In recent years, China’s robot industry, particularly the industrial robotics segment, has experienced remarkable growth, becoming a pivotal force in the nation’s advanced manufacturing strategy. However, this quantitative expansion has not automatically translated into qualitative superiority in innovation. Many new technological outcomes still face challenges related to low quality and efficiency, revealing a potential vulnerability in the face of international technological competition. This scenario underscores a critical research question: how can innovation agents—enterprises, universities, and research institutes—enhance the fundamental quality of their innovations? This study argues that the answer lies not within isolated innovation stages but in the strategic connections forged across the entire innovation chain. Focusing on China’s industrial robot sector, this paper investigates how the cross-layer embeddedness of innovation agents within collaborative networks influences innovation quality.
The innovation chain, encompassing basic research (science), applied development (technology), and commercialization (product development), represents the complete trajectory from knowledge creation to market value. Each stage demands distinct knowledge types and heterogeneous resources. It is increasingly recognized that high-quality innovation stems from the effective integration of these disparate resources, a feat difficult for any single entity to accomplish alone. Therefore, collaboration across different stages—where scientific discoveries inform technological breakthroughs, which in turn are refined through market feedback—becomes essential. This study posits that innovation agents who strategically embed themselves simultaneously in multiple layers of this chain (e.g., in both scientific and technological networks, or in both technological and product development networks) can access, integrate, and leverage a wider, more diverse set of knowledge resources, ultimately leading to higher-quality innovation outputs.
The development trajectory of China robots in the industrial domain provides a compelling context for this investigation. While the market size has expanded rapidly, the industry contends with foundational weaknesses in core components and a disconnect between scientific research, technological development, and product commercialization. This “structural imbalance” in the industrial innovation chain often leaves valuable scientific achievements underutilized. Consequently, understanding how innovation agents can bridge these gaps through cross-layer collaboration is not only an academic pursuit but a practical necessity for the sector’s sustainable, high-quality development. This research aims to shed light on this mechanism.
Theoretical Foundation and Hypothesis Development
We conceptualize the innovation ecosystem through a multi-layer network lens, corresponding to the key stages of the innovation chain:
- Scientific Collaboration Network: Constructed from co-authored publications, this network represents the basic research layer focused on theoretical knowledge creation.
- Technological Collaboration Network: Constructed from co-invented patents, this network represents the applied research and development layer focused on technological solutions.
- Product Development Collaboration Network: Constructed from joint product development projects, this network represents the commercialization layer focused on bringing innovations to market.
Cross-layer embeddedness refers to the phenomenon where an innovation agent (e.g., a company, university lab, or research institute) is simultaneously an active participant in two or more of these distinct but interconnected networks. We focus on two critical cross-layer linkages: the Science-Technology (S-T) interface and the Technology-Product (T-P) interface. The dynamics are not linear but cyclical: science fuels technology, technology application reveals new scientific questions, technology enables products, and market feedback from products highlights technological shortcomings, creating a reverse feedback loop.
To measure an agent’s position and role within a single network, we employ two fundamental concepts from social network analysis:
- Network Centrality (Degree Centrality): Measures the number of direct collaborative partners an agent has, indicating its level of activity and access to direct information flows.
$$ C_{D}(i) = \sum_{j} x_{ij} $$
where $x_{ij} = 1$ if agent $i$ is connected to agent $j$, and 0 otherwise. - Structural Holes (Constraint Index): Measures the extent to which an agent’s partners are connected to each other. A low constraint (or a high structural hole index) indicates that an agent bridges otherwise disconnected parts of the network, granting it control over information flow and access to non-redundant, diverse knowledge.
$$ C_i = \sum_j \left( p_{ij} + \sum_q p_{iq} p_{qj} \right)^2, \quad q \neq i,j $$
where $p_{ij}$ is the proportion of agent $i$’s network resources invested in the relationship with agent $j$. The structural hole index is often calculated as $ SH_i = 2 – C_i $, where a higher $SH_i$ indicates more structural holes.
We propose that the interaction between an agent’s positions in two different networks (i.e., cross-layer embeddedness) drives innovation quality. The following hypotheses are developed, as summarized in Table 1.
| Hypothesis | Relationship | Expected Sign |
|---|---|---|
| H1a | Interaction of S-T Network Centrality → Innovation Quality | Positive (+) |
| H1b | Interaction of S-T Structural Holes → Innovation Quality | Positive (+) |
| H2a | Interaction of T-P Network Centrality → Innovation Quality | Positive (+) |
| H2b | Interaction of T-P Structural Holes → Innovation Quality | Positive (+) |
| H3a | Partner Overlap (S-T) weakens H1a | Negative (-) |
| H3b | Partner Overlap (T-P) weakens H2a | Negative (-) |
| H4a | Partner Overlap (S-T) weakens H1b | Negative (-) |
| H4b | Partner Overlap (T-P) weakens H2b | Negative (-) |
Cross-layer Embeddedness in the Science-Technology (S-T) Interface
H1a & H1b: An agent deeply embedded in the scientific network (high centrality) gains access to broad, cutting-edge theoretical knowledge. When this is combined with strong embeddedness in the technological network (high centrality), the agent can more efficiently translate scientific insights into viable technological solutions, enhancing the novelty and foundational strength of its innovations. Similarly, an agent bridging structural holes in both the science and technology networks (high structural hole index in both) acts as a crucial broker between disparate scientific fields and technological domains. This position facilitates the synthesis of non-redundant, heterogeneous knowledge, fostering breakthrough ideas that significantly improve innovation quality. Thus, we hypothesize positive effects for both the centrality interaction (H1a) and the structural hole interaction (H1b) across the S-T interface.
Cross-layer Embeddedness in the Technology-Product (T-P) Interface
H2a & H2b: Strong centrality in the technology network provides an agent with diverse technical resources and solutions. Coupled with strong centrality in the product network, the agent can effectively match these technologies with market needs and user feedback, leading to innovations that are not only technically sound but also commercially viable and higher in quality. Furthermore, an agent occupying structural holes in both the technology and product networks occupies a unique brokerage position. It can identify promising technologies from disconnected R&D clusters and channel them toward specific market opportunities uncovered from disparate product development circles. This bridging role enables the integration of specialized technical knowledge with precise market intelligence, culminating in high-quality, market-ready innovations. Hence, positive effects are hypothesized for both interactions (H2a, H2b) across the T-P interface.
The Moderating Role of Partner Overlap
Partner Overlap measures the extent to which an agent collaborates with the same partners across two different network layers (e.g., S-T or T-P). While some overlap may foster trust and efficient communication, we hypothesize that high partner overlap can create rigidity. For centrality (H3a, H3b), high overlap means the agent interacts with a similar circle of partners in both networks, limiting exposure to fresh perspectives and diverse knowledge pools, which could stifle the cross-fertilization of ideas needed for high-quality innovation. For structural holes (H4a, H4b), high overlap while trying to manage many structural holes across layers can lead to information overload and excessive demands on the agent’s attention and resources to manage these similar-but-separate relationships, ultimately hampering its ability to synthesize information effectively for quality innovation.
Research Design and Methodology
Sample and Data
This study focuses on the population of innovation agents (firms, universities, research institutes) within China’s industrial robot industry from 2008 to 2022. Data was collected from multiple sources:
- Scientific Network Data: Co-authorship data from SCI-E indexed journal articles related to industrial robotics, retrieved from Web of Science.
- Technological Network Data: Co-inventorship data from invention and utility model patents related to industrial robotics, retrieved from the IncoPat database.
- Product Development Network Data: Data on joint product development, co-production, and co-marketing projects from corporate announcements, annual reports, financial news, and business databases (e.g., Qichacha).
A 3-year moving window (t-2 to t) was used to construct dynamic, cross-sectional networks for each year. The final sample consists of 509 innovation agents that are embedded in at least two of the three network layers during the observation period.
Variable Measurement
The key variables and their operationalization are detailed in Table 2.
| Variable Type | Variable Name | Symbol | Measurement |
|---|---|---|---|
| Dependent | Innovation Quality | INQ | Sum of the number of claims for all patents applied for by agent i in years t+1 to t+3. Patent claims indicate the breadth and protective scope of an innovation, serving as a proxy for its economic value and quality. |
| Independent | S-T Network Centrality Interaction | STD | $$ STD_{i,t} = C_{D}^{Science}(i,t) \times C_{D}^{Technology}(i,t) $$ where $C_{D}^{Network}$ is the degree centrality in the specified network. |
| T-P Network Centrality Interaction | TPD | $$ TPD_{i,t} = C_{D}^{Technology}(i,t) \times C_{D}^{Product}(i,t) $$ | |
| S-T Structural Hole Interaction | STSH | $$ STSH_{i,t} = SH^{Science}(i,t) \times SH^{Technology}(i,t) $$ where $SH^{Network}$ is the structural hole index (2-constraint) in the specified network. | |
| T-P Structural Hole Interaction | TPSH | $$ TPSH_{i,t} = SH^{Technology}(i,t) \times SH^{Product}(i,t) $$ | |
| Moderator | S-T Partner Overlap | wlcdd1 | $$ wlcdd1_{i,t} = \frac{M1_{i,t}}{S_{i,t} + T_{i,t} – M1_{i,t}} $$ where $M1$ is the number of overlapping direct partners in Science and Tech networks, $S$ and $T$ are the total distinct partners in each network. |
| T-P Partner Overlap | wlcdd2 | $$ wlcdd2_{i,t} = \frac{M2_{i,t}}{T_{i,t} + P_{i,t} – M2_{i,t}} $$ where $M2$ is the number of overlapping direct partners in Tech and Product networks, $T$ and $P$ are the total distinct partners in each network. | |
| Control | R&D Experience | YRD | Years since the agent’s first observed R&D activity (patent or paper) until year t. |
| R&D Team Scale | RDTS | Average number of inventors per patent for agent i in the time window. |
Empirical Model
We employ a two-way fixed effects (entity and year) panel data model to test our hypotheses, controlling for unobserved heterogeneity. The baseline models are:
$$ INQ_{i,t} = \beta_0 + \beta_1 STD_{i,t} + \beta_k \sum Control_{i,t} + \delta_i + \delta_t + \epsilon_{i,t} $$
$$ INQ_{i,t} = \beta_0 + \beta_1 TPD_{i,t} + \beta_k \sum Control_{i,t} + \delta_i + \delta_t + \epsilon_{i,t} $$
$$ INQ_{i,t} = \beta_0 + \beta_1 STSH_{i,t} + \beta_k \sum Control_{i,t} + \delta_i + \delta_t + \epsilon_{i,t} $$
$$ INQ_{i,t} = \beta_0 + \beta_1 TPSH_{i,t} + \beta_k \sum Control_{i,t} + \delta_i + \delta_t + \epsilon_{i,t} $$
To test the moderating effects, interaction terms between the cross-layer embeddedness variables and the corresponding partner overlap variables are added to the models.
Empirical Results and Analysis
Descriptive statistics and correlation analysis confirmed no severe multicollinearity issues (all VIF values < 10). The results from the two-way fixed effects regressions are presented in Table 3.
| Variable | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 (Moderated) | Model 6 (Moderated) | Model 7 (Moderated) | Model 8 (Moderated) |
|---|---|---|---|---|---|---|---|---|
| STD | 0.00148* (1.79) | -0.00062 (-0.45) | ||||||
| TPD | 0.0222 (1.09) | 0.0172 (0.76) | ||||||
| STSH | 0.504* (1.94) | 0.448* (1.74) | ||||||
| TPSH | 1.495*** (2.63) | 1.494** (2.61) | ||||||
| wlcdd1 | 9.700** (2.34) | 7.696*** (2.64) | ||||||
| wlcdd2 | 3.064 (0.57) | |||||||
| wlcdd1×STD | 0.575* (1.88) | |||||||
| wlcdd2×TPD | 0.360 (0.52) | |||||||
| wlcdd1×STSH | -0.356*** (-2.66) | |||||||
| wlcdd2×TPSH | 0.109 (0.21) | |||||||
| Controls | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
| Entity/Year FE | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
| Observations | 493 | 257 | 493 | 257 | 493 | 257 | 493 | 257 |
| R-squared | 0.478 | 0.055 | 0.486 | 0.096 | 0.479 | 0.095 | 0.492 | 0.096 |
| Notes: t-statistics in parentheses; * p<0.1, ** p<0.05, *** p<0.01. | ||||||||
Main Effects:
- H1a is supported. The interaction of Science and Technology network centrality (STD) has a positive and statistically significant effect on innovation quality (Model 1: β=0.00148, p<0.1).
- H1b is supported. The interaction of Science and Technology structural holes (STSH) also shows a positive and significant effect (Model 3: β=0.504, p<0.1).
- H2a is not supported. While the coefficient for the TPD interaction is positive, it lacks statistical significance (Model 2). This may be due to the relatively smaller size and sparser nature of the product development network in the China robot industry during the study period, limiting the flow of heterogeneous market knowledge back to the technology layer.
- H2b is supported. The interaction of Technology and Product structural holes (TPSH) has a strong positive and significant effect on innovation quality (Model 4: β=1.495, p<0.01).
Moderating Effects:
- H4a is supported. The interaction term between STSH and partner overlap (wlcdd1) is negative and significant (Model 7: β=-0.356, p<0.01). This indicates that high partner overlap weakens the positive impact of bridging structural holes across the science and technology layers, likely due to the cognitive and coordination burdens of managing similar bridging relationships in both networks.
- H3a, H3b, and H4b are not supported. The other moderating effects are not statistically significant. For centrality interactions (H3a, H3b), high partner overlap might simultaneously provide relationship stability and trust that facilitates knowledge transfer, counteracting the hypothesized negative rigidity effect. The non-significance for T-P structural hole moderation (H4b) might relate to the specific dynamics of the China robot market, where managing diverse ties across technology and product domains remains beneficial even with some partner overlap.
The results were robust to alternative specifications, including shortening the dependent variable window and winsorizing the data.
Conclusion and Implications
This study, grounded in the context of China’s industrial robot industry, elucidates the critical role of cross-layer network embeddedness in fostering high-quality innovation. The central finding is that innovation agents who strategically position themselves as central connectors or as bridges (occupying structural holes) simultaneously across two key layers of the innovation chain—particularly the Science-Technology and Technology-Product interfaces—achieve significantly higher innovation quality. This underscores the importance of proactive, multi-faceted collaboration over passive or siloed engagement within a single innovation stage. For the China robot sector, which aims to transition from scale to quality, this implies that policies and firm strategies must encourage and facilitate deep integration across the entire innovation value chain.
The findings offer specific managerial and policy implications:
- Strategic Portfolio of Collaborations: Innovation agents should consciously cultivate a diverse portfolio of partnerships spanning scientific, technological, and product development networks. Actively engaging with leading research institutions, technology pioneers, and key market players can enhance centrality and resource access across layers.
- Value of Brokerage Positions: Agents should seek to occupy brokerage positions (structural holes) that connect otherwise disconnected clusters within and between network layers. This role provides unique access to non-redundant information and offers opportunities to integrate disparate knowledge streams, a key driver of high-quality, novel innovations for China robots.
- Holistic Innovation Chain Perspective: Policymakers designing support programs for the China robot industry should incentivize collaborative projects that explicitly bridge different stages of the innovation chain (e.g., industry-university co-development projects with clear commercialization pathways). The goal should be to strengthen the feedback loops between science, technology, and the market.
- Nuanced Partner Strategy: While having some overlap in partners across networks can be efficient, agents should be cautious about excessive overlap, especially when acting as a bridge (structural hole) between science and technology. A balance between trusted, repeated ties and new, diverse connections is optimal.
This research has limitations. It focuses on a single, albeit critical, industry. Future studies could test the generalizability of these findings in other high-tech sectors within China or internationally. Furthermore, while focusing on structural embeddedness (centrality, structural holes), future work could incorporate relational aspects like tie strength or cognitive dimensions like knowledge proximity. Qualitative case studies could also provide deeper insights into the micro-processes of how specific China robot firms manage their cross-layer networks to achieve quality breakthroughs. Despite these limitations, this study provides a robust framework and empirical evidence highlighting that in the complex ecosystem of modern innovation, quality is forged in the connections between the chain’s essential links.