Synergistic Evolution or Competitive Disruption? Analysing the Dynamic Interaction Between Digital and Real Economies in Henan, China, Based on Panel Data

Abstract

In the digital transformation era, understanding the relationship between digital and real economies is vital for regional development. This study analyses the interaction between these two economies in Henan Province using panel data from 18 cities (2011–2023). It incorporates policy support intensity through fuzzy set theory, applies an integrated weighting method to measure development levels, and uses regression models to assess the digital economy’s impact on the real economy. The coupling coordination degree model, kernel density estimation, and Gini coefficient reveal the coordination status and spatial distribution, while the ecological Lotka–Volterra model identifies the symbiotic patterns. The key findings are as follows: (1) The digital economy does not directly determine the state of the real economy. For example, cities such as Zhoukou and Zhumadian have low digital economy levels but high real economy levels. However, the development of the digital economy promotes the real economy without signs of diminishing returns. (2) The two economies are generally coordinated but differ spatially, with greater coordination in the Central Plains urban agglomeration. (3) The digital and real economies exhibit both collaboration and competition, with reciprocal mutualism as the dominant mode of integration. These insights provide guidance for policymakers and offer a new perspective on the integration of both economies.

1. Introduction

The rapid rise of the digital economy (DE) has reshaped the global economic landscape, blurring the boundaries between traditional industries and digital technologies. The report of the 20th National Congress of the Communist Party of China emphasises the need to accelerate the construction of Digital China, promote the deep integration of the digital economy with the real economy (RE), and encourage the widespread application of digital technologies across various sectors of economic and social development. Guided by policies, China has emerged as one of the world’s largest digital economies and is currently at a critical juncture of transitioning from high-speed growth to high-quality development. Its vast geographic expanse, notable urban-rural disparities, and diverse and complex market environment have not only created unique opportunities to transform the digital economy and integrate it with the real economy but have also posed numerous challenges. The practical experiences and lessons accumulated during this transformation offer highly valuable references for other developing countries. By 2023, the scale of China’s digital economy reached CNY 53.9 trillion, accounting for 42.8% of the GDP and ranking second in the world. The penetration rates of the digital economy in China’s primary, secondary, and tertiary industries have reached 10.78%, 25.03%, and 45.63%, respectively, driving varying degrees of improvement across different sectors. The penetration of the digital economy into the real economy not only effectively supports stable economic growth but also indicates that the coordinated development of both is the core direction for future economic development. In this context, exploring the dynamic interaction between the digital economy and the real economy is highly important for evaluating the quality of economic development.

Henan Province is a major agricultural and heavily populated province in China that serves as a good example for studying how the digital economy and the real economy interact. Henan has a population of over 99 million with a population density of 600 people per square kilometre. Its cultivated land area accounts for 6.2% of the country’s total, and the province produces 10% of the nation’s grain. This dual identity shapes Henan’s unique economic landscape. In recent years, given the benefits of its unique geographic advantage of being located in the Central Plains, its position as a vital link that connects the east and the west as well as the south and the north, its status as a transportation hub supported by the Zhengzhou Airport Economy Comprehensive Experimental Zone, and further policy support such as the national strategy for the Rise of Central China and digital agriculture initiatives, Henan’s transformation has become increasingly clear. On the one hand, as a traditional major agricultural province, it empowers agricultural modernisation with digital technologies; on the other hand, leveraging its geographic advantages, it fosters new forms of digital economy centred on e-commerce and logistics. Nevertheless, the industrial structure, where traditional agriculture and manufacturing still account for over 40% of GDP, coupled with a dense population, has imposed particularly prominent pressure on employment restructuring during the digital transformation process, which poses challenges for the integrated development of the digital economy and the real economy. Although the high population density facilitates the rapid popularization of digital technologies, it also amplifies the demand for employment opportunities. Moreover, the reduction in jobs in the traditional real-economy industries due to the development of the digital economy further exacerbates this contradiction [1]. Balancing the relationship between the digital economy and the real economy to promote a sustainable economic development is of particular importance.

Although the literature has underscored the potential of the digital economy to drive innovation and efficiency, the nature of its interaction with the real economy remains a subject of debate, particularly across different countries and regions. In developed nations such as the United States and Germany, the digital economy has become deeply embedded in traditional industries through the industrial internet (e.g., Germany’s “Industry 4.0”) and artificial intelligence technologies, substantially increasing production efficiency [2]. However, this has also led to the automation-driven displacement of some low-skilled jobs. Scholars have noted that in developed regions, the relationship between the digital economy and the real economy generally follows an inverted-U shape. In the early stages, digital technologies significantly increase productivity, but as they enter the deployment phase, these marginal effects diminish, even giving rise to the “Solow paradox” in the new era [3]. In contrast, some developing countries, such as India, leverage their vast young labour force, abundant software talent pool, and unique resources to gain significant advantages in certain sectors of the digital economy, such as digital service outsourcing. The paths for integrating the digital economy with the real economy in these countries are diverse, yet countries are generally hindered by the lagging infrastructure, which restricts the depth and speed of the integration between the digital economy and the traditional industries [4]. In China, driven by policy initiatives, a massive market size, and rapid technological advancements, the digital economy is accelerating its integration with the real economy, albeit with regional disparities. In the eastern coastal regions, such as the Guangdong, Zhejiang, and Jiangsu provinces, favourable industrial foundations, innovative environments, and policy support have yielded remarkable results in integrating the digital economy with the real economy. New business forms, including e-commerce, intelligent manufacturing, and digital finance, have flourished, driving the transformation and upgrading of traditional industries. However, disparities in the digital infrastructure development and the digital talent reserves between the central and western regions and their eastern counterparts have resulted in a relatively lagging integrated development, highlighting the pronounced regional imbalances [5].

The digital economy has undeniably contributed to the development of traditional industries, particularly in areas such as smart manufacturing and e-commerce, where it has facilitated structural adjustments and upgrades [6,7,8]. The driving mechanisms may include the increased levels of innovation [9,10], total factor productivity [11,12], or labour productivity [13], or may result from the interaction between the digital economy and these factors, collectively advancing the progress of the real economy. Conversely, the real economy also provides the services, talent, and platforms that support the development of the digital economy, enabling it to improve resource allocation and utilisation efficiency in the real economy. As a result, we can infer that there is a mutual influence between the digital economy and the real economy [14]. Research on the coupling and coordinating relationships between the two can provide valuable insights into their mutual influence. However, these relationships often exhibit regional disparities. Driven by the digital economy, developed regions such as Zhejiang have witnessed a relatively rapid transformation and upgrading of their real economies. In contrast, in underdeveloped regions, due to a lack of infrastructure and talent resources, the coordination between the digital economy and the real economy tends to be weaker [15,16]. Henan Province in particular is considered an underdeveloped region. Moreover, due to its high population density, it is possible that the digital economy may have a non-positive impact on the development of the real economy in Henan Province. The digital economy is widely considered a virtualized form of economic activity [17]. Without effective integration into the real economy, its distinct advantages may remain unrealized. Furthermore, given the finite societal resources, inadequate coordination among the digital economy, the real economy, and the resource environment impedes their synergistic development. Thus, sustainable economic growth is driven primarily by a synergistic symbiosis between these two economies rather than by the dominance of one over the other.

To study the interaction between the digital economy and the real economy, it is essential to conduct a scientific assessment of their development levels. Foreign-related methodologies and indicator systems emphasize their international comparability and the contributions of the two economies to macroeconomic growth. For instance, the OECD focuses on approaches such as the system of health accounts and indicators, such as the investment proportion and the application efficiency of information and communication technologies (ICT) in traditional industries with an emphasis on the “inherent attributes” of the digital economy [18]. In contrast, domestic approaches in China demonstrate a greater practical adaptability, primarily utilising comprehensive indicator systems and applying methods such as entropy–TOPSIS for measurement while accounting for regional and industrial disparities. Notably, most Chinese studies on the measurement of the digital economy predominantly adhere to the classification criteria set by the Communication Institute using indicators such as digital infrastructure, digital industrialisation, and industrial digitalisation [19,20,21]. Only a few researchers have considered the impact of policies on the digital economy. Although some institutions have measured the development level of the digital economy, the results have not been fully disclosed, leaving scholars to collect and measure data independently. Consequently, some indicator systems suffer from deficiencies and lack comprehensiveness. Nevertheless, policies play a non-negligible role in the research on the digital economy and the interaction between the digital and real economies [22,23]. Setting aside the policy factors, the indicator data used by scholars are mostly from relatively developed countries or provinces with significant internal disparities [24], while research at the city level is relatively scarce, and studies specifically focusing on Henan Province are even rarer. Admittedly, the research on developed regions can serve as a guide and reference for other areas. However, less developed regions also warrant attention because they are more likely to reveal structural contradictions. Furthermore, there are numerous less developed regions like Henan Province [25], and research on Henan can provide insights for the other underdeveloped areas. Methodologically, the existing research primarily applies regression models such as fixed effects and mediation effects [26,27,28], which are limited to theoretical discussions, pathways of influence, and relationship promotion [29,30], with little focus on the symbiotic model between the two economies. Therefore, there is an urgent need for research in this area to analyse their interactive relationship systematically and comprehensively.

The contributions of this study primarily include three key aspects.

First, the evaluation index system incorporates qualitative indicators such as policy. Based on preliminary research, fuzzy set theory is used to assign values to the policy indicators, and the entropy-weighted hierarchical analysis method is applied to assign weights to the index system while considering factors such as expert position, educational background, and years of work experience.

Second, this study explores the mechanism of the digital economy’s impact on the real economy from multiple perspectives, including how the digital economy boosts the real economy, the spillover effects of the digital economy on the real economy, and the interaction between the digital economy and other factors that affect the real economy.

Third, this study examines a symbiotic model of the deep integration between the digital economy and the real economy. Current research on the interaction between the digital economy and the real economy has focused mainly on the positive effects of coordinated development with an insufficient exploration of the competitive relationships and factor constraints beyond their collaboration. This study constructs a digital economy–real economy symbiotic system that considers both the competition and the cooperation between the digital economy and the real economy and identifies the key factors for their mutual benefit and symbiosis.

The remainder of this study is structured as follows: Section 2 measures the development levels of the digital economy and the real economy. Section 3 discusses the mechanism of the digital economy’s impact on the real economy. Section 4 analyses the coordinated relationship and the spatial heterogeneity between the digital economy and the real economy. Section 5 explores a symbiotic model of a deep integration of the digital economy and the real economy. Finally, the study concludes with implications and conclusions.

2. Measurement of the Development Level of the Digital Economy and the Real Economy

2.1. Construction of the Indicator System and Data Sources

2.1.1. Indicator System Design

From a broad perspective, this study supplements the factor of “policy support intensity” in the field of digital economy, based on the research of relevant scholars [31,32,33,34], to improve the evaluation index system for the development level of the digital economy. The indicators are divided into five sections, namely the digital infrastructure, industrial digitalisation, digital industrialisation, digital innovation capability, and policy support intensity, with the specific indicators listed in

Table 1. Evaluation index system for the development level of the digital economy.

Primary Indicators	Secondary Indicators	Indicator Description and Unit	Direction	Comprehensive Weight
Digital infrastructure	Internet penetration rate	Households with broadband access/total number of households (%)	+	0.042
	Smartphone penetration rate	Mobile phone subscribers/total number of households (%)	+	0.033
	Per-household mobile telephone exchange capacity	Mobile telephone exchange capacity/total number of households (%)	+	0.040
	Logistical infrastructure’s development level	Total length of postal routes/area (kilometres per square kilometre)	+	0.114
Industry digitalisation	E-commerce sales performance	E-commerce sales per capita (CNY billions/10,000 people)	+	0.062
	Digital inclusive finance development index	Digital inclusive finance development index	+	0.027
	Website penetration rate	Number of websites per one hundred enterprises (units)	+	0.022
	Computer penetration rate	Number of computers per one hundred employees in enterprises (units)	+	0.031
Digital industrialisation	Per capita telecom service volume	Telecommunications business volume/total population (CNY/person)	+	0.047
	Number of enterprises in the digital industry	Number of enterprises in the information transmission, software, and information technology services industry (units)	+	0.073
	Number of employees in the digital industry	Average number of employees in the information transmission, software, and information technology services industry at the end of the year (persons)	+	0.063
	Per capita express delivery revenue	Volume of express delivery services/total population (parcels/person)	+	0.038
Digital innovation capability	Technology market’s transaction volume	Transaction volume of the technology market (CNY 10,000)	+	0.102
	Number of invention patents	Number of valid invention patents (units)	+	0.076
	Number of research and experimental development (R&D) personnel	Full-time equivalent (FTE) of R&D personnel (person-years)	+	0.050
	Status of R&D projects	Number of R&D projects (items)	+	0.062
Policy support intensity	Policy support intensity	Policy support intensity	+	0.118

. For the real economy, the indicators are divided into four sections, namely the development scale, innovation capability, quality and efficiency, and employment status, with the specific indicators listed in

Table 2. Evaluation index system for the development level of the real economy.

Primary Indicators	Secondary Indicators	Indicator Description and Unit	Direction	Comprehensive Weight
Development scale	Industrial output value	Value of output of all industries except the financial industry/total GDP (%)	+	0.068
	Number of enterprises	Total number of enterprises in the primary, secondary, and tertiary industries (units)	+	0.080
	Consumption level	Per capita consumption expenditure/per capita income ratio (CNY/person)	+	0.027
	Investment status	Total investment in fixed assets by the entire society except the financial industry (CNY billion)	+	0.060
Innovation capability	Agricultural modernisation	Total power of agricultural machinery (10,000 kilowatts)	+	0.058
	Industrial modernisation	R&D expenditure of industrial enterprises above the designated size (CNY 10,000)	+	0.086
	Service industry modernisation	Proportion of enterprises engaged in e-commerce (%)	+	0.049
	Status of innovation activities	Number of enterprises engaged in innovation activities above the designated size/total number of surveyed enterprises (%)	+	0.043
	Proportion of technology expenditure	Scientific and technological expenditure/total government expenditure (%)	+	0.062
Quality and efficiency	Industrial efficiency enhancement	Per capita value added in the real economy’s industries (CNY 10,000/person)	+	0.059
	Assets and liabilities	Total assets and liabilities of enterprises above the designated size in industries such as industry, construction, and real estate (CNY billion)	-	0.073
	Corporate profit	Total profit of enterprises above the designated size in wholesale and retail, accommodation, catering, etc. (CNY billion)	+	0.145
	Innovation benefits	Sales revenue of new products (CNY 10,000)	+	0.032
	Resource consumption	Energy consumption per unit of GDP (ton/CNY)	-	0.042
Employment status	Employment structure	Proportion of employees in the real economy (excluding financial industry employees) (%)	+	0.042
	Employee wages	Average wage of urban employees (CNY)	+	0.038
	Employment stability	Registered unemployment rate of each city and town (%)	-	0.037

.

In constructing the digital economy indicator system, we draw the digital infrastructure metrics from the Digital China Development Report (2021). For those indicators related to industrial digitisation and digital industrialisation, we integrate the criteria from three key sources: the Statistical Classification of Digital Economy and Its Core Industries (2021) issued by China’s National Bureau of Statistics, the aforementioned Digital China Development Report (2021), and the relevant scholarly studies [33,34]. Regarding the real economy indicator system, its core dimensions—including development scale, innovation capacity, quality and efficiency, and employment status—are primarily based on the framework established by Zeng et al. [31,32], with enhancements such as the addition of an employment stability metric.

In terms of the innovation capability indicator for the real economy, since the real economy is composed primarily of core industries across three major sectors, and particularly the secondary sector, the innovation capacity within the real economy is primarily evaluated based on the modernisation and innovation activities of agriculture, industry, and services. Notably, some studies of the quality and efficiency of the real economy consider only the assets, liabilities, and corporate profits of the secondary sector. In reality, however, in addition to the secondary sector, most parts of the primary and tertiary sectors fall within the scope of the real economy [35]. For the digital innovation capacity, this study posits that at the current stage, as a product of the new era, the innovation capacity of digital technology should advance further in terms of modernisation and technological innovation, with a particular emphasis on “scientific and technological research” as the starting point. The Global Industrial Innovation Ecosystem Development Report 2022 also highlights that the innovation capacity of digital technology is inseparable from the input and output of scientific and technological research and explicitly incorporates full-time equivalent research personnel, research and development (R&D) expenditure, the number of invention patents, and the transaction volume of technology contracts as components of the evaluation index for the regional digital innovation capacity. Therefore, this paper primarily considers these four indicators when constructing a framework for the digital innovation capacity.

Additionally, regarding those indicators related to e-commerce, compared with e-commerce sales volume, the proportion of the enterprises engaged in e-commerce transactions better reflects the structural transformation of the economic entities. Essentially, it indicates the innovation willingness of real economy enterprises, falling under the category of supply-side innovation. In contrast, the sales volume represents the demand-side expansion driven by digitalisation. According to the Statistical Classification of Digital Economy and Its Core Industries (2021), traditional manufacturing, agriculture, logistics, and other industries have seen improvements in their output and efficiency after applying digital technologies, but “the inherent attributes of these industries remain unchanged” [36]. Therefore, this paper uses the proportion of enterprises engaged in e-commerce transactions as an indicator to measure the innovation capability of the real economy and classifies the e-commerce sales volume as part of the industrial digitalisation.

2.1.2. Data Sources

First, for this study, three experts were invited to independently evaluate the policies and the indicator system. Expert one was from a government department, while experts two and three were affiliated with institutions of higher education. For detailed information on the experts’ basic profiles and the AHP calculation process, please refer to the attachments. In terms of the objective data, this study utilised panel data from 18 prefecture-level cities in Henan Province spanning the period 2011–2023 as the basis for determining the indicator weights using the entropy weight method. The relevant data originate primarily from the Henan Statistical Yearbook and statistical bulletins. For specific indicators, such as the Digital Financial Inclusion Index, data are sourced from the Digital Finance Research Centre at Peking University [37], while the number of invention patents is obtained from the Henan Provincial Intellectual Property Office. In instances of missing data, interpolation methods are applied to fill in the intermediate values, and functional methods are used for end-point values. In cases where the annual data for certain indicators are missing but the total provincial figures are available in the Henan Statistical Yearbook or the China Statistical Yearbook, estimates for the individual prefecture-level cities are derived accordingly.

With regard to the subjective data, this study collected and compiled the number of official documents related to the digital economy issued by the Henan provincial government and the governments of various prefecture-level cities from 2011 to 2023. Based on this, the three experts were invited to score the following two aspects: 1. the importance of the indicators for the digital economy and the real economy (using a scale from 1 to 9), and 2. the strength of the policy support for the digital economy (using a rating scale).

2.2. Horizontal Measurement

2.2.1. Fuzzy Set Theory

In policy evaluations, expert scoring often involves fuzzy concepts. The “policy support strength” is difficult to measure with a specific score, and different experts may have varying opinions on it (for example, some experts may tend to assign high scores, while others may lean towards low scores). Therefore, this study systematically processes expert scores using fuzzy set theory to reduce the bias introduced by subjectivity and to improve the scientific rigor and repeatability of the evaluation. The specific approach is as follows: Expert scores are mapped to fuzzy sets, and their fuzziness is quantified using triangular fuzzy numbers. Experts are assigned different weights based on their educational background, years of work experience, professional title, and relevance of expertise, which helps to reduce the impact of inconsistencies. Finally, defuzzification is conducted using the centroid method to obtain specific numerical values. Expert weights are calculated using Formulas (1) and (2), triangular fuzzy numbers are determined by Formula (3), and the defuzzification process follows Formulas (4) and (5). The scoring criteria are shown in

Table 3. Expert scoring criteria.

Factor	Category	Score
Educational background	Doctoral degree	4
	Master’s degree	3
	Bachelor’s degree	2
	Associate’s degree and below	1
Years of work experience	≥20 years	4
	10–19 years	3
	5–9 years	2
	<5 years	1
Professional title	Senior professional	4
	Associate senior professional	3
	Mid-level professional	2
	Junior professional and below	1
Relevance of expertise	Highly relevant	4
	Relatively relevant	3
	Generally relevant	2
	Barely relevant	1

, and the fuzzy function classification is presented in

Table 4. Division of fuzzy functions.

Comment Level	Triangular Fuzzy Number
I	(0, 1, 2)
II	(1, 2, 3)
III	(2, 3, 4)
IV	(3, 4, 5)
V	(4, 5, 6)
VI	(5, 6, 7)
VII	(6, 7, 8)
VIII	(7, 8, 9)
IX	(8, 9, 10)

.

$$S_i=S_{ei}+S_{si}+S_{pi}+S_{ri}$$

(1)

$$W_i=S_i/{\displaystyle \sum _{i=1}^m{S}_i}$$

(2)

where $S_i$ represents the expert’s total weighted score, $S_{ei}$ denotes the expert’s educational background, $S_{si}$ represents the expert’s years of work experience, $S_{pi}$ indicates the expert’s professional title, $S_{ri}$ refers to the expert’s relevance of expertise, and $W_i$ is the expert’s weight.

$$F(x)=\left\{\begin{array}{c}{\displaystyle \frac{x-b_{11}}{b_{12}-b_{11}}},b_{11}\le x\le b_{12}\\ {\displaystyle \frac{b_{13}-x}{b_{13}-b_{12}}},b_{12}\le x\le b_{13}\\ 0,otherwise\end{array}\right.$$

(3)

where $F(x)$ is the fuzzy function, $x$ is the fuzzy variable, $b_{11}$ is the left-side fuzzy number, $b_{12}$ is the central fuzzy number, and $b_{13}$ is the right-side fuzzy number.

$$A={\displaystyle \sum _{i=1}^m{W}_i\times }{A}_i$$

(4)

$$X={\displaystyle \frac{\int g(x)xdx}{\int g(x)dx}}$$

(5)

where $A$ is the comprehensive fuzzy number, $m$ is the number of experts, $W_i$ is the expert’s weight, $A_i$ is the expert’s fuzzy number, $X$ is the defuzzified output, $g(x)$ is the membership function, and $x$ is the output variable.

2.2.2. Entropy-Analytic Hierarchy Process Integrated Weighting Method

As previously mentioned, this study uses both objective and subjective data. The objective data are measured using the EWM, while the subjective data are measured using the AHP. The EWM calculates weights based on the data itself, exhibiting low subjectivity and a strong adaptability to diverse datasets. It can handle multiple indicators, including those of varying natures (e.g., positive and negative indicators). However, it relies entirely on the objectivity of the data. If a particular indicator has a high degree of dispersion, its corresponding weight will also be relatively large [38]. Additionally, this method may overlook implicit factors such as policies and institutional arrangements. Paradoxically, the exclusive use of objective methods can introduce a form of subjectivity. In contrast, the AHP constructs judgement matrices through expert scoring, incorporating critical yet difficult-to-quantify factors such as policies and fully leveraging the expert experience. However, the AHP is highly subjective and prone to human biases. The integration of the entropy method and the AHP represents a collaboration between data-driven patterns and human wisdom. Objectivity devoid of subjectivity is not truly objective, just as subjectivity detached from objectivity ceases to be genuinely subjective. Therefore, this study combines the EWM with the AHP, incorporating the expert weights $W_i$ from Formula (2) into the AHP. The choice of $\alpha$ = 0.5 is made, the composite weights of the digital and real economies’ indicators are calculated, and subsequently, the overall scores of the digital and real economies are determined. The specific steps are as follows:

• Calculate the subjective weight $w_a$.

(1)

Based on the experts’ scores, a first-level judgement matrix is constructed (where the policy support intensity is represented by the quantized values of the fuzzy set, while the remaining indicators utilise the original scores).

$$C=\left[\begin{array}{cccc}{c}_{11}& c_{12}& \dots & c_{1n}\\ c_{21}& c_{22}& \dots & c_{2n}\\ ⋮& ⋮& & ⋮\\ c_{n1}& c_{n2}& \dots & c_{nn}\end{array}\right]$$

(6)

where $c_{ij}$ represents the importance value of indicator $Y_i$ compared to indicator $Y_j$.

(2)

A consistency check is performed. The judgement matrix involves pairwise comparisons of multiple indicators, which may lead to contradictions. Therefore, a consistency check is required.

$$I_C={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(7)

$$R_C=I_C/I_R$$

(8)

where ${\lambda }_{\max }$ is the maximum eigenvalue of the judgement matrix, n is the number of indicators, and $I_R$ is the average random consistency index. If the consistency ratio $R_C$ < 0.1, the judgement matrix passes the consistency check.

(3)

Based on the judgement matrix, the weights of the indicators are calculated as follows. First, the arithmetic mean of each row in the judgement matrix is computed:

$$\overline{w_i}=\sqrt[n]{{\displaystyle \prod _{j=1}^n{c}_{ij}}}$$

(9)

Then, these arithmetic means are normalised to obtain the weights:

$$w_i=\overline{w_i}/{\displaystyle \sum \overline{w_i}}$$

(10)

Similarly, the weights of the secondary indicators are calculated.

(4)

Calculate the weighted overall subjective weights $w_a$.

$$w_s=w_{\mathrm{I}}{w}_{\mathrm{II}}$$

(11)

$$w_a={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m{w}_s{W}_i}$$

(12)

where m is the number of experts, $w_{\mathrm{I}}$ represents the weights of the first-level indicators, $w_{\mathrm{II}}$ represents the weights of the second-level indicators, $w_{s1}$, $w_{s2}$, and $w_{s3}$ (for s = 1, 2, etc.) denote the weights of each indicator calculated based on the scores provided by expert one, expert two, and expert three, respectively, and $W_i$ is the weight assigned to each expert.

2.

Calculate the objective weights.

(1)

Standardise the objective data. If the indicator is positive (higher values are better), use the positive standardisation:

$$a_{ij}={\displaystyle \frac{y_{ij}-\min y_{ij}}{\max y_{ij}-\min y_{ij}}}$$

(13)

If the indicator is negative (lower values are better), use the negative standardisation:

$$a_{ij}={\displaystyle \frac{\max y_{ij}-y_{ij}}{\max y_{ij}-\min y_{ij}}}$$

(14)

where $y_{ij}$ is the original data, and $a_{ij}$ represents the standardised data.

(2)

Calculate the proportion of each indicator value.

$$p_{ij}={\displaystyle \frac{a_{ij}}{{\displaystyle \sum _{i=1}^n{a}_{ij}}}}$$

(15)

(3)

Calculate the information entropy.

$$E_j=-{\displaystyle \frac{1}{\ln n}}{\displaystyle \sum _{i=1}^n{p}_{ij}}\ln p_{ij}$$

(16)

(4)

Calculate the objective weights of each indicator.

$$w_e={\displaystyle \frac{1-E_j}{{\displaystyle \sum _{i=1}^n(1-E_j)}}}$$

(17)

3.

Calculate the composite weight based on Formula (18).

$$w=\alpha w_a+(1-\alpha )w_e$$

(18)

4.

Calculate the composite score $Q_i$.

$$Q_i={\displaystyle \sum _{i=1}^n{w}_i{a}_{ij}}$$

(19)

where $a_{ij}$ represents the normalised data. The normalisation method used is min–max normalisation.

2.3. Robustness Test of Indicators

Considering the potential correlations among the indicators, this study uses principal component analysis (PCA) to extract the principal components from the indicator system and recalculates the weights of each indicator based on the indicator data. The detailed intermediate processes and results are shown in the appendices. The analysis reveals that, with the exception of the indicator “policy support intensity,” the discrepancies between the weights derived from the PCA and the comprehensive weights are all within 10%, confirming the relative robustness of the original indicator system. Notably, the differences between the weights obtained through the PCA and those from the AHP are even smaller, with some indicators showing a difference as low as 0.0001. This further corroborates the high level of expertise demonstrated by the three scoring experts selected for this study in understanding the interrelationships and relative importance of the indicators.

2.4. Measurement Results and Analysis

The comprehensive scores of the development levels of the digital economy and the real economy in Henan Province obtained using the EWM-AHP measure are shown in

Table 5. Comprehensive scores of the development levels of the digital economy and the real economy in Henan Province.

City	2011		2014		2017		2020		2023
	DE	RE	DE	RE	DE	RE	DE	RE	DE	RE
Zhengzhou	0.282	0.441	0.413	0.541	0.553	0.614	0.792	0.728	0.867	0.788
Kaifeng	0.062	0.275	0.133	0.324	0.164	0.329	0.232	0.370	0.266	0.447
Luoyang	0.130	0.334	0.220	0.369	0.289	0.407	0.379	0.483	0.409	0.554
Pingdingshan	0.068	0.254	0.142	0.286	0.197	0.298	0.261	0.301	0.288	0.318
Anyang	0.080	0.253	0.151	0.285	0.211	0.279	0.260	0.305	0.271	0.328
Hebi	0.087	0.186	0.155	0.231	0.217	0.241	0.286	0.292	0.293	0.326
Xinxiang	0.104	0.270	0.193	0.322	0.245	0.339	0.327	0.370	0.358	0.431
Jiaozuo	0.112	0.261	0.184	0.303	0.259	0.335	0.346	0.301	0.354	0.356
Puyang	0.092	0.235	0.156	0.258	0.215	0.294	0.288	0.291	0.293	0.326
Xuchang	0.069	0.282	0.134	0.333	0.193	0.349	0.276	0.388	0.276	0.426
Luohe	0.072	0.231	0.133	0.281	0.203	0.300	0.270	0.303	0.287	0.398
Sanmenxia	0.092	0.244	0.165	0.299	0.217	0.298	0.300	0.279	0.301	0.330
Nanyang	0.049	0.342	0.121	0.391	0.174	0.421	0.242	0.419	0.272	0.494
Shangqiu	0.047	0.279	0.112	0.309	0.160	0.336	0.227	0.367	0.241	0.382
Xinyang	0.040	0.246	0.095	0.275	0.139	0.302	0.204	0.342	0.247	0.429
Zhoukou	0.025	0.296	0.090	0.333	0.146	0.330	0.209	0.344	0.246	0.388
Zhumadian	0.035	0.302	0.106	0.334	0.152	0.359	0.226	0.403	0.253	0.483
Jiyuan	0.099	0.191	0.181	0.249	0.219	0.267	0.295	0.231	0.299	0.295
Average	0.086	0.274	0.160	0.318	0.220	0.339	0.301	0.362	0.323	0.417

Note: Due to space limitations, only the results from certain years are shown.

. To visualise the spatial differences in the levels of the digital economy and the real economy, ArcGIS 10.2 software was used to create maps illustrating the trends and regional differences between the two from 2011 to 2023. These are shown in Figure 1 and Figure 2.

In the temporal dimension, the development levels of the digital economy and the real economy from 2011 to 2023 have followed an overall fluctuating upward trend. According to Table 5, the digital economy grew from an average of 0.086 in 2011 to 0.323 in 2023, while the real economy increased from 0.274 to 0.417. The fluctuating upward trends of the two economies suggest the existence of a dynamic synergistic relationship between them. Existing analyses of the development trends of China’s digital economy and real economy at the national and regional levels are generally consistent with the findings of this study, but their indicator systems fail to fully consider the key impact of policy factors [39,40]. This study reveals that policy factors should not only be integrated into the logical framework for constructing indicator systems but also that they hold significant sway over the interpretability of the measurement results and the derived policy implications. Some studies have associated the growth of the digital economy and the real economy with technological progress, the expansion of market demand, and the upgrading of industrial structures [8,41]. This study argues that sustained policy empowerment is an equally indispensable factor in the growth of both the digital and real economies. Henan Province has steadily increased its annual fiscal subsidies for rural e-commerce through the “digital rural” pilot programme and has focused on supporting the construction of industrial internet platforms. The 2023 Industrial Internet Report indicates that the number of enterprises connected to industrial internet platforms across the province has surpassed 20,000. While this figure still lags behind Guangdong Province’s 120,000 and Zhejiang Province’s 100,000, it represents a 50% year-over-year increase, a growth rate that exceeds those of both the Guangdong and Zhejiang provinces. Notably, compared to the real economy, the digital economy, despite a later start, has exhibited remarkable growth. For example, in Zhengzhou City, the real economy’s index increased from 0.441 to 0.788, while the digital economy’s index surged from 0.282 to 0.867. The underlying reasons can be attributed to two main factors. On the one hand, policies have driven the advanced deployment of digital infrastructure, such as the construction of the Henan hub node in the “East Data West Computing” project, which has accelerated the technology maturation cycle. On the other hand, policy instruments such as tax incentives and innovation funds, as outlined in the relevant measures within the “Henan Provincial Digital Economy Promotion Regulations,” have effectively reduced the costs for those enterprises undergoing digital transformation. Coupled with the highly permeable nature of digital technologies, these factors have collectively forged a closed-loop mechanism of the late-mover advantage.

In the spatial dimension, Zhengzhou, which benefits from national central city policy dividends such as tax incentives for big data pilot zones and special bonds for digital infrastructure, has consistently maintained a leading position in regional digital economic development and a first-mover advantage. Its surrounding cities, such as Luoyang and Xinxiang, generally score high due to the industrial chain collaboration policies of the Zhengzhou–Luoyang–Xinxiang National Independent Innovation Demonstration Zone. In contrast, peripheral cities such as Zhoukou, which are constrained by uneven policy resource allocation and a lagging digital infrastructure, have a 5G base station density that is only approximately one-sixth that of Zhengzhou, leading to relatively slower digital economic development. This spatial pattern is essentially caused by the regional economic “siphon effect” and “diffusion effect.” As the core city, Zhengzhou creates a siphon effect through policy preferences and continuously attracts factors such as talent and capital from the peripheral areas. As Zhengzhou’s industries are upgraded, its technological spillover and data resource sharing trigger a diffusion effect. Figure 1 and Figure 2 illustrate two intriguing phenomena: (1) In some cities, there is a “downgrading phenomenon” in the development of the digital economy. For example, Sanmenxia was in a higher-value zone in 2011 but was categorized in a middle-value zone in 2023. Additionally, the number of cities in the higher-value and middle-value zones in 2023 was lower than that in 2011. This reflects the “Matthew effect” and the “catching-up effect.” Figure 1 and Table 5 together show that while the number of cities in the higher-value and middle-value zones declined in 2023, the range of digital economic development itself expanded. In other words, the “downgrading” was not equivalent to a “devaluation.” This also indicates that the stronger regions tend to become even stronger. For example, Zhengzhou, leveraging its first-mover advantage, continuously expands its resource aggregation, resulting in continuous growth in the level of the digital economy. However, some regions strive to catch up through policy interventions, leading to the “squeezing out” of certain higher-value zones and resulting in downgrading; (2) cities such as Nanyang and Zhoukou have low levels of the digital economy but strong real economies, which may indicate two issues. First, the economic structure of cities such as Nanyang, Zhoukou, and Zhumadian is lagging, with the traditional industries dominating and insufficient investment in digital transformation. Second, this may indirectly confirm that the development of the digital economy and the real economy does not necessarily follow a completely linear relationship. A higher level of development of the digital economy does not indicate a higher level of real economic development and vice versa.

Based on the above analysis, the following questions can be further raised: Is there a relationship between the digital economy and the real economy? Is their simultaneous growth driven by “coordinated development,” “unidirectional driving,” “bidirectional interaction”, or “symbiotic integration”? Is the development relationship between the digital economy and the real economy truly nonlinear? If so, does the phenomenon of “diminishing marginal returns” exist between the digital economy and the real economy? This article further examines these questions in the following sections.

3. Mechanism of the Impact of the Digital Economy on the Real Economy

3.1. Model Construction

First, to examine the impact of the digital economy on the development level of the real economy, a panel fixed-effects model is constructed:

$$R{E}_{it}={\beta }_0+{\beta }_{1}D{E}_{it}+{\beta }_2{Z}_{it}+{\alpha }_i+{\gamma }_t+{\epsilon }_{it}$$

(20)

where $R{E}_{it}$ represents the composite score of the real economy’s development level for individual $i$ at time $t$, $D{E}_{it}$ denotes the composite score of the digital economy’s development level for individual i at time t, $Z_{it}$ represents the control variables, ${\alpha }_i$ is the individual fixed effect that controls for time-invariant individual heterogeneity, ${\gamma }_t$ is the time fixed effect that controls for individual-invariant temporal heterogeneity, and ${\epsilon }_{it}$ is the random error term.

Second, to explore whether there is a nonlinear development relationship between the digital economy and the real economy, a nonlinear transformation is introduced based on the fixed-effects model. The model is as follows:

$$R{E}_{it}={\alpha }_i+{\beta }_{1}D{E}_{it}+{\beta }_2{Z}_{it}+{\beta }_{3}D{E}_{it}^2+{\gamma }_t+{\epsilon }_{it}$$

(21)

Finally, to explore whether the impact of the digital economy on the real economy varies due to other factors, interaction terms are introduced. The model is as follows:

$$R{E}_{it}={\alpha }_i+{\beta }_{1}D{E}_{it}+{\beta }_2{Z}_{it}+{\beta }_3{L}_{it}+{\beta }_4(D{E}_{it}\times L_{it})+{\gamma }_t+{\epsilon }_{it}$$

(22)

$$R{E}_{it}={\alpha }_i+{\beta }_{1}D{E}_{it}+{\beta }_2{Z}_{it}+{\beta }_3{I}_{it}+{\beta }_4(D{E}_{it}\times I_{it})+{\gamma }_t+{\epsilon }_{it}$$

(23)

$$R{E}_{it}={\alpha }_i+{\beta }_{1}D{E}_{it}+{\beta }_2{Z}_{it}+{\beta }_3{T}_{it}+{\beta }_4(D{E}_{it}\times T_{it})+{\gamma }_t+{\epsilon }_{it}$$

(24)

where $L_{it}$ represents labour productivity, measured as the ratio of regional GDP to the number of employed individuals, $D{E}_{it}\times L_{it}$ is the interaction term between the digital economy’s development level and labour productivity, $I_{it}$ represents the innovation level, measured as the ratio of new product sales revenue to R&D investment, $D{E}_{it}\times I_{it}$ is the interaction term between the digital economy’s level and the innovation level, $T_{it}$ represents the total factor productivity (TFP), and the deflated value is measured using the Cobb–Douglas production function. In this context, the capital input is denoted by the actual fixed capital stock (calculated using the perpetual inventory method), the labour input is represented by the total number of employed individuals in the region, and the output is indicated by the regional GDP.

3.2. Variable Selection and Descriptive Statistics

The core explanatory variables and the dependent variable of the model are the composite scores of the development level of the digital economy and the real economy as measured in the previous section. The relevant control variables are based on existing research. A theoretical analysis and statistical testing are performed to exclude the indicators that are highly correlated with the core explanatory variables or that overlap with the indicator system of this study to avoid information redundancy. Ultimately, four variables are selected: economic growth (GDPG), foreign investment (FDI), human capital (lnLAB), and education level (lnEDU).

Regarding the selection of interaction variables, this study briefly mentions in the theoretical analysis section that the digital economy may enhance the real economy by driving labour productivity [13], innovation [9,10], and total factor productivity (TFP) [11,12], or it may interact with these three factors to influence the real economy. As they evolve, the relationship between the digital economy and the real economy varies under different levels of labour productivity, innovation, and TFP. Conversely, the impacts of labour productivity, innovation, and TFP on the real economy may also differ under varying levels of the digital economy’s development.

• The digital economy comprehensively empowers labour factors through digital technologies, facilitating a transformation in the production mode from labour-intensive to skill-intensive [42], thereby influencing the development of the real economy. The underlying logic lies in the dual “substitution–complementarity” effects of digital technologies on labour skills: low-skilled, repetitive tasks are automated, while the demand for high-skilled positions surges [1]. In the early stages of the digital economy’s development, its enhancement of labour productivity manifests primarily as an “efficiency substitution effect.” As the digital economy advances to a mature stage, its interaction with labour productivity shifts towards a “skill complementarity effect.” Research by the World Bank (Washington, DC, USA) indicates that the role of the digital economy in boosting labour productivity is more pronounced in regions with a well-developed digital infrastructure, a scenario that requires further verification in the context of Henan Province.
• By enabling the flow of data elements and optimising the algorithms, the digital economy reconstructs the allocation mechanism of innovation resources to address the pain points of information silos and resource misallocation in the traditional economy [7]. During the early stages of the digital economy’s development, innovation activities focus on the breakthroughs in the digital technologies themselves, with their empowering effect on the real economy constrained by technological diffusion barriers. As the digital economy matures, the innovation models transition towards integrated innovation that combines the digital technologies and traditional industries. At this stage, the digital platforms serve as integrators of the innovation resources: by connecting the real economy’s entities, they reduce innovation trial-and-error costs, enable “rapid iteration” through feedback loops, and foster a positive cycle of “innovation–application–recurring innovation”, jointly driving the progress of the real economy.
• Digital technologies improve market environments, increase the total factor productivity, and promote the sustainable development of the real economy. Against the backdrop of low TFP, the digital economy’s role may be more pronounced because it can elevate the overall economic efficiency and increase the growth potential of the real economy. As the TFP improves, the digital economy may contribute further by upgrading the factor quality and optimising the factor combinations, adding value to the real economy while also fostering its own development. Moreover, the TFP may improve significantly through the full utilisation and optimised allocation of the data elements, thereby promoting the sustainable development of the real economy [43].

For these reasons, this study selects labour productivity, innovation level, and total factor productivity as the interaction variables. The specific manifestations of these interactions in Henan Province are presented in the following sections.

Table 6. Variable definitions and descriptive statistics.

	Variable	Definition	Variable Description	MIN	MAX	Mean	STD	Median
Explained variable	DE	Real economy development level	Already measured in the preceding text	0.186	0.788	0.342	0.097	0.318
Core explanatory variable	RE	Digital economy development level	Already measured in the preceding text	0.025	0.867	0.22	0.127	0.21
Interaction variable	L	Labour productivity	Regional GDP/Number of employed persons	2.059	21.167	7.791	3.86	7.014
	I	Innovation level	New product sales revenue/R&D investment	1.735	36.689	10.089	6.344	8.979
	T	TFP	Measured using the Cobb-Douglas function	0.443	2.851	1.125	0.534	0.979
Interaction variables for an alternative measurement	L1	Value added per capita	Industry value added/industry employment	2.225	21.167	7.770	3.851	7.052
	I1	Research funding’s intensity	R&D expenditure/GDP	24.827	354.469	127.868	68.469	115.763
	T1	Input-output efficiency	DEA-BCC	0.284	1.000	0.567	0.193	0.538
Instrumental variable	LDE	Level of development of the digital economy lagged by one period	Calculated from the DE’s comprehensive development level	0.162	0.805	0.285	0.121	0.261
Control variable	GDPG	Gross domestic product growth rate	(Current GDP index/Base period’s GDP index − 1) × 100%	−21	15.2	7.303	3.685	8
	FDI	Foreign investment	Actual utilised foreign investment/Regional GDP	12.84	114.27	41.206	23.609	34.565
	lnLAB	Human capital	Logarithm of the end-of-period number of employed persons in urban units	3.76	6.6	5.673	0.704	5.78
	lnEDU	Education level	Logarithm of the number of college students per 10,000 people	3.1	7	4.879	0.747	4.9

shows the descriptive statistics of the main variables in this chapter’s study.

3.3. Analysis of Empirical Results

3.3.1. Baseline Regression Analysis

In this study, a two-way fixed effects model regression was conducted using cluster-robust standard errors at the city level, and the results are shown in

Table 7. Benchmark regression results.

Variable	① RE	② RE	③ RE	④ RE	⑤ RE	⑥ RE	⑦ RE	⑧ RE	⑨ RE
	①–⑥ Are Fixed-Effects Regressions with Control Variables and Quadratic Terms Added Sequentially						⑦–⑨ Are Interaction Regressions
DE	0.613 ***	0.616 ***	0.511 ***	0.554 ***	0.544 ***	0.473 *	1.051 ***	0.538 ***	0.677 ***
	(19.402)	(19.639)	(10.521)	(8.441)	(8.098)	(1.77)	(4.546)	(7.149)	(5.625)
GDPG		0.001	0.000	0.001	0.001	0.001	0.001	0.001	0.000
		(1.058)	(0.385)	(0.535)	(0.670)	(0.662)	(1.211)	(0.702)	(0.472)
FDI			−0.001 **	−0.001 **	−0.001 **	−0.001 **	−0.001 *	−0.001 *	−0.001
			(−2.332)	(−2.206)	(−2.001)	(−2.037)	(−1.828)	(−1.816)	(−0.969)
lnLAB				−0.032	−0.033	−0.035	0.049	−0.03	0.059
				(−1.087)	(−1.096)	(−1.070)	(1.107)	(−1.045)	(1.469)
lnEDU					−0.018	−0.018	−0.016	−0.014	−0.016
					(−1.051)	(−1.043)	(−1.154)	(−0.927)	(−1.214)
DE2						0.047
						(0.25)
DE × L							−0.023 ***
							(−2.821)
DE × I								0.000
								(0.109)
DE × T									−0.059
									(−1.001)
Individual fixed effects	YES	YES	YES	YES	YES	YES	YES	YES	YES
Time fixed effects	YES	YES	YES	YES	YES	YES	YES	YES	YES
R2	0.623	0.629	0.677	0.535	0.478	0.443	0.665	0.521	0.817
Observations	234	234	234	234	234	234	234	234	234

Note: Labels ***, **, and * represent the regression results that pass the significance test at the 1%, 5%, and 10% confidence levels.

. Column ① shows the estimated results without including control variables, while columns ② to ⑤ show the estimated results with control variables such as the GDP growth rate added sequentially. The table shows that regardless of whether control variables are included, the estimated coefficients of the core explanatory variables in all the models are significantly positive at the 1% level. This result indicates that the level of the digital economy’s development has a significant promoting effect on the level of the real economy’s development.

With regard to the control variables, the regression results for the effects of the GDP growth rate, human capital, and education level on the level of the real economy’s development are not significant, indicating that in the economic development context of Henan Province, these factors may not yet constitute the core driving mechanisms of the growth of the real economy. On the other hand, foreign investment has a negative impact at the 5% significance level. The reason is that the foreign investment attracted by Henan Province is primarily market-seeking rather than efficiency-seeking, and the industrial layout competes with rather than complements the local real economy, which fails to produce technology spillover effects. According to the Henan Provincial Statistical Yearbook, foreign investment has mainly been concentrated in the traditional manufacturing industries over the years, which supports this viewpoint. Notably, this finding contrasts with the optimistic expectations in the earlier literature regarding the technology spillover effects of foreign investment [44] but is consistent with the research conclusions of some scholars [45].

In the case of a nonlinear transformation (Table 7. ⑥), the regression results for DE² are not significant, suggesting that at present, the relationship between the development of the digital economy and that of the real economy in Henan Province is closer to linear. The application of digital technology in Henan’s real economy is still in the stage of constant returns to scale. Compared to the diminishing marginal returns of digital technology that are commonly observed in developed regions, Henan’s digital transformation is still in the phase of middle-stage acceleration. Scholars such as Jiang et al. have observed that the rapid development of the digital economy generally has an “exclusion effect” on the real economy, but they also note that this exclusion effect primarily occurs in eastern China, while central regions are characterised by a “promotion effect.” Henan Province is located in the central region, which is consistent with the conclusions of this study [46]. Additionally, other scholars have proposed the concept of a catch-up dividend in the latecomer regions’ technology [47]. Together with the previous analysis, this study rules out the possibility of a nonlinear development between the digital economy and the real economy, further supporting another viewpoint: the fundamental reason for the significant lead in the development of the real economy over the digital economy in cities such as Nanyang, Zhoukou, and Zhumadian is the lag in the structural economic transformation. This finding can provide a basis for designing structural transformation policies at the meso level.

Considering the interaction terms, the interaction between the digital economy and labour productivity is characterised by a statistically significant negative relationship. This finding reveals that there is a notable suppressive synergy between the two factors in terms of their impact on the development of the real economy. Specifically, the penetration of digital technologies may weaken the positive contribution of improved labour productivity to the real economy through substitution effects. The 2023 “Henan Manufacturing Development Report” shows that after the introduction of industrial robots in Henan’s manufacturing industry, the demand for high-skilled positions increased, but the unemployment rate for low-skilled workers rose, and the overall economic efficiency did not improve accordingly. This may reflect a mismatch between the current application of digital technologies and the labour force’s skill structure. Studies have noted the role of the digital economy in driving technological innovation to promote economic development [48]. However, the empirical results of this study show that at the current stage of development in Henan Province, no significant synergy exists between the digital economy, innovation, and total factor productivity. This finding indicates that at this stage, the digital economy in Henan has not yet formed an effective collaborative mechanism with the innovation system and the improvement of total factor productivity. Thus, the penetration rate of the digital economy into the innovation processes is insufficient. The “China Digital Economy Development Research Report” shows that in 2023, the overall digital economy penetration rate in Henan Province was 21.17%, which was lower than the national average of 27.15%. The role of the digital economy in promoting the real economy may still be at the level of universal benefits and has not yet shown differentiated impacts based on the regional innovation efficiency or the efficiency of factor allocation. The above findings may reflect the structural contradictions in Henan’s digital transformation process: the rapid expansion of the digital infrastructure is not synchronized with the innovation system and market reforms, leading to a “technology–institutions” mismatch and reflecting the potential existence of “regional gradient differences.” For example, although the Central Plains urban agglomeration initially established a digital industry scale, the coverage of the digital infrastructure has remained low in southern Henan where the innovation resources are scarce, which negatively affects the overall results of the province. Therefore, this study further examines the spatial heterogeneity characteristics in the next chapter.

3.3.2. Robustness and Endogeneity Tests

The reliability of the results for the impact of the digital economy on the real economy is ensured through the following robustness checks, as shown in

Table 8. Robustness and endogeneity tests.

Variable	① RE	② RE	③ RE	④ RE	⑤ RE	⑥ DE	⑦ RE	⑧ RE	⑨ RE
	OLS	Shrinkage Treatment	Replacing the Interaction Variable Measures (FEM)			First Stage of 2SLS	Second Stage of 2SLS	GMM	PCA-FEM
DE	0.627 ***	0.545 ***	0.985 ***	0.607 **	0.666 ***		0.597 ***	0.597 ***
	(24.675)	(8.073)	(4.504)	(−2.532)	(2.963)		(−19.265)	(17.274)
GDPG	0.003 ***	0.001	0.001	0.000	0.001				0.001
	(3.52)	(0.496)	(1.039)	−0.411	(0.930)				(0.704)
FDI	0.000	−0.001 **	−0.001	−0.001 **	−0.001 **				−0.002 **
	(0.204)	(−2.059)	(−1.863)	(−2.069)	(−2.221)				(−2.122)
lnLAB	0.066 ***	−0.033	0.038	−0.033	−0.021				0.002
	(14.437)	(−1.102)	(0.767)	(−0.962)	(−0.562)				(0.048)
lnEDU	0.001	−0.017	−0.016	−0.021	−0.017				0.001
	(0.201)	(−1.030)	(−1.058)	(−1.252)	(−0.966)				(0.071)
DE × L1			−0.020 **
			(−2.469)
DE × I1				0.000
				(−0.346)
DE × T1					−0.168
					(−0.927)
LDE						1.015 ***
						(127.524)
DE(PCA)									0.690 ***
									(16.699)
Individual fixed effects	NO	YES	YES	YES	YES	NO	NO	NO	YES
Time fixed effects	NO	YES	YES	YES	YES	NO	NO	NO	YES
R2	0.856	0.477	0.694	0.477	0.443	0.986	0.623	0.623	0.699
Observations	234	234	234	234	234	234	234	234	234

Note: Labels *** and ** represent the regression results that pass the significance test at the 1% and 5% confidence levels.

. (1) Change in the estimation method: The model is re-estimated using ordinary least squares (OLS). The coefficient estimates for the digital economy variable remain statistically significant at the 1% significance level, and the direction and significance are completely consistent with the benchmark regression results, confirming the robustness of the original model. (2) Handling outliers: To reduce the potential interference of outliers on the research results, the sample data were processed. Specifically, the extreme values at both ends of the sample data were truncated at the 1% level to mitigate the impact of outliers on the statistical inference. The regression analysis results are presented in column ②, which shows that the coefficient estimate for the digital economy variable remains significant at the 1% level. The significance level is completely consistent with the benchmark model, and the regression coefficient is 0.545 with an absolute difference of only 0.001 from the benchmark estimate of 0.544, a relative deviation of less than 0.2%. This finding increases the credibility of the benchmark regression results, indicating that the positive effect of the digital economy on the real economy is both statistically and economically significant. (3) Changing the measurement of interaction variables: Labour productivity is replaced with value-added productivity, calculated as industry value-added/industry employment. Researcher density and research funding intensity are used as substitutes for the innovation level. Researcher density is represented as the number of R&D personnel/total employment, and research funding intensity is measured as R&D expenditure/GDP. Input–output efficiency is used as a substitute for total factor productivity using the calculation method of the DEA-BCC model. The regression results for these replacement variables are presented in columns ③ to ⑤. The results show that with different replacement variables, the impact of the digital economy on the real economy remains positive and significant, and the significance and direction of the interaction term’s regression coefficient are consistent with the benchmark regression results. This not only strengthens the reliability of the digital economy’s impact on the real economy but also increases the reliability of the interaction effect. (4) To mitigate issues of indicator correlation, we revised the measurement approaches for both the explanatory and the explained variables. Specifically, we re-measured the developmental levels of the variables using PCA and conducted regression analysis with a fixed-effects model. The results in column ⑨ of Table 8 show that the variable is statistically significant at the 1% level with a regression coefficient of 0.690. This confirms that the digital economy significantly promotes the development of the real economy.

This study treats endogeneity as follows. A development of the digital economy can significantly boost the real economy, but uneven development across regions may result in a “digital divide” between them [49]. For example, those regions with relatively low levels of economic development may experience slower digital economy growth due to an incomplete information infrastructure, leading to potential bidirectional causality between the digital economy and the real economy. First, we confirm the presence of endogenous variables in the model by the Hausman test. To reduce endogeneity problems, following the approach of He et al. [50], the lagged digital economy’s development level is selected as an instrumental variable, and the two-stage least squares (2SLS) method is used for the estimation. The estimation results are presented in columns ⑥ and ⑦. Both the first- and second-stage regression coefficients are significant, suggesting that the instrumental variables are valid and that the original model’s conclusions hold after accounting for endogeneity. The results show that the model’s R-squared value is 0.623, meaning that the level of the digital economy’s development can explain 62.3% of the variation in the real economy’s development level. The Wald chi-square test is performed on the model, and the model passes the Wald chi-square test (Chi = 371.139, p = 0.000 < 0.05), indicating that the level of the digital economy’s development has a significant impact on the level of the real economy’s development. The regression coefficient for the digital composite score is 0.597 (p = 0.000 < 0.01), meaning that the level of the digital economy’s development has a significant positive impact on the level of the real economy’s development. In addition, to increase the credibility of the results, we add the GMM estimation to the 2SLS method. The results are presented in column ⑧, and show that the significance and regression coefficients are comparable to those of the 2SLS method, confirming the reliability of the results.

3.3.3. Random Forest Regression

To further assess the robustness of the baseline regression model and interaction effects, the random forest method is used to regress the variables. The importance of each variable is shown in Figure 3.

According to the results, the digital economy’s development level has the highest feature weight at 62.51%, indicating that it plays a pivotal role in the model construction. This implies that among all the variables, the digital economy’s development level is a crucial factor in influencing the real economy’s development, which is consistent with our hypothesis in the benchmark regression. The interaction variables DE × I and DE × L are more important than DE × T, which is consistent with the results of our interaction model. The importance of lnLAB ranks second, yet it is not statistically significant in the benchmark regression results. Possible reasons include the following: (1) the impact of lnLAB on the real economy exhibits nonlinear and threshold effects, while a fixed-effects regression captures only the linear relationships; (2) lnLAB may interact with other factors to influence the real economy, necessitating a further exploration of the specific interaction terms; (3) in the fixed-effects model, the effect of lnLAB may be obscured by other variables, whereas the random forest method reveals its true contribution.

4. Coordinated Relationships and Spatial Heterogeneity Between the Digital Economy and the Real Economy

4.1. Research Methods

4.1.1. Coupling Coordination Degree

Based on the empirical research results presented earlier, this study has verified the impact of the digital economy on the development of the real economy. However, in the real economic system, the digital economy and the real economy do not exist in isolation; rather, they form a synergistic and coevolving organic whole through complex interaction mechanisms. To further reveal the interactive relationship between the two systems, this study draws on the paradigms established in previous research and constructs a coupling coordination degree model [51,52,53]:

$$C=2\times {\left[{\displaystyle \frac{DE\times RE}{DE+RE}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(25)

$$T=\alpha DE+\beta RE$$

(26)

$$D=\sqrt{C\times T}$$

(27)

where C represents the degree of coupling between the development systems of the digital economy and the real economy, D refers to the coupling coordination degree between the two systems, and T is the comprehensive coordination index of the subsystems of the digital economy and the real economy. DE and RE are the comprehensive indexes of the development levels of the digital economy and the real economy, respectively. $T=\alpha DE+\beta RE$ Variables $\alpha$ and $\beta$ represent the weights of the two subsystems in terms of their impact on social development, with $\alpha$ and $\beta$ both set to 0.5.

4.1.2. Kernel Density Function

Based on the coupling coordination degree values, the kernel density estimation is used to analyse the distribution pattern of the coordinated relationship between the development trends of the digital economy and the real economy in Henan Province. The kernel density function of the random variable $x_1,x_2,\dots ,x_n$ is

$$f_h(x)={\displaystyle \frac{1}{nh}}{\displaystyle \sum _{i=1}^{n}K}\left({\displaystyle \frac{x-x_i}{h}}\right)$$

(28)

where $n$ is the number of observations, $h$ is the bandwidth, $K$ is the weighting function, and $x-x_i$ represents the distance between $x$ and $x_i$.

4.1.3. Gini Coefficient

The Gini coefficient is an indicator that is commonly used to measure income disparities among the residents in a country or region [54,55,56]. In this study, the Gini coefficient and its decomposition method are utilised to explore the regional disparities in the digital economy, the real economy, and their coupling coordination degree. The specific formula for the example of the coupling coordination degree is presented below:

$$G={\displaystyle \frac{{\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|}}}}}{2n^2\stackrel{\_}{y}}}$$

(29)

$$G=G_w+G_b+G_t$$

(30)

where y_ji and y_hr represent the comprehensive scores of the coupling coordination degree between the development trends of the digital economy and the real economy in cities i and r within regions j and h, respectively; ȳ is the average value of the comprehensive coupling coordination degree score; n is the number of prefecture-level cities; k is the number of regions;  and  represent the number of prefecture-level $n_j$ and $n_h$ cities in regions j and h, respectively; $G_w$ is the within-group difference; $G_b$ is the between-group difference, and $G_t$ is the ultra-variance density.

4.2. Results and Analysis

4.2.1. Coupling Coordination Degree Results

To systematically examine regional heterogeneity, this study follows the official zoning plan outlined in the “Henan Provincial Land Spatial Planning (2021–2035)” and divides the 18 prefecture-level administrative units of Henan Province into five typical regional modules, namely the Central Plains urban agglomeration core area, the Northern Henan coordinated development area, the Western Henan transformation demonstration area, the Eastern Henan industry transfer belt, and the Southern Henan ecological economy area. The cities in each region and the quantified results of the coupling coordination degree are detailed in

Table 9. Degree of coupling coordination of the digital economy and the real economy in Henan Province.

Region	City	2011	2013	2015	2017	2019	2021	2023
Central Plains Urban Agglomeration	Zhengzhou	0.594	0.661	0.719	0.763	0.847	0.875	0.909
	Kaifeng	0.361	0.427	0.467	0.482	0.526	0.561	0.587
	Luoyang	0.456	0.510	0.553	0.585	0.640	0.652	0.690
	Pingdingshan	0.363	0.425	0.458	0.492	0.527	0.532	0.550
	Xinxiang	0.409	0.477	0.507	0.537	0.584	0.598	0.627
	Jiaozuo	0.413	0.462	0.507	0.543	0.580	0.568	0.596
	Xuchang	0.373	0.443	0.477	0.510	0.547	0.563	0.585
	Luohe	0.359	0.414	0.460	0.497	0.535	0.562	0.581
	Jiyuan	0.370	0.436	0.469	0.492	0.530	0.526	0.545
Northern Henan Region	Anyang	0.378	0.441	0.466	0.492	0.517	0.530	0.546
	Hebi	0.357	0.412	0.458	0.479	0.518	0.549	0.556
	Puyang	0.383	0.433	0.461	0.501	0.528	0.550	0.556
Western Henan Region	Sanmenxia	0.388	0.442	0.471	0.504	0.547	0.539	0.561
Eastern Henan Region	Shangqiu	0.339	0.408	0.447	0.481	0.526	0.536	0.551
	Zhoukou	0.293	0.398	0.444	0.468	0.509	0.518	0.556
Southern Henan Region	Nanyang	0.359	0.440	0.474	0.520	0.562	0.582	0.606
	Xinyang	0.315	0.380	0.424	0.453	0.498	0.528	0.571
	Zhumadian	0.321	0.393	0.451	0.483	0.526	0.564	5.591

Note: Due to space limitations, only the results from certain years are shown.

.

The results show that from 2011 to 2023, the degree of coupling coordination between the digital economy and the real economy in cities across Henan Province generally demonstrated a steady upward trend, with all cities experiencing growth to varying degrees. Although some cities experienced slight fluctuations in certain years, these fluctuations did not have a substantial impact on the overall upward trend. Notably, regional development disparities still exist. The findings of this study suggest that, compared to cities with lower levels of development, cities with higher levels of development tend to have higher degrees of coupling coordination between the different elements, which can also be verified by other studies [57,58,59]. Zhengzhou, as the capital of Henan Province, has consistently ranked first in the degree of coupling coordination, far surpassing other cities. This reflects its leading development level; it is the core of the Central Plains urban agglomeration. The northern and western regions of Henan show a moderate performance with relatively stable growth rates, indicating that the coordinated development of the economy, the society, and the environment within the urban agglomeration is gradually improving. While the initial development levels in the underdeveloped areas of Eastern and Southern Henan are low, their growth rates are remarkable; Zhoukou City has the highest growth rate in the province. This phenomenon indicates that policy support and resource allocation play a significant role in promoting the “digital–real” coupling coordination in the underdeveloped regions of Henan Province. This contrasts with the argument in the existing research that “policy dividends are concentrated in high-gradient regions” [22], suggesting that the realization of the policy effects hinges on the dual alignment of a region’s initial conditions and the adaptability of the allocated resources. Henan Province has the precisely tailored special funds and customized digital infrastructure development plans to align with local needs. In contrast, the “the strong get stronger” model adopted in other provinces has reinforced the advantages of the core cities. This regional heterogeneity indicates that the interaction between the combination of policy instruments and the structure of the resource endowments is a key factor that influences the divergence of the regional collaborative pathways. It also explains the underlying logic of the varied effects of similar policies in other countries, such as the rural broadband programme in the United States [60].

4.2.2. Kernel Density Estimation Results

This study uses Stata 17.0 and MATLAB R2021b to conduct kernel density tests on the degree of coupling coordination between the levels of development of the digital economy and the real economy in various regions. Additionally, MATLAB R2021b is used to create a 3D dynamic evolution trend chart. The six models shown in Figure 4 (ranging from the first model in the first row to the last model in the second row) represent the temporal evolution characteristics of the coupling coordination degree between the development trends of the digital economy and the real economy in Henan Province as a whole, the Central Plains urban agglomeration, and the northern, western, eastern, and southern regions of Henan.

Overall, the centre of the kernel density distribution has shifted backwards, indicating that the coupling coordination degree has been rising annually. This reflects significant progress in Henan Province’s integration of the digital economy with the real economy. The peak of the distribution reached its highest point around 2015, with the corresponding degree of coupling coordination at approximately 0.5. Thus, during this period, the coupling coordination degrees across various regions were concentrated the most, with relatively small developmental disparities among the regions. This phenomenon may be attributed to the balanced development strategy driven by policies at the end of the “12th Five-Year Plan” period, which led to a convergence of trends among cities within the province during the initial stages of the digital transformation. As time progresses, the bandwidth of the kernel density curve gradually decreases, indicating a reduction in the degree of dispersion in the coupling coordination degree across the regions. Therefore, cities within Henan Province are moving towards a more coordinated development of the digital economy and industrial integration. This convergence trend became more apparent after 2018, which coincided with the implementation of policies such as Henan’s “Big Data Development Action Plan.” This alignment suggests that policy interventions have played a crucial role in narrowing the regional digital divide. Notably, existing research often focuses on the impact of the digital divide on policy formulation [61,62], while fewer scholars have specifically examined the impact of policies on the digital divide. However, some scholars have mentioned the role of policies in addressing the digital divide, noting that policy interventions, through targeted resource allocation and institutional optimisation, can effectively reduce regional digital gaps [63]. The Gini coefficient assists us in further exploring this issue.

From the perspective of different regions, the kernel density distribution patterns of the Central Plains urban agglomeration are similar to the overall distribution, indicating that the evolution of the degree of coupling coordination in this region is highly representative and shows dynamic characteristics consistent with the overall development model of the province. In the northern, eastern, and southern parts of Henan, the kernel density centres have shifted backwards and show multiple peaks, suggesting that the coupling coordination degree in these three regions progresses in a winding manner and further revealing the developmental disparities among the cities within these areas. The western part of Henan has only a single peak with a corresponding coupling coordination degree of approximately 0.5 from 2011 to 2023.

4.2.3. Results for the Gini Coefficient

The Gini coefficient decomposition results are shown in

Table 10. Results for the Gini coefficient and contribution rates.

Category	Year	Gini Coefficient				Contribution Rate(%)
		Overall	Intra-Group Gini Coefficient	Inter-Group Gini Coefficient	Super-Variable Density Gini Coefficient	Intra-Group Contribution Rate	Inter-Group Contribution Rate	Super-Variable Density Contribution Rate
Digital economy	2011	0.294	0.087	0.182	0.024	29.71%	62.00%	8.29%
	2015	0.191	0.06	0.118	0.012	31.49%	62.06%	6.45%
	2019	0.169	0.058	0.1	0.011	34.15%	59.42%	6.43%
	2023	0.156	0.058	0.093	0.004	37.57%	59.83%	2.61%
Real economy	2011	0.108	0.035	0.043	0.031	32.26%	39.32%	28.42%
	2015	0.111	0.037	0.043	0.031	33.39%	38.86%	27.74%
	2019	0.124	0.041	0.057	0.026	33.25%	45.85%	20.90%
	2023	0.134	0.044	0.064	0.026	32.75%	47.64%	19.61%
Coupling coordination degree	2011	0.08	0.024	0.051	0.005	29.71%	64.15%	6.14%
	2015	0.054	0.019	0.032	0.002	35.67%	60.18%	4.16%
	2019	0.056	0.021	0.031	0.004	37.02%	55.87%	7.11%
	2023	0.056	0.021	0.03	0.005	37.52%	54.33%	8.15%

Note: Due to space limitations, only the results from certain years are shown.

. In terms of the overall disparity, the Gini coefficient of the digital economy decreased from 0.294 in 2011 to 0.156 in 2023, i.e., by 46.9%, indicating a significant narrowing of the regional disparities. The Gini coefficient of the real economy fluctuated slightly and increased slightly after 2020, possibly due to regional recovery capacity differentiation under the impact of the COVID-19 pandemic. Some studies suggest that large cities were more affected by the COVID-19 pandemic [64] but also had stronger recovery capabilities. The Gini coefficient of the coupling coordination degree showed little overall change during the study period and remained lower than that of the digital economy and the real economy, indicating that the coordinated development of the digital economy and the real economy was becoming more balanced.

In terms of the evolutionary trends, the contribution rate of the super-variable density of the digital economy decreased from 8.29% in 2011 to 2.61% in 2023, indicating that the cross-overlap effect between regions weakened and that the development pattern became clearer. The intergroup contribution rate of the real economy rose again after 2020, suggesting a potential risk of regional differentiation that needed to be closely monitored. The intragroup contribution rate of the coupling coordination degree has been steadily increasing, indicating that the level of coordinated development within the provincial subregions is gradually improving.

With regard to the sources of disparity, the differences in the digital economy are attributed primarily to intergroup disparities, suggesting that the development gap between urban agglomerations is the dominant factor. For the real economy, the contribution rates of intragroup, intergroup, and super-variable density are relatively balanced, indicating that the disparities are influenced by multiple factors. The disparity in the degree of coupling coordination is driven mainly by intergroup differences. These findings help us to better understand the “convergence club” phenomenon of regional coordinated development and further indicate that policies should focus on coordinating development among urban agglomerations.

5. Symbiotic Model of Deep Integration Between the Digital Economy and the Real Economy

The empirical research results mentioned earlier suggest that the digital economy and the real economy can interact and coevolve. However, whether in nature or in economic systems, cooperation and competition are not opposites; one often observes a dynamic coexistence or strategic interactions. This raises another question: when effective cooperation between the digital economy and the real economy fails, will negative effects such as competition or suppression arise?

To address this question, this study introduces the Lotka–Volterra symbiotic model based on the ecological symbiosis theory framework to construct a theoretical model of a composite symbiotic system of the digital economy and the real economy. It comprehensively considers the competitive and cooperative symbiotic patterns of the digital economy and the real economy under the constraints of the resource and environmental carrying capacity. The study also identifies the core factors that drive the mutual benefits and collaborative symbiosis between the digital economy and the real economy. This approach provides a practical and feasible reference for regions to scientifically and systematically promote the symbiotic development and deep integration of the digital economy and the real economy while considering the carrying capacity of resources and the environment.

5.1. Symbiotic System of the Digital Economy and the Real Economy

The Lotka–Volterra (L-V) model was originally used to study predator-prey relationships between biological populations [65,66,67]. In recent years, it has also been applied in fields such as economics and finance, resource management, and the environmental sciences [68,69,70]. In terms of cooperation, the digital economy and the real economy exhibit characteristics of biological mutualism. The digital economy leverages its technological and connectivity advantages and provides the real economy with efficient tools and expansive markets, facilitating its transformation and upgrading. For instance, the manufacturing sector utilises big data and artificial intelligence to enable intelligent production, enhancing efficiency and quality. Conversely, as the foundation and application scenario for the digital economy, the real economy offers a practical platform for the development and promotion of digital technologies, driving their innovation and advancement. The two sectors reinforce each other and develop together, embodying the fundamental traits of mutualism [71]. In terms of competition, the core of the L-V model is its ability to describe the dynamic interdependence between two entities under limited resources [72], which is consistent with the way the integration of the digital economy and the real economy is constrained by factors such as the labour and capital in economic systems. Based on the cooperative and competitive relationship between the digital economy and the real economy, this study constructs an L-V symbiotic model for the digital economy and the real economy as follows:

$${\displaystyle \frac{dDE(t)}{dt}}=r_{DE}DE(t){\displaystyle \frac{C-DE(t)-({\alpha }_{12}-{\beta }_{12})RE(t)}{C}}$$

(31)

$${\displaystyle \frac{dRE(t)}{dt}}=r_{RE}RE(t){\displaystyle \frac{C-RE(t)-({\alpha }_{21}-{\beta }_{21})DE(t)}{C}}$$

(32)

In this model, the meanings of DE and RE remain the same as those mentioned previously. C represents the resource and environmental carrying capacity index of the resource–environment subsystem. Variable r_DE represents the growth rate of the digital economy’s level, and r_RE is the growth rate of the real economy’s level. Variable α is the competition coefficient, indicating the mutual inhibition between the digital economy and the real economy during their development, and ${\alpha }_{12}$ and ${\alpha }_{21}$ represent the competition coefficients of the real economy’s effect on the digital economy and the digital economy’s effect on the real economy, respectively. Variable $\beta$ is the cooperation coefficient, indicating the mutual promotion and cooperation between the digital economy and the real economy, and ${\beta }_{12}$ and ${\beta }_{21}$ represent the cooperation coefficients of the real economy’s effect on the digital economy and the digital economy’s effect on the real economy, respectively. The term $\alpha -\beta$ is the synergy coefficient of the development of the digital economy and the real economy, and the force coefficient is the opposite of the synergy coefficient. Variable t represents time.

Specifically, the calculation steps for the synergy coefficient are as follows:

• Calculate $DE$ and $RE$:

  $$DE(k+1)-DE(k)={\displaystyle \frac{DE(k)-DE(k-1)}{DE(k-1)}}DE(k){\displaystyle \frac{C(k)-DE(k)-[({\alpha }_{12}-{\beta }_{12})]RE(k)}{DE(k-1)}}$$

  (33)

  $$RE(k+1)-RE(k)={\displaystyle \frac{RE(k)-RE(k-1)}{RE(k-1)}}RE(k){\displaystyle \frac{C(k)-RE(k)-[({\alpha }_{12}-{\beta }_{12})]DE(k)}{RE(k-1)}}$$

  (34)
• Calculate $\alpha -\beta$:

  $${\alpha }_{12}-{\beta }_{12}={\displaystyle \frac{{\phi }_{DE}(k)C(k)-DE(k)}{RE(k)}}$$

  (35)

  $${\alpha }_{21}-{\beta }_{21}={\displaystyle \frac{{\phi }_{RE}(k)C(k)-RE(k)}{DE(k)}}$$

  (36)

  $${\phi }_{DE}(k)=1-{\displaystyle \frac{DE(k+1)-DE(k)}{DE(k)}}\times {\displaystyle \frac{DE(k-1)}{DE(k)-DE(k-1)}}=1-{\displaystyle \frac{r_{DE}(k+1)}{r_{DE}(k)}}$$

  (37)

  $${\phi }_{RE}(k)=1-{\displaystyle \frac{RE(k+1)-RE(k)}{RE(k)}}\times {\displaystyle \frac{RE(k-1)}{RE(k)-RE(k-1)}}=1-{\displaystyle \frac{r_{RE}(k+1)}{r_{RE}(k)}}$$

  (38)

  where ${\phi }_{DE}(k)$ and ${\phi }_{RE}(k)$ represent the stability levels of the digital economy subsystem and the real economy subsystem, respectively.
• Divide $\alpha -\beta$ into different patterns based on the measured values (as shown in

  Table 11. Classification of symbiotic models of the digital economy and the real economy.

  Digital Economy	Real Economy	Symbiotic Model
  ${\alpha }_{12}-{\beta }_{12}<0,{\alpha }_{21}-{\beta }_{21}<0,({\alpha }_{12}-{\beta }_{12})({\alpha }_{21}-{\beta }_{21})>1$		Perfect symbiotic mutualism	I
  ${\alpha }_{12}-{\beta }_{12}<0,{\alpha }_{21}-{\beta }_{21}<0,({\alpha }_{12}-{\beta }_{12})({\alpha }_{21}-{\beta }_{21})<1$		Asymmetric mutualism	II
  ${\alpha }_{12}-{\beta }_{12}<0$	${\alpha }_{21}-{\beta }_{21}=0$	Digital economy-driven asymmetric mutualism	III
  ${\alpha }_{12}-{\beta }_{12}<0$	${\alpha }_{21}-{\beta }_{21}>0$	Unilateral digital economy dominance	IV
  ${\alpha }_{12}-{\beta }_{12}=0$	${\alpha }_{21}-{\beta }_{21}<0$	Real economy-driven asymmetric mutualism	V
  ${\alpha }_{12}-{\beta }_{12}=0$	${\alpha }_{21}-{\beta }_{21}=0$	No meaning	VI
  ${\alpha }_{12}-{\beta }_{12}=0$	${\alpha }_{21}-{\beta }_{21}>0$	Real economy amensalism	VII
  ${\alpha }_{12}-{\beta }_{12}>0$	${\alpha }_{21}-{\beta }_{21}<0$	Unilateral real economy dominance	VIII
  ${\alpha }_{12}-{\beta }_{12}>0$	${\alpha }_{21}-{\beta }_{21}=0$	Digital economy amensalism	IX
  ${\alpha }_{12}-{\beta }_{12}>0$	${\alpha }_{21}-{\beta }_{21}>0$	Competitive exclusion	X

  ).

Model I reflects a deep collaboration and a mutually beneficial interaction between the digital economy and the real economy. In this model, both economies not only increase the resource-environment proportion occupied by their own development through positive incentives to achieve efficient resource allocation and utilisation, but also further expand the resource-environment capacity jointly created by the market demand and government policy support, providing a broader space for their ongoing development. Model II corresponds to a mutually beneficial development trend between the digital economy and the real economy. During the interaction, both economies increase the proportion of the resources they occupy in their development, promoting resource optimisation and effective utilisation. However, compared to the perfect symbiotic mutualism model, this model has a relatively weaker role in expanding the resource-environment capacity. Model IV presents an asymmetric symbiotic relationship. In this model, the competitive effect of the real economy on the digital economy is smaller than the cooperative effect between the two, while the competitive effect of the digital economy on the real economy is greater than their cooperative effect. Thus, the real economy promotes the development of the digital economy to some extent, but the digital economy has a suppressive effect on the real economy. This asymmetrical relationship benefits the digital economy, while the real economy suffers. Correspondingly, model VIII shows that the real economy benefits while the digital economy suffers. In this model, the asymmetry of the symbiotic relationship gives the real economy a dominant position in the interactions with the digital economy and benefits from their relationship while the digital economy is suppressed and its development is negatively affected. Model X is characterised by a competitive coefficient that is significantly greater than the cooperation coefficient. In this model, the relationship between the digital economy and the real economy is mainly competitive, and the negative impacts between them outweigh the benefits of cooperation. Long-term competition and mutual harm challenge both systems, potentially leading to their decline or even disappearance, as the positive effects generated in their competitive social–ecological environment cannot offset the negative shocks caused by competition.

5.2. Empirical Analysis

5.2.1. Indicator System and Measures

The indicator system and measures for the digital economy and the real economy directly use the results from Section 3 of this article. The design of the environmental carrying capacity index refers to the studies of other scholars [73], with the specific indicators shown in

Table 12. Indicators of environmental carrying capacity.

Primary Indicator	Secondary Indicator	Tertiary-Level Indicator and Its Corresponding Units	Direction	Comprehensive Weight
Social resource status	Market resources	Total retail sales of consumer goods in each city (CNY billion)	+	0.103
		Per capita consumption expenditure (CNY)	+	0.044
	Scientific and technological resources	Internal R&D expenditure—Government funds (CNY ten thousand)	+	0.308
		Expenditure on science and technology (CNY billion)	+	0.179
	Educational resources	Number of students in regular higher education institutions (persons)	+	0.245
		Education expenditure (CNY billion)	+	0.070
Ecological environment’s pressure	Ecological environment	Total sulphur dioxide emissions (ten thousand tons)	-	0.017
		Chemical oxygen demand (ten thousand tons)	-	0.024
		General industrial solid waste generation (ten thousand tons)	-	0.010

. The method of calculating the comprehensive score for the environmental carrying capacity is the same as for the measurement of the digital economy and the real economy.

5.2.2. Synergy Coefficient and Symbiotic Model Analysis

The digital economy–real economy synergy coefficient for each province and city is calculated using the basic index. The symbiotic modes of each city are derived from the synergy coefficient (

Table 13. Synergy coefficient and symbiotic modes.

	2022–2023			2021–2022				2012–2013
	${\mathsf{\alpha }}_{12}-{\mathsf{\beta }}_{12}$	${\mathsf{\alpha }}_{21}-{\mathsf{\beta }}_{21}$	M	${\mathsf{\alpha }}_{12}-{\mathsf{\beta }}_{12}$	${\mathsf{\alpha }}_{21}-{\mathsf{\beta }}_{21}$	M	…	${\mathsf{\alpha }}_{12}-{\mathsf{\beta }}_{12}$	${\mathsf{\alpha }}_{21}-{\mathsf{\beta }}_{21}$	M
Zhengzhou	−2.099	6.696	IV	2.348	0.398	X	…	−0.344	−2.142	I
Kaifeng	−0.230	−2.076	II	−0.478	−1.336	II	…	−0.450	−4.180	I
Luoyang	−2.225	−3.464	I	0.547	−1.127	VIII	…	−0.349	−4.062	I
Pingdingshan	−0.930	1.209	IV	5.819	−0.267	VIII	…	−0.483	−2.848	I
Anyang	−0.135	−3.902	II	−3.634	0.563	IV	…	−0.599	−4.761	I
Hebi	−0.663	0.067	IV	1.751	−0.588	VIII	…	−0.547	−1.767	II
Xinxiang	−0.563	−1.490	II	1.211	−0.796	VIII	…	−0.310	−2.006	II
Jiaozuo	−1.184	−1.059	I	−0.286	−0.870	II	…	−0.832	−2.242	I
Puyang	−0.159	0.585	IV	−1.377	−0.464	II	…	−0.597	−3.217	I
Xuchang	−1.072	16.337	IV	−0.066	−1.016	II	…	−0.406	−4.004	I
Luohe	0.017	−2.505	VIII	−0.697	−0.830	II	…	−0.741	−3.438	I
Sanmenxia	−1.903	−1.535	I	−0.453	−0.898	II	…	−0.602	−2.168	I
Nanyang	−0.567	−2.361	I	−0.991	−1.212	I	…	−0.185	−5.544	I
Shangqiu	−0.841	1.124	IV	0.470	−0.508	VIII	…	−0.220	−4.166	II
Xinyang	−0.545	−3.073	I	−20.230	−1.243	I	…	−0.387	−9.168	I
Zhoukou	−0.894	−3.565	I	1.033	−1.315	VIII	…	−0.133	−6.118	II
Zhumadian	−0.723	16.146	IV	43.804	−1.169	VIII	…	−0.279	−3.954	I
Jiyuan	−4.018	−0.880	I	−0.965	−1.384	I	…	−0.660	−1.857	I

Note: Due to space limitations, only the results from certain years are shown. ”…” represents the omitted years.

). The frequency of different symbiotic modes in each year is statistically analysed, and the evolution of the symbiotic modes from 2011 to 2023 is obtained (see Figure 5 on the next page).

The results in Table 13 and a comparison with those in Table 11 show that neither the synergy coefficient of the digital economy nor that of the real economy reaches zero. The digital economy and the real economy in various provinces and municipalities have been in a state of continuous development and change, with no occurrences of one-sided development or harm. Mutualism has always been the predominant interaction pattern, indicating a coordinated development trend between the digital economy and the real economy in most regions of Henan Province, which is consistent with the results of the coupling coordination degree model mentioned earlier. The perfect pattern of symbiotic mutualism exhibits significant fluctuations; its frequency decreased to zero between 2013 and 2014, reflecting the instability of the deeply dependent relationship between the two. However, it rebounded between 2016 and 2018, suggesting a typical development pattern of digital and real mutual progress in Henan Province during this period, with both the digital economy and the real economy generally following positive development trends. According to the Chinese Academy of Information and Communication Technology, the scale of Henan’s digital economy reached CNY 1.25 trillion in 2018, accounting for approximately 26% of the GDP, while the real economy continued its growth. Moreover, in terms of the structural transformation, investment in the core industries of the digital economy has increased annually, and the digital transformation rate of the real economy and the proportion of value added in the high-tech industries have also improved. Asymmetric mutualism reached its peak between 2013 and 2014 and then fluctuated downwards, indicating a gradual decrease in the nonessential mutual relationships. The competitive exclusion pattern appeared only once between 2021 and 2022, suggesting relatively few direct conflicts between the two economies, but the risks of resource competition in the future still warrant vigilance.

Notably, during the observation period from 2019 to 2020, the frequency of the unilateral dominance pattern of the digital economy exhibited a significant surge, reaching a peak of nine occurrences (a 291% increase compared to the average of the previous cycle), while the unilateral dominance pattern of the real economy showed a downward trend during the same period. This asymmetric development pattern led directly to a systematic decline in the mutualism pattern. The reason for this is that the years 2019–2020 marked the period of the fastest development of the digital economy. Some studies suggest that the COVID-19 pandemic accelerated digitalisation [74,75]. From a macro perspective, the digital economy has become a national strategy, with significant increases in policy support. According to the “Henan Provincial Digital Economy Development Report”, in 2020 the scale of digital industrialisation in Henan Province grew by 15.6% year-over-year, and the penetration rate of the digital economy across the three industrial sectors also increased. However, due to the impact of the COVID-19 pandemic, the revenue growth rate of the real economy in Henan Province declined significantly in 2020, with some industries even experiencing negative growth. From a micro perspective, the leading enterprises in Henan Province increased their R&D investments, but the digital penetration rate among the small- and medium-sized enterprises (SMEs) remained relatively low, exhibiting the phenomenon of polarization. The intelligent transformation of the traditional industries has also led to a reduction in job opportunities, and the accelerated pace of digital transformation has caused short-term imbalances in the real economy.

From a regional comparative perspective, the distribution of mutualistic symbiosis patterns among the prefecture-level cities in Henan Province is relatively balanced. Zhengzhou, as a regional development core, exhibited a competitive exclusion pattern during the observation period of 2021–2022. This phenomenon stands in stark contrast to its characteristic high development levels in both the digital and real economies, indicating that the symbiosis pattern is not correlated significantly with the development levels of the digital and real economies. In northern Henan (in cities such as Anyang and Hebi) and eastern Henan (in cities such as Shangqiu and Zhoukou), a short-term concentration of the unilateral digital economy dominance pattern was prevalent in 2015–2016, coinciding with the policy intervention window for the digital transformation of local traditional industries. Consistent with the overall trend, the proportion of perfect mutualism patterns increased in most cities between 2016 and 2018 (e.g., Luoyang and Xinxiang), and the unilateral digital economy dominance pattern increased across the entire province between 2018 and 2019. Hence, macro policies have a strong guiding effect on the behaviour of micro entities. However, the unilateral real economy dominance pattern emerged in cities such as Luohe and Nanyang between 2019 and 2020, which may be related to the local governments’ strategy of prioritising the stability of traditional industries under the impact of the COVID-19 pandemic. Cities such as Kaifeng and Xuchang have maintained asymmetric mutualism for a long time, reflecting the gradual transformation characteristic of their industrial structures. Although this transformation is not an immediate “leapfrog” change, it is a dynamic process of stable gradual advancement. This also provides inspiration for other cities: when promoting the industrial structure’s transformation, emphasis should be placed on balance to avoid an overreliance on a single industry to achieve stable and sustained economic growth.

In addition, this study shows that the application of symbiotic patterns in the digital economy and the real economy is relatively limited. Research has explored the symbiotic relationship between the two economies using the logistic model [71]. However, this study argues that the logistic model focuses more on the development of a single element under limited resources, whereas the L-V model can describe the interactive relationship between the two elements. Therefore, it is more appropriate to use the L-V model to study the competitive and mutual symbiotic relationships between the digital economy and the real economy.

6. Conclusions, Policy Implications, and Recommendations for Future Research

6.1. Conclusions and Policy Implications

This study systematically examines the interactive relationship between the digital economy and the real economy in Henan Province, China, from 2011 to 2023. By integrating the entropy-AHP weighting, a fixed effects model, convergent cross-mapping, kernel density estimation, the Lotka–Volterra model, and other analytical frameworks, we derive critical insights into the two economies’ interaction mechanisms, spatial disparities, and symbiotic modes. Our research findings are as follows:

• The digital and real economies in Henan Province are generally growing, with indicators such as the policy support intensity and corporate profits exerting significant influences on the development levels of the economies. Zhengzhou has led in comprehensive development, creating siphon and diffusion effects. Peripheral regions, though less developed, have late-mover advantages. Some cities experience digital economy downgrades due to the Matthew effect and the catch-up effect; however, a downgrade is not the same as a devaluation.
• There are multifaceted impacts between the digital economy and the real economy. The digital economy can collaborate with multiple factors to promote the real economy; simultaneously, a coordinated and mutually reinforcing relationship of “competition and cooperation” can exist between the two economies.
• The interactive relationship between the digital economy and the real economy exhibits spatial heterogeneity and regularity across regions. This is manifested in an expanding development gap between regions but a narrowing coordination gap, with cities at the higher development levels typically demonstrating greater coupling coordination. This spatial heterogeneity stems primarily from intergroup differences, with “club convergence” effects observed among the prefecture-level cities. Research reveals that policies play a significant role in shaping spatial heterogeneity.
• The symbiotic model involves dynamic evolution and has no inherent fixed association with the development levels. During the observation period, mutual symbiosis predominated between the digital economy and the real economy across regions, although temporary asymmetric symbiosis emerged in some areas during the pandemic that exposed the vulnerabilities in resource allocation and institutional adaptability.

Based on the above conclusions, this article makes the following policy recommendations.

The diffusion effect of cities with high comprehensive development levels should be leveraged to activate the late-mover advantages of the peripheral cities. Central cities such as Zhengzhou and Luoyang, along with the leading enterprises, should be supported in creating replicable models for the integration of the digital and real economies, such as standard systems for smart factories, and royalty-free authorisation should be granted for their adoption by neighbouring cities. A modest special tax should be imposed on the additional revenue generated by the digital enterprises in Zhengzhou and other areas, with all proceeds allocated to the “Digital Advancement Fund for Peripheral Cities” to enhance policy support for digitalisation in these regions and strengthen their infrastructure development.

A “competition-cooperation navigation” mechanism should be established to guide the positive evolution of multidimensional relationships. At the same time, the health of the competition and the intensity of the collaboration should be monitored, with releases of quarterly indicators such as the rate of traditional job transitions, the proportion of employment in the new business forms, and the connectivity rate of the industrial internet platforms. Furthermore, policy interventions for the cities that show abnormalities should be initiated promptly. Through the establishment of a dedicated fund, traditional enterprises should be supported in purchasing automation equipment while concurrently conducting employee retraining, facilitating both digital transformation and employment transition.

A tiered governance should be implemented to advance the digital upgrades tailored to local conditions. The leading role of the Central Plains urban agglomeration should be leveraged by launching pilot programmes for cross-border data flows in the region. Development should be accelerated in the areas surrounding the provincial capital and western Henan, such as by advancing the “Digital Longmen” initiative in Luoyang to cultivate digital cultural tourism IP. It is important to capitalise on the catch-up effect in eastern Henan by setting and enforcing targets for intelligent transformation coverage among large-scale enterprises. The focus should also be on transforming the traditional industries in northern Henan, exemplified by Anyang Iron & Steel’s exploration of digital quota models through capacity replacement. Agricultural and ecological advantages in southern Henan should be strengthened by establishing credit guarantee funds for the live-stream e-commerce of agricultural products.

A “symbiotic resilience” system should be built to defend against asymmetric risks through three key measures: establishing risk reserve allocation standards based on the relative proportions of each city’s economic scale, deploying monitoring metrics such as resource misallocation indices on government platforms for dynamic tracking, and regularly evaluating institutional adaptability by combining policy iteration efficiency with enterprise satisfaction surveys. The construction of an emergency computing power scheduling mechanism should be advanced to prioritise the stable operation of essential cloud services (e.g., healthcare and logistics) during periods of severe regional development imbalance.

6.2. Study Limitations and Recommendations for Future Research

The limitations of this study are as follows. (1) The ability of the Lotka–Volterra model to analyse two-dimensional relationships represents both an advantage and a drawback. While it improves upon the logistic model, it fails to account for factors beyond the two analysed factors. (2) This study considered only the overall effect of the digital economy on the real economy under different factors and neglects localised relationships. Additionally, tests using random forests revealed that the role of a certain control variable was underestimated in the fixed-effects model. Future research can use a subregional regression and a quantile regression for further analysis. (3) Despite using fuzzy triangular numbers to quantify the intensity of policy support, a degree of subjectivity remains inherent in the approach, and the timeliness of policies was not considered.

Future research can explore in greater depth the following three aspects. First, the symbiotic model between the digital economy and the real economy can be explored by extending the Lotka–Volterra model from a binary system to a complex multidimensional system. This may involve incorporating multiple dimensions, such as social capital (e.g., human skill networks), and constructing a “digital–real–social capital” multivariate differential equation. Second, considering the stage and background differences across different regions, future research can overcome the limitations of single-province studies and, based on cross-province panel data, explore the dynamic relationship between the digital economy and the real economy to identify scalable synergy models. Furthermore, it would be meaningful to further examine the interaction between the local digital economy and the real economy. In the future, methods such as phased regression and threshold effect models can be applied to explore the existence of thresholds in the relationship between the two economies. Finally, measuring the intensity of policy support is crucial for evaluating the level of economic development. Therefore, a more comprehensive, multidimensional measure of policy support intensity should be developed. This could entail combining text analysis of policy tools, machine learning for causal inference of policy effects, and experimental economics for policy scenario simulations to construct a three-dimensional policy index that incorporates intensity, precision, and speed.