Digital Rural Construction and Farmers’ Income Growth: Theoretical Mechanism and Micro Experience Based on Data from China

: This study analyzes the effect of digital rural construction on farmers’ income growth and the underlying mechanism using a 2SLS instrumental variable approach based on the county digital village index developed by Peking University and AliResearch, as well as micro-survey data of farmers in China. After fully correcting for endogeneity and verifying the robustness of the models, we found that digital rural construction has a signiﬁcant positive impact on farmers’ total household income, wage income, and property income, while also inhibiting the growth of net agricultural income. Furthermore, we found that digital rural construction increases farmers’ income mainly by promoting non-agricultural employment and asset transformation. In terms of heterogeneity analysis, digital rural construction has a greater effect on increasing farmers’ income with high physical and human capital, but it is not beneﬁcial to farmers with moderate social capital. It also has a greater effect on increasing farmers’ income in villages with better infrastructure. In addition, digital rural construction more signiﬁcantly increases farmers’ income in the eastern, central, and southern regions of China compared with the western and northern regions. These ﬁndings provide new empirical evidence of the effect of digital rural construction on farmers’ income growth in China and other developing countries.


Introduction
Digital rural construction is an important measure that offers a breakthrough in empowering rural revitalization, making up for rural shortcomings, and helping farmers increase their income [1]. From the perspective of development history, digital rural construction extends the application of digital technology from urban to rural areas through continuous iterative optimization. There is a developmental wave of digital and smart villages worldwide [2][3][4]. In 2018, the Chinese government proposed to implement the digital village strategy for the first time and launched a package of policy measures, including the Outline of the Digital Rural Development Strategy, the Digital Rural Construction Guide 1.0, and the Action Plan for Digital Rural Development (2022-2025), striving to construct digital villages at different levels. After continuous investment and construction, the digital village has been deeply integrated into many aspects of farmers' daily life. It has become an important force in shaping and reconstructing rural society and directly or indirectly affecting the income growth of farmers [5]. Specifically, in terms of rural infrastructure, broadband access was available to all administrative villages in China in 2021, with an internet penetration of 57.6% in rural areas and 424,000 agricultural information centers in operation. In terms of the rural economy, the total volume of rural online retail sales was 2.05 trillion yuan in 2021, and that of agricultural products was 422.1 billion yuan, with 8.9% penetration of the agricultural digital economy. In terms of rural governance, the Sharp Eyes Project has covered 77.0% of administrative villages. Villagers do not need to leave their homes for trivial matters; they leave the village for major matters with the use of grassroots digital government affairs platforms, thereby greatly improving the efficiency of governance. In terms of rural life, there are 284 million rural internet users in China, and rural online shopping and live commerce have become new agricultural activities.
Does digital rural construction promote the income growth of farmers? Although extensive studies have examined this issue, no consensus has been reached. The main conclusions are divided into two categories: (1) digital rural construction promotes the income growth of farmers [6,7], and (2) there is no evidence that digital technology promotes residents' income [8,9]. There may be two reasons for this: on the one hand, most studies focused on the total income of farmers, and few examined the income structure. On the other hand, most data only address the effect of a single digital tool (e.g., internet, broadband, and smart phone) on farmers' income, ignoring the iterative upgrading of digital rural construction and its comprehensive impact on farmers' production and life [10,11]. Furthermore, how does digital rural construction affect farmers' income, and is there heterogeneity? Due to the heterogeneity of resource endowments, there are large differences in farmers' access to digital dividends under the same conditions of digital rural construction. There are still many obstacles to achieving inclusive growth. These questions were not answered by previous studies.
As the digital village is an important part of China's digital economy, it is of importance to investigate the impact of expanding and improving digital rural construction on farmers' income growth. Given this, we aimed to examine the impact of digital rural construction on farmers' income growth and reveal the mechanism of action using instrumental variables based on the County Digital Village Index jointly developed by Peking University and AliResearch and the micro survey data of farmers in 2018. The conclusions of this study are as follows. First, digital rural construction has a significant positive effect on the total income, wage income, and property income of farmers but an inhibitory effect on the net agricultural income. This conclusion still holds when endogeneity is considered. Second, digital rural construction increases farmers' income mainly by promoting non-agricultural employment and asset transformation. Third, digital rural construction is beneficial to farmers with high physical and human capital, as well as villages with high infrastructure levels. In addition, from the perspective of regional heterogeneity, digital rural construction has a greater effect on increasing farmers' income in the eastern, central, and southern regions of China.
The rest of this paper is organized as follows. The next section provides an overview of previous studies that have examined the impact of digital rural construction on farmers' income. Section 3 builds a theoretical model of how digital rural construction affects farmers' income growth and presents hypotheses. Section 4 presents the methodology and variables used, data sources, and the descriptive statistics of the variables. Section 5 reports the baseline regression results of the empirical model and the results of endogeneity and robustness tests. Section 6 examines how digital rural construction affects farmers' income growth. Section 7 compares the effect of digital rural construction on farmers' income growth in the context of different resource endowments, villages, and provinces. Section 8 discusses marginal contributions and points out the limitations of the study. The last section presents the conclusions and policy implications.

Literature Review
Research on digital rural construction is in its infancy. Most of the literature only considers the impact of single-application scenarios of the digital village, such as the internet, broadband, rural e-commerce, and smart phones, on farmers' income. In theory, the logic of digital rural construction to promote farmers' income is mainly reflected in four aspects. The first is to reduce transaction costs-the time and cost of farmers to search for information have been significantly reduced with the improvement of digital infrastructure and the application of digital equipment [12]. The second is to promote the accumulation of social capital, increase lending from informal sources [13], enhance the convenience of entrepreneurial financing, and improve entrepreneurial performance for farmers [14]. The third is to improve management, promote effective allocation of factors [15], increase total factor productivity, and significantly increase the sales volume and price of agricultural products [16,17], thereby increasing agricultural income. The fourth is to increase nonagricultural employment opportunities through unimpeded access to information, thereby improving the flexibility of rural labor in agricultural and non-agricultural sectors [11].
However, different conclusions have been reached concerning the effect of digital rural construction on farmers' income growth. For example, it has been reported that internet use significantly increases the wage income and total household income of rural residents [18,19]. Liu et al. (2021) argue that the policy shock of the rural broadband access project has significantly increased farmers' income [20]. However, Tang et al. (2022) found that e-commerce had little effect on the income of rural residents based on the socioeconomic data of Taobao and non-Taobao counties in 2008 and 2018 [21]. Moreover, digital rural construction has different effects on different sources of income. For example, Courtois and Subervie (2015) found that market information service contributes to increased sales volume, price, and profit rate of agricultural products, thereby increasing agricultural business income [17]. Conversely, other studies have found that informatization may inhibit agricultural business income, and this inhibitory effect decreases over time [10].
There may be three reasons for this inconsistency between theoretical expectations and empirical results. First, the existing literature mainly uses the internet, broadband, rural e-commerce, etc., as proxy variables for digital rural construction to examine the effect on farmers' income growth and ignores the diversity and integrity of farmers' participation in digital rural construction, thus resulting in omitted variables [10]. Second, there may be endogeneity of reciprocal causation between digital rural construction and farmers' income growth, leading to biased estimates [11,22]. Third and lastly, there may be a threshold effect in the application of digital rural construction [14,23]. Therefore, subsequent research not only needs to find a proper proxy variable but also needs to address the endogeneity between digital rural construction and farmers' income growth using instrumental variables.
It is worth noting that there is no consensus in the existing literature on whether farmers have fair access to digital dividends [24]. The effect of digital rural construction on farmers' income is also related to individual and household endowments, as well as the characteristics of the villages and regions where they are located, so an overall income increase does not mean a homogeneous effect on farmers with different income levels. Therefore, subsequent research needs to further investigate the heterogeneity of the effect of digital rural construction on farmers' income growth.

Theoretical Analysis and Hypotheses
Given the broad coverage of digital rural construction, it is defined in this study as promoting the modernization of agriculture and rural areas by optimizing resource allocation and stimulating the inner vitality of villages through the comprehensive application of digital technology. For farmers, digital rural construction can be regarded as an economic factor, i.e., a public service similar to rural roads, bridges, tap water, and other infrastructure. It increases farmers' income mainly by optimizing the allocation of factors for their households. As far as this study is concerned, digital rural construction may affect farmers' income growth through the following potential mechanisms.
First, by reducing the cost of searching for employment information and providing easier access to non-agricultural employment information [25], digital rural construction reduces the risk of friction in the labor market and promotes the transfer of surplus labor in rural households from the agricultural sector to non-agricultural industries with higher income, thereby increasing wage income. This may, of course, reduce agricultural inputs, thereby reducing agricultural business income.
Second, digital rural construction can revitalize existing unproductive assets of farmers and promote their capitalization, thereby increasing their benefits. For example, rural households generally have various forms of assets, but some of them, especially farmland and idle machinery, are useless and idle due to a lack of market access. The development of the external digital economy will effectively promote the establishment of local farmland transfer markets with premium prices. Farmers can use digital tools to promote farmland transfer and increase land rent, thereby increasing property income. Thus, the following hypotheses are proposed. Figure 1 provides a diagram of the theoretical framework.
land transfer and increase land rent, thereby increasing property income. Thus, the following hypotheses are proposed. Figure 1 provides a diagram of the theoretical framework.
Hypothesis 1 (H1). Digital rural construction has a significant positive effect on the total income, wage income, and property income of farmers and an inhibitory effect on net agricultural income.

Hypothesis 2 (H2). Digital rural construction increases farmers' income by promoting non-agricultural employment and accelerating farmland transfer and machine rental.
Hypothesis 3 (H3). Digital rural construction contributes to income growth for farmers with high physical, social, and human capital, and the effect of digital rural construction on promoting income growth is more significant for villages with better infrastructure.

Baseline Regression Model
To examine the effect of digital rural construction on farmers' income growth, an economic model was developed to determine farmers' income. For a farmer household, we assume that digital rural construction is a digital technology factor and that the higher the level of local digitalization, the higher the digital technology factor for the household. The household income of farmers is also affected by factors such as the individual characteristics of the household head, household characteristics, village characteristics, and the province where they are located [5,11]. Referring to the existing literature [26,27], we use

Hypothesis 1 (H1).
Digital rural construction has a significant positive effect on the total income, wage income, and property income of farmers and an inhibitory effect on net agricultural income.
Hypothesis 2 (H2). Digital rural construction increases farmers' income by promoting nonagricultural employment and accelerating farmland transfer and machine rental.

Hypothesis 3 (H3).
Digital rural construction contributes to income growth for farmers with high physical, social, and human capital, and the effect of digital rural construction on promoting income growth is more significant for villages with better infrastructure.

Baseline Regression Model
To examine the effect of digital rural construction on farmers' income growth, an economic model was developed to determine farmers' income. For a farmer household, we assume that digital rural construction is a digital technology factor and that the higher the level of local digitalization, the higher the digital technology factor for the household. The household income of farmers is also affected by factors such as the individual characteristics of the household head, household characteristics, village characteristics, and the province where they are located [5,11]. Referring to the existing literature [26,27], we use the ordinary least squares (OLS) method to estimate the mean effect of digital rural construction on farmers' income. The baseline model for determining farmers' income is expressed as: where ln Income i is the per capita household income of farmer i and is transformed into logarithms. Index i is the digital village index of the county where the farmer lives, which reflects the level of local digital rural construction. X i represents the control variables, including individual characteristics of the household head, household characteristics, and village characteristics. µ i is the province dummy variable. ε i is a residual item. The coefficient α i . is the estimated effect of interest.

Model Corrected for Endogeneity
The endogeneity needs to be addressed to accurately assess the effect of digital rural construction on farmers' income growth. Considering that the digital village index used is at the county level, it is logically difficult for reciprocal causation to occur; that is, the income change of a single farmer is unlikely to affect the level of digital rural construction in the county where they live. However, since there are many factors affecting farmers' income, it is impossible to avoid the presence of omitted variables in the baseline model specification. Referring to the existing literature [28], we use the two-stage least-squares (2SLS) method and select appropriate instrumental variables to correct for endogeneity. The resulting model is expressed as: ln where IV i is the ith instrumental variable, Index vi is the digital village index, X i represents the control variables, µ i is the province dummy variable, ε i is a residual item, and the coefficient β i is the estimated effect of interest.

Models for the Investigation of Mechanisms
To examine the mechanisms by which digital rural construction promotes income growth of farmers by affecting their labor allocation, we use the proportion of non-farm employees in the household [29] and the total non-farm work time [30] as two proxy variables for non-agricultural employment of rural households. Likewise, we use the 2SLS method to correct for endogeneity. The resulting model is expressed as: In Equation (4), Index vi is the digital village index of the county where the farmer lives, X i represents the control variables, µ i is the province dummy variable, ε i is a residual item, and the coefficient δ i is the estimated effect of interest. In Equation (5), Employperson i is the proportion of non-farm employees in the household of farmer i. In Equation (6), Employtime i is the total household non-farm work time of farmer i.
Furthermore, we also examine how digital rural construction promotes farmers' income growth by affecting the transformation of household assets. Accordingly, we use the proportion of transferred land and the resulting income [31] and machine rental income [32,33] as proxy variables for the transformation of household assets. Likewise, we use the 2SLS method to correct for endogeneity. The resulting model is expressed as: In Equation (7), Index iv is the digital village index of the county where the farmer lives. X i represents the control variables. µ i is the province dummy variable. ε i is a residual item. The coefficient ϕ i is the estimated effect of interest. In Equation (8) sidual item. The coefficient is the estimated effect of interest. In Equation represents the proportion of transferred land in the village where farm lives and the income from land transfer of farmer . In Equation (9), ℎ the machine rental income of farmer .

Dependent Variable: Farmers' Income
There are four dependent variables: per capita net income, per capita wage incom per capita net agricultural income, and per capita property income of the farmer hou holds. The per capita net income is calculated by dividing the total annual household come in 2018 by the household size. The per capita wage income is calculated by divid the sum of the migrant and local employment income of the household in 2018 by

Dependent Variable: Farmers' Income
There are four dependent variables: per capita net income, per capita wage income, per capita net agricultural income, and per capita property income of the farmer households. The per capita net income is calculated by dividing the total annual household income in 2018 by the household size. The per capita wage income is calculated by dividing the sum of the migrant and local employment income of the household in 2018 by the household size. The per capita net agricultural income is calculated by dividing the net profit from farming of the main species in 2018 by the household size. The per capita property income is calculated by the sum of household income from farmland transfer, machine rental, and house rental in 2018 by the household size. In the empirical study, the income is transformed into logarithms.

Control Variables
The control variables include household head characteristics, household characteristics, village characteristics, and province characteristics. Regarding household head characteristics, gender, education, and age were controlled for [19]. Regarding household characteristics, the skills training of household members, number of relatives and friends, contracted land area, and loan amount from banks, relatives, and friends were controlled for. Regarding village characteristics, the topography, location, and economic development level of the village were controlled for [11]. Lastly, considering the large differences in endowments between provinces, a province dummy variable was also included.

Instrumental Variables
First, referring to the existing literature, the spherical distance from the village where the farmer lives to node cities in the "Eight Vertical and Eight Horizontal" optical cable backbone network (hereinafter referred to as the "EVEH network") is included as an instrumental variable for digital rural construction (IV 1 ) [10,34]. This may be because the Chinese government focuses on building digital infrastructure in the node cities in the EVEH network. The spillover effect of the digital technology and business of these node cities decreases with the increase in distance. Therefore, the closer the spherical distance to these node cities, the higher the digital rural construction level, and vice versa. Second, the average altitude (log) of the village where the farmer lives [5] is included as another instrumental variable (IV 2 ) for digital rural construction in the county where the farmer lives to correct for endogeneity. This is because higher village altitude means greater difficulty in digital rural construction and higher management and maintenance costs. Therefore, the local government prioritizes digital rural construction in low-altitude villages. As a result, the digital rural construction level in high-altitude villages is relatively low. The empirical results below show that the instruments used in this study both pass the exogeneity and correlation tests.

Data Sources
The data used consist of three parts. The first part is data on digital rural construction in 2018. It comes from the County Digital Village Index (2018) developed by the Institute for New Rural Development of Peking University and AliResearch. This index is based on national macro statistics, industry data, and internet big data, with counties as the basic unit. It establishes a digital village index system from four dimensions, i.e., rural digital infrastructure, rural economy digitization, rural governance digitization, and rural life digitization, to accurately measure the actual level of digital rural construction.
The second part is micro data from a survey of farmers in 2019. In 2019, China Agricultural University conducted a stratified sampling survey on farmers and their villages in 11 provinces, including Jiangsu, Anhui, Jiangxi, and Hunan. The sampling plan is as follows: 2-4 counties (districts) were selected from each province, 2 administrative villages (communities) were selected from each county (district), and using a proportion of 10-30% according to the size of the resident population, 30-60 farmer households were randomly selected from each administrative region (community) to conduct one-on-one paper questionnaire interviews. After, the village cadres were interviewed to obtain basic information on local economic and social conditions. The interview covered the basic characteristics of the household head and the household, farmland transfer, and non-agricultural employment in 2018. The survey area included eastern, central, northeastern, and western China, which ensured the sample's representativeness. The data on household income, characteristics of the household head and household members, and the data used for mechanism investigation and heterogeneity analysis in this study all came from the survey.
The third part is the instrumental variable data. On the one hand, data on the two instrumental variables included in the analysis of endogeneity-spherical distance from the village where the farmer lives to node cities in the EVEH network (IV 1 ) and village altitude (IV 2 )-are from the National Bureau of Statistics of China (National Bureau of Statistics of China: http://www.stats.gov.cn (accessed on 21 July 2022)). On the other hand, data on the third instrumental variable (IV 3 ), the mean of the spherical distances from the village where the farmer lives to three core cities (Hangzhou, Beijing, and Shenzhen), included in the robustness test, were calculated from data provided by the Geographic Information System (GIS). In addition, the prefecture-level "Internet Plus" index developed by Tencent Research Institute (Tencent Research Institute: https://www.tisi.org (accessed on 19 July 2022)) is used as another proxy variable for digital rural construction for robustness testing. This index comes from the China Internet Plus Index Report (2018).
These three parts of data were combined to form the initial sample of 2181 households in this study. Next, the total sample was winsorized at the 0.5 and 99.5 percentiles, and outliers were excluded. Finally, data on 2149 farmer households from 111 counties in 11 provinces were used in the empirical analysis. Table 1 presents the sample descriptive statistics of the variables included in the models. The per capita annual net income of the sample farmer households was 22,218.17 yuan. The per capita wage income was the main source of household income, which is significantly higher than the per capita net agricultural income (13,486.94 yuan vs. 8660.72 yuan). The per capita property income was relatively low, only 905.762 yuan. The household heads were mostly male, with an average age of 52.43 years. Most of them had an education level of primary school and junior high school. Most household members had received skills training. The number of relatives and friends with whom the household had regular contact was approximately 56.98. The household contracted farmland area was approximately 10.32 mu. The households borrowed approximately 1310.87 yuan from banks, relatives, and friends. Most of the villages were not in plain areas and were not where the township government was located. The economic level of the villages was low to moderate. The demographic characteristics of the survey sample are basically consistent with the general Chinese population. Hence, the sample is suitable for the empirical statistical analysis in this study.  Figure 3 is a binned scatterplot of the correlation between digital rural construction and farmers' income. It is evident that the overall digital village index has a positive correlation with the total net income, wage income, and property income and a negative correlation with the net agricultural income of farmer households. This shows that although digital rural construction promotes farmers' overall household income, it does not mean it has the same effect on all sources of income. In the following, we empirically analyze the effect of digital rural construction on farmers' income. no = 0) Village economic level (low = 1, moderate = 2; high = 3)

Descriptive Statistics
1.822 0.733 1 3 Other variables  Figure 3 is a binned scatterplot of the correlation between digital rural construction and farmers' income. It is evident that the overall digital village index has a positive correlation with the total net income, wage income, and property income and a negative correlation with the net agricultural income of farmer households. This shows that although digital rural construction promotes farmers' overall household income, it does not mean it has the same effect on all sources of income. In the following, we empirically analyze the effect of digital rural construction on farmers' income.   Table 2 reports the empirical results of the effect of digital rural construction on farmers' household income using OLS. Specifically, the household per capita net income (log) is used as the dependent variable. The overall digital village index (Index i ) of the county where the farmer lives is used as the proxy variable for the digital rural construction level. The estimated coefficients reflect the mean effect of digital rural construction on farmers' household income. Regarding standard errors, all columns are clustered at the province level, and the identification results were resampled 300 times using the bootstrap method to obtain relatively accurate estimates. (2) ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

Baseline Regression
Variables are added to the empirical model successively using an estimation strategy of "from simple to complex". The province fixed effect is controlled for from column (1) onwards. Household head characteristics, household characteristics, and village characteristics are added successively in columns (2)-(4). The results show that the estimated coefficients of the overall digital village index are significantly positive whether the control variables are added or not. Moreover, the estimated coefficient values and significance levels increase with the successive addition of control variables. This demonstrates that digital rural construction has a positive effect on the household per capita net income of farmers.
The regression results of other control variables are also largely in line with expectations. Specifically, at the household head level, the coefficients of age (log) and education are significantly positive, which is consistent with a previous study [35]. At the household level, receiving training, the number of relatives and friends, contracted farmland area, and loan amount from banks, relatives, and friends all have a positive effect on farmers' income, which passes the 1% significance test. This conclusion is consistent with a previous study [5]. Finally, at the village level, the village economic level has a positive coefficient on farmers' household income. This may be because the better the economic condition of a village, the more employment and entrepreneurship opportunities for farmers, which promotes farmers' household income. The coefficients of whether their village is located in the plain area and whether the township government is located in their village are positive, but they do not pass the significance test.

Endogeneity Analysis
In this section, we use instrumental variables to correct for endogeneity caused by omitted variable bias. Two instrumental variables, the spherical distance from the village to node cities in the EVEH network and the average altitude (log) of the village, are used for the digital rural construction in the county where the farmer lives. Hence, we need to test the validity of the instrumental variables. Table 3 presents estimates from 2SLS regressions. Only one instrumental variable, the spherical distance from the village to node cities in the EVEH network (IV 1 ), is used in columns (1) and (2). Likewise, only the average altitude (log) of the village (IV 2 ) is used in columns (3) and (4). Both instrumental variables (IV 1 and IV 2 ) are used in columns (5) and (6) (2005) show that a critical value for a 10% bias of 16.38 strongly rejects the null hypothesis of a weak instrument), thus rejecting the weak instrument hypothesis. This indicates that the selected instrumental variables satisfy the correlation condition. Third, in terms of the exogeneity test, the p-value of Hansen's statistic is greater than 0.10, which does not reject the null hypothesis that the instrumental variables satisfy the exogeneity condition. Fourth, in terms of the overidentification test, the Sargan test shows that all instrumental variables satisfy the exogeneity condition; that is, none of the instrumental variables are correlated with the disturbance, and they are chosen well. Fifth, in terms of the endogeneity test, the p-values for the Durbin-Wu-Hausman test statistics strongly reject the null hypothesis. Hence, it is a necessary step to use instrumental variables to correct for endogeneity. All the above tests show that the two instrumental variables used in this study are valid. In terms of the second-stage estimates, the estimated coefficient of the overall digital village index is slightly greater in value and more significant, indicating that the measurement error in the independent variables is small. This further verifies that digital rural construction has a significant positive effect on the growth of farmers' household income. To ensure the reliability of the conclusions, we first substitute the instrumental variable. Referring to the existing literature [36], the instrument variable, spherical distance from the village to node cities in the EVEH network (IV 1 ), is substituted with the mean spherical distance from the village to three core cities (Hangzhou, Beijing, Shenzhen) (IV 3 ). This is mainly because Hangzhou is the location of Alibaba's headquarters, Shenzhen is where the headquarters of Tencent and Huawei are situated, Beijing has many information and communication companies, and the three sites are located in eastern China. Therefore, theoretically, the mean spherical distance from the village to the three core cities has a significant negative correlation with the digital rural construction level. Table 4 presents estimates obtained after substituting the instrumental variables. Column (1) of Table 4 presents the results of the first-stage regression. The coefficients of both instrumental variables are significantly negative. The first-stage F statistic is 113.657, which is greater than the critical empirical value, thus rejecting the null hypothesis of a weak instrument. Column (2) reports the second-stage estimates when substituting the instrumental variable (IV 1 ). It is evident that the estimated coefficient of the overall digital village index remains significantly positive and passes the 1% significance test. Therefore, we continue to use the spherical distance from the village to node cities in the EVEH network (IV 1 ) as one of the instrumental variables for empirical analysis in the subsequent research. Columns (3) and (4) present the estimates of the generalized method of moment (GMM) and limited information maximum likelihood (PLIML), which are still robust.  Table 5 presents the empirical results from 2SLS estimation when substituting the core independent variable and the dependent variable. First, the core independent variable is substituted with the prefecture-level "Internet Plus" digital economy index developed by Tencent Research Institute. Second, the dependent variable is substituted with total  Note: (1) Numbers in brackets are robust standard errors from bootstrap resampling clustered at the province level.

Substituting the Core Independent Variable and the Dependent Variable
(2) ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. (3) The control variables are the same as those of the first model and are not presented due to space limitations (the same below). Table 6 presents the empirical results from 2SLS estimation when digital village subindices are used. The sub-indices of digital rural construction are added to the model as the core independent variables to further examine the impact of digital rural construction on farmers' income in different dimensions. The sub-indices in columns (1) and (4) both have positive coefficients on farmers' household income. It is evident from the regression results that the rural economy digitalization index has the greatest impact on farmers' income, followed by the rural digital infrastructure index and then the rural life digitalization index. The rural governance digitalization index has the least impact.

Labor Allocation
To examine the impact of digital rural construction on farmers' per capita household wage income, we use the proportion of non-farm employees in the household as a proxy variable for non-agricultural employment. The empirical results are shown in column (3) of Table 7. The results show that the overall digital village index is positive at the 1% significance level. This indicates that digital rural construction significantly promotes labor allocation to non-agricultural sectors with higher income, thereby increasing household wage income. We also examine the effect of digital rural construction on the work time of farmers. As evident from columns (4) and (5) in Table 7, digital rural construction has a significant positive effect on the non-farm work time of farmers, while it has a significant inhibitory effect on the on-farm work time. Note: (1) Numbers in brackets are robust standard errors from bootstrap resampling clustered at the province level.
(2) ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. (3) The control variables are the same as those of the first model and are not presented due to space limitations (the same below).
Columns (1) and (2) of Table 7 present the regression results of the effect of digital rural construction on wage income and net agricultural income, respectively. The results show that digital rural construction significantly and positively promotes the wage income of farmers but inhibits the net agricultural income. This conclusion is consistent with the existing literature [5,10]. Furthermore, we examine the effect of digital rural construction on the net agricultural income of farmers in different regions and find a positive effect in the eastern and central regions and an inhibitory effect in the western region.

Asset Transformation
As noted above, digital rural construction promotes farmer households to reallocate labor from the agricultural sector to non-agricultural sectors, thereby increasing wage income. Then, when farmers leave agriculture partially or completely, it will inevitably increase land transfer and reliance on social services. We use the proportion of transferred farmland in the village, farmland transfer income, and machine rental income as dependent variables. Columns (2) and (3) of Table 8 present the regression results of farmland transfer. It can be seen that the higher the level of digital rural construction, the significantly greater the proportion of transferred farmland in the village, and the higher the farmland transfer income. Column (4) reports the empirical results of the effect of digital rural construction on the machine rental income of farmers. It is evident that digital rural construction promotes the income of farmers who own machines. This may be because digital rural construction reduces the cost of information search, facilitates transactions between buyers and sellers, and reduces the idle time of machines, thereby increasing machine rental income. Ultimately, digital rural construction promotes the property income of farmers, as shown in column (1) of Table 8. Inspired by a previous study [37], we use per capita net household income as a proxy variable for physical capital and equally divide the farmer households into three groups according to the per capita net household income: low, medium, and high physical capital groups. The regression results are shown in columns (1)-(3) of Table 9. It is evident that digital rural construction has the greatest effect on increasing the income of farmers with high physical capital, followed by those with low physical capital, and, lastly, those with medium physical capital. We also quantify the physical capital using the original value of productive fixed assets per capita at the end of the year according to a previous study [38]. The results are still robust, as shown in columns (4)-(6) of Table 9.

Heterogeneity of Social Capital
We further investigate the heterogeneity of the effect of digital rural construction in increasing farmers' income in terms of social capital. Intuitively, digital rural construction is more beneficial to farmers with higher social capital. To this end, we use the number of relatives and friends as a proxy variable for the social capital of farmer households. The regression results are shown in columns (1)-(3) of Table 10. It is concluded that digital rural construction is more beneficial to farmers with low and high social capital, whereas it has a small effect on farmers with medium social capital. This may be because farmers with low social capital are more willing to embrace digital rural construction and thus are more willing to expand their social capital, ultimately improving their household income. Additionally, farmers with high social capital recognize the importance of digital rural construction before it is implemented, so they are good at using digital rural construction to increase income. Referring to the existing literature [39], we also use household gift expenditure as a proxy variable for social capital and obtained the same conclusion. (2) ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. (3) The control variables are the same as those of the first model and are not presented due to space limitations (the same below).

Heterogeneity of Human Capital
We also investigate the heterogeneity of the effect of digital rural construction on increasing farmers' income in terms of human capital. To this end, education is used as a proxy variable for the human capital of farmers [5]. The total sample is divided into low, medium, and high education groups according to whether they had completed junior high school and higher education. The regression results are reported in columns (1)-(3) of Table 11. The empirical results show that digital rural construction has a significant positive effect on farmers with medium and high education levels, especially the latter, whereas no significant effect is noted for those with low education levels. This may be because farmers with medium and high education levels have a relatively strong ability to use digital technology and thus have a stronger ability to earn profits. By contrast, farmers with low education levels are relatively less able to use digital tools. As a result, they may use digital technology more for entertainment and less for profitability. Therefore, the development of basic education will help farmers take advantage of digital rural construction and increase income. In addition, the number of skills training sessions is used as another proxy variable for human capital. The conclusions are still robust, as shown in columns (4)-(6) of Table 11.

Heterogeneity of Village
To promote farmers' income growth, digital rural construction needs the support of traditional infrastructure, such as water, electricity, coal, gas, and roads in the village, and relies on new infrastructure, such as base stations, logistics, and warehousing in the village. Given this, we divide the sample into three groups for regression [35] according to the size of the fixed asset investment of the village. The estimation results are shown in columns (1)-(3) of Table 12. It is evident that digital rural construction significantly promotes farmers' income as fixed asset investment increases. In addition, the empirical results obtained by grouping according to the number of village-level courier outlets are still robust, as shown in columns (4)-(6) of Table 12.  Table 13 reports the results of the effect of digital rural construction on farmers' income in different regions. The villages where farmers live are divided into eastern, central, northeastern, western, southern, and northern villages according to their geographical location. Columns (1)-(4) present the regression results for the sample divided into eastern and western regions. Columns (5)-(6) present the regression results for the sample divided into northern and southern regions. It is evident that digital rural construction has a significantly positive effect on farmers' income in all regions. A greater positive effect is observed for farmers in the eastern, central, and southern regions than those in the western and northern regions. This may be because, on the one hand, the digital rural construction level in the eastern, central, and southern regions is higher, thus leading to a greater empowerment effect and increase in income. On the other hand, these regions also have better traditional infrastructure, which can effectively interact with digital elements, thereby increasing farmers' income. (2) ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. (3) The control variables are the same as those of the first model and are not presented due to space limitations (the same below).

Discussion
A better understanding of the impact of digital rural construction on farmers' income growth and the underlying mechanism is crucial to the development of digital economy and the improvement of farmers' welfare. Although numerous studies have focused on digital village development [40,41], few are based on whether and how digital village construction at the county level affects farm household income growth. The first contribution of this study is that we used the county digital village index as a proxy variable for digital village development to overcome the endogeneity of reciprocal causation between digital rural construction and farmers' income growth. Second, we investigated the effects of digital rural construction on farmers' total income and income from different sources, and explored the respective underlying mechanisms. Third, we examined the effects of digital rural construction on farmers' income growth at the household, village, and region levels under different conditions, thereby confirming to some extent that the same level of digital village development provides different benefits to different farmers, leading to higher reliability of the conclusions being drawn.
There are limitations in this study. First, we did not examine the effect of digital rural construction at the village level on farmers' income growth. However, the level of digital rural construction varied greatly among villages. Moreover, only one year of data was used. Therefore, a more comprehensive and extensive analysis is needed in future research. Second, digital rural construction needs to adapt to factors such as local economic development and rural mode of production and lifestyle. Therefore, the results of this study are more suitable for developing countries. Lastly, digital rural construction not only affects farmers' income growth, but also affects their income gap, relative poverty, and subjective well-being. Therefore, it is necessary to conduct interdisciplinary research combining economics and sociology in the future.

Conclusions and Policy Implications
Using the instrumental variable method based on the county digital village index and the micro-survey data of farmers, this study revealed several key findings. First, digital rural construction has a significant positive effect on the total household income of farmers. From the perspective of income structure, it has a significant positive effect on the wage income and property income of farmers, but an inhibitory effect on the net agricultural income. Second, digital rural construction increases farmers' income by promoting nonagricultural employment and asset transformation. Third, digital rural construction has a greater effect on increasing the income of farmers with higher physical and human capital. Fourth, digital rural construction also has a greater effect on increasing the income of farmers in villages with better infrastructure and higher economic level. Fifth and lastly, digital rural construction has a more significant effect on increasing the income of farmers in the eastern, central, and southern regions as compared with the western and northern regions. All these findings support the hypotheses.
Some policy implications can be drawn from these findings. First, governments at all levels in China should continue to promote the investment in digital village infrastructure and the iterative upgrading of digital village technology so that a wider range of rural residents can participate in digital rural construction. In this way, the digital rural construction action will truly become a powerful driving force for farmers' income growth. Second, while promoting digital rural construction in the developed eastern region of China, great efforts should be made to promote digital rural construction in the underdeveloped central and western regions to bridge the development gap of digital villages among regions so that all rural residents can enjoy the same level of digital infrastructure. Third, actions should be taken to accelerate informatization in China's rural areas, reduce the digital divide from multiple dimensions, and enable rural residents to fully enjoy the digital dividend, which is of great significance in narrowing the income gap within rural areas. Fourth and lastly, efforts should be made to enhance vocational training for farmers, improve their digital literacy, and improve their return on use in digital rural construction.