992:391) called "combinative capabilities." In the context of innovation and network theory, a firm that can leverage its combinative capabilities, with respect to knowledge, and control its supply chain network can generate significant innovation performance (c.f. Azadegan et al., 2008; Azadegan & Dooley, 2010; Azadegan, 2011).

In light of the above literature on innovation, as well as the network effects thereof, we define ego network innovation as follows: the collective transfer and integration of knowledge that exists within, and is derived from, the ego network in which firms are embedded that leads to innovation output for the entire ego network. This definition echoes (Narasimhan & Narayanan, 2013:28) with the explicit reference to the innovation beyond the focal firm, yet it differs in that it emphasizes the transfer and integration of knowledge by way of network structure. Effectively, by conceptualizing innovation at the network level, we contribute to the literatures on supply chain innovation (e.g., Autry & Griffis, 2008; Azadegan, 2011) as well as supply chain networks (Bastl et al., 2013; Borgatti & Li, 2009; Carnovale & Yeniyurt, 2014; Carter, Ellram & Tate, 2007). By raising the construct up to the ego network level, one can gain a better understanding of how innovation is dependent upon the network in which a firm is embedded.

Ego Network Betweenness

The core assumption behind network theory "is the concept that structure matters" (Borgatti, Mehra, Brass & Labianca, 2009:839). In studying innovation, access to information and the ability to generate increased network ties are of significant importance. Yet, the generation of network ties implies that the firm is in a position to control the access to, and facilitate the development of, such ties. Consequently, this ability is a direct result of a network construct known as betweenness (Borgatti, 2005; Freeman, 1979). Specifically, an ego's betweenness refers to "the intermediary location of a node along indirect relationships linking other nodes" (Marsden, 2002:410). As such, ego betweenness reflects the extent to which a network actor is located between other actors, that is, it is positioned on all the shortest paths (Borgatti, 2005; Borgatti & Li, 2009) connecting them (Freeman, 1982). In the context of innovation, an ego's betweenness is vitally important, as high betweenness engenders the firm to be able to facilitate communication or interaction to the other actors with which it is connected (Freeman, 1979, 1982; Marsden, 2002). Effectively, ego betweenness captures "the amount of network flow that a given node 'controls' in the sense of being able to shut it down if necessary" (Borgatti, 2005:60).

There is a substantial body of work arguing for the importance of betweenness for innovation, and it is centered on the idea that connectedness generates knowledge spillovers. These spillovers occur as firms increase their network connections, and these network connections act as resources in a facilitative capacity (Gulad, 1999) which subsequently lead to increased innovation output (Ahuja, 2000b). Additionally, firms that can navigate "large networks will be better positioned to observe more product innovations" (Skilton & Bernardes, 2014) and increase value creation (Skilton, 2014). Thus, firms occupying a more central network position have demonstrated increased firm-level innovations (Tsai, 2001) and better innovation output (Soh, 2010). In a supply chain setting, increasing a firm's betweenness means increasing the number of suppliers it works with. Increased access to innovative suppliers can render positive effects to the focal firm's innovation potential (Azadegan, 2011) should the number not grow exceedingly large (Choi & Krause, 2006). Furthermore, integrating these innovative suppliers into a focal firm's network can yield significant benefits to new product development (Wagner, 2012) as well as the firm's overall innovation strategy (Oke et al., 2013).

While most of the extant research has looked at the firm-level innovation benefits to increased network position, we expect that the effect should also apply to the ego network in which a firm is embedded. Thus, because increased network betweenness provides increased access to resources that facilitate innovation, we expect that:

H1a: Ego network betweenness has a positive effect on ego network innovation.

In addition to increasing the volume of innovation output in the ego network, betweenness should also have an effect on the distribution of innovations within the ego network by facilitating a more equitable distribution of the innovation output. Betweenness is expected to decrease the variation among network members regarding their innovation output. Increased network connections increase the knowledge transfer and absorptive capacity of the network members and result in increased levels of innovation for each member (Fosfuri & Tribo, 2008). Similarly, Yeniyurt, Henke and Yalcinkaya (2014) show that coinnovation benefits both suppliers and manufacturers in supply chain relationships. Tsai (2001) also takes a dyadic perspective on innovation and finds that firm-level absorptive capacity as well as the firm's network position (i.e., firm degree centrality) leads to increased business-unit innovation output. Increased network connections via ego betweenness centrality also increase the positive impact that the communication process has on innovation (Todorova & Durisin, 2007) and therefore lead to a decrease in the variation of the ego network members' innovation output. Given the increased levels of connectedness that arise with increased levels of betweenness, it can be expected that the variance of ego network innovation output is going to decrease.

H1b: Ego network betweenness has a negative effect on ego network innovation variance.

Ego Network Density

Another vital component of network structure that has an important role on innovation is ego network density. An ego network's density can be defined as the degree to which all actors within an ego network are connected to each other (Ahuja, 2000b; Skilton & Bernardes, 2014; Soh, 2010). Numerous studies have examined the effect of ego network density and in varying contexts. For example, McFadyen, Semadeni and Cannella (2009) studied network density in professional networks and revealed the impact that it has on knowledge creation. Burt (1992) effectively pioneered a new theory of competition by examining resource access in various industries. Additional work has looked at managerial performance (Rodan, 2010) and technological diversity (Phelps, 2010), and the role that density plays on both.

Research suggests that redundant network resources (i.e., densely connected networks) may have a positive effect on innovation. For example, Ahuja (2000b) finds that having a large number of structural holes (i.e., loosely connected, nondense network) leads to reduced innovation output. Soh (2010) echoes the results of Ahuja (2000b) and finds that innovation performance is increased as both network position and density increase. Connecting supply chain integration and supply chain structure, Defee and Stank (2005) suggest that increased density leads to positive outcomes. Given this controversy, some scholars have advocated for a contingency approach, whereby the context of the phenomenon under scrutiny is what dictates whether density's role is positive or negative (Adler & Kwon, 2002). In the context of this research, we expect that increased ego network density will lead to increased ego network innovation for the following reasons. First, ego networks that seek to increase innovation require adequate access to resources. This view echoes resource dependency theory, or the idea that views "organizations as coalitions in which structures and patterns of behavior are molded to acquire needed external resources" (Oke et al., 2013:45). Consequently, ego networks that are sparse and where numerous structural holes exist cannot take advantage of the resource acquisition possibilities that more dense networks can. Second, if innovation is dependent upon the network of potential partners of the firm (Narasimhan & Narayanan, 2013), decreasing the number of connections and interconnections within the ego network would lead to decreased levels of ego network innovation. Thus, we arrive at the following hypothesis:

H2a: Ego network density has a positive effect on ego network innovation.

It is further expected that all the members for the ego network can benefit from the advantages associated with denser networks. All the members of denser networks would have greater access to resources, and a greater ability to engage in co-innovation with and learning from other network members. Consequently, as this connectedness increases, the variance in the innovation of the ego network should decrease. Furthermore, density that fosters cooperation can significantly improve buyer-supplier relations (Wilhelm, 2011). Therefore, it is expected that as ego network density increases, all network members will enjoy greater innovation output and that the discrepancies in innovation output among network members will decrease.

H2b: Ego network density has a negative effect on ego network innovation variance.

Ego Network Brokerage

A vitally important dimension of ego network structure is the mechanism by which a firm can broker relationships between entities within the ego network. In the network literature, brokerage is a process "by which intermediary actors facilitate transactions between other actors lacking access to or trust in one another" (Marsden, 1982:202). In an ego network, brokerage opportunities exist when a firm is connected to two or more separate firms who are individually unconnected; yet they are both connected to the focal firm. In this scenario, the focal firm (i.e., broker) is in the position to connect the two firms. In a network, and in the context of innovation, brokerage increases the focal firm's access to the diverse resources of the connections for which it can broker.

As discussed above, a structural hole exists when one entity is connected to two other disjoint units. In other words, a structural hole "refers to missing relationships that inhibit information flow" between firms (Burt, 2007:119). Clearly in the context of innovation, information flows (i.e., knowledge) are vital to a firm's innovation success. A firm's ability to navigate these network disconnections can generate substantial firm's competitive advantage (Burt, 2004). In the innovation domain, firms that have the ability to span network boundaries and provide access to diverse information have been referred to as "knowledge brokers" (Billington & Davidson, 2013). Additionally, a firm that finds itself in a brokerage position can yield positive relational effects with partners in the network (Galunic, Ertug & Gargiulo, 2012) which can increase the likelihood of innovation output through increasing the interconnections that exist (Ahuja, 2000b).

Burt (2004:354) suggests that competitive advantage arises out of structural holes, in that the broker that can manage multiple connections can access nonredundant information and "translate it across groups." Vasudeva, Zaheer and Hernandez (2013) find support for the impact that network brokers have on innovation under different institutional contexts. Van Baalen, Bloemhof-Ruwaard and Van Heck (2005) find support for the role of knowledge brokers in developing knowledge portals and overcoming structural holes for increased innovation output. Kimble, Grenier and Goglio-Primard (2010) find support for the indirect positive effects of being in a brokerage position and its boundary spanning capabilities. Benassi and Di Minin (2009) find that economic benefits accrue to a broker in highly dense networks, further accentuating our hypothesis above dealing with density. Thus, brokerage is expected to have a positive impact on firm-level innovation due to the access to diverse resources and boundary spanning capabilities. Similarly, it is expected that as ego network brokerage increases, the level of innovation at the ego network will also increase.

H3a: Ego network brokerage has a positive effect on ego network innovation.

Increased ego network brokerage is expected to provide access to a diverse set of resources for ego network members, facilitating innovation across the ego network. Accordingly, Lane and Lubatkin (1998) find that knowledge flows between firms in the dyad experience heightened capacity to innovate and consequently promote a more equitable distribution of innovation. Therefore, it is expected that ego network brokerage will be beneficial for all ego network members, facilitating innovation and decreasing the discrepancies in innovation output across all member firms. Hence:

H3b: Ego network brokerage has a negative effect on ego network innovation variance.

Ego Network Weakness

Ego network weakness is the network structure dimension that is related to a firm's ability to connect otherwise unconnected subnetworks. A weak component is a subset of the overall network whereby there exist ties that connect pairs of nodes but where all nodes are not necessarily connected to each other (Everett & Krackhardt, 2012). As a network construct, ego network weakness is defined as the extent to which weak components are predominant in the network. Stated differently, ego network weakness refers to the degree to which completely connected subsets are absent from the network. Essentially, an ego network's weakness (also known as weak components) refers to the number of pairs of actors who are connected to an ego and to each other, but not to any other nodes (Scott & Carrington, 2011).

As a practical example, take General Motors (GM). In 1991, GM initiated a JV with Isuzu and a private investors group for the production of new automotive engines for GM's various models. Then in 2001, GM engaged in a joint venture with Autovaz, a Russian automotive assembler, and ERBD, an English automotive technology manufacturer. Assuming there were no connections in the network other than these JVs, Isuzu and the investor group are now a connected pair (as a result of their joint work in the JV) that is also connected to GM. Furthermore, Autovaz and ERBD also make a connected pair that is similarly connected to GM. Thus, based on the above definition, GM has two weak components in their network. The first is the Isuzu-private investor pair, and the second is the Autovaz-ERBD pair. Figure 1 shows a graphical representation of this element of network structure.

Network weakness has been studied in various contexts. Montgomery (2007) examines patronage networks (i.e., associations between patrons and clients) and demonstrates that the number of weak components in an actor's (i.e., a firm's) network has a significant effect on the dynamics of a relationship. In ego networks where there exist several weak components, a natural observation is that each weak component represents a unique subnetwork (Doreian, Lloyd & Mrvar, 2013). These separate networks are in fact triads (Bastl et al., 2013; Choi & Wu, 2009), and their examination in the context of innovation is particularly salient. The firm that can connect these networks (i.e., GM in the example above) and can leverage unique knowledge by straddling these networks can generate substantial innovation performance (Sytch & Tatarynowicz, 2014). Effectively, in so doing, the firm renders itself in a situation where it can control the access to contacts and resources. In network terminology, an actor in this position acts as a bridge. A bridge "links two components of an otherwise disconnected network" (Centola & Macy, 2007:710).

[FIGURE 1 OMITTED]

We posited above, in the section dealing with ego network density, that research has demonstrated that redundant resources lead to positive outcomes (e.g., Ahuja, 2000b; Defee & Stank, 2005; Soh, 2010). While it has been shown that density has a positive effect on innovation, suggestions have been made that loosely connected networks can generate numerous advantages for a firm. This is the case because bridges serve as connection mechanisms, through which information flow is either facilitated or restricted and much research has conducted enquiries to this end. For example, Centola and Macy (2007) find that bridges, in particular the strategic complementarities of a bridge, can influence contagion (e.g., the rapid adoption of innovations). Tucker (2008) finds that network entities that are in boundary spanning roles (i.e., bridges) significantly impact innovation adoption behavior. Sytch and Tatarynowicz (2014) study "network communities" and find that when firms have the ability to span boundaries, their innovation productivity increases. Reagans and Zuckerman (2008) study network redundancies and find that firms render themselves increasingly more powerful as they increase their ability to extract information from networks. Reagans and McEvily (2003) study the relationship between social cohesion and network range (i.e., boundary spanning capabilities) and their joint impact on knowledge transfer; they find that as both increase so too will knowledge transfer. Thus, given the key role that a firm's ability to bridge networks has on its innovation, we expect that as the weakness in the ego network increases so too will the ego network's innovation. Hence:

H4a: Ego network weakness has a positive effect on ego network innovation.

As with betweenness centrality, density, and brokerage, ego network weakness is also expected to benefit all ego network members. Increasing levels of weak components increase the bridging opportunities for firms. As we noted above, bridges serve as connection mechanisms, through which information flow is either facilitated or restricted. As the number of bridges increase, networks then generate increased opportunities to connect members. Thus, ego network weakness is expected to facilitate a more equitable distribution of the innovation output among ego network members, resulting in a decrease in the variation of the innovation output. Hence:

H4b: Ego network weakness has a negative effect on ego network innovation variance.

METHODS

The overarching question guiding this research deals specifically with raising the level of analysis of innovation, to the network rather than the firm level. To do so required three central components: (1) generation of the network structure, (2) gathering of appropriate innovation data, and (3) gathering appropriate financial and nonfinancial control variables. The following section describes how we achieved each of these components.

The construction of the network was accomplished by extracting data from the Thompson SDC Platinum database on all automotive joint ventures from the period 1985 until 2003. This dataset is a rich source of information detailing who interacted with whom and what the scope and purpose of the venture was. This allowed us to properly construct a manufacturing JV network. The total number of firms that participated in automotive JVs over the study period is 1,158 firms, both automotive manufacturers and parts suppliers observed over a 19-year period (1985-2003). The accurate construction of the network required the researcher to enumerate all possible connections and to create a binary adjacency matrix wherein all rows and columns represent the unique firms in the network, and the values of the matrix represent whether or not a firm interacted with another firm in a particular year. We constructed such matrices for each year (1985-2003) to gather the appropriate network variables. Note too that the data we have are a panel time-series dataset that encompasses innovation and network structure changes over a 19-year period. This allows for unique opportunities to gauge the development of the phenomenon under scrutiny (i.e., ego network innovation) over time. Thus, after calculating the network-level variables associated with each firm over each year, we are left with 1,158 firms multiplied with 19 years rendering a total of 22,002 observations in the initial dataset. The second necessary condition noted above was the gathering of appropriate innovation data for each firm, so that the calculation of network-level innovation could be properly operationalized. To do so, we use a dataset used for, and graciously provided, by Kogan, Papanikolaou, Seru and Stoffman (2012) (available at https://iu.app. box.com/patents). The dataset contains all granted utility patents issued by the US Patent Office from the period of 1926-2010. Utilizing this database, we identify the respective patent counts to each firm in our (V network.

Dependent Variables

The first dependent variable in this study is ego network innovation. To operationalize this variable, we first define the tie structure. To do so, we define a binary variable that takes the value 1 if firm j engaged with firm k in year t; note that j [not equal to] k. Additionally, these JVs are overwhelmingly associated with the supply of materials or services, and in our case for the explicit purposes of manufacturing automobiles. Thus, the construction of the network in this way is an appropriate representation of the supply network.

Recall that the ego network for a particular firm consists of the first-degree out connections (i.e., ties) and the interconnections between those connections. Consequently, if there is a tie between firms then firm k is in firm j's ego network and visa-versa. Thus, we operationalize ego network innovation as the summation of all granted patents for a particular ego network, for each year in the database. Accordingly, this operationalization uniquely counts all patents for a specific ego network and dynamically captures the changes over time.

The second dependent variable in this study was the variance of the patents that exist within an ego network of a particular firm. Thus, we operationalize ego network innovation variance as the logarithmic transformation of the sample variance of all granted patents for a particular ego network, for each year in the database. We use the logarithmic transformation because there exist a significant number of extreme values and a significantly large range within the data. This is a common method to deal with extreme values within a dataset (Wooldridge, 2010).

Independent Variables

All of the independent variables used in this study were calculated using UCINET 6 (Borgatti, Everett & Freeman, 2002). The first independent variable we study is ego betweenness, specifically operationalized as ego betweenness centrality. Ego betweenness centrality refers to the extent to which a firm lies on paths connecting other firms (Freeman, 1982; Marsden, 2002) or "the intermediary location of a node along indirect relationships linking other nodes" (Marsden, 2002:410). Thus, we measure ego betweenness centrality as the ratio of the sum of all paths, connecting firm j to other firms in the network, over all possible paths that exist in the network, in each year. This operationalization has been used in previous supply chain-related research (Carnovale & Yeniyurt, 2014) as well as other social network research (Freeman, 1982; Marsden, 2002).

The next component of network structure we study is the concept of ego network density. Conceptually, density refers to the connectedness of the overall network, or the ratio of the number of ties in the ego network to the overall number of pairs in the ego network. Thus, we operationalize density as the summation of all ties that a particular firm has within its ego network, over the combination of all firms (i.e., the total possible number of pairs within the ego network), for each year. Next, we examine the brokerage of firms within an ego network. The original mathematical derivation of brokerage was advanced in Gould and Fernandez (1989), and our operationalization is similarly constructed based on their work. For firm j to broker a relationship between any two other firms in the network, it must be the case that firm i is connected to firm j and firm k is also connected to firm j, yet firms i and k are not connected to each other. Figure 2 presents a graphical representation of this "ijk condition" (Gould & Fernandez, 1989) using GM, Ford, and Jaguar as an example. In Figure 2, GM (i.e., firm j) is connected to Ford (i.e., firm k) and Jaguar (i.e., firm i), yet neither Ford nor Jaguar is connected to each other. In this case, GM has the ability to broker the relationship between Ford and Jaguar. Total brokerage for a particular firm within the network is then defined as "is the number of ordered pairs (i,k) in the network for which the condition ijk holds" (Gould & Fernandez, 1989:97).

The final network construct under scrutiny in this study is ego network weakness, which we operationalize as the number of weak components in an ego network. To do so requires a similar network construction as in brokerage. Recall that a weak component is a subset of the overall network, whereby there exist ties that connect pairs of nodes but where all nodes are not necessarily connected to each other (Everett & Krackhardt, 2012). Thus, the number of weak components is the sum of unique pairs who are connected to a focal actor but not to each other (Scott & Carrington, 2011). To properly operationalize this construct analytically, we start with the same firm as in brokerage (i.e., firm j), and that firm has connections to firms i and k. In addition, and unique to weak components rather than brokerage, firms i and k are also connected to each other. Then, firm j also has connections to two additional firms, firms o and p. Similarly, firms o and p are also connected to each other and to firm j. The network structure then for a firm that has weak components in its network (such as firm j) is characterized by firm j maintaining connections to two pairs, that only share connections to firm j and each other (i.e., firms o and p are connected to each other and to firm j, and firms i and k are connected to each other and to firm j), but the pairs (i,k) and (o,p) are only to firm j (i.e., neither firms o nor p are connected to firms i or k). This renders firm j in a position to connect unconnected networks, rather than just to connect unconnected firms; as is the case with brokerage. Figure 1 presents a graphical representation of this network construct.

[FIGURE 2 OMITTED]

Control Variables

While we expect that the above variables will provide a robust picture of the role of network structure in facilitating supply chain innovation, there are several variables we need to take into account in order to ensure econometric rigor. First, there is the inherent idea of absorptive capacity and its role in the innovation process. To control for this, and for any potential autocorrelation, we include a variable that represents the innovation output of the ego network lagged by one, two, and three periods (see Empirical Model Lag Structure, in the Empirical Models section for further detail). Then, there are the related roles that firm sales and research and development (R&D) have on the innovation process. We gather these data from COMPUSTAT for each company in the database, for each year. Additionally, we include as a control variable the ego network size that each firm is associated with for each year. Then, there is the issue of focal firm size. Larger firms should have larger capital reserves as well as an increased likelihood of having access to innovative personnel; thus, we include the log of the number of employees for each firm. In addition to firm size, the age of the focal firm must also be taken into account; we thus include this variable in our model specifications. Finally, there is the issue of the temporal variations that are inherent over a 19-year dataset. Thus, we include yearly dummy variables for each year from 1986 to 2003, with 1985 as the base year. Tables 1 and 2 present a summarized explanation of the operationalization of each variable used in this study as well as the correlations and summary statistics of all the variables used in this study, respectively.

EMPIRICAL MODELS

Ego Network Innovation

The first dependent variable is ego network innovation, which is a count variable. This type of variable necessitates models that can take into account discrete, non-negative integers, and thus, ordinary techniques such as linear regression are not appropriate. The choices that are left to the modeler are the Poisson regression (e.g., Lambert, 1992), the negative binomial regression, or the family of so-called zero-inflated count data models, which include both a zero-inflated Poisson and negative binomial regression (e.g., Hall, 2000). We eliminate both the Poisson regression model and its zero-inflated counterpart due to its rather restrictive assumption that the mean of the data will equal the variance (i.e., so-called equidispersion) and given our dependent variable, using this approach will lead to the so-called over-dispersion issue (Hall, 2000) which further violates the assumptions of the Poisson regressions. The negative binomial regressions allow for an intensity parameter in the variance equation, which allows for differences between the variance and mean.

Our data, however, are characterized by a significant amount of zeros in the dependent variable. Pooling these observations into one model where there is a substantial amount of zeros will lead the model to over-predict the true number of zeros. Hence, we chose the zero-inflated negative binomial regression (ZINB). This model specification characterizes the zeros that arise in the data in two ways (Hu, Pavlicova & Nunes, 2011): (1) Some zeros arise due to choice (firms choose not to innovate) and (2) some zeros arise by chance (firms are unsuccessful at innovating).

Count data models in general predict changes to the average of the dependent variable. Thus, when parameterizing the appropriate distribution for estimation, the value of the mean is the one that is augmented (Cameron & Trivedi, 2005). We have chosen the ZINB model and thus require the use of the negative binomial distribution:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [[mu].sub.nt] = exp ([x'.sub.f,t] [beta] + [epsilon]), [alpha] > 0, [[gamma].sub.n,t] = Ego Network [Innovation.sub.n,t] and where n identifies the specific ego+ network and t identifies the year under observation. Note that f ([[gamma].sub.n,tt | [[mu].sub.n,t], [alpha]) simply expresses the functional form of the negative binomial distribution relating [[gamma].sub.n,t] (i.e., Ego Network Innovation) to the parameterized version of the mean, [[mu].sub.n,t], and the intensity parameter [alpha]. Note also that in the parameterized mean, x represents the matrix of independent variables and [beta] represents the vector of coefficients to be estimated. In our context, we specify the following parameterized [[mu].sub.n, t], for which we use maximum likelihood to estimate the coefficients:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where n identifies the specific ego network and t identifies the year under observation and CONTROLS represent all of the control variables listed above, each of which is parameterized by a coefficient in [[beta].sub.m], and as a result, the final model estimation includes two separate results: one where the parameters are estimated based on a binary choice model (probit) and the second estimates the negative binomial regression, conditional on positive outcomes of the dependent variable (Cameron & Trivedi, 2005). The binary model estimates the probability of having strictly zero values of the dependent variable, whereas the negative binomial regression, conditional on the positive outcomes, estimates the relative changes in the average of the dependent variable.

Ego Network Innovation Variance

The second dependent variable is ego network innovation variance. This variable is non-negative and continuous, and thus, the distribution upon which this model is estimated must be able to take into account non-negative, real numbers. In addition to the restriction that the model use a distribution whose support set is [0,+ [infinity]], we must consider the large number of zeros that exist within the data. Pooling these observations into one model where there are a substantial amount of zeros will lead the model to over-predict the true number of zeros. Thus, we must also consider similar zero-inflated models, but with a slight augmentation. We needed to choose a model that can handle positive real numbers with a large proportion of the observations as zeros. We thus chose a so-called two-part model (TPM) originally advanced by Cragg (1971) as a generalization of a Tobit model to deal with data characterized by left censoring; its recent developments have resulted in a model that is flexible enough to deal with an over-dispersion of zeros.

The logic of the TPM is as follows: The "first part" of the model (much like the case in the ZINB) specifies a binary choice model (probit) and estimates the probability of estimating a zero or not. Then, the second part of the model, different than the ZINB, estimates a generalized linear model (c.f. McCullagh & Nelder, 1989) with a chosen distribution and link function and estimates the coefficients of the model conditional on the dependent variable being positive. The distribution is chosen based on the empirical distribution function of the dependent variable under scrutiny. Based on nonparametric tests of fit, we chose the gamma distribution with an inverse link function.

Empirical Model Lag Structure

Given that both of the dependent variables deal with a concept that is inherently dependent upon time, the empirical models must take this into account. We do so as follows. First, in both the ZINB and the TPM, we include three model specifications that take into account 1-, 2-, and 3-year lag/lead structures of the dependent variables. In the first model for both the ZINB and the TPM, the dependent variable is estimated at one period forward (i.e., [t.sub.+1]) and all independent variables are at [t.sub.0], including the dependent variable at [t.sub.0]. In the second model for both the ZINB and the TPM, the dependent variable is estimated at two periods forward (i.e., [t.sub.+2]), all independent variables are at [t.sub.0], and the specification includes the dependent variable lagged at [t.sub.+1] and [t.sub.0]. In the third model for both the ZINB and the TPM, the dependent variable is estimated at 3 years forward (i.e., [t.sub.+3]), includes the dependent variable lagged at [t.sub.+2], [t.sub.+1], and [t.sub.0], and all other independent variables are at [t.sub.0]. Next, in both the ZINB and the TPM, we included yearly dummy variables in the model to further take into account the way in which the impact of ego network structure affects supply chain innovation over time. Doing so effectively creates a fixed effects structure, which captures the temporal variations within the data over all years in the database.

RESULTS

Ego Network Innovation

The coefficients for the final ZINB models were estimated in Stata 13 using maximum likelihood estimation. We see that the Wald [chi square] statistics for the 1-, 2-, and 3-year specifications are, respectively, 441.59, 364.67, and 637.25 with 27 degrees of freedom and are statistically significant (p < .001). Additionally, we see that the Akaike information criterion and Bayesian information criterion (AIC and BIC) are 6,689.19 and 7,067.07 for the 1-year model, 6,296.32 and 6,672.06 for the 2-year model, and 6,178.67 and 6,552.16 for the 3-year model. Finally, we see that the McFadden [R.sup.2] and Cragg-Uhler (Nagelkerke) [R.sup.2] are .26 and .44 for the 1-year model, .26 and .44 for the 2-year model, and .26 and .43 for the 3-year model. These results indicate that the final model fit to the data was quite good across multiple measures. In addition, all models were estimated using Huber-White sandwich estimators of the standard errors. This method takes into account any minor underlying heteroskedasticity or minor autocorrelation issues and provides the appropriate standard errors (Freedman, 2006).

The interpretation of the coefficients in Table 3 in their current form is slightly obfuscated. Currently, we would interpret the coefficients as a one-unit increase in each coefficient (holding all other observations constant) would increase the log of the mean of the ego network innovation by that degree. While mathematically sound, this interpretation is somewhat esoteric. To enhance the practical relevance of the results, we also calculate the incidence rate ratios (IRR). Interpretation of the IRR values is much clearer, as the IRR values describe how changes in the independent variable affect the rate at which the dependent variable occurs, while holding other predictor variables constant. Practically understood in the context of this study, the IRRs describe the rate at which ego network innovation increases (decreases) as changes in the ego network structure occur, while holding other predictor variables constant. So, IRRs that are above one indicate that as the independent variable increases by one unit, the dependent variable increases by IRR-1. Accordingly, if the IRR is below one, a one-unit increase in each independent variable produces a decrease in the dependent variable of 1-IRR. Effectively, IRRs are analogous to hazard rates with the assumption that the hazard rates are proportional as well as constant. Table 4 presents this representation of the results.

In hypothesis 1a, we suggested that as a firm increases its ego network betweenness, it would be in a better position to access information, and in the process, this would increase the ego network innovation overall. Observing the coefficients on ego network betweenness across all three specifications, in the portion of the model that relates to increases in the ego network patent counts, we see that all coefficients are negative and statistically not significant (p > .1). Furthermore, examining its IRR and corresponding impact, we see that a one-unit increase to an ego network's betweenness centrality corresponds to a proportional impact to its ego network innovation of .93 or a 6.92 percent decrease in the 1-year model, a .86 or 12.46 percent decrease in the 2-year model, and a .84 or 16.37 percent decrease in the 3-year model. Thus, hypothesis la is not supported.

In hypothesis 2a, we suggested that increases to a firm's ego network density would lead to increases in its ego network innovation. Observing the coefficients on ego network density in the 1-, 2- and 3-year models, we see that they are positive and statistically significant (p < .001) in all cases. Furthermore, we see that the proportional effect of a one-unit ego network density is 1.59 and corresponds to a 59 percent increase in the innovation generation of the ego network in the 1-year model, a proportional impact of 1.8 or 80 percent increase in the 2-year specification and a proportional impact of 1.07 or 7 percent increase in the 3-year model. Thus, hypothesis 2a is strongly supported.

Hypothesis 3a was built upon the idea that as a firm increases its connecting abilities within the network, so too would the access to knowledge flows and consequently the ego network innovation. Thus, observing the coefficients on ego network brokerage across all three models, we see that they are all positive and statistically significant [p < .001). Turning our attention to the proportional effect of a one-unit change in ego network brokerage, we see that it is 1.15 which corresponds to a 15 percent increase in ego network innovation in the 1-year model, a proportional impact of 1.22 or 22 percent increase in the 2-year model, and finally a 1.32 or 32 percent increase in the 3-year model. Thus, hypothesis 3a is supported.

Finally, in hypothesis 4a, we hypothesized that the network spanning abilities of the firm would increase the innovation output of the ego network. Thus, we expected that as the ego network's weakness (i.e., the number of weak components) increases, so too will the ego network innovation. Observing the coefficients on ego network weakness for the one- and 2-year models, we see that the coefficients are positive and statistically significant (p < .05), yet in the 3-year case, it is negative and statistically not significant (p > .1). Furthermore, the proportional effect of a one-unit increase in the level of ego network weakness in a firm's ego network is 25.8, which represents a staggering 25-fold increase in the overall innovation output of the ego network in the 1-year case and a proportional impact of 57.26 or 57-fold increase in innovation output. The 3-year case results in an approximate 53 percent decrease, yet it is not statistically significant. Thus, hypothesis 4a is partially supported.

Ego Network Innovation Variance

The coefficients for the final TPM models were estimated in Stata 13 using maximum likelihood estimation. We see that the Wald [chi square] statistics for the 1-, 2and 3-year specifications are, respectively, 172.88, 169.41, and 191.71 with 27 degrees of freedom and are statistically significant (p < .001). Additionally, we see that the Akaike information criterion and Bayesian information criterion (AIC and B1C) are 2,120.14 and 2,471.51 for the 1-year model, 1,949.90 and 2,299.27 for the 2-year model, and 1,967.87 and 2,328.25 for the 3-year model. Finally, we see that the pseudo-[R.sup.2] is .18 for the 1-year model, .19 for the 2-year model, and .17 for the 3-year model. These results indicate that the final model fit to the data was quite good across multiple measures. In addition, all models were estimated using Huber-White sandwich estimators of the standard errors. Table 4 presents these results.

In hypothesis lb, we posited that ego network betweenness would decrease the variance of the ego network patents within the ego networks of firms. Observing the coefficients on ego network betweenness on the portion of Table 5 that corresponds to increases in ego network patent variance for the 1-, 2-, and 3-year specifications, we see that only the coefficient in the 1-year model is negative, and none of the coefficients are statistically significant (p > .1). These results fail to provide support for hypothesis lb.

Hypothesis 2b states that increasing the density of the ego network would decrease the innovation variance within the ego network. Turning our attention to the coefficients of ego network density in Table 5, we see that across the 1-, 2-, and 3-year specifications, density is negative and marginally statistically significant (p<.l). Thus, the results provide weak support for hypothesis 2b.

Hypothesis 3b posits that ego network brokerage would decrease the variance of the ego network members' innovation output. Observing the coefficients for ego network brokerage in Table 5, we see that in the 2- and 3-year model specifications, the coefficients are negative; yet in the 1-year case, it is positive. In all cases, the coefficients are not statistically significant, failing to provide support for hypothesis 3b.

Finally, according to hypothesis 4b, the weakness within an ego network should decrease the variation of the innovation output of the member firms. The coefficients for ego network weakness are negative for all three model specifications (Table 5), but not statistically significant. Thus, we find no support for hypothesis 4b. Table 6 provides a summary of these results.

MODEL SELECTION AND ROBUSTNESS EVALUATION

Ego Network Innovation

The largest issue that needed to be resolved was the appropriate model choice among the three possible alternatives (i.e., zero-inflated Poisson, standard negative binomial, and zero-inflated negative binomial regression). We tested for this as follows; We first performed a likelihood ratio (LR) test on the alpha coefficient (the over-dispersion parameter) in equation (1) by specifying the null hypothesis that its value is zero and comparing it against a [chi square] distribution with one degree of freedom. The alpha coefficient represents the over-dispersion parameter in the negative binomial distribution. This is what allows the variance to exceed the mean, whereas in the Poisson regression, the mean and variance are equal; thus, alpha is equal to 0. The logic underlying this test is that should the LR statistic be statistically significant, the null hypothesis is rejected (and in fact alpha is greater than zero) and models that use a Poisson distribution (zero inflated or not) are inappropriate. We find that the value for the LR test is statistically significant (p < .001), thus eliminating the Poisson family of models.

Next, we needed to verify that the ZINB was preferred over the standard negative binomial regression. To do so, we perform a Vuong test (Vuong, 1989), which is an LR test that results in a Z-statistic and is particularly useful for comparing ZINB vs. standard negative binomial regression. The null hypothesis with this test is that the standard negative binomial regression is appropriate. We find that the Z-statistic is statistically significant (p <.001) and thus reject the null hypothesis and choose the ZINB as our final model choice. Furthermore, the results were tested with various robust standard errors, and the sign and significance levels remained stable, further validating the chosen model as the most appropriate.

Ego Network Innovation Variance

With the TPM, the largest modeling consideration that needed to me made was the appropriate choice of distribution for the second part (i.e., the GLM model). Given that our dependent variable was nonnegative and continuous, we were left with a few options for the appropriate distribution--namely the Gamma distribution and the inverse Gaussian distribution given their innate support set of [0,+oo] which was required for our dependent variable in this model. To choose the most appropriate distribution for our GLM portion of the model, we first performed a nonparametric distribution test known as the Kolmogorov-Smirnov equality-of-distributions test (Kolmogorov, 1933; Smirnov, 1933). Effectively, the test compares an empirical distribution to a theoretical distribution of interest--in our case, the gamma distribution. The result of the test showed that our distribution was indistinguishable from a gamma distribution. To be certain, we performed an LR test (much like the one described above in the case of the ZINB) against a model specification with an inverse Gaussian distribution. Both tests rendered the GLM model with the gamma distribution as the most appropriate fit to the data.

Post Hoc Analysis: Differences in Counts of Firm-level Innovation

While we examined both the counts and the distribution of innovation, we also wanted to examine whether or not the differences in firm-level innovation are significant at the extreme valued outliers (1) in the dataset; perhaps, the better positioned actors are more likely to reap the benefits of network structure. To test this, we used an interquantile regression (Koenker & Bassett, 1978), in which "quantiles of the conditional distribution of the response variable are expressed as functions of observed covariates" (Koenker & Hallock, 2001:143) and whose differences are simultaneously tested for significance. Given our interest in the extreme values (i.e., outliers) of firm-level innovation and its susceptibility to network structure in the dataset, we used the interquantile range of.01 and.99. This specification tested the differences in the effects of the characteristics of ego network structure on the outliers in the dataset. The specification for this model is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [Q.sub..99] and [Q.sub..01] represent the 99th and 1st quantiles of the dependent variable and each [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], represents the coefficient of the difference in the effect of the quantile differences and / represents each individual firm in the database. The hypothesis tests of significance of these coefficients are similar to an OLS regression, except that significance (regardless of the sign of the coefficient) implies that there is a difference in the quantile groups being tested (i.e., the outliers). The interpretation, however, is augmented slightly. If the coefficient is positive, then an increase in the independent variable to which the coefficient is attached leads to an increase in the dispersion of the difference. Stated differently, a positive coefficient means that increases in that particular network variable lead to amplified increases in the dispersion of firm-level innovation, whereas negative coefficients suggest increases in that network variable lead to decreases in the dispersion of firm-level innovation. Table 7 presents these results.

Increases in ego network density and ego network brokerage are both statistically significantly (p <.05) related to decreases in the dispersion of ego network innovations. However, in the case of ego network weakness, increases in this network variable are statistically significantly related to increases in differences in firm-level innovation output. Finally, in the case of ego network betweenness, the effect was positive, yet not statistically significant.

DISCUSSION, LIMITATIONS, AND FUTURE RESEARCH DIRECTIONS

This study began with a fundamental question: What role does network structure play in generating innovations for its members? To answer this question, we developed theoretically driven hypotheses regarding the effect of ego network structure on ego network innovation. Next, we constructed the automotive supply network based on all of the manufacturing joint ventures over a 19-year period. In so doing, we disentangled various characteristics of each firm's ego network. Specifically, we calculated ego network betweenness, density, brokerage, and weakness. We then gathered patent data and matched it with each firm. We operationalized the concept of innovation at the ego network level by aggregating the number of granted patents for each firm, in each separate ego network for each year. Additionally, the variance of innovation output among the members of each ego network for each year was calculated.

Upon testing our hypotheses, we find that network structure does in fact play a very interesting role in facilitating ego network innovations from several different perspectives. Specifically, we found the following. Ego network density is a significant driver of ego network innovation. According to our results, should an ego network increase its density by one unit, the innovation levels of that network can increase by over 59 percent, 80 percent, and 7 percent in a 1-, 2-, and 3-year period, respectively. In addition, we find marginal support for the idea that increasingly dense networks result in decreases in the variance of the innovations among member firms. This result accentuates the previous work performed by Ahuja (2000b) and Soh (2010) and advances this work by showing that cohesion among an ego network significantly increases its innovation levels. Further, our results suggest that the innovation output tends to be more equally distributed among firms that are members of dense networks; thus, we contribute to the literature on structural holes theory (Burt, 1992, 2004) and validate these ideas from the perspective of supply chain relational dynamics (e.g., Defee & Stank, 2005). Furthermore, when considering the "contingency" approach to the impact of density (c.f. Adler & Kwon, 2002), we contribute to the ongoing dialogue that attributes density as positive in innovation settings, but from a supply chain perspective.

Next, we explored the connection between brokerage and ego network innovation. We hypothesized, and subsequently validated, that as brokerage levels increase so too will the levels of ego network innovation. We find that as firms increase brokerage by one unit, they have the potential to increase their supply chain innovations by a factor of over 14 percent, 22 percent, and 32 percent, in 1, 2, and 3 years, respectively. This result further advances the notion that the boundary spanning capabilities of the firm increase its potential to take advantage of knowledge brokers (Billington & Davidson, 2013) and subsequently advance its competitive advantage (Burt, 2004; Vasudeva et al., 2013) and innovation output (Ahuja, 2000a,b).

We then explored the relatively understudied concept of network weakness, operationalized as the number weak components within an ego network. Effectively, weakness within an ego network implicitly forms subnetworks, and a firm that acts as an intermediary between each of these several subcomponents, we argued, can generate substantial benefits to supply chain innovation. Consequently, we suggested that as the level of network weakness increases so to would the supply chain innovation. We empirically validated this idea by showing that a one-unit increase in the number of weak components in an ego network would result in an over 25-fold and 57-fold increase in ego network innovation in a 1- and 2-year time period, respectively. This result validates the impact that network bridges (e.g., Centola & Macy, 2007) have on the innovation process. Consequently, we directly contribute to the network-based literature on the role of boundary spanners (Sytch & Tatarynowicz, 2014), network range and social cohesion (Reagans & McEvily, 2003), and network redundancies (Reagans & Zuckerman, 2008) by advancing that the bridging capabilities of firms within the ego network positively influence the ego network innovation.

We also explored the role of ego network betweenness and found, contrary to our hypotheses, that it has a diminishing effect on innovation. Although the effect was not statistically significant, this result justifies further inquiry. Effectively, betweenness relates to a firm's ability to inhibit or facilitate communication flows (Beauchamp, 1965). Thus, as the firm increases its connections and thereby increases its levels of involvement, there may exist administrative complexities or even issues arising from opportunistic behavior by way of other network partners. These issues may be the root of the insignificant effect of increased betweenness centrality.

The post hoc analysis also revealed some interesting findings. Specifically, network density and brokerage facilitate a more equitable distribution of innovation outcomes across the network, decreasing the differences in innovation output among firms. Conversely, ego network weakness increases the differences in firm-level innovation output. This implies that ego network weakness facilitates the concentration of innovation and some firms benefit more from their network connections than others.

These results also have significant managerial implications, specifically with respect to how a firm manages its network position. We demonstrate that increasing density increases the levels of innovation. This result highlights the importance for a firm to further enhance its connections between those in its ego network and thereby increase its innovation potential. A necessary condition for network closure (i.e., increasing levels of density) is the ability for a firm to facilitate (i.e., broker) relationships between supply chain partners. We demonstrated the multiplicative role that brokerage has on innovation performance-- for firms that can broker relationships and indirectly increase the connectedness of their ego networks, significant positive innovation results are expected. Finally, supply network innovation performance will increase as the level of network weakness in the ego network increases. Thus, triads that form with firms that can connect otherwise disconnected pairs will see significant improvements to their supply network innovation.

While we have made significant inroads to the theory of supply network innovation, there are some limitations as well as some future research directions we must consider as we move forward. First, the operationalization of the network structure was created with first-tier suppliers, and only in the automotive industry. Future research should include different industries as well as (if possible) multiple tiers of suppliers. Furthermore, future research should examine different tie structures that exist within networks, as at present, we only examine JV ties whereas other supply chain ties might reveal different results with respect to innovation. For example, Kim et al. (2011) examine direct supply ties in the automotive industry. Future research that contrasts these supply-based ties with fixed investment ties, such as JVs, has the potential to provide for a strong contribution to knowledge surrounding innovation in supply networks. Related to this is the idea of the strength of ties between network members (e.g., Granovetter, 1973). Future research should examine the impact that tie strength has on innovation within ego networks as well as the role that gatekeepers play as key actors within networks who can control access to resources that are valuable to innovation.

In addition, while we have controlled for the temporal variations that exist within ego network innovations, future research should hypothesize the causal mechanisms that impact the change over time and how network structure can address these changes. Future research should also test the diminishing effect of these variables on innovation within the ego network. Additionally, other than R&D expense and sales information, we do not consider any other financial information. Variables like current ratios as well as cost of goods sold should be considered in a line of inquiry dealing with the financial impact of innovation for the supply chain. Finally, future research should consider the impact of the role that each participant has on the overall supply network innovation.

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STEVEN CARNOVALE

Portland State University

SENGUN YENIYURT

Rutgers University

(1) We thank the associate editor for this valuable suggestion.

Steven Carnovale (Ph.D., Rutgers University) is an assistant professor in the Supply & Logistics Management Group, School of Business Administration at Portland State University. Previous research has appeared in Journal of Supply Chain Management and the European Journal of Operational Research. Current research focuses on empirical supply chain strategy, specifically network theory, risk management, supplier selection, and global sourcing strategies with a specific emphasis on equity-based partnerships. Econometric modeling activities focus on panel and time series data methods, discrete choice modeling, and event data.

Sengun Yeniyurt (Ph.D., Michigan State University) is an associate professor in Supply Chain Management and Marketing Sciences at Rutgers Business School. Dr. Yeniyurt is the founding co-director of the Center for Market Advantage and an associate professor in the Supply Chain Management and Marketing Sciences Department at Rutgers Business School, Newark and New Brunswick. Dr. Yeniyurt specializes in global strategies, innovation management, brand management, and inter-firm networks, as well as buyer-supplier relations. His work has appeared in journals such as the Journal of Supply Chain Management, Supply Chain Management Review, European Journal of Operational Research, Journal of the Academy of Marketing Science, Journal of Product Innovation Management, Journal of International Business Studies, Journal of World Business, and Marketing Letters.

Innovation is generally regarded as the creation or adoption of new ideas for processes or products (Damanpour & Gopalakrishnan, 2001) and is a vital component to a firm's strategy (Azadegan, Dooley, Carter & Carter, 2008). Accordingly, research in the supply chain management domain has identified several dimensions of innovation that play vital roles in its generation and success. One key element in the success of innovation is supply chain integration, both internally and externally, as research suggests that it plays a large role in the service innovation process (Stank, Keller & Daugherty, 2001). Additionally, collaboration with suppliers (Kim, 2000) and the increases in customer service that can arise from the innovation process (Flint, Larsson & Gammelgaard, 2008) have all been noted.

A striking commonality to the research on innovation within supply chains is that it all implicitly relies upon the network in which a firm is embedded to explain its innovative capabilities. Yet, the level of analysis in most of this research is at the firm level, rather than from the broader perspective of the firm's network. Thus, there is a significant gap in the literature regarding the effects of network structure on innovation within a firm's network. Accordingly, a more appropriate level of analysis through which to study innovation is at the network level. Hence, this study contributes to the extant literature by examining the role that network structure plays in generating innovations for the network members. We thus develop a framework for supply chain innovations using social network theory. Social network theory has recently made quite a profound ascendency and impact in supply chain research. Generally, social network theory examines relational dynamics through the lens of structure. That is to say it leverages the connections between and among entities to explain future behavior or actions (Choi & Kim, 2008; Choi & Wu, 2009). For example, scholars have studied the effect that supplier network size has on performance and trust within business relationships (Terpend & Ashenbaum, 2012) and developed conceptual frameworks that have advanced the effects of power within various network configurations (Bastl, Johnson & Choi, 2013). Particularly germane to the present research context is Kim, Choi, Yan and Dooley (2011)'s work wherein they have empirically disentangled the structure of the automotive supply network of major automotive manufacturers and find that, among other things, leveraging social network theory is useful in determining key players in various networks.

From the network perspective, innovations within the network often implicitly arise from components of the "ego network" of a particular firm. An ego network is comprised of an ego (i.e., a social unit such as a manufacturer), the ego's immediate ties (i.e., first-degree connections), and the connections among the nodes to which the ego is connected (Borgatti & Halgin, 2011; Burt, 1980; Freeman, 1982). Ego networks have been applied to various contexts such as power and influence in networks (Burt, 1992), innovation adoption (Ahuja, 2000b), and the role that ego networks have on new joint venture formations (Carnovale & Yeniyurt, 2014).

As noted above, however, most research operationalizes innovation at the firm level, rather than a network level. Thus, a primary goal of this research was to reconcile this issue and study innovation at the network level. We do so by generating the overall network structure of manufacturing-based joint ventures (JVs) in the automotive industry over a 19-year period. A joint venture can be described as the formation of a separate, autonomous entity derived from the collaboration of two or more parent organizations (Kogut, 1988). Joint ventures have long been identified as sources of positive effects on innovation (Inkpen, 1996). We then generate the ego network structures for all firms in the network, including their innovation output over the 19-year period of observation. Thus, in this study, we address the following research question: What role does network structure play in generating innovations for network members and what characteristics of network structure facilitate innovation in global supply chain networks?

The rest of the article is organized as follows. First, we review the relevant literature surrounding innovation. We then articulate several hypotheses that connect network structure to network innovations by examining ego networks in the global automotive industry. Afterward, we describe the empirical context of our study. Finally, a discussion of the results is presented followed by the limitations and future research directions.

LITERATURE REVIEW AND HYPOTHESIS DEVELOPMENT

Innovation Networks

Innovation has long been studied in the management and supply chain management domains. Broadly, innovation is generally regarded as the creation or adoption of new ideas for processes or products (Damanpour & Gopalakrishnan, 2001). Dowling and Midgley (1978) highlight the first-mover advantages to innovation, as they consider a firm to be innovative when they adopt a product or process earlier than other firms in the network. Delbecq and Mills (1985) develop a more precise definition, stating that innovation is a significant change within the organization or its line of services or products that requires a substantial adjustment in functions and/or structures, and is incorporated into the organization. Similarly, Autry and Griffis (2008:159) define the innovation orientation of a firm as "the capacity to make improvements to business processes or outcomes by leveraging new or specialized ideas, methods, or advancements." Furthermore, Soosay, Hyland and Ferrer (2008) highlight a firm's collaborative capabilities (i.e., its potential to interact within the network) as antecedents to innovation output. Accordingly, innovation is a vital component of a firm's overall strategy (Azadegan et al., 2008) and can be dichotomized into process and product innovation. A product innovation refers to a new product that serves to fill an external unmet need, whereas a process innovation refers to the integration of new elements into a firm's operations that are used to produce a product or service (Damanpour & Gopalakrishnan, 2001). Innovation in supply chain management has recently been defined as, "the process of making changes to products, processes, and services that results in new value creation to the organization and its customers by leveraging knowledge efforts of the firm and (or) that of its supply network partners" (Narasimhan & Narayanan, 2013:28). This definition highlights that innovation is an organizational process that leverages knowledge. Cohen and Levinthal (1990) articulate that a firm's ability to leverage prior knowledge significantly impacts its ability to innovate in the future; they term this as absorptive capacity.

Another vital component of the above definition of innovation (Narasimhan & Narayanan, 2013) is the potential peripheral or network effects on innovation. It has been suggested that "networks with a superior capacity for learning and knowledge transfer are able to 'out-innovate' single firms or networks with less effective knowledge-sharing routines" (Billington & Davidson, 2013:1464). Extending beyond the focal firm, Azadegan (2011) examines supplier operational innovativeness and the positive impact it has on manufacturers. In a similar line of inquiry, Wagner (2012) finds that supplier integration has a positive impact on the new product development process. Additionally, Oke, Prajogo and layaram (2013) found that supplier innovativeness has a positive impact on the innovative strategy of the firm. Autry and Griffis (2008) articulate a conceptual framework that derives propositions in support of supply chain structure as an attenuation mechanism of firm innovation and performance. Effectively, viewing the network as a resource (e.g., Zaheer, Gozubuyiik & Milanov, 2010) allows the focal firm to leverage existing tacit knowledge within the network and to integrate it within the boundaries of the firm, essentially, what Kogut and Zander (1992:391) called "combinative capabilities." In the context of innovation and network theory, a firm that can leverage its combinative capabilities, with respect to knowledge, and control its supply chain network can generate significant innovation performance (c.f. Azadegan et al., 2008; Azadegan & Dooley, 2010; Azadegan, 2011).

In light of the above literature on innovation, as well as the network effects thereof, we define ego network innovation as follows: the collective transfer and integration of knowledge that exists within, and is derived from, the ego network in which firms are embedded that leads to innovation output for the entire ego network. This definition echoes (Narasimhan & Narayanan, 2013:28) with the explicit reference to the innovation beyond the focal firm, yet it differs in that it emphasizes the transfer and integration of knowledge by way of network structure. Effectively, by conceptualizing innovation at the network level, we contribute to the literatures on supply chain innovation (e.g., Autry & Griffis, 2008; Azadegan, 2011) as well as supply chain networks (Bastl et al., 2013; Borgatti & Li, 2009; Carnovale & Yeniyurt, 2014; Carter, Ellram & Tate, 2007). By raising the construct up to the ego network level, one can gain a better understanding of how innovation is dependent upon the network in which a firm is embedded.

Ego Network Betweenness

The core assumption behind network theory "is the concept that structure matters" (Borgatti, Mehra, Brass & Labianca, 2009:839). In studying innovation, access to information and the ability to generate increased network ties are of significant importance. Yet, the generation of network ties implies that the firm is in a position to control the access to, and facilitate the development of, such ties. Consequently, this ability is a direct result of a network construct known as betweenness (Borgatti, 2005; Freeman, 1979). Specifically, an ego's betweenness refers to "the intermediary location of a node along indirect relationships linking other nodes" (Marsden, 2002:410). As such, ego betweenness reflects the extent to which a network actor is located between other actors, that is, it is positioned on all the shortest paths (Borgatti, 2005; Borgatti & Li, 2009) connecting them (Freeman, 1982). In the context of innovation, an ego's betweenness is vitally important, as high betweenness engenders the firm to be able to facilitate communication or interaction to the other actors with which it is connected (Freeman, 1979, 1982; Marsden, 2002). Effectively, ego betweenness captures "the amount of network flow that a given node 'controls' in the sense of being able to shut it down if necessary" (Borgatti, 2005:60).

There is a substantial body of work arguing for the importance of betweenness for innovation, and it is centered on the idea that connectedness generates knowledge spillovers. These spillovers occur as firms increase their network connections, and these network connections act as resources in a facilitative capacity (Gulad, 1999) which subsequently lead to increased innovation output (Ahuja, 2000b). Additionally, firms that can navigate "large networks will be better positioned to observe more product innovations" (Skilton & Bernardes, 2014) and increase value creation (Skilton, 2014). Thus, firms occupying a more central network position have demonstrated increased firm-level innovations (Tsai, 2001) and better innovation output (Soh, 2010). In a supply chain setting, increasing a firm's betweenness means increasing the number of suppliers it works with. Increased access to innovative suppliers can render positive effects to the focal firm's innovation potential (Azadegan, 2011) should the number not grow exceedingly large (Choi & Krause, 2006). Furthermore, integrating these innovative suppliers into a focal firm's network can yield significant benefits to new product development (Wagner, 2012) as well as the firm's overall innovation strategy (Oke et al., 2013).

While most of the extant research has looked at the firm-level innovation benefits to increased network position, we expect that the effect should also apply to the ego network in which a firm is embedded. Thus, because increased network betweenness provides increased access to resources that facilitate innovation, we expect that:

H1a: Ego network betweenness has a positive effect on ego network innovation.

In addition to increasing the volume of innovation output in the ego network, betweenness should also have an effect on the distribution of innovations within the ego network by facilitating a more equitable distribution of the innovation output. Betweenness is expected to decrease the variation among network members regarding their innovation output. Increased network connections increase the knowledge transfer and absorptive capacity of the network members and result in increased levels of innovation for each member (Fosfuri & Tribo, 2008). Similarly, Yeniyurt, Henke and Yalcinkaya (2014) show that coinnovation benefits both suppliers and manufacturers in supply chain relationships. Tsai (2001) also takes a dyadic perspective on innovation and finds that firm-level absorptive capacity as well as the firm's network position (i.e., firm degree centrality) leads to increased business-unit innovation output. Increased network connections via ego betweenness centrality also increase the positive impact that the communication process has on innovation (Todorova & Durisin, 2007) and therefore lead to a decrease in the variation of the ego network members' innovation output. Given the increased levels of connectedness that arise with increased levels of betweenness, it can be expected that the variance of ego network innovation output is going to decrease.

H1b: Ego network betweenness has a negative effect on ego network innovation variance.

Ego Network Density

Another vital component of network structure that has an important role on innovation is ego network density. An ego network's density can be defined as the degree to which all actors within an ego network are connected to each other (Ahuja, 2000b; Skilton & Bernardes, 2014; Soh, 2010). Numerous studies have examined the effect of ego network density and in varying contexts. For example, McFadyen, Semadeni and Cannella (2009) studied network density in professional networks and revealed the impact that it has on knowledge creation. Burt (1992) effectively pioneered a new theory of competition by examining resource access in various industries. Additional work has looked at managerial performance (Rodan, 2010) and technological diversity (Phelps, 2010), and the role that density plays on both.

Research suggests that redundant network resources (i.e., densely connected networks) may have a positive effect on innovation. For example, Ahuja (2000b) finds that having a large number of structural holes (i.e., loosely connected, nondense network) leads to reduced innovation output. Soh (2010) echoes the results of Ahuja (2000b) and finds that innovation performance is increased as both network position and density increase. Connecting supply chain integration and supply chain structure, Defee and Stank (2005) suggest that increased density leads to positive outcomes. Given this controversy, some scholars have advocated for a contingency approach, whereby the context of the phenomenon under scrutiny is what dictates whether density's role is positive or negative (Adler & Kwon, 2002). In the context of this research, we expect that increased ego network density will lead to increased ego network innovation for the following reasons. First, ego networks that seek to increase innovation require adequate access to resources. This view echoes resource dependency theory, or the idea that views "organizations as coalitions in which structures and patterns of behavior are molded to acquire needed external resources" (Oke et al., 2013:45). Consequently, ego networks that are sparse and where numerous structural holes exist cannot take advantage of the resource acquisition possibilities that more dense networks can. Second, if innovation is dependent upon the network of potential partners of the firm (Narasimhan & Narayanan, 2013), decreasing the number of connections and interconnections within the ego network would lead to decreased levels of ego network innovation. Thus, we arrive at the following hypothesis:

H2a: Ego network density has a positive effect on ego network innovation.

It is further expected that all the members for the ego network can benefit from the advantages associated with denser networks. All the members of denser networks would have greater access to resources, and a greater ability to engage in co-innovation with and learning from other network members. Consequently, as this connectedness increases, the variance in the innovation of the ego network should decrease. Furthermore, density that fosters cooperation can significantly improve buyer-supplier relations (Wilhelm, 2011). Therefore, it is expected that as ego network density increases, all network members will enjoy greater innovation output and that the discrepancies in innovation output among network members will decrease.

H2b: Ego network density has a negative effect on ego network innovation variance.

Ego Network Brokerage

A vitally important dimension of ego network structure is the mechanism by which a firm can broker relationships between entities within the ego network. In the network literature, brokerage is a process "by which intermediary actors facilitate transactions between other actors lacking access to or trust in one another" (Marsden, 1982:202). In an ego network, brokerage opportunities exist when a firm is connected to two or more separate firms who are individually unconnected; yet they are both connected to the focal firm. In this scenario, the focal firm (i.e., broker) is in the position to connect the two firms. In a network, and in the context of innovation, brokerage increases the focal firm's access to the diverse resources of the connections for which it can broker.

As discussed above, a structural hole exists when one entity is connected to two other disjoint units. In other words, a structural hole "refers to missing relationships that inhibit information flow" between firms (Burt, 2007:119). Clearly in the context of innovation, information flows (i.e., knowledge) are vital to a firm's innovation success. A firm's ability to navigate these network disconnections can generate substantial firm's competitive advantage (Burt, 2004). In the innovation domain, firms that have the ability to span network boundaries and provide access to diverse information have been referred to as "knowledge brokers" (Billington & Davidson, 2013). Additionally, a firm that finds itself in a brokerage position can yield positive relational effects with partners in the network (Galunic, Ertug & Gargiulo, 2012) which can increase the likelihood of innovation output through increasing the interconnections that exist (Ahuja, 2000b).

Burt (2004:354) suggests that competitive advantage arises out of structural holes, in that the broker that can manage multiple connections can access nonredundant information and "translate it across groups." Vasudeva, Zaheer and Hernandez (2013) find support for the impact that network brokers have on innovation under different institutional contexts. Van Baalen, Bloemhof-Ruwaard and Van Heck (2005) find support for the role of knowledge brokers in developing knowledge portals and overcoming structural holes for increased innovation output. Kimble, Grenier and Goglio-Primard (2010) find support for the indirect positive effects of being in a brokerage position and its boundary spanning capabilities. Benassi and Di Minin (2009) find that economic benefits accrue to a broker in highly dense networks, further accentuating our hypothesis above dealing with density. Thus, brokerage is expected to have a positive impact on firm-level innovation due to the access to diverse resources and boundary spanning capabilities. Similarly, it is expected that as ego network brokerage increases, the level of innovation at the ego network will also increase.

H3a: Ego network brokerage has a positive effect on ego network innovation.

Increased ego network brokerage is expected to provide access to a diverse set of resources for ego network members, facilitating innovation across the ego network. Accordingly, Lane and Lubatkin (1998) find that knowledge flows between firms in the dyad experience heightened capacity to innovate and consequently promote a more equitable distribution of innovation. Therefore, it is expected that ego network brokerage will be beneficial for all ego network members, facilitating innovation and decreasing the discrepancies in innovation output across all member firms. Hence:

H3b: Ego network brokerage has a negative effect on ego network innovation variance.

Ego Network Weakness

Ego network weakness is the network structure dimension that is related to a firm's ability to connect otherwise unconnected subnetworks. A weak component is a subset of the overall network whereby there exist ties that connect pairs of nodes but where all nodes are not necessarily connected to each other (Everett & Krackhardt, 2012). As a network construct, ego network weakness is defined as the extent to which weak components are predominant in the network. Stated differently, ego network weakness refers to the degree to which completely connected subsets are absent from the network. Essentially, an ego network's weakness (also known as weak components) refers to the number of pairs of actors who are connected to an ego and to each other, but not to any other nodes (Scott & Carrington, 2011).

As a practical example, take General Motors (GM). In 1991, GM initiated a JV with Isuzu and a private investors group for the production of new automotive engines for GM's various models. Then in 2001, GM engaged in a joint venture with Autovaz, a Russian automotive assembler, and ERBD, an English automotive technology manufacturer. Assuming there were no connections in the network other than these JVs, Isuzu and the investor group are now a connected pair (as a result of their joint work in the JV) that is also connected to GM. Furthermore, Autovaz and ERBD also make a connected pair that is similarly connected to GM. Thus, based on the above definition, GM has two weak components in their network. The first is the Isuzu-private investor pair, and the second is the Autovaz-ERBD pair. Figure 1 shows a graphical representation of this element of network structure.

Network weakness has been studied in various contexts. Montgomery (2007) examines patronage networks (i.e., associations between patrons and clients) and demonstrates that the number of weak components in an actor's (i.e., a firm's) network has a significant effect on the dynamics of a relationship. In ego networks where there exist several weak components, a natural observation is that each weak component represents a unique subnetwork (Doreian, Lloyd & Mrvar, 2013). These separate networks are in fact triads (Bastl et al., 2013; Choi & Wu, 2009), and their examination in the context of innovation is particularly salient. The firm that can connect these networks (i.e., GM in the example above) and can leverage unique knowledge by straddling these networks can generate substantial innovation performance (Sytch & Tatarynowicz, 2014). Effectively, in so doing, the firm renders itself in a situation where it can control the access to contacts and resources. In network terminology, an actor in this position acts as a bridge. A bridge "links two components of an otherwise disconnected network" (Centola & Macy, 2007:710).

[FIGURE 1 OMITTED]

We posited above, in the section dealing with ego network density, that research has demonstrated that redundant resources lead to positive outcomes (e.g., Ahuja, 2000b; Defee & Stank, 2005; Soh, 2010). While it has been shown that density has a positive effect on innovation, suggestions have been made that loosely connected networks can generate numerous advantages for a firm. This is the case because bridges serve as connection mechanisms, through which information flow is either facilitated or restricted and much research has conducted enquiries to this end. For example, Centola and Macy (2007) find that bridges, in particular the strategic complementarities of a bridge, can influence contagion (e.g., the rapid adoption of innovations). Tucker (2008) finds that network entities that are in boundary spanning roles (i.e., bridges) significantly impact innovation adoption behavior. Sytch and Tatarynowicz (2014) study "network communities" and find that when firms have the ability to span boundaries, their innovation productivity increases. Reagans and Zuckerman (2008) study network redundancies and find that firms render themselves increasingly more powerful as they increase their ability to extract information from networks. Reagans and McEvily (2003) study the relationship between social cohesion and network range (i.e., boundary spanning capabilities) and their joint impact on knowledge transfer; they find that as both increase so too will knowledge transfer. Thus, given the key role that a firm's ability to bridge networks has on its innovation, we expect that as the weakness in the ego network increases so too will the ego network's innovation. Hence:

H4a: Ego network weakness has a positive effect on ego network innovation.

As with betweenness centrality, density, and brokerage, ego network weakness is also expected to benefit all ego network members. Increasing levels of weak components increase the bridging opportunities for firms. As we noted above, bridges serve as connection mechanisms, through which information flow is either facilitated or restricted. As the number of bridges increase, networks then generate increased opportunities to connect members. Thus, ego network weakness is expected to facilitate a more equitable distribution of the innovation output among ego network members, resulting in a decrease in the variation of the innovation output. Hence:

H4b: Ego network weakness has a negative effect on ego network innovation variance.

METHODS

The overarching question guiding this research deals specifically with raising the level of analysis of innovation, to the network rather than the firm level. To do so required three central components: (1) generation of the network structure, (2) gathering of appropriate innovation data, and (3) gathering appropriate financial and nonfinancial control variables. The following section describes how we achieved each of these components.

The construction of the network was accomplished by extracting data from the Thompson SDC Platinum database on all automotive joint ventures from the period 1985 until 2003. This dataset is a rich source of information detailing who interacted with whom and what the scope and purpose of the venture was. This allowed us to properly construct a manufacturing JV network. The total number of firms that participated in automotive JVs over the study period is 1,158 firms, both automotive manufacturers and parts suppliers observed over a 19-year period (1985-2003). The accurate construction of the network required the researcher to enumerate all possible connections and to create a binary adjacency matrix wherein all rows and columns represent the unique firms in the network, and the values of the matrix represent whether or not a firm interacted with another firm in a particular year. We constructed such matrices for each year (1985-2003) to gather the appropriate network variables. Note too that the data we have are a panel time-series dataset that encompasses innovation and network structure changes over a 19-year period. This allows for unique opportunities to gauge the development of the phenomenon under scrutiny (i.e., ego network innovation) over time. Thus, after calculating the network-level variables associated with each firm over each year, we are left with 1,158 firms multiplied with 19 years rendering a total of 22,002 observations in the initial dataset. The second necessary condition noted above was the gathering of appropriate innovation data for each firm, so that the calculation of network-level innovation could be properly operationalized. To do so, we use a dataset used for, and graciously provided, by Kogan, Papanikolaou, Seru and Stoffman (2012) (available at https://iu.app. box.com/patents). The dataset contains all granted utility patents issued by the US Patent Office from the period of 1926-2010. Utilizing this database, we identify the respective patent counts to each firm in our (V network.

Dependent Variables

The first dependent variable in this study is ego network innovation. To operationalize this variable, we first define the tie structure. To do so, we define a binary variable that takes the value 1 if firm j engaged with firm k in year t; note that j [not equal to] k. Additionally, these JVs are overwhelmingly associated with the supply of materials or services, and in our case for the explicit purposes of manufacturing automobiles. Thus, the construction of the network in this way is an appropriate representation of the supply network.

Recall that the ego network for a particular firm consists of the first-degree out connections (i.e., ties) and the interconnections between those connections. Consequently, if there is a tie between firms then firm k is in firm j's ego network and visa-versa. Thus, we operationalize ego network innovation as the summation of all granted patents for a particular ego network, for each year in the database. Accordingly, this operationalization uniquely counts all patents for a specific ego network and dynamically captures the changes over time.

The second dependent variable in this study was the variance of the patents that exist within an ego network of a particular firm. Thus, we operationalize ego network innovation variance as the logarithmic transformation of the sample variance of all granted patents for a particular ego network, for each year in the database. We use the logarithmic transformation because there exist a significant number of extreme values and a significantly large range within the data. This is a common method to deal with extreme values within a dataset (Wooldridge, 2010).

Independent Variables

All of the independent variables used in this study were calculated using UCINET 6 (Borgatti, Everett & Freeman, 2002). The first independent variable we study is ego betweenness, specifically operationalized as ego betweenness centrality. Ego betweenness centrality refers to the extent to which a firm lies on paths connecting other firms (Freeman, 1982; Marsden, 2002) or "the intermediary location of a node along indirect relationships linking other nodes" (Marsden, 2002:410). Thus, we measure ego betweenness centrality as the ratio of the sum of all paths, connecting firm j to other firms in the network, over all possible paths that exist in the network, in each year. This operationalization has been used in previous supply chain-related research (Carnovale & Yeniyurt, 2014) as well as other social network research (Freeman, 1982; Marsden, 2002).

The next component of network structure we study is the concept of ego network density. Conceptually, density refers to the connectedness of the overall network, or the ratio of the number of ties in the ego network to the overall number of pairs in the ego network. Thus, we operationalize density as the summation of all ties that a particular firm has within its ego network, over the combination of all firms (i.e., the total possible number of pairs within the ego network), for each year. Next, we examine the brokerage of firms within an ego network. The original mathematical derivation of brokerage was advanced in Gould and Fernandez (1989), and our operationalization is similarly constructed based on their work. For firm j to broker a relationship between any two other firms in the network, it must be the case that firm i is connected to firm j and firm k is also connected to firm j, yet firms i and k are not connected to each other. Figure 2 presents a graphical representation of this "ijk condition" (Gould & Fernandez, 1989) using GM, Ford, and Jaguar as an example. In Figure 2, GM (i.e., firm j) is connected to Ford (i.e., firm k) and Jaguar (i.e., firm i), yet neither Ford nor Jaguar is connected to each other. In this case, GM has the ability to broker the relationship between Ford and Jaguar. Total brokerage for a particular firm within the network is then defined as "is the number of ordered pairs (i,k) in the network for which the condition ijk holds" (Gould & Fernandez, 1989:97).

The final network construct under scrutiny in this study is ego network weakness, which we operationalize as the number of weak components in an ego network. To do so requires a similar network construction as in brokerage. Recall that a weak component is a subset of the overall network, whereby there exist ties that connect pairs of nodes but where all nodes are not necessarily connected to each other (Everett & Krackhardt, 2012). Thus, the number of weak components is the sum of unique pairs who are connected to a focal actor but not to each other (Scott & Carrington, 2011). To properly operationalize this construct analytically, we start with the same firm as in brokerage (i.e., firm j), and that firm has connections to firms i and k. In addition, and unique to weak components rather than brokerage, firms i and k are also connected to each other. Then, firm j also has connections to two additional firms, firms o and p. Similarly, firms o and p are also connected to each other and to firm j. The network structure then for a firm that has weak components in its network (such as firm j) is characterized by firm j maintaining connections to two pairs, that only share connections to firm j and each other (i.e., firms o and p are connected to each other and to firm j, and firms i and k are connected to each other and to firm j), but the pairs (i,k) and (o,p) are only to firm j (i.e., neither firms o nor p are connected to firms i or k). This renders firm j in a position to connect unconnected networks, rather than just to connect unconnected firms; as is the case with brokerage. Figure 1 presents a graphical representation of this network construct.

[FIGURE 2 OMITTED]

Control Variables

While we expect that the above variables will provide a robust picture of the role of network structure in facilitating supply chain innovation, there are several variables we need to take into account in order to ensure econometric rigor. First, there is the inherent idea of absorptive capacity and its role in the innovation process. To control for this, and for any potential autocorrelation, we include a variable that represents the innovation output of the ego network lagged by one, two, and three periods (see Empirical Model Lag Structure, in the Empirical Models section for further detail). Then, there are the related roles that firm sales and research and development (R&D) have on the innovation process. We gather these data from COMPUSTAT for each company in the database, for each year. Additionally, we include as a control variable the ego network size that each firm is associated with for each year. Then, there is the issue of focal firm size. Larger firms should have larger capital reserves as well as an increased likelihood of having access to innovative personnel; thus, we include the log of the number of employees for each firm. In addition to firm size, the age of the focal firm must also be taken into account; we thus include this variable in our model specifications. Finally, there is the issue of the temporal variations that are inherent over a 19-year dataset. Thus, we include yearly dummy variables for each year from 1986 to 2003, with 1985 as the base year. Tables 1 and 2 present a summarized explanation of the operationalization of each variable used in this study as well as the correlations and summary statistics of all the variables used in this study, respectively.

EMPIRICAL MODELS

Ego Network Innovation

The first dependent variable is ego network innovation, which is a count variable. This type of variable necessitates models that can take into account discrete, non-negative integers, and thus, ordinary techniques such as linear regression are not appropriate. The choices that are left to the modeler are the Poisson regression (e.g., Lambert, 1992), the negative binomial regression, or the family of so-called zero-inflated count data models, which include both a zero-inflated Poisson and negative binomial regression (e.g., Hall, 2000). We eliminate both the Poisson regression model and its zero-inflated counterpart due to its rather restrictive assumption that the mean of the data will equal the variance (i.e., so-called equidispersion) and given our dependent variable, using this approach will lead to the so-called over-dispersion issue (Hall, 2000) which further violates the assumptions of the Poisson regressions. The negative binomial regressions allow for an intensity parameter in the variance equation, which allows for differences between the variance and mean.

Our data, however, are characterized by a significant amount of zeros in the dependent variable. Pooling these observations into one model where there is a substantial amount of zeros will lead the model to over-predict the true number of zeros. Hence, we chose the zero-inflated negative binomial regression (ZINB). This model specification characterizes the zeros that arise in the data in two ways (Hu, Pavlicova & Nunes, 2011): (1) Some zeros arise due to choice (firms choose not to innovate) and (2) some zeros arise by chance (firms are unsuccessful at innovating).

Count data models in general predict changes to the average of the dependent variable. Thus, when parameterizing the appropriate distribution for estimation, the value of the mean is the one that is augmented (Cameron & Trivedi, 2005). We have chosen the ZINB model and thus require the use of the negative binomial distribution:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [[mu].sub.nt] = exp ([x'.sub.f,t] [beta] + [epsilon]), [alpha] > 0, [[gamma].sub.n,t] = Ego Network [Innovation.sub.n,t] and where n identifies the specific ego+ network and t identifies the year under observation. Note that f ([[gamma].sub.n,tt | [[mu].sub.n,t], [alpha]) simply expresses the functional form of the negative binomial distribution relating [[gamma].sub.n,t] (i.e., Ego Network Innovation) to the parameterized version of the mean, [[mu].sub.n,t], and the intensity parameter [alpha]. Note also that in the parameterized mean, x represents the matrix of independent variables and [beta] represents the vector of coefficients to be estimated. In our context, we specify the following parameterized [[mu].sub.n, t], for which we use maximum likelihood to estimate the coefficients:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where n identifies the specific ego network and t identifies the year under observation and CONTROLS represent all of the control variables listed above, each of which is parameterized by a coefficient in [[beta].sub.m], and as a result, the final model estimation includes two separate results: one where the parameters are estimated based on a binary choice model (probit) and the second estimates the negative binomial regression, conditional on positive outcomes of the dependent variable (Cameron & Trivedi, 2005). The binary model estimates the probability of having strictly zero values of the dependent variable, whereas the negative binomial regression, conditional on the positive outcomes, estimates the relative changes in the average of the dependent variable.

Ego Network Innovation Variance

The second dependent variable is ego network innovation variance. This variable is non-negative and continuous, and thus, the distribution upon which this model is estimated must be able to take into account non-negative, real numbers. In addition to the restriction that the model use a distribution whose support set is [0,+ [infinity]], we must consider the large number of zeros that exist within the data. Pooling these observations into one model where there are a substantial amount of zeros will lead the model to over-predict the true number of zeros. Thus, we must also consider similar zero-inflated models, but with a slight augmentation. We needed to choose a model that can handle positive real numbers with a large proportion of the observations as zeros. We thus chose a so-called two-part model (TPM) originally advanced by Cragg (1971) as a generalization of a Tobit model to deal with data characterized by left censoring; its recent developments have resulted in a model that is flexible enough to deal with an over-dispersion of zeros.

The logic of the TPM is as follows: The "first part" of the model (much like the case in the ZINB) specifies a binary choice model (probit) and estimates the probability of estimating a zero or not. Then, the second part of the model, different than the ZINB, estimates a generalized linear model (c.f. McCullagh & Nelder, 1989) with a chosen distribution and link function and estimates the coefficients of the model conditional on the dependent variable being positive. The distribution is chosen based on the empirical distribution function of the dependent variable under scrutiny. Based on nonparametric tests of fit, we chose the gamma distribution with an inverse link function.

Empirical Model Lag Structure

Given that both of the dependent variables deal with a concept that is inherently dependent upon time, the empirical models must take this into account. We do so as follows. First, in both the ZINB and the TPM, we include three model specifications that take into account 1-, 2-, and 3-year lag/lead structures of the dependent variables. In the first model for both the ZINB and the TPM, the dependent variable is estimated at one period forward (i.e., [t.sub.+1]) and all independent variables are at [t.sub.0], including the dependent variable at [t.sub.0]. In the second model for both the ZINB and the TPM, the dependent variable is estimated at two periods forward (i.e., [t.sub.+2]), all independent variables are at [t.sub.0], and the specification includes the dependent variable lagged at [t.sub.+1] and [t.sub.0]. In the third model for both the ZINB and the TPM, the dependent variable is estimated at 3 years forward (i.e., [t.sub.+3]), includes the dependent variable lagged at [t.sub.+2], [t.sub.+1], and [t.sub.0], and all other independent variables are at [t.sub.0]. Next, in both the ZINB and the TPM, we included yearly dummy variables in the model to further take into account the way in which the impact of ego network structure affects supply chain innovation over time. Doing so effectively creates a fixed effects structure, which captures the temporal variations within the data over all years in the database.

RESULTS

Ego Network Innovation

The coefficients for the final ZINB models were estimated in Stata 13 using maximum likelihood estimation. We see that the Wald [chi square] statistics for the 1-, 2-, and 3-year specifications are, respectively, 441.59, 364.67, and 637.25 with 27 degrees of freedom and are statistically significant (p < .001). Additionally, we see that the Akaike information criterion and Bayesian information criterion (AIC and BIC) are 6,689.19 and 7,067.07 for the 1-year model, 6,296.32 and 6,672.06 for the 2-year model, and 6,178.67 and 6,552.16 for the 3-year model. Finally, we see that the McFadden [R.sup.2] and Cragg-Uhler (Nagelkerke) [R.sup.2] are .26 and .44 for the 1-year model, .26 and .44 for the 2-year model, and .26 and .43 for the 3-year model. These results indicate that the final model fit to the data was quite good across multiple measures. In addition, all models were estimated using Huber-White sandwich estimators of the standard errors. This method takes into account any minor underlying heteroskedasticity or minor autocorrelation issues and provides the appropriate standard errors (Freedman, 2006).

The interpretation of the coefficients in Table 3 in their current form is slightly obfuscated. Currently, we would interpret the coefficients as a one-unit increase in each coefficient (holding all other observations constant) would increase the log of the mean of the ego network innovation by that degree. While mathematically sound, this interpretation is somewhat esoteric. To enhance the practical relevance of the results, we also calculate the incidence rate ratios (IRR). Interpretation of the IRR values is much clearer, as the IRR values describe how changes in the independent variable affect the rate at which the dependent variable occurs, while holding other predictor variables constant. Practically understood in the context of this study, the IRRs describe the rate at which ego network innovation increases (decreases) as changes in the ego network structure occur, while holding other predictor variables constant. So, IRRs that are above one indicate that as the independent variable increases by one unit, the dependent variable increases by IRR-1. Accordingly, if the IRR is below one, a one-unit increase in each independent variable produces a decrease in the dependent variable of 1-IRR. Effectively, IRRs are analogous to hazard rates with the assumption that the hazard rates are proportional as well as constant. Table 4 presents this representation of the results.

In hypothesis 1a, we suggested that as a firm increases its ego network betweenness, it would be in a better position to access information, and in the process, this would increase the ego network innovation overall. Observing the coefficients on ego network betweenness across all three specifications, in the portion of the model that relates to increases in the ego network patent counts, we see that all coefficients are negative and statistically not significant (p > .1). Furthermore, examining its IRR and corresponding impact, we see that a one-unit increase to an ego network's betweenness centrality corresponds to a proportional impact to its ego network innovation of .93 or a 6.92 percent decrease in the 1-year model, a .86 or 12.46 percent decrease in the 2-year model, and a .84 or 16.37 percent decrease in the 3-year model. Thus, hypothesis la is not supported.

In hypothesis 2a, we suggested that increases to a firm's ego network density would lead to increases in its ego network innovation. Observing the coefficients on ego network density in the 1-, 2- and 3-year models, we see that they are positive and statistically significant (p < .001) in all cases. Furthermore, we see that the proportional effect of a one-unit ego network density is 1.59 and corresponds to a 59 percent increase in the innovation generation of the ego network in the 1-year model, a proportional impact of 1.8 or 80 percent increase in the 2-year specification and a proportional impact of 1.07 or 7 percent increase in the 3-year model. Thus, hypothesis 2a is strongly supported.

Hypothesis 3a was built upon the idea that as a firm increases its connecting abilities within the network, so too would the access to knowledge flows and consequently the ego network innovation. Thus, observing the coefficients on ego network brokerage across all three models, we see that they are all positive and statistically significant [p < .001). Turning our attention to the proportional effect of a one-unit change in ego network brokerage, we see that it is 1.15 which corresponds to a 15 percent increase in ego network innovation in the 1-year model, a proportional impact of 1.22 or 22 percent increase in the 2-year model, and finally a 1.32 or 32 percent increase in the 3-year model. Thus, hypothesis 3a is supported.

Finally, in hypothesis 4a, we hypothesized that the network spanning abilities of the firm would increase the innovation output of the ego network. Thus, we expected that as the ego network's weakness (i.e., the number of weak components) increases, so too will the ego network innovation. Observing the coefficients on ego network weakness for the one- and 2-year models, we see that the coefficients are positive and statistically significant (p < .05), yet in the 3-year case, it is negative and statistically not significant (p > .1). Furthermore, the proportional effect of a one-unit increase in the level of ego network weakness in a firm's ego network is 25.8, which represents a staggering 25-fold increase in the overall innovation output of the ego network in the 1-year case and a proportional impact of 57.26 or 57-fold increase in innovation output. The 3-year case results in an approximate 53 percent decrease, yet it is not statistically significant. Thus, hypothesis 4a is partially supported.

Ego Network Innovation Variance

The coefficients for the final TPM models were estimated in Stata 13 using maximum likelihood estimation. We see that the Wald [chi square] statistics for the 1-, 2and 3-year specifications are, respectively, 172.88, 169.41, and 191.71 with 27 degrees of freedom and are statistically significant (p < .001). Additionally, we see that the Akaike information criterion and Bayesian information criterion (AIC and B1C) are 2,120.14 and 2,471.51 for the 1-year model, 1,949.90 and 2,299.27 for the 2-year model, and 1,967.87 and 2,328.25 for the 3-year model. Finally, we see that the pseudo-[R.sup.2] is .18 for the 1-year model, .19 for the 2-year model, and .17 for the 3-year model. These results indicate that the final model fit to the data was quite good across multiple measures. In addition, all models were estimated using Huber-White sandwich estimators of the standard errors. Table 4 presents these results.

In hypothesis lb, we posited that ego network betweenness would decrease the variance of the ego network patents within the ego networks of firms. Observing the coefficients on ego network betweenness on the portion of Table 5 that corresponds to increases in ego network patent variance for the 1-, 2-, and 3-year specifications, we see that only the coefficient in the 1-year model is negative, and none of the coefficients are statistically significant (p > .1). These results fail to provide support for hypothesis lb.

Hypothesis 2b states that increasing the density of the ego network would decrease the innovation variance within the ego network. Turning our attention to the coefficients of ego network density in Table 5, we see that across the 1-, 2-, and 3-year specifications, density is negative and marginally statistically significant (p<.l). Thus, the results provide weak support for hypothesis 2b.

Hypothesis 3b posits that ego network brokerage would decrease the variance of the ego network members' innovation output. Observing the coefficients for ego network brokerage in Table 5, we see that in the 2- and 3-year model specifications, the coefficients are negative; yet in the 1-year case, it is positive. In all cases, the coefficients are not statistically significant, failing to provide support for hypothesis 3b.

Finally, according to hypothesis 4b, the weakness within an ego network should decrease the variation of the innovation output of the member firms. The coefficients for ego network weakness are negative for all three model specifications (Table 5), but not statistically significant. Thus, we find no support for hypothesis 4b. Table 6 provides a summary of these results.

MODEL SELECTION AND ROBUSTNESS EVALUATION

Ego Network Innovation

The largest issue that needed to be resolved was the appropriate model choice among the three possible alternatives (i.e., zero-inflated Poisson, standard negative binomial, and zero-inflated negative binomial regression). We tested for this as follows; We first performed a likelihood ratio (LR) test on the alpha coefficient (the over-dispersion parameter) in equation (1) by specifying the null hypothesis that its value is zero and comparing it against a [chi square] distribution with one degree of freedom. The alpha coefficient represents the over-dispersion parameter in the negative binomial distribution. This is what allows the variance to exceed the mean, whereas in the Poisson regression, the mean and variance are equal; thus, alpha is equal to 0. The logic underlying this test is that should the LR statistic be statistically significant, the null hypothesis is rejected (and in fact alpha is greater than zero) and models that use a Poisson distribution (zero inflated or not) are inappropriate. We find that the value for the LR test is statistically significant (p < .001), thus eliminating the Poisson family of models.

Next, we needed to verify that the ZINB was preferred over the standard negative binomial regression. To do so, we perform a Vuong test (Vuong, 1989), which is an LR test that results in a Z-statistic and is particularly useful for comparing ZINB vs. standard negative binomial regression. The null hypothesis with this test is that the standard negative binomial regression is appropriate. We find that the Z-statistic is statistically significant (p <.001) and thus reject the null hypothesis and choose the ZINB as our final model choice. Furthermore, the results were tested with various robust standard errors, and the sign and significance levels remained stable, further validating the chosen model as the most appropriate.

Ego Network Innovation Variance

With the TPM, the largest modeling consideration that needed to me made was the appropriate choice of distribution for the second part (i.e., the GLM model). Given that our dependent variable was nonnegative and continuous, we were left with a few options for the appropriate distribution--namely the Gamma distribution and the inverse Gaussian distribution given their innate support set of [0,+oo] which was required for our dependent variable in this model. To choose the most appropriate distribution for our GLM portion of the model, we first performed a nonparametric distribution test known as the Kolmogorov-Smirnov equality-of-distributions test (Kolmogorov, 1933; Smirnov, 1933). Effectively, the test compares an empirical distribution to a theoretical distribution of interest--in our case, the gamma distribution. The result of the test showed that our distribution was indistinguishable from a gamma distribution. To be certain, we performed an LR test (much like the one described above in the case of the ZINB) against a model specification with an inverse Gaussian distribution. Both tests rendered the GLM model with the gamma distribution as the most appropriate fit to the data.

Post Hoc Analysis: Differences in Counts of Firm-level Innovation

While we examined both the counts and the distribution of innovation, we also wanted to examine whether or not the differences in firm-level innovation are significant at the extreme valued outliers (1) in the dataset; perhaps, the better positioned actors are more likely to reap the benefits of network structure. To test this, we used an interquantile regression (Koenker & Bassett, 1978), in which "quantiles of the conditional distribution of the response variable are expressed as functions of observed covariates" (Koenker & Hallock, 2001:143) and whose differences are simultaneously tested for significance. Given our interest in the extreme values (i.e., outliers) of firm-level innovation and its susceptibility to network structure in the dataset, we used the interquantile range of.01 and.99. This specification tested the differences in the effects of the characteristics of ego network structure on the outliers in the dataset. The specification for this model is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [Q.sub..99] and [Q.sub..01] represent the 99th and 1st quantiles of the dependent variable and each [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], represents the coefficient of the difference in the effect of the quantile differences and / represents each individual firm in the database. The hypothesis tests of significance of these coefficients are similar to an OLS regression, except that significance (regardless of the sign of the coefficient) implies that there is a difference in the quantile groups being tested (i.e., the outliers). The interpretation, however, is augmented slightly. If the coefficient is positive, then an increase in the independent variable to which the coefficient is attached leads to an increase in the dispersion of the difference. Stated differently, a positive coefficient means that increases in that particular network variable lead to amplified increases in the dispersion of firm-level innovation, whereas negative coefficients suggest increases in that network variable lead to decreases in the dispersion of firm-level innovation. Table 7 presents these results.

Increases in ego network density and ego network brokerage are both statistically significantly (p <.05) related to decreases in the dispersion of ego network innovations. However, in the case of ego network weakness, increases in this network variable are statistically significantly related to increases in differences in firm-level innovation output. Finally, in the case of ego network betweenness, the effect was positive, yet not statistically significant.

DISCUSSION, LIMITATIONS, AND FUTURE RESEARCH DIRECTIONS

This study began with a fundamental question: What role does network structure play in generating innovations for its members? To answer this question, we developed theoretically driven hypotheses regarding the effect of ego network structure on ego network innovation. Next, we constructed the automotive supply network based on all of the manufacturing joint ventures over a 19-year period. In so doing, we disentangled various characteristics of each firm's ego network. Specifically, we calculated ego network betweenness, density, brokerage, and weakness. We then gathered patent data and matched it with each firm. We operationalized the concept of innovation at the ego network level by aggregating the number of granted patents for each firm, in each separate ego network for each year. Additionally, the variance of innovation output among the members of each ego network for each year was calculated.

Upon testing our hypotheses, we find that network structure does in fact play a very interesting role in facilitating ego network innovations from several different perspectives. Specifically, we found the following. Ego network density is a significant driver of ego network innovation. According to our results, should an ego network increase its density by one unit, the innovation levels of that network can increase by over 59 percent, 80 percent, and 7 percent in a 1-, 2-, and 3-year period, respectively. In addition, we find marginal support for the idea that increasingly dense networks result in decreases in the variance of the innovations among member firms. This result accentuates the previous work performed by Ahuja (2000b) and Soh (2010) and advances this work by showing that cohesion among an ego network significantly increases its innovation levels. Further, our results suggest that the innovation output tends to be more equally distributed among firms that are members of dense networks; thus, we contribute to the literature on structural holes theory (Burt, 1992, 2004) and validate these ideas from the perspective of supply chain relational dynamics (e.g., Defee & Stank, 2005). Furthermore, when considering the "contingency" approach to the impact of density (c.f. Adler & Kwon, 2002), we contribute to the ongoing dialogue that attributes density as positive in innovation settings, but from a supply chain perspective.

Next, we explored the connection between brokerage and ego network innovation. We hypothesized, and subsequently validated, that as brokerage levels increase so too will the levels of ego network innovation. We find that as firms increase brokerage by one unit, they have the potential to increase their supply chain innovations by a factor of over 14 percent, 22 percent, and 32 percent, in 1, 2, and 3 years, respectively. This result further advances the notion that the boundary spanning capabilities of the firm increase its potential to take advantage of knowledge brokers (Billington & Davidson, 2013) and subsequently advance its competitive advantage (Burt, 2004; Vasudeva et al., 2013) and innovation output (Ahuja, 2000a,b).

We then explored the relatively understudied concept of network weakness, operationalized as the number weak components within an ego network. Effectively, weakness within an ego network implicitly forms subnetworks, and a firm that acts as an intermediary between each of these several subcomponents, we argued, can generate substantial benefits to supply chain innovation. Consequently, we suggested that as the level of network weakness increases so to would the supply chain innovation. We empirically validated this idea by showing that a one-unit increase in the number of weak components in an ego network would result in an over 25-fold and 57-fold increase in ego network innovation in a 1- and 2-year time period, respectively. This result validates the impact that network bridges (e.g., Centola & Macy, 2007) have on the innovation process. Consequently, we directly contribute to the network-based literature on the role of boundary spanners (Sytch & Tatarynowicz, 2014), network range and social cohesion (Reagans & McEvily, 2003), and network redundancies (Reagans & Zuckerman, 2008) by advancing that the bridging capabilities of firms within the ego network positively influence the ego network innovation.

We also explored the role of ego network betweenness and found, contrary to our hypotheses, that it has a diminishing effect on innovation. Although the effect was not statistically significant, this result justifies further inquiry. Effectively, betweenness relates to a firm's ability to inhibit or facilitate communication flows (Beauchamp, 1965). Thus, as the firm increases its connections and thereby increases its levels of involvement, there may exist administrative complexities or even issues arising from opportunistic behavior by way of other network partners. These issues may be the root of the insignificant effect of increased betweenness centrality.

The post hoc analysis also revealed some interesting findings. Specifically, network density and brokerage facilitate a more equitable distribution of innovation outcomes across the network, decreasing the differences in innovation output among firms. Conversely, ego network weakness increases the differences in firm-level innovation output. This implies that ego network weakness facilitates the concentration of innovation and some firms benefit more from their network connections than others.

These results also have significant managerial implications, specifically with respect to how a firm manages its network position. We demonstrate that increasing density increases the levels of innovation. This result highlights the importance for a firm to further enhance its connections between those in its ego network and thereby increase its innovation potential. A necessary condition for network closure (i.e., increasing levels of density) is the ability for a firm to facilitate (i.e., broker) relationships between supply chain partners. We demonstrated the multiplicative role that brokerage has on innovation performance-- for firms that can broker relationships and indirectly increase the connectedness of their ego networks, significant positive innovation results are expected. Finally, supply network innovation performance will increase as the level of network weakness in the ego network increases. Thus, triads that form with firms that can connect otherwise disconnected pairs will see significant improvements to their supply network innovation.

While we have made significant inroads to the theory of supply network innovation, there are some limitations as well as some future research directions we must consider as we move forward. First, the operationalization of the network structure was created with first-tier suppliers, and only in the automotive industry. Future research should include different industries as well as (if possible) multiple tiers of suppliers. Furthermore, future research should examine different tie structures that exist within networks, as at present, we only examine JV ties whereas other supply chain ties might reveal different results with respect to innovation. For example, Kim et al. (2011) examine direct supply ties in the automotive industry. Future research that contrasts these supply-based ties with fixed investment ties, such as JVs, has the potential to provide for a strong contribution to knowledge surrounding innovation in supply networks. Related to this is the idea of the strength of ties between network members (e.g., Granovetter, 1973). Future research should examine the impact that tie strength has on innovation within ego networks as well as the role that gatekeepers play as key actors within networks who can control access to resources that are valuable to innovation.

In addition, while we have controlled for the temporal variations that exist within ego network innovations, future research should hypothesize the causal mechanisms that impact the change over time and how network structure can address these changes. Future research should also test the diminishing effect of these variables on innovation within the ego network. Additionally, other than R&D expense and sales information, we do not consider any other financial information. Variables like current ratios as well as cost of goods sold should be considered in a line of inquiry dealing with the financial impact of innovation for the supply chain. Finally, future research should consider the impact of the role that each participant has on the overall supply network innovation.

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STEVEN CARNOVALE

Portland State University

SENGUN YENIYURT

Rutgers University

(1) We thank the associate editor for this valuable suggestion.

Steven Carnovale (Ph.D., Rutgers University) is an assistant professor in the Supply & Logistics Management Group, School of Business Administration at Portland State University. Previous research has appeared in Journal of Supply Chain Management and the European Journal of Operational Research. Current research focuses on empirical supply chain strategy, specifically network theory, risk management, supplier selection, and global sourcing strategies with a specific emphasis on equity-based partnerships. Econometric modeling activities focus on panel and time series data methods, discrete choice modeling, and event data.

Sengun Yeniyurt (Ph.D., Michigan State University) is an associate professor in Supply Chain Management and Marketing Sciences at Rutgers Business School. Dr. Yeniyurt is the founding co-director of the Center for Market Advantage and an associate professor in the Supply Chain Management and Marketing Sciences Department at Rutgers Business School, Newark and New Brunswick. Dr. Yeniyurt specializes in global strategies, innovation management, brand management, and inter-firm networks, as well as buyer-supplier relations. His work has appeared in journals such as the Journal of Supply Chain Management, Supply Chain Management Review, European Journal of Operational Research, Journal of the Academy of Marketing Science, Journal of Product Innovation Management, Journal of International Business Studies, Journal of World Business, and Marketing Letters.

TABLE 1 Operationalization of Variables Variable Explanation Operationalization Network Tie * j and k represent the Tie (j, k) = {1 if firms, where j [not firms j and k enganged equal to] k, and t in a JV in year t represents the year 0 otherwise Binary Represents the binary A Adjacency adjacency matrix Matrix * whereby any JV between firms j and k is represented by a 1, otherwise a 0 Graph iAj indicates that a iAj, jAk, and i[bar.A]k Theoretic tie exists between i Brokerage and j, jAk indicates Construction that a tie exists between j and k, and finally, i[bar.A]k indicates that no tie exists between i and ijk condition * j brokers the ijk [Condition.sub.f] = relationship between {if j brokers the i and k relationship between i and k 0 otherwise Graph iAj indicates that a iAj. jAk, and iAK Theoretic tie exists between i oAj, jAp, and oAp Weak and j, jAk indicates Components that a tie exists Construction * between j and k, and iAk indicates that a tie exists between i and k. Furthermore, we introduce firms o and p. Note too that o is connected to j, j is connected to p, and o is connected to p op_j_ik o is connected to j, op_j_ik condition * j is connected to p, [Condition.sub.f] = and o is connected to {1 if j is connected p to the pairs (op) and (ik) 0 otherwise Ego Network The summation of all Ego Network Innovation granted patents, for [Innovation.sub.f,t] = (DV) a particular ego [summation over (f,t) network, in a Granted particular year [Patent.sub.f,t] where Tie(j, k) = 1 Ego Network The log of the sample Ego Network Innovation Innovation variance of all [Variance.sub.f,t] = Variance (DV) granted patents for a log [Variance (Ego particular ego Network network, for each [Innovation.sub.f,t])] year in the database Ego Network r and s are firms in the Ego Betweenness ego network of fi. N [Betweenness.sub.f,t] (IV) is the total number of = [[summation].sup.- firms in the ego N.sub.r=1] , network, [path.sub.rs] [[summation].sup.- is the total number of r-1.sub.s=1] network paths linking [path.sub.rs] (f)/ firm r and firm v, and [path.sub.rs] [path.sub.rs] (f) represents the number of those paths that include firm f, f = j, k Ego Network [summation over (f,t] Ego Density (IV) (j, k) represents the [NetworkDensity.sub.- summation of all ties f,t] = [summation for a particular firm, over [f,t] Tie(j,k)/ and [[MATHEMATICAL ([MATHEMATICAL EXPRESSION NOT EXPRESSION NOT REPRODUCIBLE IN REPRODUCIBLE IN ASCII]] represents ASCII]) the combination of all firms (i.e., the total possible number of pairs) Ego Network Total brokerage for a Brokerage particular firm within Ego Network (IV) the network is then [Brokerage.sub.f,t] = defined as "is the [1158.summation over number of ordered (f=1) (i, k) [??] pairs (i,k) in the (i, k) suchthat network for which the ijk Condition = 1 condition ijk holds" (Gould & Fernandez, 1989:97) Ego Network The largest number of Ego Network Weakness pairs of actors who [Weakness.sub.f] = (IV) are connected (Scott [N.summation over & Carrington, 2011) f=1][(I,k), (o,p)] [??](i.k), (o,p)suchthatop_j_ik- Condition = 1 * indicates a necessary element used to operationalize an independent or dependent variable, (DV) indicates a dependent variable, and (IV) indicates an independent variable. TABLE 2 Correlations Variable (* p<. 05) 1 2 3 4 1. Ego Network 1 Betweenness 2. Ego Network .0053 1 Density 3. Ego Network .3919 * .0525 * 1 Brokerage 4. Ego Network .4656 * .0775 * .3516 * 1 Weakness 5. Firm Sales .0247 * .0021 .0246 * .0510 * 6. R&D Expense .0289 * -.006 .0224 * .0569 * 7. Ego Network .4509 * .2358 * .6630 * .4952 * Size 8. Firm Size .0923 * .0883 * .0569 * .0672 * 9. Firm Age .0820 * .0372 * .0655 * .0614 * 10. Ego Network .0315 * .0027 .0372 * .0392 * Innovation (t0) 11. Ego Network .0286 * .0005 .0354 * .0778 * Innovation (t+1) 12. Ego Network .0292 * .0004 .0359 * .0762 * Innovation (t+2) 13. Ego Network .0447 * .0169 * .0394 * .0485 * Innovation Variance (t0) 14. Ego Network .0283 * -.001 .0234 * .0392 * Innovation Variance (t+1) 15. Ego Network .0198 * -.0012 .0174 * .0265 * Innovation Variance (t+2) Mean .0451 .3875 .2685 .5117 SD .5812 4.0291 3.1027 1.8422 Variable (* p<. 05) 5 6 7 8 1. Ego Network Betweenness 2. Ego Network Density 3. Ego Network Brokerage 4. Ego Network Weakness 5. Firm Sales 1 6. R&D Expense .8715 * 1 7. Ego Network .0846 * .0808 * 1 Size 8. Firm Size .1484 * .1677 * .1347 * 1 9. Firm Age .1734 * .1472 * .1393 * .2168 * 10. Ego Network .4622 * .5842 * .0879 * .1456 * Innovation (t0) 11. Ego Network .4584 * .5834 * .0751 * .1462 * Innovation (t+1) 12. Ego Network .4517 * .5776 * .0730 * .1470 * Innovation (t+2) 13. Ego Network .1956 * .2029 * .1093 * .0784 * Innovation Variance (t0) 14. Ego Network .2002 * .2052 * .0385 * .0806 * Innovation Variance (t+1) 15. Ego Network .2038 * .2076 * .0264 * .0821 * Innovation Variance (t+2) Mean .3738 .1663 .4993 4.066 SD 1.7500 .9299 .8968 .9568 Variable (* p<. 05) 9 10 11 12 1. Ego Network Betweenness 2. Ego Network Density 3. Ego Network Brokerage 4. Ego Network Weakness 5. Firm Sales 6. R&D Expense 7. Ego Network Size 8. Firm Size 9. Firm Age 1 10. Ego Network .0725 * 1 Innovation (t0) 11. Ego Network .0717 * .8581 * 1 Innovation (t+1) 12. Ego Network .0719 * .8300 * .8556 * 1 Innovation (t+2) 13. Ego Network .0267 * .3595 * .1648 * .1711 * Innovation Variance (t0) 14. Ego Network .0276 * .1492 * .3628 * .1660 * Innovation Variance (t+1) 15. Ego Network .0281 * .1649 * .1510 * .3668 * Innovation Variance (t+2) Mean 48.8045 6.9608 7.1171 7.3148 SD 36.6366 69.3110 7.5339 71.9414 Variable (* p<. 05) 13 14 15 1. Ego Network Betweenness 2. Ego Network Density 3. Ego Network Brokerage 4. Ego Network Weakness 5. Firm Sales 6. R&D Expense 7. Ego Network Size 8. Firm Size 9. Firm Age 10. Ego Network Innovation (t0) 11. Ego Network Innovation (t+1) 12. Ego Network Innovation (t+2) 13. Ego Network 1 Innovation Variance (t0) 14. Ego Network .1461 * 1 Innovation Variance (t+1) 15. Ego Network .1120 * .1462 * 1 Innovation Variance (t+2) Mean .0791 .0835 .0871 SD .7961 .8177 .8386 TABLE 3 Zero-inflated Negative Binomial Regression of Ego Network Structure on Ego Network Innovation Dependent Variable Lag Structure One Year Forward (t+1) Increases in Probability of Zero Ego Network Ego Network Innovation Innovation Independent Robust Variable (a) B SE B SE Ego Network -.0718 .1444 -.0134 .0386 Betweenness Ego Network .4659 *** .1267 .0155 .0202 Density Ego Network .1387 *** .0556 .0173 .0118 Brokerage Ego Network 3.2509 *** 1.3225 -.1343 .3824 Weakness Firm Sales -.1407 *** .0315 -.2368 *** .0544 R&D Expense .1713 *** .0457 -21.0531 *** 1.4027 Ego Network -3.4151 ** 1.3393 -.0210 .3788 Size Firm Size .6930 *** .1473 .0242 .0458 Firm Age -.0173 *** .0031 -.0007 .0011 Intercept 1.9815 *** .6649 2.1725 *** .2586 Ego Network .0031 *** .0003 -.5146 *** .1112 Innovation ([t.sub.0]) Ego Network Innovation ([t.sub.+1]) Ego Network Innovation ([t.sub.+2]) Model fit Wald [chi square] 441,59 *** (27) (DF) Log -3287.59 psuedolikelihood Over-dispersion 2.48 ([alpha]) AIC 6,689.19 BIC 7,067.07 McFadden's .26 [R.sup.2] Cragg-Uhler .44 (Nagelkerke) [R.sup.2] Observations 5,594 (zero/nonzero) (5,087/507) Dependent Variable Lag Structure Two Years Forward (t+2) Increases in Probability of Zero Ego Network Ego Network Innovation Innovation Independent Robust Variable (a) B SE B SE Ego Network -.1330 .1425 .0019 .0495 Betweenness Ego Network .5927 *** .1647 .0237 .0280 Density Ego Network .2034 *** .0598 .0277 ** .0130 Brokerage Ego Network 4.0476 ** 1.5524 -.0260 .4220 Weakness Firm Sales -.1519 ** .0466 -.3572 .3463 R&D Expense .1703 ** .0698 -.8503 1.0860 Ego Network -4.4004 ** 1.5571 -.1880 .4205 Size Firm Size .6370 *** .1556 -.0084 .1089 Firm Age -.0173 *** .0038 -.0012 .0031 Intercept 2.3127 *** .6989 2.5382 .5721 Ego Network -.0003 .0006 -.2077 .1222 Innovation ([t.sub.0]) Ego Network .0038 *** .0007 -.0013 ** .0006 Innovation ([t.sub.+1]) Ego Network Innovation ([t.sub.+2]) Model fit Wald [chi square] 364.67 (27) (DF) Log -3091.19 psuedolikelihood Over-dispersion 2.26 ([alpha]) AIC 6,296.32 BIC 6,672.06 McFadden's .26 [R.sup.2] Cragg-Uhler .44 (Nagelkerke) [R.sup.2] Observations 5,388 (zero/nonzero) (4,911/477) Dependent Variable Lag Structure Three Years Forward (t+3) Increases in Probability of Zero Ego Network Ego Network Innovation Innovation Independent Robust Variable (a) B SE B SE Ego Network -.1788 .1513 .0367 .0578 Betweenness Ego Network .0720 *** .0156 -.0188 .0243 Density Ego Network .2816 *** .0871 .0022 .0180 Brokerage Ego Network -.7476 .6505 -.7304 .6545 Weakness Firm Sales -.1477 .0335 -.2681 .0593 R&D Expense .0960 ** .0494 -1.0513 *** .3497 Ego Network .2761 .6592 .5790 .6624 Size Firm Size .8110 *** .1492 -.0183 .0487 Firm Age -.0212 *** .0028 -.0029 ** .0011 Intercept 1.9815 *** .6649 2.4373 .2568 Ego Network .0012 * .0007 .0002 .0016 Innovation ([t.sub.0]) Ego Network .0008 .0008 -.0025 ** .0010 Innovation ([t.sub.+1]) Ego Network .0016 .0008 -.0038 *** .0011 Innovation ([t.sub.+2]) Model fit Wald [chi square] 637.25 (27) (DF) Log -3032.34 psuedolikelihood Over-dispersion 1.69 ([alpha]) AIC 6,178.67 BIC 6,552.16 McFadden's .26 [R.sup.2] Cragg-Uhler .43 (Nagelkerke) [R.sup.2] Observations 5,179 (zero/nonzero) (4,717/462) (a) The models were estimated using the yearly dummy variables but were not included for space considerations, * p < .1, ** p < .05, *** p < .001 two tailed. TABLE 4 Incidence Rate Ratios and Percentage Increases in Ego Network Innovation Dependent Variable Lag Structure One Year Forward ([t.sub.+1]) Percentage Increase (Decrease) in Ego Independent Variable IRR Network Innovation Ego Network Betweenness .9308 -6.92% Ego Network Density 1.5934 59.34% Ego Network Brokerage 1.1488 14.88% Ego Network Weakness 25.8135 2481.35% Firm Sales .8687 -13.13% R&D Expense 1.1868 18.68% Ego Network Size .0329 -96.71% Firm Size 1.9996 99.96% Firm Age .9829 -1.71% Ego Network Innovation ([t.sub.0]) 1.0031 .31% Ego Network Innovation ([t.sub.+1]) Ego Network Innovation ([t.sub.+2]) Dependent Variable Lag Structure Two Years Forward ([t.sub.+2]) Percentage Increase (Decrease) in Ego Independent Variable IRR Network Innovation Ego Network Betweenness .8754 -12.46% Ego Network Density 1.8088 80.88% Ego Network Brokerage 1.2256 22.56% Ego Network Weakness 57.2612 5626.12% Firm Sales .8591 -14.09% R&D Expense 1.1856 18.56% Ego Network Size .0123 -98.77% Firm Size 1.8908 89.08% Firm Age .9829 -1.71% Ego Network Innovation ([t.sub.0]) .9997 -.03% Ego Network Innovation ([t.sub.+1]) 1.0038 .38% Ego Network Innovation ([t.sub.+2]) Dependent Variable Lag Structure Three Years Forward ([t.sub.+3]) Percentage Increase (Decrease) in Ego Independent Variable IRR Network Innovation Ego Network Betweenness .8363 -16.37% Ego Network Density 1.0747 7.47% Ego Network Brokerage 1.3252 32.52% Ego Network Weakness .4735 -52.65% Firm Sales .8627 -13.73% R&D Expense 1.1007 10.07% Ego Network Size 1.3180 31.80% Firm Size 2.2502 125.02% Firm Age .9790 -2.10% Ego Network Innovation ([t.sub.0]) 1.0012 .12% Ego Network Innovation ([t.sub.+1]) 1.0008 .08% Ego Network Innovation ([t.sub.+2]) 1.0016 .16% TABLE 5 Two-part Zero-inflated Regression Estimates of the Effect of Ego Network Structure on Ego Network Innovation Variance Dependent Variable Lag Structure One Year Forward (t+1) Probability of Increases in Zero Ego Ego Network Network Innovation Innovation Variance Variance Independent Variable (a) B SE B SE Ego Network Betweenness -.0006 .0074 .0035 .0374 Ego Network Density -.0120 * .0068 -.0115 .0213 Ego Network Brokerage .0049 .0058 -.0084 .0138 Ego Network Weakness -.0730 .1055 .2284 .3983 Firm Sales .0081 .0055 .1355 .0245 R&D Expense -.0155 .0081 -.0229 .0426 Ego Network Size .0655 .1053 -.1292 .3975 Firm Size -.0243 .0181 .0790 .0510 Firm Age .0004 .0003 -.0001 .0011 Intercept .5970 ** .2027 -2.5910 *** .2555 Ego Network Innovation -.0036 .0033 .0372 .0234 Variance (t0) Ego Network Innovation Variance (t+1) Ego Network Innovation Variance (t+2) Model fit Wald [chi square] (DF) 172.88 *** (27) Log psuedolikelihood -1007.07 AIC 2,120.14 BIC 2,471.51 Pseudo [R.sup.2] .18 Observations 5594 (5437/157) (zero/nonzero) Dependent Variable Lag Structure Two Years Forward (t+2) Probability of Increases in Zero Ego Ego Network Network Innovation Innovation Variance Variance Independent Variable (a) B SE B SE Ego Network Betweenness .0028 .0086 .0223 .0420 Ego Network Density -.0154 * .0089 -.0142 .0219 Ego Network Brokerage -.0018 .0086 -.0084 .0115 Ego Network Weakness -.1175 .1401 .0589 .3692 Firm Sales .0076 .0062 .1308 *** .0253 R&D Expense -.0170 .0094 -.0054 .0447 Ego Network Size .1218 .1398 .0206 .3581 Firm Size -.0191 .0182 .1033 * .0533 Firm Age .0008 * .0004 .0006 .0011 Intercept .2772 .0942 -2.8293 .2817 Ego Network Innovation .0024 .0018 -.0174 .0282 Variance (t0) Ego Network Innovation -.0017 .0031 .0272 .0226 Variance (t+1) Ego Network Innovation Variance (t+2) Model fit Wald [chi square] (DF) 169.41 *** (27) Log psuedolikelihood -921.95 AIC 1,949.90 BIC 2,299.27 Pseudo [R.sup.2] .19 Observations 5388 (5246/142) (zero/nonzero) Dependent Variable Lag Structure Three Years Forward (t+3) Probability of Increases in Zero Ego Ego Network Network Innovation Innovation Variance Variance Independent Variable (a) B SE B SE Ego Network Betweenness .0103 .0124 .0266 .0467 Ego Network Density -.0034 * .0020 .0151 .0210 Ego Network Brokerage -.0064 .0098 -.0035 .0139 Ego Network Weakness -.0322 .0985 .3421 .4575 Firm Sales .0057 .0050 .1134 *** .0249 R&D Expense -.0127 .0078 -.0076 .0457 Ego Network Size .0410 .0960 -.2694 .4509 Firm Size -.0116 .0178 .1165 .0523 Firm Age .0008 ** .0003 .0005 .0011 Intercept .2035 ** .0918 -2.8274 *** .2503 Ego Network Innovation -.0027 .0025 .0311 .0231 Variance (t0) Ego Network Innovation -.0009 .0023 .0231 .0289 Variance (t+1) Ego Network Innovation -.0041 .0027 .0469 ** .0212 Variance (t+2) Model fit Wald [chi square] (DF) 191.71 * (27) Log psuedolikelihood -928.94 AIC 1,967.87 BIC 2,328.25 Pseudo [R.sup.2] .17 Observations 5179 (5038/141) (zero/nonzero) (a) The models were estimated using the yearly dummy variables but were not included for space considerations. * p<.1; ** p<.05, *** p<.001. TABLE 6 Summary of Hypotheses and Results Hypothesis Number Hypothesis Result Significance H1a Ego network betweenness Not supported p >.1 has a positive effect on ego network innovation. H1b Ego network betweenness Not supported p >.1 has a negative effect on ego network innovation variance. H2a Ego network density has a Supported p <.001 positive effect on ego network innovation. H2b Ego network density has a Weakly p <.1 negative effect on ego network innovation Supported variance. H3a Ego network brokerage has Supported p <.001 a positive effect on ego network innovation. H3b Ego network brokerage has Not supported p >.1 a negative effect on ego network innovation variance. H4a Ego network weakness has Limited Mixed a positive effect on ego network innovation. Support H4b Ego network weakness has Not supported p >.1 a negative effect on ego network innovation variance. TABLE 7 Interquantile Regression of Ego Network Innovation Dispersion ([[beta].sub..99] - [[beta].sub..01]) Network Variable Sign Ego Network Betweenness Positive Ego Network Density Negative Ego Network Brokerage Negative Ego Network Weakness Positive ([[beta].sub..99] - [[beta].sub..01]) Network Variable Significance Ego Network Betweenness p > .1 Ego Network Density p < .05 Ego Network Brokerage p < .05 Ego Network Weakness p < .05 Network Variable Explanation Ego Network Betweenness Increases in ego network betweenness are not significantly related to increases in the dispersion of ego network innovations. Ego Network Density Increases in ego network density are significantly related to decreases in the dispersion of ego network innovations. Ego Network Brokerage Increases in ego network brokerage are significantly related to decreases in the dispersion of ego network innovations. Ego Network Weakness Increases in ego network weakness are significantly related to increases in the dispersion of ego network innovations.

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Author: | Carnovale, Steven; Yeniyurt, Sengun |
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Publication: | Journal of Supply Chain Management |

Date: | Apr 1, 2015 |

Words: | 15184 |

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