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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Sustain. Food Syst.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Sustainable Food Systems</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Sustain. Food Syst.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2571-581X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fsufs.2025.1728761</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Digital literacy and income inequality among farm households: evidence from China</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Zhao</surname> <given-names>Qingjun</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Formal analysis" vocab-term-identifier="https://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Funding acquisition" vocab-term-identifier="https://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
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<uri xlink:href="https://loop.frontiersin.org/people/1878356"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Fu</surname> <given-names>Cui</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Visualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/visualization/">Visualization</role>
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<uri xlink:href="https://loop.frontiersin.org/people/3214920"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname> <given-names>Hanrui</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
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<aff id="aff1"><label>1</label><institution>College of Economics and Management, Huzhou College</institution>, <city>Huzhou</city>, <country country="cn">China</country></aff>
<aff id="aff2"><label>2</label><institution>College of Economics and Management, Nanjing Agricultural University</institution>, <city>Nanjing</city>, <country country="cn">China</country></aff>
<author-notes>
<corresp id="c001"><label>&#x0002A;</label>Correspondence: Cui Fu, <email xlink:href="mailto:fucui1998@163.com">fucui1998@163.com</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-12-19">
<day>19</day>
<month>12</month>
<year>2025</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>9</volume>
<elocation-id>1728761</elocation-id>
<history>
<date date-type="received">
<day>20</day>
<month>10</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>18</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>11</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2025 Zhao, Fu and Wang.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Zhao, Fu and Wang</copyright-holder>
<license>
<ali:license_ref start_date="2025-12-19">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<sec>
<title>Background</title>
<p>The digital economy represents a pivotal pathway for mitigating rural income inequality and advancing common prosperity. As a prerequisite capability in the digital era, whether digital literacy can effectively alleviate imbalances in income distribution among rural households has emerged as a critical academic question within the context of rural revitalization.</p></sec>
<sec>
<title>Methods</title>
<p>Drawing on panel data from the China Family Panel Studies (CFPS) spanning 2014 to 2020, this study empirically examines the impact of digital literacy on rural income inequality. The Kakwani index was employed to measure income inequality, while the Two-Stage Least Squares (2SLS) method and the Extended Regression Model (ERM) were utilized to address potential endogeneity. Furthermore, heterogeneity analyses and mechanism tests were conducted.</p></sec>
<sec>
<title>Results</title>
<p>(1) Digital literacy exerts a significant inhibitory effect on rural income inequality, a finding that remains robust after controlling for endogeneity. (2) Heterogeneity analysis indicates distinct regional and demographic variations in the income-equalizing effect of digital literacy, with more pronounced impacts observed in central regions and among rural households with lower educational attainment. (3) Mechanism testing reveals that non-cognitive abilities significantly attenuate the inhibitory effect of digital literacy on income inequality; specifically, higher levels of non-cognitive abilities correspond to a diminished efficacy of digital literacy in narrowing the income gap.</p></sec>
<sec>
<title>Conclusion</title>
<p>Enhancing rural digital literacy and optimizing the allocation of new human capital constitute effective strategies for narrowing the rural income gap. Concurrently, it is essential to consider the moderating role of non-cognitive abilities. By implementing differentiated empowerment to achieve the inclusive sharing of digital dividends, this study offers theoretical support and policy references for advancing rural revitalization and common prosperity.</p></sec></abstract>
<kwd-group>
<kwd>farm households</kwd>
<kwd>digital literacy</kwd>
<kwd>income inequality</kwd>
<kwd>non-cognitive ability</kwd>
<kwd>China</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Major Humanities and Social Sciences Research Projects in Zhejiang Higher Education Institution, China (Grant No. 2024QN016).</funding-statement>
</funding-group>
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<equation-count count="5"/>
<ref-count count="24"/>
<page-count count="11"/>
<word-count count="8251"/>
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<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Agricultural and Food Economics</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="introduction" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Addressing income inequality within rural areas is a core component in advancing common prosperity. Over the past four decades, China has achieved historic milestones in rural development. Farmers&#x00027; incomes have experienced sustained growth, urban-rural income disparities have gradually narrowed, and particularly in 2020, the monumental breakthrough of eradicating absolute poverty nationwide was realized, contributing the &#x0201C;Chinese solution&#x0201D; to global poverty alleviation efforts. However, amid profound transformations in rural socio-economic structures, intertwined factors such as intensified intra-household differentiation, large-scale cross-regional migration of rural labor, and structural adjustments and upgrades in rural industries have rendered income disparities among rural residents persistently prominent, even exhibiting a trend of relative expansion (<xref ref-type="bibr" rid="B20">Wang et al., 2019</xref>). According to data from the National Bureau of Statistics of China, the absolute per capita disposable income gap between high- and low-income rural resident groups was 18,446 yuan in 2013, expanding to 48,395 yuan by 2023&#x02014;an increase of nearly 1.6-fold over the decade. This data trend not only underscores the persistence and severity of income inequality in rural areas but also reflects the ongoing challenges in narrowing relative rural income gaps and promoting equitable income distribution under the backdrop of high-quality development. With the deep penetration of internet technologies into rural areas, the digital economy&#x02014;driven primarily by online applications&#x02014;is emerging as a key instrument for addressing rural income inequality and advancing comprehensive rural revitalization. The 54th Statistical Report on China&#x00027;s Internet Development Status indicates that, as of June 2024, a cumulative 3.917 million 5G base stations have been constructed, achieving full coverage in all prefecture-level cities and county urban areas nationwide; the internet user base approaches 1.1 billion, with a penetration rate rising to 78%. However, the proliferation of infrastructure has not automatically translated into equitable sharing of developmental benefits. Currently, overall digital literacy among farmers remains generally at a low level, with significant disparities in digital capabilities within the group (<xref ref-type="bibr" rid="B23">Zhang, 2023</xref>). This results in the digital economy confronting a fundamental shift from &#x0201C;hard&#x0201D; infrastructure disparities to &#x0201C;soft&#x0201D; digital literacy gaps when fulfilling its inclusive functions (<xref ref-type="bibr" rid="B4">Chetty et al., 2018</xref>). Unlike traditional production factors such as land and labor, the value-adding effects of digital factors in agricultural production and operations are highly dependent on users possessing corresponding digital literacy (<xref ref-type="bibr" rid="B11">Liu and Zhou, 2023</xref>; <xref ref-type="bibr" rid="B19">Wang, 2025</xref>). Consequently, uneven distribution of digital literacy may cause the digital economy to objectively exacerbate income gaps between farmers while empowering income growth for a subset, thereby forming a &#x0201C;digital empowerment paradox&#x0201D; (<xref ref-type="bibr" rid="B3">Chen et al., 2024</xref>; <xref ref-type="bibr" rid="B13">Liu and Liao, 2024</xref>). Therefore, deeply investigating the mechanisms through which digital literacy influences rural income inequality has become a critical research proposition for advancing rural revitalization and achieving common prosperity in the new era.</p>
<p>The existing literature generally holds that both &#x0201C;hard&#x0201D; technological conditions, such as digital infrastructure and digital finance, and &#x0201C;soft&#x0201D; capability elements, exemplified by digital literacy, are crucial for promoting inclusive socio-economic growth in rural areas and narrowing income disparities (<xref ref-type="bibr" rid="B7">He et al., 2025</xref>; <xref ref-type="bibr" rid="B17">Perera et al., 2025</xref>). Building on this foundation, a series of studies have begun to dissect the underlying mechanisms of these influences. Existing scholars, starting from specific perspectives such as farmers&#x00027; entrepreneurship (<xref ref-type="bibr" rid="B1">Bastomi et al., 2023</xref>), e-commerce participation behavior (<xref ref-type="bibr" rid="B24">Zhang and Zhang, 2024</xref>), and digital finance usage (<xref ref-type="bibr" rid="B14">Lo Prete, 2022</xref>), have empirically examined how digital &#x0201C;hard&#x0201D; technologies influence income distribution patterns by altering farmers&#x00027; economic behaviors and opportunity structures. However, when focusing on &#x0201C;soft&#x0201D; capabilities centered on digital literacy, existing research exhibits a key limitation. Most studies either treat digital literacy as a homogeneous direct influencing variable or focus solely on its effects through single mediating pathways, such as entrepreneurship or e-commerce. A core question that has been widely overlooked is: Why do substantial individual differences persist in the income-enhancing effects of the digital economy among farmer groups with similar levels of digital literacy? This question suggests that a key endogenous moderating mechanism may exist in the transmission pathway from &#x0201C;digital literacy&#x02014;economic behavior&#x02014;income outcomes.&#x0201D; Non-cognitive abilities, such as resilience, openness, and achievement motivation&#x02014;intrinsic psychological traits&#x02014;are considered to systematically influence individuals&#x00027; learning efficiency, risk coping, opportunity recognition, and sustained utilization capabilities when confronting digital technologies (<xref ref-type="bibr" rid="B10">Karpi&#x00144;ski et al., 2023</xref>; <xref ref-type="bibr" rid="B22">Yu, 2025</xref>). Therefore, this study proposes that non-cognitive abilities likely play a pivotal &#x0201C;catalyst&#x0201D; role therein, modulating the efficiency and extent of the conversion from digital literacy to economic benefits. Furthermore, by delving into the moderating role of non-cognitive abilities, this in-depth exploration of the mechanisms through which digital literacy affects income inequality among farmers not only enriches the research outcomes in the fields of digital economy and income distribution but also provides new theoretical foundations and practical insights for formulating more targeted policies to enhance rural digital literacy and effectively narrow income gaps, thereby holding significant academic value and practical implications.</p>
<p>Compared to existing studies, the main contributions of this article are as follows: First, it overcomes the limitations of treating digital literacy as a homogeneous variable or analyzing it solely through single mediating pathways by introducing non-cognitive abilities as a key moderating variable for the first time, systematically elucidating their &#x0201C;catalyst&#x0201D; role in the transformation process from &#x0201C;digital literacy to economic outcomes&#x0201D; and revealing the intrinsic mechanisms underlying the persistent significant income differences among farmers with equivalent digital literacy levels. Second, by empirically testing the moderating effect of non-cognitive abilities on the economic returns of digital literacy, it deepens the understanding of the heterogeneous mechanisms through which digital literacy influences income inequality, thereby filling the cognitive gap in existing research regarding the moderating role of psychological traits in the digital transformation process.</p></sec>
<sec id="s2">
<label>2</label>
<title>Theoretical analysis and research hypotheses</title>
<p>As the digital economy continues to grow, the concept of digital literacy has emerged. The concept of digital literacy was first introduced in 1994 by Israeli scholar Eshet Alkalai, who defined digital literacy as the ability of understanding and utilizing digital technologies and information originating from computers, constructing a conceptual framework for digital literacy (<xref ref-type="bibr" rid="B5">Eshet, 2004</xref>). Entering the information age of the 21st century, a growing body of scholars, international bodies, and governments has sought to refine and operationalize this concept. UNESCO views it as &#x0201C;the ability to use digital technology to access and manage information for employment or entrepreneurship&#x0201D; (<xref ref-type="bibr" rid="B18">Reddy et al., 2020</xref>). In China, the Cyberspace Administration of China offers a comprehensive definition, describing it as a series of abilities required for modern life, including the ability to access, create, use, evaluate, share, and ethically engage with digital content. Fundamentally, digital literacy represents a form of &#x0201C;digital ability&#x0201D; of labor in the current era. Therefore, like land or capital, it functions as a core determinant of income returns. Furthermore, the continuous innovation within the digital economy has embedded digital technology deep within every sector and industry. This integration has not only transformed the mode of agricultural operations but has also fundamentally reshaped lifestyles, labor dynamics, and individual behaviors. For farm households, this digital transformation facilitates easier access to job market information, new skills, and social networks, which expands their avenues for generating income (<xref ref-type="bibr" rid="B15">Magesa et al., 2023</xref>; <xref ref-type="bibr" rid="B12">Liu et al., 2025</xref>). Access to information from multi-channels tends to increase the income levels of low-income farm households, leading to an improved income distribution and thereby mitigating inequality among them (<xref ref-type="bibr" rid="B9">Ji and Zhuang, 2023</xref>). Based on the above analysis, the following hypothesis is proposed:</p>
<list list-type="simple">
<list-item><p><bold>Hypothesis 1:</bold> <italic>Digital literacy has a significant negative impact on the income inequality among farm households</italic>.</p></list-item>
</list>
<p>Furthermore, the mitigating effect of digital literacy on income inequality among farmers depends on farmers&#x00027; ability to convert digital literacy into actual income growth. However, non-cognitive abilities, as deep psychological drivers of individual behavioral choices, may attenuate this mitigating effect by influencing the application efficiency and benefit distribution of digital literacy. This attenuating effect does not negate the core value of digital literacy; rather, it reveals that, in the presence of heterogeneity in non-cognitive abilities, the income distribution effects of digital literacy may diverge, thereby undermining its overall efficacy in narrowing income gaps. The income-enhancing effects of digital literacy often exhibit a &#x0201C;long-term cumulative&#x0201D; characteristic, requiring farmers to invest time in learning advanced skills and accumulating digital resources. Patience, as a non-cognitive ability reflecting individuals&#x00027; discount rates for future benefits, directly influences farmers&#x00027; willingness to make long-term investments in digital literacy (<xref ref-type="bibr" rid="B13">Liu and Liao, 2024</xref>; <xref ref-type="bibr" rid="B16">Onsomu et al., 2025</xref>). Farmers with high levels of patience can sustain time investments in upgrading digital skills, gradually deepening the application of digital literacy and thereby achieving steady income growth. In contrast, farmers with low patience levels prioritize short-term gains and may abandon in-depth learning in the early stages of digital literacy application due to inconspicuous short-term returns, remaining at the basic application level and thus failing to capture long-term income growth dividends. Such differences in patience levels cause the long-term income-enhancing effects of digital literacy to tilt toward high-patience farmers, exacerbating income disparities among farmers and thereby weakening the mitigating effect of digital literacy on income inequality. Based on the above analysis, we propose the following research hypothesis:</p>
<list list-type="simple">
<list-item><p><bold>Hypothesis 2:</bold> <italic>Non-cognitive abilities significantly attenuate the mitigating effect of digital literacy on income inequality among farmers</italic>.</p></list-item>
</list></sec>
<sec id="s3">
<label>3</label>
<title>Research design</title>
<sec>
<label>3.1</label>
<title>Data sources</title>
<p>The data for this study are drawn from four waves (2014, 2016, 2018, and 2020) of the China Family Panel Studies, implemented by the Institute of Social Science Survey of Peking University.</p>
<p>The CFPS is a nationally representative, longitudinal survey covering approximately 16,000 households across 25 provinces. It&#x00027;s research topics cover economics, education, employment, population migration, health etc. This dataset is exceptionally well-suited for our research as it provides a rich array of micro-level variables, including internet usage, new human capital (cognitive and non-cognitive abilities), demographic characteristics, and household economic endowments. To construct our analytical sample, we focused specifically on rural households First, we restricted the dataset to households with rural hukou. Second, we performed data cleaning procedures by removing observations with missing or anomalous values for the core variables. This process yielded a balanced panel dataset of 12,476 households. Additionally, this household-level data was augmented with provincial-level indicators of economic development, which were sourced from the <italic>China Statistical Yearbook</italic> for the corresponding years and merged based on each household&#x00027;s province code.</p></sec>
<sec>
<label>3.2</label>
<title>Variables</title>
<sec>
<label>3.2.1</label>
<title>Dependent variable</title>
<p>The dependent variable is income inequality among farm households. We employ the relative deprivation index developed by Kakwani to measure the dependent variable (<xref ref-type="bibr" rid="B10">Karpi&#x00144;ski et al., 2023</xref>). Within this framework, a larger index value corresponds to a higher level of income inequality experienced by a given household. The index is constructed through the following steps: First, our analysis is situated at the intra-village level; thus, each village is defined as a distinct reference group <italic>X</italic>. For a village with households <italic>n</italic>, we arrange their incomes in non-decreasing order to establish the income distribution, <italic>X</italic> &#x0003D; (<italic>x</italic><sub>1</sub>, <italic>x</italic><sub>2</sub>, &#x022EF;&#x000A0;, <italic>x</italic><sub><italic>n</italic></sub>), <italic>x</italic><sub>1</sub> &#x02264; <italic>x</italic><sub>2</sub> &#x02264; &#x022EF; &#x02264; <italic>x</italic><sub><italic>n</italic></sub>. Second, in order to avoid possible estimation bias of the empirical results caused by income extremes, we apply a winsorization process to the household income data, trimming the top and bottom 1% of the distribution. Third, following the conceptual basis of relative deprivation, the index for a specific household is calculated by comparing its income to the incomes of all other households within its village. Formally, the relative deprivation index for household <italic>i</italic> is specified as:</p>
<disp-formula id="EQ1"><mml:math id="M1"><mml:mrow><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>{</mml:mo><mml:mrow><mml:mtable equalrows='true' equalcolumns='true'><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x02212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x02004;</mml:mtext><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x0003E;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn></mml:mtd><mml:mtd><mml:mrow><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mtext>&#x02004;</mml:mtext><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x02A7D;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:math><label>(1)</label></disp-formula>
<p>Where, <italic>RD</italic>(<italic>x</italic><sub><italic>k</italic></sub>, <italic>x</italic><sub><italic>i</italic></sub>) represents the relative deprivation of household <italic>i</italic> with respect to the income of household <italic>k</italic>. By extension, the average relative deprivation for household <italic>i</italic> is given by:</p>
<disp-formula id="EQ2"><mml:math id="M2"><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>n</mml:mi><mml:msub><mml:mi>&#x003BC;</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mstyle displaystyle='true'><mml:msubsup><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:mrow><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x02212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>n</mml:mi><mml:msub><mml:mi>&#x003BC;</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle='true'><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:mrow></mml:mrow></mml:mstyle></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>&#x0003E;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x02208;</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>&#x02212;</mml:mo><mml:mstyle displaystyle='true'><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:mstyle><mml:mo>&#x0003E;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>&#x02208;</mml:mo><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math><label>(2)</label></disp-formula>
</sec>
<sec>
<label>3.2.2</label>
<title>Independent variable</title>
<p>We operationalize a household&#x00027;s digital literacy by measuring that of the household head. Our conceptualization is grounded in established international standards, including UNESCO&#x00027;s Digital Literacy Global Framework and the EU&#x00027;s Digital Competence Framework. Accordingly, we define digital literacy as the integrated ability to leverage digital technologies for learning, life, and work. This is measured through a composite index comprising five dimensions, including digital learning, social, media, business, and device literacy. Specifically, digital device literacy is operationalized based on household internet, computer, and mobile device usage. For the 2014 wave, this variable is a binary indicator, equal to 1 if household head reported using the internet and 0 otherwise. For the 2016, 2018, and 2020 waves, the variable is equal to 1 if household head answered &#x0201C;yes&#x0201D; to either of the two questions, &#x0201C;Do you use a mobile device to access the internet?&#x0201D; or &#x0201C;Do you use a computer to access the internet?&#x0201D;, and 0 if the answer to both questions was &#x0201C;no&#x0201D;. Similarly, we constructed binary variables for digital learning, social, and media literacy. These variables were operationalized based on responses to four corresponding questions in the CFPS survey. &#x0201C;How frequently do you use the internet for learning?&#x0201D;, &#x0201C;How frequently do you use the internet for business?&#x0201D;, &#x0201C;How frequently do you use the internet for social activities?&#x0201D;, and &#x0201C;How frequently do you use the internet for entertainment?&#x0201D;. For each question, we defined the variable as 0 if the answer is &#x0201C;never,&#x0201D; and 1 for all other responses (i.e., &#x0201C;rarely,&#x0201D; &#x0201C;sometimes,&#x0201D; &#x0201C;often,&#x0201D; &#x0201C;very often&#x0201D;). Finally, a composite index of overall digital literacy was created by summing the values of the five dimensions (digital device, learning, social, business, media literacy). Meanwhile, we adopted the equal weighting method to assign weights to the above five indicators, thereby obtaining the digital literacy index of farmers. The resulting index ranges from 0 to 1, with a higher score indicating a higher level of digital literacy.</p></sec>
<sec>
<label>3.2.3</label>
<title>Instrumental variable</title>
<p>Our empirical analysis of the effect of digital literacy on income inequality among farm households face two potential threats to causal inference. First, despite our efforts to control for a series of relevant factors, endogeneity may arise from omitted variable bias, as not all confounding variables can be perfectly observed or measured. Second, the relationship may suffer from simultaneity bias (reverse causality), as higher household income could plausibly increase access to digital devices and thus foster greater digital literacy. To address these endogeneity problems and obtain an unbiased estimate, we employ an instrumental variable (IV) strategy. We use the village-level internet penetration rate as an instrument for a farm household&#x00027;s digital literacy. The validity of this instrument rests on two key assumptions. On the one hand, the instrument must be correlated with the endogenous variable. This condition is met because a higher internet penetration rate at the village level fosters stronger peer effects, which encourages and increases the likelihood of digital literacy adoption by any given farmer within that village. On the other hand, the instrument must not be correlated with the error term in the primary equation. This condition is satisfied because the village-level penetration rate is a higher-level, aggregate measure. A single farm households&#x02018; digital literacy is too small to influence the digital literacy of all other villagers, and therefore cannot have a meaningful impact on the all village internet penetration rate.</p></sec>
<sec>
<label>3.2.4</label>
<title>Moderator variable</title>
<p>The measurement of non-cognitive ability is grounded in the Big Five personality traits, including Conscientiousness, Agreeableness, Extraversion, Openness, and Neuroticism (<xref ref-type="bibr" rid="B2">Borghans et al., 2008</xref>). As the specific survey items in the CFPS vary slightly across waves, we adopt an established methodology to construct a consistent indicator system (see <xref ref-type="table" rid="T1">Table 1</xref>). This involves selecting appropriate items for each of the five traits based on the available data. Each selected item is then standardized to create a dimensionless measure, and the final composite index for non-cognitive ability is computed by averaging these standardized indicators.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Indicators for evaluating non-cognitive abilities.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Year</bold></th>
<th valign="top" align="left"><bold>Dimension</bold></th>
<th valign="top" align="left"><bold>Corresponding big five personality scale questions for the CFPS questionnaire</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="5">2014</td>
<td valign="top" align="left">Conscientiousness</td>
<td valign="top" align="left">a. Neatness of attire, b. Respondent&#x00027;s impatience during the interview, c. Tendency to trust or be suspicious of others</td>
</tr>
 <tr>
<td valign="top" align="left">Extraversion</td>
<td valign="top" align="left">a. Evaluation of your personal relationship</td>
</tr>
 <tr>
<td valign="top" align="left">Agreeableness</td>
<td valign="top" align="left">a. Most people are helpful or selfish; b. Trust in strangers</td>
</tr>
 <tr>
<td valign="top" align="left">Openness</td>
<td valign="top" align="left">a. Interest in investigation</td>
</tr>
 <tr>
<td valign="top" align="left">Neuroticism</td>
<td valign="top" align="left">a. Life is meaningless; b. It&#x00027;s hard to do anything; c. I feel depressed</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="5">2016</td>
<td valign="top" align="left">Conscientiousness</td>
<td valign="top" align="left">a. Neatness of attire, b. Respondent&#x00027;s impatience during the interview, c. Tendency to trust or be suspicious of others</td>
</tr>
 <tr>
<td valign="top" align="left">Extraversion</td>
<td valign="top" align="left">a. Evaluation of your personal relationship</td>
</tr>
 <tr>
<td valign="top" align="left">Agreeableness</td>
<td valign="top" align="left">a. Most people are helpful or selfish; b. Trust in strangers</td>
</tr>
 <tr>
<td valign="top" align="left">Openness</td>
<td valign="top" align="left">a. Interest in investigation</td>
</tr>
 <tr>
<td valign="top" align="left">Neuroticism</td>
<td valign="top" align="left">a. I don&#x00027;t think life can go on; b. I felt that everything I did was an effort; c. I feel happy</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="5">2018</td>
<td valign="top" align="left">Conscientiousness</td>
<td valign="top" align="left">a. Neatness of attire, b. Respondent&#x00027;s impatience during the interview, c. Tendency to trust or be suspicious of others</td>
</tr>
 <tr>
<td valign="top" align="left">Extraversion</td>
<td valign="top" align="left">a. Evaluation of your personal relationship</td>
</tr>
 <tr>
<td valign="top" align="left">Agreeableness</td>
<td valign="top" align="left">a. Most people are helpful or selfish; b. Trust in strangers</td>
</tr>
 <tr>
<td valign="top" align="left">Openness</td>
<td valign="top" align="left">a. having children to carry on the family line</td>
</tr>
 <tr>
<td valign="top" align="left">Neuroticism</td>
<td valign="top" align="left">a. I don&#x00027;t think life can go on; b. I felt I couldn&#x00027;t do anything well; c. I feel happy</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="5">2020</td>
<td valign="top" align="left">Conscientiousness</td>
<td valign="top" align="left">a. Neatness of attire, b. Respondent&#x00027;s impatience during the interview, c. Tendency to trust or be suspicious of others</td>
</tr>
 <tr>
<td valign="top" align="left">Extraversion</td>
<td valign="top" align="left">a. Evaluation of your personal relationship</td>
</tr>
 <tr>
<td valign="top" align="left">Agreeableness</td>
<td valign="top" align="left">a. Most people are helpful or selfish; b. Trust in strangers</td>
</tr>
 <tr>
<td valign="top" align="left">Openness</td>
<td valign="top" align="left">a. having children to carry on the family line</td>
</tr>
 <tr>
<td valign="top" align="left">Neuroticism</td>
<td valign="top" align="left">a. I don&#x00027;t think life can go on; b. I felt I couldn&#x00027;t do anything well; c. I feel happy</td>
</tr></tbody>
</table>
</table-wrap>
<p>A methodological note on the measurement of non-cognitive ability is warranted. The CFPS survey items for these traits include both positively and negatively-worded indicators. To harmonize the data and ensure a consistent directional interpretation, where higher values uniformly represent more of a given trait, we reverse-scored the &#x0201C;Neuroticism&#x0201D; dimension, transforming it into positively indicators. Meanwhile, the survey items measuring Neuroticism in the 2014 wave are not identical to those used in subsequent waves. To create a longitudinally consistent measure, we identified and selected items from the 2014 questionnaire that were conceptually equivalent to those in later years. These items were then recoded to align their scales, thereby ensuring full comparability across the entire panel.</p></sec>
<sec>
<label>3.2.5</label>
<title>Control variables</title>
<p>The control variables include farmers&#x00027; individual characteristics and household characteristics. Among these, individual characteristics encompass age, age squared, education level, marital status, health status, and political affiliation. Household characteristics include household size, household land assets, household fixed assets, household financial assets, whether the household engages in individual business operations, whether the household has experienced major events, household age structure, and other related factors. Furthermore, given the variations in internet development speeds across regions, which may result in differences in farmers&#x00027; digital literacy, regional fixed effects are incorporated. The definitions and descriptive statistics of the main variables are presented in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Definition and descriptive statistics of main variables.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variable name</bold></th>
<th valign="top" align="left"><bold>Definitions and assignments</bold></th>
<th valign="top" align="center"><bold>Mean</bold></th>
<th valign="top" align="center"><bold>SD</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">RD</td>
<td valign="top" align="left">Kakwani index</td>
<td valign="top" align="center">0.369</td>
<td valign="top" align="center">0.293</td>
</tr>
<tr>
<td valign="top" align="left">LDigital</td>
<td valign="top" align="left">Digital literacy index</td>
<td valign="top" align="center">0.200</td>
<td valign="top" align="center">0.329</td>
</tr>
<tr>
<td valign="top" align="left">Age</td>
<td valign="top" align="left">Householder&#x00027;s age</td>
<td valign="top" align="center">51.97</td>
<td valign="top" align="center">12.494</td>
</tr>
<tr>
<td valign="top" align="left">Age2</td>
<td valign="top" align="left">Householder&#x00027;s age square</td>
<td valign="top" align="center">2,856.987</td>
<td valign="top" align="center">1,302.233</td>
</tr>
<tr>
<td valign="top" align="left">Edu</td>
<td valign="top" align="left">Householder&#x00027;s education</td>
<td valign="top" align="center">6.474</td>
<td valign="top" align="center">4.035</td>
</tr>
<tr>
<td valign="top" align="left">Marriage</td>
<td valign="top" align="left">Marriage = 1, else = 0</td>
<td valign="top" align="center">0.885</td>
<td valign="top" align="center">0.319</td>
</tr>
<tr>
<td valign="top" align="left">Health</td>
<td valign="top" align="left">Self-rated health</td>
<td valign="top" align="center">2.839</td>
<td valign="top" align="center">1.268</td>
</tr>
<tr>
<td valign="top" align="left">Party</td>
<td valign="top" align="left">Whether or not you are a member of the party (Yes = 1, No = 0)</td>
<td valign="top" align="center">0.044</td>
<td valign="top" align="center">0.205</td>
</tr>
<tr>
<td valign="top" align="left">Fsize</td>
<td valign="top" align="left">Number of family members</td>
<td valign="top" align="center">4.135</td>
<td valign="top" align="center">1.943</td>
</tr>
<tr>
<td valign="top" align="left">Fland</td>
<td valign="top" align="left">The log of the current value of family land assets</td>
<td valign="top" align="center">8.283</td>
<td valign="top" align="center">3.948</td>
</tr>
<tr>
<td valign="top" align="left">Ffixed</td>
<td valign="top" align="left">The log of the current value of family fixed assets</td>
<td valign="top" align="center">4.071</td>
<td valign="top" align="center">4.378</td>
</tr>
<tr>
<td valign="top" align="left">Ffinance</td>
<td valign="top" align="left">The log of the current value of family financial assets</td>
<td valign="top" align="center">6.283</td>
<td valign="top" align="center">4.832</td>
</tr>
<tr>
<td valign="top" align="left">Femploy</td>
<td valign="top" align="left">Family self-employment status (Yes = 1, No = 0)</td>
<td valign="top" align="center">0.072</td>
<td valign="top" align="center">0.258</td>
</tr>
<tr>
<td valign="top" align="left">Fthing</td>
<td valign="top" align="left">Major family events (Yes = 1, No = 0)</td>
<td valign="top" align="center">0.353</td>
<td valign="top" align="center">0.478</td>
</tr>
<tr>
<td valign="top" align="left">Elderly</td>
<td valign="top" align="left">Family elderly-to-labor-force ratio</td>
<td valign="top" align="center">0.211</td>
<td valign="top" align="center">0.418</td>
</tr>
<tr>
<td valign="top" align="left">IV</td>
<td valign="top" align="left">The share of households in the village using the internet</td>
<td valign="top" align="center">0.293</td>
<td valign="top" align="center">0.234</td>
</tr>
<tr>
<td valign="top" align="left">Ncognitive</td>
<td valign="top" align="left">Non-cognitive index</td>
<td valign="top" align="center">0.689</td>
<td valign="top" align="center">0.122</td>
</tr></tbody>
</table>
</table-wrap></sec></sec>
<sec>
<label>3.3</label>
<title>Empirical model</title>
<p>To empirically examine the effect of digital literacy on income inequality among farm households, we employ a two-way fixed effects model, using panel data from the four waves of the CFPS covering 2014 to 2020. The model is formulated as follows:</p>
<disp-formula id="EQ3"><mml:math id="M3"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003C1;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003C1;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>L</mml:mi><mml:mi>D</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mo>&#x02032;</mml:mo></mml:msubsup><mml:msub><mml:mi>&#x003C1;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003C6;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003C6;</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003C6;</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003BC;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><label>(3)</label></disp-formula>
<p>Where, <italic>RD</italic><sub><italic>ijt</italic></sub> represents the of income inequality of household <italic>i</italic>, located in province <italic>j</italic>, during year <italic>t</italic>. <italic>LDigital</italic><sub><italic>ijt</italic></sub> represents the of digital literacy of household <italic>i</italic>, located in province <italic>j</italic>, during year <italic>t</italic>. &#x003C1;<sub>1</sub> measures the impact of digital literacy on income inequality among farm households. <italic>X</italic><sub><italic>ijt</italic></sub> represents a series of control variables. &#x003C6;<sub><italic>i</italic></sub> is an individual fixed effect. &#x003C6;<sub><italic>t</italic></sub> is a year fixed effect. &#x003C6;<sub><italic>j</italic></sub> is a region fixed effect. &#x003BC;<sub><italic>ijt</italic></sub> is a randomized perturbation term.</p></sec></sec>
<sec id="s4">
<label>4</label>
<title>Empirical results</title>
<sec>
<label>4.1</label>
<title>Baseline results</title>
<p><xref ref-type="table" rid="T3">Table 3</xref> reports the baseline regression results on the impact of digital literacy on income inequality among farmers. Column (1) only considers the estimated results of the core explanatory variable, digital literacy, on income inequality among farmers; columns (2)&#x02013;(4) incorporate control variables for household head characteristics, family characteristics, and regional fixed effects, respectively. Regardless of whether control variables are included, the inhibitory effect of digital literacy on income inequality among farmers is significant at the 1% statistical level. Specifically, after incorporating relevant control variables such as household head characteristics, family characteristics, and regional fixed effects, a 1-unit increase in digital literacy level leads to a 3.4% reduction in the relative deprivation index of farmers&#x00027; income, indicating that digital literacy can mitigate income inequality among farmers and plays a non-negligible role in narrowing rural household income gaps. Thus, Hypothesis 1 is verified.</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Digital literacy and income inequality among farmers: baseline regression results.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
<th valign="top" align="center"><bold>(3)</bold></th>
<th valign="top" align="center"><bold>(4)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td valign="top" align="center">&#x02212;0.054<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.040<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.033<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.034<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="center">(0.009)</td>
<td valign="top" align="center">(0.010)</td>
<td valign="top" align="center">(0.009)</td>
<td valign="top" align="center">(0.009)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Age</td>
<td/>
<td valign="top" align="center">&#x02212;0.006<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.006<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.006<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.002)</td>
<td valign="top" align="center">(0.002)</td>
<td valign="top" align="center">(0.002)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Age2</td>
<td/>
<td valign="top" align="center">0.000<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.000<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.000<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.000)</td>
<td valign="top" align="center">(0.000)</td>
<td valign="top" align="center">(0.000)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Edu</td>
<td/>
<td valign="top" align="center">&#x02212;0.002<sup>&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.001</td>
<td valign="top" align="center">&#x02212;0.001</td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.001)</td>
<td valign="top" align="center">(0.001)</td>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Marriage</td>
<td/>
<td valign="top" align="center">&#x02212;0.032<sup>&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.000</td>
<td valign="top" align="center">0.000</td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.013)</td>
<td valign="top" align="center">(0.013)</td>
<td valign="top" align="center">(0.013)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Health</td>
<td/>
<td valign="top" align="center">&#x02212;0.001</td>
<td valign="top" align="center">0.000</td>
<td valign="top" align="center">0.000</td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.002)</td>
<td valign="top" align="center">(0.002)</td>
<td valign="top" align="center">(0.002)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Party</td>
<td/>
<td valign="top" align="center">&#x02212;0.008</td>
<td valign="top" align="center">&#x02212;0.010</td>
<td valign="top" align="center">&#x02212;0.011</td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.013)</td>
<td valign="top" align="center">(0.013)</td>
<td valign="top" align="center">(0.013)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Fsize</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.051<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.051<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.003)</td>
<td valign="top" align="center">(0.003)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Fland</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.005<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.005<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Ffixed</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.004<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.004<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Ffinance</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.004<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.004<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Femploy</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.047<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.046<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.012)</td>
<td valign="top" align="center">(0.012)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Fthing</td>
<td/>
<td/>
<td valign="top" align="center">0.017<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.017<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.006)</td>
<td valign="top" align="center">(0.006)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Elderly</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.002</td>
<td valign="top" align="center">&#x02212;0.001</td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="center">(0.008)</td>
<td valign="top" align="center">(0.008)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="center">0.414<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.575<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.824<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.650<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="center">(0.004)</td>
<td valign="top" align="center">(0.050)</td>
<td valign="top" align="center">(0.051)</td>
<td valign="top" align="center">(0.050)</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="center">NO</td>
<td valign="top" align="center">NO</td>
<td valign="top" align="center">NO</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
</tr>
<tr>
<td valign="top" align="left">Adj&#x02013;R<sup>2</sup></td>
<td valign="top" align="center">0.021</td>
<td valign="top" align="center">0.025</td>
<td valign="top" align="center">0.097</td>
<td valign="top" align="center">0.099</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup>, <sup>&#x0002A;&#x0002A;</sup>, and <sup>&#x0002A;</sup> indicate significance levels at 1%, 5%, and 10%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
<p>The estimated results for other control variables are also largely consistent with expectations and align with conclusions from the existing literature. Specifically, the estimated coefficient for the household head&#x00027;s age is negative, while that for age squared is positive. This is because, as the household head&#x00027;s age increases, their social capital gradually accumulates, leading to more channels for family income growth, a relative increase in family income levels, a reduction in income gaps with other farmers, and a consequent decrease in the degree of income inequality faced by farmers. However, once the household head&#x00027;s age reaches a certain level, labor capacity relatively weakens, family income levels decline, income gaps with other households widen, and the degree of income inequality among farmers increases. The estimated coefficient for family size is negative, indicating that larger family sizes are associated with lower degrees of income inequality among farmers. This is primarily because larger family sizes involve more income-earning members, thereby resulting in higher family incomes. The estimated coefficients for family land assets, fixed assets, financial assets, and individual business operations are all significantly negative, suggesting that greater holdings of family land assets, fixed assets, and financial assets, as well as engagement in individual business operations, are associated with lower degrees of income inequality among farmers. These factors serve as &#x0201C;income equalizers&#x0201D; and &#x0201C;risk buffers&#x0201D; within rural settings. They effectively reduce the degree of income inequality among farmers by enhancing income levels, broadening income channels, and strengthening risk resilience. This not only confirms the critical role of assets in wealth distribution, but also reveals characteristics of rural economic structural transformation. The estimated coefficients for major family events are significantly positive, indicating that the occurrence of major family events significantly increases the degree of income inequality among farmers. This is primarily because major events are typically accompanied by high expenditures or income interruptions, directly undermining family income capacities. Consequently, in farmer groups with initially small income gaps, the income disparities between affected and unaffected families widen dramatically, ultimately elevating the overall degree of income inequality.</p>
<p>Furthermore, this study employs a two-way fixed effects model to analyze the specific impacts of the five dimensions of digital literacy on income inequality among farmers, with the estimation results presented in <xref ref-type="table" rid="T4">Table 4</xref>. Columns (1) through (5) correspond to digital learning literacy, digital social literacy, digital media literacy, digital business literacy, and digital device literacy, respectively. The results indicate that the effects of the five dimensions of digital literacy on income inequality among farmers are all statistically significant at the 5% level, with negative coefficients. This implies that higher levels of digital literacy are associated with lower degrees of income inequality among farmers. This further supports Hypothesis 1.</p>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Digital literacy and income inequality among farmers: classified regression results.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variable</bold></th>
<th valign="top" align="left"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
<th valign="top" align="center"><bold>(3)</bold></th>
<th valign="top" align="center"><bold>(4)</bold></th>
<th valign="top" align="center"><bold>(5)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td valign="top" align="left">&#x02212;0.020<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.019<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.020<sup>&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.021<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">&#x02212;0.016<sup>&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.007)</td>
<td valign="top" align="center">(0.007)</td>
<td valign="top" align="center">(0.008)</td>
<td valign="top" align="center">(0.007)</td>
<td valign="top" align="center">(0.008)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="left">0.638<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.638<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.638<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.644<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.640<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.050)</td>
<td valign="top" align="center">(0.050)</td>
<td valign="top" align="center">(0.050)</td>
<td valign="top" align="center">(0.050)</td>
<td valign="top" align="center">(0.050)</td>
</tr>
<tr>
<td valign="top" align="left">Controls</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="left">12,476</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
<td valign="top" align="center">12,476</td>
</tr>
<tr>
<td valign="top" align="left">Adj&#x02013;R<sup>2</sup></td>
<td valign="top" align="left">0.099</td>
<td valign="top" align="center">0.099</td>
<td valign="top" align="center">0.098</td>
<td valign="top" align="center">0.099</td>
<td valign="top" align="center">0.098</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup> and <sup>&#x0002A;&#x0002A;</sup> indicate significance levels at 1% and 5%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap></sec>
<sec>
<label>4.2</label>
<title>Endogenous problem</title>
<p>The baseline regression results of this study confirm that digital literacy exerts a significant inhibitory effect on income inequality among farmers; however, they cannot circumvent the endogeneity issue arising from potential reverse causality. Consistent with the theoretical analysis presented earlier, digital literacy influences income inequality among farmers; conversely, it is plausible that farmers with higher income levels exhibit greater digital literacy. Accordingly, this study employs 2SLS and ERM to address the endogeneity of digital literacy. This study selects village-level internet usage rate as the instrumental variable. Influenced by peer effects, villages with higher internet penetration rates exhibit greater likelihood of internet usage among farmers, leading to elevated digital literacy levels, thereby satisfying the relevance criterion. Moreover, as internet penetration rate represents higher-level aggregate data, an individual farmer&#x00027;s digital literacy cannot influence the digital literacy levels of other villagers and thus cannot affect the village&#x00027;s internet penetration rate, fulfilling the exogeneity requirement. <xref ref-type="table" rid="T5">Table 5</xref> reports the estimation results from the 2SLS and ERM.</p>
<table-wrap position="float" id="T5">
<label>Table 5</label>
<caption><p>Digital literacy and income inequality among farmers: endogeneity test results.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center" colspan="2"><bold>TWFE-2SLS</bold></th>
<th valign="top" align="center" colspan="2"><bold>ERM</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>LDigital</bold></th>
<th valign="top" align="center"><bold>RD</bold></th>
<th valign="top" align="center"><bold>LDigital</bold></th>
<th valign="top" align="center"><bold>RD</bold></th>
</tr>
 <tr>
<th/>
<th valign="top" align="center"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
<th valign="top" align="center"><bold>(3)</bold></th>
<th valign="top" align="center"><bold>(4)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td/>
<td valign="top" align="center">&#x02212;0.051<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;0.067<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td valign="top" align="center">(0.018)</td>
<td/>
<td valign="top" align="center">(0.015)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">IV</td>
<td valign="top" align="center">0.512<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">0.668<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
</tr>
 <tr>
<td valign="top" align="center">(0.016)</td>
<td/>
<td valign="top" align="center">(0.010)</td>
<td/>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="center">0.520<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.636<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center">0.004</td>
<td valign="top" align="center">0.574<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="center">(0.067)</td>
<td valign="top" align="center">(0.137)</td>
<td valign="top" align="center">(0.005)</td>
<td valign="top" align="center">(0.130)</td>
</tr>
<tr>
<td valign="top" align="left">Controls</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="left">First-stage F statistic</td>
<td valign="top" align="center" colspan="2">2,725.237</td>
<td valign="top" align="center" colspan="2"></td>
</tr>
<tr>
<td valign="top" align="left">Kleibergen-Paap rk LM statistic</td>
<td valign="top" align="center" colspan="2">1,212.761<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center" colspan="2"></td>
</tr>
<tr>
<td valign="top" align="left">Cragg-Donald Wald F statistic</td>
<td valign="top" align="center" colspan="2">2,725.237<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="center" colspan="2"></td>
</tr>
<tr>
<td valign="top" align="left">Residual correlation</td>
<td valign="top" align="center" colspan="2"></td>
<td valign="top" align="center" colspan="2">0.049<sup>&#x0002A;&#x0002A;</sup></td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="center" colspan="2">12,476</td>
<td valign="top" align="center" colspan="2">12,476</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup> and <sup>&#x0002A;&#x0002A;</sup> indicate significance levels at 1% and 5%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
<p>Columns (1) and (2) present the estimation results from the 2SLS model. The results in column (1) indicate that the internet usage rate has a significant positive effect on farmers&#x02018; digital literacy. This suggests a strong correlation between the internet usage rate and farmers&#x00027; digital literacy levels, satisfying the relevance requirement for the instrumental variable. The first-stage F-statistic is 2,725.237, far exceeding the conventional threshold of 10, indicating no weak instrument problem. Meanwhile, the results in column (2) show that the coefficient for digital literacy is &#x02212;0.051 and significant at the 1% level; compared to the baseline regression, the absolute value of the coefficient is larger, and the standard error is also greater. This implies that the baseline regression model underestimates the inhibitory effect of digital literacy on income inequality among farmers.</p>
<p>In addition, columns (3) and (4) report the estimation results from the ERM. The results in column (3) indicate that the internet usage rate has a significant positive effect on farmers&#x02018; digital literacy, further confirming that the instrumental variable satisfies the relevance requirement. The main regression results in column (4) show that digital literacy has a significant negative effect on income inequality among farmers, with a coefficient of &#x02212;0.067; compared to the baseline regression estimate in column (1), the absolute value of the coefficient is larger, indicating that the baseline regression model indeed underestimates the inhibitory effect of digital literacy. The test for correlation of residuals indicates a significant correlation between the endogenous variable regression and the main regression, confirming that farmers&#x00027; digital literacy is indeed endogenous. After addressing endogeneity, the estimation results from the 2SLS and ERM align with the direction of effects in the two-way fixed effects model, robustly demonstrating the inhibitory effect of digital literacy on income inequality among farmers and further validating Hypothesis 1.</p></sec>
<sec>
<label>4.3</label>
<title>Robustness test</title>
<sec>
<label>4.3.1</label>
<title>Substitution of dependent variable</title>
<p>In our baseline regressions, the dependent variable, the Kakwani index, measures a household&#x00027;s comparative disadvantage within their reference group, a perspective grounded in micro-level social comparison. To test the robustness of our core findings, we conduct a further analysis using the Theil index as a substitution of dependent variable. Unlike the Kakwani index, the Theil index quantifies the deviation of a household&#x00027;s income from the overall sample mean, thus better reflecting the dispersion of the entire income distribution. We assume there are <italic>K</italic> villages, indexed by <italic>N</italic><sub><italic>k</italic></sub>, <italic>k</italic> &#x0003D; 1, &#x022EF;&#x000A0;, <italic>K</italic>. The Theil index is then given by:</p>
<disp-formula id="EQ4"><mml:math id="M4"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo class="qopname">ln</mml:mo><mml:mstyle><mml:mrow><mml:mo stretchy="true">(</mml:mo></mml:mrow></mml:mstyle><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mstyle><mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo class="qopname">ln</mml:mo><mml:mstyle><mml:mrow><mml:mo stretchy="true">(</mml:mo></mml:mrow></mml:mstyle><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mstyle><mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math><label>(4)</label></disp-formula>
<p>Where <italic>I</italic><sub><italic>k</italic></sub> and <italic>n</italic><sub><italic>k</italic></sub> represent the income and the number of households for the <italic>k</italic>-th village group, respectively, <inline-formula><mml:math id="M5"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, while <italic>w</italic><sub><italic>k</italic></sub> &#x0003D; <italic>I</italic><sub><italic>k</italic></sub>/<italic>I</italic>, and it represents the share of the <italic>k</italic>-th village income. The regression results using this alternative measure are presented in Column (1) of <xref ref-type="table" rid="T6">Table 6</xref>. We find that the estimated coefficient on digital literacy is still negative and statistically significant at the 5% level. This confirms that our baseline result is robust.</p>
<table-wrap position="float" id="T6">
<label>Table 6</label>
<caption><p>Digital literacy and income inequality among farmers: robustness test results.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="left"><bold>(1)</bold></th>
<th valign="top" align="left"><bold>(2)</bold></th>
<th valign="top" align="left"><bold>(3)</bold></th>
<th valign="top" align="left"><bold>(4)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td valign="top" align="left">&#x02212;0.010<sup>&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">&#x02212;0.056<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">&#x02212;0.029<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.005)</td>
<td/>
<td valign="top" align="left">(0.008)</td>
<td valign="top" align="left">(0.010)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Hour</td>
<td/>
<td valign="top" align="left">&#x02212;0.000<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td/>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.000)</td>
<td/>
<td/>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="left">0.300<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.630<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.577<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.631<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.027)</td>
<td valign="top" align="left">(0.049)</td>
<td valign="top" align="left">(0.131)</td>
<td valign="top" align="left">(0.088)</td>
</tr>
<tr>
<td valign="top" align="left">Controls</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="left">12,476</td>
<td valign="top" align="left">12,476</td>
<td valign="top" align="left">12,476</td>
<td valign="top" align="left">9,099</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup> and <sup>&#x0002A;&#x0002A;</sup> indicate significance levels at 1% and 5%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec>
<label>4.3.2</label>
<title>Substitution of independent variable</title>
<p>Our baseline analysis measured digital literacy using the sum of binary indicators of whether a farm household uses the internet for learning, social, business and entertainment. However, it is plausible that the intensity of internet use, not just the breadth of its application, also influences income inequality. To test this, we conduct a robustness test using the continuous variable &#x0201C;time spent online&#x0201D; to measure digital literacy. The result in Column (2) of <xref ref-type="table" rid="T6">Table 6</xref> shows a significant mitigating effect on income inequality among farm households. This finding aligns perfectly with our baseline results, confirming the robustness of our main conclusions.</p></sec>
<sec>
<label>4.3.3</label>
<title>Alternative estimation method</title>
<p>Due to the Kakwani index values are bounded between 0 and 1. To account for this data structure, we conduct a robustness test by re-estimating our model using a Panel Tobit. The results present in Column (3) of <xref ref-type="table" rid="T6">Table 6</xref>, show that the estimated coefficient on digital literacy remains significantly negative. This confirms the robustness of our main findings and provides additional support for Hypothesis 1.</p></sec>
<sec>
<label>4.3.4</label>
<title>Adjustment of sample range</title>
<p>We also re-estimate our model on a subsample restricted to households where the head of household is between 20 and 60 years old. This range corresponds to the typical working-age population in China, bounded by the legal marriage age and the official retirement age. The results presented in Column (4) of <xref ref-type="table" rid="T6">Table 6</xref>, show that the coefficient on digital literacy remains directionally consistent with our baseline findings and is statistically significant at the 1% level. This test further confirms the robustness of our results.</p></sec></sec></sec>
<sec sec-type="discussion" id="s5">
<label>5</label>
<title>Discussion</title>
<sec>
<label>5.1</label>
<title>Heterogeneity analysis</title>
<p>First, addressing imbalances in regional economic development represents a vital pathway for advancing comprehensive rural revitalization and achieving common prosperity. There exist substantial disparities in digital economic development across regions, varying levels of farmers&#x02018; internet accessibility, and differences in farmers&#x00027; digital literacy, which in turn lead to heterogeneous impacts on income inequality among farmers (<xref ref-type="bibr" rid="B21">Yang et al., 2023</xref>). To this end, this study delineates the provinces where the farmer samples are located into four regions&#x02014;Northeast, East, Central, and West&#x02014;following the classification scheme of the National Bureau of Statistics. The subsample estimation results are presented in columns (1) through (4) of <xref ref-type="table" rid="T7">Table 7</xref>. The results indicate that the negative effect of digital literacy on income inequality among farmers is significant only in the Central region. This suggests that the mitigating effect of digital literacy on income inequality among farmers is most pronounced in the Central region. This is attributable to the Central region being in a phase characterized by &#x0201C;adequate hardware but insufficient soft capabilities,&#x0201D; where policy support and economic structural transformation jointly amplify the marginal contributions of digital literacy. In contrast, the East region exhibits no significant mitigating effect due to &#x0201C;saturation of soft capabilities,&#x0201D; while the Northeast and West regions show none owing to &#x0201C;hardware deficiencies.&#x0201D;</p>
<table-wrap position="float" id="T7">
<label>Table 7</label>
<caption><p>Digital literacy and income inequality among farmers: results of heterogeneity analysis.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="left"><bold>(1)</bold></th>
<th valign="top" align="left"><bold>(2)</bold></th>
<th valign="top" align="left"><bold>(3)</bold></th>
<th valign="top" align="left"><bold>(4)</bold></th>
<th valign="top" align="left"><bold>(5)</bold></th>
<th valign="top" align="left"><bold>(6)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td valign="top" align="left">&#x02212;0.038</td>
<td valign="top" align="left">&#x02212;0.012</td>
<td valign="top" align="left">&#x02212;0.076<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">&#x02212;0.017</td>
<td valign="top" align="left">&#x02212;0.035<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">&#x02212;0.026</td>
</tr>
 <tr>
<td valign="top" align="left">(0.025)</td>
<td valign="top" align="left">(0.018)</td>
<td valign="top" align="left">(0.020)</td>
<td valign="top" align="left">(0.016)</td>
<td valign="top" align="left">(0.011)</td>
<td valign="top" align="left">(0.024)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="left">0.614<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.822<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">1.033<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.526<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.758<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.781<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.137)</td>
<td valign="top" align="left">(0.093)</td>
<td valign="top" align="left">(0.109)</td>
<td valign="top" align="left">(0.104)</td>
<td valign="top" align="left">(0.064)</td>
<td valign="top" align="left">(0.201)</td>
</tr>
<tr>
<td valign="top" align="left">Controls</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="left">1,608</td>
<td valign="top" align="left">3,258</td>
<td valign="top" align="left">3,247</td>
<td valign="top" align="left">4,363</td>
<td valign="top" align="left">10,848</td>
<td valign="top" align="left">1,628</td>
</tr>
<tr>
<td valign="top" align="left">Adj&#x02013;R<sup>2</sup></td>
<td valign="top" align="left">0.105</td>
<td valign="top" align="left">0.103</td>
<td valign="top" align="left">0.122</td>
<td valign="top" align="left">0.085</td>
<td valign="top" align="left">0.097</td>
<td valign="top" align="left">0.116</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup> indicate significance levels at 1%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
<p>Second, differences in educational attainment constitute one of the key factors influencing income inequality (<xref ref-type="bibr" rid="B6">Gregorio and Lee, 2002</xref>; <xref ref-type="bibr" rid="B8">Hendel et al., 2005</xref>). This study stratifies the sample into low-education and high-education groups based on the household head&#x00027;s years of schooling (using junior high school education as the cutoff) to examine the heterogeneous impacts of digital literacy on income inequality across different educational attainment levels among farmers. Columns (5) and (6) of <xref ref-type="table" rid="T7">Table 7</xref> present the regression results for the low-education and high-education groups, respectively. The results reveal that the negative effect of digital literacy on income inequality among farmers is significant only in the low-education group. This indicates that the mitigating effect of digital literacy on income inequality is most significant among farmers in the low-education group. For the high-education group, the income-enhancing effect of digital literacy is &#x0201C;substituted&#x0201D; or &#x0201C;masked&#x0201D; by other more potent factors. In the low-education group, however, digital literacy assumes the pivotal roles of a &#x0201C;substitute for formal education&#x0201D; and a &#x0201C;compensator for capabilities,&#x0201D; thereby generating a substantial effect in curbing income inequality. This finding carries critical policy implications, underscoring that promoting and enhancing digital literacy constitutes a highly &#x0201C;inclusive&#x0201D; and &#x0201C;equitable&#x0201D; policy, with the greatest beneficiaries being the low-education groups who are most disadvantaged under traditional development paradigms. This compellingly demonstrates the irreplaceable value of investing in rural digital literacy training for narrowing income disparities and fostering social equity.</p></sec>
<sec>
<label>5.2</label>
<title>Moderating effect analysis</title>
<p>The preceding theoretical analysis indicates that non-cognitive abilities play a pivotal moderating role between digital literacy and income inequality among farmers, such that the mitigating effect of digital literacy on income disparities exhibits significant variations contingent on differences in farmers&#x00027; non-cognitive ability levels. To this end, this study empirically tests this moderating effect by incorporating the interaction term between digital literacy and non-cognitive abilities. The estimation results are presented in <xref ref-type="table" rid="T8">Table 8</xref>.</p>
<table-wrap position="float" id="T8">
<label>Table 8</label>
<caption><p>Digital literacy and income inequality among farmers: regression results for moderating effects.</p></caption>
<table frame="box" rules="all">
<thead>
<tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="left"><bold>(1)</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="left"><bold>Cognitive</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" rowspan="2">LDigital</td>
<td valign="top" align="left">&#x02212;0.121<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.038)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Ncognitive</td>
<td valign="top" align="left">&#x02212;0.060<sup>&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.024)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">LDigital &#x000D7; Ncognitive</td>
<td valign="top" align="left">0.126<sup>&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.054)</td>
</tr>
<tr>
<td valign="top" align="left" rowspan="2">Cons.</td>
<td valign="top" align="left">0.689<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td valign="top" align="left">(0.053)</td>
</tr>
<tr>
<td valign="top" align="left">Controls</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Region FE</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Household FE</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Year FE</td>
<td valign="top" align="left">YES</td>
</tr>
<tr>
<td valign="top" align="left">Obs.</td>
<td valign="top" align="left">12,476</td>
</tr>
<tr>
<td valign="top" align="left">Adj&#x02013;<italic>R</italic><sup>2</sup></td>
<td valign="top" align="left">0.100</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>(1) <sup>&#x0002A;&#x0002A;&#x0002A;</sup> and <sup>&#x0002A;&#x0002A;</sup> indicate significance levels at 1% and 5%, respectively; (2) Robust standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
<p>The results reveal that the regression coefficient for digital literacy is significantly negative, indicating that digital literacy exerts a significant suppressive effect on income inequality among farmers. The regression coefficient for non-cognitive abilities is also significantly negative, suggesting that higher levels of non-cognitive abilities correspond to lower degrees of income inequality among farmers. The regression coefficient for the interaction term between digital literacy and non-cognitive abilities is statistically significantly positive, providing key evidence in support of this study&#x00027;s core Hypothesis 2, that non-cognitive abilities exert a significant positive moderating effect on the relationship between &#x0201C;digital literacy and income inequality.&#x0201D; Specifically, this implies that as farmers&#x00027; non-cognitive ability levels increase, the inherent capacity of digital literacy to narrow income gaps is instead systematically attenuated. This finding corroborates the theoretical inference presented earlier, namely, that non-cognitive abilities do not homogeneously empower all farmers; rather, they function as a &#x0201C;benefit amplifier,&#x0201D; substantially widening the efficiency gap in converting digital skills into economic returns between high- and low-non-cognitive-ability groups. Consequently, at the macro level, the dissemination of digital literacy, if devoid of considerations for psychological traits, will substantially diminish its inclusivity and may even potentially reinforce the structure of income inequality at the micro level by exacerbating intra-group differentiation. Thus, Hypothesis 2 is supported.</p></sec></sec>
<sec id="s6">
<label>6</label>
<title>Conclusions and implications</title>
<p>In the digital economy era, the deep penetration of internet digital technologies has reshaped agricultural production and operation models as well as farmers&#x02018; income acquisition pathways; whether these technologies can serve as an effective tool to narrow income disparities among farmers depends on the alignment between technological empowerment and farmers&#x00027; capabilities. This study, based on four waves of panel data from the CFPS spanning 2014&#x02013;2020, empirically examines the impact of digital literacy on income inequality among farmers and its boundary conditions. The main findings are as follows:</p>
<list list-type="simple">
<list-item><p>(1) Digital literacy exerts a significant suppressive effect on income inequality among farmers. Baseline regression results indicate that a one-unit increase in digital literacy level significantly reduces the relative deprivation index among farmers by 3.4%. This suggests that digital literacy can alleviate income distribution imbalances among farmers through pathways such as breaking information barriers and broadening income channels, thereby providing micro-level empirical support for the digital economy&#x00027;s role in empowering common prosperity.</p></list-item>
<list-item><p>(2) The suppressive effect of digital literacy exhibits heterogeneity across groups and regions. Heterogeneity analysis reveals that this effect is most pronounced in the central region and among farmers with low education levels. As the primary agricultural production hub, the central region benefits from greater equity in digital infrastructure and higher industrial adaptability, facilitating the more effective implementation of digital literacy&#x00027;s inclusive income-enhancing effects. For low-education farmers, the higher &#x0201C;marginal income elasticity&#x0201D; of digital literacy amplifies its effects in compensating for information asymmetries and overcoming income bottlenecks via basic digital skills; in contrast, &#x0201C;digital elite capture&#x0201D; in the eastern region and &#x0201C;weak digital foundations&#x0201D; in the western region render the effect insignificant.</p></list-item>
<list-item><p>(3) Non-cognitive abilities attenuate the income-equalizing effect of digital literacy. Interaction term tests show that the coefficient on the interaction between digital literacy and non-cognitive abilities is significantly positive, indicating that as non-cognitive abilities increase, the strength of digital literacy&#x00027;s effect in narrowing income gaps declines. This arises because farmers with high non-cognitive abilities are better positioned to aggregate resources and benefits through digital technologies, whereas those with low non-cognitive abilities, due to insufficient application initiative and weak resource integration capacities, struggle to fully realize the income-enhancing potential of digital literacy, resulting in &#x0201C;differentiated distribution of digital dividends.&#x0201D;</p></list-item>
</list>
<p>Based on the above findings, to promote digital literacy as a true &#x0201C;equalizer&#x0201D; in narrowing income disparities among farmers, the following policy implications are proposed: First, systematically strengthen digital literacy development by balancing &#x0201C;access&#x0201D; and &#x0201C;capability&#x0201D; through dual drivers. At the infrastructure level, continue to expand rural broadband and 5G network coverage to enhance internet accessibility and stability; at the capability-building level, governments should lead public-interest digital skills training, focusing on low-income farmers&#x00027; usage intentions and practical applications to ensure digital dividends shift from &#x0201C;available&#x0201D; to &#x0201C;beneficial,&#x0201D; thereby comprehensively empowering rural revitalization. Second, account for group and regional heterogeneity in formulating targeted digital development strategies. Policy design should incorporate layered mechanisms. For &#x0201C;vulnerable&#x0201D; groups in the central region and low-education farmers, implement customized online education and information subsidies to bridge the digital divide. For eastern and high-education groups, emphasize innovative integration. Through these differentiated pathways, promote regional equity and group equality while preventing digital transformation from exacerbating income polarization. Third, integrate non-cognitive ability cultivation into the digital literacy framework to enhance skill conversion efficiency. Training systems should extend beyond technical operations to incorporate social and psychological modules, leveraging internet platforms to stimulate motivation and collaboration potential, thereby addressing the social capital deficits of low non-cognitive farmers. This &#x0201C;soft-hard synergy&#x0201D; model can strengthen intermediary channels, efficiently converting digital skills into economic returns and ultimately deepening the structural alleviation of income inequality.</p></sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>Publicly available datasets were analyzed in this study. This data can be found here: <ext-link ext-link-type="uri" xlink:href="http://www.isss.pku.edu.cn/cfps">http://www.isss.pku.edu.cn/cfps</ext-link>.</p>
</sec>
<sec sec-type="ethics-statement" id="s8">
<title>Ethics statement</title>
<p>Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent from the (patients/participants OR patients/participants legal guardian/next of kin) was not required to participate in this study in accordance with the national legislation and the institutional requirements.</p>
</sec>
<sec sec-type="author-contributions" id="s9">
<title>Author contributions</title>
<p>QZ: Conceptualization, Formal analysis, Funding acquisition, Writing &#x02013; original draft. CF: Methodology, Visualization, Writing &#x02013; original draft, Writing &#x02013; review &#x00026; editing. HW: Methodology, Visualization, Writing &#x02013; original draft.</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s11">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p></sec>
<sec sec-type="disclaimer" id="s12">
<title>Publisher&#x00027;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
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<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2600066/overview">Tingting Bai</ext-link>, Yangzhou University, China</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by" id="fn0002">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1988486/overview">Jie Wang</ext-link>, Chizhou University, China</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3013328/overview">Ziyang Zhou</ext-link>, South China University of Technology, China</p>
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