New Quality Productive Forces Enabling High-Quality Development: Mechanism, Measurement, and Empirical Analysis

Abstract

To assist resource-based regions in overcoming the bottlenecks of industrial transformation and advancing high-quality development, this paper conducts an in-depth analysis of the internal mechanisms through which new quality productive forces contribute to high-quality development. Based on the construction of a measurement index system, a comprehensive measurement model is established, which includes three components: a coupling coordination degree model integrating the entropy method and grey relational analysis, an impact factor analysis model based on random effects Tobit regression, and a trend prediction model using the GM(1,1) approach. Taking Hebei Province as an example, an empirical analysis was conducted and relevant policy suggestions were proposed. The research findings are summarized as follows: (1) New quality productive forces promote high-quality development through driving, guiding, and synergistic mechanisms; (2) From 2013 to 2022, the coupling coordination degree across various cities in Hebei Province evolved from moderate imbalance to primary coordination, with the spatial pattern transitioning from “higher in the south and lower in the north” to a “central rise” phase, and finally to a stage of “all-round coordination”; (3) Forecast results indicate that inter-city coordination will continue to improve over the next five years; (4) Urbanization, scientific and technological innovation, and government intervention are identified as the core driving factors for promoting coordinated development. This study provides both theoretical methodological support and regional empirical evidence for the role of new quality productive forces in enabling high-quality development in resource-based regions.

1. Introduction

Currently, technological breakthroughs and industrial transformations centered on digitalization, technologization, and green development are rapidly reshaping the global economic landscape. Emerging technologies such as next-generation information systems and innovative energy solutions are catalyzing the emergence of “new quality productive forces.” From a theoretical perspective, new quality productive forces represent an advanced form of productivity that arises from the deep integration of technology, production factors, industrial structures, and policy frameworks. This model is driven by knowledge, data, and innovation, and incorporates principles of green development and sustainability. It is characterized by high technological content, operational efficiency, and high-quality outputs. The core value of new quality productive forces lies not only in overcoming the traditional law of diminishing marginal returns but also in establishing a robust linkage between economic growth and key dimensions of sustainable development—such as resource conservation, environmental protection, and social equity. At the technical level, it leverages cutting-edge technologies like artificial intelligence and blockchain to significantly enhance production efficiency; at the resource level, it promotes the efficient allocation and utilization of data as a substitute for excessive reliance on traditional inputs; and at the strategic level, it mitigates the ecological footprint of production through the research and application of green technologies, ultimately achieving coordinated progress in economic growth, technological sustainability, and societal well-being.

Against this backdrop, China has proactively introduced the “high-quality development” strategy, aiming to transition its economic model from one driven by rapid growth to one centered on efficiency, sustainability, and inclusiveness. This transformation is underpinned by innovation, structural optimization, and enhanced productivity. The development of new quality productive forces constitutes both an essential prerequisite and a strategic priority for achieving high-quality development. On one hand, new quality productive forces generate green and intelligent momentum that supports high-quality development; on the other hand, the guiding principles of high-quality development—innovation, coordination, environmental sustainability, openness, and shared prosperity—provide institutional frameworks and directional guidance for the cultivation of new quality productive forces. Together, they form a dynamic and interdependent “driving-supporting” system. This synergy not only reflects a necessary response to global technological transformation and domestic economic restructuring but also serves as a convergence point for theoretical advancement and practical innovation.

As a representative province with traditional industrial clusters, Hebei in China is currently under significant pressure to achieve low-carbon transformation in key sectors such as steel production and coal-based energy generation. At the same time, it is strategically positioned to benefit from the historic opportunity provided by the coordinated innovation and development strategy of the Beijing-Tianjin-Hebei region. Examining how new quality productive forces can facilitate high-quality development in Hebei not only serves as a critical demonstration for overcoming bottlenecks in energy structure transformation within resource-dependent regions and for constructing a modern regional industrial system, but also provides actionable policy insights for other regions facing similar developmental challenges.

Building upon this foundation, this paper investigates the interactive relationship between new quality productive forces and high-quality development by constructing a systematic research framework that encompasses “mechanism explanation, state measurement, and factor analysis.” On one hand, it delves into the internal mechanisms through which new quality productive forces drive high-quality development. On the other hand, it establishes a scientifically rigorous measurement system, applies the model to Hebei Province in China, and identifies the key influencing factors. The study aims to extract replicable experiences that can be applied to similar regions and to promote the integrated development of theoretical understanding and practical implementation.

The remainder of this paper is organized as follows. Section 2 presents a comprehensive review of the existing literature on new quality productive forces and high-quality development. It analyzes the current state of research on their interrelationship and lays a solid theoretical foundation for the subsequent analysis. Section 3 explores the driving, guiding, and synergistic mechanisms through which new quality productive forces promote high-quality development, with a focus on four core dimensions: technology, factors of production, industry, and policy. Section 4 constructs a coupling coordination degree model, a Tobit model, and a grey prediction model, thereby establishing a systematic and multi-dimensional analytical framework that provides rigorous tools for empirical investigation. Section 5 conducts a case study of Hebei Province, applying the aforementioned models to assess the coupling coordination between new quality productive forces and high-quality development. This includes evaluating developmental levels, analyzing spatio-temporal evolution patterns, identifying key influencing factors, and forecasting future trends, accompanied by corresponding policy recommendations. The final section provides a discussion and conclusion that summarizes the key contributions of the study, outlines its limitations, and suggests directions for future research.

2. Literature Review

2.1. New Quality Productive Forces

2.1.1. Theoretical Understandings of New Quality Productive Forces

New quality productive forces signify a qualitative leap in the development of productivity. Early theories of productivity primarily revolved around “factor input and division of labor efficiency,” emphasizing the interaction between labor and capital. Subsequently, these theories were interpreted as the contemporary evolution of Marxist productivity theory, with their essence lying in the dynamic adaptation of production factors, technological applications, and social production relations [1]. From a theoretical standpoint, this adaptability originates from the classical framework of Marxist productivity theory and aligns closely with the understanding that productivity evolves dynamically in response to factor upgrading and technological advancement [2]. In terms of fundamental attributes, new quality productive forces are distinctly marked by advanced technology, high efficiency, and high quality. Innovation serves as the central characteristic permeating the entire process of technological breakthroughs, factor reorganization, and industrial upgrading, thereby constituting the key differentiator from traditional forms of productivity [3]. The emergence of new quality productive forces is grounded in multidimensional advances in scientific and technological innovation, spearheaded by frontier technologies such as artificial intelligence, blockchain, and the Internet of Things, which collectively reshape the technological trajectory of productivity development [4].

2.1.2. Measurement Frameworks and Empirical Approaches

Building upon a clear definition of the connotation of new quality productive forces, the academic community has primarily conducted measurement and empirical research from multiple dimensions, including technology-oriented approaches, total factor productivity (TFP), and system coupling assessment. In technology-oriented research, scholars focus on both the depth and breadth of digital technology applications. Chiou (1999) proposed a technology-oriented productivity measurement model, which laid a methodological foundation for subsequent studies [5]; Qu (2025) employed a fixed-effects model to analyze the impact of digital transformation on TFP and identified artificial intelligence as a key driver of TFP improvement [6]. Xu (2025) systematically explored the mechanisms through which the digital economy promotes the development of new quality productive forces from a multi-dimensional perspective [7]. In the context of TFP research, existing literature predominantly emphasizes enhancing overall production efficiency through optimized factor allocation. Liang (2023) demonstrated that TFP improvement contributes to better environmental quality, thereby revealing an intrinsic link between production efficiency and sustainable development [8]; Rehman (2023), based on cross-national data from 67 countries, investigated the positive influence of macroeconomic factors such as energy infrastructure on TFP [9]; Pan (2022) applied pooled regression methods to confirm the existence of a significant positive nonlinear relationship between the digital economy and TFP [10]. With regard to system coupling assessment, the focus lies on the synergistic interactions among elements, structure, and function. This approach typically quantifies the alignment between the technological innovation chain and the industrial value chain using the coupling coordination degree model. For example, Dai (2025) applied an improved coupling coordination degree model to analyze the coupling characteristics across 31 Chinese provinces, revealing a regional coordination pattern characterized by a gradient distribution of “high in the east and low in the west” [11]; Qu (2024) further utilized this model to examine the coordination relationships among water resources, ecological environment, and economic development [12].

2.2. High-Quality Development

2.2.1. Theoretical Understanding of High-Quality Development

High-quality development constitutes a central theme in China’s economic development during the new era and represents a significant evolutionary direction in global development economics theory [13]. Unlike the traditional extensive development model that prioritizes GDP growth, high-quality development emphasizes innovation-driven growth, structural optimization, and sustainable, coordinated development. In recent years, scholarly research on high-quality development has become increasingly sophisticated and multidimensional. Tian (2022) constructed an analytical framework to examine how environmental regulation affects the internal structure of green total factor productivity (GTFP), highlighting that high-quality development fundamentally depends on efficiency transformation and innovation-driven strategies [14]. Chen (2025) further extended the theoretical linkage between the digital economy and enterprise-level GTFP to the micro-enterprise dimension, arguing that the key to achieving high-quality development lies in leveraging the digital economy to empower strategic emerging industries [15]. Moreover, Qayyum (2024) underscored the critical role of institutional quality in sustaining long-term development [16], while Nayak (2023) emphasized that the theory of competitive advantage offers a valuable reference for optimizing industrial structures [17]. Collectively, these theoretical contributions have facilitated a paradigm shift in high-quality development—from a singular focus on economic growth rates toward a broader framework centered on comprehensive benefit enhancement.

2.2.2. Measurement Framework and Empirical Methods

Building upon a clearly defined conceptualization of high-quality development, scholars have primarily advanced research along two methodological lines: the construction of measurement frameworks and the application of empirical methods. The measurement framework is typically structured around four key dimensions—economic efficiency, social well-being, ecological protection, and innovation-driven development. In the dimension of economic efficiency, Lin (2022) and Zhang (2024) independently investigated the impacts of foreign direct investment, energy efficiency, and economic growth on high-quality development [18,19]. Regarding social well-being, Zhang (2024) and Fatah (2025) examined the contributions of livelihood improvement and social equity to high-quality development [20,21]. In the domain of ecological protection, Wang (2022) analyzed the coordinated interactions among water resources, socio-economic factors, and the ecological environment [22]. In the innovation-driven development dimension, Zou (2024) elaborated on the multi-stage mechanisms through which technological innovation facilitates industrial upgrading [23]. In terms of empirical methodologies, recent studies exhibit a trend toward methodological diversity and analytical refinement. About measurement techniques, Wang (2023) applied the CRITIC-TOPSIS method [24], Zhong (2024) employed the Fare—Primont index method [25], and Li (2024) utilized an improved entropy weight method [26], collectively offering a range of robust quantitative tools for assessing the level of high-quality development. Concerning the analysis of influence mechanisms, Xu (2023) explored the promoting role of green finance through a spatial spillover perspective [27]. Wu (2024) investigated the empowering effects of digital transformation using a two-way fixed-effects model [28]. Ma (2025) systematically analyzed the complex interplay between carbon emissions and economic development through both the panel fixed-effects model and the spatial Durbin model [29]. Collectively, these empirical studies have significantly deepened the understanding of the internal mechanisms underlying high-quality development.

2.3. Coupling Coordination Research

Research on the coupling coordination between new quality productive forces and high-quality development has been extensively conducted from multiple theoretical and empirical perspectives. Liu (2024) examined the relationship between new quality productive forces and the transformation of economic growth models, identifying the intrinsic linkages that connect productivity evolution with high-quality development [30]. Huang (2025) investigated the innovative components embedded in new quality productive forces and explored how these components align with and reinforce the innovation-driven strategy within the framework of high-quality development [31]. Ghormare (2024) analyzed the interaction mechanism between the circular economy and ecological innovation, proposing that ecological innovation serves as a critical bridge linking productivity transformation with sustainable development goals, thereby facilitating the synergistic advancement of economic growth and environmental protection [32]. Dai (2025) explored the indirect influence of new quality productive forces on high-quality development through the optimization of industrial structure, highlighting the mediating role of structural upgrading [33]. In the realm of empirical research, Lee (2023) applied the super SBM model combined with the partial linear function coefficient method to uncover the nonlinear driving effect of digital productivity in overcoming resource and environmental constraints and advancing regional green economic transformation [34]. The study also revealed spatial and temporal variations in this effect, offering theoretical insights and policy implications for leveraging digitalization to support sustainable development [34]. Xiang (2024) constructed a comprehensive evaluation index system using the coupling coordination degree model, incorporating multiple dimensions such as innovation capacity, production efficiency, industrial structure, and ecological environment [35]. This framework enabled a quantitative assessment of the coupling coordination level between new quality productive forces and high-quality development [35]. He (2024) extended this analysis by comparing regional differences in coupling coordination and identifying the key factors contributing to regional development imbalances [36]. Wang (2024) adopted a “problem-oriented-innovative thinking-path mechanism” analytical framework to investigate how new quality productive forces drive the high-quality development of the tourism industry [37].

Despite the extensive scholarly attention given to new quality productive forces and high-quality development, significant theoretical and practical gaps remain. Current research on the theoretical framework of new quality productive forces predominantly centers on conceptual definitions and descriptions of macro-level characteristics, with limited in-depth analysis of their differentiated manifestations and specific mechanisms of action across diverse industrial contexts. While the core connotation of high-quality development has been broadly delineated, there remains a dearth of systematic investigation and empirical validation regarding its practical pathways—particularly in formulating region-specific strategies that account for varying resource endowments and stages of development. Furthermore, existing studies seldom adopt a holistic systems perspective to comprehensively examine the full spectrum of interactions between new quality productive forces and high-quality development, including the “mechanism of action–coupling measurement–influencing factors–trend prediction” framework. Instead, most research focuses on isolated components, resulting in a lack of integrative and coherent understanding. In addition, a large proportion of the literature remains confined to macro-level generalizations, with few in-depth empirical studies grounded in specific regional contexts. Given the substantial disparities among regions in terms of industrial structure, resource endowments, and policy environments, findings derived from macro-level analyses often fail to provide actionable insights for localized implementation. Accordingly, this study begins with an exploration of the mechanism through which new quality productive forces empower high-quality development. It selects Hebei Province in China as a representative case for systematic theoretical and empirical analysis, aiming to generate regionally targeted theoretical insights and policy recommendations that support the realization of high-quality development at the local level.

3. The Mechanism of New Quality Productive Forces Enabling High-Quality Development

New quality productive forces represent an advanced form of productivity characterized by high technological content, operational efficiency, and product or process quality. High-quality development refers to a model of economic growth, structural configuration, and dynamic momentum that effectively addresses the continuously evolving and authentic needs of the population [38]. In the current critical phase marked by accelerated global economic integration and industrial transformation, the ongoing emergence of new quality productive forces serves as a vital driving force for achieving high-quality development. Clarifying the internal mechanisms through which new quality productive forces contribute to high-quality development is therefore of significant theoretical and practical importance. The conceptual framework of this mechanism is illustrated in Figure 1.

3.1. Driving Mechanism

The driving mechanism through which new quality productive forces propel high-quality development is anchored in four core dimensions—technology, production factors, industry, and policy—that together constitute a multi-dimensional dynamic system. Within the technological dimension, innovation in production technologies serves as the pivotal breakthrough. By accelerating the commercialization of frontier technologies and fostering collaborative interactions among innovation entities, this dimension injects technological momentum into high-quality development, aligning with the theoretical framework that identifies technological innovation as a key driver of economic growth. The production factor dimension is grounded in the theory of production elements, emphasizing the optimization of labor structure, enhancement of capital allocation efficiency, and realization of data element value. It facilitates a transition from “quantitative input-driven” to “quality-oriented transformation,” thereby unlocking endogenous development potential. The industrial dimension is based on the theory of industrial evolution, focusing on the phased development of emerging industries, intelligent upgrading of traditional industries, strengthening of industrial chain resilience, and the cultivation of green productive forces. These initiatives drive the industrial structure toward high-end, intelligent, and sustainable development, reshaping the ecosystem of industrial growth. The policy dimension employs instruments such as public service provision, macro-level regulatory guidance, market environment construction, and coordinated resource allocation to establish a robust institutional safeguard system. It enables the government to address market failures and provide directional guidance for development across all dimensions. Through the synergistic interaction of these four dimensions, a core dynamic network is formed, effectively advancing the empowerment of high-quality development by new quality productive forces.

3.2. Guidance Mechanism

The guidance mechanism centers on policy as the primary medium, achieving precise directional regulation through systematic institutional design. Policies employ a comprehensive set of instruments: enhancing public service provision, upgrading innovation platforms and industrial infrastructure, and optimizing the overall development environment; defining strategic priorities via macro-level regulation to mitigate the inefficiencies of market self-correction; fostering a fair and competitive market environment to stimulate innovation-driven initiatives; and coordinating cross-regional resource allocation to improve factor utilization efficiency. This mechanism is grounded in the theory of collaborative governance between government and market. It addresses market shortcomings in the provision of public goods and long-term strategic planning, while aligning new quality productive forces with the objectives of high-quality development through targeted policy guidance. By doing so, it ensures that key economic activities—such as technological innovation, factor mobility, and industrial upgrading—proceed in an orderly manner within the institutional framework, thereby providing robust institutional safeguards and strategic direction for the sustainable and balanced advancement of economic and social development.

3.3. Synergy Mechanism

The synergy mechanism constitutes a dynamic interactive network centered on the interplay of technology, production elements, industries, and policies. The technology-element synergy is demonstrated through the efficient circulation of data elements enabled by digital technologies. For instance, blockchain ensures data ownership and transaction security, while artificial intelligence algorithms enhance the precision of data mining. Concurrently, technological innovation reshapes the labor force structure through skill development programs. The element-industry synergy is reflected in the emergence of new industries driven by data elements—such as industrial big data enabling personalized customization in intelligent manufacturing—as well as in the acceleration of technology industrialization through capital elements, including venture capital and industrial funds. The industry-policy synergy guides industrial transformation through adaptive policy frameworks. For example, carbon quota trading policies drive green upgrades in energy-intensive industries, while industrial chain security policies enhance technological autonomy via domestic substitution strategies. The policy-technology synergy facilitates the diffusion of technology through institutional design, such as intellectual property protection policies that incentivize corporate R&D investment and technology standardization that promotes the large-scale application of innovation outcomes. This synergy mechanism transcends the limitations of single-dimensional development, constructing a dynamic coupling system of “technology–element–industry–policy” that enables subsystems to achieve functional coordination through interaction. Ultimately, it generates a synergistic effect wherein the overall system performance surpasses the sum of its individual components, thereby advancing the synchronized evolution of new quality productive forces and high-quality development objectives.

4. Measurement Index System and Models

4.1. Construction of the Measurement Index System

Based on the principles of systematicness, simplicity, and data availability, referring to References [39,40], a coupling coordination measurement index system for enabling high-quality development through new quality productive forces was constructed. As shown in

Table 1. New quality productive forces enable the measurement index system for high-quality development and coupling coordination.

System	Primary Indicator	Secondary Indicator	Source	Attribute
New Quality Productivity Force	Digital productivity	Per capita regional GDP	Source statistics	+
		Total labor productivity	Source statistics	+
		Internet broadband access subscriptions	Source statistics	+
	Technological productivity	Level of scientific and technological inputs	R&D expenditures/GDP	+
		Percentage of education practitioners	Source statistics	+
		Percentage of persons employed in the information technology industry	Source statistics	+
		Revenue from telecommunication services	Source statistics	+
	Green Productivity	Greening coverage in built-up areas	Source statistics	+
		Number of patents granted for green inventions	Source statistics	+
		Environmental protection expenditures as a share of fiscal expenditures	Source statistics	+
		Non-hazardous treatment rate of domestic waste	Source statistics	+
High-Quality Development	Innovative development	Local revenues	General public budgets	+
		Expenditures on new product development of industrial enterprises are regular	Source statistics	+
		Full-time equivalent of R&D personnel in state-owned industrial enterprises	Source statistics	+
	Coordinated development	Ratio of disposable income per capita for urban and rural residents	Source statistics	-
		Annual disposable income of rural residents	Source statistics	+
		industrial structure	Tertiary value added/GDP	+
	Green development	Electricity consumption in transportation, storage, and postal services	Source statistics	-
		Industrial sulfur dioxide emissions	Source statistics	-
		Industrial solid waste utilization rate	Source statistics	+
	Open development	Total imports of goods	Source statistics	+
		Total exports of goods	Source statistics	+
		Foreign direct investment	Source statistics	+
	Shared development	Expenditure on education	Source statistics	+
		Cell phone penetration rate	Source statistics	+
		Road mileage	Source statistics	+

.

4.2. Measurement Modeling

4.2.1. Coupling Coordination Degree Model

The coupling coordination degree model is a mathematical framework designed to evaluate the interaction and coordination among two or more interrelated systems [41]. This study applies the model to examine whether a mutual relationship exists between new quality productive forces and high-quality development, and to assess the strength and nature of this interaction.

(1)

Standardization of Data

To eliminate dimensional discrepancies among evaluation indicators and ensure data validity, this study employs the range normalization method for standardization and further adjusts the transformed values. The procedure for model construction is outlined as follows:

Standardized treatment of positive indicators:

$$Y_{ij}=\left[\left({\displaystyle \frac{X_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}{X}_{ij}}{\mathrm{m}\mathrm{a}\mathrm{x}{X}_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}{X}_{ij}}}\right)\times 0.99\right]+0.01$$

(1)

Negative indicators of standardized treatment:

$$Y_{ij}=\left[\left({\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}{X}_{ij}-X_{ij}}{\mathrm{m}\mathrm{a}\mathrm{x}{X}_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}{X}_{ij}}}\right)\times 0.99\right]+0.01$$

(2)

In the formula, $X_{ij}$ is the value of the $i$th measurement object on the $j$th measurement index, and $Y_{ij}$ is the standardized value.

(2)

Calculation of Weights (ω_j)

This study employs an integrated two-step approach combining entropy weighting and grey relational analysis to rigorously assess the coupling and coordination between the systems of new quality productive forces and high-quality development. The methodology first applies the entropy value method to determine the objective weights of each indicator, accurately reflecting its informational contribution and variability; subsequently, grey relational analysis quantifies the degree of alignment between each indicator and the overarching objectives of both systems, thereby uncovering the intrinsic linkages in their dynamic interactions. By integrating these two techniques, the approach mitigates the biases and limitations inherent in single-weighting methods and strengthens the overall coherence and logical consistency of the evaluation framework through a mechanism that aligns weighting schemes with the underlying coupling dynamics [42].

In this paper, a sequence that ideally represents the best state of coordinated development is selected as the parent sequence, denoted as $X_0=\left(X_0\right(1),X_0(2),\cdots ,X_0(m\left)\right)$; the original index data is regarded as the child sequence, denoted as $X_i=\left(X_i\right(1),X_i(2),\cdots ,X_i(m\left)\right)$. The calculation formula is as follows.

$$P_{ij}={\displaystyle \frac{Y_{ij}}{\sum _{i=1}^n Y_{ij}}}$$

(3)

$$e_j=-{\displaystyle \frac{1}{\ln \left(n\right)}}\times \sum _{i=1}^n \left(P_{ij}\ln \left(P_{ij}\right)\right) (0\le e_j\le 1)$$

(4)

$$w_j={\displaystyle \frac{1-e_j}{\sum _{j=1}^m (1-e_j)}}$$

(5)

$${\xi }_i(k)={\displaystyle \frac{\underset{i}{\mathrm{m}\mathrm{i}\mathrm{n}} \underset{k}{\mathrm{m}\mathrm{i}\mathrm{n}} |X_0(k)-X_i(k)|+\zeta \underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}} \underset{k}{\mathrm{m}\mathrm{a}\mathrm{x}} |X_0(k)-X_i(k)|}{|X_0(k)-X_i(k)|+\zeta \underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}} \underset{k}{\mathrm{m}\mathrm{a}\mathrm{x}} |X_0(k)-X_i(k)|}}$$

(6)

$$R_i={\displaystyle \frac{1}{m}}\sum _{k=1}^m {\xi }_i(k)$$

(7)

$${\omega }_j={\displaystyle \frac{R_i\times w_j}{\sum _{j=1}^m R_i\times w_j}}$$

(8)

In the formula, n is the number of evaluated objects, m is the number of measurement indicators, $P_{ij}$ is the weighting matrix, $e_j$ is the information entropy, ${\xi }_i\left(k\right)$ is the correlation coefficient of $X_i$ to $X_0$ about the $k$ indicators, and $\zeta$ is the discrimination coefficient, which takes the value of 0.5, and $R_i$ is the degree of correlation.

(3)

Calculation of the Level of Integrated Development (U)

$$U=\sum _{j=1}^m {\omega }_j{Y}_{ij}$$

(9)

In the formula, $U_x$ is the new quality productive forces composite development index, and $U_y$ is the high-quality development composite development index.

(4)

Calculation of the Degree of Coupling Coordination (D)

$$C=2\times [{\displaystyle \frac{U_x{U}_y}{(U_x+U_y{)}^2}}{]}^{{\displaystyle \frac{1}{2}}} (0\le C\le 1)$$

(10)

$$T=\alpha U_x+\beta U_y (0\le T\le 1)$$

(11)

$$D=\sqrt{C\times T} (0\le D\le 1)$$

(12)

In the formula, $C$ denotes the coupling degree, $T$ represents the coordination index, and $D$ indicates the coupling coordination degree. Parameters $\alpha$ and $\beta$ correspond to the weights of the new quality productive forces and high-quality development systems, respectively. A significant bidirectional coupling relationship exists between new quality productive forces and high-quality development: on one hand, the former drives high-quality development through technological innovation and factor optimization; on the other hand, high-quality development facilitates the cultivation of new quality productive forces by providing policy guarantees and institutional support. Together, these two systems constitute the core driving force for regional economic transformation, with both playing equally vital roles in supporting sustainable socio-economic development. Existing studies suggest that systems exhibiting bidirectional interaction are typically assigned equal weights [43,44]. Accordingly, this study sets their weights to be equal, each with a value of 0.5. The classification criteria for the coupling coordination degree D are presented in

Table 2. Classification of the degree of coupling coordination.

D-Value Interval	Level of Coordination	Degree of Coupling Coordination	D-Value Interval	Level of Coordination	Degree of Coupling Coordination
[0.0, 0.1)	1	Extreme disorder	[0.5, 0.6)	6	Barely coordination
[0.1, 0.2)	2	Severe disorder	[0.6, 0.7)	7	Primary coordination
[0.2, 0.3)	3	Moderate disorder	[0.7, 0.8)	8	Intermediate coordination
[0.3, 0.4)	4	Mild disorder	[0.8, 0.9)	9	Good coordination
[0.4, 0.5)	5	On the verge of a disorder	[0.9, 1.0)	10	High-quality coordination

, where higher values indicate a greater degree of coordination between the two systems.

4.2.2. Tobit Model

To accurately identify the key determinants influencing the coupling coordination degree between new quality productive forces and high-quality development, this study establishes a panel Tobit model for empirical analysis. Given that the coupling coordination degree falls within the bounded interval [0, 1], it represents a typical censored continuous variable. The Tobit model is particularly effective in handling such censored data and is well-suited for parameter estimation in the context of panel data.

The coupling and coordination mechanism between new quality productive forces and high-quality development is driven by a multidimensional set of factors. Economic development provides the material foundation for system synergy, yet it also introduces transformational pressures due to path dependence. Urbanization significantly reduces institutional transaction costs through element aggregation and functional integration, thereby offering a spatial platform for system coordination. Scientific and technological R&D enhances the innovation cycle between the two systems via knowledge spillovers and technology diffusion. Optimization of the industrial structure promotes digital and green transformation on the supply side, improving structural compatibility between systems. Financial support facilitates continuous financing and incentive mechanisms for cultivating and upgrading new quality productive elements through efficient capital allocation and risk-sharing mechanisms. Government intervention plays a crucial coordinating and catalytic role during the transformation phase by providing institutional frameworks and policy guidance. These factors are interlinked and interact synergistically, collectively shaping the formation and evolution of the coupling and coordination degree.

For variable selection, this study draws upon established research [45] and incorporates contextual realities to ultimately identify six key influencing factors: economic development ($X_1$), urbanization ($X_2$), scientific and technological R&D ($X_3$), industrial structure ($X_4$), financial support ($X_5$), and government intervention ($X_6$). Detailed descriptions of each variable are provided in

Table 3. Selection of Influencing Factors for Coupling Coordination Degree.

Variable Type	Variable Name	Variable Symbol	Variable Description	Unit
The explained variable	Coupling coordination degree	$D_{it}$	The degree of coordinated development of the interaction between systems	Dimensionless
Explanatory variable	Economic development	$X_1$	Regional gross domestic product	Yuan
	Urbanization	$X_2$	Proportion of permanent urban residents in the total regional population	%
	Scientific and technological R&D	$X_3$	Full-time equivalent of R&D personnel input	Human years
	Industrial structure	$X_4$	Proportion of added value of the tertiary industry in GDP	%
	Financial support	$X_5$	Total loans issued by financial institutions to the region	Billion yuan
	Government intervention	$X_6$	Proportion of local fiscal general budget expenditure in GDP	%

.

To mitigate the effects of heteroscedasticity and multicollinearity, the natural logarithm transformation was applied to the three absolute-value variables—economic development ($X_1$), scientific and technological research and development ($X_3$), and financial support ($X_5$). In contrast, the ratio-based variables—urbanization rate ($X_2$), industrial structure ($X_4$), and government intervention intensity ($X_6$)—were retained in their original form. The model construction procedure is outlined as follows:

$$D_{it}=\alpha +\rho \mathrm{l}\mathrm{n}{X}_{1it}+\beta \mathrm{l}\mathrm{n}{X}_{2it}+\gamma \mathrm{l}\mathrm{n}{X}_{3it}+\delta \mathrm{l}\mathrm{n}{X}_{4it}+\sigma \mathrm{l}\mathrm{n}{X}_{5it}+\tau \mathrm{l}\mathrm{n}{X}_{6it}+{\epsilon }_{it}$$

(13)

In the formula, $D_{it}$ is the coupling coordination in year $t$ in region $i$, $X_{nit}$ is the data of $X$ in year $t$ in region, $\alpha ,\rho ,\beta ,\gamma ,\delta ,\sigma$, and $\tau$ are the coefficients to be estimated, and ${\epsilon }_{it}$ is the random perturbation term.

4.2.3. Grey Prediction Model

The grey prediction model $\mathrm{G}\mathrm{M}\left(\mathrm{1,1}\right)$ is a prediction method for dealing with uncertainty and incomplete information series [46]. The model is used in this study to predict the status of coupling and coordination between the two systems of new quality productive forces enabling high-quality development. The modeling process is as follows:

(1)

Rank-Ratio Test

A rank-ratio test is performed on the original sequence before modeling to verify whether the data sequence is suitable for the $\mathrm{G}\mathrm{M}\left(\mathrm{1,1}\right)$ model. Let the original sequence be $x^{\left(0\right)}=\left(x^{\left(0\right)}\left(1\right),x^{\left(0\right)}\left(2\right),\cdots x^{\left(0\right)}\left(n\right)\right)$ and $n$ be the length of the data sequence.

$$\lambda (k)={\displaystyle \frac{x^{\left(0\right)}(k-1)}{x^{\left(0\right)}\left(k\right)}},k=\mathrm{2,3},\dots ,n$$

(14)

In the formula, $\lambda \left(k\right)$ is the rank ratio value and $x^{\left(0\right)}\left(k\right)$ is the kth term of the original sequence. When $\lambda (k)\in (e^{{\displaystyle \frac{-2}{n+1}}},e^{{\displaystyle \frac{2}{n+1}}})$, then the model can be built, otherwise the transformation process is required.

(2)

Constructing the Cumulative Sequence

To weaken the original sequence’s randomness and enhance the data’s regularity, it is cumulated to obtain a new sequence $x^{\left(1\right)}$.

$$x^{\left(1\right)}=\left(x^{\left(1\right)}\left(1\right),x^{\left(1\right)}\left(2\right),\dots ,x^{\left(1\right)}\left(n\right)\right)$$

(15)

In the formula, $x^{\left(1\right)}\left(K\right)$ is the sum of the first $k$ original sequences, denoted as $\sum _{i=1}^k x^{\left(0\right)}(i),k=\mathrm{1,2},\dots ,n$.

(3)

Modeling Differential Equations

The whitening model is established by fitting the dynamics of the system through the cumulative sequence of the law of change. Define $z^{\left(1\right)}$ as the sequence generated by the immediate neighborhood mean, denoted as $z^{\left(1\right)}=\left(z^{\left(1\right)}\right(2),z^{\left(1\right)}(3),\dots ,z^{\left(1\right)}(t\left)\right)$.

$${\displaystyle \frac{\mathrm{d}{x}^{\left(1\right)}}{\mathrm{d}t}}+a{x}^{\left(1\right)}(t)=b$$

(16)

$$z^{\left(1\right)}\left(k\right)={\displaystyle \frac{1}{2}}\left(x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}\left(k-1\right)\right) k=(2,3,\dots ,n)$$

(17)

$$x^{\left(0\right)}\left(k\right)+a{z}^{\left(1\right)}\left(k\right)=b$$

(18)

In the formula, $a$ is the development coefficient and $b$ is the amount of grey role.

(4)

Parameter Estimation

The parameters in the model are estimated by the least squares method.

$$B=\left[\begin{array}{cc}-z^{\left(1\right)}\left(2\right)& 1\\ -z^{\left(1\right)}\left(3\right)& 1\\ ⋮& ⋮\\ -z^{\left(1\right)}\left(n\right)& 1\end{array}\right]$$

(19)

$$Y=\left[\begin{array}{c}{X}^{\left(0\right)}\left(2\right)\\ X^{\left(0\right)}\left(3\right)\\ ⋮\\ X^{\left(0\right)}\left(n\right)\end{array}\right]$$

(20)

$$\widehat{\theta }=[a,b{]}^{\mathrm{T}}=(B^{\mathrm{T}}B{)}^{-1}{B}^{\mathrm{T}}Y$$

(21)

In the formula, $B$ is the coefficient matrix and $Y$ is the observation vector.

(5)

Model Solving

Using the estimated parameters, the predicted future values are derived.

$${\widehat{x}}^{(1)}(k)=(x^0(1)-{\displaystyle \frac{b}{a}})e^{-a(k-1)}+{\displaystyle \frac{b}{a}}$$

(22)

$${\widehat{x}}^{(0)}(k)={\widehat{x}}^{(1)}(k)-{\widehat{x}}^{(1)}(k-1)$$

(23)

In the formula, ${\widehat{x}}^{(1)}(k)$ is the cumulative predicted value and ${\widehat{x}}^{(0)}(k)$ is the original predicted value.

(6)

Model Test

Define $\epsilon (k)$ as the absolute residual, noting $\epsilon (k)=x^{(0)}(k)-{\widehat{x}}^{(0)}(k)$.

$${\epsilon }_r(k)=(|\epsilon (k)|/x^{(0)}(k))\times 100\mathrm{\%}$$

(24)

$$C=S_{\epsilon }^2/S_0^2$$

(25)

$$S_0^2={\displaystyle \frac{1}{n}}\sum _{k=1}^n [x^{(0)}(k)-{\overline{x}}^{(0)}{]}^2$$

(26)

$$S_{\epsilon }^2={\displaystyle \frac{1}{n}}\sum _{k=1}^n [\epsilon (k)-\overline{\epsilon }(k){]}^2$$

(27)

$$P=\{|\epsilon (k)-\overline{\epsilon }(k)|\}<0.674S_0^2$$

(28)

In the formula, ${\epsilon }_r(k)$ is the relative error value, which is less than 0.2. $S_0^2$ is the original data variance, $S_{\epsilon }^2$ is the residual variance, ${\overline{x}}^{(0)}$ is the original data mean, $\overline{\epsilon }(k)$ is the residual mean, and $P$ is the probability of small error, which is greater than 0.7. $C$ is the value of a posteriori difference ratio, which is less than 0.65.

5. Empirical Analysis

5.1. Data Source

This study focuses on Hebei Province in China. The data employed in the empirical analysis are primarily sourced from authoritative publications, including the China Statistical Yearbook, Hebei Economic Yearbook, Hebei Statistical Yearbook, as well as statistical bulletins concerning national economic and social development at both provincial and municipal levels, and government work reports from various prefecture-level cities.

During the data preprocessing phase, to ensure data quality and statistical consistency, the study first performed cross-validation on raw data from multiple sources, focusing on verifying the consistency of indicator definitions and values across different statistical publications in order to minimize biases arising from source discrepancies. Next, for the very few missing data points, an inter-temporal comparison approach—consulting statistical data from adjacent years—was prioritized for imputation. When such comparisons were not feasible, linear interpolation was applied to maintain both data completeness and plausibility. Finally, potential outliers were detected through descriptive statistical analysis and scatter plot visualization. These observations were then cross-checked against original data sources for secondary validation. Upon confirmation that all identified outliers represented genuine real-world conditions, they were retained to ensure that subsequent analytical outcomes accurately reflected objective reality.

This study adopts the period from 2013 to 2022 as the observation window. This selection is primarily motivated by the proposal of the “Innovation-Driven Development Strategy” in 2012, marking the beginning of the practical implementation of China’s new development concept in 2013. This timeframe allows for a comprehensive coverage of the co-evolutionary process between new quality productive forces and high-quality development. Furthermore, after 2013, both national and Hebei Province statistical systems were significantly enhanced, with standardized and complete data now available for key indicators such as R&D investment and green development, thereby ensuring reliable measurement. It is also worth noting that annual data must undergo aggregation and verification before official release, and comprehensive data for 2023 and beyond remain unavailable. By setting 2022 as the endpoint, the study effectively balances the capture of recent developmental trends with the rigor of conclusions, while maintaining a reasonable trade-off between research timeliness and data reliability.

5.2. Comprehensive Measurement

5.2.1. Comprehensive Measurement of New Quality Productive Forces

Based on Formulas (1)–(9), the development levels of new quality productive forces in each city of Hebei Province from 2013 to 2022 were calculated, and the results are shown in Figure 2.

As illustrated in Figure 2, the level of new quality productive forces in Hebei Province exhibited a significant upward trend from 2013 to 2022, with the average value rising from 0.086 to 0.374—an increase of approximately 335%. During this period, while the growth rates and levels of new quality productive forces varied across cities, a generally positive development trend was observed. Cities such as Tangshan, Shijiazhuang, and Xingtai demonstrated relatively high levels and rapid growth rates due to their strengths in industrial foundations, scientific research and development, and industrial transformation. Tangshan, as a major industrial city, has consistently invested in high-end equipment manufacturing and intelligent upgrading of the steel industry. Its level of new quality productive forces increased from 0.092 in 2013 to 0.411 in 2022, reflecting a substantial growth trajectory. Shijiazhuang, as the provincial capital, leveraged its concentration of innovation resources and policy support, with its level rising from 0.091 to 0.397 over the same period, indicating a steady and sustained development. Xingtai advanced through industrial upgrading, achieving an increase from 0.090 to 0.367, demonstrating a commendable growth rate. Meanwhile, cities such as Zhangjiakou, Chengde, and Hengshui started with relatively lower levels of new quality productive forces, which can be attributed to weaker industrial foundations and uneven distribution of technological resources. Nevertheless, these cities have also experienced continuous growth. In recent years, they have actively promoted emerging industries and increased investments in science and technology, leading to gradual improvements. For example, Zhangjiakou’s level increased from 0.110 in 2013 to 0.330 in 2022, while Chengde’s rose from 0.072 to 0.334. Although their growth rates were somewhat slower, they have shown consistent improvement and are gradually closing the gap with more developed cities.

5.2.2. Comprehensive Measurement of High-Quality Development

Based on Formulas (1)–(9), the high-quality development levels of each city in Hebei Province from 2013 to 2022 were calculated, and the results are shown in Figure 3.

As illustrated in Figure 3, the level of high-quality development in Hebei Province exhibited a marked upward trend from 2013 to 2022. The average value increased from 0.079 in 2013 to 0.416 in 2022, representing a growth of approximately 427%. During this period, while growth rates and development levels varied across cities, a generally positive trend was observed. Cities such as Langfang, Qinhuangdao, and Baoding demonstrated relatively high levels and rapid growth due to their geographical advantages, industrial restructuring, and innovation-driven strategies. Langfang, benefiting from its proximity to Beijing, actively attracted industrial transfers and innovation resources, with its high-quality development level rising from 0.106 in 2013 to 0.380 in 2022. Qinhuangdao, leveraging its coastal location, advanced steadily in tourism and high-end manufacturing, achieving an increase from 0.043 to 0.449—showing one of the most notable growth trajectories. Baoding, driven by industrial upgrading and the spillover effects of the Xiongan New Area, saw its level rise from 0.100 to 0.431, reflecting strong development momentum. Meanwhile, cities such as Hengshui, Zhangjiakou, and Chengde started with relatively lower levels of high-quality development, which can be attributed to their initial development positioning and weaker industrial foundations. Nevertheless, these cities also experienced continuous growth. Through policy guidance and industrial transformation, they have gradually improved their development levels. For example, Hengshui’s level increased from 0.140 in 2013 to 0.370 in 2022; Zhangjiakou’s rose from 0.050 to 0.405; and Chengde’s from 0.058 to 0.417. Although these cities still lag behind more developed ones, their upward trends are evident, indicating steady progress toward the goal of high-quality development.

5.3. Spatio-Temporal Evolution of Coupling Relationship

Based on Formulas (10)–(12), the coupling coordination degree of new quality productive forces enabling high-quality development in each city of Hebei Province from 2013 to 2022 is calculated, and to intuitively analyze its spatio-temporal evolution characteristics, the coupling coordination degree data of the representative years such as 2013, 2017, and 2022 are visualized and analyzed using the ArcGIS 10.8 software, as shown in Figure 4.

As illustrated in Figure 4, the coupling and coordination types between new quality productive forces and high-quality development across cities in Hebei Province from 2013 to 2022 reveal a notable spatial evolution. Initially characterized by a “high in the south and low in the north” pattern, the region transitioned through a “rise in the central area” phase, ultimately evolving toward a “regionally coordinated” development structure.

In 2013, the overall level of coupling and coordination across the province remained relatively low. In the northern region, Zhangjiakou and Chengde—key cities within the Hebei Northern Ecological Conservation Area—were constrained by the ecological protection red line, which limited their capacity for industrial transformation and the development of new quality productive forces. These cities were classified as experiencing moderate disharmony in coupling coordination. Shijiazhuang, the provincial capital located in the central region, was burdened by a heavy traditional industrial base. Baoding was in the early stages of industrial transfer, while Cangzhou’s coastal industrial zone had yet to fully develop. In the southern region, Xingtai was characterized by a high proportion of heavy chemical industries. These cities, constrained by delayed industrial transformation and fragmented innovation resources, also fell into the category of moderate disharmony. Only a few cities—Handan in the south, which began its industrial transformation earlier as a traditional industrial base; Hengshui, transitioning from an agricultural to an industrial economy; and Qinhuangdao in the east, which had started to develop distinctive coastal industries—exhibited relatively better performance, classified as mild disharmony. These cities emerged as the few “relative high points” within the provincial spatial pattern, collectively reflecting an overall spatial characteristic of “high in the south and low in the north.”

In 2017, the overall level of coupling and coordination across Hebei Province generally improved, with region-specific characteristics increasingly shaping development patterns. In the central region, Langfang—located near Beijing—began to demonstrate initial achievements in undertaking non-capital functions. As the provincial capital, Shijiazhuang increased innovation investment following the concentration of resources. In the north, Zhangjiakou initiated the development of wind power and photovoltaic industries, marking the early stages of green energy growth. In the south, Xingtai advanced technological upgrades in traditional industries to reduce high energy consumption. These four cities were the first to achieve a state of marginal coordination. However, in the north, Chengde continued to face ecological constraints that slowed industrial development. In the east, Qinhuangdao experienced moderate progress in coastal industrial upgrading. In the south, Handan remained in a critical phase of old industrial transformation, while Hengshui continued to maintain a relatively high proportion of traditional agriculture. In the central region, Tangshan’s steel industry transformation had just begun, Baoding’s industrial transfer had not yet reached a significant scale, and Cangzhou’s port infrastructure required further improvement. The coupling and coordination types of these cities remained on the verge of imbalance. As a result, the spatial pattern evolved into a transitional phase characterized by “the rise of the central region.”

In 2022, the level of coupling and coordination across Hebei Province achieved a significant leap, with each region fully leveraging its unique advantages. In the northern region, Zhangjiakou and Chengde deepened the development of green industries, effectively aligning ecological conservation with economic growth. In the central region, Shijiazhuang capitalized on the agglomeration effect of innovation resources, establishing a modern industrial system. Langfang continued to benefit from its strategic location by attracting high-end industries. Tangshan accelerated the intelligent transformation of its industrial base and advanced the green transition of the steel industry. Baoding, driven by the radiating influence of the Xiongan New Area, successfully facilitated industrial and population inflows. In the southern region, Handan completed technological upgrades in traditional industries and enhanced its equipment manufacturing sector. Xingtai steadily progressed in industrial restructuring while increasing the share of emerging industries. Cangzhou developed a coordinated port-industry cluster, integrating petrochemical and equipment manufacturing sectors. In the eastern region, Qinhuangdao leveraged the coastal economic belt to promote the integration of cultural tourism with high-end manufacturing. All these cities transitioned into the stage of primary coordination in terms of coupling coordination types. Only Hengshui in the south lagged slightly behind, as its transformation from traditional to modern agriculture proceeded at a slower pace, and the development of new industrial formats remained insufficient. Consequently, Hengshui remained at the stage of marginal coordination, representing the sole “slightly lagging point” within the province’s overall coordinated development pattern. This evolution marked a critical breakthrough toward achieving “region-wide coordination” in spatial development.

Overall, the spatial pattern of coupling and coordination in Hebei Province from 2013 to 2022 experienced a clear evolutionary process—from a “fragmented imbalance characterized by low levels in the north and relatively higher levels in the central and southern regions” to a “partially optimized pattern marked by central breakthroughs and lagging development in the north and south,” and finally to a “region-wide coordinated state with only Hengshui exhibiting slight lag.” This trajectory clearly reflects the transformation trend of new quality productive forces driving high-quality coordinated regional development, shifting from “spatial imbalance” toward “comprehensive and highly coordinated spatial integration.”

5.4. Analysis of Coupling Coordination Degree and Influencing Factors

5.4.1. Determination of the Random Effects Model

Based on regression analysis using Formula (13), the coupling and coordination degree and its influencing factors of new quality productive forces empowering high-quality development across cities in Hebei Province were examined. Four modeling approaches fixed effects OLS, random effects OLS, mixed effects Tobit, and random effects Tobit—were implemented using Stata/MP 18 (64-bit) software. Through comprehensive diagnostic testing across multiple dimensions, the most appropriate model was selected. Detailed results are presented in

Table 4. Analysis of factors influencing the degree of coupling coordination.

Variable	Fixed Effects OLS	Random Effects OLS	Mixed Effects Tobit	Random Effects Tobit
$X_1$	0.1180 (0.1060)	−0.0368 (0.0615)	−0.0130 (0.0673)	0.0371 (0.0711)
$X_2$	0.0220 *** (0.0053)	0.0153 *** (0.0051)	0.0121 *** (0.0045)	0.0220 *** (0.0030)
$X_3$	0.1400 ** (0.0512)	0.1100 *** (0.0372)	0.0870 * (0.0448)	0.1380 *** (0.0297)
$X_4$	0.0016 (0.0051)	0.0023 (0.0047)	0.0029 (0.0041)	0.0015 (0.0026)
$X_5$	0.0269 ** (0.0088)	0.0135 (0.0120)	0.0056 (0.0145)	0.0267 ** (0.0119)
$X_6$	0.0082 * (0.0039)	0.0172 *** (0.0057)	0.0158 *** (0.0053)	0.0111 *** (0.0039)
Log-L	-	-	136.3105	166.9782
LR(chi)	-	-	-	61.3400
Prob > chi2	-	-	-	0.0000

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

.

The Hausman test yields a p-value of 0.3278, which at the 5% significance level does not allow rejection of the null hypothesis that there is no systematic difference between the fixed effects and random effects coefficients. This suggests that the random effects model better satisfies the basic assumptions of panel data. Furthermore, given that the coupling coordination degree is strictly bounded between 0 and 1, it represents censored data. Applying ordinary least squares (OLS) regression would result in biased coefficient estimates due to the failure to account for this censoring, thereby distorting the true magnitude and direction of the effects of influencing factors. Consequently, the OLS model is not suitable for the data analysis in this study. To further evaluate model appropriateness, the mixed effects Tobit model and the random effects Tobit model are compared in terms of goodness-of-fit and applicability. The log-likelihood value of the random effects Tobit model is 166.9782, significantly higher than the log-pseudo-likelihood value of 136.3105 for the mixed effects Tobit model, indicating superior explanatory power and better fit to the sample data. Additionally, the likelihood ratio test produces a statistic of 61.3400 with an associated p-value approximately equal to zero—substantially below the 0.05 significance level—leading to the rejection of the null hypothesis that the mixed effects Tobit model is more appropriate. This confirms the necessity and validity of employing the random effects Tobit model in this research.

5.4.2. Analysis of Regression Results

To ensure the robustness of the model estimation and prevent potential bias arising from high correlations among explanatory variables, this study conducted a variance inflation factor (VIF) test on all explanatory variables. The results indicate that all VIF values fall within an acceptable range, with a maximum value of 4.41—considerably below the commonly used threshold of 10—and an average VIF of 2.80. These findings provide strong evidence that multicollinearity is not a significant issue in the model, and that the explanatory variables maintain a high degree of independence. This supports the reliability and validity of the subsequent regression analysis results.

As presented in

Table 5. Regression Analysis Results of the Influencing Factors of Coupling Coordination Degree Estimation.

Variable	Coefficient Estimates	Standard Error	Z Value	p-Value
$X_1$	0.0371	0.0710677	0.52	0.602
$X_2$	0.0220 ***	0.0029149	7.56	0.000
$X_3$	0.1378 ***	0.0296719	4.64	0.000
$X_4$	0.0015	0.0026231	0.59	0.556
$X_5$	0.0267 **	0.0118581	2.25	0.024
$X_6$	0.0111 ***	0.0039	2.83	0.005
Cons	−1.8911	0.2874	−6.58	0.000

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

, the impact of each variable on the coupling and coordination degree demonstrates notable variation. Specifically, urbanization development ${(X}_2$), scientific and technological R&D ($X_3$), and government intervention ($X_6$) are statistically significant at the 1% significance level, with p-values below 0.01. All corresponding coefficients are positive, indicating a positive influence on the coupling and coordination degree. Among these, scientific and technological R&D ($X_3$) exhibits the highest coefficient, suggesting the strongest positive promoting effect. Financial support ($X_5$) is also statistically significant, though at the 5% level (p = 0.024), with a positive coefficient. In contrast, economic development ($X_1$) and industrial structure ($X_4$) yield p-values of 0.602 and 0.556, respectively—both exceeding the 0.1 significance threshold—indicating that their effects on the coupling and coordination degree are not statistically significant.

In summary, urbanization development ($X_2$), scientific and technological R&D ($X_3$), financial support ($X_5$), and government intervention ($X_6$) are identified as key significant determinants of the coupling and coordination degree, all exerting positive influences. The effects of economic development ($X_1$) and industrial structure ($X_4$), however, are not statistically significant.

5.4.3. Test for Potential Endogeneity

Although the regression results of the random effects Tobit model indicate that economic development ($X_1$) does not have a statistically significant effect on the coupling coordination degree ($D_{it}$) between new quality productive forces and high-quality development, a potential causal relationship between these two variables cannot be ruled out. This implies the need to examine possible endogeneity issues associated with $X_1$. If the endogeneity of $X_1$ is overlooked, its correlation with the error term may lead to biased estimates of other key explanatory variables—such as urbanization development ($X_2$), scientific and scientific and technological R&D ($X_3$), and government intervention ($X_6$)—thereby under mining the reliability of the core findings. To address this concern and ensure the robustness of the estimation results, this study conducts an endogeneity test for $X_1$ using the control function approach within the framework of the random effects Tobit model. Specifically, the Resid $X_1$ is introduced to capture and remove any potential endogenous component, thereby validating the stability and reliability of the overall model estimates.

As presented in

Table 6. Potential Endogeneity Test.

Variable	Random Effects Tobit	Control Function Approach Tobit Model
$X_1$	0.0371 (0.0711)	−0.0086 (0.0736)
$X_2$	0.0220 *** (0.0029)	0.0108 ** (0.0044)
$X_3$	0.1378 *** (0.0297)	0.0783 * (0.0454)
$X_4$	0.0015 (0.0026)	0.0028 (0.0039)
$X_5$	0.0267 ** (0.0119)	0.0217 (0.0164)
$X_6$	0.0111 *** (0.0039)	0.0140 *** (0.0049)
Resid $X_1$	-	0.0683 (0.0863)
Cons	−1.8911 *** (0.2874)	−0.8775 *** (0.3142)

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

, the results of the endogeneity analysis for the coupling coordination degree are summarized. In the random effects Tobit model, urbanization development ($X_2$), scientific and technological R&D ($X_3$), financial support ($X_5$), and government intervention ($X_6$) are statistically significant at the 1%, 1%, 5%, and 1% levels, respectively, all demonstrating positive effects. Among these variables, scientific and technological research and development ($X_3$) exhibits the largest coefficient, indicating the strongest promoting influence. In contrast, economic development ($X_1$) and industrial structure ($X_4$) do not show statistical significance. When applying the control function method to the Tobit model by introducing the residual term Resid $X_1$ to address potential endogeneity, urbanization development ($X_2$) remains significant at the 5% level, scientific and technological R&D ($X_3$) at the 10% level, and government intervention ($X_6$) at the 1% level, with all continuing to display positive effects. Notably, the coefficient of economic development ($X_1$) shifts from positive to negative and becomes statistically insignificant, while industrial structure ($X_4$), financial support ($X_5$), and the residual term Resid $X_1$ also fail to reach significance. Based on the overall endogeneity testing procedure, these findings suggest that the endogeneity associated with economic development ($X_1$) exerts only a limited influence on the estimation results. Consequently, the estimates derived from the random effects Tobit model demonstrate a high degree of robustness, supporting the validity and reliability of the empirical conclusions.

In summary, urbanization development ($X_2$), scientific and technological R&D ($X_3$) and government intervention ($X_6$) are identified as the core explanatory variables with statistically significant positive effects on the coupling coordination degree. Among these factors, scientific and technological R&D ($X_3$) demonstrates the strongest promoting effect, followed by government intervention ($X_6$), with urbanization development ($X_2$) exhibiting the weakest but still meaningful positive influence.

5.5. Prediction of Coupling Coordination Degree

The predicted values of the coupling coordination degree of new quality productive forces enabling high-quality development in each city of Hebei Province in 2023–2027 are derived from Equations (14)–(27), as shown in Figure 5. According to the calculation, the relative error values are all less than 0.2, the a posteriori difference ratios C values are all less than 0.1, and the probability of small error p values is all 1, indicating high prediction accuracy.

As illustrated in Figure 5, the coupling coordination degree values reflecting the empowerment of high-quality development by new quality productive forces in all cities of Hebei Province from 2023 to 2027 exhibit a consistently upward trend. In 2023, the provincial average stood at approximately 0.690, indicating a primary coordination level. Among the cities, Tangshan, Xingtai, Baoding, and Cangzhou had already reached the intermediate coordination level. By 2024, the provincial average had increased to approximately 0.737, reaching the intermediate coordination level, with Cangzhou being the first to transition to the good coordination level. In 2025, the average further rose to approximately 0.786, remaining at the intermediate level, while Tangshan, Baoding, and Cangzhou advanced to the good coordination level. In 2026, the provincial average reached approximately 0.838, indicating a good coordination level, with Tangshan and Cangzhou approaching high-quality coordination. By 2027, the provincial average had increased to approximately 0.891, maintaining the good coordination level. Tangshan and Cangzhou remained at the high-quality coordination level, while Qinhuangdao, Baoding, and several other cities were at the good coordination level. Only Zhangjiakou and Hengshui remained at the intermediate coordination level.

Overall, during the forecast period, the coupling coordination status across cities in Hebei Province transitioned from primary coordination to intermediate, good, and even high-quality coordination. Among these cities, Tangshan—leveraging industrial restructuring and the Cao Feidian industrial cluster advantages—and Cangzhou—benefiting from the Bohai New Area’s port-oriented industrial layout and the industrial transfer and reception dividends of the Beijing-Tianjin-Hebei region—emerged as the leading “pioneers” in advancing coordination levels. In contrast, Zhangjiakou, constrained by ecological protection policies, and Hengshui, hindered by a traditional industrial structure, experienced relatively slower progress in coordination improvement. This spatial disparity clearly illustrates the significant influence of industrial foundations, policy guidance, and locational advantages on the coupling coordination degree between regional new quality productive forces and high-quality development.

5.6. Policy Recommendations for Development

Drawing upon the empirical findings, core driving factors, and projected trends in the coupling and coordination between new quality productive forces and high-quality development in Hebei Province, this section proposes targeted policy recommendations centered on the four key dimensions of “talent—innovation—digital—ecology.” These recommendations aim to advance the coordinated development of the two systems toward a higher and more sustainable level.

5.6.1. Focusing on Industrial Foundations and Implementing Location-Specific Talent Attraction and Cultivation Strategies

Talent serves as the core driver for the high-quality development of new quality productive forces. Given the diverse development foundations and industrial structures across cities, talent attraction and cultivation policies should be designed in alignment with each city’s unique industrial characteristics. For example, Tangshan, as a key hub for the steel industry, should prioritize the recruitment of technical and managerial talents in steel production and equipment manufacturing. Meanwhile, Shijiazhuang, as the center for digital economy development in Hebei Province, should strengthen its efforts to attract professionals in information technology and artificial intelligence. To facilitate the inflow of high-end talents, local governments can implement incentive policies such as tax exemptions and housing subsidies. Furthermore, by collaborating with local universities and vocational institutions, they can cultivate industry-specific talents in a targeted and systematic manner.

5.6.2. Promoting Innovation-Driven Transformation and Supporting Industrial Upgrading Across Cities

Innovation serves as the core driver for the development of new quality productive forces and high-quality growth. Given the heterogeneous innovation demands across cities, innovation investments should be strategically aligned with the technological breakthrough needs of local characteristic industries. For example, Handan should intensify its support for low-carbon transformation technologies in traditional coal and steel industries, while Shijiazhuang ought to accelerate the integration of digital technologies into manufacturing processes. Cangzhou, on the other hand, can prioritize technological innovation in the environmental protection sector. To facilitate such transitions, it is recommended to establish a dedicated innovation fund aimed at encouraging enterprises to deepen collaboration with research institutions, particularly in the development of key enabling technologies—such as intelligent manufacturing and green technologies—that are critical for advancing traditional industries toward high value-added, low-carbon, and environmentally sustainable pathways.

5.6.3. Accelerating Digital Transformation and Promoting Economic Structural Optimization

The digital economy serves as a critical vehicle for advancing new quality productive forces. Given the uneven progress of digitalization across cities, policy interventions should be tailored to local conditions to maximize effectiveness. For example, as the provincial capital, Shijiazhuang should expedite the deployment of 5G infrastructure and artificial intelligence applications to position itself as a regional leader in the digital economy. In contrast, cities such as Xingtai and Baoding can focus on digitizing agriculture and traditional industries to improve production efficiency and increase product value-added. It is recommended to establish a province-wide integrated digital platform to enhance data resource sharing, while encouraging cities to develop localized demonstration zones in key areas such as smart cities, intelligent manufacturing, and smart agriculture based on their unique developmental contexts.

5.6.4. Strengthen Green Development and Promote Ecological Civilization Construction

A sound ecological environment serves as the cornerstone for achieving high-quality development. Given the diverse ecological challenges faced by different cities, tailored policy support should be formulated in accordance with local conditions. For example, Zhangjiakou, with its potential in eco-tourism and renewable energy, should prioritize investments in these areas to drive the growth of green industries. Chengde can concentrate on advancing green agriculture, making full use of its natural resources to improve the sustainability of its regional economy. In heavily polluted cities such as Tangshan and Handan, greater efforts should be directed toward facilitating the green transformation of high-pollution industries through financial incentives and technological upgrades, while also enforcing strict controls on pollutant emissions to ensure a balanced relationship between ecological conservation and industrial development.

6. Discussion and Conclusions

6.1. Discussion

Compared to previous studies, the innovative contribution of this paper lies in three key aspects: the systematic design of the research framework, the original integration of methodologies, and the targeted application of the approach to specific scenarios.

(1)

A systematic perspective on the research framework. While existing literature primarily examines either new-quality productive forces or high-quality development in isolation, or only addresses their partial impacts, this study adopts a comprehensive approach grounded in the context of Hebei Province. It establishes a full-chain research framework encompassing “coupling mechanism—measurement—influencing factors—trend prediction.” First, the coupling mechanism between new-quality productive forces and high-quality development is systematically analyzed from four dimensions—technology, elements, industry, and policy—to clarify the internal logic of their interaction. Subsequently, the current state of regional coordination is assessed using the coupling coordination degree model, with spatial visualization techniques employed to illustrate the dynamic evolution of coordination patterns. Finally, through the identification of driving factors and trend forecasting, the study offers a multidimensional analysis of the interactive relationship, addressing the limitations of prior research that tends to emphasize individual dimensions while overlooking systemic synergy. This framework provides a more holistic analytical paradigm for investigating the interplay between new-quality productive forces and high-quality development at the regional level.

(2)

Integration and innovation of research methods. While existing studies on the relationship between new-quality productive forces and high-quality development largely remain at the stage of calculating the coupling coordination degree, lacking quantitative verification of driving mechanisms and projections of future trends, this study innovatively integrates three analytical tools—the coupling coordination degree model, the random effects Tobit model, and the Grey GM (1,1) model. Centered on the coupling coordination degree model, the study first assesses the coordination status of the two systems using a combined weighting system based on the entropy value and grey relational analysis. The resulting coordination index is then introduced as the dependent variable into the random effects Tobit model to identify key influencing factors. Finally, the Grey GM (1,1) model is employed to forecast future development trends. This integrated approach establishes a “measurement–explanation–prediction” closed-loop paradigm, offering a more systematic and coherent methodological reference for similar studies.

(3)

The targeted value of the research scenario. While existing studies predominantly focus on regions such as the Yangtze River Delta or adopt a national-level perspective, few specifically examine resource-based provinces characterized by the high concentration of traditional industries and significant transformation pressures. As a result, the practical applicability of their findings remains limited in such regions. This study selects Hebei Province as a representative case. As a core region for China’s steel and coal industries, Hebei not only confronts stringent constraints in ecological and environmental protection but also faces the urgent challenge of accelerating the transformation and upgrading of its traditional industrial base. Therefore, the research context offers enhanced practical relevance. The findings of this study not only serve as a scientific reference for policy formulation in Hebei but also provide an actionable pathway for other similar resource-based regions seeking to promote the coordinated development of new-quality productive forces and high-quality growth.

Although this study has achieved certain advancements, several limitations remain to be addressed:

(1)

Limitations in the construction of the indicator system. As a dynamically evolving and advanced form of productive forces, new-quality productive forces are measured in this study through a framework based on three dimensions—digitalization, technology, and sustainability. However, due to the rapid development of emerging fields such as data elements and large-scale artificial intelligence models, the selected indicators may not fully capture all aspects of their evolving nature. Similarly, in the evaluation of high-quality development, although an indicator system has been established across five dimensions—innovation, coordination, environmental sustainability, openness, and inclusiveness—it remains challenging to account for all potential influencing factors.

(2)

Limitations in data acquisition. This study primarily relies on macro-level statistical data from provincial and municipal sources, which effectively captures broad regional trends. However, critical micro-level information—such as enterprise innovation input structures and technology conversion efficiency—remains difficult to access due to commercial confidentiality. Additionally, qualitative data reflecting residents’ subjective experiences of high-quality development are limited in availability, as constraints related to survey costs and sample representativeness hinder the systematic collection of such information within the analytical framework.

(3)

Limitations of the research scope. This study selects Hebei Province as a case for analysis. As a resource-based province characterized by the agglomeration of traditional industries, Hebei demonstrates a certain degree of representativeness in the cultivation of new-quality productive forces and the transition toward high-quality development, offering a concrete example for addressing the bottlenecks in kinetic energy transformation within resource-dependent regions. However, China’s regional development exhibits significant heterogeneity. In the eastern coastal regions, new-quality productive forces are primarily driven by the integration of digital technologies and high-end industries, whereas in the western regions, the development of such productive forces emphasizes green transformation and the upgrading of distinctive local industries.

Future research can be further expanded in several aspects:

(1)

Establish a dynamic and adaptive mechanism for indicator updates. By collaborating with universities, research institutions, and government statistical departments, this approach should reference authoritative standards such as the National Bureau of Statistics’ “Classification of New Industries, New Business Forms, and New Models.” It aims to monitor evolving trends in frontier areas such as the digital economy and green technologies, and to update system indicators on a phased and systematic basis.

(2)

Explore pathways for acquiring microdata and qualitative data. To obtain enterprise-level microdata, collaborations can be formed with the Hebei Provincial Department of Industry and Information Technology and the Department of Science and Technology. These partnerships would enable targeted surveys in key industries such as steel production, equipment manufacturing, and green energy, while ensuring data confidentiality through formal agreements to protect enterprise information. For subjective data from residents, Python 3. 10. 0-based web scraping techniques can be employed to extract textual content from social media platforms, which can then be quantified using sentiment analysis models. This approach would help address the current gap in qualitative data within existing research.

(3)

Strengthen cross-regional comparative research. Building on the case study of Hebei Province, this research recommends conducting comparative analyses across other representative regions, such as the eastern coastal and western regions, to uncover spatial patterns of coupling and coordination between new-quality productive forces and high-quality development. This approach would help identify the contextual applicability of distinct development models—such as “digital integration-driven” and “green transformation-driven”—and provide more comprehensive theoretical foundations for formulating differentiated policies at the national level.

6.2. Conclusions

Grounded in the international context of global economic restructuring and the rapid transformation of the science and technology industry, as well as the domestic background of China’s high-quality development strategy and the ongoing transformation of traditional industries in Hebei Province, this study investigates the interactive relationship between new quality productive forces and high-quality development. A comprehensive research framework is established, encompassing “mechanism analysis—coupling measurement—spatiotemporal evolution—factor analysis—trend prediction.” This framework elucidates the coupling mechanisms and developmental patterns between these two dimensions. Based on a multi-dimensional indicator system and the integration of multiple models, empirical analyses are conducted, offering theoretical insights and methodological references to help resource-dependent regions overcome bottlenecks in transforming their economic driving forces.

At the application level, a sequential analytical approach was implemented using the coupling coordination degree model, the Tobit model, and the grey prediction model. The coupling coordination degree model revealed that the average coordination level increased from moderate disharmony in 2013 to primary coordination in 2022, representing a three-grade advancement over the decade. Spatiotemporal evolution analysis further illustrated a transformation in regional coordination patterns—from an imbalanced “south-high-north-low” distribution to a “central region rise” phase, and ultimately toward a trend of “province-wide synergy.” The random effects Tobit model confirmed that urbanization development ($X_2$), scientific and technological R&D ($X_3$), and government intervention ($X_6$) are the key drivers through which new quality productive forces enhance high-quality development. Additionally, the grey prediction model projected that the coupling coordination degree across cities in Hebei Province would grow at an average annual rate of 6.6% over the next five years. By 2027, the provincial average is expected to reach a “good coordination” level, with certain regions advancing to the “high-quality coordination” stage, thereby forming a comprehensive trend of synergistic optimization in high-quality development.

From a practical perspective, this study offers a scientifically rigorous theoretical foundation for the formulation of differentiated regional development policies in Hebei Province. Taking Tangshan City as an example, which has demonstrated a high level of regional coordination, the city can leverage the strategic location advantage of Caofeidian District to establish a green and intelligent steel research and development base. This objective can be achieved through the allocation of dedicated funding to support the research, development, and application of digital twin factories and hydrogen metallurgy technologies, thereby advancing industrial intelligence and fostering the growth of green and sustainable industries. Benefiting from the spillover effects of innovation resources from the Xiongan New Area, Baoding City can facilitate the construction of vehicle-infrastructure coordination platforms by new energy vehicle enterprises and promote breakthroughs in core battery technologies. Supported by scientific and technological innovation, these efforts will accelerate the cultivation and development of high-end industrial clusters. For regions with relatively low coordination levels, such as Zhangjiakou, it is recommended to fully utilize the policy opportunities associated with the ecological barrier construction in northern Hebei by integrating local ecological resources and clean energy advantages to drive industrial structure optimization and upgrading. Furthermore, based on the functional positioning of the ecological conservation zone in northern Hebei, policy priorities should focus on establishing mechanisms for ecological value conversion and cultivating renewable energy industries. These differentiated policy pathways not only align with the unique resource endowments and development foundations of each region but also center on core driving factors such as technological innovation and green transformation. They collectively provide an actionable and replicable model for promoting the synergistic development of new quality productive forces and high-quality growth in Hebei Province and similar resource-based regions.