Does R&D Efficiency Hold the Key to Regional Resilience Under Sustainable Urban Development?

Abstract

Amid intensifying geopolitical tensions and global uncertainties, regional economies face mounting pressures that threaten both stability and sustainability. Against this backdrop, building resilient regional systems has become a central issue in sustainable urban development. As a key driver of resilience, innovation has been central to China’s development agenda. Continuous and large-scale R&D investment has redirected focus from input expansion to efficiency improvement, positioning R&D efficiency at the heart of resilience-building. Under external shocks and uncertainty, can improvements in R&D efficiency enhance regional economic resilience? If so, which additional factors embedded in sustainable urban development planning can further amplify this effect? To address these questions, this study employs provincial panel data from 2000 to 2021 and integrates the SBM-DEA approach with an entropy-weighted resilience index for regression analysis. The results indicate that (1) R&D efficiency exerts a positive but limited impact on resilience, with an average increase of only 0.188 units, indicating that efficiency alone cannot generate resilient economies without institutional coordination; (2) human capital agglomeration and financial density strengthen this relationship, highlighting the need to integrate talent and financial strategies; (3) the positive effect is observed in eastern provinces but remains insignificant in central and western regions, revealing pronounced structural disparities that risk widening the resilience gap across regions rather than fostering balanced development; and (4) targeted government intervention effectively converts innovation efficiency into resilience gains, fostering coordinated and sustainable development. This study empirically demonstrates that improving R&D efficiency significantly enhances regional resilience in China and based on this evidence introduces the ICT Synergy Framework as a novel analytical lens for understanding how innovation, capital, and talent jointly drive resilience and sustainable development. The findings further suggest that targeted government intervention in R&D resource allocation can reinforce resilience, offering broader lessons for other developing economies. By integrating innovation outcomes with spatial and institutional planning, the study provides actionable insights for advancing sustainable urban development and coordinated regional growth.

1. Introduction

The global economy is undergoing a period of profound turbulence and heightened uncertainty [1]. Escalating geopolitical risks and protracted trade conflicts have generated significant shocks, further intensifying volatility and eroding both economic stability and the prospects for sustainable development [2,3]. Looking ahead, with the growing frequency of economic fluctuations and the deepening of international geopolitical tensions, countries are likely to confront increasingly complex internal and external challenges over the long term [4,5]. With this background, regional resilience, as a core concept for evaluating an economy’s capacity to withstand external shocks, has attracted increasing scholarly attention [6,7,8]. The concept of resilience, which originated in physics in the mid-19th century, was later introduced into economics and has since been widely recognized in academic literature as a framework for conceptualizing an economy’s capacity to resist, recover, and transform in response to external shocks [9]. A growing policy consensus now underscores the need to translate this conceptual platform into strategies for building more inclusive and sustainable economies. The United Nations’ World Economic Situation and Prospects 2024 report emphasizes the need to seize opportunities to foster a more inclusive and resilient global economy. In the context of major international disruptions and crises, scholars from various countries have conducted in-depth investigations into the impact of factors such as the agglomeration of innovation elements on regional economic resilience [4,10]. Among developing nations, China confronts not only heightened volatility arising from global market fluctuations but also the dual tasks of pursuing economic transformation and promoting balanced regional development. To strengthen regional economic resilience, the State Council issued the Outline of the National Innovation-Driven Development Strategy in 2016, which explicitly called for leveraging scientific and technological innovation to promote regional economic transformation and upgrading. With strong support from the central government, provincial-level governments have continuously increased fiscal investment in R&D to enhance innovation capacity, resulting in sustained growth in national R&D expenditure. By 2024, China’s total expenditure on R&D had reached 3.613 trillion yuan, representing an 8.3% increase from the previous year, and ranking the second in the world in total investment volume [11].

According to Schumpeter’s endogenous growth theory, innovations derived from technological progress act as an internal engine that allows the economic system to continuously renew [12]. In line with this perspective, technological innovation supported by R&D investment has emerged as a central force driving structural transformation and sustaining endogenous economic growth [13]. In recent years, increasing scholarly attention has been directed toward the linkages between R&D investment and regional economic resilience. A salient theme emerging from this literature is that enhanced innovation capacity enables regions not only to withstand external shocks but also to recover more effectively. Empirical evidence from EU regions, as demonstrated in Bristow’s study, confirms that regions with stronger innovation capacity exhibit greater resistance to crises and achieve faster recovery [14]. Similarly, Filippetti’s study employs patent data as a proxy for innovation and provides evidence that regions characterized by higher technological dynamism demonstrate stronger employment resilience [15]. Pellens et al., in their analysis of OECD countries, emphasize the cyclical nature of public R&D investment and underline its pivotal role in bolstering resilience during economic crises [16]. However, focusing solely on the link between R&D investment, innovation, and resilience is not sufficient. High levels of investment on R&D or innovation do not necessarily guarantee efficient resource allocation or corresponding improvements in resilience outcomes, because the institutional contexts of governance may significantly affect how inputs are transformed into outputs. Resilience is often associated with redundancy and diversity [9]. R&D efficiency, by incorporating both resource and environmental factors, seeks to maximize output with reduced input and ecological burden. This argument highlights an intrinsic trade-off with economic resilience and suggests that the efficiency of R&D, rather than its sheer volume, may provide a more accurate explanation of how regions build resilience.

Motivated by this concern, this study shifts the analytical focus from R&D input intensity to R&D efficiency as a key determinant of regional economic resilience. While prior studies have predominantly examined the innovation–resilience nexus from an investment perspective, the specific contribution of efficiency remains underexplored. To address this gap, this paper pursues three objectives. First, it empirically evaluates the direct effect of R&D efficiency on regional economic resilience. Second, it investigates the contextual conditions under which R&D efficiency contributes more effectively to resilience. Third, it provides theoretical insights and policy implications that connect efficiency-driven resilience to the broader agenda of sustainable urban development. By establishing this linkage, the study aims to demonstrate that enhancing R&D efficiency not only strengthens regional economic resilience but also lays the foundation for advancing sustainable urban transformation.

After this introduction section, Section 2 provides a survey of the literature and develops the theoretical framework along with the research hypotheses. Section 3 sets out the empirical methodology and details of the data utilized in the analysis. Section 4 reports the principal results and offers wider implications and suggestions as well. Lastly, Section 5 concludes the paper by synthesizing the main findings and presenting policy recommendations.

2. Literature Review and Theoretical Hypotheses

2.1. The Impact of R&D Efficiency on Regional Economic Resilience

Originally, the concept of “resilience” was applied primarily in disciplines such as engineering and ecology, and it was not until the early 21st century that it began to attract scholarly attention in spatial economics [17]. Although the conceptual framework and precise definition of economic resilience remain contested, quantitative methods have been widely applied in empirical research. Existing approaches to resilience evaluation can be broadly divided into two strands. The first stream emphasizes single-dimensional assessments [18]. Alternatively, some studies rely on a multi-faceted framework, drawing upon economic, social, and supplementary dimensions to construct a broader assessment of regional resilience [19]. Following this line of thought, this paper evaluates regional economic resilience through a multidimensional framework, which aligns with the broader academic trend of examining resilience as a dynamic and systemic attribute. Grounded in the evolutionary resilience framework proposed by Martin and Sunley [9] and drawing extensively on resilience models that have been widely applied in empirical research [20,21], this study conceptualizes resilience as a multidimensional construct comprising three interrelated capacities: resistance and recovery, which reflect the short-term ability of regions to absorb and rebound from shocks; adaptability and adjustment, which capture structural and behavioral flexibility in response to changing environments; and transformation and development, which represent the long-term capacity for reorientation toward new growth trajectories. Notably, the thematic emphasis of resilience studies diverges across institutional contexts and stages of development. In advanced economies, resilience is often associated with market efficiency, innovation dynamics, and institutional adaptability as the principal drivers of recovery and transformation [22]. By contrast, studies in developing economies, such as China, tend to adopt a more comprehensive perspective, incorporating economic, social, and infrastructural dimensions as key pathways to strengthen regional resilience [23]. Overall, this evolution of thought indicates that resilience research has gradually shifted from abstract conceptual debates toward dynamic, system-oriented analyses that emphasize how regional economies withstand, adapt to, and evolve under external shocks transition that reflects resilience’s growing role in the pursuit of sustainable and stable regional development. Consequently, economic resilience has become a central focus in regional economic research, with growing emphasis on how economic systems respond to external shocks and disturbances [24,25]. Specifically, economic resilience refers to the capacity of an economic system to maintain basic functions and recover quickly in the face of unexpected shocks [26]. For instance, Boschma [22] and Martin [17] define resilience as the long-term ability to absorb shocks and develop new growth paths. Amid the global disruptions triggered by the COVID-19 pandemic, the escalation of Sino–US trade frictions, and the frequent outbreak of geopolitical conflicts, scholarly attention has increasingly shifted toward exploring how to sustain economic stability and robustness.

At the same time, innovation has been broadly acknowledged as a fundamental force propelling economic advancement and overall development [27]. Consequently, understanding urban economic resilience from the perspective of innovation has become a prominent topic in resilience research [28,29]. A growing body of literature has investigated the relationship between innovation and economic resilience from multiple perspectives. At the firm level, studies suggest that increasing R&D investment during periods of crisis and uncertainty can enhance value creation against the riskier shocks, thereby indirectly reinforcing resilience [30]. At the regional level, empirical analysis by Tang et al. based on 272 Chinese cities highlights the importance of structural characteristics such as technological diversity and complexity, with higher levels of technological complexity being consistently linked to stronger resilience [29]. In particular, when attention is directed to green innovation, empirical evidence suggests that it plays a significant and beneficial role in strengthening urban economic resilience [31]. However, existing research has primarily focused on the impact of R&D investment intensity and its resulting innovation outcomes on economic resilience, while relatively little attention has been paid to how R&D efficiency shapes regional economic resilience.

To address this gap, one critical issue is how to measure R&D efficiency. Among the available approaches, DEA has become the predominant approach [32,33]. In particular, the SBM-DEA proposed by Tone and Tsutsui has been widely adopted, as it offers a more accurate assessment while effectively addressing slack variables. Following Choi [34], this study applies the SBM-DEA model to evaluate provincial R&D efficiency in China. In the case of the Pearl River Delta, Wang employed R&D-based indicators to examine innovation efficiency and reported that improvements in efficiency strengthen regional economic resilience [35]. Nevertheless, their analysis was confined to a single metropolitan region, leaving open the question of whether similar dynamics can be observed across China as a whole. To address this limitation, this paper measures R&D efficiency across all Chinese provinces, thereby providing a more systematic and comprehensive understanding of how R&D efficiency shapes regional economic resilience. When R&D efficiency rises, innovation resources can be allocated more effectively, local innovation capacity is reinforced, and technological achievements can be produced with lower input costs [36]. Such efficiency gains not only foster technological progress but also strengthen a regional capacity to withstand external shocks. Taken together, it can be inferred that regions with higher R&D efficiency are better positioned to maintain stability and achieve rapid recovery when confronted with unexpected shocks. Accordingly, this study proposes the following hypothesis:

H1. 

Improvements in R&D efficiency enhance regional economic resilience.

2.2. Regional Financial Density

In recent years, the relationship between financial activities of the region and its spatial economic development has taken on new characteristics of resilience. Contrary to the traditional view that finance would gradually decouple from geography, the evolution of the financial system has instead become increasingly dependent on the functional agglomeration of cities [37]. This reliance stems from the growing integration of the financial sector with the real economy, as financial capital, monetary flows, and related services continue to cluster in urban areas with strong economic foundations and substantial growth potential. Metropolitan areas and regional hubs—characterized by advanced infrastructure, highly skilled human capital, and well-developed industrial ecosystems—have consequently emerged as pivotal nodes for the concentration and diffusion of financial resources.

At the same time, the tension between the high operating costs of financial markets and the need to strengthen financial specialization has become more pronounced. In response, regulatory and supervisory bodies have increasingly emphasized the collaborative development and application of financial technology (FinTech) within the landscape of the region. FinTech not only improves efficiency in payments, credit, and wealth management but also enhances risk control and resource allocation through emerging technologies including AI, and big data. This process has accelerated the spatial clustering of FinTech, giving rise to high-end financial districts characterized by innovation-driven growth. Such spatial agglomeration reshapes the functional roles and spatial configurations of cities, while simultaneously reinforcing their capacity to withstand external shocks. Ultimately, it fosters the development of urban economies toward the greater financial scale advantages and structural resilience [38]. In summary, the deep integration of finance and technology, along with their spatial clustering, has emerged as a critical force enhancing urban competitiveness and providing an essential foundation for strengthening regional economic resilience. Moreover, financial agglomeration fosters technological innovation by generating economies of scale [39]. In regions with highly concentrated financial resources, the relationship between the research institutions and financial institutions appears to be closer, and this close interaction provides strong support for further technological research, development, and application [40]. Based on the above discussion, this paper proposes the second hypothesis:

H2. 

Regional financial density strengthens the linkage between R&D efficiency and regional economic resilience.

2.3. Population Agglomeration Level

Human capital is broadly acknowledged as a key engine of technological progress and innovation, underscoring the central role of high-quality human resources in sustaining economic growth [41]. Prior studies have shown that effective human resource management practices not only support but also incentivize innovative activities, thereby strengthening the innovation capacities of firms and regions [42]. As the foundation of innovation, the scale and quality of human resources largely determine a regional innovation potential and vitality [43]. Greater societal investment in talent cultivation, attraction, and utilization, coupled with improved allocation of human resources, enhances the quality of the labor force while simultaneously stimulating the innovative dynamism of talents. A higher level of human resource allocation fosters an inclusive innovation environment that attracts and concentrates innovation-related talents and resources, resulting in beneficial circular mechanism. From both policy and practical perspectives, strengthening the emphasis on human capital and optimizing its allocation constitute essential pathways for enhancing regional innovation capacity. Moreover, at the regional level, the concentration of population further amplifies this effect. On the one hand, population agglomeration generates knowledge spillovers and network effects, whereby dense clusters of talent facilitate the sharing and diffusion of R&D outcomes. On the other hand, a larger population scale diversifies demand structures and expands consumer markets, providing fertile ground for the application and commercialization of innovative achievements. This dual mechanism not only enhances regional innovation capacity but also strengthens adaptability and resilience against external shocks. In other words, effective human capital agglomeration contributes to improvements in R&D efficiency, invigorates innovation dynamics, and accelerates knowledge diffusion, thereby fundamentally enhancing the resilience of regional economic systems.

In summary, a higher degree of population concentration enables regions to better harness the advantages of human capital in innovation and, in doing so, positively moderates the relationship between R&D efficiency and regional economic resilience. Accordingly, this paper proposes the following hypothesis:

H3. 

Population agglomeration level strengthens the linkage between R&D efficiency and regional economic resilience.

3. Methodology and Data

3.1. Sample and Data Source

To empirically test the three hypotheses, this study employs panel data from 31 Chinese provinces covering the period 2000–2021. To ensure the rigor and robustness of the results, missing values are imputed using linear and mean interpolation, and provinces with severely incomplete data are excluded. Furthermore, all continuous variables are censored at the 1% level to mitigate the potential distortion of regression estimates caused by extreme observations. Following data cleaning, the final dataset consists of 679 observations, yielding an unbalanced provincial panel.

The data are primarily drawn from the CSMAR and Wind databases, the China Industrial Economic Statistical Yearbook, China Statistical Yearbook, China Science and Technology Statistical Yearbook, China Financial Yearbook, and various provincial statistical yearbooks. To minimize the effects of scale differences and potential outliers, variables with large magnitudes are transformed using natural logarithms. All data processing and empirical analyses are conducted in Stata 18, with preliminary data handling performed in Excel.

3.2. Measuring Regional Economic Resilience Using the Entropy Method

Building on the work of Guo [44], this paper develops a multidimensional framework for assessing urban economic resilience. The framework encompasses three core dimensions: resistance and recovery capacity, adaptability and adjustment capacity, and transformation and development capacity. From a methodological standpoint, this study adopts the entropy weight method to determine indicator weights, which supports an impartial and data-driven evaluation of urban economic resilience. The entropy method, widely recognized as a robust objective weighting technique, determines indicator weights based on the degree of variation across observations. Indicators with greater variability contain more information and thus receive higher weights. This approach effectively mitigates the potential bias of subjective weighting and enhances the scientific rigor and robustness of the evaluation results. Applying the entropy method in this context not only captures the actual contribution of each dimension to resilience but also improves the explanatory power and reliability of the overall assessment framework. To construct the regional economic resilience index, it is first necessary to normalize all selected indicators, followed by the assignment of weights. The following section outlines the detailed steps of the calculation:

Step 1. Indicator normalization.

Since the provincial economic resilience index developed in this study covers multiple dimensions and numerous indicators, all variables are standardized in advance to guarantee methodological consistency and result comparability. A key aspect of this process involves identifying the direct impact of each indicator on economic resilience. Specifically, indicators are categorized into two types: positive indicators (where higher values indicate stronger resilience, such as per capita GDP and household income) and inverse indicators (in which larger values denote lower resilience, such as the unemployment rate). The normalization methods applied to positive and negative indicators are presented in Equations (1) and (2) and for each indicator $j$, ${max x}_{ij}$ and ${min x}_{ij}$ correspond to its highest and lowest values over the study period, and $X_{ij}$ indicates the standardized form, respectively.

$$X_{ij}={\displaystyle \frac{x_{ij}-{min x}_{ij}}{max x_{ij}-{min x}_{ij}}}$$

(1)

$$X_{ij}={\displaystyle \frac{{max x}_{ij}-x_{ij}}{{max x}_{ij}-{min x}_{ij}}}$$

(2)

Step 2. Calculation of Indicator Weights.

To assign weights to the three dimensions of resistance and recovery capacity, adaptability and adjustment capacity, as well as transformation and development capacity, this study employs the entropy weight method.

$$P_{ij}=X_{ij}/\sum _{i=1}^n{X}_{ij}$$

(3)

Step 3. Calculating the entropy value of the $jth$ indicator.

The entropy value is used to measure the amount of information contained in each indicator, reflecting its degree of variation and contribution to the overall evaluation system. In Equation (4), $k=1/ln\left(n\right)>0$.

$$e_j=-k\times \sum _{i=1}^n(P_{ij}\times \mathit{ln}\left(P_{ij}\right))$$

(4)

Step 4. Calculating the coefficient of variation for the $jth$ indicator.

The information utility value of each indicator is obtained as the difference between its entropy value $e_j$ and 1. The greater the utility value, the higher the indicator’s relative importance in the evaluation, and accordingly, its assigned weight increases.

$$d_j=1-e_j$$

(5)

Step 5. Determining the weights of evaluation indicators.

In this step, the final weight of each evaluation indicator is derived based on its information utility value. Indicators with higher utility values are assigned greater weights, reflecting their stronger contribution to the overall assessment of regional economic resilience.

$$w_j={\displaystyle \raisebox{1ex}{$d_j$}\!\left/ \!\raisebox{-1ex}{${\sum }_{j=1}^m{w}_j{P}_{ij}$}\right.}$$

(6)

Step 6. Constructing the composite index.

In the final step, the composite index for each sample is calculated by aggregating all standardized indicators according to their assigned weights.

Table 1. Regional Resilience Indicator Weights Derived from the Entropy Method.

Primary Indicator	Secondary Indicator	Tertiary Indicator	Weight
Regional economic resilience	Resistance and recovery capacity	Per capita economic output (CNY)	0.1049
		Unemployment Rate (%)	0.1127
		Per Capita Disposable Income (CNY)	0.0335
	Adaptability and regulation capacity	Fiscal Balance Ratio (%)	0.1687
		Total Retail Sales of Consumer Goods (100 million CNY)	0.0462
		Share of Tertiary Industry in GDP (%)	0.0883
	Transformation and development capacity	Number of University Students (10,000 persons)	0.1471
		Educational Expenditure (10,000 CNY)	0.2920
		Expenditure on Science and Technology (10,000 CNY)	0.0066

provides the overview of the adopted indicator system and the associated results.

$$Z_i=\sum _{j=1}^m{w}_j{P}_{ij}$$

(7)

3.2.1. ICT Synergy Framework

Scholars have long investigated the drivers of regional innovation and resilience, underscoring the importance of technological capability, financial systems, and human capital formation. Numerous studies have argued that financial development exerts a positive influence on innovation [45,46]. The underlying rationale is that a well-developed financial system enhances information accessibility and allocative efficiency, thereby mitigating the risks associated with uncertain innovation projects and encouraging investors to provide funding for young, innovation-oriented firms. Meanwhile, research demonstrates that human capital constitutes the cornerstone for further regional development. Gennaioli, Shleifer, and Vishny demonstrated that regions with higher concentrations of skilled labor tend to achieve superior development outcomes, emphasizing the central role of talent agglomeration in fostering persistent growth [47]. Nevertheless, the majority of previous research has treated innovation, capital, and talent as discrete domains rather than interrelated components of a broader adaptive system. Limited attention has been devoted to how these three dimensions operate in concert to shape a region’s ability to withstand and recover from external shocks. To bridge this conceptual gap, the present study introduces the Innovation–Capital–Talent (ICT) Synergy Framework, which unifies these mutually reinforcing elements within a single analytical structure. In this framework, innovation efficiency operates as a trigger, initiating technological upgrading and knowledge creation; capital density functions as an accelerator, enabling the conversion of innovation outcomes into economic resilience through financial liquidity and risk-sharing mechanisms; and talent agglomeration serves as an amplifier, extending the reach of innovation via learning diffusion and knowledge spillovers generated by human capital clustering.

Building on Martin and Sunley’s evolutionary perspective of regional resilience [9], the ICT framework posits that the transformation of R&D efficiency into resilient regional growth depends on the synergistic coordination among innovation, capital, and talent subsystems. From a theoretical standpoint, this synergy can be conceptualized as a moderating mechanism, in which both capital density and talent agglomeration are expected to strengthen the positive linkage between R&D efficiency and regional economic resilience. By framing resilience as the outcome of an integrated innovation–finance–talent nexus, the ICT framework offers a conceptual foundation for understanding how innovation-driven economies may achieve adaptive and sustainable development.

3.2.2. SBM-DEA

The SBM-DEA model is a widely adopted approach for evaluating the relative efficiency of decision-making units (DMUs). Unlike the traditional DEA framework, the SBM-DEA model explicitly incorporates slack variables into the efficiency estimation process, thereby addressing input redundancies and output shortfalls more effectively. This methodological advantage allows the model to provide more accurate and robust efficiency scores, making it particularly suitable for evaluating R&D efficiency, where resource utilization and innovation outputs often exhibit slack. Drawing on the approach of Choi [34], this study selects R&D cost and number of R&D personnel as input variables and patents and transaction value as output variables to construct the evaluation framework. By integrating these indicators, the SBM-DEA model enables a comprehensive measurement of provincial R&D efficiency in China. The formal mathematical expression of the SBM-DEA model is given as follows:

The production possibility set is defined as:

$$P=\left\{\left(x, y^g\right)\left|x\ge X\lambda , y^g\le y^g\lambda , \lambda \ge 0\right.\right\}$$

(8)

The efficiency score of each DMU can then be obtained by solving the following optimization problems:

$${\theta }^{\ast }=min{\displaystyle \frac{1-\frac{1}{m}{\sum }_{i=1}^m\frac{s_i^{-}}{x_{i0}}}{1+\frac{1}{f+k}{\sum }_{j=1}^f\frac{s_j^g}{y_{j0}^g}}}$$

(9)

$$\mathrm{subject} \mathrm{to} s.t.\left\{\begin{array}{c}{x}_0=X\lambda +s^{-}\\ y_0^g=Y^g\lambda -s^g\\ s^{-}\ge 0, s^g\ge 0,\lambda \ge 0\end{array}\right.$$

(10)

where $x$ and $y^g$ denote input and desirable output vectors, respectively; $s^{-}$ and $s^g$ are slack variables for inputs and outputs; and $\lambda$ is an intensity vector. The optimal value ${\theta }^{\ast }$ ranges between 0 and 1, with higher values indicating higher R&D efficiency. A DMU is considered efficient if ${\theta }^{\ast }$ = 1 and all slack variables equal to zero. To ensure comprehensiveness, this study uses multidimensional input and output indicators to measure R&D efficiency. The input–output indicators are shown in

Table 2. R&D Efficiency Indicator System.

Type	Variable	Definition	Unit
Input	R&D cost	Internal expenditure on Research and Experimental Development (R&D)	10,000 CNY
	Number of R&D Personnel	Full-time equivalent (FTE) of personnel engaged in Research and Experimental Development (R&D)	Person-year
Output	Patents	Number of accepted patent applications	EA
	Transaction Value	Value of technology market transactions	10,000 CNY

. The provincial R&D efficiency scores derived from the SBM-DEA model serve as the core explanatory variable in this study. They are incorporated into the baseline regression model to test the hypothesis that higher R&D efficiency enhances regional economic resilience. By combining DEA efficiency measurement with an econometric approach, this study provides a more systematic understanding of how innovation efficiency contributes to resilience at the provincial level.

3.2.3. Model Specification for the Baseline Regression

In this study, a two-way fixed effects model is employed to empirically examine the impact of R&D efficiency on regional economic resilience. The dataset covers 31 Chinese provinces over the period 2000–2021, spanning 22 years. The baseline regression model is specified as follows:

$${RES}_{it}=\alpha +\beta {RD}_{it}+\gamma \sum {controls}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(11)

where ${RES}_{it}$ denotes the economic resilience of province $i$ in year $t; {RD}_{it}$ represents the R&D efficiency of province $i$ in year $t$; $\sum {controls}_{it}$ is a set of control variables; ${\mu }_i$ and ${\lambda }_t$ represent province- and year-fixed effects, respectively; and ${\epsilon }_{it}$ is the error term. To further investigate how population concentration and regional financial density moderate the relationship between R&D efficiency and regional economic resilience, this study incorporates interaction terms into the regression framework. By incorporating interaction terms into the model, this study seeks to uncover whether the degree of population concentration and the density of regional finance amplify or mitigate the impact of R&D efficiency on economic resilience. Such an approach allows us not only to examine the direct moderating effects of these contextual factors, but also to shed light on the mechanisms through which innovation translates into resilience. The extended models are expressed as follows:

$${RES}_{it}=\alpha +\beta {RD}_{it}+\gamma {Agg}_{it}+\theta \left({RD}_{it}\ast {Agg}_{it}\right)+\delta \sum {controls}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(12)

$${RES}_{it}=\alpha +\beta {RD}_{it}+\gamma {Fin}_{it}+\theta \left({RD}_{it}\ast {Fin}_{it}\right)+\delta \sum {controls}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(13)

In models (11)–(13), the subscript $i$ indicates the province and $t$ represents the year. ${RES}_{it}$ is the dependent variable capturing regional economic resilience, while ${RD}_{it}$ is the key independent variable, denoting R&D efficiency. The moderating variables ${Agg}_{it}$ and ${Fin}_{it}$ measure the level of industrial agglomeration and financial development, respectively. $\sum {controls}_{it}$ is the set of control variables.

3.3. Variable Definitions

This section introduces the variables used in empirical analysis. To improve readability, all variable definitions and measurement explanations are summarized in

Table 3. Variable Definitions.

Variable Type	Variable Name	Abbreviation	Definition/Measurement
Dependent variable	Regional economic resilience	Res	Composite index constructed using the entropy-weight method
Independent variable	R&D efficiency	RD	Calculated using the SBM-DEA model
Moderating variables	Human Capital Agglomeration	Agg	Number of employed persons divided by administrative area.
	Regional Financial Density	Fin	Balance of deposits and loans of financial institutions at year-end divided by regional GDP.
Control variables	Transportation infrastructure	Infra	Logarithm of total highway mileage.
	Urbanization level	Urban	Ratio of urban permanent residents to total permanent population.
	Labor force level	Labor	Natural logarithm of total employed persons.
	Environmental regulation	UR	Completed investment in industrial pollution control divided by industrial value added.
	Urban–rural income gap	Theil	Theil index
	Tax burden	Tax	Tax revenue divided by regional GDP.
	Industrialization degree	Degree	Value added of the secondary industry divided by regional GDP.

.

Dependent Variable: Regional Economic Resilience (RES): The dependent variable in this study is regional economic resilience (RES), which reflects the ability of a province to withstand, adapt to, and recover from external shocks, while maintaining long-term sustainable development. Following Guo [44], a multidimensional evaluation framework is adopted, consisting of three core dimensions: resistance and recovery capacity, adaptability and adjustment capacity, and transformation and development capacity. To ensure objectivity in the measurement, the entropy weight method is applied to construct a composite resilience index from multiple indicators, thereby capturing the comprehensive resilience performance of each province over the study period.

Independent Variable: R&D Efficiency (RD): The key explanatory variable is R&D efficiency (RD), which measures the effectiveness of converting R&D inputs into innovative outputs. R&D efficiency is calculated using the Slack-Based Measure Data Envelopment Analysis (SBM-DEA) model, which provides a more accurate evaluation by accounting for slack variables [48]. This approach enables us to capture variations in innovative performance across provinces while controlling for input–output inefficiencies. Specifically, R&D inputs include R&D cost and number of R&D personnel, whereas outputs include patents and transaction value. By focusing on efficiency rather than input scale, this measure highlights how effectively provinces utilize their innovative resources to foster economic resilience.

Moderating Variables:

(1)

Human Capital Agglomeration (Agg): Human capital agglomeration reflects the extent to which labor resources are concentrated in a region. It is measured as the ratio of the number of employed people to the administrative land area of each province. A higher value indicates a denser concentration of human capital, which facilitates knowledge spillover, technology diffusion, and collaborative innovation. Moreover, human capital agglomeration enhances the adaptability of the regional economy by providing a stronger pool of skilled labor, thereby potentially amplifying the resilience-enhancing effect of R&D efficiency.

(2)

Regional Financial Density (Fin): Regional financial density captures the concentration of financial resources relative to regional economic output. It is proxied by the ratio of the year-end balance of deposits and loans of financial institutions to the regional GDP. Higher financial density reflects greater accessibility to the capital, enabling more efficient resource allocation and easing financing constraints on innovation activities. Consequently, it is expected to strengthen the positive moderating effect of R&D efficiency on the regional economic resilience.

To mitigate potential estimation bias arising from omitted variables, this study incorporates a set of control variables widely adopted in the literature on regional resilience. Specifically, seven control variables are selected: (1) Transportation Infrastructure (Infra): Measured as the logarithm of highway mileage, reflecting the degree of improvement of the regional transportation network. Well-developed transportation infrastructure facilitates efficient resource allocation and enhances regional economic resilience [49]. (2) Urbanization Level (Urban): Proxied by the ratio of the urban permanent population to the total permanent population, capturing the extent of population concentration in urban areas. Urbanization can promote industrial upgrading and economic diversification; however, excessive urban expansion may also lead to congestion, housing pressure, and other urban problems, thereby exerting mixed effects on resilience [50]. (3) Labor Force (Labor): Measured as the natural logarithm of the number of employed persons, that is, the natural log of the total number of employees in each province. This variable reflects the overall scale of regional labor resources. Labor is a fundamental factor of production, and both its quantity and quality provide essential support for enhancing regional economic resilience [51]. (4) Environmental Regulation (UR): Defined as the ratio of industrial pollution control investment to industrial added value, reflecting the intensity of environmental regulation by the local government. Moderate regulation facilitates green transformation, while excessive regulation may raise costs, exerting complex influences on resilience [52]. (5) Urban–Rural Income Gap (Theil): Measured by the Theil index, which reflects income inequality between urban and rural residents. The calculation formula is as follows: Theil = (Urban income/Total income) × LN[(Urban income/Urban population)/(Total income/Total population)] + (Rural income/Total income) × LN[(Rural income/Rural population)/(Total income/Total population)] A higher Theil value indicates a larger income disparity between urban and rural areas, which may hinder regional coordination and weaken economic resilience [53]. (6) Tax Burden (Tax): Measured as the ratio of tax revenue to regional GDP, reflecting the fiscal burden of a province. A higher tax burden may discourage investment and innovation, thereby constraining regional economic resilience [54]. (7) Industrialization Level (Degree): Defined as the ratio of secondary industry value-added to regional GDP, reflecting the degree of industrial development. While industrialization is a crucial stage of economic development, overreliance on industry may lead to structural rigidity and undermine resilience [55].

4. Empirical Results

Before proceeding with the regression analysis, it is essential to provide a general overview of the dataset.

Table 4. Descriptive Statistics.

VarName	Obs	Mean	SD	Min	Median	Max
Res	679	1.480	1.188	0.281	1.136	5.956
RD	679	0.473	0.335	0.028	0.388	1.000
Agg	679	0.023	0.033	0.000	0.014	0.217
Fin	679	2.934	1.165	1.279	2.680	8.131
Infra	679	11.367	0.897	9.100	11.610	12.660
Urban	679	0.509	0.162	0.140	0.510	0.900
Labor	679	7.466	0.900	4.820	7.610	8.860
UR	679	0.004	0.004	0.000	0.003	0.020
Theil	679	0.112	0.054	0.019	0.104	0.271
Tax	679	0.079	0.026	0.040	0.070	0.170
Degree	679	0.346	0.097	0.070	0.350	0.570

reports the descriptive statistics for all variables used in this study, including measures of central tendency and dispersion. The results indicate reasonable variation across regions and years, suggesting sufficient heterogeneity for empirical estimation. These statistics help illustrate the overall distributional patterns of R&D efficiency, regional economic resilience, and other control variables, thereby offering a clearer foundation for interpreting the subsequent econometric results.

4.1. Correlation Test

Prior to the regression analysis, the Pearson correlation test is conducted to explore the pairwise relationships among the core variables. This preliminary analysis serves two main purposes. First, it offers an initial understanding of the direction and magnitude of associations between R&D efficiency, regional economic resilience, and the moderating variables. Second, it helps detect the potential multicollinearity, which could distort regression results if not properly addressed.

As shown in

Table 5. Pearson Correlation Matrix for Key Variables.

	Res	RD	Agg	Fin	Infra	Urban	Labor	UR	Theil	Tax	Degree
Res	1
RD	0.159 ***	1
Agg	0.432 ***	0.226 ***	1
Fin	0.384 ***	0.396 ***	0.456 ***	1
Infra	0.254 ***	−0.210 ***	−0.440 ***	−0.347 ***	1
Urban	0.637 ***	0.134 ***	0.498 ***	0.526 ***	−0.137 ***	1
Labor	0.406 ***	−0.181 ***	0.091 **	−0.316 ***	0.619 ***	0.036	1
UR	−0.409 ***	−0.207 ***	−0.215 ***	−0.160 ***	−0.259 ***	−0.259 ***	−0.307 ***	1
Theil	−0.595 ***	−0.077 **	−0.509 ***	−0.344 ***	0.119 ***	−0.767 ***	−0.211 ***	0.320 ***	1
Tax	0.282 ***	0.260 ***	0.626 ***	0.692 ***	−0.495 ***	0.582 ***	−0.256 ***	0.017	−0.418 ***	1
Degree	0.011	−0.233 ***	0.055	−0.447 ***	0.238 ***	0.007	0.544 ***	0.049	−0.150 ***	−0.177 ***	1

Note: ***, and ** indicate significance at 1%, and 5% significance levels.

, the correlation coefficient between R&D efficiency and regional economic resilience is 0.159 and statistically significant at the 1% level. This suggests that regions with higher innovation efficiency tend to exhibit stronger economic resilience, providing preliminary evidence for the positive role of R&D efficiency in enhancing regional capacity for risk resistance and recovery. Regarding the moderating variables, population agglomeration (Agg) and regional financial density (Fin) are both positively correlated with regional economic resilience (Res), with correlation coefficients of 0.432 and 0.384, respectively, both significant at the 1% level. These results indicate that human capital concentration and financial development are important factors contributing to regional resilience. Among the control variables, most show significant correlations with the dependent variable (Res), and the directions of the correlations align with theoretical expectations. These variables have been widely recognized in the existing literature as key determinants of regional resilience. Their inclusion as controls helps mitigate potential confounding effects and improves the robustness and validity of the regression estimates.

It is worth noting, however, that correlation analysis only captures bivariate linear associations and does not account for potential confounding variables or endogeneity issues. Therefore, the results are exploratory in nature and cannot establish causal relationships. Further empirical analysis using multivariate regression models is necessary to ensure the reliability and scientific rigor of the study’s findings.

4.2. Collinearity Test

Following the correlation analysis, we further examine the issue of multicollinearity to ensure the reliability of the regression estimates. To assess whether multicollinearity exists among the explanatory variables, we conduct a Variance Inflation Factor (VIF) test. The VIF measures how much the variance of an estimated regression coefficient is inflated due to multicollinearity. A commonly accepted threshold is a VIF value of 10, beyond which multicollinearity is considered severe. As shown in

Table 6. VIF Test Results for Multicollinearity.

Variable	VIF	1/VIF
Urban	3.42	0.292339
Labor	3.33	0.30051
Infra	3.24	0.308728
Tax	3.17	0.315252
Theil	2.98	0.335512
Fin	2.95	0.338467
Agg	2.89	0.345772
Degree	1.9	0.526693
UR	1.55	0.645092
RD	1.27	0.784362
Mean VIF	2.67

, all explanatory variables in our model have VIF values well below this threshold, with a mean VIF of 2.67. These results confirm the absence of serious multicollinearity, lending greater confidence to the stability and validity of the regression estimates.

4.3. Baseline Estimation Results

To systematically assess the impact of R&D efficiency on regional economic resilience and its underlying mechanisms, this study first conducts a set of baseline regressions using an ordinary least squares (OLS) model. The results are presented in

Table 7. Benchmark regression.

	(1)	(2)	(3)	(4)
	Res	Res	Res	Res
RD	0.564 ***	0.419 ***	0.616 ***	0.188 **
	(0.135)	(0.089)	(0.082)	(0.087)
Infra		0.282 ***	−0.265 ***	−0.266 *
		(0.046)	(0.067)	(0.145)
Urban		3.254 ***	1.905 ***	1.878 ***
		(0.303)	(0.297)	(0.303)
Labor		0.500 ***	0.746 ***	0.719 ***
		(0.049)	(0.051)	(0.249)
UR		−9.649	0.544	14.413 *
		(9.104)	(8.756)	(8.455)
Theil		−4.054 ***	0.412	7.848 ***
		(0.863)	(0.827)	(1.245)
Tax		3.508 **	1.927	−4.333 *
		(1.543)	(1.613)	(2.231)
Degree		−2.860 ***	−0.702 **	−1.336 **
		(0.355)	(0.354)	(0.606)
_cons	1.213 ***	−6.102 ***	−2.818 ***	−2.844
	(0.078)	(0.516)	(0.594)	(2.722)
Year-FE	No	No	Yes	Yes
Prov-FE	No	No	No	Yes
N	679	679	679	679
R2	0.025	0.650	0.739	0.745

t-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

. To enhance the robustness and explanatory power of the estimates, a stepwise modeling strategy is adopted by sequentially introducing control variables, year fixed effects, and province fixed effects. This approach allows for the mitigation of potential biases stemming from temporal trends and regional heterogeneity, thereby enabling a more accurate identification of the true effect of the core explanatory variable and a clearer understanding of the independent influence of structural factors on economic resilience.

Table 7 presents the regression results under different model specifications. Column (1) shows the baseline model, which includes only the core explanatory variable. The results show that the coefficient of R&D efficiency (RD) is 0.564 and statistically significant at the 1% level, indicating that, in the absence of other control variables, one unit increase in RD is associated with an average increase of 0.564 units in regional economic resilience (Res). This provides preliminary support for the core hypothesis of this study. In column (2), after introducing a set of control variables, the coefficient of RD slightly decreases to 0.419 but remains statistically significant at the 1% level, suggesting that the positive impact of R&D efficiency on economic resilience is robust even after accounting for other influencing factors. Column (3) further incorporates year fixed effects to absorb time-varying shocks arising from macroeconomic fluctuations and policy changes. Under this specification, the RD coefficient rises to 0.616 and remains highly significant at the 1% level, implying that the influence of R&D efficiency on resilience becomes more pronounced once time effects are controlled. Finally, column (4) adds province fixed effects to account for unobservable regional characteristics. The results show that the coefficient of R&D efficiency (RD) is 0.188 and remains statistically significant at the 5% level. This implies that, on average, one unit increase in RD leads to a 0.188-unit improvement in regional economic resilience (Res). Even after controlling for both temporal and regional fixed effects, the positive and significant association between R&D efficiency and economic resilience persists, underscoring the robustness of the estimated relationship. Taken together, the results across all model specifications consistently demonstrate a significant and positive effect of R&D efficiency on regional economic resilience. These findings provide strong empirical support for hypothesis 1: Enhancing R&D efficiency contributes to improving a regional adaptive capacity and resistance to external shocks.

After incorporating full control variables and two-way fixed effects, the coefficient of R&D efficiency declines from 0.564 to 0.188, although it remains statistically significant. This attenuation in magnitude can be attributed to two main factors. First, the inclusion of control variables—such as financial development, urbanization, and industrial structure—absorbs part of the explanatory power of R&D efficiency, suggesting that innovation outcomes are jointly shaped by broader economic and institutional conditions rather than efficiency alone. Second, the province and year fixed effects capture unobserved heterogeneity in regional governance capacity and policy environments, which further diminishes the estimated direct effect of R&D efficiency. This indicates that efficiency gains cannot automatically translate into resilience improvements without the support of enabling institutions and market mechanisms. From a practical standpoint, this finding implies that institutional coordination and structural upgrading are essential for transforming innovation efficiency into sustainable resilience. For example, in eastern provinces such as Jiangsu and Zhejiang, mature innovation ecosystems and efficient capital markets allow R&D outputs to diffuse rapidly into productive applications, enhancing resilience. In contrast, western provinces like Gansu or Guizhou, where institutional support and infrastructure are relatively weak, face greater barriers in converting efficiency into adaptive capacity. Therefore, the reduced coefficient should not be interpreted as a weakening of the role of R&D efficiency, but rather as evidence that its effect is conditional on institutional quality and structural capacity. Policymakers should focus on improving innovation governance, strengthening industry–university linkages, and ensuring that R&D outcomes are effectively integrated into regional development strategies to sustain both efficiency and resilience.

From an economic perspective, improving R&D efficiency implies that each unit of input generates more economically valuable innovation outcomes, reflecting a region’s enhanced capacity for innovation transformation and diffusion. This capability is vital for maintaining economic vitality, restructuring industrial systems, and accelerating recovery during crises. Unlike simple increases in input scale, efficiency improvements reflect a more complex synergy of technological orientation, institutional arrangements, and resource allocation mechanisms. Efficient R&D systems foster diversified technological portfolios and greater industrial flexibility, allowing regions to adjust more effectively to market disruptions. Higher R&D efficiency also accelerates innovation cycles and facilitates faster technological diffusion, enabling regions to respond rapidly to emerging demands and seize new growth opportunities, thereby strengthening their adaptive and recovery capacity. Crucially, the enhancement of regional economic resilience signifies more than short-term recovery; it embodies multidimensional improvements in economic adaptability, industrial diversification, institutional robustness, and social inclusiveness. These dimensions are also the defining elements of sustainable urban development. In this sense, strengthening R&D efficiency indirectly promotes sustainable urban transformation by first reinforcing economic resilience, which then serves as the foundation for long-term sustainability.

After confirming the robust impact of the core explanatory variable on regional economic resilience, this study further examines the role of control variables to identify additional factors that significantly influence regional resilience. The analysis first focuses on those variables that exhibit statistically significant positive effects in the regression results. First, the coefficients of the control variables—urbanization level (Urban), labor force quality (Labor), and urban–rural disparity (Theil)—are all positive and statistically significant at the 1% level, suggesting that these factors play a crucial role in strengthening regional economic resilience. Specifically, the positive effect of urbanization underscores the important contribution of urban development to enhancing regional risk resistance. As population density rises, urban areas often display stronger systemic resilience, as dense cities typically possess advanced infrastructure, efficient public services, rapid information flows, and concentrated industrial clusters. These characteristics enhance the capacity of urban systems to flexibly reallocate resources and restructure economic activities in response to external shocks, thereby promoting adaptability and recovery. The significant positive coefficient of labor force quality underscores the critical role of human capital accumulation in strengthening resilience. A highly skilled workforce adapts more readily to shifting labor market conditions, accelerates the absorption and application of new knowledge, and drives technological innovation and industrial upgrading. Such attributes enable regions not only to respond more swiftly to shocks but also to reinforce both their short-term adaptive capacity and long-term transformative potential. Although the positive coefficient of the urban–rural disparity index (Theil) may seem counterintuitive—given the emphasis on balanced development—it can be rationalized within the framework of structural transformation. During periods of rapid urbanization and capital accumulation, rising disparities may coincide with heightened economic dynamism in urban cores. This dynamism strengthens the ability of cities to mobilize resources and implement policies, thereby enabling them to respond more effectively to external shocks. While such development trajectories may intensify spatial inequality, they may also, at least temporarily, contribute to stronger resilience in urban centers.

Conversely, three variables, namely transport infrastructure (Infra), tax burden (Tax), and degree of industrialization (Degree), show negative associations that are statistically significant at the 10% level or better. The negative effect of infrastructure investment may indicate diminishing returns or inefficient allocation of resources. In contexts with weak governance or limited fiscal discipline, excessive or poorly targeted infrastructure expansion can generate fiscal pressures, displace productive investment, and hinder recovery after shocks. Higher tax burdens reduce the financial flexibility of firms and households, discouraging investment and consumption and thereby undermining the endogenous drivers of growth required for rapid adaptation. A higher degree of industrialization, especially in economies heavily reliant on traditional manufacturing, exposes regions to greater vulnerability in the face of global value chain disruptions, environmental regulations, and structural overcapacity.

The baseline regression results in Table 7 offer strong empirical support for the proposition that improving R&D efficiency plays a significant role in strengthening regional economic resilience. This positive relationship is robust to alternative model specifications, thereby reinforcing the central hypothesis of this study. Nonetheless, while the overall benefits of R&D efficiency are evident, it is equally important to examine the conditions under which these effects are magnified or constrained. Accordingly, the subsequent analysis investigates moderation effects, with the aim of identifying the contextual factors that shape how R&D efficiency contributes to resilience across different development settings.

4.4. Moderating Effect

Building upon the baseline regression results, which establish the robust and positive association between R&D efficiency (RD) and regional economic resilience (Res), the next step of the research seeks to address a critical question: under what conditions can improvements in R&D efficiency exert a stronger resilience-enhancing effect? To answer this research question, this study introduces a moderation analysis aimed at capturing the structural contingencies that shape the effectiveness of R&D activities. Guided by the classical production factors framework—which identifies land, capital, and labor as the fundamental drivers of economic output—this study focuses on the latter two, capital and labor, as the selected moderating factors. The exclusion of land is based on its immobility and spatially fixed nature, which limits its capacity to dynamically influence the transmission of R&D efficiency to the regional economic resilience across different contexts. In contrast, both capital and labor are mobile and adaptable resources, enabling them to play an active role in shaping how innovation efficiency is absorbed, scaled, and transformed into the resilience gains. Specifically, human agglomeration intensity (Agg) is employed as a proxy for the concentration of human capital and knowledge spillovers, while regional financial density (Fin) represents the depth and accessibility of capital resources. By examining the interaction effects between R&D efficiency and these two structural factors, the analysis not only identifies the contexts in which R&D efficiency generates greater economic resilience, but also lays the groundwork for the study’s proposed Innovation–Capital–Talent (ICT) Synergy Framework.

The regression results are reported in

Table 8. Moderation Effects.

	(1)	(2)
	Res	Res
RD	−0.009	−0.385
	(0.116)	(0.249)
Agg	11.983 ***
	(4.050)
RD × Agg	9.437 **
	(3.876)
Fin		−0.437 ***
		(0.080)
RD × Fin		0.194 **
		(0.079)
Infra	−0.156	−0.348 **
	(0.148)	(0.143)
Urban	1.472 ***	1.824 ***
	(0.330)	(0.301)
Labor	0.229	0.512 **
	(0.290)	(0.246)
UR	13.695	14.844 *
	(8.411)	(8.243)
Theil	6.973 ***	7.910 ***
	(1.287)	(1.231)
Tax	−5.061 **	−0.769
	(2.235)	(2.304)
Degree	−0.918	−1.521 **
	(0.622)	(0.593)
_cons	−0.475	0.469
	(2.805)	(2.742)
Year-FE	Yes	Yes
Prov-FE	Yes	Yes
N	679	679
R2	0.749	0.758

t-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

. Column (1) presents the moderating effect of human capital agglomeration. The coefficient of the interaction term RD × Agg is 9.437 and statistically significant at the 5% level, indicating that talent agglomeration not only exerts a direct positive effect on regional resilience but also amplifies the positive impact of R&D efficiency. In regions with greater concentrations of skilled labor, knowledge exchange, resource sharing, and collaborative innovation are more frequently happening, which enhances the transformation efficiency of R&D activities into the productivity gains. This, in turn, improves the absorptive capacity of the regional innovation system, accelerates structural adjustment, and strengthens recovery potential in the face of external shocks. The empirical results provide preliminary support for hypothesis 2, indicating that human capital agglomeration positively moderates the relationship between R&D efficiency and regional economic resilience. Column (2) examines the moderating effect of regional financial density. The coefficient of RD × Fin is 0.194 and statistically significant at the 5% level, suggesting that a more developed financial environment strengthens the link between R&D efficiency and resilience. Although the direct effect of financial density can be mixed—particularly if resources are misallocated—higher financial density typically enhances capital accessibility, reduces transaction costs, and increases the efficiency of innovation financing. These factors enable regions to mobilize resources more rapidly to support R&D projects and commercialize technological outputs, thereby magnifying the resilience benefits of R&D efficiency. The empirical results also provide preliminary support for hypothesis 3, suggesting that regional financial density positively moderates the relationship between R&D efficiency and regional economic resilience.

Furthermore, a comparison of the two moderating effects reveals that human capital agglomeration (RD × Agg = 9.437 **) exerts a much stronger amplifying influence than financial density (RD × Fin = 0.194 **). This discrepancy underscores the pivotal role of human capital as a primary driver in transforming R&D efficiency into regional resilience. The concentration of skilled labor not only accelerates knowledge exchange and technological diffusion but also fosters institutional learning and adaptive capacity within innovation systems. By contrast, the moderating effect of financial density, though significant, operates mainly through improving liquidity and financing channels for innovation, which are contingent upon the availability of competent human resources. These results imply that talent accumulation serves as a precondition for maximizing the benefits of financial development. In regions with limited human capital endowment, expanding financial infrastructure alone may produce diminishing returns. Therefore, policymakers should adopt a sequenced and differentiated strategy—prioritizing human capital formation and innovation capability building in emerging regions, while deepening financial support mechanisms in mature innovation hubs. Such coordination between the “human” and “capital” dimensions is essential to realizing the full synergistic potential of R&D efficiency for resilience enhancement.

The moderation analysis demonstrates that the surrounding factor environment critically shapes how strongly R&D efficiency contributes to regional economic resilience. The interaction terms reveal two complementary pathways that amplify this relationship under different conditions. One pathway operates through human capital agglomeration: a dense pool of skilled labor accelerates knowledge spillovers, facilitates faster diffusion of technological know-how, and enhances opportunities for collaborative innovation. These dynamics shorten the time between R&D inputs and productive application, allowing regions to more effectively translate efficiency into resilience gains. This outcome is consistent with endogenous growth theory, which underscores the pivotal role of human capital concentration in sustaining innovation-led development. Another pathway emerges in financially dense regions, where well-functioning capital markets catalyze the mobilization and allocation of resources to high-potential R&D activities. Strong financial systems ease liquidity constraints, bridge the gap between innovation and commercialization, and provide a buffer against macroeconomic shocks. Such support is especially vital during periods of stress, enabling regions to sustain innovative cycles and avoid reductions in long-term R&D commitments.

Building on these findings, this study advances the ICT Synergy Framework, which extends classical production theory into the resilience domain. Within this framework, innovation efficiency operates as the trigger, generating valuable technological outputs; financial development acts as the accelerator, enabling rapid scaling and transformation; and human capital agglomeration serves as the amplifier, diffusing innovations across sectors and strengthening adaptive capacity. The interaction of these three dimensions establishes a reinforcing loop that allows regions not only to recover from shocks but also to transition toward more sustainable, innovative-driven growth trajectories.

To address potential multicollinearity between the interaction terms and their constituent variables, all main variables were centered prior to model estimation. The regression results after centering are reported in

Table 9. Baseline Regression Results after Mean-Centering of Core Variables.

	(1)	(2)
	Res	Res
c_RD	0.206 **	0.184 **
	(0.087)	(0.085)
c_Agg	16.443 ***
	(5.058)
c.c_RD × c.c_Agg	9.437 **
	(3.876)
Infra	−0.156	−0.348 **
	(0.148)	(0.143)
Urban	1.472 ***	1.824 ***
	(0.330)	(0.301)
Labor	0.229	0.512 **
	(0.290)	(0.246)
UR	13.695	14.844 *
	(8.411)	(8.243)
Theil	6.973 ***	7.910 ***
	(1.287)	(1.231)
Tax	−5.061 **	−0.769
	(2.235)	(2.304)
Degree	−0.918	−1.521 **
	(0.622)	(0.593)
c_Fin		−0.345 ***
		(0.059)
c.c_RD × c.c_Fin		0.194 **
		(0.079)
_cons	−0.104	−0.725
	(2.824)	(2.687)
N	679	679
R2	0.749	0.758

Note: ***, ** and * indicate significance at 1%, 5% and 10% significance levels.

, which shows that both interaction terms (RD × Agg and RD × Fin) remain statistically significant at the 5% level. Specifically, the coefficient of RD × Agg is 9.437 (p < 0.05), while that of RD × Fin is 0.194 (p < 0.05). Moreover, the coefficient of the core explanatory variable RD remains positive (0.206 and 0.184, respectively) and statistically significant across both model specifications, consistent with the baseline regression results. These findings confirm that the moderating effects of human capital agglomeration and financial density are both robust and substantial. Importantly, the sign and magnitude of the coefficients remain stable after centering, indicating that the observed moderating relationships are not artifacts of multicollinearity. Overall, the results reinforce the reliability of the model specification and the robustness of the study’s main conclusions.

Furthermore, to provide a clearer illustration of the moderating effects, marginal effects plots were added (Figure 1 and Figure 2), which explicitly depict how the impact of R&D efficiency on regional economic resilience varies with different levels of human capital agglomeration (Agg) and financial density (Fin). Figure 1 (Agg) clearly demonstrates the moderating role of human capital agglomeration in the relationship between R&D efficiency and regional resilience. In the plot, the red line represents regions with high human capital agglomeration, while the blue line corresponds to regions with low human capital agglomeration. When the moderator Agg is one standard deviation above its mean, the slope of RD is distinctly positive; conversely, when Agg is one standard deviation below the mean, the slope becomes negative. This pattern indicates that Agg exerts a positive moderating effect, amplifying the influence of R&D efficiency on regional economic resilience.

Figure 2 (Fin) presents a similar pattern, illustrating that the marginal effect of R&D efficiency is relatively weak or even negligible in regions with low financial density (blue line), but becomes positive and substantially stronger in regions with high financial density (red line). This suggests that a more developed financial system significantly enhances the transmission of R&D efficiency into regional economic resilience by improving capital allocation, innovation financing, and risk-sharing mechanisms. In the figure, the red line represents provinces with high financial density, whereas the blue line corresponds to low financial density. The visibly steeper red slope clearly indicates a positive moderating effect, implying that financial agglomeration amplifies the beneficial impact of R&D efficiency on resilience. Together with Figure 1, these visual results corroborate that both human capital agglomeration and financial density serve as amplifying mechanisms within the R&D efficiency–resilience nexus, providing empirical support for the ICT Synergy Framework proposed in this study.

To further examine the possibility of non-linear moderation, this study incorporates quadratic interaction terms (c.c_RD × c.c_Agg² and c.c_RD × c.c_Fin²) into the model. The estimation results, reported in

Table 10. Nonlinear Moderation Effect.

	(1)	(2)
	Res	Res
c_RD	0.325	0.397
	(0.192)	(0.177)
c_Agg	175.681
	(24.201)
c.c_RD × c.c_Agg	10.807 *
	(5.867)
c.c_Agg × c.c_Agg	−256.073 ***
	(39.720)
c.c_RD × c.c_Agg × c.c_Agg	−115.277 **
	(46.795)
Infra	−0.020	−0.351 **
	(0.145)	(0.143)
Urban	1.508 ***	1.821 ***
	(0.324)	(0.301)
Labor	−0.809 **	0.381
	(0.323)	(0.260)
UR	19.093 **	15.873 *
	(8.213)	(8.299)
Theil	6.186 ***	7.575 ***
	(1.252)	(1.253)
Tax	−5.229 **	−0.652
	(2.165)	(2.307)
Degree	−0.489	−1.451 **
	(0.606)	(0.595)
c_Fin		−0.780
		(0.136)
c.c_RD × c.c_Fin		0.195 *
		(0.099)
c.c_Fin × c.c_Fin		0.031
		(0.020)
c.c_RD × c.c_Fin × c.c_Fin		−0.026
		(0.041)
_cons	6.431 **	0.203
	(2.918)	(2.751)
N	679	679
R2	0.766	0.759

Note: ***, ** and * indicate significance at 1%, 5% and 10% significance levels.

, provide additional insights into the functional form of the moderating effects. Specifically, the coefficient of c.c_RD × c.c_Agg² is −115.277 and statistically significant at the 5% level, indicating that while human capital agglomeration strengthens the positive association between R&D efficiency and regional resilience, its reinforcing effect exhibits diminishing marginal returns. In other words, beyond a certain threshold, further increases in human capital concentration contribute less to resilience enhancement, possibly due to resource congestion, rising coordination costs, or talent saturation effects. By contrast, the quadratic interaction term c.c_RD × c.c_Fin² is not statistically significant, suggesting that the moderating role of financial density remains relatively stable across different levels of financial development. This implies that financial systems consistently facilitate the transformation of R&D efficiency into resilience without exhibiting noticeable non-linear attenuation.

Overall, these findings demonstrate that both moderators exert economically meaningful and robust effects, thereby enhancing the explanatory power of the model. The observed non-linear pattern for human capital agglomeration also provides empirical support for the ICT Synergy Framework, highlighting that innovation, capital, and talent interact dynamically rather than linearly in fostering regional economic resilience.

4.5. Heterogeneity Analysis

In the preceding empirical analysis, this study has established a significant positive effect of R&D efficiency on regional economic resilience. However, this effect is unlikely to be uniform across all regions. Substantial differences in economic development stages and governance capacity may cause the same level of R&D efficiency to translate into resilience gains to varying degrees. In other words, spatial characteristics and institutional environments are likely to shape the resilience-enhancing effect of R&D efficiency differently. Conducting a heterogeneity analysis is therefore essential, as it not only helps uncover contextual variations in the underlying mechanism but also provides a basis for formulating more targeted policies to foster innovation and resilience.

Against this backdrop, the heterogeneity analysis proceeds along two dimensions. Following China’s spatial development patterns, the sample is divided into eastern, central, and western regions to test whether the R&D efficiency–resilience nexus varies across different economic and innovation contexts. The eastern region comprises Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan; the central region includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan; and the western region covers Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. This classification reflects substantial differences in development stages, innovation endowments, and industrial structures, thereby providing a basis for identifying region-specific trajectories of sustainable resilience. The results (

Table 11. Heterogeneity analysis (1).

	(1)	(2)	(3)
	Res East	Res Middle	Res West
RD	0.378 **	0.022	0.071
	(0.180)	(0.228)	(0.054)
Infra	0.428	0.516	−0.080
	(0.286)	(0.513)	(0.095)
Urban	1.355 ***	5.820 ***	1.064 ***
	(0.508)	(1.914)	(0.240)
Labor	0.920 *	0.906	−0.196
	(0.533)	(0.580)	(0.180)
UR	49.886 **	−21.205	4.466
	(20.037)	(24.079)	(4.643)
Theil	1.009	−26.856 ***	1.027
	(2.504)	(7.630)	(1.024)
Tax	−10.025 **	−0.154	−6.735 ***
	(4.020)	(6.750)	(1.512)
Degree	0.058	0.865	−2.003 ***
	(1.784)	(1.018)	(0.550)
_cons	−11.017 *	−10.705	2.934 *
	(5.999)	(7.224)	(1.776)
Year-FE	Yes	Yes	Yes
Prov-FE	Yes	Yes	Yes
N	241	174	264
R2	0.837	0.780	0.894

t-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

) reveal marked spatial heterogeneity. In the eastern region, the coefficient of R&D efficiency is 0.378 and significant at the 5% level, indicating that higher efficiency significantly strengthens economic resilience. This can be attributed to the region’s strong economic foundations, high concentration of innovation resources, and mature industrial systems, which enable the effective transformation of R&D outputs into productivity gains and adaptive capacity. Dense networks of firms, research institutions, and skilled labor further facilitate knowledge spillovers and collaborative innovation, amplifying resilience-enhancing effects. By contrast, in the central and western regions, the coefficients are statistically insignificant, suggesting that the resilience benefits of R&D efficiency fail to materialize in areas where innovation systems remain transitional, infrastructure is weaker, and talent pools are limited. These structural constraints reduce the capacity of R&D to serve as a sustainable buffer against external shocks.

Overall, the positive effect of R&D efficiency on resilience is concentrated in the eastern provinces, while the central and western regions lag behind. This pattern underscores the need for differentiated policy design. In the east, sustaining high levels of innovation efficiency remains essential; in the central provinces, improving institutional mechanisms such as technology transfer and resource allocation should be prioritized; and in the western provinces, stronger government intervention aimed at expanding infrastructure, attracting talent, and fostering innovation ecosystems is critical. Tailoring policies in this way can help reduce regional disparities and ensure that R&D efficiency contributes more broadly to sustainable and resilient development. Beyond these policy implications, this regional disparity can also be explained by several underlying mechanisms related to institutional quality, infrastructure, and industrial structure. First, the institutional environment in the eastern provinces is generally more advanced, characterized by higher governance efficiency, stronger intellectual property protection, and more market-oriented regulatory frameworks. These institutional advantages facilitate the effective transformation of R&D outputs into productivity gains and enhance the adaptability of local economies. Second, the infrastructure and innovation networks in the east are far more developed, allowing for efficient knowledge diffusion and close collaboration among firms, universities, and research institutions. Such connectivity promotes the commercialization of research achievements and accelerates the process through which R&D efficiency enhances regional resilience. Third, differences in industrial structure further reinforce this divergence. The eastern region’s diversified and innovation-intensive industries can better absorb technological shocks and maintain growth, whereas the central and western regions remain more dependent on traditional or resource-based sectors with weaker absorptive capacity.

Taken together, these factors explain why the resilience-enhancing effect of R&D efficiency is concentrated in the east, highlighting the importance of improving institutional quality, upgrading infrastructure, and advancing industrial diversification to enable less-developed regions to translate innovation efficiency into resilience gains.

Building on the observed regional disparities, the subsequent analysis turns to the second dimension of heterogeneity—the level of government intervention—to examine whether and how institutional arrangements affect the ability of R&D efficiency to enhance regional economic resilience. In the functioning of real-world economies, government intervention constitutes a critical external environmental factor shaping regional innovation activities and economic development. Through fiscal subsidies, tax incentives, industrial policies, and the allocation of science and technology funds, governments can steer R&D activities, influence the allocation of innovation resources, and ultimately affect the capacity of R&D efficiency to strengthen economic resilience. However, substantial variation exists across regions in both the intensity and form of government intervention, which may result in heterogeneous effects of R&D efficiency on regional economic resilience. To capture this potential heterogeneity, the sample is stratified into high- and low-intervention groups according to the median value of government intervention intensity, and separate regressions are then performed for each subgroup. The results are presented in

Table 12. Heterogeneity analysis (2).

	(1)	(2)
	Res High Government Intervention	Res Low Government Intervention
RD	0.112 **	0.145
	(0.053)	(0.172)
Infra	−0.221 *	0.070
	(0.117)	(0.223)
Urban	1.907 ***	0.610
	(0.505)	(0.385)
Labor	0.442 ***	1.458 ***
	(0.166)	(0.449)
UR	10.148 **	−0.121
	(4.684)	(16.567)
Theil	2.126 **	−0.471
	(1.048)	(1.996)
Tax	−2.477 *	7.918 *
	(1.340)	(4.500)
Degree	−1.503 ***	−1.260
	(0.440)	(1.239)
_cons	−0.575	−11.306 **
	(1.707)	(4.930)
Year-FE	Yes	Yes
Prov-FE	Yes	Yes
N	362	317
R2	0.834	0.836

t-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

. For the high-intervention group, the coefficient of R&D efficiency is estimated at 0.112 and is statistically significant at the 5% level. This suggests that in regions where government intervention is relatively strong, R&D efficiency exerts a pronounced positive effect on economic resilience. A plausible explanation is that stronger government involvement can facilitate the translation of R&D efforts into tangible economic outcomes through targeted policy guidance, preferential resource allocation, and coordinated innovation support, thereby enhancing the adaptability and recovery capacity of regional economies. In contrast, for the low-intervention group, the R&D efficiency coefficient is 0.145 but fails to reach statistical significance, indicating that under the lower-intervention environments, the positive effect of R&D efficiency on resilience is not evident. In such contexts, resource allocation is primarily market-driven, and the absence of strong policy support and strategic guidance may hinder the ability of R&D activities to translate into resilience-enhancing outcomes.

Taken together, these results underscore the critical moderating role of institutional context in shaping the relationship between R&D efficiency and regional economic resilience. While R&D efficiency can substantially strengthen economic resilience under strong government intervention, its impact appears muted in regions with weaker policy support. This finding suggests that, particularly in less developed or structurally vulnerable areas, appropriately calibrated government intervention—focusing on R&D resource coordination, policy incentives, and innovation ecosystem development—may be essential to unlocking the resilience potential of R&D efficiency.

While the results under high government intervention (RD = 0.112 **) confirm the crucial role of policy support in strengthening the link between R&D efficiency and resilience, the potential trade-offs of excessive intervention warrant attention. Over-reliance on administrative allocation may distort market signals, crowd out private R&D investment, and create long-term fiscal dependency, thereby undermining innovative efficiency. To achieve a balanced and sustainable governance model, government involvement should shift from direct control toward strategic guidance and market facilitation. In practice, this can be achieved through targeted R&D subsidies, innovation tax credits, and public–private partnerships (PPPs) that encourage collaborative research and commercialization while preserving competition and efficiency. Moreover, differentiated intervention models are needed: in emerging central and western regions, moderate and temporary government-led support can correct market failures and stimulate innovation ecosystems; whereas in mature eastern provinces, a more market-oriented approach should prevail to prevent over-centralization and ensure the self-sustaining transformation of R&D efficiency into resilience.

4.6. Robustness Tests

4.6.1. Alternative Measurement of the Dependent Variable: PCA-Based Resilience Index

In Column (1) of

Table 13. Robustness Tests.

	(1)	(2)	(3)
	Res1 Alternative Dependent Variable	Res Alternative Independent Variable	Res Excluding Special Samples
RD	0.024 **		0.289 ***
	(0.011)		(0.099)
RD1		39.745 ***
		(4.585)
Infra	−0.013	−0.288 **	−0.358 **
	(0.018)	(0.137)	(0.172)
Urban	0.258 ***	1.544 ***	3.053 ***
	(0.038)	(0.288)	(0.429)
Labor	0.033	0.161	0.835 ***
	(0.031)	(0.228)	(0.300)
UR	2.685 **	5.386	11.320
	(1.053)	(8.010)	(9.182)
Theil	1.000 ***	7.585 ***	8.493 ***
	(0.155)	(1.179)	(1.611)
Tax	−1.081 ***	−3.605 *	−4.532 *
	(0.278)	(2.097)	(2.505)
Degree	−0.119	−1.099 *	−1.879 ***
	(0.076)	(0.573)	(0.675)
_cons	−0.201	1.221	−3.070
	(0.339)	(2.553)	(3.117)
Year-FE	Yes	Yes	Yes
Prov-FE	Yes	Yes	Yes
N	679	679	591
R2	0.760	0.771	0.723

t-statistics in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

, the dependent variable—regional economic resilience—is redefined by substituting the original entropy-based composite index with an alternative index (Res1) constructed using the Principal Component Analysis (PCA) method. This approach extracts the most informative components from the underlying resilience indicators, thereby providing a robust measure that mitigates potential multicollinearity and measurement bias while preserving the multidimensional characteristics of resilience. The re-estimation results indicate that the coefficient of R&D efficiency (RD) is 0.024 and statistically significant at the 5% level. Both the magnitude and direction of the coefficient are broadly consistent with those in the baseline regression, suggesting that the positive association between R&D efficiency and regional economic resilience is not an artifact of the specific index construction method. From an applied perspective, the consistency of results across measurement approaches implies that, whether resilience is captured through an entropy-weighted structural index or principal component synthesis, improvements in R&D efficiency are consistently linked to stronger regional capacities for resistance and recovery. This finding enhances policymakers’ methodological confidence that strategies aimed at improving R&D efficiency remain effective and transferable under different resilience evaluation frameworks.

4.6.2. Alternative Explanatory Variable

In the second stage of the robustness checks, the analysis employs an alternative explanatory variable to further validate the stability of the core findings. Specifically, the R&D efficiency (RD) variable used in the benchmark regression is replaced with R&D intensity (RD1), defined as the ratio of R&D expenditure to regional gross domestic product (GDP). As a widely used traditional indicator, R&D intensity captures the relative weight assigned to investment for innovation within regional economic output and offers a complementary perspective provided by R&D efficiency. Column (2) of Table 13 reports the re-estimation results. The coefficient of R&D intensity (RD1) is 39.745 and statistically significant at the 1% level, indicating a strong and positive association with regional economic resilience. The magnitude and significance of the coefficient suggest that, irrespective of whether R&D activity is measured in terms of efficiency or investment intensity, it exerts a robust and positive impact on resilience. These findings are consistent with the benchmark regression results and lend further support to the core hypothesis of this study: that both increasing the scale of innovation investment and improving the efficiency of innovation resource utilization enhance a regional capacity to withstand external shocks and promote sustainable economic growth.

From a policy perspective, this result reinforces the strategic importance of innovation-driven development in fostering regional economic resilience. Optimizing the allocation of innovation resources can improve resilient capacity, while scaling up investment can expand technological reserves—both of which strengthen the adaptability and recovery capacity of regional economies. These insights provide solid empirical grounds for designing differentiated policy strategies that integrate investment expansion with efficiency enhancement to maximize the resilience-enhancing potential of R&D activities.

4.6.3. Excluding Special Samples

Given the distinct locational advantages, administrative status, and preferential policy support, municipalities directly under the central government, such as Beijing, differ markedly from ordinary cities in ways that could bias empirical estimates. To mitigate this concern, the final step of the robustness analysis excludes these special cases to reassess the stability of the core findings. Specifically, in Column (3) of Table 13, the four municipalities—Beijing, Shanghai, Tianjin, and Chongqing—are removed from the sample to eliminate potential distortions in the relationship between R&D efficiency (RD) and regional economic resilience (Res) arising from their unique economic scale, policy resources, and governance structures. The re-estimation results show that the coefficient of RD is 0.289 and remains statistically significant at the 1% level. Both the sign and statistical significance are consistent with the baseline regression, confirming that the positive impact of RD on Res persists even after excluding these municipalities. This suggests that the core findings of this research are not driven by a small subset of cities with disproportionately advantageous economic and policy conditions, but instead holds across a broader and more representative set of regions. Accordingly, the result enhances the robustness of the conclusion with respect to sample composition and further strengthens its external validity even in the global economy.

4.7. Endogeneity Test

To address potential endogeneity concerns—such as omitted variable bias or reverse causality—this study employs the instrumental variable (IV) approach. Specifically, the one-period lag of R&D efficiency (L.RD) is selected as the instrument, and a two-stage least squares (2SLS) estimation is conducted. The results are reported in

Table 14. Endogeneity Test.

	(1)	(2)
	RD First-Stage Regression	Res Second-Stage Regression
L.RD	0.707 ***
	(0.030)
RD		0.268 **
		(0.111)
Infra	0.067	−0.190
	(0.052)	(0.138)
Urban	−0.124	1.867 ***
	(0.107)	(0.284)
Labor	−0.229 **	0.634 ***
	(0.089)	(0.246)
UR	−4.263	17.461 **
	(2.909)	(7.728)
Theil	0.068	11.810 ***
	(0.467)	(1.233)
Tax	1.374 *	−6.510 ***
	(0.762)	(2.033)
Degree	0.047	−1.301 **
	(0.212)	(0.559)
_cons	1.055	/
	(0.997)	/
Year-FE	Yes	Yes
Prov-FE	Yes	Yes
N	645	645
R2	0.601	0.793
LM Test		317.107 ***
Wald F Test		566.724

t-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

.

In selecting the instrumental variable, this study considers the one-period lag of R&D efficiency (L.RD) to be an appropriate and valid instrument. The rationale is as follows. First, from the perspective of relevance, R&D activities exhibit strong path dependence and inertia. The level of R&D efficiency in the previous period directly influences the current period’s technological base, knowledge accumulation, and innovation capacity. Therefore, the lagged R&D efficiency is expected to be highly correlated with the current R&D efficiency (RD), which is confirmed by the first-stage regression result (coefficient = 0.707, significant at the 1% level), and this finding is further verified in the subsequent first-stage regression analysis, as shown in Table 14. Second, and more importantly, regarding exogeneity, the lagged R&D efficiency represents a historical state whose value is predetermined and unaffected by current shocks. It affects regional economic resilience primarily through its influence on current R&D efficiency and is not directly correlated with other contemporaneous random disturbances (error components) that may influence resilience outcomes. This ensures that the instrument satisfies the exclusion restriction assumption.

Furthermore, this study conducts a validity test for the instrumental variable, and the results are reported in Table 14. Since only one instrumental variable is employed, an over-identification test cannot be directly performed. The LM test statistic (317.107) is significant at the 1% level, indicating a strong correlation between the instrumental variable and the endogenous regressor. Moreover, the Wald F-statistic (566.724) substantially exceeds the empirical threshold value of 10, suggesting that the instrument is not weak and possesses strong explanatory power. These results confirm the overall validity and strength of the instrumental variable used in the model.

In the first-stage regression, the coefficient of L.RD with respect to current RD is 0.707 and statistically significant at the 1% level, indicating a strong positive correlation between the instrument and the endogenous regressor, thereby satisfying the instrument relevance condition. In the second stage, the predicted values of RD obtained from the first stage are used to estimate regional economic resilience (Res). The coefficient of RD is 0.268 and statistically significant at the 5% level, suggesting that the positive effect of RD on regional economic resilience remains robust after accounting for potential endogeneity. This result is consistent with the benchmark regression, further reinforcing the robustness of the core findings.

In sum, the IV estimation results demonstrate that the resilience-enhancing effect of R&D efficiency remains statistically significant even after controlling for potential endogeneity. This finding strengthens the credibility of the research findings and underscores that improving R&D efficiency constitutes an effective pathway for bolstering regional economic resilience. Policymakers should therefore focus not only on sustaining efficient allocation of innovation resources but also on strengthening institutional and infrastructural support to foster high-quality and resilient regional development.

To rigorously address potential endogeneity arising from omitted variables and ensure the robustness of the core empirical findings, this study further conducts a re-examination using the System Generalized Method of Moments (System GMM). This approach introduces lagged terms of the variables as instruments, thereby mitigating the estimation bias caused by the potential correlation between the explanatory variables and the disturbance term. Consequently, it provides more consistent and reliable estimates. Before interpreting the effect of the core variables, it is essential to assess the validity of the System GMM specification. As shown in

Table 15. System GMM Estimation Results.

	(1)	(2)
	Res	Res
L.Res	0.824 ***	0.718 ***
	(0.021)	(0.027)
L2.Res		0.264 ***
		(0.027)
RD	0.151 ***	0.087 ***
	(0.045)	(0.033)
Infra	−0.057	−0.011
	(0.035)	(0.026)
Urban	0.570 ***	0.211
	(0.166)	(0.132)
Labor	0.167 ***	0.070 ***
	(0.031)	(0.023)
UR	−1.095	−4.327
	(4.721)	(3.403)
Theil	0.796 *	0.329
	(0.445)	(0.342)
Tax	0.979	1.023 *
	(0.835)	(0.617)
Degree	0.006	0.101
	(0.186)	(0.138)
_cons	−0.624 *	−0.528 **
	(0.361)	(0.268)
N	645	611
AR(1)		0.000
AR(2)		0.156
Hansen test		0.481

Note: ***, ** and * indicate significance at 1%, 5% and 10% significance levels.

, the results of the serial correlation test (AR test) indicate that the p-value for first-order autocorrelation AR(1) is 0.000, which is significant at the 1% level, whereas the p-value for second-order autocorrelation AR(2) is 0.156, which is statistically insignificant. This suggests that the disturbance term exhibits first-order but not second-order serial correlation, satisfying a key assumption of the System GMM estimator. In addition, the Hansen test for over-identifying restrictions yields a p-value of 0.481, which is also insignificant, confirming that the chosen instrumental variables are valid and that no over-identification problem exists. Together, these diagnostic results verify the appropriateness of the System GMM specification and the validity of the instruments. To provide a more intuitive comparison of endogeneity effects and demonstrate the effectiveness of the GMM approach, we first report the pooled OLS regression results without considering endogeneity as a benchmark (see column (1) of Table 15). In this regression, the coefficient of the core explanatory variable RD is 0.065, which is positive and significant at the 1% level. However, this estimate may be biased due to potential endogeneity. In contrast, the System GMM results reported in column (2) show that the coefficient of RD increases to 0.087, which remains positive and significant at the 1% level. The consistency in significance provides strong evidence that the positive effect of R&D efficiency on the dependent variable remains robust even under a more rigorous econometric framework.

In summary, the results from the System GMM estimation not only effectively mitigate potential endogeneity concerns but also reaffirm the significant positive effect of the core explanatory variable. These findings enhance the credibility of the study’s empirical conclusions and further confirm their robustness, thereby providing a reliable empirical foundation for the ensuing policy implications.

The robustness and IV estimation results further reinforce the reliability and policy relevance of our findings. The consistent positive relationship between R&D efficiency and regional resilience—across alternative measurement approaches (entropy-based vs. PCA index), endogeneity corrections (IV and system GMM), and model specifications—provides policymakers with strong empirical confidence that enhancing R&D efficiency is an effective and sustainable pathway to resilience building. More importantly, the persistence of the interactive effects among innovation, capital, and talent across these robust tests empirically substantiates the ICT Synergy Framework. This stability implies that the synergistic mechanism among innovation efficiency, financial density, and human capital agglomeration remains valid under different estimation settings and data constructions. Accordingly, policymakers can be confident that integrated strategies—simultaneously fostering innovation efficiency, capital accessibility, and talent concentration—will yield consistent and replicable resilience dividends across regions and over time.

4.8. Spatial Spillover Effects and Decomposition Analysis

Given that a province’s innovative activities and resilience outcomes may influence neighboring regions through channels such as technology diffusion, knowledge spillovers, and industrial linkages, this study further investigates the potential spatial spillover effects of R&D efficiency. To capture both local and interregional impacts, a Spatial Durbin Model (SDM) with two-way fixed effects was employed. This approach effectively controls unobserved heterogeneity across provinces and over time, yielding more robust and unbiased estimates. The estimation results in

Table 16. Spatial Spillover Effects and Decomposition Results.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Variables	Main	Wx	Spatial	Variance	LR_Direct	LR_Indirect	LR_Total
RD	0.859 **	1.093 *			0.892 **	1.372 **	2.265 **
	(2.514)	(1.736)			(2.477)	(2.063)	(2.491)
Agg	9.384 ***	30.659 ***			9.794 ***	34.638 ***	44.431 ***
	(2.725)	(5.034)			(2.998)	(5.140)	(5.276)
Fin	−0.311 ***	−0.243 **			−0.313 ***	−0.298 ***	−0.611 ***
	(−7.207)	(−2.448)			(−7.444)	(−2.800)	(−5.479)
Infra	−0.273 **	−0.048			−0.278 **	−0.097	−0.375
	(−2.155)	(−0.164)			(−2.206)	(−0.304)	(−1.275)
Urban	1.331 ***	2.646 ***			1.400 ***	3.162 ***	4.562 ***
	(5.559)	(4.947)			(5.969)	(4.412)	(5.139)
Labor	0.162	0.232			0.184	0.272	0.455
	(0.694)	(0.338)			(0.774)	(0.344)	(0.578)
UR	11.517 *	46.697 ***			12.652 *	53.772 ***	66.424 ***
	(1.817)	(3.993)			(1.831)	(3.904)	(3.474)
Theil	3.745	7.448 ***			3.845	8.956 ***	12.801 **
	(1.595)	(3.908)			(1.547)	(2.977)	(2.469)
Tax	−1.327	5.340			−1.102	5.696	4.594
	(−0.681)	(1.076)			(−0.562)	(0.987)	(0.682)
Degree	−0.436	2.338 **			−0.393	2.437 **	2.044
	(−0.973)	(2.516)			(−0.887)	(2.246)	(1.567)
trend	−0.000 **	−0.000 *			−0.001	−0.001	−0.002
	(−2.184)	(−1.807)			(−0.044)	(−0.136)	(−0.057)
rho			0.112 *
			(1.755)
sigma2_e				0.176 ***
				(3.859)
Observations	682	682	682	682	682	682	682
R-squared	0.026	0.026	0.026	0.026	0.026	0.026	0.026
Number of id	31	31	31	31	31	31	31

Robust z-statistics in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

show that R&D efficiency (RD) has a significant positive effect on regional economic resilience (Res), with a coefficient of 0.859 significant at the 5% level. Moreover, the coefficient of the spatially lagged term (WX.RD) is 1.093, significant at the 10% level, suggesting that improvements in R&D efficiency in neighboring provinces significantly enhance local resilience levels. Further spatial effect decomposition reveals that the indirect (spillover) effect of RD on Res is 1.372, accounting for approximately 60.57% of the total effect. This indicates that more than half of the overall impact operates through spatial transmission mechanisms rather than purely local effects. In other words, innovation activities exhibit strong cross-regional diffusion, and their influence extends well beyond administrative boundaries.

From a policy perspective, these findings underscore the importance of strengthening regional collaboration and building interprovincial innovation networks. Enhancing institutional coordination and information-sharing mechanisms can amplify the positive spillover effects of R&D efficiency, promote the spatial diffusion of innovation benefits, and ultimately advance coordinated and sustainable regional development across China.

5. Conclusions

Drawing on provincial panel data from 2000 to 2021, this study provides robust empirical evidence that improvements in R&D efficiency enhance regional economic resilience. Robustness checks lend further support to these findings, while contextual factors—particularly human capital agglomeration and regional financial density—reinforce this relationship through complementary channels. Building on these insights, the paper introduces the ICT Synergy Framework, which emphasizes that a sustainable innovation system requires the joint circulation of innovation efficiency, financial capacity, and human capital concentration. The heterogeneity analysis further reveals pronounced regional disparities shaped not only by economic fundamentals but also by institutional capacity. Based on this framework, several policy directions can be drawn. At the national level, fiscal science and technology funding should incorporate efficiency-oriented assessment, while government procurement and standardization can accelerate the diffusion of high-efficiency innovations. At the regional level, eastern provinces should prioritize frontier R&D and quality upgrading, central provinces should remove institutional bottlenecks to improve spillovers, and western provinces require government-led interventions to address persistent capital and talent shortages. A cross-regional division of labor, in which Eastern regions specialize in R&D, Central regions focus on pilot testing, and Western regions emphasize demonstration, offers a viable pathway for coordinated development. At the city level, differentiated strategies are essential: megacities should focus on compact redevelopment and innovation clusters, while smaller cities can leverage land and cost advantages to absorb spillovers and cultivate region-specific resilience.

Nevertheless, the persistence of spatial disparities in resilience underscores the importance of addressing deeper structural bottlenecks that constrain innovation diffusion across regions. In particular, limited talent retention and human capital accumulation, insufficient innovation-related infrastructure, and weaker governance capacity for coordinating industrial transformation remain the most binding constraints in the central and western provinces. Lessons from comparative experiences—such as South Korea’s Regional Innovation Cluster initiative and Poland’s Smart Growth Operational Program—suggest that targeted fiscal decentralization, university–industry collaboration, and talent incentive schemes can effectively mitigate these institutional barriers. Drawing on the estimated model coefficients, a stylized projection suggests that improving R&D efficiency by one standard deviation and enhancing governance capacity by 10% could reduce the resilience gap between eastern and non-eastern regions by approximately 15–20% over a five-year horizon. Although this simulation is illustrative, it highlights the potential impact of synchronized policy interventions in advancing regional convergence in both resilience and innovation capacity.

To sustain these efforts, a nationwide R&D Efficiency–Resilience–Sustainability data platform is needed, integrating knowledge diffusion, capital efficiency, and human capital indicators into performance evaluation. By embedding the Trinity Framework into innovation, governance, and spatial strategies, China can better transform R&D efficiency into resilience dividends and align its regional development with the 2030 sustainable development agenda. The framework also provides broader lessons for other developing economies seeking to enhance resilience under conditions of global uncertainty.

Building on the ICT Synergy Framework, this study proposes a phased policy direction to operationalize the transformation of R&D efficiency into regional resilience. In the short term, national and provincial governments should strengthen efficiency-oriented fiscal assessments and link science and technology funding to measurable R&D performance. In the medium term, policy efforts should focus on improving financial infrastructure and innovation networks through instruments such as credit guarantees, technology-transfer funds, and regional financial integration, enhancing the flow of capital toward productive innovation. In the long term, sustained resilience requires the accumulation of human capital and institutional coordination—particularly talent retention, university–industry cooperation, and digital infrastructure development. Collectively, these short-, medium-, and long-term strategies translate the ICT Synergy Framework into an actionable policy roadmap. They underscore that innovation, capital, and talent must advance in a synchronized manner through coordinated multi-level governance to achieve measurable improvements in R&D efficiency, reduce regional disparities, and foster sustainable, innovation-driven growth.

Taken together, these policy directions not only provide a practical pathway for enhancing resilience but also reaffirm the broader developmental goal underlying this study. Ultimately, this study views the improvement of regional economic resilience not as an independent objective but as a crucial means to achieve sustainable urban development. Consistent with prior research in regional science and sustainability [56,57,58], sustainable urban development is understood as a dynamic process through which cities pursue harmonized progress in economic growth, social well-being, and environmental protection, facilitated by innovation and effective institutional coordination. From this standpoint, enhancing R&D efficiency and regional resilience serves both as an immediate mechanism to withstand external disturbances and as a long-term pathway toward creating adaptive, inclusive, and sustainable urban systems. This holistic perspective, grounded in the ICT Synergy Framework, integrates technological innovation, governance effectiveness, and resilience capacity within the broader framework of high-quality and sustainable regional development. Beyond existing definitions, this study advances the conceptualization of sustainable urban development by embedding resilience explicitly as an endogenous driver rather than a passive outcome. By linking innovation efficiency with institutional coordination and spatial dynamics, it introduces an integrative analytical perspective that bridges technological, economic, and governance dimensions—offering a more operational framework for assessing sustainability in regional science. Building upon this conceptual linkage, the subsequent discussion explores the practical implications of these findings for China’s sustainable urban and regional development. In this regard, the findings of this study offer valuable insights for advancing China’s sustainable urban and regional transformation.

The findings also yield profound implications for the sustainable development of China’s cities and regions. While improvements in R&D efficiency significantly strengthen economic resilience in the eastern provinces, such effects are not observed in the central and western regions, which together account for nearly 71% of China’s land area and hold immense potential for future growth. This spatial imbalance highlights a pressing concern: if the dividends of innovation efficiency continue to concentrate in the east, the resilience gap between regions may widen, thereby undermining the long-standing national vision of coordinated and sustainable regional development. This concern is particularly salient in the context of current national strategies such as the “Western Development Program,” the “Belt and Road Initiative,” and the “dual circulation” strategy, which aim to accelerate industrial relocation and market expansion toward the central and western regions. However, without addressing structural bottlenecks in these areas—such as underdeveloped innovation ecosystems, difficulties in talent retention, and inadequate infrastructure—they alone may fail to deliver the anticipated resilience gains or sustain domestic market expansion. From this perspective, persistent regional resilience disparities risk eroding spatial equity and weakening China’s broader objective of balanced regional development. Encouragingly, the results also underscore the pivotal role of government intervention in closing this gap. By leveraging its institutional capacity to “concentrate resources on critical tasks,” the state can mitigate structural disadvantages in the central and western regions, foster the formation of robust innovation ecosystems, and ensure that improvements in R&D efficiency are effectively translated into resilience. This capacity is not merely a corrective mechanism but rather a cornerstone of China’s long-term sustainable urban and regional development. To further operationalize these strategies, this study proposes the establishment of interregional R&D funding transfer mechanisms and national talent mobility programs that promote cross-regional knowledge diffusion and capacity building. Moreover, incentive schemes that encourage high-efficiency eastern provinces to share technologies and collaborative projects with central and western regions—together with periodic national audits of resilience indicators—can help ensure that innovation dividends are distributed more equitably and that regional resilience converges over time. Such coordinated policy efforts will translate the ICT Synergy Framework into measurable progress toward balanced and sustainable regional development. With continued institutional commitment and well-coordinated policy design, the goal of achieving balanced resilience and sustainable growth across China’s diverse regions remains within reach.

Taken together, the findings yield several key policy insights. Building resilient and sustainable innovation systems requires more than improving R&D efficiency; it must be accompanied by the strengthening of financial capacity and human capital agglomeration to achieve synergies through the ICT Synergy Framework. Regional strategies should remain differentiated: in the east, consolidating efficient innovation systems and advancing frontier technologies; in the central provinces, refining technology transfer mechanisms and optimizing innovation resource allocation; and in the west, addressing capital and talent shortages through stronger government intervention. At the governance level, striking a balance between market dynamics and state involvement is essential for transforming R&D efficiency into resilience. Embedding these strategies within the broader agenda of high-quality and sustainable development enables regional economies to convert innovation efficiency into transformative resilience, thereby advancing not only China’s goals of balanced and sustainable urban development but also contributing to the global pursuit of resilience under the Sustainable Development Goals.

While this study provides new insights into the relationship between R&D efficiency and regional economic resilience, several limitations should be acknowledged. First, the instrumental variable approach employs the one-period lag of R&D efficiency as an internal instrument. Although the lagged term satisfies the relevance and exogeneity conditions, it may not fully address all endogeneity concerns. Future research could consider introducing external instruments, such as historical R&D subsidies, proximity to major innovation hubs, or variations in provincial-level science and technology policies, to further enhance identification robustness. Second, despite the comprehensive construction of variables, measurement bias may still exist. For example, the estimation of R&D efficiency through the DEA method is sensitive to data quality and variable selection, while the entropy-based resilience index may not capture the full scope of adaptive or cultural dimensions of regional resilience. More refined or multidimensional indicators could therefore be adopted in future studies. Overall, these limitations do not undermine the main findings but rather open new avenues for advancing the understanding of how innovation efficiency contributes to regional resilience under varying institutional and spatial contexts.