Overview of the study region
In the process of China’s active promotion of digital inclusive finance development and the common prosperity goals, different regions have exhibited differentiated development trends. Eastern coastal provinces represented by Zhejiang Province have demonstrated particularly outstanding performance. Benefiting from a vibrant private economy, well-developed digital infrastructure, and strong policy support, Zhejiang has witnessed rapid growth in digital inclusive finance, with innovative services such as mobile payments and online lending becoming widely adopted. This has not only significantly improved financial service accessibility but also facilitated its designation as the nation’s first common prosperity demonstration zone. First-tier cities like Beijing, Shanghai, and Shenzhen, leveraging their robust economic strength and technological innovation advantages, have utilized digital inclusive finance to drive industrial upgrading and foster innovation and entrepreneurship, achieving remarkable results in resident income growth and social security system improvement. Meanwhile, nationwide, digital inclusive finance supported by technologies such as mobile payments, big data, and blockchain has significantly expanded financial service coverage, effectively alleviating financing difficulties for traditionally underserved groups such as small and micro enterprises and low-income populations. It has become a crucial tool in narrowing urban-rural and regional disparities. Against this backdrop, this study focuses on the development trajectory of 245 Chinese cities from 2012 to 2022, a period marking the critical phase from the emergence to the rapid expansion of digital inclusive finance in China. Given the spatial interdependence of economic phenomena, the research constructs an economic distance matrix to incorporate intercity economic linkages into the analytical framework, thoroughly examining the mechanisms through which digital inclusive finance influences common prosperity and its spatial heterogeneity. Despite persistent challenges in regional balance, data security, and regulatory compliance, the continuous innovation in digital inclusive finance by lowering service barriers and optimizing resource allocation is providing vital support for China’s pursuit of common prosperity.
Research method
Setting the weighting matrix
To measure spatial correlation, an economic distance matrix is constructed as a spatial weighting matrix W. By comparing the per capita gross domestic product (GDP) of the cities, the utilization of the economic matrix facilitates the computation of the economic distance between them. The economic distance is shortest when there is more frequent economic transit between cities. The expression is:
$${W}_{{ij}}=\left\{\begin{array}{c}\frac{1}{\left|{G}_{i}-{G}_{j}\right|},i\ne j\\ 0, i=j\end{array}\right.$$
(1)
The equation in formula (1) depicts the GDP per capita of city i in 2021.
Spatial correlation
Global spatial correlation refers to the distribution characteristics of the analyzed spatial data throughout the study area, and to determine the correlation coefficients between observations and geographically lagged variables, the global Moran’s I index is frequently utilized, which is calculated using the following formula:
$${{I}}=\frac{\mathop{\sum }\limits_{{{i}}=1}^{{{n}}}\mathop{\sum }\limits_{j=1}^{n}{W}_{ij}({X}_{i}-\overline{X})({X}_{j}-\overline{X})}{{S}^{2}\mathop{\sum }\limits_{{{i}}=1}^{{{n}}}\mathop{\sum }\limits_{j=1}^{n}{W}_{ij}}$$
(2)
Where the global Moran’s I measures spatial autocorrelation, n signifies the total number of regions, xi and xj indicate the level of common prosperity in regions i and j, respectively, and Wij represents the spatial weight matrix that captures the relationships between these regions.
Local spatial correlation is used to test for spatial aggregation in local areas. The Local Indicator Spatial Association (LISA), sometimes referred to as the local Moran’s I, is employed in this study to show the level of geographical connection in a region.
$${{LISA}}=\frac{({X}_{i}-\overline{X})}{{S}_{X}^{2}}{\sum }_{i=1}^{n}[{W}_{ij}-({X}_{i}-\overline{X})]$$
(3)
Where “high-high” and “low-low” aggregation are included in a positive LISA, suggesting that the high and low values within the research unit tend to cluster with similarly high and low values in their surroundings. Conversely, in a negative LISA, the high (or low) values of the research unit are encircled by low (or high) values, exhibiting a “high-low” or “low-high” aggregation pattern.
Spatial econometric model
The SAR, SEM, and SDM are the most widely utilized spatial measurement models. The specific models are shown below:
$$y=\rho Wy+\beta X+\theta WX+\mu$$
(4)
$$\mu =\lambda W\mu +\varepsilon$$
(5)
$$\varepsilon \sim N(0,{\sigma }^{2}{I}_{n})$$
(6)
where y is the explanatory variable, X is the n × k dimensional matrix of explanatory variables, W is the spatial weight matrix, in the dependent variable, the spatial autocorrelation coefficient is denoted by ρ; in the independent variables, it is represented by θ; in the vector of correlation parameters, by β; and in the spatial error coefficient, by λ,\(\,{\rm{\alpha }}\) is the constant term, the random error terms are μ and ε, and the nth-order unit matrix is denoted as In.
(1) The SAR model is obtained when \({{\rho }}\) ≠ 0 and \({\rm{\theta }}\) = 0, \({{\lambda }}\) = 0;
(2) The model is an SEM when λ ≠ 0, ρ = 0, and \({\rm{\theta }}\) = 0;
(3) The model is an SDM when ρ ≠ 0, \({\rm{\theta }}\) ≠ 0, and λ = 0.
Variable selection
Explained variables
Common prosperity is the explanatory factor (cp). The evaluation index system for common prosperity is constructed around two core dimensions: “commonness” and “prosperity.” It systematically assesses the degree of economic development (“prosperity”) while scientifically measuring the level of sharing development outcomes (“commonness”). The “commonness” dimension focuses on the inclusive sharing of development achievements, encompassing both prosperity disparity and sharing mechanisms. By measuring disparities among regions, urban-rural areas, and different social groups, it reflects the realization of social equity and justice. The “prosperity” dimension emphasizes the coordinated development of material and spiritual civilization. It comprehensively characterizes the provision level of basic public services and ecological environment resources across multiple aspects, including economic development, cultural education, social security, ecological environment, and income-consumption patterns.
Based on existing research findings and data availability, this study establishes an evaluation system comprising 4 first-level indicators, 9 second-level indicators, and 12 third-level indicators (as shown in Table 1). To ensure the objectivity of indicator weighting, the entropy method is employed to scientifically calculate and synthesize the common prosperity development index for each city (Chen et al., 2021; Han et al., 2023).
Core explanatory variables
The development level of digital financial inclusion (dif) is measured using the Digital Financial Inclusion Index calculated by the Peking University Digital Finance Research Center and Ant Group. This index encompasses three key dimensions: coverage breadth (coverage), usage depth (usage), and digitalization level (digital). It covers 31 provinces, 337 prefecture-level cities, and 2800 counties in China, demonstrating strong credibility and reliability. To ensure the accuracy of regression results, all data values are divided by 100 to reduce scale differences among the variables (Fang, 2023).
Control variables
In this research, the study incorporates the use of the following control variables: industrial structure (is), as determined by the tertiary industry’s added value as a percentage of the city’s GDP; the maturity of traditional financial systems (loan), as measured by the proportion of the end-of-year financial institution loan balance to the regional GDP; innovation capacity (ino), represented as the number of awarded patents logarithmically; innovation capacity, expressed as the logarithm of the number of patents granted; proportion of total foreign trade that reflects a country’s degree of openness to the outside world; the total amount of import and export, expressed as a proportion of regional GDP; the level of technology (tech), stated as a percentage of the local GDP to the amount spent on research and technology; the government regulation (gov), expressed as a proportion of the public budgetary expenditure of the cities to regional GDP; and the basic education (edu), expressed as the logarithmic ratio of elementary and secondary school teachers to 10,000 urban residents.
Moderating variables
The access, usage, and efficiency divides are the three categories into which the digital divide may be split. The access divide (ac- divide) is caused by differences in “digital access,” which is characterized by differences in the density of fiber-optic cables, the density of mobile base stations, and the number of Internet broadband accesses in different regions. This hardware difference is also called the “hard divide” (Qiu et al., 2023). The inverse of Internet broadband coverage was chosen to gauge the degree of “access” in each region, examining the access divide.
The usage divide (us- divide) refers to the difference in the utilization of digital technologies based on the different conditions of digital infrastructure (Wei et al., 2011). This variable is mainly measured by the internet penetration rate and the popularity of smartphones, including both frequency and method of use. The inverse of the year-end number of users of cell phones per 100 individuals was chosen to measure the usage divide.
The efficiency divide (ef- divide) refers to individual differences in the level of access to and the use of digital technology due to educational differences and differences in economic capacity. Thus, the efficiency divide is closely related to individual cultural literacy, and the inverse of the proportion of the population with a general education degree or higher was chosen to measure the capability gap. The larger the three indicators, the deeper the digital divide.
Data description
Based on data availability and completeness, this study utilizes panel data from 245 prefecture-level cities spanning 2012 to 2022, comprising a total of 2695 sample observations. Data on digital financial inclusion were obtained from the Peking University Digital Financial Inclusion Index (2011–2023), while other variables were primarily sourced from the China Statistical Yearbook, China City Statistical Yearbook (2013–2023), as well as provincial and municipal statistical yearbooks and bulletins. Missing values for specific indicators were addressed using interpolation methods. To mitigate the influence of outliers, the core explanatory variable (common prosperity) and control variables were winsorized at the 1% level. The descriptive statistics for all variables are presented in Table 2 below.