Unveiling the Temporal Dynamics: The Impact of Knowledge Source Structure on Innovation through Time-Series Analysis

Unveiling the Temporal Dynamics: The Impact of Knowledge Source Structure on Innovation through Time-Series Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Unveiling the Temporal Dynamics: The Impact of Knowledge Source Structure on Innovation through Time-Series Analysis Yue Li, Jiaxing Li, Lele Kang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8119156/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Disruptive innovation plays a critical role in driving technological progress and reshaping industries by challenging established paradigms and fostering new opportunities for growth. While previous research has largely focused on the static relationship between knowledge characteristics and disruptive innovation, the temporal dynamics of how knowledge structures influence disruptive innovation remain unclear. This study addresses this gap by examining the absorptive capacity process, distinguishing between Potential (PAC) and Realized (RAC) absorptive capacities. Using global patents spanning 1980 to 2010, we employed Autoregressive Distributed Lag (ARDL) and Granger causality tests to analyze the long-run, short-run, and causal relationships. The ARDL findings reveal a temporal conflict. In the long-run, PAC, as measured by knowledge source diversity, promotes disruptive innovation. In contrast, an exploratory path of RAC, measured by knowledge breadth, is detrimental. These effects are reversed in the short-run. Here, PAC negatively impacts disruptive innovation, whereas RAC, when measured by knowledge depth, provides a positive impact. The Granger causality tests further uncover a bidirectional feedback loop between PAC and disruptive innovation, and reveal that disruptions are an endogenous driver of the exploratory RAC path. These findings underscore the importance of aligning knowledge management strategies with temporal dynamics to foster sustained innovation. Disruptive innovation Knowledge structure Temporal dynamic Figures Figure 1 Figure 2 Introduction Disruptive innovation (DI), which reshapes existing technological paradigms and drives progress in entirely new directions, has historically been a cornerstone of transformative development. However, recent studies reveal a worrying trend: the disruptive potential of innovations is steadily declining. Park et al. ( 2023 ) quantified this phenomenon using the CD index, a metric that captures the disruptiveness of patents and scientific publications by assessing their impact on subsequent citation patterns. Their findings highlighted a consistent decline in disruptiveness across technological fields, raising critical questions about the factors driving this shift. Despite growing attention to this phenomenon, it remains unclear whether and how different structures of knowledge influence this decline. Existing studies have investigated various factors influencing innovation, including institutional frameworks such as intellectual property rights regime (Thakur-Wernzet al., 2022) and funding mechanisms (Irfan et al., 2022 ), technological ecosystems such as industry clusters (Kim et al., 2023 )d networks (Wen et al., 2021 ), and organizational characteristics such as team size (Wuchty et al., 2007 ), leadership styles (Alblooshi et al., 2021 ), and knowledge management practices (Darroch, 2005 ; Mardani et al., 2018 ). Among these factors, knowledge emerges as a cornerstone of the innovation process, enabling both exploration and exploitation, which form the basis for novel recombination and technical refinement (Grant, 1996 ). Evolutionary economics reinforces this perspective by emphasizing the cumulative nature of knowledge, where its recombination drives disruptions (Nelson, 1985 ). Despite these insights, most research adopts a static perspective, overlooking how the continuous evolution of knowledge influences disruptive innovation (Volberda et al., 2010 ). As innovation systems mature, the complexity of integrating and applying knowledge evolves, potentially reshaping its impact on innovation outcomes (Fleming et al., 2001). This highlights the need to examine how the dynamic restructuring of knowledge affects the trajectory of DI. Innovation is inherently dynamic, shaped by the transformation of knowledge and its interplay with external factors like technological advancements and market dynamics (Teece et al., 1997 ; Ganguly et al., 2022 ). Within a dynamic capability view, absorptive capacity provides microfoundations through two analytically separable components (Zahra & George, 2002 ). Potential Absorptive Capacity (PAC) captures what knowledge is sourced and reflects the heterogeneity of external prior art an invention taps. Realized Absorptive Capacity (RAC) captures how knowledge is applied and reflects the actualized knowledge structure manifested within the patent itself. Greater PAC enlarges the space for novel recombination (Rosenkopf & Almeida, 2003 ) but increases screening and assimilation costs (Fleming, 2001 ); RAC that spans fields supports exploration yet risks fragmentation, whereas concentration streamlines exploitation yet raises lock in risk (Volberda et al., 2010 ). These opposing effects indicate that the link between knowledge structure and DI evolves as knowledge is accessed and applied, which motivates examining their dynamic relationship. To better understand the dynamic relationship between DI and the knowledge absorptive capacity (e.g., PAC and RAC) this study employs the Autoregressive Distributed Lag (ARDL) model (Pesaran, et al., 2001 ). In contrast to traditional static models, the ARDL approach enables the simultaneous estimation of short-run adjustments and long-run equilibrium relationships, providing deeper insights into the evolving impact of knowledge on DI. By distinguishing between short-run fluctuations and long-run trends, the ARDL model offers valuable insights into how DI responds to changes in knowledge structure over different time horizons. The short-run analysis reveals immediate responses to shifts in knowledge, while the long-run analysis captures persistent influences that shape innovation trajectories. This comprehensive approach contributes to a deeper understanding of how knowledge recombination and application influence DI. This study analyzed annual patent data from 1980 to 2010. First, we applied unit root tests, including the Augmented Dickey-Fuller and Phillips-Perron tests, to ensure the stationarity of the variables. Second, given the mixed integration order of the data, we utilized the ARDL bounds test to determine the presence of long-run relationships. Third, we conducted Granger-causality tests to examine the dynamic feedback loops. The empirical findings indicate that, over the long run, PAC is the sole significant positive driver of disruptive innovation, while a specific pathway of RAC, namely exploratory transformation measured by knowledge breadth, has a significant adverse effect. This core long-run finding is robust to alternative estimation methods. In the short run, however, the system’s incentives are reversed: investments in PAC present immediate challenges, while the exploitative pathway of RAC, measured by knowledge depth, fosters innovation. Furthermore, our Granger causality analysis uncovers a bidirectional feedback loop between PAC and disruptive innovation. It also reveals that disruptions act as a strong endogenous driver of future RAC configurations, particularly by fuelling the expansion of the exploratory transformation path represented by knowledge breadth. Building on these findings, this study makes several contributions to the literature. First, they provide a deeper understanding of the mechanisms underlying the observed decline in disruptiveness, highlighting the lack of sufficient analysis on the temporal evolution of knowledge structures. Second, by employing the ARDL model, this study offers a methodological advancement that allows for the investigation of DI from a dynamic perspective, capturing both short-run adjustments and long-run equilibrium relationships. Third, our study reveals the co-evolutionary dynamics between knowledge structures and innovation. By uncovering a feedback loop between PAC and disruptive outcomes, we show that innovation is not merely an endpoint but an active agent that reshapes its own knowledge environment. This provides a novel, systemic explanation for how innovation trajectories are endogenously formed and sustained over time. Related Work Disruptive innovation The theory of disruptive innovation was first proposed by Christensen ( 1997 ), characterized by its non-linear technological trajectory. Unlike traditional mainstream technologies, disruptive innovation advances through differentiated strategies to achieve competitive advantage (Hang et al., 2015 ). Existing studies have defined the concept from various perspectives, including technological characteristics (Nagy et al., 2016 ; Reinhardt & Gurtner, 2015 ), innovation processes (Levina, 2017 ), and innovation impacts (Suseno, 2018 ). These studies have also explored disruptive innovation across multiple levels, including the individual (Osiyevskyy & Dewald, 2015 ), firm (Van Balen et al., 2019 ), industry (Chevalier-Roignant et al., 2019 ), and network or ecosystem levels (Ruan et al., 2014 ). A significant challenge in this field has been the empirical measurement of an innovation’s disruptive impact. Early work relied primarily on qualitative cases and industry-level histories; a major advance came with the use of patent citations to quantify technological influence (Trajtenberg, 1990 ; Jaffe & Trajtenberg, 2002 ). Within this tradition, originality and generality capture, respectively, the dispersion of an invention’s knowledge inputs and the breadth of its downstream reach. One family of subsequent measures remains rooted in this recombinant view, extending beyond input-output dispersion to the rarity of knowledge pairings: atypical combinations identified from co-classification matrices or topic models, and other indicators of cognitive novelty, anticipate disruptive potential even before diffusion is fully observed (Uzzi et al., 2013 ; Kaplan & Vakili, 2015 ). Another family of measures locates inventions in a technological or semantic knowledge space and tracks how far they move relative to their prior art or how strongly they bridge previously separated clusters. Distance-based and bridging metrics, implemented with classification hierarchies, vector embeddings, or citation geodesics, emphasize structural relocation and reconfiguration as hallmarks of disruption (Rosenkopf & Nerkar, 2001 ; Youn et al., 2015 ; Wang et al., 2023 ; Wang, 2024 ). More recently, a network-based approach has emerged to measure creative destruction directly in citation behavior. The disruption-consolidation framework operates by analyzing subsequent citation behavior. It identifies evidence of displacement if later works citing a focal contribution simultaneously omit its antecedents. Conversely, it identifies evidence of consolidation if these later works co-cite both the focal contribution and its intellectual predecessors. The CD index operationalizes this logic at scale and underpins large-sample findings, including the widely cited evidence of declining disruptiveness across science and technology (Wu et al., 2019 ; Park et al., 2023 ). Related dynamic network measures trace how downstream citation flows are reoriented after a focal invention, complementing CD by capturing redirection in the broader knowledge graph (Funk & Owen‑Smith, 2017). Potential absorptive capacity and realized absorptive capacity While the aforementioned measurement traditions provide powerful tools to quantify what constitutes a disruptive innovation, a deeper theoretical framework is needed to explain why and how these knowledge dynamics unfold. The theory of absorptive capacity, introduced by Cohen and Levinthal ( 1990 ), provides the dominant framework for this inquiry. It argues that an innovation’s potential is not merely a function of the available knowledge components, but of an entity’s capacity to value, assimilate, and apply new external knowledge. A key development in this theory was the reconceptualization by Zahra and George ( 2002 ), who decomposed absorptive capacity into Potential Absorptive Capacity (PAC) and Realized Absorptive Capacity (RAC). PAC encompasses the processes of knowledge acquisition and assimilation, representing the potential to learn from external knowledge. RAC, in contrast, covers the subsequent processes of transformation and exploitation, representing the ability to convert that potential into innovation outcomes. Grounded in this framework, a vast body of prior research has explored how different facets of absorptive capacity influence innovation performance. For example, numerous studies have investigated the PAC stage by examining the role of external knowledge sourcing strategies. Scholars have found that the breadth of external search (Laursen & Salter, 2006 ), boundary-spanning activities into distant knowledge domains (Rosenkopf & Nerkar, 2001 ), and the diversity of external knowledge partners are critical for firm innovation (Jiang et al., 2020 ; Powell et al., 1996 ). Research on the RAC stage emphasizes how internal knowledge structures are reconfigured to realize value. Changes in knowledge couplings among a firm’s domains shape innovation outcomes, contingent on domain complexity (Yayavaram & Chen, 2015 ). Breakthrough invention benefits from recombination when internal coherence is maintained, highlighting the integration challenge of synthesizing disparate knowledge components (Kaplan & Vakili, 2015 ). Within this body of research, the structure of knowledge itself has emerged as a crucial lens for operationalizing and understanding these capabilities. Numerous scholars have adopted this lens to empirically study absorptive capacity. Research investigating the PAC has frequently focused on the role of external knowledge sourcing. Therefore, we conceptualize knowledge source diversity, which measures the variety of an innovation’s external knowledge inputs, as a direct and tangible indicator of this external driving force for innovation. A rich body of literature has explored the dual impacts of sourcing from diverse knowledge bases. On one hand, a high KSD enriches opportunities for novel technological combinations and enhances overall innovation capacity (Dogru et al., 2019 ). It provides the necessary resilience and adaptability for disruptive innovation by enabling systems to address path dependency and uncertainties (Luo et al., 2024 ). On the other hand, excessive diversity in knowledge sources can increase coordination challenges and integration costs, thereby negatively impacting innovation efficiency. Some studies have even identified an inverted U-shaped relationship, suggesting that moderate diversity is optimal while excessive diversity leads to managerial complexity (Hajialibeigi, 2023 ). The specific categories of knowledge sources, such as public versus private sector knowledge, also appear to have differential impacts (Abdul Basit & Medase, 2019 ). The RAC, which reflects the internal processing and application of knowledge, can be understood through knowledge breadth and knowledge depth. These represent the strategic trade-offs in how acquired knowledge is exploited. Knowledge breadth, the integration of knowledge from multiple internal fields, is found to facilitate disruptive innovation by enabling diverse combinations and cross-domain integration (Xu et al., 2015). However, the literature also warns that excessive breadth may lead to resource dispersion and coordination complexities, ultimately hindering innovation efficiency (Jin et al., 2015 ). In contrast, Knowledge depth, representing specialization within a specific field, is shown to strengthen technological advantages and support incremental innovation (Boh et al., 2014 ). Yet, an over-reliance on depth can limit a firm’s adaptability to emerging technologies, a significant risk in rapidly changing environments. Data and Method Data and variables To investigate the short-run and long-run dynamics between disruptive innovation, knowledge source diversity, breadth and depth, this study utilizes patent data obtained from the PatentView database. This comprehensive database includes detailed information on patents from 1976 to 2024, encompassing inventor details, patent and application metadata, assignee and location information, as well as International Patent Classification (IPC) data. The database further provides access to the full text of patents, which includes three key sections: abstract, claims, and description. The claims section outlines the scope of the legal protection granted to the patent, while the description section provides a detailed explanation of the invention or innovation’s technical characteristics. The abstract offers a summary of the content in both the claims and description sections. To analyse the genuine technological attributes of patented inventions, this study exclusively relies on the description section. The variables in this study are designed to capture the core constructs of our theoretical framework. The dependent variable is disruptive innovation. The independent variables operationalize the two stages of absorptive capacity: potential absorptive capacity is measured by knowledge source diversity , while realized absorptive capacity is measured through the distinct pathways of knowledge breadth and knowledge depth . The specific measurement of each variable is detailed below. Disruptive Innovation . Disruptive innovation is measured using the CD index, which was developed by Funk and Owen-Smith ( 2017 ) and later applied by Park et al. ( 2023 ). The CD index quantitatively captures whether a patent consolidates existing knowledge or disrupts the technological status quo. Consolidating patents build upon prior knowledge and reinforce established trajectories, whereas disruptive patents render earlier work obsolete and chart new technological directions. The CD index ranges from − 1 to 1, where − 1 indicates a highly consolidating innovation, and 1 signifies a highly disruptive innovation. This study adopts the five-year post-publication window used by Park et al. ( 2023 ), referred to as CD 5 , to evaluate the disruptive potential of patents. The starting year of analysis is 1980, aligns with Park et al.’s dataset to ensure consistency in the time window and methodology. The calculation of the CD index also follows the exact formula proposed by Park et al. ( 2023 ). Using this standardized approach ensures comparability with prior studies and allows for robust exploration of the relationships between disruptive innovation and knowledge structures, including breadth, depth, and source diversity. Knowledge Source Diversity (KSD) . The knowledge source diversity measures the extent to which a patent integrates knowledge from multiple technological categories, based on the NBER two-digit technology classification. The NBER classification system, developed by Hall et al. ( 2001 ), provides a standardized framework for categorizing patents into broad technological fields, facilitating cross-field comparisons, and enabling robust analyses of knowledge diversity. In this study, the classification of patents into NBER technology categories is obtained directly from the PatentView database, ensuring consistency and reliability in the analysis. To calculate KSD, the references cited by each patent are analysed to determine their distribution across NBER technology categories. The diversity of these references is quantified using an entropy-based approach, which accounts for both the number of categories referenced and the balance among them. Patents with higher KSD indicate a greater reliance on knowledge inputs from multiple distinct technological fields, reflecting their ability to integrate diverse sources of knowledge. This diversity is hypothesized to enhance the potential for creative recombination of ideas, which is often a critical driver of disruptive innovation. Knowledge Breadth (KB) . The knowledge breadth is defined as the extent to which a patent draws upon vocabulary from multiple technological fields. Following the methodology outlined in Bowen et al. ( 2023 ), this metric is constructed by first calculating the frequency of word usage across technological fields for each year. A word is tagged as specialized in a particular field if its usage in that field exceeds 150% of its usage in the second most prominent field during the same year. Words that do not meet this criterion are classified as unspecialized and excluded from further analysis. For each patent, the fraction of specialized words classified into each field is then calculated, with these fractions summing to one for every patent. Using this classification, technological breadth is defined as one minus the concentration of specialized words, thereby reflecting the diversity of fields from which a patent draws its vocabulary. Patents with high knowledge breadth integrate terminology from a wider range of fields, indicating a more diverse knowledge base: Knowledge Depth (KD). The knowledge depth measures the extent of focus within a single technological field, and is calculated based on the concentration of a patent’s classification within a specific four-digit International Patent Classification (IPC4) code. The IPC4 system provides a highly granular framework for categorizing patents, often used as a proxy for defining technological fields. By examining the proportion of a patent’s classifications that fall within its most dominant IPC4 category, knowledge depth captures the degree to which a patent concentrates on a single technological field. Patents with high knowledge depth often exhibit a deliberate emphasis on advancing a particular field, suggesting a refined specialization that may impact incremental innovations or significant technical improvements within that domain. By anchoring the measurement of depth in the IPC4 classification, the analysis ensures precision in capturing the technical focus of each patent. This reliance on established knowledge structures may enhance efficiency in knowledge utilization. All variables and their description are shown in Table 1 . Table 1 Variables description. Variables Description Disruptive Innovation (DI) CD Measured using the CD index, developed by Funk and Owen-Smith ( 2017 ) and applied by Park et al. ( 2023 ). The index ranges from − 1 (highly consolidating) to 1 (highly disruptive), with CD 5 calculated over a five-year post-publication window to evaluate a patent’s influence on obsolescing or reinforcing prior knowledge. Potential Absorptive Capacity (PAC) Knowledge Source Diversity (KSD) Reflects the variety of technological categories from which a patent integrates knowledge. Based on the NBER two-digit technology classification and calculated using entropy to measure the diversity of references cited by each patent across multiple fields. Realized Absorptive Capacity (RAC) Knowledge Breadth (KB) Captures the diversity of technological fields from which a patent draws its vocabulary. Calculated as one minus the concentration of a patent’s classification into six broad fields, reflecting the extent to which the patent spans multiple domains. Derived using field-specific data from the patent text and classification systems. Knowledge Depth (KD) Measures the extent of focus within a single technological field. Calculated based on the proportion of a patent’s classifications concentrated within its most dominant IPC4 code, representing a refined specialization in a specific domain. The rationale for employing distinct operational measures for KSD, KB, and KD is grounded in their theoretical separation, empirical complementarity, and granular alignment with the conceptual constructs. Although these structures are interrelated, they reflect fundamentally different structural layers of knowledge, which necessitates differentiated yet coherent measurement strategies. First, KSD captures the diversity of technological origins, for which the NBER 2-digit classification is particularly suited. Its coarse granularity reflects broader source fields (e.g., Chemicals, Electronics, Drugs), and has been widely used to proxy knowledge origin variety in macro-level innovation studies (Hall et al., 2001 ). NBER codes aggregate IPC-based patent classes according to economically meaningful technological sectors, thus aligning closely with the idea of where knowledge comes from. Second, KD is intended to reflect technological specialization, which demands greater classification precision. The IPC 4-digit level provides such fine-grained technical delineation, enabling us to observe how concentrated a patent’s technical focus is. Compared with higher-level IPC or NBER codes, IPC4 provides domain stability and domain resolution, making it the most valid proxy for focused depth within a technological field. Third, KB concerns the semantic recombination and interdisciplinary expression of knowledge within the patent text. To this end, a vocabulary-based approach is employed, tracking the field-specific concentration of technical terms used in abstracts and claims. This textual metric captures horizontal conceptual integration at a finer level than taxonomic classifications, especially in domains where innovation involves hybrid or emergent concepts not yet classified in IPC/NBER systems. While the data sources and granularity differ across these three variables, they are intentionally selected to match the theoretical domain of each construct: broad origin domains (KSD), fine technical depth (KD), and semantic conceptual spread (KB). These differences do not imply inconsistency but rather reflect the layered nature of knowledge structures in innovation. We explicitly acknowledge that the classification schemes are non-nested and differ in dimensional logic. However, their temporal aggregation into annual panel data and their independent derivation from non-overlapping sources reduce concerns about collinearity or semantic redundancy. Moreover, our ARDL model framework allows for distinct lag structures, further reducing risks of artificial convergence. Methodology and model specification Econometric methods that investigate the temporal dynamics of innovation processes are essential for understanding how variables interact over time. These approaches enable the analysis of both short-run fluctuations and long-run equilibrium relationships, offering valuable insights into the mechanisms impacting disruptive innovation and its connections to knowledge structures such as source diversity, breadth and depth. Given the need to examine these dynamics comprehensively, this study adopts the Autoregressive Distributed Lag (ARDL) bounds testing model, introduced by Pesaran et al. ( 1999 ) and later developed further (Pesaran, et al., 2001 ), to explore the cointegration processes and temporal interactions among the variables. The ARDL approach not only estimates cointegration and long-run equilibrium relationships but also captures dynamic effects in both time horizons, offering a comprehensive framework for understanding temporal interactions. The ARDL methodology is particularly advantageous for several reasons. First, it is highly flexible and can accommodate variables with mixed integration orders, whether I(0) or I(1). Second, the single-equation setup simplifies implementation and interpretation compared to traditional cointegration methods. Third, it allows for different lag lengths to be specified for different variables, enhancing the model’s adaptability to the data. Fourth, the method is well-suited for small sample sizes, providing robust estimates of long-run relationships and parameters. Finally, the ARDL model effectively addresses potential issues of autocorrelation and endogeneity, ensuring unbiased and reliable results (Harris & Sollis, 2003 ; Jalil & Ma, 2008 ). Given these strengths, the ARDL approach is employed in this study to examine the temporal dynamics between disruptive innovation and its key regressors, such as knowledge source diversity, breadth and depth. The method is applied to identify both the long-run equilibrium relationships and the short-run adjustments that occur in response to deviations from equilibrium. The subsequent steps for verifying these dynamics within the ARDL framework are outlined in the following sections. Stationarity test . Stationarity is a critical consideration in time-series analysis, as it ensures the validity of econometric models and the reliability of their results. Time-series data have diverse applications across various fields, and identifying the appropriate trend structure of the data represents an essential econometric task (Mushtaq, 2011 ). To determine the stationarity of the variables, this study employs the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests. These tests are widely used to identify whether variables are stationary at their levels or become stationary after differencing. The results of these tests guide the appropriate application of the Autoregressive Distributed Lag (ARDL) approach, which is capable of handling variables integrated at different orders. Specifically, the ARDL model can accommodate variables that are stationary at level (I(0)), at first difference (I(1)), or a combination of the two, making it a robust method for analysing the cointegration and temporal dynamics among time-series variables. Autoregressive Distributed Lag bounds test . The bounds testing procedure is utilized in this study to examine whether a single long-run relationship exists among the variables under investigation. The ARDL bounds test evaluates cointegration by testing the joint significance of the coefficients of the lagged levels of the variables in a single-equation model. The model for the bounds test is specified as follows: $$\:\varDelta\:{CD}_{t}=\alpha\:+\sum\:_{i=1}^{p}{\beta\:}_{i}\varDelta\:{CD}_{t-i}+\sum\:_{i=0}^{q}{\gamma\:}_{i}\varDelta\:{KB}_{t-i}+\sum\:_{i=0}^{r}{\delta\:}_{i}\varDelta\:{KD}_{t-i}+\sum\:_{i=0}^{s}{\eta\:}_{i}\varDelta\:{KSD}_{t-i}$$ $$\:+{\theta\:}_{1}{CD}_{t-1}+{\theta\:}_{2}{lnKB}_{t-1}+{\theta\:}_{3}{lnKD}_{t-1}+{\theta\:}_{4}{lnKSD}_{t-1}+{ϵ}_{t}$$ In this equation, Δ denotes the first-difference operator, CD t is the disruptive innovation index, and KB t , KD t , and KSD t represent knowledge breadth, depth, and source diversity, respectively. The optimal lag lengths (p, q, r, s) are determined using the Akaike Information Criterion (AIC), which minimizes information loss and ensures the model is parsimonious while retaining explanatory power. The coefficients \(\:{\theta\:}_{1}\) , \(\:{\theta\:}_{2}\) , \(\:{\theta\:}_{3}\) , \(\:{\theta\:}_{4}\) capture the long-run equilibrium relationships, while the summations account for short-run dynamics. The term \(\:{ϵ}_{t}\) captures any variations unexplained by the model, ensuring the robustness of the estimation process. To evaluate the existence of a cointegration relationship, the ARDL bounds test is applied. This test compares the calculated F-statistic to critical bounds for the null hypothesis (H 0 ), which assumes no cointegration among the variables, and the alternative hypothesis (H 1 ), which posits the presence of cointegration. A rejection of H 0 occurs when the F-statistic exceeds the upper critical bound, indicating a stable long-run relationship among the variables. Conversely, if the F-statistic falls below the lower bound, the null hypothesis cannot be rejected. When the F-statistic lies between the bounds, the result is inconclusive, requiring further investigation. Once a long-run relationship is confirmed through the ARDL bounds testing approach, the model is re-specified into an Error Correction Model (ECM) to estimate both short-run dynamics and the speed of adjustment back to the long-run equilibrium. The ECM effectively integrates short-run fluctuations and long-run relationships within a single framework, ensuring the model captures both immediate and equilibrium effects of the independent variables on disruptive innovation. The ECM for this study is specified as follows: $$\:\varDelta\:{CD}_{t}=\alpha\:+\sum\:_{i=1}^{p}{\beta\:}_{i}\varDelta\:{CD}_{t-i}+\sum\:_{i=0}^{q}{\gamma\:}_{i}\varDelta\:{KB}_{t-i}+\sum\:_{i=0}^{r}{\delta\:}_{i}\varDelta\:{KD}_{t-i}+\sum\:_{i=0}^{s}{\eta\:}_{i}\varDelta\:{KSD}_{t-i}+\tau\:{ECT}_{t-1}+{ϵ}_{t}$$ The ECM framework is particularly valuable because it allows the separation of short-run dynamics from long-run equilibrium behaviour while maintaining a consistent representation of the temporal relationships among variables. The short-run effects are captured by the coefficients of the lagged differences, which provide insights into the immediate impacts of changes in knowledge structures on disruptive innovation. Meanwhile, the Error Correction Term (ECT) integrates the short-run adjustments with the long-run relationship, ensuring that deviations from equilibrium are systematically corrected over time. By applying the ECM within the ARDL framework, this study is able to investigate not only how knowledge breadth, depth, and source diversity influence disruptive innovation in the long run, but also how these variables interact dynamically in the short run. This dual focus provides a comprehensive understanding of the temporal mechanisms impacting innovation processes. Stability test . Ensuring the stability of regression models is critical when working with autoregressive structures, as stability confirms the robustness of estimated coefficients over time. In this study, the CUSUM of squares approach, as proposed by Brown et al. ( 1975 ), is employed to evaluate the dynamic stability of the model. The CUSUM of squares test provides a graphical representation of stability, where the plotted test statistic is compared against a confidence interval. If the test statistic remains within the confidence bounds, the model is considered stable, indicating no significant changes in the regression coefficients over time. Conversely, if the statistic crosses the bounds, it suggests potential instability, requiring further investigation. Empirical findings This study employs multivariate time-series data from 1980 to 2010, with annual observations to mitigate the influence of seasonal variations. The annual data are derived by calculating patent-level indicators for each year and then averaging these values at the yearly level, ensuring a consistent representation of trends over time. The analysis focuses on identifying the relationships between disruptive innovation and various knowledge structures over time. Summary statistics The descriptive statistics for the key study variables is provided in Table 2 , including disruptive innovation (CD), knowledge breadth (lnKB), knowledge depth (lnKD), and knowledge source diversity (lnKSD). The mean value of CD is 0.127, with a standard deviation of 0.098, indicating moderate variation in disruptive innovation across the sample period. The minimum and maximum values of CD range from 0.030 to 0.388, reflecting substantial differences in the disruptiveness of innovations over time. Knowledge breadth (lnKB) exhibits a mean value of 0.364 with relatively low variability (S.D. = 0.023), suggesting a consistent level of knowledge integration across patents. Knowledge depth (lnKD) has a slightly higher mean of 0.528 and also demonstrates low variability (S.D. = 0.017), highlighting the stable specialization within individual technological fields. In contrast, knowledge source diversity (lnKSD) shows the highest mean of 0.684 with minimal variation (S.D. = 0.003), indicating that patents consistently rely on a diverse set of external knowledge sources. Table 2 Summary statistics of study variables. Variables Mean S.D. Min Max CD 0.127 0.098 0.030 0.388 lnKB 0.364 0.023 0.313 0.397 lnKD 0.528 0.017 0.488 0.561 lnKSD 0.684 0.003 0.677 0.687 Together, these descriptive statistics and time trends highlight the dynamic relationships between disruptive innovation and the key knowledge structure, providing a foundation for exploring their short-run and long-run interactions in subsequent analyses. Stationarity test In this study, stationarity of the variables was tested using both the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests, with the results summarized in Table 3 . The stationarity test results reveal that, except for the variable CD, all variables become stationary after applying the first difference. Specifically, the results indicate that at the level, none of the variables, except for CD, exhibit stationarity. However, after taking the first difference, all variables—namely the logarithms of knowledge breadth (lnKB), knowledge depth (lnKD), and knowledge source diversity (lnKSD)—become stationary. The variable CD, on the other hand, is stationary at the level, confirming that it does not require differencing. This mixed order of integration among the variables suggests that an Autoregressive Distributed Lag (ARDL) bound approach is appropriate for modeling the relationship between the variables, as it can accommodate variables with different integration orders (i.e., I(0) and I(1)). Table 3 Stationarity test statistics. Variables ADF Test PP Test Stationary Remark Level First difference Level First difference CD -4.873*** (0.000) - -3.870*** (0.013) - I(0) lnKB -0.191 (0.992) -5.894*** (0.000) -0.196 (0.992) -5.872*** (0.000) I(1) lnKD -2.676 (0.246) -4.637*** (0.001) -2.722 (0.227) -4.574*** (0.001) I(1) lnKSD -1.596 (0.794) -7.120*** (0.000) -1.325 (0.882) -7.105 (0.000) I(1) Note : An intercept term and a trend term have been included in all unit-root tests. Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. ARDL bounds test To determine the optimal lag length for the model, the Akaike Information Criterion (AIC) was utilized. Based on this criterion, the chosen model is ARDL(1, 0, 2, 2). This means that the optimum lag lengths for the variables CD, lnKB, lnKD, and lnKSD are p = 1, q = 0, r = 2 and s = 2, respectively. The results of the ARDL bounds test are presented in Table 4 , which includes the F-statistics values for testing the presence of a long-run relationship between the variables. Table 4 ARDL bounds test (F-statistic). F-statistic Value Null hypothesis: no levels of relationship Significance level I(0) I(1) Value of F-statistic 31.232 10.0% 2.72 3.77 K 3 5.0% 3.23 4.35 Critical Value Bounds 0.1 − 0.01 2.5% 3.69 4.89 1.0% 4.29 5.61 Since the F-statistic value exceeds the critical values for both I(0) and I(1), this provides strong evidence of a long-run relationship among the variables. The results suggest that the knowledge structures are jointly influencing disruptive innovation in the long-run, while the variables move together toward an equilibrium over time. ARDL adjustment estimation, long-run and short-run relationships The ARDL adjustment estimates is reported in Table 5 , indicating how the variables align with the long-run equilibrium following deviations. The coefficient of CD L1 is − 0.135, which is negative and statistically significant at the 1% level. This value reflects the proportion of the adjustment toward long-run equilibrium in response to deviations. Specifically, approximately 13.5% of the disequilibrium is corrected within one year, indicating that the variables are gradually realigned with their long-run equilibrium. The statistically significant negative coefficient also suggests a stable long-run relationship, with adjustments occurring systematically over time. Table 5 ARDL adjustment estimates. D.CD Coef. Std.error T P >|t| [95% Conf. Interval] CD. L1. -0.135*** 0.023 -5.98 0.00 -0.181 -0.088 Note : Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. The long-run estimates obtained from the ARDL model is presented in Table 6 , illustrating the sustained relationships between disruptive innovation and the knowledge sturcture: breadth, depth, and source diversity. The coefficient of knowledge breadth (lnKB) is negative and statistically significant at the 1% level. This indicates that in the long run, an increase in knowledge breadth is associated with a reduction in disruptive innovation. This may reflect the trade-off between generalization and specialization, where increased knowledge breadth could dilute the focus needed for achieving disruption. The coefficient of knowledge depth (lnKD) is negative but not statistically significant. This result implies that knowledge depth does not show a strong long-run influence on disruptive innovation during the study period. This finding may suggest that depth alone is insufficient to drive innovation without the complementary effects of breadth or diversity. The coefficient of knowledge source diversity (lnKSD) is positive and statistically significant at the 1% level. This indicates a strong positive long-run relationship between knowledge source diversity and disruptive innovation. The result suggests that integrating diverse sources of knowledge significantly enhances the potential for disruption, potentially due to the cross-pollination of ideas from different fields or disciplines. Table 6 ARDL long-run estimates. Variables Coef. Std.error T P >|t| [95% Conf. Interval] lnKB -1.276*** 0.396 -3.23 0.004 -2.101 -0.451 lnKD -0.558 0.988 -0.57 0.578 -2.619 1.503 lnKSD 18.942*** 4.209 4.50 0.000 10.161 27.722 Note : Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. Table 7 reports the short-run estimates from the ARDL model, capturing the immediate effects of knowledge structuress on disruptive innovation. The results indicate that the variable knowledge breadth (lnKB) does not return significant short-run coefficients, suggesting that it may not play a measurable role in influencing disruptive innovation within the short-run time horizon. This lack of significant results could be attributed to the inherently gradual nature of the effects of knowledge breadth, which may require longer periods to manifest its impact on innovation outcomes. For knowledge depth (lnKD), the results reveal a positive and statistically significant short-run relationship with disruptive innovation. At lag order 0, the coefficient is 0.270, significant at the 1% level, indicating that an immediate increase in knowledge depth is associated with a rise in disruptive innovation. This positive relationship persists at lag order 1, with a smaller coefficient of 0.185, which is significant at the 10% level. These findings suggest that while knowledge depth contributes positively to disruptive innovation in the short run, the magnitude of its impact diminishes slightly over time. In contrast, knowledge source diversity (lnKSD) shows a consistently negative and statistically significant short-run relationship with disruptive innovation. At lag order 0, the coefficient is -4.829, significant at the 1% level, indicating that an increase in knowledge source diversity imposes short-run challenges on innovation processes. This negative impact persists at lag order 1, with a coefficient of -4.953, also significant at the 1% level. The consistent short-run negative effects of knowledge diversity suggest that the integration of diverse knowledge sources may introduce complexities and inefficiencies that hinder immediate innovation outcomes, despite its positive influence in the long run. The overall model demonstrates a strong fit, as reflected by the R-squared value of 0.936, which indicates that 93.6% of the variation in disruptive innovation can be explained by the short-run dynamics of the model. Table 7 ARDL short-run estimates. Variables Coefficient Estimates Lag order 0 1 ΔlnKB - - ΔlnKD 0.270** (0.011) 0.185* (0.092) ΔlnKSD -4.829*** (0.001) -4.953*** (0.000) R 2 0.936 Note : Short-run estimators for first lagged have been depicted by Δ. Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. Stability test findings The cumulative sum of squares (CUSUM square) plot is illustrated in Fig. 1 , which is used to assess the stability of the regression coefficients in the specified model. The test was conducted with a 5% significance level, and the shaded area represents the confidence interval under the null hypothesis of stability. The red plot line indicates the recursive cumulative sum of squares. The stability of the model is determined by examining whether the red plot line remains within the shaded confidence bands throughout the observation period. As shown in Fig. 1 , the cumulative sum of squares stays entirely within the 95% confidence interval. This confirms that there is no significant deviation from stability over the study period. At the 5% significance level, the results provide evidence of the stability of the regression coefficients. The findings indicate that the model is robust and the relationships among the variables remain consistent over time. DOLS findings To ensure the robustness of our long-run findings from the ARDL model, we employed an alternative cointegration estimation method: Dynamic Ordinary Least Squares (DOLS). The DOLS estimator is known for its reliability in small samples and its effectiveness in correcting for endogeneity by including leads and lags of the first-differenced regressors. The results are presented in Table 8 . Table 8 DOLS Results Variables DOLS Coef. Std. Err. p-value lnKB -2.373*** 0.478 0.001 lnKD 3.194*** 0.826 0.003 lnKSD 13.360* 7.100 0.089 Constant -9.874* 0.058 R2 0.961 Adjusted R2 0.902 Note : Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. The DOLS estimates provide strong support for our primary long-run conclusions. Specifically, the coefficient for KB remains negative and highly significant (-2.16, p < 0.01), while the coefficient for KSD remains positive and highly significant (25.80, p < 0.01). This confirms that the detrimental long-run effect of internal knowledge fragmentation and the beneficial long-run effect of external knowledge sourcing are robust findings, independent of the specific estimation methodology. Granger causality test To further investigate the dynamic interplay and temporal precedence among the variables, we conducted Granger-causality tests within a Vector Autoregression (VAR) framework. Based on the Schwarz Bayesian Information Criterion, a VAR model with one lag was selected. The results of the pairwise Granger-causality Wald tests are summarized in Table 9 . Table 9 Granger causality test results Direction of causality CD KB KD KSD CD - 16.277*** 0.709 8.366*** CD→KB; CD→KSD KB 0.054 - 0.081 0.347 KD 1.469 0.209 - 0.005 KSD 7.400*** 2.765 2.831* - KSD→CD; KSD→KD Note : Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively. First, we find evidence of a bidirectional causality between KSD and CD. As shown in Table 9 , the null hypothesis that KSD does not Granger-cause CD is rejected at the 1% significance level (χ² = 7.400, p = 0.007). Conversely, the hypothesis that CD does not Granger-cause KSD is also rejected at the 1% level (χ² = 8.366, p = 0.004). This indicates a powerful, self-reinforcing feedback loop between the diversity of external knowledge inputs and disruptive outputs. Second, we uncover a unidirectional shock effect originating from disruptive innovation. The test results show that CD is a highly significant Granger-cause of KB (χ² = 16.277, p = 0.000). However, the reverse causality from KB to CD is not significant (p = 0.817). This suggests that successful disruptions act as a powerful catalyst that subsequently drives the expansion of internal knowledge breadth. Third, the results point to a weaker, internal knowledge cascade. KSD is found to be a weak Granger-cause of both KB (p = 0.096) and KD (p = 0.092) at the 10% significance level. This suggests that the introduction of diverse external knowledge tends to precede adjustments in the internal knowledge structure. Notably, neither KB nor KD are found to be significant Granger-causes of CD in our model. In summary, our Granger-causality analysis moves beyond the structural dynamics identified in the ARDL model to reveal the directional pathways and feedback loops of the innovation system. The findings paint a picture not of a simple linear process, but of a co-evolutionary system dominated by a core feedback loop between external knowledge sourcing and disruptive outcomes, and a strong reshaping effect that successful innovations exert on the internal knowledge landscape. The implications of these dynamic mechanisms, particularly the interplay between the virtuous feedback loop and the potentially detrimental consequences of success-driven knowledge expansion, will be explored in the following Discussion section. Discussion The two clocks of innovation: short-term payoffs and long-run potential Our findings, summarized in Table 10 , reveal that the path to disruptive innovation is governed by two conflicting temporal logics running at different speeds and rewarding different strategies. The first is a short-term clock geared towards immediate, predictable payoffs, while the second is a long-term clock that cultivates uncertain, yet transformative, potential. We argue that this tension is deeply embedded in the absorptive capacity process, creating a fundamental conflict between the behavioral imperatives of Realized Absorptive Capacity (RAC) and the structural investments required for a robust Potential Absorptive Capacity (PAC). Table 10 Long-run and short-run effects of different variables. Dependent Variable: CD Long-run estimate Short-run estimate lnKB Significant negative - lnKD - Significant positive lnKSD Significant positive Significant negative The short-term clock rewards the efficient deployment of RAC, particularly through its exploitative pathway. As shown in Table 10 , our results indicate that Knowledge Depth (KD), which represents this exploitative refinement, emerges as a significant positive factor in the short run. This underscores the power of specialization to provide focused pathways for immediate technical advancements, enabling the swift resolution of well-defined technical challenges. Conversely, this short-term logic actively penalizes investments in PAC. Our analysis shows that Knowledge Source Diversity (KSD), the empirical proxy for PAC, exhibits a significant negative effect in the short term. This creates a temporal integration burden, where the cognitive and coordination costs of assimilating diverse external knowledge suppress immediate innovation performance. Thus, the incentives of the short-term clock systematically favor a narrow, exploitative RAC while discouraging the foundational investments in PAC. The long-run clock, in contrast, is driven almost entirely by sustained investment in PAC. Our findings underscore the transformative power of KSD, which in the long run becomes the sole significant positive driver of disruptive innovation. This reflects the delayed yet powerful rewards of leveraging external diversity, which enriches the innovation process with novel ideas and fosters the cross-boundary synergies necessary for paradigm shifts. However, the long-run clock also reveals the perils of a specific pathway within RAC Knowledge Breadth (KB), representing an exploratory internal integration, exerts a significant negative long-run impact. This suggests that an overly broad internal knowledge base, while promising interdisciplinary disruption, ultimately leads to resource dispersion and a fragmented innovation process. Over time, the challenges of managing this internal complexity outweigh the benefits, resulting in incremental rather than disruptive outcomes. Taken together, these findings paint a picture of a systemic dilemma within the absorptive capacity framework. The strategies rewarded by the short-term clock (exploitative RAC via KD) are, at best, inconsequential for long-term disruption. Meanwhile, the crucial investment for long-term potential (PAC via KSD) is actively penalized in the short run. Furthermore, even the seemingly beneficial exploratory pathway of RAC (KB) proves to be a long-term trap, leading to fragmentation rather than disruptions. This fundamental misalignment between the two clocks of innovation highlights the immense challenge of managing knowledge for sustained disruptiveness, providing a deep structural explanation for why innovation systems may naturally drift towards incrementalism over time. Consistent with Park et al. ( 2023 ), who link the decline in disruptiveness to a narrowing use of prior knowledge, our results identify external knowledge diversity (KSD) as the only sustained long-run lever for disruption. The entropy of success: how disruptive innovation breed complexity and stagnation While the preceding analysis illuminated the temporal trade-offs inherent in the innovation system, this section delves deeper into its dynamic evolution. The findings from our Granger causality analysis allow us to move beyond viewing innovation as a mere outcome and to examine its role as an active antecedent that shapes the future knowledge landscape. The results reveal the presence of feedback mechanisms, suggesting that disruptive innovation is not only a product of its knowledge inputs but also an endogenous driver of subsequent changes in knowledge structure. This section, therefore, explores these dynamics, with a particular focus on how the consequences of success may, in turn, create the structural conditions that affect the potential for future disruptions. Our analysis first uncovers a potentially virtuous, self-reinforcing mechanism at the core of the innovation system. The Granger causality tests reveal a bidirectional feedback loop between KSD and disruptive innovation. This suggests that while the infusion of diverse external knowledge serves as a critical antecedent to disruptive outputs, these disruptions in turn stimulate a broader search for novel external knowledge. A successful disruption appears to legitimize new knowledge combinations and shift technological paradigms, thereby compelling the ecosystem to expand its PAC and fueling the engine for subsequent rounds of innovation. However, this virtuous cycle is accompanied by a problematic dynamic. The consequence of a disruptive innovation, as revealed by our Granger causality results, is its role in driving the expansion of internal KB. A disruptive innovation success inherently triggers a phase of widespread application and exploitation. This process necessitates the integration of knowledge from various complementary fields, leading to an unavoidable increase in the complexity and diversity of the internal knowledge base. This expansion of KB represents a systemic shift in RAC towards a more exploratory and multifaceted internal structure. This success-driven expansion of internal knowledge breadth ultimately closes a systemic trap. By linking this powerful dynamic finding with our long-run ARDL estimates, the paradox becomes clear. Our long-run analysis has already established that high levels of KB are structurally detrimental to the generation of future disruptive innovation, likely due to the challenges of resource fragmentation and loss of strategic focus. Consequently, the innovation system appears to contain an endogenous mechanism for its own potential stagnation: the very success of a disruptive innovation triggers a systemic increase in knowledge breadth, which in turn erodes the structural conditions required for the next disruption. Therefore, the decline in disruptive potential can be understood as a risk emerging from this cumulative process, a form of systemic entropy where past success, if left unmanaged, can become a primary driver of future stagnation. However, understanding these entropic forces illuminates potential pathways to counteract them. The challenge of success-driven complexity in KB, for instance, can be mitigated through strategic modularity in organizational design, which structurally insulates exploratory teams from the inertia of mature business units. Furthermore, the inward-looking tendencies that follow success can be counterbalanced by a conscious and continuous investment in PAC, institutionalizing the search for external knowledge to ensure a steady supply of novel sparks. Finally, overcoming the path dependency created by success requires dynamic evaluation and an embrace of creative destruction, fostering a culture that is willing to challenge and even cannibalize its own successful products. By actively managing the consequences of success through these mechanisms, organizations and policymakers can work to sustain the vitality of the innovation ecosystem against its natural drift towards stagnation. Conclusion This study set out to provide a dynamic understanding of the declining potential of disruptive innovation. By applying a suite of time-series methods to global patent data from 1980 to 2010 and grounding our analysis in absorptive capacity theory, we move beyond static explanations to reveal a complex, co-evolutionary system fraught with temporal trade-offs and feedback loops. Our ARDL analysis first uncovers a fundamental conflict between the short-term behaviors and long-term structural requirements of the innovation process. We find that Potential Absorptive Capacity (PAC), measured by KSD, is the sole significant positive driver of disruptive innovation in the long run, yet it incurs immediate costs in the short run. Conversely, the exploitative pathway of Realized Absorptive Capacity (RAC), measured by KD, offers immediate payoffs but is inconsequential over the long term. Meanwhile, the exploratory pathway of RAC, measured by KB, proves to be detrimental in the long run, suggesting that excessive internal diversification erodes disruptive potential. Moreover, Granger causality analysis reveals the dynamic engine of this system. We uncover a bidirectional feedback loop between PAC and disruptive innovation, indicating a self-reinforcing co-evolution. We also identify a critical dynamic whereby successful disruptions act as a strong endogenous driver of the detrimental exploratory RAC path, measured by KB. This suggests that the very success of a disruptive event can trigger a systemic shift towards a more complex and fragmented knowledge structure that is less conducive to future disruption. These findings offer critical insights for policymakers and innovation managers aiming to foster sustained disruptive innovation. The core challenge lies in reconciling the temporal trade-offs and managing the endogenous dynamics revealed in our study. First, the conflict between the short-term costs and long-term benefits of PAC underscores the need for governance structures that function as temporal bridges. Innovation infrastructures must be designed to buffer early-stage integration inefficiencies while preserving long-term recombinability. To achieve this, governments and funding agencies can support modular, phase-based mechanisms such as two-stage R&D consortia and develop platform-based digital infrastructures to reduce search and alignment costs. Second, managing the dynamic consequences of success requires a conscious strategy of strategic modularity to counteract the detrimental long-run effects of KB. Knowledge integration within organizations should be governed to avoid wholesale internal diffusion. Funding programs should encourage bounded, selective integration through mechanisms like matrix organizational structures, rather than undirected interdisciplinarity. Mid-term evaluation checkpoints can also help prevent the over-extension of an innovation’s internal knowledge base. Finally, the transient role of KD highlights that short-term technical expertise alone is insufficient to sustain disruptive trajectories. Policy frameworks should incentivize depth-to-diversity transitions over time. Project funding, for example, can adopt tapered incentive schemes that reward initial technical depth but make renewal or scaling-up contingent on demonstrable cross-domain expansion. Career development tracks in public R&D institutions can also be designed to encourage this temporal diversification, ensuring that individual-level knowledge accumulation aligns with systemic innovation needs. This study has several limitations that open avenues for future investigation. First, our analysis relies on the CD index as the sole measure of disruptive innovation; future research could explore the robustness of our findings by triangulating our results with alternative metrics. Second, while our analysis reveals a dynamic link between disruptive events and KB, the precise mechanisms driving this success-driven fragmentation warrant deeper investigation. Lastly, and most importantly, our study is conducted at an aggregate level, which may mask significant heterogeneity across different technological fields. Future research employing dynamic panel techniques is therefore needed to explore these cross-sectional dynamics and identify the boundary conditions of our findings. Declarations Author Contribution Yue Li: Conceptualization, Methodology, Data Curation, WritingLele Kang: Conceptualization, Writing, Resources, ValidationJiaxing Li: Supervision, Project administration, Validation Acknowledgments National Social Science Fund of China. Research on the Formation Mechanism and Collaborative Governance of Health Information Poverty among Older Adults (Grant No. 23CTQ010) Data Availability Data available on request due to privacy. References Abdul Basit, S., & Medase, K. (2019). The diversity of knowledge sources and its impact on firm-level innovation: Evidence from Germany. European Journal of Innovation Management, 22(4), 681–714. Alblooshi, M., Shamsuzzaman, M., & Haridy, S. (2021). The relationship between leadership styles and organisational innovation: A systematic literature review and narrative synthesis. European Journal of Innovation Management, 24(2), 338–370. Boh, W. F., Evaristo, R., & Ouderkirk, A. (2014). 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1","display":"","copyAsset":false,"role":"figure","size":4348,"visible":true,"origin":"","legend":"\u003cp\u003eCUSUM Squares Plot with a 5 % level of significance\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8119156/v1/dedc54efc7ada6c4d045fdf8.png"},{"id":98215673,"identity":"b59766d3-5959-46da-ac28-e82eef17e3cd","added_by":"auto","created_at":"2025-12-15 10:33:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":56834,"visible":true,"origin":"","legend":"\u003cp\u003eThe co-evolutionary dynamics of knowledge and disruptive innovation\u003c/p\u003e","description":"","filename":"floatimage222.png","url":"https://assets-eu.researchsquare.com/files/rs-8119156/v1/16144e505f655038283865cd.png"},{"id":98622372,"identity":"cfe74022-1211-43ce-b270-3be1e7891f76","added_by":"auto","created_at":"2025-12-19 16:53:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1130172,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8119156/v1/6065797b-eeea-41de-97e6-6b765780cde0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Unveiling the Temporal Dynamics: The Impact of Knowledge Source Structure on Innovation through Time-Series Analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDisruptive innovation (DI), which reshapes existing technological paradigms and drives progress in entirely new directions, has historically been a cornerstone of transformative development. However, recent studies reveal a worrying trend: the disruptive potential of innovations is steadily declining. Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) quantified this phenomenon using the CD index, a metric that captures the disruptiveness of patents and scientific publications by assessing their impact on subsequent citation patterns. Their findings highlighted a consistent decline in disruptiveness across technological fields, raising critical questions about the factors driving this shift. Despite growing attention to this phenomenon, it remains unclear whether and how different structures of knowledge influence this decline.\u003c/p\u003e\u003cp\u003eExisting studies have investigated various factors influencing innovation, including institutional frameworks such as intellectual property rights regime (Thakur-Wernzet al., 2022) and funding mechanisms (Irfan et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), technological ecosystems such as industry clusters (Kim et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)d networks (Wen et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and organizational characteristics such as team size (Wuchty et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), leadership styles (Alblooshi et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and knowledge management practices (Darroch, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Mardani et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Among these factors, knowledge emerges as a cornerstone of the innovation process, enabling both exploration and exploitation, which form the basis for novel recombination and technical refinement (Grant, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). Evolutionary economics reinforces this perspective by emphasizing the cumulative nature of knowledge, where its recombination drives disruptions (Nelson, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1985\u003c/span\u003e). Despite these insights, most research adopts a static perspective, overlooking how the continuous evolution of knowledge influences disruptive innovation (Volberda et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). As innovation systems mature, the complexity of integrating and applying knowledge evolves, potentially reshaping its impact on innovation outcomes (Fleming et al., 2001). This highlights the need to examine how the dynamic restructuring of knowledge affects the trajectory of DI.\u003c/p\u003e\u003cp\u003eInnovation is inherently dynamic, shaped by the transformation of knowledge and its interplay with external factors like technological advancements and market dynamics (Teece et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Ganguly et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Within a dynamic capability view, absorptive capacity provides microfoundations through two analytically separable components (Zahra \u0026amp; George, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Potential Absorptive Capacity (PAC) captures what knowledge is sourced and reflects the heterogeneity of external prior art an invention taps. Realized Absorptive Capacity (RAC) captures how knowledge is applied and reflects the actualized knowledge structure manifested within the patent itself. Greater PAC enlarges the space for novel recombination (Rosenkopf \u0026amp; Almeida, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) but increases screening and assimilation costs (Fleming, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2001\u003c/span\u003e); RAC that spans fields supports exploration yet risks fragmentation, whereas concentration streamlines exploitation yet raises lock in risk (Volberda et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). These opposing effects indicate that the link between knowledge structure and DI evolves as knowledge is accessed and applied, which motivates examining their dynamic relationship.\u003c/p\u003e\u003cp\u003eTo better understand the dynamic relationship between DI and the knowledge absorptive capacity (e.g., PAC and RAC) this study employs the Autoregressive Distributed Lag (ARDL) model (Pesaran, et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). In contrast to traditional static models, the ARDL approach enables the simultaneous estimation of short-run adjustments and long-run equilibrium relationships, providing deeper insights into the evolving impact of knowledge on DI. By distinguishing between short-run fluctuations and long-run trends, the ARDL model offers valuable insights into how DI responds to changes in knowledge structure over different time horizons. The short-run analysis reveals immediate responses to shifts in knowledge, while the long-run analysis captures persistent influences that shape innovation trajectories. This comprehensive approach contributes to a deeper understanding of how knowledge recombination and application influence DI.\u003c/p\u003e\u003cp\u003eThis study analyzed annual patent data from 1980 to 2010. First, we applied unit root tests, including the Augmented Dickey-Fuller and Phillips-Perron tests, to ensure the stationarity of the variables. Second, given the mixed integration order of the data, we utilized the ARDL bounds test to determine the presence of long-run relationships. Third, we conducted Granger-causality tests to examine the dynamic feedback loops. The empirical findings indicate that, over the long run, PAC is the sole significant positive driver of disruptive innovation, while a specific pathway of RAC, namely exploratory transformation measured by knowledge breadth, has a significant adverse effect. This core long-run finding is robust to alternative estimation methods. In the short run, however, the system\u0026rsquo;s incentives are reversed: investments in PAC present immediate challenges, while the exploitative pathway of RAC, measured by knowledge depth, fosters innovation. Furthermore, our Granger causality analysis uncovers a bidirectional feedback loop between PAC and disruptive innovation. It also reveals that disruptions act as a strong endogenous driver of future RAC configurations, particularly by fuelling the expansion of the exploratory transformation path represented by knowledge breadth.\u003c/p\u003e\u003cp\u003eBuilding on these findings, this study makes several contributions to the literature. First, they provide a deeper understanding of the mechanisms underlying the observed decline in disruptiveness, highlighting the lack of sufficient analysis on the temporal evolution of knowledge structures. Second, by employing the ARDL model, this study offers a methodological advancement that allows for the investigation of DI from a dynamic perspective, capturing both short-run adjustments and long-run equilibrium relationships. Third, our study reveals the co-evolutionary dynamics between knowledge structures and innovation. By uncovering a feedback loop between PAC and disruptive outcomes, we show that innovation is not merely an endpoint but an active agent that reshapes its own knowledge environment. This provides a novel, systemic explanation for how innovation trajectories are endogenously formed and sustained over time.\u003c/p\u003e\n\u003ch3\u003eRelated Work\u003c/h3\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eDisruptive innovation\u003c/h2\u003e\u003cp\u003eThe theory of disruptive innovation was first proposed by Christensen (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), characterized by its non-linear technological trajectory. Unlike traditional mainstream technologies, disruptive innovation advances through differentiated strategies to achieve competitive advantage (Hang et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Existing studies have defined the concept from various perspectives, including technological characteristics (Nagy et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Reinhardt \u0026amp; Gurtner, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), innovation processes (Levina, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and innovation impacts (Suseno, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). These studies have also explored disruptive innovation across multiple levels, including the individual (Osiyevskyy \u0026amp; Dewald, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), firm (Van Balen et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), industry (Chevalier-Roignant et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and network or ecosystem levels (Ruan et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA significant challenge in this field has been the empirical measurement of an innovation\u0026rsquo;s disruptive impact. Early work relied primarily on qualitative cases and industry-level histories; a major advance came with the use of patent citations to quantify technological influence (Trajtenberg, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Jaffe \u0026amp; Trajtenberg, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Within this tradition, originality and generality capture, respectively, the dispersion of an invention\u0026rsquo;s knowledge inputs and the breadth of its downstream reach. One family of subsequent measures remains rooted in this recombinant view, extending beyond input-output dispersion to the rarity of knowledge pairings: atypical combinations identified from co-classification matrices or topic models, and other indicators of cognitive novelty, anticipate disruptive potential even before diffusion is fully observed (Uzzi et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kaplan \u0026amp; Vakili, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAnother family of measures locates inventions in a technological or semantic knowledge space and tracks how far they move relative to their prior art or how strongly they bridge previously separated clusters. Distance-based and bridging metrics, implemented with classification hierarchies, vector embeddings, or citation geodesics, emphasize structural relocation and reconfiguration as hallmarks of disruption (Rosenkopf \u0026amp; Nerkar, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Youn et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eMore recently, a network-based approach has emerged to measure creative destruction directly in citation behavior. The disruption-consolidation framework operates by analyzing subsequent citation behavior. It identifies evidence of displacement if later works citing a focal contribution simultaneously omit its antecedents. Conversely, it identifies evidence of consolidation if these later works co-cite both the focal contribution and its intellectual predecessors. The CD index operationalizes this logic at scale and underpins large-sample findings, including the widely cited evidence of declining disruptiveness across science and technology (Wu et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Park et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Related dynamic network measures trace how downstream citation flows are reoriented after a focal invention, complementing CD by capturing redirection in the broader knowledge graph (Funk \u0026amp; Owen‑Smith, 2017).\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003ePotential absorptive capacity and realized absorptive capacity\u003c/h3\u003e\n\u003cp\u003eWhile the aforementioned measurement traditions provide powerful tools to quantify what constitutes a disruptive innovation, a deeper theoretical framework is needed to explain why and how these knowledge dynamics unfold. The theory of absorptive capacity, introduced by Cohen and Levinthal (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1990\u003c/span\u003e), provides the dominant framework for this inquiry. It argues that an innovation\u0026rsquo;s potential is not merely a function of the available knowledge components, but of an entity\u0026rsquo;s capacity to value, assimilate, and apply new external knowledge. A key development in this theory was the reconceptualization by Zahra and George (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), who decomposed absorptive capacity into Potential Absorptive Capacity (PAC) and Realized Absorptive Capacity (RAC). PAC encompasses the processes of knowledge acquisition and assimilation, representing the potential to learn from external knowledge. RAC, in contrast, covers the subsequent processes of transformation and exploitation, representing the ability to convert that potential into innovation outcomes.\u003c/p\u003e\u003cp\u003eGrounded in this framework, a vast body of prior research has explored how different facets of absorptive capacity influence innovation performance. For example, numerous studies have investigated the PAC stage by examining the role of external knowledge sourcing strategies. Scholars have found that the breadth of external search (Laursen \u0026amp; Salter, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), boundary-spanning activities into distant knowledge domains (Rosenkopf \u0026amp; Nerkar, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), and the diversity of external knowledge partners are critical for firm innovation (Jiang et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Powell et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). Research on the RAC stage emphasizes how internal knowledge structures are reconfigured to realize value. Changes in knowledge couplings among a firm\u0026rsquo;s domains shape innovation outcomes, contingent on domain complexity (Yayavaram \u0026amp; Chen, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Breakthrough invention benefits from recombination when internal coherence is maintained, highlighting the integration challenge of synthesizing disparate knowledge components (Kaplan \u0026amp; Vakili, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWithin this body of research, the structure of knowledge itself has emerged as a crucial lens for operationalizing and understanding these capabilities. Numerous scholars have adopted this lens to empirically study absorptive capacity. Research investigating the PAC has frequently focused on the role of external knowledge sourcing. Therefore, we conceptualize knowledge source diversity, which measures the variety of an innovation\u0026rsquo;s external knowledge inputs, as a direct and tangible indicator of this external driving force for innovation. A rich body of literature has explored the dual impacts of sourcing from diverse knowledge bases. On one hand, a high KSD enriches opportunities for novel technological combinations and enhances overall innovation capacity (Dogru et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). It provides the necessary resilience and adaptability for disruptive innovation by enabling systems to address path dependency and uncertainties (Luo et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). On the other hand, excessive diversity in knowledge sources can increase coordination challenges and integration costs, thereby negatively impacting innovation efficiency. Some studies have even identified an inverted U-shaped relationship, suggesting that moderate diversity is optimal while excessive diversity leads to managerial complexity (Hajialibeigi, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The specific categories of knowledge sources, such as public versus private sector knowledge, also appear to have differential impacts (Abdul Basit \u0026amp; Medase, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe RAC, which reflects the internal processing and application of knowledge, can be understood through knowledge breadth and knowledge depth. These represent the strategic trade-offs in how acquired knowledge is exploited. Knowledge breadth, the integration of knowledge from multiple internal fields, is found to facilitate disruptive innovation by enabling diverse combinations and cross-domain integration (Xu et al., 2015). However, the literature also warns that excessive breadth may lead to resource dispersion and coordination complexities, ultimately hindering innovation efficiency (Jin et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In contrast, Knowledge depth, representing specialization within a specific field, is shown to strengthen technological advantages and support incremental innovation (Boh et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Yet, an over-reliance on depth can limit a firm\u0026rsquo;s adaptability to emerging technologies, a significant risk in rapidly changing environments.\u003c/p\u003e"},{"header":"Data and Method","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003eData and variables\u003c/h2\u003e\u003cp\u003eTo investigate the short-run and long-run dynamics between disruptive innovation, knowledge source diversity, breadth and depth, this study utilizes patent data obtained from the PatentView database. This comprehensive database includes detailed information on patents from 1976 to 2024, encompassing inventor details, patent and application metadata, assignee and location information, as well as International Patent Classification (IPC) data.\u003c/p\u003e\u003cp\u003eThe database further provides access to the full text of patents, which includes three key sections: abstract, claims, and description. The claims section outlines the scope of the legal protection granted to the patent, while the description section provides a detailed explanation of the invention or innovation’s technical characteristics. The abstract offers a summary of the content in both the claims and description sections. To analyse the genuine technological attributes of patented inventions, this study exclusively relies on the description section.\u003c/p\u003e\u003cp\u003eThe variables in this study are designed to capture the core constructs of our theoretical framework. The dependent variable is disruptive innovation. The independent variables operationalize the two stages of absorptive capacity: \u003cem\u003epotential absorptive capacity\u003c/em\u003e is measured by \u003cem\u003eknowledge source diversity\u003c/em\u003e, while \u003cem\u003erealized absorptive capacity\u003c/em\u003e is measured through the distinct pathways of \u003cem\u003eknowledge breadth\u003c/em\u003e and \u003cem\u003eknowledge depth\u003c/em\u003e. The specific measurement of each variable is detailed below.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDisruptive Innovation\u003c/b\u003e. Disruptive innovation is measured using the CD index, which was developed by Funk and Owen-Smith (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and later applied by Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The CD index quantitatively captures whether a patent consolidates existing knowledge or disrupts the technological status quo. Consolidating patents build upon prior knowledge and reinforce established trajectories, whereas disruptive patents render earlier work obsolete and chart new technological directions. The CD index ranges from − 1 to 1, where − 1 indicates a highly consolidating innovation, and 1 signifies a highly disruptive innovation.\u003c/p\u003e\u003cp\u003eThis study adopts the five-year post-publication window used by Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), referred to as CD\u003csub\u003e5\u003c/sub\u003e, to evaluate the disruptive potential of patents. The starting year of analysis is 1980, aligns with Park et al.’s dataset to ensure consistency in the time window and methodology. The calculation of the CD index also follows the exact formula proposed by Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Using this standardized approach ensures comparability with prior studies and allows for robust exploration of the relationships between disruptive innovation and knowledge structures, including breadth, depth, and source diversity.\u003c/p\u003e\u003cp\u003e\u003cb\u003eKnowledge Source Diversity (KSD)\u003c/b\u003e. The knowledge source diversity measures the extent to which a patent integrates knowledge from multiple technological categories, based on the NBER two-digit technology classification. The NBER classification system, developed by Hall et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), provides a standardized framework for categorizing patents into broad technological fields, facilitating cross-field comparisons, and enabling robust analyses of knowledge diversity. In this study, the classification of patents into NBER technology categories is obtained directly from the PatentView database, ensuring consistency and reliability in the analysis. To calculate KSD, the references cited by each patent are analysed to determine their distribution across NBER technology categories. The diversity of these references is quantified using an entropy-based approach, which accounts for both the number of categories referenced and the balance among them. Patents with higher KSD indicate a greater reliance on knowledge inputs from multiple distinct technological fields, reflecting their ability to integrate diverse sources of knowledge. This diversity is hypothesized to enhance the potential for creative recombination of ideas, which is often a critical driver of disruptive innovation.\u003c/p\u003e\u003cp\u003e\u003cb\u003eKnowledge Breadth (KB)\u003c/b\u003e. The knowledge breadth is defined as the extent to which a patent draws upon vocabulary from multiple technological fields. Following the methodology outlined in Bowen et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), this metric is constructed by first calculating the frequency of word usage across technological fields for each year. A word is tagged as \u003cem\u003especialized\u003c/em\u003e in a particular field if its usage in that field exceeds 150% of its usage in the second most prominent field during the same year. Words that do not meet this criterion are classified as \u003cem\u003eunspecialized\u003c/em\u003e and excluded from further analysis. For each patent, the fraction of specialized words classified into each field is then calculated, with these fractions summing to one for every patent. Using this classification, technological breadth is defined as one minus the concentration of specialized words, thereby reflecting the diversity of fields from which a patent draws its vocabulary. Patents with high knowledge breadth integrate terminology from a wider range of fields, indicating a more diverse knowledge base:\u003c/p\u003e\u003cp\u003e\u003cb\u003eKnowledge Depth (KD).\u003c/b\u003e The knowledge depth measures the extent of focus within a single technological field, and is calculated based on the concentration of a patent’s classification within a specific four-digit International Patent Classification (IPC4) code. The IPC4 system provides a highly granular framework for categorizing patents, often used as a proxy for defining technological fields. By examining the proportion of a patent’s classifications that fall within its most dominant IPC4 category, knowledge depth captures the degree to which a patent concentrates on a single technological field. Patents with high knowledge depth often exhibit a deliberate emphasis on advancing a particular field, suggesting a refined specialization that may impact incremental innovations or significant technical improvements within that domain. By anchoring the measurement of depth in the IPC4 classification, the analysis ensures precision in capturing the technical focus of each patent. This reliance on established knowledge structures may enhance efficiency in knowledge utilization. All variables and their description are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eVariables description.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eDescription\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDisruptive Innovation (DI)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMeasured using the CD index, developed by Funk and Owen-Smith (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and applied by Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The index ranges from − 1 (highly consolidating) to 1 (highly disruptive), with CD\u003csub\u003e5\u003c/sub\u003e calculated over a five-year post-publication window to evaluate a patent’s influence on obsolescing or reinforcing prior knowledge.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePotential Absorptive Capacity (PAC)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKnowledge Source Diversity (KSD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eReflects the variety of technological categories from which a patent integrates knowledge. Based on the NBER two-digit technology classification and calculated using entropy to measure the diversity of references cited by each patent across multiple fields.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eRealized Absorptive Capacity (RAC)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKnowledge Breadth (KB)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCaptures the diversity of technological fields from which a patent draws its vocabulary. Calculated as one minus the concentration of a patent’s classification into six broad fields, reflecting the extent to which the patent spans multiple domains. Derived using field-specific data from the patent text and classification systems.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKnowledge\u003c/p\u003e\u003cp\u003eDepth (KD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMeasures the extent of focus within a single technological field. Calculated based on the proportion of a patent’s classifications concentrated within its most dominant IPC4 code, representing a refined specialization in a specific domain.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe rationale for employing distinct operational measures for KSD, KB, and KD is grounded in their theoretical separation, empirical complementarity, and granular alignment with the conceptual constructs. Although these structures are interrelated, they reflect fundamentally different structural layers of knowledge, which necessitates differentiated yet coherent measurement strategies. First, KSD captures the diversity of technological origins, for which the NBER 2-digit classification is particularly suited. Its coarse granularity reflects broader source fields (e.g., Chemicals, Electronics, Drugs), and has been widely used to proxy knowledge origin variety in macro-level innovation studies (Hall et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). NBER codes aggregate IPC-based patent classes according to economically meaningful technological sectors, thus aligning closely with the idea of where knowledge comes from.\u003c/p\u003e\u003cp\u003eSecond, KD is intended to reflect technological specialization, which demands greater classification precision. The IPC 4-digit level provides such fine-grained technical delineation, enabling us to observe how concentrated a patent’s technical focus is. Compared with higher-level IPC or NBER codes, IPC4 provides domain stability and domain resolution, making it the most valid proxy for focused depth within a technological field.\u003c/p\u003e\u003cp\u003eThird, KB concerns the semantic recombination and interdisciplinary expression of knowledge within the patent text. To this end, a vocabulary-based approach is employed, tracking the field-specific concentration of technical terms used in abstracts and claims. This textual metric captures horizontal conceptual integration at a finer level than taxonomic classifications, especially in domains where innovation involves hybrid or emergent concepts not yet classified in IPC/NBER systems.\u003c/p\u003e\u003cp\u003eWhile the data sources and granularity differ across these three variables, they are intentionally selected to match the theoretical domain of each construct: broad origin domains (KSD), fine technical depth (KD), and semantic conceptual spread (KB). These differences do not imply inconsistency but rather reflect the layered nature of knowledge structures in innovation. We explicitly acknowledge that the classification schemes are non-nested and differ in dimensional logic. However, their temporal aggregation into annual panel data and their independent derivation from non-overlapping sources reduce concerns about collinearity or semantic redundancy. Moreover, our ARDL model framework allows for distinct lag structures, further reducing risks of artificial convergence.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eMethodology and model specification\u003c/h3\u003e\n\u003cp\u003eEconometric methods that investigate the temporal dynamics of innovation processes are essential for understanding how variables interact over time. These approaches enable the analysis of both short-run fluctuations and long-run equilibrium relationships, offering valuable insights into the mechanisms impacting disruptive innovation and its connections to knowledge structures such as source diversity, breadth and depth. Given the need to examine these dynamics comprehensively, this study adopts the Autoregressive Distributed Lag (ARDL) bounds testing model, introduced by Pesaran et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) and later developed further (Pesaran, et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), to explore the cointegration processes and temporal interactions among the variables. The ARDL approach not only estimates cointegration and long-run equilibrium relationships but also captures dynamic effects in both time horizons, offering a comprehensive framework for understanding temporal interactions.\u003c/p\u003e\u003cp\u003eThe ARDL methodology is particularly advantageous for several reasons. First, it is highly flexible and can accommodate variables with mixed integration orders, whether I(0) or I(1). Second, the single-equation setup simplifies implementation and interpretation compared to traditional cointegration methods. Third, it allows for different lag lengths to be specified for different variables, enhancing the model’s adaptability to the data. Fourth, the method is well-suited for small sample sizes, providing robust estimates of long-run relationships and parameters. Finally, the ARDL model effectively addresses potential issues of autocorrelation and endogeneity, ensuring unbiased and reliable results (Harris \u0026amp; Sollis, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Jalil \u0026amp; Ma, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eGiven these strengths, the ARDL approach is employed in this study to examine the temporal dynamics between disruptive innovation and its key regressors, such as knowledge source diversity, breadth and depth. The method is applied to identify both the long-run equilibrium relationships and the short-run adjustments that occur in response to deviations from equilibrium. The subsequent steps for verifying these dynamics within the ARDL framework are outlined in the following sections.\u003c/p\u003e\u003cp\u003e\u003cb\u003eStationarity test\u003c/b\u003e. Stationarity is a critical consideration in time-series analysis, as it ensures the validity of econometric models and the reliability of their results. Time-series data have diverse applications across various fields, and identifying the appropriate trend structure of the data represents an essential econometric task (Mushtaq, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). To determine the stationarity of the variables, this study employs the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests. These tests are widely used to identify whether variables are stationary at their levels or become stationary after differencing. The results of these tests guide the appropriate application of the Autoregressive Distributed Lag (ARDL) approach, which is capable of handling variables integrated at different orders. Specifically, the ARDL model can accommodate variables that are stationary at level (I(0)), at first difference (I(1)), or a combination of the two, making it a robust method for analysing the cointegration and temporal dynamics among time-series variables.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAutoregressive Distributed Lag bounds test\u003c/b\u003e. The bounds testing procedure is utilized in this study to examine whether a single long-run relationship exists among the variables under investigation. The ARDL bounds test evaluates cointegration by testing the joint significance of the coefficients of the lagged levels of the variables in a single-equation model. The model for the bounds test is specified as follows:\u003c/p\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:{CD}_{t}=\\alpha\\:+\\sum\\:_{i=1}^{p}{\\beta\\:}_{i}\\varDelta\\:{CD}_{t-i}+\\sum\\:_{i=0}^{q}{\\gamma\\:}_{i}\\varDelta\\:{KB}_{t-i}+\\sum\\:_{i=0}^{r}{\\delta\\:}_{i}\\varDelta\\:{KD}_{t-i}+\\sum\\:_{i=0}^{s}{\\eta\\:}_{i}\\varDelta\\:{KSD}_{t-i}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:+{\\theta\\:}_{1}{CD}_{t-1}+{\\theta\\:}_{2}{lnKB}_{t-1}+{\\theta\\:}_{3}{lnKD}_{t-1}+{\\theta\\:}_{4}{lnKSD}_{t-1}+{ϵ}_{t}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn this equation, Δ denotes the first-difference operator, CD\u003csub\u003et\u003c/sub\u003e is the disruptive innovation index, and KB\u003csub\u003et\u003c/sub\u003e, KD\u003csub\u003et\u003c/sub\u003e, and KSD\u003csub\u003et\u003c/sub\u003e represent knowledge breadth, depth, and source diversity, respectively. The optimal lag lengths (p, q, r, s) are determined using the Akaike Information Criterion (AIC), which minimizes information loss and ensures the model is parsimonious while retaining explanatory power. The coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{3}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{4}\\)\u003c/span\u003e\u003c/span\u003e capture the long-run equilibrium relationships, while the summations account for short-run dynamics. The term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ϵ}_{t}\\)\u003c/span\u003e\u003c/span\u003e captures any variations unexplained by the model, ensuring the robustness of the estimation process.\u003c/p\u003e\u003cp\u003eTo evaluate the existence of a cointegration relationship, the ARDL bounds test is applied. This test compares the calculated F-statistic to critical bounds for the null hypothesis (H\u003csub\u003e0\u003c/sub\u003e), which assumes no cointegration among the variables, and the alternative hypothesis (H\u003csub\u003e1\u003c/sub\u003e), which posits the presence of cointegration. A rejection of H\u003csub\u003e0\u003c/sub\u003e occurs when the F-statistic exceeds the upper critical bound, indicating a stable long-run relationship among the variables. Conversely, if the F-statistic falls below the lower bound, the null hypothesis cannot be rejected. When the F-statistic lies between the bounds, the result is inconclusive, requiring further investigation.\u003c/p\u003e\u003cp\u003eOnce a long-run relationship is confirmed through the ARDL bounds testing approach, the model is re-specified into an Error Correction Model (ECM) to estimate both short-run dynamics and the speed of adjustment back to the long-run equilibrium. The ECM effectively integrates short-run fluctuations and long-run relationships within a single framework, ensuring the model captures both immediate and equilibrium effects of the independent variables on disruptive innovation. The ECM for this study is specified as follows:\u003c/p\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:{CD}_{t}=\\alpha\\:+\\sum\\:_{i=1}^{p}{\\beta\\:}_{i}\\varDelta\\:{CD}_{t-i}+\\sum\\:_{i=0}^{q}{\\gamma\\:}_{i}\\varDelta\\:{KB}_{t-i}+\\sum\\:_{i=0}^{r}{\\delta\\:}_{i}\\varDelta\\:{KD}_{t-i}+\\sum\\:_{i=0}^{s}{\\eta\\:}_{i}\\varDelta\\:{KSD}_{t-i}+\\tau\\:{ECT}_{t-1}+{ϵ}_{t}$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe ECM framework is particularly valuable because it allows the separation of short-run dynamics from long-run equilibrium behaviour while maintaining a consistent representation of the temporal relationships among variables. The short-run effects are captured by the coefficients of the lagged differences, which provide insights into the immediate impacts of changes in knowledge structures on disruptive innovation. Meanwhile, the Error Correction Term (ECT) integrates the short-run adjustments with the long-run relationship, ensuring that deviations from equilibrium are systematically corrected over time.\u003c/p\u003e\u003cp\u003eBy applying the ECM within the ARDL framework, this study is able to investigate not only how knowledge breadth, depth, and source diversity influence disruptive innovation in the long run, but also how these variables interact dynamically in the short run. This dual focus provides a comprehensive understanding of the temporal mechanisms impacting innovation processes.\u003c/p\u003e\u003cp\u003e\u003cb\u003eStability test\u003c/b\u003e. Ensuring the stability of regression models is critical when working with autoregressive structures, as stability confirms the robustness of estimated coefficients over time. In this study, the CUSUM of squares approach, as proposed by Brown et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1975\u003c/span\u003e), is employed to evaluate the dynamic stability of the model. The CUSUM of squares test provides a graphical representation of stability, where the plotted test statistic is compared against a confidence interval. If the test statistic remains within the confidence bounds, the model is considered stable, indicating no significant changes in the regression coefficients over time. Conversely, if the statistic crosses the bounds, it suggests potential instability, requiring further investigation.\u003c/p\u003e"},{"header":"Empirical findings","content":"\u003cp\u003eThis study employs multivariate time-series data from 1980 to 2010, with annual observations to mitigate the influence of seasonal variations. The annual data are derived by calculating patent-level indicators for each year and then averaging these values at the yearly level, ensuring a consistent representation of trends over time. The analysis focuses on identifying the relationships between disruptive innovation and various knowledge structures over time.\u003c/p\u003e\u003ch3\u003eSummary statistics\u003c/h3\u003e\u003cp\u003eThe descriptive statistics for the key study variables is provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, including disruptive innovation (CD), knowledge breadth (lnKB), knowledge depth (lnKD), and knowledge source diversity (lnKSD). The mean value of CD is 0.127, with a standard deviation of 0.098, indicating moderate variation in disruptive innovation across the sample period. The minimum and maximum values of CD range from 0.030 to 0.388, reflecting substantial differences in the disruptiveness of innovations over time. Knowledge breadth (lnKB) exhibits a mean value of 0.364 with relatively low variability (S.D. = 0.023), suggesting a consistent level of knowledge integration across patents. Knowledge depth (lnKD) has a slightly higher mean of 0.528 and also demonstrates low variability (S.D. = 0.017), highlighting the stable specialization within individual technological fields. In contrast, knowledge source diversity (lnKSD) shows the highest mean of 0.684 with minimal variation (S.D. = 0.003), indicating that patents consistently rely on a diverse set of external knowledge sources.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary statistics of study variables.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eMean\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eS.D.\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003eMin\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eMax\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.127\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.098\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.030\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.388\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.364\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.023\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.397\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.528\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.017\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.488\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.561\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.684\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.687\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTogether, these descriptive statistics and time trends highlight the dynamic relationships between disruptive innovation and the key knowledge structure, providing a foundation for exploring their short-run and long-run interactions in subsequent analyses.\u003c/p\u003e\u003ch3\u003eStationarity test\u003c/h3\u003e\u003cp\u003eIn this study, stationarity of the variables was tested using both the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests, with the results summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The stationarity test results reveal that, except for the variable CD, all variables become stationary after applying the first difference. Specifically, the results indicate that at the level, none of the variables, except for CD, exhibit stationarity. However, after taking the first difference, all variables—namely the logarithms of knowledge breadth (lnKB), knowledge depth (lnKD), and knowledge source diversity (lnKSD)—become stationary. The variable CD, on the other hand, is stationary at the level, confirming that it does not require differencing. This mixed order of integration among the variables suggests that an Autoregressive Distributed Lag (ARDL) bound approach is appropriate for modeling the relationship between the variables, as it can accommodate variables with different integration orders (i.e., I(0) and I(1)).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eStationarity test statistics.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003e\u003cem\u003eADF Test\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e\u003cem\u003ePP Test\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eStationary\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003eRemark\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eLevel\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eFirst difference\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eLevel\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003eFirst difference\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-4.873***\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-3.870***\u003c/p\u003e\u003cp\u003e(0.013)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eI(0)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.191\u003c/p\u003e\u003cp\u003e(0.992)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-5.894***\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-0.196\u003c/p\u003e\u003cp\u003e(0.992)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-5.872***\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eI(1)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-2.676\u003c/p\u003e\u003cp\u003e(0.246)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-4.637***\u003c/p\u003e\u003cp\u003e(0.001)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-2.722\u003c/p\u003e\u003cp\u003e(0.227)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-4.574***\u003c/p\u003e\u003cp\u003e(0.001)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eI(1)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1.596\u003c/p\u003e\u003cp\u003e(0.794)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-7.120***\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-1.325\u003c/p\u003e\u003cp\u003e(0.882)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-7.105\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eI(1)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote\u003c/em\u003e: An intercept term and a trend term have been included in all unit-root tests. Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003ch2\u003eARDL bounds test\u003c/h2\u003e\u003cp\u003eTo determine the optimal lag length for the model, the Akaike Information Criterion (AIC) was utilized. Based on this criterion, the chosen model is ARDL(1, 0, 2, 2). This means that the optimum lag lengths for the variables CD, lnKB, lnKD, and lnKSD are p = 1, q = 0, r = 2 and s = 2, respectively. The results of the ARDL bounds test are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which includes the F-statistics values for testing the presence of a long-run relationship between the variables.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eARDL bounds test (F-statistic).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eF-statistic\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eValue\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cem\u003eNull hypothesis: no levels of relationship\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eSignificance level\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003eI(0)\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cem\u003eI(1)\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eValue of F-statistic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e31.232\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e10.0%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e2.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e3.77\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eK\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e5.0%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e4.35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCritical Value Bounds\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.1 − 0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.5%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e3.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e4.89\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.0%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e4.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e5.61\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSince the F-statistic value exceeds the critical values for both I(0) and I(1), this provides strong evidence of a long-run relationship among the variables. The results suggest that the knowledge structures are jointly influencing disruptive innovation in the long-run, while the variables move together toward an equilibrium over time.\u003c/p\u003e\u003ch2\u003eARDL adjustment estimation, long-run and short-run relationships\u003c/h2\u003e\u003cp\u003eThe ARDL adjustment estimates is reported in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, indicating how the variables align with the long-run equilibrium following deviations. The coefficient of CD L1 is − 0.135, which is negative and statistically significant at the 1% level. This value reflects the proportion of the adjustment toward long-run equilibrium in response to deviations. Specifically, approximately 13.5% of the disequilibrium is corrected within one year, indicating that the variables are gradually realigned with their long-run equilibrium. The statistically significant negative coefficient also suggests a stable long-run relationship, with adjustments occurring systematically over time.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eARDL adjustment estimates.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eD.CD\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eCoef.\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eStd.error\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eP \u0026gt;|t|\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003e[95% Conf. Interval]\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCD. L1.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.135***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.023\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-5.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.181 -0.088\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote\u003c/em\u003e: Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe long-run estimates obtained from the ARDL model is presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, illustrating the sustained relationships between disruptive innovation and the knowledge sturcture: breadth, depth, and source diversity. The coefficient of knowledge breadth (lnKB) is negative and statistically significant at the 1% level. This indicates that in the long run, an increase in knowledge breadth is associated with a reduction in disruptive innovation. This may reflect the trade-off between generalization and specialization, where increased knowledge breadth could dilute the focus needed for achieving disruption. The coefficient of knowledge depth (lnKD) is negative but not statistically significant. This result implies that knowledge depth does not show a strong long-run influence on disruptive innovation during the study period. This finding may suggest that depth alone is insufficient to drive innovation without the complementary effects of breadth or diversity. The coefficient of knowledge source diversity (lnKSD) is positive and statistically significant at the 1% level. This indicates a strong positive long-run relationship between knowledge source diversity and disruptive innovation. The result suggests that integrating diverse sources of knowledge significantly enhances the potential for disruption, potentially due to the cross-pollination of ideas from different fields or disciplines.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eARDL long-run estimates.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eCoef.\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eStd.error\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eP \u0026gt;|t|\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003e[95% Conf. Interval]\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-1.276***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.396\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-3.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-2.101 -0.451\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.558\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.988\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.578\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-2.619 1.503\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e18.942***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.209\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e10.161 27.722\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote\u003c/em\u003e: Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e reports the short-run estimates from the ARDL model, capturing the immediate effects of knowledge structuress on disruptive innovation. The results indicate that the variable knowledge breadth (lnKB) does not return significant short-run coefficients, suggesting that it may not play a measurable role in influencing disruptive innovation within the short-run time horizon. This lack of significant results could be attributed to the inherently gradual nature of the effects of knowledge breadth, which may require longer periods to manifest its impact on innovation outcomes. For knowledge depth (lnKD), the results reveal a positive and statistically significant short-run relationship with disruptive innovation. At lag order 0, the coefficient is 0.270, significant at the 1% level, indicating that an immediate increase in knowledge depth is associated with a rise in disruptive innovation. This positive relationship persists at lag order 1, with a smaller coefficient of 0.185, which is significant at the 10% level. These findings suggest that while knowledge depth contributes positively to disruptive innovation in the short run, the magnitude of its impact diminishes slightly over time. In contrast, knowledge source diversity (lnKSD) shows a consistently negative and statistically significant short-run relationship with disruptive innovation. At lag order 0, the coefficient is -4.829, significant at the 1% level, indicating that an increase in knowledge source diversity imposes short-run challenges on innovation processes. This negative impact persists at lag order 1, with a coefficient of -4.953, also significant at the 1% level. The consistent short-run negative effects of knowledge diversity suggest that the integration of diverse knowledge sources may introduce complexities and inefficiencies that hinder immediate innovation outcomes, despite its positive influence in the long run. The overall model demonstrates a strong fit, as reflected by the R-squared value of 0.936, which indicates that 93.6% of the variation in disruptive innovation can be explained by the short-run dynamics of the model.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eARDL short-run estimates.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eCoefficient\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eEstimates\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLag order\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eΔlnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eΔlnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.270**\u003c/p\u003e\u003cp\u003e(0.011)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.185*\u003c/p\u003e\u003cp\u003e(0.092)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eΔlnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-4.829***\u003c/p\u003e\u003cp\u003e(0.001)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-4.953***\u003c/p\u003e\u003cp\u003e(0.000)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.936\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003cem\u003eNote\u003c/em\u003e: Short-run estimators for first lagged have been depicted by Δ. Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003ch2\u003eStability test findings\u003c/h2\u003e\u003cp\u003eThe cumulative sum of squares (CUSUM square) plot is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, which is used to assess the stability of the regression coefficients in the specified model. The test was conducted with a 5% significance level, and the shaded area represents the confidence interval under the null hypothesis of stability. The red plot line indicates the recursive cumulative sum of squares. The stability of the model is determined by examining whether the red plot line remains within the shaded confidence bands throughout the observation period. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the cumulative sum of squares stays entirely within the 95% confidence interval. This confirms that there is no significant deviation from stability over the study period. At the 5% significance level, the results provide evidence of the stability of the regression coefficients. The findings indicate that the model is robust and the relationships among the variables remain consistent over time.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003ch2\u003eDOLS findings\u003c/h2\u003e\u003cp\u003eTo ensure the robustness of our long-run findings from the ARDL model, we employed an alternative cointegration estimation method: Dynamic Ordinary Least Squares (DOLS). The DOLS estimator is known for its reliability in small samples and its effectiveness in correcting for endogeneity by including leads and lags of the first-differenced regressors. The results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDOLS Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariables\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDOLS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCoef.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStd. Err.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ep-value\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-2.373***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.478\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3.194***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.826\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e13.360*\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7.100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.089\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-9.874*\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.058\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eR2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.961\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAdjusted R2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.902\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNote\u003c/em\u003e: Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe DOLS estimates provide strong support for our primary long-run conclusions. Specifically, the coefficient for KB remains negative and highly significant (-2.16, p \u0026lt; 0.01), while the coefficient for KSD remains positive and highly significant (25.80, p \u0026lt; 0.01). This confirms that the detrimental long-run effect of internal knowledge fragmentation and the beneficial long-run effect of external knowledge sourcing are robust findings, independent of the specific estimation methodology.\u003c/p\u003e\u003ch2\u003eGranger causality test\u003c/h2\u003e\u003cp\u003eTo further investigate the dynamic interplay and temporal precedence among the variables, we conducted Granger-causality tests within a Vector Autoregression (VAR) framework. Based on the Schwarz Bayesian Information Criterion, a VAR model with one lag was selected. The results of the pairwise Granger-causality Wald tests are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eGranger causality test results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eDirection of causality\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eKB\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eKD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eKSD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e16.277***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.709\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8.366***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCD→KB; CD→KSD\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.054\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.081\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.347\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.469\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.209\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.005\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7.400***\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.765\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.831*\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eKSD→CD; KSD→KD\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote\u003c/em\u003e: Significance levels are denoted as 1%, 5%, and 10% with ***, **, and * respectively.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFirst, we find evidence of a bidirectional causality between KSD and CD. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the null hypothesis that KSD does not Granger-cause CD is rejected at the 1% significance level (χ² = 7.400, p = 0.007). Conversely, the hypothesis that CD does not Granger-cause KSD is also rejected at the 1% level (χ² = 8.366, p = 0.004). This indicates a powerful, self-reinforcing feedback loop between the diversity of external knowledge inputs and disruptive outputs.\u003c/p\u003e\u003cp\u003eSecond, we uncover a unidirectional shock effect originating from disruptive innovation. The test results show that CD is a highly significant Granger-cause of KB (χ² = 16.277, p = 0.000). However, the reverse causality from KB to CD is not significant (p = 0.817). This suggests that successful disruptions act as a powerful catalyst that subsequently drives the expansion of internal knowledge breadth.\u003c/p\u003e\u003cp\u003eThird, the results point to a weaker, internal knowledge cascade. KSD is found to be a weak Granger-cause of both KB (p = 0.096) and KD (p = 0.092) at the 10% significance level. This suggests that the introduction of diverse external knowledge tends to precede adjustments in the internal knowledge structure. Notably, neither KB nor KD are found to be significant Granger-causes of CD in our model.\u003c/p\u003e\u003cp\u003eIn summary, our Granger-causality analysis moves beyond the structural dynamics identified in the ARDL model to reveal the directional pathways and feedback loops of the innovation system. The findings paint a picture not of a simple linear process, but of a co-evolutionary system dominated by a core feedback loop between external knowledge sourcing and disruptive outcomes, and a strong reshaping effect that successful innovations exert on the internal knowledge landscape. The implications of these dynamic mechanisms, particularly the interplay between the virtuous feedback loop and the potentially detrimental consequences of success-driven knowledge expansion, will be explored in the following Discussion section.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003eThe two clocks of innovation: short-term payoffs and long-run potential\u003c/h2\u003e\u003cp\u003eOur findings, summarized in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, reveal that the path to disruptive innovation is governed by two conflicting temporal logics running at different speeds and rewarding different strategies. The first is a short-term clock geared towards immediate, predictable payoffs, while the second is a long-term clock that cultivates uncertain, yet transformative, potential. We argue that this tension is deeply embedded in the absorptive capacity process, creating a fundamental conflict between the behavioral imperatives of Realized Absorptive Capacity (RAC) and the structural investments required for a robust Potential Absorptive Capacity (PAC).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eLong-run and short-run effects of different variables.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eDependent Variable: CD\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eLong-run estimate\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eShort-run estimate\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSignificant negative\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSignificant positive\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003elnKSD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSignificant positive\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSignificant negative\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe short-term clock rewards the efficient deployment of RAC, particularly through its exploitative pathway. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, our results indicate that Knowledge Depth (KD), which represents this exploitative refinement, emerges as a significant positive factor in the short run. This underscores the power of specialization to provide focused pathways for immediate technical advancements, enabling the swift resolution of well-defined technical challenges. Conversely, this short-term logic actively penalizes investments in PAC. Our analysis shows that Knowledge Source Diversity (KSD), the empirical proxy for PAC, exhibits a significant negative effect in the short term. This creates a temporal integration burden, where the cognitive and coordination costs of assimilating diverse external knowledge suppress immediate innovation performance. Thus, the incentives of the short-term clock systematically favor a narrow, exploitative RAC while discouraging the foundational investments in PAC.\u003c/p\u003e\u003cp\u003eThe long-run clock, in contrast, is driven almost entirely by sustained investment in PAC. Our findings underscore the transformative power of KSD, which in the long run becomes the sole significant positive driver of disruptive innovation. This reflects the delayed yet powerful rewards of leveraging external diversity, which enriches the innovation process with novel ideas and fosters the cross-boundary synergies necessary for paradigm shifts. However, the long-run clock also reveals the perils of a specific pathway within RAC Knowledge Breadth (KB), representing an exploratory internal integration, exerts a significant negative long-run impact. This suggests that an overly broad internal knowledge base, while promising interdisciplinary disruption, ultimately leads to resource dispersion and a fragmented innovation process. Over time, the challenges of managing this internal complexity outweigh the benefits, resulting in incremental rather than disruptive outcomes.\u003c/p\u003e\u003cp\u003eTaken together, these findings paint a picture of a systemic dilemma within the absorptive capacity framework. The strategies rewarded by the short-term clock (exploitative RAC via KD) are, at best, inconsequential for long-term disruption. Meanwhile, the crucial investment for long-term potential (PAC via KSD) is actively penalized in the short run. Furthermore, even the seemingly beneficial exploratory pathway of RAC (KB) proves to be a long-term trap, leading to fragmentation rather than disruptions. This fundamental misalignment between the two clocks of innovation highlights the immense challenge of managing knowledge for sustained disruptiveness, providing a deep structural explanation for why innovation systems may naturally drift towards incrementalism over time. Consistent with Park et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), who link the decline in disruptiveness to a narrowing use of prior knowledge, our results identify external knowledge diversity (KSD) as the only sustained long-run lever for disruption.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003eThe entropy of success: how disruptive innovation breed complexity and stagnation\u003c/h2\u003e\u003cp\u003eWhile the preceding analysis illuminated the temporal trade-offs inherent in the innovation system, this section delves deeper into its dynamic evolution. The findings from our Granger causality analysis allow us to move beyond viewing innovation as a mere outcome and to examine its role as an active antecedent that shapes the future knowledge landscape. The results reveal the presence of feedback mechanisms, suggesting that disruptive innovation is not only a product of its knowledge inputs but also an endogenous driver of subsequent changes in knowledge structure. This section, therefore, explores these dynamics, with a particular focus on how the consequences of success may, in turn, create the structural conditions that affect the potential for future disruptions.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eOur analysis first uncovers a potentially virtuous, self-reinforcing mechanism at the core of the innovation system. The Granger causality tests reveal a bidirectional feedback loop between KSD and disruptive innovation. This suggests that while the infusion of diverse external knowledge serves as a critical antecedent to disruptive outputs, these disruptions in turn stimulate a broader search for novel external knowledge. A successful disruption appears to legitimize new knowledge combinations and shift technological paradigms, thereby compelling the ecosystem to expand its PAC and fueling the engine for subsequent rounds of innovation.\u003c/p\u003e\u003cp\u003eHowever, this virtuous cycle is accompanied by a problematic dynamic. The consequence of a disruptive innovation, as revealed by our Granger causality results, is its role in driving the expansion of internal KB. A disruptive innovation success inherently triggers a phase of widespread application and exploitation. This process necessitates the integration of knowledge from various complementary fields, leading to an unavoidable increase in the complexity and diversity of the internal knowledge base. This expansion of KB represents a systemic shift in RAC towards a more exploratory and multifaceted internal structure.\u003c/p\u003e\u003cp\u003eThis success-driven expansion of internal knowledge breadth ultimately closes a systemic trap. By linking this powerful dynamic finding with our long-run ARDL estimates, the paradox becomes clear. Our long-run analysis has already established that high levels of KB are structurally detrimental to the generation of future disruptive innovation, likely due to the challenges of resource fragmentation and loss of strategic focus. Consequently, the innovation system appears to contain an endogenous mechanism for its own potential stagnation: the very success of a disruptive innovation triggers a systemic increase in knowledge breadth, which in turn erodes the structural conditions required for the next disruption. Therefore, the decline in disruptive potential can be understood as a risk emerging from this cumulative process, a form of systemic entropy where past success, if left unmanaged, can become a primary driver of future stagnation.\u003c/p\u003e\u003cp\u003eHowever, understanding these entropic forces illuminates potential pathways to counteract them. The challenge of success-driven complexity in KB, for instance, can be mitigated through strategic modularity in organizational design, which structurally insulates exploratory teams from the inertia of mature business units. Furthermore, the inward-looking tendencies that follow success can be counterbalanced by a conscious and continuous investment in PAC, institutionalizing the search for external knowledge to ensure a steady supply of novel sparks. Finally, overcoming the path dependency created by success requires dynamic evaluation and an embrace of creative destruction, fostering a culture that is willing to challenge and even cannibalize its own successful products. By actively managing the consequences of success through these mechanisms, organizations and policymakers can work to sustain the vitality of the innovation ecosystem against its natural drift towards stagnation.\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study set out to provide a dynamic understanding of the declining potential of disruptive innovation. By applying a suite of time-series methods to global patent data from 1980 to 2010 and grounding our analysis in absorptive capacity theory, we move beyond static explanations to reveal a complex, co-evolutionary system fraught with temporal trade-offs and feedback loops.\u003c/p\u003e\u003cp\u003eOur ARDL analysis first uncovers a fundamental conflict between the short-term behaviors and long-term structural requirements of the innovation process. We find that Potential Absorptive Capacity (PAC), measured by KSD, is the sole significant positive driver of disruptive innovation in the long run, yet it incurs immediate costs in the short run. Conversely, the exploitative pathway of Realized Absorptive Capacity (RAC), measured by KD, offers immediate payoffs but is inconsequential over the long term. Meanwhile, the exploratory pathway of RAC, measured by KB, proves to be detrimental in the long run, suggesting that excessive internal diversification erodes disruptive potential.\u003c/p\u003e\u003cp\u003eMoreover, Granger causality analysis reveals the dynamic engine of this system. We uncover a bidirectional feedback loop between PAC and disruptive innovation, indicating a self-reinforcing co-evolution. We also identify a critical dynamic whereby successful disruptions act as a strong endogenous driver of the detrimental exploratory RAC path, measured by KB. This suggests that the very success of a disruptive event can trigger a systemic shift towards a more complex and fragmented knowledge structure that is less conducive to future disruption.\u003c/p\u003e\u003cp\u003eThese findings offer critical insights for policymakers and innovation managers aiming to foster sustained disruptive innovation. The core challenge lies in reconciling the temporal trade-offs and managing the endogenous dynamics revealed in our study. First, the conflict between the short-term costs and long-term benefits of PAC underscores the need for governance structures that function as temporal bridges. Innovation infrastructures must be designed to buffer early-stage integration inefficiencies while preserving long-term recombinability. To achieve this, governments and funding agencies can support modular, phase-based mechanisms such as two-stage R\u0026amp;D consortia and develop platform-based digital infrastructures to reduce search and alignment costs. Second, managing the dynamic consequences of success requires a conscious strategy of strategic modularity to counteract the detrimental long-run effects of KB. Knowledge integration within organizations should be governed to avoid wholesale internal diffusion. Funding programs should encourage bounded, selective integration through mechanisms like matrix organizational structures, rather than undirected interdisciplinarity. Mid-term evaluation checkpoints can also help prevent the over-extension of an innovation\u0026rsquo;s internal knowledge base. Finally, the transient role of KD highlights that short-term technical expertise alone is insufficient to sustain disruptive trajectories. Policy frameworks should incentivize depth-to-diversity transitions over time. Project funding, for example, can adopt tapered incentive schemes that reward initial technical depth but make renewal or scaling-up contingent on demonstrable cross-domain expansion. Career development tracks in public R\u0026amp;D institutions can also be designed to encourage this temporal diversification, ensuring that individual-level knowledge accumulation aligns with systemic innovation needs.\u003c/p\u003e\u003cp\u003eThis study has several limitations that open avenues for future investigation. First, our analysis relies on the CD index as the sole measure of disruptive innovation; future research could explore the robustness of our findings by triangulating our results with alternative metrics. Second, while our analysis reveals a dynamic link between disruptive events and KB, the precise mechanisms driving this success-driven fragmentation warrant deeper investigation. Lastly, and most importantly, our study is conducted at an aggregate level, which may mask significant heterogeneity across different technological fields. Future research employing dynamic panel techniques is therefore needed to explore these cross-sectional dynamics and identify the boundary conditions of our findings.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eYue Li: Conceptualization, Methodology, Data Curation, WritingLele Kang: Conceptualization, Writing, Resources, ValidationJiaxing Li: Supervision, Project administration, Validation\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eNational Social Science Fund of China. Research on the Formation Mechanism and Collaborative Governance of Health Information Poverty among Older Adults (Grant No. 23CTQ010)\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData available on request due to privacy.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbdul Basit, S., \u0026amp; Medase, K. (2019). 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Academy of management review, 27(2), 185\u0026ndash;203.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Disruptive innovation, Knowledge structure, Temporal dynamic","lastPublishedDoi":"10.21203/rs.3.rs-8119156/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8119156/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDisruptive innovation plays a critical role in driving technological progress and reshaping industries by challenging established paradigms and fostering new opportunities for growth. While previous research has largely focused on the static relationship between knowledge characteristics and disruptive innovation, the temporal dynamics of how knowledge structures influence disruptive innovation remain unclear. This study addresses this gap by examining the absorptive capacity process, distinguishing between Potential (PAC) and Realized (RAC) absorptive capacities. Using global patents spanning 1980 to 2010, we employed Autoregressive Distributed Lag (ARDL) and Granger causality tests to analyze the long-run, short-run, and causal relationships. The ARDL findings reveal a temporal conflict. In the long-run, PAC, as measured by knowledge source diversity, promotes disruptive innovation. In contrast, an exploratory path of RAC, measured by knowledge breadth, is detrimental. These effects are reversed in the short-run. Here, PAC negatively impacts disruptive innovation, whereas RAC, when measured by knowledge depth, provides a positive impact. The Granger causality tests further uncover a bidirectional feedback loop between PAC and disruptive innovation, and reveal that disruptions are an endogenous driver of the exploratory RAC path. These findings underscore the importance of aligning knowledge management strategies with temporal dynamics to foster sustained innovation.\u003c/p\u003e","manuscriptTitle":"Unveiling the Temporal Dynamics: The Impact of Knowledge Source Structure on Innovation through Time-Series Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-15 10:33:05","doi":"10.21203/rs.3.rs-8119156/v1","editorialEvents":[{"type":"communityComments","content":1}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b93b7aea-3efd-45cc-a4bc-9de269864439","owner":[],"postedDate":"December 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-15T10:33:06+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-15 10:33:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8119156","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8119156","identity":"rs-8119156","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}