1. Introduction

Financial development has become one of the critical determinants of economic growth and social fairness in the modern global economy. With the introduction of inclusive financial systems, which seek to provide financial services to a broader range of society, the financial landscape has experienced profound changes. This change has been especially pertinent when considering China, which has seen tremendous urbanization and economic expansion in recent years.

China's economic system transitioned from planned to market following the 1978 reform and opening-up. This restructuring has propelled China's economic ascent while elevating living standards nationwide. From 1978 to 2022, GDP grew from 367.870 billion yuan to 1,210,207.24 billion yuan, and per capita GDP rose from 384.74 yuan to 85,698.11 yuan. Disposable income per capita increased from 171.17 yuan to 36,883.28 yuan. However, sustained income growth has been accompanied by rising inter-resident inequality. Ravallion and Chen [1] pointed out that income inequality is rising in China. As reported by the National Bureau of Statistics, the Gini coefficient of disposable income per capita was 0.473 in 2004, 0.490 in 2009, and 0.467 in 2022, exceeding 0.4, the threshold set by the relevant United Nations organizations. This discrepancy is especially noticeable between rural and urban areas, where disparities in opportunity and financial services accessibility can deepen existing economic gaps. As the economy grows and urbanization deepens, a more comprehensive range of financial needs will emerge.

As a reaction to these difficulties, "inclusive finance" has become popular. A system that offers financial services to all social segments and groups in a complete, adequate, and economical manner is known as inclusive finance, and it was first introduced by the UN in 2005 [2]. As inclusive finance has the potential to increase financial inclusion and decrease economic disparities, it is a topic of great interest that could help close the urban-rural income gap.

Therefore, this research aims to explore the effect of inclusive financial development on the urban-rural income inequality. The main contribution is that this study will use the Thiel index to measure urban-rural income inequality by province since less literature uses the Thiel index.

2. Literature review

Defined by the United Nations in 2005, inclusive finance initially advocated for universal access to responsible and sustainable financial services. Today, it has evolved into a comprehensive framework that delivers efficient, affordable financial solutions to all segments of society with financial needs [3]. Some research has created an index to measure various aspects of financial inclusion instead of depending just on one metric. Sarma and Pais [4] measured the level of financial inclusion development through three dimensions: service penetration, service availability, and utilization utility. They gave a formula for calculating the financial inclusion index (Ifl). Amidzic et al [5]. pioneered a composite metric for assessing financial inclusion, which takes into account three factors: utilization (loans and deposits), outreach (demographic and geographic penetration), and quality (cost of usage, dispute resolution, and transparency requirement). Zhou et al [6].identified a threshold effect in the relationship between inclusive finance and high-quality economic development. Specifically, economic advancement is dampened when the financial inclusion index falls below 0.358. Within the intermediate range of 0.358 and 0.522, inclusive finance positively yet modestly contributes to economic quality. Once the index surpasses 0.522, however, it exerts a significantly stronger promotive effect on high-quality development.

Some research concluded that inclusive finance contributes to economic growth and shared prosperity[7-9]. However, these studies have differing views on the role of coverage breadth, usage depth, and digital transformation. Zhou et al [10]. concluded that usage depth had the most significant impact, coverage breadth the next greatest, and digital transformation the least. Zhang et al [9].believed that they all influence shared prosperity. Different from these two conclusions, Ji et al [11]. empirically demonstrated that solely financial inclusion's coverage breadth exerts a significant mitigating effect on the urban-rural income gap, whereas usage depth and digitalization show statistically insignificant impacts.

Empirical evidence confirms that inclusive finance serves as a catalyst for rural revitalization and its associated industries^[12-13]. Financial inclusion significantly impacts rural households' developmental consumption but not rural households' subsistence and hedonic consumption[14]. Li et al [15]. empirically established that the expansion of inclusive finance significantly accelerates rural human capital accumulation through broader service coverage.

Additionally, inclusive finance positively impacts rural incomes[16-17]. It can narrow the urban-rural income inequality [18]. Yu et al [19]. demonstrated that inclusive finance significantly narrows urban-rural disparities in wage, property, and transfer income, yet exerts minimal influence on net business income differentials. Conversely, Ge et al [20]. found that financial inclusion has positively affected rural people's income, particularly by boosting wage, business, and transfer incomes, while it has harmed property incomes.

Inclusive finance exerts a significant spatial spillover effect, advancing high-quality economic development both locally and in geographically proximate regions with comparable economic conditions[21-22]. However, the efficacy of financial inclusion exhibits heterogeneous regional effects, with significantly stronger impacts on farmer income in eastern and central China than in western regions. This disparity is attributable to variations in economic development, infrastructure, and financial literacy [20]. Zhou et al [10]. demonstrated pronounced heterogeneity in financial inclusion's economic contribution: it is significantly stronger in regions with advanced economies, high digital financial inclusion, and technologically adept populations, yet markedly weaker in underdeveloped areas with limited financial access and technological capacity. Conversely, Zhang et al [13].empirically revealed an inverse efficacy pattern, where financial inclusion's impact on narrowing the urban-rural income gap intensifies in regions with greater socioeconomic deprivation.

3. Data and variables

3.1. Data collecting, cleaning, and matching

Thirty-one provinces (excluding Hong Kong, Macau, and Taiwan) in China were selected as sample regions for the Mobile Financial Inclusion Indicators and the Thiel Index. China's 31 provinces encompass a spectrum of development levels, from the advanced eastern seaboard to less developed central and western regions, exhibiting substantial provincial variations in economic growth, urban-rural income disparity, and financial landscapes. This geographic and socioeconomic heterogeneity enables a more comprehensive analysis of inclusive finance's impact on income gaps.

Statistical data from 2018 to 2022 for China's 31 provinces are relatively complete. Institutions such as the National Bureau of Statistics (NBS), the China Statistical Yearbook, Peking University, and the WIND database provide a wealth of provincial-level economic and financial data, including total population, balance of deposits and loans of financial institutions, premium income, agricultural loans in local and foreign currencies, GDP, land area, Tyrell's index and so on, making the database for the study more reliable and actionable.

Here, data that consist of the Inclusive Finance Index are cleaned based on the following steps: (1) standardizing raw data; (2) using the coefficient of variation method to determine the weights of indicators; (3) weighted to calculate the Financial Inclusion Index. Consequently, 155 Inclusive Finance Index remained between 2018-2022. Meanwhile, the Thiel Indexes are cleaned based on the following steps: (1) total income for towns is calculated using disposable income per capita for towns and the population of towns; (2) total rural income is calculated using disposable rural income per capita and rural population; (3) calculating the Thiel Index. Consequently, 155 observations are retained. The control variables are cleaned based on the following steps: (1) using fiscal expenditure and GDP data to calculate the government behavior, which represents the extent to which local governments are involved in economic activity; (2) using total exports and imports to calculate the degree of openness to the outside world; (3) using secondary GDP, tertiary GDP, and GDP to calculate the industrial structure. Consequently, 465 observations are retained.

Because the Inclusive Finance Index, the Thiel Index, and the control variables are separate, their provinces and years should be consistent. Here, two methods were adopted: matching by location and matching by year. Accordingly, 930 observations were matched.

3.2. Variables

3.2.1. Dependent variable

According to the previous content, the Thiel Index (Gap) is the dependent variable. This research employs the Thiel Index to quantify provincial-level urban-rural income disparities. Therefore,  $$ {Gap}_t$$  is measured by the equation as follows:

$$$ \begin{array}{c}{Gap}_t=\sum _{j=1}^2\left(\frac{y_{jt}}{y_t}\right)\ln \left(\frac{y_{jt}}{y_t}/\frac{p_{jt}}{p_t}\right),\end{array}$$$(1)

For urban (j=1) and rural (j=2) areas respectively,  $$ y_{jt }$$ denotes annual aggregate income of each sector, while  $$ y_t $$ represents combined urban-rural income in year t. Correspondingly,  $$ p_{jt} $$ signifies sectoral population, and  $$ p_{t }$$ the total regional population annually.

3.2.2. Independent variable

The Inclusive Finance Index (IFL) was considered independent variable for research aim. This paper will select ten specific evaluation indicators from three aspects of service availability, service utilization and service quality, and use the calculation method of Sarma and Paris [4] to comprehensively analysis the level of inclusive financial development.

This study employs the coefficient of variation method to assign indicator weights, and the financial inclusion index is calculated using the Euclidean distance method. Firstly, standardize the raw data:

$$$ \begin{array}{c}{X}_{ij}^{\text{'}}=\frac{X_{ij}-\min \left\{X_j\right\}}{\max \left\{X_j\right\}-\min \left\{X_j\right\}}\end{array}$$$(2)

Where  $$ X_{ij}$$  represents the actual value of indicator j in year i, min{ $$ X_j$$ } and max{ $$ X_j$$ } denote the minimum and maximum values in the jth indicator, i=1,2,…n, and j=1,2,…k.

The next step is to calculate the coefficient of variation for each evaluation indicator:

$$$ \begin{array}{c}{V}_j=\frac{s_j}{\stackrel{-}{A_j}}\end{array}$$$(3)

For the jth evaluation indicator,  $$ V_j$$  denotes its coefficient of variation,  $$ s_j$$  is the standard deviation, and  $$ \stackrel{-}{A_j}$$  represents the mean value.

Each indicator's weight is derived from its coefficient of variation. Denoting the jth indicator's weight as  $$ W_j$$ , the dimensionless value  $$ D_{ij}$$  is computed as:

$$$ \begin{array}{c}{W}_j=\frac{V_j}{{\sum }_{j=1}^k{V}_j}\end{array}$$$(4)

$$$ \begin{array}{c}{D}_{ij}=W_j\ast X_{ij}^{\text{'}}\end{array}$$$(5)

The final step is calculating the inclusive finance index using the Euclidean distance method:

$$$ \begin{array}{c}{IFL}_i=1-\frac{\sqrt{{\left(W_1-D_{i1}\right)}^2+{\left(W_2-D_{i2}\right)}^2+\dots +{\left(W_k-D_{ik}\right)}^2}}{\sqrt{{\left(W_1\right)}^2+{\left(W_2\right)}^2+\dots +{\left(W_k\right)}^2}}\end{array}$$$(6)

3.2.3. Control variables

About control variables, existing studies have explored four critical factors influencing the urban-rural income gap. According to previous studies, this paper chooses Level of economic development (GDP) [23], government behavior (GOV) [18], degree of openness to the outside world (OPE) [24], and industrial structure (IS) [25].

4. Panel data model estimation and analysis

4.1. Panel data model

Drawing on empirical data and extant literature, this research employs panel modeling to analyze inclusive finance's influence on the urban-rural income disparity. The specification is formalized as:

$$$ \begin{array}{c}{Gap}_{i,t}={\beta }_1{IFL}_{i,t}+{\beta }_2{GDP}_{i,t}+{\beta }_3{GOV}_{i.t}+{\beta }_4{OPE}_{i,t}+{\beta }_5{IS}_{i,t}+{\beta }_7+{\epsilon }_{i,t}\end{array}$$$(7)

Where  $$ {Gap}_{i,t}$$  represents the urban-rural income disparity in ith province in period t,  $$ {IFL}_{i,t}$$  denotes the level of inclusive financial development in the ith province in period t,  $$ {GDP}_{i,t}$$  denotes the GDP per capita of the ith province in period t,  $$ {GOV}_{i,t}$$  denotes the share of public fiscal expenditure in GDP in period t for the ith province,  $$ {OPE}_{i,t}$$  denotes the share of total imports and exports of the ith province in GDP in period t,  $$ {IS}_{i,t}$$  denotes the sum of the value added of the secondary industry and the tertiary industry of the ith province in period t as a share of GDP,  $$ {\epsilon }_{i,t}$$  represents the random error term.

4.2. Statistical profiles and associations

Table 2 reports descriptive statistics for all variables. The variable Gap shows substantial dispersion (mean=0.073, SD=0.032) across observations, while IFL exhibits significant interprovincial variation (mean=0.134, SD=0.124). With a mean of 73871.088 and a standard deviation of 33262.669,  $$ GDP$$  per capita has the most significant diversity among the studied regions, indicating substantial economic differences. The average and standard deviation of  $$ GOV$$  are 0.282 and 0.194, respectively. The  $$ IS$$  has a mean of 0.908 with very low variability (SD = 0.052), whereas the  $$ OPE$$  has a mean of 0.239 and a standard deviation of 0.230.

Table 3 shows the correlations of all the variables. A lower urban-rural income gap is connected with better levels of inclusive financial development, economic growth, openness, and industrial structure, as indicated by the  $$ Gap$$ 's negative correlations with  $$ IFL$$  (-0.6080),  $$ GDP$$  (-0.6854),  $$ OPE$$  (-0.6984), and  $$ IS$$  (-0.4134). On the other hand, there is a positive correlation between the  $$ Gap$$  and  $$ GOV$$  (0.5350), indicating that greater government participation in the economy is linked to a broader income disparity.

Table 4 shows the weights and descriptive statistical values for each evaluation indicator. Within the ten inclusive finance metrics, three spatial penetration indicators carry notably higher weights, namely financial outlet density (0.1892), employee density (0.2282), and insurance density (0.1015) per 10,000 square kilometers. This shows that the number of employees in financial institutions significantly impacts inclusive finance and reduces the urban-rural income disparity. The distribution and density of financial institutions' outlets also attach importance to promoting financial inclusion, as more outlets mean that residents have easier access to financial services, especially in rural and remote areas, which can decrease the urban-rural income disparity. Insurance density reflects the popularity of insurance products among population, and higher insurance density can provide better risk protection and enhance the population's economic stability and risk resistance, thus helping to promote economic equity. The weighting of innovative Internet finance situations suggests that digital financial inclusion significantly impacts urban-rural income disparity.

4.3. Model regression results and analysis

The R-squared values represent the dependent variable's variance as a function of the independent factors. The R-squared values for the inside, between, and overall categories are 0.7362, 0.4034, and 0.4137, respectively. A moderately negative correlation (-0.5469) exists between the fixed effects and the independent variables.

The coefficients for  $$ IFL$$ ,  $$ GDP$$ ,  $$ GOV$$ , and  $$ IS$$  are statistically significant at 1% level. The negative coefficient for  $$ IFL$$  (-0.2165) suggests that the higher financial inclusion development, the lower urban-rural income disparity. Other things being equal, a one-unit increase in inclusive finance can reduce the urban-rural income disparity by 0.2165 units.

Among control variables, GDP's coefficient (-3.14e-07) places China on the declining segment of the inverted U-curve (Kuznets hypothesis), indicating that higher economic development levels correlate with reduced income inequality. The coefficient of government behavior influence on the urban-rural income disparity is 0.0832 and is significant. This implies that increased government fiscal expenditure on towns and cities has widened the urban-rural income disparity. A lower income difference is linked to a more sophisticated industrial structure, as indicated by the positive coefficient for  $$ IS$$  (0.5946). However, the coefficient of OPE is not statistically significant at 5% level, showing that trade openness exerts no significant influence on urban-rural income inequality.

*** p<0.01, ** p<0.05, * p<0.1

5. Conclusions and discussions

5.1. Main findings

Inclusive financial development has emerged as a critical determinant of urban-rural income disparities. This research leverages provincial panel data in China from 2018 to 2022 to empirically assess financial inclusion's impact on such disparities, yielding three key insights. First, advancing inclusive finance significantly narrows the rural-urban income divide. Second, enhancing financial institution staffing, service outlets, and insurance density improves financial accessibility and service quality, fostering both economic growth and social equity. Digital financial innovation further contributes meaningfully to reducing interregional income inequality. Third, while heightened economic development and trade openness alleviate income inequality, increased public expenditure share in GDP and industrial and service sectors' economic contributions inadvertently amplify the disparity.

5.2. Policy recommendations

Combined with the actual situation of China's inclusive financial development and the results of this paper's researchers, it mainly puts forward policy recommendations from the following four aspects.

First, governments should increase their investment in and support inclusive finance and promote inclusive financial services. On the one hand, the government should increase financial investment in developing inclusive finance, including financial support, tax incentives, and operating subsidies, to encourage more financial institutions to participate actively in inclusive financial services. On the other hand, investment in building financial infrastructure in rural and remote areas, such as automated teller machines (ATMs), mobile banking, and electronic payment terminals, improves access to financial services.

Second, increasing the number of employees in financial institutions, expanding their business outlets, and increasing the popularity of insurance products. Governments should encourage and fund financial education programs, especially in rural and remote areas, to train more financial professionals. Governments can also attract financial professionals to work in rural and less developed areas by providing financial incentives and welfare policies. In addition, the government should improve the infrastructure in rural and remote areas and create conditions for establishing financial institutions' business outlets. The government should also increase insurance education and publicity, innovate insurance products that meet the specific needs of rural and low-income populations, and encourage more residents to purchase insurance through policy incentives.

Third, the coverage of digital financial services should be expanded, and the digital financial literacy of the population should be enhanced. Governments should invest in Internet and mobile communications infrastructure in rural and remote areas to ensure residents can access digital financial services easily. At the same time, extensive financial literacy and digital skills training has been carried out, especially for rural residents, the elderly, and low-income groups, to help them acquire basic skills in using digital financial tools.

5.3. Limitations and further work

While relatively robust, the fixed effects model used in this study has limitations and may not be able to fully explain all of the unobserved heterogeneity or potential endogeneity between financial inclusion and income disparity. Moreover, this study is limited to a specific geographic context, and the results may not apply to other regions or countries with different economic structures, financial systems, and regulatory environments.

Future research should aim to collect more comprehensive and detailed data over longer time horizons and in different regions to provide a more nuanced understanding of the relationship between inclusive financial development and income disparity.