Spatial Spillover Effect and Threshold Effect of Digital Financial Inclusion on Farmers’ Income Growth—Based on Provincial Data of China

Abstract

The effect of digital financial inclusion on farmers’ income growth is worth theoretical discussion and empirical testing. Based on the sample data of 30 provinces in the Chinese mainland from 2011 to 2019, this paper adopted the spatial Durbin model and the panel threshold model to empirically study the impact of digital financial inclusion on the growth of farmers’ income; furthermore, the heterogeneity of the impact was studied in terms of the difference of provincial economic development level. The results showed that: first, digital financial inclusion can significantly promote farmers’ income growth; second, digital financial inclusion has a positive spatial spillover effect on farmers’ income growth; third, the impact of digital financial inclusion on farmers’ income growth has a double threshold effect: farmers’ income growth increases with the development of digital financial inclusion; and fourth, the impact of digital financial inclusion on farmers’ income growth is heterogeneous in terms of provincial economic development level.

1. Introduction

The growth of farmers’ income is of great practical significance to the development of rural economy and the stability of farmers’ lives. In recent years, with rapid economic development, economic development imbalance exists among regions as well as between urban and rural areas in China. The income gap between urban and rural areas of China has become one of the critical issues concerned by many scholars. There are many factors affecting farmers’ income, such as natural conditions [1], infrastructure gap [2,3], urbanization level, and even capital stock difference [4,5], which may influence farmers’ income to a certain extent. From the perspective of financial development, since the traditional financial mode (set physical outlets, etc.) is greatly limited by transportation and geographical location, the financial needs (credit lines for the purchase of machinery, etc.) of rural areas cannot be met in time. In addition, the high threshold and high transaction cost of traditional finance cause rural residents’ borrowing difficulties, hindering rural economic development and limiting farmers’ income growth. Digital finance, which combines digital information technology with traditional finance, innovates the financial development model, broadens the development space of the financial market, and further promotes the development of financial inclusion, bringing convenience and welfare to people. On the basis of overcoming high cost and low return, digital financial inclusion can optimize the allocation of financial resources through digital technology and provide financial service support for economically underdeveloped areas.

Farmers’ income growth is the key to realizing the coordinated development of urban and rural economies. Financial development has an impact on farmers’ income growth, and the development of digital financial inclusion based on digitization is more important to increase farmers’ income. Studies have shown that in the context of digital dividends, that is, digitalization brings convenience and welfare to people’s lives, and digital financial inclusion is conducive to promoting inclusive growth in rural areas, thus improving farmers’ income. The development of digital financial inclusion has a phased and in-depth impact on farmers’ income, mainly reflected in the following aspects. First, financial development will improve farmers’ income. Luo et al. found differences in the impact of rural financial scale and financial efficiency on farmers’ income in different regions [6]. There is a significant causal relationship between rural financial development efficiency and farmers’ income [7]. Obtaining funds through finance can reduce income inequality and alleviate rural poverty [8,9], thus improving farmers’ income. Second, digital financial inclusion promotes economic growth in rural areas and increases farmers’ income. Digital financial inclusion is attached to network and information technology to reasonably allocate financial resources in rural areas and provide people in remote areas such as rural areas with the possibility of accessing financial services. Ma adopted the panel regression model to find that petty loans encourage farmers to start businesses and thus increase farmers’ income, indicating that financial behavior can promote farmers’ income growth [10,11], and it also has a significant contribution to promoting economic growth [12,13,14]. Third, the development of inclusive finance has narrowed the income gap between urban and rural areas while raising farmers’ income. Yu and Wang found that inclusive finance can reduce wage income, promote the growth of farmers’ income, and narrow the income gap between urban and rural areas [15]. Liu et al. found that inclusive finance promotes farmers’ income growth through the mediating role of industrial structure upgrading, realizing the integration of farmers and modern agricultural industry through technological innovation in the process of industrial upgrading, and the modern agricultural industry is agriculture based on modern industry and modern science and technology [16,17].

As an emerging financial development mode, digital financial inclusion not only meets people’s needs but also expands the depth of poor farmers’ financial use and effectively alleviates financial exclusion. On the one hand, the credit support provided by digital financial inclusion helps farmers solve capital constraints and helps promote the development of rural economy and industry [18,19]. From the perspective of space, the network features of digital financial inclusion increase the coverage of rural financial services and provide more income increase opportunities for poor farmers. Digital financial inclusion not only reduces the income gap between urban and rural areas but also contributes to farmers’ income growth and helping the poor escape poverty at an early date.

This paper studied the impact of digital financial inclusion on farmers’ income growth, focusing on its spatial effect and threshold effect. The significant contributions are as follows. First, the relationship between digital financial inclusion and farmers’ income growth as well as the impact mechanism and effect were explored through theoretical analysis and empirical research. Second, from the perspective of space, this paper empirically tested the spatial spillover effect of digital financial inclusion on farmers’ income growth using the spatial Durbin model. Third, from the angle of nonlinear impact, this paper constructed a panel threshold model and took digital financial inclusion as the threshold variable to test its threshold effect on farmers’ income growth. Fourth, considering the factor of unbalanced regional economic development, all sample areas were divided into economic development areas and economically underdeveloped areas to study the heterogeneous impact of digital financial inclusion on farmers’ income growth.

The rest of this paper is mainly arranged as follows. Section 2 elaborates the theoretical analysis and research hypotheses, theoretically analyzing the growth effect, spatial spillover effect, threshold effect, and spatial heterogeneity of digital financial inclusion on farmers’ income, and proposing research hypotheses accordingly. Section 3 describes the model design and indicator selection, including the construction of the spatial Durbin model and panel threshold model, and the introduction of indicator selection and data sources. Section 4 presents and analyzes the empirical results, including the spatial correlation test of variables, the spatial spillover effect test, and the threshold effect test. Section 5 concludes the research, comments on the results and the effectiveness of the chosen models, and proposes political implications.

2. Theoretical Analysis and Research Hypotheses

2.1. The Effect of Digital Financial Inclusion on Farmers’ Income Growth

Finance is closely linked with rural economic development and farmers’ income, and financial development promotes rapid growth of the rural economy [12,20]. Economic growth theories hold that capital is an essential factor of growth, so better capital allocation brought by rural financial development will greatly promote farmers’ income growth. However, due to the lack of financial services for a long time, the financial needs of the poor in rural areas are often not well met. With the help of a series of network connection advantages such as the Internet and big data, digital financial inclusion has a more favorable communication space than traditional finance. Solving the loan problem of rural people and encouraging farmers to start business investment can promote farmers’ income growth.

Digital financial inclusion is the combination of digital finance and inclusive finance. With the support of information technology, it reduces the problem of information asymmetry and realizes low-cost transactions [21,22], greatly reducing the threshold for people to participate in financial transactions and providing financial services for low-income and vulnerable groups more conveniently. Firstly, there is a one-way causal relationship between agricultural loans and agricultural output value: the increase of agricultural loans promotes the improvement of agricultural output value [23,24], while fintech helps reduce credit risk [18,19]. Wang et al. used a quantile regression method to study the relationship between credit constraints, credit adjustment, and farmers’ income growth. The empirical results showed that rural people face severe credit constraints, and farmers’ credit plays a role in the sustainable growth of farmers’ income [25]. Secondly, compared with the rural financial structure, the development efficiency and construction scale of rural finance make a more prominent contribution to farmers’ income growth [26,27]. Digital financial inclusion has effectively alleviated financial exclusion in rural areas, improved the inclusion of financial services, and promoted inclusive economic growth. By reducing transaction costs, time, and information costs, digital financial inclusion meets the financial needs of people in rural areas, improves the confidence of poor people in financial institutions, and helps the poor escape poverty as soon as possible [28,29].

The network characteristics of digital financial inclusion have also promoted farmers’ income growth. Digital financial inclusion is more inclusive than traditional finance and covers a broader range of people with the help of digital technology and Internet technology. Traditional finance is a limited and relatively single financial activity, which only includes the three traditional businesses of deposit, loan, and settlement. Traditional finance relies on setting up physical outlets to develop financial institutions, while digital financial inclusion relies on digital technology to exert the zero-marginal cost effect of network and promote the rapid and inclusive development of digital finance in remote areas. Digital financial inclusion promotes economic growth with the Internet threshold effect [12]. In areas with good network conditions, inclusive financial services can promote economic growth and help vulnerable farmers reduce poverty [30,31]. Kelikume used the systematic generalized moment method to study and found that with the increase of Internet usage, inclusive finance has a significant impact on improving poverty reduction efficiency [32]. Financial services can reduce income inequality among countries and reduce the credit constraints of low-income people through the development of digital financial inclusion, and fintech can help boost productivity in industries such as agriculture so as to effectively increase farmers’ income [33,34,35]. It can be seen that the rapid development of digital finance has brought a series of impacts on the economy, society, and people’s lives. Digital financial inclusion has greatly contributed to poverty reduction in remote areas and the growth of rural residents’ income. Therefore, this paper puts forward the first hypothesis.

Hypothesis 1.

Digital financial inclusion has a positive effect on farmers’ income growth.

2.2. The Spatial Spillover Effect of Digital Financial Inclusion on Farmers’ Income Growth

The impact of digital financial inclusion on farmers’ income growth is also affected by spatial factors and has spatial spillover effects. Firstly, with the maturity of digital technology and the popularization of the Internet, spatial connections among regions have become closer, the network characteristics of digital financial inclusion have become increasingly prominent, and cross-regional services have become more convenient so that developed provinces can easily drive financial activities in other provinces through network spillover [21,36,37]. Secondly, the development of digital financial inclusion has an upstream and downstream pulling effect. When the financial demand in a certain area is strong, it is bound to drive the development of the upstream and downstream financial industries in the surrounding areas. Therefore, in order to prevent underestimating the impact of digital financial inclusion on farmers’ income growth, considering the spatial spillover effect of digital financial inclusion, this paper proposes the second hypothesis.

Hypothesis 2.

Digital financial inclusion has a spatial spillover effect on farmers’ income growth.

2.3. The Threshold Effect of Digital Financial Inclusion on Farmers’ Income Growth

Digital financial inclusion has different effects on regional economic growth at different stages of its development. Affected by factors such as residents’ cultural quality and Internet penetration, the main participants of digital financial inclusion in the early stages of development are urban residents, and the participation of rural residents is low. With the development of the Internet and the improvement of rural infrastructure, digital financial inclusion does not need to rely on physical outlets to provide financial services for people. Therefore, the number of financial users in remote areas such as rural areas grows rapidly. Additionally, digital financial inclusion investment is a problem; for different service objects, digital financial inclusion has different impacts on them. So, through financial support for the reasonable and avoiding the mismatching of financial resources, which are beneficial to the combination of the combination of digital inclusive finance and farmers’ production and farmers’ production, farmers’ income growth increases.

When the rural financial market was underdeveloped, financial services were insufficient and financial products were single, and farmers were less willing to participate in financial activities. At this time, the impact of digital financial inclusion on farmers’ income growth was limited. With the gradual penetration of digital financial inclusion in rural areas and the lowering of financial service thresholds, rural residents are more likely to access the benefits brought by the improvement of financial development. When the threshold of digital financial inclusion is crossed, that is, with the application of digital technologies such as digital verification technology and mobile terminals, the impact of digital financial inclusion on farmers’ income growth will increase. In general, as the development of digital financial inclusion continues to mature, it will provide financial services and low usage costs in rural areas and increases farmers’ income by promoting rural economic growth and industrial development. Therefore, the impact of digital financial inclusion on farmers’ income growth has a threshold feature. Therefore, the third hypothesis is put forward.

Hypothesis 3.

The impact of digital financial inclusion on farmers’ income growth has a threshold effect depending on its development level.

2.4. Spatial Heterogeneity of the Impact of Digital Financial Inclusion on Farmers’ Income Growth

Digital financial inclusion has different effects on farmers’ income growth in regions with different economic foundations, and the economic conditions of different regions have different effects on the development trend of digital financial inclusion [38,39,40]. Xie et al. found that the in-depth development of digital financial inclusion will promote rural entrepreneurship, which can have more abundant human resources and government support to save costs; the impact of financial development on farmers’ entrepreneurship is regionally heterogeneous, and the promotion of the central region is significantly better than that of the eastern and western regions [41]. In addition, there are significant differences in China’s regional economic development level and financial level. Although digital financial inclusion has expanded financial coverage in rural areas, due to regional differences, its impact on farmers’ income growth also has regional heterogeneity. Therefore, based on the differences in regional development and the imbalance in financial allocation, it is of great practical significance to explore the differences in the impact of digital financial inclusion on farmers’ income growth. Thus, this paper proposes the fourth hypothesis.

Hypothesis 4.

The impact of digital financial inclusion on farmers’ income growth is spatially heterogeneous in terms of regional economic characteristics.

3. Model Specification and Indicator Selection

3.1. Model Specification

3.1.1. Moran’s I

In order to study the spatial relationship between digital financial inclusion and farmers’ income, it is necessary to test the spatial correlation between the two first. This paper selected the commonly used global $Mora{n}^{\prime }s I$ to verify it. The form of the global $Mora{n}^{\prime }s I$ is as follows:

$$Mora{n}^{\prime }s I=\frac{n{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{w}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}{{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{\left(x_i-\overline{x}\right)}^2}$$

(1)

where $n$ represents the number of regions in the research sample (the number of provinces in this paper), and $w_{ij}$ is a spatial weight matrix; $x_i$, $x_j$ represent the digital financial inclusion or farmers’ income in province $i$ and province $j$ respectively; $\overline{x}$ is the average value of digital financial inclusion or farmers’ income in the corresponding year. The data of farmers’ income and digital financial inclusion are based on the data of 30 Provinces in China from 2011 to 2019 (Tibet was excluded because serious data were missing). The selection and sources of specific indicators are shown in

Table 1. Variable definition and data source.

Variable	Abbreviation	Unit	Measurement	Source
Farmers’ income	FII	Ten thousand yuan	Per capita disposable income of rural residents	Statistical yearbook of Chinese provinces 2012–2020
Digital financial inclusion	DIF	/	Peking University Digital Financial Inclusion Index	Institute of Digital Finance Peking University
Economic development level	LED	One thousand yuan	Regional per capita GDP	Statistical yearbook of Chinese provinces 2012–2020
Industrial structure	IS	%	Added value of the secondary industry/GDP	Statistical yearbook of Chinese provinces 2012–2020
Urbanization level	UL	%	Permanent urban population/population	Statistical yearbook of Chinese provinces 2012–2020
Production factors	AM	kilowatts	Total power of agricultural machinery	EPS database
Human capital	HC	/	calculation	EPS database
Farmers’ investment	IF	billion	Farmers’ capital investment—residential investment	EPS database

. $Mora{n}^{\prime }s I$ takes a value between −1 and 1, and when it approaches 0, it indicates that there is no spatial correlation between the variables; if it is greater than 0, it means that the variable has a positive auto-correlation; otherwise, there is a negative auto-correlation.

In this paper, the inverse distance matrix was selected as the spatial weight matrix, and the reciprocal of the distance between any two provinces was used as the weight of the inverse distance matrix. The greater the distance between the two provinces, the smaller the weight. The calculation formula of the inverse distance matrix set in this paper is shown in Equation (2):

$$w_{ij}=\{\begin{array}{c}\frac{1}{d_{ij}} , i\ne j\\ 0 , i=j\end{array}$$

(2)

where $d_{ij}$ is the distance between provincial capital cities calculated according to latitude and longitude.

3.1.2. Spatial Durbin Model

According to the previous analysis, digital financial inclusion has spatial features. General econometric models usually regard samples as independent and homogeneous in geographical space, and do not consider the possible spatial dependence of samples so as to obtain biased estimation. However, spatial panel model improves the validity of parameter estimation by combining spatial panel data observed in a certain spatial unit time series. In order to comprehensively study the impact of digital financial inclusion on farmers’ income growth, this paper considered the spatial spillover effect of digital financial inclusion and selected the spatial Durbin model for empirical analysis by referring to the research on the spatial spillover effect of digital financial inclusion [21,42]. The basic expression of the spatial Durbin model is:

$$y=\alpha {\theta }_n+\gamma Wy+X\beta +WX\delta +\epsilon$$

(3)

Therefore, the expression of the spatial Durbin model constructed according to the variables selected in this paper is:

$$\begin{array}{c}FI{I}_{it}=\alpha {\theta }_n+\gamma wFI{I}_{it}+{\beta }_{1}DI{F}_{it}+{\beta }_{2}I{S}_{it}+{\beta }_{3}U{L}_{it}+{\beta }_{4}A{M}_{it}+{\beta }_{5}H{C}_{it}+{\beta }_{6}I{F}_{it}+{\delta }_{1}wDI{F}_{it}+{\delta }_{2}wI{S}_{it}\\ +{\delta }_{3}wU{L}_{it}+{\delta }_{4}wA{M}_{it}+{\delta }_{5}wH{C}_{it}+{\delta }_{6}wI{F}_{it}+{\epsilon }_{it}\end{array}$$

(4)

In Equation (4), $FI{I}_{it}$ is the explained variable, which represents the farmers’ income in each province. As an explanatory variable, $DI{F}_{it}$ represents digital financial inclusion. The control variables included industrial structure, urbanization level, production factors, human capital, and farmers’ investment. The details of the selection of variables and data sources are shown in Table 1. $\gamma$ is the spatial lag term coefficient of farmers’ income. ${\beta }_i$ is the elastic coefficient of variable $i$ to the farmers’ income growth in local province, and ${\delta }_i$ is the spatial interaction term coefficient of variable $i$, which characterizes the impact of the variable on the farmers’ income growth in surrounding provinces. $\alpha$ is the constant term. ${\theta }_n$ is the $n\times 1$ identity matrix. $n$ is the number of provinces observed, and ${\epsilon }_{it}$ is the error term.

The spatial Durbin model was used to analyze the spatial spillover effect of digital financial inclusion on farmers’ income growth. Due to the spatial dependence between variables, it is better to study the direct effect of the development and change of digital financial inclusion on the local province and the indirect effect on the surrounding provinces. The effect decomposition formulas are as follows:

$$Y={\left(I-\gamma W\right)}^{-1}\alpha {\theta }_n+{\left(I-\gamma W\right)}^{-1}\left(X\beta +WX\delta \right)+{\left(I-\gamma W\right)}^{-1}\epsilon$$

(5)

$$\begin{array}{c}Y={\displaystyle \sum _{r=1}^n}{S}_r\left(W\right)X_r+V\left(W\right){\theta }_n\alpha +V\left(W\right)\epsilon \\ S_r\left(W\right)=V\left(W\right)\left(I_n{\beta }_r+W{\delta }_r\right),V\left(W\right)={\left(I-\gamma W\right)}^{-1}\end{array}$$

(6)

$$\left[\begin{array}{c}\begin{array}{c}{Y}_1\\ Y_2\end{array}\\ \begin{array}{c}⋮\\ Y_n\end{array}\end{array}\right]={\displaystyle \sum }_{r=1}^n\left[\begin{array}{cc}\begin{array}{ccc}{S}_r{\left(W\right)}_{11}& S_r{\left(W\right)}_{12}& \dots \\ S_r{\left(W\right)}_{21}& S_r{\left(W\right)}_{22}& \dots \end{array}& \begin{array}{c}{S}_r{\left(W\right)}_{1n}\\ S_r{\left(W\right)}_{2n}\end{array}\\ \begin{array}{ccc}⋮& ⋮& \ddots \\ S_r{\left(W\right)}_{n1}& S_r{\left(W\right)}_{n2}& \dots \end{array}& \begin{array}{c}⋮\\ S_r{\left(W\right)}_{nn}\end{array}\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{X}_{1r}\\ X_{2r}\end{array}\\ \begin{array}{c}⋮\\ X_{nr}\end{array}\end{array}\right]+V{\left(W\right)}_{\epsilon }$$

(7)

In Equation (7), $S_r{\left(W\right)}_{ij}$ represents the impact of variable $r$ in province $j$ on the farmers’ income of surrounding provinces, i.e., the indirect effect. $S_r{\left(W\right)}_{ii}$ represents the impact of variable $r$ in the local province on local farmers’ income, i.e., the direct effect. The sum of direct effect $S_r{\left(W\right)}_{ii}$ and indirect effect $S_r{\left(W\right)}_{ii}$ is the total effect.

3.1.3. Panel Threshold Model

Digital financial inclusion impacts farmers’ income growth, and regional differences make its impact complex. The resource allocation in each province is different, and the development gap of digital financial inclusion between provinces has different effects on farmers’ income growth. The development of digital financial inclusion is uneven in space, and it has different influences on farmers’ income growth in different development degrees. Therefore, it is necessary to study the non-linear influence of digital financial inclusion on farmers’ income growth. Therefore, based on the panel threshold model proposed by Hansen (1999), this paper constructed an econometric model to study the phased impact of digital financial inclusion on farmers’ income growth. The threshold effect was verified by the threshold model, and the existence of several digital financial inclusion thresholds was determined by the threshold value estimated by the model so as to analyze the influence of different digital financial inclusion development degrees on farmers’ income growth. The expression of the panel threshold model constructed in this paper is as follows:

$$\begin{array}{c}FI{I}_{it}={\mu }_i+{\alpha }_{1}DI{F}_{it}I\left(q\le {\gamma }_1\right)+{\alpha }_{2}DI{F}_{it}I\left({\gamma }_1\le q\le {\gamma }_2\right)+\dots +{\alpha }_{n}DI{F}_{it}I\left({\gamma }_{n-1}\le q\le {\gamma }_n\right)+{\beta }_{1}I{S}_{it}+{\beta }_{2}U{L}_{it}\\ +{\beta }_{3}A{M}_{it}+{\beta }_{4}H{C}_{it}+{\beta }_{5}I{F}_{it}+{\epsilon }_{it}\end{array}$$

(8)

In Equation (8), $i, t$ represent province and time, respectively; $FII$ is the explained variable: farmers’ income, and $DIF$ is the core explanatory variable: digital financial inclusion, which is also a threshold variable. The rest are a series of control variables, including $IS$: the industrial structure, $UL$: the level of urbanization, $AM$: the production factor, $HC$: the human capital, and $IF$: the investment of farmers. $I(·)$ is an indicator function. When the condition in the bracket is met, $I(·)$ = 1, otherwise it is 0. ${\gamma }_i$ is the estimated threshold value of threshold $i$. ${\mu }_i$ is the individual fixed effect, and ${\epsilon }_{it}$ is the error term.

According to the given estimation method, the threshold model was estimated first, and then the threshold effect significance was tested by the minimum threshold value and slope value of the estimated sum of squared residuals. The asymptotic distribution was simulated by Bootstrapping. The threshold effect significance and the authenticity of the threshold estimates were inspected according to statistics $F$ and the likelihood ratio (LR).

3.2. Indicator Selection and Data Source

The explanatory variable of this paper was farmers’ income. Referring to most relevant research papers, this paper selected the per capita disposable income of rural residents in various provinces to measure farmers’ income. According to the available statistical data, since 2013, the National Bureau of Statistics has implemented the reform of urban-rural integrated household income and expenditure survey, replacing the net income of rural residents with disposable income. However, after analysis and comparison, little difference was found in the statistical caliber between the two. Therefore, this paper selected the data of rural residents’ net income from 2011 to 2012 and rural residents’ disposable income from 2013 to 2019, which are collectively referred to as rural residents’ per capita disposable income.

The core explanatory variable of this paper was digital financial inclusion, and the Digital Financial Inclusion Index of China (DFIIC) published by the Institute of Digital Finance Peking University was selected as the representative [43]. The index was compiled from digital financial services data provided by tech company Alibaba Ant Financial, and it constructs an index system from three dimensions of breadth, usage depth, and digitalization, including data of counties, cities, and provinces. According to the research theme and objectives, this paper chose provincial data for research. It followed the compilation principles of comprehensiveness, balance, comparability, continuity, and feasibility, and reflects the overall development and changing trend of digital technology-assisted finance. The breadth of coverage was measured by the number of electronic accounts. Digital financial inclusion can better provide financial services because it does not need physical outlets and is cross-regional. The depth of use mainly reflects the development depth of digital financial inclusion by combining different types of financial services and products, and its measurement indicators include the actual total use (the number of users per 10,000 users), the degree of active use (the number of transactions per capita), and the intensity of use (the amount of transactions per capita). The degree of digitization reflects the situation that digital financial inclusion provides financial services to the masses by lowering the threshold and improving the convenience.

The selected control variables included (1) Industrial structure. The industrial structure has an important impact on residents’ income. When production efficiency is higher, residents’ living standards also improve. This paper selected the proportion of the added value of the secondary industry in the GDP of each province to measure the corresponding industrial structure. (2) Urbanization level. More and more rural laborers are migrating to cities, and the flow of rural laborers will impact their income. This paper selected the proportion of permanent urban residents in the total population of each province to measure the level of urbanization. (3) Production factors. When the agricultural production mode changes, the income structure of farmers will also be affected. This paper selected the total power of agricultural machinery to measure production factors. (4) Human capital. Generally speaking, the rural population has a low level of education, which obviously affects their income level. Based on the practice of Du Jiang et al. [44], this paper selected the average education level to measure rural human capital (the specific calculation is the weighted average of the education level of each academic level, that is: average education level = primary school proportion × 6 + junior middle school proportion × 9 + senior high school proportion × 12 + junior college and above proportion × 16. The education years of each academic level were taken as 6, 9, 12, and 16, respectively). (5) Farmers’ investment. In general, the improvement of farmers’ investment level can increase farmers’ income. This paper, referring to the practice of Wang Yongcang [45], selected farmers’ fixed asset investment minus residential investment to measure farmers’ investment level.

The definitions and data sources of screened variables selected in this paper are shown in Table 1.

The data samples of this study were 30 provinces in the Chinese mainland. (Tibet’s data were seriously missing, so it was excluded). Peking University’s Digital Financial Inclusion Index is widely used in digital financial inclusion-related research [12,15,22], which can well reflect the overall development and change trend of digital technology-assisted finance. Since the DFIIC was released in 2011, and the statistical indicators required to construct the DFIIC are not comprehensive enough before 2011, combined with the data available for other control variables, this paper finally selected the data from 2011 to 2019 for research. The time frequency of the data was set as annual. The data of farmers’ income came from the statistical yearbook of each province from 2012 to 2020, the data of digital financial inclusion came from the digital financial inclusion Index released by the Research Center for Digital Finance of Peking University, and the data of other control variables came from the EPS (Economy Prediction System) database and the statistical yearbook of each province from 2012 to 2020. See Table 1 for details. We collected and measured the data of all variables according to data sources, and the descriptive statistics of main variables are shown in

Table 2. Descriptive statistics of main variables.

Variable	Obs	Mean	Std. Dev.	Min	Max
FII	270	12.039	5.137	3.909	33.195
DIF	270	203.358	91.568	18.33	410.281
IS	270	0.438	0.086	0.162	0.59
UL	270	0.576	0.122	0.35	0.896
AM	270	34.01	29.364	.94	133.53
HC	270	8.904	.827	7.165	12.028
IF	270	1.268	.991	.001	5.639

.

Table 2 describes the basic characteristics of the data of 30 Provinces in China from 2011 to 2019 by means of the average, standard deviation, and minimum and maximum values of statistical data. The standard deviation of digital financial inclusion was the largest, followed by production factors. The maximum value of digital financial inclusion was 410.281, which differs greatly from the minimum value of 18.33. This shows that the development of digital financial inclusion has significant differences among different regions. With the continuous advancement of the digital era, the development of digital financial inclusion goes deep into poverty areas, provides financial service support for poverty people, and brings a series of impacts on the development of related industries. There are also significant differences in production factors. Farmers in different regions have different production modes. Therefore, improving production modes has an impact on increasing farmers’ income. The analysis of large standard deviation shows that heterogeneity research has practical significance in the field of digital financial inclusion and farmers’ income growth.

4. Empirical Results

4.1. Spatial Correlation Test

This paper first used the global Moran’s I to test the spatial correlation between farmers’ income and digital financial inclusion in 30 provinces in the Chinese mainland from 2011 to 2019. The results of the spatial correlation test of the two variables are shown in

Table 3. Moran’s I test results.

Year	Farmers’ Income	Digital Financial Inclusion	Year	Farmers’ Income	Digital Financial Inclusion
2011	0.031 **	0.051 **	2016	0.046 ***	0.043 *
2012	0.031 **	0.072 **	2017	0.049 ***	0.067 **
2013	0.039 ***	0.049 **	2018	0.049 ***	0.082 ***
2014	0.041 ***	0.058 **	2019	0.050 ***	0.089 ***
2015	0.044 ***	0.018

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

.

There was a significant positive spatial correlation between farmers’ income growth and digital financial inclusion. According to Table 3, the global Moran’s I values of both farmers’ income and digital financial inclusion were greater than 0, mostly passing the test at the 5% level. There was a positive spatial correlation between provincial farmers’ income growth and digital financial inclusion, and the correlation degree increases with the change of time. This showed that both farmers’ income growth and digital financial inclusion have spatial heterogeneity at the provincial scale. It is necessary to further study the spatial spillover effect of digital financial inclusion on Farmers’ income growth.

4.2. Spatial Spillover Test

This subsection used the spatial Durbin model to study the spatial spillover effect of digital financial inclusion on farmers’ income growth based on their significant positive spatial correlation. Firstly, the Wald and LR tests results showed that the SDM (Spatial Durbin Model) will not degenerate into the SLM (Spatial Lag Model) or the SEM (Spatial Error Model); secondly, according to the Hausman test results, the original hypothesis is rejected, so the fixed effect Durbin model was selected for estimation. The estimation results are shown in

Table 4. Empirical results of the spatial spillover test.

Variable	Spatial Fixed Effect	Time Fixed Effect	Spatial and Time Fixed
DIF	0.0545 ***	0.0963 ***	0.0508 ***
	(8.2788)	(14.2384)	(7.9716)
IS	0.0298 *	0.0034	0.0555 ***
	(1.7189)	(0.2405)	(2.9843)
UL	−0.3176 ***	0.1282 ***	−0.3806 ***
	(−10.4620)	(9.4354)	(−10.5912)
AM	−0.0000	−0.0001 *	−0.0000
	(−0.6950)	(−1.7354)	(−0.3266)
HC	0.3069	−0.2106 **	0.4591 *
	(1.2903)	(−2.0331)	(1.9393)
IF	0.0020 *	0.0031 **	0.0019 *
	(1.7960)	(2.0237)	(1.7706)
W*DIF	−0.0636 ***	0.1985 ***	0.0703*
	(−8.3709)	(4.3037)	(1.7224)
W*IS	0.1855 ***	0.1031	0.5842 ***
	(2.9348)	(0.8030)	(4.3486)
W*UL	1.1667 ***	−0.2082 **	0.4060
	(8.6218)	(−2.1464)	(1.4608)
W*AM	0.0010 ***	0.0019 ***	0.0014 *
	(3.0739)	(4.9157)	(1.9359)
W*HC	−0.5373	2.4240 ***	1.9844
	(−1.1583)	(3.2121)	(1.1304)
W*IF	−0.0047	−0.0090	0.0004
	(−0.7515)	(−0.6478)	(0.0466)
Spatial rho	0.7430 ***	−0.8520 ***	0.0456
	(10.3851)	(−3.2980)	(0.2131)
Variance sigma2_e	0.3073 ***	1.5859 ***	0.2684 ***
	(11.4222)	(11.9284)	(11.6079)
N	270	270	270

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

.

As can be seen from Table 4, digital financial inclusion has a significant promotion effect and a spatial spillover effect on farmers’ income growth. Under the spatial and time-fixed effect, the elastic coefficient of digital financial inclusion on farmers’ income growth was 0.0508, which passes the significance test, indicating that digital financial inclusion has a significant positive impact on farmers’ income growth. The spatial interaction term coefficient of digital financial inclusion was 0.0703 and significant, indicating that the development of peripheral digital financial inclusion has a significant positive spillover effect on the income growth of local farmers. Based on the above empirical results, Hypotheses 1 and 2 are verified. Farmers’ income growth is highly and positively affected by the development of digital financial inclusion. The development of digital financial inclusion has a spillover effect on farmers’ income growth: it improves farmers’ income growth within the province as well as in the neighboring provinces.

Among the control variables, industrial structure, human capital, and farmers’ investment had a significantly positive impact on farmers’ income growth, while urbanization level had a significantly negative impact on farmers’ income growth, and production factors had no significant impact on farmers’ income growth. With the optimization of the industrial structure, the production efficiency increases, and with the input of manpower and capital, farmers’ income has been greatly improved. It can be seen from Table 4 that a series of control variables, such as industrial structure and human capital, have a significant impact on farmers’ income growth in the surrounding areas, while the impact of farmers’ investment on farmers’ income growth in the surrounding areas is not significant.

Above, the spillover effect of digital financial inclusion on farmers’ income growth was studied through the estimated coefficients of the spatial Durbin model. Next, the spatial Durbin model was decomposed into the direct effect, the spatial effect, and the total effect to specifically reflect the effects of digital financial inclusion on farmers’ income growth. The results are shown in

Table 5. Effect decomposition of the SDM.

Variable	Direct Effect	Indirect Effect	Total Effect
DIF	0.0513 ***	0.0783 *	0.1295 ***
	(7.8465)	(1.7413)	(2.8885)
IS	0.0570 ***	0.6347 ***	0.6917 ***
	(3.0977)	(3.1353)	(3.2882)
UL	−0.3739 ***	0.4823	0.1084
	(−10.4066)	(1.4104)	(0.2973)
AM	−0.0000	0.0016 *	0.0015 *
	(−0.2433)	(1.9537)	(1.8208)
HC	0.4676 **	2.1260	2.5936
	(1.9776)	(1.0069)	(1.1786)
IF	0.0020 *	0.0017	0.0038
	(1.8372)	(0.1598)	(0.3349)

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

.

According to Table 5, in the direct effect column, the impact coefficient of digital financial inclusion on farmers’ income growth was 0.0513, indicating that digital financial inclusion development helps improve farmers’ income. In the indirect effect column, the elasticity coefficient of digital financial inclusion was 0.0783, which shows that the development and change of digital financial inclusion have potentially promoted farmers’ income growth in the surrounding areas by changing the spatial interaction, that is, they have a significant positive spatial spillover effect. According to the regression results, the development of digital financial inclusion plays a synergistic role in promoting farmers’ income growth in the local province and surrounding provinces, and the economic growth effect on farmers in surrounding provinces is greater than that on farmers in the local province. On the one hand, digital financial inclusion provides credit support for rural residents, increases the possibility of farmers’ investment and entrepreneurship, and makes it possible for farmers to obtain income not only from pure agriculture but also from other sources. On the other hand, digital financial inclusion broadens the coverage of financial services through its network characteristics, enabling more low-income people to use simple financial services more efficiently, thus improving farmers’ income.

4.3. Threshold Effect Test of Digital Financial Inclusion on Farmers’ Income Growth

Due to the uneven development of digital financial inclusion across provinces in China, the relationship between digital financial inclusion and farmers’ income growth is complicated, and its promoting effect on farmers’ income growth may be significant only when its development crosses a certain stage, that is, there is a “threshold effect” in its impact on farmers’ income growth. Due to economic development differences among provinces, all sample provinces were divided into high development and low development areas according to their economic development levels based on the differences in regional per capita GDP (the economic development level was classified by the average value of regional per capita GDP of each province during the investigation period. The provinces with the top 50% of per capita GDP were classified as areas with high economic development level, and the other provinces were classified as areas with low economic development level).

Table 6. Threshold effect test results.

Area	Threshold	Fstat	Prob	Crit1	Crit5	Crit10
Total area	Single	136.02 ***	0.0000	41.4027	32.7646	29.4189
	Double	80.85 ***	0.0000	26.7035	22.6912	21.2210
High economic development areas	Single	66.05 ***	0.0000	33.8678	26.3330	23.4820
	Double	31.26 ***	0.0000	17.2860	13.5463	11.1534
Low economic development areas	Single	73.05 ***	0.0000	37.7659	29.0000	25.5976
	Double	29.38 **	0.0133	32.0530	24.2651	20.0738

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

and

Table 7. Threshold estimation results and confidence intervals.

Area	Threshold Value 1		Threshold Value 2
	Estimated Value	95% Confidence Interval	Estimated Value	95% Confidence Interval
Total area	267.7968	(266.0130,272.5073)	344.4025	(336.6506,359.0265)
High economic development areas	231.4107	(225.8829,232.5660)	344.4358	(331.9826,336.6506)
Low economic development areas	24.91	(18.8400,28.4000)	289.1405	(285.7906,289.2483)

present the threshold effect test and threshold value estimation results.

As can be seen from Table 6 and Table 7, under all samples, both the single threshold test and the double threshold test of digital financial inclusion passed the test at the 1% significance level, so there was a double threshold effect, and the threshold values were 267.7968 and 344.4025. Similarly, digital financial inclusion also had double threshold effects in both high-quality and low-quality areas in terms of economic development level, passing the significance test. The threshold values in high-quality areas were 231.4107 and 344.4358, and those in low-quality areas were 24.91 and 289.1405.

Digital financial inclusion was taken as the threshold variable, and the panel threshold model was used for testing. The regression results of the whole sample and sub-samples are shown in

Table 8. Threshold regression results.

Variable	Total Area	High Economic Development Areas	Low Economic Development Areas
	FII	FII	FII
IS	−0.0272	−0.0409	−0.0234 *
	(−1.5491)	(−1.1712)	(−1.7743)
UL	−0.1651 ***	−0.1920 ***	0.1424 ***
	(−5.1733)	(−3.6716)	(3.7814)
AM	−0.0002 *	−0.0002 *	0.0000
	(−1.9188)	(−1.9339)	(0.5715)
HC	−0.3731 *	−0.1006	−0.0339
	(−1.7203)	(−0.2813)	(−0.1956)
IF	−0.0004	0.0017	0.0011
	(−0.2780)	(0.7590)	(1.0768)
DIF	0.0303 ***	0.0295 ***	0.0672 ***
($\gamma$ $< {\gamma }_1$)	(21.2207)	(13.0348)	(6.8512)
DIF	0.0347 ***	0.0345 ***	0.0204 ***
(${\gamma }_1 \le \gamma \le {\gamma }_2$)	(24.4207)	(15.6853)	(11.5477)
DIF	0.0417 ***	0.0412 ***	0.0230 ***
($\gamma$ $> {\gamma }_2$)	(32.8224)	(21.1640)	(12.5099)
_cons	19.9951 ***	23.0280 ***	−0.2933
	(7.5403)	(4.9814)	(−0.1213)
N	270	135	135

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

.

According to the regression results in Table 8, with digital financial inclusion as the threshold variable, the impact of digital financial inclusion on farmers’ income growth has a threshold effect, and Hypothesis 3 is verified. In the whole sample test, the three-stage impact coefficients of digital financial inclusion on farmers’ income were 0.0303, 0.0347, and 0.0417, respectively, and they were significant, indicating that the impact of digital financial inclusion on farmers’ income growth rises step by step. When the development of digital financial inclusion crosses the threshold of 344.4025, the impact will be significantly enhanced. With the in-depth development of digital financial inclusion, its impact on farmers’ income growth has increased, and the rational allocation of financial resources in rural areas has a significant impact on farmers’ income. The development of digital financial inclusion is conducive to promoting the construction of financial serving the real economy and contributing to the improvement of economy, culture, and ecology in rural areas. Therefore, it is possible to adjust the threshold of digital financial services and expand the coverage of digital financial services by means of the Internet and big data so that more farmers can enjoy the economic dividend of income growth brought about by the development of digital financial inclusion.

According to Table 8, the impact of digital financial inclusion on farmers’ income growth is also heterogeneous in terms of regional economic development characteristics. In areas with a high level of economic development, the three-stage impact coefficients of digital financial inclusion on farmers’ income were 0.0295, 0.0345, and 0.0412, respectively, and they were significant, indicating that with the continuous improvement of the digital financial inclusion system, the promoting effect of financial services on farmers’ income gradually increases. Therefore, it is necessary to continuously strengthen the input of digital financial inclusion and strengthen its progressive trend of promoting farmers’ income growth. In areas with low levels of economic development, the three-stage impact coefficients of digital financial inclusion on farmers’ income were 0.0672, 0.0204, and 0.0230, respectively, and they were significant, indicating that the development of digital financial inclusion has a U-shaped effect on farmers’ income growth.

Based on the above empirical results, the role of digital financial inclusion in promoting farmers’ income growth varies with regional economic development levels, so Hypothesis 4 has been verified. In areas with high levels of economic development, rural financial services are relatively mature, and financial services to the real economy are relatively developed. Digital financial inclusion provides financial service support to those with low income to promote farmers’ income growth. In economically underdeveloped areas, farmers cannot enjoy financial services due to the lack of financial services and the blocking of financial markets. When such areas first start to access digital financial services, the elasticity is very large, and then it conforms to the law of diminishing returns to scale; when digital financial inclusion reaches a certain level, the impact of financial services on farmers’ income gradually decreases to a flat trend.

5. Conclusions and Policy Implications

Based on the panel data of 30 provinces in the Chinese mainland from 2011 to 2019, this paper constructed a spatial Durbin model and a panel threshold regression model with digital financial inclusion as the threshold variable to analyze the spatial spillover effect and the threshold effect of digital financial inclusion on farmers’ income growth. The conclusions are as follows:

First, digital financial inclusion has a significant promotion effect and a positive spatial spillover effect on farmers’ income growth. Digital financial inclusion, through its network characteristics, improves the coverage of financial services and the investment enthusiasm of farmers by providing credit support, thereby increasing farmers’ income and narrowing the income gap between urban and rural residents. Digital financial inclusion has obvious spatial spillover effects on farmers’ income growth. Therefore, it is necessary to rationally allocate financial resources among different regions and achieve coordinated development through inter-regional communication and cooperation so as to promote high-quality economic development in rural areas.

Second, the impact of digital financial inclusion on farmers’ income growth has a double threshold effect, and farmers’ income increases with the development of digital financial inclusion. Financial demand is the key to rural agricultural development, and social capital factors are introduced into rural areas through Internet finance to provide financial support for rural agricultural development. Single financial products and low-level financial services often limit the role of digital financial inclusion. Therefore, it is necessary to strengthen rural financial reforms, promote the diversification of financial products, and increase support for digital financial inclusion through policies.

Third, the impact of digital financial inclusion on farmers’ income growth is heterogeneous in terms of regional economic development levels. In areas with relatively high economic levels, efficient financial service has a significant impact on regional economic growth, while in economically underdeveloped areas, digital financial inclusion has a limited role in promoting farmers’ income growth. Therefore, under the premise of improving regional economic development level, strengthening investment in financial services can significantly increase farmers’ income.

However, the deficiency of this study is that due to the incomplete statistics of index data in each county, the study samples were temporarily confined to the provincial level. Considering the impact of major events, the impact of the development of digital financial inclusion after COVID-19’s impact on the growth of farmers’ income will also be an important direction of future research. Based on the above conclusions, in order to further play the role of digital financial inclusion in increasing farmers’ income, this paper draws the following policy implications. (1) Improve inter-regional interaction and cooperation for the regionalization of digital financial inclusion. Regional economic interaction facilitates financial penetration, which enhances the spatial correlation of digital financial inclusion so as to give full play to the regional radiation effect of digital financial inclusion among provinces to promote farmers’ income growth. (2) Attention should be paid to the threshold effect of digital financial inclusion on farmers’ income growth. Financial resources should be allocated reasonably according to the characteristics of regional economic development so as to improve farmers’ income more effectively. (3) Increase government financial support for the development of digital financial inclusion. The construction of a sound financial service system brings strong financial support to farmers, which is conducive to rural technology innovation, and the need to “train” farmers on digital tools, thus contributing to local economic development and improving farmers’ income.